Date: 2019-12-25 21:31:16 CET, cola version: 1.3.2
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All available functions which can be applied to this res_list object:
res_list
#> A 'ConsensusPartitionList' object with 24 methods.
#> On a matrix with 27425 rows and 90 columns.
#> Top rows are extracted by 'SD, CV, MAD, ATC' methods.
#> Subgroups are detected by 'hclust, kmeans, skmeans, pam, mclust, NMF' method.
#> Number of partitions are tried for k = 2, 3, 4, 5, 6.
#> Performed in total 30000 partitions by row resampling.
#>
#> Following methods can be applied to this 'ConsensusPartitionList' object:
#> [1] "cola_report" "collect_classes" "collect_plots" "collect_stats"
#> [5] "colnames" "functional_enrichment" "get_anno_col" "get_anno"
#> [9] "get_classes" "get_matrix" "get_membership" "get_stats"
#> [13] "is_best_k" "is_stable_k" "ncol" "nrow"
#> [17] "rownames" "show" "suggest_best_k" "test_to_known_factors"
#> [21] "top_rows_heatmap" "top_rows_overlap"
#>
#> You can get result for a single method by, e.g. object["SD", "hclust"] or object["SD:hclust"]
#> or a subset of methods by object[c("SD", "CV")], c("hclust", "kmeans")]
The call of run_all_consensus_partition_methods() was:
#> run_all_consensus_partition_methods(data = mat, mc.cores = 4, anno = anno)
Dimension of the input matrix:
mat = get_matrix(res_list)
dim(mat)
#> [1] 27425 90
The density distribution for each sample is visualized as in one column in the following heatmap. The clustering is based on the distance which is the Kolmogorov-Smirnov statistic between two distributions.
library(ComplexHeatmap)
densityHeatmap(mat, top_annotation = HeatmapAnnotation(df = get_anno(res_list),
col = get_anno_col(res_list)), ylab = "value", cluster_columns = TRUE, show_column_names = FALSE,
mc.cores = 4)
Folowing table shows the best k (number of partitions) for each combination
of top-value methods and partition methods. Clicking on the method name in
the table goes to the section for a single combination of methods.
The cola vignette explains the definition of the metrics used for determining the best number of partitions.
suggest_best_k(res_list)
| The best k | 1-PAC | Mean silhouette | Concordance | Optional k | ||
|---|---|---|---|---|---|---|
| SD:pam | 2 | 1.000 | 0.988 | 0.995 | ** | |
| SD:NMF | 3 | 1.000 | 0.965 | 0.985 | ** | 2 |
| MAD:skmeans | 3 | 1.000 | 0.947 | 0.980 | ** | 2 |
| ATC:kmeans | 2 | 1.000 | 0.992 | 0.997 | ** | |
| ATC:mclust | 2 | 1.000 | 0.989 | 0.995 | ** | |
| ATC:NMF | 2 | 1.000 | 0.985 | 0.994 | ** | |
| MAD:NMF | 3 | 1.000 | 0.977 | 0.990 | ** | 2 |
| SD:hclust | 2 | 0.979 | 0.951 | 0.975 | ** | |
| CV:kmeans | 4 | 0.974 | 0.928 | 0.969 | ** | 2,3 |
| ATC:pam | 4 | 0.969 | 0.936 | 0.975 | ** | 2 |
| CV:pam | 6 | 0.968 | 0.911 | 0.958 | ** | 2,4 |
| CV:skmeans | 4 | 0.961 | 0.915 | 0.966 | ** | 2,3 |
| MAD:mclust | 4 | 0.961 | 0.920 | 0.968 | ** | 2 |
| SD:skmeans | 4 | 0.957 | 0.918 | 0.967 | ** | 2,3 |
| MAD:pam | 4 | 0.947 | 0.914 | 0.966 | * | 2 |
| CV:NMF | 4 | 0.937 | 0.904 | 0.959 | * | 2,3 |
| MAD:hclust | 2 | 0.930 | 0.926 | 0.969 | * | |
| SD:kmeans | 4 | 0.927 | 0.876 | 0.951 | * | 2,3 |
| CV:mclust | 4 | 0.917 | 0.893 | 0.938 | * | |
| MAD:kmeans | 4 | 0.916 | 0.870 | 0.945 | * | 2,3 |
| ATC:hclust | 2 | 0.910 | 0.957 | 0.981 | * | |
| ATC:skmeans | 5 | 0.903 | 0.891 | 0.943 | * | 2 |
| SD:mclust | 4 | 0.890 | 0.885 | 0.945 | ||
| CV:hclust | 3 | 0.696 | 0.706 | 0.878 |
**: 1-PAC > 0.95, *: 1-PAC > 0.9
Cumulative distribution function curves of consensus matrix for all methods.
collect_plots(res_list, fun = plot_ecdf)
Consensus heatmaps for all methods. (What is a consensus heatmap?)
collect_plots(res_list, k = 2, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 3, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 4, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 5, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 6, fun = consensus_heatmap, mc.cores = 4)
Membership heatmaps for all methods. (What is a membership heatmap?)
collect_plots(res_list, k = 2, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 3, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 4, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 5, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 6, fun = membership_heatmap, mc.cores = 4)
Signature heatmaps for all methods. (What is a signature heatmap?)
Note in following heatmaps, rows are scaled.
collect_plots(res_list, k = 2, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 3, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 4, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 5, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 6, fun = get_signatures, mc.cores = 4)
The statistics used for measuring the stability of consensus partitioning. (How are they defined?)
get_stats(res_list, k = 2)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 2 1.000 0.966 0.987 0.422 0.585 0.585
#> CV:NMF 2 0.999 0.964 0.985 0.436 0.567 0.567
#> MAD:NMF 2 1.000 0.977 0.990 0.428 0.575 0.575
#> ATC:NMF 2 1.000 0.985 0.994 0.412 0.585 0.585
#> SD:skmeans 2 0.954 0.950 0.979 0.477 0.525 0.525
#> CV:skmeans 2 1.000 0.949 0.980 0.485 0.515 0.515
#> MAD:skmeans 2 0.976 0.939 0.977 0.483 0.519 0.519
#> ATC:skmeans 2 1.000 0.987 0.995 0.439 0.558 0.558
#> SD:mclust 2 0.810 0.941 0.968 0.415 0.594 0.594
#> CV:mclust 2 0.754 0.804 0.922 0.445 0.594 0.594
#> MAD:mclust 2 1.000 0.975 0.986 0.409 0.594 0.594
#> ATC:mclust 2 1.000 0.989 0.995 0.429 0.575 0.575
#> SD:kmeans 2 1.000 0.972 0.985 0.393 0.615 0.615
#> CV:kmeans 2 1.000 0.969 0.986 0.406 0.604 0.604
#> MAD:kmeans 2 1.000 0.966 0.987 0.400 0.604 0.604
#> ATC:kmeans 2 1.000 0.992 0.997 0.388 0.615 0.615
#> SD:pam 2 1.000 0.988 0.995 0.413 0.585 0.585
#> CV:pam 2 0.931 0.924 0.970 0.433 0.585 0.585
#> MAD:pam 2 1.000 0.981 0.993 0.418 0.585 0.585
#> ATC:pam 2 1.000 1.000 1.000 0.406 0.594 0.594
#> SD:hclust 2 0.979 0.951 0.975 0.348 0.676 0.676
#> CV:hclust 2 0.860 0.870 0.950 0.375 0.626 0.626
#> MAD:hclust 2 0.930 0.926 0.969 0.368 0.626 0.626
#> ATC:hclust 2 0.910 0.957 0.981 0.375 0.626 0.626
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 1.000 0.965 0.985 0.542 0.721 0.539
#> CV:NMF 3 0.970 0.957 0.981 0.492 0.756 0.578
#> MAD:NMF 3 1.000 0.977 0.990 0.530 0.758 0.584
#> ATC:NMF 3 0.720 0.855 0.913 0.430 0.788 0.644
#> SD:skmeans 3 1.000 0.956 0.982 0.378 0.733 0.528
#> CV:skmeans 3 0.945 0.948 0.978 0.352 0.768 0.574
#> MAD:skmeans 3 1.000 0.947 0.980 0.364 0.747 0.545
#> ATC:skmeans 3 0.656 0.811 0.876 0.408 0.773 0.601
#> SD:mclust 3 0.778 0.859 0.904 0.533 0.716 0.533
#> CV:mclust 3 0.781 0.889 0.941 0.466 0.713 0.529
#> MAD:mclust 3 0.790 0.859 0.914 0.557 0.716 0.533
#> ATC:mclust 3 0.774 0.893 0.947 0.447 0.766 0.610
#> SD:kmeans 3 0.966 0.940 0.975 0.577 0.765 0.619
#> CV:kmeans 3 0.951 0.959 0.982 0.560 0.736 0.572
#> MAD:kmeans 3 0.965 0.924 0.970 0.602 0.725 0.554
#> ATC:kmeans 3 0.602 0.787 0.879 0.571 0.722 0.553
#> SD:pam 3 0.748 0.828 0.913 0.567 0.690 0.498
#> CV:pam 3 0.749 0.851 0.912 0.494 0.690 0.497
#> MAD:pam 3 0.736 0.765 0.910 0.552 0.741 0.561
#> ATC:pam 3 0.848 0.858 0.943 0.415 0.787 0.649
#> SD:hclust 3 0.735 0.792 0.898 0.705 0.776 0.669
#> CV:hclust 3 0.696 0.706 0.878 0.634 0.768 0.629
#> MAD:hclust 3 0.718 0.853 0.925 0.596 0.792 0.668
#> ATC:hclust 3 0.814 0.874 0.937 0.121 0.986 0.977
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.899 0.903 0.956 0.1397 0.838 0.578
#> CV:NMF 4 0.937 0.904 0.959 0.1311 0.834 0.569
#> MAD:NMF 4 0.874 0.872 0.942 0.1352 0.844 0.587
#> ATC:NMF 4 0.725 0.591 0.796 0.2134 0.697 0.394
#> SD:skmeans 4 0.957 0.918 0.967 0.0913 0.926 0.789
#> CV:skmeans 4 0.961 0.915 0.966 0.0906 0.930 0.800
#> MAD:skmeans 4 0.893 0.890 0.956 0.0961 0.913 0.753
#> ATC:skmeans 4 0.780 0.826 0.897 0.1722 0.794 0.494
#> SD:mclust 4 0.890 0.885 0.945 0.1309 0.919 0.768
#> CV:mclust 4 0.917 0.893 0.938 0.0926 0.886 0.690
#> MAD:mclust 4 0.961 0.920 0.968 0.1266 0.931 0.802
#> ATC:mclust 4 0.855 0.857 0.930 0.1590 0.853 0.630
#> SD:kmeans 4 0.927 0.876 0.951 0.1637 0.858 0.647
#> CV:kmeans 4 0.974 0.928 0.969 0.1387 0.869 0.660
#> MAD:kmeans 4 0.916 0.870 0.945 0.1410 0.849 0.608
#> ATC:kmeans 4 0.626 0.778 0.849 0.1500 0.895 0.714
#> SD:pam 4 0.893 0.916 0.962 0.1368 0.914 0.750
#> CV:pam 4 0.975 0.957 0.981 0.1463 0.911 0.742
#> MAD:pam 4 0.947 0.914 0.966 0.1332 0.856 0.614
#> ATC:pam 4 0.969 0.936 0.975 0.0928 0.944 0.867
#> SD:hclust 4 0.699 0.875 0.874 0.1695 0.824 0.612
#> CV:hclust 4 0.683 0.797 0.844 0.1231 0.857 0.655
#> MAD:hclust 4 0.636 0.649 0.808 0.1517 0.921 0.812
#> ATC:hclust 4 0.745 0.827 0.919 0.1825 0.931 0.887
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.790 0.747 0.868 0.0497 0.946 0.800
#> CV:NMF 5 0.799 0.809 0.866 0.0532 0.940 0.785
#> MAD:NMF 5 0.772 0.724 0.863 0.0479 0.942 0.789
#> ATC:NMF 5 0.666 0.617 0.815 0.0471 0.877 0.645
#> SD:skmeans 5 0.806 0.772 0.846 0.0936 0.893 0.642
#> CV:skmeans 5 0.788 0.767 0.826 0.0944 0.898 0.660
#> MAD:skmeans 5 0.792 0.668 0.852 0.0822 0.913 0.698
#> ATC:skmeans 5 0.903 0.891 0.943 0.0587 0.847 0.523
#> SD:mclust 5 0.757 0.752 0.862 0.0538 0.906 0.704
#> CV:mclust 5 0.681 0.641 0.808 0.0748 0.911 0.709
#> MAD:mclust 5 0.796 0.790 0.889 0.0595 0.909 0.705
#> ATC:mclust 5 0.753 0.767 0.862 0.0498 0.912 0.707
#> SD:kmeans 5 0.733 0.636 0.822 0.0771 0.919 0.723
#> CV:kmeans 5 0.747 0.662 0.826 0.0756 0.918 0.722
#> MAD:kmeans 5 0.732 0.695 0.757 0.0658 0.935 0.788
#> ATC:kmeans 5 0.699 0.693 0.770 0.0840 0.951 0.831
#> SD:pam 5 0.789 0.684 0.865 0.0846 0.860 0.532
#> CV:pam 5 0.858 0.894 0.926 0.0754 0.886 0.600
#> MAD:pam 5 0.843 0.816 0.906 0.0873 0.893 0.622
#> ATC:pam 5 0.650 0.772 0.857 0.1401 0.898 0.734
#> SD:hclust 5 0.777 0.831 0.885 0.0601 1.000 1.000
#> CV:hclust 5 0.726 0.732 0.858 0.0442 0.971 0.904
#> MAD:hclust 5 0.712 0.650 0.809 0.0828 0.880 0.660
#> ATC:hclust 5 0.585 0.698 0.852 0.1296 0.907 0.832
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.853 0.738 0.890 0.0451 0.913 0.653
#> CV:NMF 6 0.864 0.748 0.892 0.0502 0.914 0.657
#> MAD:NMF 6 0.857 0.765 0.890 0.0443 0.900 0.613
#> ATC:NMF 6 0.691 0.699 0.831 0.0408 0.914 0.699
#> SD:skmeans 6 0.781 0.658 0.821 0.0419 0.958 0.810
#> CV:skmeans 6 0.766 0.576 0.762 0.0426 0.982 0.913
#> MAD:skmeans 6 0.766 0.601 0.785 0.0430 0.911 0.634
#> ATC:skmeans 6 0.825 0.783 0.877 0.0274 0.968 0.866
#> SD:mclust 6 0.699 0.644 0.775 0.0587 0.884 0.585
#> CV:mclust 6 0.734 0.685 0.792 0.0485 0.884 0.571
#> MAD:mclust 6 0.725 0.611 0.759 0.0520 0.928 0.714
#> ATC:mclust 6 0.806 0.695 0.856 0.0530 0.897 0.631
#> SD:kmeans 6 0.713 0.584 0.738 0.0469 0.939 0.746
#> CV:kmeans 6 0.726 0.591 0.767 0.0437 0.931 0.715
#> MAD:kmeans 6 0.707 0.613 0.760 0.0438 0.910 0.685
#> ATC:kmeans 6 0.752 0.581 0.751 0.0531 0.975 0.899
#> SD:pam 6 0.803 0.592 0.753 0.0322 0.891 0.537
#> CV:pam 6 0.968 0.911 0.958 0.0213 0.982 0.911
#> MAD:pam 6 0.845 0.798 0.904 0.0206 0.982 0.910
#> ATC:pam 6 0.762 0.784 0.829 0.1124 0.821 0.448
#> SD:hclust 6 0.765 0.809 0.875 0.0516 0.928 0.741
#> CV:hclust 6 0.714 0.689 0.822 0.0432 0.961 0.867
#> MAD:hclust 6 0.730 0.736 0.840 0.0503 0.917 0.690
#> ATC:hclust 6 0.638 0.630 0.777 0.1978 0.828 0.628
Following heatmap plots the partition for each combination of methods and the lightness correspond to the silhouette scores for samples in each method. On top the consensus subgroup is inferred from all methods by taking the mean silhouette scores as weight.
collect_stats(res_list, k = 2)
collect_stats(res_list, k = 3)
collect_stats(res_list, k = 4)
collect_stats(res_list, k = 5)
collect_stats(res_list, k = 6)
Collect partitions from all methods:
collect_classes(res_list, k = 2)
collect_classes(res_list, k = 3)
collect_classes(res_list, k = 4)
collect_classes(res_list, k = 5)
collect_classes(res_list, k = 6)
Overlap of top rows from different top-row methods:
top_rows_overlap(res_list, top_n = 1000, method = "euler")
top_rows_overlap(res_list, top_n = 2000, method = "euler")
top_rows_overlap(res_list, top_n = 3000, method = "euler")
top_rows_overlap(res_list, top_n = 4000, method = "euler")
top_rows_overlap(res_list, top_n = 5000, method = "euler")
Also visualize the correspondance of rankings between different top-row methods:
top_rows_overlap(res_list, top_n = 1000, method = "correspondance")
top_rows_overlap(res_list, top_n = 2000, method = "correspondance")
top_rows_overlap(res_list, top_n = 3000, method = "correspondance")
top_rows_overlap(res_list, top_n = 4000, method = "correspondance")
top_rows_overlap(res_list, top_n = 5000, method = "correspondance")
Heatmaps of the top rows:
top_rows_heatmap(res_list, top_n = 1000)
top_rows_heatmap(res_list, top_n = 2000)
top_rows_heatmap(res_list, top_n = 3000)
top_rows_heatmap(res_list, top_n = 4000)
top_rows_heatmap(res_list, top_n = 5000)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res_list, k = 2)
#> n tissue(p) disease.state(p) individual(p) k
#> SD:NMF 89 5.55e-05 0.219 0.616 2
#> CV:NMF 89 1.04e-05 0.188 0.726 2
#> MAD:NMF 90 3.47e-05 0.176 0.644 2
#> ATC:NMF 89 1.62e-05 0.236 0.559 2
#> SD:skmeans 88 4.87e-06 0.547 0.842 2
#> CV:skmeans 87 9.67e-07 0.475 0.831 2
#> MAD:skmeans 87 2.96e-06 0.521 0.864 2
#> ATC:skmeans 89 1.99e-05 0.227 0.726 2
#> SD:mclust 89 3.70e-05 0.193 0.501 2
#> CV:mclust 77 9.27e-07 0.353 0.768 2
#> MAD:mclust 90 2.27e-05 0.143 0.530 2
#> ATC:mclust 89 5.58e-06 0.237 0.672 2
#> SD:kmeans 88 6.08e-05 0.209 0.473 2
#> CV:kmeans 89 3.70e-05 0.223 0.501 2
#> MAD:kmeans 88 6.08e-05 0.209 0.473 2
#> ATC:kmeans 90 1.10e-04 0.296 0.417 2
#> SD:pam 90 7.70e-05 0.240 0.587 2
#> CV:pam 87 2.74e-05 0.222 0.674 2
#> MAD:pam 89 5.55e-05 0.219 0.616 2
#> ATC:pam 90 2.27e-05 0.233 0.530 2
#> SD:hclust 90 3.75e-03 0.160 0.178 2
#> CV:hclust 83 3.62e-04 0.218 0.382 2
#> MAD:hclust 86 8.01e-04 0.195 0.306 2
#> ATC:hclust 90 2.34e-04 0.285 0.363 2
test_to_known_factors(res_list, k = 3)
#> n tissue(p) disease.state(p) individual(p) k
#> SD:NMF 89 3.41e-11 0.244 0.695 3
#> CV:NMF 89 3.41e-11 0.244 0.695 3
#> MAD:NMF 90 9.16e-11 0.259 0.733 3
#> ATC:NMF 84 9.89e-05 0.232 0.142 3
#> SD:skmeans 88 2.59e-10 0.172 0.735 3
#> CV:skmeans 88 1.71e-10 0.166 0.653 3
#> MAD:skmeans 88 2.59e-10 0.172 0.735 3
#> ATC:skmeans 83 5.53e-06 0.131 0.319 3
#> SD:mclust 90 1.63e-10 0.402 0.570 3
#> CV:mclust 87 1.24e-10 0.371 0.568 3
#> MAD:mclust 88 4.17e-10 0.459 0.513 3
#> ATC:mclust 89 2.72e-09 0.106 0.405 3
#> SD:kmeans 87 6.75e-09 0.122 0.360 3
#> CV:kmeans 90 1.20e-10 0.312 0.574 3
#> MAD:kmeans 86 3.75e-11 0.308 0.623 3
#> ATC:kmeans 80 3.20e-07 0.504 0.488 3
#> SD:pam 85 7.04e-11 0.482 0.801 3
#> CV:pam 88 4.99e-11 0.404 0.753 3
#> MAD:pam 79 2.25e-10 0.343 0.657 3
#> ATC:pam 79 5.23e-05 0.588 0.417 3
#> SD:hclust 79 2.47e-08 0.123 0.490 3
#> CV:hclust 70 1.90e-08 0.159 0.643 3
#> MAD:hclust 85 2.23e-07 0.121 0.486 3
#> ATC:hclust 89 6.25e-04 0.273 0.311 3
test_to_known_factors(res_list, k = 4)
#> n tissue(p) disease.state(p) individual(p) k
#> SD:NMF 88 3.24e-08 0.1629 0.420 4
#> CV:NMF 86 8.20e-08 0.1927 0.483 4
#> MAD:NMF 86 3.48e-08 0.1845 0.329 4
#> ATC:NMF 70 1.13e-08 0.1970 0.526 4
#> SD:skmeans 86 9.38e-10 0.2772 0.303 4
#> CV:skmeans 86 8.89e-10 0.2582 0.304 4
#> MAD:skmeans 86 3.07e-09 0.3459 0.328 4
#> ATC:skmeans 87 1.01e-08 0.1270 0.585 4
#> SD:mclust 86 1.14e-09 0.1160 0.429 4
#> CV:mclust 86 9.29e-10 0.1184 0.560 4
#> MAD:mclust 87 1.42e-10 0.1061 0.527 4
#> ATC:mclust 87 3.52e-09 0.1548 0.466 4
#> SD:kmeans 83 2.78e-09 0.1177 0.321 4
#> CV:kmeans 87 4.74e-09 0.1091 0.315 4
#> MAD:kmeans 83 5.91e-09 0.1221 0.362 4
#> ATC:kmeans 85 5.03e-06 0.3688 0.383 4
#> SD:pam 88 4.01e-10 0.1419 0.549 4
#> CV:pam 90 3.70e-10 0.1306 0.503 4
#> MAD:pam 87 7.89e-10 0.1313 0.413 4
#> ATC:pam 88 4.96e-05 0.0964 0.465 4
#> SD:hclust 90 1.19e-09 0.0989 0.348 4
#> CV:hclust 80 7.97e-09 0.2004 0.345 4
#> MAD:hclust 76 1.23e-08 0.2914 0.357 4
#> ATC:hclust 88 1.53e-04 0.4415 0.428 4
test_to_known_factors(res_list, k = 5)
#> n tissue(p) disease.state(p) individual(p) k
#> SD:NMF 76 2.61e-08 0.1476 0.274 5
#> CV:NMF 84 4.64e-09 0.0432 0.307 5
#> MAD:NMF 76 7.56e-09 0.2252 0.259 5
#> ATC:NMF 63 1.58e-08 0.1852 0.506 5
#> SD:skmeans 83 3.11e-08 0.1453 0.108 5
#> CV:skmeans 81 1.85e-08 0.1698 0.177 5
#> MAD:skmeans 70 1.50e-07 0.1701 0.198 5
#> ATC:skmeans 88 4.44e-08 0.2393 0.369 5
#> SD:mclust 81 5.58e-08 0.1066 0.423 5
#> CV:mclust 69 1.07e-07 0.0452 0.491 5
#> MAD:mclust 83 2.10e-08 0.0328 0.381 5
#> ATC:mclust 82 3.16e-09 0.3893 0.178 5
#> SD:kmeans 71 1.99e-07 0.1041 0.147 5
#> CV:kmeans 74 7.56e-07 0.1242 0.143 5
#> MAD:kmeans 79 4.70e-09 0.1205 0.273 5
#> ATC:kmeans 76 4.61e-06 0.0658 0.272 5
#> SD:pam 72 4.01e-07 0.1846 0.210 5
#> CV:pam 88 1.23e-08 0.1024 0.298 5
#> MAD:pam 83 8.12e-08 0.1455 0.221 5
#> ATC:pam 84 2.02e-05 0.0221 0.175 5
#> SD:hclust 87 3.92e-09 0.0651 0.389 5
#> CV:hclust 75 2.02e-08 0.0888 0.359 5
#> MAD:hclust 75 5.45e-07 0.1257 0.279 5
#> ATC:hclust 75 3.66e-04 0.6750 0.413 5
test_to_known_factors(res_list, k = 6)
#> n tissue(p) disease.state(p) individual(p) k
#> SD:NMF 74 1.28e-06 0.1336 0.226 6
#> CV:NMF 75 1.39e-06 0.1377 0.157 6
#> MAD:NMF 78 1.77e-07 0.2662 0.200 6
#> ATC:NMF 67 3.43e-07 0.3627 0.782 6
#> SD:skmeans 68 8.62e-07 0.0593 0.013 6
#> CV:skmeans 53 4.95e-06 0.3984 0.184 6
#> MAD:skmeans 57 6.73e-06 0.1744 0.395 6
#> ATC:skmeans 83 4.02e-07 0.1472 0.333 6
#> SD:mclust 77 1.25e-08 0.1094 0.216 6
#> CV:mclust 78 1.96e-08 0.0660 0.273 6
#> MAD:mclust 72 3.14e-07 0.0460 0.200 6
#> ATC:mclust 80 2.89e-07 0.0544 0.197 6
#> SD:kmeans 70 1.06e-07 0.2721 0.237 6
#> CV:kmeans 70 9.17e-07 0.1770 0.193 6
#> MAD:kmeans 70 9.12e-08 0.2648 0.400 6
#> ATC:kmeans 68 5.00e-05 0.1443 0.473 6
#> SD:pam 70 1.48e-06 0.1795 0.355 6
#> CV:pam 87 4.00e-08 0.1128 0.240 6
#> MAD:pam 84 2.21e-08 0.1779 0.197 6
#> ATC:pam 87 2.04e-07 0.0785 0.324 6
#> SD:hclust 85 1.13e-08 0.0425 0.431 6
#> CV:hclust 74 9.32e-08 0.0379 0.205 6
#> MAD:hclust 72 8.66e-08 0.1514 0.558 6
#> ATC:hclust 68 3.69e-07 0.4445 0.554 6
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "hclust"]
# you can also extract it by
# res = res_list["SD:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 27425 rows and 90 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.979 0.951 0.975 0.3479 0.676 0.676
#> 3 3 0.735 0.792 0.898 0.7051 0.776 0.669
#> 4 4 0.699 0.875 0.874 0.1695 0.824 0.612
#> 5 5 0.777 0.831 0.885 0.0601 1.000 1.000
#> 6 6 0.765 0.809 0.875 0.0516 0.928 0.741
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM711936 2 0.0376 0.995 0.004 0.996
#> GSM711938 2 0.0000 0.998 0.000 1.000
#> GSM711950 1 0.0000 0.969 1.000 0.000
#> GSM711956 1 0.0000 0.969 1.000 0.000
#> GSM711958 1 0.0000 0.969 1.000 0.000
#> GSM711960 1 0.0000 0.969 1.000 0.000
#> GSM711964 1 0.0000 0.969 1.000 0.000
#> GSM711966 1 0.0000 0.969 1.000 0.000
#> GSM711968 1 0.0000 0.969 1.000 0.000
#> GSM711972 1 0.0000 0.969 1.000 0.000
#> GSM711976 1 0.0000 0.969 1.000 0.000
#> GSM711980 1 0.0000 0.969 1.000 0.000
#> GSM711986 1 0.0000 0.969 1.000 0.000
#> GSM711904 1 0.0000 0.969 1.000 0.000
#> GSM711906 1 0.0000 0.969 1.000 0.000
#> GSM711908 1 0.0000 0.969 1.000 0.000
#> GSM711910 1 0.0000 0.969 1.000 0.000
#> GSM711914 1 0.0000 0.969 1.000 0.000
#> GSM711916 1 0.0000 0.969 1.000 0.000
#> GSM711922 1 0.0000 0.969 1.000 0.000
#> GSM711924 1 0.0000 0.969 1.000 0.000
#> GSM711926 1 0.3584 0.924 0.932 0.068
#> GSM711928 1 0.0000 0.969 1.000 0.000
#> GSM711930 1 0.0000 0.969 1.000 0.000
#> GSM711932 1 0.0000 0.969 1.000 0.000
#> GSM711934 1 0.0000 0.969 1.000 0.000
#> GSM711940 1 0.0000 0.969 1.000 0.000
#> GSM711942 1 0.0000 0.969 1.000 0.000
#> GSM711944 1 0.0000 0.969 1.000 0.000
#> GSM711946 1 0.2778 0.939 0.952 0.048
#> GSM711948 1 0.0000 0.969 1.000 0.000
#> GSM711952 1 0.0000 0.969 1.000 0.000
#> GSM711954 1 0.0000 0.969 1.000 0.000
#> GSM711962 1 0.0000 0.969 1.000 0.000
#> GSM711970 1 0.0000 0.969 1.000 0.000
#> GSM711974 1 0.0000 0.969 1.000 0.000
#> GSM711978 1 0.2603 0.942 0.956 0.044
#> GSM711988 1 0.0000 0.969 1.000 0.000
#> GSM711990 1 0.0000 0.969 1.000 0.000
#> GSM711992 1 0.3584 0.924 0.932 0.068
#> GSM711982 1 0.0000 0.969 1.000 0.000
#> GSM711984 2 0.0000 0.998 0.000 1.000
#> GSM711912 1 0.0000 0.969 1.000 0.000
#> GSM711918 1 0.0000 0.969 1.000 0.000
#> GSM711920 1 0.0000 0.969 1.000 0.000
#> GSM711937 2 0.0376 0.995 0.004 0.996
#> GSM711939 2 0.0000 0.998 0.000 1.000
#> GSM711951 1 0.9000 0.590 0.684 0.316
#> GSM711957 1 0.0000 0.969 1.000 0.000
#> GSM711959 2 0.0000 0.998 0.000 1.000
#> GSM711961 2 0.0000 0.998 0.000 1.000
#> GSM711965 1 0.0000 0.969 1.000 0.000
#> GSM711967 1 0.0000 0.969 1.000 0.000
#> GSM711969 2 0.0376 0.995 0.004 0.996
#> GSM711973 1 0.0000 0.969 1.000 0.000
#> GSM711977 1 0.0000 0.969 1.000 0.000
#> GSM711981 1 0.4022 0.914 0.920 0.080
#> GSM711987 2 0.0000 0.998 0.000 1.000
#> GSM711905 2 0.0000 0.998 0.000 1.000
#> GSM711907 1 0.9248 0.542 0.660 0.340
#> GSM711909 1 0.0000 0.969 1.000 0.000
#> GSM711911 1 0.0000 0.969 1.000 0.000
#> GSM711915 1 0.0000 0.969 1.000 0.000
#> GSM711917 2 0.1414 0.979 0.020 0.980
#> GSM711923 1 0.2423 0.945 0.960 0.040
#> GSM711925 2 0.0000 0.998 0.000 1.000
#> GSM711927 1 0.0000 0.969 1.000 0.000
#> GSM711929 2 0.0000 0.998 0.000 1.000
#> GSM711931 1 0.5178 0.879 0.884 0.116
#> GSM711933 1 0.0000 0.969 1.000 0.000
#> GSM711935 2 0.0000 0.998 0.000 1.000
#> GSM711941 1 0.0000 0.969 1.000 0.000
#> GSM711943 1 0.2423 0.945 0.960 0.040
#> GSM711945 1 0.2778 0.939 0.952 0.048
#> GSM711947 1 0.5629 0.864 0.868 0.132
#> GSM711949 2 0.0000 0.998 0.000 1.000
#> GSM711953 2 0.0000 0.998 0.000 1.000
#> GSM711955 1 0.0000 0.969 1.000 0.000
#> GSM711963 2 0.0000 0.998 0.000 1.000
#> GSM711971 1 0.0000 0.969 1.000 0.000
#> GSM711975 1 0.9000 0.590 0.684 0.316
#> GSM711979 1 0.2603 0.942 0.956 0.044
#> GSM711989 1 0.9000 0.590 0.684 0.316
#> GSM711991 1 0.4022 0.914 0.920 0.080
#> GSM711993 1 0.4022 0.914 0.920 0.080
#> GSM711983 1 0.0000 0.969 1.000 0.000
#> GSM711985 2 0.0000 0.998 0.000 1.000
#> GSM711913 1 0.0000 0.969 1.000 0.000
#> GSM711919 1 0.0000 0.969 1.000 0.000
#> GSM711921 1 0.0000 0.969 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM711936 2 0.0237 0.9945 0.000 0.996 0.004
#> GSM711938 2 0.0000 0.9977 0.000 1.000 0.000
#> GSM711950 1 0.0892 0.8298 0.980 0.000 0.020
#> GSM711956 1 0.0000 0.8341 1.000 0.000 0.000
#> GSM711958 1 0.0592 0.8318 0.988 0.000 0.012
#> GSM711960 1 0.1643 0.8164 0.956 0.000 0.044
#> GSM711964 1 0.0000 0.8341 1.000 0.000 0.000
#> GSM711966 1 0.0000 0.8341 1.000 0.000 0.000
#> GSM711968 1 0.0000 0.8341 1.000 0.000 0.000
#> GSM711972 1 0.0000 0.8341 1.000 0.000 0.000
#> GSM711976 1 0.0592 0.8318 0.988 0.000 0.012
#> GSM711980 1 0.0592 0.8318 0.988 0.000 0.012
#> GSM711986 1 0.0000 0.8341 1.000 0.000 0.000
#> GSM711904 1 0.0237 0.8335 0.996 0.000 0.004
#> GSM711906 1 0.0000 0.8341 1.000 0.000 0.000
#> GSM711908 1 0.0000 0.8341 1.000 0.000 0.000
#> GSM711910 3 0.0000 0.9424 0.000 0.000 1.000
#> GSM711914 1 0.0000 0.8341 1.000 0.000 0.000
#> GSM711916 1 0.0000 0.8341 1.000 0.000 0.000
#> GSM711922 1 0.0000 0.8341 1.000 0.000 0.000
#> GSM711924 1 0.0000 0.8341 1.000 0.000 0.000
#> GSM711926 1 0.7764 0.5002 0.604 0.068 0.328
#> GSM711928 1 0.0000 0.8341 1.000 0.000 0.000
#> GSM711930 1 0.0000 0.8341 1.000 0.000 0.000
#> GSM711932 1 0.0000 0.8341 1.000 0.000 0.000
#> GSM711934 1 0.0592 0.8318 0.988 0.000 0.012
#> GSM711940 1 0.5968 0.5280 0.636 0.000 0.364
#> GSM711942 1 0.0000 0.8341 1.000 0.000 0.000
#> GSM711944 3 0.3816 0.8245 0.148 0.000 0.852
#> GSM711946 1 0.7648 0.4140 0.552 0.048 0.400
#> GSM711948 1 0.1411 0.8228 0.964 0.000 0.036
#> GSM711952 1 0.0000 0.8341 1.000 0.000 0.000
#> GSM711954 1 0.0592 0.8318 0.988 0.000 0.012
#> GSM711962 1 0.0000 0.8341 1.000 0.000 0.000
#> GSM711970 1 0.0424 0.8328 0.992 0.000 0.008
#> GSM711974 1 0.0592 0.8318 0.988 0.000 0.012
#> GSM711978 1 0.7138 0.5493 0.644 0.044 0.312
#> GSM711988 1 0.0592 0.8318 0.988 0.000 0.012
#> GSM711990 3 0.1411 0.9359 0.036 0.000 0.964
#> GSM711992 1 0.7618 0.5448 0.628 0.068 0.304
#> GSM711982 1 0.0000 0.8341 1.000 0.000 0.000
#> GSM711984 2 0.0000 0.9977 0.000 1.000 0.000
#> GSM711912 1 0.0000 0.8341 1.000 0.000 0.000
#> GSM711918 1 0.0000 0.8341 1.000 0.000 0.000
#> GSM711920 1 0.0000 0.8341 1.000 0.000 0.000
#> GSM711937 2 0.0237 0.9945 0.000 0.996 0.004
#> GSM711939 2 0.0000 0.9977 0.000 1.000 0.000
#> GSM711951 1 0.9981 0.0562 0.364 0.316 0.320
#> GSM711957 1 0.1411 0.8203 0.964 0.000 0.036
#> GSM711959 2 0.0000 0.9977 0.000 1.000 0.000
#> GSM711961 2 0.0000 0.9977 0.000 1.000 0.000
#> GSM711965 1 0.6062 0.4961 0.616 0.000 0.384
#> GSM711967 1 0.0000 0.8341 1.000 0.000 0.000
#> GSM711969 2 0.0237 0.9945 0.000 0.996 0.004
#> GSM711973 3 0.4235 0.7826 0.176 0.000 0.824
#> GSM711977 3 0.0892 0.9404 0.020 0.000 0.980
#> GSM711981 1 0.7992 0.4845 0.592 0.080 0.328
#> GSM711987 2 0.0000 0.9977 0.000 1.000 0.000
#> GSM711905 2 0.0000 0.9977 0.000 1.000 0.000
#> GSM711907 1 0.9990 0.0192 0.348 0.340 0.312
#> GSM711909 3 0.0000 0.9424 0.000 0.000 1.000
#> GSM711911 3 0.0000 0.9424 0.000 0.000 1.000
#> GSM711915 3 0.0000 0.9424 0.000 0.000 1.000
#> GSM711917 2 0.1015 0.9766 0.008 0.980 0.012
#> GSM711923 1 0.7346 0.4798 0.592 0.040 0.368
#> GSM711925 2 0.0000 0.9977 0.000 1.000 0.000
#> GSM711927 3 0.0000 0.9424 0.000 0.000 1.000
#> GSM711929 2 0.0000 0.9977 0.000 1.000 0.000
#> GSM711931 1 0.8573 0.4306 0.556 0.116 0.328
#> GSM711933 1 0.0892 0.8292 0.980 0.000 0.020
#> GSM711935 2 0.0000 0.9977 0.000 1.000 0.000
#> GSM711941 1 0.5968 0.5280 0.636 0.000 0.364
#> GSM711943 1 0.7271 0.5056 0.608 0.040 0.352
#> GSM711945 1 0.7648 0.4140 0.552 0.048 0.400
#> GSM711947 3 0.4128 0.8409 0.012 0.132 0.856
#> GSM711949 2 0.0000 0.9977 0.000 1.000 0.000
#> GSM711953 2 0.0000 0.9977 0.000 1.000 0.000
#> GSM711955 1 0.1643 0.8186 0.956 0.000 0.044
#> GSM711963 2 0.0000 0.9977 0.000 1.000 0.000
#> GSM711971 3 0.1411 0.9359 0.036 0.000 0.964
#> GSM711975 1 0.9981 0.0562 0.364 0.316 0.320
#> GSM711979 1 0.7138 0.5493 0.644 0.044 0.312
#> GSM711989 1 0.9981 0.0562 0.364 0.316 0.320
#> GSM711991 3 0.3802 0.8748 0.032 0.080 0.888
#> GSM711993 1 0.7992 0.4845 0.592 0.080 0.328
#> GSM711983 3 0.1411 0.9359 0.036 0.000 0.964
#> GSM711985 2 0.0000 0.9977 0.000 1.000 0.000
#> GSM711913 3 0.0892 0.9404 0.020 0.000 0.980
#> GSM711919 3 0.0000 0.9424 0.000 0.000 1.000
#> GSM711921 3 0.0000 0.9424 0.000 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM711936 2 0.0188 0.994 0.000 0.996 0.000 0.004
#> GSM711938 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM711950 1 0.1488 0.935 0.956 0.000 0.012 0.032
#> GSM711956 1 0.0188 0.946 0.996 0.000 0.000 0.004
#> GSM711958 1 0.1174 0.941 0.968 0.000 0.012 0.020
#> GSM711960 1 0.2111 0.919 0.932 0.000 0.044 0.024
#> GSM711964 1 0.0188 0.946 0.996 0.000 0.000 0.004
#> GSM711966 1 0.2345 0.902 0.900 0.000 0.000 0.100
#> GSM711968 1 0.0336 0.946 0.992 0.000 0.000 0.008
#> GSM711972 1 0.2345 0.902 0.900 0.000 0.000 0.100
#> GSM711976 1 0.1284 0.940 0.964 0.000 0.012 0.024
#> GSM711980 1 0.1284 0.940 0.964 0.000 0.012 0.024
#> GSM711986 1 0.2216 0.907 0.908 0.000 0.000 0.092
#> GSM711904 1 0.0524 0.946 0.988 0.000 0.004 0.008
#> GSM711906 1 0.1211 0.932 0.960 0.000 0.000 0.040
#> GSM711908 1 0.2408 0.900 0.896 0.000 0.000 0.104
#> GSM711910 3 0.0000 0.909 0.000 0.000 1.000 0.000
#> GSM711914 1 0.0188 0.946 0.996 0.000 0.000 0.004
#> GSM711916 1 0.2408 0.900 0.896 0.000 0.000 0.104
#> GSM711922 1 0.0336 0.946 0.992 0.000 0.000 0.008
#> GSM711924 1 0.0188 0.946 0.996 0.000 0.000 0.004
#> GSM711926 4 0.7228 0.752 0.088 0.068 0.200 0.644
#> GSM711928 1 0.0188 0.946 0.996 0.000 0.000 0.004
#> GSM711930 1 0.2408 0.900 0.896 0.000 0.000 0.104
#> GSM711932 1 0.1637 0.910 0.940 0.000 0.000 0.060
#> GSM711934 1 0.1284 0.940 0.964 0.000 0.012 0.024
#> GSM711940 4 0.7458 0.673 0.240 0.000 0.252 0.508
#> GSM711942 1 0.0188 0.946 0.996 0.000 0.000 0.004
#> GSM711944 3 0.3324 0.742 0.136 0.000 0.852 0.012
#> GSM711946 4 0.7824 0.735 0.120 0.048 0.280 0.552
#> GSM711948 1 0.2021 0.922 0.936 0.000 0.024 0.040
#> GSM711952 1 0.2408 0.900 0.896 0.000 0.000 0.104
#> GSM711954 1 0.1284 0.940 0.964 0.000 0.012 0.024
#> GSM711962 1 0.0469 0.945 0.988 0.000 0.000 0.012
#> GSM711970 1 0.1151 0.941 0.968 0.000 0.008 0.024
#> GSM711974 1 0.1174 0.941 0.968 0.000 0.012 0.020
#> GSM711978 4 0.7615 0.760 0.156 0.044 0.200 0.600
#> GSM711988 1 0.1284 0.940 0.964 0.000 0.012 0.024
#> GSM711990 3 0.1209 0.892 0.032 0.000 0.964 0.004
#> GSM711992 4 0.8933 0.566 0.324 0.068 0.204 0.404
#> GSM711982 1 0.2408 0.900 0.896 0.000 0.000 0.104
#> GSM711984 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM711912 1 0.2408 0.900 0.896 0.000 0.000 0.104
#> GSM711918 1 0.2408 0.900 0.896 0.000 0.000 0.104
#> GSM711920 1 0.0188 0.946 0.996 0.000 0.000 0.004
#> GSM711937 2 0.0188 0.994 0.000 0.996 0.000 0.004
#> GSM711939 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM711951 4 0.7963 0.599 0.016 0.316 0.196 0.472
#> GSM711957 4 0.3569 0.520 0.196 0.000 0.000 0.804
#> GSM711959 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM711961 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM711965 4 0.7389 0.677 0.212 0.000 0.272 0.516
#> GSM711967 1 0.0469 0.945 0.988 0.000 0.000 0.012
#> GSM711969 2 0.0188 0.994 0.000 0.996 0.000 0.004
#> GSM711973 3 0.4388 0.699 0.132 0.000 0.808 0.060
#> GSM711977 3 0.0707 0.900 0.000 0.000 0.980 0.020
#> GSM711981 4 0.7237 0.748 0.076 0.080 0.200 0.644
#> GSM711987 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM711905 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM711907 4 0.7973 0.575 0.016 0.340 0.188 0.456
#> GSM711909 3 0.0000 0.909 0.000 0.000 1.000 0.000
#> GSM711911 3 0.0000 0.909 0.000 0.000 1.000 0.000
#> GSM711915 3 0.0000 0.909 0.000 0.000 1.000 0.000
#> GSM711917 2 0.0804 0.975 0.000 0.980 0.012 0.008
#> GSM711923 4 0.8018 0.739 0.168 0.040 0.256 0.536
#> GSM711925 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM711927 3 0.0000 0.909 0.000 0.000 1.000 0.000
#> GSM711929 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM711931 4 0.7176 0.723 0.044 0.116 0.200 0.640
#> GSM711933 1 0.1624 0.933 0.952 0.000 0.020 0.028
#> GSM711935 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM711941 4 0.7458 0.673 0.240 0.000 0.252 0.508
#> GSM711943 4 0.7994 0.744 0.176 0.040 0.240 0.544
#> GSM711945 4 0.7824 0.735 0.120 0.048 0.280 0.552
#> GSM711947 3 0.5253 0.636 0.012 0.132 0.772 0.084
#> GSM711949 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM711953 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM711955 1 0.2313 0.911 0.924 0.000 0.032 0.044
#> GSM711963 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM711971 3 0.1209 0.892 0.032 0.000 0.964 0.004
#> GSM711975 4 0.7963 0.599 0.016 0.316 0.196 0.472
#> GSM711979 4 0.7615 0.760 0.156 0.044 0.200 0.600
#> GSM711989 4 0.7963 0.599 0.016 0.316 0.196 0.472
#> GSM711991 3 0.5188 0.623 0.012 0.080 0.776 0.132
#> GSM711993 4 0.7237 0.748 0.076 0.080 0.200 0.644
#> GSM711983 3 0.1209 0.892 0.032 0.000 0.964 0.004
#> GSM711985 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM711913 3 0.0707 0.900 0.000 0.000 0.980 0.020
#> GSM711919 3 0.0000 0.909 0.000 0.000 1.000 0.000
#> GSM711921 3 0.0000 0.909 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM711936 2 0.0609 0.986 0.000 0.980 0.000 0.020 NA
#> GSM711938 2 0.0510 0.988 0.000 0.984 0.000 0.016 NA
#> GSM711950 1 0.1356 0.889 0.956 0.000 0.012 0.028 NA
#> GSM711956 1 0.0162 0.899 0.996 0.000 0.000 0.000 NA
#> GSM711958 1 0.1299 0.894 0.960 0.000 0.012 0.020 NA
#> GSM711960 1 0.2095 0.877 0.928 0.000 0.028 0.020 NA
#> GSM711964 1 0.0162 0.899 0.996 0.000 0.000 0.000 NA
#> GSM711966 1 0.3242 0.810 0.784 0.000 0.000 0.000 NA
#> GSM711968 1 0.0162 0.899 0.996 0.000 0.000 0.000 NA
#> GSM711972 1 0.3452 0.794 0.756 0.000 0.000 0.000 NA
#> GSM711976 1 0.1173 0.893 0.964 0.000 0.012 0.020 NA
#> GSM711980 1 0.1173 0.893 0.964 0.000 0.012 0.020 NA
#> GSM711986 1 0.3612 0.778 0.732 0.000 0.000 0.000 NA
#> GSM711904 1 0.0932 0.898 0.972 0.000 0.004 0.004 NA
#> GSM711906 1 0.2127 0.866 0.892 0.000 0.000 0.000 NA
#> GSM711908 1 0.3730 0.763 0.712 0.000 0.000 0.000 NA
#> GSM711910 3 0.0404 0.846 0.000 0.000 0.988 0.000 NA
#> GSM711914 1 0.0162 0.899 0.996 0.000 0.000 0.000 NA
#> GSM711916 1 0.3508 0.788 0.748 0.000 0.000 0.000 NA
#> GSM711922 1 0.0162 0.899 0.996 0.000 0.000 0.000 NA
#> GSM711924 1 0.0162 0.899 0.996 0.000 0.000 0.000 NA
#> GSM711926 4 0.2158 0.773 0.052 0.008 0.000 0.920 NA
#> GSM711928 1 0.0162 0.899 0.996 0.000 0.000 0.000 NA
#> GSM711930 1 0.3730 0.763 0.712 0.000 0.000 0.000 NA
#> GSM711932 1 0.1270 0.877 0.948 0.000 0.000 0.052 NA
#> GSM711934 1 0.1173 0.893 0.964 0.000 0.012 0.020 NA
#> GSM711940 4 0.5079 0.708 0.232 0.000 0.040 0.700 NA
#> GSM711942 1 0.0162 0.899 0.996 0.000 0.000 0.000 NA
#> GSM711944 3 0.3197 0.746 0.140 0.000 0.836 0.000 NA
#> GSM711946 4 0.4593 0.767 0.112 0.008 0.072 0.788 NA
#> GSM711948 1 0.1885 0.877 0.936 0.000 0.020 0.032 NA
#> GSM711952 1 0.3730 0.763 0.712 0.000 0.000 0.000 NA
#> GSM711954 1 0.1173 0.893 0.964 0.000 0.012 0.020 NA
#> GSM711962 1 0.1270 0.889 0.948 0.000 0.000 0.000 NA
#> GSM711970 1 0.1059 0.894 0.968 0.000 0.008 0.020 NA
#> GSM711974 1 0.1299 0.894 0.960 0.000 0.012 0.020 NA
#> GSM711978 4 0.3246 0.783 0.120 0.008 0.000 0.848 NA
#> GSM711988 1 0.1173 0.893 0.964 0.000 0.012 0.020 NA
#> GSM711990 3 0.1469 0.839 0.036 0.000 0.948 0.000 NA
#> GSM711992 4 0.4483 0.595 0.308 0.008 0.012 0.672 NA
#> GSM711982 1 0.3508 0.788 0.748 0.000 0.000 0.000 NA
#> GSM711984 2 0.0510 0.988 0.000 0.984 0.000 0.016 NA
#> GSM711912 1 0.3730 0.763 0.712 0.000 0.000 0.000 NA
#> GSM711918 1 0.3730 0.763 0.712 0.000 0.000 0.000 NA
#> GSM711920 1 0.0162 0.899 0.996 0.000 0.000 0.000 NA
#> GSM711937 2 0.0609 0.986 0.000 0.980 0.000 0.020 NA
#> GSM711939 2 0.0510 0.988 0.000 0.984 0.000 0.016 NA
#> GSM711951 4 0.3452 0.662 0.000 0.244 0.000 0.756 NA
#> GSM711957 4 0.5557 0.406 0.068 0.000 0.000 0.472 NA
#> GSM711959 2 0.0510 0.988 0.000 0.984 0.000 0.016 NA
#> GSM711961 2 0.0000 0.989 0.000 1.000 0.000 0.000 NA
#> GSM711965 4 0.5153 0.716 0.208 0.000 0.060 0.708 NA
#> GSM711967 1 0.1197 0.890 0.952 0.000 0.000 0.000 NA
#> GSM711969 2 0.0609 0.986 0.000 0.980 0.000 0.020 NA
#> GSM711973 3 0.6674 0.626 0.136 0.000 0.592 0.056 NA
#> GSM711977 3 0.3829 0.775 0.000 0.000 0.776 0.028 NA
#> GSM711981 4 0.2011 0.770 0.044 0.008 0.000 0.928 NA
#> GSM711987 2 0.0000 0.989 0.000 1.000 0.000 0.000 NA
#> GSM711905 2 0.0000 0.989 0.000 1.000 0.000 0.000 NA
#> GSM711907 4 0.3612 0.630 0.000 0.268 0.000 0.732 NA
#> GSM711909 3 0.0000 0.848 0.000 0.000 1.000 0.000 NA
#> GSM711911 3 0.0000 0.848 0.000 0.000 1.000 0.000 NA
#> GSM711915 3 0.3690 0.775 0.000 0.000 0.764 0.012 NA
#> GSM711917 2 0.1043 0.967 0.000 0.960 0.000 0.040 NA
#> GSM711923 4 0.4731 0.764 0.160 0.008 0.048 0.764 NA
#> GSM711925 2 0.0000 0.989 0.000 1.000 0.000 0.000 NA
#> GSM711927 3 0.0000 0.848 0.000 0.000 1.000 0.000 NA
#> GSM711929 2 0.0000 0.989 0.000 1.000 0.000 0.000 NA
#> GSM711931 4 0.2011 0.749 0.008 0.044 0.000 0.928 NA
#> GSM711933 1 0.1518 0.888 0.952 0.000 0.016 0.020 NA
#> GSM711935 2 0.0000 0.989 0.000 1.000 0.000 0.000 NA
#> GSM711941 4 0.5079 0.708 0.232 0.000 0.040 0.700 NA
#> GSM711943 4 0.4475 0.768 0.164 0.008 0.032 0.776 NA
#> GSM711945 4 0.4593 0.767 0.112 0.008 0.072 0.788 NA
#> GSM711947 3 0.6230 0.253 0.000 0.060 0.528 0.372 NA
#> GSM711949 2 0.0000 0.989 0.000 1.000 0.000 0.000 NA
#> GSM711953 2 0.0000 0.989 0.000 1.000 0.000 0.000 NA
#> GSM711955 1 0.2180 0.868 0.924 0.000 0.024 0.032 NA
#> GSM711963 2 0.0000 0.989 0.000 1.000 0.000 0.000 NA
#> GSM711971 3 0.1469 0.839 0.036 0.000 0.948 0.000 NA
#> GSM711975 4 0.3452 0.662 0.000 0.244 0.000 0.756 NA
#> GSM711979 4 0.3246 0.783 0.120 0.008 0.000 0.848 NA
#> GSM711989 4 0.3452 0.662 0.000 0.244 0.000 0.756 NA
#> GSM711991 3 0.5453 0.198 0.000 0.008 0.528 0.420 NA
#> GSM711993 4 0.1934 0.768 0.040 0.008 0.000 0.932 NA
#> GSM711983 3 0.1469 0.839 0.036 0.000 0.948 0.000 NA
#> GSM711985 2 0.0510 0.988 0.000 0.984 0.000 0.016 NA
#> GSM711913 3 0.3829 0.775 0.000 0.000 0.776 0.028 NA
#> GSM711919 3 0.0000 0.848 0.000 0.000 1.000 0.000 NA
#> GSM711921 3 0.0404 0.846 0.000 0.000 0.988 0.000 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM711936 2 0.0603 0.985 0.000 0.980 0.000 0.016 0.000 0.004
#> GSM711938 2 0.0458 0.987 0.000 0.984 0.000 0.016 0.000 0.000
#> GSM711950 1 0.0260 0.933 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM711956 1 0.1075 0.932 0.952 0.000 0.000 0.000 0.000 0.048
#> GSM711958 1 0.0146 0.938 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM711960 1 0.0972 0.913 0.964 0.000 0.008 0.000 0.028 0.000
#> GSM711964 1 0.1075 0.932 0.952 0.000 0.000 0.000 0.000 0.048
#> GSM711966 6 0.3672 0.771 0.368 0.000 0.000 0.000 0.000 0.632
#> GSM711968 1 0.0865 0.937 0.964 0.000 0.000 0.000 0.000 0.036
#> GSM711972 6 0.3482 0.857 0.316 0.000 0.000 0.000 0.000 0.684
#> GSM711976 1 0.0000 0.938 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711980 1 0.0000 0.938 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711986 6 0.3244 0.864 0.268 0.000 0.000 0.000 0.000 0.732
#> GSM711904 1 0.1267 0.923 0.940 0.000 0.000 0.000 0.000 0.060
#> GSM711906 1 0.3266 0.514 0.728 0.000 0.000 0.000 0.000 0.272
#> GSM711908 6 0.2762 0.890 0.196 0.000 0.000 0.000 0.000 0.804
#> GSM711910 3 0.0551 0.768 0.000 0.000 0.984 0.004 0.008 0.004
#> GSM711914 1 0.1075 0.932 0.952 0.000 0.000 0.000 0.000 0.048
#> GSM711916 6 0.3390 0.874 0.296 0.000 0.000 0.000 0.000 0.704
#> GSM711922 1 0.0865 0.937 0.964 0.000 0.000 0.000 0.000 0.036
#> GSM711924 1 0.1007 0.934 0.956 0.000 0.000 0.000 0.000 0.044
#> GSM711926 4 0.1007 0.708 0.044 0.000 0.000 0.956 0.000 0.000
#> GSM711928 1 0.1075 0.932 0.952 0.000 0.000 0.000 0.000 0.048
#> GSM711930 6 0.2762 0.890 0.196 0.000 0.000 0.000 0.000 0.804
#> GSM711932 1 0.2066 0.895 0.908 0.000 0.000 0.052 0.000 0.040
#> GSM711934 1 0.0000 0.938 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711940 4 0.4607 0.644 0.268 0.000 0.016 0.676 0.036 0.004
#> GSM711942 1 0.1007 0.934 0.956 0.000 0.000 0.000 0.000 0.044
#> GSM711944 3 0.3094 0.639 0.140 0.000 0.824 0.000 0.036 0.000
#> GSM711946 4 0.4196 0.724 0.144 0.000 0.056 0.772 0.024 0.004
#> GSM711948 1 0.0820 0.915 0.972 0.000 0.000 0.012 0.016 0.000
#> GSM711952 6 0.2762 0.890 0.196 0.000 0.000 0.000 0.000 0.804
#> GSM711954 1 0.0000 0.938 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711962 1 0.2092 0.844 0.876 0.000 0.000 0.000 0.000 0.124
#> GSM711970 1 0.0146 0.939 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM711974 1 0.0146 0.938 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM711978 4 0.2243 0.723 0.112 0.000 0.000 0.880 0.004 0.004
#> GSM711988 1 0.0000 0.938 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711990 3 0.1572 0.759 0.036 0.000 0.936 0.000 0.028 0.000
#> GSM711992 4 0.3578 0.496 0.340 0.000 0.000 0.660 0.000 0.000
#> GSM711982 6 0.3390 0.874 0.296 0.000 0.000 0.000 0.000 0.704
#> GSM711984 2 0.0458 0.987 0.000 0.984 0.000 0.016 0.000 0.000
#> GSM711912 6 0.2762 0.890 0.196 0.000 0.000 0.000 0.000 0.804
#> GSM711918 6 0.2762 0.890 0.196 0.000 0.000 0.000 0.000 0.804
#> GSM711920 1 0.1007 0.934 0.956 0.000 0.000 0.000 0.000 0.044
#> GSM711937 2 0.0603 0.985 0.000 0.980 0.000 0.016 0.000 0.004
#> GSM711939 2 0.0458 0.987 0.000 0.984 0.000 0.016 0.000 0.000
#> GSM711951 4 0.3189 0.571 0.000 0.236 0.000 0.760 0.000 0.004
#> GSM711957 5 0.4915 0.000 0.000 0.000 0.000 0.188 0.656 0.156
#> GSM711959 2 0.0458 0.987 0.000 0.984 0.000 0.016 0.000 0.000
#> GSM711961 2 0.0000 0.987 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711965 4 0.4821 0.655 0.240 0.000 0.036 0.684 0.036 0.004
#> GSM711967 1 0.2003 0.855 0.884 0.000 0.000 0.000 0.000 0.116
#> GSM711969 2 0.0603 0.985 0.000 0.980 0.000 0.016 0.000 0.004
#> GSM711973 3 0.6371 0.390 0.136 0.000 0.500 0.044 0.316 0.004
#> GSM711977 3 0.3840 0.601 0.000 0.000 0.696 0.020 0.284 0.000
#> GSM711981 4 0.0865 0.703 0.036 0.000 0.000 0.964 0.000 0.000
#> GSM711987 2 0.0000 0.987 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711905 2 0.0000 0.987 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711907 4 0.3337 0.538 0.000 0.260 0.000 0.736 0.000 0.004
#> GSM711909 3 0.0000 0.771 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711911 3 0.0000 0.771 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711915 3 0.3721 0.595 0.000 0.000 0.684 0.004 0.308 0.004
#> GSM711917 2 0.0937 0.961 0.000 0.960 0.000 0.040 0.000 0.000
#> GSM711923 4 0.4218 0.716 0.192 0.000 0.032 0.748 0.024 0.004
#> GSM711925 2 0.0000 0.987 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711927 3 0.0000 0.771 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711929 2 0.0000 0.987 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711931 4 0.1010 0.667 0.000 0.036 0.000 0.960 0.000 0.004
#> GSM711933 1 0.0363 0.931 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM711935 2 0.0000 0.987 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711941 4 0.4607 0.644 0.268 0.000 0.016 0.676 0.036 0.004
#> GSM711943 4 0.3939 0.718 0.196 0.000 0.016 0.760 0.024 0.004
#> GSM711945 4 0.4196 0.724 0.144 0.000 0.056 0.772 0.024 0.004
#> GSM711947 3 0.6064 0.156 0.000 0.052 0.504 0.380 0.028 0.036
#> GSM711949 2 0.0000 0.987 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711953 2 0.0000 0.987 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711955 1 0.1074 0.902 0.960 0.000 0.000 0.012 0.028 0.000
#> GSM711963 2 0.0000 0.987 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711971 3 0.1572 0.759 0.036 0.000 0.936 0.000 0.028 0.000
#> GSM711975 4 0.3189 0.571 0.000 0.236 0.000 0.760 0.000 0.004
#> GSM711979 4 0.2243 0.723 0.112 0.000 0.000 0.880 0.004 0.004
#> GSM711989 4 0.3189 0.571 0.000 0.236 0.000 0.760 0.000 0.004
#> GSM711991 3 0.5291 0.147 0.000 0.000 0.504 0.424 0.032 0.040
#> GSM711993 4 0.0935 0.698 0.032 0.000 0.000 0.964 0.000 0.004
#> GSM711983 3 0.1572 0.759 0.036 0.000 0.936 0.000 0.028 0.000
#> GSM711985 2 0.0458 0.987 0.000 0.984 0.000 0.016 0.000 0.000
#> GSM711913 3 0.3840 0.601 0.000 0.000 0.696 0.020 0.284 0.000
#> GSM711919 3 0.0000 0.771 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711921 3 0.0551 0.768 0.000 0.000 0.984 0.004 0.008 0.004
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) disease.state(p) individual(p) k
#> SD:hclust 90 3.75e-03 0.1604 0.178 2
#> SD:hclust 79 2.47e-08 0.1225 0.490 3
#> SD:hclust 90 1.19e-09 0.0989 0.348 4
#> SD:hclust 87 3.92e-09 0.0651 0.389 5
#> SD:hclust 85 1.13e-08 0.0425 0.431 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "kmeans"]
# you can also extract it by
# res = res_list["SD:kmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 27425 rows and 90 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.972 0.985 0.3933 0.615 0.615
#> 3 3 0.966 0.940 0.975 0.5770 0.765 0.619
#> 4 4 0.927 0.876 0.951 0.1637 0.858 0.647
#> 5 5 0.733 0.636 0.822 0.0771 0.919 0.723
#> 6 6 0.713 0.584 0.738 0.0469 0.939 0.746
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 2 3
There is also optional best \(k\) = 2 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM711936 2 0.0938 1.000 0.012 0.988
#> GSM711938 2 0.0938 1.000 0.012 0.988
#> GSM711950 1 0.0000 0.984 1.000 0.000
#> GSM711956 1 0.0000 0.984 1.000 0.000
#> GSM711958 1 0.0376 0.983 0.996 0.004
#> GSM711960 1 0.0938 0.979 0.988 0.012
#> GSM711964 1 0.0000 0.984 1.000 0.000
#> GSM711966 1 0.0000 0.984 1.000 0.000
#> GSM711968 1 0.0000 0.984 1.000 0.000
#> GSM711972 1 0.0000 0.984 1.000 0.000
#> GSM711976 1 0.0000 0.984 1.000 0.000
#> GSM711980 1 0.0000 0.984 1.000 0.000
#> GSM711986 1 0.0000 0.984 1.000 0.000
#> GSM711904 1 0.0000 0.984 1.000 0.000
#> GSM711906 1 0.0000 0.984 1.000 0.000
#> GSM711908 1 0.0000 0.984 1.000 0.000
#> GSM711910 1 0.0938 0.979 0.988 0.012
#> GSM711914 1 0.0000 0.984 1.000 0.000
#> GSM711916 1 0.0000 0.984 1.000 0.000
#> GSM711922 1 0.0000 0.984 1.000 0.000
#> GSM711924 1 0.0000 0.984 1.000 0.000
#> GSM711926 1 0.0376 0.982 0.996 0.004
#> GSM711928 1 0.0000 0.984 1.000 0.000
#> GSM711930 1 0.0000 0.984 1.000 0.000
#> GSM711932 1 0.0000 0.984 1.000 0.000
#> GSM711934 1 0.0000 0.984 1.000 0.000
#> GSM711940 1 0.0000 0.984 1.000 0.000
#> GSM711942 1 0.0000 0.984 1.000 0.000
#> GSM711944 1 0.0938 0.979 0.988 0.012
#> GSM711946 1 0.0376 0.983 0.996 0.004
#> GSM711948 1 0.0000 0.984 1.000 0.000
#> GSM711952 1 0.0000 0.984 1.000 0.000
#> GSM711954 1 0.0000 0.984 1.000 0.000
#> GSM711962 1 0.0000 0.984 1.000 0.000
#> GSM711970 1 0.0000 0.984 1.000 0.000
#> GSM711974 1 0.0000 0.984 1.000 0.000
#> GSM711978 1 0.0000 0.984 1.000 0.000
#> GSM711988 1 0.0000 0.984 1.000 0.000
#> GSM711990 1 0.0938 0.979 0.988 0.012
#> GSM711992 1 0.0000 0.984 1.000 0.000
#> GSM711982 1 0.0000 0.984 1.000 0.000
#> GSM711984 2 0.0938 1.000 0.012 0.988
#> GSM711912 1 0.0000 0.984 1.000 0.000
#> GSM711918 1 0.0000 0.984 1.000 0.000
#> GSM711920 1 0.0000 0.984 1.000 0.000
#> GSM711937 2 0.0938 1.000 0.012 0.988
#> GSM711939 2 0.0938 1.000 0.012 0.988
#> GSM711951 2 0.0938 1.000 0.012 0.988
#> GSM711957 1 0.0000 0.984 1.000 0.000
#> GSM711959 2 0.0938 1.000 0.012 0.988
#> GSM711961 2 0.0938 1.000 0.012 0.988
#> GSM711965 1 0.0938 0.979 0.988 0.012
#> GSM711967 1 0.0000 0.984 1.000 0.000
#> GSM711969 2 0.0938 1.000 0.012 0.988
#> GSM711973 1 0.0000 0.984 1.000 0.000
#> GSM711977 1 0.0938 0.979 0.988 0.012
#> GSM711981 1 0.0376 0.982 0.996 0.004
#> GSM711987 2 0.0938 1.000 0.012 0.988
#> GSM711905 2 0.0938 1.000 0.012 0.988
#> GSM711907 2 0.0938 1.000 0.012 0.988
#> GSM711909 1 0.0938 0.979 0.988 0.012
#> GSM711911 1 0.0938 0.979 0.988 0.012
#> GSM711915 1 0.0938 0.979 0.988 0.012
#> GSM711917 2 0.0938 1.000 0.012 0.988
#> GSM711923 1 0.0000 0.984 1.000 0.000
#> GSM711925 2 0.0938 1.000 0.012 0.988
#> GSM711927 1 0.0938 0.979 0.988 0.012
#> GSM711929 2 0.0938 1.000 0.012 0.988
#> GSM711931 2 0.0938 1.000 0.012 0.988
#> GSM711933 1 0.0000 0.984 1.000 0.000
#> GSM711935 2 0.0938 1.000 0.012 0.988
#> GSM711941 1 0.0000 0.984 1.000 0.000
#> GSM711943 1 0.0000 0.984 1.000 0.000
#> GSM711945 1 0.0672 0.981 0.992 0.008
#> GSM711947 1 0.9850 0.282 0.572 0.428
#> GSM711949 2 0.0938 1.000 0.012 0.988
#> GSM711953 2 0.0938 1.000 0.012 0.988
#> GSM711955 1 0.0376 0.983 0.996 0.004
#> GSM711963 2 0.0938 1.000 0.012 0.988
#> GSM711971 1 0.0938 0.979 0.988 0.012
#> GSM711975 2 0.0938 1.000 0.012 0.988
#> GSM711979 1 0.0000 0.984 1.000 0.000
#> GSM711989 2 0.0938 1.000 0.012 0.988
#> GSM711991 1 0.1184 0.977 0.984 0.016
#> GSM711993 1 0.9635 0.363 0.612 0.388
#> GSM711983 1 0.0938 0.979 0.988 0.012
#> GSM711985 2 0.0938 1.000 0.012 0.988
#> GSM711913 1 0.0938 0.979 0.988 0.012
#> GSM711919 1 0.0938 0.979 0.988 0.012
#> GSM711921 1 0.0938 0.979 0.988 0.012
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM711936 2 0.0000 0.998 0.000 1.000 0.000
#> GSM711938 2 0.0000 0.998 0.000 1.000 0.000
#> GSM711950 1 0.0237 0.968 0.996 0.000 0.004
#> GSM711956 1 0.0000 0.971 1.000 0.000 0.000
#> GSM711958 1 0.0000 0.971 1.000 0.000 0.000
#> GSM711960 1 0.5138 0.652 0.748 0.000 0.252
#> GSM711964 1 0.0000 0.971 1.000 0.000 0.000
#> GSM711966 1 0.0000 0.971 1.000 0.000 0.000
#> GSM711968 1 0.0000 0.971 1.000 0.000 0.000
#> GSM711972 1 0.0000 0.971 1.000 0.000 0.000
#> GSM711976 1 0.0000 0.971 1.000 0.000 0.000
#> GSM711980 1 0.0000 0.971 1.000 0.000 0.000
#> GSM711986 1 0.0000 0.971 1.000 0.000 0.000
#> GSM711904 1 0.0000 0.971 1.000 0.000 0.000
#> GSM711906 1 0.0000 0.971 1.000 0.000 0.000
#> GSM711908 1 0.0000 0.971 1.000 0.000 0.000
#> GSM711910 3 0.0592 0.943 0.012 0.000 0.988
#> GSM711914 1 0.0000 0.971 1.000 0.000 0.000
#> GSM711916 1 0.0000 0.971 1.000 0.000 0.000
#> GSM711922 1 0.0000 0.971 1.000 0.000 0.000
#> GSM711924 1 0.0000 0.971 1.000 0.000 0.000
#> GSM711926 1 0.0592 0.962 0.988 0.000 0.012
#> GSM711928 1 0.0000 0.971 1.000 0.000 0.000
#> GSM711930 1 0.0000 0.971 1.000 0.000 0.000
#> GSM711932 1 0.0000 0.971 1.000 0.000 0.000
#> GSM711934 1 0.0000 0.971 1.000 0.000 0.000
#> GSM711940 1 0.0000 0.971 1.000 0.000 0.000
#> GSM711942 1 0.0000 0.971 1.000 0.000 0.000
#> GSM711944 3 0.0592 0.943 0.012 0.000 0.988
#> GSM711946 3 0.0000 0.935 0.000 0.000 1.000
#> GSM711948 1 0.0000 0.971 1.000 0.000 0.000
#> GSM711952 1 0.0000 0.971 1.000 0.000 0.000
#> GSM711954 1 0.0000 0.971 1.000 0.000 0.000
#> GSM711962 1 0.0000 0.971 1.000 0.000 0.000
#> GSM711970 1 0.0000 0.971 1.000 0.000 0.000
#> GSM711974 1 0.0000 0.971 1.000 0.000 0.000
#> GSM711978 1 0.0592 0.962 0.988 0.000 0.012
#> GSM711988 1 0.0000 0.971 1.000 0.000 0.000
#> GSM711990 3 0.0592 0.943 0.012 0.000 0.988
#> GSM711992 1 0.0592 0.962 0.988 0.000 0.012
#> GSM711982 1 0.0000 0.971 1.000 0.000 0.000
#> GSM711984 2 0.0000 0.998 0.000 1.000 0.000
#> GSM711912 1 0.0000 0.971 1.000 0.000 0.000
#> GSM711918 1 0.0000 0.971 1.000 0.000 0.000
#> GSM711920 1 0.0000 0.971 1.000 0.000 0.000
#> GSM711937 2 0.0000 0.998 0.000 1.000 0.000
#> GSM711939 2 0.0000 0.998 0.000 1.000 0.000
#> GSM711951 2 0.0592 0.990 0.000 0.988 0.012
#> GSM711957 1 0.0000 0.971 1.000 0.000 0.000
#> GSM711959 2 0.0000 0.998 0.000 1.000 0.000
#> GSM711961 2 0.0000 0.998 0.000 1.000 0.000
#> GSM711965 3 0.0237 0.938 0.004 0.000 0.996
#> GSM711967 1 0.0000 0.971 1.000 0.000 0.000
#> GSM711969 2 0.0000 0.998 0.000 1.000 0.000
#> GSM711973 1 0.3941 0.804 0.844 0.000 0.156
#> GSM711977 3 0.0592 0.943 0.012 0.000 0.988
#> GSM711981 1 0.4121 0.798 0.832 0.000 0.168
#> GSM711987 2 0.0000 0.998 0.000 1.000 0.000
#> GSM711905 2 0.0000 0.998 0.000 1.000 0.000
#> GSM711907 2 0.0592 0.990 0.000 0.988 0.012
#> GSM711909 3 0.0592 0.943 0.012 0.000 0.988
#> GSM711911 3 0.0592 0.943 0.012 0.000 0.988
#> GSM711915 3 0.0592 0.943 0.012 0.000 0.988
#> GSM711917 2 0.0000 0.998 0.000 1.000 0.000
#> GSM711923 3 0.6140 0.312 0.404 0.000 0.596
#> GSM711925 2 0.0000 0.998 0.000 1.000 0.000
#> GSM711927 3 0.0592 0.943 0.012 0.000 0.988
#> GSM711929 2 0.0000 0.998 0.000 1.000 0.000
#> GSM711931 2 0.0592 0.990 0.000 0.988 0.012
#> GSM711933 1 0.0000 0.971 1.000 0.000 0.000
#> GSM711935 2 0.0000 0.998 0.000 1.000 0.000
#> GSM711941 1 0.0592 0.962 0.988 0.000 0.012
#> GSM711943 3 0.6154 0.301 0.408 0.000 0.592
#> GSM711945 3 0.0000 0.935 0.000 0.000 1.000
#> GSM711947 3 0.0237 0.933 0.000 0.004 0.996
#> GSM711949 2 0.0000 0.998 0.000 1.000 0.000
#> GSM711953 2 0.0000 0.998 0.000 1.000 0.000
#> GSM711955 1 0.4399 0.758 0.812 0.000 0.188
#> GSM711963 2 0.0000 0.998 0.000 1.000 0.000
#> GSM711971 3 0.0592 0.943 0.012 0.000 0.988
#> GSM711975 2 0.0237 0.996 0.000 0.996 0.004
#> GSM711979 1 0.0592 0.962 0.988 0.000 0.012
#> GSM711989 2 0.0237 0.996 0.000 0.996 0.004
#> GSM711991 3 0.0000 0.935 0.000 0.000 1.000
#> GSM711993 1 0.6632 0.341 0.596 0.392 0.012
#> GSM711983 3 0.0592 0.943 0.012 0.000 0.988
#> GSM711985 2 0.0000 0.998 0.000 1.000 0.000
#> GSM711913 3 0.0592 0.943 0.012 0.000 0.988
#> GSM711919 3 0.0592 0.943 0.012 0.000 0.988
#> GSM711921 3 0.0592 0.943 0.012 0.000 0.988
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM711936 2 0.0188 0.9562 0.000 0.996 0.000 0.004
#> GSM711938 2 0.0000 0.9593 0.000 1.000 0.000 0.000
#> GSM711950 4 0.3688 0.6856 0.208 0.000 0.000 0.792
#> GSM711956 1 0.0000 0.9619 1.000 0.000 0.000 0.000
#> GSM711958 1 0.0188 0.9617 0.996 0.000 0.000 0.004
#> GSM711960 1 0.0779 0.9504 0.980 0.000 0.016 0.004
#> GSM711964 1 0.0000 0.9619 1.000 0.000 0.000 0.000
#> GSM711966 1 0.0188 0.9617 0.996 0.000 0.000 0.004
#> GSM711968 1 0.0188 0.9613 0.996 0.000 0.000 0.004
#> GSM711972 1 0.0188 0.9617 0.996 0.000 0.000 0.004
#> GSM711976 1 0.1557 0.9186 0.944 0.000 0.000 0.056
#> GSM711980 1 0.0000 0.9619 1.000 0.000 0.000 0.000
#> GSM711986 1 0.0188 0.9613 0.996 0.000 0.000 0.004
#> GSM711904 1 0.0188 0.9613 0.996 0.000 0.000 0.004
#> GSM711906 1 0.0188 0.9617 0.996 0.000 0.000 0.004
#> GSM711908 1 0.0188 0.9613 0.996 0.000 0.000 0.004
#> GSM711910 3 0.0000 0.9700 0.000 0.000 1.000 0.000
#> GSM711914 1 0.0000 0.9619 1.000 0.000 0.000 0.000
#> GSM711916 1 0.0188 0.9617 0.996 0.000 0.000 0.004
#> GSM711922 1 0.0188 0.9613 0.996 0.000 0.000 0.004
#> GSM711924 1 0.0188 0.9617 0.996 0.000 0.000 0.004
#> GSM711926 4 0.0469 0.8520 0.012 0.000 0.000 0.988
#> GSM711928 1 0.0188 0.9613 0.996 0.000 0.000 0.004
#> GSM711930 1 0.0188 0.9617 0.996 0.000 0.000 0.004
#> GSM711932 1 0.2081 0.8882 0.916 0.000 0.000 0.084
#> GSM711934 1 0.0000 0.9619 1.000 0.000 0.000 0.000
#> GSM711940 1 0.3311 0.7731 0.828 0.000 0.000 0.172
#> GSM711942 1 0.0188 0.9617 0.996 0.000 0.000 0.004
#> GSM711944 3 0.0188 0.9665 0.004 0.000 0.996 0.000
#> GSM711946 4 0.0592 0.8460 0.000 0.000 0.016 0.984
#> GSM711948 4 0.4916 0.2578 0.424 0.000 0.000 0.576
#> GSM711952 1 0.0188 0.9613 0.996 0.000 0.000 0.004
#> GSM711954 1 0.0188 0.9613 0.996 0.000 0.000 0.004
#> GSM711962 1 0.0188 0.9617 0.996 0.000 0.000 0.004
#> GSM711970 1 0.0188 0.9613 0.996 0.000 0.000 0.004
#> GSM711974 1 0.0188 0.9617 0.996 0.000 0.000 0.004
#> GSM711978 4 0.0469 0.8520 0.012 0.000 0.000 0.988
#> GSM711988 1 0.0592 0.9517 0.984 0.000 0.000 0.016
#> GSM711990 3 0.0000 0.9700 0.000 0.000 1.000 0.000
#> GSM711992 4 0.0469 0.8520 0.012 0.000 0.000 0.988
#> GSM711982 1 0.0188 0.9617 0.996 0.000 0.000 0.004
#> GSM711984 2 0.0000 0.9593 0.000 1.000 0.000 0.000
#> GSM711912 1 0.0188 0.9613 0.996 0.000 0.000 0.004
#> GSM711918 1 0.0188 0.9613 0.996 0.000 0.000 0.004
#> GSM711920 1 0.0000 0.9619 1.000 0.000 0.000 0.000
#> GSM711937 2 0.0000 0.9593 0.000 1.000 0.000 0.000
#> GSM711939 2 0.0000 0.9593 0.000 1.000 0.000 0.000
#> GSM711951 4 0.0592 0.8450 0.000 0.016 0.000 0.984
#> GSM711957 1 0.4967 0.1181 0.548 0.000 0.000 0.452
#> GSM711959 2 0.0000 0.9593 0.000 1.000 0.000 0.000
#> GSM711961 2 0.0000 0.9593 0.000 1.000 0.000 0.000
#> GSM711965 4 0.5000 -0.0915 0.000 0.000 0.496 0.504
#> GSM711967 1 0.0188 0.9617 0.996 0.000 0.000 0.004
#> GSM711969 2 0.0000 0.9593 0.000 1.000 0.000 0.000
#> GSM711973 4 0.4222 0.5970 0.272 0.000 0.000 0.728
#> GSM711977 3 0.0188 0.9683 0.000 0.000 0.996 0.004
#> GSM711981 4 0.0336 0.8516 0.008 0.000 0.000 0.992
#> GSM711987 2 0.0000 0.9593 0.000 1.000 0.000 0.000
#> GSM711905 2 0.0000 0.9593 0.000 1.000 0.000 0.000
#> GSM711907 2 0.4830 0.3922 0.000 0.608 0.000 0.392
#> GSM711909 3 0.0000 0.9700 0.000 0.000 1.000 0.000
#> GSM711911 3 0.0000 0.9700 0.000 0.000 1.000 0.000
#> GSM711915 3 0.0188 0.9683 0.000 0.000 0.996 0.004
#> GSM711917 2 0.0000 0.9593 0.000 1.000 0.000 0.000
#> GSM711923 4 0.0524 0.8496 0.004 0.000 0.008 0.988
#> GSM711925 2 0.0000 0.9593 0.000 1.000 0.000 0.000
#> GSM711927 3 0.0000 0.9700 0.000 0.000 1.000 0.000
#> GSM711929 2 0.0000 0.9593 0.000 1.000 0.000 0.000
#> GSM711931 4 0.4877 0.1754 0.000 0.408 0.000 0.592
#> GSM711933 1 0.0188 0.9617 0.996 0.000 0.000 0.004
#> GSM711935 2 0.0000 0.9593 0.000 1.000 0.000 0.000
#> GSM711941 4 0.0469 0.8510 0.012 0.000 0.000 0.988
#> GSM711943 4 0.0524 0.8496 0.004 0.000 0.008 0.988
#> GSM711945 4 0.0469 0.8466 0.000 0.000 0.012 0.988
#> GSM711947 3 0.4149 0.7818 0.000 0.028 0.804 0.168
#> GSM711949 2 0.0000 0.9593 0.000 1.000 0.000 0.000
#> GSM711953 2 0.0000 0.9593 0.000 1.000 0.000 0.000
#> GSM711955 1 0.5253 0.3808 0.624 0.000 0.016 0.360
#> GSM711963 2 0.0000 0.9593 0.000 1.000 0.000 0.000
#> GSM711971 3 0.0000 0.9700 0.000 0.000 1.000 0.000
#> GSM711975 2 0.4661 0.4813 0.000 0.652 0.000 0.348
#> GSM711979 4 0.0336 0.8520 0.008 0.000 0.000 0.992
#> GSM711989 2 0.1118 0.9283 0.000 0.964 0.000 0.036
#> GSM711991 3 0.3569 0.7661 0.000 0.000 0.804 0.196
#> GSM711993 4 0.0524 0.8503 0.004 0.008 0.000 0.988
#> GSM711983 3 0.0000 0.9700 0.000 0.000 1.000 0.000
#> GSM711985 2 0.0000 0.9593 0.000 1.000 0.000 0.000
#> GSM711913 3 0.0188 0.9683 0.000 0.000 0.996 0.004
#> GSM711919 3 0.0000 0.9700 0.000 0.000 1.000 0.000
#> GSM711921 3 0.0000 0.9700 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM711936 2 0.3779 0.8249 0.000 0.752 0.000 0.012 0.236
#> GSM711938 2 0.0000 0.9127 0.000 1.000 0.000 0.000 0.000
#> GSM711950 4 0.5376 0.1664 0.424 0.000 0.000 0.520 0.056
#> GSM711956 1 0.0880 0.6075 0.968 0.000 0.000 0.000 0.032
#> GSM711958 1 0.2179 0.5667 0.888 0.000 0.000 0.000 0.112
#> GSM711960 1 0.4486 0.5100 0.784 0.000 0.052 0.032 0.132
#> GSM711964 1 0.3003 0.3268 0.812 0.000 0.000 0.000 0.188
#> GSM711966 5 0.4304 0.9654 0.484 0.000 0.000 0.000 0.516
#> GSM711968 1 0.1608 0.5737 0.928 0.000 0.000 0.000 0.072
#> GSM711972 5 0.4304 0.9654 0.484 0.000 0.000 0.000 0.516
#> GSM711976 1 0.2574 0.5620 0.876 0.000 0.000 0.112 0.012
#> GSM711980 1 0.0451 0.6194 0.988 0.000 0.000 0.008 0.004
#> GSM711986 1 0.4294 -0.7998 0.532 0.000 0.000 0.000 0.468
#> GSM711904 1 0.2605 0.4542 0.852 0.000 0.000 0.000 0.148
#> GSM711906 5 0.4291 0.9569 0.464 0.000 0.000 0.000 0.536
#> GSM711908 5 0.4297 0.9236 0.472 0.000 0.000 0.000 0.528
#> GSM711910 3 0.0510 0.9145 0.000 0.000 0.984 0.000 0.016
#> GSM711914 1 0.3003 0.3314 0.812 0.000 0.000 0.000 0.188
#> GSM711916 5 0.4302 0.9666 0.480 0.000 0.000 0.000 0.520
#> GSM711922 1 0.0290 0.6185 0.992 0.000 0.000 0.000 0.008
#> GSM711924 1 0.2127 0.5535 0.892 0.000 0.000 0.000 0.108
#> GSM711926 4 0.2124 0.7517 0.004 0.000 0.000 0.900 0.096
#> GSM711928 1 0.2127 0.5212 0.892 0.000 0.000 0.000 0.108
#> GSM711930 5 0.4291 0.9569 0.464 0.000 0.000 0.000 0.536
#> GSM711932 1 0.2189 0.5869 0.904 0.000 0.000 0.084 0.012
#> GSM711934 1 0.0510 0.6172 0.984 0.000 0.000 0.000 0.016
#> GSM711940 1 0.5082 0.3820 0.664 0.000 0.000 0.260 0.076
#> GSM711942 1 0.2127 0.5535 0.892 0.000 0.000 0.000 0.108
#> GSM711944 3 0.5467 0.6589 0.164 0.000 0.712 0.048 0.076
#> GSM711946 4 0.1764 0.7490 0.008 0.000 0.000 0.928 0.064
#> GSM711948 1 0.5396 0.1873 0.560 0.000 0.000 0.376 0.064
#> GSM711952 1 0.4294 -0.7998 0.532 0.000 0.000 0.000 0.468
#> GSM711954 1 0.0798 0.6183 0.976 0.000 0.000 0.008 0.016
#> GSM711962 1 0.3177 0.3550 0.792 0.000 0.000 0.000 0.208
#> GSM711970 1 0.0451 0.6191 0.988 0.000 0.000 0.004 0.008
#> GSM711974 1 0.2471 0.5345 0.864 0.000 0.000 0.000 0.136
#> GSM711978 4 0.1364 0.7667 0.012 0.000 0.000 0.952 0.036
#> GSM711988 1 0.1764 0.5996 0.928 0.000 0.000 0.064 0.008
#> GSM711990 3 0.1205 0.9119 0.000 0.000 0.956 0.004 0.040
#> GSM711992 4 0.1364 0.7667 0.012 0.000 0.000 0.952 0.036
#> GSM711982 5 0.4304 0.9654 0.484 0.000 0.000 0.000 0.516
#> GSM711984 2 0.1851 0.9012 0.000 0.912 0.000 0.000 0.088
#> GSM711912 1 0.4294 -0.7998 0.532 0.000 0.000 0.000 0.468
#> GSM711918 1 0.4294 -0.7998 0.532 0.000 0.000 0.000 0.468
#> GSM711920 1 0.1197 0.6013 0.952 0.000 0.000 0.000 0.048
#> GSM711937 2 0.3551 0.8405 0.000 0.772 0.000 0.008 0.220
#> GSM711939 2 0.2424 0.8887 0.000 0.868 0.000 0.000 0.132
#> GSM711951 4 0.3689 0.6640 0.000 0.004 0.000 0.740 0.256
#> GSM711957 1 0.4558 0.4309 0.740 0.000 0.000 0.180 0.080
#> GSM711959 2 0.2424 0.8887 0.000 0.868 0.000 0.000 0.132
#> GSM711961 2 0.0000 0.9127 0.000 1.000 0.000 0.000 0.000
#> GSM711965 4 0.6467 -0.0751 0.012 0.000 0.408 0.452 0.128
#> GSM711967 1 0.3209 0.4197 0.812 0.000 0.000 0.008 0.180
#> GSM711969 2 0.3582 0.8379 0.000 0.768 0.000 0.008 0.224
#> GSM711973 4 0.6233 0.3028 0.344 0.000 0.008 0.524 0.124
#> GSM711977 3 0.2513 0.8867 0.000 0.000 0.876 0.008 0.116
#> GSM711981 4 0.1282 0.7644 0.004 0.000 0.000 0.952 0.044
#> GSM711987 2 0.0000 0.9127 0.000 1.000 0.000 0.000 0.000
#> GSM711905 2 0.0000 0.9127 0.000 1.000 0.000 0.000 0.000
#> GSM711907 4 0.6526 0.2722 0.000 0.260 0.000 0.484 0.256
#> GSM711909 3 0.0404 0.9148 0.000 0.000 0.988 0.000 0.012
#> GSM711911 3 0.0865 0.9147 0.000 0.000 0.972 0.004 0.024
#> GSM711915 3 0.1732 0.8982 0.000 0.000 0.920 0.000 0.080
#> GSM711917 2 0.3582 0.8379 0.000 0.768 0.000 0.008 0.224
#> GSM711923 4 0.1522 0.7566 0.012 0.000 0.000 0.944 0.044
#> GSM711925 2 0.0000 0.9127 0.000 1.000 0.000 0.000 0.000
#> GSM711927 3 0.0290 0.9152 0.000 0.000 0.992 0.000 0.008
#> GSM711929 2 0.0000 0.9127 0.000 1.000 0.000 0.000 0.000
#> GSM711931 4 0.5841 0.4893 0.000 0.148 0.000 0.596 0.256
#> GSM711933 1 0.2077 0.6027 0.920 0.000 0.000 0.040 0.040
#> GSM711935 2 0.0000 0.9127 0.000 1.000 0.000 0.000 0.000
#> GSM711941 4 0.1893 0.7514 0.024 0.000 0.000 0.928 0.048
#> GSM711943 4 0.0693 0.7650 0.012 0.000 0.000 0.980 0.008
#> GSM711945 4 0.1671 0.7514 0.000 0.000 0.000 0.924 0.076
#> GSM711947 3 0.4680 0.7297 0.000 0.008 0.752 0.152 0.088
#> GSM711949 2 0.0000 0.9127 0.000 1.000 0.000 0.000 0.000
#> GSM711953 2 0.0000 0.9127 0.000 1.000 0.000 0.000 0.000
#> GSM711955 1 0.5503 0.2946 0.596 0.000 0.004 0.328 0.072
#> GSM711963 2 0.0000 0.9127 0.000 1.000 0.000 0.000 0.000
#> GSM711971 3 0.0865 0.9147 0.000 0.000 0.972 0.004 0.024
#> GSM711975 4 0.6651 0.1629 0.000 0.300 0.000 0.444 0.256
#> GSM711979 4 0.0404 0.7660 0.012 0.000 0.000 0.988 0.000
#> GSM711989 2 0.5215 0.7124 0.000 0.656 0.000 0.088 0.256
#> GSM711991 3 0.4270 0.7067 0.000 0.000 0.748 0.204 0.048
#> GSM711993 4 0.2179 0.7500 0.004 0.000 0.000 0.896 0.100
#> GSM711983 3 0.1205 0.9119 0.000 0.000 0.956 0.004 0.040
#> GSM711985 2 0.1965 0.8995 0.000 0.904 0.000 0.000 0.096
#> GSM711913 3 0.2513 0.8867 0.000 0.000 0.876 0.008 0.116
#> GSM711919 3 0.0290 0.9152 0.000 0.000 0.992 0.000 0.008
#> GSM711921 3 0.0510 0.9145 0.000 0.000 0.984 0.000 0.016
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM711936 2 0.4335 0.1410 0.000 0.508 0.000 0.020 0.472 0.000
#> GSM711938 2 0.1082 0.7706 0.040 0.956 0.000 0.000 0.004 0.000
#> GSM711950 4 0.5389 0.0968 0.444 0.000 0.000 0.456 0.096 0.004
#> GSM711956 1 0.4270 0.6659 0.684 0.000 0.000 0.000 0.052 0.264
#> GSM711958 1 0.5025 0.5846 0.560 0.000 0.000 0.000 0.084 0.356
#> GSM711960 1 0.6504 0.4835 0.540 0.000 0.108 0.008 0.080 0.264
#> GSM711964 1 0.5015 0.3976 0.504 0.000 0.000 0.000 0.072 0.424
#> GSM711966 6 0.0603 0.7694 0.016 0.000 0.000 0.000 0.004 0.980
#> GSM711968 1 0.4687 0.6211 0.632 0.000 0.000 0.000 0.072 0.296
#> GSM711972 6 0.0458 0.7708 0.016 0.000 0.000 0.000 0.000 0.984
#> GSM711976 1 0.5371 0.5987 0.684 0.000 0.000 0.136 0.076 0.104
#> GSM711980 1 0.3558 0.6825 0.736 0.000 0.000 0.000 0.016 0.248
#> GSM711986 6 0.3792 0.6976 0.108 0.000 0.000 0.000 0.112 0.780
#> GSM711904 1 0.5157 0.5060 0.544 0.000 0.000 0.000 0.096 0.360
#> GSM711906 6 0.0405 0.7701 0.004 0.000 0.000 0.000 0.008 0.988
#> GSM711908 6 0.2309 0.7494 0.028 0.000 0.000 0.000 0.084 0.888
#> GSM711910 3 0.0260 0.8680 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM711914 1 0.5087 0.4231 0.508 0.000 0.000 0.000 0.080 0.412
#> GSM711916 6 0.0363 0.7714 0.012 0.000 0.000 0.000 0.000 0.988
#> GSM711922 1 0.4022 0.6740 0.708 0.000 0.000 0.000 0.040 0.252
#> GSM711924 1 0.5045 0.5142 0.512 0.000 0.000 0.000 0.076 0.412
#> GSM711926 4 0.2980 0.4642 0.008 0.000 0.000 0.800 0.192 0.000
#> GSM711928 1 0.4697 0.5945 0.612 0.000 0.000 0.000 0.064 0.324
#> GSM711930 6 0.0405 0.7701 0.004 0.000 0.000 0.000 0.008 0.988
#> GSM711932 1 0.5377 0.6386 0.684 0.000 0.000 0.100 0.080 0.136
#> GSM711934 1 0.3695 0.6780 0.712 0.000 0.000 0.000 0.016 0.272
#> GSM711940 1 0.6276 0.3969 0.544 0.000 0.000 0.264 0.068 0.124
#> GSM711942 1 0.5045 0.5142 0.512 0.000 0.000 0.000 0.076 0.412
#> GSM711944 3 0.6412 0.4244 0.268 0.000 0.516 0.056 0.160 0.000
#> GSM711946 4 0.2571 0.6394 0.060 0.000 0.000 0.876 0.064 0.000
#> GSM711948 1 0.5652 0.3058 0.576 0.000 0.000 0.292 0.104 0.028
#> GSM711952 6 0.3792 0.6976 0.108 0.000 0.000 0.000 0.112 0.780
#> GSM711954 1 0.4085 0.6761 0.704 0.000 0.000 0.000 0.044 0.252
#> GSM711962 6 0.4563 -0.1944 0.368 0.000 0.000 0.000 0.044 0.588
#> GSM711970 1 0.3841 0.6794 0.724 0.000 0.000 0.000 0.032 0.244
#> GSM711974 1 0.4709 0.5451 0.540 0.000 0.000 0.000 0.048 0.412
#> GSM711978 4 0.1950 0.6209 0.024 0.000 0.000 0.912 0.064 0.000
#> GSM711988 1 0.5003 0.6504 0.708 0.000 0.000 0.068 0.064 0.160
#> GSM711990 3 0.1938 0.8621 0.036 0.000 0.920 0.004 0.040 0.000
#> GSM711992 4 0.2088 0.6203 0.028 0.000 0.000 0.904 0.068 0.000
#> GSM711982 6 0.0603 0.7694 0.016 0.000 0.000 0.000 0.004 0.980
#> GSM711984 2 0.2703 0.7017 0.004 0.824 0.000 0.000 0.172 0.000
#> GSM711912 6 0.3747 0.7019 0.104 0.000 0.000 0.000 0.112 0.784
#> GSM711918 6 0.3747 0.7019 0.104 0.000 0.000 0.000 0.112 0.784
#> GSM711920 1 0.4767 0.6271 0.620 0.000 0.000 0.000 0.076 0.304
#> GSM711937 2 0.3966 0.3026 0.000 0.552 0.000 0.004 0.444 0.000
#> GSM711939 2 0.4044 0.6227 0.040 0.704 0.000 0.000 0.256 0.000
#> GSM711951 4 0.3991 -0.4285 0.000 0.004 0.000 0.524 0.472 0.000
#> GSM711957 1 0.5627 0.5460 0.656 0.000 0.000 0.144 0.128 0.072
#> GSM711959 2 0.3717 0.6071 0.016 0.708 0.000 0.000 0.276 0.000
#> GSM711961 2 0.0937 0.7702 0.040 0.960 0.000 0.000 0.000 0.000
#> GSM711965 4 0.6981 0.2634 0.112 0.000 0.188 0.472 0.228 0.000
#> GSM711967 6 0.4978 -0.2911 0.396 0.000 0.000 0.000 0.072 0.532
#> GSM711969 2 0.3975 0.2834 0.000 0.544 0.000 0.004 0.452 0.000
#> GSM711973 4 0.6387 0.3410 0.324 0.000 0.000 0.408 0.252 0.016
#> GSM711977 3 0.4672 0.7766 0.088 0.000 0.716 0.020 0.176 0.000
#> GSM711981 4 0.1588 0.6130 0.004 0.000 0.000 0.924 0.072 0.000
#> GSM711987 2 0.0000 0.7721 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711905 2 0.0713 0.7708 0.028 0.972 0.000 0.000 0.000 0.000
#> GSM711907 5 0.4929 0.5116 0.000 0.064 0.000 0.428 0.508 0.000
#> GSM711909 3 0.0146 0.8685 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM711911 3 0.1261 0.8670 0.024 0.000 0.952 0.000 0.024 0.000
#> GSM711915 3 0.3934 0.8000 0.068 0.000 0.780 0.012 0.140 0.000
#> GSM711917 2 0.3975 0.2834 0.000 0.544 0.000 0.004 0.452 0.000
#> GSM711923 4 0.2325 0.6440 0.060 0.000 0.000 0.892 0.048 0.000
#> GSM711925 2 0.0291 0.7725 0.004 0.992 0.000 0.000 0.004 0.000
#> GSM711927 3 0.0000 0.8687 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711929 2 0.0713 0.7708 0.028 0.972 0.000 0.000 0.000 0.000
#> GSM711931 4 0.4758 -0.5913 0.000 0.048 0.000 0.476 0.476 0.000
#> GSM711933 1 0.4838 0.6531 0.676 0.000 0.000 0.012 0.088 0.224
#> GSM711935 2 0.0291 0.7725 0.004 0.992 0.000 0.000 0.004 0.000
#> GSM711941 4 0.3006 0.6273 0.064 0.000 0.000 0.844 0.092 0.000
#> GSM711943 4 0.1007 0.6485 0.044 0.000 0.000 0.956 0.000 0.000
#> GSM711945 4 0.2740 0.6224 0.076 0.000 0.000 0.864 0.060 0.000
#> GSM711947 3 0.5016 0.6911 0.040 0.004 0.716 0.124 0.116 0.000
#> GSM711949 2 0.0291 0.7725 0.004 0.992 0.000 0.000 0.004 0.000
#> GSM711953 2 0.0937 0.7702 0.040 0.960 0.000 0.000 0.000 0.000
#> GSM711955 1 0.5851 0.3192 0.584 0.000 0.008 0.264 0.120 0.024
#> GSM711963 2 0.0291 0.7725 0.004 0.992 0.000 0.000 0.004 0.000
#> GSM711971 3 0.1418 0.8661 0.024 0.000 0.944 0.000 0.032 0.000
#> GSM711975 5 0.5449 0.6247 0.000 0.128 0.000 0.368 0.504 0.000
#> GSM711979 4 0.1010 0.6463 0.036 0.000 0.000 0.960 0.004 0.000
#> GSM711989 5 0.5341 0.1493 0.000 0.380 0.000 0.112 0.508 0.000
#> GSM711991 3 0.4673 0.6664 0.040 0.000 0.708 0.208 0.044 0.000
#> GSM711993 4 0.2558 0.5206 0.004 0.000 0.000 0.840 0.156 0.000
#> GSM711983 3 0.1938 0.8621 0.036 0.000 0.920 0.004 0.040 0.000
#> GSM711985 2 0.3259 0.6713 0.012 0.772 0.000 0.000 0.216 0.000
#> GSM711913 3 0.4672 0.7766 0.088 0.000 0.716 0.020 0.176 0.000
#> GSM711919 3 0.0000 0.8687 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711921 3 0.0260 0.8680 0.008 0.000 0.992 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) disease.state(p) individual(p) k
#> SD:kmeans 88 6.08e-05 0.209 0.473 2
#> SD:kmeans 87 6.75e-09 0.122 0.360 3
#> SD:kmeans 83 2.78e-09 0.118 0.321 4
#> SD:kmeans 71 1.99e-07 0.104 0.147 5
#> SD:kmeans 70 1.06e-07 0.272 0.237 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "skmeans"]
# you can also extract it by
# res = res_list["SD:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 27425 rows and 90 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.954 0.950 0.979 0.4769 0.525 0.525
#> 3 3 1.000 0.956 0.982 0.3779 0.733 0.528
#> 4 4 0.957 0.918 0.967 0.0913 0.926 0.789
#> 5 5 0.806 0.772 0.846 0.0936 0.893 0.642
#> 6 6 0.781 0.658 0.821 0.0419 0.958 0.810
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 2 3
There is also optional best \(k\) = 2 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM711936 2 0.000 0.974 0.000 1.000
#> GSM711938 2 0.000 0.974 0.000 1.000
#> GSM711950 1 0.000 0.981 1.000 0.000
#> GSM711956 1 0.000 0.981 1.000 0.000
#> GSM711958 1 0.000 0.981 1.000 0.000
#> GSM711960 1 0.000 0.981 1.000 0.000
#> GSM711964 1 0.000 0.981 1.000 0.000
#> GSM711966 1 0.000 0.981 1.000 0.000
#> GSM711968 1 0.000 0.981 1.000 0.000
#> GSM711972 1 0.000 0.981 1.000 0.000
#> GSM711976 1 0.000 0.981 1.000 0.000
#> GSM711980 1 0.000 0.981 1.000 0.000
#> GSM711986 1 0.000 0.981 1.000 0.000
#> GSM711904 1 0.000 0.981 1.000 0.000
#> GSM711906 1 0.000 0.981 1.000 0.000
#> GSM711908 1 0.000 0.981 1.000 0.000
#> GSM711910 1 0.000 0.981 1.000 0.000
#> GSM711914 1 0.000 0.981 1.000 0.000
#> GSM711916 1 0.000 0.981 1.000 0.000
#> GSM711922 1 0.000 0.981 1.000 0.000
#> GSM711924 1 0.000 0.981 1.000 0.000
#> GSM711926 2 0.000 0.974 0.000 1.000
#> GSM711928 1 0.000 0.981 1.000 0.000
#> GSM711930 1 0.000 0.981 1.000 0.000
#> GSM711932 1 0.000 0.981 1.000 0.000
#> GSM711934 1 0.000 0.981 1.000 0.000
#> GSM711940 1 0.000 0.981 1.000 0.000
#> GSM711942 1 0.000 0.981 1.000 0.000
#> GSM711944 1 0.000 0.981 1.000 0.000
#> GSM711946 1 0.722 0.750 0.800 0.200
#> GSM711948 1 0.000 0.981 1.000 0.000
#> GSM711952 1 0.000 0.981 1.000 0.000
#> GSM711954 1 0.000 0.981 1.000 0.000
#> GSM711962 1 0.000 0.981 1.000 0.000
#> GSM711970 1 0.000 0.981 1.000 0.000
#> GSM711974 1 0.000 0.981 1.000 0.000
#> GSM711978 2 0.000 0.974 0.000 1.000
#> GSM711988 1 0.000 0.981 1.000 0.000
#> GSM711990 1 0.000 0.981 1.000 0.000
#> GSM711992 2 0.000 0.974 0.000 1.000
#> GSM711982 1 0.000 0.981 1.000 0.000
#> GSM711984 2 0.000 0.974 0.000 1.000
#> GSM711912 1 0.000 0.981 1.000 0.000
#> GSM711918 1 0.000 0.981 1.000 0.000
#> GSM711920 1 0.000 0.981 1.000 0.000
#> GSM711937 2 0.000 0.974 0.000 1.000
#> GSM711939 2 0.000 0.974 0.000 1.000
#> GSM711951 2 0.000 0.974 0.000 1.000
#> GSM711957 2 0.991 0.226 0.444 0.556
#> GSM711959 2 0.000 0.974 0.000 1.000
#> GSM711961 2 0.000 0.974 0.000 1.000
#> GSM711965 1 0.000 0.981 1.000 0.000
#> GSM711967 1 0.000 0.981 1.000 0.000
#> GSM711969 2 0.000 0.974 0.000 1.000
#> GSM711973 1 0.000 0.981 1.000 0.000
#> GSM711977 1 0.000 0.981 1.000 0.000
#> GSM711981 2 0.000 0.974 0.000 1.000
#> GSM711987 2 0.000 0.974 0.000 1.000
#> GSM711905 2 0.000 0.974 0.000 1.000
#> GSM711907 2 0.000 0.974 0.000 1.000
#> GSM711909 1 0.000 0.981 1.000 0.000
#> GSM711911 1 0.000 0.981 1.000 0.000
#> GSM711915 2 0.714 0.754 0.196 0.804
#> GSM711917 2 0.000 0.974 0.000 1.000
#> GSM711923 1 0.745 0.733 0.788 0.212
#> GSM711925 2 0.000 0.974 0.000 1.000
#> GSM711927 1 0.000 0.981 1.000 0.000
#> GSM711929 2 0.000 0.974 0.000 1.000
#> GSM711931 2 0.000 0.974 0.000 1.000
#> GSM711933 1 0.000 0.981 1.000 0.000
#> GSM711935 2 0.000 0.974 0.000 1.000
#> GSM711941 1 0.000 0.981 1.000 0.000
#> GSM711943 1 0.971 0.348 0.600 0.400
#> GSM711945 2 0.000 0.974 0.000 1.000
#> GSM711947 2 0.000 0.974 0.000 1.000
#> GSM711949 2 0.000 0.974 0.000 1.000
#> GSM711953 2 0.000 0.974 0.000 1.000
#> GSM711955 1 0.000 0.981 1.000 0.000
#> GSM711963 2 0.000 0.974 0.000 1.000
#> GSM711971 1 0.000 0.981 1.000 0.000
#> GSM711975 2 0.000 0.974 0.000 1.000
#> GSM711979 1 0.745 0.733 0.788 0.212
#> GSM711989 2 0.000 0.974 0.000 1.000
#> GSM711991 2 0.000 0.974 0.000 1.000
#> GSM711993 2 0.000 0.974 0.000 1.000
#> GSM711983 1 0.000 0.981 1.000 0.000
#> GSM711985 2 0.000 0.974 0.000 1.000
#> GSM711913 2 0.722 0.749 0.200 0.800
#> GSM711919 1 0.000 0.981 1.000 0.000
#> GSM711921 1 0.000 0.981 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM711936 2 0.0000 1.000 0.000 1.000 0.000
#> GSM711938 2 0.0000 1.000 0.000 1.000 0.000
#> GSM711950 1 0.0000 0.982 1.000 0.000 0.000
#> GSM711956 1 0.0000 0.982 1.000 0.000 0.000
#> GSM711958 1 0.0000 0.982 1.000 0.000 0.000
#> GSM711960 3 0.6095 0.395 0.392 0.000 0.608
#> GSM711964 1 0.0000 0.982 1.000 0.000 0.000
#> GSM711966 1 0.0000 0.982 1.000 0.000 0.000
#> GSM711968 1 0.0000 0.982 1.000 0.000 0.000
#> GSM711972 1 0.0000 0.982 1.000 0.000 0.000
#> GSM711976 1 0.0000 0.982 1.000 0.000 0.000
#> GSM711980 1 0.0000 0.982 1.000 0.000 0.000
#> GSM711986 1 0.0000 0.982 1.000 0.000 0.000
#> GSM711904 1 0.0000 0.982 1.000 0.000 0.000
#> GSM711906 1 0.0000 0.982 1.000 0.000 0.000
#> GSM711908 1 0.0000 0.982 1.000 0.000 0.000
#> GSM711910 3 0.0000 0.953 0.000 0.000 1.000
#> GSM711914 1 0.0000 0.982 1.000 0.000 0.000
#> GSM711916 1 0.0000 0.982 1.000 0.000 0.000
#> GSM711922 1 0.0000 0.982 1.000 0.000 0.000
#> GSM711924 1 0.0000 0.982 1.000 0.000 0.000
#> GSM711926 2 0.0000 1.000 0.000 1.000 0.000
#> GSM711928 1 0.0000 0.982 1.000 0.000 0.000
#> GSM711930 1 0.0000 0.982 1.000 0.000 0.000
#> GSM711932 1 0.0000 0.982 1.000 0.000 0.000
#> GSM711934 1 0.0000 0.982 1.000 0.000 0.000
#> GSM711940 1 0.0000 0.982 1.000 0.000 0.000
#> GSM711942 1 0.0000 0.982 1.000 0.000 0.000
#> GSM711944 3 0.0000 0.953 0.000 0.000 1.000
#> GSM711946 3 0.0000 0.953 0.000 0.000 1.000
#> GSM711948 1 0.0000 0.982 1.000 0.000 0.000
#> GSM711952 1 0.0000 0.982 1.000 0.000 0.000
#> GSM711954 1 0.0000 0.982 1.000 0.000 0.000
#> GSM711962 1 0.0000 0.982 1.000 0.000 0.000
#> GSM711970 1 0.0000 0.982 1.000 0.000 0.000
#> GSM711974 1 0.0000 0.982 1.000 0.000 0.000
#> GSM711978 2 0.0000 1.000 0.000 1.000 0.000
#> GSM711988 1 0.0000 0.982 1.000 0.000 0.000
#> GSM711990 3 0.0000 0.953 0.000 0.000 1.000
#> GSM711992 1 0.6204 0.270 0.576 0.424 0.000
#> GSM711982 1 0.0000 0.982 1.000 0.000 0.000
#> GSM711984 2 0.0000 1.000 0.000 1.000 0.000
#> GSM711912 1 0.0000 0.982 1.000 0.000 0.000
#> GSM711918 1 0.0000 0.982 1.000 0.000 0.000
#> GSM711920 1 0.0000 0.982 1.000 0.000 0.000
#> GSM711937 2 0.0000 1.000 0.000 1.000 0.000
#> GSM711939 2 0.0000 1.000 0.000 1.000 0.000
#> GSM711951 2 0.0000 1.000 0.000 1.000 0.000
#> GSM711957 1 0.0237 0.978 0.996 0.004 0.000
#> GSM711959 2 0.0000 1.000 0.000 1.000 0.000
#> GSM711961 2 0.0000 1.000 0.000 1.000 0.000
#> GSM711965 3 0.0000 0.953 0.000 0.000 1.000
#> GSM711967 1 0.0000 0.982 1.000 0.000 0.000
#> GSM711969 2 0.0000 1.000 0.000 1.000 0.000
#> GSM711973 3 0.0000 0.953 0.000 0.000 1.000
#> GSM711977 3 0.0000 0.953 0.000 0.000 1.000
#> GSM711981 2 0.0000 1.000 0.000 1.000 0.000
#> GSM711987 2 0.0000 1.000 0.000 1.000 0.000
#> GSM711905 2 0.0000 1.000 0.000 1.000 0.000
#> GSM711907 2 0.0000 1.000 0.000 1.000 0.000
#> GSM711909 3 0.0000 0.953 0.000 0.000 1.000
#> GSM711911 3 0.0000 0.953 0.000 0.000 1.000
#> GSM711915 3 0.0000 0.953 0.000 0.000 1.000
#> GSM711917 2 0.0000 1.000 0.000 1.000 0.000
#> GSM711923 3 0.0237 0.951 0.000 0.004 0.996
#> GSM711925 2 0.0000 1.000 0.000 1.000 0.000
#> GSM711927 3 0.0000 0.953 0.000 0.000 1.000
#> GSM711929 2 0.0000 1.000 0.000 1.000 0.000
#> GSM711931 2 0.0000 1.000 0.000 1.000 0.000
#> GSM711933 1 0.0000 0.982 1.000 0.000 0.000
#> GSM711935 2 0.0000 1.000 0.000 1.000 0.000
#> GSM711941 3 0.0237 0.951 0.004 0.000 0.996
#> GSM711943 3 0.2066 0.907 0.000 0.060 0.940
#> GSM711945 3 0.1753 0.917 0.000 0.048 0.952
#> GSM711947 3 0.4555 0.742 0.000 0.200 0.800
#> GSM711949 2 0.0000 1.000 0.000 1.000 0.000
#> GSM711953 2 0.0000 1.000 0.000 1.000 0.000
#> GSM711955 3 0.5529 0.600 0.296 0.000 0.704
#> GSM711963 2 0.0000 1.000 0.000 1.000 0.000
#> GSM711971 3 0.0000 0.953 0.000 0.000 1.000
#> GSM711975 2 0.0000 1.000 0.000 1.000 0.000
#> GSM711979 1 0.4605 0.736 0.796 0.204 0.000
#> GSM711989 2 0.0000 1.000 0.000 1.000 0.000
#> GSM711991 3 0.0000 0.953 0.000 0.000 1.000
#> GSM711993 2 0.0000 1.000 0.000 1.000 0.000
#> GSM711983 3 0.0000 0.953 0.000 0.000 1.000
#> GSM711985 2 0.0000 1.000 0.000 1.000 0.000
#> GSM711913 3 0.0000 0.953 0.000 0.000 1.000
#> GSM711919 3 0.0000 0.953 0.000 0.000 1.000
#> GSM711921 3 0.0000 0.953 0.000 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM711936 2 0.0000 0.9931 0.000 1.000 0.000 0.000
#> GSM711938 2 0.0000 0.9931 0.000 1.000 0.000 0.000
#> GSM711950 4 0.3942 0.6466 0.236 0.000 0.000 0.764
#> GSM711956 1 0.0188 0.9805 0.996 0.000 0.000 0.004
#> GSM711958 1 0.0000 0.9814 1.000 0.000 0.000 0.000
#> GSM711960 3 0.4543 0.4984 0.324 0.000 0.676 0.000
#> GSM711964 1 0.0000 0.9814 1.000 0.000 0.000 0.000
#> GSM711966 1 0.0000 0.9814 1.000 0.000 0.000 0.000
#> GSM711968 1 0.0188 0.9805 0.996 0.000 0.000 0.004
#> GSM711972 1 0.0000 0.9814 1.000 0.000 0.000 0.000
#> GSM711976 1 0.0817 0.9660 0.976 0.000 0.000 0.024
#> GSM711980 1 0.0188 0.9805 0.996 0.000 0.000 0.004
#> GSM711986 1 0.0000 0.9814 1.000 0.000 0.000 0.000
#> GSM711904 1 0.0188 0.9805 0.996 0.000 0.000 0.004
#> GSM711906 1 0.0000 0.9814 1.000 0.000 0.000 0.000
#> GSM711908 1 0.0000 0.9814 1.000 0.000 0.000 0.000
#> GSM711910 3 0.0000 0.8951 0.000 0.000 1.000 0.000
#> GSM711914 1 0.0000 0.9814 1.000 0.000 0.000 0.000
#> GSM711916 1 0.0000 0.9814 1.000 0.000 0.000 0.000
#> GSM711922 1 0.0188 0.9805 0.996 0.000 0.000 0.004
#> GSM711924 1 0.0000 0.9814 1.000 0.000 0.000 0.000
#> GSM711926 4 0.2408 0.8488 0.000 0.104 0.000 0.896
#> GSM711928 1 0.0188 0.9805 0.996 0.000 0.000 0.004
#> GSM711930 1 0.0000 0.9814 1.000 0.000 0.000 0.000
#> GSM711932 1 0.1022 0.9597 0.968 0.000 0.000 0.032
#> GSM711934 1 0.0188 0.9805 0.996 0.000 0.000 0.004
#> GSM711940 1 0.0469 0.9758 0.988 0.000 0.000 0.012
#> GSM711942 1 0.0000 0.9814 1.000 0.000 0.000 0.000
#> GSM711944 3 0.0000 0.8951 0.000 0.000 1.000 0.000
#> GSM711946 3 0.4804 0.4189 0.000 0.000 0.616 0.384
#> GSM711948 1 0.4994 0.0653 0.520 0.000 0.000 0.480
#> GSM711952 1 0.0000 0.9814 1.000 0.000 0.000 0.000
#> GSM711954 1 0.0188 0.9805 0.996 0.000 0.000 0.004
#> GSM711962 1 0.0000 0.9814 1.000 0.000 0.000 0.000
#> GSM711970 1 0.0188 0.9805 0.996 0.000 0.000 0.004
#> GSM711974 1 0.0000 0.9814 1.000 0.000 0.000 0.000
#> GSM711978 4 0.0000 0.9398 0.000 0.000 0.000 1.000
#> GSM711988 1 0.0817 0.9660 0.976 0.000 0.000 0.024
#> GSM711990 3 0.0000 0.8951 0.000 0.000 1.000 0.000
#> GSM711992 4 0.0000 0.9398 0.000 0.000 0.000 1.000
#> GSM711982 1 0.0000 0.9814 1.000 0.000 0.000 0.000
#> GSM711984 2 0.0000 0.9931 0.000 1.000 0.000 0.000
#> GSM711912 1 0.0000 0.9814 1.000 0.000 0.000 0.000
#> GSM711918 1 0.0000 0.9814 1.000 0.000 0.000 0.000
#> GSM711920 1 0.0000 0.9814 1.000 0.000 0.000 0.000
#> GSM711937 2 0.0000 0.9931 0.000 1.000 0.000 0.000
#> GSM711939 2 0.0000 0.9931 0.000 1.000 0.000 0.000
#> GSM711951 2 0.2973 0.8243 0.000 0.856 0.000 0.144
#> GSM711957 1 0.1109 0.9599 0.968 0.004 0.000 0.028
#> GSM711959 2 0.0000 0.9931 0.000 1.000 0.000 0.000
#> GSM711961 2 0.0000 0.9931 0.000 1.000 0.000 0.000
#> GSM711965 3 0.0000 0.8951 0.000 0.000 1.000 0.000
#> GSM711967 1 0.0000 0.9814 1.000 0.000 0.000 0.000
#> GSM711969 2 0.0000 0.9931 0.000 1.000 0.000 0.000
#> GSM711973 3 0.1302 0.8620 0.000 0.000 0.956 0.044
#> GSM711977 3 0.0000 0.8951 0.000 0.000 1.000 0.000
#> GSM711981 4 0.0336 0.9380 0.000 0.008 0.000 0.992
#> GSM711987 2 0.0000 0.9931 0.000 1.000 0.000 0.000
#> GSM711905 2 0.0000 0.9931 0.000 1.000 0.000 0.000
#> GSM711907 2 0.0000 0.9931 0.000 1.000 0.000 0.000
#> GSM711909 3 0.0000 0.8951 0.000 0.000 1.000 0.000
#> GSM711911 3 0.0000 0.8951 0.000 0.000 1.000 0.000
#> GSM711915 3 0.0000 0.8951 0.000 0.000 1.000 0.000
#> GSM711917 2 0.0000 0.9931 0.000 1.000 0.000 0.000
#> GSM711923 4 0.0817 0.9272 0.000 0.000 0.024 0.976
#> GSM711925 2 0.0000 0.9931 0.000 1.000 0.000 0.000
#> GSM711927 3 0.0000 0.8951 0.000 0.000 1.000 0.000
#> GSM711929 2 0.0000 0.9931 0.000 1.000 0.000 0.000
#> GSM711931 2 0.0000 0.9931 0.000 1.000 0.000 0.000
#> GSM711933 1 0.0336 0.9785 0.992 0.000 0.000 0.008
#> GSM711935 2 0.0000 0.9931 0.000 1.000 0.000 0.000
#> GSM711941 4 0.0000 0.9398 0.000 0.000 0.000 1.000
#> GSM711943 4 0.0817 0.9272 0.000 0.000 0.024 0.976
#> GSM711945 3 0.4977 0.2317 0.000 0.000 0.540 0.460
#> GSM711947 3 0.4331 0.5842 0.000 0.288 0.712 0.000
#> GSM711949 2 0.0000 0.9931 0.000 1.000 0.000 0.000
#> GSM711953 2 0.0000 0.9931 0.000 1.000 0.000 0.000
#> GSM711955 3 0.4313 0.5867 0.260 0.000 0.736 0.004
#> GSM711963 2 0.0000 0.9931 0.000 1.000 0.000 0.000
#> GSM711971 3 0.0000 0.8951 0.000 0.000 1.000 0.000
#> GSM711975 2 0.0000 0.9931 0.000 1.000 0.000 0.000
#> GSM711979 4 0.0000 0.9398 0.000 0.000 0.000 1.000
#> GSM711989 2 0.0000 0.9931 0.000 1.000 0.000 0.000
#> GSM711991 3 0.0000 0.8951 0.000 0.000 1.000 0.000
#> GSM711993 4 0.0336 0.9380 0.000 0.008 0.000 0.992
#> GSM711983 3 0.0000 0.8951 0.000 0.000 1.000 0.000
#> GSM711985 2 0.0000 0.9931 0.000 1.000 0.000 0.000
#> GSM711913 3 0.0000 0.8951 0.000 0.000 1.000 0.000
#> GSM711919 3 0.0000 0.8951 0.000 0.000 1.000 0.000
#> GSM711921 3 0.0000 0.8951 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM711936 2 0.0000 0.9856 0.000 1.000 0.000 0.000 0.000
#> GSM711938 2 0.0000 0.9856 0.000 1.000 0.000 0.000 0.000
#> GSM711950 1 0.1282 0.5455 0.952 0.000 0.000 0.044 0.004
#> GSM711956 1 0.4150 0.6510 0.612 0.000 0.000 0.000 0.388
#> GSM711958 5 0.4291 -0.0433 0.464 0.000 0.000 0.000 0.536
#> GSM711960 1 0.6641 0.1679 0.448 0.000 0.296 0.000 0.256
#> GSM711964 1 0.4306 0.5091 0.508 0.000 0.000 0.000 0.492
#> GSM711966 5 0.0290 0.8083 0.008 0.000 0.000 0.000 0.992
#> GSM711968 1 0.4256 0.6108 0.564 0.000 0.000 0.000 0.436
#> GSM711972 5 0.0000 0.8073 0.000 0.000 0.000 0.000 1.000
#> GSM711976 1 0.3636 0.6718 0.728 0.000 0.000 0.000 0.272
#> GSM711980 1 0.3752 0.6812 0.708 0.000 0.000 0.000 0.292
#> GSM711986 5 0.1908 0.7518 0.092 0.000 0.000 0.000 0.908
#> GSM711904 1 0.4268 0.5961 0.556 0.000 0.000 0.000 0.444
#> GSM711906 5 0.0162 0.8063 0.004 0.000 0.000 0.000 0.996
#> GSM711908 5 0.0290 0.8064 0.008 0.000 0.000 0.000 0.992
#> GSM711910 3 0.0000 0.8896 0.000 0.000 1.000 0.000 0.000
#> GSM711914 1 0.4300 0.5398 0.524 0.000 0.000 0.000 0.476
#> GSM711916 5 0.0404 0.8077 0.012 0.000 0.000 0.000 0.988
#> GSM711922 1 0.4101 0.6526 0.628 0.000 0.000 0.000 0.372
#> GSM711924 5 0.3508 0.5723 0.252 0.000 0.000 0.000 0.748
#> GSM711926 4 0.1043 0.9101 0.000 0.040 0.000 0.960 0.000
#> GSM711928 1 0.4235 0.6211 0.576 0.000 0.000 0.000 0.424
#> GSM711930 5 0.0162 0.8085 0.004 0.000 0.000 0.000 0.996
#> GSM711932 1 0.3994 0.6645 0.772 0.000 0.000 0.040 0.188
#> GSM711934 1 0.3586 0.6788 0.736 0.000 0.000 0.000 0.264
#> GSM711940 1 0.4307 0.1232 0.500 0.000 0.000 0.000 0.500
#> GSM711942 5 0.3274 0.6171 0.220 0.000 0.000 0.000 0.780
#> GSM711944 3 0.1965 0.8305 0.096 0.000 0.904 0.000 0.000
#> GSM711946 3 0.6188 0.3375 0.160 0.000 0.524 0.316 0.000
#> GSM711948 1 0.0992 0.5507 0.968 0.000 0.000 0.024 0.008
#> GSM711952 5 0.1851 0.7554 0.088 0.000 0.000 0.000 0.912
#> GSM711954 1 0.4161 0.6342 0.608 0.000 0.000 0.000 0.392
#> GSM711962 5 0.1965 0.7603 0.096 0.000 0.000 0.000 0.904
#> GSM711970 1 0.4060 0.6480 0.640 0.000 0.000 0.000 0.360
#> GSM711974 5 0.4074 0.2009 0.364 0.000 0.000 0.000 0.636
#> GSM711978 4 0.0000 0.9373 0.000 0.000 0.000 1.000 0.000
#> GSM711988 1 0.3003 0.6705 0.812 0.000 0.000 0.000 0.188
#> GSM711990 3 0.0000 0.8896 0.000 0.000 1.000 0.000 0.000
#> GSM711992 4 0.0162 0.9361 0.004 0.000 0.000 0.996 0.000
#> GSM711982 5 0.0290 0.8083 0.008 0.000 0.000 0.000 0.992
#> GSM711984 2 0.0000 0.9856 0.000 1.000 0.000 0.000 0.000
#> GSM711912 5 0.1341 0.7860 0.056 0.000 0.000 0.000 0.944
#> GSM711918 5 0.1478 0.7798 0.064 0.000 0.000 0.000 0.936
#> GSM711920 5 0.3949 0.3592 0.332 0.000 0.000 0.000 0.668
#> GSM711937 2 0.0000 0.9856 0.000 1.000 0.000 0.000 0.000
#> GSM711939 2 0.0000 0.9856 0.000 1.000 0.000 0.000 0.000
#> GSM711951 2 0.2471 0.8346 0.000 0.864 0.000 0.136 0.000
#> GSM711957 1 0.5341 0.6178 0.664 0.000 0.000 0.124 0.212
#> GSM711959 2 0.0000 0.9856 0.000 1.000 0.000 0.000 0.000
#> GSM711961 2 0.0000 0.9856 0.000 1.000 0.000 0.000 0.000
#> GSM711965 3 0.2732 0.8094 0.160 0.000 0.840 0.000 0.000
#> GSM711967 5 0.1410 0.7830 0.060 0.000 0.000 0.000 0.940
#> GSM711969 2 0.0000 0.9856 0.000 1.000 0.000 0.000 0.000
#> GSM711973 3 0.4127 0.6693 0.312 0.000 0.680 0.008 0.000
#> GSM711977 3 0.2020 0.8491 0.100 0.000 0.900 0.000 0.000
#> GSM711981 4 0.1638 0.9257 0.064 0.004 0.000 0.932 0.000
#> GSM711987 2 0.0000 0.9856 0.000 1.000 0.000 0.000 0.000
#> GSM711905 2 0.0000 0.9856 0.000 1.000 0.000 0.000 0.000
#> GSM711907 2 0.0000 0.9856 0.000 1.000 0.000 0.000 0.000
#> GSM711909 3 0.0000 0.8896 0.000 0.000 1.000 0.000 0.000
#> GSM711911 3 0.0000 0.8896 0.000 0.000 1.000 0.000 0.000
#> GSM711915 3 0.0404 0.8862 0.012 0.000 0.988 0.000 0.000
#> GSM711917 2 0.0000 0.9856 0.000 1.000 0.000 0.000 0.000
#> GSM711923 4 0.2798 0.8800 0.140 0.000 0.008 0.852 0.000
#> GSM711925 2 0.0000 0.9856 0.000 1.000 0.000 0.000 0.000
#> GSM711927 3 0.0000 0.8896 0.000 0.000 1.000 0.000 0.000
#> GSM711929 2 0.0000 0.9856 0.000 1.000 0.000 0.000 0.000
#> GSM711931 2 0.2852 0.8013 0.000 0.828 0.000 0.172 0.000
#> GSM711933 1 0.3424 0.6588 0.760 0.000 0.000 0.000 0.240
#> GSM711935 2 0.0000 0.9856 0.000 1.000 0.000 0.000 0.000
#> GSM711941 4 0.3534 0.8079 0.256 0.000 0.000 0.744 0.000
#> GSM711943 4 0.1478 0.9259 0.064 0.000 0.000 0.936 0.000
#> GSM711945 3 0.6282 0.2012 0.156 0.000 0.476 0.368 0.000
#> GSM711947 3 0.3177 0.6766 0.000 0.208 0.792 0.000 0.000
#> GSM711949 2 0.0000 0.9856 0.000 1.000 0.000 0.000 0.000
#> GSM711953 2 0.0000 0.9856 0.000 1.000 0.000 0.000 0.000
#> GSM711955 1 0.2771 0.5027 0.860 0.000 0.128 0.000 0.012
#> GSM711963 2 0.0000 0.9856 0.000 1.000 0.000 0.000 0.000
#> GSM711971 3 0.0000 0.8896 0.000 0.000 1.000 0.000 0.000
#> GSM711975 2 0.0000 0.9856 0.000 1.000 0.000 0.000 0.000
#> GSM711979 4 0.0000 0.9373 0.000 0.000 0.000 1.000 0.000
#> GSM711989 2 0.0000 0.9856 0.000 1.000 0.000 0.000 0.000
#> GSM711991 3 0.0162 0.8886 0.004 0.000 0.996 0.000 0.000
#> GSM711993 4 0.0000 0.9373 0.000 0.000 0.000 1.000 0.000
#> GSM711983 3 0.0000 0.8896 0.000 0.000 1.000 0.000 0.000
#> GSM711985 2 0.0000 0.9856 0.000 1.000 0.000 0.000 0.000
#> GSM711913 3 0.1965 0.8513 0.096 0.000 0.904 0.000 0.000
#> GSM711919 3 0.0000 0.8896 0.000 0.000 1.000 0.000 0.000
#> GSM711921 3 0.0000 0.8896 0.000 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM711936 2 0.0000 0.9765 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711938 2 0.0000 0.9765 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711950 1 0.3857 0.4020 0.532 0.000 0.000 0.000 0.468 0.000
#> GSM711956 1 0.3062 0.6734 0.824 0.000 0.000 0.000 0.032 0.144
#> GSM711958 6 0.5725 0.1624 0.416 0.000 0.000 0.000 0.164 0.420
#> GSM711960 6 0.7638 0.0905 0.268 0.000 0.280 0.000 0.172 0.280
#> GSM711964 1 0.3314 0.6011 0.740 0.000 0.000 0.000 0.004 0.256
#> GSM711966 6 0.0363 0.6591 0.012 0.000 0.000 0.000 0.000 0.988
#> GSM711968 1 0.3202 0.6466 0.800 0.000 0.000 0.000 0.024 0.176
#> GSM711972 6 0.0458 0.6584 0.016 0.000 0.000 0.000 0.000 0.984
#> GSM711976 1 0.4520 0.6333 0.688 0.000 0.000 0.000 0.220 0.092
#> GSM711980 1 0.3006 0.6765 0.844 0.000 0.000 0.000 0.064 0.092
#> GSM711986 6 0.4508 0.2395 0.396 0.000 0.000 0.000 0.036 0.568
#> GSM711904 1 0.4065 0.6100 0.724 0.000 0.000 0.000 0.056 0.220
#> GSM711906 6 0.0363 0.6579 0.012 0.000 0.000 0.000 0.000 0.988
#> GSM711908 6 0.2858 0.5855 0.124 0.000 0.000 0.000 0.032 0.844
#> GSM711910 3 0.0000 0.8253 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711914 1 0.3817 0.5891 0.720 0.000 0.000 0.000 0.028 0.252
#> GSM711916 6 0.0458 0.6578 0.016 0.000 0.000 0.000 0.000 0.984
#> GSM711922 1 0.2573 0.6720 0.864 0.000 0.000 0.000 0.024 0.112
#> GSM711924 6 0.5304 0.4360 0.276 0.000 0.000 0.000 0.144 0.580
#> GSM711926 4 0.1010 0.8072 0.000 0.036 0.000 0.960 0.004 0.000
#> GSM711928 1 0.3551 0.6480 0.772 0.000 0.000 0.000 0.036 0.192
#> GSM711930 6 0.0260 0.6582 0.008 0.000 0.000 0.000 0.000 0.992
#> GSM711932 1 0.4297 0.6435 0.752 0.000 0.000 0.032 0.168 0.048
#> GSM711934 1 0.4232 0.5916 0.732 0.000 0.000 0.000 0.168 0.100
#> GSM711940 6 0.5451 0.2460 0.328 0.000 0.000 0.000 0.140 0.532
#> GSM711942 6 0.5065 0.4710 0.260 0.000 0.000 0.000 0.124 0.616
#> GSM711944 3 0.4044 0.4865 0.076 0.000 0.744 0.000 0.180 0.000
#> GSM711946 5 0.5627 0.4444 0.004 0.000 0.380 0.132 0.484 0.000
#> GSM711948 1 0.3996 0.3982 0.512 0.000 0.000 0.000 0.484 0.004
#> GSM711952 6 0.4552 0.2526 0.388 0.000 0.000 0.000 0.040 0.572
#> GSM711954 1 0.3062 0.6595 0.816 0.000 0.000 0.000 0.024 0.160
#> GSM711962 6 0.2112 0.6330 0.088 0.000 0.000 0.000 0.016 0.896
#> GSM711970 1 0.2888 0.6570 0.852 0.000 0.000 0.000 0.056 0.092
#> GSM711974 6 0.5486 0.2423 0.372 0.000 0.000 0.000 0.132 0.496
#> GSM711978 4 0.0146 0.8410 0.004 0.000 0.000 0.996 0.000 0.000
#> GSM711988 1 0.4044 0.6088 0.704 0.000 0.000 0.000 0.256 0.040
#> GSM711990 3 0.0260 0.8251 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM711992 4 0.0436 0.8371 0.004 0.000 0.000 0.988 0.004 0.004
#> GSM711982 6 0.0363 0.6591 0.012 0.000 0.000 0.000 0.000 0.988
#> GSM711984 2 0.0000 0.9765 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711912 6 0.4396 0.3356 0.352 0.000 0.000 0.000 0.036 0.612
#> GSM711918 6 0.4408 0.3279 0.356 0.000 0.000 0.000 0.036 0.608
#> GSM711920 1 0.5624 -0.0576 0.488 0.000 0.000 0.000 0.156 0.356
#> GSM711937 2 0.0000 0.9765 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711939 2 0.0000 0.9765 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711951 2 0.2912 0.7313 0.000 0.784 0.000 0.216 0.000 0.000
#> GSM711957 1 0.4294 0.6067 0.768 0.000 0.000 0.080 0.120 0.032
#> GSM711959 2 0.0000 0.9765 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711961 2 0.0000 0.9765 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711965 3 0.3982 -0.0976 0.004 0.000 0.536 0.000 0.460 0.000
#> GSM711967 6 0.2510 0.6290 0.100 0.000 0.000 0.000 0.028 0.872
#> GSM711969 2 0.0000 0.9765 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711973 5 0.4209 0.2371 0.020 0.000 0.384 0.000 0.596 0.000
#> GSM711977 3 0.2941 0.6211 0.000 0.000 0.780 0.000 0.220 0.000
#> GSM711981 4 0.2362 0.7547 0.000 0.004 0.000 0.860 0.136 0.000
#> GSM711987 2 0.0000 0.9765 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711905 2 0.0000 0.9765 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711907 2 0.0000 0.9765 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711909 3 0.0000 0.8253 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711911 3 0.0260 0.8251 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM711915 3 0.2300 0.7152 0.000 0.000 0.856 0.000 0.144 0.000
#> GSM711917 2 0.0000 0.9765 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711923 4 0.4171 0.3880 0.012 0.000 0.004 0.604 0.380 0.000
#> GSM711925 2 0.0000 0.9765 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711927 3 0.0000 0.8253 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711929 2 0.0000 0.9765 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711931 2 0.3309 0.6323 0.000 0.720 0.000 0.280 0.000 0.000
#> GSM711933 1 0.4924 0.4474 0.652 0.000 0.000 0.000 0.204 0.144
#> GSM711935 2 0.0000 0.9765 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711941 5 0.4453 -0.2672 0.028 0.000 0.000 0.444 0.528 0.000
#> GSM711943 4 0.3714 0.6103 0.008 0.000 0.008 0.720 0.264 0.000
#> GSM711945 5 0.5549 0.5177 0.000 0.000 0.304 0.164 0.532 0.000
#> GSM711947 3 0.3776 0.4634 0.000 0.196 0.756 0.000 0.048 0.000
#> GSM711949 2 0.0000 0.9765 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711953 2 0.0000 0.9765 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711955 1 0.5218 0.3180 0.464 0.000 0.068 0.000 0.460 0.008
#> GSM711963 2 0.0000 0.9765 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711971 3 0.0260 0.8251 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM711975 2 0.0363 0.9667 0.000 0.988 0.000 0.012 0.000 0.000
#> GSM711979 4 0.0692 0.8378 0.004 0.000 0.000 0.976 0.020 0.000
#> GSM711989 2 0.0000 0.9765 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711991 3 0.2454 0.6551 0.000 0.000 0.840 0.000 0.160 0.000
#> GSM711993 4 0.0000 0.8406 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM711983 3 0.0260 0.8251 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM711985 2 0.0000 0.9765 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711913 3 0.2883 0.6345 0.000 0.000 0.788 0.000 0.212 0.000
#> GSM711919 3 0.0000 0.8253 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711921 3 0.0000 0.8253 0.000 0.000 1.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) disease.state(p) individual(p) k
#> SD:skmeans 88 4.87e-06 0.5469 0.842 2
#> SD:skmeans 88 2.59e-10 0.1724 0.735 3
#> SD:skmeans 86 9.38e-10 0.2772 0.303 4
#> SD:skmeans 83 3.11e-08 0.1453 0.108 5
#> SD:skmeans 68 8.62e-07 0.0593 0.013 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "pam"]
# you can also extract it by
# res = res_list["SD:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 27425 rows and 90 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.988 0.995 0.4130 0.585 0.585
#> 3 3 0.748 0.828 0.913 0.5666 0.690 0.498
#> 4 4 0.893 0.916 0.962 0.1368 0.914 0.750
#> 5 5 0.789 0.684 0.865 0.0846 0.860 0.532
#> 6 6 0.803 0.592 0.753 0.0322 0.891 0.537
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM711936 2 0.0000 0.985 0.000 1.000
#> GSM711938 2 0.0000 0.985 0.000 1.000
#> GSM711950 1 0.0000 0.999 1.000 0.000
#> GSM711956 1 0.0000 0.999 1.000 0.000
#> GSM711958 1 0.0000 0.999 1.000 0.000
#> GSM711960 1 0.0000 0.999 1.000 0.000
#> GSM711964 1 0.0000 0.999 1.000 0.000
#> GSM711966 1 0.0000 0.999 1.000 0.000
#> GSM711968 1 0.0000 0.999 1.000 0.000
#> GSM711972 1 0.0000 0.999 1.000 0.000
#> GSM711976 1 0.0000 0.999 1.000 0.000
#> GSM711980 1 0.0000 0.999 1.000 0.000
#> GSM711986 1 0.0000 0.999 1.000 0.000
#> GSM711904 1 0.0000 0.999 1.000 0.000
#> GSM711906 1 0.0000 0.999 1.000 0.000
#> GSM711908 1 0.0000 0.999 1.000 0.000
#> GSM711910 1 0.0000 0.999 1.000 0.000
#> GSM711914 1 0.0000 0.999 1.000 0.000
#> GSM711916 1 0.0000 0.999 1.000 0.000
#> GSM711922 1 0.0000 0.999 1.000 0.000
#> GSM711924 1 0.0000 0.999 1.000 0.000
#> GSM711926 2 0.9129 0.517 0.328 0.672
#> GSM711928 1 0.0000 0.999 1.000 0.000
#> GSM711930 1 0.0000 0.999 1.000 0.000
#> GSM711932 1 0.0000 0.999 1.000 0.000
#> GSM711934 1 0.0000 0.999 1.000 0.000
#> GSM711940 1 0.0000 0.999 1.000 0.000
#> GSM711942 1 0.0000 0.999 1.000 0.000
#> GSM711944 1 0.0000 0.999 1.000 0.000
#> GSM711946 1 0.0000 0.999 1.000 0.000
#> GSM711948 1 0.0000 0.999 1.000 0.000
#> GSM711952 1 0.0000 0.999 1.000 0.000
#> GSM711954 1 0.0000 0.999 1.000 0.000
#> GSM711962 1 0.0000 0.999 1.000 0.000
#> GSM711970 1 0.0000 0.999 1.000 0.000
#> GSM711974 1 0.0000 0.999 1.000 0.000
#> GSM711978 1 0.0376 0.995 0.996 0.004
#> GSM711988 1 0.0000 0.999 1.000 0.000
#> GSM711990 1 0.0000 0.999 1.000 0.000
#> GSM711992 1 0.0376 0.995 0.996 0.004
#> GSM711982 1 0.0000 0.999 1.000 0.000
#> GSM711984 2 0.0000 0.985 0.000 1.000
#> GSM711912 1 0.0000 0.999 1.000 0.000
#> GSM711918 1 0.0000 0.999 1.000 0.000
#> GSM711920 1 0.0000 0.999 1.000 0.000
#> GSM711937 2 0.0000 0.985 0.000 1.000
#> GSM711939 2 0.0000 0.985 0.000 1.000
#> GSM711951 2 0.0000 0.985 0.000 1.000
#> GSM711957 1 0.0000 0.999 1.000 0.000
#> GSM711959 2 0.0000 0.985 0.000 1.000
#> GSM711961 2 0.0000 0.985 0.000 1.000
#> GSM711965 1 0.0000 0.999 1.000 0.000
#> GSM711967 1 0.0000 0.999 1.000 0.000
#> GSM711969 2 0.0000 0.985 0.000 1.000
#> GSM711973 1 0.0000 0.999 1.000 0.000
#> GSM711977 1 0.0000 0.999 1.000 0.000
#> GSM711981 1 0.1184 0.984 0.984 0.016
#> GSM711987 2 0.0000 0.985 0.000 1.000
#> GSM711905 2 0.0000 0.985 0.000 1.000
#> GSM711907 2 0.0000 0.985 0.000 1.000
#> GSM711909 1 0.0000 0.999 1.000 0.000
#> GSM711911 1 0.0000 0.999 1.000 0.000
#> GSM711915 1 0.0672 0.992 0.992 0.008
#> GSM711917 2 0.0000 0.985 0.000 1.000
#> GSM711923 1 0.0000 0.999 1.000 0.000
#> GSM711925 2 0.0000 0.985 0.000 1.000
#> GSM711927 1 0.0000 0.999 1.000 0.000
#> GSM711929 2 0.0000 0.985 0.000 1.000
#> GSM711931 2 0.0000 0.985 0.000 1.000
#> GSM711933 1 0.0000 0.999 1.000 0.000
#> GSM711935 2 0.0000 0.985 0.000 1.000
#> GSM711941 1 0.0000 0.999 1.000 0.000
#> GSM711943 1 0.0000 0.999 1.000 0.000
#> GSM711945 1 0.1414 0.980 0.980 0.020
#> GSM711947 2 0.1843 0.961 0.028 0.972
#> GSM711949 2 0.0000 0.985 0.000 1.000
#> GSM711953 2 0.0000 0.985 0.000 1.000
#> GSM711955 1 0.0000 0.999 1.000 0.000
#> GSM711963 2 0.0000 0.985 0.000 1.000
#> GSM711971 1 0.0000 0.999 1.000 0.000
#> GSM711975 2 0.0000 0.985 0.000 1.000
#> GSM711979 1 0.0000 0.999 1.000 0.000
#> GSM711989 2 0.0000 0.985 0.000 1.000
#> GSM711991 1 0.1843 0.972 0.972 0.028
#> GSM711993 2 0.1633 0.965 0.024 0.976
#> GSM711983 1 0.0000 0.999 1.000 0.000
#> GSM711985 2 0.0000 0.985 0.000 1.000
#> GSM711913 1 0.0000 0.999 1.000 0.000
#> GSM711919 1 0.0000 0.999 1.000 0.000
#> GSM711921 1 0.0000 0.999 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM711936 2 0.0000 0.989 0.000 1.000 0.000
#> GSM711938 2 0.0000 0.989 0.000 1.000 0.000
#> GSM711950 3 0.6095 0.585 0.392 0.000 0.608
#> GSM711956 1 0.0000 0.955 1.000 0.000 0.000
#> GSM711958 1 0.5650 0.350 0.688 0.000 0.312
#> GSM711960 1 0.5529 0.512 0.704 0.000 0.296
#> GSM711964 1 0.0000 0.955 1.000 0.000 0.000
#> GSM711966 1 0.0000 0.955 1.000 0.000 0.000
#> GSM711968 1 0.0000 0.955 1.000 0.000 0.000
#> GSM711972 1 0.0000 0.955 1.000 0.000 0.000
#> GSM711976 1 0.0000 0.955 1.000 0.000 0.000
#> GSM711980 1 0.0000 0.955 1.000 0.000 0.000
#> GSM711986 1 0.0000 0.955 1.000 0.000 0.000
#> GSM711904 1 0.0000 0.955 1.000 0.000 0.000
#> GSM711906 1 0.0000 0.955 1.000 0.000 0.000
#> GSM711908 1 0.0000 0.955 1.000 0.000 0.000
#> GSM711910 3 0.0000 0.789 0.000 0.000 1.000
#> GSM711914 1 0.0000 0.955 1.000 0.000 0.000
#> GSM711916 1 0.0000 0.955 1.000 0.000 0.000
#> GSM711922 1 0.0000 0.955 1.000 0.000 0.000
#> GSM711924 1 0.0000 0.955 1.000 0.000 0.000
#> GSM711926 3 0.6095 0.585 0.392 0.000 0.608
#> GSM711928 1 0.0000 0.955 1.000 0.000 0.000
#> GSM711930 1 0.0000 0.955 1.000 0.000 0.000
#> GSM711932 1 0.6260 -0.183 0.552 0.000 0.448
#> GSM711934 1 0.0000 0.955 1.000 0.000 0.000
#> GSM711940 3 0.6095 0.585 0.392 0.000 0.608
#> GSM711942 1 0.0000 0.955 1.000 0.000 0.000
#> GSM711944 3 0.0237 0.789 0.004 0.000 0.996
#> GSM711946 3 0.0424 0.789 0.008 0.000 0.992
#> GSM711948 3 0.6111 0.579 0.396 0.000 0.604
#> GSM711952 1 0.0000 0.955 1.000 0.000 0.000
#> GSM711954 1 0.0000 0.955 1.000 0.000 0.000
#> GSM711962 1 0.0000 0.955 1.000 0.000 0.000
#> GSM711970 1 0.0000 0.955 1.000 0.000 0.000
#> GSM711974 1 0.0000 0.955 1.000 0.000 0.000
#> GSM711978 3 0.6095 0.585 0.392 0.000 0.608
#> GSM711988 1 0.0592 0.941 0.988 0.000 0.012
#> GSM711990 3 0.0000 0.789 0.000 0.000 1.000
#> GSM711992 3 0.6095 0.585 0.392 0.000 0.608
#> GSM711982 1 0.0000 0.955 1.000 0.000 0.000
#> GSM711984 2 0.0000 0.989 0.000 1.000 0.000
#> GSM711912 1 0.0000 0.955 1.000 0.000 0.000
#> GSM711918 1 0.0000 0.955 1.000 0.000 0.000
#> GSM711920 1 0.0000 0.955 1.000 0.000 0.000
#> GSM711937 2 0.0000 0.989 0.000 1.000 0.000
#> GSM711939 2 0.0000 0.989 0.000 1.000 0.000
#> GSM711951 3 0.6095 0.415 0.000 0.392 0.608
#> GSM711957 3 0.6111 0.579 0.396 0.000 0.604
#> GSM711959 2 0.0000 0.989 0.000 1.000 0.000
#> GSM711961 2 0.0000 0.989 0.000 1.000 0.000
#> GSM711965 3 0.0000 0.789 0.000 0.000 1.000
#> GSM711967 3 0.6111 0.579 0.396 0.000 0.604
#> GSM711969 2 0.0000 0.989 0.000 1.000 0.000
#> GSM711973 3 0.6008 0.605 0.372 0.000 0.628
#> GSM711977 3 0.0000 0.789 0.000 0.000 1.000
#> GSM711981 3 0.6079 0.590 0.388 0.000 0.612
#> GSM711987 2 0.0000 0.989 0.000 1.000 0.000
#> GSM711905 2 0.0000 0.989 0.000 1.000 0.000
#> GSM711907 2 0.4504 0.713 0.000 0.804 0.196
#> GSM711909 3 0.0000 0.789 0.000 0.000 1.000
#> GSM711911 3 0.0000 0.789 0.000 0.000 1.000
#> GSM711915 3 0.0000 0.789 0.000 0.000 1.000
#> GSM711917 2 0.0000 0.989 0.000 1.000 0.000
#> GSM711923 3 0.2959 0.770 0.100 0.000 0.900
#> GSM711925 2 0.0000 0.989 0.000 1.000 0.000
#> GSM711927 3 0.0000 0.789 0.000 0.000 1.000
#> GSM711929 2 0.0000 0.989 0.000 1.000 0.000
#> GSM711931 2 0.0000 0.989 0.000 1.000 0.000
#> GSM711933 3 0.6111 0.579 0.396 0.000 0.604
#> GSM711935 2 0.0000 0.989 0.000 1.000 0.000
#> GSM711941 3 0.5254 0.690 0.264 0.000 0.736
#> GSM711943 3 0.2959 0.770 0.100 0.000 0.900
#> GSM711945 3 0.1647 0.786 0.036 0.004 0.960
#> GSM711947 3 0.6079 0.422 0.000 0.388 0.612
#> GSM711949 2 0.0000 0.989 0.000 1.000 0.000
#> GSM711953 2 0.0000 0.989 0.000 1.000 0.000
#> GSM711955 3 0.4555 0.728 0.200 0.000 0.800
#> GSM711963 2 0.0000 0.989 0.000 1.000 0.000
#> GSM711971 3 0.0000 0.789 0.000 0.000 1.000
#> GSM711975 2 0.0000 0.989 0.000 1.000 0.000
#> GSM711979 3 0.6095 0.585 0.392 0.000 0.608
#> GSM711989 2 0.0000 0.989 0.000 1.000 0.000
#> GSM711991 3 0.0000 0.789 0.000 0.000 1.000
#> GSM711993 3 0.6095 0.415 0.000 0.392 0.608
#> GSM711983 3 0.0000 0.789 0.000 0.000 1.000
#> GSM711985 2 0.0000 0.989 0.000 1.000 0.000
#> GSM711913 3 0.0000 0.789 0.000 0.000 1.000
#> GSM711919 3 0.0000 0.789 0.000 0.000 1.000
#> GSM711921 3 0.0000 0.789 0.000 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM711936 2 0.0707 0.968 0.000 0.980 0.000 0.020
#> GSM711938 2 0.0000 0.978 0.000 1.000 0.000 0.000
#> GSM711950 4 0.2589 0.864 0.116 0.000 0.000 0.884
#> GSM711956 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM711958 1 0.4477 0.479 0.688 0.000 0.000 0.312
#> GSM711960 3 0.3024 0.803 0.148 0.000 0.852 0.000
#> GSM711964 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM711966 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM711968 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM711972 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM711976 1 0.0188 0.966 0.996 0.000 0.000 0.004
#> GSM711980 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM711986 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM711904 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM711906 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM711908 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM711910 3 0.0000 0.968 0.000 0.000 1.000 0.000
#> GSM711914 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM711916 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM711922 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM711924 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM711926 4 0.0000 0.907 0.000 0.000 0.000 1.000
#> GSM711928 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM711930 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM711932 1 0.4999 -0.111 0.508 0.000 0.000 0.492
#> GSM711934 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM711940 4 0.2589 0.864 0.116 0.000 0.000 0.884
#> GSM711942 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM711944 3 0.3355 0.800 0.004 0.000 0.836 0.160
#> GSM711946 4 0.0336 0.904 0.000 0.000 0.008 0.992
#> GSM711948 4 0.4730 0.509 0.364 0.000 0.000 0.636
#> GSM711952 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM711954 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM711962 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM711970 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM711974 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM711978 4 0.0000 0.907 0.000 0.000 0.000 1.000
#> GSM711988 1 0.0469 0.958 0.988 0.000 0.000 0.012
#> GSM711990 3 0.0000 0.968 0.000 0.000 1.000 0.000
#> GSM711992 4 0.0000 0.907 0.000 0.000 0.000 1.000
#> GSM711982 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM711984 2 0.0000 0.978 0.000 1.000 0.000 0.000
#> GSM711912 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM711918 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM711920 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM711937 2 0.0707 0.968 0.000 0.980 0.000 0.020
#> GSM711939 2 0.0000 0.978 0.000 1.000 0.000 0.000
#> GSM711951 4 0.0000 0.907 0.000 0.000 0.000 1.000
#> GSM711957 4 0.2868 0.851 0.136 0.000 0.000 0.864
#> GSM711959 2 0.0000 0.978 0.000 1.000 0.000 0.000
#> GSM711961 2 0.0000 0.978 0.000 1.000 0.000 0.000
#> GSM711965 4 0.1557 0.878 0.000 0.000 0.056 0.944
#> GSM711967 4 0.2921 0.848 0.140 0.000 0.000 0.860
#> GSM711969 2 0.0000 0.978 0.000 1.000 0.000 0.000
#> GSM711973 4 0.4552 0.816 0.128 0.000 0.072 0.800
#> GSM711977 3 0.0921 0.951 0.000 0.000 0.972 0.028
#> GSM711981 4 0.0000 0.907 0.000 0.000 0.000 1.000
#> GSM711987 2 0.0000 0.978 0.000 1.000 0.000 0.000
#> GSM711905 2 0.0000 0.978 0.000 1.000 0.000 0.000
#> GSM711907 2 0.4277 0.620 0.000 0.720 0.000 0.280
#> GSM711909 3 0.0000 0.968 0.000 0.000 1.000 0.000
#> GSM711911 3 0.0000 0.968 0.000 0.000 1.000 0.000
#> GSM711915 3 0.0000 0.968 0.000 0.000 1.000 0.000
#> GSM711917 2 0.0000 0.978 0.000 1.000 0.000 0.000
#> GSM711923 4 0.0000 0.907 0.000 0.000 0.000 1.000
#> GSM711925 2 0.0000 0.978 0.000 1.000 0.000 0.000
#> GSM711927 3 0.0000 0.968 0.000 0.000 1.000 0.000
#> GSM711929 2 0.0000 0.978 0.000 1.000 0.000 0.000
#> GSM711931 2 0.1637 0.934 0.000 0.940 0.000 0.060
#> GSM711933 4 0.3907 0.753 0.232 0.000 0.000 0.768
#> GSM711935 2 0.0000 0.978 0.000 1.000 0.000 0.000
#> GSM711941 4 0.0707 0.903 0.020 0.000 0.000 0.980
#> GSM711943 4 0.0000 0.907 0.000 0.000 0.000 1.000
#> GSM711945 4 0.0000 0.907 0.000 0.000 0.000 1.000
#> GSM711947 4 0.4194 0.757 0.000 0.172 0.028 0.800
#> GSM711949 2 0.0000 0.978 0.000 1.000 0.000 0.000
#> GSM711953 2 0.0000 0.978 0.000 1.000 0.000 0.000
#> GSM711955 4 0.3674 0.852 0.116 0.000 0.036 0.848
#> GSM711963 2 0.0000 0.978 0.000 1.000 0.000 0.000
#> GSM711971 3 0.0000 0.968 0.000 0.000 1.000 0.000
#> GSM711975 2 0.1022 0.959 0.000 0.968 0.000 0.032
#> GSM711979 4 0.0000 0.907 0.000 0.000 0.000 1.000
#> GSM711989 2 0.0707 0.968 0.000 0.980 0.000 0.020
#> GSM711991 4 0.0592 0.901 0.000 0.000 0.016 0.984
#> GSM711993 4 0.0000 0.907 0.000 0.000 0.000 1.000
#> GSM711983 3 0.0188 0.966 0.000 0.000 0.996 0.004
#> GSM711985 2 0.0000 0.978 0.000 1.000 0.000 0.000
#> GSM711913 3 0.0921 0.951 0.000 0.000 0.972 0.028
#> GSM711919 3 0.0000 0.968 0.000 0.000 1.000 0.000
#> GSM711921 3 0.0000 0.968 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM711936 2 0.1410 0.9041 0.000 0.940 0.000 0.060 0.000
#> GSM711938 2 0.0000 0.9555 0.000 1.000 0.000 0.000 0.000
#> GSM711950 5 0.4297 -0.2564 0.000 0.000 0.000 0.472 0.528
#> GSM711956 1 0.0404 0.8966 0.988 0.000 0.000 0.000 0.012
#> GSM711958 5 0.1410 0.6793 0.060 0.000 0.000 0.000 0.940
#> GSM711960 5 0.1697 0.6794 0.060 0.000 0.008 0.000 0.932
#> GSM711964 1 0.0000 0.9008 1.000 0.000 0.000 0.000 0.000
#> GSM711966 1 0.0000 0.9008 1.000 0.000 0.000 0.000 0.000
#> GSM711968 1 0.0290 0.8987 0.992 0.000 0.000 0.000 0.008
#> GSM711972 1 0.0000 0.9008 1.000 0.000 0.000 0.000 0.000
#> GSM711976 1 0.5663 0.0363 0.508 0.000 0.000 0.080 0.412
#> GSM711980 5 0.4114 0.3769 0.376 0.000 0.000 0.000 0.624
#> GSM711986 1 0.0000 0.9008 1.000 0.000 0.000 0.000 0.000
#> GSM711904 1 0.1270 0.8708 0.948 0.000 0.000 0.000 0.052
#> GSM711906 5 0.4306 0.1346 0.492 0.000 0.000 0.000 0.508
#> GSM711908 1 0.1043 0.8765 0.960 0.000 0.000 0.000 0.040
#> GSM711910 3 0.0000 0.8887 0.000 0.000 1.000 0.000 0.000
#> GSM711914 1 0.0290 0.8987 0.992 0.000 0.000 0.000 0.008
#> GSM711916 1 0.0000 0.9008 1.000 0.000 0.000 0.000 0.000
#> GSM711922 1 0.3837 0.4520 0.692 0.000 0.000 0.000 0.308
#> GSM711924 5 0.1671 0.6797 0.076 0.000 0.000 0.000 0.924
#> GSM711926 4 0.0000 0.7249 0.000 0.000 0.000 1.000 0.000
#> GSM711928 1 0.1043 0.8813 0.960 0.000 0.000 0.000 0.040
#> GSM711930 1 0.0404 0.8964 0.988 0.000 0.000 0.000 0.012
#> GSM711932 5 0.3612 0.5109 0.000 0.000 0.000 0.268 0.732
#> GSM711934 1 0.4015 0.3545 0.652 0.000 0.000 0.000 0.348
#> GSM711940 5 0.4825 0.0184 0.024 0.000 0.000 0.408 0.568
#> GSM711942 5 0.4283 0.2258 0.456 0.000 0.000 0.000 0.544
#> GSM711944 5 0.1197 0.6214 0.000 0.000 0.048 0.000 0.952
#> GSM711946 4 0.4030 0.4885 0.000 0.000 0.000 0.648 0.352
#> GSM711948 5 0.1965 0.6288 0.096 0.000 0.000 0.000 0.904
#> GSM711952 1 0.0000 0.9008 1.000 0.000 0.000 0.000 0.000
#> GSM711954 5 0.4273 0.2331 0.448 0.000 0.000 0.000 0.552
#> GSM711962 5 0.3395 0.5680 0.236 0.000 0.000 0.000 0.764
#> GSM711970 5 0.4305 0.1403 0.488 0.000 0.000 0.000 0.512
#> GSM711974 1 0.2561 0.7512 0.856 0.000 0.000 0.000 0.144
#> GSM711978 4 0.0000 0.7249 0.000 0.000 0.000 1.000 0.000
#> GSM711988 5 0.1597 0.6754 0.048 0.000 0.000 0.012 0.940
#> GSM711990 3 0.3612 0.7259 0.000 0.000 0.732 0.000 0.268
#> GSM711992 4 0.0000 0.7249 0.000 0.000 0.000 1.000 0.000
#> GSM711982 1 0.0000 0.9008 1.000 0.000 0.000 0.000 0.000
#> GSM711984 2 0.0000 0.9555 0.000 1.000 0.000 0.000 0.000
#> GSM711912 1 0.0000 0.9008 1.000 0.000 0.000 0.000 0.000
#> GSM711918 1 0.0000 0.9008 1.000 0.000 0.000 0.000 0.000
#> GSM711920 5 0.3180 0.6594 0.068 0.000 0.000 0.076 0.856
#> GSM711937 2 0.1270 0.9118 0.000 0.948 0.000 0.052 0.000
#> GSM711939 2 0.0000 0.9555 0.000 1.000 0.000 0.000 0.000
#> GSM711951 4 0.0000 0.7249 0.000 0.000 0.000 1.000 0.000
#> GSM711957 5 0.3612 0.5109 0.000 0.000 0.000 0.268 0.732
#> GSM711959 2 0.0000 0.9555 0.000 1.000 0.000 0.000 0.000
#> GSM711961 2 0.0000 0.9555 0.000 1.000 0.000 0.000 0.000
#> GSM711965 4 0.5450 0.3030 0.000 0.000 0.060 0.496 0.444
#> GSM711967 5 0.3612 0.5109 0.000 0.000 0.000 0.268 0.732
#> GSM711969 2 0.0000 0.9555 0.000 1.000 0.000 0.000 0.000
#> GSM711973 5 0.4356 0.0875 0.012 0.000 0.000 0.340 0.648
#> GSM711977 3 0.4150 0.5437 0.000 0.000 0.612 0.000 0.388
#> GSM711981 4 0.0000 0.7249 0.000 0.000 0.000 1.000 0.000
#> GSM711987 2 0.0000 0.9555 0.000 1.000 0.000 0.000 0.000
#> GSM711905 2 0.0000 0.9555 0.000 1.000 0.000 0.000 0.000
#> GSM711907 4 0.4291 -0.0581 0.000 0.464 0.000 0.536 0.000
#> GSM711909 3 0.0000 0.8887 0.000 0.000 1.000 0.000 0.000
#> GSM711911 3 0.0000 0.8887 0.000 0.000 1.000 0.000 0.000
#> GSM711915 3 0.1410 0.8673 0.000 0.000 0.940 0.000 0.060
#> GSM711917 2 0.0000 0.9555 0.000 1.000 0.000 0.000 0.000
#> GSM711923 4 0.2891 0.6270 0.000 0.000 0.000 0.824 0.176
#> GSM711925 2 0.0000 0.9555 0.000 1.000 0.000 0.000 0.000
#> GSM711927 3 0.0000 0.8887 0.000 0.000 1.000 0.000 0.000
#> GSM711929 2 0.0000 0.9555 0.000 1.000 0.000 0.000 0.000
#> GSM711931 4 0.4306 -0.1480 0.000 0.492 0.000 0.508 0.000
#> GSM711933 5 0.1410 0.6793 0.060 0.000 0.000 0.000 0.940
#> GSM711935 2 0.0000 0.9555 0.000 1.000 0.000 0.000 0.000
#> GSM711941 4 0.3857 0.5171 0.000 0.000 0.000 0.688 0.312
#> GSM711943 4 0.0000 0.7249 0.000 0.000 0.000 1.000 0.000
#> GSM711945 4 0.3274 0.6081 0.000 0.000 0.000 0.780 0.220
#> GSM711947 4 0.6257 0.2224 0.000 0.148 0.392 0.460 0.000
#> GSM711949 2 0.0000 0.9555 0.000 1.000 0.000 0.000 0.000
#> GSM711953 2 0.0000 0.9555 0.000 1.000 0.000 0.000 0.000
#> GSM711955 5 0.0000 0.6415 0.000 0.000 0.000 0.000 1.000
#> GSM711963 2 0.0000 0.9555 0.000 1.000 0.000 0.000 0.000
#> GSM711971 3 0.0000 0.8887 0.000 0.000 1.000 0.000 0.000
#> GSM711975 2 0.4235 0.3075 0.000 0.576 0.000 0.424 0.000
#> GSM711979 4 0.2891 0.6270 0.000 0.000 0.000 0.824 0.176
#> GSM711989 2 0.3395 0.6906 0.000 0.764 0.000 0.236 0.000
#> GSM711991 4 0.5772 0.3555 0.000 0.000 0.328 0.564 0.108
#> GSM711993 4 0.0000 0.7249 0.000 0.000 0.000 1.000 0.000
#> GSM711983 3 0.3612 0.7259 0.000 0.000 0.732 0.000 0.268
#> GSM711985 2 0.0000 0.9555 0.000 1.000 0.000 0.000 0.000
#> GSM711913 3 0.2230 0.8434 0.000 0.000 0.884 0.000 0.116
#> GSM711919 3 0.0000 0.8887 0.000 0.000 1.000 0.000 0.000
#> GSM711921 3 0.0000 0.8887 0.000 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM711936 5 0.3737 0.0857 0.000 0.392 0.000 0.000 0.608 0.000
#> GSM711938 2 0.3620 0.5868 0.000 0.648 0.000 0.000 0.352 0.000
#> GSM711950 4 0.2135 0.6941 0.128 0.000 0.000 0.872 0.000 0.000
#> GSM711956 6 0.0363 0.9339 0.012 0.000 0.000 0.000 0.000 0.988
#> GSM711958 1 0.0000 0.8576 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711960 1 0.0000 0.8576 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711964 6 0.0000 0.9385 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM711966 6 0.0000 0.9385 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM711968 6 0.0260 0.9362 0.008 0.000 0.000 0.000 0.000 0.992
#> GSM711972 6 0.0000 0.9385 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM711976 6 0.4780 0.5484 0.112 0.000 0.000 0.000 0.228 0.660
#> GSM711980 1 0.1444 0.8564 0.928 0.000 0.000 0.000 0.000 0.072
#> GSM711986 6 0.0000 0.9385 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM711904 6 0.0790 0.9222 0.032 0.000 0.000 0.000 0.000 0.968
#> GSM711906 1 0.2664 0.7976 0.816 0.000 0.000 0.000 0.000 0.184
#> GSM711908 6 0.0547 0.9281 0.020 0.000 0.000 0.000 0.000 0.980
#> GSM711910 3 0.0000 0.8716 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711914 6 0.0260 0.9362 0.008 0.000 0.000 0.000 0.000 0.992
#> GSM711916 6 0.0000 0.9385 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM711922 1 0.3659 0.5091 0.636 0.000 0.000 0.000 0.000 0.364
#> GSM711924 1 0.0458 0.8597 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM711926 5 0.3851 -0.4866 0.000 0.000 0.000 0.460 0.540 0.000
#> GSM711928 6 0.0632 0.9285 0.024 0.000 0.000 0.000 0.000 0.976
#> GSM711930 6 0.0363 0.9337 0.012 0.000 0.000 0.000 0.000 0.988
#> GSM711932 1 0.1349 0.8420 0.940 0.000 0.000 0.004 0.056 0.000
#> GSM711934 1 0.3578 0.5594 0.660 0.000 0.000 0.000 0.000 0.340
#> GSM711940 4 0.3864 0.2455 0.480 0.000 0.000 0.520 0.000 0.000
#> GSM711942 1 0.1910 0.8440 0.892 0.000 0.000 0.000 0.000 0.108
#> GSM711944 1 0.0547 0.8533 0.980 0.000 0.020 0.000 0.000 0.000
#> GSM711946 4 0.2006 0.7128 0.080 0.000 0.000 0.904 0.016 0.000
#> GSM711948 1 0.1910 0.8208 0.892 0.000 0.000 0.000 0.000 0.108
#> GSM711952 6 0.0000 0.9385 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM711954 1 0.2378 0.8227 0.848 0.000 0.000 0.000 0.000 0.152
#> GSM711962 1 0.0865 0.8609 0.964 0.000 0.000 0.000 0.000 0.036
#> GSM711970 1 0.2048 0.8385 0.880 0.000 0.000 0.000 0.000 0.120
#> GSM711974 6 0.3864 -0.1079 0.480 0.000 0.000 0.000 0.000 0.520
#> GSM711978 4 0.3499 0.6725 0.000 0.000 0.000 0.680 0.320 0.000
#> GSM711988 1 0.0000 0.8576 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711990 3 0.5284 0.6178 0.080 0.040 0.652 0.228 0.000 0.000
#> GSM711992 4 0.3789 0.5952 0.000 0.000 0.000 0.584 0.416 0.000
#> GSM711982 6 0.0000 0.9385 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM711984 2 0.3620 0.5868 0.000 0.648 0.000 0.000 0.352 0.000
#> GSM711912 6 0.0000 0.9385 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM711918 6 0.0000 0.9385 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM711920 1 0.0909 0.8596 0.968 0.000 0.000 0.000 0.020 0.012
#> GSM711937 5 0.3789 0.0496 0.000 0.416 0.000 0.000 0.584 0.000
#> GSM711939 5 0.3789 0.0496 0.000 0.416 0.000 0.000 0.584 0.000
#> GSM711951 5 0.3620 -0.3307 0.000 0.000 0.000 0.352 0.648 0.000
#> GSM711957 1 0.3426 0.6024 0.720 0.000 0.000 0.004 0.276 0.000
#> GSM711959 5 0.3843 -0.0775 0.000 0.452 0.000 0.000 0.548 0.000
#> GSM711961 2 0.3620 0.5868 0.000 0.648 0.000 0.000 0.352 0.000
#> GSM711965 4 0.1908 0.7069 0.096 0.004 0.000 0.900 0.000 0.000
#> GSM711967 1 0.3534 0.5963 0.716 0.000 0.000 0.008 0.276 0.000
#> GSM711969 5 0.3789 0.0496 0.000 0.416 0.000 0.000 0.584 0.000
#> GSM711973 4 0.5395 0.2125 0.096 0.328 0.000 0.564 0.000 0.012
#> GSM711977 2 0.6127 -0.4578 0.000 0.352 0.328 0.320 0.000 0.000
#> GSM711981 5 0.3854 -0.4963 0.000 0.000 0.000 0.464 0.536 0.000
#> GSM711987 2 0.3620 0.5868 0.000 0.648 0.000 0.000 0.352 0.000
#> GSM711905 2 0.3620 0.5868 0.000 0.648 0.000 0.000 0.352 0.000
#> GSM711907 5 0.1075 0.3855 0.000 0.000 0.000 0.048 0.952 0.000
#> GSM711909 3 0.0000 0.8716 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711911 3 0.1007 0.8539 0.000 0.044 0.956 0.000 0.000 0.000
#> GSM711915 2 0.6127 -0.4578 0.000 0.352 0.328 0.320 0.000 0.000
#> GSM711917 5 0.3789 0.0496 0.000 0.416 0.000 0.000 0.584 0.000
#> GSM711923 4 0.4087 0.6866 0.036 0.000 0.000 0.688 0.276 0.000
#> GSM711925 2 0.3620 0.5868 0.000 0.648 0.000 0.000 0.352 0.000
#> GSM711927 3 0.0000 0.8716 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711929 2 0.3620 0.5868 0.000 0.648 0.000 0.000 0.352 0.000
#> GSM711931 5 0.0260 0.3849 0.000 0.000 0.000 0.008 0.992 0.000
#> GSM711933 1 0.0000 0.8576 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711935 2 0.3620 0.5868 0.000 0.648 0.000 0.000 0.352 0.000
#> GSM711941 4 0.2134 0.7255 0.044 0.000 0.000 0.904 0.052 0.000
#> GSM711943 4 0.3499 0.6725 0.000 0.000 0.000 0.680 0.320 0.000
#> GSM711945 4 0.2070 0.7171 0.048 0.000 0.000 0.908 0.044 0.000
#> GSM711947 3 0.5137 0.3436 0.000 0.000 0.552 0.096 0.352 0.000
#> GSM711949 2 0.3620 0.5868 0.000 0.648 0.000 0.000 0.352 0.000
#> GSM711953 2 0.3620 0.5868 0.000 0.648 0.000 0.000 0.352 0.000
#> GSM711955 1 0.1863 0.7878 0.896 0.000 0.000 0.104 0.000 0.000
#> GSM711963 2 0.3620 0.5868 0.000 0.648 0.000 0.000 0.352 0.000
#> GSM711971 3 0.0000 0.8716 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711975 5 0.0937 0.3738 0.000 0.040 0.000 0.000 0.960 0.000
#> GSM711979 4 0.4127 0.6829 0.036 0.000 0.000 0.680 0.284 0.000
#> GSM711989 5 0.3288 0.2089 0.000 0.276 0.000 0.000 0.724 0.000
#> GSM711991 4 0.1913 0.6765 0.012 0.000 0.080 0.908 0.000 0.000
#> GSM711993 4 0.3864 0.5305 0.000 0.000 0.000 0.520 0.480 0.000
#> GSM711983 3 0.4247 0.6405 0.060 0.000 0.700 0.240 0.000 0.000
#> GSM711985 2 0.3620 0.5868 0.000 0.648 0.000 0.000 0.352 0.000
#> GSM711913 2 0.6127 -0.4578 0.000 0.352 0.328 0.320 0.000 0.000
#> GSM711919 3 0.0000 0.8716 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711921 3 0.0000 0.8716 0.000 0.000 1.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) disease.state(p) individual(p) k
#> SD:pam 90 7.70e-05 0.240 0.587 2
#> SD:pam 85 7.04e-11 0.482 0.801 3
#> SD:pam 88 4.01e-10 0.142 0.549 4
#> SD:pam 72 4.01e-07 0.185 0.210 5
#> SD:pam 70 1.48e-06 0.179 0.355 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "mclust"]
# you can also extract it by
# res = res_list["SD:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 27425 rows and 90 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.810 0.941 0.968 0.4150 0.594 0.594
#> 3 3 0.778 0.859 0.904 0.5328 0.716 0.533
#> 4 4 0.890 0.885 0.945 0.1309 0.919 0.768
#> 5 5 0.757 0.752 0.862 0.0538 0.906 0.704
#> 6 6 0.699 0.644 0.775 0.0587 0.884 0.585
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM711936 2 0.000 0.973 0.000 1.000
#> GSM711938 2 0.000 0.973 0.000 1.000
#> GSM711950 1 0.000 0.963 1.000 0.000
#> GSM711956 1 0.000 0.963 1.000 0.000
#> GSM711958 1 0.000 0.963 1.000 0.000
#> GSM711960 1 0.000 0.963 1.000 0.000
#> GSM711964 1 0.000 0.963 1.000 0.000
#> GSM711966 1 0.000 0.963 1.000 0.000
#> GSM711968 1 0.000 0.963 1.000 0.000
#> GSM711972 1 0.000 0.963 1.000 0.000
#> GSM711976 1 0.000 0.963 1.000 0.000
#> GSM711980 1 0.000 0.963 1.000 0.000
#> GSM711986 1 0.000 0.963 1.000 0.000
#> GSM711904 1 0.000 0.963 1.000 0.000
#> GSM711906 1 0.000 0.963 1.000 0.000
#> GSM711908 1 0.000 0.963 1.000 0.000
#> GSM711910 1 0.529 0.894 0.880 0.120
#> GSM711914 1 0.000 0.963 1.000 0.000
#> GSM711916 1 0.000 0.963 1.000 0.000
#> GSM711922 1 0.000 0.963 1.000 0.000
#> GSM711924 1 0.000 0.963 1.000 0.000
#> GSM711926 1 0.242 0.944 0.960 0.040
#> GSM711928 1 0.000 0.963 1.000 0.000
#> GSM711930 1 0.000 0.963 1.000 0.000
#> GSM711932 1 0.000 0.963 1.000 0.000
#> GSM711934 1 0.000 0.963 1.000 0.000
#> GSM711940 1 0.000 0.963 1.000 0.000
#> GSM711942 1 0.000 0.963 1.000 0.000
#> GSM711944 1 0.000 0.963 1.000 0.000
#> GSM711946 1 0.456 0.915 0.904 0.096
#> GSM711948 1 0.000 0.963 1.000 0.000
#> GSM711952 1 0.000 0.963 1.000 0.000
#> GSM711954 1 0.000 0.963 1.000 0.000
#> GSM711962 1 0.000 0.963 1.000 0.000
#> GSM711970 1 0.000 0.963 1.000 0.000
#> GSM711974 1 0.000 0.963 1.000 0.000
#> GSM711978 1 0.242 0.944 0.960 0.040
#> GSM711988 1 0.000 0.963 1.000 0.000
#> GSM711990 1 0.456 0.912 0.904 0.096
#> GSM711992 1 0.242 0.944 0.960 0.040
#> GSM711982 1 0.000 0.963 1.000 0.000
#> GSM711984 2 0.000 0.973 0.000 1.000
#> GSM711912 1 0.000 0.963 1.000 0.000
#> GSM711918 1 0.000 0.963 1.000 0.000
#> GSM711920 1 0.000 0.963 1.000 0.000
#> GSM711937 2 0.000 0.973 0.000 1.000
#> GSM711939 2 0.000 0.973 0.000 1.000
#> GSM711951 2 0.000 0.973 0.000 1.000
#> GSM711957 1 0.000 0.963 1.000 0.000
#> GSM711959 2 0.000 0.973 0.000 1.000
#> GSM711961 2 0.000 0.973 0.000 1.000
#> GSM711965 1 0.343 0.933 0.936 0.064
#> GSM711967 1 0.000 0.963 1.000 0.000
#> GSM711969 2 0.000 0.973 0.000 1.000
#> GSM711973 1 0.000 0.963 1.000 0.000
#> GSM711977 1 0.430 0.918 0.912 0.088
#> GSM711981 2 0.981 0.265 0.420 0.580
#> GSM711987 2 0.000 0.973 0.000 1.000
#> GSM711905 2 0.000 0.973 0.000 1.000
#> GSM711907 2 0.000 0.973 0.000 1.000
#> GSM711909 1 0.529 0.894 0.880 0.120
#> GSM711911 1 0.529 0.894 0.880 0.120
#> GSM711915 1 0.529 0.894 0.880 0.120
#> GSM711917 2 0.000 0.973 0.000 1.000
#> GSM711923 1 0.260 0.942 0.956 0.044
#> GSM711925 2 0.000 0.973 0.000 1.000
#> GSM711927 1 0.529 0.894 0.880 0.120
#> GSM711929 2 0.000 0.973 0.000 1.000
#> GSM711931 2 0.000 0.973 0.000 1.000
#> GSM711933 1 0.000 0.963 1.000 0.000
#> GSM711935 2 0.000 0.973 0.000 1.000
#> GSM711941 1 0.242 0.944 0.960 0.040
#> GSM711943 1 0.311 0.937 0.944 0.056
#> GSM711945 1 0.625 0.863 0.844 0.156
#> GSM711947 1 0.634 0.859 0.840 0.160
#> GSM711949 2 0.000 0.973 0.000 1.000
#> GSM711953 2 0.000 0.973 0.000 1.000
#> GSM711955 1 0.000 0.963 1.000 0.000
#> GSM711963 2 0.000 0.973 0.000 1.000
#> GSM711971 1 0.529 0.894 0.880 0.120
#> GSM711975 2 0.000 0.973 0.000 1.000
#> GSM711979 1 0.242 0.944 0.960 0.040
#> GSM711989 2 0.000 0.973 0.000 1.000
#> GSM711991 1 0.634 0.859 0.840 0.160
#> GSM711993 2 0.722 0.738 0.200 0.800
#> GSM711983 1 0.529 0.894 0.880 0.120
#> GSM711985 2 0.000 0.973 0.000 1.000
#> GSM711913 1 0.430 0.918 0.912 0.088
#> GSM711919 1 0.529 0.894 0.880 0.120
#> GSM711921 1 0.529 0.894 0.880 0.120
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM711936 2 0.0000 0.982 0.000 1.000 0.000
#> GSM711938 2 0.0000 0.982 0.000 1.000 0.000
#> GSM711950 3 0.6154 0.652 0.408 0.000 0.592
#> GSM711956 1 0.1753 0.941 0.952 0.000 0.048
#> GSM711958 1 0.2165 0.941 0.936 0.000 0.064
#> GSM711960 1 0.5178 0.668 0.744 0.000 0.256
#> GSM711964 1 0.1289 0.937 0.968 0.000 0.032
#> GSM711966 1 0.2066 0.942 0.940 0.000 0.060
#> GSM711968 1 0.1411 0.939 0.964 0.000 0.036
#> GSM711972 1 0.2165 0.941 0.936 0.000 0.064
#> GSM711976 1 0.0000 0.923 1.000 0.000 0.000
#> GSM711980 1 0.0237 0.925 0.996 0.000 0.004
#> GSM711986 1 0.2165 0.941 0.936 0.000 0.064
#> GSM711904 1 0.2165 0.941 0.936 0.000 0.064
#> GSM711906 1 0.2537 0.933 0.920 0.000 0.080
#> GSM711908 1 0.2711 0.927 0.912 0.000 0.088
#> GSM711910 3 0.0000 0.771 0.000 0.000 1.000
#> GSM711914 1 0.2066 0.942 0.940 0.000 0.060
#> GSM711916 1 0.2261 0.939 0.932 0.000 0.068
#> GSM711922 1 0.0000 0.923 1.000 0.000 0.000
#> GSM711924 1 0.2356 0.937 0.928 0.000 0.072
#> GSM711926 3 0.6600 0.680 0.384 0.012 0.604
#> GSM711928 1 0.0000 0.923 1.000 0.000 0.000
#> GSM711930 1 0.2711 0.927 0.912 0.000 0.088
#> GSM711932 1 0.4452 0.642 0.808 0.000 0.192
#> GSM711934 1 0.1411 0.939 0.964 0.000 0.036
#> GSM711940 1 0.0000 0.923 1.000 0.000 0.000
#> GSM711942 1 0.2261 0.939 0.932 0.000 0.068
#> GSM711944 3 0.5591 0.679 0.304 0.000 0.696
#> GSM711946 3 0.6062 0.683 0.384 0.000 0.616
#> GSM711948 1 0.0237 0.923 0.996 0.000 0.004
#> GSM711952 1 0.2165 0.941 0.936 0.000 0.064
#> GSM711954 1 0.0000 0.923 1.000 0.000 0.000
#> GSM711962 1 0.2066 0.942 0.940 0.000 0.060
#> GSM711970 1 0.0000 0.923 1.000 0.000 0.000
#> GSM711974 1 0.2165 0.941 0.936 0.000 0.064
#> GSM711978 3 0.6600 0.680 0.384 0.012 0.604
#> GSM711988 1 0.0000 0.923 1.000 0.000 0.000
#> GSM711990 3 0.0237 0.772 0.004 0.000 0.996
#> GSM711992 3 0.6600 0.680 0.384 0.012 0.604
#> GSM711982 1 0.2165 0.941 0.936 0.000 0.064
#> GSM711984 2 0.0000 0.982 0.000 1.000 0.000
#> GSM711912 1 0.2537 0.933 0.920 0.000 0.080
#> GSM711918 1 0.2537 0.933 0.920 0.000 0.080
#> GSM711920 1 0.2165 0.941 0.936 0.000 0.064
#> GSM711937 2 0.0000 0.982 0.000 1.000 0.000
#> GSM711939 2 0.0000 0.982 0.000 1.000 0.000
#> GSM711951 2 0.4062 0.784 0.000 0.836 0.164
#> GSM711957 3 0.5785 0.658 0.332 0.000 0.668
#> GSM711959 2 0.0000 0.982 0.000 1.000 0.000
#> GSM711961 2 0.0000 0.982 0.000 1.000 0.000
#> GSM711965 3 0.6008 0.693 0.372 0.000 0.628
#> GSM711967 1 0.0000 0.923 1.000 0.000 0.000
#> GSM711969 2 0.0000 0.982 0.000 1.000 0.000
#> GSM711973 3 0.5733 0.663 0.324 0.000 0.676
#> GSM711977 3 0.0000 0.771 0.000 0.000 1.000
#> GSM711981 3 0.8608 0.654 0.192 0.204 0.604
#> GSM711987 2 0.0000 0.982 0.000 1.000 0.000
#> GSM711905 2 0.0000 0.982 0.000 1.000 0.000
#> GSM711907 2 0.0000 0.982 0.000 1.000 0.000
#> GSM711909 3 0.0000 0.771 0.000 0.000 1.000
#> GSM711911 3 0.0000 0.771 0.000 0.000 1.000
#> GSM711915 3 0.0000 0.771 0.000 0.000 1.000
#> GSM711917 2 0.0000 0.982 0.000 1.000 0.000
#> GSM711923 3 0.6062 0.683 0.384 0.000 0.616
#> GSM711925 2 0.0000 0.982 0.000 1.000 0.000
#> GSM711927 3 0.0000 0.771 0.000 0.000 1.000
#> GSM711929 2 0.0000 0.982 0.000 1.000 0.000
#> GSM711931 2 0.4291 0.760 0.000 0.820 0.180
#> GSM711933 1 0.0237 0.923 0.996 0.000 0.004
#> GSM711935 2 0.0000 0.982 0.000 1.000 0.000
#> GSM711941 3 0.6111 0.668 0.396 0.000 0.604
#> GSM711943 3 0.6062 0.683 0.384 0.000 0.616
#> GSM711945 3 0.6667 0.691 0.368 0.016 0.616
#> GSM711947 3 0.0747 0.764 0.000 0.016 0.984
#> GSM711949 2 0.0000 0.982 0.000 1.000 0.000
#> GSM711953 2 0.0000 0.982 0.000 1.000 0.000
#> GSM711955 1 0.4702 0.598 0.788 0.000 0.212
#> GSM711963 2 0.0000 0.982 0.000 1.000 0.000
#> GSM711971 3 0.0000 0.771 0.000 0.000 1.000
#> GSM711975 2 0.0000 0.982 0.000 1.000 0.000
#> GSM711979 3 0.6600 0.680 0.384 0.012 0.604
#> GSM711989 2 0.0000 0.982 0.000 1.000 0.000
#> GSM711991 3 0.1774 0.772 0.024 0.016 0.960
#> GSM711993 3 0.8258 0.548 0.112 0.284 0.604
#> GSM711983 3 0.0237 0.772 0.004 0.000 0.996
#> GSM711985 2 0.0000 0.982 0.000 1.000 0.000
#> GSM711913 3 0.0000 0.771 0.000 0.000 1.000
#> GSM711919 3 0.0000 0.771 0.000 0.000 1.000
#> GSM711921 3 0.0000 0.771 0.000 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM711936 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM711938 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM711950 4 0.3219 0.726 0.164 0.000 0.000 0.836
#> GSM711956 1 0.0592 0.938 0.984 0.000 0.000 0.016
#> GSM711958 1 0.0336 0.938 0.992 0.000 0.000 0.008
#> GSM711960 1 0.2921 0.812 0.860 0.000 0.000 0.140
#> GSM711964 1 0.0592 0.938 0.984 0.000 0.000 0.016
#> GSM711966 1 0.0336 0.939 0.992 0.000 0.000 0.008
#> GSM711968 1 0.0817 0.936 0.976 0.000 0.000 0.024
#> GSM711972 1 0.0000 0.939 1.000 0.000 0.000 0.000
#> GSM711976 1 0.2469 0.890 0.892 0.000 0.000 0.108
#> GSM711980 1 0.1867 0.917 0.928 0.000 0.000 0.072
#> GSM711986 1 0.0336 0.939 0.992 0.000 0.000 0.008
#> GSM711904 1 0.0817 0.937 0.976 0.000 0.000 0.024
#> GSM711906 1 0.0188 0.938 0.996 0.000 0.000 0.004
#> GSM711908 1 0.0188 0.938 0.996 0.000 0.000 0.004
#> GSM711910 3 0.0188 0.885 0.000 0.000 0.996 0.004
#> GSM711914 1 0.0188 0.939 0.996 0.000 0.000 0.004
#> GSM711916 1 0.0000 0.939 1.000 0.000 0.000 0.000
#> GSM711922 1 0.1940 0.915 0.924 0.000 0.000 0.076
#> GSM711924 1 0.0000 0.939 1.000 0.000 0.000 0.000
#> GSM711926 4 0.0469 0.894 0.000 0.012 0.000 0.988
#> GSM711928 1 0.1389 0.927 0.952 0.000 0.000 0.048
#> GSM711930 1 0.0188 0.938 0.996 0.000 0.000 0.004
#> GSM711932 4 0.4967 0.122 0.452 0.000 0.000 0.548
#> GSM711934 1 0.0336 0.939 0.992 0.000 0.000 0.008
#> GSM711940 1 0.3074 0.848 0.848 0.000 0.000 0.152
#> GSM711942 1 0.0000 0.939 1.000 0.000 0.000 0.000
#> GSM711944 1 0.6016 0.182 0.544 0.000 0.044 0.412
#> GSM711946 4 0.1022 0.881 0.000 0.000 0.032 0.968
#> GSM711948 1 0.3074 0.848 0.848 0.000 0.000 0.152
#> GSM711952 1 0.0469 0.939 0.988 0.000 0.000 0.012
#> GSM711954 1 0.2921 0.860 0.860 0.000 0.000 0.140
#> GSM711962 1 0.0188 0.939 0.996 0.000 0.000 0.004
#> GSM711970 1 0.1940 0.915 0.924 0.000 0.000 0.076
#> GSM711974 1 0.0000 0.939 1.000 0.000 0.000 0.000
#> GSM711978 4 0.0469 0.894 0.000 0.012 0.000 0.988
#> GSM711988 1 0.1867 0.917 0.928 0.000 0.000 0.072
#> GSM711990 3 0.3933 0.744 0.008 0.000 0.792 0.200
#> GSM711992 4 0.0469 0.894 0.000 0.012 0.000 0.988
#> GSM711982 1 0.0000 0.939 1.000 0.000 0.000 0.000
#> GSM711984 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM711912 1 0.0188 0.938 0.996 0.000 0.000 0.004
#> GSM711918 1 0.0188 0.938 0.996 0.000 0.000 0.004
#> GSM711920 1 0.0000 0.939 1.000 0.000 0.000 0.000
#> GSM711937 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM711939 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM711951 2 0.1389 0.950 0.000 0.952 0.000 0.048
#> GSM711957 4 0.4419 0.735 0.152 0.004 0.040 0.804
#> GSM711959 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM711961 2 0.0188 0.991 0.000 0.996 0.004 0.000
#> GSM711965 4 0.0592 0.892 0.000 0.000 0.016 0.984
#> GSM711967 1 0.1940 0.915 0.924 0.000 0.000 0.076
#> GSM711969 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM711973 4 0.4224 0.746 0.144 0.000 0.044 0.812
#> GSM711977 3 0.4866 0.354 0.000 0.000 0.596 0.404
#> GSM711981 4 0.0469 0.894 0.000 0.012 0.000 0.988
#> GSM711987 2 0.0524 0.989 0.000 0.988 0.004 0.008
#> GSM711905 2 0.0524 0.989 0.000 0.988 0.004 0.008
#> GSM711907 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM711909 3 0.0188 0.885 0.000 0.000 0.996 0.004
#> GSM711911 3 0.0188 0.885 0.000 0.000 0.996 0.004
#> GSM711915 3 0.0188 0.885 0.000 0.000 0.996 0.004
#> GSM711917 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM711923 4 0.0592 0.892 0.000 0.000 0.016 0.984
#> GSM711925 2 0.0188 0.991 0.000 0.996 0.004 0.000
#> GSM711927 3 0.0188 0.885 0.000 0.000 0.996 0.004
#> GSM711929 2 0.0524 0.989 0.000 0.988 0.004 0.008
#> GSM711931 2 0.1211 0.958 0.000 0.960 0.000 0.040
#> GSM711933 1 0.1792 0.919 0.932 0.000 0.000 0.068
#> GSM711935 2 0.0524 0.989 0.000 0.988 0.004 0.008
#> GSM711941 4 0.0657 0.891 0.012 0.000 0.004 0.984
#> GSM711943 4 0.0592 0.892 0.000 0.000 0.016 0.984
#> GSM711945 4 0.0592 0.892 0.000 0.000 0.016 0.984
#> GSM711947 3 0.0188 0.885 0.000 0.000 0.996 0.004
#> GSM711949 2 0.0524 0.989 0.000 0.988 0.004 0.008
#> GSM711953 2 0.0524 0.989 0.000 0.988 0.004 0.008
#> GSM711955 1 0.4872 0.502 0.640 0.000 0.004 0.356
#> GSM711963 2 0.0524 0.989 0.000 0.988 0.004 0.008
#> GSM711971 3 0.3088 0.808 0.008 0.000 0.864 0.128
#> GSM711975 2 0.0592 0.980 0.000 0.984 0.000 0.016
#> GSM711979 4 0.0469 0.894 0.000 0.012 0.000 0.988
#> GSM711989 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM711991 3 0.0336 0.883 0.000 0.000 0.992 0.008
#> GSM711993 4 0.0707 0.888 0.000 0.020 0.000 0.980
#> GSM711983 3 0.3933 0.744 0.008 0.000 0.792 0.200
#> GSM711985 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM711913 3 0.4866 0.354 0.000 0.000 0.596 0.404
#> GSM711919 3 0.0188 0.885 0.000 0.000 0.996 0.004
#> GSM711921 3 0.0188 0.885 0.000 0.000 0.996 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM711936 2 0.0609 0.929 0.000 0.980 0.000 0.020 0.000
#> GSM711938 2 0.0912 0.935 0.000 0.972 0.000 0.012 0.016
#> GSM711950 1 0.4238 0.654 0.768 0.000 0.000 0.164 0.068
#> GSM711956 1 0.0404 0.822 0.988 0.000 0.000 0.000 0.012
#> GSM711958 1 0.4171 0.117 0.604 0.000 0.000 0.000 0.396
#> GSM711960 5 0.3838 0.854 0.280 0.000 0.000 0.004 0.716
#> GSM711964 1 0.0693 0.825 0.980 0.000 0.000 0.012 0.008
#> GSM711966 1 0.0671 0.822 0.980 0.000 0.000 0.004 0.016
#> GSM711968 1 0.0579 0.825 0.984 0.000 0.000 0.008 0.008
#> GSM711972 1 0.1197 0.811 0.952 0.000 0.000 0.000 0.048
#> GSM711976 1 0.2580 0.782 0.892 0.000 0.000 0.044 0.064
#> GSM711980 1 0.0880 0.826 0.968 0.000 0.000 0.032 0.000
#> GSM711986 1 0.2516 0.750 0.860 0.000 0.000 0.000 0.140
#> GSM711904 1 0.2997 0.736 0.840 0.000 0.000 0.012 0.148
#> GSM711906 5 0.3480 0.900 0.248 0.000 0.000 0.000 0.752
#> GSM711908 5 0.3003 0.932 0.188 0.000 0.000 0.000 0.812
#> GSM711910 3 0.0000 0.779 0.000 0.000 1.000 0.000 0.000
#> GSM711914 1 0.1043 0.813 0.960 0.000 0.000 0.000 0.040
#> GSM711916 5 0.3210 0.934 0.212 0.000 0.000 0.000 0.788
#> GSM711922 1 0.0880 0.826 0.968 0.000 0.000 0.032 0.000
#> GSM711924 1 0.3242 0.624 0.784 0.000 0.000 0.000 0.216
#> GSM711926 4 0.2713 0.810 0.020 0.008 0.008 0.896 0.068
#> GSM711928 1 0.0955 0.826 0.968 0.000 0.000 0.028 0.004
#> GSM711930 5 0.3003 0.932 0.188 0.000 0.000 0.000 0.812
#> GSM711932 1 0.1740 0.813 0.932 0.000 0.000 0.056 0.012
#> GSM711934 1 0.2230 0.769 0.884 0.000 0.000 0.000 0.116
#> GSM711940 1 0.1121 0.822 0.956 0.000 0.000 0.044 0.000
#> GSM711942 1 0.1608 0.801 0.928 0.000 0.000 0.000 0.072
#> GSM711944 4 0.6840 0.183 0.396 0.000 0.100 0.456 0.048
#> GSM711946 4 0.0807 0.811 0.012 0.000 0.012 0.976 0.000
#> GSM711948 1 0.3183 0.783 0.872 0.000 0.020 0.060 0.048
#> GSM711952 1 0.2852 0.708 0.828 0.000 0.000 0.000 0.172
#> GSM711954 1 0.1121 0.822 0.956 0.000 0.000 0.044 0.000
#> GSM711962 1 0.1430 0.812 0.944 0.000 0.000 0.004 0.052
#> GSM711970 1 0.0880 0.826 0.968 0.000 0.000 0.032 0.000
#> GSM711974 1 0.4114 0.137 0.624 0.000 0.000 0.000 0.376
#> GSM711978 4 0.2304 0.811 0.020 0.004 0.000 0.908 0.068
#> GSM711988 1 0.0880 0.826 0.968 0.000 0.000 0.032 0.000
#> GSM711990 3 0.6355 0.214 0.060 0.000 0.484 0.412 0.044
#> GSM711992 4 0.2304 0.811 0.020 0.004 0.000 0.908 0.068
#> GSM711982 1 0.1197 0.810 0.952 0.000 0.000 0.000 0.048
#> GSM711984 2 0.0000 0.935 0.000 1.000 0.000 0.000 0.000
#> GSM711912 1 0.4306 -0.226 0.508 0.000 0.000 0.000 0.492
#> GSM711918 1 0.4307 -0.239 0.504 0.000 0.000 0.000 0.496
#> GSM711920 1 0.2280 0.768 0.880 0.000 0.000 0.000 0.120
#> GSM711937 2 0.0000 0.935 0.000 1.000 0.000 0.000 0.000
#> GSM711939 2 0.0000 0.935 0.000 1.000 0.000 0.000 0.000
#> GSM711951 2 0.2660 0.862 0.000 0.864 0.000 0.128 0.008
#> GSM711957 4 0.5296 0.682 0.100 0.000 0.036 0.728 0.136
#> GSM711959 2 0.0000 0.935 0.000 1.000 0.000 0.000 0.000
#> GSM711961 2 0.2573 0.923 0.000 0.880 0.000 0.016 0.104
#> GSM711965 4 0.1877 0.787 0.064 0.000 0.012 0.924 0.000
#> GSM711967 1 0.1043 0.824 0.960 0.000 0.000 0.040 0.000
#> GSM711969 2 0.0000 0.935 0.000 1.000 0.000 0.000 0.000
#> GSM711973 4 0.5627 0.520 0.240 0.000 0.044 0.664 0.052
#> GSM711977 3 0.4201 0.444 0.000 0.000 0.592 0.408 0.000
#> GSM711981 4 0.2833 0.805 0.020 0.024 0.000 0.888 0.068
#> GSM711987 2 0.2964 0.916 0.000 0.856 0.000 0.024 0.120
#> GSM711905 2 0.2964 0.916 0.000 0.856 0.000 0.024 0.120
#> GSM711907 2 0.0609 0.929 0.000 0.980 0.000 0.020 0.000
#> GSM711909 3 0.0000 0.779 0.000 0.000 1.000 0.000 0.000
#> GSM711911 3 0.3999 0.541 0.000 0.000 0.656 0.344 0.000
#> GSM711915 3 0.0000 0.779 0.000 0.000 1.000 0.000 0.000
#> GSM711917 2 0.0000 0.935 0.000 1.000 0.000 0.000 0.000
#> GSM711923 4 0.0912 0.811 0.016 0.000 0.012 0.972 0.000
#> GSM711925 2 0.2573 0.923 0.000 0.880 0.000 0.016 0.104
#> GSM711927 3 0.0000 0.779 0.000 0.000 1.000 0.000 0.000
#> GSM711929 2 0.2964 0.916 0.000 0.856 0.000 0.024 0.120
#> GSM711931 2 0.2645 0.870 0.000 0.888 0.000 0.044 0.068
#> GSM711933 1 0.1772 0.823 0.940 0.000 0.020 0.032 0.008
#> GSM711935 2 0.2964 0.916 0.000 0.856 0.000 0.024 0.120
#> GSM711941 1 0.4677 0.617 0.732 0.000 0.004 0.196 0.068
#> GSM711943 4 0.0807 0.811 0.012 0.000 0.012 0.976 0.000
#> GSM711945 4 0.0807 0.811 0.012 0.000 0.012 0.976 0.000
#> GSM711947 3 0.1410 0.756 0.000 0.000 0.940 0.060 0.000
#> GSM711949 2 0.2964 0.916 0.000 0.856 0.000 0.024 0.120
#> GSM711953 2 0.2964 0.916 0.000 0.856 0.000 0.024 0.120
#> GSM711955 1 0.2761 0.779 0.872 0.000 0.024 0.104 0.000
#> GSM711963 2 0.2964 0.916 0.000 0.856 0.000 0.024 0.120
#> GSM711971 3 0.4679 0.589 0.012 0.000 0.700 0.260 0.028
#> GSM711975 2 0.1043 0.923 0.000 0.960 0.000 0.040 0.000
#> GSM711979 1 0.5124 0.534 0.668 0.004 0.000 0.260 0.068
#> GSM711989 2 0.0609 0.929 0.000 0.980 0.000 0.020 0.000
#> GSM711991 3 0.1965 0.746 0.000 0.000 0.904 0.096 0.000
#> GSM711993 4 0.4064 0.738 0.012 0.100 0.004 0.816 0.068
#> GSM711983 3 0.6247 0.229 0.052 0.000 0.492 0.412 0.044
#> GSM711985 2 0.0162 0.935 0.000 0.996 0.000 0.000 0.004
#> GSM711913 3 0.4150 0.475 0.000 0.000 0.612 0.388 0.000
#> GSM711919 3 0.0162 0.777 0.000 0.000 0.996 0.000 0.004
#> GSM711921 3 0.0000 0.779 0.000 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM711936 5 0.3756 0.8510 0.000 0.400 0.000 0.000 0.600 0.000
#> GSM711938 2 0.3765 -0.4332 0.000 0.596 0.000 0.000 0.404 0.000
#> GSM711950 4 0.3706 0.3314 0.380 0.000 0.000 0.620 0.000 0.000
#> GSM711956 1 0.2972 0.7388 0.836 0.000 0.000 0.036 0.000 0.128
#> GSM711958 1 0.4567 0.4596 0.616 0.000 0.000 0.052 0.000 0.332
#> GSM711960 6 0.6380 0.2579 0.268 0.000 0.148 0.060 0.000 0.524
#> GSM711964 1 0.2278 0.7345 0.868 0.000 0.000 0.000 0.004 0.128
#> GSM711966 1 0.2135 0.7355 0.872 0.000 0.000 0.000 0.000 0.128
#> GSM711968 1 0.2191 0.7379 0.876 0.000 0.000 0.000 0.004 0.120
#> GSM711972 1 0.2454 0.7206 0.840 0.000 0.000 0.000 0.000 0.160
#> GSM711976 1 0.1765 0.7041 0.904 0.000 0.000 0.096 0.000 0.000
#> GSM711980 1 0.0632 0.7366 0.976 0.000 0.000 0.024 0.000 0.000
#> GSM711986 6 0.3050 0.7163 0.236 0.000 0.000 0.000 0.000 0.764
#> GSM711904 6 0.5688 0.4121 0.384 0.000 0.000 0.140 0.004 0.472
#> GSM711906 6 0.3562 0.7569 0.168 0.000 0.000 0.040 0.004 0.788
#> GSM711908 6 0.0363 0.6740 0.000 0.000 0.000 0.000 0.012 0.988
#> GSM711910 3 0.0000 0.8590 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711914 1 0.2402 0.7301 0.856 0.000 0.000 0.000 0.004 0.140
#> GSM711916 6 0.3691 0.6551 0.192 0.000 0.000 0.036 0.004 0.768
#> GSM711922 1 0.1285 0.7327 0.944 0.000 0.000 0.052 0.000 0.004
#> GSM711924 1 0.3864 0.6877 0.744 0.000 0.000 0.048 0.000 0.208
#> GSM711926 4 0.1858 0.7136 0.004 0.000 0.000 0.904 0.092 0.000
#> GSM711928 1 0.1141 0.7456 0.948 0.000 0.000 0.000 0.000 0.052
#> GSM711930 6 0.0632 0.6692 0.000 0.000 0.000 0.000 0.024 0.976
#> GSM711932 1 0.2996 0.5718 0.772 0.000 0.000 0.228 0.000 0.000
#> GSM711934 1 0.4644 0.4900 0.628 0.000 0.000 0.052 0.004 0.316
#> GSM711940 1 0.1141 0.7309 0.948 0.000 0.000 0.052 0.000 0.000
#> GSM711942 1 0.2703 0.7141 0.824 0.000 0.000 0.000 0.004 0.172
#> GSM711944 1 0.7562 0.0575 0.392 0.000 0.260 0.252 0.040 0.056
#> GSM711946 4 0.4332 0.6534 0.000 0.000 0.040 0.644 0.316 0.000
#> GSM711948 1 0.4722 0.0755 0.512 0.000 0.016 0.452 0.000 0.020
#> GSM711952 6 0.4280 0.7234 0.232 0.000 0.000 0.056 0.004 0.708
#> GSM711954 1 0.0000 0.7346 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711962 1 0.2260 0.7334 0.860 0.000 0.000 0.000 0.000 0.140
#> GSM711970 1 0.0000 0.7346 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711974 1 0.4292 0.5177 0.628 0.000 0.000 0.032 0.000 0.340
#> GSM711978 4 0.2234 0.7332 0.004 0.000 0.000 0.872 0.124 0.000
#> GSM711988 1 0.1141 0.7309 0.948 0.000 0.000 0.052 0.000 0.000
#> GSM711990 3 0.5043 0.7654 0.024 0.000 0.740 0.080 0.104 0.052
#> GSM711992 4 0.2442 0.7331 0.004 0.000 0.000 0.852 0.144 0.000
#> GSM711982 1 0.3221 0.6295 0.736 0.000 0.000 0.000 0.000 0.264
#> GSM711984 5 0.3851 0.7618 0.000 0.460 0.000 0.000 0.540 0.000
#> GSM711912 6 0.3758 0.7579 0.176 0.000 0.000 0.048 0.004 0.772
#> GSM711918 6 0.3804 0.7580 0.176 0.000 0.000 0.044 0.008 0.772
#> GSM711920 1 0.2933 0.6940 0.796 0.000 0.000 0.000 0.004 0.200
#> GSM711937 5 0.3756 0.8510 0.000 0.400 0.000 0.000 0.600 0.000
#> GSM711939 5 0.3774 0.8432 0.000 0.408 0.000 0.000 0.592 0.000
#> GSM711951 2 0.6075 -0.3346 0.000 0.396 0.000 0.324 0.280 0.000
#> GSM711957 4 0.4611 0.6646 0.072 0.000 0.016 0.772 0.080 0.060
#> GSM711959 5 0.3847 0.7701 0.000 0.456 0.000 0.000 0.544 0.000
#> GSM711961 2 0.1814 0.6135 0.000 0.900 0.000 0.000 0.100 0.000
#> GSM711965 4 0.5998 0.4219 0.012 0.000 0.180 0.492 0.316 0.000
#> GSM711967 1 0.0508 0.7360 0.984 0.000 0.000 0.012 0.000 0.004
#> GSM711969 5 0.3756 0.8510 0.000 0.400 0.000 0.000 0.600 0.000
#> GSM711973 4 0.5566 0.5947 0.200 0.000 0.016 0.664 0.064 0.056
#> GSM711977 3 0.3601 0.7330 0.000 0.000 0.684 0.004 0.312 0.000
#> GSM711981 4 0.2053 0.7355 0.004 0.000 0.000 0.888 0.108 0.000
#> GSM711987 2 0.0000 0.7451 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711905 2 0.0000 0.7451 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711907 5 0.3756 0.8510 0.000 0.400 0.000 0.000 0.600 0.000
#> GSM711909 3 0.0146 0.8597 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM711911 3 0.2838 0.8127 0.000 0.000 0.808 0.004 0.188 0.000
#> GSM711915 3 0.0000 0.8590 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711917 5 0.3756 0.8510 0.000 0.400 0.000 0.000 0.600 0.000
#> GSM711923 4 0.3446 0.6915 0.000 0.000 0.000 0.692 0.308 0.000
#> GSM711925 2 0.0713 0.7195 0.000 0.972 0.000 0.000 0.028 0.000
#> GSM711927 3 0.0146 0.8597 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM711929 2 0.0000 0.7451 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711931 5 0.6012 0.3522 0.000 0.256 0.000 0.320 0.424 0.000
#> GSM711933 1 0.4601 0.5571 0.708 0.000 0.016 0.204 0.000 0.072
#> GSM711935 2 0.0000 0.7451 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711941 4 0.3151 0.5474 0.252 0.000 0.000 0.748 0.000 0.000
#> GSM711943 4 0.3446 0.7064 0.000 0.000 0.000 0.692 0.308 0.000
#> GSM711945 4 0.4541 0.6543 0.000 0.000 0.044 0.596 0.360 0.000
#> GSM711947 3 0.2121 0.8064 0.000 0.000 0.892 0.096 0.012 0.000
#> GSM711949 2 0.0000 0.7451 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711953 2 0.0000 0.7451 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711955 1 0.5485 0.1579 0.528 0.000 0.056 0.388 0.008 0.020
#> GSM711963 2 0.0000 0.7451 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711971 3 0.3939 0.8180 0.016 0.000 0.808 0.020 0.104 0.052
#> GSM711975 5 0.5818 0.5180 0.000 0.392 0.000 0.184 0.424 0.000
#> GSM711979 4 0.2300 0.6732 0.144 0.000 0.000 0.856 0.000 0.000
#> GSM711989 5 0.3756 0.8510 0.000 0.400 0.000 0.000 0.600 0.000
#> GSM711991 3 0.4125 0.7268 0.000 0.000 0.748 0.124 0.128 0.000
#> GSM711993 4 0.2737 0.6863 0.004 0.004 0.000 0.832 0.160 0.000
#> GSM711983 3 0.5043 0.7654 0.024 0.000 0.740 0.080 0.104 0.052
#> GSM711985 2 0.3868 -0.6952 0.000 0.504 0.000 0.000 0.496 0.000
#> GSM711913 3 0.3601 0.7330 0.000 0.000 0.684 0.004 0.312 0.000
#> GSM711919 3 0.0713 0.8522 0.000 0.000 0.972 0.000 0.000 0.028
#> GSM711921 3 0.0000 0.8590 0.000 0.000 1.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) disease.state(p) individual(p) k
#> SD:mclust 89 3.70e-05 0.193 0.501 2
#> SD:mclust 90 1.63e-10 0.402 0.570 3
#> SD:mclust 86 1.14e-09 0.116 0.429 4
#> SD:mclust 81 5.58e-08 0.107 0.423 5
#> SD:mclust 77 1.25e-08 0.109 0.216 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "NMF"]
# you can also extract it by
# res = res_list["SD:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 27425 rows and 90 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.966 0.987 0.4221 0.585 0.585
#> 3 3 1.000 0.965 0.985 0.5422 0.721 0.539
#> 4 4 0.899 0.903 0.956 0.1397 0.838 0.578
#> 5 5 0.790 0.747 0.868 0.0497 0.946 0.800
#> 6 6 0.853 0.738 0.890 0.0451 0.913 0.653
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
#> attr(,"optional")
#> [1] 2
There is also optional best \(k\) = 2 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM711936 2 0.0000 0.990 0.000 1.000
#> GSM711938 2 0.0000 0.990 0.000 1.000
#> GSM711950 1 0.0000 0.984 1.000 0.000
#> GSM711956 1 0.0000 0.984 1.000 0.000
#> GSM711958 1 0.0000 0.984 1.000 0.000
#> GSM711960 1 0.0000 0.984 1.000 0.000
#> GSM711964 1 0.0000 0.984 1.000 0.000
#> GSM711966 1 0.0000 0.984 1.000 0.000
#> GSM711968 1 0.0000 0.984 1.000 0.000
#> GSM711972 1 0.0000 0.984 1.000 0.000
#> GSM711976 1 0.0000 0.984 1.000 0.000
#> GSM711980 1 0.0000 0.984 1.000 0.000
#> GSM711986 1 0.0000 0.984 1.000 0.000
#> GSM711904 1 0.0000 0.984 1.000 0.000
#> GSM711906 1 0.0000 0.984 1.000 0.000
#> GSM711908 1 0.0000 0.984 1.000 0.000
#> GSM711910 1 0.0000 0.984 1.000 0.000
#> GSM711914 1 0.0000 0.984 1.000 0.000
#> GSM711916 1 0.0000 0.984 1.000 0.000
#> GSM711922 1 0.0000 0.984 1.000 0.000
#> GSM711924 1 0.0000 0.984 1.000 0.000
#> GSM711926 2 0.7219 0.745 0.200 0.800
#> GSM711928 1 0.0000 0.984 1.000 0.000
#> GSM711930 1 0.0000 0.984 1.000 0.000
#> GSM711932 1 0.0000 0.984 1.000 0.000
#> GSM711934 1 0.0000 0.984 1.000 0.000
#> GSM711940 1 0.0000 0.984 1.000 0.000
#> GSM711942 1 0.0000 0.984 1.000 0.000
#> GSM711944 1 0.0000 0.984 1.000 0.000
#> GSM711946 1 0.0000 0.984 1.000 0.000
#> GSM711948 1 0.0000 0.984 1.000 0.000
#> GSM711952 1 0.0000 0.984 1.000 0.000
#> GSM711954 1 0.0000 0.984 1.000 0.000
#> GSM711962 1 0.0000 0.984 1.000 0.000
#> GSM711970 1 0.0000 0.984 1.000 0.000
#> GSM711974 1 0.0000 0.984 1.000 0.000
#> GSM711978 1 0.1184 0.970 0.984 0.016
#> GSM711988 1 0.0000 0.984 1.000 0.000
#> GSM711990 1 0.0000 0.984 1.000 0.000
#> GSM711992 1 0.0000 0.984 1.000 0.000
#> GSM711982 1 0.0000 0.984 1.000 0.000
#> GSM711984 2 0.0000 0.990 0.000 1.000
#> GSM711912 1 0.0000 0.984 1.000 0.000
#> GSM711918 1 0.0000 0.984 1.000 0.000
#> GSM711920 1 0.0000 0.984 1.000 0.000
#> GSM711937 2 0.0000 0.990 0.000 1.000
#> GSM711939 2 0.0000 0.990 0.000 1.000
#> GSM711951 2 0.0000 0.990 0.000 1.000
#> GSM711957 1 0.0000 0.984 1.000 0.000
#> GSM711959 2 0.0000 0.990 0.000 1.000
#> GSM711961 2 0.0000 0.990 0.000 1.000
#> GSM711965 1 0.0000 0.984 1.000 0.000
#> GSM711967 1 0.0000 0.984 1.000 0.000
#> GSM711969 2 0.0000 0.990 0.000 1.000
#> GSM711973 1 0.0000 0.984 1.000 0.000
#> GSM711977 1 0.0000 0.984 1.000 0.000
#> GSM711981 1 0.9970 0.124 0.532 0.468
#> GSM711987 2 0.0000 0.990 0.000 1.000
#> GSM711905 2 0.0000 0.990 0.000 1.000
#> GSM711907 2 0.0000 0.990 0.000 1.000
#> GSM711909 1 0.0000 0.984 1.000 0.000
#> GSM711911 1 0.0000 0.984 1.000 0.000
#> GSM711915 1 0.0000 0.984 1.000 0.000
#> GSM711917 2 0.0000 0.990 0.000 1.000
#> GSM711923 1 0.0000 0.984 1.000 0.000
#> GSM711925 2 0.0000 0.990 0.000 1.000
#> GSM711927 1 0.0000 0.984 1.000 0.000
#> GSM711929 2 0.0000 0.990 0.000 1.000
#> GSM711931 2 0.0000 0.990 0.000 1.000
#> GSM711933 1 0.0000 0.984 1.000 0.000
#> GSM711935 2 0.0000 0.990 0.000 1.000
#> GSM711941 1 0.0000 0.984 1.000 0.000
#> GSM711943 1 0.0672 0.977 0.992 0.008
#> GSM711945 1 0.8144 0.663 0.748 0.252
#> GSM711947 2 0.0376 0.986 0.004 0.996
#> GSM711949 2 0.0000 0.990 0.000 1.000
#> GSM711953 2 0.0000 0.990 0.000 1.000
#> GSM711955 1 0.0000 0.984 1.000 0.000
#> GSM711963 2 0.0000 0.990 0.000 1.000
#> GSM711971 1 0.0000 0.984 1.000 0.000
#> GSM711975 2 0.0000 0.990 0.000 1.000
#> GSM711979 1 0.0000 0.984 1.000 0.000
#> GSM711989 2 0.0000 0.990 0.000 1.000
#> GSM711991 1 0.7602 0.716 0.780 0.220
#> GSM711993 2 0.2603 0.948 0.044 0.956
#> GSM711983 1 0.0000 0.984 1.000 0.000
#> GSM711985 2 0.0000 0.990 0.000 1.000
#> GSM711913 1 0.0000 0.984 1.000 0.000
#> GSM711919 1 0.0000 0.984 1.000 0.000
#> GSM711921 1 0.0000 0.984 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM711936 2 0.0000 1.000 0.000 1.000 0.000
#> GSM711938 2 0.0000 1.000 0.000 1.000 0.000
#> GSM711950 1 0.0000 0.983 1.000 0.000 0.000
#> GSM711956 1 0.0000 0.983 1.000 0.000 0.000
#> GSM711958 1 0.0000 0.983 1.000 0.000 0.000
#> GSM711960 3 0.3879 0.828 0.152 0.000 0.848
#> GSM711964 1 0.0000 0.983 1.000 0.000 0.000
#> GSM711966 1 0.0000 0.983 1.000 0.000 0.000
#> GSM711968 1 0.0000 0.983 1.000 0.000 0.000
#> GSM711972 1 0.0000 0.983 1.000 0.000 0.000
#> GSM711976 1 0.0000 0.983 1.000 0.000 0.000
#> GSM711980 1 0.0000 0.983 1.000 0.000 0.000
#> GSM711986 1 0.0000 0.983 1.000 0.000 0.000
#> GSM711904 1 0.0000 0.983 1.000 0.000 0.000
#> GSM711906 1 0.0000 0.983 1.000 0.000 0.000
#> GSM711908 1 0.0000 0.983 1.000 0.000 0.000
#> GSM711910 3 0.0000 0.967 0.000 0.000 1.000
#> GSM711914 1 0.0000 0.983 1.000 0.000 0.000
#> GSM711916 1 0.0000 0.983 1.000 0.000 0.000
#> GSM711922 1 0.0000 0.983 1.000 0.000 0.000
#> GSM711924 1 0.0000 0.983 1.000 0.000 0.000
#> GSM711926 1 0.6260 0.203 0.552 0.448 0.000
#> GSM711928 1 0.0000 0.983 1.000 0.000 0.000
#> GSM711930 1 0.0000 0.983 1.000 0.000 0.000
#> GSM711932 1 0.0000 0.983 1.000 0.000 0.000
#> GSM711934 1 0.0000 0.983 1.000 0.000 0.000
#> GSM711940 1 0.0000 0.983 1.000 0.000 0.000
#> GSM711942 1 0.0000 0.983 1.000 0.000 0.000
#> GSM711944 3 0.0000 0.967 0.000 0.000 1.000
#> GSM711946 3 0.0000 0.967 0.000 0.000 1.000
#> GSM711948 1 0.0237 0.980 0.996 0.000 0.004
#> GSM711952 1 0.0000 0.983 1.000 0.000 0.000
#> GSM711954 1 0.0000 0.983 1.000 0.000 0.000
#> GSM711962 1 0.0000 0.983 1.000 0.000 0.000
#> GSM711970 1 0.0000 0.983 1.000 0.000 0.000
#> GSM711974 1 0.0000 0.983 1.000 0.000 0.000
#> GSM711978 1 0.3116 0.873 0.892 0.108 0.000
#> GSM711988 1 0.0000 0.983 1.000 0.000 0.000
#> GSM711990 3 0.0000 0.967 0.000 0.000 1.000
#> GSM711992 1 0.0424 0.976 0.992 0.008 0.000
#> GSM711982 1 0.0000 0.983 1.000 0.000 0.000
#> GSM711984 2 0.0000 1.000 0.000 1.000 0.000
#> GSM711912 1 0.0000 0.983 1.000 0.000 0.000
#> GSM711918 1 0.0000 0.983 1.000 0.000 0.000
#> GSM711920 1 0.0000 0.983 1.000 0.000 0.000
#> GSM711937 2 0.0000 1.000 0.000 1.000 0.000
#> GSM711939 2 0.0000 1.000 0.000 1.000 0.000
#> GSM711951 2 0.0000 1.000 0.000 1.000 0.000
#> GSM711957 1 0.0000 0.983 1.000 0.000 0.000
#> GSM711959 2 0.0000 1.000 0.000 1.000 0.000
#> GSM711961 2 0.0000 1.000 0.000 1.000 0.000
#> GSM711965 3 0.0000 0.967 0.000 0.000 1.000
#> GSM711967 1 0.0000 0.983 1.000 0.000 0.000
#> GSM711969 2 0.0000 1.000 0.000 1.000 0.000
#> GSM711973 3 0.0424 0.962 0.008 0.000 0.992
#> GSM711977 3 0.0000 0.967 0.000 0.000 1.000
#> GSM711981 2 0.0424 0.992 0.000 0.992 0.008
#> GSM711987 2 0.0000 1.000 0.000 1.000 0.000
#> GSM711905 2 0.0000 1.000 0.000 1.000 0.000
#> GSM711907 2 0.0000 1.000 0.000 1.000 0.000
#> GSM711909 3 0.0000 0.967 0.000 0.000 1.000
#> GSM711911 3 0.0000 0.967 0.000 0.000 1.000
#> GSM711915 3 0.0000 0.967 0.000 0.000 1.000
#> GSM711917 2 0.0000 1.000 0.000 1.000 0.000
#> GSM711923 3 0.0237 0.965 0.000 0.004 0.996
#> GSM711925 2 0.0000 1.000 0.000 1.000 0.000
#> GSM711927 3 0.0000 0.967 0.000 0.000 1.000
#> GSM711929 2 0.0000 1.000 0.000 1.000 0.000
#> GSM711931 2 0.0000 1.000 0.000 1.000 0.000
#> GSM711933 1 0.0000 0.983 1.000 0.000 0.000
#> GSM711935 2 0.0000 1.000 0.000 1.000 0.000
#> GSM711941 3 0.4887 0.732 0.228 0.000 0.772
#> GSM711943 3 0.1289 0.944 0.000 0.032 0.968
#> GSM711945 3 0.0592 0.960 0.000 0.012 0.988
#> GSM711947 3 0.0747 0.957 0.000 0.016 0.984
#> GSM711949 2 0.0000 1.000 0.000 1.000 0.000
#> GSM711953 2 0.0000 1.000 0.000 1.000 0.000
#> GSM711955 3 0.4931 0.726 0.232 0.000 0.768
#> GSM711963 2 0.0000 1.000 0.000 1.000 0.000
#> GSM711971 3 0.0000 0.967 0.000 0.000 1.000
#> GSM711975 2 0.0000 1.000 0.000 1.000 0.000
#> GSM711979 1 0.2165 0.921 0.936 0.064 0.000
#> GSM711989 2 0.0000 1.000 0.000 1.000 0.000
#> GSM711991 3 0.0000 0.967 0.000 0.000 1.000
#> GSM711993 2 0.0000 1.000 0.000 1.000 0.000
#> GSM711983 3 0.0000 0.967 0.000 0.000 1.000
#> GSM711985 2 0.0000 1.000 0.000 1.000 0.000
#> GSM711913 3 0.0000 0.967 0.000 0.000 1.000
#> GSM711919 3 0.0000 0.967 0.000 0.000 1.000
#> GSM711921 3 0.0000 0.967 0.000 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM711936 2 0.0000 0.9875 0.000 1.000 0.000 0.000
#> GSM711938 2 0.0000 0.9875 0.000 1.000 0.000 0.000
#> GSM711950 4 0.0000 0.8791 0.000 0.000 0.000 1.000
#> GSM711956 1 0.0000 0.9641 1.000 0.000 0.000 0.000
#> GSM711958 1 0.0000 0.9641 1.000 0.000 0.000 0.000
#> GSM711960 3 0.0336 0.9577 0.008 0.000 0.992 0.000
#> GSM711964 1 0.0000 0.9641 1.000 0.000 0.000 0.000
#> GSM711966 1 0.0000 0.9641 1.000 0.000 0.000 0.000
#> GSM711968 1 0.0000 0.9641 1.000 0.000 0.000 0.000
#> GSM711972 1 0.0000 0.9641 1.000 0.000 0.000 0.000
#> GSM711976 4 0.4040 0.6753 0.248 0.000 0.000 0.752
#> GSM711980 1 0.0000 0.9641 1.000 0.000 0.000 0.000
#> GSM711986 1 0.0000 0.9641 1.000 0.000 0.000 0.000
#> GSM711904 1 0.0000 0.9641 1.000 0.000 0.000 0.000
#> GSM711906 1 0.0000 0.9641 1.000 0.000 0.000 0.000
#> GSM711908 1 0.0000 0.9641 1.000 0.000 0.000 0.000
#> GSM711910 3 0.0000 0.9624 0.000 0.000 1.000 0.000
#> GSM711914 1 0.0000 0.9641 1.000 0.000 0.000 0.000
#> GSM711916 1 0.0000 0.9641 1.000 0.000 0.000 0.000
#> GSM711922 1 0.0188 0.9614 0.996 0.000 0.000 0.004
#> GSM711924 1 0.0000 0.9641 1.000 0.000 0.000 0.000
#> GSM711926 4 0.1004 0.8745 0.004 0.024 0.000 0.972
#> GSM711928 1 0.0000 0.9641 1.000 0.000 0.000 0.000
#> GSM711930 1 0.0188 0.9612 0.996 0.000 0.004 0.000
#> GSM711932 4 0.1302 0.8633 0.044 0.000 0.000 0.956
#> GSM711934 1 0.0000 0.9641 1.000 0.000 0.000 0.000
#> GSM711940 4 0.4250 0.6385 0.276 0.000 0.000 0.724
#> GSM711942 1 0.0000 0.9641 1.000 0.000 0.000 0.000
#> GSM711944 3 0.0817 0.9578 0.000 0.000 0.976 0.024
#> GSM711946 4 0.3942 0.6798 0.000 0.000 0.236 0.764
#> GSM711948 4 0.0000 0.8791 0.000 0.000 0.000 1.000
#> GSM711952 1 0.0000 0.9641 1.000 0.000 0.000 0.000
#> GSM711954 1 0.1118 0.9337 0.964 0.000 0.000 0.036
#> GSM711962 1 0.0000 0.9641 1.000 0.000 0.000 0.000
#> GSM711970 1 0.0188 0.9614 0.996 0.000 0.000 0.004
#> GSM711974 1 0.0000 0.9641 1.000 0.000 0.000 0.000
#> GSM711978 4 0.0592 0.8757 0.016 0.000 0.000 0.984
#> GSM711988 1 0.3649 0.7326 0.796 0.000 0.000 0.204
#> GSM711990 3 0.0469 0.9634 0.000 0.000 0.988 0.012
#> GSM711992 4 0.3975 0.6939 0.240 0.000 0.000 0.760
#> GSM711982 1 0.0000 0.9641 1.000 0.000 0.000 0.000
#> GSM711984 2 0.0000 0.9875 0.000 1.000 0.000 0.000
#> GSM711912 1 0.0000 0.9641 1.000 0.000 0.000 0.000
#> GSM711918 1 0.0000 0.9641 1.000 0.000 0.000 0.000
#> GSM711920 1 0.0000 0.9641 1.000 0.000 0.000 0.000
#> GSM711937 2 0.0000 0.9875 0.000 1.000 0.000 0.000
#> GSM711939 2 0.0000 0.9875 0.000 1.000 0.000 0.000
#> GSM711951 4 0.0921 0.8729 0.000 0.028 0.000 0.972
#> GSM711957 1 0.4996 0.0229 0.516 0.000 0.000 0.484
#> GSM711959 2 0.0000 0.9875 0.000 1.000 0.000 0.000
#> GSM711961 2 0.0000 0.9875 0.000 1.000 0.000 0.000
#> GSM711965 4 0.3649 0.7205 0.000 0.000 0.204 0.796
#> GSM711967 1 0.3356 0.7672 0.824 0.000 0.000 0.176
#> GSM711969 2 0.0000 0.9875 0.000 1.000 0.000 0.000
#> GSM711973 4 0.3975 0.6498 0.000 0.000 0.240 0.760
#> GSM711977 3 0.1637 0.9265 0.000 0.000 0.940 0.060
#> GSM711981 4 0.0000 0.8791 0.000 0.000 0.000 1.000
#> GSM711987 2 0.0000 0.9875 0.000 1.000 0.000 0.000
#> GSM711905 2 0.0000 0.9875 0.000 1.000 0.000 0.000
#> GSM711907 2 0.3801 0.6974 0.000 0.780 0.000 0.220
#> GSM711909 3 0.0188 0.9637 0.000 0.000 0.996 0.004
#> GSM711911 3 0.0469 0.9634 0.000 0.000 0.988 0.012
#> GSM711915 3 0.0000 0.9624 0.000 0.000 1.000 0.000
#> GSM711917 2 0.0000 0.9875 0.000 1.000 0.000 0.000
#> GSM711923 4 0.0000 0.8791 0.000 0.000 0.000 1.000
#> GSM711925 2 0.0000 0.9875 0.000 1.000 0.000 0.000
#> GSM711927 3 0.0336 0.9638 0.000 0.000 0.992 0.008
#> GSM711929 2 0.0000 0.9875 0.000 1.000 0.000 0.000
#> GSM711931 4 0.1211 0.8672 0.000 0.040 0.000 0.960
#> GSM711933 1 0.2647 0.8436 0.880 0.000 0.000 0.120
#> GSM711935 2 0.0000 0.9875 0.000 1.000 0.000 0.000
#> GSM711941 4 0.0000 0.8791 0.000 0.000 0.000 1.000
#> GSM711943 4 0.0000 0.8791 0.000 0.000 0.000 1.000
#> GSM711945 4 0.4222 0.6259 0.000 0.000 0.272 0.728
#> GSM711947 3 0.0336 0.9585 0.000 0.008 0.992 0.000
#> GSM711949 2 0.0000 0.9875 0.000 1.000 0.000 0.000
#> GSM711953 2 0.0000 0.9875 0.000 1.000 0.000 0.000
#> GSM711955 3 0.5217 0.3318 0.012 0.000 0.608 0.380
#> GSM711963 2 0.0000 0.9875 0.000 1.000 0.000 0.000
#> GSM711971 3 0.0469 0.9634 0.000 0.000 0.988 0.012
#> GSM711975 4 0.3764 0.7015 0.000 0.216 0.000 0.784
#> GSM711979 4 0.0000 0.8791 0.000 0.000 0.000 1.000
#> GSM711989 2 0.0000 0.9875 0.000 1.000 0.000 0.000
#> GSM711991 3 0.0188 0.9637 0.000 0.000 0.996 0.004
#> GSM711993 4 0.0592 0.8765 0.000 0.016 0.000 0.984
#> GSM711983 3 0.0592 0.9620 0.000 0.000 0.984 0.016
#> GSM711985 2 0.0000 0.9875 0.000 1.000 0.000 0.000
#> GSM711913 3 0.0817 0.9578 0.000 0.000 0.976 0.024
#> GSM711919 3 0.0000 0.9624 0.000 0.000 1.000 0.000
#> GSM711921 3 0.0188 0.9637 0.000 0.000 0.996 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM711936 2 0.0000 0.9800 0.000 1.000 0.000 0.000 0.000
#> GSM711938 2 0.0000 0.9800 0.000 1.000 0.000 0.000 0.000
#> GSM711950 4 0.3424 0.5500 0.000 0.000 0.000 0.760 0.240
#> GSM711956 1 0.3730 0.7274 0.712 0.000 0.000 0.000 0.288
#> GSM711958 1 0.4436 0.3077 0.596 0.000 0.396 0.000 0.008
#> GSM711960 3 0.0579 0.9218 0.008 0.000 0.984 0.000 0.008
#> GSM711964 1 0.0000 0.8439 1.000 0.000 0.000 0.000 0.000
#> GSM711966 1 0.0162 0.8433 0.996 0.000 0.000 0.000 0.004
#> GSM711968 1 0.3895 0.7047 0.680 0.000 0.000 0.000 0.320
#> GSM711972 1 0.0000 0.8439 1.000 0.000 0.000 0.000 0.000
#> GSM711976 1 0.4808 0.3737 0.576 0.000 0.000 0.400 0.024
#> GSM711980 1 0.3074 0.7789 0.804 0.000 0.000 0.000 0.196
#> GSM711986 1 0.0000 0.8439 1.000 0.000 0.000 0.000 0.000
#> GSM711904 1 0.3242 0.7694 0.784 0.000 0.000 0.000 0.216
#> GSM711906 1 0.0000 0.8439 1.000 0.000 0.000 0.000 0.000
#> GSM711908 1 0.0000 0.8439 1.000 0.000 0.000 0.000 0.000
#> GSM711910 3 0.0000 0.9311 0.000 0.000 1.000 0.000 0.000
#> GSM711914 1 0.0290 0.8436 0.992 0.000 0.000 0.000 0.008
#> GSM711916 1 0.0162 0.8433 0.996 0.000 0.000 0.000 0.004
#> GSM711922 1 0.4135 0.6878 0.656 0.000 0.000 0.004 0.340
#> GSM711924 1 0.3508 0.7251 0.748 0.000 0.000 0.000 0.252
#> GSM711926 4 0.3940 0.6292 0.000 0.024 0.000 0.756 0.220
#> GSM711928 1 0.0703 0.8408 0.976 0.000 0.000 0.000 0.024
#> GSM711930 1 0.0290 0.8419 0.992 0.000 0.000 0.000 0.008
#> GSM711932 4 0.5082 0.5279 0.076 0.000 0.000 0.664 0.260
#> GSM711934 1 0.3109 0.7813 0.800 0.000 0.000 0.000 0.200
#> GSM711940 4 0.3177 0.5963 0.208 0.000 0.000 0.792 0.000
#> GSM711942 1 0.3395 0.7408 0.764 0.000 0.000 0.000 0.236
#> GSM711944 3 0.0992 0.9116 0.000 0.000 0.968 0.008 0.024
#> GSM711946 4 0.2491 0.7001 0.000 0.000 0.068 0.896 0.036
#> GSM711948 4 0.3039 0.6566 0.012 0.000 0.000 0.836 0.152
#> GSM711952 1 0.0290 0.8436 0.992 0.000 0.000 0.000 0.008
#> GSM711954 1 0.3146 0.7681 0.844 0.000 0.000 0.128 0.028
#> GSM711962 1 0.0000 0.8439 1.000 0.000 0.000 0.000 0.000
#> GSM711970 1 0.4467 0.6716 0.640 0.000 0.000 0.016 0.344
#> GSM711974 1 0.0162 0.8433 0.996 0.000 0.000 0.000 0.004
#> GSM711978 4 0.1443 0.7490 0.004 0.004 0.000 0.948 0.044
#> GSM711988 1 0.3194 0.7478 0.832 0.000 0.000 0.148 0.020
#> GSM711990 3 0.0771 0.9131 0.000 0.000 0.976 0.004 0.020
#> GSM711992 4 0.2605 0.6688 0.148 0.000 0.000 0.852 0.000
#> GSM711982 1 0.0162 0.8433 0.996 0.000 0.000 0.000 0.004
#> GSM711984 2 0.0000 0.9800 0.000 1.000 0.000 0.000 0.000
#> GSM711912 1 0.0000 0.8439 1.000 0.000 0.000 0.000 0.000
#> GSM711918 1 0.0162 0.8436 0.996 0.000 0.000 0.000 0.004
#> GSM711920 1 0.4855 0.5759 0.552 0.000 0.000 0.024 0.424
#> GSM711937 2 0.0000 0.9800 0.000 1.000 0.000 0.000 0.000
#> GSM711939 2 0.0000 0.9800 0.000 1.000 0.000 0.000 0.000
#> GSM711951 4 0.1544 0.7291 0.000 0.068 0.000 0.932 0.000
#> GSM711957 5 0.6493 -0.0994 0.248 0.000 0.000 0.260 0.492
#> GSM711959 2 0.0000 0.9800 0.000 1.000 0.000 0.000 0.000
#> GSM711961 2 0.0000 0.9800 0.000 1.000 0.000 0.000 0.000
#> GSM711965 5 0.4890 0.0385 0.000 0.000 0.024 0.452 0.524
#> GSM711967 1 0.5467 0.2183 0.548 0.000 0.000 0.384 0.068
#> GSM711969 2 0.0000 0.9800 0.000 1.000 0.000 0.000 0.000
#> GSM711973 5 0.6101 0.4456 0.000 0.000 0.164 0.284 0.552
#> GSM711977 5 0.5838 0.4666 0.000 0.000 0.336 0.112 0.552
#> GSM711981 4 0.1965 0.7141 0.000 0.000 0.000 0.904 0.096
#> GSM711987 2 0.0000 0.9800 0.000 1.000 0.000 0.000 0.000
#> GSM711905 2 0.0000 0.9800 0.000 1.000 0.000 0.000 0.000
#> GSM711907 2 0.3876 0.4646 0.000 0.684 0.000 0.316 0.000
#> GSM711909 3 0.0000 0.9311 0.000 0.000 1.000 0.000 0.000
#> GSM711911 3 0.0451 0.9269 0.000 0.000 0.988 0.008 0.004
#> GSM711915 5 0.4451 0.1586 0.000 0.000 0.492 0.004 0.504
#> GSM711917 2 0.0000 0.9800 0.000 1.000 0.000 0.000 0.000
#> GSM711923 4 0.0324 0.7476 0.000 0.000 0.004 0.992 0.004
#> GSM711925 2 0.0000 0.9800 0.000 1.000 0.000 0.000 0.000
#> GSM711927 3 0.0000 0.9311 0.000 0.000 1.000 0.000 0.000
#> GSM711929 2 0.0000 0.9800 0.000 1.000 0.000 0.000 0.000
#> GSM711931 4 0.3110 0.7135 0.000 0.080 0.000 0.860 0.060
#> GSM711933 4 0.6912 0.2027 0.208 0.000 0.016 0.464 0.312
#> GSM711935 2 0.0000 0.9800 0.000 1.000 0.000 0.000 0.000
#> GSM711941 4 0.0404 0.7440 0.000 0.000 0.000 0.988 0.012
#> GSM711943 4 0.1670 0.7376 0.000 0.000 0.052 0.936 0.012
#> GSM711945 4 0.4066 0.3761 0.000 0.000 0.004 0.672 0.324
#> GSM711947 3 0.0898 0.9072 0.000 0.020 0.972 0.000 0.008
#> GSM711949 2 0.0000 0.9800 0.000 1.000 0.000 0.000 0.000
#> GSM711953 2 0.0000 0.9800 0.000 1.000 0.000 0.000 0.000
#> GSM711955 3 0.6595 -0.0489 0.116 0.000 0.508 0.348 0.028
#> GSM711963 2 0.0000 0.9800 0.000 1.000 0.000 0.000 0.000
#> GSM711971 3 0.0000 0.9311 0.000 0.000 1.000 0.000 0.000
#> GSM711975 4 0.4302 0.1228 0.000 0.480 0.000 0.520 0.000
#> GSM711979 4 0.1430 0.7472 0.000 0.000 0.004 0.944 0.052
#> GSM711989 2 0.0000 0.9800 0.000 1.000 0.000 0.000 0.000
#> GSM711991 3 0.0404 0.9272 0.000 0.000 0.988 0.000 0.012
#> GSM711993 4 0.0912 0.7512 0.000 0.012 0.000 0.972 0.016
#> GSM711983 3 0.0290 0.9284 0.000 0.000 0.992 0.008 0.000
#> GSM711985 2 0.0000 0.9800 0.000 1.000 0.000 0.000 0.000
#> GSM711913 5 0.5458 0.4097 0.000 0.000 0.380 0.068 0.552
#> GSM711919 3 0.0162 0.9300 0.000 0.000 0.996 0.000 0.004
#> GSM711921 3 0.0000 0.9311 0.000 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM711936 2 0.0146 0.9571 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM711938 2 0.0000 0.9593 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711950 5 0.4208 0.1807 0.008 0.000 0.000 0.452 0.536 0.004
#> GSM711956 1 0.3823 0.3981 0.564 0.000 0.000 0.000 0.000 0.436
#> GSM711958 3 0.2805 0.7392 0.000 0.000 0.828 0.000 0.012 0.160
#> GSM711960 3 0.0000 0.9272 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711964 6 0.0291 0.8113 0.004 0.000 0.000 0.000 0.004 0.992
#> GSM711966 6 0.0622 0.8100 0.008 0.000 0.000 0.000 0.012 0.980
#> GSM711968 1 0.3309 0.6142 0.720 0.000 0.000 0.000 0.000 0.280
#> GSM711972 6 0.0363 0.8120 0.000 0.000 0.000 0.000 0.012 0.988
#> GSM711976 6 0.5858 -0.0140 0.084 0.000 0.000 0.036 0.424 0.456
#> GSM711980 1 0.3868 0.2414 0.504 0.000 0.000 0.000 0.000 0.496
#> GSM711986 6 0.0363 0.8096 0.012 0.000 0.000 0.000 0.000 0.988
#> GSM711904 6 0.3819 0.1367 0.372 0.000 0.000 0.000 0.004 0.624
#> GSM711906 6 0.0508 0.8113 0.004 0.000 0.000 0.000 0.012 0.984
#> GSM711908 6 0.0363 0.8120 0.000 0.000 0.000 0.000 0.012 0.988
#> GSM711910 3 0.0000 0.9272 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711914 6 0.0508 0.8091 0.012 0.000 0.000 0.000 0.004 0.984
#> GSM711916 6 0.0914 0.8049 0.016 0.000 0.000 0.000 0.016 0.968
#> GSM711922 1 0.3592 0.5565 0.656 0.000 0.000 0.000 0.000 0.344
#> GSM711924 1 0.5401 0.3518 0.552 0.000 0.092 0.000 0.012 0.344
#> GSM711926 4 0.2773 0.7807 0.152 0.008 0.000 0.836 0.000 0.004
#> GSM711928 6 0.0935 0.7998 0.032 0.000 0.000 0.000 0.004 0.964
#> GSM711930 6 0.0820 0.8052 0.016 0.000 0.000 0.000 0.012 0.972
#> GSM711932 1 0.4412 -0.0904 0.572 0.000 0.000 0.404 0.008 0.016
#> GSM711934 6 0.3563 0.2639 0.336 0.000 0.000 0.000 0.000 0.664
#> GSM711940 4 0.1442 0.8604 0.012 0.000 0.000 0.944 0.004 0.040
#> GSM711942 6 0.4177 -0.1544 0.468 0.000 0.000 0.000 0.012 0.520
#> GSM711944 3 0.1265 0.8969 0.044 0.000 0.948 0.000 0.008 0.000
#> GSM711946 4 0.0665 0.8847 0.008 0.000 0.008 0.980 0.004 0.000
#> GSM711948 4 0.4167 0.3409 0.012 0.000 0.000 0.636 0.344 0.008
#> GSM711952 6 0.0865 0.7964 0.036 0.000 0.000 0.000 0.000 0.964
#> GSM711954 6 0.4616 0.2543 0.060 0.000 0.000 0.316 0.000 0.624
#> GSM711962 6 0.0508 0.8113 0.004 0.000 0.000 0.000 0.012 0.984
#> GSM711970 1 0.3265 0.6258 0.748 0.000 0.000 0.004 0.000 0.248
#> GSM711974 6 0.0405 0.8121 0.004 0.000 0.000 0.000 0.008 0.988
#> GSM711978 4 0.0291 0.8870 0.004 0.004 0.000 0.992 0.000 0.000
#> GSM711988 6 0.2309 0.7344 0.084 0.000 0.000 0.028 0.000 0.888
#> GSM711990 3 0.0632 0.9128 0.000 0.000 0.976 0.000 0.024 0.000
#> GSM711992 4 0.0767 0.8845 0.008 0.004 0.000 0.976 0.000 0.012
#> GSM711982 6 0.0622 0.8100 0.008 0.000 0.000 0.000 0.012 0.980
#> GSM711984 2 0.0000 0.9593 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711912 6 0.0363 0.8096 0.012 0.000 0.000 0.000 0.000 0.988
#> GSM711918 6 0.0547 0.8069 0.020 0.000 0.000 0.000 0.000 0.980
#> GSM711920 1 0.1367 0.5515 0.944 0.000 0.000 0.000 0.012 0.044
#> GSM711937 2 0.0000 0.9593 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711939 2 0.0000 0.9593 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711951 4 0.1075 0.8587 0.000 0.048 0.000 0.952 0.000 0.000
#> GSM711957 1 0.0748 0.5256 0.976 0.000 0.000 0.004 0.004 0.016
#> GSM711959 2 0.0000 0.9593 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711961 2 0.0146 0.9569 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM711965 5 0.0935 0.7892 0.000 0.000 0.004 0.032 0.964 0.000
#> GSM711967 6 0.4459 0.2310 0.016 0.000 0.000 0.384 0.012 0.588
#> GSM711969 2 0.0000 0.9593 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711973 5 0.0891 0.7906 0.000 0.000 0.008 0.024 0.968 0.000
#> GSM711977 5 0.0909 0.7897 0.000 0.000 0.020 0.012 0.968 0.000
#> GSM711981 4 0.3601 0.4655 0.004 0.000 0.000 0.684 0.312 0.000
#> GSM711987 2 0.0000 0.9593 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711905 2 0.0146 0.9569 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM711907 2 0.3647 0.4068 0.000 0.640 0.000 0.360 0.000 0.000
#> GSM711909 3 0.0000 0.9272 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711911 3 0.0146 0.9260 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM711915 5 0.1753 0.7431 0.004 0.000 0.084 0.000 0.912 0.000
#> GSM711917 2 0.0260 0.9545 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM711923 4 0.0146 0.8876 0.000 0.000 0.004 0.996 0.000 0.000
#> GSM711925 2 0.0000 0.9593 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711927 3 0.0000 0.9272 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711929 2 0.0000 0.9593 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711931 4 0.3182 0.7427 0.036 0.124 0.000 0.832 0.008 0.000
#> GSM711933 3 0.6539 0.3413 0.180 0.000 0.516 0.248 0.004 0.052
#> GSM711935 2 0.0000 0.9593 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711941 4 0.0260 0.8862 0.000 0.000 0.000 0.992 0.008 0.000
#> GSM711943 4 0.0363 0.8858 0.000 0.000 0.012 0.988 0.000 0.000
#> GSM711945 5 0.3979 0.1964 0.004 0.000 0.000 0.456 0.540 0.000
#> GSM711947 3 0.0146 0.9249 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM711949 2 0.0000 0.9593 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711953 2 0.0000 0.9593 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711955 3 0.4314 0.6368 0.024 0.000 0.728 0.220 0.012 0.016
#> GSM711963 2 0.0000 0.9593 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711971 3 0.0000 0.9272 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711975 2 0.3482 0.5279 0.000 0.684 0.000 0.316 0.000 0.000
#> GSM711979 4 0.0603 0.8845 0.016 0.000 0.000 0.980 0.004 0.000
#> GSM711989 2 0.0260 0.9545 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM711991 3 0.0146 0.9254 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM711993 4 0.0000 0.8874 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM711983 3 0.0000 0.9272 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711985 2 0.0000 0.9593 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711913 5 0.0891 0.7876 0.000 0.000 0.024 0.008 0.968 0.000
#> GSM711919 3 0.0000 0.9272 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711921 3 0.0000 0.9272 0.000 0.000 1.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) disease.state(p) individual(p) k
#> SD:NMF 89 5.55e-05 0.219 0.616 2
#> SD:NMF 89 3.41e-11 0.244 0.695 3
#> SD:NMF 88 3.24e-08 0.163 0.420 4
#> SD:NMF 76 2.61e-08 0.148 0.274 5
#> SD:NMF 74 1.28e-06 0.134 0.226 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "hclust"]
# you can also extract it by
# res = res_list["CV:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 27425 rows and 90 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.860 0.870 0.950 0.3748 0.626 0.626
#> 3 3 0.696 0.706 0.878 0.6344 0.768 0.629
#> 4 4 0.683 0.797 0.844 0.1231 0.857 0.655
#> 5 5 0.726 0.732 0.858 0.0442 0.971 0.904
#> 6 6 0.714 0.689 0.822 0.0432 0.961 0.867
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM711936 2 0.416 0.8508 0.084 0.916
#> GSM711938 2 0.000 0.8984 0.000 1.000
#> GSM711950 1 0.000 0.9571 1.000 0.000
#> GSM711956 1 0.000 0.9571 1.000 0.000
#> GSM711958 1 0.000 0.9571 1.000 0.000
#> GSM711960 1 0.000 0.9571 1.000 0.000
#> GSM711964 1 0.000 0.9571 1.000 0.000
#> GSM711966 1 0.000 0.9571 1.000 0.000
#> GSM711968 1 0.000 0.9571 1.000 0.000
#> GSM711972 1 0.000 0.9571 1.000 0.000
#> GSM711976 1 0.000 0.9571 1.000 0.000
#> GSM711980 1 0.000 0.9571 1.000 0.000
#> GSM711986 1 0.000 0.9571 1.000 0.000
#> GSM711904 1 0.000 0.9571 1.000 0.000
#> GSM711906 1 0.000 0.9571 1.000 0.000
#> GSM711908 1 0.000 0.9571 1.000 0.000
#> GSM711910 1 0.000 0.9571 1.000 0.000
#> GSM711914 1 0.000 0.9571 1.000 0.000
#> GSM711916 1 0.000 0.9571 1.000 0.000
#> GSM711922 1 0.000 0.9571 1.000 0.000
#> GSM711924 1 0.000 0.9571 1.000 0.000
#> GSM711926 1 0.891 0.5218 0.692 0.308
#> GSM711928 1 0.000 0.9571 1.000 0.000
#> GSM711930 1 0.000 0.9571 1.000 0.000
#> GSM711932 1 0.000 0.9571 1.000 0.000
#> GSM711934 1 0.000 0.9571 1.000 0.000
#> GSM711940 1 0.000 0.9571 1.000 0.000
#> GSM711942 1 0.000 0.9571 1.000 0.000
#> GSM711944 1 0.000 0.9571 1.000 0.000
#> GSM711946 1 0.242 0.9244 0.960 0.040
#> GSM711948 1 0.000 0.9571 1.000 0.000
#> GSM711952 1 0.000 0.9571 1.000 0.000
#> GSM711954 1 0.000 0.9571 1.000 0.000
#> GSM711962 1 0.000 0.9571 1.000 0.000
#> GSM711970 1 0.000 0.9571 1.000 0.000
#> GSM711974 1 0.000 0.9571 1.000 0.000
#> GSM711978 1 0.358 0.8975 0.932 0.068
#> GSM711988 1 0.000 0.9571 1.000 0.000
#> GSM711990 1 0.000 0.9571 1.000 0.000
#> GSM711992 1 0.529 0.8378 0.880 0.120
#> GSM711982 1 0.000 0.9571 1.000 0.000
#> GSM711984 2 0.000 0.8984 0.000 1.000
#> GSM711912 1 0.000 0.9571 1.000 0.000
#> GSM711918 1 0.000 0.9571 1.000 0.000
#> GSM711920 1 0.000 0.9571 1.000 0.000
#> GSM711937 2 0.416 0.8508 0.084 0.916
#> GSM711939 2 0.000 0.8984 0.000 1.000
#> GSM711951 2 0.995 0.2113 0.460 0.540
#> GSM711957 1 0.000 0.9571 1.000 0.000
#> GSM711959 2 0.000 0.8984 0.000 1.000
#> GSM711961 2 0.000 0.8984 0.000 1.000
#> GSM711965 1 0.000 0.9571 1.000 0.000
#> GSM711967 1 0.000 0.9571 1.000 0.000
#> GSM711969 2 0.358 0.8624 0.068 0.932
#> GSM711973 1 0.000 0.9571 1.000 0.000
#> GSM711977 1 0.000 0.9571 1.000 0.000
#> GSM711981 1 0.722 0.7248 0.800 0.200
#> GSM711987 2 0.000 0.8984 0.000 1.000
#> GSM711905 2 0.000 0.8984 0.000 1.000
#> GSM711907 2 0.904 0.5465 0.320 0.680
#> GSM711909 1 0.000 0.9571 1.000 0.000
#> GSM711911 1 0.000 0.9571 1.000 0.000
#> GSM711915 1 0.000 0.9571 1.000 0.000
#> GSM711917 2 0.184 0.8855 0.028 0.972
#> GSM711923 1 0.242 0.9244 0.960 0.040
#> GSM711925 2 0.000 0.8984 0.000 1.000
#> GSM711927 1 0.000 0.9571 1.000 0.000
#> GSM711929 2 0.000 0.8984 0.000 1.000
#> GSM711931 1 0.917 0.4664 0.668 0.332
#> GSM711933 1 0.000 0.9571 1.000 0.000
#> GSM711935 2 0.000 0.8984 0.000 1.000
#> GSM711941 1 0.000 0.9571 1.000 0.000
#> GSM711943 1 0.242 0.9244 0.960 0.040
#> GSM711945 1 0.242 0.9244 0.960 0.040
#> GSM711947 1 1.000 -0.0487 0.512 0.488
#> GSM711949 2 0.000 0.8984 0.000 1.000
#> GSM711953 2 0.000 0.8984 0.000 1.000
#> GSM711955 1 0.000 0.9571 1.000 0.000
#> GSM711963 2 0.000 0.8984 0.000 1.000
#> GSM711971 1 0.000 0.9571 1.000 0.000
#> GSM711975 2 0.995 0.2113 0.460 0.540
#> GSM711979 1 0.358 0.8975 0.932 0.068
#> GSM711989 2 0.995 0.2113 0.460 0.540
#> GSM711991 1 0.999 -0.0168 0.520 0.480
#> GSM711993 1 0.913 0.4760 0.672 0.328
#> GSM711983 1 0.000 0.9571 1.000 0.000
#> GSM711985 2 0.000 0.8984 0.000 1.000
#> GSM711913 1 0.000 0.9571 1.000 0.000
#> GSM711919 1 0.000 0.9571 1.000 0.000
#> GSM711921 1 0.000 0.9571 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM711936 2 0.3155 0.8230 0.040 0.916 0.044
#> GSM711938 2 0.0000 0.8806 0.000 1.000 0.000
#> GSM711950 1 0.2165 0.8324 0.936 0.000 0.064
#> GSM711956 1 0.0592 0.8589 0.988 0.000 0.012
#> GSM711958 1 0.0424 0.8591 0.992 0.000 0.008
#> GSM711960 1 0.0592 0.8585 0.988 0.000 0.012
#> GSM711964 1 0.0424 0.8591 0.992 0.000 0.008
#> GSM711966 1 0.0000 0.8573 1.000 0.000 0.000
#> GSM711968 1 0.0592 0.8589 0.988 0.000 0.012
#> GSM711972 1 0.0000 0.8573 1.000 0.000 0.000
#> GSM711976 1 0.1289 0.8513 0.968 0.000 0.032
#> GSM711980 1 0.0424 0.8591 0.992 0.000 0.008
#> GSM711986 1 0.0000 0.8573 1.000 0.000 0.000
#> GSM711904 1 0.0592 0.8589 0.988 0.000 0.012
#> GSM711906 1 0.0000 0.8573 1.000 0.000 0.000
#> GSM711908 1 0.0000 0.8573 1.000 0.000 0.000
#> GSM711910 3 0.0000 0.8132 0.000 0.000 1.000
#> GSM711914 1 0.0424 0.8591 0.992 0.000 0.008
#> GSM711916 1 0.0000 0.8573 1.000 0.000 0.000
#> GSM711922 1 0.0592 0.8589 0.988 0.000 0.012
#> GSM711924 1 0.0237 0.8586 0.996 0.000 0.004
#> GSM711926 3 0.9940 0.2214 0.304 0.308 0.388
#> GSM711928 1 0.0592 0.8589 0.988 0.000 0.012
#> GSM711930 1 0.0000 0.8573 1.000 0.000 0.000
#> GSM711932 1 0.1411 0.8485 0.964 0.000 0.036
#> GSM711934 1 0.0592 0.8589 0.988 0.000 0.012
#> GSM711940 1 0.6235 0.3328 0.564 0.000 0.436
#> GSM711942 1 0.0237 0.8586 0.996 0.000 0.004
#> GSM711944 3 0.3482 0.7078 0.128 0.000 0.872
#> GSM711946 1 0.7566 0.2251 0.512 0.040 0.448
#> GSM711948 1 0.2448 0.8239 0.924 0.000 0.076
#> GSM711952 1 0.0000 0.8573 1.000 0.000 0.000
#> GSM711954 1 0.0592 0.8589 0.988 0.000 0.012
#> GSM711962 1 0.0237 0.8586 0.996 0.000 0.004
#> GSM711970 1 0.0592 0.8589 0.988 0.000 0.012
#> GSM711974 1 0.0424 0.8591 0.992 0.000 0.008
#> GSM711978 1 0.8066 0.2677 0.528 0.068 0.404
#> GSM711988 1 0.1411 0.8494 0.964 0.000 0.036
#> GSM711990 3 0.0592 0.8099 0.012 0.000 0.988
#> GSM711992 1 0.8503 0.3773 0.576 0.120 0.304
#> GSM711982 1 0.0000 0.8573 1.000 0.000 0.000
#> GSM711984 2 0.0000 0.8806 0.000 1.000 0.000
#> GSM711912 1 0.0000 0.8573 1.000 0.000 0.000
#> GSM711918 1 0.0000 0.8573 1.000 0.000 0.000
#> GSM711920 1 0.0237 0.8586 0.996 0.000 0.004
#> GSM711937 2 0.3155 0.8230 0.040 0.916 0.044
#> GSM711939 2 0.0000 0.8806 0.000 1.000 0.000
#> GSM711951 2 0.8645 0.1896 0.116 0.540 0.344
#> GSM711957 1 0.4504 0.7125 0.804 0.000 0.196
#> GSM711959 2 0.0000 0.8806 0.000 1.000 0.000
#> GSM711961 2 0.0000 0.8806 0.000 1.000 0.000
#> GSM711965 1 0.6309 0.1763 0.500 0.000 0.500
#> GSM711967 1 0.0237 0.8586 0.996 0.000 0.004
#> GSM711969 2 0.2689 0.8362 0.036 0.932 0.032
#> GSM711973 3 0.0892 0.8044 0.020 0.000 0.980
#> GSM711977 3 0.0000 0.8132 0.000 0.000 1.000
#> GSM711981 1 0.9602 -0.0973 0.400 0.200 0.400
#> GSM711987 2 0.0000 0.8806 0.000 1.000 0.000
#> GSM711905 2 0.0000 0.8806 0.000 1.000 0.000
#> GSM711907 2 0.7259 0.4903 0.072 0.680 0.248
#> GSM711909 3 0.0000 0.8132 0.000 0.000 1.000
#> GSM711911 3 0.0000 0.8132 0.000 0.000 1.000
#> GSM711915 3 0.0000 0.8132 0.000 0.000 1.000
#> GSM711917 2 0.1315 0.8644 0.008 0.972 0.020
#> GSM711923 1 0.7566 0.2251 0.512 0.040 0.448
#> GSM711925 2 0.0000 0.8806 0.000 1.000 0.000
#> GSM711927 3 0.0000 0.8132 0.000 0.000 1.000
#> GSM711929 2 0.0000 0.8806 0.000 1.000 0.000
#> GSM711931 3 0.9932 0.1984 0.284 0.332 0.384
#> GSM711933 1 0.1643 0.8457 0.956 0.000 0.044
#> GSM711935 2 0.0000 0.8806 0.000 1.000 0.000
#> GSM711941 1 0.6235 0.3328 0.564 0.000 0.436
#> GSM711943 1 0.7566 0.2251 0.512 0.040 0.448
#> GSM711945 1 0.7581 0.1807 0.496 0.040 0.464
#> GSM711947 3 0.6307 0.0158 0.000 0.488 0.512
#> GSM711949 2 0.0000 0.8806 0.000 1.000 0.000
#> GSM711953 2 0.0000 0.8806 0.000 1.000 0.000
#> GSM711955 1 0.2537 0.8220 0.920 0.000 0.080
#> GSM711963 2 0.0000 0.8806 0.000 1.000 0.000
#> GSM711971 3 0.0592 0.8099 0.012 0.000 0.988
#> GSM711975 2 0.8645 0.1896 0.116 0.540 0.344
#> GSM711979 1 0.8066 0.2677 0.528 0.068 0.404
#> GSM711989 2 0.8645 0.1896 0.116 0.540 0.344
#> GSM711991 3 0.6302 0.0436 0.000 0.480 0.520
#> GSM711993 3 0.9937 0.2027 0.288 0.328 0.384
#> GSM711983 3 0.0592 0.8099 0.012 0.000 0.988
#> GSM711985 2 0.0000 0.8806 0.000 1.000 0.000
#> GSM711913 3 0.0000 0.8132 0.000 0.000 1.000
#> GSM711919 3 0.0000 0.8132 0.000 0.000 1.000
#> GSM711921 3 0.0000 0.8132 0.000 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM711936 2 0.2520 0.790 0.004 0.904 0.004 0.088
#> GSM711938 2 0.0000 0.843 0.000 1.000 0.000 0.000
#> GSM711950 1 0.2466 0.850 0.900 0.000 0.004 0.096
#> GSM711956 1 0.0707 0.916 0.980 0.000 0.000 0.020
#> GSM711958 1 0.0336 0.917 0.992 0.000 0.000 0.008
#> GSM711960 1 0.0524 0.917 0.988 0.000 0.004 0.008
#> GSM711964 1 0.0469 0.917 0.988 0.000 0.000 0.012
#> GSM711966 1 0.2589 0.865 0.884 0.000 0.000 0.116
#> GSM711968 1 0.0707 0.916 0.980 0.000 0.000 0.020
#> GSM711972 1 0.2589 0.865 0.884 0.000 0.000 0.116
#> GSM711976 1 0.1398 0.904 0.956 0.000 0.004 0.040
#> GSM711980 1 0.0469 0.917 0.988 0.000 0.000 0.012
#> GSM711986 1 0.2704 0.859 0.876 0.000 0.000 0.124
#> GSM711904 1 0.0707 0.916 0.980 0.000 0.000 0.020
#> GSM711906 1 0.1211 0.904 0.960 0.000 0.000 0.040
#> GSM711908 1 0.2760 0.857 0.872 0.000 0.000 0.128
#> GSM711910 3 0.0000 0.966 0.000 0.000 1.000 0.000
#> GSM711914 1 0.0469 0.917 0.988 0.000 0.000 0.012
#> GSM711916 1 0.2589 0.865 0.884 0.000 0.000 0.116
#> GSM711922 1 0.0707 0.916 0.980 0.000 0.000 0.020
#> GSM711924 1 0.0336 0.916 0.992 0.000 0.000 0.008
#> GSM711926 4 0.7965 0.478 0.028 0.296 0.168 0.508
#> GSM711928 1 0.0707 0.916 0.980 0.000 0.000 0.020
#> GSM711930 1 0.2760 0.857 0.872 0.000 0.000 0.128
#> GSM711932 1 0.1474 0.906 0.948 0.000 0.000 0.052
#> GSM711934 1 0.0707 0.916 0.980 0.000 0.000 0.020
#> GSM711940 4 0.7468 0.742 0.304 0.000 0.204 0.492
#> GSM711942 1 0.0336 0.916 0.992 0.000 0.000 0.008
#> GSM711944 3 0.2944 0.777 0.128 0.000 0.868 0.004
#> GSM711946 4 0.8381 0.789 0.256 0.040 0.220 0.484
#> GSM711948 1 0.2654 0.835 0.888 0.000 0.004 0.108
#> GSM711952 1 0.2760 0.857 0.872 0.000 0.000 0.128
#> GSM711954 1 0.0817 0.917 0.976 0.000 0.000 0.024
#> GSM711962 1 0.0469 0.915 0.988 0.000 0.000 0.012
#> GSM711970 1 0.0817 0.917 0.976 0.000 0.000 0.024
#> GSM711974 1 0.0336 0.917 0.992 0.000 0.000 0.008
#> GSM711978 4 0.8475 0.787 0.256 0.056 0.192 0.496
#> GSM711988 1 0.1489 0.902 0.952 0.000 0.004 0.044
#> GSM711990 3 0.0657 0.961 0.012 0.000 0.984 0.004
#> GSM711992 1 0.8779 -0.376 0.480 0.112 0.128 0.280
#> GSM711982 1 0.2589 0.865 0.884 0.000 0.000 0.116
#> GSM711984 2 0.0000 0.843 0.000 1.000 0.000 0.000
#> GSM711912 1 0.2760 0.857 0.872 0.000 0.000 0.128
#> GSM711918 1 0.2760 0.857 0.872 0.000 0.000 0.128
#> GSM711920 1 0.0336 0.916 0.992 0.000 0.000 0.008
#> GSM711937 2 0.2520 0.790 0.004 0.904 0.004 0.088
#> GSM711939 2 0.0000 0.843 0.000 1.000 0.000 0.000
#> GSM711951 2 0.7262 0.154 0.004 0.528 0.148 0.320
#> GSM711957 4 0.3688 0.529 0.208 0.000 0.000 0.792
#> GSM711959 2 0.0000 0.843 0.000 1.000 0.000 0.000
#> GSM711961 2 0.0000 0.843 0.000 1.000 0.000 0.000
#> GSM711965 4 0.7536 0.742 0.244 0.000 0.264 0.492
#> GSM711967 1 0.0469 0.915 0.988 0.000 0.000 0.012
#> GSM711969 2 0.2164 0.804 0.004 0.924 0.004 0.068
#> GSM711973 3 0.2256 0.905 0.020 0.000 0.924 0.056
#> GSM711977 3 0.0895 0.953 0.004 0.000 0.976 0.020
#> GSM711981 4 0.8770 0.671 0.120 0.188 0.176 0.516
#> GSM711987 2 0.0000 0.843 0.000 1.000 0.000 0.000
#> GSM711905 2 0.0000 0.843 0.000 1.000 0.000 0.000
#> GSM711907 2 0.5822 0.485 0.004 0.668 0.056 0.272
#> GSM711909 3 0.0000 0.966 0.000 0.000 1.000 0.000
#> GSM711911 3 0.0188 0.965 0.000 0.000 0.996 0.004
#> GSM711915 3 0.0000 0.966 0.000 0.000 1.000 0.000
#> GSM711917 2 0.1042 0.828 0.000 0.972 0.020 0.008
#> GSM711923 4 0.8381 0.789 0.256 0.040 0.220 0.484
#> GSM711925 2 0.0000 0.843 0.000 1.000 0.000 0.000
#> GSM711927 3 0.0000 0.966 0.000 0.000 1.000 0.000
#> GSM711929 2 0.0000 0.843 0.000 1.000 0.000 0.000
#> GSM711931 4 0.7874 0.425 0.020 0.320 0.168 0.492
#> GSM711933 1 0.1576 0.899 0.948 0.000 0.004 0.048
#> GSM711935 2 0.0000 0.843 0.000 1.000 0.000 0.000
#> GSM711941 4 0.7468 0.742 0.304 0.000 0.204 0.492
#> GSM711943 4 0.8381 0.789 0.256 0.040 0.220 0.484
#> GSM711945 4 0.8391 0.780 0.240 0.040 0.236 0.484
#> GSM711947 2 0.6607 0.190 0.000 0.476 0.444 0.080
#> GSM711949 2 0.0000 0.843 0.000 1.000 0.000 0.000
#> GSM711953 2 0.0000 0.843 0.000 1.000 0.000 0.000
#> GSM711955 1 0.2737 0.836 0.888 0.000 0.008 0.104
#> GSM711963 2 0.0000 0.843 0.000 1.000 0.000 0.000
#> GSM711971 3 0.0657 0.961 0.012 0.000 0.984 0.004
#> GSM711975 2 0.7262 0.154 0.004 0.528 0.148 0.320
#> GSM711979 4 0.8475 0.787 0.256 0.056 0.192 0.496
#> GSM711989 2 0.7262 0.154 0.004 0.528 0.148 0.320
#> GSM711991 2 0.6659 0.173 0.000 0.468 0.448 0.084
#> GSM711993 4 0.7951 0.437 0.024 0.316 0.168 0.492
#> GSM711983 3 0.0657 0.961 0.012 0.000 0.984 0.004
#> GSM711985 2 0.0000 0.843 0.000 1.000 0.000 0.000
#> GSM711913 3 0.0895 0.953 0.004 0.000 0.976 0.020
#> GSM711919 3 0.0000 0.966 0.000 0.000 1.000 0.000
#> GSM711921 3 0.0000 0.966 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM711936 2 0.2329 0.8018 0.000 0.876 0.000 0.124 0.000
#> GSM711938 2 0.0609 0.8728 0.000 0.980 0.000 0.020 0.000
#> GSM711950 1 0.2293 0.8354 0.900 0.000 0.000 0.084 0.016
#> GSM711956 1 0.0693 0.8950 0.980 0.000 0.000 0.012 0.008
#> GSM711958 1 0.0290 0.8961 0.992 0.000 0.000 0.008 0.000
#> GSM711960 1 0.0451 0.8962 0.988 0.000 0.004 0.008 0.000
#> GSM711964 1 0.0510 0.8964 0.984 0.000 0.000 0.016 0.000
#> GSM711966 1 0.2723 0.8253 0.864 0.000 0.000 0.012 0.124
#> GSM711968 1 0.0693 0.8950 0.980 0.000 0.000 0.012 0.008
#> GSM711972 1 0.2723 0.8253 0.864 0.000 0.000 0.012 0.124
#> GSM711976 1 0.1300 0.8841 0.956 0.000 0.000 0.028 0.016
#> GSM711980 1 0.0404 0.8959 0.988 0.000 0.000 0.012 0.000
#> GSM711986 1 0.4316 0.7414 0.772 0.000 0.000 0.108 0.120
#> GSM711904 1 0.0693 0.8950 0.980 0.000 0.000 0.012 0.008
#> GSM711906 1 0.1408 0.8763 0.948 0.000 0.000 0.008 0.044
#> GSM711908 1 0.4457 0.7291 0.760 0.000 0.000 0.116 0.124
#> GSM711910 3 0.0510 0.8985 0.000 0.000 0.984 0.000 0.016
#> GSM711914 1 0.0510 0.8964 0.984 0.000 0.000 0.016 0.000
#> GSM711916 1 0.2723 0.8253 0.864 0.000 0.000 0.012 0.124
#> GSM711922 1 0.0693 0.8950 0.980 0.000 0.000 0.012 0.008
#> GSM711924 1 0.0290 0.8943 0.992 0.000 0.000 0.000 0.008
#> GSM711926 4 0.3690 0.4232 0.012 0.224 0.000 0.764 0.000
#> GSM711928 1 0.0693 0.8950 0.980 0.000 0.000 0.012 0.008
#> GSM711930 1 0.4457 0.7291 0.760 0.000 0.000 0.116 0.124
#> GSM711932 1 0.1493 0.8852 0.948 0.000 0.000 0.028 0.024
#> GSM711934 1 0.0693 0.8950 0.980 0.000 0.000 0.012 0.008
#> GSM711940 4 0.5165 0.4775 0.304 0.000 0.036 0.644 0.016
#> GSM711942 1 0.0290 0.8943 0.992 0.000 0.000 0.000 0.008
#> GSM711944 3 0.2536 0.7328 0.128 0.000 0.868 0.004 0.000
#> GSM711946 4 0.5064 0.5458 0.256 0.008 0.048 0.684 0.004
#> GSM711948 1 0.2464 0.8222 0.888 0.000 0.000 0.096 0.016
#> GSM711952 1 0.4361 0.7379 0.768 0.000 0.000 0.108 0.124
#> GSM711954 1 0.0807 0.8959 0.976 0.000 0.000 0.012 0.012
#> GSM711962 1 0.0404 0.8934 0.988 0.000 0.000 0.000 0.012
#> GSM711970 1 0.0807 0.8959 0.976 0.000 0.000 0.012 0.012
#> GSM711974 1 0.0290 0.8961 0.992 0.000 0.000 0.008 0.000
#> GSM711978 4 0.4467 0.5422 0.240 0.012 0.024 0.724 0.000
#> GSM711988 1 0.1386 0.8820 0.952 0.000 0.000 0.032 0.016
#> GSM711990 3 0.0854 0.8967 0.012 0.000 0.976 0.008 0.004
#> GSM711992 1 0.5697 -0.2805 0.480 0.068 0.000 0.448 0.004
#> GSM711982 1 0.2723 0.8253 0.864 0.000 0.000 0.012 0.124
#> GSM711984 2 0.0162 0.8766 0.000 0.996 0.000 0.000 0.004
#> GSM711912 1 0.4457 0.7291 0.760 0.000 0.000 0.116 0.124
#> GSM711918 1 0.4457 0.7291 0.760 0.000 0.000 0.116 0.124
#> GSM711920 1 0.0290 0.8943 0.992 0.000 0.000 0.000 0.008
#> GSM711937 2 0.2329 0.8018 0.000 0.876 0.000 0.124 0.000
#> GSM711939 2 0.0609 0.8728 0.000 0.980 0.000 0.020 0.000
#> GSM711951 4 0.4283 0.1751 0.000 0.456 0.000 0.544 0.000
#> GSM711957 5 0.5309 0.0000 0.060 0.000 0.000 0.364 0.576
#> GSM711959 2 0.0703 0.8715 0.000 0.976 0.000 0.024 0.000
#> GSM711961 2 0.0162 0.8766 0.000 0.996 0.000 0.000 0.004
#> GSM711965 4 0.5650 0.4924 0.244 0.000 0.084 0.652 0.020
#> GSM711967 1 0.0404 0.8934 0.988 0.000 0.000 0.000 0.012
#> GSM711969 2 0.2074 0.8199 0.000 0.896 0.000 0.104 0.000
#> GSM711973 3 0.4817 0.7479 0.016 0.000 0.728 0.052 0.204
#> GSM711977 3 0.3710 0.7956 0.000 0.000 0.784 0.024 0.192
#> GSM711981 4 0.4917 0.4773 0.104 0.140 0.008 0.744 0.004
#> GSM711987 2 0.0162 0.8766 0.000 0.996 0.000 0.000 0.004
#> GSM711905 2 0.0162 0.8766 0.000 0.996 0.000 0.000 0.004
#> GSM711907 2 0.4192 0.2465 0.000 0.596 0.000 0.404 0.000
#> GSM711909 3 0.0162 0.9015 0.000 0.000 0.996 0.000 0.004
#> GSM711911 3 0.0324 0.9013 0.000 0.000 0.992 0.004 0.004
#> GSM711915 3 0.3074 0.8100 0.000 0.000 0.804 0.000 0.196
#> GSM711917 2 0.1197 0.8588 0.000 0.952 0.000 0.048 0.000
#> GSM711923 4 0.5064 0.5458 0.256 0.008 0.048 0.684 0.004
#> GSM711925 2 0.0162 0.8766 0.000 0.996 0.000 0.000 0.004
#> GSM711927 3 0.0162 0.9015 0.000 0.000 0.996 0.000 0.004
#> GSM711929 2 0.0162 0.8766 0.000 0.996 0.000 0.000 0.004
#> GSM711931 4 0.3635 0.4109 0.004 0.248 0.000 0.748 0.000
#> GSM711933 1 0.1547 0.8798 0.948 0.000 0.004 0.032 0.016
#> GSM711935 2 0.0162 0.8766 0.000 0.996 0.000 0.000 0.004
#> GSM711941 4 0.5165 0.4775 0.304 0.000 0.036 0.644 0.016
#> GSM711943 4 0.5064 0.5458 0.256 0.008 0.048 0.684 0.004
#> GSM711945 4 0.5271 0.5376 0.240 0.008 0.060 0.684 0.008
#> GSM711947 2 0.8153 -0.0664 0.000 0.340 0.256 0.300 0.104
#> GSM711949 2 0.0162 0.8766 0.000 0.996 0.000 0.000 0.004
#> GSM711953 2 0.0162 0.8766 0.000 0.996 0.000 0.000 0.004
#> GSM711955 1 0.2568 0.8229 0.888 0.000 0.004 0.092 0.016
#> GSM711963 2 0.0162 0.8766 0.000 0.996 0.000 0.000 0.004
#> GSM711971 3 0.0854 0.8967 0.012 0.000 0.976 0.008 0.004
#> GSM711975 4 0.4283 0.1751 0.000 0.456 0.000 0.544 0.000
#> GSM711979 4 0.4467 0.5422 0.240 0.012 0.024 0.724 0.000
#> GSM711989 4 0.4283 0.1751 0.000 0.456 0.000 0.544 0.000
#> GSM711991 2 0.8158 -0.0845 0.000 0.332 0.256 0.308 0.104
#> GSM711993 4 0.3728 0.4152 0.008 0.244 0.000 0.748 0.000
#> GSM711983 3 0.0854 0.8967 0.012 0.000 0.976 0.008 0.004
#> GSM711985 2 0.0609 0.8728 0.000 0.980 0.000 0.020 0.000
#> GSM711913 3 0.3710 0.7956 0.000 0.000 0.784 0.024 0.192
#> GSM711919 3 0.0162 0.9015 0.000 0.000 0.996 0.000 0.004
#> GSM711921 3 0.0510 0.8985 0.000 0.000 0.984 0.000 0.016
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM711936 2 0.3428 0.7272 0.000 0.696 0.000 0.304 NA 0.000
#> GSM711938 2 0.2631 0.8297 0.000 0.820 0.000 0.180 NA 0.000
#> GSM711950 1 0.1995 0.7833 0.912 0.000 0.000 0.052 NA 0.000
#> GSM711956 1 0.0508 0.8467 0.984 0.000 0.000 0.004 NA 0.000
#> GSM711958 1 0.0260 0.8467 0.992 0.000 0.000 0.000 NA 0.000
#> GSM711960 1 0.0405 0.8466 0.988 0.000 0.004 0.000 NA 0.000
#> GSM711964 1 0.0935 0.8465 0.964 0.000 0.000 0.004 NA 0.000
#> GSM711966 1 0.3482 0.6755 0.684 0.000 0.000 0.000 NA 0.000
#> GSM711968 1 0.0508 0.8467 0.984 0.000 0.000 0.004 NA 0.000
#> GSM711972 1 0.3499 0.6740 0.680 0.000 0.000 0.000 NA 0.000
#> GSM711976 1 0.0891 0.8321 0.968 0.000 0.000 0.008 NA 0.000
#> GSM711980 1 0.0405 0.8461 0.988 0.000 0.000 0.004 NA 0.000
#> GSM711986 1 0.3828 0.5393 0.560 0.000 0.000 0.000 NA 0.000
#> GSM711904 1 0.0692 0.8454 0.976 0.000 0.000 0.004 NA 0.000
#> GSM711906 1 0.2340 0.7953 0.852 0.000 0.000 0.000 NA 0.000
#> GSM711908 1 0.3867 0.4811 0.512 0.000 0.000 0.000 NA 0.000
#> GSM711910 3 0.0508 0.8767 0.000 0.000 0.984 0.000 NA 0.012
#> GSM711914 1 0.0935 0.8465 0.964 0.000 0.000 0.004 NA 0.000
#> GSM711916 1 0.3499 0.6740 0.680 0.000 0.000 0.000 NA 0.000
#> GSM711922 1 0.0405 0.8467 0.988 0.000 0.000 0.004 NA 0.000
#> GSM711924 1 0.0790 0.8451 0.968 0.000 0.000 0.000 NA 0.000
#> GSM711926 4 0.0972 0.4397 0.008 0.028 0.000 0.964 NA 0.000
#> GSM711928 1 0.0603 0.8467 0.980 0.000 0.000 0.004 NA 0.000
#> GSM711930 1 0.3867 0.4811 0.512 0.000 0.000 0.000 NA 0.000
#> GSM711932 1 0.1462 0.8362 0.936 0.000 0.000 0.008 NA 0.000
#> GSM711934 1 0.0405 0.8457 0.988 0.000 0.000 0.004 NA 0.000
#> GSM711940 4 0.5148 0.5075 0.316 0.000 0.028 0.604 NA 0.000
#> GSM711942 1 0.0790 0.8451 0.968 0.000 0.000 0.000 NA 0.000
#> GSM711944 3 0.2278 0.7342 0.128 0.000 0.868 0.000 NA 0.000
#> GSM711946 4 0.4879 0.5464 0.264 0.000 0.040 0.660 NA 0.000
#> GSM711948 1 0.2190 0.7711 0.900 0.000 0.000 0.060 NA 0.000
#> GSM711952 1 0.3851 0.5175 0.540 0.000 0.000 0.000 NA 0.000
#> GSM711954 1 0.0291 0.8459 0.992 0.000 0.000 0.004 NA 0.000
#> GSM711962 1 0.1204 0.8394 0.944 0.000 0.000 0.000 NA 0.000
#> GSM711970 1 0.0291 0.8459 0.992 0.000 0.000 0.004 NA 0.000
#> GSM711974 1 0.0260 0.8467 0.992 0.000 0.000 0.000 NA 0.000
#> GSM711978 4 0.3892 0.5436 0.236 0.000 0.024 0.732 NA 0.000
#> GSM711988 1 0.0972 0.8298 0.964 0.000 0.000 0.008 NA 0.000
#> GSM711990 3 0.1074 0.8754 0.012 0.000 0.960 0.000 NA 0.000
#> GSM711992 4 0.4127 0.2394 0.484 0.004 0.000 0.508 NA 0.000
#> GSM711982 1 0.3499 0.6740 0.680 0.000 0.000 0.000 NA 0.000
#> GSM711984 2 0.0146 0.8671 0.000 0.996 0.000 0.004 NA 0.000
#> GSM711912 1 0.3866 0.4870 0.516 0.000 0.000 0.000 NA 0.000
#> GSM711918 1 0.3866 0.4870 0.516 0.000 0.000 0.000 NA 0.000
#> GSM711920 1 0.0790 0.8451 0.968 0.000 0.000 0.000 NA 0.000
#> GSM711937 2 0.3428 0.7272 0.000 0.696 0.000 0.304 NA 0.000
#> GSM711939 2 0.2631 0.8297 0.000 0.820 0.000 0.180 NA 0.000
#> GSM711951 4 0.3175 0.3434 0.000 0.256 0.000 0.744 NA 0.000
#> GSM711957 6 0.2135 0.0000 0.000 0.000 0.000 0.128 NA 0.872
#> GSM711959 2 0.2793 0.8183 0.000 0.800 0.000 0.200 NA 0.000
#> GSM711961 2 0.0000 0.8674 0.000 1.000 0.000 0.000 NA 0.000
#> GSM711965 4 0.5676 0.5159 0.260 0.000 0.068 0.612 NA 0.004
#> GSM711967 1 0.1204 0.8394 0.944 0.000 0.000 0.000 NA 0.000
#> GSM711969 2 0.3330 0.7489 0.000 0.716 0.000 0.284 NA 0.000
#> GSM711973 3 0.5529 0.6930 0.024 0.000 0.672 0.060 NA 0.048
#> GSM711977 3 0.4610 0.7447 0.000 0.000 0.736 0.056 NA 0.048
#> GSM711981 4 0.2963 0.4978 0.100 0.016 0.008 0.860 NA 0.000
#> GSM711987 2 0.0000 0.8674 0.000 1.000 0.000 0.000 NA 0.000
#> GSM711905 2 0.0000 0.8674 0.000 1.000 0.000 0.000 NA 0.000
#> GSM711907 4 0.3756 -0.0624 0.000 0.400 0.000 0.600 NA 0.000
#> GSM711909 3 0.0146 0.8804 0.000 0.000 0.996 0.000 NA 0.004
#> GSM711911 3 0.0291 0.8802 0.000 0.000 0.992 0.000 NA 0.004
#> GSM711915 3 0.4289 0.7603 0.000 0.000 0.756 0.032 NA 0.052
#> GSM711917 2 0.2912 0.8091 0.000 0.784 0.000 0.216 NA 0.000
#> GSM711923 4 0.4879 0.5464 0.264 0.000 0.040 0.660 NA 0.000
#> GSM711925 2 0.0000 0.8674 0.000 1.000 0.000 0.000 NA 0.000
#> GSM711927 3 0.0146 0.8804 0.000 0.000 0.996 0.000 NA 0.004
#> GSM711929 2 0.0000 0.8674 0.000 1.000 0.000 0.000 NA 0.000
#> GSM711931 4 0.1075 0.4283 0.000 0.048 0.000 0.952 NA 0.000
#> GSM711933 1 0.1080 0.8281 0.960 0.000 0.004 0.004 NA 0.000
#> GSM711935 2 0.0000 0.8674 0.000 1.000 0.000 0.000 NA 0.000
#> GSM711941 4 0.5148 0.5075 0.316 0.000 0.028 0.604 NA 0.000
#> GSM711943 4 0.4879 0.5464 0.264 0.000 0.040 0.660 NA 0.000
#> GSM711945 4 0.5110 0.5426 0.248 0.000 0.052 0.660 NA 0.004
#> GSM711947 4 0.7977 -0.2853 0.000 0.052 0.256 0.312 NA 0.080
#> GSM711949 2 0.0000 0.8674 0.000 1.000 0.000 0.000 NA 0.000
#> GSM711953 2 0.0000 0.8674 0.000 1.000 0.000 0.000 NA 0.000
#> GSM711955 1 0.2272 0.7719 0.900 0.000 0.004 0.056 NA 0.000
#> GSM711963 2 0.0000 0.8674 0.000 1.000 0.000 0.000 NA 0.000
#> GSM711971 3 0.1074 0.8754 0.012 0.000 0.960 0.000 NA 0.000
#> GSM711975 4 0.3175 0.3434 0.000 0.256 0.000 0.744 NA 0.000
#> GSM711979 4 0.3892 0.5436 0.236 0.000 0.024 0.732 NA 0.000
#> GSM711989 4 0.3175 0.3434 0.000 0.256 0.000 0.744 NA 0.000
#> GSM711991 4 0.7894 -0.2824 0.000 0.044 0.256 0.316 NA 0.080
#> GSM711993 4 0.1152 0.4322 0.004 0.044 0.000 0.952 NA 0.000
#> GSM711983 3 0.1074 0.8754 0.012 0.000 0.960 0.000 NA 0.000
#> GSM711985 2 0.2562 0.8327 0.000 0.828 0.000 0.172 NA 0.000
#> GSM711913 3 0.4610 0.7447 0.000 0.000 0.736 0.056 NA 0.048
#> GSM711919 3 0.0146 0.8804 0.000 0.000 0.996 0.000 NA 0.004
#> GSM711921 3 0.0508 0.8767 0.000 0.000 0.984 0.000 NA 0.012
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) disease.state(p) individual(p) k
#> CV:hclust 83 3.62e-04 0.2181 0.382 2
#> CV:hclust 70 1.90e-08 0.1587 0.643 3
#> CV:hclust 80 7.97e-09 0.2004 0.345 4
#> CV:hclust 75 2.02e-08 0.0888 0.359 5
#> CV:hclust 74 9.32e-08 0.0379 0.205 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "kmeans"]
# you can also extract it by
# res = res_list["CV:kmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 27425 rows and 90 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.969 0.986 0.4063 0.604 0.604
#> 3 3 0.951 0.959 0.982 0.5604 0.736 0.572
#> 4 4 0.974 0.928 0.969 0.1387 0.869 0.660
#> 5 5 0.747 0.662 0.826 0.0756 0.918 0.722
#> 6 6 0.726 0.591 0.767 0.0437 0.931 0.715
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 2 3
There is also optional best \(k\) = 2 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM711936 2 0.0376 0.9997 0.004 0.996
#> GSM711938 2 0.0376 0.9997 0.004 0.996
#> GSM711950 1 0.0000 0.9822 1.000 0.000
#> GSM711956 1 0.0000 0.9822 1.000 0.000
#> GSM711958 1 0.0000 0.9822 1.000 0.000
#> GSM711960 1 0.0376 0.9806 0.996 0.004
#> GSM711964 1 0.0000 0.9822 1.000 0.000
#> GSM711966 1 0.0000 0.9822 1.000 0.000
#> GSM711968 1 0.0000 0.9822 1.000 0.000
#> GSM711972 1 0.0000 0.9822 1.000 0.000
#> GSM711976 1 0.0000 0.9822 1.000 0.000
#> GSM711980 1 0.0000 0.9822 1.000 0.000
#> GSM711986 1 0.0000 0.9822 1.000 0.000
#> GSM711904 1 0.0000 0.9822 1.000 0.000
#> GSM711906 1 0.0000 0.9822 1.000 0.000
#> GSM711908 1 0.0000 0.9822 1.000 0.000
#> GSM711910 1 0.0376 0.9806 0.996 0.004
#> GSM711914 1 0.0000 0.9822 1.000 0.000
#> GSM711916 1 0.0000 0.9822 1.000 0.000
#> GSM711922 1 0.0000 0.9822 1.000 0.000
#> GSM711924 1 0.0000 0.9822 1.000 0.000
#> GSM711926 1 0.0938 0.9722 0.988 0.012
#> GSM711928 1 0.0000 0.9822 1.000 0.000
#> GSM711930 1 0.0000 0.9822 1.000 0.000
#> GSM711932 1 0.0000 0.9822 1.000 0.000
#> GSM711934 1 0.0000 0.9822 1.000 0.000
#> GSM711940 1 0.0000 0.9822 1.000 0.000
#> GSM711942 1 0.0000 0.9822 1.000 0.000
#> GSM711944 1 0.0376 0.9806 0.996 0.004
#> GSM711946 1 0.0376 0.9806 0.996 0.004
#> GSM711948 1 0.0000 0.9822 1.000 0.000
#> GSM711952 1 0.0000 0.9822 1.000 0.000
#> GSM711954 1 0.0000 0.9822 1.000 0.000
#> GSM711962 1 0.0000 0.9822 1.000 0.000
#> GSM711970 1 0.0000 0.9822 1.000 0.000
#> GSM711974 1 0.0000 0.9822 1.000 0.000
#> GSM711978 1 0.0000 0.9822 1.000 0.000
#> GSM711988 1 0.0000 0.9822 1.000 0.000
#> GSM711990 1 0.0376 0.9806 0.996 0.004
#> GSM711992 1 0.0000 0.9822 1.000 0.000
#> GSM711982 1 0.0000 0.9822 1.000 0.000
#> GSM711984 2 0.0376 0.9997 0.004 0.996
#> GSM711912 1 0.0000 0.9822 1.000 0.000
#> GSM711918 1 0.0000 0.9822 1.000 0.000
#> GSM711920 1 0.0000 0.9822 1.000 0.000
#> GSM711937 2 0.0376 0.9997 0.004 0.996
#> GSM711939 2 0.0376 0.9997 0.004 0.996
#> GSM711951 2 0.0376 0.9997 0.004 0.996
#> GSM711957 1 0.0000 0.9822 1.000 0.000
#> GSM711959 2 0.0376 0.9997 0.004 0.996
#> GSM711961 2 0.0376 0.9997 0.004 0.996
#> GSM711965 1 0.0376 0.9806 0.996 0.004
#> GSM711967 1 0.0000 0.9822 1.000 0.000
#> GSM711969 2 0.0376 0.9997 0.004 0.996
#> GSM711973 1 0.0376 0.9806 0.996 0.004
#> GSM711977 1 0.0376 0.9806 0.996 0.004
#> GSM711981 1 0.6973 0.7713 0.812 0.188
#> GSM711987 2 0.0376 0.9997 0.004 0.996
#> GSM711905 2 0.0376 0.9997 0.004 0.996
#> GSM711907 2 0.0376 0.9997 0.004 0.996
#> GSM711909 1 0.0376 0.9806 0.996 0.004
#> GSM711911 1 0.0376 0.9806 0.996 0.004
#> GSM711915 1 0.0376 0.9806 0.996 0.004
#> GSM711917 2 0.0376 0.9997 0.004 0.996
#> GSM711923 1 0.0000 0.9822 1.000 0.000
#> GSM711925 2 0.0376 0.9997 0.004 0.996
#> GSM711927 1 0.0376 0.9806 0.996 0.004
#> GSM711929 2 0.0376 0.9997 0.004 0.996
#> GSM711931 2 0.0376 0.9997 0.004 0.996
#> GSM711933 1 0.0000 0.9822 1.000 0.000
#> GSM711935 2 0.0376 0.9997 0.004 0.996
#> GSM711941 1 0.0000 0.9822 1.000 0.000
#> GSM711943 1 0.0000 0.9822 1.000 0.000
#> GSM711945 1 0.7056 0.7712 0.808 0.192
#> GSM711947 2 0.0376 0.9942 0.004 0.996
#> GSM711949 2 0.0376 0.9997 0.004 0.996
#> GSM711953 2 0.0376 0.9997 0.004 0.996
#> GSM711955 1 0.0376 0.9806 0.996 0.004
#> GSM711963 2 0.0376 0.9997 0.004 0.996
#> GSM711971 1 0.0376 0.9806 0.996 0.004
#> GSM711975 2 0.0376 0.9997 0.004 0.996
#> GSM711979 1 0.0000 0.9822 1.000 0.000
#> GSM711989 2 0.0376 0.9997 0.004 0.996
#> GSM711991 1 0.7056 0.7712 0.808 0.192
#> GSM711993 1 1.0000 0.0408 0.504 0.496
#> GSM711983 1 0.0376 0.9806 0.996 0.004
#> GSM711985 2 0.0376 0.9997 0.004 0.996
#> GSM711913 1 0.0376 0.9806 0.996 0.004
#> GSM711919 1 0.0376 0.9806 0.996 0.004
#> GSM711921 1 0.0376 0.9806 0.996 0.004
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM711936 2 0.000 0.982 0.000 1.000 0.000
#> GSM711938 2 0.000 0.982 0.000 1.000 0.000
#> GSM711950 1 0.000 0.989 1.000 0.000 0.000
#> GSM711956 1 0.000 0.989 1.000 0.000 0.000
#> GSM711958 1 0.000 0.989 1.000 0.000 0.000
#> GSM711960 1 0.196 0.932 0.944 0.000 0.056
#> GSM711964 1 0.000 0.989 1.000 0.000 0.000
#> GSM711966 1 0.000 0.989 1.000 0.000 0.000
#> GSM711968 1 0.000 0.989 1.000 0.000 0.000
#> GSM711972 1 0.000 0.989 1.000 0.000 0.000
#> GSM711976 1 0.000 0.989 1.000 0.000 0.000
#> GSM711980 1 0.000 0.989 1.000 0.000 0.000
#> GSM711986 1 0.000 0.989 1.000 0.000 0.000
#> GSM711904 1 0.000 0.989 1.000 0.000 0.000
#> GSM711906 1 0.000 0.989 1.000 0.000 0.000
#> GSM711908 1 0.000 0.989 1.000 0.000 0.000
#> GSM711910 3 0.000 0.957 0.000 0.000 1.000
#> GSM711914 1 0.000 0.989 1.000 0.000 0.000
#> GSM711916 1 0.000 0.989 1.000 0.000 0.000
#> GSM711922 1 0.000 0.989 1.000 0.000 0.000
#> GSM711924 1 0.000 0.989 1.000 0.000 0.000
#> GSM711926 1 0.000 0.989 1.000 0.000 0.000
#> GSM711928 1 0.000 0.989 1.000 0.000 0.000
#> GSM711930 1 0.000 0.989 1.000 0.000 0.000
#> GSM711932 1 0.000 0.989 1.000 0.000 0.000
#> GSM711934 1 0.000 0.989 1.000 0.000 0.000
#> GSM711940 1 0.000 0.989 1.000 0.000 0.000
#> GSM711942 1 0.000 0.989 1.000 0.000 0.000
#> GSM711944 3 0.000 0.957 0.000 0.000 1.000
#> GSM711946 3 0.000 0.957 0.000 0.000 1.000
#> GSM711948 1 0.000 0.989 1.000 0.000 0.000
#> GSM711952 1 0.000 0.989 1.000 0.000 0.000
#> GSM711954 1 0.000 0.989 1.000 0.000 0.000
#> GSM711962 1 0.000 0.989 1.000 0.000 0.000
#> GSM711970 1 0.000 0.989 1.000 0.000 0.000
#> GSM711974 1 0.000 0.989 1.000 0.000 0.000
#> GSM711978 1 0.000 0.989 1.000 0.000 0.000
#> GSM711988 1 0.000 0.989 1.000 0.000 0.000
#> GSM711990 3 0.000 0.957 0.000 0.000 1.000
#> GSM711992 1 0.000 0.989 1.000 0.000 0.000
#> GSM711982 1 0.000 0.989 1.000 0.000 0.000
#> GSM711984 2 0.000 0.982 0.000 1.000 0.000
#> GSM711912 1 0.000 0.989 1.000 0.000 0.000
#> GSM711918 1 0.000 0.989 1.000 0.000 0.000
#> GSM711920 1 0.000 0.989 1.000 0.000 0.000
#> GSM711937 2 0.000 0.982 0.000 1.000 0.000
#> GSM711939 2 0.000 0.982 0.000 1.000 0.000
#> GSM711951 2 0.000 0.982 0.000 1.000 0.000
#> GSM711957 1 0.000 0.989 1.000 0.000 0.000
#> GSM711959 2 0.000 0.982 0.000 1.000 0.000
#> GSM711961 2 0.000 0.982 0.000 1.000 0.000
#> GSM711965 3 0.000 0.957 0.000 0.000 1.000
#> GSM711967 1 0.000 0.989 1.000 0.000 0.000
#> GSM711969 2 0.000 0.982 0.000 1.000 0.000
#> GSM711973 3 0.362 0.838 0.136 0.000 0.864
#> GSM711977 3 0.000 0.957 0.000 0.000 1.000
#> GSM711981 3 0.802 0.625 0.156 0.188 0.656
#> GSM711987 2 0.000 0.982 0.000 1.000 0.000
#> GSM711905 2 0.000 0.982 0.000 1.000 0.000
#> GSM711907 2 0.000 0.982 0.000 1.000 0.000
#> GSM711909 3 0.000 0.957 0.000 0.000 1.000
#> GSM711911 3 0.000 0.957 0.000 0.000 1.000
#> GSM711915 3 0.000 0.957 0.000 0.000 1.000
#> GSM711917 2 0.000 0.982 0.000 1.000 0.000
#> GSM711923 3 0.394 0.817 0.156 0.000 0.844
#> GSM711925 2 0.000 0.982 0.000 1.000 0.000
#> GSM711927 3 0.000 0.957 0.000 0.000 1.000
#> GSM711929 2 0.000 0.982 0.000 1.000 0.000
#> GSM711931 2 0.000 0.982 0.000 1.000 0.000
#> GSM711933 1 0.000 0.989 1.000 0.000 0.000
#> GSM711935 2 0.000 0.982 0.000 1.000 0.000
#> GSM711941 1 0.412 0.792 0.832 0.000 0.168
#> GSM711943 3 0.394 0.817 0.156 0.000 0.844
#> GSM711945 3 0.000 0.957 0.000 0.000 1.000
#> GSM711947 3 0.153 0.925 0.000 0.040 0.960
#> GSM711949 2 0.000 0.982 0.000 1.000 0.000
#> GSM711953 2 0.000 0.982 0.000 1.000 0.000
#> GSM711955 1 0.489 0.693 0.772 0.000 0.228
#> GSM711963 2 0.000 0.982 0.000 1.000 0.000
#> GSM711971 3 0.000 0.957 0.000 0.000 1.000
#> GSM711975 2 0.000 0.982 0.000 1.000 0.000
#> GSM711979 1 0.000 0.989 1.000 0.000 0.000
#> GSM711989 2 0.000 0.982 0.000 1.000 0.000
#> GSM711991 3 0.000 0.957 0.000 0.000 1.000
#> GSM711993 2 0.576 0.508 0.328 0.672 0.000
#> GSM711983 3 0.000 0.957 0.000 0.000 1.000
#> GSM711985 2 0.000 0.982 0.000 1.000 0.000
#> GSM711913 3 0.000 0.957 0.000 0.000 1.000
#> GSM711919 3 0.000 0.957 0.000 0.000 1.000
#> GSM711921 3 0.000 0.957 0.000 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM711936 2 0.0000 0.967 0.000 1.000 0.000 0.000
#> GSM711938 2 0.0000 0.967 0.000 1.000 0.000 0.000
#> GSM711950 4 0.1302 0.866 0.044 0.000 0.000 0.956
#> GSM711956 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM711958 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM711960 1 0.0188 0.988 0.996 0.000 0.004 0.000
#> GSM711964 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM711966 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM711968 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM711972 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM711976 1 0.1867 0.920 0.928 0.000 0.000 0.072
#> GSM711980 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM711986 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM711904 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM711906 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM711908 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM711910 3 0.0000 0.970 0.000 0.000 1.000 0.000
#> GSM711914 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM711916 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM711922 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM711924 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM711926 4 0.0336 0.894 0.008 0.000 0.000 0.992
#> GSM711928 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM711930 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM711932 1 0.1867 0.920 0.928 0.000 0.000 0.072
#> GSM711934 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM711940 1 0.0592 0.978 0.984 0.000 0.000 0.016
#> GSM711942 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM711944 3 0.0000 0.970 0.000 0.000 1.000 0.000
#> GSM711946 4 0.0336 0.890 0.000 0.000 0.008 0.992
#> GSM711948 4 0.4543 0.542 0.324 0.000 0.000 0.676
#> GSM711952 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM711954 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM711962 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM711970 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM711974 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM711978 4 0.0336 0.894 0.008 0.000 0.000 0.992
#> GSM711988 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM711990 3 0.0000 0.970 0.000 0.000 1.000 0.000
#> GSM711992 4 0.0336 0.894 0.008 0.000 0.000 0.992
#> GSM711982 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM711984 2 0.0000 0.967 0.000 1.000 0.000 0.000
#> GSM711912 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM711918 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM711920 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM711937 2 0.0000 0.967 0.000 1.000 0.000 0.000
#> GSM711939 2 0.0000 0.967 0.000 1.000 0.000 0.000
#> GSM711951 4 0.0469 0.886 0.000 0.012 0.000 0.988
#> GSM711957 1 0.2281 0.895 0.904 0.000 0.000 0.096
#> GSM711959 2 0.0000 0.967 0.000 1.000 0.000 0.000
#> GSM711961 2 0.0000 0.967 0.000 1.000 0.000 0.000
#> GSM711965 4 0.4643 0.430 0.000 0.000 0.344 0.656
#> GSM711967 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM711969 2 0.0000 0.967 0.000 1.000 0.000 0.000
#> GSM711973 4 0.4054 0.719 0.016 0.000 0.188 0.796
#> GSM711977 3 0.0188 0.968 0.000 0.000 0.996 0.004
#> GSM711981 4 0.0188 0.893 0.004 0.000 0.000 0.996
#> GSM711987 2 0.0000 0.967 0.000 1.000 0.000 0.000
#> GSM711905 2 0.0000 0.967 0.000 1.000 0.000 0.000
#> GSM711907 2 0.2281 0.883 0.000 0.904 0.000 0.096
#> GSM711909 3 0.0000 0.970 0.000 0.000 1.000 0.000
#> GSM711911 3 0.0000 0.970 0.000 0.000 1.000 0.000
#> GSM711915 3 0.0188 0.968 0.000 0.000 0.996 0.004
#> GSM711917 2 0.0000 0.967 0.000 1.000 0.000 0.000
#> GSM711923 4 0.0376 0.893 0.004 0.000 0.004 0.992
#> GSM711925 2 0.0000 0.967 0.000 1.000 0.000 0.000
#> GSM711927 3 0.0000 0.970 0.000 0.000 1.000 0.000
#> GSM711929 2 0.0000 0.967 0.000 1.000 0.000 0.000
#> GSM711931 2 0.4746 0.466 0.000 0.632 0.000 0.368
#> GSM711933 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM711935 2 0.0000 0.967 0.000 1.000 0.000 0.000
#> GSM711941 4 0.0336 0.894 0.008 0.000 0.000 0.992
#> GSM711943 4 0.0376 0.893 0.004 0.000 0.004 0.992
#> GSM711945 4 0.0188 0.890 0.000 0.000 0.004 0.996
#> GSM711947 3 0.4285 0.773 0.000 0.156 0.804 0.040
#> GSM711949 2 0.0000 0.967 0.000 1.000 0.000 0.000
#> GSM711953 2 0.0000 0.967 0.000 1.000 0.000 0.000
#> GSM711955 4 0.5112 0.271 0.436 0.000 0.004 0.560
#> GSM711963 2 0.0000 0.967 0.000 1.000 0.000 0.000
#> GSM711971 3 0.0000 0.970 0.000 0.000 1.000 0.000
#> GSM711975 2 0.3907 0.712 0.000 0.768 0.000 0.232
#> GSM711979 4 0.0336 0.894 0.008 0.000 0.000 0.992
#> GSM711989 2 0.0000 0.967 0.000 1.000 0.000 0.000
#> GSM711991 3 0.3569 0.759 0.000 0.000 0.804 0.196
#> GSM711993 4 0.0336 0.894 0.008 0.000 0.000 0.992
#> GSM711983 3 0.0000 0.970 0.000 0.000 1.000 0.000
#> GSM711985 2 0.0000 0.967 0.000 1.000 0.000 0.000
#> GSM711913 3 0.0188 0.968 0.000 0.000 0.996 0.004
#> GSM711919 3 0.0000 0.970 0.000 0.000 1.000 0.000
#> GSM711921 3 0.0000 0.970 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM711936 2 0.3563 0.83704 0.000 0.780 0.000 0.012 0.208
#> GSM711938 2 0.0000 0.89308 0.000 1.000 0.000 0.000 0.000
#> GSM711950 4 0.3994 0.71387 0.188 0.000 0.000 0.772 0.040
#> GSM711956 1 0.0963 0.62588 0.964 0.000 0.000 0.000 0.036
#> GSM711958 1 0.1792 0.61578 0.916 0.000 0.000 0.000 0.084
#> GSM711960 1 0.3191 0.59147 0.860 0.000 0.052 0.004 0.084
#> GSM711964 1 0.3636 0.00664 0.728 0.000 0.000 0.000 0.272
#> GSM711966 5 0.4273 0.98888 0.448 0.000 0.000 0.000 0.552
#> GSM711968 1 0.1792 0.58248 0.916 0.000 0.000 0.000 0.084
#> GSM711972 5 0.4273 0.98888 0.448 0.000 0.000 0.000 0.552
#> GSM711976 1 0.2777 0.55669 0.864 0.000 0.000 0.120 0.016
#> GSM711980 1 0.0000 0.64502 1.000 0.000 0.000 0.000 0.000
#> GSM711986 1 0.4283 -0.71857 0.544 0.000 0.000 0.000 0.456
#> GSM711904 1 0.3143 0.31242 0.796 0.000 0.000 0.000 0.204
#> GSM711906 5 0.4268 0.98648 0.444 0.000 0.000 0.000 0.556
#> GSM711908 5 0.4273 0.96941 0.448 0.000 0.000 0.000 0.552
#> GSM711910 3 0.0290 0.90377 0.000 0.000 0.992 0.000 0.008
#> GSM711914 1 0.3636 0.01167 0.728 0.000 0.000 0.000 0.272
#> GSM711916 5 0.4273 0.98888 0.448 0.000 0.000 0.000 0.552
#> GSM711922 1 0.0000 0.64502 1.000 0.000 0.000 0.000 0.000
#> GSM711924 1 0.2605 0.53322 0.852 0.000 0.000 0.000 0.148
#> GSM711926 4 0.2390 0.82316 0.020 0.000 0.000 0.896 0.084
#> GSM711928 1 0.2732 0.42917 0.840 0.000 0.000 0.000 0.160
#> GSM711930 5 0.4262 0.98032 0.440 0.000 0.000 0.000 0.560
#> GSM711932 1 0.1444 0.63147 0.948 0.000 0.000 0.040 0.012
#> GSM711934 1 0.0290 0.64521 0.992 0.000 0.000 0.000 0.008
#> GSM711940 1 0.4437 0.48423 0.760 0.000 0.000 0.140 0.100
#> GSM711942 1 0.2690 0.52353 0.844 0.000 0.000 0.000 0.156
#> GSM711944 3 0.5200 0.62953 0.228 0.000 0.688 0.012 0.072
#> GSM711946 4 0.1518 0.83927 0.004 0.000 0.004 0.944 0.048
#> GSM711948 1 0.4836 0.33290 0.652 0.000 0.000 0.304 0.044
#> GSM711952 1 0.4283 -0.71857 0.544 0.000 0.000 0.000 0.456
#> GSM711954 1 0.0324 0.64521 0.992 0.000 0.000 0.004 0.004
#> GSM711962 1 0.3336 0.36454 0.772 0.000 0.000 0.000 0.228
#> GSM711970 1 0.0162 0.64536 0.996 0.000 0.000 0.004 0.000
#> GSM711974 1 0.2377 0.56994 0.872 0.000 0.000 0.000 0.128
#> GSM711978 4 0.0865 0.85269 0.024 0.000 0.000 0.972 0.004
#> GSM711988 1 0.1195 0.63748 0.960 0.000 0.000 0.028 0.012
#> GSM711990 3 0.1357 0.90284 0.000 0.000 0.948 0.004 0.048
#> GSM711992 4 0.0955 0.85252 0.028 0.000 0.000 0.968 0.004
#> GSM711982 5 0.4273 0.98888 0.448 0.000 0.000 0.000 0.552
#> GSM711984 2 0.1544 0.88874 0.000 0.932 0.000 0.000 0.068
#> GSM711912 1 0.4291 -0.73949 0.536 0.000 0.000 0.000 0.464
#> GSM711918 1 0.4291 -0.73949 0.536 0.000 0.000 0.000 0.464
#> GSM711920 1 0.1043 0.63495 0.960 0.000 0.000 0.000 0.040
#> GSM711937 2 0.3421 0.84165 0.000 0.788 0.000 0.008 0.204
#> GSM711939 2 0.2020 0.88276 0.000 0.900 0.000 0.000 0.100
#> GSM711951 4 0.3663 0.72009 0.000 0.016 0.000 0.776 0.208
#> GSM711957 1 0.2446 0.60124 0.900 0.000 0.000 0.056 0.044
#> GSM711959 2 0.2074 0.88182 0.000 0.896 0.000 0.000 0.104
#> GSM711961 2 0.0000 0.89308 0.000 1.000 0.000 0.000 0.000
#> GSM711965 4 0.6308 0.22825 0.004 0.000 0.308 0.528 0.160
#> GSM711967 1 0.3300 0.41868 0.792 0.000 0.000 0.004 0.204
#> GSM711969 2 0.3455 0.83940 0.000 0.784 0.000 0.008 0.208
#> GSM711973 4 0.6220 0.61731 0.068 0.000 0.112 0.656 0.164
#> GSM711977 3 0.3449 0.85454 0.000 0.000 0.812 0.024 0.164
#> GSM711981 4 0.0566 0.84872 0.004 0.000 0.000 0.984 0.012
#> GSM711987 2 0.0000 0.89308 0.000 1.000 0.000 0.000 0.000
#> GSM711905 2 0.0000 0.89308 0.000 1.000 0.000 0.000 0.000
#> GSM711907 2 0.5958 0.61804 0.000 0.592 0.000 0.200 0.208
#> GSM711909 3 0.0290 0.90377 0.000 0.000 0.992 0.000 0.008
#> GSM711911 3 0.1282 0.90327 0.000 0.000 0.952 0.004 0.044
#> GSM711915 3 0.2969 0.86722 0.000 0.000 0.852 0.020 0.128
#> GSM711917 2 0.3421 0.84162 0.000 0.788 0.000 0.008 0.204
#> GSM711923 4 0.1403 0.84946 0.024 0.000 0.000 0.952 0.024
#> GSM711925 2 0.0000 0.89308 0.000 1.000 0.000 0.000 0.000
#> GSM711927 3 0.0290 0.90377 0.000 0.000 0.992 0.000 0.008
#> GSM711929 2 0.0000 0.89308 0.000 1.000 0.000 0.000 0.000
#> GSM711931 4 0.6487 0.07059 0.000 0.316 0.000 0.476 0.208
#> GSM711933 1 0.1168 0.64431 0.960 0.000 0.000 0.008 0.032
#> GSM711935 2 0.0000 0.89308 0.000 1.000 0.000 0.000 0.000
#> GSM711941 4 0.1668 0.84606 0.028 0.000 0.000 0.940 0.032
#> GSM711943 4 0.0992 0.85296 0.024 0.000 0.000 0.968 0.008
#> GSM711945 4 0.1502 0.83846 0.000 0.000 0.004 0.940 0.056
#> GSM711947 3 0.4806 0.75922 0.000 0.092 0.776 0.056 0.076
#> GSM711949 2 0.0000 0.89308 0.000 1.000 0.000 0.000 0.000
#> GSM711953 2 0.0000 0.89308 0.000 1.000 0.000 0.000 0.000
#> GSM711955 1 0.5009 0.33469 0.652 0.000 0.000 0.288 0.060
#> GSM711963 2 0.0000 0.89308 0.000 1.000 0.000 0.000 0.000
#> GSM711971 3 0.1282 0.90327 0.000 0.000 0.952 0.004 0.044
#> GSM711975 2 0.6584 0.17817 0.000 0.412 0.000 0.380 0.208
#> GSM711979 4 0.0794 0.85250 0.028 0.000 0.000 0.972 0.000
#> GSM711989 2 0.4161 0.81668 0.000 0.752 0.000 0.040 0.208
#> GSM711991 3 0.3995 0.73067 0.000 0.000 0.776 0.180 0.044
#> GSM711993 4 0.2293 0.82341 0.016 0.000 0.000 0.900 0.084
#> GSM711983 3 0.1357 0.90284 0.000 0.000 0.948 0.004 0.048
#> GSM711985 2 0.1732 0.88698 0.000 0.920 0.000 0.000 0.080
#> GSM711913 3 0.3449 0.85454 0.000 0.000 0.812 0.024 0.164
#> GSM711919 3 0.0290 0.90377 0.000 0.000 0.992 0.000 0.008
#> GSM711921 3 0.0290 0.90377 0.000 0.000 0.992 0.000 0.008
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM711936 2 0.3807 0.4461 0.000 0.628 0.000 0.004 0.368 0.000
#> GSM711938 2 0.0632 0.7797 0.024 0.976 0.000 0.000 0.000 0.000
#> GSM711950 4 0.4333 0.3218 0.376 0.000 0.000 0.596 0.028 0.000
#> GSM711956 1 0.4606 0.6207 0.656 0.000 0.000 0.000 0.076 0.268
#> GSM711958 1 0.5012 0.6119 0.576 0.000 0.000 0.000 0.088 0.336
#> GSM711960 1 0.5701 0.5884 0.612 0.000 0.060 0.000 0.084 0.244
#> GSM711964 6 0.5187 -0.1555 0.440 0.000 0.000 0.000 0.088 0.472
#> GSM711966 6 0.0291 0.6835 0.004 0.000 0.000 0.000 0.004 0.992
#> GSM711968 1 0.5030 0.5189 0.588 0.000 0.000 0.000 0.096 0.316
#> GSM711972 6 0.0291 0.6835 0.004 0.000 0.000 0.000 0.004 0.992
#> GSM711976 1 0.5392 0.6401 0.676 0.000 0.000 0.116 0.060 0.148
#> GSM711980 1 0.3189 0.6996 0.760 0.000 0.000 0.000 0.004 0.236
#> GSM711986 6 0.4204 0.6136 0.132 0.000 0.000 0.000 0.128 0.740
#> GSM711904 1 0.5217 0.3243 0.512 0.000 0.000 0.000 0.096 0.392
#> GSM711906 6 0.0603 0.6810 0.004 0.000 0.000 0.000 0.016 0.980
#> GSM711908 6 0.1908 0.6756 0.028 0.000 0.000 0.000 0.056 0.916
#> GSM711910 3 0.0291 0.8343 0.004 0.000 0.992 0.000 0.004 0.000
#> GSM711914 6 0.5226 -0.1836 0.444 0.000 0.000 0.000 0.092 0.464
#> GSM711916 6 0.0146 0.6850 0.000 0.000 0.000 0.000 0.004 0.996
#> GSM711922 1 0.4059 0.6792 0.720 0.000 0.000 0.000 0.052 0.228
#> GSM711924 1 0.5260 0.4407 0.464 0.000 0.000 0.000 0.096 0.440
#> GSM711926 4 0.2389 0.6087 0.008 0.000 0.000 0.864 0.128 0.000
#> GSM711928 1 0.5112 0.3855 0.536 0.000 0.000 0.000 0.088 0.376
#> GSM711930 6 0.0458 0.6838 0.000 0.000 0.000 0.000 0.016 0.984
#> GSM711932 1 0.4678 0.6979 0.712 0.000 0.000 0.048 0.040 0.200
#> GSM711934 1 0.3617 0.7001 0.736 0.000 0.000 0.000 0.020 0.244
#> GSM711940 1 0.5816 0.5288 0.576 0.000 0.000 0.200 0.020 0.204
#> GSM711942 1 0.5260 0.4407 0.464 0.000 0.000 0.000 0.096 0.440
#> GSM711944 3 0.6109 0.3991 0.324 0.000 0.500 0.028 0.148 0.000
#> GSM711946 4 0.1334 0.7001 0.020 0.000 0.000 0.948 0.032 0.000
#> GSM711948 1 0.5093 0.4993 0.656 0.000 0.000 0.248 0.040 0.056
#> GSM711952 6 0.4204 0.6136 0.132 0.000 0.000 0.000 0.128 0.740
#> GSM711954 1 0.4050 0.6747 0.716 0.000 0.000 0.000 0.048 0.236
#> GSM711962 6 0.4949 -0.2643 0.380 0.000 0.000 0.000 0.072 0.548
#> GSM711970 1 0.3974 0.6939 0.728 0.000 0.000 0.000 0.048 0.224
#> GSM711974 1 0.5179 0.5383 0.516 0.000 0.000 0.000 0.092 0.392
#> GSM711978 4 0.1421 0.7025 0.028 0.000 0.000 0.944 0.028 0.000
#> GSM711988 1 0.4293 0.7006 0.728 0.000 0.000 0.036 0.024 0.212
#> GSM711990 3 0.2680 0.8348 0.048 0.000 0.880 0.012 0.060 0.000
#> GSM711992 4 0.1421 0.7025 0.028 0.000 0.000 0.944 0.028 0.000
#> GSM711982 6 0.0291 0.6835 0.004 0.000 0.000 0.000 0.004 0.992
#> GSM711984 2 0.2668 0.7151 0.004 0.828 0.000 0.000 0.168 0.000
#> GSM711912 6 0.4204 0.6136 0.132 0.000 0.000 0.000 0.128 0.740
#> GSM711918 6 0.4204 0.6136 0.132 0.000 0.000 0.000 0.128 0.740
#> GSM711920 1 0.4980 0.6413 0.608 0.000 0.000 0.000 0.100 0.292
#> GSM711937 2 0.3769 0.4750 0.000 0.640 0.000 0.004 0.356 0.000
#> GSM711939 2 0.3333 0.6967 0.024 0.784 0.000 0.000 0.192 0.000
#> GSM711951 4 0.3841 -0.0786 0.000 0.004 0.000 0.616 0.380 0.000
#> GSM711957 1 0.5249 0.6201 0.680 0.000 0.000 0.040 0.152 0.128
#> GSM711959 2 0.3023 0.6784 0.004 0.784 0.000 0.000 0.212 0.000
#> GSM711961 2 0.0858 0.7749 0.028 0.968 0.000 0.000 0.004 0.000
#> GSM711965 4 0.7055 0.1273 0.104 0.000 0.196 0.444 0.256 0.000
#> GSM711967 6 0.5209 -0.2347 0.360 0.000 0.000 0.004 0.088 0.548
#> GSM711969 2 0.3905 0.4701 0.004 0.636 0.000 0.004 0.356 0.000
#> GSM711973 4 0.6708 0.3229 0.188 0.000 0.052 0.472 0.284 0.004
#> GSM711977 3 0.5591 0.7033 0.108 0.000 0.596 0.028 0.268 0.000
#> GSM711981 4 0.1075 0.6925 0.000 0.000 0.000 0.952 0.048 0.000
#> GSM711987 2 0.0000 0.7807 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711905 2 0.0858 0.7749 0.028 0.968 0.000 0.000 0.004 0.000
#> GSM711907 5 0.6100 0.8024 0.000 0.304 0.000 0.312 0.384 0.000
#> GSM711909 3 0.0146 0.8346 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM711911 3 0.2546 0.8354 0.040 0.000 0.888 0.012 0.060 0.000
#> GSM711915 3 0.5187 0.7225 0.092 0.000 0.628 0.016 0.264 0.000
#> GSM711917 2 0.3905 0.4701 0.004 0.636 0.000 0.004 0.356 0.000
#> GSM711923 4 0.1418 0.7058 0.032 0.000 0.000 0.944 0.024 0.000
#> GSM711925 2 0.0000 0.7807 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711927 3 0.0260 0.8348 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM711929 2 0.0858 0.7749 0.028 0.968 0.000 0.000 0.004 0.000
#> GSM711931 4 0.5555 -0.6572 0.000 0.140 0.000 0.480 0.380 0.000
#> GSM711933 1 0.4948 0.6746 0.648 0.000 0.000 0.008 0.092 0.252
#> GSM711935 2 0.0000 0.7807 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711941 4 0.1492 0.7005 0.036 0.000 0.000 0.940 0.024 0.000
#> GSM711943 4 0.0909 0.7080 0.020 0.000 0.000 0.968 0.012 0.000
#> GSM711945 4 0.1984 0.6811 0.032 0.000 0.000 0.912 0.056 0.000
#> GSM711947 3 0.4841 0.6996 0.032 0.032 0.752 0.068 0.116 0.000
#> GSM711949 2 0.0000 0.7807 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711953 2 0.0858 0.7749 0.028 0.968 0.000 0.000 0.004 0.000
#> GSM711955 1 0.5021 0.5089 0.688 0.000 0.004 0.212 0.048 0.048
#> GSM711963 2 0.0000 0.7807 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711971 3 0.2614 0.8353 0.044 0.000 0.884 0.012 0.060 0.000
#> GSM711975 5 0.6026 0.8108 0.000 0.244 0.000 0.376 0.380 0.000
#> GSM711979 4 0.0713 0.7075 0.028 0.000 0.000 0.972 0.000 0.000
#> GSM711989 2 0.4343 0.3314 0.000 0.592 0.000 0.028 0.380 0.000
#> GSM711991 3 0.4614 0.6600 0.028 0.000 0.720 0.188 0.064 0.000
#> GSM711993 4 0.2377 0.6059 0.004 0.004 0.000 0.868 0.124 0.000
#> GSM711983 3 0.2680 0.8348 0.048 0.000 0.880 0.012 0.060 0.000
#> GSM711985 2 0.2362 0.7350 0.004 0.860 0.000 0.000 0.136 0.000
#> GSM711913 3 0.5591 0.7033 0.108 0.000 0.596 0.028 0.268 0.000
#> GSM711919 3 0.0363 0.8346 0.012 0.000 0.988 0.000 0.000 0.000
#> GSM711921 3 0.0291 0.8343 0.004 0.000 0.992 0.000 0.004 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) disease.state(p) individual(p) k
#> CV:kmeans 89 3.70e-05 0.223 0.501 2
#> CV:kmeans 90 1.20e-10 0.312 0.574 3
#> CV:kmeans 87 4.74e-09 0.109 0.315 4
#> CV:kmeans 74 7.56e-07 0.124 0.143 5
#> CV:kmeans 70 9.17e-07 0.177 0.193 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "skmeans"]
# you can also extract it by
# res = res_list["CV:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 27425 rows and 90 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.949 0.980 0.4846 0.515 0.515
#> 3 3 0.945 0.948 0.978 0.3524 0.768 0.574
#> 4 4 0.961 0.915 0.966 0.0906 0.930 0.800
#> 5 5 0.788 0.767 0.826 0.0944 0.898 0.660
#> 6 6 0.766 0.576 0.762 0.0426 0.982 0.913
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 2 3
There is also optional best \(k\) = 2 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM711936 2 0.000 0.972 0.000 1.000
#> GSM711938 2 0.000 0.972 0.000 1.000
#> GSM711950 1 0.000 0.984 1.000 0.000
#> GSM711956 1 0.000 0.984 1.000 0.000
#> GSM711958 1 0.000 0.984 1.000 0.000
#> GSM711960 1 0.000 0.984 1.000 0.000
#> GSM711964 1 0.000 0.984 1.000 0.000
#> GSM711966 1 0.000 0.984 1.000 0.000
#> GSM711968 1 0.000 0.984 1.000 0.000
#> GSM711972 1 0.000 0.984 1.000 0.000
#> GSM711976 1 0.000 0.984 1.000 0.000
#> GSM711980 1 0.000 0.984 1.000 0.000
#> GSM711986 1 0.000 0.984 1.000 0.000
#> GSM711904 1 0.000 0.984 1.000 0.000
#> GSM711906 1 0.000 0.984 1.000 0.000
#> GSM711908 1 0.000 0.984 1.000 0.000
#> GSM711910 1 0.000 0.984 1.000 0.000
#> GSM711914 1 0.000 0.984 1.000 0.000
#> GSM711916 1 0.000 0.984 1.000 0.000
#> GSM711922 1 0.000 0.984 1.000 0.000
#> GSM711924 1 0.000 0.984 1.000 0.000
#> GSM711926 2 0.000 0.972 0.000 1.000
#> GSM711928 1 0.000 0.984 1.000 0.000
#> GSM711930 1 0.000 0.984 1.000 0.000
#> GSM711932 1 0.000 0.984 1.000 0.000
#> GSM711934 1 0.000 0.984 1.000 0.000
#> GSM711940 1 0.000 0.984 1.000 0.000
#> GSM711942 1 0.000 0.984 1.000 0.000
#> GSM711944 1 0.000 0.984 1.000 0.000
#> GSM711946 2 0.991 0.197 0.444 0.556
#> GSM711948 1 0.000 0.984 1.000 0.000
#> GSM711952 1 0.000 0.984 1.000 0.000
#> GSM711954 1 0.000 0.984 1.000 0.000
#> GSM711962 1 0.000 0.984 1.000 0.000
#> GSM711970 1 0.000 0.984 1.000 0.000
#> GSM711974 1 0.000 0.984 1.000 0.000
#> GSM711978 2 0.000 0.972 0.000 1.000
#> GSM711988 1 0.000 0.984 1.000 0.000
#> GSM711990 1 0.000 0.984 1.000 0.000
#> GSM711992 2 0.000 0.972 0.000 1.000
#> GSM711982 1 0.000 0.984 1.000 0.000
#> GSM711984 2 0.000 0.972 0.000 1.000
#> GSM711912 1 0.000 0.984 1.000 0.000
#> GSM711918 1 0.000 0.984 1.000 0.000
#> GSM711920 1 0.000 0.984 1.000 0.000
#> GSM711937 2 0.000 0.972 0.000 1.000
#> GSM711939 2 0.000 0.972 0.000 1.000
#> GSM711951 2 0.000 0.972 0.000 1.000
#> GSM711957 1 0.000 0.984 1.000 0.000
#> GSM711959 2 0.000 0.972 0.000 1.000
#> GSM711961 2 0.000 0.972 0.000 1.000
#> GSM711965 1 0.000 0.984 1.000 0.000
#> GSM711967 1 0.000 0.984 1.000 0.000
#> GSM711969 2 0.000 0.972 0.000 1.000
#> GSM711973 1 0.000 0.984 1.000 0.000
#> GSM711977 2 0.814 0.671 0.252 0.748
#> GSM711981 2 0.000 0.972 0.000 1.000
#> GSM711987 2 0.000 0.972 0.000 1.000
#> GSM711905 2 0.000 0.972 0.000 1.000
#> GSM711907 2 0.000 0.972 0.000 1.000
#> GSM711909 1 0.000 0.984 1.000 0.000
#> GSM711911 1 0.000 0.984 1.000 0.000
#> GSM711915 2 0.311 0.924 0.056 0.944
#> GSM711917 2 0.000 0.972 0.000 1.000
#> GSM711923 1 0.971 0.317 0.600 0.400
#> GSM711925 2 0.000 0.972 0.000 1.000
#> GSM711927 1 0.000 0.984 1.000 0.000
#> GSM711929 2 0.000 0.972 0.000 1.000
#> GSM711931 2 0.000 0.972 0.000 1.000
#> GSM711933 1 0.000 0.984 1.000 0.000
#> GSM711935 2 0.000 0.972 0.000 1.000
#> GSM711941 1 0.204 0.952 0.968 0.032
#> GSM711943 2 0.605 0.819 0.148 0.852
#> GSM711945 2 0.000 0.972 0.000 1.000
#> GSM711947 2 0.000 0.972 0.000 1.000
#> GSM711949 2 0.000 0.972 0.000 1.000
#> GSM711953 2 0.000 0.972 0.000 1.000
#> GSM711955 1 0.000 0.984 1.000 0.000
#> GSM711963 2 0.000 0.972 0.000 1.000
#> GSM711971 1 0.000 0.984 1.000 0.000
#> GSM711975 2 0.000 0.972 0.000 1.000
#> GSM711979 1 0.971 0.317 0.600 0.400
#> GSM711989 2 0.000 0.972 0.000 1.000
#> GSM711991 2 0.000 0.972 0.000 1.000
#> GSM711993 2 0.000 0.972 0.000 1.000
#> GSM711983 1 0.000 0.984 1.000 0.000
#> GSM711985 2 0.000 0.972 0.000 1.000
#> GSM711913 2 0.327 0.920 0.060 0.940
#> GSM711919 1 0.000 0.984 1.000 0.000
#> GSM711921 1 0.000 0.984 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM711936 2 0.000 0.993 0.000 1.000 0.000
#> GSM711938 2 0.000 0.993 0.000 1.000 0.000
#> GSM711950 1 0.000 0.982 1.000 0.000 0.000
#> GSM711956 1 0.000 0.982 1.000 0.000 0.000
#> GSM711958 1 0.000 0.982 1.000 0.000 0.000
#> GSM711960 1 0.465 0.716 0.792 0.000 0.208
#> GSM711964 1 0.000 0.982 1.000 0.000 0.000
#> GSM711966 1 0.000 0.982 1.000 0.000 0.000
#> GSM711968 1 0.000 0.982 1.000 0.000 0.000
#> GSM711972 1 0.000 0.982 1.000 0.000 0.000
#> GSM711976 1 0.000 0.982 1.000 0.000 0.000
#> GSM711980 1 0.000 0.982 1.000 0.000 0.000
#> GSM711986 1 0.000 0.982 1.000 0.000 0.000
#> GSM711904 1 0.000 0.982 1.000 0.000 0.000
#> GSM711906 1 0.000 0.982 1.000 0.000 0.000
#> GSM711908 1 0.000 0.982 1.000 0.000 0.000
#> GSM711910 3 0.000 0.942 0.000 0.000 1.000
#> GSM711914 1 0.000 0.982 1.000 0.000 0.000
#> GSM711916 1 0.000 0.982 1.000 0.000 0.000
#> GSM711922 1 0.000 0.982 1.000 0.000 0.000
#> GSM711924 1 0.000 0.982 1.000 0.000 0.000
#> GSM711926 2 0.000 0.993 0.000 1.000 0.000
#> GSM711928 1 0.000 0.982 1.000 0.000 0.000
#> GSM711930 1 0.000 0.982 1.000 0.000 0.000
#> GSM711932 1 0.000 0.982 1.000 0.000 0.000
#> GSM711934 1 0.000 0.982 1.000 0.000 0.000
#> GSM711940 1 0.000 0.982 1.000 0.000 0.000
#> GSM711942 1 0.000 0.982 1.000 0.000 0.000
#> GSM711944 3 0.000 0.942 0.000 0.000 1.000
#> GSM711946 3 0.000 0.942 0.000 0.000 1.000
#> GSM711948 1 0.000 0.982 1.000 0.000 0.000
#> GSM711952 1 0.000 0.982 1.000 0.000 0.000
#> GSM711954 1 0.000 0.982 1.000 0.000 0.000
#> GSM711962 1 0.000 0.982 1.000 0.000 0.000
#> GSM711970 1 0.000 0.982 1.000 0.000 0.000
#> GSM711974 1 0.000 0.982 1.000 0.000 0.000
#> GSM711978 2 0.000 0.993 0.000 1.000 0.000
#> GSM711988 1 0.000 0.982 1.000 0.000 0.000
#> GSM711990 3 0.000 0.942 0.000 0.000 1.000
#> GSM711992 2 0.394 0.794 0.156 0.844 0.000
#> GSM711982 1 0.000 0.982 1.000 0.000 0.000
#> GSM711984 2 0.000 0.993 0.000 1.000 0.000
#> GSM711912 1 0.000 0.982 1.000 0.000 0.000
#> GSM711918 1 0.000 0.982 1.000 0.000 0.000
#> GSM711920 1 0.000 0.982 1.000 0.000 0.000
#> GSM711937 2 0.000 0.993 0.000 1.000 0.000
#> GSM711939 2 0.000 0.993 0.000 1.000 0.000
#> GSM711951 2 0.000 0.993 0.000 1.000 0.000
#> GSM711957 1 0.000 0.982 1.000 0.000 0.000
#> GSM711959 2 0.000 0.993 0.000 1.000 0.000
#> GSM711961 2 0.000 0.993 0.000 1.000 0.000
#> GSM711965 3 0.000 0.942 0.000 0.000 1.000
#> GSM711967 1 0.000 0.982 1.000 0.000 0.000
#> GSM711969 2 0.000 0.993 0.000 1.000 0.000
#> GSM711973 3 0.000 0.942 0.000 0.000 1.000
#> GSM711977 3 0.000 0.942 0.000 0.000 1.000
#> GSM711981 2 0.000 0.993 0.000 1.000 0.000
#> GSM711987 2 0.000 0.993 0.000 1.000 0.000
#> GSM711905 2 0.000 0.993 0.000 1.000 0.000
#> GSM711907 2 0.000 0.993 0.000 1.000 0.000
#> GSM711909 3 0.000 0.942 0.000 0.000 1.000
#> GSM711911 3 0.000 0.942 0.000 0.000 1.000
#> GSM711915 3 0.000 0.942 0.000 0.000 1.000
#> GSM711917 2 0.000 0.993 0.000 1.000 0.000
#> GSM711923 3 0.435 0.791 0.000 0.184 0.816
#> GSM711925 2 0.000 0.993 0.000 1.000 0.000
#> GSM711927 3 0.000 0.942 0.000 0.000 1.000
#> GSM711929 2 0.000 0.993 0.000 1.000 0.000
#> GSM711931 2 0.000 0.993 0.000 1.000 0.000
#> GSM711933 1 0.000 0.982 1.000 0.000 0.000
#> GSM711935 2 0.000 0.993 0.000 1.000 0.000
#> GSM711941 3 0.000 0.942 0.000 0.000 1.000
#> GSM711943 3 0.455 0.773 0.000 0.200 0.800
#> GSM711945 3 0.455 0.773 0.000 0.200 0.800
#> GSM711947 3 0.460 0.768 0.000 0.204 0.796
#> GSM711949 2 0.000 0.993 0.000 1.000 0.000
#> GSM711953 2 0.000 0.993 0.000 1.000 0.000
#> GSM711955 3 0.610 0.365 0.392 0.000 0.608
#> GSM711963 2 0.000 0.993 0.000 1.000 0.000
#> GSM711971 3 0.000 0.942 0.000 0.000 1.000
#> GSM711975 2 0.000 0.993 0.000 1.000 0.000
#> GSM711979 1 0.800 0.306 0.568 0.360 0.072
#> GSM711989 2 0.000 0.993 0.000 1.000 0.000
#> GSM711991 3 0.153 0.916 0.000 0.040 0.960
#> GSM711993 2 0.000 0.993 0.000 1.000 0.000
#> GSM711983 3 0.000 0.942 0.000 0.000 1.000
#> GSM711985 2 0.000 0.993 0.000 1.000 0.000
#> GSM711913 3 0.000 0.942 0.000 0.000 1.000
#> GSM711919 3 0.000 0.942 0.000 0.000 1.000
#> GSM711921 3 0.000 0.942 0.000 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM711936 2 0.0000 0.993 0.000 1.000 0.000 0.000
#> GSM711938 2 0.0000 0.993 0.000 1.000 0.000 0.000
#> GSM711950 4 0.3907 0.646 0.232 0.000 0.000 0.768
#> GSM711956 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM711958 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM711960 1 0.4382 0.557 0.704 0.000 0.296 0.000
#> GSM711964 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM711966 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM711968 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM711972 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM711976 1 0.0188 0.973 0.996 0.000 0.000 0.004
#> GSM711980 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM711986 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM711904 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM711906 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM711908 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM711910 3 0.0000 0.895 0.000 0.000 1.000 0.000
#> GSM711914 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM711916 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM711922 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM711924 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM711926 4 0.2281 0.854 0.000 0.096 0.000 0.904
#> GSM711928 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM711930 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM711932 1 0.0469 0.966 0.988 0.000 0.000 0.012
#> GSM711934 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM711940 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM711942 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM711944 3 0.0000 0.895 0.000 0.000 1.000 0.000
#> GSM711946 3 0.4967 0.293 0.000 0.000 0.548 0.452
#> GSM711948 1 0.4985 0.104 0.532 0.000 0.000 0.468
#> GSM711952 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM711954 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM711962 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM711970 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM711974 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM711978 4 0.0000 0.945 0.000 0.000 0.000 1.000
#> GSM711988 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM711990 3 0.0000 0.895 0.000 0.000 1.000 0.000
#> GSM711992 4 0.0336 0.942 0.000 0.008 0.000 0.992
#> GSM711982 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM711984 2 0.0000 0.993 0.000 1.000 0.000 0.000
#> GSM711912 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM711918 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM711920 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM711937 2 0.0000 0.993 0.000 1.000 0.000 0.000
#> GSM711939 2 0.0000 0.993 0.000 1.000 0.000 0.000
#> GSM711951 2 0.2973 0.824 0.000 0.856 0.000 0.144
#> GSM711957 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM711959 2 0.0000 0.993 0.000 1.000 0.000 0.000
#> GSM711961 2 0.0000 0.993 0.000 1.000 0.000 0.000
#> GSM711965 3 0.0336 0.890 0.000 0.000 0.992 0.008
#> GSM711967 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM711969 2 0.0000 0.993 0.000 1.000 0.000 0.000
#> GSM711973 3 0.2216 0.828 0.000 0.000 0.908 0.092
#> GSM711977 3 0.0000 0.895 0.000 0.000 1.000 0.000
#> GSM711981 4 0.0000 0.945 0.000 0.000 0.000 1.000
#> GSM711987 2 0.0000 0.993 0.000 1.000 0.000 0.000
#> GSM711905 2 0.0000 0.993 0.000 1.000 0.000 0.000
#> GSM711907 2 0.0000 0.993 0.000 1.000 0.000 0.000
#> GSM711909 3 0.0000 0.895 0.000 0.000 1.000 0.000
#> GSM711911 3 0.0000 0.895 0.000 0.000 1.000 0.000
#> GSM711915 3 0.0000 0.895 0.000 0.000 1.000 0.000
#> GSM711917 2 0.0000 0.993 0.000 1.000 0.000 0.000
#> GSM711923 4 0.0000 0.945 0.000 0.000 0.000 1.000
#> GSM711925 2 0.0000 0.993 0.000 1.000 0.000 0.000
#> GSM711927 3 0.0000 0.895 0.000 0.000 1.000 0.000
#> GSM711929 2 0.0000 0.993 0.000 1.000 0.000 0.000
#> GSM711931 2 0.0000 0.993 0.000 1.000 0.000 0.000
#> GSM711933 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM711935 2 0.0000 0.993 0.000 1.000 0.000 0.000
#> GSM711941 4 0.0000 0.945 0.000 0.000 0.000 1.000
#> GSM711943 4 0.0188 0.943 0.000 0.000 0.004 0.996
#> GSM711945 3 0.4972 0.283 0.000 0.000 0.544 0.456
#> GSM711947 3 0.4331 0.588 0.000 0.288 0.712 0.000
#> GSM711949 2 0.0000 0.993 0.000 1.000 0.000 0.000
#> GSM711953 2 0.0000 0.993 0.000 1.000 0.000 0.000
#> GSM711955 3 0.4973 0.432 0.348 0.000 0.644 0.008
#> GSM711963 2 0.0000 0.993 0.000 1.000 0.000 0.000
#> GSM711971 3 0.0000 0.895 0.000 0.000 1.000 0.000
#> GSM711975 2 0.0000 0.993 0.000 1.000 0.000 0.000
#> GSM711979 4 0.0000 0.945 0.000 0.000 0.000 1.000
#> GSM711989 2 0.0000 0.993 0.000 1.000 0.000 0.000
#> GSM711991 3 0.2988 0.807 0.000 0.012 0.876 0.112
#> GSM711993 4 0.0336 0.942 0.000 0.008 0.000 0.992
#> GSM711983 3 0.0000 0.895 0.000 0.000 1.000 0.000
#> GSM711985 2 0.0000 0.993 0.000 1.000 0.000 0.000
#> GSM711913 3 0.0000 0.895 0.000 0.000 1.000 0.000
#> GSM711919 3 0.0000 0.895 0.000 0.000 1.000 0.000
#> GSM711921 3 0.0000 0.895 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM711936 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000
#> GSM711938 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000
#> GSM711950 1 0.5426 0.430 0.640 0.000 0.000 0.108 0.252
#> GSM711956 1 0.1732 0.685 0.920 0.000 0.000 0.000 0.080
#> GSM711958 1 0.3876 0.177 0.684 0.000 0.000 0.000 0.316
#> GSM711960 1 0.6661 0.162 0.440 0.000 0.256 0.000 0.304
#> GSM711964 1 0.3143 0.548 0.796 0.000 0.000 0.000 0.204
#> GSM711966 5 0.3730 0.845 0.288 0.000 0.000 0.000 0.712
#> GSM711968 1 0.2471 0.643 0.864 0.000 0.000 0.000 0.136
#> GSM711972 5 0.3730 0.845 0.288 0.000 0.000 0.000 0.712
#> GSM711976 1 0.2424 0.669 0.868 0.000 0.000 0.000 0.132
#> GSM711980 1 0.1341 0.693 0.944 0.000 0.000 0.000 0.056
#> GSM711986 5 0.4283 0.665 0.456 0.000 0.000 0.000 0.544
#> GSM711904 1 0.2648 0.617 0.848 0.000 0.000 0.000 0.152
#> GSM711906 5 0.3707 0.843 0.284 0.000 0.000 0.000 0.716
#> GSM711908 5 0.3857 0.838 0.312 0.000 0.000 0.000 0.688
#> GSM711910 3 0.0000 0.852 0.000 0.000 1.000 0.000 0.000
#> GSM711914 1 0.3039 0.566 0.808 0.000 0.000 0.000 0.192
#> GSM711916 5 0.3816 0.841 0.304 0.000 0.000 0.000 0.696
#> GSM711922 1 0.1544 0.691 0.932 0.000 0.000 0.000 0.068
#> GSM711924 5 0.4307 0.556 0.496 0.000 0.000 0.000 0.504
#> GSM711926 4 0.1124 0.910 0.000 0.036 0.000 0.960 0.004
#> GSM711928 1 0.2471 0.635 0.864 0.000 0.000 0.000 0.136
#> GSM711930 5 0.3796 0.842 0.300 0.000 0.000 0.000 0.700
#> GSM711932 1 0.1608 0.680 0.928 0.000 0.000 0.000 0.072
#> GSM711934 1 0.1121 0.688 0.956 0.000 0.000 0.000 0.044
#> GSM711940 5 0.4321 0.722 0.396 0.000 0.000 0.004 0.600
#> GSM711942 5 0.4300 0.614 0.476 0.000 0.000 0.000 0.524
#> GSM711944 3 0.2390 0.784 0.084 0.000 0.896 0.000 0.020
#> GSM711946 3 0.6628 0.130 0.000 0.000 0.408 0.372 0.220
#> GSM711948 1 0.4479 0.488 0.700 0.000 0.000 0.036 0.264
#> GSM711952 5 0.4256 0.704 0.436 0.000 0.000 0.000 0.564
#> GSM711954 1 0.2179 0.662 0.888 0.000 0.000 0.000 0.112
#> GSM711962 5 0.4015 0.790 0.348 0.000 0.000 0.000 0.652
#> GSM711970 1 0.1410 0.688 0.940 0.000 0.000 0.000 0.060
#> GSM711974 1 0.4030 0.060 0.648 0.000 0.000 0.000 0.352
#> GSM711978 4 0.0162 0.935 0.000 0.000 0.000 0.996 0.004
#> GSM711988 1 0.1410 0.680 0.940 0.000 0.000 0.000 0.060
#> GSM711990 3 0.0000 0.852 0.000 0.000 1.000 0.000 0.000
#> GSM711992 4 0.0566 0.929 0.012 0.000 0.000 0.984 0.004
#> GSM711982 5 0.3730 0.845 0.288 0.000 0.000 0.000 0.712
#> GSM711984 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000
#> GSM711912 5 0.4182 0.762 0.400 0.000 0.000 0.000 0.600
#> GSM711918 5 0.4219 0.740 0.416 0.000 0.000 0.000 0.584
#> GSM711920 1 0.3774 0.215 0.704 0.000 0.000 0.000 0.296
#> GSM711937 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000
#> GSM711939 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000
#> GSM711951 2 0.2377 0.843 0.000 0.872 0.000 0.128 0.000
#> GSM711957 1 0.1568 0.684 0.944 0.000 0.000 0.020 0.036
#> GSM711959 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000
#> GSM711961 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000
#> GSM711965 3 0.3521 0.749 0.000 0.000 0.764 0.004 0.232
#> GSM711967 5 0.3999 0.805 0.344 0.000 0.000 0.000 0.656
#> GSM711969 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000
#> GSM711973 3 0.4090 0.714 0.000 0.000 0.716 0.016 0.268
#> GSM711977 3 0.3177 0.767 0.000 0.000 0.792 0.000 0.208
#> GSM711981 4 0.2891 0.857 0.000 0.000 0.000 0.824 0.176
#> GSM711987 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000
#> GSM711905 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000
#> GSM711907 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000
#> GSM711909 3 0.0000 0.852 0.000 0.000 1.000 0.000 0.000
#> GSM711911 3 0.0000 0.852 0.000 0.000 1.000 0.000 0.000
#> GSM711915 3 0.0880 0.845 0.000 0.000 0.968 0.000 0.032
#> GSM711917 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000
#> GSM711923 4 0.2074 0.900 0.000 0.000 0.000 0.896 0.104
#> GSM711925 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000
#> GSM711927 3 0.0000 0.852 0.000 0.000 1.000 0.000 0.000
#> GSM711929 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000
#> GSM711931 2 0.3366 0.712 0.000 0.768 0.000 0.232 0.000
#> GSM711933 1 0.2280 0.632 0.880 0.000 0.000 0.000 0.120
#> GSM711935 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000
#> GSM711941 4 0.3210 0.829 0.000 0.000 0.000 0.788 0.212
#> GSM711943 4 0.0290 0.935 0.000 0.000 0.000 0.992 0.008
#> GSM711945 3 0.6655 0.128 0.000 0.000 0.404 0.368 0.228
#> GSM711947 3 0.3612 0.580 0.000 0.268 0.732 0.000 0.000
#> GSM711949 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000
#> GSM711953 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000
#> GSM711955 1 0.5578 0.443 0.644 0.000 0.176 0.000 0.180
#> GSM711963 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000
#> GSM711971 3 0.0000 0.852 0.000 0.000 1.000 0.000 0.000
#> GSM711975 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000
#> GSM711979 4 0.0000 0.936 0.000 0.000 0.000 1.000 0.000
#> GSM711989 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000
#> GSM711991 3 0.2623 0.791 0.000 0.016 0.884 0.096 0.004
#> GSM711993 4 0.0000 0.936 0.000 0.000 0.000 1.000 0.000
#> GSM711983 3 0.0000 0.852 0.000 0.000 1.000 0.000 0.000
#> GSM711985 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000
#> GSM711913 3 0.3177 0.767 0.000 0.000 0.792 0.000 0.208
#> GSM711919 3 0.0000 0.852 0.000 0.000 1.000 0.000 0.000
#> GSM711921 3 0.0000 0.852 0.000 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM711936 2 0.0000 0.97486 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711938 2 0.0000 0.97486 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711950 1 0.6331 0.35300 0.516 0.000 0.208 0.028 0.244 0.004
#> GSM711956 1 0.3420 0.60593 0.748 0.000 0.000 0.000 0.012 0.240
#> GSM711958 1 0.5368 0.05888 0.508 0.000 0.000 0.000 0.116 0.376
#> GSM711960 5 0.6122 0.09383 0.288 0.000 0.012 0.000 0.480 0.220
#> GSM711964 1 0.3890 0.43814 0.596 0.000 0.000 0.000 0.004 0.400
#> GSM711966 6 0.0146 0.71788 0.004 0.000 0.000 0.000 0.000 0.996
#> GSM711968 1 0.3534 0.58124 0.716 0.000 0.000 0.000 0.008 0.276
#> GSM711972 6 0.0146 0.71788 0.004 0.000 0.000 0.000 0.000 0.996
#> GSM711976 1 0.5059 0.57575 0.652 0.000 0.000 0.004 0.168 0.176
#> GSM711980 1 0.2668 0.63117 0.828 0.000 0.000 0.000 0.004 0.168
#> GSM711986 6 0.3634 0.40096 0.296 0.000 0.000 0.000 0.008 0.696
#> GSM711904 1 0.4052 0.48589 0.628 0.000 0.000 0.000 0.016 0.356
#> GSM711906 6 0.1285 0.69932 0.052 0.000 0.000 0.000 0.004 0.944
#> GSM711908 6 0.1398 0.68947 0.052 0.000 0.000 0.000 0.008 0.940
#> GSM711910 3 0.3862 0.24866 0.000 0.000 0.524 0.000 0.476 0.000
#> GSM711914 1 0.4066 0.44817 0.596 0.000 0.000 0.000 0.012 0.392
#> GSM711916 6 0.0363 0.71509 0.012 0.000 0.000 0.000 0.000 0.988
#> GSM711922 1 0.3133 0.61995 0.780 0.000 0.000 0.000 0.008 0.212
#> GSM711924 6 0.5353 0.20849 0.388 0.000 0.000 0.000 0.112 0.500
#> GSM711926 4 0.0858 0.83573 0.000 0.028 0.000 0.968 0.004 0.000
#> GSM711928 1 0.3905 0.54083 0.668 0.000 0.000 0.000 0.016 0.316
#> GSM711930 6 0.0363 0.71509 0.012 0.000 0.000 0.000 0.000 0.988
#> GSM711932 1 0.3834 0.58764 0.780 0.000 0.000 0.004 0.140 0.076
#> GSM711934 1 0.3108 0.61913 0.828 0.000 0.000 0.000 0.044 0.128
#> GSM711940 6 0.4061 0.52307 0.248 0.000 0.000 0.000 0.044 0.708
#> GSM711942 6 0.5250 0.29385 0.352 0.000 0.000 0.000 0.108 0.540
#> GSM711944 5 0.4932 0.01364 0.072 0.000 0.372 0.000 0.556 0.000
#> GSM711946 3 0.5896 -0.02129 0.024 0.000 0.564 0.168 0.244 0.000
#> GSM711948 1 0.5406 0.48583 0.624 0.000 0.104 0.012 0.252 0.008
#> GSM711952 6 0.3608 0.44919 0.272 0.000 0.000 0.000 0.012 0.716
#> GSM711954 1 0.3841 0.58826 0.716 0.000 0.000 0.000 0.028 0.256
#> GSM711962 6 0.3171 0.59753 0.204 0.000 0.000 0.000 0.012 0.784
#> GSM711970 1 0.3190 0.60579 0.820 0.000 0.000 0.000 0.044 0.136
#> GSM711974 1 0.5153 0.09962 0.464 0.000 0.000 0.000 0.084 0.452
#> GSM711978 4 0.0260 0.85213 0.000 0.000 0.000 0.992 0.008 0.000
#> GSM711988 1 0.4338 0.60048 0.732 0.000 0.000 0.004 0.164 0.100
#> GSM711990 3 0.3860 0.24970 0.000 0.000 0.528 0.000 0.472 0.000
#> GSM711992 4 0.0405 0.84912 0.004 0.000 0.000 0.988 0.008 0.000
#> GSM711982 6 0.0146 0.71788 0.004 0.000 0.000 0.000 0.000 0.996
#> GSM711984 2 0.0000 0.97486 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711912 6 0.3468 0.47111 0.264 0.000 0.000 0.000 0.008 0.728
#> GSM711918 6 0.3468 0.47015 0.264 0.000 0.000 0.000 0.008 0.728
#> GSM711920 1 0.5164 0.23512 0.584 0.000 0.000 0.000 0.116 0.300
#> GSM711937 2 0.0000 0.97486 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711939 2 0.0000 0.97486 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711951 2 0.2454 0.80588 0.000 0.840 0.000 0.160 0.000 0.000
#> GSM711957 1 0.3966 0.56732 0.792 0.000 0.000 0.028 0.116 0.064
#> GSM711959 2 0.0000 0.97486 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711961 2 0.0000 0.97486 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711965 3 0.2260 0.25110 0.000 0.000 0.860 0.000 0.140 0.000
#> GSM711967 6 0.3253 0.60585 0.192 0.000 0.000 0.000 0.020 0.788
#> GSM711969 2 0.0000 0.97486 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711973 3 0.2912 0.20037 0.000 0.000 0.784 0.000 0.216 0.000
#> GSM711977 3 0.0000 0.28576 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711981 4 0.4416 0.72516 0.000 0.004 0.212 0.708 0.076 0.000
#> GSM711987 2 0.0000 0.97486 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711905 2 0.0000 0.97486 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711907 2 0.0000 0.97486 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711909 3 0.3862 0.24866 0.000 0.000 0.524 0.000 0.476 0.000
#> GSM711911 3 0.3860 0.24970 0.000 0.000 0.528 0.000 0.472 0.000
#> GSM711915 3 0.2697 0.23041 0.000 0.000 0.812 0.000 0.188 0.000
#> GSM711917 2 0.0000 0.97486 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711923 4 0.4915 0.75953 0.024 0.000 0.092 0.692 0.192 0.000
#> GSM711925 2 0.0000 0.97486 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711927 3 0.3862 0.24866 0.000 0.000 0.524 0.000 0.476 0.000
#> GSM711929 2 0.0000 0.97486 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711931 2 0.3659 0.45348 0.000 0.636 0.000 0.364 0.000 0.000
#> GSM711933 1 0.4449 0.46393 0.712 0.000 0.000 0.000 0.124 0.164
#> GSM711935 2 0.0000 0.97486 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711941 4 0.6263 0.58349 0.028 0.000 0.176 0.480 0.316 0.000
#> GSM711943 4 0.3239 0.81530 0.024 0.000 0.004 0.808 0.164 0.000
#> GSM711945 3 0.5142 -0.00528 0.000 0.000 0.620 0.156 0.224 0.000
#> GSM711947 5 0.6013 0.07587 0.004 0.228 0.304 0.000 0.464 0.000
#> GSM711949 2 0.0000 0.97486 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711953 2 0.0000 0.97486 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711955 1 0.5242 0.34045 0.516 0.000 0.100 0.000 0.384 0.000
#> GSM711963 2 0.0000 0.97486 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711971 3 0.3860 0.24970 0.000 0.000 0.528 0.000 0.472 0.000
#> GSM711975 2 0.0547 0.95850 0.000 0.980 0.000 0.020 0.000 0.000
#> GSM711979 4 0.1049 0.85196 0.008 0.000 0.000 0.960 0.032 0.000
#> GSM711989 2 0.0000 0.97486 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711991 5 0.4818 -0.14983 0.004 0.004 0.388 0.040 0.564 0.000
#> GSM711993 4 0.0405 0.85230 0.000 0.004 0.000 0.988 0.008 0.000
#> GSM711983 3 0.3860 0.24970 0.000 0.000 0.528 0.000 0.472 0.000
#> GSM711985 2 0.0000 0.97486 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711913 3 0.0260 0.28571 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM711919 3 0.3862 0.24866 0.000 0.000 0.524 0.000 0.476 0.000
#> GSM711921 3 0.3862 0.24866 0.000 0.000 0.524 0.000 0.476 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) disease.state(p) individual(p) k
#> CV:skmeans 87 9.67e-07 0.475 0.831 2
#> CV:skmeans 88 1.71e-10 0.166 0.653 3
#> CV:skmeans 86 8.89e-10 0.258 0.304 4
#> CV:skmeans 81 1.85e-08 0.170 0.177 5
#> CV:skmeans 53 4.95e-06 0.398 0.184 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "pam"]
# you can also extract it by
# res = res_list["CV:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 27425 rows and 90 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.931 0.924 0.970 0.4329 0.585 0.585
#> 3 3 0.749 0.851 0.912 0.4943 0.690 0.497
#> 4 4 0.975 0.957 0.981 0.1463 0.911 0.742
#> 5 5 0.858 0.894 0.926 0.0754 0.886 0.600
#> 6 6 0.968 0.911 0.958 0.0213 0.982 0.911
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2 4
There is also optional best \(k\) = 2 4 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM711936 2 0.0000 0.987 0.000 1.000
#> GSM711938 2 0.0000 0.987 0.000 1.000
#> GSM711950 1 0.0000 0.960 1.000 0.000
#> GSM711956 1 0.0000 0.960 1.000 0.000
#> GSM711958 1 0.0000 0.960 1.000 0.000
#> GSM711960 1 0.0000 0.960 1.000 0.000
#> GSM711964 1 0.0000 0.960 1.000 0.000
#> GSM711966 1 0.0000 0.960 1.000 0.000
#> GSM711968 1 0.0000 0.960 1.000 0.000
#> GSM711972 1 0.0000 0.960 1.000 0.000
#> GSM711976 1 0.0000 0.960 1.000 0.000
#> GSM711980 1 0.0000 0.960 1.000 0.000
#> GSM711986 1 0.0000 0.960 1.000 0.000
#> GSM711904 1 0.0000 0.960 1.000 0.000
#> GSM711906 1 0.0000 0.960 1.000 0.000
#> GSM711908 1 0.0000 0.960 1.000 0.000
#> GSM711910 1 0.0000 0.960 1.000 0.000
#> GSM711914 1 0.0000 0.960 1.000 0.000
#> GSM711916 1 0.0000 0.960 1.000 0.000
#> GSM711922 1 0.0000 0.960 1.000 0.000
#> GSM711924 1 0.0000 0.960 1.000 0.000
#> GSM711926 2 0.8813 0.539 0.300 0.700
#> GSM711928 1 0.0000 0.960 1.000 0.000
#> GSM711930 1 0.0000 0.960 1.000 0.000
#> GSM711932 1 0.0000 0.960 1.000 0.000
#> GSM711934 1 0.0000 0.960 1.000 0.000
#> GSM711940 1 0.0000 0.960 1.000 0.000
#> GSM711942 1 0.0000 0.960 1.000 0.000
#> GSM711944 1 0.0000 0.960 1.000 0.000
#> GSM711946 1 0.0000 0.960 1.000 0.000
#> GSM711948 1 0.0000 0.960 1.000 0.000
#> GSM711952 1 0.0000 0.960 1.000 0.000
#> GSM711954 1 0.0000 0.960 1.000 0.000
#> GSM711962 1 0.0000 0.960 1.000 0.000
#> GSM711970 1 0.0000 0.960 1.000 0.000
#> GSM711974 1 0.0000 0.960 1.000 0.000
#> GSM711978 1 0.8555 0.623 0.720 0.280
#> GSM711988 1 0.0000 0.960 1.000 0.000
#> GSM711990 1 0.0000 0.960 1.000 0.000
#> GSM711992 1 0.7950 0.688 0.760 0.240
#> GSM711982 1 0.0000 0.960 1.000 0.000
#> GSM711984 2 0.0000 0.987 0.000 1.000
#> GSM711912 1 0.0000 0.960 1.000 0.000
#> GSM711918 1 0.0000 0.960 1.000 0.000
#> GSM711920 1 0.0000 0.960 1.000 0.000
#> GSM711937 2 0.0000 0.987 0.000 1.000
#> GSM711939 2 0.0000 0.987 0.000 1.000
#> GSM711951 2 0.0000 0.987 0.000 1.000
#> GSM711957 1 0.0000 0.960 1.000 0.000
#> GSM711959 2 0.0000 0.987 0.000 1.000
#> GSM711961 2 0.0000 0.987 0.000 1.000
#> GSM711965 1 0.0000 0.960 1.000 0.000
#> GSM711967 1 0.0000 0.960 1.000 0.000
#> GSM711969 2 0.0000 0.987 0.000 1.000
#> GSM711973 1 0.0000 0.960 1.000 0.000
#> GSM711977 1 0.0000 0.960 1.000 0.000
#> GSM711981 1 0.9909 0.255 0.556 0.444
#> GSM711987 2 0.0000 0.987 0.000 1.000
#> GSM711905 2 0.0000 0.987 0.000 1.000
#> GSM711907 2 0.0000 0.987 0.000 1.000
#> GSM711909 1 0.0000 0.960 1.000 0.000
#> GSM711911 1 0.0000 0.960 1.000 0.000
#> GSM711915 1 0.8713 0.603 0.708 0.292
#> GSM711917 2 0.0000 0.987 0.000 1.000
#> GSM711923 1 0.0000 0.960 1.000 0.000
#> GSM711925 2 0.0000 0.987 0.000 1.000
#> GSM711927 1 0.0000 0.960 1.000 0.000
#> GSM711929 2 0.0000 0.987 0.000 1.000
#> GSM711931 2 0.0000 0.987 0.000 1.000
#> GSM711933 1 0.0000 0.960 1.000 0.000
#> GSM711935 2 0.0000 0.987 0.000 1.000
#> GSM711941 1 0.0000 0.960 1.000 0.000
#> GSM711943 1 0.0376 0.957 0.996 0.004
#> GSM711945 1 0.9977 0.168 0.528 0.472
#> GSM711947 2 0.0000 0.987 0.000 1.000
#> GSM711949 2 0.0000 0.987 0.000 1.000
#> GSM711953 2 0.0000 0.987 0.000 1.000
#> GSM711955 1 0.0000 0.960 1.000 0.000
#> GSM711963 2 0.0000 0.987 0.000 1.000
#> GSM711971 1 0.0000 0.960 1.000 0.000
#> GSM711975 2 0.0000 0.987 0.000 1.000
#> GSM711979 1 0.0000 0.960 1.000 0.000
#> GSM711989 2 0.0000 0.987 0.000 1.000
#> GSM711991 1 0.9988 0.141 0.520 0.480
#> GSM711993 2 0.0000 0.987 0.000 1.000
#> GSM711983 1 0.0000 0.960 1.000 0.000
#> GSM711985 2 0.0000 0.987 0.000 1.000
#> GSM711913 1 0.7453 0.728 0.788 0.212
#> GSM711919 1 0.0000 0.960 1.000 0.000
#> GSM711921 1 0.0000 0.960 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM711936 2 0.0000 0.999 0.000 1.000 0.000
#> GSM711938 2 0.0000 0.999 0.000 1.000 0.000
#> GSM711950 3 0.6095 0.607 0.392 0.000 0.608
#> GSM711956 1 0.0000 0.967 1.000 0.000 0.000
#> GSM711958 1 0.5138 0.527 0.748 0.000 0.252
#> GSM711960 1 0.5327 0.586 0.728 0.000 0.272
#> GSM711964 1 0.0000 0.967 1.000 0.000 0.000
#> GSM711966 1 0.0000 0.967 1.000 0.000 0.000
#> GSM711968 1 0.0000 0.967 1.000 0.000 0.000
#> GSM711972 1 0.0000 0.967 1.000 0.000 0.000
#> GSM711976 1 0.0000 0.967 1.000 0.000 0.000
#> GSM711980 1 0.0000 0.967 1.000 0.000 0.000
#> GSM711986 1 0.0000 0.967 1.000 0.000 0.000
#> GSM711904 1 0.0000 0.967 1.000 0.000 0.000
#> GSM711906 1 0.0000 0.967 1.000 0.000 0.000
#> GSM711908 1 0.0000 0.967 1.000 0.000 0.000
#> GSM711910 3 0.0000 0.790 0.000 0.000 1.000
#> GSM711914 1 0.0000 0.967 1.000 0.000 0.000
#> GSM711916 1 0.0000 0.967 1.000 0.000 0.000
#> GSM711922 1 0.0000 0.967 1.000 0.000 0.000
#> GSM711924 1 0.0000 0.967 1.000 0.000 0.000
#> GSM711926 3 0.7741 0.652 0.324 0.068 0.608
#> GSM711928 1 0.0000 0.967 1.000 0.000 0.000
#> GSM711930 1 0.0000 0.967 1.000 0.000 0.000
#> GSM711932 3 0.6095 0.607 0.392 0.000 0.608
#> GSM711934 1 0.0000 0.967 1.000 0.000 0.000
#> GSM711940 3 0.6095 0.607 0.392 0.000 0.608
#> GSM711942 1 0.0000 0.967 1.000 0.000 0.000
#> GSM711944 3 0.0000 0.790 0.000 0.000 1.000
#> GSM711946 3 0.2711 0.784 0.088 0.000 0.912
#> GSM711948 3 0.6192 0.556 0.420 0.000 0.580
#> GSM711952 1 0.0000 0.967 1.000 0.000 0.000
#> GSM711954 1 0.0000 0.967 1.000 0.000 0.000
#> GSM711962 1 0.0000 0.967 1.000 0.000 0.000
#> GSM711970 1 0.0000 0.967 1.000 0.000 0.000
#> GSM711974 1 0.0000 0.967 1.000 0.000 0.000
#> GSM711978 3 0.7683 0.650 0.328 0.064 0.608
#> GSM711988 1 0.4974 0.568 0.764 0.000 0.236
#> GSM711990 3 0.0000 0.790 0.000 0.000 1.000
#> GSM711992 3 0.6451 0.614 0.384 0.008 0.608
#> GSM711982 1 0.0000 0.967 1.000 0.000 0.000
#> GSM711984 2 0.0000 0.999 0.000 1.000 0.000
#> GSM711912 1 0.0000 0.967 1.000 0.000 0.000
#> GSM711918 1 0.0000 0.967 1.000 0.000 0.000
#> GSM711920 1 0.0000 0.967 1.000 0.000 0.000
#> GSM711937 2 0.0000 0.999 0.000 1.000 0.000
#> GSM711939 2 0.0000 0.999 0.000 1.000 0.000
#> GSM711951 3 0.6095 0.437 0.000 0.392 0.608
#> GSM711957 3 0.6095 0.607 0.392 0.000 0.608
#> GSM711959 2 0.0000 0.999 0.000 1.000 0.000
#> GSM711961 2 0.0000 0.999 0.000 1.000 0.000
#> GSM711965 3 0.0000 0.790 0.000 0.000 1.000
#> GSM711967 3 0.6095 0.607 0.392 0.000 0.608
#> GSM711969 2 0.0000 0.999 0.000 1.000 0.000
#> GSM711973 3 0.5497 0.705 0.292 0.000 0.708
#> GSM711977 3 0.0000 0.790 0.000 0.000 1.000
#> GSM711981 3 0.6018 0.692 0.308 0.008 0.684
#> GSM711987 2 0.0000 0.999 0.000 1.000 0.000
#> GSM711905 2 0.0000 0.999 0.000 1.000 0.000
#> GSM711907 2 0.0424 0.991 0.000 0.992 0.008
#> GSM711909 3 0.0000 0.790 0.000 0.000 1.000
#> GSM711911 3 0.0000 0.790 0.000 0.000 1.000
#> GSM711915 3 0.0000 0.790 0.000 0.000 1.000
#> GSM711917 2 0.0000 0.999 0.000 1.000 0.000
#> GSM711923 3 0.4353 0.771 0.156 0.008 0.836
#> GSM711925 2 0.0000 0.999 0.000 1.000 0.000
#> GSM711927 3 0.0000 0.790 0.000 0.000 1.000
#> GSM711929 2 0.0000 0.999 0.000 1.000 0.000
#> GSM711931 2 0.0237 0.995 0.000 0.996 0.004
#> GSM711933 3 0.6140 0.586 0.404 0.000 0.596
#> GSM711935 2 0.0000 0.999 0.000 1.000 0.000
#> GSM711941 3 0.4399 0.759 0.188 0.000 0.812
#> GSM711943 3 0.4353 0.771 0.156 0.008 0.836
#> GSM711945 3 0.2955 0.786 0.080 0.008 0.912
#> GSM711947 3 0.6291 0.256 0.000 0.468 0.532
#> GSM711949 2 0.0000 0.999 0.000 1.000 0.000
#> GSM711953 2 0.0000 0.999 0.000 1.000 0.000
#> GSM711955 3 0.5327 0.717 0.272 0.000 0.728
#> GSM711963 2 0.0000 0.999 0.000 1.000 0.000
#> GSM711971 3 0.0000 0.790 0.000 0.000 1.000
#> GSM711975 2 0.0000 0.999 0.000 1.000 0.000
#> GSM711979 3 0.6129 0.678 0.324 0.008 0.668
#> GSM711989 2 0.0000 0.999 0.000 1.000 0.000
#> GSM711991 3 0.0237 0.789 0.000 0.004 0.996
#> GSM711993 3 0.7850 0.562 0.076 0.316 0.608
#> GSM711983 3 0.0000 0.790 0.000 0.000 1.000
#> GSM711985 2 0.0000 0.999 0.000 1.000 0.000
#> GSM711913 3 0.0000 0.790 0.000 0.000 1.000
#> GSM711919 3 0.0000 0.790 0.000 0.000 1.000
#> GSM711921 3 0.0000 0.790 0.000 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM711936 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM711938 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM711950 4 0.0188 0.951 0.004 0.000 0.000 0.996
#> GSM711956 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> GSM711958 1 0.4250 0.608 0.724 0.000 0.000 0.276
#> GSM711960 3 0.2760 0.848 0.128 0.000 0.872 0.000
#> GSM711964 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> GSM711966 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> GSM711968 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> GSM711972 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> GSM711976 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> GSM711980 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> GSM711986 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> GSM711904 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> GSM711906 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> GSM711908 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> GSM711910 3 0.0000 0.988 0.000 0.000 1.000 0.000
#> GSM711914 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> GSM711916 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> GSM711922 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> GSM711924 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> GSM711926 4 0.0000 0.952 0.000 0.000 0.000 1.000
#> GSM711928 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> GSM711930 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> GSM711932 4 0.1302 0.918 0.044 0.000 0.000 0.956
#> GSM711934 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> GSM711940 4 0.0188 0.951 0.004 0.000 0.000 0.996
#> GSM711942 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> GSM711944 3 0.0376 0.982 0.004 0.000 0.992 0.004
#> GSM711946 4 0.0000 0.952 0.000 0.000 0.000 1.000
#> GSM711948 4 0.3837 0.720 0.224 0.000 0.000 0.776
#> GSM711952 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> GSM711954 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> GSM711962 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> GSM711970 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> GSM711974 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> GSM711978 4 0.0000 0.952 0.000 0.000 0.000 1.000
#> GSM711988 1 0.4103 0.646 0.744 0.000 0.000 0.256
#> GSM711990 3 0.0000 0.988 0.000 0.000 1.000 0.000
#> GSM711992 4 0.0000 0.952 0.000 0.000 0.000 1.000
#> GSM711982 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> GSM711984 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM711912 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> GSM711918 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> GSM711920 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> GSM711937 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM711939 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM711951 4 0.0000 0.952 0.000 0.000 0.000 1.000
#> GSM711957 4 0.0188 0.951 0.004 0.000 0.000 0.996
#> GSM711959 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM711961 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM711965 4 0.0188 0.950 0.000 0.000 0.004 0.996
#> GSM711967 4 0.0188 0.951 0.004 0.000 0.000 0.996
#> GSM711969 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM711973 4 0.4095 0.774 0.024 0.000 0.172 0.804
#> GSM711977 3 0.0000 0.988 0.000 0.000 1.000 0.000
#> GSM711981 4 0.0000 0.952 0.000 0.000 0.000 1.000
#> GSM711987 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM711905 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM711907 2 0.0469 0.988 0.000 0.988 0.000 0.012
#> GSM711909 3 0.0000 0.988 0.000 0.000 1.000 0.000
#> GSM711911 3 0.0000 0.988 0.000 0.000 1.000 0.000
#> GSM711915 3 0.0000 0.988 0.000 0.000 1.000 0.000
#> GSM711917 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM711923 4 0.0000 0.952 0.000 0.000 0.000 1.000
#> GSM711925 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM711927 3 0.0000 0.988 0.000 0.000 1.000 0.000
#> GSM711929 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM711931 2 0.0336 0.992 0.000 0.992 0.000 0.008
#> GSM711933 4 0.3311 0.785 0.172 0.000 0.000 0.828
#> GSM711935 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM711941 4 0.0000 0.952 0.000 0.000 0.000 1.000
#> GSM711943 4 0.0000 0.952 0.000 0.000 0.000 1.000
#> GSM711945 4 0.0000 0.952 0.000 0.000 0.000 1.000
#> GSM711947 4 0.4564 0.534 0.000 0.328 0.000 0.672
#> GSM711949 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM711953 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM711955 4 0.0376 0.949 0.004 0.000 0.004 0.992
#> GSM711963 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM711971 3 0.0000 0.988 0.000 0.000 1.000 0.000
#> GSM711975 2 0.0188 0.995 0.000 0.996 0.000 0.004
#> GSM711979 4 0.0000 0.952 0.000 0.000 0.000 1.000
#> GSM711989 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM711991 4 0.0000 0.952 0.000 0.000 0.000 1.000
#> GSM711993 4 0.0000 0.952 0.000 0.000 0.000 1.000
#> GSM711983 3 0.0000 0.988 0.000 0.000 1.000 0.000
#> GSM711985 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM711913 3 0.0000 0.988 0.000 0.000 1.000 0.000
#> GSM711919 3 0.0000 0.988 0.000 0.000 1.000 0.000
#> GSM711921 3 0.0000 0.988 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM711936 2 0.0880 0.960 0.000 0.968 0.000 0.032 0.000
#> GSM711938 2 0.0000 0.974 0.000 1.000 0.000 0.000 0.000
#> GSM711950 4 0.2516 0.859 0.000 0.000 0.000 0.860 0.140
#> GSM711956 1 0.0000 0.969 1.000 0.000 0.000 0.000 0.000
#> GSM711958 5 0.2516 0.890 0.140 0.000 0.000 0.000 0.860
#> GSM711960 5 0.2516 0.890 0.140 0.000 0.000 0.000 0.860
#> GSM711964 1 0.0000 0.969 1.000 0.000 0.000 0.000 0.000
#> GSM711966 1 0.0000 0.969 1.000 0.000 0.000 0.000 0.000
#> GSM711968 1 0.0000 0.969 1.000 0.000 0.000 0.000 0.000
#> GSM711972 1 0.0000 0.969 1.000 0.000 0.000 0.000 0.000
#> GSM711976 1 0.1197 0.910 0.952 0.000 0.000 0.048 0.000
#> GSM711980 5 0.2516 0.890 0.140 0.000 0.000 0.000 0.860
#> GSM711986 1 0.0000 0.969 1.000 0.000 0.000 0.000 0.000
#> GSM711904 1 0.0000 0.969 1.000 0.000 0.000 0.000 0.000
#> GSM711906 5 0.2516 0.890 0.140 0.000 0.000 0.000 0.860
#> GSM711908 1 0.0000 0.969 1.000 0.000 0.000 0.000 0.000
#> GSM711910 3 0.0000 0.939 0.000 0.000 1.000 0.000 0.000
#> GSM711914 1 0.0000 0.969 1.000 0.000 0.000 0.000 0.000
#> GSM711916 1 0.0000 0.969 1.000 0.000 0.000 0.000 0.000
#> GSM711922 5 0.4074 0.623 0.364 0.000 0.000 0.000 0.636
#> GSM711924 5 0.2516 0.890 0.140 0.000 0.000 0.000 0.860
#> GSM711926 4 0.0000 0.897 0.000 0.000 0.000 1.000 0.000
#> GSM711928 1 0.0000 0.969 1.000 0.000 0.000 0.000 0.000
#> GSM711930 1 0.0000 0.969 1.000 0.000 0.000 0.000 0.000
#> GSM711932 5 0.2516 0.819 0.000 0.000 0.000 0.140 0.860
#> GSM711934 5 0.4060 0.628 0.360 0.000 0.000 0.000 0.640
#> GSM711940 4 0.2278 0.847 0.060 0.000 0.000 0.908 0.032
#> GSM711942 5 0.2516 0.890 0.140 0.000 0.000 0.000 0.860
#> GSM711944 5 0.0404 0.805 0.000 0.000 0.012 0.000 0.988
#> GSM711946 4 0.2516 0.859 0.000 0.000 0.000 0.860 0.140
#> GSM711948 5 0.3109 0.684 0.200 0.000 0.000 0.000 0.800
#> GSM711952 1 0.0000 0.969 1.000 0.000 0.000 0.000 0.000
#> GSM711954 5 0.3336 0.822 0.228 0.000 0.000 0.000 0.772
#> GSM711962 5 0.2516 0.890 0.140 0.000 0.000 0.000 0.860
#> GSM711970 5 0.2891 0.869 0.176 0.000 0.000 0.000 0.824
#> GSM711974 1 0.4088 0.206 0.632 0.000 0.000 0.000 0.368
#> GSM711978 4 0.0000 0.897 0.000 0.000 0.000 1.000 0.000
#> GSM711988 5 0.3297 0.872 0.084 0.000 0.000 0.068 0.848
#> GSM711990 3 0.2929 0.878 0.000 0.000 0.820 0.000 0.180
#> GSM711992 4 0.0000 0.897 0.000 0.000 0.000 1.000 0.000
#> GSM711982 1 0.0000 0.969 1.000 0.000 0.000 0.000 0.000
#> GSM711984 2 0.0000 0.974 0.000 1.000 0.000 0.000 0.000
#> GSM711912 1 0.0000 0.969 1.000 0.000 0.000 0.000 0.000
#> GSM711918 1 0.0000 0.969 1.000 0.000 0.000 0.000 0.000
#> GSM711920 5 0.3116 0.873 0.076 0.000 0.000 0.064 0.860
#> GSM711937 2 0.0880 0.960 0.000 0.968 0.000 0.032 0.000
#> GSM711939 2 0.0162 0.973 0.000 0.996 0.000 0.004 0.000
#> GSM711951 4 0.0000 0.897 0.000 0.000 0.000 1.000 0.000
#> GSM711957 5 0.2516 0.819 0.000 0.000 0.000 0.140 0.860
#> GSM711959 2 0.0000 0.974 0.000 1.000 0.000 0.000 0.000
#> GSM711961 2 0.0000 0.974 0.000 1.000 0.000 0.000 0.000
#> GSM711965 4 0.3445 0.834 0.000 0.000 0.036 0.824 0.140
#> GSM711967 5 0.2561 0.816 0.000 0.000 0.000 0.144 0.856
#> GSM711969 2 0.0794 0.962 0.000 0.972 0.000 0.028 0.000
#> GSM711973 4 0.5245 0.664 0.000 0.000 0.080 0.640 0.280
#> GSM711977 3 0.2798 0.899 0.000 0.000 0.852 0.008 0.140
#> GSM711981 4 0.0000 0.897 0.000 0.000 0.000 1.000 0.000
#> GSM711987 2 0.0000 0.974 0.000 1.000 0.000 0.000 0.000
#> GSM711905 2 0.0000 0.974 0.000 1.000 0.000 0.000 0.000
#> GSM711907 2 0.2561 0.862 0.000 0.856 0.000 0.144 0.000
#> GSM711909 3 0.0000 0.939 0.000 0.000 1.000 0.000 0.000
#> GSM711911 3 0.0000 0.939 0.000 0.000 1.000 0.000 0.000
#> GSM711915 3 0.2516 0.904 0.000 0.000 0.860 0.000 0.140
#> GSM711917 2 0.0162 0.973 0.000 0.996 0.000 0.004 0.000
#> GSM711923 4 0.0000 0.897 0.000 0.000 0.000 1.000 0.000
#> GSM711925 2 0.0000 0.974 0.000 1.000 0.000 0.000 0.000
#> GSM711927 3 0.0000 0.939 0.000 0.000 1.000 0.000 0.000
#> GSM711929 2 0.0000 0.974 0.000 1.000 0.000 0.000 0.000
#> GSM711931 2 0.2891 0.825 0.000 0.824 0.000 0.176 0.000
#> GSM711933 5 0.2516 0.890 0.140 0.000 0.000 0.000 0.860
#> GSM711935 2 0.0000 0.974 0.000 1.000 0.000 0.000 0.000
#> GSM711941 4 0.2179 0.873 0.000 0.000 0.000 0.888 0.112
#> GSM711943 4 0.0000 0.897 0.000 0.000 0.000 1.000 0.000
#> GSM711945 4 0.2516 0.859 0.000 0.000 0.000 0.860 0.140
#> GSM711947 4 0.6109 0.387 0.000 0.320 0.148 0.532 0.000
#> GSM711949 2 0.0000 0.974 0.000 1.000 0.000 0.000 0.000
#> GSM711953 2 0.0000 0.974 0.000 1.000 0.000 0.000 0.000
#> GSM711955 5 0.0000 0.802 0.000 0.000 0.000 0.000 1.000
#> GSM711963 2 0.0000 0.974 0.000 1.000 0.000 0.000 0.000
#> GSM711971 3 0.0000 0.939 0.000 0.000 1.000 0.000 0.000
#> GSM711975 2 0.1908 0.914 0.000 0.908 0.000 0.092 0.000
#> GSM711979 4 0.0290 0.893 0.000 0.000 0.000 0.992 0.008
#> GSM711989 2 0.0880 0.960 0.000 0.968 0.000 0.032 0.000
#> GSM711991 4 0.2516 0.859 0.000 0.000 0.000 0.860 0.140
#> GSM711993 4 0.0000 0.897 0.000 0.000 0.000 1.000 0.000
#> GSM711983 3 0.2338 0.913 0.000 0.000 0.884 0.004 0.112
#> GSM711985 2 0.0000 0.974 0.000 1.000 0.000 0.000 0.000
#> GSM711913 3 0.2516 0.904 0.000 0.000 0.860 0.000 0.140
#> GSM711919 3 0.0000 0.939 0.000 0.000 1.000 0.000 0.000
#> GSM711921 3 0.0000 0.939 0.000 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM711936 2 0.1807 0.949 0.000 0.920 0.000 0.020 0.060 0.000
#> GSM711938 2 0.0260 0.963 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM711950 4 0.0000 0.970 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM711956 6 0.0000 0.961 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM711958 1 0.0000 0.941 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711960 1 0.0000 0.941 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711964 6 0.0000 0.961 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM711966 6 0.0000 0.961 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM711968 6 0.0000 0.961 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM711972 6 0.0000 0.961 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM711976 6 0.0260 0.953 0.000 0.000 0.000 0.008 0.000 0.992
#> GSM711980 1 0.0000 0.941 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711986 6 0.0000 0.961 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM711904 6 0.0000 0.961 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM711906 1 0.0000 0.941 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711908 6 0.0000 0.961 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM711910 3 0.0000 0.865 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711914 6 0.0000 0.961 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM711916 6 0.0000 0.961 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM711922 1 0.3076 0.690 0.760 0.000 0.000 0.000 0.000 0.240
#> GSM711924 1 0.0000 0.941 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711926 4 0.0000 0.970 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM711928 6 0.0000 0.961 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM711930 6 0.0000 0.961 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM711932 1 0.0000 0.941 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711934 1 0.2941 0.721 0.780 0.000 0.000 0.000 0.000 0.220
#> GSM711940 4 0.1267 0.924 0.060 0.000 0.000 0.940 0.000 0.000
#> GSM711942 1 0.0000 0.941 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711944 1 0.0000 0.941 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711946 4 0.0937 0.960 0.000 0.000 0.000 0.960 0.040 0.000
#> GSM711948 1 0.2793 0.747 0.800 0.000 0.000 0.000 0.000 0.200
#> GSM711952 6 0.0000 0.961 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM711954 1 0.2135 0.825 0.872 0.000 0.000 0.000 0.000 0.128
#> GSM711962 1 0.0000 0.941 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711970 1 0.0865 0.918 0.964 0.000 0.000 0.000 0.000 0.036
#> GSM711974 6 0.3869 -0.102 0.500 0.000 0.000 0.000 0.000 0.500
#> GSM711978 4 0.0000 0.970 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM711988 1 0.0363 0.935 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM711990 3 0.2214 0.763 0.096 0.000 0.888 0.000 0.016 0.000
#> GSM711992 4 0.0000 0.970 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM711982 6 0.0000 0.961 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM711984 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711912 6 0.0000 0.961 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM711918 6 0.0000 0.961 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM711920 1 0.0000 0.941 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711937 2 0.1807 0.949 0.000 0.920 0.000 0.020 0.060 0.000
#> GSM711939 2 0.1267 0.955 0.000 0.940 0.000 0.000 0.060 0.000
#> GSM711951 4 0.1814 0.908 0.000 0.000 0.000 0.900 0.100 0.000
#> GSM711957 1 0.0632 0.926 0.976 0.000 0.000 0.024 0.000 0.000
#> GSM711959 2 0.1267 0.955 0.000 0.940 0.000 0.000 0.060 0.000
#> GSM711961 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711965 4 0.1267 0.948 0.000 0.000 0.000 0.940 0.060 0.000
#> GSM711967 1 0.0937 0.913 0.960 0.000 0.000 0.040 0.000 0.000
#> GSM711969 2 0.1807 0.949 0.000 0.920 0.000 0.020 0.060 0.000
#> GSM711973 5 0.1349 0.907 0.000 0.000 0.004 0.056 0.940 0.000
#> GSM711977 5 0.1387 0.959 0.000 0.000 0.068 0.000 0.932 0.000
#> GSM711981 4 0.1007 0.959 0.000 0.000 0.000 0.956 0.044 0.000
#> GSM711987 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711905 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711907 2 0.2309 0.927 0.000 0.888 0.000 0.028 0.084 0.000
#> GSM711909 3 0.0000 0.865 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711911 3 0.1610 0.806 0.000 0.000 0.916 0.000 0.084 0.000
#> GSM711915 5 0.1267 0.965 0.000 0.000 0.060 0.000 0.940 0.000
#> GSM711917 2 0.1267 0.955 0.000 0.940 0.000 0.000 0.060 0.000
#> GSM711923 4 0.0000 0.970 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM711925 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711927 3 0.0000 0.865 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711929 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711931 2 0.2512 0.919 0.000 0.880 0.000 0.060 0.060 0.000
#> GSM711933 1 0.0000 0.941 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711935 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711941 4 0.0547 0.957 0.020 0.000 0.000 0.980 0.000 0.000
#> GSM711943 4 0.0000 0.970 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM711945 4 0.0937 0.960 0.000 0.000 0.000 0.960 0.040 0.000
#> GSM711947 3 0.5031 0.496 0.000 0.196 0.680 0.024 0.100 0.000
#> GSM711949 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711953 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711955 1 0.0000 0.941 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711963 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711971 3 0.0000 0.865 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711975 2 0.1890 0.947 0.000 0.916 0.000 0.024 0.060 0.000
#> GSM711979 4 0.0260 0.966 0.008 0.000 0.000 0.992 0.000 0.000
#> GSM711989 2 0.1807 0.949 0.000 0.920 0.000 0.020 0.060 0.000
#> GSM711991 4 0.1082 0.959 0.000 0.000 0.004 0.956 0.040 0.000
#> GSM711993 4 0.0000 0.970 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM711983 3 0.3592 0.406 0.000 0.000 0.656 0.344 0.000 0.000
#> GSM711985 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711913 5 0.1267 0.965 0.000 0.000 0.060 0.000 0.940 0.000
#> GSM711919 3 0.0000 0.865 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711921 3 0.0000 0.865 0.000 0.000 1.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) disease.state(p) individual(p) k
#> CV:pam 87 2.74e-05 0.222 0.674 2
#> CV:pam 88 4.99e-11 0.404 0.753 3
#> CV:pam 90 3.70e-10 0.131 0.503 4
#> CV:pam 88 1.23e-08 0.102 0.298 5
#> CV:pam 87 4.00e-08 0.113 0.240 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "mclust"]
# you can also extract it by
# res = res_list["CV:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 27425 rows and 90 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.754 0.804 0.922 0.4445 0.594 0.594
#> 3 3 0.781 0.889 0.941 0.4665 0.713 0.529
#> 4 4 0.917 0.893 0.938 0.0926 0.886 0.690
#> 5 5 0.681 0.641 0.808 0.0748 0.911 0.709
#> 6 6 0.734 0.685 0.792 0.0485 0.884 0.571
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM711936 2 0.0000 0.966 0.000 1.000
#> GSM711938 2 0.0000 0.966 0.000 1.000
#> GSM711950 1 0.0376 0.889 0.996 0.004
#> GSM711956 1 0.0000 0.891 1.000 0.000
#> GSM711958 1 0.0000 0.891 1.000 0.000
#> GSM711960 1 0.0000 0.891 1.000 0.000
#> GSM711964 1 0.0000 0.891 1.000 0.000
#> GSM711966 1 0.0000 0.891 1.000 0.000
#> GSM711968 1 0.0000 0.891 1.000 0.000
#> GSM711972 1 0.0000 0.891 1.000 0.000
#> GSM711976 1 0.0000 0.891 1.000 0.000
#> GSM711980 1 0.0000 0.891 1.000 0.000
#> GSM711986 1 0.0000 0.891 1.000 0.000
#> GSM711904 1 0.0000 0.891 1.000 0.000
#> GSM711906 1 0.0000 0.891 1.000 0.000
#> GSM711908 1 0.0000 0.891 1.000 0.000
#> GSM711910 1 0.9944 0.271 0.544 0.456
#> GSM711914 1 0.0000 0.891 1.000 0.000
#> GSM711916 1 0.0000 0.891 1.000 0.000
#> GSM711922 1 0.0000 0.891 1.000 0.000
#> GSM711924 1 0.0000 0.891 1.000 0.000
#> GSM711926 1 0.2778 0.864 0.952 0.048
#> GSM711928 1 0.0000 0.891 1.000 0.000
#> GSM711930 1 0.0000 0.891 1.000 0.000
#> GSM711932 1 0.0000 0.891 1.000 0.000
#> GSM711934 1 0.0000 0.891 1.000 0.000
#> GSM711940 1 0.0000 0.891 1.000 0.000
#> GSM711942 1 0.0000 0.891 1.000 0.000
#> GSM711944 1 0.0000 0.891 1.000 0.000
#> GSM711946 1 0.3431 0.855 0.936 0.064
#> GSM711948 1 0.0000 0.891 1.000 0.000
#> GSM711952 1 0.0000 0.891 1.000 0.000
#> GSM711954 1 0.0000 0.891 1.000 0.000
#> GSM711962 1 0.0000 0.891 1.000 0.000
#> GSM711970 1 0.0000 0.891 1.000 0.000
#> GSM711974 1 0.0000 0.891 1.000 0.000
#> GSM711978 1 0.2778 0.864 0.952 0.048
#> GSM711988 1 0.0000 0.891 1.000 0.000
#> GSM711990 1 0.9944 0.271 0.544 0.456
#> GSM711992 1 0.2778 0.864 0.952 0.048
#> GSM711982 1 0.0000 0.891 1.000 0.000
#> GSM711984 2 0.0000 0.966 0.000 1.000
#> GSM711912 1 0.0000 0.891 1.000 0.000
#> GSM711918 1 0.0000 0.891 1.000 0.000
#> GSM711920 1 0.0000 0.891 1.000 0.000
#> GSM711937 2 0.0000 0.966 0.000 1.000
#> GSM711939 2 0.0000 0.966 0.000 1.000
#> GSM711951 2 0.0000 0.966 0.000 1.000
#> GSM711957 1 0.0000 0.891 1.000 0.000
#> GSM711959 2 0.0000 0.966 0.000 1.000
#> GSM711961 2 0.0000 0.966 0.000 1.000
#> GSM711965 1 0.1184 0.884 0.984 0.016
#> GSM711967 1 0.0000 0.891 1.000 0.000
#> GSM711969 2 0.0000 0.966 0.000 1.000
#> GSM711973 1 0.0000 0.891 1.000 0.000
#> GSM711977 1 0.1633 0.879 0.976 0.024
#> GSM711981 1 0.9996 0.103 0.512 0.488
#> GSM711987 2 0.0000 0.966 0.000 1.000
#> GSM711905 2 0.0000 0.966 0.000 1.000
#> GSM711907 2 0.0000 0.966 0.000 1.000
#> GSM711909 1 0.9944 0.271 0.544 0.456
#> GSM711911 1 0.9944 0.271 0.544 0.456
#> GSM711915 1 0.9944 0.271 0.544 0.456
#> GSM711917 2 0.0000 0.966 0.000 1.000
#> GSM711923 1 0.2948 0.862 0.948 0.052
#> GSM711925 2 0.0000 0.966 0.000 1.000
#> GSM711927 1 0.9944 0.271 0.544 0.456
#> GSM711929 2 0.0000 0.966 0.000 1.000
#> GSM711931 2 0.0000 0.966 0.000 1.000
#> GSM711933 1 0.0000 0.891 1.000 0.000
#> GSM711935 2 0.0000 0.966 0.000 1.000
#> GSM711941 1 0.2778 0.864 0.952 0.048
#> GSM711943 1 0.2948 0.862 0.948 0.052
#> GSM711945 1 0.8763 0.597 0.704 0.296
#> GSM711947 2 1.0000 -0.205 0.500 0.500
#> GSM711949 2 0.0000 0.966 0.000 1.000
#> GSM711953 2 0.0000 0.966 0.000 1.000
#> GSM711955 1 0.0000 0.891 1.000 0.000
#> GSM711963 2 0.0000 0.966 0.000 1.000
#> GSM711971 1 0.9944 0.271 0.544 0.456
#> GSM711975 2 0.0000 0.966 0.000 1.000
#> GSM711979 1 0.2778 0.864 0.952 0.048
#> GSM711989 2 0.0000 0.966 0.000 1.000
#> GSM711991 1 1.0000 0.159 0.500 0.500
#> GSM711993 2 0.7056 0.715 0.192 0.808
#> GSM711983 1 0.9944 0.271 0.544 0.456
#> GSM711985 2 0.0000 0.966 0.000 1.000
#> GSM711913 1 0.2423 0.869 0.960 0.040
#> GSM711919 1 0.9944 0.271 0.544 0.456
#> GSM711921 1 0.9944 0.271 0.544 0.456
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM711936 2 0.0000 0.9764 0.000 1.000 0.000
#> GSM711938 2 0.0000 0.9764 0.000 1.000 0.000
#> GSM711950 3 0.5465 0.7241 0.288 0.000 0.712
#> GSM711956 1 0.0000 0.9607 1.000 0.000 0.000
#> GSM711958 1 0.0237 0.9591 0.996 0.000 0.004
#> GSM711960 3 0.6308 0.1251 0.492 0.000 0.508
#> GSM711964 1 0.0000 0.9607 1.000 0.000 0.000
#> GSM711966 1 0.0000 0.9607 1.000 0.000 0.000
#> GSM711968 1 0.0000 0.9607 1.000 0.000 0.000
#> GSM711972 1 0.0000 0.9607 1.000 0.000 0.000
#> GSM711976 1 0.0000 0.9607 1.000 0.000 0.000
#> GSM711980 1 0.0000 0.9607 1.000 0.000 0.000
#> GSM711986 1 0.0592 0.9553 0.988 0.000 0.012
#> GSM711904 1 0.0000 0.9607 1.000 0.000 0.000
#> GSM711906 1 0.1753 0.9307 0.952 0.000 0.048
#> GSM711908 1 0.1964 0.9234 0.944 0.000 0.056
#> GSM711910 3 0.0000 0.8700 0.000 0.000 1.000
#> GSM711914 1 0.0000 0.9607 1.000 0.000 0.000
#> GSM711916 1 0.1031 0.9488 0.976 0.000 0.024
#> GSM711922 1 0.0000 0.9607 1.000 0.000 0.000
#> GSM711924 1 0.1643 0.9341 0.956 0.000 0.044
#> GSM711926 3 0.4589 0.8532 0.172 0.008 0.820
#> GSM711928 1 0.0000 0.9607 1.000 0.000 0.000
#> GSM711930 1 0.2165 0.9187 0.936 0.000 0.064
#> GSM711932 1 0.5216 0.5637 0.740 0.000 0.260
#> GSM711934 1 0.0000 0.9607 1.000 0.000 0.000
#> GSM711940 1 0.0000 0.9607 1.000 0.000 0.000
#> GSM711942 1 0.0892 0.9511 0.980 0.000 0.020
#> GSM711944 3 0.2796 0.8564 0.092 0.000 0.908
#> GSM711946 3 0.4178 0.8544 0.172 0.000 0.828
#> GSM711948 1 0.2878 0.8571 0.904 0.000 0.096
#> GSM711952 1 0.0000 0.9607 1.000 0.000 0.000
#> GSM711954 1 0.0000 0.9607 1.000 0.000 0.000
#> GSM711962 1 0.0000 0.9607 1.000 0.000 0.000
#> GSM711970 1 0.0000 0.9607 1.000 0.000 0.000
#> GSM711974 1 0.0000 0.9607 1.000 0.000 0.000
#> GSM711978 3 0.4589 0.8532 0.172 0.008 0.820
#> GSM711988 1 0.0000 0.9607 1.000 0.000 0.000
#> GSM711990 3 0.0000 0.8700 0.000 0.000 1.000
#> GSM711992 3 0.4589 0.8532 0.172 0.008 0.820
#> GSM711982 1 0.0747 0.9533 0.984 0.000 0.016
#> GSM711984 2 0.0000 0.9764 0.000 1.000 0.000
#> GSM711912 1 0.1289 0.9432 0.968 0.000 0.032
#> GSM711918 1 0.1964 0.9234 0.944 0.000 0.056
#> GSM711920 1 0.0000 0.9607 1.000 0.000 0.000
#> GSM711937 2 0.0000 0.9764 0.000 1.000 0.000
#> GSM711939 2 0.0000 0.9764 0.000 1.000 0.000
#> GSM711951 2 0.3619 0.8192 0.000 0.864 0.136
#> GSM711957 3 0.5678 0.6706 0.316 0.000 0.684
#> GSM711959 2 0.0000 0.9764 0.000 1.000 0.000
#> GSM711961 2 0.0000 0.9764 0.000 1.000 0.000
#> GSM711965 3 0.3879 0.8609 0.152 0.000 0.848
#> GSM711967 1 0.0000 0.9607 1.000 0.000 0.000
#> GSM711969 2 0.0000 0.9764 0.000 1.000 0.000
#> GSM711973 3 0.4346 0.8349 0.184 0.000 0.816
#> GSM711977 3 0.0000 0.8700 0.000 0.000 1.000
#> GSM711981 3 0.6380 0.7702 0.076 0.164 0.760
#> GSM711987 2 0.0000 0.9764 0.000 1.000 0.000
#> GSM711905 2 0.0000 0.9764 0.000 1.000 0.000
#> GSM711907 2 0.0000 0.9764 0.000 1.000 0.000
#> GSM711909 3 0.0000 0.8700 0.000 0.000 1.000
#> GSM711911 3 0.0000 0.8700 0.000 0.000 1.000
#> GSM711915 3 0.0000 0.8700 0.000 0.000 1.000
#> GSM711917 2 0.0000 0.9764 0.000 1.000 0.000
#> GSM711923 3 0.4178 0.8544 0.172 0.000 0.828
#> GSM711925 2 0.0000 0.9764 0.000 1.000 0.000
#> GSM711927 3 0.0000 0.8700 0.000 0.000 1.000
#> GSM711929 2 0.0000 0.9764 0.000 1.000 0.000
#> GSM711931 2 0.5785 0.4508 0.000 0.668 0.332
#> GSM711933 1 0.0000 0.9607 1.000 0.000 0.000
#> GSM711935 2 0.0000 0.9764 0.000 1.000 0.000
#> GSM711941 3 0.4178 0.8544 0.172 0.000 0.828
#> GSM711943 3 0.4178 0.8544 0.172 0.000 0.828
#> GSM711945 3 0.4178 0.8544 0.172 0.000 0.828
#> GSM711947 3 0.0000 0.8700 0.000 0.000 1.000
#> GSM711949 2 0.0000 0.9764 0.000 1.000 0.000
#> GSM711953 2 0.0000 0.9764 0.000 1.000 0.000
#> GSM711955 1 0.6215 0.0275 0.572 0.000 0.428
#> GSM711963 2 0.0000 0.9764 0.000 1.000 0.000
#> GSM711971 3 0.0000 0.8700 0.000 0.000 1.000
#> GSM711975 2 0.0000 0.9764 0.000 1.000 0.000
#> GSM711979 3 0.4589 0.8532 0.172 0.008 0.820
#> GSM711989 2 0.0000 0.9764 0.000 1.000 0.000
#> GSM711991 3 0.0424 0.8695 0.008 0.000 0.992
#> GSM711993 3 0.6522 0.6307 0.032 0.272 0.696
#> GSM711983 3 0.0000 0.8700 0.000 0.000 1.000
#> GSM711985 2 0.0000 0.9764 0.000 1.000 0.000
#> GSM711913 3 0.0000 0.8700 0.000 0.000 1.000
#> GSM711919 3 0.0000 0.8700 0.000 0.000 1.000
#> GSM711921 3 0.0000 0.8700 0.000 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM711936 2 0.0000 0.953 0.000 1.000 0.000 0.000
#> GSM711938 2 0.0000 0.953 0.000 1.000 0.000 0.000
#> GSM711950 4 0.2149 0.807 0.088 0.000 0.000 0.912
#> GSM711956 1 0.0336 0.954 0.992 0.000 0.000 0.008
#> GSM711958 1 0.0336 0.953 0.992 0.000 0.000 0.008
#> GSM711960 1 0.0469 0.952 0.988 0.000 0.000 0.012
#> GSM711964 1 0.1389 0.952 0.952 0.000 0.000 0.048
#> GSM711966 1 0.1302 0.953 0.956 0.000 0.000 0.044
#> GSM711968 1 0.1867 0.946 0.928 0.000 0.000 0.072
#> GSM711972 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM711976 1 0.3400 0.839 0.820 0.000 0.000 0.180
#> GSM711980 1 0.2011 0.943 0.920 0.000 0.000 0.080
#> GSM711986 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM711904 1 0.1637 0.949 0.940 0.000 0.000 0.060
#> GSM711906 1 0.0188 0.952 0.996 0.000 0.000 0.004
#> GSM711908 1 0.0188 0.952 0.996 0.000 0.000 0.004
#> GSM711910 3 0.0000 0.928 0.000 0.000 1.000 0.000
#> GSM711914 1 0.1118 0.954 0.964 0.000 0.000 0.036
#> GSM711916 1 0.0188 0.952 0.996 0.000 0.000 0.004
#> GSM711922 1 0.2011 0.943 0.920 0.000 0.000 0.080
#> GSM711924 1 0.0336 0.953 0.992 0.000 0.000 0.008
#> GSM711926 4 0.1863 0.850 0.004 0.040 0.012 0.944
#> GSM711928 1 0.2011 0.943 0.920 0.000 0.000 0.080
#> GSM711930 1 0.0188 0.952 0.996 0.000 0.000 0.004
#> GSM711932 4 0.4746 0.386 0.368 0.000 0.000 0.632
#> GSM711934 1 0.0188 0.952 0.996 0.000 0.000 0.004
#> GSM711940 1 0.2149 0.939 0.912 0.000 0.000 0.088
#> GSM711942 1 0.0188 0.952 0.996 0.000 0.000 0.004
#> GSM711944 1 0.4467 0.726 0.788 0.000 0.040 0.172
#> GSM711946 4 0.1716 0.853 0.000 0.000 0.064 0.936
#> GSM711948 1 0.2402 0.936 0.912 0.000 0.012 0.076
#> GSM711952 1 0.1474 0.951 0.948 0.000 0.000 0.052
#> GSM711954 1 0.2149 0.939 0.912 0.000 0.000 0.088
#> GSM711962 1 0.0707 0.954 0.980 0.000 0.000 0.020
#> GSM711970 1 0.2011 0.943 0.920 0.000 0.000 0.080
#> GSM711974 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM711978 4 0.1863 0.850 0.004 0.040 0.012 0.944
#> GSM711988 1 0.2011 0.943 0.920 0.000 0.000 0.080
#> GSM711990 3 0.4105 0.817 0.032 0.000 0.812 0.156
#> GSM711992 4 0.1863 0.850 0.004 0.040 0.012 0.944
#> GSM711982 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM711984 2 0.0000 0.953 0.000 1.000 0.000 0.000
#> GSM711912 1 0.0188 0.952 0.996 0.000 0.000 0.004
#> GSM711918 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM711920 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM711937 2 0.0000 0.953 0.000 1.000 0.000 0.000
#> GSM711939 2 0.0000 0.953 0.000 1.000 0.000 0.000
#> GSM711951 2 0.0336 0.950 0.000 0.992 0.000 0.008
#> GSM711957 4 0.3577 0.750 0.156 0.000 0.012 0.832
#> GSM711959 2 0.0000 0.953 0.000 1.000 0.000 0.000
#> GSM711961 2 0.0188 0.953 0.000 0.996 0.000 0.004
#> GSM711965 4 0.1716 0.853 0.000 0.000 0.064 0.936
#> GSM711967 1 0.2081 0.941 0.916 0.000 0.000 0.084
#> GSM711969 2 0.0000 0.953 0.000 1.000 0.000 0.000
#> GSM711973 4 0.4237 0.761 0.152 0.000 0.040 0.808
#> GSM711977 4 0.4103 0.646 0.000 0.000 0.256 0.744
#> GSM711981 2 0.5417 0.294 0.000 0.572 0.016 0.412
#> GSM711987 2 0.1118 0.944 0.000 0.964 0.000 0.036
#> GSM711905 2 0.1118 0.944 0.000 0.964 0.000 0.036
#> GSM711907 2 0.0000 0.953 0.000 1.000 0.000 0.000
#> GSM711909 3 0.0000 0.928 0.000 0.000 1.000 0.000
#> GSM711911 3 0.3052 0.848 0.004 0.000 0.860 0.136
#> GSM711915 3 0.0000 0.928 0.000 0.000 1.000 0.000
#> GSM711917 2 0.0000 0.953 0.000 1.000 0.000 0.000
#> GSM711923 4 0.1743 0.856 0.004 0.000 0.056 0.940
#> GSM711925 2 0.1118 0.944 0.000 0.964 0.000 0.036
#> GSM711927 3 0.0000 0.928 0.000 0.000 1.000 0.000
#> GSM711929 2 0.1118 0.944 0.000 0.964 0.000 0.036
#> GSM711931 2 0.0336 0.950 0.000 0.992 0.000 0.008
#> GSM711933 1 0.1978 0.945 0.928 0.000 0.004 0.068
#> GSM711935 2 0.1118 0.944 0.000 0.964 0.000 0.036
#> GSM711941 4 0.1576 0.856 0.004 0.000 0.048 0.948
#> GSM711943 4 0.1824 0.855 0.004 0.000 0.060 0.936
#> GSM711945 4 0.1716 0.853 0.000 0.000 0.064 0.936
#> GSM711947 3 0.0000 0.928 0.000 0.000 1.000 0.000
#> GSM711949 2 0.1118 0.944 0.000 0.964 0.000 0.036
#> GSM711953 2 0.1118 0.944 0.000 0.964 0.000 0.036
#> GSM711955 1 0.2522 0.933 0.908 0.000 0.016 0.076
#> GSM711963 2 0.1118 0.944 0.000 0.964 0.000 0.036
#> GSM711971 3 0.3813 0.831 0.024 0.000 0.828 0.148
#> GSM711975 2 0.0188 0.952 0.000 0.996 0.000 0.004
#> GSM711979 4 0.1771 0.851 0.004 0.036 0.012 0.948
#> GSM711989 2 0.0000 0.953 0.000 1.000 0.000 0.000
#> GSM711991 3 0.0336 0.925 0.000 0.000 0.992 0.008
#> GSM711993 2 0.5093 0.454 0.000 0.640 0.012 0.348
#> GSM711983 3 0.3910 0.823 0.024 0.000 0.820 0.156
#> GSM711985 2 0.0000 0.953 0.000 1.000 0.000 0.000
#> GSM711913 4 0.4877 0.409 0.000 0.000 0.408 0.592
#> GSM711919 3 0.0188 0.926 0.004 0.000 0.996 0.000
#> GSM711921 3 0.0000 0.928 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM711936 2 0.0510 0.9259 0.000 0.984 0.000 0.000 0.016
#> GSM711938 2 0.0671 0.9283 0.000 0.980 0.000 0.004 0.016
#> GSM711950 1 0.6307 -0.3075 0.464 0.000 0.008 0.408 0.120
#> GSM711956 1 0.1608 0.6470 0.928 0.000 0.000 0.000 0.072
#> GSM711958 1 0.3752 0.4382 0.708 0.000 0.000 0.000 0.292
#> GSM711960 1 0.4620 0.2057 0.612 0.000 0.012 0.004 0.372
#> GSM711964 1 0.2605 0.6128 0.852 0.000 0.000 0.000 0.148
#> GSM711966 1 0.3366 0.5239 0.768 0.000 0.000 0.000 0.232
#> GSM711968 1 0.1341 0.6485 0.944 0.000 0.000 0.000 0.056
#> GSM711972 1 0.2813 0.5963 0.832 0.000 0.000 0.000 0.168
#> GSM711976 1 0.2997 0.5218 0.840 0.000 0.000 0.012 0.148
#> GSM711980 1 0.0000 0.6539 1.000 0.000 0.000 0.000 0.000
#> GSM711986 5 0.4210 0.7715 0.412 0.000 0.000 0.000 0.588
#> GSM711904 1 0.4397 -0.3598 0.564 0.000 0.000 0.004 0.432
#> GSM711906 5 0.3774 0.8331 0.296 0.000 0.000 0.000 0.704
#> GSM711908 5 0.3461 0.7890 0.224 0.000 0.000 0.004 0.772
#> GSM711910 3 0.0000 0.8129 0.000 0.000 1.000 0.000 0.000
#> GSM711914 1 0.2074 0.6355 0.896 0.000 0.000 0.000 0.104
#> GSM711916 5 0.3707 0.8286 0.284 0.000 0.000 0.000 0.716
#> GSM711922 1 0.0609 0.6559 0.980 0.000 0.000 0.000 0.020
#> GSM711924 1 0.3730 0.4469 0.712 0.000 0.000 0.000 0.288
#> GSM711926 4 0.7564 0.5354 0.164 0.180 0.004 0.532 0.120
#> GSM711928 1 0.0609 0.6557 0.980 0.000 0.000 0.000 0.020
#> GSM711930 5 0.3461 0.7890 0.224 0.000 0.000 0.004 0.772
#> GSM711932 1 0.3565 0.4915 0.816 0.000 0.000 0.144 0.040
#> GSM711934 1 0.3534 0.4920 0.744 0.000 0.000 0.000 0.256
#> GSM711940 1 0.0324 0.6528 0.992 0.000 0.000 0.004 0.004
#> GSM711942 1 0.3707 0.4500 0.716 0.000 0.000 0.000 0.284
#> GSM711944 1 0.6831 0.1582 0.512 0.000 0.112 0.328 0.048
#> GSM711946 4 0.0566 0.6246 0.004 0.000 0.012 0.984 0.000
#> GSM711948 1 0.5406 0.3634 0.684 0.000 0.012 0.200 0.104
#> GSM711952 5 0.4278 0.7034 0.452 0.000 0.000 0.000 0.548
#> GSM711954 1 0.0771 0.6481 0.976 0.000 0.000 0.004 0.020
#> GSM711962 1 0.3274 0.5373 0.780 0.000 0.000 0.000 0.220
#> GSM711970 1 0.1124 0.6397 0.960 0.000 0.000 0.004 0.036
#> GSM711974 1 0.3752 0.4397 0.708 0.000 0.000 0.000 0.292
#> GSM711978 4 0.5253 0.6256 0.172 0.008 0.000 0.700 0.120
#> GSM711988 1 0.0451 0.6511 0.988 0.000 0.000 0.004 0.008
#> GSM711990 3 0.7050 0.3759 0.164 0.000 0.476 0.324 0.036
#> GSM711992 4 0.5441 0.6242 0.176 0.008 0.004 0.692 0.120
#> GSM711982 1 0.3586 0.4691 0.736 0.000 0.000 0.000 0.264
#> GSM711984 2 0.0000 0.9281 0.000 1.000 0.000 0.000 0.000
#> GSM711912 5 0.4114 0.8117 0.376 0.000 0.000 0.000 0.624
#> GSM711918 5 0.4150 0.8017 0.388 0.000 0.000 0.000 0.612
#> GSM711920 1 0.3452 0.5070 0.756 0.000 0.000 0.000 0.244
#> GSM711937 2 0.0510 0.9259 0.000 0.984 0.000 0.000 0.016
#> GSM711939 2 0.0290 0.9273 0.000 0.992 0.000 0.000 0.008
#> GSM711951 2 0.2777 0.8491 0.000 0.864 0.000 0.120 0.016
#> GSM711957 4 0.6620 0.5476 0.312 0.000 0.016 0.512 0.160
#> GSM711959 2 0.0000 0.9281 0.000 1.000 0.000 0.000 0.000
#> GSM711961 2 0.0703 0.9280 0.000 0.976 0.000 0.000 0.024
#> GSM711965 4 0.3427 0.5616 0.108 0.000 0.056 0.836 0.000
#> GSM711967 1 0.1041 0.6389 0.964 0.000 0.000 0.004 0.032
#> GSM711969 2 0.0510 0.9259 0.000 0.984 0.000 0.000 0.016
#> GSM711973 4 0.5286 0.4965 0.220 0.000 0.036 0.696 0.048
#> GSM711977 4 0.4126 0.0755 0.000 0.000 0.380 0.620 0.000
#> GSM711981 4 0.6393 0.3966 0.024 0.296 0.000 0.560 0.120
#> GSM711987 2 0.2136 0.9149 0.000 0.904 0.000 0.008 0.088
#> GSM711905 2 0.2136 0.9149 0.000 0.904 0.000 0.008 0.088
#> GSM711907 2 0.0510 0.9259 0.000 0.984 0.000 0.000 0.016
#> GSM711909 3 0.0000 0.8129 0.000 0.000 1.000 0.000 0.000
#> GSM711911 3 0.5041 0.5524 0.016 0.000 0.632 0.328 0.024
#> GSM711915 3 0.0000 0.8129 0.000 0.000 1.000 0.000 0.000
#> GSM711917 2 0.0290 0.9273 0.000 0.992 0.000 0.000 0.008
#> GSM711923 4 0.0579 0.6266 0.008 0.000 0.008 0.984 0.000
#> GSM711925 2 0.2011 0.9159 0.000 0.908 0.000 0.004 0.088
#> GSM711927 3 0.0000 0.8129 0.000 0.000 1.000 0.000 0.000
#> GSM711929 2 0.2136 0.9149 0.000 0.904 0.000 0.008 0.088
#> GSM711931 2 0.2969 0.8210 0.000 0.852 0.000 0.020 0.128
#> GSM711933 1 0.2783 0.6195 0.868 0.000 0.012 0.004 0.116
#> GSM711935 2 0.2136 0.9149 0.000 0.904 0.000 0.008 0.088
#> GSM711941 4 0.6244 0.4535 0.364 0.000 0.008 0.508 0.120
#> GSM711943 4 0.0566 0.6246 0.004 0.000 0.012 0.984 0.000
#> GSM711945 4 0.0566 0.6246 0.004 0.000 0.012 0.984 0.000
#> GSM711947 3 0.0000 0.8129 0.000 0.000 1.000 0.000 0.000
#> GSM711949 2 0.2136 0.9149 0.000 0.904 0.000 0.008 0.088
#> GSM711953 2 0.2136 0.9149 0.000 0.904 0.000 0.008 0.088
#> GSM711955 1 0.3967 0.4439 0.724 0.000 0.012 0.264 0.000
#> GSM711963 2 0.2136 0.9149 0.000 0.904 0.000 0.008 0.088
#> GSM711971 3 0.5880 0.5219 0.060 0.000 0.588 0.324 0.028
#> GSM711975 2 0.1117 0.9212 0.000 0.964 0.000 0.020 0.016
#> GSM711979 4 0.5906 0.5867 0.268 0.008 0.000 0.604 0.120
#> GSM711989 2 0.0510 0.9259 0.000 0.984 0.000 0.000 0.016
#> GSM711991 3 0.0963 0.7939 0.000 0.000 0.964 0.036 0.000
#> GSM711993 2 0.7821 -0.0608 0.152 0.444 0.000 0.284 0.120
#> GSM711983 3 0.6765 0.3913 0.164 0.000 0.492 0.324 0.020
#> GSM711985 2 0.0404 0.9284 0.000 0.988 0.000 0.000 0.012
#> GSM711913 4 0.4307 -0.1464 0.000 0.000 0.496 0.504 0.000
#> GSM711919 3 0.0771 0.8014 0.004 0.000 0.976 0.000 0.020
#> GSM711921 3 0.0000 0.8129 0.000 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM711936 2 0.0000 0.7765 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711938 2 0.2941 0.4557 0.000 0.780 0.000 0.000 0.220 0.000
#> GSM711950 4 0.2261 0.7794 0.104 0.000 0.004 0.884 0.008 0.000
#> GSM711956 1 0.3213 0.7497 0.784 0.000 0.000 0.008 0.004 0.204
#> GSM711958 1 0.5806 0.5363 0.592 0.000 0.132 0.020 0.008 0.248
#> GSM711960 3 0.5918 0.0685 0.068 0.000 0.472 0.036 0.008 0.416
#> GSM711964 1 0.3023 0.7476 0.784 0.000 0.000 0.004 0.000 0.212
#> GSM711966 1 0.3109 0.7450 0.772 0.000 0.000 0.004 0.000 0.224
#> GSM711968 1 0.2838 0.7487 0.808 0.000 0.000 0.004 0.000 0.188
#> GSM711972 1 0.3050 0.7370 0.764 0.000 0.000 0.000 0.000 0.236
#> GSM711976 1 0.3292 0.4335 0.784 0.000 0.000 0.200 0.008 0.008
#> GSM711980 1 0.0692 0.6993 0.976 0.000 0.000 0.004 0.000 0.020
#> GSM711986 6 0.2996 0.7315 0.228 0.000 0.000 0.000 0.000 0.772
#> GSM711904 1 0.3684 0.6529 0.692 0.000 0.000 0.004 0.004 0.300
#> GSM711906 1 0.3769 0.5734 0.640 0.000 0.000 0.000 0.004 0.356
#> GSM711908 6 0.0458 0.6700 0.016 0.000 0.000 0.000 0.000 0.984
#> GSM711910 3 0.3699 0.7581 0.000 0.000 0.660 0.000 0.336 0.004
#> GSM711914 1 0.2912 0.7443 0.784 0.000 0.000 0.000 0.000 0.216
#> GSM711916 6 0.3999 -0.3255 0.496 0.000 0.000 0.000 0.004 0.500
#> GSM711922 1 0.0806 0.6869 0.972 0.000 0.000 0.020 0.008 0.000
#> GSM711924 1 0.3863 0.7292 0.728 0.000 0.000 0.020 0.008 0.244
#> GSM711926 4 0.0951 0.8003 0.008 0.004 0.000 0.968 0.020 0.000
#> GSM711928 1 0.1806 0.7264 0.908 0.000 0.000 0.004 0.000 0.088
#> GSM711930 6 0.0603 0.6696 0.016 0.000 0.000 0.000 0.004 0.980
#> GSM711932 1 0.3878 0.2746 0.688 0.000 0.000 0.296 0.008 0.008
#> GSM711934 1 0.4112 0.7325 0.728 0.000 0.008 0.024 0.008 0.232
#> GSM711940 1 0.1262 0.6804 0.956 0.000 0.000 0.020 0.008 0.016
#> GSM711942 1 0.3076 0.7339 0.760 0.000 0.000 0.000 0.000 0.240
#> GSM711944 3 0.4845 0.4811 0.204 0.000 0.700 0.072 0.008 0.016
#> GSM711946 4 0.3043 0.7334 0.000 0.000 0.196 0.796 0.004 0.004
#> GSM711948 4 0.5148 0.4901 0.332 0.000 0.060 0.592 0.008 0.008
#> GSM711952 6 0.3023 0.7278 0.232 0.000 0.000 0.000 0.000 0.768
#> GSM711954 1 0.0508 0.6848 0.984 0.000 0.000 0.004 0.000 0.012
#> GSM711962 1 0.3023 0.7392 0.768 0.000 0.000 0.000 0.000 0.232
#> GSM711970 1 0.0508 0.6848 0.984 0.000 0.000 0.004 0.000 0.012
#> GSM711974 1 0.3672 0.5371 0.632 0.000 0.000 0.000 0.000 0.368
#> GSM711978 4 0.0806 0.8009 0.008 0.000 0.000 0.972 0.020 0.000
#> GSM711988 1 0.1251 0.6800 0.956 0.000 0.000 0.024 0.008 0.012
#> GSM711990 3 0.2144 0.6730 0.004 0.000 0.908 0.068 0.008 0.012
#> GSM711992 4 0.0806 0.8009 0.008 0.000 0.000 0.972 0.020 0.000
#> GSM711982 1 0.3023 0.7381 0.768 0.000 0.000 0.000 0.000 0.232
#> GSM711984 2 0.1267 0.7561 0.000 0.940 0.000 0.000 0.060 0.000
#> GSM711912 6 0.2883 0.7384 0.212 0.000 0.000 0.000 0.000 0.788
#> GSM711918 6 0.2883 0.7387 0.212 0.000 0.000 0.000 0.000 0.788
#> GSM711920 1 0.3189 0.7373 0.760 0.000 0.000 0.004 0.000 0.236
#> GSM711937 2 0.0000 0.7765 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711939 2 0.1007 0.7676 0.000 0.956 0.000 0.000 0.044 0.000
#> GSM711951 2 0.3810 0.1956 0.000 0.572 0.000 0.428 0.000 0.000
#> GSM711957 4 0.4154 0.7204 0.136 0.000 0.004 0.776 0.020 0.064
#> GSM711959 2 0.1075 0.7651 0.000 0.952 0.000 0.000 0.048 0.000
#> GSM711961 2 0.3126 0.3848 0.000 0.752 0.000 0.000 0.248 0.000
#> GSM711965 3 0.4084 0.1271 0.000 0.000 0.588 0.400 0.012 0.000
#> GSM711967 1 0.0405 0.6862 0.988 0.000 0.000 0.004 0.000 0.008
#> GSM711969 2 0.0000 0.7765 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711973 4 0.3538 0.7283 0.036 0.000 0.116 0.824 0.008 0.016
#> GSM711977 3 0.3419 0.7062 0.000 0.000 0.820 0.088 0.088 0.004
#> GSM711981 4 0.2734 0.7018 0.000 0.148 0.008 0.840 0.004 0.000
#> GSM711987 5 0.3737 0.9644 0.000 0.392 0.000 0.000 0.608 0.000
#> GSM711905 5 0.3684 0.9902 0.000 0.372 0.000 0.000 0.628 0.000
#> GSM711907 2 0.0000 0.7765 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711909 3 0.3699 0.7581 0.000 0.000 0.660 0.000 0.336 0.004
#> GSM711911 3 0.1053 0.7052 0.000 0.000 0.964 0.020 0.004 0.012
#> GSM711915 3 0.3578 0.7579 0.000 0.000 0.660 0.000 0.340 0.000
#> GSM711917 2 0.0937 0.7694 0.000 0.960 0.000 0.000 0.040 0.000
#> GSM711923 4 0.3154 0.7412 0.000 0.000 0.184 0.800 0.012 0.004
#> GSM711925 5 0.3717 0.9770 0.000 0.384 0.000 0.000 0.616 0.000
#> GSM711927 3 0.3699 0.7581 0.000 0.000 0.660 0.000 0.336 0.004
#> GSM711929 5 0.3684 0.9902 0.000 0.372 0.000 0.000 0.628 0.000
#> GSM711931 2 0.3695 0.3366 0.000 0.624 0.000 0.376 0.000 0.000
#> GSM711933 1 0.5174 0.5149 0.712 0.000 0.136 0.056 0.008 0.088
#> GSM711935 5 0.3684 0.9902 0.000 0.372 0.000 0.000 0.628 0.000
#> GSM711941 4 0.1049 0.8019 0.032 0.000 0.000 0.960 0.008 0.000
#> GSM711943 4 0.3056 0.7421 0.000 0.000 0.184 0.804 0.008 0.004
#> GSM711945 4 0.3121 0.7366 0.000 0.000 0.192 0.796 0.008 0.004
#> GSM711947 3 0.5024 0.7223 0.000 0.000 0.572 0.088 0.340 0.000
#> GSM711949 5 0.3684 0.9902 0.000 0.372 0.000 0.000 0.628 0.000
#> GSM711953 5 0.3695 0.9874 0.000 0.376 0.000 0.000 0.624 0.000
#> GSM711955 4 0.6028 0.3527 0.356 0.000 0.148 0.480 0.008 0.008
#> GSM711963 5 0.3684 0.9902 0.000 0.372 0.000 0.000 0.628 0.000
#> GSM711971 3 0.1723 0.6915 0.004 0.000 0.932 0.048 0.004 0.012
#> GSM711975 2 0.1610 0.6964 0.000 0.916 0.000 0.084 0.000 0.000
#> GSM711979 4 0.0508 0.8022 0.004 0.000 0.000 0.984 0.012 0.000
#> GSM711989 2 0.0000 0.7765 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711991 3 0.5094 0.7188 0.000 0.000 0.568 0.096 0.336 0.000
#> GSM711993 4 0.3206 0.6703 0.008 0.172 0.004 0.808 0.008 0.000
#> GSM711983 3 0.2086 0.6750 0.004 0.000 0.912 0.064 0.008 0.012
#> GSM711985 2 0.2340 0.6258 0.000 0.852 0.000 0.000 0.148 0.000
#> GSM711913 3 0.3138 0.7188 0.000 0.000 0.840 0.060 0.096 0.004
#> GSM711919 3 0.3984 0.7569 0.000 0.000 0.648 0.000 0.336 0.016
#> GSM711921 3 0.3699 0.7581 0.000 0.000 0.660 0.000 0.336 0.004
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) disease.state(p) individual(p) k
#> CV:mclust 77 9.27e-07 0.3528 0.768 2
#> CV:mclust 87 1.24e-10 0.3713 0.568 3
#> CV:mclust 86 9.29e-10 0.1184 0.560 4
#> CV:mclust 69 1.07e-07 0.0452 0.491 5
#> CV:mclust 78 1.96e-08 0.0660 0.273 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "NMF"]
# you can also extract it by
# res = res_list["CV:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 27425 rows and 90 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.999 0.964 0.985 0.4365 0.567 0.567
#> 3 3 0.970 0.957 0.981 0.4923 0.756 0.578
#> 4 4 0.937 0.904 0.959 0.1311 0.834 0.569
#> 5 5 0.799 0.809 0.866 0.0532 0.940 0.785
#> 6 6 0.864 0.748 0.892 0.0502 0.914 0.657
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 2 3
There is also optional best \(k\) = 2 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM711936 2 0.000 0.982 0.000 1.000
#> GSM711938 2 0.000 0.982 0.000 1.000
#> GSM711950 1 0.000 0.986 1.000 0.000
#> GSM711956 1 0.000 0.986 1.000 0.000
#> GSM711958 1 0.000 0.986 1.000 0.000
#> GSM711960 1 0.000 0.986 1.000 0.000
#> GSM711964 1 0.000 0.986 1.000 0.000
#> GSM711966 1 0.000 0.986 1.000 0.000
#> GSM711968 1 0.000 0.986 1.000 0.000
#> GSM711972 1 0.000 0.986 1.000 0.000
#> GSM711976 1 0.000 0.986 1.000 0.000
#> GSM711980 1 0.000 0.986 1.000 0.000
#> GSM711986 1 0.000 0.986 1.000 0.000
#> GSM711904 1 0.000 0.986 1.000 0.000
#> GSM711906 1 0.000 0.986 1.000 0.000
#> GSM711908 1 0.000 0.986 1.000 0.000
#> GSM711910 1 0.000 0.986 1.000 0.000
#> GSM711914 1 0.000 0.986 1.000 0.000
#> GSM711916 1 0.000 0.986 1.000 0.000
#> GSM711922 1 0.000 0.986 1.000 0.000
#> GSM711924 1 0.000 0.986 1.000 0.000
#> GSM711926 2 0.402 0.907 0.080 0.920
#> GSM711928 1 0.000 0.986 1.000 0.000
#> GSM711930 1 0.000 0.986 1.000 0.000
#> GSM711932 1 0.000 0.986 1.000 0.000
#> GSM711934 1 0.000 0.986 1.000 0.000
#> GSM711940 1 0.000 0.986 1.000 0.000
#> GSM711942 1 0.000 0.986 1.000 0.000
#> GSM711944 1 0.000 0.986 1.000 0.000
#> GSM711946 1 0.224 0.954 0.964 0.036
#> GSM711948 1 0.000 0.986 1.000 0.000
#> GSM711952 1 0.000 0.986 1.000 0.000
#> GSM711954 1 0.000 0.986 1.000 0.000
#> GSM711962 1 0.000 0.986 1.000 0.000
#> GSM711970 1 0.000 0.986 1.000 0.000
#> GSM711974 1 0.000 0.986 1.000 0.000
#> GSM711978 1 0.482 0.881 0.896 0.104
#> GSM711988 1 0.000 0.986 1.000 0.000
#> GSM711990 1 0.000 0.986 1.000 0.000
#> GSM711992 1 0.295 0.938 0.948 0.052
#> GSM711982 1 0.000 0.986 1.000 0.000
#> GSM711984 2 0.000 0.982 0.000 1.000
#> GSM711912 1 0.000 0.986 1.000 0.000
#> GSM711918 1 0.000 0.986 1.000 0.000
#> GSM711920 1 0.000 0.986 1.000 0.000
#> GSM711937 2 0.000 0.982 0.000 1.000
#> GSM711939 2 0.000 0.982 0.000 1.000
#> GSM711951 2 0.000 0.982 0.000 1.000
#> GSM711957 1 0.000 0.986 1.000 0.000
#> GSM711959 2 0.000 0.982 0.000 1.000
#> GSM711961 2 0.000 0.982 0.000 1.000
#> GSM711965 1 0.000 0.986 1.000 0.000
#> GSM711967 1 0.000 0.986 1.000 0.000
#> GSM711969 2 0.000 0.982 0.000 1.000
#> GSM711973 1 0.000 0.986 1.000 0.000
#> GSM711977 1 0.000 0.986 1.000 0.000
#> GSM711981 2 0.343 0.924 0.064 0.936
#> GSM711987 2 0.000 0.982 0.000 1.000
#> GSM711905 2 0.000 0.982 0.000 1.000
#> GSM711907 2 0.000 0.982 0.000 1.000
#> GSM711909 1 0.000 0.986 1.000 0.000
#> GSM711911 1 0.000 0.986 1.000 0.000
#> GSM711915 1 0.000 0.986 1.000 0.000
#> GSM711917 2 0.000 0.982 0.000 1.000
#> GSM711923 1 0.141 0.969 0.980 0.020
#> GSM711925 2 0.000 0.982 0.000 1.000
#> GSM711927 1 0.000 0.986 1.000 0.000
#> GSM711929 2 0.000 0.982 0.000 1.000
#> GSM711931 2 0.000 0.982 0.000 1.000
#> GSM711933 1 0.000 0.986 1.000 0.000
#> GSM711935 2 0.000 0.982 0.000 1.000
#> GSM711941 1 0.000 0.986 1.000 0.000
#> GSM711943 1 0.653 0.797 0.832 0.168
#> GSM711945 2 0.904 0.523 0.320 0.680
#> GSM711947 2 0.000 0.982 0.000 1.000
#> GSM711949 2 0.000 0.982 0.000 1.000
#> GSM711953 2 0.000 0.982 0.000 1.000
#> GSM711955 1 0.000 0.986 1.000 0.000
#> GSM711963 2 0.000 0.982 0.000 1.000
#> GSM711971 1 0.000 0.986 1.000 0.000
#> GSM711975 2 0.000 0.982 0.000 1.000
#> GSM711979 1 0.141 0.969 0.980 0.020
#> GSM711989 2 0.000 0.982 0.000 1.000
#> GSM711991 1 0.994 0.153 0.544 0.456
#> GSM711993 2 0.000 0.982 0.000 1.000
#> GSM711983 1 0.000 0.986 1.000 0.000
#> GSM711985 2 0.000 0.982 0.000 1.000
#> GSM711913 1 0.000 0.986 1.000 0.000
#> GSM711919 1 0.000 0.986 1.000 0.000
#> GSM711921 1 0.000 0.986 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM711936 2 0.0000 0.982 0.000 1.000 0.000
#> GSM711938 2 0.0000 0.982 0.000 1.000 0.000
#> GSM711950 1 0.0000 0.990 1.000 0.000 0.000
#> GSM711956 1 0.0000 0.990 1.000 0.000 0.000
#> GSM711958 1 0.0000 0.990 1.000 0.000 0.000
#> GSM711960 3 0.4796 0.746 0.220 0.000 0.780
#> GSM711964 1 0.0000 0.990 1.000 0.000 0.000
#> GSM711966 1 0.0000 0.990 1.000 0.000 0.000
#> GSM711968 1 0.0000 0.990 1.000 0.000 0.000
#> GSM711972 1 0.0000 0.990 1.000 0.000 0.000
#> GSM711976 1 0.0000 0.990 1.000 0.000 0.000
#> GSM711980 1 0.0000 0.990 1.000 0.000 0.000
#> GSM711986 1 0.0000 0.990 1.000 0.000 0.000
#> GSM711904 1 0.0000 0.990 1.000 0.000 0.000
#> GSM711906 1 0.0000 0.990 1.000 0.000 0.000
#> GSM711908 1 0.0000 0.990 1.000 0.000 0.000
#> GSM711910 3 0.0000 0.952 0.000 0.000 1.000
#> GSM711914 1 0.0000 0.990 1.000 0.000 0.000
#> GSM711916 1 0.0000 0.990 1.000 0.000 0.000
#> GSM711922 1 0.0000 0.990 1.000 0.000 0.000
#> GSM711924 1 0.0000 0.990 1.000 0.000 0.000
#> GSM711926 2 0.5988 0.403 0.368 0.632 0.000
#> GSM711928 1 0.0000 0.990 1.000 0.000 0.000
#> GSM711930 1 0.0000 0.990 1.000 0.000 0.000
#> GSM711932 1 0.0000 0.990 1.000 0.000 0.000
#> GSM711934 1 0.0000 0.990 1.000 0.000 0.000
#> GSM711940 1 0.0000 0.990 1.000 0.000 0.000
#> GSM711942 1 0.0000 0.990 1.000 0.000 0.000
#> GSM711944 3 0.0000 0.952 0.000 0.000 1.000
#> GSM711946 3 0.0000 0.952 0.000 0.000 1.000
#> GSM711948 1 0.0424 0.983 0.992 0.000 0.008
#> GSM711952 1 0.0000 0.990 1.000 0.000 0.000
#> GSM711954 1 0.0000 0.990 1.000 0.000 0.000
#> GSM711962 1 0.0000 0.990 1.000 0.000 0.000
#> GSM711970 1 0.0000 0.990 1.000 0.000 0.000
#> GSM711974 1 0.0000 0.990 1.000 0.000 0.000
#> GSM711978 1 0.4291 0.780 0.820 0.180 0.000
#> GSM711988 1 0.0000 0.990 1.000 0.000 0.000
#> GSM711990 3 0.0000 0.952 0.000 0.000 1.000
#> GSM711992 1 0.1289 0.959 0.968 0.032 0.000
#> GSM711982 1 0.0000 0.990 1.000 0.000 0.000
#> GSM711984 2 0.0000 0.982 0.000 1.000 0.000
#> GSM711912 1 0.0000 0.990 1.000 0.000 0.000
#> GSM711918 1 0.0000 0.990 1.000 0.000 0.000
#> GSM711920 1 0.0000 0.990 1.000 0.000 0.000
#> GSM711937 2 0.0000 0.982 0.000 1.000 0.000
#> GSM711939 2 0.0000 0.982 0.000 1.000 0.000
#> GSM711951 2 0.0000 0.982 0.000 1.000 0.000
#> GSM711957 1 0.0000 0.990 1.000 0.000 0.000
#> GSM711959 2 0.0000 0.982 0.000 1.000 0.000
#> GSM711961 2 0.0000 0.982 0.000 1.000 0.000
#> GSM711965 3 0.0000 0.952 0.000 0.000 1.000
#> GSM711967 1 0.0000 0.990 1.000 0.000 0.000
#> GSM711969 2 0.0000 0.982 0.000 1.000 0.000
#> GSM711973 3 0.0000 0.952 0.000 0.000 1.000
#> GSM711977 3 0.0000 0.952 0.000 0.000 1.000
#> GSM711981 2 0.0000 0.982 0.000 1.000 0.000
#> GSM711987 2 0.0000 0.982 0.000 1.000 0.000
#> GSM711905 2 0.0000 0.982 0.000 1.000 0.000
#> GSM711907 2 0.0000 0.982 0.000 1.000 0.000
#> GSM711909 3 0.0000 0.952 0.000 0.000 1.000
#> GSM711911 3 0.0000 0.952 0.000 0.000 1.000
#> GSM711915 3 0.0000 0.952 0.000 0.000 1.000
#> GSM711917 2 0.0000 0.982 0.000 1.000 0.000
#> GSM711923 3 0.1753 0.923 0.000 0.048 0.952
#> GSM711925 2 0.0000 0.982 0.000 1.000 0.000
#> GSM711927 3 0.0000 0.952 0.000 0.000 1.000
#> GSM711929 2 0.0000 0.982 0.000 1.000 0.000
#> GSM711931 2 0.0000 0.982 0.000 1.000 0.000
#> GSM711933 1 0.0000 0.990 1.000 0.000 0.000
#> GSM711935 2 0.0000 0.982 0.000 1.000 0.000
#> GSM711941 3 0.4842 0.743 0.224 0.000 0.776
#> GSM711943 3 0.3686 0.833 0.000 0.140 0.860
#> GSM711945 3 0.2261 0.906 0.000 0.068 0.932
#> GSM711947 3 0.1860 0.920 0.000 0.052 0.948
#> GSM711949 2 0.0000 0.982 0.000 1.000 0.000
#> GSM711953 2 0.0000 0.982 0.000 1.000 0.000
#> GSM711955 3 0.5254 0.681 0.264 0.000 0.736
#> GSM711963 2 0.0000 0.982 0.000 1.000 0.000
#> GSM711971 3 0.0000 0.952 0.000 0.000 1.000
#> GSM711975 2 0.0000 0.982 0.000 1.000 0.000
#> GSM711979 1 0.3686 0.835 0.860 0.140 0.000
#> GSM711989 2 0.0000 0.982 0.000 1.000 0.000
#> GSM711991 3 0.0000 0.952 0.000 0.000 1.000
#> GSM711993 2 0.0000 0.982 0.000 1.000 0.000
#> GSM711983 3 0.0000 0.952 0.000 0.000 1.000
#> GSM711985 2 0.0000 0.982 0.000 1.000 0.000
#> GSM711913 3 0.0000 0.952 0.000 0.000 1.000
#> GSM711919 3 0.0000 0.952 0.000 0.000 1.000
#> GSM711921 3 0.0000 0.952 0.000 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM711936 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM711938 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM711950 4 0.0000 0.845 0.000 0.000 0.000 1.000
#> GSM711956 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM711958 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM711960 3 0.1118 0.934 0.036 0.000 0.964 0.000
#> GSM711964 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM711966 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM711968 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM711972 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM711976 4 0.4624 0.532 0.340 0.000 0.000 0.660
#> GSM711980 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM711986 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM711904 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM711906 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM711908 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM711910 3 0.0000 0.969 0.000 0.000 1.000 0.000
#> GSM711914 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM711916 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM711922 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM711924 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM711926 4 0.1452 0.829 0.008 0.036 0.000 0.956
#> GSM711928 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM711930 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM711932 4 0.4431 0.586 0.304 0.000 0.000 0.696
#> GSM711934 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM711940 4 0.4843 0.400 0.396 0.000 0.000 0.604
#> GSM711942 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM711944 3 0.0000 0.969 0.000 0.000 1.000 0.000
#> GSM711946 4 0.0817 0.836 0.000 0.000 0.024 0.976
#> GSM711948 4 0.0188 0.844 0.004 0.000 0.000 0.996
#> GSM711952 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM711954 1 0.0817 0.968 0.976 0.000 0.000 0.024
#> GSM711962 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM711970 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM711974 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM711978 4 0.0000 0.845 0.000 0.000 0.000 1.000
#> GSM711988 1 0.1211 0.951 0.960 0.000 0.000 0.040
#> GSM711990 3 0.0000 0.969 0.000 0.000 1.000 0.000
#> GSM711992 4 0.5000 0.107 0.496 0.000 0.000 0.504
#> GSM711982 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM711984 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM711912 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM711918 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM711920 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM711937 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM711939 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM711951 4 0.0188 0.844 0.000 0.004 0.000 0.996
#> GSM711957 1 0.1118 0.956 0.964 0.000 0.000 0.036
#> GSM711959 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM711961 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM711965 4 0.0921 0.834 0.000 0.000 0.028 0.972
#> GSM711967 1 0.3266 0.776 0.832 0.000 0.000 0.168
#> GSM711969 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM711973 4 0.3486 0.676 0.000 0.000 0.188 0.812
#> GSM711977 3 0.4304 0.598 0.000 0.000 0.716 0.284
#> GSM711981 4 0.0000 0.845 0.000 0.000 0.000 1.000
#> GSM711987 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM711905 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM711907 2 0.4040 0.647 0.000 0.752 0.000 0.248
#> GSM711909 3 0.0000 0.969 0.000 0.000 1.000 0.000
#> GSM711911 3 0.0000 0.969 0.000 0.000 1.000 0.000
#> GSM711915 3 0.0000 0.969 0.000 0.000 1.000 0.000
#> GSM711917 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM711923 4 0.0000 0.845 0.000 0.000 0.000 1.000
#> GSM711925 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM711927 3 0.0000 0.969 0.000 0.000 1.000 0.000
#> GSM711929 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM711931 4 0.3172 0.735 0.000 0.160 0.000 0.840
#> GSM711933 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM711935 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM711941 4 0.0000 0.845 0.000 0.000 0.000 1.000
#> GSM711943 4 0.0000 0.845 0.000 0.000 0.000 1.000
#> GSM711945 4 0.0817 0.836 0.000 0.000 0.024 0.976
#> GSM711947 3 0.1940 0.898 0.000 0.076 0.924 0.000
#> GSM711949 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM711953 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM711955 4 0.5428 0.325 0.020 0.000 0.380 0.600
#> GSM711963 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM711971 3 0.0000 0.969 0.000 0.000 1.000 0.000
#> GSM711975 4 0.4661 0.444 0.000 0.348 0.000 0.652
#> GSM711979 4 0.0000 0.845 0.000 0.000 0.000 1.000
#> GSM711989 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM711991 3 0.0000 0.969 0.000 0.000 1.000 0.000
#> GSM711993 4 0.0000 0.845 0.000 0.000 0.000 1.000
#> GSM711983 3 0.0000 0.969 0.000 0.000 1.000 0.000
#> GSM711985 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM711913 3 0.1118 0.942 0.000 0.000 0.964 0.036
#> GSM711919 3 0.0000 0.969 0.000 0.000 1.000 0.000
#> GSM711921 3 0.0000 0.969 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM711936 2 0.0000 0.9695 0.000 1.000 0.000 0.000 0.000
#> GSM711938 2 0.0000 0.9695 0.000 1.000 0.000 0.000 0.000
#> GSM711950 4 0.4235 0.0628 0.000 0.000 0.000 0.576 0.424
#> GSM711956 1 0.3305 0.8156 0.776 0.000 0.000 0.000 0.224
#> GSM711958 1 0.3807 0.6523 0.748 0.000 0.240 0.000 0.012
#> GSM711960 3 0.0451 0.9787 0.008 0.000 0.988 0.000 0.004
#> GSM711964 1 0.0290 0.8749 0.992 0.000 0.000 0.000 0.008
#> GSM711966 1 0.0290 0.8740 0.992 0.000 0.000 0.000 0.008
#> GSM711968 1 0.3305 0.8156 0.776 0.000 0.000 0.000 0.224
#> GSM711972 1 0.0290 0.8740 0.992 0.000 0.000 0.000 0.008
#> GSM711976 1 0.5329 0.5941 0.656 0.000 0.000 0.236 0.108
#> GSM711980 1 0.3519 0.8160 0.776 0.000 0.000 0.008 0.216
#> GSM711986 1 0.0000 0.8744 1.000 0.000 0.000 0.000 0.000
#> GSM711904 1 0.3003 0.8286 0.812 0.000 0.000 0.000 0.188
#> GSM711906 1 0.0290 0.8740 0.992 0.000 0.000 0.000 0.008
#> GSM711908 1 0.0290 0.8740 0.992 0.000 0.000 0.000 0.008
#> GSM711910 3 0.0000 0.9927 0.000 0.000 1.000 0.000 0.000
#> GSM711914 1 0.0880 0.8734 0.968 0.000 0.000 0.000 0.032
#> GSM711916 1 0.0290 0.8740 0.992 0.000 0.000 0.000 0.008
#> GSM711922 1 0.4080 0.7903 0.728 0.000 0.000 0.020 0.252
#> GSM711924 1 0.3210 0.8380 0.860 0.000 0.008 0.040 0.092
#> GSM711926 4 0.2439 0.7011 0.000 0.004 0.000 0.876 0.120
#> GSM711928 1 0.1851 0.8630 0.912 0.000 0.000 0.000 0.088
#> GSM711930 1 0.0290 0.8740 0.992 0.000 0.000 0.000 0.008
#> GSM711932 4 0.4559 0.5833 0.152 0.000 0.000 0.748 0.100
#> GSM711934 1 0.3274 0.8171 0.780 0.000 0.000 0.000 0.220
#> GSM711940 4 0.2690 0.6795 0.156 0.000 0.000 0.844 0.000
#> GSM711942 1 0.2570 0.8489 0.888 0.000 0.000 0.028 0.084
#> GSM711944 3 0.0000 0.9927 0.000 0.000 1.000 0.000 0.000
#> GSM711946 4 0.3110 0.6996 0.000 0.000 0.060 0.860 0.080
#> GSM711948 4 0.3327 0.6910 0.028 0.000 0.000 0.828 0.144
#> GSM711952 1 0.0510 0.8750 0.984 0.000 0.000 0.000 0.016
#> GSM711954 1 0.4247 0.7849 0.776 0.000 0.000 0.132 0.092
#> GSM711962 1 0.0290 0.8740 0.992 0.000 0.000 0.000 0.008
#> GSM711970 1 0.5028 0.7477 0.668 0.000 0.000 0.072 0.260
#> GSM711974 1 0.0162 0.8741 0.996 0.000 0.000 0.000 0.004
#> GSM711978 4 0.0290 0.7543 0.000 0.000 0.000 0.992 0.008
#> GSM711988 1 0.1741 0.8663 0.936 0.000 0.000 0.040 0.024
#> GSM711990 3 0.0290 0.9856 0.000 0.000 0.992 0.000 0.008
#> GSM711992 4 0.2674 0.6927 0.140 0.000 0.000 0.856 0.004
#> GSM711982 1 0.0290 0.8740 0.992 0.000 0.000 0.000 0.008
#> GSM711984 2 0.0000 0.9695 0.000 1.000 0.000 0.000 0.000
#> GSM711912 1 0.0290 0.8749 0.992 0.000 0.000 0.000 0.008
#> GSM711918 1 0.0290 0.8751 0.992 0.000 0.000 0.000 0.008
#> GSM711920 1 0.4689 0.7627 0.688 0.000 0.000 0.048 0.264
#> GSM711937 2 0.0000 0.9695 0.000 1.000 0.000 0.000 0.000
#> GSM711939 2 0.0000 0.9695 0.000 1.000 0.000 0.000 0.000
#> GSM711951 4 0.2376 0.7276 0.000 0.052 0.000 0.904 0.044
#> GSM711957 1 0.6787 0.1900 0.380 0.000 0.000 0.332 0.288
#> GSM711959 2 0.0000 0.9695 0.000 1.000 0.000 0.000 0.000
#> GSM711961 2 0.0000 0.9695 0.000 1.000 0.000 0.000 0.000
#> GSM711965 5 0.4016 0.5890 0.000 0.000 0.012 0.272 0.716
#> GSM711967 1 0.4167 0.6610 0.724 0.000 0.000 0.252 0.024
#> GSM711969 2 0.0000 0.9695 0.000 1.000 0.000 0.000 0.000
#> GSM711973 5 0.4761 0.7118 0.000 0.000 0.104 0.168 0.728
#> GSM711977 5 0.4637 0.7413 0.000 0.000 0.196 0.076 0.728
#> GSM711981 4 0.3838 0.4978 0.000 0.004 0.000 0.716 0.280
#> GSM711987 2 0.0000 0.9695 0.000 1.000 0.000 0.000 0.000
#> GSM711905 2 0.0000 0.9695 0.000 1.000 0.000 0.000 0.000
#> GSM711907 2 0.3586 0.6160 0.000 0.736 0.000 0.264 0.000
#> GSM711909 3 0.0000 0.9927 0.000 0.000 1.000 0.000 0.000
#> GSM711911 3 0.0000 0.9927 0.000 0.000 1.000 0.000 0.000
#> GSM711915 5 0.4060 0.5178 0.000 0.000 0.360 0.000 0.640
#> GSM711917 2 0.0162 0.9665 0.000 0.996 0.000 0.004 0.000
#> GSM711923 4 0.0794 0.7525 0.000 0.000 0.000 0.972 0.028
#> GSM711925 2 0.0000 0.9695 0.000 1.000 0.000 0.000 0.000
#> GSM711927 3 0.0000 0.9927 0.000 0.000 1.000 0.000 0.000
#> GSM711929 2 0.0000 0.9695 0.000 1.000 0.000 0.000 0.000
#> GSM711931 4 0.3132 0.6137 0.000 0.172 0.000 0.820 0.008
#> GSM711933 4 0.6712 0.3369 0.232 0.000 0.020 0.536 0.212
#> GSM711935 2 0.0000 0.9695 0.000 1.000 0.000 0.000 0.000
#> GSM711941 4 0.1341 0.7419 0.000 0.000 0.000 0.944 0.056
#> GSM711943 4 0.0798 0.7544 0.000 0.000 0.016 0.976 0.008
#> GSM711945 5 0.4632 0.2505 0.000 0.000 0.012 0.448 0.540
#> GSM711947 3 0.0963 0.9399 0.000 0.036 0.964 0.000 0.000
#> GSM711949 2 0.0000 0.9695 0.000 1.000 0.000 0.000 0.000
#> GSM711953 2 0.0000 0.9695 0.000 1.000 0.000 0.000 0.000
#> GSM711955 4 0.5973 0.1880 0.080 0.000 0.384 0.524 0.012
#> GSM711963 2 0.0000 0.9695 0.000 1.000 0.000 0.000 0.000
#> GSM711971 3 0.0000 0.9927 0.000 0.000 1.000 0.000 0.000
#> GSM711975 2 0.3480 0.6573 0.000 0.752 0.000 0.248 0.000
#> GSM711979 4 0.0162 0.7546 0.000 0.000 0.000 0.996 0.004
#> GSM711989 2 0.0162 0.9665 0.000 0.996 0.000 0.004 0.000
#> GSM711991 3 0.0000 0.9927 0.000 0.000 1.000 0.000 0.000
#> GSM711993 4 0.0510 0.7549 0.000 0.000 0.000 0.984 0.016
#> GSM711983 3 0.0000 0.9927 0.000 0.000 1.000 0.000 0.000
#> GSM711985 2 0.0000 0.9695 0.000 1.000 0.000 0.000 0.000
#> GSM711913 5 0.4197 0.6986 0.000 0.000 0.244 0.028 0.728
#> GSM711919 3 0.0000 0.9927 0.000 0.000 1.000 0.000 0.000
#> GSM711921 3 0.0000 0.9927 0.000 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM711936 2 0.0146 0.9621 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM711938 2 0.0000 0.9638 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711950 5 0.3961 0.2182 0.004 0.000 0.000 0.440 0.556 0.000
#> GSM711956 1 0.4167 0.5475 0.612 0.000 0.000 0.000 0.020 0.368
#> GSM711958 3 0.3450 0.6501 0.012 0.000 0.772 0.000 0.008 0.208
#> GSM711960 3 0.0000 0.9128 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711964 6 0.1176 0.8235 0.024 0.000 0.000 0.000 0.020 0.956
#> GSM711966 6 0.0146 0.8294 0.000 0.000 0.000 0.000 0.004 0.996
#> GSM711968 1 0.3986 0.5920 0.664 0.000 0.000 0.000 0.020 0.316
#> GSM711972 6 0.0146 0.8294 0.000 0.000 0.000 0.000 0.004 0.996
#> GSM711976 6 0.5509 0.0454 0.100 0.000 0.000 0.008 0.416 0.476
#> GSM711980 1 0.4415 0.4456 0.556 0.000 0.000 0.004 0.020 0.420
#> GSM711986 6 0.1257 0.8218 0.028 0.000 0.000 0.000 0.020 0.952
#> GSM711904 6 0.4322 -0.2166 0.452 0.000 0.000 0.000 0.020 0.528
#> GSM711906 6 0.0146 0.8294 0.000 0.000 0.000 0.000 0.004 0.996
#> GSM711908 6 0.0146 0.8294 0.000 0.000 0.000 0.000 0.004 0.996
#> GSM711910 3 0.0000 0.9128 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711914 6 0.1334 0.8198 0.032 0.000 0.000 0.000 0.020 0.948
#> GSM711916 6 0.0146 0.8294 0.000 0.000 0.000 0.000 0.004 0.996
#> GSM711922 1 0.4105 0.5730 0.632 0.000 0.000 0.000 0.020 0.348
#> GSM711924 1 0.5023 0.2080 0.560 0.000 0.060 0.008 0.000 0.372
#> GSM711926 4 0.2149 0.8407 0.080 0.016 0.000 0.900 0.004 0.000
#> GSM711928 6 0.2581 0.7279 0.120 0.000 0.000 0.000 0.020 0.860
#> GSM711930 6 0.0291 0.8269 0.004 0.000 0.000 0.000 0.004 0.992
#> GSM711932 1 0.4315 -0.2751 0.524 0.000 0.000 0.460 0.008 0.008
#> GSM711934 1 0.4362 0.5079 0.584 0.000 0.000 0.004 0.020 0.392
#> GSM711940 4 0.0777 0.8875 0.004 0.000 0.000 0.972 0.000 0.024
#> GSM711942 6 0.3782 0.1328 0.412 0.000 0.000 0.000 0.000 0.588
#> GSM711944 3 0.1204 0.8784 0.056 0.000 0.944 0.000 0.000 0.000
#> GSM711946 4 0.0603 0.8953 0.000 0.000 0.004 0.980 0.016 0.000
#> GSM711948 4 0.3368 0.6152 0.012 0.000 0.000 0.756 0.232 0.000
#> GSM711952 6 0.1528 0.8128 0.048 0.000 0.000 0.000 0.016 0.936
#> GSM711954 6 0.5886 0.0803 0.160 0.000 0.000 0.292 0.016 0.532
#> GSM711962 6 0.0146 0.8294 0.000 0.000 0.000 0.000 0.004 0.996
#> GSM711970 1 0.3534 0.6093 0.740 0.000 0.000 0.016 0.000 0.244
#> GSM711974 6 0.0363 0.8294 0.012 0.000 0.000 0.000 0.000 0.988
#> GSM711978 4 0.0000 0.9001 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM711988 6 0.1974 0.8048 0.048 0.000 0.000 0.012 0.020 0.920
#> GSM711990 3 0.0146 0.9110 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM711992 4 0.0653 0.8959 0.012 0.004 0.000 0.980 0.000 0.004
#> GSM711982 6 0.0146 0.8294 0.000 0.000 0.000 0.000 0.004 0.996
#> GSM711984 2 0.0000 0.9638 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711912 6 0.1088 0.8244 0.024 0.000 0.000 0.000 0.016 0.960
#> GSM711918 6 0.1074 0.8249 0.028 0.000 0.000 0.000 0.012 0.960
#> GSM711920 1 0.0837 0.4967 0.972 0.000 0.000 0.004 0.004 0.020
#> GSM711937 2 0.0000 0.9638 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711939 2 0.0000 0.9638 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711951 4 0.0520 0.8980 0.000 0.008 0.000 0.984 0.008 0.000
#> GSM711957 1 0.0520 0.4818 0.984 0.000 0.000 0.000 0.008 0.008
#> GSM711959 2 0.0000 0.9638 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711961 2 0.0000 0.9638 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711965 5 0.1245 0.8080 0.000 0.000 0.016 0.032 0.952 0.000
#> GSM711967 6 0.3166 0.6263 0.024 0.000 0.000 0.156 0.004 0.816
#> GSM711969 2 0.0146 0.9621 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM711973 5 0.0909 0.8110 0.000 0.000 0.020 0.012 0.968 0.000
#> GSM711977 5 0.0858 0.8110 0.000 0.000 0.028 0.004 0.968 0.000
#> GSM711981 4 0.3887 0.3261 0.008 0.000 0.000 0.632 0.360 0.000
#> GSM711987 2 0.0000 0.9638 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711905 2 0.0000 0.9638 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711907 2 0.3727 0.3313 0.000 0.612 0.000 0.388 0.000 0.000
#> GSM711909 3 0.0000 0.9128 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711911 3 0.0146 0.9115 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM711915 5 0.1327 0.7875 0.000 0.000 0.064 0.000 0.936 0.000
#> GSM711917 2 0.0146 0.9621 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM711923 4 0.0000 0.9001 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM711925 2 0.0000 0.9638 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711927 3 0.0000 0.9128 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711929 2 0.0000 0.9638 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711931 4 0.3776 0.6329 0.052 0.188 0.000 0.760 0.000 0.000
#> GSM711933 3 0.5971 0.4475 0.152 0.000 0.564 0.256 0.004 0.024
#> GSM711935 2 0.0000 0.9638 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711941 4 0.0508 0.8982 0.004 0.000 0.000 0.984 0.012 0.000
#> GSM711943 4 0.0146 0.8998 0.000 0.000 0.004 0.996 0.000 0.000
#> GSM711945 5 0.3782 0.3361 0.000 0.000 0.000 0.412 0.588 0.000
#> GSM711947 3 0.0405 0.9061 0.004 0.008 0.988 0.000 0.000 0.000
#> GSM711949 2 0.0000 0.9638 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711953 2 0.0000 0.9638 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711955 3 0.4495 0.3211 0.028 0.000 0.580 0.388 0.000 0.004
#> GSM711963 2 0.0000 0.9638 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711971 3 0.0000 0.9128 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711975 2 0.2941 0.7093 0.000 0.780 0.000 0.220 0.000 0.000
#> GSM711979 4 0.0363 0.8991 0.012 0.000 0.000 0.988 0.000 0.000
#> GSM711989 2 0.0260 0.9591 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM711991 3 0.0146 0.9115 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM711993 4 0.0260 0.8994 0.008 0.000 0.000 0.992 0.000 0.000
#> GSM711983 3 0.0000 0.9128 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711985 2 0.0146 0.9621 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM711913 5 0.0858 0.8110 0.000 0.000 0.028 0.004 0.968 0.000
#> GSM711919 3 0.0000 0.9128 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711921 3 0.0000 0.9128 0.000 0.000 1.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) disease.state(p) individual(p) k
#> CV:NMF 89 1.04e-05 0.1877 0.726 2
#> CV:NMF 89 3.41e-11 0.2443 0.695 3
#> CV:NMF 86 8.20e-08 0.1927 0.483 4
#> CV:NMF 84 4.64e-09 0.0432 0.307 5
#> CV:NMF 75 1.39e-06 0.1377 0.157 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "hclust"]
# you can also extract it by
# res = res_list["MAD:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 27425 rows and 90 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.930 0.926 0.969 0.3676 0.626 0.626
#> 3 3 0.718 0.853 0.925 0.5958 0.792 0.668
#> 4 4 0.636 0.649 0.808 0.1517 0.921 0.812
#> 5 5 0.712 0.650 0.809 0.0828 0.880 0.660
#> 6 6 0.730 0.736 0.840 0.0503 0.917 0.690
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM711936 2 0.1414 0.913 0.020 0.980
#> GSM711938 2 0.0000 0.923 0.000 1.000
#> GSM711950 1 0.0000 0.980 1.000 0.000
#> GSM711956 1 0.0000 0.980 1.000 0.000
#> GSM711958 1 0.0000 0.980 1.000 0.000
#> GSM711960 1 0.0000 0.980 1.000 0.000
#> GSM711964 1 0.0000 0.980 1.000 0.000
#> GSM711966 1 0.0000 0.980 1.000 0.000
#> GSM711968 1 0.0000 0.980 1.000 0.000
#> GSM711972 1 0.0000 0.980 1.000 0.000
#> GSM711976 1 0.0000 0.980 1.000 0.000
#> GSM711980 1 0.0000 0.980 1.000 0.000
#> GSM711986 1 0.0000 0.980 1.000 0.000
#> GSM711904 1 0.0000 0.980 1.000 0.000
#> GSM711906 1 0.0000 0.980 1.000 0.000
#> GSM711908 1 0.0000 0.980 1.000 0.000
#> GSM711910 1 0.0000 0.980 1.000 0.000
#> GSM711914 1 0.0000 0.980 1.000 0.000
#> GSM711916 1 0.0000 0.980 1.000 0.000
#> GSM711922 1 0.0000 0.980 1.000 0.000
#> GSM711924 1 0.0000 0.980 1.000 0.000
#> GSM711926 1 0.2423 0.944 0.960 0.040
#> GSM711928 1 0.0000 0.980 1.000 0.000
#> GSM711930 1 0.0000 0.980 1.000 0.000
#> GSM711932 1 0.0000 0.980 1.000 0.000
#> GSM711934 1 0.0000 0.980 1.000 0.000
#> GSM711940 1 0.0000 0.980 1.000 0.000
#> GSM711942 1 0.0000 0.980 1.000 0.000
#> GSM711944 1 0.0000 0.980 1.000 0.000
#> GSM711946 1 0.1633 0.960 0.976 0.024
#> GSM711948 1 0.0000 0.980 1.000 0.000
#> GSM711952 1 0.0000 0.980 1.000 0.000
#> GSM711954 1 0.0000 0.980 1.000 0.000
#> GSM711962 1 0.0000 0.980 1.000 0.000
#> GSM711970 1 0.0000 0.980 1.000 0.000
#> GSM711974 1 0.0000 0.980 1.000 0.000
#> GSM711978 1 0.0000 0.980 1.000 0.000
#> GSM711988 1 0.0000 0.980 1.000 0.000
#> GSM711990 1 0.0000 0.980 1.000 0.000
#> GSM711992 1 0.2043 0.952 0.968 0.032
#> GSM711982 1 0.0000 0.980 1.000 0.000
#> GSM711984 2 0.0000 0.923 0.000 1.000
#> GSM711912 1 0.0000 0.980 1.000 0.000
#> GSM711918 1 0.0000 0.980 1.000 0.000
#> GSM711920 1 0.0000 0.980 1.000 0.000
#> GSM711937 2 0.1414 0.913 0.020 0.980
#> GSM711939 2 0.0000 0.923 0.000 1.000
#> GSM711951 2 0.9775 0.360 0.412 0.588
#> GSM711957 1 0.0000 0.980 1.000 0.000
#> GSM711959 2 0.0000 0.923 0.000 1.000
#> GSM711961 2 0.0000 0.923 0.000 1.000
#> GSM711965 1 0.0000 0.980 1.000 0.000
#> GSM711967 1 0.0000 0.980 1.000 0.000
#> GSM711969 2 0.1414 0.913 0.020 0.980
#> GSM711973 1 0.0000 0.980 1.000 0.000
#> GSM711977 1 0.0000 0.980 1.000 0.000
#> GSM711981 1 0.4298 0.891 0.912 0.088
#> GSM711987 2 0.0000 0.923 0.000 1.000
#> GSM711905 2 0.0000 0.923 0.000 1.000
#> GSM711907 2 0.8016 0.678 0.244 0.756
#> GSM711909 1 0.0000 0.980 1.000 0.000
#> GSM711911 1 0.0000 0.980 1.000 0.000
#> GSM711915 1 0.0000 0.980 1.000 0.000
#> GSM711917 2 0.0000 0.923 0.000 1.000
#> GSM711923 1 0.0672 0.973 0.992 0.008
#> GSM711925 2 0.0000 0.923 0.000 1.000
#> GSM711927 1 0.0000 0.980 1.000 0.000
#> GSM711929 2 0.0000 0.923 0.000 1.000
#> GSM711931 1 0.9686 0.285 0.604 0.396
#> GSM711933 1 0.0000 0.980 1.000 0.000
#> GSM711935 2 0.0000 0.923 0.000 1.000
#> GSM711941 1 0.0000 0.980 1.000 0.000
#> GSM711943 1 0.0672 0.973 0.992 0.008
#> GSM711945 1 0.1633 0.960 0.976 0.024
#> GSM711947 1 0.7453 0.715 0.788 0.212
#> GSM711949 2 0.0000 0.923 0.000 1.000
#> GSM711953 2 0.0000 0.923 0.000 1.000
#> GSM711955 1 0.0000 0.980 1.000 0.000
#> GSM711963 2 0.0000 0.923 0.000 1.000
#> GSM711971 1 0.0000 0.980 1.000 0.000
#> GSM711975 2 0.9775 0.360 0.412 0.588
#> GSM711979 1 0.0000 0.980 1.000 0.000
#> GSM711989 2 0.9775 0.360 0.412 0.588
#> GSM711991 1 0.5737 0.830 0.864 0.136
#> GSM711993 1 0.8267 0.627 0.740 0.260
#> GSM711983 1 0.0000 0.980 1.000 0.000
#> GSM711985 2 0.0000 0.923 0.000 1.000
#> GSM711913 1 0.0000 0.980 1.000 0.000
#> GSM711919 1 0.0000 0.980 1.000 0.000
#> GSM711921 1 0.0000 0.980 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM711936 2 0.0983 0.892 0.016 0.980 0.004
#> GSM711938 2 0.0000 0.903 0.000 1.000 0.000
#> GSM711950 1 0.1860 0.907 0.948 0.000 0.052
#> GSM711956 1 0.0000 0.915 1.000 0.000 0.000
#> GSM711958 1 0.1860 0.906 0.948 0.000 0.052
#> GSM711960 1 0.3686 0.857 0.860 0.000 0.140
#> GSM711964 1 0.0000 0.915 1.000 0.000 0.000
#> GSM711966 1 0.0237 0.914 0.996 0.000 0.004
#> GSM711968 1 0.0000 0.915 1.000 0.000 0.000
#> GSM711972 1 0.0237 0.914 0.996 0.000 0.004
#> GSM711976 1 0.1860 0.907 0.948 0.000 0.052
#> GSM711980 1 0.1860 0.907 0.948 0.000 0.052
#> GSM711986 1 0.0237 0.914 0.996 0.000 0.004
#> GSM711904 1 0.0892 0.913 0.980 0.000 0.020
#> GSM711906 1 0.0237 0.914 0.996 0.000 0.004
#> GSM711908 1 0.0237 0.914 0.996 0.000 0.004
#> GSM711910 3 0.0237 0.923 0.004 0.000 0.996
#> GSM711914 1 0.0000 0.915 1.000 0.000 0.000
#> GSM711916 1 0.0237 0.914 0.996 0.000 0.004
#> GSM711922 1 0.0000 0.915 1.000 0.000 0.000
#> GSM711924 1 0.0000 0.915 1.000 0.000 0.000
#> GSM711926 1 0.5028 0.814 0.828 0.040 0.132
#> GSM711928 1 0.0000 0.915 1.000 0.000 0.000
#> GSM711930 1 0.0237 0.914 0.996 0.000 0.004
#> GSM711932 1 0.0237 0.915 0.996 0.000 0.004
#> GSM711934 1 0.1753 0.907 0.952 0.000 0.048
#> GSM711940 1 0.4504 0.806 0.804 0.000 0.196
#> GSM711942 1 0.0000 0.915 1.000 0.000 0.000
#> GSM711944 3 0.2165 0.898 0.064 0.000 0.936
#> GSM711946 1 0.6180 0.710 0.716 0.024 0.260
#> GSM711948 1 0.1964 0.906 0.944 0.000 0.056
#> GSM711952 1 0.0237 0.914 0.996 0.000 0.004
#> GSM711954 1 0.1860 0.907 0.948 0.000 0.052
#> GSM711962 1 0.0237 0.915 0.996 0.000 0.004
#> GSM711970 1 0.1411 0.911 0.964 0.000 0.036
#> GSM711974 1 0.1860 0.906 0.948 0.000 0.052
#> GSM711978 1 0.3412 0.851 0.876 0.000 0.124
#> GSM711988 1 0.1860 0.907 0.948 0.000 0.052
#> GSM711990 3 0.1643 0.913 0.044 0.000 0.956
#> GSM711992 1 0.4591 0.856 0.848 0.032 0.120
#> GSM711982 1 0.0237 0.914 0.996 0.000 0.004
#> GSM711984 2 0.0000 0.903 0.000 1.000 0.000
#> GSM711912 1 0.0237 0.914 0.996 0.000 0.004
#> GSM711918 1 0.0237 0.914 0.996 0.000 0.004
#> GSM711920 1 0.0000 0.915 1.000 0.000 0.000
#> GSM711937 2 0.0983 0.892 0.016 0.980 0.004
#> GSM711939 2 0.0000 0.903 0.000 1.000 0.000
#> GSM711951 2 0.8362 0.424 0.300 0.588 0.112
#> GSM711957 1 0.1289 0.909 0.968 0.000 0.032
#> GSM711959 2 0.0000 0.903 0.000 1.000 0.000
#> GSM711961 2 0.0000 0.903 0.000 1.000 0.000
#> GSM711965 1 0.4654 0.793 0.792 0.000 0.208
#> GSM711967 1 0.0237 0.915 0.996 0.000 0.004
#> GSM711969 2 0.0983 0.892 0.016 0.980 0.004
#> GSM711973 3 0.4002 0.801 0.160 0.000 0.840
#> GSM711977 3 0.0592 0.922 0.012 0.000 0.988
#> GSM711981 1 0.6079 0.766 0.784 0.088 0.128
#> GSM711987 2 0.0000 0.903 0.000 1.000 0.000
#> GSM711905 2 0.0000 0.903 0.000 1.000 0.000
#> GSM711907 2 0.6336 0.647 0.180 0.756 0.064
#> GSM711909 3 0.0237 0.923 0.004 0.000 0.996
#> GSM711911 3 0.0237 0.923 0.004 0.000 0.996
#> GSM711915 3 0.0237 0.923 0.004 0.000 0.996
#> GSM711917 2 0.0000 0.903 0.000 1.000 0.000
#> GSM711923 1 0.5292 0.765 0.764 0.008 0.228
#> GSM711925 2 0.0000 0.903 0.000 1.000 0.000
#> GSM711927 3 0.0237 0.923 0.004 0.000 0.996
#> GSM711929 2 0.0000 0.903 0.000 1.000 0.000
#> GSM711931 1 0.8747 0.102 0.492 0.396 0.112
#> GSM711933 1 0.1860 0.907 0.948 0.000 0.052
#> GSM711935 2 0.0000 0.903 0.000 1.000 0.000
#> GSM711941 1 0.4504 0.806 0.804 0.000 0.196
#> GSM711943 1 0.5247 0.770 0.768 0.008 0.224
#> GSM711945 1 0.6180 0.710 0.716 0.024 0.260
#> GSM711947 3 0.7762 0.585 0.120 0.212 0.668
#> GSM711949 2 0.0000 0.903 0.000 1.000 0.000
#> GSM711953 2 0.0000 0.903 0.000 1.000 0.000
#> GSM711955 1 0.1964 0.906 0.944 0.000 0.056
#> GSM711963 2 0.0000 0.903 0.000 1.000 0.000
#> GSM711971 3 0.1643 0.913 0.044 0.000 0.956
#> GSM711975 2 0.8362 0.424 0.300 0.588 0.112
#> GSM711979 1 0.3412 0.851 0.876 0.000 0.124
#> GSM711989 2 0.8362 0.424 0.300 0.588 0.112
#> GSM711991 3 0.7739 0.620 0.188 0.136 0.676
#> GSM711993 1 0.8202 0.497 0.620 0.260 0.120
#> GSM711983 3 0.1643 0.913 0.044 0.000 0.956
#> GSM711985 2 0.0000 0.903 0.000 1.000 0.000
#> GSM711913 3 0.0592 0.922 0.012 0.000 0.988
#> GSM711919 3 0.0237 0.923 0.004 0.000 0.996
#> GSM711921 3 0.0237 0.923 0.004 0.000 0.996
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM711936 2 0.0779 0.8984 0.004 0.980 0.000 0.016
#> GSM711938 2 0.0000 0.9094 0.000 1.000 0.000 0.000
#> GSM711950 1 0.2197 0.7215 0.928 0.000 0.048 0.024
#> GSM711956 1 0.0592 0.7387 0.984 0.000 0.000 0.016
#> GSM711958 1 0.1938 0.7294 0.936 0.000 0.052 0.012
#> GSM711960 1 0.3377 0.6494 0.848 0.000 0.140 0.012
#> GSM711964 1 0.0592 0.7387 0.984 0.000 0.000 0.016
#> GSM711966 1 0.3975 0.6110 0.760 0.000 0.000 0.240
#> GSM711968 1 0.0592 0.7387 0.984 0.000 0.000 0.016
#> GSM711972 1 0.3907 0.6148 0.768 0.000 0.000 0.232
#> GSM711976 1 0.2089 0.7239 0.932 0.000 0.048 0.020
#> GSM711980 1 0.1975 0.7258 0.936 0.000 0.048 0.016
#> GSM711986 1 0.3801 0.6234 0.780 0.000 0.000 0.220
#> GSM711904 1 0.1520 0.7403 0.956 0.000 0.020 0.024
#> GSM711906 1 0.2469 0.6954 0.892 0.000 0.000 0.108
#> GSM711908 1 0.3975 0.6110 0.760 0.000 0.000 0.240
#> GSM711910 3 0.0000 0.9071 0.000 0.000 1.000 0.000
#> GSM711914 1 0.0592 0.7387 0.984 0.000 0.000 0.016
#> GSM711916 1 0.3975 0.6110 0.760 0.000 0.000 0.240
#> GSM711922 1 0.0592 0.7387 0.984 0.000 0.000 0.016
#> GSM711924 1 0.0188 0.7393 0.996 0.000 0.000 0.004
#> GSM711926 4 0.7712 0.6909 0.348 0.040 0.100 0.512
#> GSM711928 1 0.0592 0.7387 0.984 0.000 0.000 0.016
#> GSM711930 1 0.3975 0.6110 0.760 0.000 0.000 0.240
#> GSM711932 1 0.1022 0.7294 0.968 0.000 0.000 0.032
#> GSM711934 1 0.1854 0.7276 0.940 0.000 0.048 0.012
#> GSM711940 1 0.7254 -0.2579 0.524 0.000 0.176 0.300
#> GSM711942 1 0.0188 0.7393 0.996 0.000 0.000 0.004
#> GSM711944 3 0.1716 0.8703 0.064 0.000 0.936 0.000
#> GSM711946 1 0.8232 -0.3832 0.464 0.024 0.232 0.280
#> GSM711948 1 0.3301 0.6759 0.876 0.000 0.048 0.076
#> GSM711952 1 0.3907 0.6148 0.768 0.000 0.000 0.232
#> GSM711954 1 0.2089 0.7242 0.932 0.000 0.048 0.020
#> GSM711962 1 0.0592 0.7394 0.984 0.000 0.000 0.016
#> GSM711970 1 0.1488 0.7337 0.956 0.000 0.032 0.012
#> GSM711974 1 0.1938 0.7294 0.936 0.000 0.052 0.012
#> GSM711978 4 0.6745 0.6054 0.428 0.000 0.092 0.480
#> GSM711988 1 0.2089 0.7239 0.932 0.000 0.048 0.020
#> GSM711990 3 0.1302 0.8893 0.044 0.000 0.956 0.000
#> GSM711992 1 0.7082 0.0746 0.612 0.032 0.092 0.264
#> GSM711982 1 0.3975 0.6110 0.760 0.000 0.000 0.240
#> GSM711984 2 0.0000 0.9094 0.000 1.000 0.000 0.000
#> GSM711912 1 0.3907 0.6148 0.768 0.000 0.000 0.232
#> GSM711918 1 0.3907 0.6148 0.768 0.000 0.000 0.232
#> GSM711920 1 0.0188 0.7393 0.996 0.000 0.000 0.004
#> GSM711937 2 0.0779 0.8984 0.004 0.980 0.000 0.016
#> GSM711939 2 0.0000 0.9094 0.000 1.000 0.000 0.000
#> GSM711951 2 0.7890 0.2256 0.108 0.588 0.084 0.220
#> GSM711957 4 0.4008 0.5915 0.244 0.000 0.000 0.756
#> GSM711959 2 0.0000 0.9094 0.000 1.000 0.000 0.000
#> GSM711961 2 0.0000 0.9094 0.000 1.000 0.000 0.000
#> GSM711965 1 0.7373 -0.3201 0.500 0.000 0.184 0.316
#> GSM711967 1 0.0336 0.7377 0.992 0.000 0.000 0.008
#> GSM711969 2 0.0779 0.8984 0.004 0.980 0.000 0.016
#> GSM711973 3 0.4163 0.7724 0.076 0.000 0.828 0.096
#> GSM711977 3 0.0336 0.9053 0.000 0.000 0.992 0.008
#> GSM711981 4 0.8297 0.7071 0.304 0.088 0.100 0.508
#> GSM711987 2 0.0000 0.9094 0.000 1.000 0.000 0.000
#> GSM711905 2 0.0000 0.9094 0.000 1.000 0.000 0.000
#> GSM711907 2 0.5837 0.6085 0.080 0.756 0.048 0.116
#> GSM711909 3 0.0000 0.9071 0.000 0.000 1.000 0.000
#> GSM711911 3 0.0000 0.9071 0.000 0.000 1.000 0.000
#> GSM711915 3 0.0000 0.9071 0.000 0.000 1.000 0.000
#> GSM711917 2 0.0000 0.9094 0.000 1.000 0.000 0.000
#> GSM711923 1 0.7709 -0.3271 0.496 0.008 0.200 0.296
#> GSM711925 2 0.0000 0.9094 0.000 1.000 0.000 0.000
#> GSM711927 3 0.0000 0.9071 0.000 0.000 1.000 0.000
#> GSM711929 2 0.0000 0.9094 0.000 1.000 0.000 0.000
#> GSM711931 4 0.8626 0.2234 0.120 0.396 0.084 0.400
#> GSM711933 1 0.1975 0.7258 0.936 0.000 0.048 0.016
#> GSM711935 2 0.0000 0.9094 0.000 1.000 0.000 0.000
#> GSM711941 1 0.7254 -0.2579 0.524 0.000 0.176 0.300
#> GSM711943 1 0.7682 -0.3191 0.500 0.008 0.196 0.296
#> GSM711945 1 0.8232 -0.3832 0.464 0.024 0.232 0.280
#> GSM711947 3 0.7014 0.4008 0.108 0.212 0.644 0.036
#> GSM711949 2 0.0000 0.9094 0.000 1.000 0.000 0.000
#> GSM711953 2 0.0000 0.9094 0.000 1.000 0.000 0.000
#> GSM711955 1 0.3301 0.6759 0.876 0.000 0.048 0.076
#> GSM711963 2 0.0000 0.9094 0.000 1.000 0.000 0.000
#> GSM711971 3 0.1302 0.8893 0.044 0.000 0.956 0.000
#> GSM711975 2 0.7890 0.2256 0.108 0.588 0.084 0.220
#> GSM711979 4 0.6745 0.6054 0.428 0.000 0.092 0.480
#> GSM711989 2 0.7890 0.2256 0.108 0.588 0.084 0.220
#> GSM711991 3 0.7426 0.4122 0.128 0.136 0.648 0.088
#> GSM711993 4 0.9248 0.6026 0.248 0.260 0.092 0.400
#> GSM711983 3 0.1302 0.8893 0.044 0.000 0.956 0.000
#> GSM711985 2 0.0000 0.9094 0.000 1.000 0.000 0.000
#> GSM711913 3 0.0336 0.9053 0.000 0.000 0.992 0.008
#> GSM711919 3 0.0000 0.9071 0.000 0.000 1.000 0.000
#> GSM711921 3 0.0000 0.9071 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM711936 2 0.1205 0.890 0.000 0.956 0.000 0.040 0.004
#> GSM711938 2 0.0510 0.900 0.000 0.984 0.000 0.016 0.000
#> GSM711950 1 0.1960 0.738 0.928 0.000 0.048 0.020 0.004
#> GSM711956 1 0.0510 0.729 0.984 0.000 0.000 0.000 0.016
#> GSM711958 1 0.1717 0.743 0.936 0.000 0.052 0.008 0.004
#> GSM711960 1 0.2956 0.637 0.848 0.000 0.140 0.008 0.004
#> GSM711964 1 0.0510 0.729 0.984 0.000 0.000 0.000 0.016
#> GSM711966 5 0.4307 1.000 0.496 0.000 0.000 0.000 0.504
#> GSM711968 1 0.0703 0.723 0.976 0.000 0.000 0.000 0.024
#> GSM711972 1 0.4150 -0.667 0.612 0.000 0.000 0.000 0.388
#> GSM711976 1 0.1862 0.741 0.932 0.000 0.048 0.016 0.004
#> GSM711980 1 0.1757 0.743 0.936 0.000 0.048 0.012 0.004
#> GSM711986 1 0.4101 -0.609 0.628 0.000 0.000 0.000 0.372
#> GSM711904 1 0.1405 0.743 0.956 0.000 0.020 0.008 0.016
#> GSM711906 1 0.3242 0.199 0.784 0.000 0.000 0.000 0.216
#> GSM711908 5 0.4307 1.000 0.496 0.000 0.000 0.000 0.504
#> GSM711910 3 0.1041 0.876 0.000 0.000 0.964 0.004 0.032
#> GSM711914 1 0.0510 0.729 0.984 0.000 0.000 0.000 0.016
#> GSM711916 5 0.4307 1.000 0.496 0.000 0.000 0.000 0.504
#> GSM711922 1 0.0703 0.723 0.976 0.000 0.000 0.000 0.024
#> GSM711924 1 0.0162 0.739 0.996 0.000 0.000 0.000 0.004
#> GSM711926 4 0.3883 0.705 0.216 0.016 0.000 0.764 0.004
#> GSM711928 1 0.0510 0.729 0.984 0.000 0.000 0.000 0.016
#> GSM711930 5 0.4307 1.000 0.496 0.000 0.000 0.000 0.504
#> GSM711932 1 0.0955 0.735 0.968 0.000 0.000 0.028 0.004
#> GSM711934 1 0.1597 0.744 0.940 0.000 0.048 0.012 0.000
#> GSM711940 4 0.5908 0.664 0.404 0.000 0.080 0.508 0.008
#> GSM711942 1 0.0162 0.739 0.996 0.000 0.000 0.000 0.004
#> GSM711944 3 0.1478 0.855 0.064 0.000 0.936 0.000 0.000
#> GSM711946 4 0.6467 0.705 0.352 0.008 0.132 0.504 0.004
#> GSM711948 1 0.3126 0.679 0.868 0.000 0.048 0.076 0.008
#> GSM711952 1 0.4307 -0.985 0.504 0.000 0.000 0.000 0.496
#> GSM711954 1 0.2100 0.742 0.924 0.000 0.048 0.016 0.012
#> GSM711962 1 0.0771 0.735 0.976 0.000 0.000 0.004 0.020
#> GSM711970 1 0.1329 0.747 0.956 0.000 0.032 0.008 0.004
#> GSM711974 1 0.1717 0.743 0.936 0.000 0.052 0.008 0.004
#> GSM711978 4 0.3990 0.701 0.308 0.000 0.000 0.688 0.004
#> GSM711988 1 0.1862 0.741 0.932 0.000 0.048 0.016 0.004
#> GSM711990 3 0.1121 0.872 0.044 0.000 0.956 0.000 0.000
#> GSM711992 1 0.5628 -0.275 0.540 0.008 0.048 0.400 0.004
#> GSM711982 5 0.4307 1.000 0.496 0.000 0.000 0.000 0.504
#> GSM711984 2 0.0771 0.898 0.000 0.976 0.000 0.020 0.004
#> GSM711912 1 0.4307 -0.985 0.504 0.000 0.000 0.000 0.496
#> GSM711918 1 0.4307 -0.985 0.504 0.000 0.000 0.000 0.496
#> GSM711920 1 0.0162 0.739 0.996 0.000 0.000 0.000 0.004
#> GSM711937 2 0.1205 0.890 0.000 0.956 0.000 0.040 0.004
#> GSM711939 2 0.0510 0.900 0.000 0.984 0.000 0.016 0.000
#> GSM711951 2 0.4443 0.301 0.000 0.524 0.000 0.472 0.004
#> GSM711957 4 0.5510 0.275 0.072 0.000 0.000 0.548 0.380
#> GSM711959 2 0.0510 0.900 0.000 0.984 0.000 0.016 0.000
#> GSM711961 2 0.0162 0.900 0.000 0.996 0.000 0.000 0.004
#> GSM711965 4 0.5846 0.695 0.380 0.000 0.088 0.528 0.004
#> GSM711967 1 0.0451 0.741 0.988 0.000 0.000 0.004 0.008
#> GSM711969 2 0.1205 0.890 0.000 0.956 0.000 0.040 0.004
#> GSM711973 3 0.4547 0.758 0.076 0.000 0.792 0.088 0.044
#> GSM711977 3 0.1251 0.877 0.000 0.000 0.956 0.008 0.036
#> GSM711981 4 0.4114 0.674 0.176 0.044 0.000 0.776 0.004
#> GSM711987 2 0.0162 0.900 0.000 0.996 0.000 0.000 0.004
#> GSM711905 2 0.0162 0.900 0.000 0.996 0.000 0.000 0.004
#> GSM711907 2 0.4102 0.611 0.000 0.692 0.004 0.300 0.004
#> GSM711909 3 0.0000 0.885 0.000 0.000 1.000 0.000 0.000
#> GSM711911 3 0.0000 0.885 0.000 0.000 1.000 0.000 0.000
#> GSM711915 3 0.2286 0.841 0.000 0.000 0.888 0.004 0.108
#> GSM711917 2 0.0510 0.900 0.000 0.984 0.000 0.016 0.000
#> GSM711923 4 0.5958 0.703 0.372 0.004 0.100 0.524 0.000
#> GSM711925 2 0.0162 0.900 0.000 0.996 0.000 0.000 0.004
#> GSM711927 3 0.0000 0.885 0.000 0.000 1.000 0.000 0.000
#> GSM711929 2 0.0162 0.900 0.000 0.996 0.000 0.000 0.004
#> GSM711931 4 0.4253 0.092 0.004 0.332 0.000 0.660 0.004
#> GSM711933 1 0.1757 0.743 0.936 0.000 0.048 0.012 0.004
#> GSM711935 2 0.0162 0.900 0.000 0.996 0.000 0.000 0.004
#> GSM711941 4 0.5908 0.664 0.404 0.000 0.080 0.508 0.008
#> GSM711943 4 0.5924 0.701 0.376 0.004 0.096 0.524 0.000
#> GSM711945 4 0.6467 0.705 0.352 0.008 0.132 0.504 0.004
#> GSM711947 3 0.7425 0.288 0.000 0.148 0.472 0.304 0.076
#> GSM711949 2 0.0162 0.900 0.000 0.996 0.000 0.000 0.004
#> GSM711953 2 0.0162 0.900 0.000 0.996 0.000 0.000 0.004
#> GSM711955 1 0.3126 0.679 0.868 0.000 0.048 0.076 0.008
#> GSM711963 2 0.0162 0.900 0.000 0.996 0.000 0.000 0.004
#> GSM711971 3 0.1121 0.872 0.044 0.000 0.956 0.000 0.000
#> GSM711975 2 0.4443 0.301 0.000 0.524 0.000 0.472 0.004
#> GSM711979 4 0.3990 0.701 0.308 0.000 0.000 0.688 0.004
#> GSM711989 2 0.4443 0.301 0.000 0.524 0.000 0.472 0.004
#> GSM711991 3 0.7292 0.272 0.016 0.072 0.472 0.364 0.076
#> GSM711993 4 0.5457 0.494 0.132 0.196 0.000 0.668 0.004
#> GSM711983 3 0.1121 0.872 0.044 0.000 0.956 0.000 0.000
#> GSM711985 2 0.0510 0.900 0.000 0.984 0.000 0.016 0.000
#> GSM711913 3 0.1251 0.877 0.000 0.000 0.956 0.008 0.036
#> GSM711919 3 0.0000 0.885 0.000 0.000 1.000 0.000 0.000
#> GSM711921 3 0.1041 0.876 0.000 0.000 0.964 0.004 0.032
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM711936 2 0.1398 0.92141 0.000 0.940 0.000 0.052 0.000 0.008
#> GSM711938 2 0.0547 0.94242 0.000 0.980 0.000 0.020 0.000 0.000
#> GSM711950 1 0.0405 0.88311 0.988 0.000 0.004 0.008 0.000 0.000
#> GSM711956 1 0.1714 0.88124 0.908 0.000 0.000 0.000 0.000 0.092
#> GSM711958 1 0.0717 0.88946 0.976 0.000 0.008 0.000 0.000 0.016
#> GSM711960 1 0.1970 0.80135 0.900 0.000 0.092 0.000 0.000 0.008
#> GSM711964 1 0.1714 0.88124 0.908 0.000 0.000 0.000 0.000 0.092
#> GSM711966 6 0.2003 0.92740 0.116 0.000 0.000 0.000 0.000 0.884
#> GSM711968 1 0.1863 0.87490 0.896 0.000 0.000 0.000 0.000 0.104
#> GSM711972 6 0.3126 0.77550 0.248 0.000 0.000 0.000 0.000 0.752
#> GSM711976 1 0.0291 0.88444 0.992 0.000 0.004 0.004 0.000 0.000
#> GSM711980 1 0.0146 0.88622 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM711986 6 0.3244 0.73792 0.268 0.000 0.000 0.000 0.000 0.732
#> GSM711904 1 0.1531 0.89068 0.928 0.000 0.004 0.000 0.000 0.068
#> GSM711906 1 0.3860 -0.03783 0.528 0.000 0.000 0.000 0.000 0.472
#> GSM711908 6 0.1863 0.92304 0.104 0.000 0.000 0.000 0.000 0.896
#> GSM711910 3 0.2452 0.84577 0.000 0.000 0.892 0.044 0.056 0.008
#> GSM711914 1 0.1714 0.88124 0.908 0.000 0.000 0.000 0.000 0.092
#> GSM711916 6 0.2003 0.92740 0.116 0.000 0.000 0.000 0.000 0.884
#> GSM711922 1 0.1863 0.87490 0.896 0.000 0.000 0.000 0.000 0.104
#> GSM711924 1 0.1444 0.89054 0.928 0.000 0.000 0.000 0.000 0.072
#> GSM711926 4 0.2902 0.43499 0.196 0.000 0.000 0.800 0.000 0.004
#> GSM711928 1 0.1714 0.88124 0.908 0.000 0.000 0.000 0.000 0.092
#> GSM711930 6 0.1863 0.92304 0.104 0.000 0.000 0.000 0.000 0.896
#> GSM711932 1 0.1845 0.88626 0.920 0.000 0.000 0.028 0.000 0.052
#> GSM711934 1 0.0405 0.88844 0.988 0.000 0.004 0.000 0.000 0.008
#> GSM711940 4 0.4808 0.45951 0.444 0.000 0.036 0.512 0.000 0.008
#> GSM711942 1 0.1444 0.89054 0.928 0.000 0.000 0.000 0.000 0.072
#> GSM711944 3 0.1471 0.86555 0.064 0.000 0.932 0.000 0.000 0.004
#> GSM711946 4 0.5589 0.52847 0.392 0.004 0.088 0.504 0.000 0.012
#> GSM711948 1 0.1674 0.82115 0.924 0.000 0.004 0.068 0.000 0.004
#> GSM711952 6 0.2048 0.92760 0.120 0.000 0.000 0.000 0.000 0.880
#> GSM711954 1 0.0862 0.88644 0.972 0.000 0.004 0.008 0.000 0.016
#> GSM711962 1 0.1663 0.88104 0.912 0.000 0.000 0.000 0.000 0.088
#> GSM711970 1 0.0922 0.89294 0.968 0.000 0.004 0.004 0.000 0.024
#> GSM711974 1 0.0717 0.88946 0.976 0.000 0.008 0.000 0.000 0.016
#> GSM711978 4 0.3489 0.45283 0.288 0.000 0.000 0.708 0.000 0.004
#> GSM711988 1 0.0291 0.88444 0.992 0.000 0.004 0.004 0.000 0.000
#> GSM711990 3 0.1152 0.88473 0.044 0.000 0.952 0.000 0.000 0.004
#> GSM711992 1 0.4063 -0.06977 0.572 0.000 0.004 0.420 0.000 0.004
#> GSM711982 6 0.2003 0.92740 0.116 0.000 0.000 0.000 0.000 0.884
#> GSM711984 2 0.0972 0.93570 0.000 0.964 0.000 0.028 0.000 0.008
#> GSM711912 6 0.2048 0.92760 0.120 0.000 0.000 0.000 0.000 0.880
#> GSM711918 6 0.2048 0.92760 0.120 0.000 0.000 0.000 0.000 0.880
#> GSM711920 1 0.1444 0.89054 0.928 0.000 0.000 0.000 0.000 0.072
#> GSM711937 2 0.1398 0.92141 0.000 0.940 0.000 0.052 0.000 0.008
#> GSM711939 2 0.0547 0.94242 0.000 0.980 0.000 0.020 0.000 0.000
#> GSM711951 4 0.4093 0.00081 0.000 0.476 0.000 0.516 0.000 0.008
#> GSM711957 5 0.3161 0.00000 0.008 0.000 0.000 0.216 0.776 0.000
#> GSM711959 2 0.0632 0.94154 0.000 0.976 0.000 0.024 0.000 0.000
#> GSM711961 2 0.0632 0.94320 0.000 0.976 0.000 0.000 0.000 0.024
#> GSM711965 4 0.4893 0.49639 0.416 0.000 0.044 0.532 0.000 0.008
#> GSM711967 1 0.1531 0.88950 0.928 0.000 0.000 0.004 0.000 0.068
#> GSM711969 2 0.1398 0.92141 0.000 0.940 0.000 0.052 0.000 0.008
#> GSM711973 3 0.5093 0.71765 0.084 0.000 0.728 0.128 0.028 0.032
#> GSM711977 3 0.2886 0.84242 0.000 0.000 0.872 0.060 0.028 0.040
#> GSM711981 4 0.2810 0.39693 0.156 0.008 0.000 0.832 0.000 0.004
#> GSM711987 2 0.0632 0.94320 0.000 0.976 0.000 0.000 0.000 0.024
#> GSM711905 2 0.0632 0.94320 0.000 0.976 0.000 0.000 0.000 0.024
#> GSM711907 2 0.3955 0.44434 0.000 0.648 0.000 0.340 0.004 0.008
#> GSM711909 3 0.0000 0.89230 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711911 3 0.0000 0.89230 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711915 3 0.5189 0.66506 0.000 0.000 0.676 0.072 0.200 0.052
#> GSM711917 2 0.0632 0.94154 0.000 0.976 0.000 0.024 0.000 0.000
#> GSM711923 4 0.5065 0.51581 0.404 0.004 0.056 0.532 0.000 0.004
#> GSM711925 2 0.0632 0.94320 0.000 0.976 0.000 0.000 0.000 0.024
#> GSM711927 3 0.0000 0.89230 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711929 2 0.0632 0.94320 0.000 0.976 0.000 0.000 0.000 0.024
#> GSM711931 4 0.3713 0.16052 0.004 0.284 0.000 0.704 0.000 0.008
#> GSM711933 1 0.0291 0.88552 0.992 0.000 0.004 0.004 0.000 0.000
#> GSM711935 2 0.0632 0.94320 0.000 0.976 0.000 0.000 0.000 0.024
#> GSM711941 4 0.4808 0.45951 0.444 0.000 0.036 0.512 0.000 0.008
#> GSM711943 4 0.5020 0.51147 0.408 0.004 0.052 0.532 0.000 0.004
#> GSM711945 4 0.5589 0.52847 0.392 0.004 0.088 0.504 0.000 0.012
#> GSM711947 4 0.7595 -0.15026 0.000 0.100 0.252 0.424 0.196 0.028
#> GSM711949 2 0.0632 0.94320 0.000 0.976 0.000 0.000 0.000 0.024
#> GSM711953 2 0.0632 0.94320 0.000 0.976 0.000 0.000 0.000 0.024
#> GSM711955 1 0.1674 0.82115 0.924 0.000 0.004 0.068 0.000 0.004
#> GSM711963 2 0.0632 0.94320 0.000 0.976 0.000 0.000 0.000 0.024
#> GSM711971 3 0.1152 0.88473 0.044 0.000 0.952 0.000 0.000 0.004
#> GSM711975 4 0.4093 0.00081 0.000 0.476 0.000 0.516 0.000 0.008
#> GSM711979 4 0.3489 0.45283 0.288 0.000 0.000 0.708 0.000 0.004
#> GSM711989 4 0.4093 0.00081 0.000 0.476 0.000 0.516 0.000 0.008
#> GSM711991 4 0.6844 -0.13696 0.004 0.024 0.252 0.496 0.196 0.028
#> GSM711993 4 0.4635 0.32434 0.132 0.148 0.000 0.712 0.000 0.008
#> GSM711983 3 0.1152 0.88473 0.044 0.000 0.952 0.000 0.000 0.004
#> GSM711985 2 0.0632 0.94154 0.000 0.976 0.000 0.024 0.000 0.000
#> GSM711913 3 0.2886 0.84242 0.000 0.000 0.872 0.060 0.028 0.040
#> GSM711919 3 0.0000 0.89230 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711921 3 0.2452 0.84577 0.000 0.000 0.892 0.044 0.056 0.008
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) disease.state(p) individual(p) k
#> MAD:hclust 86 8.01e-04 0.195 0.306 2
#> MAD:hclust 85 2.23e-07 0.121 0.486 3
#> MAD:hclust 76 1.23e-08 0.291 0.357 4
#> MAD:hclust 75 5.45e-07 0.126 0.279 5
#> MAD:hclust 72 8.66e-08 0.151 0.558 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "kmeans"]
# you can also extract it by
# res = res_list["MAD:kmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 27425 rows and 90 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.966 0.987 0.4001 0.604 0.604
#> 3 3 0.965 0.924 0.970 0.6017 0.725 0.554
#> 4 4 0.916 0.870 0.945 0.1410 0.849 0.608
#> 5 5 0.732 0.695 0.757 0.0658 0.935 0.788
#> 6 6 0.707 0.613 0.760 0.0438 0.910 0.685
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 2 3
There is also optional best \(k\) = 2 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM711936 2 0.000 0.983 0.000 1.000
#> GSM711938 2 0.000 0.983 0.000 1.000
#> GSM711950 1 0.000 0.987 1.000 0.000
#> GSM711956 1 0.000 0.987 1.000 0.000
#> GSM711958 1 0.000 0.987 1.000 0.000
#> GSM711960 1 0.000 0.987 1.000 0.000
#> GSM711964 1 0.000 0.987 1.000 0.000
#> GSM711966 1 0.000 0.987 1.000 0.000
#> GSM711968 1 0.000 0.987 1.000 0.000
#> GSM711972 1 0.000 0.987 1.000 0.000
#> GSM711976 1 0.000 0.987 1.000 0.000
#> GSM711980 1 0.000 0.987 1.000 0.000
#> GSM711986 1 0.000 0.987 1.000 0.000
#> GSM711904 1 0.000 0.987 1.000 0.000
#> GSM711906 1 0.000 0.987 1.000 0.000
#> GSM711908 1 0.000 0.987 1.000 0.000
#> GSM711910 1 0.000 0.987 1.000 0.000
#> GSM711914 1 0.000 0.987 1.000 0.000
#> GSM711916 1 0.000 0.987 1.000 0.000
#> GSM711922 1 0.000 0.987 1.000 0.000
#> GSM711924 1 0.000 0.987 1.000 0.000
#> GSM711926 1 0.814 0.661 0.748 0.252
#> GSM711928 1 0.000 0.987 1.000 0.000
#> GSM711930 1 0.000 0.987 1.000 0.000
#> GSM711932 1 0.000 0.987 1.000 0.000
#> GSM711934 1 0.000 0.987 1.000 0.000
#> GSM711940 1 0.000 0.987 1.000 0.000
#> GSM711942 1 0.000 0.987 1.000 0.000
#> GSM711944 1 0.000 0.987 1.000 0.000
#> GSM711946 1 0.000 0.987 1.000 0.000
#> GSM711948 1 0.000 0.987 1.000 0.000
#> GSM711952 1 0.000 0.987 1.000 0.000
#> GSM711954 1 0.000 0.987 1.000 0.000
#> GSM711962 1 0.000 0.987 1.000 0.000
#> GSM711970 1 0.000 0.987 1.000 0.000
#> GSM711974 1 0.000 0.987 1.000 0.000
#> GSM711978 1 0.000 0.987 1.000 0.000
#> GSM711988 1 0.000 0.987 1.000 0.000
#> GSM711990 1 0.000 0.987 1.000 0.000
#> GSM711992 1 0.000 0.987 1.000 0.000
#> GSM711982 1 0.000 0.987 1.000 0.000
#> GSM711984 2 0.000 0.983 0.000 1.000
#> GSM711912 1 0.000 0.987 1.000 0.000
#> GSM711918 1 0.000 0.987 1.000 0.000
#> GSM711920 1 0.000 0.987 1.000 0.000
#> GSM711937 2 0.000 0.983 0.000 1.000
#> GSM711939 2 0.000 0.983 0.000 1.000
#> GSM711951 2 0.000 0.983 0.000 1.000
#> GSM711957 1 0.000 0.987 1.000 0.000
#> GSM711959 2 0.000 0.983 0.000 1.000
#> GSM711961 2 0.000 0.983 0.000 1.000
#> GSM711965 1 0.000 0.987 1.000 0.000
#> GSM711967 1 0.000 0.987 1.000 0.000
#> GSM711969 2 0.000 0.983 0.000 1.000
#> GSM711973 1 0.000 0.987 1.000 0.000
#> GSM711977 1 0.000 0.987 1.000 0.000
#> GSM711981 1 0.529 0.858 0.880 0.120
#> GSM711987 2 0.000 0.983 0.000 1.000
#> GSM711905 2 0.000 0.983 0.000 1.000
#> GSM711907 2 0.000 0.983 0.000 1.000
#> GSM711909 1 0.000 0.987 1.000 0.000
#> GSM711911 1 0.000 0.987 1.000 0.000
#> GSM711915 1 0.000 0.987 1.000 0.000
#> GSM711917 2 0.000 0.983 0.000 1.000
#> GSM711923 1 0.000 0.987 1.000 0.000
#> GSM711925 2 0.000 0.983 0.000 1.000
#> GSM711927 1 0.000 0.987 1.000 0.000
#> GSM711929 2 0.000 0.983 0.000 1.000
#> GSM711931 2 0.000 0.983 0.000 1.000
#> GSM711933 1 0.000 0.987 1.000 0.000
#> GSM711935 2 0.000 0.983 0.000 1.000
#> GSM711941 1 0.000 0.987 1.000 0.000
#> GSM711943 1 0.000 0.987 1.000 0.000
#> GSM711945 1 0.141 0.969 0.980 0.020
#> GSM711947 2 0.955 0.376 0.376 0.624
#> GSM711949 2 0.000 0.983 0.000 1.000
#> GSM711953 2 0.000 0.983 0.000 1.000
#> GSM711955 1 0.000 0.987 1.000 0.000
#> GSM711963 2 0.000 0.983 0.000 1.000
#> GSM711971 1 0.000 0.987 1.000 0.000
#> GSM711975 2 0.000 0.983 0.000 1.000
#> GSM711979 1 0.000 0.987 1.000 0.000
#> GSM711989 2 0.000 0.983 0.000 1.000
#> GSM711991 1 0.141 0.969 0.980 0.020
#> GSM711993 1 0.975 0.308 0.592 0.408
#> GSM711983 1 0.000 0.987 1.000 0.000
#> GSM711985 2 0.000 0.983 0.000 1.000
#> GSM711913 1 0.000 0.987 1.000 0.000
#> GSM711919 1 0.000 0.987 1.000 0.000
#> GSM711921 1 0.000 0.987 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM711936 2 0.000 0.977 0.000 1.000 0.000
#> GSM711938 2 0.000 0.977 0.000 1.000 0.000
#> GSM711950 1 0.000 0.982 1.000 0.000 0.000
#> GSM711956 1 0.000 0.982 1.000 0.000 0.000
#> GSM711958 1 0.000 0.982 1.000 0.000 0.000
#> GSM711960 3 0.622 0.308 0.432 0.000 0.568
#> GSM711964 1 0.000 0.982 1.000 0.000 0.000
#> GSM711966 1 0.000 0.982 1.000 0.000 0.000
#> GSM711968 1 0.000 0.982 1.000 0.000 0.000
#> GSM711972 1 0.000 0.982 1.000 0.000 0.000
#> GSM711976 1 0.000 0.982 1.000 0.000 0.000
#> GSM711980 1 0.000 0.982 1.000 0.000 0.000
#> GSM711986 1 0.000 0.982 1.000 0.000 0.000
#> GSM711904 1 0.000 0.982 1.000 0.000 0.000
#> GSM711906 1 0.000 0.982 1.000 0.000 0.000
#> GSM711908 1 0.000 0.982 1.000 0.000 0.000
#> GSM711910 3 0.000 0.921 0.000 0.000 1.000
#> GSM711914 1 0.000 0.982 1.000 0.000 0.000
#> GSM711916 1 0.000 0.982 1.000 0.000 0.000
#> GSM711922 1 0.000 0.982 1.000 0.000 0.000
#> GSM711924 1 0.000 0.982 1.000 0.000 0.000
#> GSM711926 1 0.502 0.667 0.760 0.240 0.000
#> GSM711928 1 0.000 0.982 1.000 0.000 0.000
#> GSM711930 1 0.000 0.982 1.000 0.000 0.000
#> GSM711932 1 0.000 0.982 1.000 0.000 0.000
#> GSM711934 1 0.000 0.982 1.000 0.000 0.000
#> GSM711940 1 0.000 0.982 1.000 0.000 0.000
#> GSM711942 1 0.000 0.982 1.000 0.000 0.000
#> GSM711944 3 0.000 0.921 0.000 0.000 1.000
#> GSM711946 3 0.000 0.921 0.000 0.000 1.000
#> GSM711948 1 0.000 0.982 1.000 0.000 0.000
#> GSM711952 1 0.000 0.982 1.000 0.000 0.000
#> GSM711954 1 0.000 0.982 1.000 0.000 0.000
#> GSM711962 1 0.000 0.982 1.000 0.000 0.000
#> GSM711970 1 0.000 0.982 1.000 0.000 0.000
#> GSM711974 1 0.000 0.982 1.000 0.000 0.000
#> GSM711978 1 0.000 0.982 1.000 0.000 0.000
#> GSM711988 1 0.000 0.982 1.000 0.000 0.000
#> GSM711990 3 0.000 0.921 0.000 0.000 1.000
#> GSM711992 1 0.000 0.982 1.000 0.000 0.000
#> GSM711982 1 0.000 0.982 1.000 0.000 0.000
#> GSM711984 2 0.000 0.977 0.000 1.000 0.000
#> GSM711912 1 0.000 0.982 1.000 0.000 0.000
#> GSM711918 1 0.000 0.982 1.000 0.000 0.000
#> GSM711920 1 0.000 0.982 1.000 0.000 0.000
#> GSM711937 2 0.000 0.977 0.000 1.000 0.000
#> GSM711939 2 0.000 0.977 0.000 1.000 0.000
#> GSM711951 2 0.000 0.977 0.000 1.000 0.000
#> GSM711957 1 0.000 0.982 1.000 0.000 0.000
#> GSM711959 2 0.000 0.977 0.000 1.000 0.000
#> GSM711961 2 0.000 0.977 0.000 1.000 0.000
#> GSM711965 3 0.000 0.921 0.000 0.000 1.000
#> GSM711967 1 0.000 0.982 1.000 0.000 0.000
#> GSM711969 2 0.000 0.977 0.000 1.000 0.000
#> GSM711973 3 0.493 0.708 0.232 0.000 0.768
#> GSM711977 3 0.000 0.921 0.000 0.000 1.000
#> GSM711981 3 0.888 0.511 0.212 0.212 0.576
#> GSM711987 2 0.000 0.977 0.000 1.000 0.000
#> GSM711905 2 0.000 0.977 0.000 1.000 0.000
#> GSM711907 2 0.000 0.977 0.000 1.000 0.000
#> GSM711909 3 0.000 0.921 0.000 0.000 1.000
#> GSM711911 3 0.000 0.921 0.000 0.000 1.000
#> GSM711915 3 0.000 0.921 0.000 0.000 1.000
#> GSM711917 2 0.000 0.977 0.000 1.000 0.000
#> GSM711923 3 0.196 0.883 0.056 0.000 0.944
#> GSM711925 2 0.000 0.977 0.000 1.000 0.000
#> GSM711927 3 0.000 0.921 0.000 0.000 1.000
#> GSM711929 2 0.000 0.977 0.000 1.000 0.000
#> GSM711931 2 0.000 0.977 0.000 1.000 0.000
#> GSM711933 1 0.000 0.982 1.000 0.000 0.000
#> GSM711935 2 0.000 0.977 0.000 1.000 0.000
#> GSM711941 1 0.620 0.179 0.576 0.000 0.424
#> GSM711943 3 0.263 0.861 0.084 0.000 0.916
#> GSM711945 3 0.000 0.921 0.000 0.000 1.000
#> GSM711947 3 0.103 0.903 0.000 0.024 0.976
#> GSM711949 2 0.000 0.977 0.000 1.000 0.000
#> GSM711953 2 0.000 0.977 0.000 1.000 0.000
#> GSM711955 3 0.608 0.429 0.388 0.000 0.612
#> GSM711963 2 0.000 0.977 0.000 1.000 0.000
#> GSM711971 3 0.000 0.921 0.000 0.000 1.000
#> GSM711975 2 0.000 0.977 0.000 1.000 0.000
#> GSM711979 1 0.000 0.982 1.000 0.000 0.000
#> GSM711989 2 0.000 0.977 0.000 1.000 0.000
#> GSM711991 3 0.000 0.921 0.000 0.000 1.000
#> GSM711993 2 0.619 0.258 0.420 0.580 0.000
#> GSM711983 3 0.000 0.921 0.000 0.000 1.000
#> GSM711985 2 0.000 0.977 0.000 1.000 0.000
#> GSM711913 3 0.000 0.921 0.000 0.000 1.000
#> GSM711919 3 0.000 0.921 0.000 0.000 1.000
#> GSM711921 3 0.000 0.921 0.000 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM711936 2 0.0000 0.968 0.000 1.000 0.000 0.000
#> GSM711938 2 0.0000 0.968 0.000 1.000 0.000 0.000
#> GSM711950 4 0.1302 0.840 0.044 0.000 0.000 0.956
#> GSM711956 1 0.0000 0.951 1.000 0.000 0.000 0.000
#> GSM711958 1 0.1022 0.945 0.968 0.000 0.000 0.032
#> GSM711960 1 0.2521 0.894 0.912 0.000 0.064 0.024
#> GSM711964 1 0.0000 0.951 1.000 0.000 0.000 0.000
#> GSM711966 1 0.0188 0.951 0.996 0.000 0.000 0.004
#> GSM711968 1 0.0188 0.951 0.996 0.000 0.000 0.004
#> GSM711972 1 0.0188 0.951 0.996 0.000 0.000 0.004
#> GSM711976 4 0.4994 0.119 0.480 0.000 0.000 0.520
#> GSM711980 1 0.0921 0.945 0.972 0.000 0.000 0.028
#> GSM711986 1 0.0188 0.951 0.996 0.000 0.000 0.004
#> GSM711904 1 0.0188 0.951 0.996 0.000 0.000 0.004
#> GSM711906 1 0.0336 0.951 0.992 0.000 0.000 0.008
#> GSM711908 1 0.0188 0.951 0.996 0.000 0.000 0.004
#> GSM711910 3 0.0000 0.939 0.000 0.000 1.000 0.000
#> GSM711914 1 0.0000 0.951 1.000 0.000 0.000 0.000
#> GSM711916 1 0.0188 0.951 0.996 0.000 0.000 0.004
#> GSM711922 1 0.1022 0.944 0.968 0.000 0.000 0.032
#> GSM711924 1 0.1022 0.945 0.968 0.000 0.000 0.032
#> GSM711926 4 0.0188 0.857 0.004 0.000 0.000 0.996
#> GSM711928 1 0.0000 0.951 1.000 0.000 0.000 0.000
#> GSM711930 1 0.0188 0.951 0.996 0.000 0.000 0.004
#> GSM711932 1 0.4888 0.244 0.588 0.000 0.000 0.412
#> GSM711934 1 0.1022 0.945 0.968 0.000 0.000 0.032
#> GSM711940 1 0.4843 0.294 0.604 0.000 0.000 0.396
#> GSM711942 1 0.1118 0.944 0.964 0.000 0.000 0.036
#> GSM711944 3 0.0817 0.918 0.000 0.000 0.976 0.024
#> GSM711946 4 0.1211 0.834 0.000 0.000 0.040 0.960
#> GSM711948 4 0.3726 0.700 0.212 0.000 0.000 0.788
#> GSM711952 1 0.0188 0.951 0.996 0.000 0.000 0.004
#> GSM711954 1 0.1022 0.944 0.968 0.000 0.000 0.032
#> GSM711962 1 0.0188 0.951 0.996 0.000 0.000 0.004
#> GSM711970 1 0.1022 0.944 0.968 0.000 0.000 0.032
#> GSM711974 1 0.0188 0.951 0.996 0.000 0.000 0.004
#> GSM711978 4 0.0188 0.857 0.004 0.000 0.000 0.996
#> GSM711988 1 0.3528 0.745 0.808 0.000 0.000 0.192
#> GSM711990 3 0.0000 0.939 0.000 0.000 1.000 0.000
#> GSM711992 4 0.0188 0.857 0.004 0.000 0.000 0.996
#> GSM711982 1 0.0188 0.951 0.996 0.000 0.000 0.004
#> GSM711984 2 0.0000 0.968 0.000 1.000 0.000 0.000
#> GSM711912 1 0.0188 0.951 0.996 0.000 0.000 0.004
#> GSM711918 1 0.0188 0.951 0.996 0.000 0.000 0.004
#> GSM711920 1 0.1118 0.944 0.964 0.000 0.000 0.036
#> GSM711937 2 0.0000 0.968 0.000 1.000 0.000 0.000
#> GSM711939 2 0.0000 0.968 0.000 1.000 0.000 0.000
#> GSM711951 4 0.1118 0.830 0.000 0.036 0.000 0.964
#> GSM711957 4 0.4888 0.321 0.412 0.000 0.000 0.588
#> GSM711959 2 0.0000 0.968 0.000 1.000 0.000 0.000
#> GSM711961 2 0.0000 0.968 0.000 1.000 0.000 0.000
#> GSM711965 3 0.4981 0.198 0.000 0.000 0.536 0.464
#> GSM711967 1 0.1211 0.942 0.960 0.000 0.000 0.040
#> GSM711969 2 0.0000 0.968 0.000 1.000 0.000 0.000
#> GSM711973 4 0.3205 0.780 0.024 0.000 0.104 0.872
#> GSM711977 3 0.0000 0.939 0.000 0.000 1.000 0.000
#> GSM711981 4 0.0188 0.857 0.004 0.000 0.000 0.996
#> GSM711987 2 0.0000 0.968 0.000 1.000 0.000 0.000
#> GSM711905 2 0.0000 0.968 0.000 1.000 0.000 0.000
#> GSM711907 2 0.1940 0.908 0.000 0.924 0.000 0.076
#> GSM711909 3 0.0000 0.939 0.000 0.000 1.000 0.000
#> GSM711911 3 0.0000 0.939 0.000 0.000 1.000 0.000
#> GSM711915 3 0.0000 0.939 0.000 0.000 1.000 0.000
#> GSM711917 2 0.0000 0.968 0.000 1.000 0.000 0.000
#> GSM711923 4 0.0188 0.856 0.000 0.000 0.004 0.996
#> GSM711925 2 0.0000 0.968 0.000 1.000 0.000 0.000
#> GSM711927 3 0.0000 0.939 0.000 0.000 1.000 0.000
#> GSM711929 2 0.0000 0.968 0.000 1.000 0.000 0.000
#> GSM711931 2 0.4804 0.428 0.000 0.616 0.000 0.384
#> GSM711933 1 0.1022 0.945 0.968 0.000 0.000 0.032
#> GSM711935 2 0.0000 0.968 0.000 1.000 0.000 0.000
#> GSM711941 4 0.0188 0.856 0.004 0.000 0.000 0.996
#> GSM711943 4 0.0000 0.857 0.000 0.000 0.000 1.000
#> GSM711945 4 0.1637 0.814 0.000 0.000 0.060 0.940
#> GSM711947 3 0.4621 0.770 0.000 0.128 0.796 0.076
#> GSM711949 2 0.0000 0.968 0.000 1.000 0.000 0.000
#> GSM711953 2 0.0000 0.968 0.000 1.000 0.000 0.000
#> GSM711955 4 0.6367 0.318 0.392 0.000 0.068 0.540
#> GSM711963 2 0.0000 0.968 0.000 1.000 0.000 0.000
#> GSM711971 3 0.0000 0.939 0.000 0.000 1.000 0.000
#> GSM711975 2 0.3266 0.808 0.000 0.832 0.000 0.168
#> GSM711979 4 0.0000 0.857 0.000 0.000 0.000 1.000
#> GSM711989 2 0.0921 0.948 0.000 0.972 0.000 0.028
#> GSM711991 3 0.3688 0.747 0.000 0.000 0.792 0.208
#> GSM711993 4 0.0188 0.856 0.000 0.004 0.000 0.996
#> GSM711983 3 0.0000 0.939 0.000 0.000 1.000 0.000
#> GSM711985 2 0.0000 0.968 0.000 1.000 0.000 0.000
#> GSM711913 3 0.0000 0.939 0.000 0.000 1.000 0.000
#> GSM711919 3 0.0000 0.939 0.000 0.000 1.000 0.000
#> GSM711921 3 0.0000 0.939 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM711936 2 0.4552 0.77464 0.000 0.696 0.000 0.040 NA
#> GSM711938 2 0.0000 0.87528 0.000 1.000 0.000 0.000 NA
#> GSM711950 4 0.5275 0.52041 0.276 0.000 0.000 0.640 NA
#> GSM711956 1 0.1121 0.73401 0.956 0.000 0.000 0.000 NA
#> GSM711958 1 0.1792 0.72694 0.916 0.000 0.000 0.000 NA
#> GSM711960 1 0.4351 0.64977 0.784 0.000 0.104 0.008 NA
#> GSM711964 1 0.4088 0.68107 0.632 0.000 0.000 0.000 NA
#> GSM711966 1 0.4294 0.65131 0.532 0.000 0.000 0.000 NA
#> GSM711968 1 0.2648 0.73125 0.848 0.000 0.000 0.000 NA
#> GSM711972 1 0.4291 0.64995 0.536 0.000 0.000 0.000 NA
#> GSM711976 1 0.4527 0.41150 0.700 0.000 0.000 0.260 NA
#> GSM711980 1 0.0404 0.72420 0.988 0.000 0.000 0.000 NA
#> GSM711986 1 0.4273 0.64896 0.552 0.000 0.000 0.000 NA
#> GSM711904 1 0.2813 0.72725 0.832 0.000 0.000 0.000 NA
#> GSM711906 1 0.4294 0.64766 0.532 0.000 0.000 0.000 NA
#> GSM711908 1 0.4287 0.64602 0.540 0.000 0.000 0.000 NA
#> GSM711910 3 0.0000 0.87440 0.000 0.000 1.000 0.000 NA
#> GSM711914 1 0.3895 0.69502 0.680 0.000 0.000 0.000 NA
#> GSM711916 1 0.4294 0.65131 0.532 0.000 0.000 0.000 NA
#> GSM711922 1 0.0162 0.72576 0.996 0.000 0.000 0.000 NA
#> GSM711924 1 0.1671 0.72999 0.924 0.000 0.000 0.000 NA
#> GSM711926 4 0.2233 0.75692 0.004 0.000 0.000 0.892 NA
#> GSM711928 1 0.2471 0.73175 0.864 0.000 0.000 0.000 NA
#> GSM711930 1 0.4297 0.64827 0.528 0.000 0.000 0.000 NA
#> GSM711932 1 0.4240 0.49124 0.736 0.000 0.000 0.228 NA
#> GSM711934 1 0.0963 0.72396 0.964 0.000 0.000 0.000 NA
#> GSM711940 1 0.5405 0.24343 0.596 0.000 0.000 0.328 NA
#> GSM711942 1 0.1478 0.73202 0.936 0.000 0.000 0.000 NA
#> GSM711944 3 0.7078 0.28377 0.340 0.000 0.484 0.064 NA
#> GSM711946 4 0.2871 0.75893 0.004 0.000 0.032 0.876 NA
#> GSM711948 1 0.5876 -0.09676 0.488 0.000 0.000 0.412 NA
#> GSM711952 1 0.4273 0.64896 0.552 0.000 0.000 0.000 NA
#> GSM711954 1 0.0798 0.72701 0.976 0.000 0.000 0.008 NA
#> GSM711962 1 0.2074 0.73569 0.896 0.000 0.000 0.000 NA
#> GSM711970 1 0.0671 0.72319 0.980 0.000 0.000 0.004 NA
#> GSM711974 1 0.2773 0.73453 0.836 0.000 0.000 0.000 NA
#> GSM711978 4 0.1386 0.79093 0.032 0.000 0.000 0.952 NA
#> GSM711988 1 0.3565 0.58399 0.816 0.000 0.000 0.144 NA
#> GSM711990 3 0.0703 0.87314 0.000 0.000 0.976 0.000 NA
#> GSM711992 4 0.1469 0.79072 0.036 0.000 0.000 0.948 NA
#> GSM711982 1 0.4294 0.65131 0.532 0.000 0.000 0.000 NA
#> GSM711984 2 0.1908 0.86564 0.000 0.908 0.000 0.000 NA
#> GSM711912 1 0.4273 0.64896 0.552 0.000 0.000 0.000 NA
#> GSM711918 1 0.4273 0.64896 0.552 0.000 0.000 0.000 NA
#> GSM711920 1 0.1410 0.73255 0.940 0.000 0.000 0.000 NA
#> GSM711937 2 0.4380 0.78433 0.000 0.708 0.000 0.032 NA
#> GSM711939 2 0.2516 0.85577 0.000 0.860 0.000 0.000 NA
#> GSM711951 4 0.3661 0.62834 0.000 0.000 0.000 0.724 NA
#> GSM711957 1 0.5304 0.34045 0.640 0.000 0.000 0.272 NA
#> GSM711959 2 0.2516 0.85577 0.000 0.860 0.000 0.000 NA
#> GSM711961 2 0.0000 0.87528 0.000 1.000 0.000 0.000 NA
#> GSM711965 3 0.6161 0.11056 0.000 0.000 0.444 0.424 NA
#> GSM711967 1 0.1830 0.73244 0.924 0.000 0.000 0.008 NA
#> GSM711969 2 0.4380 0.78433 0.000 0.708 0.000 0.032 NA
#> GSM711973 4 0.6554 0.51462 0.248 0.000 0.024 0.564 NA
#> GSM711977 3 0.2583 0.83564 0.000 0.000 0.864 0.004 NA
#> GSM711981 4 0.0963 0.78051 0.000 0.000 0.000 0.964 NA
#> GSM711987 2 0.0000 0.87528 0.000 1.000 0.000 0.000 NA
#> GSM711905 2 0.0000 0.87528 0.000 1.000 0.000 0.000 NA
#> GSM711907 2 0.6638 0.38756 0.000 0.452 0.000 0.272 NA
#> GSM711909 3 0.0000 0.87440 0.000 0.000 1.000 0.000 NA
#> GSM711911 3 0.0510 0.87393 0.000 0.000 0.984 0.000 NA
#> GSM711915 3 0.1792 0.85186 0.000 0.000 0.916 0.000 NA
#> GSM711917 2 0.4380 0.78433 0.000 0.708 0.000 0.032 NA
#> GSM711923 4 0.2344 0.77755 0.032 0.000 0.000 0.904 NA
#> GSM711925 2 0.0000 0.87528 0.000 1.000 0.000 0.000 NA
#> GSM711927 3 0.0000 0.87440 0.000 0.000 1.000 0.000 NA
#> GSM711929 2 0.0000 0.87528 0.000 1.000 0.000 0.000 NA
#> GSM711931 4 0.6518 0.18441 0.000 0.240 0.000 0.484 NA
#> GSM711933 1 0.2236 0.69646 0.908 0.000 0.000 0.024 NA
#> GSM711935 2 0.0000 0.87528 0.000 1.000 0.000 0.000 NA
#> GSM711941 4 0.2616 0.77135 0.036 0.000 0.000 0.888 NA
#> GSM711943 4 0.1386 0.78972 0.032 0.000 0.000 0.952 NA
#> GSM711945 4 0.2879 0.75624 0.000 0.000 0.032 0.868 NA
#> GSM711947 3 0.4875 0.72124 0.000 0.044 0.768 0.096 NA
#> GSM711949 2 0.0000 0.87528 0.000 1.000 0.000 0.000 NA
#> GSM711953 2 0.0000 0.87528 0.000 1.000 0.000 0.000 NA
#> GSM711955 1 0.6848 -0.00765 0.496 0.000 0.044 0.344 NA
#> GSM711963 2 0.0000 0.87528 0.000 1.000 0.000 0.000 NA
#> GSM711971 3 0.0609 0.87361 0.000 0.000 0.980 0.000 NA
#> GSM711975 4 0.6673 0.04679 0.000 0.284 0.000 0.440 NA
#> GSM711979 4 0.0963 0.79092 0.036 0.000 0.000 0.964 NA
#> GSM711989 2 0.5467 0.69875 0.000 0.624 0.000 0.100 NA
#> GSM711991 3 0.3988 0.70466 0.000 0.000 0.768 0.196 NA
#> GSM711993 4 0.2280 0.74834 0.000 0.000 0.000 0.880 NA
#> GSM711983 3 0.0703 0.87314 0.000 0.000 0.976 0.000 NA
#> GSM711985 2 0.2377 0.85885 0.000 0.872 0.000 0.000 NA
#> GSM711913 3 0.2583 0.83564 0.000 0.000 0.864 0.004 NA
#> GSM711919 3 0.0000 0.87440 0.000 0.000 1.000 0.000 NA
#> GSM711921 3 0.0000 0.87440 0.000 0.000 1.000 0.000 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM711936 2 0.4348 0.3961 0.000 0.600 0.000 0.016 0.376 0.008
#> GSM711938 2 0.1124 0.7901 0.000 0.956 0.000 0.000 0.036 0.008
#> GSM711950 4 0.6110 0.3229 0.292 0.000 0.000 0.544 0.104 0.060
#> GSM711956 1 0.2179 0.6547 0.900 0.000 0.000 0.000 0.064 0.036
#> GSM711958 1 0.2812 0.6439 0.856 0.000 0.000 0.000 0.048 0.096
#> GSM711960 1 0.5319 0.5586 0.688 0.000 0.112 0.004 0.048 0.148
#> GSM711964 1 0.4607 -0.0163 0.616 0.000 0.000 0.000 0.056 0.328
#> GSM711966 6 0.3784 0.8803 0.308 0.000 0.000 0.000 0.012 0.680
#> GSM711968 1 0.3883 0.5298 0.768 0.000 0.000 0.000 0.088 0.144
#> GSM711972 6 0.3650 0.8928 0.280 0.000 0.000 0.000 0.012 0.708
#> GSM711976 1 0.5418 0.5469 0.652 0.000 0.000 0.204 0.100 0.044
#> GSM711980 1 0.0520 0.6802 0.984 0.000 0.000 0.000 0.008 0.008
#> GSM711986 6 0.4671 0.8631 0.304 0.000 0.000 0.000 0.068 0.628
#> GSM711904 1 0.4046 0.4602 0.748 0.000 0.000 0.000 0.084 0.168
#> GSM711906 6 0.3383 0.8898 0.268 0.000 0.000 0.000 0.004 0.728
#> GSM711908 6 0.4190 0.8863 0.260 0.000 0.000 0.000 0.048 0.692
#> GSM711910 3 0.0692 0.8450 0.000 0.000 0.976 0.000 0.004 0.020
#> GSM711914 1 0.4652 0.1506 0.640 0.000 0.000 0.000 0.072 0.288
#> GSM711916 6 0.3766 0.8842 0.304 0.000 0.000 0.000 0.012 0.684
#> GSM711922 1 0.1921 0.6703 0.916 0.000 0.000 0.000 0.052 0.032
#> GSM711924 1 0.3225 0.6456 0.828 0.000 0.000 0.000 0.092 0.080
#> GSM711926 4 0.3244 0.2689 0.000 0.000 0.000 0.732 0.268 0.000
#> GSM711928 1 0.3551 0.5265 0.792 0.000 0.000 0.000 0.060 0.148
#> GSM711930 6 0.3448 0.8909 0.280 0.000 0.000 0.000 0.004 0.716
#> GSM711932 1 0.4517 0.6260 0.744 0.000 0.000 0.116 0.116 0.024
#> GSM711934 1 0.0914 0.6803 0.968 0.000 0.000 0.000 0.016 0.016
#> GSM711940 1 0.5791 0.3431 0.560 0.000 0.000 0.312 0.052 0.076
#> GSM711942 1 0.3225 0.6456 0.828 0.000 0.000 0.000 0.092 0.080
#> GSM711944 3 0.7761 0.1559 0.308 0.000 0.400 0.068 0.148 0.076
#> GSM711946 4 0.3768 0.5981 0.008 0.000 0.004 0.796 0.136 0.056
#> GSM711948 1 0.6386 0.1940 0.488 0.000 0.000 0.332 0.112 0.068
#> GSM711952 6 0.4829 0.8524 0.308 0.000 0.000 0.000 0.080 0.612
#> GSM711954 1 0.1777 0.6725 0.928 0.000 0.000 0.004 0.044 0.024
#> GSM711962 1 0.3385 0.5667 0.788 0.000 0.000 0.000 0.032 0.180
#> GSM711970 1 0.1320 0.6812 0.948 0.000 0.000 0.000 0.036 0.016
#> GSM711974 1 0.3352 0.5684 0.792 0.000 0.000 0.000 0.032 0.176
#> GSM711978 4 0.1531 0.5847 0.004 0.000 0.000 0.928 0.068 0.000
#> GSM711988 1 0.4271 0.6216 0.772 0.000 0.000 0.116 0.076 0.036
#> GSM711990 3 0.1672 0.8438 0.000 0.000 0.932 0.004 0.048 0.016
#> GSM711992 4 0.1643 0.5874 0.008 0.000 0.000 0.924 0.068 0.000
#> GSM711982 6 0.3766 0.8842 0.304 0.000 0.000 0.000 0.012 0.684
#> GSM711984 2 0.2771 0.7633 0.000 0.852 0.000 0.000 0.116 0.032
#> GSM711912 6 0.4735 0.8667 0.296 0.000 0.000 0.000 0.076 0.628
#> GSM711918 6 0.4735 0.8667 0.296 0.000 0.000 0.000 0.076 0.628
#> GSM711920 1 0.3167 0.6490 0.832 0.000 0.000 0.000 0.096 0.072
#> GSM711937 2 0.4034 0.4621 0.000 0.624 0.000 0.004 0.364 0.008
#> GSM711939 2 0.2768 0.7401 0.000 0.832 0.000 0.000 0.156 0.012
#> GSM711951 4 0.3774 -0.1717 0.000 0.000 0.000 0.592 0.408 0.000
#> GSM711957 1 0.6514 0.4412 0.524 0.000 0.000 0.180 0.228 0.068
#> GSM711959 2 0.2981 0.7372 0.000 0.820 0.000 0.000 0.160 0.020
#> GSM711961 2 0.0000 0.7943 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711965 4 0.7087 0.2642 0.004 0.000 0.208 0.460 0.232 0.096
#> GSM711967 1 0.3479 0.6397 0.820 0.000 0.000 0.008 0.084 0.088
#> GSM711969 2 0.4115 0.4655 0.000 0.624 0.000 0.004 0.360 0.012
#> GSM711973 4 0.6806 0.4085 0.148 0.000 0.000 0.480 0.272 0.100
#> GSM711977 3 0.4591 0.7430 0.000 0.000 0.688 0.004 0.224 0.084
#> GSM711981 4 0.1765 0.5674 0.000 0.000 0.000 0.904 0.096 0.000
#> GSM711987 2 0.0547 0.7934 0.000 0.980 0.000 0.000 0.000 0.020
#> GSM711905 2 0.0000 0.7943 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711907 5 0.5963 0.7456 0.000 0.276 0.000 0.272 0.452 0.000
#> GSM711909 3 0.0291 0.8464 0.000 0.000 0.992 0.000 0.004 0.004
#> GSM711911 3 0.1226 0.8464 0.000 0.000 0.952 0.004 0.040 0.004
#> GSM711915 3 0.4174 0.7671 0.000 0.000 0.736 0.000 0.172 0.092
#> GSM711917 2 0.4115 0.4655 0.000 0.624 0.000 0.004 0.360 0.012
#> GSM711923 4 0.2978 0.6137 0.012 0.000 0.000 0.860 0.072 0.056
#> GSM711925 2 0.0260 0.7944 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM711927 3 0.0000 0.8472 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711929 2 0.0000 0.7943 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711931 4 0.5744 -0.7985 0.000 0.168 0.000 0.424 0.408 0.000
#> GSM711933 1 0.2765 0.6720 0.872 0.000 0.000 0.008 0.064 0.056
#> GSM711935 2 0.0632 0.7932 0.000 0.976 0.000 0.000 0.000 0.024
#> GSM711941 4 0.3439 0.6023 0.016 0.000 0.000 0.828 0.096 0.060
#> GSM711943 4 0.0976 0.6140 0.008 0.000 0.000 0.968 0.016 0.008
#> GSM711945 4 0.3685 0.5889 0.000 0.000 0.004 0.796 0.120 0.080
#> GSM711947 3 0.5637 0.6426 0.000 0.008 0.672 0.092 0.148 0.080
#> GSM711949 2 0.0632 0.7932 0.000 0.976 0.000 0.000 0.000 0.024
#> GSM711953 2 0.0000 0.7943 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711955 1 0.6535 0.2558 0.524 0.000 0.008 0.284 0.108 0.076
#> GSM711963 2 0.0632 0.7932 0.000 0.976 0.000 0.000 0.000 0.024
#> GSM711971 3 0.1511 0.8453 0.000 0.000 0.940 0.004 0.044 0.012
#> GSM711975 5 0.5753 0.7254 0.000 0.172 0.000 0.384 0.444 0.000
#> GSM711979 4 0.0405 0.6133 0.008 0.000 0.000 0.988 0.004 0.000
#> GSM711989 2 0.5260 -0.2382 0.000 0.464 0.000 0.096 0.440 0.000
#> GSM711991 3 0.5355 0.6118 0.000 0.000 0.660 0.208 0.064 0.068
#> GSM711993 4 0.3198 0.3047 0.000 0.000 0.000 0.740 0.260 0.000
#> GSM711983 3 0.1672 0.8438 0.000 0.000 0.932 0.004 0.048 0.016
#> GSM711985 2 0.2730 0.7473 0.000 0.836 0.000 0.000 0.152 0.012
#> GSM711913 3 0.4591 0.7430 0.000 0.000 0.688 0.004 0.224 0.084
#> GSM711919 3 0.0000 0.8472 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711921 3 0.0692 0.8450 0.000 0.000 0.976 0.000 0.004 0.020
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) disease.state(p) individual(p) k
#> MAD:kmeans 88 6.08e-05 0.209 0.473 2
#> MAD:kmeans 86 3.75e-11 0.308 0.623 3
#> MAD:kmeans 83 5.91e-09 0.122 0.362 4
#> MAD:kmeans 79 4.70e-09 0.121 0.273 5
#> MAD:kmeans 70 9.12e-08 0.265 0.400 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "skmeans"]
# you can also extract it by
# res = res_list["MAD:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 27425 rows and 90 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.976 0.939 0.977 0.4827 0.519 0.519
#> 3 3 1.000 0.947 0.980 0.3639 0.747 0.545
#> 4 4 0.893 0.890 0.956 0.0961 0.913 0.753
#> 5 5 0.792 0.668 0.852 0.0822 0.913 0.698
#> 6 6 0.766 0.601 0.785 0.0430 0.911 0.634
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
#> attr(,"optional")
#> [1] 2
There is also optional best \(k\) = 2 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM711936 2 0.0000 0.97446 0.000 1.000
#> GSM711938 2 0.0000 0.97446 0.000 1.000
#> GSM711950 1 0.0000 0.97511 1.000 0.000
#> GSM711956 1 0.0000 0.97511 1.000 0.000
#> GSM711958 1 0.0000 0.97511 1.000 0.000
#> GSM711960 1 0.0000 0.97511 1.000 0.000
#> GSM711964 1 0.0000 0.97511 1.000 0.000
#> GSM711966 1 0.0000 0.97511 1.000 0.000
#> GSM711968 1 0.0000 0.97511 1.000 0.000
#> GSM711972 1 0.0000 0.97511 1.000 0.000
#> GSM711976 1 0.0000 0.97511 1.000 0.000
#> GSM711980 1 0.0000 0.97511 1.000 0.000
#> GSM711986 1 0.0000 0.97511 1.000 0.000
#> GSM711904 1 0.0000 0.97511 1.000 0.000
#> GSM711906 1 0.0000 0.97511 1.000 0.000
#> GSM711908 1 0.0000 0.97511 1.000 0.000
#> GSM711910 1 0.0000 0.97511 1.000 0.000
#> GSM711914 1 0.0000 0.97511 1.000 0.000
#> GSM711916 1 0.0000 0.97511 1.000 0.000
#> GSM711922 1 0.0000 0.97511 1.000 0.000
#> GSM711924 1 0.0000 0.97511 1.000 0.000
#> GSM711926 2 0.0000 0.97446 0.000 1.000
#> GSM711928 1 0.0000 0.97511 1.000 0.000
#> GSM711930 1 0.0000 0.97511 1.000 0.000
#> GSM711932 1 0.0000 0.97511 1.000 0.000
#> GSM711934 1 0.0000 0.97511 1.000 0.000
#> GSM711940 1 0.0000 0.97511 1.000 0.000
#> GSM711942 1 0.0000 0.97511 1.000 0.000
#> GSM711944 1 0.0000 0.97511 1.000 0.000
#> GSM711946 1 0.8443 0.62694 0.728 0.272
#> GSM711948 1 0.0000 0.97511 1.000 0.000
#> GSM711952 1 0.0000 0.97511 1.000 0.000
#> GSM711954 1 0.0000 0.97511 1.000 0.000
#> GSM711962 1 0.0000 0.97511 1.000 0.000
#> GSM711970 1 0.0000 0.97511 1.000 0.000
#> GSM711974 1 0.0000 0.97511 1.000 0.000
#> GSM711978 2 0.0000 0.97446 0.000 1.000
#> GSM711988 1 0.0000 0.97511 1.000 0.000
#> GSM711990 1 0.0000 0.97511 1.000 0.000
#> GSM711992 2 0.0000 0.97446 0.000 1.000
#> GSM711982 1 0.0000 0.97511 1.000 0.000
#> GSM711984 2 0.0000 0.97446 0.000 1.000
#> GSM711912 1 0.0000 0.97511 1.000 0.000
#> GSM711918 1 0.0000 0.97511 1.000 0.000
#> GSM711920 1 0.0000 0.97511 1.000 0.000
#> GSM711937 2 0.0000 0.97446 0.000 1.000
#> GSM711939 2 0.0000 0.97446 0.000 1.000
#> GSM711951 2 0.0000 0.97446 0.000 1.000
#> GSM711957 2 0.9209 0.48521 0.336 0.664
#> GSM711959 2 0.0000 0.97446 0.000 1.000
#> GSM711961 2 0.0000 0.97446 0.000 1.000
#> GSM711965 1 0.0000 0.97511 1.000 0.000
#> GSM711967 1 0.0000 0.97511 1.000 0.000
#> GSM711969 2 0.0000 0.97446 0.000 1.000
#> GSM711973 1 0.0000 0.97511 1.000 0.000
#> GSM711977 1 0.9710 0.34514 0.600 0.400
#> GSM711981 2 0.0000 0.97446 0.000 1.000
#> GSM711987 2 0.0000 0.97446 0.000 1.000
#> GSM711905 2 0.0000 0.97446 0.000 1.000
#> GSM711907 2 0.0000 0.97446 0.000 1.000
#> GSM711909 1 0.0000 0.97511 1.000 0.000
#> GSM711911 1 0.0000 0.97511 1.000 0.000
#> GSM711915 2 0.0376 0.97097 0.004 0.996
#> GSM711917 2 0.0000 0.97446 0.000 1.000
#> GSM711923 1 0.8861 0.56810 0.696 0.304
#> GSM711925 2 0.0000 0.97446 0.000 1.000
#> GSM711927 1 0.0000 0.97511 1.000 0.000
#> GSM711929 2 0.0000 0.97446 0.000 1.000
#> GSM711931 2 0.0000 0.97446 0.000 1.000
#> GSM711933 1 0.0000 0.97511 1.000 0.000
#> GSM711935 2 0.0000 0.97446 0.000 1.000
#> GSM711941 1 0.0000 0.97511 1.000 0.000
#> GSM711943 2 0.9993 0.00872 0.484 0.516
#> GSM711945 2 0.0000 0.97446 0.000 1.000
#> GSM711947 2 0.0000 0.97446 0.000 1.000
#> GSM711949 2 0.0000 0.97446 0.000 1.000
#> GSM711953 2 0.0000 0.97446 0.000 1.000
#> GSM711955 1 0.0000 0.97511 1.000 0.000
#> GSM711963 2 0.0000 0.97446 0.000 1.000
#> GSM711971 1 0.0000 0.97511 1.000 0.000
#> GSM711975 2 0.0000 0.97446 0.000 1.000
#> GSM711979 1 0.8909 0.56037 0.692 0.308
#> GSM711989 2 0.0000 0.97446 0.000 1.000
#> GSM711991 2 0.0000 0.97446 0.000 1.000
#> GSM711993 2 0.0000 0.97446 0.000 1.000
#> GSM711983 1 0.0000 0.97511 1.000 0.000
#> GSM711985 2 0.0000 0.97446 0.000 1.000
#> GSM711913 2 0.0376 0.97097 0.004 0.996
#> GSM711919 1 0.0000 0.97511 1.000 0.000
#> GSM711921 1 0.0000 0.97511 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM711936 2 0.000 0.97843 0.000 1.000 0.000
#> GSM711938 2 0.000 0.97843 0.000 1.000 0.000
#> GSM711950 1 0.000 0.98853 1.000 0.000 0.000
#> GSM711956 1 0.000 0.98853 1.000 0.000 0.000
#> GSM711958 1 0.000 0.98853 1.000 0.000 0.000
#> GSM711960 3 0.613 0.36297 0.400 0.000 0.600
#> GSM711964 1 0.000 0.98853 1.000 0.000 0.000
#> GSM711966 1 0.000 0.98853 1.000 0.000 0.000
#> GSM711968 1 0.000 0.98853 1.000 0.000 0.000
#> GSM711972 1 0.000 0.98853 1.000 0.000 0.000
#> GSM711976 1 0.000 0.98853 1.000 0.000 0.000
#> GSM711980 1 0.000 0.98853 1.000 0.000 0.000
#> GSM711986 1 0.000 0.98853 1.000 0.000 0.000
#> GSM711904 1 0.000 0.98853 1.000 0.000 0.000
#> GSM711906 1 0.000 0.98853 1.000 0.000 0.000
#> GSM711908 1 0.000 0.98853 1.000 0.000 0.000
#> GSM711910 3 0.000 0.95709 0.000 0.000 1.000
#> GSM711914 1 0.000 0.98853 1.000 0.000 0.000
#> GSM711916 1 0.000 0.98853 1.000 0.000 0.000
#> GSM711922 1 0.000 0.98853 1.000 0.000 0.000
#> GSM711924 1 0.000 0.98853 1.000 0.000 0.000
#> GSM711926 2 0.000 0.97843 0.000 1.000 0.000
#> GSM711928 1 0.000 0.98853 1.000 0.000 0.000
#> GSM711930 1 0.000 0.98853 1.000 0.000 0.000
#> GSM711932 1 0.000 0.98853 1.000 0.000 0.000
#> GSM711934 1 0.000 0.98853 1.000 0.000 0.000
#> GSM711940 1 0.000 0.98853 1.000 0.000 0.000
#> GSM711942 1 0.000 0.98853 1.000 0.000 0.000
#> GSM711944 3 0.000 0.95709 0.000 0.000 1.000
#> GSM711946 3 0.000 0.95709 0.000 0.000 1.000
#> GSM711948 1 0.000 0.98853 1.000 0.000 0.000
#> GSM711952 1 0.000 0.98853 1.000 0.000 0.000
#> GSM711954 1 0.000 0.98853 1.000 0.000 0.000
#> GSM711962 1 0.000 0.98853 1.000 0.000 0.000
#> GSM711970 1 0.000 0.98853 1.000 0.000 0.000
#> GSM711974 1 0.000 0.98853 1.000 0.000 0.000
#> GSM711978 2 0.000 0.97843 0.000 1.000 0.000
#> GSM711988 1 0.000 0.98853 1.000 0.000 0.000
#> GSM711990 3 0.000 0.95709 0.000 0.000 1.000
#> GSM711992 2 0.631 -0.00082 0.496 0.504 0.000
#> GSM711982 1 0.000 0.98853 1.000 0.000 0.000
#> GSM711984 2 0.000 0.97843 0.000 1.000 0.000
#> GSM711912 1 0.000 0.98853 1.000 0.000 0.000
#> GSM711918 1 0.000 0.98853 1.000 0.000 0.000
#> GSM711920 1 0.000 0.98853 1.000 0.000 0.000
#> GSM711937 2 0.000 0.97843 0.000 1.000 0.000
#> GSM711939 2 0.000 0.97843 0.000 1.000 0.000
#> GSM711951 2 0.000 0.97843 0.000 1.000 0.000
#> GSM711957 1 0.236 0.91305 0.928 0.072 0.000
#> GSM711959 2 0.000 0.97843 0.000 1.000 0.000
#> GSM711961 2 0.000 0.97843 0.000 1.000 0.000
#> GSM711965 3 0.000 0.95709 0.000 0.000 1.000
#> GSM711967 1 0.000 0.98853 1.000 0.000 0.000
#> GSM711969 2 0.000 0.97843 0.000 1.000 0.000
#> GSM711973 3 0.000 0.95709 0.000 0.000 1.000
#> GSM711977 3 0.000 0.95709 0.000 0.000 1.000
#> GSM711981 2 0.000 0.97843 0.000 1.000 0.000
#> GSM711987 2 0.000 0.97843 0.000 1.000 0.000
#> GSM711905 2 0.000 0.97843 0.000 1.000 0.000
#> GSM711907 2 0.000 0.97843 0.000 1.000 0.000
#> GSM711909 3 0.000 0.95709 0.000 0.000 1.000
#> GSM711911 3 0.000 0.95709 0.000 0.000 1.000
#> GSM711915 3 0.000 0.95709 0.000 0.000 1.000
#> GSM711917 2 0.000 0.97843 0.000 1.000 0.000
#> GSM711923 3 0.000 0.95709 0.000 0.000 1.000
#> GSM711925 2 0.000 0.97843 0.000 1.000 0.000
#> GSM711927 3 0.000 0.95709 0.000 0.000 1.000
#> GSM711929 2 0.000 0.97843 0.000 1.000 0.000
#> GSM711931 2 0.000 0.97843 0.000 1.000 0.000
#> GSM711933 1 0.000 0.98853 1.000 0.000 0.000
#> GSM711935 2 0.000 0.97843 0.000 1.000 0.000
#> GSM711941 3 0.000 0.95709 0.000 0.000 1.000
#> GSM711943 3 0.116 0.93370 0.000 0.028 0.972
#> GSM711945 3 0.000 0.95709 0.000 0.000 1.000
#> GSM711947 3 0.553 0.57601 0.000 0.296 0.704
#> GSM711949 2 0.000 0.97843 0.000 1.000 0.000
#> GSM711953 2 0.000 0.97843 0.000 1.000 0.000
#> GSM711955 3 0.455 0.74724 0.200 0.000 0.800
#> GSM711963 2 0.000 0.97843 0.000 1.000 0.000
#> GSM711971 3 0.000 0.95709 0.000 0.000 1.000
#> GSM711975 2 0.000 0.97843 0.000 1.000 0.000
#> GSM711979 1 0.697 0.52145 0.668 0.288 0.044
#> GSM711989 2 0.000 0.97843 0.000 1.000 0.000
#> GSM711991 3 0.000 0.95709 0.000 0.000 1.000
#> GSM711993 2 0.000 0.97843 0.000 1.000 0.000
#> GSM711983 3 0.000 0.95709 0.000 0.000 1.000
#> GSM711985 2 0.000 0.97843 0.000 1.000 0.000
#> GSM711913 3 0.000 0.95709 0.000 0.000 1.000
#> GSM711919 3 0.000 0.95709 0.000 0.000 1.000
#> GSM711921 3 0.000 0.95709 0.000 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM711936 2 0.0000 0.9885 0.000 1.000 0.000 0.000
#> GSM711938 2 0.0000 0.9885 0.000 1.000 0.000 0.000
#> GSM711950 4 0.2760 0.7299 0.128 0.000 0.000 0.872
#> GSM711956 1 0.0000 0.9793 1.000 0.000 0.000 0.000
#> GSM711958 1 0.0188 0.9769 0.996 0.000 0.000 0.004
#> GSM711960 3 0.3942 0.6000 0.236 0.000 0.764 0.000
#> GSM711964 1 0.0000 0.9793 1.000 0.000 0.000 0.000
#> GSM711966 1 0.0000 0.9793 1.000 0.000 0.000 0.000
#> GSM711968 1 0.0000 0.9793 1.000 0.000 0.000 0.000
#> GSM711972 1 0.0000 0.9793 1.000 0.000 0.000 0.000
#> GSM711976 1 0.3074 0.8293 0.848 0.000 0.000 0.152
#> GSM711980 1 0.0000 0.9793 1.000 0.000 0.000 0.000
#> GSM711986 1 0.0000 0.9793 1.000 0.000 0.000 0.000
#> GSM711904 1 0.0000 0.9793 1.000 0.000 0.000 0.000
#> GSM711906 1 0.0000 0.9793 1.000 0.000 0.000 0.000
#> GSM711908 1 0.0000 0.9793 1.000 0.000 0.000 0.000
#> GSM711910 3 0.0000 0.8957 0.000 0.000 1.000 0.000
#> GSM711914 1 0.0000 0.9793 1.000 0.000 0.000 0.000
#> GSM711916 1 0.0000 0.9793 1.000 0.000 0.000 0.000
#> GSM711922 1 0.0000 0.9793 1.000 0.000 0.000 0.000
#> GSM711924 1 0.0188 0.9769 0.996 0.000 0.000 0.004
#> GSM711926 4 0.3837 0.6278 0.000 0.224 0.000 0.776
#> GSM711928 1 0.0000 0.9793 1.000 0.000 0.000 0.000
#> GSM711930 1 0.0000 0.9793 1.000 0.000 0.000 0.000
#> GSM711932 1 0.3219 0.8144 0.836 0.000 0.000 0.164
#> GSM711934 1 0.0188 0.9769 0.996 0.000 0.000 0.004
#> GSM711940 1 0.0707 0.9643 0.980 0.000 0.000 0.020
#> GSM711942 1 0.0000 0.9793 1.000 0.000 0.000 0.000
#> GSM711944 3 0.0188 0.8930 0.000 0.000 0.996 0.004
#> GSM711946 3 0.4713 0.4028 0.000 0.000 0.640 0.360
#> GSM711948 4 0.4804 0.3083 0.384 0.000 0.000 0.616
#> GSM711952 1 0.0000 0.9793 1.000 0.000 0.000 0.000
#> GSM711954 1 0.0000 0.9793 1.000 0.000 0.000 0.000
#> GSM711962 1 0.0000 0.9793 1.000 0.000 0.000 0.000
#> GSM711970 1 0.0000 0.9793 1.000 0.000 0.000 0.000
#> GSM711974 1 0.0000 0.9793 1.000 0.000 0.000 0.000
#> GSM711978 4 0.0188 0.8255 0.000 0.004 0.000 0.996
#> GSM711988 1 0.3024 0.8342 0.852 0.000 0.000 0.148
#> GSM711990 3 0.0000 0.8957 0.000 0.000 1.000 0.000
#> GSM711992 4 0.0188 0.8247 0.004 0.000 0.000 0.996
#> GSM711982 1 0.0000 0.9793 1.000 0.000 0.000 0.000
#> GSM711984 2 0.0000 0.9885 0.000 1.000 0.000 0.000
#> GSM711912 1 0.0000 0.9793 1.000 0.000 0.000 0.000
#> GSM711918 1 0.0000 0.9793 1.000 0.000 0.000 0.000
#> GSM711920 1 0.0000 0.9793 1.000 0.000 0.000 0.000
#> GSM711937 2 0.0000 0.9885 0.000 1.000 0.000 0.000
#> GSM711939 2 0.0000 0.9885 0.000 1.000 0.000 0.000
#> GSM711951 2 0.3942 0.6729 0.000 0.764 0.000 0.236
#> GSM711957 1 0.3711 0.8174 0.836 0.024 0.000 0.140
#> GSM711959 2 0.0000 0.9885 0.000 1.000 0.000 0.000
#> GSM711961 2 0.0000 0.9885 0.000 1.000 0.000 0.000
#> GSM711965 3 0.0000 0.8957 0.000 0.000 1.000 0.000
#> GSM711967 1 0.0000 0.9793 1.000 0.000 0.000 0.000
#> GSM711969 2 0.0000 0.9885 0.000 1.000 0.000 0.000
#> GSM711973 3 0.3444 0.6972 0.000 0.000 0.816 0.184
#> GSM711977 3 0.0000 0.8957 0.000 0.000 1.000 0.000
#> GSM711981 4 0.0188 0.8255 0.000 0.004 0.000 0.996
#> GSM711987 2 0.0000 0.9885 0.000 1.000 0.000 0.000
#> GSM711905 2 0.0000 0.9885 0.000 1.000 0.000 0.000
#> GSM711907 2 0.0000 0.9885 0.000 1.000 0.000 0.000
#> GSM711909 3 0.0000 0.8957 0.000 0.000 1.000 0.000
#> GSM711911 3 0.0000 0.8957 0.000 0.000 1.000 0.000
#> GSM711915 3 0.0000 0.8957 0.000 0.000 1.000 0.000
#> GSM711917 2 0.0000 0.9885 0.000 1.000 0.000 0.000
#> GSM711923 4 0.2973 0.7275 0.000 0.000 0.144 0.856
#> GSM711925 2 0.0000 0.9885 0.000 1.000 0.000 0.000
#> GSM711927 3 0.0000 0.8957 0.000 0.000 1.000 0.000
#> GSM711929 2 0.0000 0.9885 0.000 1.000 0.000 0.000
#> GSM711931 2 0.0000 0.9885 0.000 1.000 0.000 0.000
#> GSM711933 1 0.0188 0.9769 0.996 0.000 0.000 0.004
#> GSM711935 2 0.0000 0.9885 0.000 1.000 0.000 0.000
#> GSM711941 4 0.0000 0.8249 0.000 0.000 0.000 1.000
#> GSM711943 4 0.2973 0.7275 0.000 0.000 0.144 0.856
#> GSM711945 4 0.4996 -0.0228 0.000 0.000 0.484 0.516
#> GSM711947 3 0.4941 0.2635 0.000 0.436 0.564 0.000
#> GSM711949 2 0.0000 0.9885 0.000 1.000 0.000 0.000
#> GSM711953 2 0.0000 0.9885 0.000 1.000 0.000 0.000
#> GSM711955 3 0.3791 0.6518 0.200 0.000 0.796 0.004
#> GSM711963 2 0.0000 0.9885 0.000 1.000 0.000 0.000
#> GSM711971 3 0.0000 0.8957 0.000 0.000 1.000 0.000
#> GSM711975 2 0.0000 0.9885 0.000 1.000 0.000 0.000
#> GSM711979 4 0.0000 0.8249 0.000 0.000 0.000 1.000
#> GSM711989 2 0.0000 0.9885 0.000 1.000 0.000 0.000
#> GSM711991 3 0.2281 0.8191 0.000 0.000 0.904 0.096
#> GSM711993 4 0.0188 0.8255 0.000 0.004 0.000 0.996
#> GSM711983 3 0.0000 0.8957 0.000 0.000 1.000 0.000
#> GSM711985 2 0.0000 0.9885 0.000 1.000 0.000 0.000
#> GSM711913 3 0.0000 0.8957 0.000 0.000 1.000 0.000
#> GSM711919 3 0.0000 0.8957 0.000 0.000 1.000 0.000
#> GSM711921 3 0.0000 0.8957 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM711936 2 0.0000 0.9750 0.000 1.000 0.000 0.000 0.000
#> GSM711938 2 0.0000 0.9750 0.000 1.000 0.000 0.000 0.000
#> GSM711950 5 0.1041 0.5045 0.004 0.000 0.000 0.032 0.964
#> GSM711956 1 0.4306 -0.1675 0.508 0.000 0.000 0.000 0.492
#> GSM711958 1 0.3857 0.4444 0.688 0.000 0.000 0.000 0.312
#> GSM711960 3 0.6824 -0.2670 0.324 0.000 0.344 0.000 0.332
#> GSM711964 1 0.3949 0.3532 0.668 0.000 0.000 0.000 0.332
#> GSM711966 1 0.0963 0.6991 0.964 0.000 0.000 0.000 0.036
#> GSM711968 1 0.4219 0.0351 0.584 0.000 0.000 0.000 0.416
#> GSM711972 1 0.0000 0.7005 1.000 0.000 0.000 0.000 0.000
#> GSM711976 5 0.3636 0.5601 0.272 0.000 0.000 0.000 0.728
#> GSM711980 5 0.4262 0.2773 0.440 0.000 0.000 0.000 0.560
#> GSM711986 1 0.0880 0.7031 0.968 0.000 0.000 0.000 0.032
#> GSM711904 1 0.4201 0.1001 0.592 0.000 0.000 0.000 0.408
#> GSM711906 1 0.0000 0.7005 1.000 0.000 0.000 0.000 0.000
#> GSM711908 1 0.0290 0.7012 0.992 0.000 0.000 0.000 0.008
#> GSM711910 3 0.0000 0.8231 0.000 0.000 1.000 0.000 0.000
#> GSM711914 1 0.3876 0.3887 0.684 0.000 0.000 0.000 0.316
#> GSM711916 1 0.1043 0.6984 0.960 0.000 0.000 0.000 0.040
#> GSM711922 5 0.4307 0.1362 0.496 0.000 0.000 0.000 0.504
#> GSM711924 1 0.3480 0.5349 0.752 0.000 0.000 0.000 0.248
#> GSM711926 4 0.1121 0.8747 0.000 0.044 0.000 0.956 0.000
#> GSM711928 1 0.4287 -0.0603 0.540 0.000 0.000 0.000 0.460
#> GSM711930 1 0.0510 0.7015 0.984 0.000 0.000 0.000 0.016
#> GSM711932 5 0.4850 0.5606 0.232 0.000 0.000 0.072 0.696
#> GSM711934 5 0.4182 0.3816 0.400 0.000 0.000 0.000 0.600
#> GSM711940 5 0.3966 0.4176 0.336 0.000 0.000 0.000 0.664
#> GSM711942 1 0.3242 0.5718 0.784 0.000 0.000 0.000 0.216
#> GSM711944 3 0.3003 0.7094 0.000 0.000 0.812 0.000 0.188
#> GSM711946 3 0.6354 0.3313 0.000 0.000 0.520 0.264 0.216
#> GSM711948 5 0.0579 0.5256 0.008 0.000 0.000 0.008 0.984
#> GSM711952 1 0.0880 0.7031 0.968 0.000 0.000 0.000 0.032
#> GSM711954 1 0.4300 -0.1344 0.524 0.000 0.000 0.000 0.476
#> GSM711962 1 0.1965 0.6768 0.904 0.000 0.000 0.000 0.096
#> GSM711970 5 0.4305 0.1492 0.488 0.000 0.000 0.000 0.512
#> GSM711974 1 0.3109 0.6107 0.800 0.000 0.000 0.000 0.200
#> GSM711978 4 0.0000 0.9033 0.000 0.000 0.000 1.000 0.000
#> GSM711988 5 0.3336 0.5784 0.228 0.000 0.000 0.000 0.772
#> GSM711990 3 0.0000 0.8231 0.000 0.000 1.000 0.000 0.000
#> GSM711992 4 0.0162 0.9029 0.000 0.000 0.000 0.996 0.004
#> GSM711982 1 0.0963 0.6991 0.964 0.000 0.000 0.000 0.036
#> GSM711984 2 0.0000 0.9750 0.000 1.000 0.000 0.000 0.000
#> GSM711912 1 0.0880 0.7026 0.968 0.000 0.000 0.000 0.032
#> GSM711918 1 0.0880 0.7026 0.968 0.000 0.000 0.000 0.032
#> GSM711920 1 0.3480 0.5395 0.752 0.000 0.000 0.000 0.248
#> GSM711937 2 0.0000 0.9750 0.000 1.000 0.000 0.000 0.000
#> GSM711939 2 0.0000 0.9750 0.000 1.000 0.000 0.000 0.000
#> GSM711951 2 0.3480 0.6537 0.000 0.752 0.000 0.248 0.000
#> GSM711957 5 0.6519 0.3982 0.300 0.004 0.000 0.196 0.500
#> GSM711959 2 0.0000 0.9750 0.000 1.000 0.000 0.000 0.000
#> GSM711961 2 0.0000 0.9750 0.000 1.000 0.000 0.000 0.000
#> GSM711965 3 0.3305 0.6950 0.000 0.000 0.776 0.000 0.224
#> GSM711967 1 0.1121 0.6918 0.956 0.000 0.000 0.000 0.044
#> GSM711969 2 0.0000 0.9750 0.000 1.000 0.000 0.000 0.000
#> GSM711973 3 0.4294 0.4495 0.000 0.000 0.532 0.000 0.468
#> GSM711977 3 0.1608 0.7977 0.000 0.000 0.928 0.000 0.072
#> GSM711981 4 0.1809 0.8896 0.000 0.012 0.000 0.928 0.060
#> GSM711987 2 0.0000 0.9750 0.000 1.000 0.000 0.000 0.000
#> GSM711905 2 0.0000 0.9750 0.000 1.000 0.000 0.000 0.000
#> GSM711907 2 0.0000 0.9750 0.000 1.000 0.000 0.000 0.000
#> GSM711909 3 0.0000 0.8231 0.000 0.000 1.000 0.000 0.000
#> GSM711911 3 0.0000 0.8231 0.000 0.000 1.000 0.000 0.000
#> GSM711915 3 0.0000 0.8231 0.000 0.000 1.000 0.000 0.000
#> GSM711917 2 0.0000 0.9750 0.000 1.000 0.000 0.000 0.000
#> GSM711923 4 0.4240 0.7580 0.000 0.000 0.036 0.736 0.228
#> GSM711925 2 0.0000 0.9750 0.000 1.000 0.000 0.000 0.000
#> GSM711927 3 0.0000 0.8231 0.000 0.000 1.000 0.000 0.000
#> GSM711929 2 0.0000 0.9750 0.000 1.000 0.000 0.000 0.000
#> GSM711931 2 0.3684 0.6254 0.000 0.720 0.000 0.280 0.000
#> GSM711933 5 0.4101 0.4503 0.372 0.000 0.000 0.000 0.628
#> GSM711935 2 0.0000 0.9750 0.000 1.000 0.000 0.000 0.000
#> GSM711941 4 0.4210 0.6425 0.000 0.000 0.000 0.588 0.412
#> GSM711943 4 0.1740 0.8878 0.000 0.000 0.012 0.932 0.056
#> GSM711945 3 0.6588 -0.0459 0.000 0.000 0.396 0.396 0.208
#> GSM711947 3 0.3816 0.5045 0.000 0.304 0.696 0.000 0.000
#> GSM711949 2 0.0000 0.9750 0.000 1.000 0.000 0.000 0.000
#> GSM711953 2 0.0000 0.9750 0.000 1.000 0.000 0.000 0.000
#> GSM711955 5 0.2843 0.4653 0.008 0.000 0.144 0.000 0.848
#> GSM711963 2 0.0000 0.9750 0.000 1.000 0.000 0.000 0.000
#> GSM711971 3 0.0000 0.8231 0.000 0.000 1.000 0.000 0.000
#> GSM711975 2 0.0000 0.9750 0.000 1.000 0.000 0.000 0.000
#> GSM711979 4 0.0000 0.9033 0.000 0.000 0.000 1.000 0.000
#> GSM711989 2 0.0000 0.9750 0.000 1.000 0.000 0.000 0.000
#> GSM711991 3 0.2286 0.7537 0.000 0.000 0.888 0.108 0.004
#> GSM711993 4 0.0162 0.9025 0.000 0.004 0.000 0.996 0.000
#> GSM711983 3 0.0000 0.8231 0.000 0.000 1.000 0.000 0.000
#> GSM711985 2 0.0000 0.9750 0.000 1.000 0.000 0.000 0.000
#> GSM711913 3 0.1608 0.7977 0.000 0.000 0.928 0.000 0.072
#> GSM711919 3 0.0000 0.8231 0.000 0.000 1.000 0.000 0.000
#> GSM711921 3 0.0000 0.8231 0.000 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM711936 2 0.0000 0.9638 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711938 2 0.0000 0.9638 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711950 5 0.4260 0.0970 0.472 0.000 0.000 0.016 0.512 0.000
#> GSM711956 1 0.4180 0.4293 0.628 0.000 0.000 0.000 0.024 0.348
#> GSM711958 1 0.4660 0.0854 0.540 0.000 0.000 0.000 0.044 0.416
#> GSM711960 1 0.6868 0.1244 0.368 0.000 0.316 0.000 0.048 0.268
#> GSM711964 6 0.3860 -0.1071 0.472 0.000 0.000 0.000 0.000 0.528
#> GSM711966 6 0.1141 0.6472 0.052 0.000 0.000 0.000 0.000 0.948
#> GSM711968 1 0.3765 0.3504 0.596 0.000 0.000 0.000 0.000 0.404
#> GSM711972 6 0.0363 0.6544 0.012 0.000 0.000 0.000 0.000 0.988
#> GSM711976 1 0.5475 0.4570 0.588 0.000 0.000 0.004 0.224 0.184
#> GSM711980 1 0.3404 0.5226 0.760 0.000 0.000 0.000 0.016 0.224
#> GSM711986 6 0.2912 0.5918 0.172 0.000 0.000 0.000 0.012 0.816
#> GSM711904 1 0.4456 0.2349 0.524 0.000 0.000 0.000 0.028 0.448
#> GSM711906 6 0.0260 0.6519 0.008 0.000 0.000 0.000 0.000 0.992
#> GSM711908 6 0.2070 0.6309 0.092 0.000 0.000 0.000 0.012 0.896
#> GSM711910 3 0.0000 0.8533 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711914 6 0.4147 -0.0262 0.436 0.000 0.000 0.000 0.012 0.552
#> GSM711916 6 0.1075 0.6490 0.048 0.000 0.000 0.000 0.000 0.952
#> GSM711922 1 0.3175 0.4986 0.744 0.000 0.000 0.000 0.000 0.256
#> GSM711924 6 0.4986 -0.0111 0.444 0.000 0.000 0.000 0.068 0.488
#> GSM711926 4 0.0508 0.8956 0.004 0.012 0.000 0.984 0.000 0.000
#> GSM711928 1 0.4301 0.3530 0.584 0.000 0.000 0.000 0.024 0.392
#> GSM711930 6 0.0937 0.6507 0.040 0.000 0.000 0.000 0.000 0.960
#> GSM711932 1 0.4285 0.4988 0.772 0.000 0.000 0.040 0.116 0.072
#> GSM711934 1 0.4000 0.5152 0.724 0.000 0.000 0.000 0.048 0.228
#> GSM711940 1 0.5737 0.2410 0.460 0.000 0.000 0.000 0.172 0.368
#> GSM711942 6 0.4921 0.0590 0.420 0.000 0.000 0.000 0.064 0.516
#> GSM711944 3 0.3997 0.6049 0.108 0.000 0.760 0.000 0.132 0.000
#> GSM711946 5 0.5181 0.3597 0.020 0.000 0.308 0.068 0.604 0.000
#> GSM711948 5 0.3869 0.0338 0.500 0.000 0.000 0.000 0.500 0.000
#> GSM711952 6 0.2841 0.5906 0.164 0.000 0.000 0.000 0.012 0.824
#> GSM711954 1 0.3528 0.4688 0.700 0.000 0.000 0.000 0.004 0.296
#> GSM711962 6 0.3271 0.4864 0.232 0.000 0.000 0.000 0.008 0.760
#> GSM711970 1 0.3202 0.5024 0.800 0.000 0.000 0.000 0.024 0.176
#> GSM711974 6 0.4514 0.1545 0.372 0.000 0.000 0.000 0.040 0.588
#> GSM711978 4 0.0000 0.9075 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM711988 1 0.4843 0.4683 0.652 0.000 0.000 0.000 0.232 0.116
#> GSM711990 3 0.0000 0.8533 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711992 4 0.0000 0.9075 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM711982 6 0.1007 0.6496 0.044 0.000 0.000 0.000 0.000 0.956
#> GSM711984 2 0.0000 0.9638 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711912 6 0.2877 0.5852 0.168 0.000 0.000 0.000 0.012 0.820
#> GSM711918 6 0.2877 0.5852 0.168 0.000 0.000 0.000 0.012 0.820
#> GSM711920 1 0.4971 0.0278 0.508 0.000 0.000 0.000 0.068 0.424
#> GSM711937 2 0.0000 0.9638 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711939 2 0.0000 0.9638 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711951 2 0.3515 0.5321 0.000 0.676 0.000 0.324 0.000 0.000
#> GSM711957 1 0.5885 0.3859 0.636 0.004 0.000 0.144 0.068 0.148
#> GSM711959 2 0.0000 0.9638 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711961 2 0.0000 0.9638 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711965 5 0.3819 0.2124 0.004 0.000 0.372 0.000 0.624 0.000
#> GSM711967 6 0.3645 0.4514 0.236 0.000 0.000 0.000 0.024 0.740
#> GSM711969 2 0.0000 0.9638 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711973 5 0.4544 0.3306 0.052 0.000 0.292 0.004 0.652 0.000
#> GSM711977 3 0.3448 0.5799 0.004 0.000 0.716 0.000 0.280 0.000
#> GSM711981 4 0.2320 0.7996 0.000 0.004 0.000 0.864 0.132 0.000
#> GSM711987 2 0.0000 0.9638 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711905 2 0.0000 0.9638 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711907 2 0.0000 0.9638 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711909 3 0.0000 0.8533 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711911 3 0.0000 0.8533 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711915 3 0.2520 0.7440 0.004 0.000 0.844 0.000 0.152 0.000
#> GSM711917 2 0.0000 0.9638 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711923 5 0.4827 -0.0534 0.028 0.000 0.016 0.420 0.536 0.000
#> GSM711925 2 0.0000 0.9638 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711927 3 0.0000 0.8533 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711929 2 0.0000 0.9638 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711931 2 0.3923 0.3089 0.004 0.580 0.000 0.416 0.000 0.000
#> GSM711933 1 0.3983 0.4263 0.736 0.000 0.000 0.000 0.056 0.208
#> GSM711935 2 0.0000 0.9638 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711941 5 0.4380 0.3228 0.080 0.000 0.000 0.220 0.700 0.000
#> GSM711943 4 0.4235 0.5252 0.020 0.000 0.012 0.672 0.296 0.000
#> GSM711945 5 0.4530 0.4449 0.000 0.000 0.208 0.100 0.692 0.000
#> GSM711947 3 0.4348 0.4185 0.000 0.268 0.676 0.000 0.056 0.000
#> GSM711949 2 0.0000 0.9638 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711953 2 0.0000 0.9638 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711955 1 0.5514 -0.1962 0.464 0.000 0.112 0.000 0.420 0.004
#> GSM711963 2 0.0000 0.9638 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711971 3 0.0000 0.8533 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711975 2 0.0865 0.9322 0.000 0.964 0.000 0.036 0.000 0.000
#> GSM711979 4 0.0146 0.9061 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM711989 2 0.0000 0.9638 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711991 3 0.3541 0.5502 0.000 0.000 0.728 0.012 0.260 0.000
#> GSM711993 4 0.0000 0.9075 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM711983 3 0.0146 0.8511 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM711985 2 0.0000 0.9638 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711913 3 0.3405 0.5939 0.004 0.000 0.724 0.000 0.272 0.000
#> GSM711919 3 0.0000 0.8533 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711921 3 0.0000 0.8533 0.000 0.000 1.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) disease.state(p) individual(p) k
#> MAD:skmeans 87 2.96e-06 0.521 0.864 2
#> MAD:skmeans 88 2.59e-10 0.172 0.735 3
#> MAD:skmeans 86 3.07e-09 0.346 0.328 4
#> MAD:skmeans 70 1.50e-07 0.170 0.198 5
#> MAD:skmeans 57 6.73e-06 0.174 0.395 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "pam"]
# you can also extract it by
# res = res_list["MAD:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 27425 rows and 90 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.981 0.993 0.4182 0.585 0.585
#> 3 3 0.736 0.765 0.910 0.5516 0.741 0.561
#> 4 4 0.947 0.914 0.966 0.1332 0.856 0.614
#> 5 5 0.843 0.816 0.906 0.0873 0.893 0.622
#> 6 6 0.845 0.798 0.904 0.0206 0.982 0.910
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 2
There is also optional best \(k\) = 2 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM711936 2 0.0000 0.991 0.000 1.000
#> GSM711938 2 0.0000 0.991 0.000 1.000
#> GSM711950 1 0.0000 0.993 1.000 0.000
#> GSM711956 1 0.0000 0.993 1.000 0.000
#> GSM711958 1 0.0000 0.993 1.000 0.000
#> GSM711960 1 0.0000 0.993 1.000 0.000
#> GSM711964 1 0.0000 0.993 1.000 0.000
#> GSM711966 1 0.0000 0.993 1.000 0.000
#> GSM711968 1 0.0000 0.993 1.000 0.000
#> GSM711972 1 0.0000 0.993 1.000 0.000
#> GSM711976 1 0.0000 0.993 1.000 0.000
#> GSM711980 1 0.0000 0.993 1.000 0.000
#> GSM711986 1 0.0000 0.993 1.000 0.000
#> GSM711904 1 0.0000 0.993 1.000 0.000
#> GSM711906 1 0.0000 0.993 1.000 0.000
#> GSM711908 1 0.0000 0.993 1.000 0.000
#> GSM711910 1 0.0000 0.993 1.000 0.000
#> GSM711914 1 0.0000 0.993 1.000 0.000
#> GSM711916 1 0.0000 0.993 1.000 0.000
#> GSM711922 1 0.0000 0.993 1.000 0.000
#> GSM711924 1 0.0000 0.993 1.000 0.000
#> GSM711926 2 0.1633 0.970 0.024 0.976
#> GSM711928 1 0.0000 0.993 1.000 0.000
#> GSM711930 1 0.0000 0.993 1.000 0.000
#> GSM711932 1 0.0000 0.993 1.000 0.000
#> GSM711934 1 0.0000 0.993 1.000 0.000
#> GSM711940 1 0.0000 0.993 1.000 0.000
#> GSM711942 1 0.0000 0.993 1.000 0.000
#> GSM711944 1 0.0000 0.993 1.000 0.000
#> GSM711946 1 0.0000 0.993 1.000 0.000
#> GSM711948 1 0.0000 0.993 1.000 0.000
#> GSM711952 1 0.0000 0.993 1.000 0.000
#> GSM711954 1 0.0000 0.993 1.000 0.000
#> GSM711962 1 0.0000 0.993 1.000 0.000
#> GSM711970 1 0.0000 0.993 1.000 0.000
#> GSM711974 1 0.0000 0.993 1.000 0.000
#> GSM711978 1 0.0000 0.993 1.000 0.000
#> GSM711988 1 0.0000 0.993 1.000 0.000
#> GSM711990 1 0.0000 0.993 1.000 0.000
#> GSM711992 1 0.0000 0.993 1.000 0.000
#> GSM711982 1 0.0000 0.993 1.000 0.000
#> GSM711984 2 0.0000 0.991 0.000 1.000
#> GSM711912 1 0.0000 0.993 1.000 0.000
#> GSM711918 1 0.0000 0.993 1.000 0.000
#> GSM711920 1 0.0000 0.993 1.000 0.000
#> GSM711937 2 0.0000 0.991 0.000 1.000
#> GSM711939 2 0.0000 0.991 0.000 1.000
#> GSM711951 2 0.0000 0.991 0.000 1.000
#> GSM711957 1 0.0000 0.993 1.000 0.000
#> GSM711959 2 0.0000 0.991 0.000 1.000
#> GSM711961 2 0.0000 0.991 0.000 1.000
#> GSM711965 1 0.0000 0.993 1.000 0.000
#> GSM711967 1 0.0000 0.993 1.000 0.000
#> GSM711969 2 0.0000 0.991 0.000 1.000
#> GSM711973 1 0.0000 0.993 1.000 0.000
#> GSM711977 1 0.0000 0.993 1.000 0.000
#> GSM711981 1 0.9754 0.301 0.592 0.408
#> GSM711987 2 0.0000 0.991 0.000 1.000
#> GSM711905 2 0.0000 0.991 0.000 1.000
#> GSM711907 2 0.0000 0.991 0.000 1.000
#> GSM711909 1 0.0000 0.993 1.000 0.000
#> GSM711911 1 0.0000 0.993 1.000 0.000
#> GSM711915 1 0.0376 0.989 0.996 0.004
#> GSM711917 2 0.0000 0.991 0.000 1.000
#> GSM711923 1 0.0000 0.993 1.000 0.000
#> GSM711925 2 0.0000 0.991 0.000 1.000
#> GSM711927 1 0.0000 0.993 1.000 0.000
#> GSM711929 2 0.0000 0.991 0.000 1.000
#> GSM711931 2 0.0000 0.991 0.000 1.000
#> GSM711933 1 0.0000 0.993 1.000 0.000
#> GSM711935 2 0.0000 0.991 0.000 1.000
#> GSM711941 1 0.0000 0.993 1.000 0.000
#> GSM711943 1 0.0000 0.993 1.000 0.000
#> GSM711945 1 0.0376 0.989 0.996 0.004
#> GSM711947 2 0.6801 0.779 0.180 0.820
#> GSM711949 2 0.0000 0.991 0.000 1.000
#> GSM711953 2 0.0000 0.991 0.000 1.000
#> GSM711955 1 0.0000 0.993 1.000 0.000
#> GSM711963 2 0.0000 0.991 0.000 1.000
#> GSM711971 1 0.0000 0.993 1.000 0.000
#> GSM711975 2 0.0000 0.991 0.000 1.000
#> GSM711979 1 0.0000 0.993 1.000 0.000
#> GSM711989 2 0.0000 0.991 0.000 1.000
#> GSM711991 1 0.2236 0.957 0.964 0.036
#> GSM711993 2 0.0672 0.985 0.008 0.992
#> GSM711983 1 0.0000 0.993 1.000 0.000
#> GSM711985 2 0.0000 0.991 0.000 1.000
#> GSM711913 1 0.0376 0.989 0.996 0.004
#> GSM711919 1 0.0000 0.993 1.000 0.000
#> GSM711921 1 0.0000 0.993 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM711936 2 0.0000 0.92132 0.000 1.000 0.000
#> GSM711938 2 0.0000 0.92132 0.000 1.000 0.000
#> GSM711950 3 0.6309 0.01724 0.496 0.000 0.504
#> GSM711956 1 0.0000 0.89655 1.000 0.000 0.000
#> GSM711958 1 0.3752 0.76501 0.856 0.000 0.144
#> GSM711960 3 0.5968 0.45252 0.364 0.000 0.636
#> GSM711964 1 0.0000 0.89655 1.000 0.000 0.000
#> GSM711966 1 0.0000 0.89655 1.000 0.000 0.000
#> GSM711968 1 0.0000 0.89655 1.000 0.000 0.000
#> GSM711972 1 0.0000 0.89655 1.000 0.000 0.000
#> GSM711976 1 0.0747 0.88525 0.984 0.000 0.016
#> GSM711980 1 0.0000 0.89655 1.000 0.000 0.000
#> GSM711986 1 0.0000 0.89655 1.000 0.000 0.000
#> GSM711904 1 0.0000 0.89655 1.000 0.000 0.000
#> GSM711906 1 0.0000 0.89655 1.000 0.000 0.000
#> GSM711908 1 0.0000 0.89655 1.000 0.000 0.000
#> GSM711910 3 0.1031 0.85867 0.024 0.000 0.976
#> GSM711914 1 0.0000 0.89655 1.000 0.000 0.000
#> GSM711916 1 0.0000 0.89655 1.000 0.000 0.000
#> GSM711922 1 0.0000 0.89655 1.000 0.000 0.000
#> GSM711924 1 0.0000 0.89655 1.000 0.000 0.000
#> GSM711926 3 0.7394 0.05719 0.472 0.032 0.496
#> GSM711928 1 0.0000 0.89655 1.000 0.000 0.000
#> GSM711930 1 0.0000 0.89655 1.000 0.000 0.000
#> GSM711932 1 0.4555 0.69453 0.800 0.000 0.200
#> GSM711934 1 0.0000 0.89655 1.000 0.000 0.000
#> GSM711940 1 0.6308 -0.03890 0.508 0.000 0.492
#> GSM711942 1 0.0000 0.89655 1.000 0.000 0.000
#> GSM711944 3 0.2066 0.85029 0.060 0.000 0.940
#> GSM711946 3 0.0747 0.85393 0.016 0.000 0.984
#> GSM711948 1 0.6286 0.04046 0.536 0.000 0.464
#> GSM711952 1 0.0000 0.89655 1.000 0.000 0.000
#> GSM711954 1 0.0000 0.89655 1.000 0.000 0.000
#> GSM711962 1 0.0000 0.89655 1.000 0.000 0.000
#> GSM711970 1 0.0000 0.89655 1.000 0.000 0.000
#> GSM711974 1 0.0000 0.89655 1.000 0.000 0.000
#> GSM711978 1 0.6309 -0.06364 0.500 0.000 0.500
#> GSM711988 1 0.1860 0.85642 0.948 0.000 0.052
#> GSM711990 3 0.1031 0.85867 0.024 0.000 0.976
#> GSM711992 1 0.6309 -0.04835 0.504 0.000 0.496
#> GSM711982 1 0.0000 0.89655 1.000 0.000 0.000
#> GSM711984 2 0.0000 0.92132 0.000 1.000 0.000
#> GSM711912 1 0.0000 0.89655 1.000 0.000 0.000
#> GSM711918 1 0.0000 0.89655 1.000 0.000 0.000
#> GSM711920 1 0.0000 0.89655 1.000 0.000 0.000
#> GSM711937 2 0.0000 0.92132 0.000 1.000 0.000
#> GSM711939 2 0.0000 0.92132 0.000 1.000 0.000
#> GSM711951 2 0.6309 0.03483 0.000 0.504 0.496
#> GSM711957 1 0.5058 0.62810 0.756 0.000 0.244
#> GSM711959 2 0.0000 0.92132 0.000 1.000 0.000
#> GSM711961 2 0.0000 0.92132 0.000 1.000 0.000
#> GSM711965 3 0.0424 0.85265 0.008 0.000 0.992
#> GSM711967 1 0.5058 0.62810 0.756 0.000 0.244
#> GSM711969 2 0.0000 0.92132 0.000 1.000 0.000
#> GSM711973 3 0.5431 0.60921 0.284 0.000 0.716
#> GSM711977 3 0.0000 0.84905 0.000 0.000 1.000
#> GSM711981 3 0.8163 0.52625 0.124 0.248 0.628
#> GSM711987 2 0.0000 0.92132 0.000 1.000 0.000
#> GSM711905 2 0.0000 0.92132 0.000 1.000 0.000
#> GSM711907 2 0.4605 0.69114 0.000 0.796 0.204
#> GSM711909 3 0.1031 0.85867 0.024 0.000 0.976
#> GSM711911 3 0.1031 0.85867 0.024 0.000 0.976
#> GSM711915 3 0.0000 0.84905 0.000 0.000 1.000
#> GSM711917 2 0.0000 0.92132 0.000 1.000 0.000
#> GSM711923 3 0.2959 0.82144 0.100 0.000 0.900
#> GSM711925 2 0.0000 0.92132 0.000 1.000 0.000
#> GSM711927 3 0.1031 0.85867 0.024 0.000 0.976
#> GSM711929 2 0.0000 0.92132 0.000 1.000 0.000
#> GSM711931 2 0.0000 0.92132 0.000 1.000 0.000
#> GSM711933 1 0.4974 0.64125 0.764 0.000 0.236
#> GSM711935 2 0.0000 0.92132 0.000 1.000 0.000
#> GSM711941 3 0.3340 0.80637 0.120 0.000 0.880
#> GSM711943 3 0.3192 0.81360 0.112 0.000 0.888
#> GSM711945 3 0.0424 0.85265 0.008 0.000 0.992
#> GSM711947 2 0.6299 0.08555 0.000 0.524 0.476
#> GSM711949 2 0.0000 0.92132 0.000 1.000 0.000
#> GSM711953 2 0.0000 0.92132 0.000 1.000 0.000
#> GSM711955 3 0.3752 0.79496 0.144 0.000 0.856
#> GSM711963 2 0.0000 0.92132 0.000 1.000 0.000
#> GSM711971 3 0.1031 0.85867 0.024 0.000 0.976
#> GSM711975 2 0.0000 0.92132 0.000 1.000 0.000
#> GSM711979 3 0.6309 0.00134 0.500 0.000 0.500
#> GSM711989 2 0.0000 0.92132 0.000 1.000 0.000
#> GSM711991 3 0.0000 0.84905 0.000 0.000 1.000
#> GSM711993 2 0.6309 0.03483 0.000 0.504 0.496
#> GSM711983 3 0.1031 0.85867 0.024 0.000 0.976
#> GSM711985 2 0.0000 0.92132 0.000 1.000 0.000
#> GSM711913 3 0.0000 0.84905 0.000 0.000 1.000
#> GSM711919 3 0.1031 0.85867 0.024 0.000 0.976
#> GSM711921 3 0.1031 0.85867 0.024 0.000 0.976
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM711936 2 0.0000 0.9886 0.000 1.000 0.000 0.000
#> GSM711938 2 0.0000 0.9886 0.000 1.000 0.000 0.000
#> GSM711950 4 0.0336 0.8954 0.008 0.000 0.000 0.992
#> GSM711956 1 0.0000 0.9772 1.000 0.000 0.000 0.000
#> GSM711958 1 0.2216 0.8838 0.908 0.000 0.000 0.092
#> GSM711960 3 0.1211 0.9158 0.040 0.000 0.960 0.000
#> GSM711964 1 0.0000 0.9772 1.000 0.000 0.000 0.000
#> GSM711966 1 0.0000 0.9772 1.000 0.000 0.000 0.000
#> GSM711968 1 0.0000 0.9772 1.000 0.000 0.000 0.000
#> GSM711972 1 0.0000 0.9772 1.000 0.000 0.000 0.000
#> GSM711976 1 0.0921 0.9542 0.972 0.000 0.000 0.028
#> GSM711980 1 0.0000 0.9772 1.000 0.000 0.000 0.000
#> GSM711986 1 0.0000 0.9772 1.000 0.000 0.000 0.000
#> GSM711904 1 0.0000 0.9772 1.000 0.000 0.000 0.000
#> GSM711906 1 0.0000 0.9772 1.000 0.000 0.000 0.000
#> GSM711908 1 0.0000 0.9772 1.000 0.000 0.000 0.000
#> GSM711910 3 0.0000 0.9563 0.000 0.000 1.000 0.000
#> GSM711914 1 0.0000 0.9772 1.000 0.000 0.000 0.000
#> GSM711916 1 0.0000 0.9772 1.000 0.000 0.000 0.000
#> GSM711922 1 0.0000 0.9772 1.000 0.000 0.000 0.000
#> GSM711924 1 0.0000 0.9772 1.000 0.000 0.000 0.000
#> GSM711926 4 0.0000 0.8987 0.000 0.000 0.000 1.000
#> GSM711928 1 0.0000 0.9772 1.000 0.000 0.000 0.000
#> GSM711930 1 0.0000 0.9772 1.000 0.000 0.000 0.000
#> GSM711932 1 0.4164 0.6306 0.736 0.000 0.000 0.264
#> GSM711934 1 0.0000 0.9772 1.000 0.000 0.000 0.000
#> GSM711940 4 0.0592 0.8911 0.016 0.000 0.000 0.984
#> GSM711942 1 0.0000 0.9772 1.000 0.000 0.000 0.000
#> GSM711944 3 0.4985 0.0668 0.000 0.000 0.532 0.468
#> GSM711946 4 0.0469 0.8938 0.000 0.000 0.012 0.988
#> GSM711948 4 0.4543 0.5456 0.324 0.000 0.000 0.676
#> GSM711952 1 0.0000 0.9772 1.000 0.000 0.000 0.000
#> GSM711954 1 0.0000 0.9772 1.000 0.000 0.000 0.000
#> GSM711962 1 0.0000 0.9772 1.000 0.000 0.000 0.000
#> GSM711970 1 0.0000 0.9772 1.000 0.000 0.000 0.000
#> GSM711974 1 0.0000 0.9772 1.000 0.000 0.000 0.000
#> GSM711978 4 0.0000 0.8987 0.000 0.000 0.000 1.000
#> GSM711988 1 0.0817 0.9566 0.976 0.000 0.000 0.024
#> GSM711990 3 0.0000 0.9563 0.000 0.000 1.000 0.000
#> GSM711992 4 0.0000 0.8987 0.000 0.000 0.000 1.000
#> GSM711982 1 0.0000 0.9772 1.000 0.000 0.000 0.000
#> GSM711984 2 0.0000 0.9886 0.000 1.000 0.000 0.000
#> GSM711912 1 0.0000 0.9772 1.000 0.000 0.000 0.000
#> GSM711918 1 0.0000 0.9772 1.000 0.000 0.000 0.000
#> GSM711920 1 0.0000 0.9772 1.000 0.000 0.000 0.000
#> GSM711937 2 0.0000 0.9886 0.000 1.000 0.000 0.000
#> GSM711939 2 0.0000 0.9886 0.000 1.000 0.000 0.000
#> GSM711951 4 0.0000 0.8987 0.000 0.000 0.000 1.000
#> GSM711957 4 0.4817 0.3713 0.388 0.000 0.000 0.612
#> GSM711959 2 0.0000 0.9886 0.000 1.000 0.000 0.000
#> GSM711961 2 0.0000 0.9886 0.000 1.000 0.000 0.000
#> GSM711965 4 0.1302 0.8723 0.000 0.000 0.044 0.956
#> GSM711967 4 0.4855 0.3365 0.400 0.000 0.000 0.600
#> GSM711969 2 0.0000 0.9886 0.000 1.000 0.000 0.000
#> GSM711973 4 0.3311 0.7429 0.000 0.000 0.172 0.828
#> GSM711977 3 0.0592 0.9436 0.000 0.000 0.984 0.016
#> GSM711981 4 0.0000 0.8987 0.000 0.000 0.000 1.000
#> GSM711987 2 0.0000 0.9886 0.000 1.000 0.000 0.000
#> GSM711905 2 0.0000 0.9886 0.000 1.000 0.000 0.000
#> GSM711907 2 0.3688 0.7266 0.000 0.792 0.000 0.208
#> GSM711909 3 0.0000 0.9563 0.000 0.000 1.000 0.000
#> GSM711911 3 0.0000 0.9563 0.000 0.000 1.000 0.000
#> GSM711915 3 0.0000 0.9563 0.000 0.000 1.000 0.000
#> GSM711917 2 0.0000 0.9886 0.000 1.000 0.000 0.000
#> GSM711923 4 0.0000 0.8987 0.000 0.000 0.000 1.000
#> GSM711925 2 0.0000 0.9886 0.000 1.000 0.000 0.000
#> GSM711927 3 0.0000 0.9563 0.000 0.000 1.000 0.000
#> GSM711929 2 0.0000 0.9886 0.000 1.000 0.000 0.000
#> GSM711931 2 0.0188 0.9851 0.000 0.996 0.000 0.004
#> GSM711933 1 0.3975 0.6650 0.760 0.000 0.000 0.240
#> GSM711935 2 0.0000 0.9886 0.000 1.000 0.000 0.000
#> GSM711941 4 0.0000 0.8987 0.000 0.000 0.000 1.000
#> GSM711943 4 0.0000 0.8987 0.000 0.000 0.000 1.000
#> GSM711945 4 0.0000 0.8987 0.000 0.000 0.000 1.000
#> GSM711947 4 0.4136 0.7011 0.000 0.196 0.016 0.788
#> GSM711949 2 0.0000 0.9886 0.000 1.000 0.000 0.000
#> GSM711953 2 0.0000 0.9886 0.000 1.000 0.000 0.000
#> GSM711955 4 0.2988 0.8114 0.012 0.000 0.112 0.876
#> GSM711963 2 0.0000 0.9886 0.000 1.000 0.000 0.000
#> GSM711971 3 0.0000 0.9563 0.000 0.000 1.000 0.000
#> GSM711975 2 0.0188 0.9851 0.000 0.996 0.000 0.004
#> GSM711979 4 0.0000 0.8987 0.000 0.000 0.000 1.000
#> GSM711989 2 0.0000 0.9886 0.000 1.000 0.000 0.000
#> GSM711991 4 0.0469 0.8938 0.000 0.000 0.012 0.988
#> GSM711993 4 0.0000 0.8987 0.000 0.000 0.000 1.000
#> GSM711983 3 0.0000 0.9563 0.000 0.000 1.000 0.000
#> GSM711985 2 0.0000 0.9886 0.000 1.000 0.000 0.000
#> GSM711913 3 0.0000 0.9563 0.000 0.000 1.000 0.000
#> GSM711919 3 0.0000 0.9563 0.000 0.000 1.000 0.000
#> GSM711921 3 0.0000 0.9563 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM711936 2 0.1965 0.891 0.000 0.904 0.000 0.096 0.000
#> GSM711938 2 0.0000 0.951 0.000 1.000 0.000 0.000 0.000
#> GSM711950 4 0.3752 0.738 0.000 0.000 0.000 0.708 0.292
#> GSM711956 1 0.0000 0.936 1.000 0.000 0.000 0.000 0.000
#> GSM711958 5 0.0162 0.797 0.004 0.000 0.000 0.000 0.996
#> GSM711960 5 0.1638 0.770 0.004 0.000 0.064 0.000 0.932
#> GSM711964 1 0.0000 0.936 1.000 0.000 0.000 0.000 0.000
#> GSM711966 1 0.0000 0.936 1.000 0.000 0.000 0.000 0.000
#> GSM711968 1 0.0000 0.936 1.000 0.000 0.000 0.000 0.000
#> GSM711972 1 0.0000 0.936 1.000 0.000 0.000 0.000 0.000
#> GSM711976 1 0.4475 0.485 0.692 0.000 0.000 0.032 0.276
#> GSM711980 5 0.3707 0.653 0.284 0.000 0.000 0.000 0.716
#> GSM711986 1 0.0000 0.936 1.000 0.000 0.000 0.000 0.000
#> GSM711904 1 0.0000 0.936 1.000 0.000 0.000 0.000 0.000
#> GSM711906 5 0.4262 0.383 0.440 0.000 0.000 0.000 0.560
#> GSM711908 1 0.0000 0.936 1.000 0.000 0.000 0.000 0.000
#> GSM711910 3 0.0000 0.950 0.000 0.000 1.000 0.000 0.000
#> GSM711914 1 0.0000 0.936 1.000 0.000 0.000 0.000 0.000
#> GSM711916 1 0.0000 0.936 1.000 0.000 0.000 0.000 0.000
#> GSM711922 5 0.4307 0.169 0.500 0.000 0.000 0.000 0.500
#> GSM711924 5 0.0162 0.797 0.004 0.000 0.000 0.000 0.996
#> GSM711926 4 0.0000 0.802 0.000 0.000 0.000 1.000 0.000
#> GSM711928 1 0.0000 0.936 1.000 0.000 0.000 0.000 0.000
#> GSM711930 1 0.0162 0.932 0.996 0.000 0.000 0.000 0.004
#> GSM711932 5 0.0880 0.789 0.000 0.000 0.000 0.032 0.968
#> GSM711934 1 0.3837 0.462 0.692 0.000 0.000 0.000 0.308
#> GSM711940 4 0.4390 0.560 0.004 0.000 0.000 0.568 0.428
#> GSM711942 5 0.3752 0.645 0.292 0.000 0.000 0.000 0.708
#> GSM711944 5 0.0000 0.795 0.000 0.000 0.000 0.000 1.000
#> GSM711946 4 0.3586 0.784 0.000 0.000 0.020 0.792 0.188
#> GSM711948 5 0.0000 0.795 0.000 0.000 0.000 0.000 1.000
#> GSM711952 1 0.0000 0.936 1.000 0.000 0.000 0.000 0.000
#> GSM711954 5 0.4030 0.566 0.352 0.000 0.000 0.000 0.648
#> GSM711962 5 0.3586 0.671 0.264 0.000 0.000 0.000 0.736
#> GSM711970 5 0.3752 0.645 0.292 0.000 0.000 0.000 0.708
#> GSM711974 1 0.3816 0.456 0.696 0.000 0.000 0.000 0.304
#> GSM711978 4 0.0000 0.802 0.000 0.000 0.000 1.000 0.000
#> GSM711988 5 0.0162 0.795 0.000 0.000 0.000 0.004 0.996
#> GSM711990 3 0.1121 0.927 0.000 0.000 0.956 0.000 0.044
#> GSM711992 4 0.0000 0.802 0.000 0.000 0.000 1.000 0.000
#> GSM711982 1 0.0000 0.936 1.000 0.000 0.000 0.000 0.000
#> GSM711984 2 0.0000 0.951 0.000 1.000 0.000 0.000 0.000
#> GSM711912 1 0.0000 0.936 1.000 0.000 0.000 0.000 0.000
#> GSM711918 1 0.0000 0.936 1.000 0.000 0.000 0.000 0.000
#> GSM711920 5 0.0880 0.789 0.000 0.000 0.000 0.032 0.968
#> GSM711937 2 0.0290 0.947 0.000 0.992 0.000 0.008 0.000
#> GSM711939 2 0.0000 0.951 0.000 1.000 0.000 0.000 0.000
#> GSM711951 4 0.0000 0.802 0.000 0.000 0.000 1.000 0.000
#> GSM711957 5 0.1732 0.767 0.000 0.000 0.000 0.080 0.920
#> GSM711959 2 0.0000 0.951 0.000 1.000 0.000 0.000 0.000
#> GSM711961 2 0.0000 0.951 0.000 1.000 0.000 0.000 0.000
#> GSM711965 4 0.4025 0.734 0.000 0.000 0.008 0.700 0.292
#> GSM711967 5 0.1732 0.767 0.000 0.000 0.000 0.080 0.920
#> GSM711969 2 0.0162 0.949 0.000 0.996 0.000 0.004 0.000
#> GSM711973 4 0.4307 0.427 0.000 0.000 0.000 0.500 0.500
#> GSM711977 3 0.5037 0.590 0.000 0.000 0.684 0.088 0.228
#> GSM711981 4 0.0000 0.802 0.000 0.000 0.000 1.000 0.000
#> GSM711987 2 0.0000 0.951 0.000 1.000 0.000 0.000 0.000
#> GSM711905 2 0.0000 0.951 0.000 1.000 0.000 0.000 0.000
#> GSM711907 2 0.3452 0.763 0.000 0.756 0.000 0.244 0.000
#> GSM711909 3 0.0000 0.950 0.000 0.000 1.000 0.000 0.000
#> GSM711911 3 0.0000 0.950 0.000 0.000 1.000 0.000 0.000
#> GSM711915 3 0.0162 0.948 0.000 0.000 0.996 0.000 0.004
#> GSM711917 2 0.0000 0.951 0.000 1.000 0.000 0.000 0.000
#> GSM711923 4 0.3177 0.770 0.000 0.000 0.000 0.792 0.208
#> GSM711925 2 0.0000 0.951 0.000 1.000 0.000 0.000 0.000
#> GSM711927 3 0.0000 0.950 0.000 0.000 1.000 0.000 0.000
#> GSM711929 2 0.0000 0.951 0.000 1.000 0.000 0.000 0.000
#> GSM711931 2 0.3534 0.749 0.000 0.744 0.000 0.256 0.000
#> GSM711933 5 0.0162 0.797 0.004 0.000 0.000 0.000 0.996
#> GSM711935 2 0.0000 0.951 0.000 1.000 0.000 0.000 0.000
#> GSM711941 4 0.3730 0.736 0.000 0.000 0.000 0.712 0.288
#> GSM711943 4 0.0000 0.802 0.000 0.000 0.000 1.000 0.000
#> GSM711945 4 0.0880 0.797 0.000 0.000 0.000 0.968 0.032
#> GSM711947 4 0.6386 0.298 0.000 0.188 0.320 0.492 0.000
#> GSM711949 2 0.0000 0.951 0.000 1.000 0.000 0.000 0.000
#> GSM711953 2 0.0000 0.951 0.000 1.000 0.000 0.000 0.000
#> GSM711955 5 0.0000 0.795 0.000 0.000 0.000 0.000 1.000
#> GSM711963 2 0.0000 0.951 0.000 1.000 0.000 0.000 0.000
#> GSM711971 3 0.0000 0.950 0.000 0.000 1.000 0.000 0.000
#> GSM711975 2 0.3336 0.780 0.000 0.772 0.000 0.228 0.000
#> GSM711979 4 0.3210 0.768 0.000 0.000 0.000 0.788 0.212
#> GSM711989 2 0.3274 0.788 0.000 0.780 0.000 0.220 0.000
#> GSM711991 4 0.4250 0.629 0.000 0.000 0.252 0.720 0.028
#> GSM711993 4 0.0000 0.802 0.000 0.000 0.000 1.000 0.000
#> GSM711983 3 0.0880 0.934 0.000 0.000 0.968 0.000 0.032
#> GSM711985 2 0.0000 0.951 0.000 1.000 0.000 0.000 0.000
#> GSM711913 3 0.2127 0.855 0.000 0.000 0.892 0.000 0.108
#> GSM711919 3 0.0000 0.950 0.000 0.000 1.000 0.000 0.000
#> GSM711921 3 0.0000 0.950 0.000 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM711936 2 0.0622 0.936 0.000 0.980 0.000 0.008 0.012 0.000
#> GSM711938 2 0.0000 0.949 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711950 4 0.4982 0.633 0.176 0.000 0.000 0.648 0.176 0.000
#> GSM711956 6 0.0000 0.923 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM711958 1 0.0000 0.814 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711960 1 0.0000 0.814 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711964 6 0.0000 0.923 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM711966 6 0.0000 0.923 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM711968 6 0.0000 0.923 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM711972 6 0.0000 0.923 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM711976 6 0.4515 0.457 0.056 0.000 0.000 0.304 0.000 0.640
#> GSM711980 1 0.2300 0.777 0.856 0.000 0.000 0.000 0.000 0.144
#> GSM711986 6 0.0000 0.923 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM711904 6 0.0000 0.923 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM711906 1 0.3547 0.572 0.668 0.000 0.000 0.000 0.000 0.332
#> GSM711908 6 0.0000 0.923 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM711910 3 0.0000 0.861 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711914 6 0.0000 0.923 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM711916 6 0.0000 0.923 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM711922 1 0.3717 0.437 0.616 0.000 0.000 0.000 0.000 0.384
#> GSM711924 1 0.0000 0.814 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711926 4 0.0790 0.763 0.000 0.000 0.000 0.968 0.032 0.000
#> GSM711928 6 0.0000 0.923 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM711930 6 0.0146 0.919 0.004 0.000 0.000 0.000 0.000 0.996
#> GSM711932 1 0.2300 0.763 0.856 0.000 0.000 0.144 0.000 0.000
#> GSM711934 6 0.3620 0.370 0.352 0.000 0.000 0.000 0.000 0.648
#> GSM711940 4 0.3869 0.283 0.500 0.000 0.000 0.500 0.000 0.000
#> GSM711942 1 0.2597 0.759 0.824 0.000 0.000 0.000 0.000 0.176
#> GSM711944 1 0.0000 0.814 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711946 4 0.5035 0.629 0.168 0.000 0.000 0.640 0.192 0.000
#> GSM711948 1 0.0000 0.814 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711952 6 0.0000 0.923 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM711954 1 0.3221 0.685 0.736 0.000 0.000 0.000 0.000 0.264
#> GSM711962 1 0.0790 0.809 0.968 0.000 0.000 0.000 0.000 0.032
#> GSM711970 1 0.2597 0.759 0.824 0.000 0.000 0.000 0.000 0.176
#> GSM711974 6 0.3797 0.173 0.420 0.000 0.000 0.000 0.000 0.580
#> GSM711978 4 0.0000 0.770 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM711988 1 0.0000 0.814 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711990 3 0.4953 0.484 0.172 0.000 0.652 0.000 0.176 0.000
#> GSM711992 4 0.0790 0.763 0.000 0.000 0.000 0.968 0.032 0.000
#> GSM711982 6 0.0000 0.923 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM711984 2 0.0000 0.949 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711912 6 0.0000 0.923 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM711918 6 0.0000 0.923 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM711920 1 0.2300 0.763 0.856 0.000 0.000 0.144 0.000 0.000
#> GSM711937 2 0.0146 0.946 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM711939 2 0.0000 0.949 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711951 4 0.1075 0.764 0.000 0.000 0.000 0.952 0.048 0.000
#> GSM711957 1 0.3499 0.579 0.680 0.000 0.000 0.320 0.000 0.000
#> GSM711959 2 0.0000 0.949 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711961 2 0.0000 0.949 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711965 4 0.5093 0.625 0.176 0.000 0.000 0.632 0.192 0.000
#> GSM711967 1 0.3515 0.573 0.676 0.000 0.000 0.324 0.000 0.000
#> GSM711969 2 0.0000 0.949 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711973 5 0.0790 0.945 0.000 0.000 0.000 0.032 0.968 0.000
#> GSM711977 5 0.1075 0.961 0.000 0.000 0.048 0.000 0.952 0.000
#> GSM711981 4 0.1075 0.764 0.000 0.000 0.000 0.952 0.048 0.000
#> GSM711987 2 0.0000 0.949 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711905 2 0.0000 0.949 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711907 2 0.4313 0.587 0.000 0.668 0.000 0.284 0.048 0.000
#> GSM711909 3 0.0000 0.861 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711911 3 0.0000 0.861 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711915 5 0.0790 0.975 0.000 0.000 0.032 0.000 0.968 0.000
#> GSM711917 2 0.0000 0.949 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711923 4 0.1151 0.764 0.032 0.000 0.000 0.956 0.012 0.000
#> GSM711925 2 0.0000 0.949 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711927 3 0.0000 0.861 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711929 2 0.0000 0.949 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711931 2 0.4319 0.512 0.000 0.620 0.000 0.348 0.032 0.000
#> GSM711933 1 0.0000 0.814 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711935 2 0.0000 0.949 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711941 4 0.4235 0.677 0.084 0.000 0.000 0.724 0.192 0.000
#> GSM711943 4 0.0000 0.770 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM711945 4 0.4843 0.633 0.144 0.000 0.000 0.664 0.192 0.000
#> GSM711947 3 0.4681 0.534 0.000 0.188 0.708 0.088 0.016 0.000
#> GSM711949 2 0.0000 0.949 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711953 2 0.0000 0.949 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711955 1 0.2378 0.664 0.848 0.000 0.000 0.000 0.152 0.000
#> GSM711963 2 0.0000 0.949 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711971 3 0.0000 0.861 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711975 2 0.3139 0.784 0.000 0.816 0.000 0.152 0.032 0.000
#> GSM711979 4 0.0790 0.765 0.032 0.000 0.000 0.968 0.000 0.000
#> GSM711989 2 0.1789 0.892 0.000 0.924 0.000 0.044 0.032 0.000
#> GSM711991 4 0.5620 0.611 0.136 0.000 0.040 0.632 0.192 0.000
#> GSM711993 4 0.0790 0.763 0.000 0.000 0.000 0.968 0.032 0.000
#> GSM711983 3 0.4728 0.515 0.144 0.000 0.680 0.000 0.176 0.000
#> GSM711985 2 0.0000 0.949 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711913 5 0.0790 0.975 0.000 0.000 0.032 0.000 0.968 0.000
#> GSM711919 3 0.0000 0.861 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711921 3 0.0000 0.861 0.000 0.000 1.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) disease.state(p) individual(p) k
#> MAD:pam 89 5.55e-05 0.219 0.616 2
#> MAD:pam 79 2.25e-10 0.343 0.657 3
#> MAD:pam 87 7.89e-10 0.131 0.413 4
#> MAD:pam 83 8.12e-08 0.145 0.221 5
#> MAD:pam 84 2.21e-08 0.178 0.197 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "mclust"]
# you can also extract it by
# res = res_list["MAD:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 27425 rows and 90 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.975 0.986 0.4092 0.594 0.594
#> 3 3 0.790 0.859 0.914 0.5566 0.716 0.533
#> 4 4 0.961 0.920 0.968 0.1266 0.931 0.802
#> 5 5 0.796 0.790 0.889 0.0595 0.909 0.705
#> 6 6 0.725 0.611 0.759 0.0520 0.928 0.714
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 2
There is also optional best \(k\) = 2 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM711936 2 0.000 0.987 0.000 1.000
#> GSM711938 2 0.000 0.987 0.000 1.000
#> GSM711950 1 0.000 0.984 1.000 0.000
#> GSM711956 1 0.000 0.984 1.000 0.000
#> GSM711958 1 0.000 0.984 1.000 0.000
#> GSM711960 1 0.000 0.984 1.000 0.000
#> GSM711964 1 0.000 0.984 1.000 0.000
#> GSM711966 1 0.000 0.984 1.000 0.000
#> GSM711968 1 0.000 0.984 1.000 0.000
#> GSM711972 1 0.000 0.984 1.000 0.000
#> GSM711976 1 0.000 0.984 1.000 0.000
#> GSM711980 1 0.000 0.984 1.000 0.000
#> GSM711986 1 0.000 0.984 1.000 0.000
#> GSM711904 1 0.000 0.984 1.000 0.000
#> GSM711906 1 0.000 0.984 1.000 0.000
#> GSM711908 1 0.000 0.984 1.000 0.000
#> GSM711910 1 0.343 0.948 0.936 0.064
#> GSM711914 1 0.000 0.984 1.000 0.000
#> GSM711916 1 0.000 0.984 1.000 0.000
#> GSM711922 1 0.000 0.984 1.000 0.000
#> GSM711924 1 0.000 0.984 1.000 0.000
#> GSM711926 1 0.000 0.984 1.000 0.000
#> GSM711928 1 0.000 0.984 1.000 0.000
#> GSM711930 1 0.000 0.984 1.000 0.000
#> GSM711932 1 0.000 0.984 1.000 0.000
#> GSM711934 1 0.000 0.984 1.000 0.000
#> GSM711940 1 0.000 0.984 1.000 0.000
#> GSM711942 1 0.000 0.984 1.000 0.000
#> GSM711944 1 0.000 0.984 1.000 0.000
#> GSM711946 1 0.311 0.953 0.944 0.056
#> GSM711948 1 0.000 0.984 1.000 0.000
#> GSM711952 1 0.000 0.984 1.000 0.000
#> GSM711954 1 0.000 0.984 1.000 0.000
#> GSM711962 1 0.000 0.984 1.000 0.000
#> GSM711970 1 0.000 0.984 1.000 0.000
#> GSM711974 1 0.000 0.984 1.000 0.000
#> GSM711978 1 0.000 0.984 1.000 0.000
#> GSM711988 1 0.000 0.984 1.000 0.000
#> GSM711990 1 0.242 0.964 0.960 0.040
#> GSM711992 1 0.000 0.984 1.000 0.000
#> GSM711982 1 0.000 0.984 1.000 0.000
#> GSM711984 2 0.000 0.987 0.000 1.000
#> GSM711912 1 0.000 0.984 1.000 0.000
#> GSM711918 1 0.000 0.984 1.000 0.000
#> GSM711920 1 0.000 0.984 1.000 0.000
#> GSM711937 2 0.000 0.987 0.000 1.000
#> GSM711939 2 0.000 0.987 0.000 1.000
#> GSM711951 2 0.000 0.987 0.000 1.000
#> GSM711957 1 0.000 0.984 1.000 0.000
#> GSM711959 2 0.000 0.987 0.000 1.000
#> GSM711961 2 0.000 0.987 0.000 1.000
#> GSM711965 1 0.118 0.977 0.984 0.016
#> GSM711967 1 0.000 0.984 1.000 0.000
#> GSM711969 2 0.000 0.987 0.000 1.000
#> GSM711973 1 0.000 0.984 1.000 0.000
#> GSM711977 1 0.295 0.956 0.948 0.052
#> GSM711981 2 0.644 0.806 0.164 0.836
#> GSM711987 2 0.000 0.987 0.000 1.000
#> GSM711905 2 0.000 0.987 0.000 1.000
#> GSM711907 2 0.000 0.987 0.000 1.000
#> GSM711909 1 0.343 0.948 0.936 0.064
#> GSM711911 1 0.343 0.948 0.936 0.064
#> GSM711915 1 0.343 0.948 0.936 0.064
#> GSM711917 2 0.000 0.987 0.000 1.000
#> GSM711923 1 0.000 0.984 1.000 0.000
#> GSM711925 2 0.000 0.987 0.000 1.000
#> GSM711927 1 0.343 0.948 0.936 0.064
#> GSM711929 2 0.000 0.987 0.000 1.000
#> GSM711931 2 0.000 0.987 0.000 1.000
#> GSM711933 1 0.000 0.984 1.000 0.000
#> GSM711935 2 0.000 0.987 0.000 1.000
#> GSM711941 1 0.000 0.984 1.000 0.000
#> GSM711943 1 0.204 0.968 0.968 0.032
#> GSM711945 1 0.224 0.966 0.964 0.036
#> GSM711947 1 0.343 0.948 0.936 0.064
#> GSM711949 2 0.000 0.987 0.000 1.000
#> GSM711953 2 0.000 0.987 0.000 1.000
#> GSM711955 1 0.000 0.984 1.000 0.000
#> GSM711963 2 0.000 0.987 0.000 1.000
#> GSM711971 1 0.343 0.948 0.936 0.064
#> GSM711975 2 0.000 0.987 0.000 1.000
#> GSM711979 1 0.000 0.984 1.000 0.000
#> GSM711989 2 0.000 0.987 0.000 1.000
#> GSM711991 1 0.343 0.948 0.936 0.064
#> GSM711993 2 0.574 0.846 0.136 0.864
#> GSM711983 1 0.343 0.948 0.936 0.064
#> GSM711985 2 0.000 0.987 0.000 1.000
#> GSM711913 1 0.295 0.956 0.948 0.052
#> GSM711919 1 0.343 0.948 0.936 0.064
#> GSM711921 1 0.343 0.948 0.936 0.064
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM711936 2 0.0000 0.961 0.000 1.000 0.000
#> GSM711938 2 0.0000 0.961 0.000 1.000 0.000
#> GSM711950 3 0.5968 0.699 0.364 0.000 0.636
#> GSM711956 1 0.0000 0.949 1.000 0.000 0.000
#> GSM711958 1 0.1643 0.954 0.956 0.000 0.044
#> GSM711960 1 0.2711 0.922 0.912 0.000 0.088
#> GSM711964 1 0.0000 0.949 1.000 0.000 0.000
#> GSM711966 1 0.0237 0.950 0.996 0.000 0.004
#> GSM711968 1 0.0424 0.951 0.992 0.000 0.008
#> GSM711972 1 0.1643 0.954 0.956 0.000 0.044
#> GSM711976 1 0.0000 0.949 1.000 0.000 0.000
#> GSM711980 1 0.0000 0.949 1.000 0.000 0.000
#> GSM711986 1 0.1860 0.951 0.948 0.000 0.052
#> GSM711904 1 0.1643 0.954 0.956 0.000 0.044
#> GSM711906 1 0.1860 0.951 0.948 0.000 0.052
#> GSM711908 1 0.1860 0.951 0.948 0.000 0.052
#> GSM711910 3 0.0000 0.778 0.000 0.000 1.000
#> GSM711914 1 0.1643 0.954 0.956 0.000 0.044
#> GSM711916 1 0.1860 0.951 0.948 0.000 0.052
#> GSM711922 1 0.0000 0.949 1.000 0.000 0.000
#> GSM711924 1 0.1860 0.951 0.948 0.000 0.052
#> GSM711926 3 0.6126 0.713 0.352 0.004 0.644
#> GSM711928 1 0.0000 0.949 1.000 0.000 0.000
#> GSM711930 1 0.1860 0.951 0.948 0.000 0.052
#> GSM711932 1 0.4974 0.558 0.764 0.000 0.236
#> GSM711934 1 0.0424 0.951 0.992 0.000 0.008
#> GSM711940 1 0.0000 0.949 1.000 0.000 0.000
#> GSM711942 1 0.1860 0.951 0.948 0.000 0.052
#> GSM711944 3 0.5560 0.710 0.300 0.000 0.700
#> GSM711946 3 0.5882 0.718 0.348 0.000 0.652
#> GSM711948 1 0.1411 0.921 0.964 0.000 0.036
#> GSM711952 1 0.1860 0.951 0.948 0.000 0.052
#> GSM711954 1 0.0000 0.949 1.000 0.000 0.000
#> GSM711962 1 0.1643 0.954 0.956 0.000 0.044
#> GSM711970 1 0.0000 0.949 1.000 0.000 0.000
#> GSM711974 1 0.1643 0.954 0.956 0.000 0.044
#> GSM711978 3 0.6126 0.713 0.352 0.004 0.644
#> GSM711988 1 0.0000 0.949 1.000 0.000 0.000
#> GSM711990 3 0.0000 0.778 0.000 0.000 1.000
#> GSM711992 3 0.6126 0.713 0.352 0.004 0.644
#> GSM711982 1 0.1860 0.951 0.948 0.000 0.052
#> GSM711984 2 0.0000 0.961 0.000 1.000 0.000
#> GSM711912 1 0.1860 0.951 0.948 0.000 0.052
#> GSM711918 1 0.1860 0.951 0.948 0.000 0.052
#> GSM711920 1 0.1643 0.954 0.956 0.000 0.044
#> GSM711937 2 0.0000 0.961 0.000 1.000 0.000
#> GSM711939 2 0.0000 0.961 0.000 1.000 0.000
#> GSM711951 2 0.6079 0.315 0.000 0.612 0.388
#> GSM711957 3 0.5835 0.660 0.340 0.000 0.660
#> GSM711959 2 0.0000 0.961 0.000 1.000 0.000
#> GSM711961 2 0.0000 0.961 0.000 1.000 0.000
#> GSM711965 3 0.5882 0.718 0.348 0.000 0.652
#> GSM711967 1 0.0000 0.949 1.000 0.000 0.000
#> GSM711969 2 0.0000 0.961 0.000 1.000 0.000
#> GSM711973 3 0.5591 0.707 0.304 0.000 0.696
#> GSM711977 3 0.0000 0.778 0.000 0.000 1.000
#> GSM711981 3 0.7778 0.577 0.092 0.264 0.644
#> GSM711987 2 0.0000 0.961 0.000 1.000 0.000
#> GSM711905 2 0.0000 0.961 0.000 1.000 0.000
#> GSM711907 2 0.0000 0.961 0.000 1.000 0.000
#> GSM711909 3 0.0000 0.778 0.000 0.000 1.000
#> GSM711911 3 0.0000 0.778 0.000 0.000 1.000
#> GSM711915 3 0.0000 0.778 0.000 0.000 1.000
#> GSM711917 2 0.0000 0.961 0.000 1.000 0.000
#> GSM711923 3 0.5905 0.714 0.352 0.000 0.648
#> GSM711925 2 0.0000 0.961 0.000 1.000 0.000
#> GSM711927 3 0.0000 0.778 0.000 0.000 1.000
#> GSM711929 2 0.0000 0.961 0.000 1.000 0.000
#> GSM711931 2 0.6045 0.337 0.000 0.620 0.380
#> GSM711933 1 0.0000 0.949 1.000 0.000 0.000
#> GSM711935 2 0.0000 0.961 0.000 1.000 0.000
#> GSM711941 3 0.5926 0.710 0.356 0.000 0.644
#> GSM711943 3 0.5905 0.714 0.352 0.000 0.648
#> GSM711945 3 0.5882 0.718 0.348 0.000 0.652
#> GSM711947 3 0.0000 0.778 0.000 0.000 1.000
#> GSM711949 2 0.0000 0.961 0.000 1.000 0.000
#> GSM711953 2 0.0000 0.961 0.000 1.000 0.000
#> GSM711955 1 0.4002 0.733 0.840 0.000 0.160
#> GSM711963 2 0.0000 0.961 0.000 1.000 0.000
#> GSM711971 3 0.0000 0.778 0.000 0.000 1.000
#> GSM711975 2 0.0000 0.961 0.000 1.000 0.000
#> GSM711979 3 0.6126 0.713 0.352 0.004 0.644
#> GSM711989 2 0.0000 0.961 0.000 1.000 0.000
#> GSM711991 3 0.0592 0.779 0.012 0.000 0.988
#> GSM711993 3 0.7558 0.546 0.072 0.284 0.644
#> GSM711983 3 0.0000 0.778 0.000 0.000 1.000
#> GSM711985 2 0.0000 0.961 0.000 1.000 0.000
#> GSM711913 3 0.0000 0.778 0.000 0.000 1.000
#> GSM711919 3 0.0000 0.778 0.000 0.000 1.000
#> GSM711921 3 0.0000 0.778 0.000 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM711936 2 0.0000 0.9984 0.000 1.000 0.000 0.000
#> GSM711938 2 0.0000 0.9984 0.000 1.000 0.000 0.000
#> GSM711950 4 0.0336 0.9469 0.008 0.000 0.000 0.992
#> GSM711956 1 0.0000 0.9553 1.000 0.000 0.000 0.000
#> GSM711958 1 0.0000 0.9553 1.000 0.000 0.000 0.000
#> GSM711960 1 0.0921 0.9323 0.972 0.000 0.000 0.028
#> GSM711964 1 0.0000 0.9553 1.000 0.000 0.000 0.000
#> GSM711966 1 0.0000 0.9553 1.000 0.000 0.000 0.000
#> GSM711968 1 0.0000 0.9553 1.000 0.000 0.000 0.000
#> GSM711972 1 0.0000 0.9553 1.000 0.000 0.000 0.000
#> GSM711976 1 0.1211 0.9238 0.960 0.000 0.000 0.040
#> GSM711980 1 0.0000 0.9553 1.000 0.000 0.000 0.000
#> GSM711986 1 0.0000 0.9553 1.000 0.000 0.000 0.000
#> GSM711904 1 0.0000 0.9553 1.000 0.000 0.000 0.000
#> GSM711906 1 0.0000 0.9553 1.000 0.000 0.000 0.000
#> GSM711908 1 0.0000 0.9553 1.000 0.000 0.000 0.000
#> GSM711910 3 0.0000 0.9410 0.000 0.000 1.000 0.000
#> GSM711914 1 0.0000 0.9553 1.000 0.000 0.000 0.000
#> GSM711916 1 0.0000 0.9553 1.000 0.000 0.000 0.000
#> GSM711922 1 0.0000 0.9553 1.000 0.000 0.000 0.000
#> GSM711924 1 0.0000 0.9553 1.000 0.000 0.000 0.000
#> GSM711926 4 0.0188 0.9514 0.000 0.004 0.000 0.996
#> GSM711928 1 0.0000 0.9553 1.000 0.000 0.000 0.000
#> GSM711930 1 0.0000 0.9553 1.000 0.000 0.000 0.000
#> GSM711932 1 0.4916 0.2462 0.576 0.000 0.000 0.424
#> GSM711934 1 0.0000 0.9553 1.000 0.000 0.000 0.000
#> GSM711940 1 0.0817 0.9373 0.976 0.000 0.000 0.024
#> GSM711942 1 0.0000 0.9553 1.000 0.000 0.000 0.000
#> GSM711944 1 0.5510 0.0197 0.504 0.000 0.016 0.480
#> GSM711946 4 0.0188 0.9516 0.000 0.000 0.004 0.996
#> GSM711948 1 0.2647 0.8428 0.880 0.000 0.000 0.120
#> GSM711952 1 0.0000 0.9553 1.000 0.000 0.000 0.000
#> GSM711954 1 0.0469 0.9465 0.988 0.000 0.000 0.012
#> GSM711962 1 0.0000 0.9553 1.000 0.000 0.000 0.000
#> GSM711970 1 0.0000 0.9553 1.000 0.000 0.000 0.000
#> GSM711974 1 0.0000 0.9553 1.000 0.000 0.000 0.000
#> GSM711978 4 0.0188 0.9514 0.000 0.004 0.000 0.996
#> GSM711988 1 0.0000 0.9553 1.000 0.000 0.000 0.000
#> GSM711990 3 0.0921 0.9251 0.000 0.000 0.972 0.028
#> GSM711992 4 0.0188 0.9514 0.000 0.004 0.000 0.996
#> GSM711982 1 0.0000 0.9553 1.000 0.000 0.000 0.000
#> GSM711984 2 0.0000 0.9984 0.000 1.000 0.000 0.000
#> GSM711912 1 0.0000 0.9553 1.000 0.000 0.000 0.000
#> GSM711918 1 0.0000 0.9553 1.000 0.000 0.000 0.000
#> GSM711920 1 0.0000 0.9553 1.000 0.000 0.000 0.000
#> GSM711937 2 0.0000 0.9984 0.000 1.000 0.000 0.000
#> GSM711939 2 0.0000 0.9984 0.000 1.000 0.000 0.000
#> GSM711951 2 0.0188 0.9952 0.000 0.996 0.000 0.004
#> GSM711957 4 0.3751 0.7263 0.196 0.000 0.004 0.800
#> GSM711959 2 0.0000 0.9984 0.000 1.000 0.000 0.000
#> GSM711961 2 0.0000 0.9984 0.000 1.000 0.000 0.000
#> GSM711965 4 0.0188 0.9516 0.000 0.000 0.004 0.996
#> GSM711967 1 0.0000 0.9553 1.000 0.000 0.000 0.000
#> GSM711969 2 0.0000 0.9984 0.000 1.000 0.000 0.000
#> GSM711973 4 0.4012 0.7344 0.184 0.000 0.016 0.800
#> GSM711977 3 0.4543 0.5501 0.000 0.000 0.676 0.324
#> GSM711981 4 0.0469 0.9458 0.000 0.012 0.000 0.988
#> GSM711987 2 0.0188 0.9971 0.000 0.996 0.000 0.004
#> GSM711905 2 0.0188 0.9971 0.000 0.996 0.000 0.004
#> GSM711907 2 0.0000 0.9984 0.000 1.000 0.000 0.000
#> GSM711909 3 0.0000 0.9410 0.000 0.000 1.000 0.000
#> GSM711911 3 0.0188 0.9395 0.000 0.000 0.996 0.004
#> GSM711915 3 0.0000 0.9410 0.000 0.000 1.000 0.000
#> GSM711917 2 0.0000 0.9984 0.000 1.000 0.000 0.000
#> GSM711923 4 0.0188 0.9516 0.000 0.000 0.004 0.996
#> GSM711925 2 0.0000 0.9984 0.000 1.000 0.000 0.000
#> GSM711927 3 0.0000 0.9410 0.000 0.000 1.000 0.000
#> GSM711929 2 0.0188 0.9971 0.000 0.996 0.000 0.004
#> GSM711931 2 0.0188 0.9952 0.000 0.996 0.000 0.004
#> GSM711933 1 0.0000 0.9553 1.000 0.000 0.000 0.000
#> GSM711935 2 0.0188 0.9971 0.000 0.996 0.000 0.004
#> GSM711941 4 0.0188 0.9516 0.000 0.000 0.004 0.996
#> GSM711943 4 0.0188 0.9516 0.000 0.000 0.004 0.996
#> GSM711945 4 0.0188 0.9516 0.000 0.000 0.004 0.996
#> GSM711947 3 0.0000 0.9410 0.000 0.000 1.000 0.000
#> GSM711949 2 0.0188 0.9971 0.000 0.996 0.000 0.004
#> GSM711953 2 0.0188 0.9971 0.000 0.996 0.000 0.004
#> GSM711955 1 0.4925 0.2493 0.572 0.000 0.000 0.428
#> GSM711963 2 0.0188 0.9971 0.000 0.996 0.000 0.004
#> GSM711971 3 0.0336 0.9377 0.000 0.000 0.992 0.008
#> GSM711975 2 0.0000 0.9984 0.000 1.000 0.000 0.000
#> GSM711979 4 0.0188 0.9514 0.000 0.004 0.000 0.996
#> GSM711989 2 0.0000 0.9984 0.000 1.000 0.000 0.000
#> GSM711991 3 0.0000 0.9410 0.000 0.000 1.000 0.000
#> GSM711993 4 0.1637 0.8956 0.000 0.060 0.000 0.940
#> GSM711983 3 0.1022 0.9229 0.000 0.000 0.968 0.032
#> GSM711985 2 0.0000 0.9984 0.000 1.000 0.000 0.000
#> GSM711913 3 0.4543 0.5501 0.000 0.000 0.676 0.324
#> GSM711919 3 0.0000 0.9410 0.000 0.000 1.000 0.000
#> GSM711921 3 0.0000 0.9410 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM711936 2 0.0290 0.9649 0.000 0.992 0.000 0.008 0.000
#> GSM711938 2 0.0000 0.9671 0.000 1.000 0.000 0.000 0.000
#> GSM711950 1 0.2707 0.7663 0.876 0.000 0.000 0.100 0.024
#> GSM711956 1 0.0510 0.8636 0.984 0.000 0.000 0.000 0.016
#> GSM711958 1 0.3395 0.6516 0.764 0.000 0.000 0.000 0.236
#> GSM711960 5 0.3300 0.7629 0.204 0.000 0.004 0.000 0.792
#> GSM711964 1 0.0162 0.8648 0.996 0.000 0.000 0.000 0.004
#> GSM711966 1 0.1121 0.8569 0.956 0.000 0.000 0.000 0.044
#> GSM711968 1 0.0880 0.8613 0.968 0.000 0.000 0.000 0.032
#> GSM711972 1 0.1341 0.8550 0.944 0.000 0.000 0.000 0.056
#> GSM711976 1 0.0703 0.8539 0.976 0.000 0.000 0.000 0.024
#> GSM711980 1 0.0162 0.8653 0.996 0.000 0.000 0.000 0.004
#> GSM711986 1 0.3452 0.6421 0.756 0.000 0.000 0.000 0.244
#> GSM711904 1 0.4138 0.1090 0.616 0.000 0.000 0.000 0.384
#> GSM711906 5 0.2127 0.7875 0.108 0.000 0.000 0.000 0.892
#> GSM711908 5 0.1851 0.7746 0.088 0.000 0.000 0.000 0.912
#> GSM711910 3 0.0000 0.7802 0.000 0.000 1.000 0.000 0.000
#> GSM711914 1 0.1197 0.8543 0.952 0.000 0.000 0.000 0.048
#> GSM711916 5 0.2773 0.7940 0.164 0.000 0.000 0.000 0.836
#> GSM711922 1 0.0000 0.8646 1.000 0.000 0.000 0.000 0.000
#> GSM711924 1 0.1851 0.8377 0.912 0.000 0.000 0.000 0.088
#> GSM711926 4 0.3207 0.8386 0.056 0.048 0.000 0.872 0.024
#> GSM711928 1 0.0000 0.8646 1.000 0.000 0.000 0.000 0.000
#> GSM711930 5 0.1851 0.7746 0.088 0.000 0.000 0.000 0.912
#> GSM711932 1 0.1386 0.8408 0.952 0.000 0.000 0.032 0.016
#> GSM711934 1 0.1121 0.8562 0.956 0.000 0.000 0.000 0.044
#> GSM711940 1 0.0000 0.8646 1.000 0.000 0.000 0.000 0.000
#> GSM711942 1 0.2179 0.8234 0.888 0.000 0.000 0.000 0.112
#> GSM711944 1 0.6784 0.0603 0.488 0.000 0.036 0.356 0.120
#> GSM711946 4 0.0771 0.8654 0.020 0.000 0.004 0.976 0.000
#> GSM711948 1 0.2230 0.8308 0.912 0.000 0.000 0.044 0.044
#> GSM711952 5 0.4307 0.2269 0.500 0.000 0.000 0.000 0.500
#> GSM711954 1 0.0000 0.8646 1.000 0.000 0.000 0.000 0.000
#> GSM711962 1 0.1732 0.8440 0.920 0.000 0.000 0.000 0.080
#> GSM711970 1 0.0000 0.8646 1.000 0.000 0.000 0.000 0.000
#> GSM711974 1 0.3796 0.5205 0.700 0.000 0.000 0.000 0.300
#> GSM711978 4 0.1943 0.8554 0.056 0.000 0.000 0.924 0.020
#> GSM711988 1 0.0000 0.8646 1.000 0.000 0.000 0.000 0.000
#> GSM711990 3 0.6152 0.3192 0.008 0.000 0.524 0.356 0.112
#> GSM711992 4 0.1628 0.8579 0.056 0.000 0.000 0.936 0.008
#> GSM711982 1 0.2329 0.8184 0.876 0.000 0.000 0.000 0.124
#> GSM711984 2 0.0000 0.9671 0.000 1.000 0.000 0.000 0.000
#> GSM711912 5 0.3796 0.7196 0.300 0.000 0.000 0.000 0.700
#> GSM711918 5 0.3684 0.7437 0.280 0.000 0.000 0.000 0.720
#> GSM711920 1 0.1792 0.8415 0.916 0.000 0.000 0.000 0.084
#> GSM711937 2 0.0000 0.9671 0.000 1.000 0.000 0.000 0.000
#> GSM711939 2 0.0000 0.9671 0.000 1.000 0.000 0.000 0.000
#> GSM711951 2 0.1851 0.9112 0.000 0.912 0.000 0.088 0.000
#> GSM711957 4 0.4528 0.7147 0.104 0.000 0.000 0.752 0.144
#> GSM711959 2 0.0000 0.9671 0.000 1.000 0.000 0.000 0.000
#> GSM711961 2 0.0162 0.9670 0.000 0.996 0.000 0.000 0.004
#> GSM711965 4 0.1082 0.8631 0.028 0.000 0.008 0.964 0.000
#> GSM711967 1 0.0290 0.8652 0.992 0.000 0.000 0.000 0.008
#> GSM711969 2 0.0000 0.9671 0.000 1.000 0.000 0.000 0.000
#> GSM711973 4 0.5505 0.5394 0.208 0.000 0.004 0.660 0.128
#> GSM711977 3 0.4305 0.2443 0.000 0.000 0.512 0.488 0.000
#> GSM711981 4 0.3601 0.7699 0.024 0.124 0.000 0.832 0.020
#> GSM711987 2 0.2171 0.9469 0.000 0.912 0.000 0.024 0.064
#> GSM711905 2 0.2171 0.9469 0.000 0.912 0.000 0.024 0.064
#> GSM711907 2 0.0290 0.9649 0.000 0.992 0.000 0.008 0.000
#> GSM711909 3 0.0000 0.7802 0.000 0.000 1.000 0.000 0.000
#> GSM711911 3 0.3983 0.5111 0.000 0.000 0.660 0.340 0.000
#> GSM711915 3 0.0000 0.7802 0.000 0.000 1.000 0.000 0.000
#> GSM711917 2 0.0000 0.9671 0.000 1.000 0.000 0.000 0.000
#> GSM711923 4 0.0865 0.8659 0.024 0.000 0.004 0.972 0.000
#> GSM711925 2 0.1410 0.9552 0.000 0.940 0.000 0.000 0.060
#> GSM711927 3 0.0000 0.7802 0.000 0.000 1.000 0.000 0.000
#> GSM711929 2 0.2171 0.9469 0.000 0.912 0.000 0.024 0.064
#> GSM711931 2 0.1012 0.9526 0.000 0.968 0.000 0.012 0.020
#> GSM711933 1 0.1270 0.8542 0.948 0.000 0.000 0.000 0.052
#> GSM711935 2 0.2171 0.9469 0.000 0.912 0.000 0.024 0.064
#> GSM711941 1 0.3779 0.6482 0.776 0.000 0.000 0.200 0.024
#> GSM711943 4 0.0771 0.8654 0.020 0.000 0.004 0.976 0.000
#> GSM711945 4 0.0771 0.8654 0.020 0.000 0.004 0.976 0.000
#> GSM711947 3 0.0963 0.7688 0.000 0.000 0.964 0.036 0.000
#> GSM711949 2 0.2171 0.9469 0.000 0.912 0.000 0.024 0.064
#> GSM711953 2 0.2171 0.9469 0.000 0.912 0.000 0.024 0.064
#> GSM711955 1 0.2585 0.8284 0.896 0.000 0.004 0.064 0.036
#> GSM711963 2 0.2171 0.9469 0.000 0.912 0.000 0.024 0.064
#> GSM711971 3 0.4425 0.6716 0.004 0.000 0.772 0.112 0.112
#> GSM711975 2 0.0404 0.9639 0.000 0.988 0.000 0.012 0.000
#> GSM711979 1 0.4086 0.5923 0.736 0.000 0.000 0.240 0.024
#> GSM711989 2 0.0290 0.9649 0.000 0.992 0.000 0.008 0.000
#> GSM711991 3 0.2516 0.7326 0.000 0.000 0.860 0.140 0.000
#> GSM711993 4 0.4320 0.7568 0.052 0.132 0.000 0.792 0.024
#> GSM711983 3 0.6152 0.3192 0.008 0.000 0.524 0.356 0.112
#> GSM711985 2 0.0000 0.9671 0.000 1.000 0.000 0.000 0.000
#> GSM711913 3 0.4291 0.2998 0.000 0.000 0.536 0.464 0.000
#> GSM711919 3 0.0404 0.7777 0.000 0.000 0.988 0.000 0.012
#> GSM711921 3 0.0000 0.7802 0.000 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM711936 2 0.0146 0.78240 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM711938 2 0.0547 0.77826 0.000 0.980 0.000 0.000 0.020 0.000
#> GSM711950 4 0.6130 0.46921 0.272 0.000 0.000 0.432 0.292 0.004
#> GSM711956 1 0.0000 0.76211 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711958 1 0.2164 0.71513 0.900 0.000 0.000 0.032 0.000 0.068
#> GSM711960 6 0.6584 0.25830 0.284 0.000 0.256 0.032 0.000 0.428
#> GSM711964 1 0.0000 0.76211 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711966 1 0.0000 0.76211 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711968 1 0.0000 0.76211 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711972 1 0.0547 0.75376 0.980 0.000 0.000 0.000 0.000 0.020
#> GSM711976 1 0.2846 0.72792 0.856 0.000 0.000 0.060 0.000 0.084
#> GSM711980 1 0.1663 0.75421 0.912 0.000 0.000 0.000 0.000 0.088
#> GSM711986 6 0.3810 0.58931 0.428 0.000 0.000 0.000 0.000 0.572
#> GSM711904 1 0.4697 0.24386 0.688 0.000 0.000 0.004 0.108 0.200
#> GSM711906 6 0.3595 0.66849 0.288 0.000 0.000 0.000 0.008 0.704
#> GSM711908 6 0.1610 0.56556 0.084 0.000 0.000 0.000 0.000 0.916
#> GSM711910 3 0.0000 0.83433 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711914 1 0.0000 0.76211 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711916 6 0.3890 0.39024 0.400 0.000 0.000 0.000 0.004 0.596
#> GSM711922 1 0.2060 0.75186 0.900 0.000 0.000 0.016 0.000 0.084
#> GSM711924 1 0.1257 0.75070 0.952 0.000 0.000 0.020 0.000 0.028
#> GSM711926 4 0.4086 0.67486 0.000 0.008 0.000 0.528 0.464 0.000
#> GSM711928 1 0.1610 0.75266 0.916 0.000 0.000 0.000 0.000 0.084
#> GSM711930 6 0.1610 0.56556 0.084 0.000 0.000 0.000 0.000 0.916
#> GSM711932 1 0.7028 -0.18841 0.384 0.000 0.000 0.340 0.192 0.084
#> GSM711934 1 0.1755 0.74256 0.932 0.000 0.000 0.032 0.008 0.028
#> GSM711940 1 0.2639 0.74511 0.876 0.000 0.000 0.032 0.008 0.084
#> GSM711942 1 0.1610 0.70097 0.916 0.000 0.000 0.000 0.000 0.084
#> GSM711944 1 0.6632 -0.05076 0.460 0.000 0.336 0.112 0.000 0.092
#> GSM711946 4 0.0000 0.66881 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM711948 1 0.5338 0.12156 0.508 0.000 0.000 0.416 0.044 0.032
#> GSM711952 6 0.4697 0.60912 0.404 0.000 0.000 0.000 0.048 0.548
#> GSM711954 1 0.1610 0.75266 0.916 0.000 0.000 0.000 0.000 0.084
#> GSM711962 1 0.0363 0.75749 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM711970 1 0.1610 0.75266 0.916 0.000 0.000 0.000 0.000 0.084
#> GSM711974 1 0.3515 0.28435 0.676 0.000 0.000 0.000 0.000 0.324
#> GSM711978 4 0.3126 0.70434 0.000 0.000 0.000 0.752 0.248 0.000
#> GSM711988 1 0.2527 0.74621 0.880 0.000 0.000 0.032 0.004 0.084
#> GSM711990 3 0.3508 0.77637 0.000 0.000 0.800 0.132 0.000 0.068
#> GSM711992 4 0.3101 0.70420 0.000 0.000 0.000 0.756 0.244 0.000
#> GSM711982 1 0.3482 0.30493 0.684 0.000 0.000 0.000 0.000 0.316
#> GSM711984 2 0.1075 0.74744 0.000 0.952 0.000 0.000 0.048 0.000
#> GSM711912 6 0.3975 0.63218 0.392 0.000 0.000 0.000 0.008 0.600
#> GSM711918 6 0.4301 0.63068 0.392 0.000 0.000 0.000 0.024 0.584
#> GSM711920 1 0.1007 0.74061 0.956 0.000 0.000 0.000 0.000 0.044
#> GSM711937 2 0.0000 0.78404 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711939 2 0.0260 0.78333 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM711951 2 0.4131 0.19155 0.000 0.624 0.000 0.356 0.020 0.000
#> GSM711957 4 0.5786 0.62510 0.020 0.000 0.000 0.440 0.436 0.104
#> GSM711959 2 0.0632 0.77284 0.000 0.976 0.000 0.000 0.024 0.000
#> GSM711961 2 0.3266 0.19201 0.000 0.728 0.000 0.000 0.272 0.000
#> GSM711965 4 0.3489 0.00522 0.000 0.000 0.288 0.708 0.004 0.000
#> GSM711967 1 0.1918 0.75400 0.904 0.000 0.000 0.000 0.008 0.088
#> GSM711969 2 0.0260 0.78333 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM711973 4 0.5875 0.62069 0.100 0.000 0.000 0.624 0.188 0.088
#> GSM711977 3 0.3864 0.46938 0.000 0.000 0.520 0.480 0.000 0.000
#> GSM711981 4 0.4712 0.67947 0.000 0.052 0.000 0.564 0.384 0.000
#> GSM711987 5 0.3860 0.71857 0.000 0.472 0.000 0.000 0.528 0.000
#> GSM711905 5 0.3860 0.71857 0.000 0.472 0.000 0.000 0.528 0.000
#> GSM711907 2 0.0146 0.78240 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM711909 3 0.0363 0.83627 0.000 0.000 0.988 0.012 0.000 0.000
#> GSM711911 3 0.3446 0.67791 0.000 0.000 0.692 0.308 0.000 0.000
#> GSM711915 3 0.0000 0.83433 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711917 2 0.0000 0.78404 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711923 4 0.0000 0.66881 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM711925 2 0.3782 -0.41943 0.000 0.588 0.000 0.000 0.412 0.000
#> GSM711927 3 0.0363 0.83627 0.000 0.000 0.988 0.012 0.000 0.000
#> GSM711929 5 0.3860 0.71857 0.000 0.472 0.000 0.000 0.528 0.000
#> GSM711931 2 0.4915 0.30557 0.000 0.632 0.000 0.108 0.260 0.000
#> GSM711933 1 0.2177 0.72529 0.908 0.000 0.000 0.052 0.008 0.032
#> GSM711935 5 0.3860 0.71857 0.000 0.472 0.000 0.000 0.528 0.000
#> GSM711941 4 0.5549 0.60780 0.168 0.000 0.000 0.536 0.296 0.000
#> GSM711943 4 0.1714 0.68970 0.000 0.000 0.000 0.908 0.092 0.000
#> GSM711945 4 0.1074 0.66428 0.000 0.000 0.012 0.960 0.028 0.000
#> GSM711947 3 0.1349 0.80918 0.000 0.000 0.940 0.056 0.004 0.000
#> GSM711949 5 0.3860 0.71857 0.000 0.472 0.000 0.000 0.528 0.000
#> GSM711953 5 0.3860 0.71857 0.000 0.472 0.000 0.000 0.528 0.000
#> GSM711955 1 0.5580 0.23113 0.552 0.000 0.064 0.344 0.000 0.040
#> GSM711963 5 0.3860 0.71857 0.000 0.472 0.000 0.000 0.528 0.000
#> GSM711971 3 0.3013 0.80100 0.000 0.000 0.844 0.088 0.000 0.068
#> GSM711975 2 0.2263 0.64884 0.000 0.884 0.000 0.100 0.016 0.000
#> GSM711979 4 0.5276 0.65089 0.124 0.000 0.000 0.564 0.312 0.000
#> GSM711989 2 0.0000 0.78404 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711991 3 0.3215 0.70993 0.000 0.000 0.756 0.240 0.004 0.000
#> GSM711993 5 0.5387 -0.66962 0.000 0.112 0.000 0.424 0.464 0.000
#> GSM711983 3 0.3508 0.77637 0.000 0.000 0.800 0.132 0.000 0.068
#> GSM711985 2 0.1141 0.74396 0.000 0.948 0.000 0.000 0.052 0.000
#> GSM711913 3 0.3862 0.47581 0.000 0.000 0.524 0.476 0.000 0.000
#> GSM711919 3 0.0547 0.83162 0.000 0.000 0.980 0.000 0.000 0.020
#> GSM711921 3 0.0000 0.83433 0.000 0.000 1.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) disease.state(p) individual(p) k
#> MAD:mclust 90 2.27e-05 0.1428 0.530 2
#> MAD:mclust 88 4.17e-10 0.4595 0.513 3
#> MAD:mclust 87 1.42e-10 0.1061 0.527 4
#> MAD:mclust 83 2.10e-08 0.0328 0.381 5
#> MAD:mclust 72 3.14e-07 0.0460 0.200 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "NMF"]
# you can also extract it by
# res = res_list["MAD:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 27425 rows and 90 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.977 0.990 0.4276 0.575 0.575
#> 3 3 1.000 0.977 0.990 0.5303 0.758 0.584
#> 4 4 0.874 0.872 0.942 0.1352 0.844 0.587
#> 5 5 0.772 0.724 0.863 0.0479 0.942 0.789
#> 6 6 0.857 0.765 0.890 0.0443 0.900 0.613
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
#> attr(,"optional")
#> [1] 2
There is also optional best \(k\) = 2 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM711936 2 0.0000 0.989 0.000 1.000
#> GSM711938 2 0.0000 0.989 0.000 1.000
#> GSM711950 1 0.0000 0.990 1.000 0.000
#> GSM711956 1 0.0000 0.990 1.000 0.000
#> GSM711958 1 0.0000 0.990 1.000 0.000
#> GSM711960 1 0.0000 0.990 1.000 0.000
#> GSM711964 1 0.0000 0.990 1.000 0.000
#> GSM711966 1 0.0000 0.990 1.000 0.000
#> GSM711968 1 0.0000 0.990 1.000 0.000
#> GSM711972 1 0.0000 0.990 1.000 0.000
#> GSM711976 1 0.0000 0.990 1.000 0.000
#> GSM711980 1 0.0000 0.990 1.000 0.000
#> GSM711986 1 0.0000 0.990 1.000 0.000
#> GSM711904 1 0.0000 0.990 1.000 0.000
#> GSM711906 1 0.0000 0.990 1.000 0.000
#> GSM711908 1 0.0000 0.990 1.000 0.000
#> GSM711910 1 0.0000 0.990 1.000 0.000
#> GSM711914 1 0.0000 0.990 1.000 0.000
#> GSM711916 1 0.0000 0.990 1.000 0.000
#> GSM711922 1 0.0000 0.990 1.000 0.000
#> GSM711924 1 0.0000 0.990 1.000 0.000
#> GSM711926 2 0.2948 0.939 0.052 0.948
#> GSM711928 1 0.0000 0.990 1.000 0.000
#> GSM711930 1 0.0000 0.990 1.000 0.000
#> GSM711932 1 0.0000 0.990 1.000 0.000
#> GSM711934 1 0.0000 0.990 1.000 0.000
#> GSM711940 1 0.0000 0.990 1.000 0.000
#> GSM711942 1 0.0000 0.990 1.000 0.000
#> GSM711944 1 0.0000 0.990 1.000 0.000
#> GSM711946 1 0.0000 0.990 1.000 0.000
#> GSM711948 1 0.0000 0.990 1.000 0.000
#> GSM711952 1 0.0000 0.990 1.000 0.000
#> GSM711954 1 0.0000 0.990 1.000 0.000
#> GSM711962 1 0.0000 0.990 1.000 0.000
#> GSM711970 1 0.0000 0.990 1.000 0.000
#> GSM711974 1 0.0000 0.990 1.000 0.000
#> GSM711978 1 0.1843 0.963 0.972 0.028
#> GSM711988 1 0.0000 0.990 1.000 0.000
#> GSM711990 1 0.0000 0.990 1.000 0.000
#> GSM711992 1 0.0000 0.990 1.000 0.000
#> GSM711982 1 0.0000 0.990 1.000 0.000
#> GSM711984 2 0.0000 0.989 0.000 1.000
#> GSM711912 1 0.0000 0.990 1.000 0.000
#> GSM711918 1 0.0000 0.990 1.000 0.000
#> GSM711920 1 0.0000 0.990 1.000 0.000
#> GSM711937 2 0.0000 0.989 0.000 1.000
#> GSM711939 2 0.0000 0.989 0.000 1.000
#> GSM711951 2 0.0000 0.989 0.000 1.000
#> GSM711957 1 0.0000 0.990 1.000 0.000
#> GSM711959 2 0.0000 0.989 0.000 1.000
#> GSM711961 2 0.0000 0.989 0.000 1.000
#> GSM711965 1 0.0000 0.990 1.000 0.000
#> GSM711967 1 0.0000 0.990 1.000 0.000
#> GSM711969 2 0.0000 0.989 0.000 1.000
#> GSM711973 1 0.0000 0.990 1.000 0.000
#> GSM711977 1 0.0000 0.990 1.000 0.000
#> GSM711981 2 0.7815 0.695 0.232 0.768
#> GSM711987 2 0.0000 0.989 0.000 1.000
#> GSM711905 2 0.0000 0.989 0.000 1.000
#> GSM711907 2 0.0000 0.989 0.000 1.000
#> GSM711909 1 0.0000 0.990 1.000 0.000
#> GSM711911 1 0.0000 0.990 1.000 0.000
#> GSM711915 1 0.0000 0.990 1.000 0.000
#> GSM711917 2 0.0000 0.989 0.000 1.000
#> GSM711923 1 0.0000 0.990 1.000 0.000
#> GSM711925 2 0.0000 0.989 0.000 1.000
#> GSM711927 1 0.0000 0.990 1.000 0.000
#> GSM711929 2 0.0000 0.989 0.000 1.000
#> GSM711931 2 0.0000 0.989 0.000 1.000
#> GSM711933 1 0.0000 0.990 1.000 0.000
#> GSM711935 2 0.0000 0.989 0.000 1.000
#> GSM711941 1 0.0000 0.990 1.000 0.000
#> GSM711943 1 0.1184 0.975 0.984 0.016
#> GSM711945 1 0.9000 0.538 0.684 0.316
#> GSM711947 2 0.0000 0.989 0.000 1.000
#> GSM711949 2 0.0000 0.989 0.000 1.000
#> GSM711953 2 0.0000 0.989 0.000 1.000
#> GSM711955 1 0.0000 0.990 1.000 0.000
#> GSM711963 2 0.0000 0.989 0.000 1.000
#> GSM711971 1 0.0000 0.990 1.000 0.000
#> GSM711975 2 0.0000 0.989 0.000 1.000
#> GSM711979 1 0.0000 0.990 1.000 0.000
#> GSM711989 2 0.0000 0.989 0.000 1.000
#> GSM711991 1 0.7883 0.690 0.764 0.236
#> GSM711993 2 0.0672 0.982 0.008 0.992
#> GSM711983 1 0.0000 0.990 1.000 0.000
#> GSM711985 2 0.0000 0.989 0.000 1.000
#> GSM711913 1 0.0000 0.990 1.000 0.000
#> GSM711919 1 0.0000 0.990 1.000 0.000
#> GSM711921 1 0.0000 0.990 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM711936 2 0.0000 0.991 0.000 1.000 0.000
#> GSM711938 2 0.0000 0.991 0.000 1.000 0.000
#> GSM711950 1 0.0000 0.991 1.000 0.000 0.000
#> GSM711956 1 0.0000 0.991 1.000 0.000 0.000
#> GSM711958 1 0.0000 0.991 1.000 0.000 0.000
#> GSM711960 3 0.2537 0.910 0.080 0.000 0.920
#> GSM711964 1 0.0000 0.991 1.000 0.000 0.000
#> GSM711966 1 0.0000 0.991 1.000 0.000 0.000
#> GSM711968 1 0.0000 0.991 1.000 0.000 0.000
#> GSM711972 1 0.0000 0.991 1.000 0.000 0.000
#> GSM711976 1 0.0000 0.991 1.000 0.000 0.000
#> GSM711980 1 0.0000 0.991 1.000 0.000 0.000
#> GSM711986 1 0.0000 0.991 1.000 0.000 0.000
#> GSM711904 1 0.0000 0.991 1.000 0.000 0.000
#> GSM711906 1 0.0000 0.991 1.000 0.000 0.000
#> GSM711908 1 0.0000 0.991 1.000 0.000 0.000
#> GSM711910 3 0.0000 0.981 0.000 0.000 1.000
#> GSM711914 1 0.0000 0.991 1.000 0.000 0.000
#> GSM711916 1 0.0000 0.991 1.000 0.000 0.000
#> GSM711922 1 0.0000 0.991 1.000 0.000 0.000
#> GSM711924 1 0.0000 0.991 1.000 0.000 0.000
#> GSM711926 2 0.4452 0.757 0.192 0.808 0.000
#> GSM711928 1 0.0000 0.991 1.000 0.000 0.000
#> GSM711930 1 0.0000 0.991 1.000 0.000 0.000
#> GSM711932 1 0.0000 0.991 1.000 0.000 0.000
#> GSM711934 1 0.0000 0.991 1.000 0.000 0.000
#> GSM711940 1 0.0000 0.991 1.000 0.000 0.000
#> GSM711942 1 0.0000 0.991 1.000 0.000 0.000
#> GSM711944 3 0.0000 0.981 0.000 0.000 1.000
#> GSM711946 3 0.0000 0.981 0.000 0.000 1.000
#> GSM711948 1 0.2066 0.931 0.940 0.000 0.060
#> GSM711952 1 0.0000 0.991 1.000 0.000 0.000
#> GSM711954 1 0.0000 0.991 1.000 0.000 0.000
#> GSM711962 1 0.0000 0.991 1.000 0.000 0.000
#> GSM711970 1 0.0000 0.991 1.000 0.000 0.000
#> GSM711974 1 0.0000 0.991 1.000 0.000 0.000
#> GSM711978 1 0.4235 0.788 0.824 0.176 0.000
#> GSM711988 1 0.0000 0.991 1.000 0.000 0.000
#> GSM711990 3 0.0000 0.981 0.000 0.000 1.000
#> GSM711992 1 0.0592 0.980 0.988 0.012 0.000
#> GSM711982 1 0.0000 0.991 1.000 0.000 0.000
#> GSM711984 2 0.0000 0.991 0.000 1.000 0.000
#> GSM711912 1 0.0000 0.991 1.000 0.000 0.000
#> GSM711918 1 0.0000 0.991 1.000 0.000 0.000
#> GSM711920 1 0.0000 0.991 1.000 0.000 0.000
#> GSM711937 2 0.0000 0.991 0.000 1.000 0.000
#> GSM711939 2 0.0000 0.991 0.000 1.000 0.000
#> GSM711951 2 0.0000 0.991 0.000 1.000 0.000
#> GSM711957 1 0.0000 0.991 1.000 0.000 0.000
#> GSM711959 2 0.0000 0.991 0.000 1.000 0.000
#> GSM711961 2 0.0000 0.991 0.000 1.000 0.000
#> GSM711965 3 0.0000 0.981 0.000 0.000 1.000
#> GSM711967 1 0.0000 0.991 1.000 0.000 0.000
#> GSM711969 2 0.0000 0.991 0.000 1.000 0.000
#> GSM711973 3 0.0000 0.981 0.000 0.000 1.000
#> GSM711977 3 0.0000 0.981 0.000 0.000 1.000
#> GSM711981 2 0.0000 0.991 0.000 1.000 0.000
#> GSM711987 2 0.0000 0.991 0.000 1.000 0.000
#> GSM711905 2 0.0000 0.991 0.000 1.000 0.000
#> GSM711907 2 0.0000 0.991 0.000 1.000 0.000
#> GSM711909 3 0.0000 0.981 0.000 0.000 1.000
#> GSM711911 3 0.0000 0.981 0.000 0.000 1.000
#> GSM711915 3 0.0000 0.981 0.000 0.000 1.000
#> GSM711917 2 0.0000 0.991 0.000 1.000 0.000
#> GSM711923 3 0.0000 0.981 0.000 0.000 1.000
#> GSM711925 2 0.0000 0.991 0.000 1.000 0.000
#> GSM711927 3 0.0000 0.981 0.000 0.000 1.000
#> GSM711929 2 0.0000 0.991 0.000 1.000 0.000
#> GSM711931 2 0.0000 0.991 0.000 1.000 0.000
#> GSM711933 1 0.0000 0.991 1.000 0.000 0.000
#> GSM711935 2 0.0000 0.991 0.000 1.000 0.000
#> GSM711941 3 0.2356 0.918 0.072 0.000 0.928
#> GSM711943 3 0.1753 0.940 0.000 0.048 0.952
#> GSM711945 3 0.0000 0.981 0.000 0.000 1.000
#> GSM711947 3 0.0000 0.981 0.000 0.000 1.000
#> GSM711949 2 0.0000 0.991 0.000 1.000 0.000
#> GSM711953 2 0.0000 0.991 0.000 1.000 0.000
#> GSM711955 3 0.4452 0.776 0.192 0.000 0.808
#> GSM711963 2 0.0000 0.991 0.000 1.000 0.000
#> GSM711971 3 0.0000 0.981 0.000 0.000 1.000
#> GSM711975 2 0.0000 0.991 0.000 1.000 0.000
#> GSM711979 1 0.2878 0.893 0.904 0.096 0.000
#> GSM711989 2 0.0000 0.991 0.000 1.000 0.000
#> GSM711991 3 0.0000 0.981 0.000 0.000 1.000
#> GSM711993 2 0.0000 0.991 0.000 1.000 0.000
#> GSM711983 3 0.0000 0.981 0.000 0.000 1.000
#> GSM711985 2 0.0000 0.991 0.000 1.000 0.000
#> GSM711913 3 0.0000 0.981 0.000 0.000 1.000
#> GSM711919 3 0.0000 0.981 0.000 0.000 1.000
#> GSM711921 3 0.0000 0.981 0.000 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM711936 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM711938 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM711950 4 0.0469 0.842 0.012 0.000 0.000 0.988
#> GSM711956 1 0.0336 0.962 0.992 0.000 0.000 0.008
#> GSM711958 1 0.0000 0.963 1.000 0.000 0.000 0.000
#> GSM711960 3 0.0895 0.895 0.020 0.000 0.976 0.004
#> GSM711964 1 0.0188 0.963 0.996 0.000 0.000 0.004
#> GSM711966 1 0.0000 0.963 1.000 0.000 0.000 0.000
#> GSM711968 1 0.0336 0.962 0.992 0.000 0.000 0.008
#> GSM711972 1 0.0000 0.963 1.000 0.000 0.000 0.000
#> GSM711976 4 0.3266 0.770 0.168 0.000 0.000 0.832
#> GSM711980 1 0.0188 0.963 0.996 0.000 0.000 0.004
#> GSM711986 1 0.0000 0.963 1.000 0.000 0.000 0.000
#> GSM711904 1 0.0336 0.962 0.992 0.000 0.000 0.008
#> GSM711906 1 0.0000 0.963 1.000 0.000 0.000 0.000
#> GSM711908 1 0.0000 0.963 1.000 0.000 0.000 0.000
#> GSM711910 3 0.0188 0.908 0.000 0.000 0.996 0.004
#> GSM711914 1 0.0188 0.963 0.996 0.000 0.000 0.004
#> GSM711916 1 0.0000 0.963 1.000 0.000 0.000 0.000
#> GSM711922 1 0.0336 0.961 0.992 0.000 0.000 0.008
#> GSM711924 1 0.0000 0.963 1.000 0.000 0.000 0.000
#> GSM711926 4 0.1792 0.831 0.000 0.068 0.000 0.932
#> GSM711928 1 0.0188 0.963 0.996 0.000 0.000 0.004
#> GSM711930 1 0.0188 0.961 0.996 0.000 0.000 0.004
#> GSM711932 4 0.3074 0.781 0.152 0.000 0.000 0.848
#> GSM711934 1 0.0188 0.963 0.996 0.000 0.000 0.004
#> GSM711940 4 0.4605 0.535 0.336 0.000 0.000 0.664
#> GSM711942 1 0.0188 0.962 0.996 0.000 0.000 0.004
#> GSM711944 3 0.0592 0.904 0.000 0.000 0.984 0.016
#> GSM711946 3 0.4972 0.261 0.000 0.000 0.544 0.456
#> GSM711948 4 0.0524 0.841 0.008 0.000 0.004 0.988
#> GSM711952 1 0.0188 0.963 0.996 0.000 0.000 0.004
#> GSM711954 1 0.2589 0.855 0.884 0.000 0.000 0.116
#> GSM711962 1 0.0000 0.963 1.000 0.000 0.000 0.000
#> GSM711970 1 0.2345 0.876 0.900 0.000 0.000 0.100
#> GSM711974 1 0.0000 0.963 1.000 0.000 0.000 0.000
#> GSM711978 4 0.1411 0.844 0.020 0.020 0.000 0.960
#> GSM711988 1 0.5000 -0.120 0.500 0.000 0.000 0.500
#> GSM711990 3 0.0188 0.909 0.000 0.000 0.996 0.004
#> GSM711992 4 0.4761 0.539 0.332 0.004 0.000 0.664
#> GSM711982 1 0.0000 0.963 1.000 0.000 0.000 0.000
#> GSM711984 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM711912 1 0.0000 0.963 1.000 0.000 0.000 0.000
#> GSM711918 1 0.0000 0.963 1.000 0.000 0.000 0.000
#> GSM711920 1 0.0336 0.962 0.992 0.000 0.000 0.008
#> GSM711937 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM711939 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM711951 4 0.2149 0.821 0.000 0.088 0.000 0.912
#> GSM711957 4 0.4008 0.693 0.244 0.000 0.000 0.756
#> GSM711959 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM711961 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM711965 4 0.4543 0.404 0.000 0.000 0.324 0.676
#> GSM711967 1 0.1867 0.902 0.928 0.000 0.000 0.072
#> GSM711969 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM711973 4 0.3356 0.709 0.000 0.000 0.176 0.824
#> GSM711977 3 0.3123 0.790 0.000 0.000 0.844 0.156
#> GSM711981 4 0.0921 0.841 0.000 0.028 0.000 0.972
#> GSM711987 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM711905 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM711907 2 0.1792 0.920 0.000 0.932 0.000 0.068
#> GSM711909 3 0.0000 0.909 0.000 0.000 1.000 0.000
#> GSM711911 3 0.0188 0.909 0.000 0.000 0.996 0.004
#> GSM711915 3 0.0000 0.909 0.000 0.000 1.000 0.000
#> GSM711917 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM711923 4 0.0469 0.837 0.000 0.000 0.012 0.988
#> GSM711925 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM711927 3 0.0000 0.909 0.000 0.000 1.000 0.000
#> GSM711929 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM711931 4 0.3528 0.744 0.000 0.192 0.000 0.808
#> GSM711933 1 0.3074 0.804 0.848 0.000 0.000 0.152
#> GSM711935 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM711941 4 0.0524 0.839 0.004 0.000 0.008 0.988
#> GSM711943 4 0.1284 0.836 0.000 0.012 0.024 0.964
#> GSM711945 3 0.5000 0.116 0.000 0.000 0.500 0.500
#> GSM711947 3 0.1004 0.894 0.000 0.024 0.972 0.004
#> GSM711949 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM711953 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM711955 3 0.5184 0.552 0.024 0.000 0.672 0.304
#> GSM711963 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM711971 3 0.0000 0.909 0.000 0.000 1.000 0.000
#> GSM711975 4 0.4356 0.607 0.000 0.292 0.000 0.708
#> GSM711979 4 0.0524 0.842 0.008 0.004 0.000 0.988
#> GSM711989 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM711991 3 0.0000 0.909 0.000 0.000 1.000 0.000
#> GSM711993 4 0.1022 0.841 0.000 0.032 0.000 0.968
#> GSM711983 3 0.0188 0.909 0.000 0.000 0.996 0.004
#> GSM711985 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM711913 3 0.1118 0.893 0.000 0.000 0.964 0.036
#> GSM711919 3 0.0188 0.908 0.000 0.000 0.996 0.004
#> GSM711921 3 0.0188 0.908 0.000 0.000 0.996 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM711936 2 0.0000 0.97867 0.000 1.000 0.000 0.000 0.000
#> GSM711938 2 0.0000 0.97867 0.000 1.000 0.000 0.000 0.000
#> GSM711950 4 0.3177 0.64273 0.000 0.000 0.000 0.792 0.208
#> GSM711956 1 0.2648 0.78460 0.848 0.000 0.000 0.000 0.152
#> GSM711958 1 0.4321 0.30400 0.600 0.000 0.396 0.000 0.004
#> GSM711960 3 0.0955 0.88063 0.028 0.000 0.968 0.000 0.004
#> GSM711964 1 0.0000 0.82438 1.000 0.000 0.000 0.000 0.000
#> GSM711966 1 0.0404 0.82359 0.988 0.000 0.000 0.000 0.012
#> GSM711968 1 0.3177 0.75371 0.792 0.000 0.000 0.000 0.208
#> GSM711972 1 0.0290 0.82389 0.992 0.000 0.000 0.000 0.008
#> GSM711976 1 0.5467 0.29692 0.548 0.000 0.000 0.384 0.068
#> GSM711980 1 0.2136 0.80823 0.904 0.000 0.000 0.008 0.088
#> GSM711986 1 0.0000 0.82438 1.000 0.000 0.000 0.000 0.000
#> GSM711904 1 0.2377 0.79534 0.872 0.000 0.000 0.000 0.128
#> GSM711906 1 0.0404 0.82359 0.988 0.000 0.000 0.000 0.012
#> GSM711908 1 0.0404 0.82359 0.988 0.000 0.000 0.000 0.012
#> GSM711910 3 0.0000 0.91534 0.000 0.000 1.000 0.000 0.000
#> GSM711914 1 0.0290 0.82459 0.992 0.000 0.000 0.000 0.008
#> GSM711916 1 0.0404 0.82359 0.988 0.000 0.000 0.000 0.012
#> GSM711922 1 0.3671 0.73041 0.756 0.000 0.000 0.008 0.236
#> GSM711924 1 0.4416 0.57763 0.632 0.000 0.000 0.012 0.356
#> GSM711926 4 0.4498 0.44794 0.000 0.032 0.000 0.688 0.280
#> GSM711928 1 0.0703 0.82274 0.976 0.000 0.000 0.000 0.024
#> GSM711930 1 0.0404 0.82359 0.988 0.000 0.000 0.000 0.012
#> GSM711932 5 0.6320 -0.03533 0.156 0.000 0.000 0.404 0.440
#> GSM711934 1 0.2329 0.79714 0.876 0.000 0.000 0.000 0.124
#> GSM711940 4 0.2732 0.61443 0.160 0.000 0.000 0.840 0.000
#> GSM711942 1 0.4066 0.63294 0.672 0.000 0.000 0.004 0.324
#> GSM711944 3 0.0992 0.89264 0.000 0.000 0.968 0.008 0.024
#> GSM711946 4 0.3543 0.65122 0.000 0.000 0.112 0.828 0.060
#> GSM711948 4 0.2233 0.71691 0.004 0.000 0.000 0.892 0.104
#> GSM711952 1 0.1608 0.81291 0.928 0.000 0.000 0.000 0.072
#> GSM711954 1 0.3829 0.67223 0.776 0.000 0.000 0.196 0.028
#> GSM711962 1 0.0404 0.82359 0.988 0.000 0.000 0.000 0.012
#> GSM711970 1 0.5441 0.60110 0.624 0.000 0.000 0.096 0.280
#> GSM711974 1 0.0404 0.82359 0.988 0.000 0.000 0.000 0.012
#> GSM711978 4 0.1412 0.73644 0.004 0.008 0.000 0.952 0.036
#> GSM711988 1 0.4413 0.61141 0.724 0.000 0.000 0.232 0.044
#> GSM711990 3 0.0000 0.91534 0.000 0.000 1.000 0.000 0.000
#> GSM711992 4 0.2921 0.62107 0.148 0.004 0.000 0.844 0.004
#> GSM711982 1 0.0404 0.82359 0.988 0.000 0.000 0.000 0.012
#> GSM711984 2 0.0000 0.97867 0.000 1.000 0.000 0.000 0.000
#> GSM711912 1 0.0290 0.82428 0.992 0.000 0.000 0.000 0.008
#> GSM711918 1 0.0510 0.82490 0.984 0.000 0.000 0.000 0.016
#> GSM711920 1 0.4924 0.50241 0.552 0.000 0.000 0.028 0.420
#> GSM711937 2 0.0000 0.97867 0.000 1.000 0.000 0.000 0.000
#> GSM711939 2 0.0000 0.97867 0.000 1.000 0.000 0.000 0.000
#> GSM711951 4 0.2020 0.69983 0.000 0.100 0.000 0.900 0.000
#> GSM711957 5 0.6236 0.14529 0.208 0.000 0.000 0.248 0.544
#> GSM711959 2 0.0000 0.97867 0.000 1.000 0.000 0.000 0.000
#> GSM711961 2 0.0000 0.97867 0.000 1.000 0.000 0.000 0.000
#> GSM711965 4 0.5071 0.23677 0.000 0.000 0.036 0.540 0.424
#> GSM711967 1 0.5979 0.22698 0.520 0.000 0.000 0.360 0.120
#> GSM711969 2 0.0000 0.97867 0.000 1.000 0.000 0.000 0.000
#> GSM711973 5 0.5630 -0.00640 0.000 0.000 0.088 0.352 0.560
#> GSM711977 5 0.6002 0.23892 0.000 0.000 0.308 0.140 0.552
#> GSM711981 4 0.3882 0.62377 0.000 0.020 0.000 0.756 0.224
#> GSM711987 2 0.0000 0.97867 0.000 1.000 0.000 0.000 0.000
#> GSM711905 2 0.0000 0.97867 0.000 1.000 0.000 0.000 0.000
#> GSM711907 2 0.2230 0.84495 0.000 0.884 0.000 0.116 0.000
#> GSM711909 3 0.0000 0.91534 0.000 0.000 1.000 0.000 0.000
#> GSM711911 3 0.0000 0.91534 0.000 0.000 1.000 0.000 0.000
#> GSM711915 3 0.4268 0.13820 0.000 0.000 0.556 0.000 0.444
#> GSM711917 2 0.0000 0.97867 0.000 1.000 0.000 0.000 0.000
#> GSM711923 4 0.0162 0.74293 0.000 0.000 0.000 0.996 0.004
#> GSM711925 2 0.0000 0.97867 0.000 1.000 0.000 0.000 0.000
#> GSM711927 3 0.0000 0.91534 0.000 0.000 1.000 0.000 0.000
#> GSM711929 2 0.0000 0.97867 0.000 1.000 0.000 0.000 0.000
#> GSM711931 4 0.6220 0.26241 0.000 0.272 0.000 0.540 0.188
#> GSM711933 1 0.7359 -0.00661 0.384 0.000 0.028 0.324 0.264
#> GSM711935 2 0.0000 0.97867 0.000 1.000 0.000 0.000 0.000
#> GSM711941 4 0.0162 0.74259 0.000 0.000 0.000 0.996 0.004
#> GSM711943 4 0.1768 0.71879 0.000 0.000 0.072 0.924 0.004
#> GSM711945 4 0.4025 0.51509 0.000 0.000 0.008 0.700 0.292
#> GSM711947 3 0.0794 0.88395 0.000 0.028 0.972 0.000 0.000
#> GSM711949 2 0.0000 0.97867 0.000 1.000 0.000 0.000 0.000
#> GSM711953 2 0.0000 0.97867 0.000 1.000 0.000 0.000 0.000
#> GSM711955 3 0.5676 0.26013 0.048 0.000 0.620 0.300 0.032
#> GSM711963 2 0.0000 0.97867 0.000 1.000 0.000 0.000 0.000
#> GSM711971 3 0.0000 0.91534 0.000 0.000 1.000 0.000 0.000
#> GSM711975 2 0.3635 0.63989 0.000 0.748 0.000 0.248 0.004
#> GSM711979 4 0.1544 0.72518 0.000 0.000 0.000 0.932 0.068
#> GSM711989 2 0.0000 0.97867 0.000 1.000 0.000 0.000 0.000
#> GSM711991 3 0.0000 0.91534 0.000 0.000 1.000 0.000 0.000
#> GSM711993 4 0.0693 0.74344 0.000 0.008 0.000 0.980 0.012
#> GSM711983 3 0.0000 0.91534 0.000 0.000 1.000 0.000 0.000
#> GSM711985 2 0.0000 0.97867 0.000 1.000 0.000 0.000 0.000
#> GSM711913 5 0.5177 -0.13695 0.000 0.000 0.472 0.040 0.488
#> GSM711919 3 0.0000 0.91534 0.000 0.000 1.000 0.000 0.000
#> GSM711921 3 0.0000 0.91534 0.000 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM711936 2 0.0260 0.9739 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM711938 2 0.0000 0.9754 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711950 5 0.4046 0.4114 0.008 0.000 0.000 0.368 0.620 0.004
#> GSM711956 1 0.3804 0.3662 0.656 0.000 0.000 0.000 0.008 0.336
#> GSM711958 3 0.3292 0.6940 0.200 0.000 0.784 0.008 0.008 0.000
#> GSM711960 3 0.0924 0.9163 0.008 0.000 0.972 0.008 0.008 0.004
#> GSM711964 1 0.0508 0.8525 0.984 0.000 0.000 0.000 0.012 0.004
#> GSM711966 1 0.1049 0.8403 0.960 0.000 0.000 0.000 0.008 0.032
#> GSM711968 6 0.4091 0.2736 0.472 0.000 0.000 0.000 0.008 0.520
#> GSM711972 1 0.0405 0.8526 0.988 0.000 0.000 0.000 0.004 0.008
#> GSM711976 5 0.5373 -0.0507 0.392 0.000 0.000 0.016 0.520 0.072
#> GSM711980 1 0.3714 0.3690 0.656 0.000 0.000 0.000 0.004 0.340
#> GSM711986 1 0.0458 0.8519 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM711904 1 0.3470 0.5841 0.740 0.000 0.000 0.000 0.012 0.248
#> GSM711906 1 0.0622 0.8491 0.980 0.000 0.000 0.000 0.008 0.012
#> GSM711908 1 0.0146 0.8527 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM711910 3 0.0000 0.9233 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711914 1 0.1124 0.8472 0.956 0.000 0.000 0.000 0.008 0.036
#> GSM711916 1 0.1151 0.8418 0.956 0.000 0.000 0.000 0.012 0.032
#> GSM711922 6 0.3823 0.4007 0.436 0.000 0.000 0.000 0.000 0.564
#> GSM711924 6 0.4236 0.6426 0.184 0.000 0.056 0.000 0.016 0.744
#> GSM711926 4 0.3791 0.6385 0.000 0.032 0.000 0.732 0.000 0.236
#> GSM711928 1 0.1225 0.8459 0.952 0.000 0.000 0.000 0.012 0.036
#> GSM711930 1 0.1297 0.8317 0.948 0.000 0.000 0.000 0.012 0.040
#> GSM711932 6 0.3962 0.4303 0.044 0.000 0.000 0.196 0.008 0.752
#> GSM711934 1 0.3133 0.6502 0.780 0.000 0.000 0.000 0.008 0.212
#> GSM711940 4 0.1410 0.8001 0.044 0.000 0.000 0.944 0.004 0.008
#> GSM711942 6 0.3672 0.6254 0.304 0.000 0.000 0.000 0.008 0.688
#> GSM711944 3 0.1900 0.8836 0.000 0.000 0.916 0.008 0.008 0.068
#> GSM711946 4 0.1296 0.8073 0.000 0.000 0.032 0.952 0.012 0.004
#> GSM711948 4 0.4126 0.3224 0.008 0.000 0.000 0.624 0.360 0.008
#> GSM711952 1 0.1556 0.8211 0.920 0.000 0.000 0.000 0.000 0.080
#> GSM711954 1 0.4493 0.2430 0.596 0.000 0.000 0.364 0.000 0.040
#> GSM711962 1 0.0717 0.8478 0.976 0.000 0.000 0.000 0.008 0.016
#> GSM711970 6 0.5028 0.5573 0.340 0.000 0.000 0.060 0.012 0.588
#> GSM711974 1 0.0870 0.8498 0.972 0.000 0.004 0.000 0.012 0.012
#> GSM711978 4 0.0260 0.8227 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM711988 1 0.3499 0.7135 0.812 0.000 0.000 0.044 0.012 0.132
#> GSM711990 3 0.0405 0.9218 0.000 0.000 0.988 0.004 0.008 0.000
#> GSM711992 4 0.0767 0.8209 0.008 0.012 0.000 0.976 0.004 0.000
#> GSM711982 1 0.0972 0.8410 0.964 0.000 0.000 0.000 0.008 0.028
#> GSM711984 2 0.0260 0.9739 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM711912 1 0.1075 0.8424 0.952 0.000 0.000 0.000 0.000 0.048
#> GSM711918 1 0.1075 0.8430 0.952 0.000 0.000 0.000 0.000 0.048
#> GSM711920 6 0.2112 0.6372 0.088 0.000 0.000 0.000 0.016 0.896
#> GSM711937 2 0.0146 0.9748 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM711939 2 0.0000 0.9754 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711951 4 0.1285 0.7938 0.000 0.052 0.000 0.944 0.004 0.000
#> GSM711957 6 0.1010 0.5936 0.036 0.000 0.004 0.000 0.000 0.960
#> GSM711959 2 0.0260 0.9739 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM711961 2 0.0000 0.9754 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711965 5 0.1088 0.7399 0.000 0.000 0.016 0.024 0.960 0.000
#> GSM711967 4 0.4751 0.1303 0.400 0.000 0.000 0.556 0.008 0.036
#> GSM711969 2 0.0260 0.9739 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM711973 5 0.1078 0.7370 0.000 0.000 0.016 0.012 0.964 0.008
#> GSM711977 5 0.1082 0.7367 0.000 0.000 0.040 0.000 0.956 0.004
#> GSM711981 5 0.4280 0.2706 0.000 0.008 0.000 0.428 0.556 0.008
#> GSM711987 2 0.0000 0.9754 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711905 2 0.0000 0.9754 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711907 2 0.2527 0.7901 0.000 0.832 0.000 0.168 0.000 0.000
#> GSM711909 3 0.0000 0.9233 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711911 3 0.0508 0.9204 0.000 0.000 0.984 0.000 0.004 0.012
#> GSM711915 5 0.1714 0.7101 0.000 0.000 0.092 0.000 0.908 0.000
#> GSM711917 2 0.0260 0.9739 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM711923 4 0.0405 0.8218 0.000 0.000 0.008 0.988 0.000 0.004
#> GSM711925 2 0.0000 0.9754 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711927 3 0.0146 0.9230 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM711929 2 0.0000 0.9754 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711931 4 0.5501 0.3548 0.000 0.320 0.000 0.552 0.008 0.120
#> GSM711933 3 0.6022 0.5041 0.032 0.000 0.592 0.208 0.008 0.160
#> GSM711935 2 0.0000 0.9754 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711941 4 0.1151 0.8145 0.000 0.000 0.000 0.956 0.032 0.012
#> GSM711943 4 0.0363 0.8211 0.000 0.000 0.012 0.988 0.000 0.000
#> GSM711945 5 0.3490 0.5796 0.000 0.000 0.008 0.268 0.724 0.000
#> GSM711947 3 0.0603 0.9141 0.000 0.016 0.980 0.000 0.000 0.004
#> GSM711949 2 0.0000 0.9754 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711953 2 0.0000 0.9754 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711955 3 0.4494 0.6059 0.012 0.000 0.700 0.244 0.036 0.008
#> GSM711963 2 0.0000 0.9754 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711971 3 0.0291 0.9228 0.000 0.000 0.992 0.004 0.004 0.000
#> GSM711975 2 0.3023 0.7208 0.000 0.784 0.000 0.212 0.000 0.004
#> GSM711979 4 0.0692 0.8214 0.000 0.000 0.000 0.976 0.004 0.020
#> GSM711989 2 0.0547 0.9659 0.000 0.980 0.000 0.020 0.000 0.000
#> GSM711991 3 0.0291 0.9230 0.000 0.000 0.992 0.004 0.000 0.004
#> GSM711993 4 0.0665 0.8219 0.000 0.008 0.000 0.980 0.004 0.008
#> GSM711983 3 0.0551 0.9220 0.000 0.000 0.984 0.008 0.004 0.004
#> GSM711985 2 0.0260 0.9739 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM711913 5 0.1007 0.7364 0.000 0.000 0.044 0.000 0.956 0.000
#> GSM711919 3 0.0146 0.9230 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM711921 3 0.0000 0.9233 0.000 0.000 1.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) disease.state(p) individual(p) k
#> MAD:NMF 90 3.47e-05 0.176 0.644 2
#> MAD:NMF 90 9.16e-11 0.259 0.733 3
#> MAD:NMF 86 3.48e-08 0.185 0.329 4
#> MAD:NMF 76 7.56e-09 0.225 0.259 5
#> MAD:NMF 78 1.77e-07 0.266 0.200 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "hclust"]
# you can also extract it by
# res = res_list["ATC:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 27425 rows and 90 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.910 0.957 0.981 0.375 0.626 0.626
#> 3 3 0.814 0.874 0.937 0.121 0.986 0.977
#> 4 4 0.745 0.827 0.919 0.183 0.931 0.887
#> 5 5 0.585 0.698 0.852 0.130 0.907 0.832
#> 6 6 0.638 0.630 0.777 0.198 0.828 0.628
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM711936 2 0.0000 0.961 0.000 1.000
#> GSM711938 2 0.0000 0.961 0.000 1.000
#> GSM711950 1 0.0000 0.985 1.000 0.000
#> GSM711956 1 0.0000 0.985 1.000 0.000
#> GSM711958 1 0.0000 0.985 1.000 0.000
#> GSM711960 1 0.0000 0.985 1.000 0.000
#> GSM711964 1 0.0000 0.985 1.000 0.000
#> GSM711966 1 0.0000 0.985 1.000 0.000
#> GSM711968 1 0.0000 0.985 1.000 0.000
#> GSM711972 1 0.0000 0.985 1.000 0.000
#> GSM711976 1 0.0000 0.985 1.000 0.000
#> GSM711980 1 0.0000 0.985 1.000 0.000
#> GSM711986 1 0.0000 0.985 1.000 0.000
#> GSM711904 1 0.0000 0.985 1.000 0.000
#> GSM711906 1 0.0000 0.985 1.000 0.000
#> GSM711908 1 0.0000 0.985 1.000 0.000
#> GSM711910 1 0.0000 0.985 1.000 0.000
#> GSM711914 1 0.0000 0.985 1.000 0.000
#> GSM711916 1 0.0000 0.985 1.000 0.000
#> GSM711922 1 0.0000 0.985 1.000 0.000
#> GSM711924 1 0.0000 0.985 1.000 0.000
#> GSM711926 1 0.0938 0.974 0.988 0.012
#> GSM711928 1 0.0000 0.985 1.000 0.000
#> GSM711930 1 0.0000 0.985 1.000 0.000
#> GSM711932 1 0.0000 0.985 1.000 0.000
#> GSM711934 1 0.0000 0.985 1.000 0.000
#> GSM711940 1 0.0000 0.985 1.000 0.000
#> GSM711942 1 0.0000 0.985 1.000 0.000
#> GSM711944 1 0.0000 0.985 1.000 0.000
#> GSM711946 1 0.0000 0.985 1.000 0.000
#> GSM711948 1 0.0000 0.985 1.000 0.000
#> GSM711952 1 0.0000 0.985 1.000 0.000
#> GSM711954 1 0.0000 0.985 1.000 0.000
#> GSM711962 1 0.0000 0.985 1.000 0.000
#> GSM711970 1 0.0000 0.985 1.000 0.000
#> GSM711974 1 0.0000 0.985 1.000 0.000
#> GSM711978 1 0.0000 0.985 1.000 0.000
#> GSM711988 1 0.0000 0.985 1.000 0.000
#> GSM711990 1 0.0000 0.985 1.000 0.000
#> GSM711992 1 0.0000 0.985 1.000 0.000
#> GSM711982 1 0.0000 0.985 1.000 0.000
#> GSM711984 2 0.0000 0.961 0.000 1.000
#> GSM711912 1 0.0000 0.985 1.000 0.000
#> GSM711918 1 0.0000 0.985 1.000 0.000
#> GSM711920 1 0.0000 0.985 1.000 0.000
#> GSM711937 2 0.0000 0.961 0.000 1.000
#> GSM711939 2 0.0000 0.961 0.000 1.000
#> GSM711951 1 0.8555 0.606 0.720 0.280
#> GSM711957 1 0.0000 0.985 1.000 0.000
#> GSM711959 2 0.0000 0.961 0.000 1.000
#> GSM711961 2 0.0000 0.961 0.000 1.000
#> GSM711965 1 0.0000 0.985 1.000 0.000
#> GSM711967 1 0.0000 0.985 1.000 0.000
#> GSM711969 2 0.0000 0.961 0.000 1.000
#> GSM711973 1 0.0000 0.985 1.000 0.000
#> GSM711977 1 0.0000 0.985 1.000 0.000
#> GSM711981 1 0.0000 0.985 1.000 0.000
#> GSM711987 2 0.0000 0.961 0.000 1.000
#> GSM711905 2 0.0000 0.961 0.000 1.000
#> GSM711907 2 0.7139 0.785 0.196 0.804
#> GSM711909 1 0.0000 0.985 1.000 0.000
#> GSM711911 1 0.0000 0.985 1.000 0.000
#> GSM711915 2 0.7139 0.785 0.196 0.804
#> GSM711917 2 0.0000 0.961 0.000 1.000
#> GSM711923 1 0.0000 0.985 1.000 0.000
#> GSM711925 2 0.0000 0.961 0.000 1.000
#> GSM711927 1 0.0000 0.985 1.000 0.000
#> GSM711929 2 0.0000 0.961 0.000 1.000
#> GSM711931 1 0.8443 0.621 0.728 0.272
#> GSM711933 1 0.0000 0.985 1.000 0.000
#> GSM711935 2 0.0000 0.961 0.000 1.000
#> GSM711941 1 0.0000 0.985 1.000 0.000
#> GSM711943 1 0.0000 0.985 1.000 0.000
#> GSM711945 1 0.0938 0.974 0.988 0.012
#> GSM711947 2 0.7139 0.785 0.196 0.804
#> GSM711949 2 0.0000 0.961 0.000 1.000
#> GSM711953 2 0.0000 0.961 0.000 1.000
#> GSM711955 1 0.0000 0.985 1.000 0.000
#> GSM711963 2 0.0000 0.961 0.000 1.000
#> GSM711971 1 0.0000 0.985 1.000 0.000
#> GSM711975 1 0.8555 0.606 0.720 0.280
#> GSM711979 1 0.0000 0.985 1.000 0.000
#> GSM711989 2 0.7219 0.774 0.200 0.800
#> GSM711991 1 0.4815 0.875 0.896 0.104
#> GSM711993 1 0.0000 0.985 1.000 0.000
#> GSM711983 1 0.0000 0.985 1.000 0.000
#> GSM711985 2 0.0000 0.961 0.000 1.000
#> GSM711913 1 0.0000 0.985 1.000 0.000
#> GSM711919 1 0.0000 0.985 1.000 0.000
#> GSM711921 1 0.0000 0.985 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM711936 2 0.6111 0.5078 0.000 0.604 0.396
#> GSM711938 2 0.4291 0.7235 0.000 0.820 0.180
#> GSM711950 1 0.0000 0.9671 1.000 0.000 0.000
#> GSM711956 1 0.0000 0.9671 1.000 0.000 0.000
#> GSM711958 1 0.0000 0.9671 1.000 0.000 0.000
#> GSM711960 1 0.0000 0.9671 1.000 0.000 0.000
#> GSM711964 1 0.0000 0.9671 1.000 0.000 0.000
#> GSM711966 1 0.0000 0.9671 1.000 0.000 0.000
#> GSM711968 1 0.0000 0.9671 1.000 0.000 0.000
#> GSM711972 1 0.0000 0.9671 1.000 0.000 0.000
#> GSM711976 1 0.0000 0.9671 1.000 0.000 0.000
#> GSM711980 1 0.0000 0.9671 1.000 0.000 0.000
#> GSM711986 1 0.0000 0.9671 1.000 0.000 0.000
#> GSM711904 1 0.1289 0.9423 0.968 0.000 0.032
#> GSM711906 1 0.0000 0.9671 1.000 0.000 0.000
#> GSM711908 1 0.4504 0.7758 0.804 0.000 0.196
#> GSM711910 1 0.0000 0.9671 1.000 0.000 0.000
#> GSM711914 1 0.0000 0.9671 1.000 0.000 0.000
#> GSM711916 1 0.4504 0.7758 0.804 0.000 0.196
#> GSM711922 1 0.0000 0.9671 1.000 0.000 0.000
#> GSM711924 1 0.0000 0.9671 1.000 0.000 0.000
#> GSM711926 1 0.0592 0.9577 0.988 0.000 0.012
#> GSM711928 1 0.0000 0.9671 1.000 0.000 0.000
#> GSM711930 1 0.4504 0.7758 0.804 0.000 0.196
#> GSM711932 1 0.0000 0.9671 1.000 0.000 0.000
#> GSM711934 1 0.0000 0.9671 1.000 0.000 0.000
#> GSM711940 1 0.0000 0.9671 1.000 0.000 0.000
#> GSM711942 1 0.0000 0.9671 1.000 0.000 0.000
#> GSM711944 1 0.0000 0.9671 1.000 0.000 0.000
#> GSM711946 1 0.0000 0.9671 1.000 0.000 0.000
#> GSM711948 1 0.0000 0.9671 1.000 0.000 0.000
#> GSM711952 1 0.4452 0.7808 0.808 0.000 0.192
#> GSM711954 1 0.0000 0.9671 1.000 0.000 0.000
#> GSM711962 1 0.0000 0.9671 1.000 0.000 0.000
#> GSM711970 1 0.4452 0.7808 0.808 0.000 0.192
#> GSM711974 1 0.0000 0.9671 1.000 0.000 0.000
#> GSM711978 1 0.0000 0.9671 1.000 0.000 0.000
#> GSM711988 1 0.0000 0.9671 1.000 0.000 0.000
#> GSM711990 1 0.0000 0.9671 1.000 0.000 0.000
#> GSM711992 1 0.0000 0.9671 1.000 0.000 0.000
#> GSM711982 1 0.0000 0.9671 1.000 0.000 0.000
#> GSM711984 2 0.0000 0.7719 0.000 1.000 0.000
#> GSM711912 1 0.0000 0.9671 1.000 0.000 0.000
#> GSM711918 1 0.0000 0.9671 1.000 0.000 0.000
#> GSM711920 1 0.0000 0.9671 1.000 0.000 0.000
#> GSM711937 2 0.6111 0.5078 0.000 0.604 0.396
#> GSM711939 2 0.4291 0.7235 0.000 0.820 0.180
#> GSM711951 1 0.6621 0.6274 0.720 0.052 0.228
#> GSM711957 1 0.0000 0.9671 1.000 0.000 0.000
#> GSM711959 2 0.0000 0.7719 0.000 1.000 0.000
#> GSM711961 2 0.0000 0.7719 0.000 1.000 0.000
#> GSM711965 1 0.0000 0.9671 1.000 0.000 0.000
#> GSM711967 1 0.0000 0.9671 1.000 0.000 0.000
#> GSM711969 2 0.6111 0.5078 0.000 0.604 0.396
#> GSM711973 1 0.0000 0.9671 1.000 0.000 0.000
#> GSM711977 1 0.0000 0.9671 1.000 0.000 0.000
#> GSM711981 1 0.0000 0.9671 1.000 0.000 0.000
#> GSM711987 2 0.4291 0.7235 0.000 0.820 0.180
#> GSM711905 2 0.0000 0.7719 0.000 1.000 0.000
#> GSM711907 3 0.5621 0.8576 0.000 0.308 0.692
#> GSM711909 1 0.0000 0.9671 1.000 0.000 0.000
#> GSM711911 1 0.0000 0.9671 1.000 0.000 0.000
#> GSM711915 3 0.3752 0.7651 0.000 0.144 0.856
#> GSM711917 2 0.6111 0.5078 0.000 0.604 0.396
#> GSM711923 1 0.0000 0.9671 1.000 0.000 0.000
#> GSM711925 2 0.0000 0.7719 0.000 1.000 0.000
#> GSM711927 1 0.0000 0.9671 1.000 0.000 0.000
#> GSM711929 2 0.0000 0.7719 0.000 1.000 0.000
#> GSM711931 1 0.6535 0.6410 0.728 0.052 0.220
#> GSM711933 1 0.0000 0.9671 1.000 0.000 0.000
#> GSM711935 2 0.0000 0.7719 0.000 1.000 0.000
#> GSM711941 1 0.0000 0.9671 1.000 0.000 0.000
#> GSM711943 1 0.0000 0.9671 1.000 0.000 0.000
#> GSM711945 1 0.0592 0.9580 0.988 0.000 0.012
#> GSM711947 3 0.5621 0.8576 0.000 0.308 0.692
#> GSM711949 2 0.0000 0.7719 0.000 1.000 0.000
#> GSM711953 2 0.0000 0.7719 0.000 1.000 0.000
#> GSM711955 1 0.0000 0.9671 1.000 0.000 0.000
#> GSM711963 2 0.0000 0.7719 0.000 1.000 0.000
#> GSM711971 1 0.0000 0.9671 1.000 0.000 0.000
#> GSM711975 1 0.6621 0.6274 0.720 0.052 0.228
#> GSM711979 1 0.0000 0.9671 1.000 0.000 0.000
#> GSM711989 2 0.9602 0.0292 0.200 0.404 0.396
#> GSM711991 1 0.5363 0.6608 0.724 0.000 0.276
#> GSM711993 1 0.0000 0.9671 1.000 0.000 0.000
#> GSM711983 1 0.0000 0.9671 1.000 0.000 0.000
#> GSM711985 2 0.4291 0.7235 0.000 0.820 0.180
#> GSM711913 1 0.0000 0.9671 1.000 0.000 0.000
#> GSM711919 1 0.0000 0.9671 1.000 0.000 0.000
#> GSM711921 1 0.0000 0.9671 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM711936 2 0.7113 0.520 0.000 0.552 0.172 0.276
#> GSM711938 2 0.3907 0.734 0.000 0.768 0.000 0.232
#> GSM711950 1 0.0000 0.944 1.000 0.000 0.000 0.000
#> GSM711956 1 0.0000 0.944 1.000 0.000 0.000 0.000
#> GSM711958 1 0.0000 0.944 1.000 0.000 0.000 0.000
#> GSM711960 1 0.0000 0.944 1.000 0.000 0.000 0.000
#> GSM711964 1 0.0000 0.944 1.000 0.000 0.000 0.000
#> GSM711966 1 0.0000 0.944 1.000 0.000 0.000 0.000
#> GSM711968 1 0.0000 0.944 1.000 0.000 0.000 0.000
#> GSM711972 1 0.0000 0.944 1.000 0.000 0.000 0.000
#> GSM711976 1 0.0000 0.944 1.000 0.000 0.000 0.000
#> GSM711980 1 0.0000 0.944 1.000 0.000 0.000 0.000
#> GSM711986 1 0.0000 0.944 1.000 0.000 0.000 0.000
#> GSM711904 1 0.1022 0.925 0.968 0.000 0.032 0.000
#> GSM711906 1 0.0000 0.944 1.000 0.000 0.000 0.000
#> GSM711908 1 0.3569 0.765 0.804 0.000 0.196 0.000
#> GSM711910 1 0.0188 0.943 0.996 0.000 0.000 0.004
#> GSM711914 1 0.0000 0.944 1.000 0.000 0.000 0.000
#> GSM711916 1 0.3569 0.765 0.804 0.000 0.196 0.000
#> GSM711922 1 0.0000 0.944 1.000 0.000 0.000 0.000
#> GSM711924 1 0.0000 0.944 1.000 0.000 0.000 0.000
#> GSM711926 1 0.4500 0.580 0.684 0.000 0.000 0.316
#> GSM711928 1 0.0000 0.944 1.000 0.000 0.000 0.000
#> GSM711930 1 0.3569 0.765 0.804 0.000 0.196 0.000
#> GSM711932 1 0.0000 0.944 1.000 0.000 0.000 0.000
#> GSM711934 1 0.0000 0.944 1.000 0.000 0.000 0.000
#> GSM711940 1 0.0000 0.944 1.000 0.000 0.000 0.000
#> GSM711942 1 0.0000 0.944 1.000 0.000 0.000 0.000
#> GSM711944 1 0.0000 0.944 1.000 0.000 0.000 0.000
#> GSM711946 1 0.1637 0.911 0.940 0.000 0.000 0.060
#> GSM711948 1 0.0000 0.944 1.000 0.000 0.000 0.000
#> GSM711952 1 0.3528 0.770 0.808 0.000 0.192 0.000
#> GSM711954 1 0.0000 0.944 1.000 0.000 0.000 0.000
#> GSM711962 1 0.0000 0.944 1.000 0.000 0.000 0.000
#> GSM711970 1 0.3528 0.770 0.808 0.000 0.192 0.000
#> GSM711974 1 0.0000 0.944 1.000 0.000 0.000 0.000
#> GSM711978 1 0.3074 0.829 0.848 0.000 0.000 0.152
#> GSM711988 1 0.0000 0.944 1.000 0.000 0.000 0.000
#> GSM711990 1 0.0188 0.943 0.996 0.000 0.000 0.004
#> GSM711992 1 0.1637 0.911 0.940 0.000 0.000 0.060
#> GSM711982 1 0.0000 0.944 1.000 0.000 0.000 0.000
#> GSM711984 2 0.0000 0.803 0.000 1.000 0.000 0.000
#> GSM711912 1 0.0000 0.944 1.000 0.000 0.000 0.000
#> GSM711918 1 0.0000 0.944 1.000 0.000 0.000 0.000
#> GSM711920 1 0.0000 0.944 1.000 0.000 0.000 0.000
#> GSM711937 2 0.7113 0.520 0.000 0.552 0.172 0.276
#> GSM711939 2 0.3907 0.734 0.000 0.768 0.000 0.232
#> GSM711951 4 0.0524 0.541 0.008 0.000 0.004 0.988
#> GSM711957 4 0.4331 0.205 0.288 0.000 0.000 0.712
#> GSM711959 2 0.0000 0.803 0.000 1.000 0.000 0.000
#> GSM711961 2 0.0000 0.803 0.000 1.000 0.000 0.000
#> GSM711965 1 0.0188 0.943 0.996 0.000 0.000 0.004
#> GSM711967 1 0.0000 0.944 1.000 0.000 0.000 0.000
#> GSM711969 2 0.7113 0.520 0.000 0.552 0.172 0.276
#> GSM711973 1 0.1716 0.907 0.936 0.000 0.000 0.064
#> GSM711977 1 0.2704 0.855 0.876 0.000 0.000 0.124
#> GSM711981 1 0.4072 0.693 0.748 0.000 0.000 0.252
#> GSM711987 2 0.3907 0.734 0.000 0.768 0.000 0.232
#> GSM711905 2 0.0000 0.803 0.000 1.000 0.000 0.000
#> GSM711907 3 0.4462 0.838 0.000 0.164 0.792 0.044
#> GSM711909 1 0.0188 0.943 0.996 0.000 0.000 0.004
#> GSM711911 1 0.0188 0.943 0.996 0.000 0.000 0.004
#> GSM711915 3 0.0000 0.686 0.000 0.000 1.000 0.000
#> GSM711917 2 0.7113 0.520 0.000 0.552 0.172 0.276
#> GSM711923 1 0.3024 0.833 0.852 0.000 0.000 0.148
#> GSM711925 2 0.0000 0.803 0.000 1.000 0.000 0.000
#> GSM711927 1 0.0188 0.943 0.996 0.000 0.000 0.004
#> GSM711929 2 0.0000 0.803 0.000 1.000 0.000 0.000
#> GSM711931 4 0.0188 0.543 0.004 0.000 0.000 0.996
#> GSM711933 1 0.0000 0.944 1.000 0.000 0.000 0.000
#> GSM711935 2 0.0000 0.803 0.000 1.000 0.000 0.000
#> GSM711941 1 0.0000 0.944 1.000 0.000 0.000 0.000
#> GSM711943 1 0.1637 0.911 0.940 0.000 0.000 0.060
#> GSM711945 1 0.2101 0.903 0.928 0.000 0.012 0.060
#> GSM711947 3 0.4462 0.838 0.000 0.164 0.792 0.044
#> GSM711949 2 0.0000 0.803 0.000 1.000 0.000 0.000
#> GSM711953 2 0.0000 0.803 0.000 1.000 0.000 0.000
#> GSM711955 1 0.0000 0.944 1.000 0.000 0.000 0.000
#> GSM711963 2 0.0000 0.803 0.000 1.000 0.000 0.000
#> GSM711971 1 0.0188 0.943 0.996 0.000 0.000 0.004
#> GSM711975 4 0.0188 0.538 0.000 0.000 0.004 0.996
#> GSM711979 1 0.3975 0.710 0.760 0.000 0.000 0.240
#> GSM711989 4 0.7384 -0.241 0.000 0.352 0.172 0.476
#> GSM711991 1 0.5742 0.571 0.664 0.000 0.276 0.060
#> GSM711993 1 0.4072 0.693 0.748 0.000 0.000 0.252
#> GSM711983 1 0.0188 0.943 0.996 0.000 0.000 0.004
#> GSM711985 2 0.3907 0.734 0.000 0.768 0.000 0.232
#> GSM711913 1 0.2704 0.855 0.876 0.000 0.000 0.124
#> GSM711919 1 0.0188 0.943 0.996 0.000 0.000 0.004
#> GSM711921 1 0.0188 0.943 0.996 0.000 0.000 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM711936 5 0.6671 -0.2978 0.000 0.372 0.000 0.232 0.396
#> GSM711938 2 0.3849 0.7283 0.000 0.752 0.000 0.232 0.016
#> GSM711950 1 0.0324 0.8732 0.992 0.000 0.000 0.004 0.004
#> GSM711956 1 0.0162 0.8733 0.996 0.000 0.000 0.000 0.004
#> GSM711958 1 0.0162 0.8733 0.996 0.000 0.000 0.000 0.004
#> GSM711960 1 0.0794 0.8690 0.972 0.000 0.000 0.000 0.028
#> GSM711964 1 0.0794 0.8687 0.972 0.000 0.000 0.000 0.028
#> GSM711966 1 0.0162 0.8733 0.996 0.000 0.000 0.000 0.004
#> GSM711968 1 0.0290 0.8721 0.992 0.000 0.000 0.000 0.008
#> GSM711972 1 0.0162 0.8733 0.996 0.000 0.000 0.000 0.004
#> GSM711976 1 0.0324 0.8732 0.992 0.000 0.000 0.004 0.004
#> GSM711980 1 0.0290 0.8721 0.992 0.000 0.000 0.000 0.008
#> GSM711986 1 0.0162 0.8733 0.996 0.000 0.000 0.000 0.004
#> GSM711904 1 0.3796 0.5551 0.700 0.000 0.000 0.000 0.300
#> GSM711906 1 0.0162 0.8733 0.996 0.000 0.000 0.000 0.004
#> GSM711908 5 0.4300 0.1601 0.476 0.000 0.000 0.000 0.524
#> GSM711910 1 0.2690 0.7844 0.844 0.000 0.000 0.000 0.156
#> GSM711914 1 0.0162 0.8733 0.996 0.000 0.000 0.000 0.004
#> GSM711916 5 0.4300 0.1601 0.476 0.000 0.000 0.000 0.524
#> GSM711922 1 0.0290 0.8721 0.992 0.000 0.000 0.000 0.008
#> GSM711924 1 0.0324 0.8732 0.992 0.000 0.000 0.004 0.004
#> GSM711926 1 0.4987 0.3840 0.616 0.000 0.000 0.340 0.044
#> GSM711928 1 0.0290 0.8721 0.992 0.000 0.000 0.000 0.008
#> GSM711930 5 0.4300 0.1601 0.476 0.000 0.000 0.000 0.524
#> GSM711932 1 0.0324 0.8732 0.992 0.000 0.000 0.004 0.004
#> GSM711934 1 0.0404 0.8712 0.988 0.000 0.000 0.000 0.012
#> GSM711940 1 0.0703 0.8687 0.976 0.000 0.000 0.000 0.024
#> GSM711942 1 0.0290 0.8727 0.992 0.000 0.000 0.000 0.008
#> GSM711944 1 0.0324 0.8732 0.992 0.000 0.000 0.004 0.004
#> GSM711946 1 0.3825 0.7603 0.804 0.000 0.000 0.060 0.136
#> GSM711948 1 0.0324 0.8732 0.992 0.000 0.000 0.004 0.004
#> GSM711952 5 0.4302 0.1483 0.480 0.000 0.000 0.000 0.520
#> GSM711954 1 0.0963 0.8667 0.964 0.000 0.000 0.000 0.036
#> GSM711962 1 0.0162 0.8733 0.996 0.000 0.000 0.000 0.004
#> GSM711970 5 0.4302 0.1483 0.480 0.000 0.000 0.000 0.520
#> GSM711974 1 0.0794 0.8690 0.972 0.000 0.000 0.000 0.028
#> GSM711978 1 0.4096 0.7057 0.772 0.000 0.000 0.176 0.052
#> GSM711988 1 0.0324 0.8732 0.992 0.000 0.000 0.004 0.004
#> GSM711990 1 0.2561 0.7966 0.856 0.000 0.000 0.000 0.144
#> GSM711992 1 0.3493 0.7900 0.832 0.000 0.000 0.060 0.108
#> GSM711982 1 0.0162 0.8733 0.996 0.000 0.000 0.000 0.004
#> GSM711984 2 0.0000 0.9066 0.000 1.000 0.000 0.000 0.000
#> GSM711912 1 0.0609 0.8696 0.980 0.000 0.000 0.000 0.020
#> GSM711918 1 0.0609 0.8696 0.980 0.000 0.000 0.000 0.020
#> GSM711920 1 0.0324 0.8732 0.992 0.000 0.000 0.004 0.004
#> GSM711937 5 0.6671 -0.2978 0.000 0.372 0.000 0.232 0.396
#> GSM711939 2 0.3849 0.7283 0.000 0.752 0.000 0.232 0.016
#> GSM711951 4 0.1557 0.6434 0.008 0.000 0.000 0.940 0.052
#> GSM711957 4 0.4385 0.3195 0.180 0.000 0.000 0.752 0.068
#> GSM711959 2 0.0000 0.9066 0.000 1.000 0.000 0.000 0.000
#> GSM711961 2 0.0000 0.9066 0.000 1.000 0.000 0.000 0.000
#> GSM711965 1 0.2561 0.7966 0.856 0.000 0.000 0.000 0.144
#> GSM711967 1 0.0324 0.8732 0.992 0.000 0.000 0.004 0.004
#> GSM711969 5 0.6671 -0.2978 0.000 0.372 0.000 0.232 0.396
#> GSM711973 1 0.2707 0.8040 0.876 0.000 0.000 0.100 0.024
#> GSM711977 1 0.3449 0.7296 0.812 0.000 0.000 0.164 0.024
#> GSM711981 1 0.4603 0.4952 0.668 0.000 0.000 0.300 0.032
#> GSM711987 2 0.3849 0.7283 0.000 0.752 0.000 0.232 0.016
#> GSM711905 2 0.0000 0.9066 0.000 1.000 0.000 0.000 0.000
#> GSM711907 3 0.4126 0.7790 0.000 0.000 0.620 0.000 0.380
#> GSM711909 1 0.2690 0.7844 0.844 0.000 0.000 0.000 0.156
#> GSM711911 1 0.2690 0.7844 0.844 0.000 0.000 0.000 0.156
#> GSM711915 3 0.0000 0.5758 0.000 0.000 1.000 0.000 0.000
#> GSM711917 5 0.6671 -0.2978 0.000 0.372 0.000 0.232 0.396
#> GSM711923 1 0.4430 0.6927 0.752 0.000 0.000 0.172 0.076
#> GSM711925 2 0.0000 0.9066 0.000 1.000 0.000 0.000 0.000
#> GSM711927 1 0.2690 0.7844 0.844 0.000 0.000 0.000 0.156
#> GSM711929 2 0.0000 0.9066 0.000 1.000 0.000 0.000 0.000
#> GSM711931 4 0.1121 0.6439 0.000 0.000 0.000 0.956 0.044
#> GSM711933 1 0.0404 0.8712 0.988 0.000 0.000 0.000 0.012
#> GSM711935 2 0.0000 0.9066 0.000 1.000 0.000 0.000 0.000
#> GSM711941 1 0.0324 0.8732 0.992 0.000 0.000 0.004 0.004
#> GSM711943 1 0.3825 0.7603 0.804 0.000 0.000 0.060 0.136
#> GSM711945 1 0.4421 0.7210 0.772 0.000 0.012 0.060 0.156
#> GSM711947 3 0.4126 0.7790 0.000 0.000 0.620 0.000 0.380
#> GSM711949 2 0.0000 0.9066 0.000 1.000 0.000 0.000 0.000
#> GSM711953 2 0.0000 0.9066 0.000 1.000 0.000 0.000 0.000
#> GSM711955 1 0.0404 0.8712 0.988 0.000 0.000 0.000 0.012
#> GSM711963 2 0.0000 0.9066 0.000 1.000 0.000 0.000 0.000
#> GSM711971 1 0.2516 0.7980 0.860 0.000 0.000 0.000 0.140
#> GSM711975 4 0.1270 0.6440 0.000 0.000 0.000 0.948 0.052
#> GSM711979 1 0.4452 0.5450 0.696 0.000 0.000 0.272 0.032
#> GSM711989 4 0.6415 0.0346 0.000 0.172 0.000 0.428 0.400
#> GSM711991 1 0.7195 0.0885 0.508 0.000 0.276 0.060 0.156
#> GSM711993 1 0.4603 0.4952 0.668 0.000 0.000 0.300 0.032
#> GSM711983 1 0.2516 0.7980 0.860 0.000 0.000 0.000 0.140
#> GSM711985 2 0.3849 0.7283 0.000 0.752 0.000 0.232 0.016
#> GSM711913 1 0.3449 0.7296 0.812 0.000 0.000 0.164 0.024
#> GSM711919 1 0.2690 0.7844 0.844 0.000 0.000 0.000 0.156
#> GSM711921 1 0.2690 0.7844 0.844 0.000 0.000 0.000 0.156
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM711936 6 0.5971 -0.059700 0.000 0.344 0.000 0.232 0.000 0.424
#> GSM711938 2 0.3964 0.689049 0.000 0.724 0.000 0.232 0.000 0.044
#> GSM711950 1 0.0405 0.817068 0.988 0.000 0.008 0.000 0.000 0.004
#> GSM711956 1 0.0000 0.819171 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711958 1 0.0000 0.819171 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711960 1 0.1176 0.798197 0.956 0.000 0.020 0.000 0.000 0.024
#> GSM711964 1 0.1720 0.770090 0.928 0.000 0.040 0.000 0.000 0.032
#> GSM711966 1 0.0000 0.819171 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711968 1 0.0820 0.810020 0.972 0.000 0.016 0.000 0.000 0.012
#> GSM711972 1 0.0000 0.819171 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711976 1 0.0405 0.817068 0.988 0.000 0.008 0.000 0.000 0.004
#> GSM711980 1 0.0520 0.814634 0.984 0.000 0.008 0.000 0.000 0.008
#> GSM711986 1 0.0000 0.819171 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711904 3 0.5962 0.436480 0.364 0.000 0.412 0.000 0.000 0.224
#> GSM711906 1 0.0000 0.819171 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711908 6 0.5576 0.338783 0.144 0.000 0.376 0.000 0.000 0.480
#> GSM711910 3 0.3717 0.869447 0.384 0.000 0.616 0.000 0.000 0.000
#> GSM711914 1 0.0000 0.819171 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711916 6 0.5576 0.338783 0.144 0.000 0.376 0.000 0.000 0.480
#> GSM711922 1 0.0520 0.814634 0.984 0.000 0.008 0.000 0.000 0.008
#> GSM711924 1 0.0291 0.818374 0.992 0.000 0.004 0.000 0.000 0.004
#> GSM711926 1 0.6418 -0.006389 0.464 0.000 0.228 0.280 0.000 0.028
#> GSM711928 1 0.0909 0.807248 0.968 0.000 0.020 0.000 0.000 0.012
#> GSM711930 6 0.5576 0.338783 0.144 0.000 0.376 0.000 0.000 0.480
#> GSM711932 1 0.0405 0.817068 0.988 0.000 0.008 0.000 0.000 0.004
#> GSM711934 1 0.0508 0.815231 0.984 0.000 0.004 0.000 0.000 0.012
#> GSM711940 1 0.0858 0.807227 0.968 0.000 0.004 0.000 0.000 0.028
#> GSM711942 1 0.0146 0.818345 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM711944 1 0.0291 0.818374 0.992 0.000 0.004 0.000 0.000 0.004
#> GSM711946 3 0.3607 0.834211 0.348 0.000 0.652 0.000 0.000 0.000
#> GSM711948 1 0.0405 0.817068 0.988 0.000 0.008 0.000 0.000 0.004
#> GSM711952 6 0.5603 0.330355 0.148 0.000 0.376 0.000 0.000 0.476
#> GSM711954 1 0.2457 0.699905 0.880 0.000 0.084 0.000 0.000 0.036
#> GSM711962 1 0.0000 0.819171 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711970 6 0.5603 0.330355 0.148 0.000 0.376 0.000 0.000 0.476
#> GSM711974 1 0.1176 0.798197 0.956 0.000 0.020 0.000 0.000 0.024
#> GSM711978 1 0.5642 -0.411811 0.468 0.000 0.420 0.096 0.000 0.016
#> GSM711988 1 0.0405 0.817068 0.988 0.000 0.008 0.000 0.000 0.004
#> GSM711990 3 0.3937 0.843247 0.424 0.000 0.572 0.000 0.000 0.004
#> GSM711992 3 0.4115 0.815929 0.360 0.000 0.624 0.004 0.000 0.012
#> GSM711982 1 0.0000 0.819171 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711984 2 0.0000 0.894919 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711912 1 0.1461 0.774963 0.940 0.000 0.044 0.000 0.000 0.016
#> GSM711918 1 0.1088 0.798659 0.960 0.000 0.024 0.000 0.000 0.016
#> GSM711920 1 0.0291 0.818374 0.992 0.000 0.004 0.000 0.000 0.004
#> GSM711937 6 0.5971 -0.059700 0.000 0.344 0.000 0.232 0.000 0.424
#> GSM711939 2 0.3964 0.689049 0.000 0.724 0.000 0.232 0.000 0.044
#> GSM711951 4 0.1625 0.674410 0.000 0.000 0.060 0.928 0.000 0.012
#> GSM711957 4 0.5528 0.328872 0.036 0.000 0.252 0.616 0.000 0.096
#> GSM711959 2 0.0000 0.894919 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711961 2 0.0000 0.894919 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711965 3 0.3937 0.843247 0.424 0.000 0.572 0.000 0.000 0.004
#> GSM711967 1 0.0291 0.818374 0.992 0.000 0.004 0.000 0.000 0.004
#> GSM711969 6 0.5971 -0.059700 0.000 0.344 0.000 0.232 0.000 0.424
#> GSM711973 1 0.5033 -0.000292 0.596 0.000 0.336 0.044 0.000 0.024
#> GSM711977 1 0.5765 -0.248045 0.504 0.000 0.372 0.100 0.000 0.024
#> GSM711981 1 0.6226 0.094452 0.516 0.000 0.232 0.224 0.000 0.028
#> GSM711987 2 0.3964 0.689049 0.000 0.724 0.000 0.232 0.000 0.044
#> GSM711905 2 0.0000 0.894919 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711907 5 0.3706 0.772371 0.000 0.000 0.000 0.000 0.620 0.380
#> GSM711909 3 0.3727 0.869720 0.388 0.000 0.612 0.000 0.000 0.000
#> GSM711911 3 0.3756 0.864356 0.400 0.000 0.600 0.000 0.000 0.000
#> GSM711915 5 0.0000 0.550722 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM711917 6 0.5971 -0.059700 0.000 0.344 0.000 0.232 0.000 0.424
#> GSM711923 1 0.5353 -0.466404 0.464 0.000 0.440 0.092 0.000 0.004
#> GSM711925 2 0.0000 0.894919 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711927 3 0.3727 0.869720 0.388 0.000 0.612 0.000 0.000 0.000
#> GSM711929 2 0.0000 0.894919 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711931 4 0.1411 0.676001 0.000 0.000 0.060 0.936 0.000 0.004
#> GSM711933 1 0.0993 0.802407 0.964 0.000 0.024 0.000 0.000 0.012
#> GSM711935 2 0.0000 0.894919 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711941 1 0.0405 0.817068 0.988 0.000 0.008 0.000 0.000 0.004
#> GSM711943 3 0.3607 0.834211 0.348 0.000 0.652 0.000 0.000 0.000
#> GSM711945 3 0.3784 0.810041 0.308 0.000 0.680 0.000 0.012 0.000
#> GSM711947 5 0.3706 0.772371 0.000 0.000 0.000 0.000 0.620 0.380
#> GSM711949 2 0.0000 0.894919 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711953 2 0.0000 0.894919 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711955 1 0.0508 0.815231 0.984 0.000 0.004 0.000 0.000 0.012
#> GSM711963 2 0.0000 0.894919 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711971 3 0.3823 0.827364 0.436 0.000 0.564 0.000 0.000 0.000
#> GSM711975 4 0.1500 0.676792 0.000 0.000 0.052 0.936 0.000 0.012
#> GSM711979 1 0.6069 0.142034 0.548 0.000 0.212 0.212 0.000 0.028
#> GSM711989 4 0.5612 0.043801 0.000 0.144 0.000 0.432 0.000 0.424
#> GSM711991 3 0.5207 0.311322 0.132 0.000 0.592 0.000 0.276 0.000
#> GSM711993 1 0.6226 0.094452 0.516 0.000 0.232 0.224 0.000 0.028
#> GSM711983 3 0.3823 0.827364 0.436 0.000 0.564 0.000 0.000 0.000
#> GSM711985 2 0.3964 0.689049 0.000 0.724 0.000 0.232 0.000 0.044
#> GSM711913 1 0.5765 -0.248045 0.504 0.000 0.372 0.100 0.000 0.024
#> GSM711919 3 0.3727 0.869720 0.388 0.000 0.612 0.000 0.000 0.000
#> GSM711921 3 0.3717 0.869447 0.384 0.000 0.616 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) disease.state(p) individual(p) k
#> ATC:hclust 90 2.34e-04 0.285 0.363 2
#> ATC:hclust 89 6.25e-04 0.273 0.311 3
#> ATC:hclust 88 1.53e-04 0.442 0.428 4
#> ATC:hclust 75 3.66e-04 0.675 0.413 5
#> ATC:hclust 68 3.69e-07 0.444 0.554 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "kmeans"]
# you can also extract it by
# res = res_list["ATC:kmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 27425 rows and 90 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.992 0.997 0.3884 0.615 0.615
#> 3 3 0.602 0.787 0.879 0.5714 0.722 0.553
#> 4 4 0.626 0.778 0.849 0.1500 0.895 0.714
#> 5 5 0.699 0.693 0.770 0.0840 0.951 0.831
#> 6 6 0.752 0.581 0.751 0.0531 0.975 0.899
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM711936 2 0.000 1.000 0.000 1.000
#> GSM711938 2 0.000 1.000 0.000 1.000
#> GSM711950 1 0.000 0.996 1.000 0.000
#> GSM711956 1 0.000 0.996 1.000 0.000
#> GSM711958 1 0.000 0.996 1.000 0.000
#> GSM711960 1 0.000 0.996 1.000 0.000
#> GSM711964 1 0.000 0.996 1.000 0.000
#> GSM711966 1 0.000 0.996 1.000 0.000
#> GSM711968 1 0.000 0.996 1.000 0.000
#> GSM711972 1 0.000 0.996 1.000 0.000
#> GSM711976 1 0.000 0.996 1.000 0.000
#> GSM711980 1 0.000 0.996 1.000 0.000
#> GSM711986 1 0.000 0.996 1.000 0.000
#> GSM711904 1 0.000 0.996 1.000 0.000
#> GSM711906 1 0.000 0.996 1.000 0.000
#> GSM711908 1 0.000 0.996 1.000 0.000
#> GSM711910 1 0.000 0.996 1.000 0.000
#> GSM711914 1 0.000 0.996 1.000 0.000
#> GSM711916 1 0.000 0.996 1.000 0.000
#> GSM711922 1 0.000 0.996 1.000 0.000
#> GSM711924 1 0.000 0.996 1.000 0.000
#> GSM711926 1 0.000 0.996 1.000 0.000
#> GSM711928 1 0.000 0.996 1.000 0.000
#> GSM711930 1 0.000 0.996 1.000 0.000
#> GSM711932 1 0.000 0.996 1.000 0.000
#> GSM711934 1 0.000 0.996 1.000 0.000
#> GSM711940 1 0.000 0.996 1.000 0.000
#> GSM711942 1 0.000 0.996 1.000 0.000
#> GSM711944 1 0.000 0.996 1.000 0.000
#> GSM711946 1 0.000 0.996 1.000 0.000
#> GSM711948 1 0.000 0.996 1.000 0.000
#> GSM711952 1 0.000 0.996 1.000 0.000
#> GSM711954 1 0.000 0.996 1.000 0.000
#> GSM711962 1 0.000 0.996 1.000 0.000
#> GSM711970 1 0.000 0.996 1.000 0.000
#> GSM711974 1 0.000 0.996 1.000 0.000
#> GSM711978 1 0.000 0.996 1.000 0.000
#> GSM711988 1 0.000 0.996 1.000 0.000
#> GSM711990 1 0.000 0.996 1.000 0.000
#> GSM711992 1 0.000 0.996 1.000 0.000
#> GSM711982 1 0.000 0.996 1.000 0.000
#> GSM711984 2 0.000 1.000 0.000 1.000
#> GSM711912 1 0.000 0.996 1.000 0.000
#> GSM711918 1 0.000 0.996 1.000 0.000
#> GSM711920 1 0.000 0.996 1.000 0.000
#> GSM711937 2 0.000 1.000 0.000 1.000
#> GSM711939 2 0.000 1.000 0.000 1.000
#> GSM711951 1 0.861 0.603 0.716 0.284
#> GSM711957 1 0.000 0.996 1.000 0.000
#> GSM711959 2 0.000 1.000 0.000 1.000
#> GSM711961 2 0.000 1.000 0.000 1.000
#> GSM711965 1 0.000 0.996 1.000 0.000
#> GSM711967 1 0.000 0.996 1.000 0.000
#> GSM711969 2 0.000 1.000 0.000 1.000
#> GSM711973 1 0.000 0.996 1.000 0.000
#> GSM711977 1 0.000 0.996 1.000 0.000
#> GSM711981 1 0.000 0.996 1.000 0.000
#> GSM711987 2 0.000 1.000 0.000 1.000
#> GSM711905 2 0.000 1.000 0.000 1.000
#> GSM711907 2 0.000 1.000 0.000 1.000
#> GSM711909 1 0.000 0.996 1.000 0.000
#> GSM711911 1 0.000 0.996 1.000 0.000
#> GSM711915 2 0.000 1.000 0.000 1.000
#> GSM711917 2 0.000 1.000 0.000 1.000
#> GSM711923 1 0.000 0.996 1.000 0.000
#> GSM711925 2 0.000 1.000 0.000 1.000
#> GSM711927 1 0.000 0.996 1.000 0.000
#> GSM711929 2 0.000 1.000 0.000 1.000
#> GSM711931 1 0.000 0.996 1.000 0.000
#> GSM711933 1 0.000 0.996 1.000 0.000
#> GSM711935 2 0.000 1.000 0.000 1.000
#> GSM711941 1 0.000 0.996 1.000 0.000
#> GSM711943 1 0.000 0.996 1.000 0.000
#> GSM711945 1 0.000 0.996 1.000 0.000
#> GSM711947 2 0.000 1.000 0.000 1.000
#> GSM711949 2 0.000 1.000 0.000 1.000
#> GSM711953 2 0.000 1.000 0.000 1.000
#> GSM711955 1 0.000 0.996 1.000 0.000
#> GSM711963 2 0.000 1.000 0.000 1.000
#> GSM711971 1 0.000 0.996 1.000 0.000
#> GSM711975 2 0.000 1.000 0.000 1.000
#> GSM711979 1 0.000 0.996 1.000 0.000
#> GSM711989 2 0.000 1.000 0.000 1.000
#> GSM711991 1 0.000 0.996 1.000 0.000
#> GSM711993 1 0.000 0.996 1.000 0.000
#> GSM711983 1 0.000 0.996 1.000 0.000
#> GSM711985 2 0.000 1.000 0.000 1.000
#> GSM711913 1 0.000 0.996 1.000 0.000
#> GSM711919 1 0.000 0.996 1.000 0.000
#> GSM711921 1 0.000 0.996 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM711936 2 0.3038 0.914 0.000 0.896 0.104
#> GSM711938 2 0.0000 0.952 0.000 1.000 0.000
#> GSM711950 1 0.0592 0.916 0.988 0.000 0.012
#> GSM711956 1 0.0000 0.923 1.000 0.000 0.000
#> GSM711958 1 0.0000 0.923 1.000 0.000 0.000
#> GSM711960 1 0.4399 0.655 0.812 0.000 0.188
#> GSM711964 1 0.0000 0.923 1.000 0.000 0.000
#> GSM711966 1 0.0000 0.923 1.000 0.000 0.000
#> GSM711968 1 0.0000 0.923 1.000 0.000 0.000
#> GSM711972 1 0.0000 0.923 1.000 0.000 0.000
#> GSM711976 1 0.0237 0.921 0.996 0.000 0.004
#> GSM711980 1 0.0000 0.923 1.000 0.000 0.000
#> GSM711986 1 0.0000 0.923 1.000 0.000 0.000
#> GSM711904 3 0.6299 0.477 0.476 0.000 0.524
#> GSM711906 1 0.0000 0.923 1.000 0.000 0.000
#> GSM711908 3 0.6309 0.417 0.500 0.000 0.500
#> GSM711910 3 0.6008 0.642 0.372 0.000 0.628
#> GSM711914 1 0.0000 0.923 1.000 0.000 0.000
#> GSM711916 1 0.4887 0.570 0.772 0.000 0.228
#> GSM711922 1 0.0000 0.923 1.000 0.000 0.000
#> GSM711924 1 0.0237 0.921 0.996 0.000 0.004
#> GSM711926 3 0.4605 0.708 0.204 0.000 0.796
#> GSM711928 1 0.0000 0.923 1.000 0.000 0.000
#> GSM711930 3 0.6305 0.458 0.484 0.000 0.516
#> GSM711932 1 0.0237 0.921 0.996 0.000 0.004
#> GSM711934 1 0.0000 0.923 1.000 0.000 0.000
#> GSM711940 1 0.0000 0.923 1.000 0.000 0.000
#> GSM711942 1 0.0000 0.923 1.000 0.000 0.000
#> GSM711944 1 0.0592 0.916 0.988 0.000 0.012
#> GSM711946 3 0.3816 0.729 0.148 0.000 0.852
#> GSM711948 1 0.0592 0.916 0.988 0.000 0.012
#> GSM711952 1 0.4291 0.652 0.820 0.000 0.180
#> GSM711954 1 0.4235 0.662 0.824 0.000 0.176
#> GSM711962 1 0.0000 0.923 1.000 0.000 0.000
#> GSM711970 3 0.6168 0.596 0.412 0.000 0.588
#> GSM711974 1 0.0237 0.920 0.996 0.000 0.004
#> GSM711978 3 0.5016 0.711 0.240 0.000 0.760
#> GSM711988 1 0.0237 0.921 0.996 0.000 0.004
#> GSM711990 1 0.6309 -0.417 0.504 0.000 0.496
#> GSM711992 3 0.4178 0.722 0.172 0.000 0.828
#> GSM711982 1 0.0000 0.923 1.000 0.000 0.000
#> GSM711984 2 0.0000 0.952 0.000 1.000 0.000
#> GSM711912 1 0.0000 0.923 1.000 0.000 0.000
#> GSM711918 1 0.0000 0.923 1.000 0.000 0.000
#> GSM711920 1 0.0237 0.921 0.996 0.000 0.004
#> GSM711937 2 0.0237 0.951 0.000 0.996 0.004
#> GSM711939 2 0.0000 0.952 0.000 1.000 0.000
#> GSM711951 3 0.0000 0.622 0.000 0.000 1.000
#> GSM711957 3 0.6307 0.310 0.488 0.000 0.512
#> GSM711959 2 0.0000 0.952 0.000 1.000 0.000
#> GSM711961 2 0.0000 0.952 0.000 1.000 0.000
#> GSM711965 3 0.5926 0.654 0.356 0.000 0.644
#> GSM711967 1 0.0237 0.921 0.996 0.000 0.004
#> GSM711969 2 0.3116 0.912 0.000 0.892 0.108
#> GSM711973 1 0.2625 0.835 0.916 0.000 0.084
#> GSM711977 3 0.5497 0.703 0.292 0.000 0.708
#> GSM711981 3 0.5016 0.711 0.240 0.000 0.760
#> GSM711987 2 0.0000 0.952 0.000 1.000 0.000
#> GSM711905 2 0.0000 0.952 0.000 1.000 0.000
#> GSM711907 2 0.3551 0.900 0.000 0.868 0.132
#> GSM711909 3 0.6008 0.642 0.372 0.000 0.628
#> GSM711911 3 0.6291 0.473 0.468 0.000 0.532
#> GSM711915 3 0.4002 0.480 0.000 0.160 0.840
#> GSM711917 2 0.3116 0.912 0.000 0.892 0.108
#> GSM711923 3 0.5216 0.708 0.260 0.000 0.740
#> GSM711925 2 0.0000 0.952 0.000 1.000 0.000
#> GSM711927 3 0.6045 0.632 0.380 0.000 0.620
#> GSM711929 2 0.0000 0.952 0.000 1.000 0.000
#> GSM711931 3 0.3116 0.652 0.108 0.000 0.892
#> GSM711933 1 0.0000 0.923 1.000 0.000 0.000
#> GSM711935 2 0.0000 0.952 0.000 1.000 0.000
#> GSM711941 1 0.1964 0.870 0.944 0.000 0.056
#> GSM711943 3 0.3551 0.725 0.132 0.000 0.868
#> GSM711945 3 0.0237 0.628 0.004 0.000 0.996
#> GSM711947 2 0.4062 0.878 0.000 0.836 0.164
#> GSM711949 2 0.0000 0.952 0.000 1.000 0.000
#> GSM711953 2 0.0000 0.952 0.000 1.000 0.000
#> GSM711955 1 0.0424 0.918 0.992 0.000 0.008
#> GSM711963 2 0.0000 0.952 0.000 1.000 0.000
#> GSM711971 1 0.5591 0.372 0.696 0.000 0.304
#> GSM711975 2 0.6302 0.444 0.000 0.520 0.480
#> GSM711979 1 0.4002 0.706 0.840 0.000 0.160
#> GSM711989 2 0.3686 0.895 0.000 0.860 0.140
#> GSM711991 3 0.0237 0.624 0.004 0.000 0.996
#> GSM711993 3 0.5497 0.668 0.292 0.000 0.708
#> GSM711983 1 0.3752 0.747 0.856 0.000 0.144
#> GSM711985 2 0.0237 0.951 0.000 0.996 0.004
#> GSM711913 3 0.3816 0.729 0.148 0.000 0.852
#> GSM711919 3 0.6308 0.415 0.492 0.000 0.508
#> GSM711921 3 0.6008 0.642 0.372 0.000 0.628
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM711936 2 0.5631 0.826 0.000 0.700 0.076 0.224
#> GSM711938 2 0.2450 0.871 0.000 0.912 0.016 0.072
#> GSM711950 1 0.2949 0.855 0.888 0.000 0.024 0.088
#> GSM711956 1 0.0000 0.904 1.000 0.000 0.000 0.000
#> GSM711958 1 0.0657 0.901 0.984 0.000 0.004 0.012
#> GSM711960 3 0.4477 0.713 0.312 0.000 0.688 0.000
#> GSM711964 1 0.0707 0.899 0.980 0.000 0.020 0.000
#> GSM711966 1 0.0469 0.902 0.988 0.000 0.012 0.000
#> GSM711968 1 0.0707 0.899 0.980 0.000 0.020 0.000
#> GSM711972 1 0.0188 0.904 0.996 0.000 0.000 0.004
#> GSM711976 1 0.2197 0.875 0.916 0.000 0.004 0.080
#> GSM711980 1 0.0000 0.904 1.000 0.000 0.000 0.000
#> GSM711986 1 0.0592 0.901 0.984 0.000 0.016 0.000
#> GSM711904 3 0.4283 0.761 0.256 0.000 0.740 0.004
#> GSM711906 1 0.0336 0.903 0.992 0.000 0.008 0.000
#> GSM711908 3 0.4482 0.753 0.264 0.000 0.728 0.008
#> GSM711910 3 0.3557 0.781 0.108 0.000 0.856 0.036
#> GSM711914 1 0.0000 0.904 1.000 0.000 0.000 0.000
#> GSM711916 3 0.4632 0.715 0.308 0.000 0.688 0.004
#> GSM711922 1 0.0000 0.904 1.000 0.000 0.000 0.000
#> GSM711924 1 0.1743 0.887 0.940 0.000 0.004 0.056
#> GSM711926 4 0.5265 0.785 0.092 0.000 0.160 0.748
#> GSM711928 1 0.0707 0.899 0.980 0.000 0.020 0.000
#> GSM711930 3 0.4283 0.761 0.256 0.000 0.740 0.004
#> GSM711932 1 0.2197 0.875 0.916 0.000 0.004 0.080
#> GSM711934 1 0.0000 0.904 1.000 0.000 0.000 0.000
#> GSM711940 1 0.0469 0.902 0.988 0.000 0.012 0.000
#> GSM711942 1 0.0000 0.904 1.000 0.000 0.000 0.000
#> GSM711944 1 0.2949 0.855 0.888 0.000 0.024 0.088
#> GSM711946 3 0.3999 0.636 0.036 0.000 0.824 0.140
#> GSM711948 1 0.2949 0.855 0.888 0.000 0.024 0.088
#> GSM711952 1 0.5147 -0.209 0.536 0.000 0.460 0.004
#> GSM711954 1 0.5147 -0.209 0.536 0.000 0.460 0.004
#> GSM711962 1 0.0188 0.904 0.996 0.000 0.004 0.000
#> GSM711970 3 0.4328 0.765 0.244 0.000 0.748 0.008
#> GSM711974 1 0.0921 0.894 0.972 0.000 0.028 0.000
#> GSM711978 4 0.5265 0.785 0.092 0.000 0.160 0.748
#> GSM711988 1 0.2197 0.875 0.916 0.000 0.004 0.080
#> GSM711990 3 0.3763 0.797 0.144 0.000 0.832 0.024
#> GSM711992 4 0.5240 0.772 0.072 0.000 0.188 0.740
#> GSM711982 1 0.0469 0.902 0.988 0.000 0.012 0.000
#> GSM711984 2 0.0000 0.868 0.000 1.000 0.000 0.000
#> GSM711912 1 0.0707 0.899 0.980 0.000 0.020 0.000
#> GSM711918 1 0.0707 0.899 0.980 0.000 0.020 0.000
#> GSM711920 1 0.1902 0.884 0.932 0.000 0.004 0.064
#> GSM711937 2 0.5432 0.833 0.000 0.716 0.068 0.216
#> GSM711939 2 0.5180 0.841 0.000 0.740 0.064 0.196
#> GSM711951 4 0.2216 0.655 0.000 0.000 0.092 0.908
#> GSM711957 4 0.5327 0.673 0.220 0.000 0.060 0.720
#> GSM711959 2 0.0000 0.868 0.000 1.000 0.000 0.000
#> GSM711961 2 0.0000 0.868 0.000 1.000 0.000 0.000
#> GSM711965 3 0.3978 0.775 0.108 0.000 0.836 0.056
#> GSM711967 1 0.1902 0.884 0.932 0.000 0.004 0.064
#> GSM711969 2 0.5631 0.826 0.000 0.700 0.076 0.224
#> GSM711973 1 0.4617 0.703 0.764 0.000 0.032 0.204
#> GSM711977 4 0.6946 0.610 0.212 0.000 0.200 0.588
#> GSM711981 4 0.5265 0.785 0.092 0.000 0.160 0.748
#> GSM711987 2 0.2450 0.871 0.000 0.912 0.016 0.072
#> GSM711905 2 0.0000 0.868 0.000 1.000 0.000 0.000
#> GSM711907 2 0.6397 0.794 0.000 0.648 0.144 0.208
#> GSM711909 3 0.3842 0.795 0.128 0.000 0.836 0.036
#> GSM711911 3 0.4307 0.784 0.144 0.000 0.808 0.048
#> GSM711915 3 0.3074 0.515 0.000 0.000 0.848 0.152
#> GSM711917 2 0.5631 0.826 0.000 0.700 0.076 0.224
#> GSM711923 4 0.5551 0.770 0.112 0.000 0.160 0.728
#> GSM711925 2 0.0000 0.868 0.000 1.000 0.000 0.000
#> GSM711927 3 0.3842 0.795 0.128 0.000 0.836 0.036
#> GSM711929 2 0.0000 0.868 0.000 1.000 0.000 0.000
#> GSM711931 4 0.1209 0.679 0.004 0.000 0.032 0.964
#> GSM711933 1 0.0000 0.904 1.000 0.000 0.000 0.000
#> GSM711935 2 0.0000 0.868 0.000 1.000 0.000 0.000
#> GSM711941 1 0.3485 0.824 0.856 0.000 0.028 0.116
#> GSM711943 4 0.5359 0.686 0.036 0.000 0.288 0.676
#> GSM711945 4 0.4522 0.672 0.000 0.000 0.320 0.680
#> GSM711947 2 0.7010 0.722 0.000 0.576 0.184 0.240
#> GSM711949 2 0.0000 0.868 0.000 1.000 0.000 0.000
#> GSM711953 2 0.2376 0.871 0.000 0.916 0.016 0.068
#> GSM711955 1 0.1284 0.894 0.964 0.000 0.024 0.012
#> GSM711963 2 0.0000 0.868 0.000 1.000 0.000 0.000
#> GSM711971 3 0.5912 0.344 0.440 0.000 0.524 0.036
#> GSM711975 4 0.4104 0.514 0.000 0.080 0.088 0.832
#> GSM711979 1 0.4993 0.604 0.712 0.000 0.028 0.260
#> GSM711989 2 0.5935 0.803 0.000 0.664 0.080 0.256
#> GSM711991 3 0.4222 0.310 0.000 0.000 0.728 0.272
#> GSM711993 4 0.5247 0.748 0.148 0.000 0.100 0.752
#> GSM711983 1 0.4290 0.732 0.800 0.000 0.164 0.036
#> GSM711985 2 0.5218 0.840 0.000 0.736 0.064 0.200
#> GSM711913 4 0.5912 0.435 0.036 0.000 0.440 0.524
#> GSM711919 3 0.3749 0.796 0.128 0.000 0.840 0.032
#> GSM711921 3 0.3876 0.792 0.124 0.000 0.836 0.040
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM711936 2 0.5925 0.76395 0.000 0.584 0.004 0.124 0.288
#> GSM711938 2 0.4010 0.80683 0.000 0.792 0.000 0.072 0.136
#> GSM711950 1 0.2102 0.79069 0.916 0.000 0.012 0.068 0.004
#> GSM711956 1 0.1502 0.81067 0.940 0.000 0.004 0.000 0.056
#> GSM711958 1 0.1041 0.80525 0.964 0.000 0.004 0.032 0.000
#> GSM711960 3 0.6215 -0.57341 0.152 0.000 0.500 0.000 0.348
#> GSM711964 1 0.4768 0.34381 0.592 0.000 0.024 0.000 0.384
#> GSM711966 1 0.2286 0.78897 0.888 0.000 0.004 0.000 0.108
#> GSM711968 1 0.4768 0.34763 0.592 0.000 0.024 0.000 0.384
#> GSM711972 1 0.0566 0.81062 0.984 0.000 0.000 0.004 0.012
#> GSM711976 1 0.1864 0.79538 0.924 0.000 0.004 0.068 0.004
#> GSM711980 1 0.1704 0.80799 0.928 0.000 0.004 0.000 0.068
#> GSM711986 1 0.2719 0.76190 0.852 0.000 0.004 0.000 0.144
#> GSM711904 5 0.6152 0.88878 0.112 0.000 0.356 0.008 0.524
#> GSM711906 1 0.2179 0.79362 0.896 0.000 0.004 0.000 0.100
#> GSM711908 5 0.6152 0.88878 0.112 0.000 0.356 0.008 0.524
#> GSM711910 3 0.1205 0.71405 0.040 0.000 0.956 0.000 0.004
#> GSM711914 1 0.1502 0.81067 0.940 0.000 0.004 0.000 0.056
#> GSM711916 5 0.5974 0.86608 0.132 0.000 0.320 0.000 0.548
#> GSM711922 1 0.1341 0.81123 0.944 0.000 0.000 0.000 0.056
#> GSM711924 1 0.1638 0.79810 0.932 0.000 0.004 0.064 0.000
#> GSM711926 4 0.3342 0.82032 0.048 0.000 0.100 0.848 0.004
#> GSM711928 1 0.4768 0.34381 0.592 0.000 0.024 0.000 0.384
#> GSM711930 5 0.5942 0.88289 0.116 0.000 0.360 0.000 0.524
#> GSM711932 1 0.1864 0.79538 0.924 0.000 0.004 0.068 0.004
#> GSM711934 1 0.1571 0.80995 0.936 0.000 0.004 0.000 0.060
#> GSM711940 1 0.2338 0.78675 0.884 0.000 0.004 0.000 0.112
#> GSM711942 1 0.1704 0.80799 0.928 0.000 0.004 0.000 0.068
#> GSM711944 1 0.1942 0.79278 0.920 0.000 0.012 0.068 0.000
#> GSM711946 3 0.2339 0.67017 0.004 0.000 0.892 0.100 0.004
#> GSM711948 1 0.1942 0.79278 0.920 0.000 0.012 0.068 0.000
#> GSM711952 5 0.6408 0.82315 0.188 0.000 0.256 0.008 0.548
#> GSM711954 5 0.6518 0.78551 0.212 0.000 0.248 0.008 0.532
#> GSM711962 1 0.1768 0.80665 0.924 0.000 0.004 0.000 0.072
#> GSM711970 5 0.6152 0.88878 0.112 0.000 0.356 0.008 0.524
#> GSM711974 1 0.6132 0.00461 0.508 0.000 0.140 0.000 0.352
#> GSM711978 4 0.3466 0.82037 0.048 0.000 0.100 0.844 0.008
#> GSM711988 1 0.1704 0.79678 0.928 0.000 0.004 0.068 0.000
#> GSM711990 3 0.1774 0.69639 0.052 0.000 0.932 0.000 0.016
#> GSM711992 4 0.3404 0.80941 0.024 0.000 0.124 0.840 0.012
#> GSM711982 1 0.2286 0.78897 0.888 0.000 0.004 0.000 0.108
#> GSM711984 2 0.0162 0.79878 0.000 0.996 0.004 0.000 0.000
#> GSM711912 1 0.4779 0.33757 0.588 0.000 0.024 0.000 0.388
#> GSM711918 1 0.4768 0.34763 0.592 0.000 0.024 0.000 0.384
#> GSM711920 1 0.1638 0.79810 0.932 0.000 0.004 0.064 0.000
#> GSM711937 2 0.5754 0.76632 0.000 0.588 0.000 0.120 0.292
#> GSM711939 2 0.5579 0.77798 0.000 0.620 0.000 0.116 0.264
#> GSM711951 4 0.2984 0.70992 0.000 0.000 0.032 0.860 0.108
#> GSM711957 4 0.3682 0.75641 0.120 0.000 0.040 0.828 0.012
#> GSM711959 2 0.0162 0.79878 0.000 0.996 0.004 0.000 0.000
#> GSM711961 2 0.0510 0.80010 0.000 0.984 0.000 0.000 0.016
#> GSM711965 3 0.1285 0.71475 0.036 0.000 0.956 0.004 0.004
#> GSM711967 1 0.1638 0.79845 0.932 0.000 0.000 0.064 0.004
#> GSM711969 2 0.5925 0.76395 0.000 0.584 0.004 0.124 0.288
#> GSM711973 1 0.3219 0.72810 0.840 0.000 0.020 0.136 0.004
#> GSM711977 3 0.6264 -0.10543 0.128 0.000 0.460 0.408 0.004
#> GSM711981 4 0.3237 0.81996 0.048 0.000 0.104 0.848 0.000
#> GSM711987 2 0.4010 0.80683 0.000 0.792 0.000 0.072 0.136
#> GSM711905 2 0.0000 0.79872 0.000 1.000 0.000 0.000 0.000
#> GSM711907 2 0.6547 0.67736 0.000 0.484 0.032 0.096 0.388
#> GSM711909 3 0.1205 0.71405 0.040 0.000 0.956 0.000 0.004
#> GSM711911 3 0.1628 0.70773 0.056 0.000 0.936 0.008 0.000
#> GSM711915 3 0.5215 0.31769 0.000 0.000 0.576 0.052 0.372
#> GSM711917 2 0.5925 0.76395 0.000 0.584 0.004 0.124 0.288
#> GSM711923 4 0.4835 0.73711 0.084 0.000 0.188 0.724 0.004
#> GSM711925 2 0.0162 0.79878 0.000 0.996 0.004 0.000 0.000
#> GSM711927 3 0.1205 0.71405 0.040 0.000 0.956 0.000 0.004
#> GSM711929 2 0.0000 0.79872 0.000 1.000 0.000 0.000 0.000
#> GSM711931 4 0.1981 0.75062 0.000 0.000 0.028 0.924 0.048
#> GSM711933 1 0.2046 0.80455 0.916 0.000 0.016 0.000 0.068
#> GSM711935 2 0.0000 0.79872 0.000 1.000 0.000 0.000 0.000
#> GSM711941 1 0.2429 0.77994 0.900 0.000 0.020 0.076 0.004
#> GSM711943 4 0.4122 0.63198 0.004 0.000 0.304 0.688 0.004
#> GSM711945 4 0.4132 0.68392 0.000 0.000 0.260 0.720 0.020
#> GSM711947 2 0.7294 0.60665 0.000 0.420 0.080 0.108 0.392
#> GSM711949 2 0.0000 0.79872 0.000 1.000 0.000 0.000 0.000
#> GSM711953 2 0.4010 0.80683 0.000 0.792 0.000 0.072 0.136
#> GSM711955 1 0.1836 0.80958 0.932 0.000 0.032 0.000 0.036
#> GSM711963 2 0.0162 0.79878 0.000 0.996 0.004 0.000 0.000
#> GSM711971 3 0.3696 0.47746 0.212 0.000 0.772 0.000 0.016
#> GSM711975 4 0.4516 0.49228 0.000 0.016 0.012 0.696 0.276
#> GSM711979 1 0.3742 0.66815 0.788 0.000 0.020 0.188 0.004
#> GSM711989 2 0.6308 0.72502 0.000 0.528 0.004 0.160 0.308
#> GSM711991 3 0.5382 0.40670 0.000 0.000 0.644 0.252 0.104
#> GSM711993 4 0.3362 0.80249 0.080 0.000 0.076 0.844 0.000
#> GSM711983 1 0.4836 0.22841 0.568 0.000 0.412 0.008 0.012
#> GSM711985 2 0.5579 0.77798 0.000 0.620 0.000 0.116 0.264
#> GSM711913 3 0.4434 0.26184 0.008 0.000 0.640 0.348 0.004
#> GSM711919 3 0.1357 0.70953 0.048 0.000 0.948 0.000 0.004
#> GSM711921 3 0.1124 0.71564 0.036 0.000 0.960 0.004 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM711936 2 0.6169 0.4406 0.000 0.480 0.000 0.016 0.296 0.208
#> GSM711938 2 0.4915 0.5926 0.000 0.676 0.000 0.008 0.128 0.188
#> GSM711950 1 0.4170 0.6613 0.660 0.000 0.000 0.032 0.308 0.000
#> GSM711956 1 0.0146 0.7083 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM711958 1 0.3104 0.6967 0.800 0.000 0.000 0.016 0.184 0.000
#> GSM711960 3 0.6069 -0.3574 0.324 0.000 0.440 0.000 0.004 0.232
#> GSM711964 1 0.4032 -0.1112 0.572 0.000 0.008 0.000 0.000 0.420
#> GSM711966 1 0.0777 0.6967 0.972 0.000 0.000 0.000 0.004 0.024
#> GSM711968 1 0.4364 -0.1279 0.556 0.000 0.008 0.000 0.012 0.424
#> GSM711972 1 0.2772 0.6990 0.816 0.000 0.000 0.000 0.180 0.004
#> GSM711976 1 0.4289 0.6622 0.660 0.000 0.000 0.032 0.304 0.004
#> GSM711980 1 0.0363 0.7059 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM711986 1 0.1320 0.6886 0.948 0.000 0.000 0.000 0.016 0.036
#> GSM711904 6 0.4503 0.8538 0.084 0.000 0.232 0.000 0.000 0.684
#> GSM711906 1 0.1003 0.7019 0.964 0.000 0.000 0.000 0.020 0.016
#> GSM711908 6 0.4743 0.8543 0.088 0.000 0.224 0.000 0.008 0.680
#> GSM711910 3 0.0260 0.7449 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM711914 1 0.0363 0.7039 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM711916 6 0.5491 0.7777 0.232 0.000 0.180 0.000 0.004 0.584
#> GSM711922 1 0.0291 0.7086 0.992 0.000 0.000 0.000 0.004 0.004
#> GSM711924 1 0.4099 0.6770 0.696 0.000 0.000 0.024 0.272 0.008
#> GSM711926 4 0.0653 0.8614 0.004 0.000 0.012 0.980 0.000 0.004
#> GSM711928 1 0.4045 -0.1291 0.564 0.000 0.008 0.000 0.000 0.428
#> GSM711930 6 0.4525 0.8558 0.088 0.000 0.228 0.000 0.000 0.684
#> GSM711932 1 0.4428 0.6587 0.648 0.000 0.000 0.032 0.312 0.008
#> GSM711934 1 0.0260 0.7055 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM711940 1 0.0972 0.6948 0.964 0.000 0.000 0.000 0.008 0.028
#> GSM711942 1 0.0622 0.7073 0.980 0.000 0.000 0.000 0.012 0.008
#> GSM711944 1 0.4152 0.6626 0.664 0.000 0.000 0.032 0.304 0.000
#> GSM711946 3 0.1333 0.7223 0.000 0.000 0.944 0.048 0.008 0.000
#> GSM711948 1 0.4170 0.6613 0.660 0.000 0.000 0.032 0.308 0.000
#> GSM711952 6 0.4878 0.8245 0.164 0.000 0.144 0.000 0.008 0.684
#> GSM711954 6 0.5324 0.6616 0.340 0.000 0.120 0.000 0.000 0.540
#> GSM711962 1 0.0291 0.7076 0.992 0.000 0.000 0.000 0.004 0.004
#> GSM711970 6 0.4503 0.8538 0.084 0.000 0.232 0.000 0.000 0.684
#> GSM711974 1 0.5630 -0.1740 0.560 0.000 0.196 0.000 0.004 0.240
#> GSM711978 4 0.0748 0.8627 0.004 0.000 0.016 0.976 0.004 0.000
#> GSM711988 1 0.4135 0.6639 0.668 0.000 0.000 0.032 0.300 0.000
#> GSM711990 3 0.1036 0.7447 0.024 0.000 0.964 0.000 0.004 0.008
#> GSM711992 4 0.0922 0.8619 0.004 0.000 0.024 0.968 0.004 0.000
#> GSM711982 1 0.0777 0.6967 0.972 0.000 0.000 0.000 0.004 0.024
#> GSM711984 2 0.0000 0.6373 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711912 1 0.4380 -0.1546 0.544 0.000 0.008 0.000 0.012 0.436
#> GSM711918 1 0.4457 -0.1502 0.544 0.000 0.008 0.000 0.016 0.432
#> GSM711920 1 0.4193 0.6745 0.688 0.000 0.000 0.028 0.276 0.008
#> GSM711937 2 0.6116 0.4450 0.000 0.480 0.000 0.012 0.292 0.216
#> GSM711939 2 0.6024 0.4644 0.000 0.492 0.000 0.008 0.268 0.232
#> GSM711951 4 0.1624 0.8287 0.000 0.000 0.004 0.936 0.040 0.020
#> GSM711957 4 0.3106 0.7608 0.016 0.000 0.000 0.840 0.120 0.024
#> GSM711959 2 0.0291 0.6366 0.000 0.992 0.000 0.000 0.004 0.004
#> GSM711961 2 0.1934 0.6308 0.000 0.916 0.000 0.000 0.044 0.040
#> GSM711965 3 0.0653 0.7494 0.012 0.000 0.980 0.004 0.004 0.000
#> GSM711967 1 0.4173 0.6758 0.692 0.000 0.000 0.028 0.272 0.008
#> GSM711969 2 0.6243 0.4355 0.000 0.476 0.000 0.020 0.296 0.208
#> GSM711973 1 0.5603 0.5728 0.544 0.000 0.000 0.120 0.324 0.012
#> GSM711977 3 0.6458 -0.0216 0.012 0.000 0.396 0.388 0.192 0.012
#> GSM711981 4 0.0603 0.8628 0.004 0.000 0.016 0.980 0.000 0.000
#> GSM711987 2 0.4915 0.5926 0.000 0.676 0.000 0.008 0.128 0.188
#> GSM711905 2 0.0000 0.6373 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711907 5 0.5164 0.3770 0.000 0.268 0.008 0.004 0.628 0.092
#> GSM711909 3 0.0458 0.7504 0.016 0.000 0.984 0.000 0.000 0.000
#> GSM711911 3 0.1592 0.7403 0.020 0.000 0.940 0.000 0.032 0.008
#> GSM711915 5 0.6130 0.1767 0.000 0.000 0.292 0.004 0.432 0.272
#> GSM711917 2 0.6243 0.4355 0.000 0.476 0.000 0.020 0.296 0.208
#> GSM711923 4 0.3405 0.7729 0.012 0.000 0.136 0.816 0.036 0.000
#> GSM711925 2 0.0000 0.6373 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711927 3 0.0458 0.7504 0.016 0.000 0.984 0.000 0.000 0.000
#> GSM711929 2 0.0146 0.6373 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM711931 4 0.1148 0.8396 0.000 0.000 0.004 0.960 0.016 0.020
#> GSM711933 1 0.0508 0.7028 0.984 0.000 0.004 0.000 0.000 0.012
#> GSM711935 2 0.0000 0.6373 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711941 1 0.4476 0.6482 0.640 0.000 0.000 0.052 0.308 0.000
#> GSM711943 4 0.3012 0.7368 0.000 0.000 0.196 0.796 0.008 0.000
#> GSM711945 4 0.2980 0.7444 0.000 0.000 0.192 0.800 0.008 0.000
#> GSM711947 5 0.5968 0.4948 0.000 0.208 0.064 0.012 0.624 0.092
#> GSM711949 2 0.0000 0.6373 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711953 2 0.4915 0.5926 0.000 0.676 0.000 0.008 0.128 0.188
#> GSM711955 1 0.1382 0.7054 0.948 0.000 0.008 0.000 0.036 0.008
#> GSM711963 2 0.0000 0.6373 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711971 3 0.2791 0.6773 0.096 0.000 0.864 0.000 0.032 0.008
#> GSM711975 4 0.5462 0.2514 0.000 0.000 0.004 0.592 0.204 0.200
#> GSM711979 1 0.5474 0.5751 0.552 0.000 0.000 0.132 0.312 0.004
#> GSM711989 2 0.7396 0.1851 0.000 0.364 0.004 0.112 0.312 0.208
#> GSM711991 3 0.6590 0.0758 0.000 0.000 0.424 0.292 0.252 0.032
#> GSM711993 4 0.0653 0.8617 0.004 0.000 0.012 0.980 0.004 0.000
#> GSM711983 3 0.4901 0.4313 0.260 0.000 0.648 0.000 0.084 0.008
#> GSM711985 2 0.6024 0.4644 0.000 0.492 0.000 0.008 0.268 0.232
#> GSM711913 3 0.4358 0.3005 0.000 0.000 0.620 0.352 0.020 0.008
#> GSM711919 3 0.0837 0.7480 0.020 0.000 0.972 0.000 0.004 0.004
#> GSM711921 3 0.0458 0.7504 0.016 0.000 0.984 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) disease.state(p) individual(p) k
#> ATC:kmeans 90 1.10e-04 0.2961 0.417 2
#> ATC:kmeans 80 3.20e-07 0.5042 0.488 3
#> ATC:kmeans 85 5.03e-06 0.3688 0.383 4
#> ATC:kmeans 76 4.61e-06 0.0658 0.272 5
#> ATC:kmeans 68 5.00e-05 0.1443 0.473 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "skmeans"]
# you can also extract it by
# res = res_list["ATC:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 27425 rows and 90 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 5.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.987 0.995 0.4388 0.558 0.558
#> 3 3 0.656 0.811 0.876 0.4076 0.773 0.601
#> 4 4 0.780 0.826 0.897 0.1722 0.794 0.494
#> 5 5 0.903 0.891 0.943 0.0587 0.847 0.523
#> 6 6 0.825 0.783 0.877 0.0274 0.968 0.866
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
#> attr(,"optional")
#> [1] 2
There is also optional best \(k\) = 2 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM711936 2 0.000 0.985 0.000 1.000
#> GSM711938 2 0.000 0.985 0.000 1.000
#> GSM711950 1 0.000 1.000 1.000 0.000
#> GSM711956 1 0.000 1.000 1.000 0.000
#> GSM711958 1 0.000 1.000 1.000 0.000
#> GSM711960 1 0.000 1.000 1.000 0.000
#> GSM711964 1 0.000 1.000 1.000 0.000
#> GSM711966 1 0.000 1.000 1.000 0.000
#> GSM711968 1 0.000 1.000 1.000 0.000
#> GSM711972 1 0.000 1.000 1.000 0.000
#> GSM711976 1 0.000 1.000 1.000 0.000
#> GSM711980 1 0.000 1.000 1.000 0.000
#> GSM711986 1 0.000 1.000 1.000 0.000
#> GSM711904 1 0.000 1.000 1.000 0.000
#> GSM711906 1 0.000 1.000 1.000 0.000
#> GSM711908 1 0.000 1.000 1.000 0.000
#> GSM711910 1 0.000 1.000 1.000 0.000
#> GSM711914 1 0.000 1.000 1.000 0.000
#> GSM711916 1 0.000 1.000 1.000 0.000
#> GSM711922 1 0.000 1.000 1.000 0.000
#> GSM711924 1 0.000 1.000 1.000 0.000
#> GSM711926 2 0.000 0.985 0.000 1.000
#> GSM711928 1 0.000 1.000 1.000 0.000
#> GSM711930 1 0.000 1.000 1.000 0.000
#> GSM711932 1 0.000 1.000 1.000 0.000
#> GSM711934 1 0.000 1.000 1.000 0.000
#> GSM711940 1 0.000 1.000 1.000 0.000
#> GSM711942 1 0.000 1.000 1.000 0.000
#> GSM711944 1 0.000 1.000 1.000 0.000
#> GSM711946 1 0.000 1.000 1.000 0.000
#> GSM711948 1 0.000 1.000 1.000 0.000
#> GSM711952 1 0.000 1.000 1.000 0.000
#> GSM711954 1 0.000 1.000 1.000 0.000
#> GSM711962 1 0.000 1.000 1.000 0.000
#> GSM711970 1 0.000 1.000 1.000 0.000
#> GSM711974 1 0.000 1.000 1.000 0.000
#> GSM711978 1 0.000 1.000 1.000 0.000
#> GSM711988 1 0.000 1.000 1.000 0.000
#> GSM711990 1 0.000 1.000 1.000 0.000
#> GSM711992 2 0.983 0.264 0.424 0.576
#> GSM711982 1 0.000 1.000 1.000 0.000
#> GSM711984 2 0.000 0.985 0.000 1.000
#> GSM711912 1 0.000 1.000 1.000 0.000
#> GSM711918 1 0.000 1.000 1.000 0.000
#> GSM711920 1 0.000 1.000 1.000 0.000
#> GSM711937 2 0.000 0.985 0.000 1.000
#> GSM711939 2 0.000 0.985 0.000 1.000
#> GSM711951 2 0.000 0.985 0.000 1.000
#> GSM711957 1 0.000 1.000 1.000 0.000
#> GSM711959 2 0.000 0.985 0.000 1.000
#> GSM711961 2 0.000 0.985 0.000 1.000
#> GSM711965 1 0.000 1.000 1.000 0.000
#> GSM711967 1 0.000 1.000 1.000 0.000
#> GSM711969 2 0.000 0.985 0.000 1.000
#> GSM711973 1 0.000 1.000 1.000 0.000
#> GSM711977 1 0.000 1.000 1.000 0.000
#> GSM711981 1 0.000 1.000 1.000 0.000
#> GSM711987 2 0.000 0.985 0.000 1.000
#> GSM711905 2 0.000 0.985 0.000 1.000
#> GSM711907 2 0.000 0.985 0.000 1.000
#> GSM711909 1 0.000 1.000 1.000 0.000
#> GSM711911 1 0.000 1.000 1.000 0.000
#> GSM711915 2 0.000 0.985 0.000 1.000
#> GSM711917 2 0.000 0.985 0.000 1.000
#> GSM711923 1 0.000 1.000 1.000 0.000
#> GSM711925 2 0.000 0.985 0.000 1.000
#> GSM711927 1 0.000 1.000 1.000 0.000
#> GSM711929 2 0.000 0.985 0.000 1.000
#> GSM711931 2 0.000 0.985 0.000 1.000
#> GSM711933 1 0.000 1.000 1.000 0.000
#> GSM711935 2 0.000 0.985 0.000 1.000
#> GSM711941 1 0.000 1.000 1.000 0.000
#> GSM711943 1 0.000 1.000 1.000 0.000
#> GSM711945 2 0.000 0.985 0.000 1.000
#> GSM711947 2 0.000 0.985 0.000 1.000
#> GSM711949 2 0.000 0.985 0.000 1.000
#> GSM711953 2 0.000 0.985 0.000 1.000
#> GSM711955 1 0.000 1.000 1.000 0.000
#> GSM711963 2 0.000 0.985 0.000 1.000
#> GSM711971 1 0.000 1.000 1.000 0.000
#> GSM711975 2 0.000 0.985 0.000 1.000
#> GSM711979 1 0.000 1.000 1.000 0.000
#> GSM711989 2 0.000 0.985 0.000 1.000
#> GSM711991 2 0.000 0.985 0.000 1.000
#> GSM711993 1 0.000 1.000 1.000 0.000
#> GSM711983 1 0.000 1.000 1.000 0.000
#> GSM711985 2 0.000 0.985 0.000 1.000
#> GSM711913 1 0.000 1.000 1.000 0.000
#> GSM711919 1 0.000 1.000 1.000 0.000
#> GSM711921 1 0.000 1.000 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM711936 2 0.0000 0.958 0.000 1.000 0.000
#> GSM711938 2 0.0000 0.958 0.000 1.000 0.000
#> GSM711950 1 0.4178 0.846 0.828 0.000 0.172
#> GSM711956 1 0.5327 0.883 0.728 0.000 0.272
#> GSM711958 1 0.5327 0.883 0.728 0.000 0.272
#> GSM711960 3 0.0237 0.804 0.004 0.000 0.996
#> GSM711964 1 0.5327 0.883 0.728 0.000 0.272
#> GSM711966 1 0.5327 0.883 0.728 0.000 0.272
#> GSM711968 1 0.5327 0.883 0.728 0.000 0.272
#> GSM711972 1 0.5327 0.883 0.728 0.000 0.272
#> GSM711976 1 0.4121 0.847 0.832 0.000 0.168
#> GSM711980 1 0.5327 0.883 0.728 0.000 0.272
#> GSM711986 1 0.5327 0.883 0.728 0.000 0.272
#> GSM711904 3 0.6026 0.194 0.376 0.000 0.624
#> GSM711906 1 0.5327 0.883 0.728 0.000 0.272
#> GSM711908 3 0.6126 0.087 0.400 0.000 0.600
#> GSM711910 3 0.0000 0.806 0.000 0.000 1.000
#> GSM711914 1 0.5327 0.883 0.728 0.000 0.272
#> GSM711916 3 0.5948 0.252 0.360 0.000 0.640
#> GSM711922 1 0.5327 0.883 0.728 0.000 0.272
#> GSM711924 1 0.5138 0.878 0.748 0.000 0.252
#> GSM711926 2 0.5327 0.713 0.272 0.728 0.000
#> GSM711928 1 0.5327 0.883 0.728 0.000 0.272
#> GSM711930 3 0.4291 0.650 0.180 0.000 0.820
#> GSM711932 1 0.4121 0.847 0.832 0.000 0.168
#> GSM711934 1 0.5327 0.883 0.728 0.000 0.272
#> GSM711940 1 0.5327 0.883 0.728 0.000 0.272
#> GSM711942 1 0.5327 0.883 0.728 0.000 0.272
#> GSM711944 1 0.4178 0.846 0.828 0.000 0.172
#> GSM711946 3 0.0000 0.806 0.000 0.000 1.000
#> GSM711948 1 0.4178 0.846 0.828 0.000 0.172
#> GSM711952 1 0.5327 0.883 0.728 0.000 0.272
#> GSM711954 1 0.5327 0.883 0.728 0.000 0.272
#> GSM711962 1 0.5327 0.883 0.728 0.000 0.272
#> GSM711970 3 0.4974 0.562 0.236 0.000 0.764
#> GSM711974 3 0.5988 0.225 0.368 0.000 0.632
#> GSM711978 1 0.0000 0.680 1.000 0.000 0.000
#> GSM711988 1 0.4121 0.847 0.832 0.000 0.168
#> GSM711990 3 0.0000 0.806 0.000 0.000 1.000
#> GSM711992 1 0.1163 0.651 0.972 0.028 0.000
#> GSM711982 1 0.5327 0.883 0.728 0.000 0.272
#> GSM711984 2 0.0000 0.958 0.000 1.000 0.000
#> GSM711912 1 0.5327 0.883 0.728 0.000 0.272
#> GSM711918 1 0.5327 0.883 0.728 0.000 0.272
#> GSM711920 1 0.4452 0.858 0.808 0.000 0.192
#> GSM711937 2 0.0000 0.958 0.000 1.000 0.000
#> GSM711939 2 0.0000 0.958 0.000 1.000 0.000
#> GSM711951 2 0.0000 0.958 0.000 1.000 0.000
#> GSM711957 1 0.0000 0.680 1.000 0.000 0.000
#> GSM711959 2 0.0000 0.958 0.000 1.000 0.000
#> GSM711961 2 0.0000 0.958 0.000 1.000 0.000
#> GSM711965 3 0.0000 0.806 0.000 0.000 1.000
#> GSM711967 1 0.4121 0.847 0.832 0.000 0.168
#> GSM711969 2 0.0000 0.958 0.000 1.000 0.000
#> GSM711973 1 0.4178 0.846 0.828 0.000 0.172
#> GSM711977 3 0.6225 0.202 0.432 0.000 0.568
#> GSM711981 1 0.0424 0.674 0.992 0.000 0.008
#> GSM711987 2 0.0000 0.958 0.000 1.000 0.000
#> GSM711905 2 0.0000 0.958 0.000 1.000 0.000
#> GSM711907 2 0.0000 0.958 0.000 1.000 0.000
#> GSM711909 3 0.0000 0.806 0.000 0.000 1.000
#> GSM711911 3 0.0000 0.806 0.000 0.000 1.000
#> GSM711915 2 0.0000 0.958 0.000 1.000 0.000
#> GSM711917 2 0.0000 0.958 0.000 1.000 0.000
#> GSM711923 1 0.2711 0.737 0.912 0.000 0.088
#> GSM711925 2 0.0000 0.958 0.000 1.000 0.000
#> GSM711927 3 0.0000 0.806 0.000 0.000 1.000
#> GSM711929 2 0.0000 0.958 0.000 1.000 0.000
#> GSM711931 2 0.3551 0.857 0.132 0.868 0.000
#> GSM711933 1 0.5327 0.883 0.728 0.000 0.272
#> GSM711935 2 0.0000 0.958 0.000 1.000 0.000
#> GSM711941 1 0.4178 0.846 0.828 0.000 0.172
#> GSM711943 3 0.5760 0.581 0.328 0.000 0.672
#> GSM711945 2 0.6783 0.437 0.016 0.588 0.396
#> GSM711947 2 0.0000 0.958 0.000 1.000 0.000
#> GSM711949 2 0.0000 0.958 0.000 1.000 0.000
#> GSM711953 2 0.0000 0.958 0.000 1.000 0.000
#> GSM711955 1 0.5363 0.880 0.724 0.000 0.276
#> GSM711963 2 0.0000 0.958 0.000 1.000 0.000
#> GSM711971 3 0.0000 0.806 0.000 0.000 1.000
#> GSM711975 2 0.0000 0.958 0.000 1.000 0.000
#> GSM711979 1 0.0237 0.678 0.996 0.000 0.004
#> GSM711989 2 0.0000 0.958 0.000 1.000 0.000
#> GSM711991 2 0.6095 0.463 0.000 0.608 0.392
#> GSM711993 1 0.0237 0.678 0.996 0.000 0.004
#> GSM711983 3 0.2448 0.755 0.076 0.000 0.924
#> GSM711985 2 0.0000 0.958 0.000 1.000 0.000
#> GSM711913 3 0.3038 0.722 0.104 0.000 0.896
#> GSM711919 3 0.0000 0.806 0.000 0.000 1.000
#> GSM711921 3 0.0000 0.806 0.000 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM711936 2 0.0000 0.985 0.000 1.000 0.000 0.000
#> GSM711938 2 0.0000 0.985 0.000 1.000 0.000 0.000
#> GSM711950 4 0.4776 0.763 0.376 0.000 0.000 0.624
#> GSM711956 1 0.0469 0.886 0.988 0.000 0.000 0.012
#> GSM711958 1 0.2530 0.742 0.888 0.000 0.000 0.112
#> GSM711960 1 0.4406 0.619 0.700 0.000 0.300 0.000
#> GSM711964 1 0.0000 0.886 1.000 0.000 0.000 0.000
#> GSM711966 1 0.0336 0.887 0.992 0.000 0.000 0.008
#> GSM711968 1 0.0000 0.886 1.000 0.000 0.000 0.000
#> GSM711972 1 0.0469 0.886 0.988 0.000 0.000 0.012
#> GSM711976 4 0.4776 0.763 0.376 0.000 0.000 0.624
#> GSM711980 1 0.0469 0.886 0.988 0.000 0.000 0.012
#> GSM711986 1 0.0336 0.887 0.992 0.000 0.000 0.008
#> GSM711904 1 0.4103 0.681 0.744 0.000 0.256 0.000
#> GSM711906 1 0.0469 0.886 0.988 0.000 0.000 0.012
#> GSM711908 1 0.4103 0.681 0.744 0.000 0.256 0.000
#> GSM711910 3 0.0000 0.871 0.000 0.000 1.000 0.000
#> GSM711914 1 0.0469 0.886 0.988 0.000 0.000 0.012
#> GSM711916 1 0.4222 0.661 0.728 0.000 0.272 0.000
#> GSM711922 1 0.0469 0.886 0.988 0.000 0.000 0.012
#> GSM711924 4 0.4972 0.637 0.456 0.000 0.000 0.544
#> GSM711926 4 0.0336 0.641 0.000 0.008 0.000 0.992
#> GSM711928 1 0.0000 0.886 1.000 0.000 0.000 0.000
#> GSM711930 1 0.4250 0.655 0.724 0.000 0.276 0.000
#> GSM711932 4 0.4776 0.763 0.376 0.000 0.000 0.624
#> GSM711934 1 0.0469 0.886 0.988 0.000 0.000 0.012
#> GSM711940 1 0.0469 0.886 0.988 0.000 0.000 0.012
#> GSM711942 1 0.0469 0.886 0.988 0.000 0.000 0.012
#> GSM711944 4 0.4776 0.763 0.376 0.000 0.000 0.624
#> GSM711946 3 0.0000 0.871 0.000 0.000 1.000 0.000
#> GSM711948 4 0.4776 0.763 0.376 0.000 0.000 0.624
#> GSM711952 1 0.0592 0.877 0.984 0.000 0.016 0.000
#> GSM711954 1 0.0188 0.884 0.996 0.000 0.004 0.000
#> GSM711962 1 0.0469 0.886 0.988 0.000 0.000 0.012
#> GSM711970 1 0.4222 0.661 0.728 0.000 0.272 0.000
#> GSM711974 1 0.4134 0.676 0.740 0.000 0.260 0.000
#> GSM711978 4 0.0000 0.649 0.000 0.000 0.000 1.000
#> GSM711988 4 0.4776 0.763 0.376 0.000 0.000 0.624
#> GSM711990 3 0.0000 0.871 0.000 0.000 1.000 0.000
#> GSM711992 4 0.0188 0.645 0.000 0.004 0.000 0.996
#> GSM711982 1 0.0336 0.887 0.992 0.000 0.000 0.008
#> GSM711984 2 0.0000 0.985 0.000 1.000 0.000 0.000
#> GSM711912 1 0.0000 0.886 1.000 0.000 0.000 0.000
#> GSM711918 1 0.0000 0.886 1.000 0.000 0.000 0.000
#> GSM711920 4 0.4967 0.645 0.452 0.000 0.000 0.548
#> GSM711937 2 0.0000 0.985 0.000 1.000 0.000 0.000
#> GSM711939 2 0.0000 0.985 0.000 1.000 0.000 0.000
#> GSM711951 2 0.0000 0.985 0.000 1.000 0.000 0.000
#> GSM711957 4 0.0188 0.651 0.004 0.000 0.000 0.996
#> GSM711959 2 0.0000 0.985 0.000 1.000 0.000 0.000
#> GSM711961 2 0.0000 0.985 0.000 1.000 0.000 0.000
#> GSM711965 3 0.0000 0.871 0.000 0.000 1.000 0.000
#> GSM711967 4 0.4830 0.743 0.392 0.000 0.000 0.608
#> GSM711969 2 0.0000 0.985 0.000 1.000 0.000 0.000
#> GSM711973 4 0.4761 0.764 0.372 0.000 0.000 0.628
#> GSM711977 4 0.6691 0.705 0.236 0.000 0.152 0.612
#> GSM711981 4 0.0000 0.649 0.000 0.000 0.000 1.000
#> GSM711987 2 0.0000 0.985 0.000 1.000 0.000 0.000
#> GSM711905 2 0.0000 0.985 0.000 1.000 0.000 0.000
#> GSM711907 2 0.0000 0.985 0.000 1.000 0.000 0.000
#> GSM711909 3 0.0000 0.871 0.000 0.000 1.000 0.000
#> GSM711911 3 0.0000 0.871 0.000 0.000 1.000 0.000
#> GSM711915 2 0.0000 0.985 0.000 1.000 0.000 0.000
#> GSM711917 2 0.0000 0.985 0.000 1.000 0.000 0.000
#> GSM711923 4 0.3791 0.757 0.200 0.000 0.004 0.796
#> GSM711925 2 0.0000 0.985 0.000 1.000 0.000 0.000
#> GSM711927 3 0.0000 0.871 0.000 0.000 1.000 0.000
#> GSM711929 2 0.0000 0.985 0.000 1.000 0.000 0.000
#> GSM711931 2 0.4730 0.540 0.000 0.636 0.000 0.364
#> GSM711933 1 0.0469 0.886 0.988 0.000 0.000 0.012
#> GSM711935 2 0.0000 0.985 0.000 1.000 0.000 0.000
#> GSM711941 4 0.4761 0.764 0.372 0.000 0.000 0.628
#> GSM711943 3 0.6475 0.490 0.172 0.000 0.644 0.184
#> GSM711945 3 0.5132 0.237 0.000 0.448 0.548 0.004
#> GSM711947 2 0.0000 0.985 0.000 1.000 0.000 0.000
#> GSM711949 2 0.0000 0.985 0.000 1.000 0.000 0.000
#> GSM711953 2 0.0000 0.985 0.000 1.000 0.000 0.000
#> GSM711955 1 0.0937 0.879 0.976 0.000 0.012 0.012
#> GSM711963 2 0.0000 0.985 0.000 1.000 0.000 0.000
#> GSM711971 3 0.0188 0.868 0.004 0.000 0.996 0.000
#> GSM711975 2 0.0000 0.985 0.000 1.000 0.000 0.000
#> GSM711979 4 0.3400 0.749 0.180 0.000 0.000 0.820
#> GSM711989 2 0.0000 0.985 0.000 1.000 0.000 0.000
#> GSM711991 3 0.4981 0.195 0.000 0.464 0.536 0.000
#> GSM711993 4 0.0000 0.649 0.000 0.000 0.000 1.000
#> GSM711983 3 0.3907 0.569 0.232 0.000 0.768 0.000
#> GSM711985 2 0.0000 0.985 0.000 1.000 0.000 0.000
#> GSM711913 3 0.0657 0.861 0.012 0.000 0.984 0.004
#> GSM711919 3 0.0000 0.871 0.000 0.000 1.000 0.000
#> GSM711921 3 0.0000 0.871 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM711936 2 0.0000 0.9764 0.000 1.000 0.000 0.000 0.000
#> GSM711938 2 0.0000 0.9764 0.000 1.000 0.000 0.000 0.000
#> GSM711950 1 0.0963 0.9248 0.964 0.000 0.000 0.036 0.000
#> GSM711956 1 0.1043 0.9339 0.960 0.000 0.000 0.000 0.040
#> GSM711958 1 0.0290 0.9352 0.992 0.000 0.000 0.000 0.008
#> GSM711960 5 0.4465 0.5878 0.024 0.000 0.304 0.000 0.672
#> GSM711964 5 0.2516 0.8503 0.140 0.000 0.000 0.000 0.860
#> GSM711966 1 0.1608 0.9161 0.928 0.000 0.000 0.000 0.072
#> GSM711968 5 0.3143 0.8073 0.204 0.000 0.000 0.000 0.796
#> GSM711972 1 0.0703 0.9356 0.976 0.000 0.000 0.000 0.024
#> GSM711976 1 0.0880 0.9267 0.968 0.000 0.000 0.032 0.000
#> GSM711980 1 0.1121 0.9331 0.956 0.000 0.000 0.000 0.044
#> GSM711986 1 0.3366 0.7018 0.768 0.000 0.000 0.000 0.232
#> GSM711904 5 0.0992 0.8570 0.008 0.000 0.024 0.000 0.968
#> GSM711906 1 0.1608 0.9162 0.928 0.000 0.000 0.000 0.072
#> GSM711908 5 0.0955 0.8552 0.004 0.000 0.028 0.000 0.968
#> GSM711910 3 0.0162 0.9083 0.000 0.000 0.996 0.000 0.004
#> GSM711914 1 0.1121 0.9331 0.956 0.000 0.000 0.000 0.044
#> GSM711916 5 0.1041 0.8544 0.004 0.000 0.032 0.000 0.964
#> GSM711922 1 0.1121 0.9331 0.956 0.000 0.000 0.000 0.044
#> GSM711924 1 0.0162 0.9349 0.996 0.000 0.000 0.000 0.004
#> GSM711926 4 0.0290 0.9765 0.008 0.000 0.000 0.992 0.000
#> GSM711928 5 0.2891 0.8340 0.176 0.000 0.000 0.000 0.824
#> GSM711930 5 0.0955 0.8552 0.004 0.000 0.028 0.000 0.968
#> GSM711932 1 0.0963 0.9248 0.964 0.000 0.000 0.036 0.000
#> GSM711934 1 0.1121 0.9331 0.956 0.000 0.000 0.000 0.044
#> GSM711940 1 0.1544 0.9192 0.932 0.000 0.000 0.000 0.068
#> GSM711942 1 0.1121 0.9331 0.956 0.000 0.000 0.000 0.044
#> GSM711944 1 0.0880 0.9267 0.968 0.000 0.000 0.032 0.000
#> GSM711946 3 0.0290 0.9025 0.000 0.000 0.992 0.000 0.008
#> GSM711948 1 0.0880 0.9267 0.968 0.000 0.000 0.032 0.000
#> GSM711952 5 0.0963 0.8615 0.036 0.000 0.000 0.000 0.964
#> GSM711954 5 0.1043 0.8623 0.040 0.000 0.000 0.000 0.960
#> GSM711962 1 0.1121 0.9331 0.956 0.000 0.000 0.000 0.044
#> GSM711970 5 0.0955 0.8552 0.004 0.000 0.028 0.000 0.968
#> GSM711974 5 0.4555 0.7739 0.200 0.000 0.068 0.000 0.732
#> GSM711978 4 0.0290 0.9765 0.008 0.000 0.000 0.992 0.000
#> GSM711988 1 0.0880 0.9267 0.968 0.000 0.000 0.032 0.000
#> GSM711990 3 0.0162 0.9083 0.000 0.000 0.996 0.000 0.004
#> GSM711992 4 0.0693 0.9721 0.008 0.000 0.000 0.980 0.012
#> GSM711982 1 0.2127 0.8813 0.892 0.000 0.000 0.000 0.108
#> GSM711984 2 0.0000 0.9764 0.000 1.000 0.000 0.000 0.000
#> GSM711912 5 0.2773 0.8401 0.164 0.000 0.000 0.000 0.836
#> GSM711918 5 0.2966 0.8262 0.184 0.000 0.000 0.000 0.816
#> GSM711920 1 0.0162 0.9339 0.996 0.000 0.000 0.004 0.000
#> GSM711937 2 0.0000 0.9764 0.000 1.000 0.000 0.000 0.000
#> GSM711939 2 0.0000 0.9764 0.000 1.000 0.000 0.000 0.000
#> GSM711951 2 0.0000 0.9764 0.000 1.000 0.000 0.000 0.000
#> GSM711957 4 0.0963 0.9516 0.036 0.000 0.000 0.964 0.000
#> GSM711959 2 0.0000 0.9764 0.000 1.000 0.000 0.000 0.000
#> GSM711961 2 0.0000 0.9764 0.000 1.000 0.000 0.000 0.000
#> GSM711965 3 0.0162 0.9083 0.000 0.000 0.996 0.000 0.004
#> GSM711967 1 0.0162 0.9339 0.996 0.000 0.000 0.004 0.000
#> GSM711969 2 0.0000 0.9764 0.000 1.000 0.000 0.000 0.000
#> GSM711973 1 0.1197 0.9175 0.952 0.000 0.000 0.048 0.000
#> GSM711977 3 0.3255 0.7721 0.100 0.000 0.848 0.052 0.000
#> GSM711981 4 0.0290 0.9765 0.008 0.000 0.000 0.992 0.000
#> GSM711987 2 0.0000 0.9764 0.000 1.000 0.000 0.000 0.000
#> GSM711905 2 0.0000 0.9764 0.000 1.000 0.000 0.000 0.000
#> GSM711907 2 0.0000 0.9764 0.000 1.000 0.000 0.000 0.000
#> GSM711909 3 0.0162 0.9083 0.000 0.000 0.996 0.000 0.004
#> GSM711911 3 0.0162 0.9083 0.000 0.000 0.996 0.000 0.004
#> GSM711915 2 0.0898 0.9536 0.000 0.972 0.000 0.008 0.020
#> GSM711917 2 0.0000 0.9764 0.000 1.000 0.000 0.000 0.000
#> GSM711923 1 0.2583 0.8386 0.864 0.000 0.004 0.132 0.000
#> GSM711925 2 0.0000 0.9764 0.000 1.000 0.000 0.000 0.000
#> GSM711927 3 0.0162 0.9083 0.000 0.000 0.996 0.000 0.004
#> GSM711929 2 0.0000 0.9764 0.000 1.000 0.000 0.000 0.000
#> GSM711931 4 0.1544 0.9015 0.000 0.068 0.000 0.932 0.000
#> GSM711933 1 0.1121 0.9331 0.956 0.000 0.000 0.000 0.044
#> GSM711935 2 0.0000 0.9764 0.000 1.000 0.000 0.000 0.000
#> GSM711941 1 0.1197 0.9175 0.952 0.000 0.000 0.048 0.000
#> GSM711943 3 0.5125 0.5955 0.184 0.000 0.708 0.100 0.008
#> GSM711945 3 0.5710 0.0875 0.000 0.448 0.492 0.028 0.032
#> GSM711947 2 0.0290 0.9702 0.000 0.992 0.000 0.008 0.000
#> GSM711949 2 0.0000 0.9764 0.000 1.000 0.000 0.000 0.000
#> GSM711953 2 0.0000 0.9764 0.000 1.000 0.000 0.000 0.000
#> GSM711955 1 0.0290 0.9352 0.992 0.000 0.000 0.000 0.008
#> GSM711963 2 0.0000 0.9764 0.000 1.000 0.000 0.000 0.000
#> GSM711971 3 0.0162 0.9083 0.000 0.000 0.996 0.000 0.004
#> GSM711975 2 0.0000 0.9764 0.000 1.000 0.000 0.000 0.000
#> GSM711979 1 0.3774 0.5996 0.704 0.000 0.000 0.296 0.000
#> GSM711989 2 0.0000 0.9764 0.000 1.000 0.000 0.000 0.000
#> GSM711991 2 0.5286 0.0413 0.000 0.516 0.444 0.008 0.032
#> GSM711993 4 0.0290 0.9765 0.008 0.000 0.000 0.992 0.000
#> GSM711983 3 0.1544 0.8476 0.068 0.000 0.932 0.000 0.000
#> GSM711985 2 0.0000 0.9764 0.000 1.000 0.000 0.000 0.000
#> GSM711913 3 0.0162 0.9046 0.000 0.000 0.996 0.004 0.000
#> GSM711919 3 0.0162 0.9083 0.000 0.000 0.996 0.000 0.004
#> GSM711921 3 0.0162 0.9083 0.000 0.000 0.996 0.000 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM711936 2 0.0000 0.9732 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711938 2 0.0000 0.9732 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711950 1 0.3318 0.7508 0.796 0.000 0.000 0.032 0.172 0.000
#> GSM711956 1 0.1444 0.7857 0.928 0.000 0.000 0.000 0.000 0.072
#> GSM711958 1 0.0865 0.7912 0.964 0.000 0.000 0.000 0.036 0.000
#> GSM711960 3 0.5614 0.3041 0.112 0.000 0.568 0.000 0.020 0.300
#> GSM711964 6 0.3690 0.6803 0.308 0.000 0.000 0.000 0.008 0.684
#> GSM711966 1 0.2118 0.7646 0.888 0.000 0.000 0.000 0.008 0.104
#> GSM711968 6 0.3907 0.5386 0.408 0.000 0.000 0.000 0.004 0.588
#> GSM711972 1 0.1075 0.7895 0.952 0.000 0.000 0.000 0.000 0.048
#> GSM711976 1 0.3168 0.7552 0.804 0.000 0.000 0.024 0.172 0.000
#> GSM711980 1 0.1858 0.7762 0.904 0.000 0.000 0.000 0.004 0.092
#> GSM711986 1 0.2442 0.7244 0.852 0.000 0.000 0.000 0.004 0.144
#> GSM711904 6 0.0000 0.7370 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM711906 1 0.2053 0.7663 0.888 0.000 0.000 0.000 0.004 0.108
#> GSM711908 6 0.0260 0.7320 0.000 0.000 0.000 0.000 0.008 0.992
#> GSM711910 3 0.0260 0.8633 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM711914 1 0.1644 0.7844 0.920 0.000 0.000 0.000 0.004 0.076
#> GSM711916 6 0.0717 0.7376 0.008 0.000 0.000 0.000 0.016 0.976
#> GSM711922 1 0.1501 0.7844 0.924 0.000 0.000 0.000 0.000 0.076
#> GSM711924 1 0.2048 0.7801 0.880 0.000 0.000 0.000 0.120 0.000
#> GSM711926 4 0.0000 0.9394 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM711928 6 0.3934 0.6010 0.376 0.000 0.000 0.000 0.008 0.616
#> GSM711930 6 0.0363 0.7345 0.000 0.000 0.000 0.000 0.012 0.988
#> GSM711932 1 0.3279 0.7520 0.796 0.000 0.000 0.028 0.176 0.000
#> GSM711934 1 0.1858 0.7762 0.904 0.000 0.000 0.000 0.004 0.092
#> GSM711940 1 0.2405 0.7630 0.880 0.000 0.004 0.000 0.016 0.100
#> GSM711942 1 0.1714 0.7777 0.908 0.000 0.000 0.000 0.000 0.092
#> GSM711944 1 0.3088 0.7569 0.808 0.000 0.000 0.020 0.172 0.000
#> GSM711946 3 0.2003 0.7993 0.000 0.000 0.884 0.000 0.116 0.000
#> GSM711948 1 0.3245 0.7531 0.800 0.000 0.000 0.028 0.172 0.000
#> GSM711952 6 0.0000 0.7370 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM711954 6 0.1918 0.7367 0.088 0.000 0.000 0.000 0.008 0.904
#> GSM711962 1 0.1714 0.7780 0.908 0.000 0.000 0.000 0.000 0.092
#> GSM711970 6 0.0000 0.7370 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM711974 1 0.5294 -0.2055 0.508 0.000 0.056 0.000 0.020 0.416
#> GSM711978 4 0.0260 0.9397 0.000 0.000 0.000 0.992 0.008 0.000
#> GSM711988 1 0.3245 0.7531 0.800 0.000 0.000 0.028 0.172 0.000
#> GSM711990 3 0.0458 0.8608 0.000 0.000 0.984 0.000 0.016 0.000
#> GSM711992 4 0.1444 0.9064 0.000 0.000 0.000 0.928 0.072 0.000
#> GSM711982 1 0.2302 0.7487 0.872 0.000 0.000 0.000 0.008 0.120
#> GSM711984 2 0.0146 0.9721 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM711912 6 0.3684 0.6556 0.332 0.000 0.000 0.000 0.004 0.664
#> GSM711918 6 0.3881 0.5622 0.396 0.000 0.000 0.000 0.004 0.600
#> GSM711920 1 0.2135 0.7787 0.872 0.000 0.000 0.000 0.128 0.000
#> GSM711937 2 0.0000 0.9732 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711939 2 0.0000 0.9732 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711951 2 0.0000 0.9732 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711957 4 0.2579 0.8293 0.040 0.000 0.000 0.872 0.088 0.000
#> GSM711959 2 0.0146 0.9721 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM711961 2 0.0146 0.9721 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM711965 3 0.0260 0.8623 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM711967 1 0.2048 0.7808 0.880 0.000 0.000 0.000 0.120 0.000
#> GSM711969 2 0.0000 0.9732 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711973 1 0.4117 0.6934 0.716 0.000 0.000 0.056 0.228 0.000
#> GSM711977 3 0.5762 0.4602 0.104 0.000 0.608 0.052 0.236 0.000
#> GSM711981 4 0.0146 0.9402 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM711987 2 0.0000 0.9732 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711905 2 0.0146 0.9721 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM711907 2 0.0865 0.9345 0.000 0.964 0.000 0.000 0.036 0.000
#> GSM711909 3 0.0260 0.8633 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM711911 3 0.0146 0.8635 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM711915 5 0.3915 0.4460 0.000 0.412 0.004 0.000 0.584 0.000
#> GSM711917 2 0.0000 0.9732 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711923 1 0.5373 0.5614 0.596 0.000 0.004 0.152 0.248 0.000
#> GSM711925 2 0.0146 0.9721 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM711927 3 0.0260 0.8633 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM711929 2 0.0146 0.9721 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM711931 4 0.1444 0.8505 0.000 0.072 0.000 0.928 0.000 0.000
#> GSM711933 1 0.1858 0.7762 0.904 0.000 0.000 0.000 0.004 0.092
#> GSM711935 2 0.0146 0.9721 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM711941 1 0.3646 0.7371 0.776 0.000 0.000 0.052 0.172 0.000
#> GSM711943 3 0.6210 0.4669 0.108 0.000 0.596 0.132 0.164 0.000
#> GSM711945 5 0.4523 0.6343 0.000 0.084 0.112 0.048 0.756 0.000
#> GSM711947 2 0.3717 0.0541 0.000 0.616 0.000 0.000 0.384 0.000
#> GSM711949 2 0.0146 0.9721 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM711953 2 0.0000 0.9732 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711955 1 0.1382 0.7914 0.948 0.000 0.008 0.000 0.036 0.008
#> GSM711963 2 0.0000 0.9732 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711971 3 0.0363 0.8615 0.000 0.000 0.988 0.000 0.012 0.000
#> GSM711975 2 0.0000 0.9732 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711979 1 0.5645 0.3340 0.508 0.000 0.000 0.320 0.172 0.000
#> GSM711989 2 0.0000 0.9732 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711991 5 0.4308 0.7080 0.000 0.152 0.120 0.000 0.728 0.000
#> GSM711993 4 0.0260 0.9401 0.000 0.000 0.000 0.992 0.008 0.000
#> GSM711983 3 0.2134 0.8028 0.052 0.000 0.904 0.000 0.044 0.000
#> GSM711985 2 0.0000 0.9732 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711913 3 0.2333 0.7932 0.004 0.000 0.872 0.004 0.120 0.000
#> GSM711919 3 0.0146 0.8632 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM711921 3 0.0260 0.8633 0.000 0.000 0.992 0.000 0.008 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) disease.state(p) individual(p) k
#> ATC:skmeans 89 1.99e-05 0.227 0.726 2
#> ATC:skmeans 83 5.53e-06 0.131 0.319 3
#> ATC:skmeans 87 1.01e-08 0.127 0.585 4
#> ATC:skmeans 88 4.44e-08 0.239 0.369 5
#> ATC:skmeans 83 4.02e-07 0.147 0.333 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "pam"]
# you can also extract it by
# res = res_list["ATC:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 27425 rows and 90 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4063 0.594 0.594
#> 3 3 0.848 0.858 0.943 0.4147 0.787 0.649
#> 4 4 0.969 0.936 0.975 0.0928 0.944 0.867
#> 5 5 0.650 0.772 0.857 0.1401 0.898 0.734
#> 6 6 0.762 0.784 0.829 0.1124 0.821 0.448
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 2
There is also optional best \(k\) = 2 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM711936 2 0.0000 1.000 0.000 1.000
#> GSM711938 2 0.0000 1.000 0.000 1.000
#> GSM711950 1 0.0000 1.000 1.000 0.000
#> GSM711956 1 0.0000 1.000 1.000 0.000
#> GSM711958 1 0.0000 1.000 1.000 0.000
#> GSM711960 1 0.0000 1.000 1.000 0.000
#> GSM711964 1 0.0000 1.000 1.000 0.000
#> GSM711966 1 0.0000 1.000 1.000 0.000
#> GSM711968 1 0.0000 1.000 1.000 0.000
#> GSM711972 1 0.0000 1.000 1.000 0.000
#> GSM711976 1 0.0000 1.000 1.000 0.000
#> GSM711980 1 0.0000 1.000 1.000 0.000
#> GSM711986 1 0.0000 1.000 1.000 0.000
#> GSM711904 1 0.0000 1.000 1.000 0.000
#> GSM711906 1 0.0000 1.000 1.000 0.000
#> GSM711908 1 0.0000 1.000 1.000 0.000
#> GSM711910 1 0.0000 1.000 1.000 0.000
#> GSM711914 1 0.0000 1.000 1.000 0.000
#> GSM711916 1 0.0000 1.000 1.000 0.000
#> GSM711922 1 0.0000 1.000 1.000 0.000
#> GSM711924 1 0.0000 1.000 1.000 0.000
#> GSM711926 1 0.0000 1.000 1.000 0.000
#> GSM711928 1 0.0000 1.000 1.000 0.000
#> GSM711930 1 0.0000 1.000 1.000 0.000
#> GSM711932 1 0.0000 1.000 1.000 0.000
#> GSM711934 1 0.0000 1.000 1.000 0.000
#> GSM711940 1 0.0000 1.000 1.000 0.000
#> GSM711942 1 0.0000 1.000 1.000 0.000
#> GSM711944 1 0.0000 1.000 1.000 0.000
#> GSM711946 1 0.0000 1.000 1.000 0.000
#> GSM711948 1 0.0000 1.000 1.000 0.000
#> GSM711952 1 0.0000 1.000 1.000 0.000
#> GSM711954 1 0.0000 1.000 1.000 0.000
#> GSM711962 1 0.0000 1.000 1.000 0.000
#> GSM711970 1 0.0000 1.000 1.000 0.000
#> GSM711974 1 0.0000 1.000 1.000 0.000
#> GSM711978 1 0.0000 1.000 1.000 0.000
#> GSM711988 1 0.0000 1.000 1.000 0.000
#> GSM711990 1 0.0000 1.000 1.000 0.000
#> GSM711992 1 0.0000 1.000 1.000 0.000
#> GSM711982 1 0.0000 1.000 1.000 0.000
#> GSM711984 2 0.0000 1.000 0.000 1.000
#> GSM711912 1 0.0000 1.000 1.000 0.000
#> GSM711918 1 0.0000 1.000 1.000 0.000
#> GSM711920 1 0.0000 1.000 1.000 0.000
#> GSM711937 2 0.0000 1.000 0.000 1.000
#> GSM711939 2 0.0000 1.000 0.000 1.000
#> GSM711951 2 0.0000 1.000 0.000 1.000
#> GSM711957 1 0.0000 1.000 1.000 0.000
#> GSM711959 2 0.0000 1.000 0.000 1.000
#> GSM711961 2 0.0000 1.000 0.000 1.000
#> GSM711965 1 0.0000 1.000 1.000 0.000
#> GSM711967 1 0.0000 1.000 1.000 0.000
#> GSM711969 2 0.0000 1.000 0.000 1.000
#> GSM711973 1 0.0000 1.000 1.000 0.000
#> GSM711977 1 0.0000 1.000 1.000 0.000
#> GSM711981 1 0.0000 1.000 1.000 0.000
#> GSM711987 2 0.0000 1.000 0.000 1.000
#> GSM711905 2 0.0000 1.000 0.000 1.000
#> GSM711907 2 0.0000 1.000 0.000 1.000
#> GSM711909 1 0.0000 1.000 1.000 0.000
#> GSM711911 1 0.0000 1.000 1.000 0.000
#> GSM711915 2 0.0376 0.996 0.004 0.996
#> GSM711917 2 0.0000 1.000 0.000 1.000
#> GSM711923 1 0.0000 1.000 1.000 0.000
#> GSM711925 2 0.0000 1.000 0.000 1.000
#> GSM711927 1 0.0000 1.000 1.000 0.000
#> GSM711929 2 0.0000 1.000 0.000 1.000
#> GSM711931 2 0.0000 1.000 0.000 1.000
#> GSM711933 1 0.0000 1.000 1.000 0.000
#> GSM711935 2 0.0000 1.000 0.000 1.000
#> GSM711941 1 0.0000 1.000 1.000 0.000
#> GSM711943 1 0.0000 1.000 1.000 0.000
#> GSM711945 1 0.0000 1.000 1.000 0.000
#> GSM711947 2 0.0000 1.000 0.000 1.000
#> GSM711949 2 0.0000 1.000 0.000 1.000
#> GSM711953 2 0.0000 1.000 0.000 1.000
#> GSM711955 1 0.0000 1.000 1.000 0.000
#> GSM711963 2 0.0000 1.000 0.000 1.000
#> GSM711971 1 0.0000 1.000 1.000 0.000
#> GSM711975 2 0.0000 1.000 0.000 1.000
#> GSM711979 1 0.0000 1.000 1.000 0.000
#> GSM711989 2 0.0000 1.000 0.000 1.000
#> GSM711991 1 0.0000 1.000 1.000 0.000
#> GSM711993 1 0.0000 1.000 1.000 0.000
#> GSM711983 1 0.0000 1.000 1.000 0.000
#> GSM711985 2 0.0000 1.000 0.000 1.000
#> GSM711913 1 0.0000 1.000 1.000 0.000
#> GSM711919 1 0.0000 1.000 1.000 0.000
#> GSM711921 1 0.0000 1.000 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM711936 2 0.0000 0.9351 0.000 1.000 0.000
#> GSM711938 2 0.0000 0.9351 0.000 1.000 0.000
#> GSM711950 1 0.0000 0.9812 1.000 0.000 0.000
#> GSM711956 1 0.0000 0.9812 1.000 0.000 0.000
#> GSM711958 1 0.0000 0.9812 1.000 0.000 0.000
#> GSM711960 1 0.0000 0.9812 1.000 0.000 0.000
#> GSM711964 1 0.0000 0.9812 1.000 0.000 0.000
#> GSM711966 1 0.0000 0.9812 1.000 0.000 0.000
#> GSM711968 1 0.0000 0.9812 1.000 0.000 0.000
#> GSM711972 1 0.0000 0.9812 1.000 0.000 0.000
#> GSM711976 1 0.0000 0.9812 1.000 0.000 0.000
#> GSM711980 1 0.0000 0.9812 1.000 0.000 0.000
#> GSM711986 1 0.0000 0.9812 1.000 0.000 0.000
#> GSM711904 1 0.0000 0.9812 1.000 0.000 0.000
#> GSM711906 1 0.0000 0.9812 1.000 0.000 0.000
#> GSM711908 1 0.6180 0.0854 0.584 0.000 0.416
#> GSM711910 1 0.0000 0.9812 1.000 0.000 0.000
#> GSM711914 1 0.0000 0.9812 1.000 0.000 0.000
#> GSM711916 1 0.0000 0.9812 1.000 0.000 0.000
#> GSM711922 1 0.0000 0.9812 1.000 0.000 0.000
#> GSM711924 1 0.0000 0.9812 1.000 0.000 0.000
#> GSM711926 3 0.0000 0.7228 0.000 0.000 1.000
#> GSM711928 1 0.0000 0.9812 1.000 0.000 0.000
#> GSM711930 1 0.0000 0.9812 1.000 0.000 0.000
#> GSM711932 1 0.0000 0.9812 1.000 0.000 0.000
#> GSM711934 1 0.0000 0.9812 1.000 0.000 0.000
#> GSM711940 1 0.0000 0.9812 1.000 0.000 0.000
#> GSM711942 1 0.0000 0.9812 1.000 0.000 0.000
#> GSM711944 1 0.0000 0.9812 1.000 0.000 0.000
#> GSM711946 1 0.5291 0.5391 0.732 0.000 0.268
#> GSM711948 1 0.0000 0.9812 1.000 0.000 0.000
#> GSM711952 3 0.6180 0.4398 0.416 0.000 0.584
#> GSM711954 1 0.0000 0.9812 1.000 0.000 0.000
#> GSM711962 1 0.0000 0.9812 1.000 0.000 0.000
#> GSM711970 3 0.6180 0.4398 0.416 0.000 0.584
#> GSM711974 1 0.0000 0.9812 1.000 0.000 0.000
#> GSM711978 3 0.0000 0.7228 0.000 0.000 1.000
#> GSM711988 1 0.0000 0.9812 1.000 0.000 0.000
#> GSM711990 1 0.0000 0.9812 1.000 0.000 0.000
#> GSM711992 3 0.0000 0.7228 0.000 0.000 1.000
#> GSM711982 1 0.0000 0.9812 1.000 0.000 0.000
#> GSM711984 2 0.0000 0.9351 0.000 1.000 0.000
#> GSM711912 1 0.1964 0.9176 0.944 0.000 0.056
#> GSM711918 1 0.0424 0.9730 0.992 0.000 0.008
#> GSM711920 1 0.0000 0.9812 1.000 0.000 0.000
#> GSM711937 2 0.0000 0.9351 0.000 1.000 0.000
#> GSM711939 2 0.0000 0.9351 0.000 1.000 0.000
#> GSM711951 3 0.0000 0.7228 0.000 0.000 1.000
#> GSM711957 3 0.4002 0.6822 0.160 0.000 0.840
#> GSM711959 2 0.0000 0.9351 0.000 1.000 0.000
#> GSM711961 2 0.0000 0.9351 0.000 1.000 0.000
#> GSM711965 1 0.0000 0.9812 1.000 0.000 0.000
#> GSM711967 1 0.1289 0.9465 0.968 0.000 0.032
#> GSM711969 2 0.0000 0.9351 0.000 1.000 0.000
#> GSM711973 1 0.0000 0.9812 1.000 0.000 0.000
#> GSM711977 1 0.0000 0.9812 1.000 0.000 0.000
#> GSM711981 3 0.0000 0.7228 0.000 0.000 1.000
#> GSM711987 2 0.0000 0.9351 0.000 1.000 0.000
#> GSM711905 2 0.0000 0.9351 0.000 1.000 0.000
#> GSM711907 2 0.6180 0.4332 0.000 0.584 0.416
#> GSM711909 1 0.0000 0.9812 1.000 0.000 0.000
#> GSM711911 1 0.0000 0.9812 1.000 0.000 0.000
#> GSM711915 3 0.5291 0.3724 0.000 0.268 0.732
#> GSM711917 2 0.0000 0.9351 0.000 1.000 0.000
#> GSM711923 3 0.6180 0.4398 0.416 0.000 0.584
#> GSM711925 2 0.0000 0.9351 0.000 1.000 0.000
#> GSM711927 1 0.0000 0.9812 1.000 0.000 0.000
#> GSM711929 2 0.0000 0.9351 0.000 1.000 0.000
#> GSM711931 3 0.0000 0.7228 0.000 0.000 1.000
#> GSM711933 1 0.0000 0.9812 1.000 0.000 0.000
#> GSM711935 2 0.0000 0.9351 0.000 1.000 0.000
#> GSM711941 1 0.0000 0.9812 1.000 0.000 0.000
#> GSM711943 3 0.6180 0.4398 0.416 0.000 0.584
#> GSM711945 3 0.0000 0.7228 0.000 0.000 1.000
#> GSM711947 2 0.6180 0.4332 0.000 0.584 0.416
#> GSM711949 2 0.0000 0.9351 0.000 1.000 0.000
#> GSM711953 2 0.0000 0.9351 0.000 1.000 0.000
#> GSM711955 1 0.0000 0.9812 1.000 0.000 0.000
#> GSM711963 2 0.0000 0.9351 0.000 1.000 0.000
#> GSM711971 1 0.0000 0.9812 1.000 0.000 0.000
#> GSM711975 3 0.6045 0.0861 0.000 0.380 0.620
#> GSM711979 3 0.6180 0.4398 0.416 0.000 0.584
#> GSM711989 2 0.6180 0.4332 0.000 0.584 0.416
#> GSM711991 3 0.0000 0.7228 0.000 0.000 1.000
#> GSM711993 3 0.0000 0.7228 0.000 0.000 1.000
#> GSM711983 1 0.0000 0.9812 1.000 0.000 0.000
#> GSM711985 2 0.0000 0.9351 0.000 1.000 0.000
#> GSM711913 3 0.5098 0.6390 0.248 0.000 0.752
#> GSM711919 1 0.0000 0.9812 1.000 0.000 0.000
#> GSM711921 1 0.0000 0.9812 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM711936 2 0.0000 0.963 0.000 1.000 0.000 0.000
#> GSM711938 2 0.0000 0.963 0.000 1.000 0.000 0.000
#> GSM711950 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM711956 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM711958 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM711960 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM711964 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM711966 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM711968 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM711972 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM711976 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM711980 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM711986 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM711904 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM711906 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM711908 4 0.3726 0.641 0.212 0.000 0.000 0.788
#> GSM711910 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM711914 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM711916 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM711922 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM711924 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM711926 4 0.0000 0.929 0.000 0.000 0.000 1.000
#> GSM711928 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM711930 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM711932 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM711934 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM711940 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM711942 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM711944 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM711946 1 0.4304 0.582 0.716 0.000 0.000 0.284
#> GSM711948 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM711952 4 0.0817 0.920 0.024 0.000 0.000 0.976
#> GSM711954 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM711962 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM711970 4 0.0817 0.920 0.024 0.000 0.000 0.976
#> GSM711974 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM711978 4 0.0000 0.929 0.000 0.000 0.000 1.000
#> GSM711988 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM711990 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM711992 4 0.0000 0.929 0.000 0.000 0.000 1.000
#> GSM711982 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM711984 3 0.0000 0.996 0.000 0.000 1.000 0.000
#> GSM711912 1 0.4713 0.423 0.640 0.000 0.000 0.360
#> GSM711918 1 0.3074 0.807 0.848 0.000 0.000 0.152
#> GSM711920 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM711937 2 0.0000 0.963 0.000 1.000 0.000 0.000
#> GSM711939 2 0.0000 0.963 0.000 1.000 0.000 0.000
#> GSM711951 4 0.0000 0.929 0.000 0.000 0.000 1.000
#> GSM711957 4 0.0188 0.928 0.004 0.000 0.000 0.996
#> GSM711959 2 0.2814 0.849 0.000 0.868 0.132 0.000
#> GSM711961 2 0.1302 0.935 0.000 0.956 0.044 0.000
#> GSM711965 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM711967 1 0.4193 0.623 0.732 0.000 0.000 0.268
#> GSM711969 2 0.0000 0.963 0.000 1.000 0.000 0.000
#> GSM711973 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM711977 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM711981 4 0.0000 0.929 0.000 0.000 0.000 1.000
#> GSM711987 2 0.0000 0.963 0.000 1.000 0.000 0.000
#> GSM711905 3 0.0000 0.996 0.000 0.000 1.000 0.000
#> GSM711907 2 0.0817 0.954 0.000 0.976 0.000 0.024
#> GSM711909 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM711911 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM711915 2 0.3837 0.720 0.000 0.776 0.000 0.224
#> GSM711917 2 0.0000 0.963 0.000 1.000 0.000 0.000
#> GSM711923 4 0.0817 0.920 0.024 0.000 0.000 0.976
#> GSM711925 3 0.0000 0.996 0.000 0.000 1.000 0.000
#> GSM711927 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM711929 3 0.0817 0.978 0.000 0.024 0.976 0.000
#> GSM711931 4 0.0000 0.929 0.000 0.000 0.000 1.000
#> GSM711933 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM711935 3 0.0000 0.996 0.000 0.000 1.000 0.000
#> GSM711941 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM711943 4 0.0817 0.920 0.024 0.000 0.000 0.976
#> GSM711945 4 0.0000 0.929 0.000 0.000 0.000 1.000
#> GSM711947 2 0.0817 0.954 0.000 0.976 0.000 0.024
#> GSM711949 3 0.0000 0.996 0.000 0.000 1.000 0.000
#> GSM711953 2 0.0000 0.963 0.000 1.000 0.000 0.000
#> GSM711955 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM711963 3 0.0000 0.996 0.000 0.000 1.000 0.000
#> GSM711971 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM711975 2 0.1211 0.943 0.000 0.960 0.000 0.040
#> GSM711979 4 0.0817 0.920 0.024 0.000 0.000 0.976
#> GSM711989 2 0.0817 0.954 0.000 0.976 0.000 0.024
#> GSM711991 4 0.0000 0.929 0.000 0.000 0.000 1.000
#> GSM711993 4 0.0000 0.929 0.000 0.000 0.000 1.000
#> GSM711983 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM711985 2 0.0000 0.963 0.000 1.000 0.000 0.000
#> GSM711913 4 0.4643 0.423 0.344 0.000 0.000 0.656
#> GSM711919 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM711921 1 0.0000 0.976 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM711936 2 0.2377 0.8670 0.000 0.872 0.128 0.000 0.000
#> GSM711938 2 0.0000 0.8794 0.000 1.000 0.000 0.000 0.000
#> GSM711950 1 0.2674 0.8230 0.856 0.000 0.004 0.140 0.000
#> GSM711956 1 0.2471 0.8255 0.864 0.000 0.000 0.136 0.000
#> GSM711958 1 0.0404 0.8375 0.988 0.000 0.012 0.000 0.000
#> GSM711960 1 0.0000 0.8355 1.000 0.000 0.000 0.000 0.000
#> GSM711964 1 0.1851 0.8148 0.912 0.000 0.088 0.000 0.000
#> GSM711966 1 0.1851 0.8148 0.912 0.000 0.088 0.000 0.000
#> GSM711968 1 0.1608 0.8220 0.928 0.000 0.072 0.000 0.000
#> GSM711972 1 0.4334 0.7927 0.768 0.000 0.092 0.140 0.000
#> GSM711976 1 0.2674 0.8230 0.856 0.000 0.004 0.140 0.000
#> GSM711980 1 0.0000 0.8355 1.000 0.000 0.000 0.000 0.000
#> GSM711986 1 0.4334 0.7927 0.768 0.000 0.092 0.140 0.000
#> GSM711904 1 0.1608 0.8220 0.928 0.000 0.072 0.000 0.000
#> GSM711906 1 0.1121 0.8331 0.956 0.000 0.044 0.000 0.000
#> GSM711908 4 0.6323 0.2898 0.220 0.000 0.252 0.528 0.000
#> GSM711910 3 0.4060 0.7996 0.360 0.000 0.640 0.000 0.000
#> GSM711914 1 0.4104 0.8043 0.788 0.000 0.088 0.124 0.000
#> GSM711916 1 0.1851 0.8148 0.912 0.000 0.088 0.000 0.000
#> GSM711922 1 0.2909 0.8219 0.848 0.000 0.012 0.140 0.000
#> GSM711924 1 0.2674 0.8230 0.856 0.000 0.004 0.140 0.000
#> GSM711926 4 0.2516 0.7936 0.000 0.000 0.140 0.860 0.000
#> GSM711928 1 0.1608 0.8220 0.928 0.000 0.072 0.000 0.000
#> GSM711930 3 0.3895 0.7077 0.320 0.000 0.680 0.000 0.000
#> GSM711932 1 0.2674 0.8230 0.856 0.000 0.004 0.140 0.000
#> GSM711934 1 0.0162 0.8361 0.996 0.000 0.004 0.000 0.000
#> GSM711940 1 0.0000 0.8355 1.000 0.000 0.000 0.000 0.000
#> GSM711942 1 0.0000 0.8355 1.000 0.000 0.000 0.000 0.000
#> GSM711944 1 0.2674 0.8230 0.856 0.000 0.004 0.140 0.000
#> GSM711946 1 0.4249 0.0269 0.568 0.000 0.000 0.432 0.000
#> GSM711948 1 0.2674 0.8230 0.856 0.000 0.004 0.140 0.000
#> GSM711952 4 0.4054 0.6831 0.140 0.000 0.072 0.788 0.000
#> GSM711954 1 0.1608 0.8220 0.928 0.000 0.072 0.000 0.000
#> GSM711962 1 0.0510 0.8362 0.984 0.000 0.016 0.000 0.000
#> GSM711970 4 0.6220 0.0476 0.140 0.000 0.428 0.432 0.000
#> GSM711974 1 0.0000 0.8355 1.000 0.000 0.000 0.000 0.000
#> GSM711978 4 0.2516 0.7936 0.000 0.000 0.140 0.860 0.000
#> GSM711988 1 0.2674 0.8230 0.856 0.000 0.004 0.140 0.000
#> GSM711990 3 0.4192 0.7588 0.404 0.000 0.596 0.000 0.000
#> GSM711992 4 0.2516 0.7936 0.000 0.000 0.140 0.860 0.000
#> GSM711982 1 0.1851 0.8148 0.912 0.000 0.088 0.000 0.000
#> GSM711984 5 0.0000 0.9735 0.000 0.000 0.000 0.000 1.000
#> GSM711912 1 0.3416 0.7530 0.840 0.000 0.088 0.072 0.000
#> GSM711918 1 0.3962 0.8099 0.800 0.000 0.088 0.112 0.000
#> GSM711920 1 0.2674 0.8230 0.856 0.000 0.004 0.140 0.000
#> GSM711937 2 0.0000 0.8794 0.000 1.000 0.000 0.000 0.000
#> GSM711939 2 0.0000 0.8794 0.000 1.000 0.000 0.000 0.000
#> GSM711951 4 0.3612 0.7066 0.000 0.000 0.268 0.732 0.000
#> GSM711957 4 0.0000 0.7672 0.000 0.000 0.000 1.000 0.000
#> GSM711959 2 0.2852 0.7573 0.000 0.828 0.000 0.000 0.172
#> GSM711961 2 0.0794 0.8643 0.000 0.972 0.000 0.000 0.028
#> GSM711965 1 0.3039 0.5638 0.808 0.000 0.192 0.000 0.000
#> GSM711967 1 0.3724 0.7783 0.776 0.000 0.020 0.204 0.000
#> GSM711969 2 0.2377 0.8670 0.000 0.872 0.128 0.000 0.000
#> GSM711973 1 0.2674 0.8230 0.856 0.000 0.004 0.140 0.000
#> GSM711977 1 0.3928 0.6544 0.700 0.000 0.004 0.296 0.000
#> GSM711981 4 0.0000 0.7672 0.000 0.000 0.000 1.000 0.000
#> GSM711987 2 0.0000 0.8794 0.000 1.000 0.000 0.000 0.000
#> GSM711905 5 0.0000 0.9735 0.000 0.000 0.000 0.000 1.000
#> GSM711907 2 0.4268 0.7929 0.000 0.708 0.268 0.024 0.000
#> GSM711909 3 0.4060 0.7996 0.360 0.000 0.640 0.000 0.000
#> GSM711911 3 0.4227 0.7316 0.420 0.000 0.580 0.000 0.000
#> GSM711915 3 0.2260 0.3706 0.000 0.064 0.908 0.028 0.000
#> GSM711917 2 0.2377 0.8670 0.000 0.872 0.128 0.000 0.000
#> GSM711923 4 0.2773 0.7133 0.164 0.000 0.000 0.836 0.000
#> GSM711925 5 0.0000 0.9735 0.000 0.000 0.000 0.000 1.000
#> GSM711927 3 0.4060 0.7996 0.360 0.000 0.640 0.000 0.000
#> GSM711929 5 0.2732 0.8185 0.000 0.160 0.000 0.000 0.840
#> GSM711931 4 0.2516 0.7936 0.000 0.000 0.140 0.860 0.000
#> GSM711933 1 0.0000 0.8355 1.000 0.000 0.000 0.000 0.000
#> GSM711935 5 0.0000 0.9735 0.000 0.000 0.000 0.000 1.000
#> GSM711941 1 0.2674 0.8230 0.856 0.000 0.004 0.140 0.000
#> GSM711943 4 0.2773 0.7133 0.164 0.000 0.000 0.836 0.000
#> GSM711945 4 0.2516 0.7936 0.000 0.000 0.140 0.860 0.000
#> GSM711947 2 0.4268 0.7929 0.000 0.708 0.268 0.024 0.000
#> GSM711949 5 0.0000 0.9735 0.000 0.000 0.000 0.000 1.000
#> GSM711953 2 0.0000 0.8794 0.000 1.000 0.000 0.000 0.000
#> GSM711955 1 0.0000 0.8355 1.000 0.000 0.000 0.000 0.000
#> GSM711963 5 0.0000 0.9735 0.000 0.000 0.000 0.000 1.000
#> GSM711971 1 0.2690 0.6418 0.844 0.000 0.156 0.000 0.000
#> GSM711975 2 0.4350 0.7897 0.000 0.704 0.268 0.028 0.000
#> GSM711979 4 0.0865 0.7482 0.024 0.000 0.004 0.972 0.000
#> GSM711989 2 0.4268 0.7929 0.000 0.708 0.268 0.024 0.000
#> GSM711991 3 0.4114 -0.0741 0.000 0.000 0.624 0.376 0.000
#> GSM711993 4 0.0000 0.7672 0.000 0.000 0.000 1.000 0.000
#> GSM711983 1 0.0000 0.8355 1.000 0.000 0.000 0.000 0.000
#> GSM711985 2 0.0000 0.8794 0.000 1.000 0.000 0.000 0.000
#> GSM711913 3 0.4973 0.4216 0.048 0.000 0.632 0.320 0.000
#> GSM711919 3 0.4060 0.7996 0.360 0.000 0.640 0.000 0.000
#> GSM711921 3 0.4060 0.7996 0.360 0.000 0.640 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM711936 2 0.3364 0.7655 0.000 0.780 0.024 0.000 0.196 0.000
#> GSM711938 2 0.0000 0.7933 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711950 5 0.2823 0.9174 0.204 0.000 0.000 0.000 0.796 0.000
#> GSM711956 5 0.3390 0.8510 0.296 0.000 0.000 0.000 0.704 0.000
#> GSM711958 5 0.2996 0.9083 0.228 0.000 0.000 0.000 0.772 0.000
#> GSM711960 1 0.0632 0.8835 0.976 0.000 0.000 0.000 0.024 0.000
#> GSM711964 1 0.0000 0.8898 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711966 1 0.0146 0.8895 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM711968 1 0.0260 0.8890 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM711972 5 0.2854 0.9135 0.208 0.000 0.000 0.000 0.792 0.000
#> GSM711976 5 0.2762 0.9172 0.196 0.000 0.000 0.000 0.804 0.000
#> GSM711980 5 0.3672 0.7501 0.368 0.000 0.000 0.000 0.632 0.000
#> GSM711986 1 0.1444 0.8433 0.928 0.000 0.000 0.000 0.072 0.000
#> GSM711904 1 0.0000 0.8898 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711906 1 0.0790 0.8844 0.968 0.000 0.000 0.000 0.032 0.000
#> GSM711908 1 0.4209 0.6253 0.736 0.000 0.160 0.104 0.000 0.000
#> GSM711910 3 0.0632 0.8623 0.000 0.000 0.976 0.000 0.024 0.000
#> GSM711914 1 0.0937 0.8762 0.960 0.000 0.000 0.000 0.040 0.000
#> GSM711916 1 0.0000 0.8898 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711922 5 0.2854 0.9158 0.208 0.000 0.000 0.000 0.792 0.000
#> GSM711924 5 0.2793 0.9173 0.200 0.000 0.000 0.000 0.800 0.000
#> GSM711926 4 0.0000 0.7738 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM711928 1 0.0260 0.8890 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM711930 1 0.3390 0.5343 0.704 0.000 0.296 0.000 0.000 0.000
#> GSM711932 5 0.2762 0.9172 0.196 0.000 0.000 0.000 0.804 0.000
#> GSM711934 1 0.3747 0.0397 0.604 0.000 0.000 0.000 0.396 0.000
#> GSM711940 1 0.0713 0.8813 0.972 0.000 0.000 0.000 0.028 0.000
#> GSM711942 1 0.0937 0.8798 0.960 0.000 0.000 0.000 0.040 0.000
#> GSM711944 5 0.2854 0.9172 0.208 0.000 0.000 0.000 0.792 0.000
#> GSM711946 4 0.5460 0.4528 0.072 0.000 0.256 0.624 0.048 0.000
#> GSM711948 5 0.2762 0.9172 0.196 0.000 0.000 0.000 0.804 0.000
#> GSM711952 1 0.3595 0.5223 0.704 0.000 0.000 0.288 0.008 0.000
#> GSM711954 1 0.0000 0.8898 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711962 1 0.1814 0.8045 0.900 0.000 0.000 0.000 0.100 0.000
#> GSM711970 1 0.3547 0.5250 0.696 0.000 0.300 0.004 0.000 0.000
#> GSM711974 1 0.0632 0.8835 0.976 0.000 0.000 0.000 0.024 0.000
#> GSM711978 4 0.0000 0.7738 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM711988 5 0.2823 0.9174 0.204 0.000 0.000 0.000 0.796 0.000
#> GSM711990 3 0.1890 0.8389 0.060 0.000 0.916 0.000 0.024 0.000
#> GSM711992 4 0.0000 0.7738 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM711982 1 0.0260 0.8902 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM711984 6 0.0000 0.9535 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM711912 1 0.0260 0.8890 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM711918 1 0.0260 0.8890 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM711920 5 0.2793 0.9157 0.200 0.000 0.000 0.000 0.800 0.000
#> GSM711937 2 0.0146 0.7934 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM711939 2 0.0000 0.7933 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711951 4 0.3284 0.5596 0.000 0.000 0.020 0.784 0.196 0.000
#> GSM711957 4 0.3351 0.6561 0.000 0.000 0.000 0.712 0.288 0.000
#> GSM711959 2 0.2854 0.6341 0.000 0.792 0.000 0.000 0.000 0.208
#> GSM711961 2 0.0547 0.7809 0.000 0.980 0.000 0.000 0.000 0.020
#> GSM711965 3 0.3743 0.6372 0.252 0.000 0.724 0.000 0.024 0.000
#> GSM711967 5 0.2762 0.9172 0.196 0.000 0.000 0.000 0.804 0.000
#> GSM711969 2 0.3364 0.7655 0.000 0.780 0.024 0.000 0.196 0.000
#> GSM711973 5 0.2823 0.9174 0.204 0.000 0.000 0.000 0.796 0.000
#> GSM711977 5 0.3287 0.9033 0.220 0.000 0.000 0.012 0.768 0.000
#> GSM711981 4 0.3659 0.5282 0.000 0.000 0.000 0.636 0.364 0.000
#> GSM711987 2 0.0000 0.7933 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711905 6 0.0000 0.9535 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM711907 2 0.6193 0.6071 0.000 0.504 0.024 0.276 0.196 0.000
#> GSM711909 3 0.0632 0.8623 0.000 0.000 0.976 0.000 0.024 0.000
#> GSM711911 3 0.1890 0.8321 0.060 0.000 0.916 0.000 0.024 0.000
#> GSM711915 3 0.0000 0.8372 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM711917 2 0.3364 0.7655 0.000 0.780 0.024 0.000 0.196 0.000
#> GSM711923 4 0.3351 0.6561 0.000 0.000 0.000 0.712 0.288 0.000
#> GSM711925 6 0.0000 0.9535 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM711927 3 0.0632 0.8623 0.000 0.000 0.976 0.000 0.024 0.000
#> GSM711929 6 0.3221 0.6442 0.000 0.264 0.000 0.000 0.000 0.736
#> GSM711931 4 0.0000 0.7738 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM711933 1 0.0632 0.8835 0.976 0.000 0.000 0.000 0.024 0.000
#> GSM711935 6 0.0000 0.9535 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM711941 5 0.2823 0.9174 0.204 0.000 0.000 0.000 0.796 0.000
#> GSM711943 4 0.0000 0.7738 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM711945 4 0.0000 0.7738 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM711947 2 0.6231 0.5956 0.000 0.492 0.024 0.288 0.196 0.000
#> GSM711949 6 0.0000 0.9535 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM711953 2 0.0000 0.7933 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711955 5 0.3371 0.8543 0.292 0.000 0.000 0.000 0.708 0.000
#> GSM711963 6 0.0000 0.9535 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM711971 3 0.3897 0.5963 0.280 0.000 0.696 0.000 0.024 0.000
#> GSM711975 2 0.6254 0.5847 0.000 0.484 0.024 0.296 0.196 0.000
#> GSM711979 5 0.2996 0.5230 0.000 0.000 0.000 0.228 0.772 0.000
#> GSM711989 2 0.6231 0.5956 0.000 0.492 0.024 0.288 0.196 0.000
#> GSM711991 3 0.3151 0.5964 0.000 0.000 0.748 0.252 0.000 0.000
#> GSM711993 4 0.3351 0.6561 0.000 0.000 0.000 0.712 0.288 0.000
#> GSM711983 5 0.3371 0.8543 0.292 0.000 0.000 0.000 0.708 0.000
#> GSM711985 2 0.0000 0.7933 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711913 5 0.4471 0.0392 0.000 0.000 0.472 0.028 0.500 0.000
#> GSM711919 3 0.0632 0.8623 0.000 0.000 0.976 0.000 0.024 0.000
#> GSM711921 3 0.0632 0.8623 0.000 0.000 0.976 0.000 0.024 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) disease.state(p) individual(p) k
#> ATC:pam 90 2.27e-05 0.2329 0.530 2
#> ATC:pam 79 5.23e-05 0.5878 0.417 3
#> ATC:pam 88 4.96e-05 0.0964 0.465 4
#> ATC:pam 84 2.02e-05 0.0221 0.175 5
#> ATC:pam 87 2.04e-07 0.0785 0.324 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "mclust"]
# you can also extract it by
# res = res_list["ATC:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 27425 rows and 90 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.989 0.995 0.4289 0.575 0.575
#> 3 3 0.774 0.893 0.947 0.4474 0.766 0.610
#> 4 4 0.855 0.857 0.930 0.1590 0.853 0.630
#> 5 5 0.753 0.767 0.862 0.0498 0.912 0.707
#> 6 6 0.806 0.695 0.856 0.0530 0.897 0.631
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM711936 2 0.0000 1.000 0.000 1.000
#> GSM711938 2 0.0000 1.000 0.000 1.000
#> GSM711950 1 0.0000 0.993 1.000 0.000
#> GSM711956 1 0.0000 0.993 1.000 0.000
#> GSM711958 1 0.0000 0.993 1.000 0.000
#> GSM711960 1 0.0000 0.993 1.000 0.000
#> GSM711964 1 0.0000 0.993 1.000 0.000
#> GSM711966 1 0.0000 0.993 1.000 0.000
#> GSM711968 1 0.0000 0.993 1.000 0.000
#> GSM711972 1 0.0000 0.993 1.000 0.000
#> GSM711976 1 0.0000 0.993 1.000 0.000
#> GSM711980 1 0.0000 0.993 1.000 0.000
#> GSM711986 1 0.0000 0.993 1.000 0.000
#> GSM711904 1 0.0000 0.993 1.000 0.000
#> GSM711906 1 0.0000 0.993 1.000 0.000
#> GSM711908 1 0.0000 0.993 1.000 0.000
#> GSM711910 1 0.9209 0.496 0.664 0.336
#> GSM711914 1 0.0000 0.993 1.000 0.000
#> GSM711916 1 0.0000 0.993 1.000 0.000
#> GSM711922 1 0.0000 0.993 1.000 0.000
#> GSM711924 1 0.0000 0.993 1.000 0.000
#> GSM711926 1 0.0000 0.993 1.000 0.000
#> GSM711928 1 0.0000 0.993 1.000 0.000
#> GSM711930 1 0.0000 0.993 1.000 0.000
#> GSM711932 1 0.0000 0.993 1.000 0.000
#> GSM711934 1 0.0000 0.993 1.000 0.000
#> GSM711940 1 0.0000 0.993 1.000 0.000
#> GSM711942 1 0.0000 0.993 1.000 0.000
#> GSM711944 1 0.0000 0.993 1.000 0.000
#> GSM711946 1 0.0000 0.993 1.000 0.000
#> GSM711948 1 0.0000 0.993 1.000 0.000
#> GSM711952 1 0.0000 0.993 1.000 0.000
#> GSM711954 1 0.0000 0.993 1.000 0.000
#> GSM711962 1 0.0000 0.993 1.000 0.000
#> GSM711970 1 0.0000 0.993 1.000 0.000
#> GSM711974 1 0.0000 0.993 1.000 0.000
#> GSM711978 1 0.0000 0.993 1.000 0.000
#> GSM711988 1 0.0000 0.993 1.000 0.000
#> GSM711990 1 0.0000 0.993 1.000 0.000
#> GSM711992 1 0.0000 0.993 1.000 0.000
#> GSM711982 1 0.0000 0.993 1.000 0.000
#> GSM711984 2 0.0000 1.000 0.000 1.000
#> GSM711912 1 0.0000 0.993 1.000 0.000
#> GSM711918 1 0.0000 0.993 1.000 0.000
#> GSM711920 1 0.0000 0.993 1.000 0.000
#> GSM711937 2 0.0000 1.000 0.000 1.000
#> GSM711939 2 0.0000 1.000 0.000 1.000
#> GSM711951 2 0.0000 1.000 0.000 1.000
#> GSM711957 1 0.0000 0.993 1.000 0.000
#> GSM711959 2 0.0000 1.000 0.000 1.000
#> GSM711961 2 0.0000 1.000 0.000 1.000
#> GSM711965 1 0.0000 0.993 1.000 0.000
#> GSM711967 1 0.0000 0.993 1.000 0.000
#> GSM711969 2 0.0000 1.000 0.000 1.000
#> GSM711973 1 0.0000 0.993 1.000 0.000
#> GSM711977 1 0.0000 0.993 1.000 0.000
#> GSM711981 1 0.0376 0.990 0.996 0.004
#> GSM711987 2 0.0000 1.000 0.000 1.000
#> GSM711905 2 0.0000 1.000 0.000 1.000
#> GSM711907 2 0.0000 1.000 0.000 1.000
#> GSM711909 1 0.0376 0.990 0.996 0.004
#> GSM711911 1 0.0000 0.993 1.000 0.000
#> GSM711915 2 0.0000 1.000 0.000 1.000
#> GSM711917 2 0.0000 1.000 0.000 1.000
#> GSM711923 1 0.0000 0.993 1.000 0.000
#> GSM711925 2 0.0000 1.000 0.000 1.000
#> GSM711927 1 0.0000 0.993 1.000 0.000
#> GSM711929 2 0.0000 1.000 0.000 1.000
#> GSM711931 2 0.0000 1.000 0.000 1.000
#> GSM711933 1 0.0000 0.993 1.000 0.000
#> GSM711935 2 0.0000 1.000 0.000 1.000
#> GSM711941 1 0.0000 0.993 1.000 0.000
#> GSM711943 1 0.0000 0.993 1.000 0.000
#> GSM711945 2 0.0000 1.000 0.000 1.000
#> GSM711947 2 0.0000 1.000 0.000 1.000
#> GSM711949 2 0.0000 1.000 0.000 1.000
#> GSM711953 2 0.0000 1.000 0.000 1.000
#> GSM711955 1 0.0000 0.993 1.000 0.000
#> GSM711963 2 0.0000 1.000 0.000 1.000
#> GSM711971 1 0.0000 0.993 1.000 0.000
#> GSM711975 2 0.0000 1.000 0.000 1.000
#> GSM711979 1 0.0000 0.993 1.000 0.000
#> GSM711989 2 0.0000 1.000 0.000 1.000
#> GSM711991 2 0.0000 1.000 0.000 1.000
#> GSM711993 1 0.0000 0.993 1.000 0.000
#> GSM711983 1 0.0000 0.993 1.000 0.000
#> GSM711985 2 0.0000 1.000 0.000 1.000
#> GSM711913 1 0.3733 0.919 0.928 0.072
#> GSM711919 1 0.0000 0.993 1.000 0.000
#> GSM711921 1 0.0000 0.993 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM711936 2 0.0000 0.951 0.000 1.000 0.000
#> GSM711938 2 0.0000 0.951 0.000 1.000 0.000
#> GSM711950 1 0.5016 0.740 0.760 0.000 0.240
#> GSM711956 1 0.0000 0.924 1.000 0.000 0.000
#> GSM711958 1 0.0000 0.924 1.000 0.000 0.000
#> GSM711960 1 0.0000 0.924 1.000 0.000 0.000
#> GSM711964 1 0.0000 0.924 1.000 0.000 0.000
#> GSM711966 1 0.0000 0.924 1.000 0.000 0.000
#> GSM711968 1 0.0000 0.924 1.000 0.000 0.000
#> GSM711972 1 0.0000 0.924 1.000 0.000 0.000
#> GSM711976 1 0.2165 0.888 0.936 0.000 0.064
#> GSM711980 1 0.0000 0.924 1.000 0.000 0.000
#> GSM711986 1 0.0000 0.924 1.000 0.000 0.000
#> GSM711904 1 0.0000 0.924 1.000 0.000 0.000
#> GSM711906 1 0.0000 0.924 1.000 0.000 0.000
#> GSM711908 1 0.0000 0.924 1.000 0.000 0.000
#> GSM711910 3 0.0000 0.968 0.000 0.000 1.000
#> GSM711914 1 0.0000 0.924 1.000 0.000 0.000
#> GSM711916 1 0.0000 0.924 1.000 0.000 0.000
#> GSM711922 1 0.0000 0.924 1.000 0.000 0.000
#> GSM711924 1 0.0000 0.924 1.000 0.000 0.000
#> GSM711926 1 0.8853 0.457 0.568 0.168 0.264
#> GSM711928 1 0.0000 0.924 1.000 0.000 0.000
#> GSM711930 1 0.0000 0.924 1.000 0.000 0.000
#> GSM711932 1 0.3941 0.822 0.844 0.000 0.156
#> GSM711934 1 0.0000 0.924 1.000 0.000 0.000
#> GSM711940 1 0.0000 0.924 1.000 0.000 0.000
#> GSM711942 1 0.0000 0.924 1.000 0.000 0.000
#> GSM711944 1 0.3752 0.832 0.856 0.000 0.144
#> GSM711946 3 0.0000 0.968 0.000 0.000 1.000
#> GSM711948 1 0.3941 0.822 0.844 0.000 0.156
#> GSM711952 1 0.0000 0.924 1.000 0.000 0.000
#> GSM711954 1 0.0000 0.924 1.000 0.000 0.000
#> GSM711962 1 0.0000 0.924 1.000 0.000 0.000
#> GSM711970 1 0.0000 0.924 1.000 0.000 0.000
#> GSM711974 1 0.0000 0.924 1.000 0.000 0.000
#> GSM711978 1 0.5254 0.712 0.736 0.000 0.264
#> GSM711988 1 0.0237 0.922 0.996 0.000 0.004
#> GSM711990 3 0.3482 0.841 0.128 0.000 0.872
#> GSM711992 1 0.5812 0.700 0.724 0.012 0.264
#> GSM711982 1 0.0000 0.924 1.000 0.000 0.000
#> GSM711984 2 0.0000 0.951 0.000 1.000 0.000
#> GSM711912 1 0.0000 0.924 1.000 0.000 0.000
#> GSM711918 1 0.0000 0.924 1.000 0.000 0.000
#> GSM711920 1 0.0000 0.924 1.000 0.000 0.000
#> GSM711937 2 0.0000 0.951 0.000 1.000 0.000
#> GSM711939 2 0.0000 0.951 0.000 1.000 0.000
#> GSM711951 2 0.4504 0.754 0.000 0.804 0.196
#> GSM711957 1 0.5216 0.717 0.740 0.000 0.260
#> GSM711959 2 0.0000 0.951 0.000 1.000 0.000
#> GSM711961 2 0.0000 0.951 0.000 1.000 0.000
#> GSM711965 3 0.4121 0.784 0.168 0.000 0.832
#> GSM711967 1 0.0000 0.924 1.000 0.000 0.000
#> GSM711969 2 0.0000 0.951 0.000 1.000 0.000
#> GSM711973 1 0.5098 0.731 0.752 0.000 0.248
#> GSM711977 3 0.0237 0.965 0.004 0.000 0.996
#> GSM711981 2 0.6452 0.602 0.032 0.704 0.264
#> GSM711987 2 0.0000 0.951 0.000 1.000 0.000
#> GSM711905 2 0.0000 0.951 0.000 1.000 0.000
#> GSM711907 2 0.4346 0.785 0.000 0.816 0.184
#> GSM711909 3 0.0000 0.968 0.000 0.000 1.000
#> GSM711911 3 0.1964 0.918 0.056 0.000 0.944
#> GSM711915 3 0.0892 0.952 0.000 0.020 0.980
#> GSM711917 2 0.0000 0.951 0.000 1.000 0.000
#> GSM711923 1 0.5254 0.712 0.736 0.000 0.264
#> GSM711925 2 0.0000 0.951 0.000 1.000 0.000
#> GSM711927 3 0.0000 0.968 0.000 0.000 1.000
#> GSM711929 2 0.0000 0.951 0.000 1.000 0.000
#> GSM711931 2 0.3412 0.842 0.000 0.876 0.124
#> GSM711933 1 0.0000 0.924 1.000 0.000 0.000
#> GSM711935 2 0.0000 0.951 0.000 1.000 0.000
#> GSM711941 1 0.5058 0.736 0.756 0.000 0.244
#> GSM711943 1 0.5254 0.712 0.736 0.000 0.264
#> GSM711945 3 0.0000 0.968 0.000 0.000 1.000
#> GSM711947 3 0.0892 0.952 0.000 0.020 0.980
#> GSM711949 2 0.0000 0.951 0.000 1.000 0.000
#> GSM711953 2 0.0000 0.951 0.000 1.000 0.000
#> GSM711955 1 0.1411 0.905 0.964 0.000 0.036
#> GSM711963 2 0.0000 0.951 0.000 1.000 0.000
#> GSM711971 3 0.0000 0.968 0.000 0.000 1.000
#> GSM711975 2 0.0000 0.951 0.000 1.000 0.000
#> GSM711979 1 0.5216 0.717 0.740 0.000 0.260
#> GSM711989 2 0.0000 0.951 0.000 1.000 0.000
#> GSM711991 3 0.0000 0.968 0.000 0.000 1.000
#> GSM711993 2 0.5480 0.640 0.004 0.732 0.264
#> GSM711983 3 0.0000 0.968 0.000 0.000 1.000
#> GSM711985 2 0.0000 0.951 0.000 1.000 0.000
#> GSM711913 3 0.0000 0.968 0.000 0.000 1.000
#> GSM711919 3 0.0000 0.968 0.000 0.000 1.000
#> GSM711921 3 0.0000 0.968 0.000 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM711936 2 0.0000 0.97866 0.000 1.000 0.000 0.000
#> GSM711938 2 0.0336 0.97844 0.000 0.992 0.000 0.008
#> GSM711950 4 0.4431 0.69829 0.304 0.000 0.000 0.696
#> GSM711956 1 0.0000 0.95109 1.000 0.000 0.000 0.000
#> GSM711958 1 0.0469 0.94801 0.988 0.000 0.000 0.012
#> GSM711960 1 0.1022 0.93327 0.968 0.000 0.000 0.032
#> GSM711964 1 0.0707 0.94294 0.980 0.000 0.000 0.020
#> GSM711966 1 0.0469 0.94801 0.988 0.000 0.000 0.012
#> GSM711968 1 0.0000 0.95109 1.000 0.000 0.000 0.000
#> GSM711972 1 0.0000 0.95109 1.000 0.000 0.000 0.000
#> GSM711976 4 0.4730 0.62466 0.364 0.000 0.000 0.636
#> GSM711980 1 0.0000 0.95109 1.000 0.000 0.000 0.000
#> GSM711986 1 0.0000 0.95109 1.000 0.000 0.000 0.000
#> GSM711904 1 0.0336 0.94980 0.992 0.000 0.000 0.008
#> GSM711906 1 0.0000 0.95109 1.000 0.000 0.000 0.000
#> GSM711908 1 0.0336 0.94980 0.992 0.000 0.000 0.008
#> GSM711910 3 0.0188 0.89370 0.004 0.000 0.996 0.000
#> GSM711914 1 0.0000 0.95109 1.000 0.000 0.000 0.000
#> GSM711916 1 0.0921 0.93660 0.972 0.000 0.000 0.028
#> GSM711922 1 0.0000 0.95109 1.000 0.000 0.000 0.000
#> GSM711924 1 0.4564 0.35451 0.672 0.000 0.000 0.328
#> GSM711926 4 0.0000 0.74372 0.000 0.000 0.000 1.000
#> GSM711928 1 0.0000 0.95109 1.000 0.000 0.000 0.000
#> GSM711930 1 0.0921 0.93660 0.972 0.000 0.000 0.028
#> GSM711932 4 0.4522 0.68305 0.320 0.000 0.000 0.680
#> GSM711934 1 0.0469 0.94801 0.988 0.000 0.000 0.012
#> GSM711940 1 0.0000 0.95109 1.000 0.000 0.000 0.000
#> GSM711942 1 0.0000 0.95109 1.000 0.000 0.000 0.000
#> GSM711944 4 0.4746 0.61708 0.368 0.000 0.000 0.632
#> GSM711946 3 0.1743 0.87973 0.004 0.000 0.940 0.056
#> GSM711948 4 0.4477 0.69101 0.312 0.000 0.000 0.688
#> GSM711952 1 0.0336 0.94980 0.992 0.000 0.000 0.008
#> GSM711954 1 0.0000 0.95109 1.000 0.000 0.000 0.000
#> GSM711962 1 0.0000 0.95109 1.000 0.000 0.000 0.000
#> GSM711970 1 0.0336 0.94980 0.992 0.000 0.000 0.008
#> GSM711974 1 0.1022 0.93327 0.968 0.000 0.000 0.032
#> GSM711978 4 0.0000 0.74372 0.000 0.000 0.000 1.000
#> GSM711988 4 0.4804 0.58558 0.384 0.000 0.000 0.616
#> GSM711990 3 0.5497 0.56797 0.284 0.000 0.672 0.044
#> GSM711992 4 0.0469 0.74228 0.000 0.000 0.012 0.988
#> GSM711982 1 0.0921 0.93660 0.972 0.000 0.000 0.028
#> GSM711984 2 0.0000 0.97866 0.000 1.000 0.000 0.000
#> GSM711912 1 0.0000 0.95109 1.000 0.000 0.000 0.000
#> GSM711918 1 0.0000 0.95109 1.000 0.000 0.000 0.000
#> GSM711920 4 0.4992 0.35549 0.476 0.000 0.000 0.524
#> GSM711937 2 0.0336 0.97844 0.000 0.992 0.000 0.008
#> GSM711939 2 0.0336 0.97844 0.000 0.992 0.000 0.008
#> GSM711951 2 0.3958 0.81822 0.000 0.816 0.024 0.160
#> GSM711957 4 0.0469 0.74772 0.012 0.000 0.000 0.988
#> GSM711959 2 0.0000 0.97866 0.000 1.000 0.000 0.000
#> GSM711961 2 0.0000 0.97866 0.000 1.000 0.000 0.000
#> GSM711965 3 0.5498 0.58233 0.272 0.000 0.680 0.048
#> GSM711967 1 0.4898 -0.00181 0.584 0.000 0.000 0.416
#> GSM711969 2 0.0336 0.97844 0.000 0.992 0.000 0.008
#> GSM711973 4 0.3873 0.73706 0.228 0.000 0.000 0.772
#> GSM711977 3 0.0188 0.89341 0.000 0.000 0.996 0.004
#> GSM711981 4 0.0817 0.73878 0.000 0.000 0.024 0.976
#> GSM711987 2 0.0336 0.97844 0.000 0.992 0.000 0.008
#> GSM711905 2 0.0000 0.97866 0.000 1.000 0.000 0.000
#> GSM711907 2 0.0188 0.97658 0.000 0.996 0.004 0.000
#> GSM711909 3 0.0188 0.89253 0.000 0.000 0.996 0.004
#> GSM711911 3 0.4877 0.69237 0.204 0.000 0.752 0.044
#> GSM711915 3 0.0817 0.88229 0.000 0.024 0.976 0.000
#> GSM711917 2 0.0336 0.97844 0.000 0.992 0.000 0.008
#> GSM711923 4 0.1388 0.74258 0.012 0.000 0.028 0.960
#> GSM711925 2 0.0000 0.97866 0.000 1.000 0.000 0.000
#> GSM711927 3 0.0000 0.89204 0.000 0.000 1.000 0.000
#> GSM711929 2 0.0000 0.97866 0.000 1.000 0.000 0.000
#> GSM711931 2 0.4387 0.77131 0.000 0.776 0.024 0.200
#> GSM711933 1 0.0000 0.95109 1.000 0.000 0.000 0.000
#> GSM711935 2 0.0000 0.97866 0.000 1.000 0.000 0.000
#> GSM711941 4 0.4431 0.69829 0.304 0.000 0.000 0.696
#> GSM711943 4 0.0921 0.73732 0.000 0.000 0.028 0.972
#> GSM711945 3 0.1211 0.88587 0.000 0.000 0.960 0.040
#> GSM711947 3 0.0817 0.88229 0.000 0.024 0.976 0.000
#> GSM711949 2 0.0000 0.97866 0.000 1.000 0.000 0.000
#> GSM711953 2 0.0336 0.97844 0.000 0.992 0.000 0.008
#> GSM711955 1 0.3569 0.69380 0.804 0.000 0.000 0.196
#> GSM711963 2 0.0000 0.97866 0.000 1.000 0.000 0.000
#> GSM711971 3 0.2385 0.86827 0.052 0.000 0.920 0.028
#> GSM711975 2 0.1151 0.95959 0.000 0.968 0.024 0.008
#> GSM711979 4 0.0188 0.74604 0.004 0.000 0.000 0.996
#> GSM711989 2 0.0336 0.97844 0.000 0.992 0.000 0.008
#> GSM711991 3 0.0188 0.89161 0.000 0.004 0.996 0.000
#> GSM711993 4 0.0000 0.74372 0.000 0.000 0.000 1.000
#> GSM711983 3 0.3803 0.79001 0.132 0.000 0.836 0.032
#> GSM711985 2 0.0336 0.97844 0.000 0.992 0.000 0.008
#> GSM711913 3 0.0469 0.89318 0.000 0.000 0.988 0.012
#> GSM711919 3 0.2300 0.87100 0.048 0.000 0.924 0.028
#> GSM711921 3 0.0188 0.89253 0.000 0.000 0.996 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM711936 5 0.3932 0.8530 0.000 0.328 0.000 0.000 0.672
#> GSM711938 2 0.2966 0.7632 0.000 0.848 0.000 0.016 0.136
#> GSM711950 4 0.4367 0.4798 0.372 0.000 0.008 0.620 0.000
#> GSM711956 1 0.0000 0.8490 1.000 0.000 0.000 0.000 0.000
#> GSM711958 1 0.0290 0.8470 0.992 0.000 0.000 0.008 0.000
#> GSM711960 1 0.3459 0.8007 0.844 0.000 0.004 0.080 0.072
#> GSM711964 1 0.2338 0.8139 0.884 0.000 0.000 0.004 0.112
#> GSM711966 1 0.0000 0.8490 1.000 0.000 0.000 0.000 0.000
#> GSM711968 1 0.1892 0.8316 0.916 0.000 0.000 0.004 0.080
#> GSM711972 1 0.2020 0.8196 0.900 0.000 0.000 0.000 0.100
#> GSM711976 1 0.3983 0.3387 0.660 0.000 0.000 0.340 0.000
#> GSM711980 1 0.0000 0.8490 1.000 0.000 0.000 0.000 0.000
#> GSM711986 1 0.2233 0.8172 0.892 0.000 0.000 0.004 0.104
#> GSM711904 1 0.3048 0.7770 0.820 0.000 0.000 0.004 0.176
#> GSM711906 1 0.2233 0.8172 0.892 0.000 0.000 0.004 0.104
#> GSM711908 1 0.3838 0.7242 0.716 0.000 0.000 0.004 0.280
#> GSM711910 3 0.0000 0.9314 0.000 0.000 1.000 0.000 0.000
#> GSM711914 1 0.0000 0.8490 1.000 0.000 0.000 0.000 0.000
#> GSM711916 1 0.2890 0.7870 0.836 0.000 0.000 0.004 0.160
#> GSM711922 1 0.0000 0.8490 1.000 0.000 0.000 0.000 0.000
#> GSM711924 1 0.0290 0.8469 0.992 0.000 0.000 0.008 0.000
#> GSM711926 4 0.0290 0.7759 0.000 0.000 0.008 0.992 0.000
#> GSM711928 1 0.0609 0.8468 0.980 0.000 0.000 0.000 0.020
#> GSM711930 1 0.3048 0.7770 0.820 0.000 0.000 0.004 0.176
#> GSM711932 1 0.4283 -0.0882 0.544 0.000 0.000 0.456 0.000
#> GSM711934 1 0.0000 0.8490 1.000 0.000 0.000 0.000 0.000
#> GSM711940 1 0.0162 0.8485 0.996 0.000 0.004 0.000 0.000
#> GSM711942 1 0.0000 0.8490 1.000 0.000 0.000 0.000 0.000
#> GSM711944 1 0.4557 -0.1026 0.516 0.000 0.008 0.476 0.000
#> GSM711946 3 0.0510 0.9284 0.000 0.000 0.984 0.016 0.000
#> GSM711948 4 0.4560 0.1411 0.484 0.000 0.008 0.508 0.000
#> GSM711952 1 0.3838 0.7242 0.716 0.000 0.000 0.004 0.280
#> GSM711954 1 0.3048 0.7770 0.820 0.000 0.000 0.004 0.176
#> GSM711962 1 0.0000 0.8490 1.000 0.000 0.000 0.000 0.000
#> GSM711970 1 0.3048 0.7770 0.820 0.000 0.000 0.004 0.176
#> GSM711974 1 0.0162 0.8484 0.996 0.000 0.004 0.000 0.000
#> GSM711978 4 0.0404 0.7760 0.000 0.000 0.012 0.988 0.000
#> GSM711988 1 0.4009 0.4053 0.684 0.000 0.004 0.312 0.000
#> GSM711990 3 0.5233 0.5872 0.192 0.000 0.680 0.000 0.128
#> GSM711992 4 0.0404 0.7760 0.000 0.000 0.012 0.988 0.000
#> GSM711982 1 0.0000 0.8490 1.000 0.000 0.000 0.000 0.000
#> GSM711984 2 0.0404 0.8757 0.000 0.988 0.000 0.000 0.012
#> GSM711912 1 0.3635 0.7511 0.748 0.000 0.000 0.004 0.248
#> GSM711918 1 0.2930 0.8013 0.832 0.000 0.000 0.004 0.164
#> GSM711920 1 0.2377 0.7437 0.872 0.000 0.000 0.128 0.000
#> GSM711937 5 0.4738 0.5411 0.000 0.464 0.000 0.016 0.520
#> GSM711939 2 0.3789 0.5904 0.000 0.760 0.000 0.016 0.224
#> GSM711951 5 0.5400 0.7931 0.000 0.220 0.008 0.100 0.672
#> GSM711957 4 0.2625 0.7184 0.108 0.000 0.000 0.876 0.016
#> GSM711959 2 0.2813 0.6707 0.000 0.832 0.000 0.000 0.168
#> GSM711961 2 0.1638 0.8556 0.000 0.932 0.000 0.004 0.064
#> GSM711965 3 0.4994 0.6545 0.152 0.000 0.720 0.004 0.124
#> GSM711967 1 0.1018 0.8440 0.968 0.000 0.000 0.016 0.016
#> GSM711969 5 0.4329 0.8625 0.000 0.312 0.000 0.016 0.672
#> GSM711973 4 0.3759 0.7113 0.220 0.000 0.016 0.764 0.000
#> GSM711977 3 0.0290 0.9305 0.000 0.000 0.992 0.008 0.000
#> GSM711981 4 0.0451 0.7750 0.000 0.000 0.008 0.988 0.004
#> GSM711987 2 0.1549 0.8649 0.000 0.944 0.000 0.016 0.040
#> GSM711905 2 0.0000 0.8792 0.000 1.000 0.000 0.000 0.000
#> GSM711907 5 0.4003 0.8357 0.000 0.288 0.008 0.000 0.704
#> GSM711909 3 0.0000 0.9314 0.000 0.000 1.000 0.000 0.000
#> GSM711911 3 0.1732 0.8627 0.080 0.000 0.920 0.000 0.000
#> GSM711915 3 0.1591 0.9035 0.000 0.004 0.940 0.004 0.052
#> GSM711917 5 0.4290 0.8678 0.000 0.304 0.000 0.016 0.680
#> GSM711923 4 0.1571 0.7614 0.000 0.000 0.060 0.936 0.004
#> GSM711925 2 0.0000 0.8792 0.000 1.000 0.000 0.000 0.000
#> GSM711927 3 0.0000 0.9314 0.000 0.000 1.000 0.000 0.000
#> GSM711929 2 0.0000 0.8792 0.000 1.000 0.000 0.000 0.000
#> GSM711931 5 0.5781 0.6738 0.000 0.164 0.004 0.200 0.632
#> GSM711933 1 0.0000 0.8490 1.000 0.000 0.000 0.000 0.000
#> GSM711935 2 0.0000 0.8792 0.000 1.000 0.000 0.000 0.000
#> GSM711941 4 0.4613 0.5009 0.360 0.000 0.020 0.620 0.000
#> GSM711943 4 0.1430 0.7640 0.000 0.000 0.052 0.944 0.004
#> GSM711945 3 0.0609 0.9270 0.000 0.000 0.980 0.020 0.000
#> GSM711947 3 0.2424 0.8386 0.000 0.000 0.868 0.000 0.132
#> GSM711949 2 0.0000 0.8792 0.000 1.000 0.000 0.000 0.000
#> GSM711953 2 0.1774 0.8564 0.000 0.932 0.000 0.016 0.052
#> GSM711955 1 0.4430 0.3152 0.628 0.000 0.012 0.360 0.000
#> GSM711963 2 0.0000 0.8792 0.000 1.000 0.000 0.000 0.000
#> GSM711971 3 0.0290 0.9301 0.008 0.000 0.992 0.000 0.000
#> GSM711975 5 0.4617 0.8672 0.000 0.304 0.004 0.024 0.668
#> GSM711979 4 0.3013 0.7379 0.160 0.000 0.008 0.832 0.000
#> GSM711989 5 0.4290 0.8678 0.000 0.304 0.000 0.016 0.680
#> GSM711991 3 0.0162 0.9307 0.000 0.000 0.996 0.004 0.000
#> GSM711993 4 0.0324 0.7747 0.000 0.000 0.004 0.992 0.004
#> GSM711983 3 0.0609 0.9234 0.020 0.000 0.980 0.000 0.000
#> GSM711985 2 0.4161 0.4413 0.000 0.704 0.000 0.016 0.280
#> GSM711913 3 0.0290 0.9305 0.000 0.000 0.992 0.008 0.000
#> GSM711919 3 0.0290 0.9301 0.008 0.000 0.992 0.000 0.000
#> GSM711921 3 0.0000 0.9314 0.000 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM711936 2 0.2491 0.585 0.000 0.836 0.000 0.000 0.164 0.000
#> GSM711938 2 0.3810 0.535 0.000 0.572 0.000 0.000 0.428 0.000
#> GSM711950 4 0.4454 0.612 0.348 0.000 0.004 0.616 0.000 0.032
#> GSM711956 1 0.0000 0.792 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711958 1 0.2221 0.695 0.896 0.000 0.000 0.072 0.000 0.032
#> GSM711960 1 0.3998 -0.389 0.504 0.000 0.004 0.492 0.000 0.000
#> GSM711964 1 0.0458 0.783 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM711966 1 0.0000 0.792 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711968 1 0.3756 -0.186 0.600 0.000 0.000 0.000 0.000 0.400
#> GSM711972 1 0.3789 -0.284 0.584 0.000 0.000 0.000 0.000 0.416
#> GSM711976 1 0.0458 0.783 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM711980 1 0.0000 0.792 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711986 6 0.3817 0.588 0.432 0.000 0.000 0.000 0.000 0.568
#> GSM711904 1 0.3634 0.385 0.644 0.000 0.000 0.000 0.000 0.356
#> GSM711906 6 0.3857 0.520 0.468 0.000 0.000 0.000 0.000 0.532
#> GSM711908 6 0.1151 0.513 0.012 0.000 0.000 0.032 0.000 0.956
#> GSM711910 3 0.0146 0.960 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM711914 1 0.0000 0.792 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711916 1 0.3405 0.492 0.724 0.000 0.000 0.004 0.000 0.272
#> GSM711922 1 0.0146 0.790 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM711924 1 0.0000 0.792 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711926 4 0.2001 0.625 0.092 0.004 0.004 0.900 0.000 0.000
#> GSM711928 1 0.0146 0.790 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM711930 1 0.4461 0.273 0.564 0.000 0.000 0.032 0.000 0.404
#> GSM711932 1 0.0260 0.788 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM711934 1 0.0000 0.792 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711940 1 0.0291 0.788 0.992 0.000 0.004 0.004 0.000 0.000
#> GSM711942 1 0.0146 0.790 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM711944 4 0.4454 0.612 0.348 0.000 0.004 0.616 0.000 0.032
#> GSM711946 3 0.0260 0.959 0.000 0.000 0.992 0.008 0.000 0.000
#> GSM711948 4 0.4454 0.612 0.348 0.000 0.004 0.616 0.000 0.032
#> GSM711952 6 0.1151 0.513 0.012 0.000 0.000 0.032 0.000 0.956
#> GSM711954 1 0.3634 0.385 0.644 0.000 0.000 0.000 0.000 0.356
#> GSM711962 1 0.0000 0.792 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711970 1 0.4400 0.322 0.592 0.000 0.000 0.032 0.000 0.376
#> GSM711974 1 0.0260 0.789 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM711978 4 0.2101 0.625 0.100 0.004 0.004 0.892 0.000 0.000
#> GSM711988 1 0.2726 0.643 0.856 0.000 0.000 0.112 0.000 0.032
#> GSM711990 3 0.1370 0.936 0.012 0.000 0.948 0.004 0.000 0.036
#> GSM711992 4 0.1958 0.623 0.100 0.004 0.000 0.896 0.000 0.000
#> GSM711982 1 0.0000 0.792 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711984 5 0.0000 0.999 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM711912 6 0.3499 0.671 0.320 0.000 0.000 0.000 0.000 0.680
#> GSM711918 6 0.3647 0.658 0.360 0.000 0.000 0.000 0.000 0.640
#> GSM711920 1 0.0000 0.792 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711937 2 0.3804 0.538 0.000 0.576 0.000 0.000 0.424 0.000
#> GSM711939 2 0.3810 0.535 0.000 0.572 0.000 0.000 0.428 0.000
#> GSM711951 2 0.1082 0.677 0.000 0.956 0.004 0.040 0.000 0.000
#> GSM711957 1 0.4199 0.299 0.600 0.000 0.000 0.380 0.000 0.020
#> GSM711959 5 0.0000 0.999 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM711961 2 0.3810 0.535 0.000 0.572 0.000 0.000 0.428 0.000
#> GSM711965 3 0.1265 0.936 0.000 0.000 0.948 0.008 0.000 0.044
#> GSM711967 1 0.0363 0.786 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM711969 2 0.0000 0.683 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711973 4 0.4532 0.619 0.340 0.000 0.008 0.620 0.000 0.032
#> GSM711977 3 0.3198 0.714 0.000 0.000 0.740 0.260 0.000 0.000
#> GSM711981 4 0.0665 0.641 0.004 0.008 0.008 0.980 0.000 0.000
#> GSM711987 2 0.3847 0.483 0.000 0.544 0.000 0.000 0.456 0.000
#> GSM711905 5 0.0000 0.999 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM711907 2 0.4072 0.534 0.000 0.756 0.004 0.040 0.188 0.012
#> GSM711909 3 0.0146 0.960 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM711911 3 0.0405 0.955 0.008 0.000 0.988 0.004 0.000 0.000
#> GSM711915 3 0.2403 0.910 0.000 0.032 0.904 0.044 0.008 0.012
#> GSM711917 2 0.0000 0.683 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM711923 4 0.1462 0.633 0.000 0.008 0.056 0.936 0.000 0.000
#> GSM711925 5 0.0000 0.999 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM711927 3 0.0146 0.960 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM711929 5 0.0146 0.994 0.000 0.004 0.000 0.000 0.996 0.000
#> GSM711931 2 0.1219 0.674 0.000 0.948 0.004 0.048 0.000 0.000
#> GSM711933 1 0.0000 0.792 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM711935 5 0.0000 0.999 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM711941 4 0.4624 0.618 0.340 0.000 0.012 0.616 0.000 0.032
#> GSM711943 4 0.1668 0.632 0.004 0.008 0.060 0.928 0.000 0.000
#> GSM711945 3 0.0937 0.941 0.000 0.000 0.960 0.040 0.000 0.000
#> GSM711947 3 0.2360 0.905 0.000 0.044 0.900 0.044 0.000 0.012
#> GSM711949 5 0.0000 0.999 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM711953 2 0.3810 0.535 0.000 0.572 0.000 0.000 0.428 0.000
#> GSM711955 4 0.3996 0.608 0.352 0.000 0.004 0.636 0.000 0.008
#> GSM711963 5 0.0000 0.999 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM711971 3 0.0146 0.960 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM711975 2 0.1082 0.677 0.000 0.956 0.004 0.040 0.000 0.000
#> GSM711979 4 0.3690 0.631 0.308 0.000 0.008 0.684 0.000 0.000
#> GSM711989 2 0.0508 0.683 0.000 0.984 0.004 0.012 0.000 0.000
#> GSM711991 3 0.1082 0.940 0.000 0.000 0.956 0.040 0.000 0.004
#> GSM711993 4 0.0665 0.641 0.004 0.008 0.008 0.980 0.000 0.000
#> GSM711983 3 0.0146 0.960 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM711985 2 0.3810 0.535 0.000 0.572 0.000 0.000 0.428 0.000
#> GSM711913 3 0.0260 0.959 0.000 0.000 0.992 0.008 0.000 0.000
#> GSM711919 3 0.0146 0.960 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM711921 3 0.0146 0.960 0.000 0.000 0.996 0.004 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) disease.state(p) individual(p) k
#> ATC:mclust 89 5.58e-06 0.2370 0.672 2
#> ATC:mclust 89 2.72e-09 0.1055 0.405 3
#> ATC:mclust 87 3.52e-09 0.1548 0.466 4
#> ATC:mclust 82 3.16e-09 0.3893 0.178 5
#> ATC:mclust 80 2.89e-07 0.0544 0.197 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "NMF"]
# you can also extract it by
# res = res_list["ATC:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 27425 rows and 90 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.985 0.994 0.4124 0.585 0.585
#> 3 3 0.720 0.855 0.913 0.4303 0.788 0.644
#> 4 4 0.725 0.591 0.796 0.2134 0.697 0.394
#> 5 5 0.666 0.617 0.815 0.0471 0.877 0.645
#> 6 6 0.691 0.699 0.831 0.0408 0.914 0.699
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM711936 2 0.000 0.982 0.000 1.000
#> GSM711938 2 0.000 0.982 0.000 1.000
#> GSM711950 1 0.000 0.999 1.000 0.000
#> GSM711956 1 0.000 0.999 1.000 0.000
#> GSM711958 1 0.000 0.999 1.000 0.000
#> GSM711960 1 0.000 0.999 1.000 0.000
#> GSM711964 1 0.000 0.999 1.000 0.000
#> GSM711966 1 0.000 0.999 1.000 0.000
#> GSM711968 1 0.000 0.999 1.000 0.000
#> GSM711972 1 0.000 0.999 1.000 0.000
#> GSM711976 1 0.000 0.999 1.000 0.000
#> GSM711980 1 0.000 0.999 1.000 0.000
#> GSM711986 1 0.000 0.999 1.000 0.000
#> GSM711904 1 0.000 0.999 1.000 0.000
#> GSM711906 1 0.000 0.999 1.000 0.000
#> GSM711908 1 0.000 0.999 1.000 0.000
#> GSM711910 1 0.000 0.999 1.000 0.000
#> GSM711914 1 0.000 0.999 1.000 0.000
#> GSM711916 1 0.000 0.999 1.000 0.000
#> GSM711922 1 0.000 0.999 1.000 0.000
#> GSM711924 1 0.000 0.999 1.000 0.000
#> GSM711926 1 0.224 0.962 0.964 0.036
#> GSM711928 1 0.000 0.999 1.000 0.000
#> GSM711930 1 0.000 0.999 1.000 0.000
#> GSM711932 1 0.000 0.999 1.000 0.000
#> GSM711934 1 0.000 0.999 1.000 0.000
#> GSM711940 1 0.000 0.999 1.000 0.000
#> GSM711942 1 0.000 0.999 1.000 0.000
#> GSM711944 1 0.000 0.999 1.000 0.000
#> GSM711946 1 0.000 0.999 1.000 0.000
#> GSM711948 1 0.000 0.999 1.000 0.000
#> GSM711952 1 0.000 0.999 1.000 0.000
#> GSM711954 1 0.000 0.999 1.000 0.000
#> GSM711962 1 0.000 0.999 1.000 0.000
#> GSM711970 1 0.000 0.999 1.000 0.000
#> GSM711974 1 0.000 0.999 1.000 0.000
#> GSM711978 1 0.000 0.999 1.000 0.000
#> GSM711988 1 0.000 0.999 1.000 0.000
#> GSM711990 1 0.000 0.999 1.000 0.000
#> GSM711992 1 0.000 0.999 1.000 0.000
#> GSM711982 1 0.000 0.999 1.000 0.000
#> GSM711984 2 0.000 0.982 0.000 1.000
#> GSM711912 1 0.000 0.999 1.000 0.000
#> GSM711918 1 0.000 0.999 1.000 0.000
#> GSM711920 1 0.000 0.999 1.000 0.000
#> GSM711937 2 0.000 0.982 0.000 1.000
#> GSM711939 2 0.000 0.982 0.000 1.000
#> GSM711951 2 0.000 0.982 0.000 1.000
#> GSM711957 1 0.000 0.999 1.000 0.000
#> GSM711959 2 0.000 0.982 0.000 1.000
#> GSM711961 2 0.000 0.982 0.000 1.000
#> GSM711965 1 0.000 0.999 1.000 0.000
#> GSM711967 1 0.000 0.999 1.000 0.000
#> GSM711969 2 0.000 0.982 0.000 1.000
#> GSM711973 1 0.000 0.999 1.000 0.000
#> GSM711977 1 0.000 0.999 1.000 0.000
#> GSM711981 1 0.000 0.999 1.000 0.000
#> GSM711987 2 0.000 0.982 0.000 1.000
#> GSM711905 2 0.000 0.982 0.000 1.000
#> GSM711907 2 0.000 0.982 0.000 1.000
#> GSM711909 1 0.000 0.999 1.000 0.000
#> GSM711911 1 0.000 0.999 1.000 0.000
#> GSM711915 2 0.000 0.982 0.000 1.000
#> GSM711917 2 0.000 0.982 0.000 1.000
#> GSM711923 1 0.000 0.999 1.000 0.000
#> GSM711925 2 0.000 0.982 0.000 1.000
#> GSM711927 1 0.000 0.999 1.000 0.000
#> GSM711929 2 0.000 0.982 0.000 1.000
#> GSM711931 2 0.000 0.982 0.000 1.000
#> GSM711933 1 0.000 0.999 1.000 0.000
#> GSM711935 2 0.000 0.982 0.000 1.000
#> GSM711941 1 0.000 0.999 1.000 0.000
#> GSM711943 1 0.000 0.999 1.000 0.000
#> GSM711945 1 0.204 0.967 0.968 0.032
#> GSM711947 2 0.000 0.982 0.000 1.000
#> GSM711949 2 0.000 0.982 0.000 1.000
#> GSM711953 2 0.000 0.982 0.000 1.000
#> GSM711955 1 0.000 0.999 1.000 0.000
#> GSM711963 2 0.000 0.982 0.000 1.000
#> GSM711971 1 0.000 0.999 1.000 0.000
#> GSM711975 2 0.000 0.982 0.000 1.000
#> GSM711979 1 0.000 0.999 1.000 0.000
#> GSM711989 2 0.000 0.982 0.000 1.000
#> GSM711991 2 0.990 0.211 0.440 0.560
#> GSM711993 1 0.000 0.999 1.000 0.000
#> GSM711983 1 0.000 0.999 1.000 0.000
#> GSM711985 2 0.000 0.982 0.000 1.000
#> GSM711913 1 0.000 0.999 1.000 0.000
#> GSM711919 1 0.000 0.999 1.000 0.000
#> GSM711921 1 0.000 0.999 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM711936 2 0.0747 0.961 0.000 0.984 0.016
#> GSM711938 2 0.0000 0.962 0.000 1.000 0.000
#> GSM711950 1 0.0000 0.915 1.000 0.000 0.000
#> GSM711956 1 0.0237 0.915 0.996 0.000 0.004
#> GSM711958 1 0.0000 0.915 1.000 0.000 0.000
#> GSM711960 3 0.5016 0.880 0.240 0.000 0.760
#> GSM711964 1 0.6045 0.191 0.620 0.000 0.380
#> GSM711966 1 0.1163 0.911 0.972 0.000 0.028
#> GSM711968 1 0.1411 0.906 0.964 0.000 0.036
#> GSM711972 1 0.0000 0.915 1.000 0.000 0.000
#> GSM711976 1 0.0000 0.915 1.000 0.000 0.000
#> GSM711980 1 0.0892 0.914 0.980 0.000 0.020
#> GSM711986 1 0.0892 0.914 0.980 0.000 0.020
#> GSM711904 3 0.4702 0.901 0.212 0.000 0.788
#> GSM711906 1 0.0892 0.914 0.980 0.000 0.020
#> GSM711908 3 0.3340 0.855 0.120 0.000 0.880
#> GSM711910 3 0.4121 0.891 0.168 0.000 0.832
#> GSM711914 1 0.0892 0.914 0.980 0.000 0.020
#> GSM711916 3 0.4796 0.899 0.220 0.000 0.780
#> GSM711922 1 0.0000 0.915 1.000 0.000 0.000
#> GSM711924 1 0.0000 0.915 1.000 0.000 0.000
#> GSM711926 1 0.7015 0.291 0.584 0.392 0.024
#> GSM711928 1 0.2165 0.883 0.936 0.000 0.064
#> GSM711930 3 0.4178 0.893 0.172 0.000 0.828
#> GSM711932 1 0.0237 0.914 0.996 0.000 0.004
#> GSM711934 1 0.1031 0.912 0.976 0.000 0.024
#> GSM711940 1 0.1163 0.911 0.972 0.000 0.028
#> GSM711942 1 0.1289 0.909 0.968 0.000 0.032
#> GSM711944 1 0.0000 0.915 1.000 0.000 0.000
#> GSM711946 1 0.3116 0.833 0.892 0.000 0.108
#> GSM711948 1 0.0000 0.915 1.000 0.000 0.000
#> GSM711952 3 0.4887 0.892 0.228 0.000 0.772
#> GSM711954 1 0.3816 0.777 0.852 0.000 0.148
#> GSM711962 1 0.0892 0.914 0.980 0.000 0.020
#> GSM711970 3 0.4178 0.893 0.172 0.000 0.828
#> GSM711974 3 0.6309 0.293 0.496 0.000 0.504
#> GSM711978 1 0.0237 0.914 0.996 0.000 0.004
#> GSM711988 1 0.0000 0.915 1.000 0.000 0.000
#> GSM711990 3 0.4796 0.899 0.220 0.000 0.780
#> GSM711992 1 0.1411 0.890 0.964 0.036 0.000
#> GSM711982 1 0.1289 0.909 0.968 0.000 0.032
#> GSM711984 2 0.2878 0.929 0.000 0.904 0.096
#> GSM711912 1 0.1753 0.897 0.952 0.000 0.048
#> GSM711918 1 0.1289 0.909 0.968 0.000 0.032
#> GSM711920 1 0.0000 0.915 1.000 0.000 0.000
#> GSM711937 2 0.0000 0.962 0.000 1.000 0.000
#> GSM711939 2 0.0000 0.962 0.000 1.000 0.000
#> GSM711951 2 0.1031 0.955 0.000 0.976 0.024
#> GSM711957 1 0.1031 0.899 0.976 0.000 0.024
#> GSM711959 2 0.2625 0.936 0.000 0.916 0.084
#> GSM711961 2 0.0747 0.961 0.000 0.984 0.016
#> GSM711965 3 0.5138 0.865 0.252 0.000 0.748
#> GSM711967 1 0.0000 0.915 1.000 0.000 0.000
#> GSM711969 2 0.0592 0.960 0.000 0.988 0.012
#> GSM711973 1 0.0237 0.914 0.996 0.000 0.004
#> GSM711977 1 0.0237 0.914 0.996 0.000 0.004
#> GSM711981 1 0.1620 0.888 0.964 0.012 0.024
#> GSM711987 2 0.0892 0.957 0.000 0.980 0.020
#> GSM711905 2 0.2959 0.927 0.000 0.900 0.100
#> GSM711907 2 0.5948 0.628 0.000 0.640 0.360
#> GSM711909 3 0.4605 0.901 0.204 0.000 0.796
#> GSM711911 1 0.5560 0.458 0.700 0.000 0.300
#> GSM711915 3 0.1031 0.702 0.000 0.024 0.976
#> GSM711917 2 0.0237 0.962 0.000 0.996 0.004
#> GSM711923 1 0.0000 0.915 1.000 0.000 0.000
#> GSM711925 2 0.1964 0.948 0.000 0.944 0.056
#> GSM711927 3 0.4654 0.901 0.208 0.000 0.792
#> GSM711929 2 0.0747 0.961 0.000 0.984 0.016
#> GSM711931 2 0.1620 0.948 0.012 0.964 0.024
#> GSM711933 1 0.1289 0.909 0.968 0.000 0.032
#> GSM711935 2 0.1964 0.948 0.000 0.944 0.056
#> GSM711941 1 0.0237 0.914 0.996 0.000 0.004
#> GSM711943 1 0.0000 0.915 1.000 0.000 0.000
#> GSM711945 1 0.9822 -0.259 0.428 0.280 0.292
#> GSM711947 3 0.2959 0.621 0.000 0.100 0.900
#> GSM711949 2 0.2796 0.932 0.000 0.908 0.092
#> GSM711953 2 0.0237 0.962 0.000 0.996 0.004
#> GSM711955 1 0.1163 0.911 0.972 0.000 0.028
#> GSM711963 2 0.0424 0.962 0.000 0.992 0.008
#> GSM711971 1 0.6062 0.174 0.616 0.000 0.384
#> GSM711975 2 0.1031 0.955 0.000 0.976 0.024
#> GSM711979 1 0.1031 0.899 0.976 0.000 0.024
#> GSM711989 2 0.0592 0.960 0.000 0.988 0.012
#> GSM711991 3 0.4270 0.848 0.116 0.024 0.860
#> GSM711993 1 0.4045 0.772 0.872 0.104 0.024
#> GSM711983 1 0.0892 0.914 0.980 0.000 0.020
#> GSM711985 2 0.0592 0.960 0.000 0.988 0.012
#> GSM711913 1 0.3267 0.821 0.884 0.000 0.116
#> GSM711919 3 0.4796 0.899 0.220 0.000 0.780
#> GSM711921 3 0.4842 0.896 0.224 0.000 0.776
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM711936 2 0.4817 0.5820 0.000 0.612 0.000 0.388
#> GSM711938 2 0.4804 0.5857 0.000 0.616 0.000 0.384
#> GSM711950 2 0.7892 -0.4961 0.292 0.368 0.340 0.000
#> GSM711956 1 0.0188 0.8632 0.996 0.000 0.004 0.000
#> GSM711958 1 0.1004 0.8528 0.972 0.024 0.004 0.000
#> GSM711960 3 0.4332 0.5735 0.032 0.000 0.792 0.176
#> GSM711964 1 0.0188 0.8631 0.996 0.000 0.000 0.004
#> GSM711966 1 0.0188 0.8632 0.996 0.000 0.004 0.000
#> GSM711968 1 0.0188 0.8631 0.996 0.000 0.000 0.004
#> GSM711972 1 0.0188 0.8632 0.996 0.000 0.004 0.000
#> GSM711976 1 0.2334 0.8132 0.908 0.088 0.004 0.000
#> GSM711980 1 0.0188 0.8632 0.996 0.000 0.004 0.000
#> GSM711986 1 0.0188 0.8631 0.996 0.000 0.000 0.004
#> GSM711904 1 0.6119 0.6152 0.680 0.000 0.152 0.168
#> GSM711906 1 0.0188 0.8631 0.996 0.000 0.000 0.004
#> GSM711908 1 0.6869 0.5211 0.596 0.000 0.180 0.224
#> GSM711910 3 0.3266 0.5919 0.000 0.000 0.832 0.168
#> GSM711914 1 0.0000 0.8632 1.000 0.000 0.000 0.000
#> GSM711916 1 0.6583 0.5610 0.632 0.000 0.192 0.176
#> GSM711922 1 0.0188 0.8631 0.996 0.000 0.000 0.004
#> GSM711924 1 0.0336 0.8617 0.992 0.008 0.000 0.000
#> GSM711926 2 0.5250 0.2036 0.080 0.744 0.000 0.176
#> GSM711928 1 0.0188 0.8631 0.996 0.000 0.000 0.004
#> GSM711930 1 0.7566 0.3367 0.480 0.000 0.292 0.228
#> GSM711932 1 0.3306 0.7611 0.840 0.156 0.004 0.000
#> GSM711934 1 0.0188 0.8632 0.996 0.000 0.004 0.000
#> GSM711940 1 0.0336 0.8619 0.992 0.000 0.008 0.000
#> GSM711942 1 0.0188 0.8631 0.996 0.000 0.000 0.004
#> GSM711944 3 0.7020 0.6576 0.136 0.332 0.532 0.000
#> GSM711946 3 0.4769 0.7487 0.008 0.308 0.684 0.000
#> GSM711948 1 0.7912 -0.2379 0.356 0.336 0.308 0.000
#> GSM711952 1 0.0188 0.8631 0.996 0.000 0.000 0.004
#> GSM711954 1 0.0188 0.8631 0.996 0.000 0.000 0.004
#> GSM711962 1 0.0000 0.8632 1.000 0.000 0.000 0.000
#> GSM711970 1 0.7627 0.3317 0.472 0.000 0.272 0.256
#> GSM711974 1 0.5165 0.6940 0.752 0.000 0.168 0.080
#> GSM711978 1 0.5010 0.6691 0.728 0.244 0.012 0.016
#> GSM711988 1 0.6618 0.4410 0.604 0.272 0.124 0.000
#> GSM711990 3 0.3024 0.6114 0.000 0.000 0.852 0.148
#> GSM711992 1 0.6731 0.3497 0.608 0.236 0.000 0.156
#> GSM711982 1 0.0188 0.8632 0.996 0.000 0.004 0.000
#> GSM711984 4 0.4624 0.2793 0.000 0.340 0.000 0.660
#> GSM711912 1 0.0188 0.8631 0.996 0.000 0.000 0.004
#> GSM711918 1 0.0188 0.8631 0.996 0.000 0.000 0.004
#> GSM711920 1 0.0336 0.8617 0.992 0.008 0.000 0.000
#> GSM711937 2 0.4804 0.5857 0.000 0.616 0.000 0.384
#> GSM711939 2 0.4804 0.5857 0.000 0.616 0.000 0.384
#> GSM711951 2 0.4730 0.5656 0.000 0.636 0.000 0.364
#> GSM711957 1 0.2647 0.7941 0.880 0.120 0.000 0.000
#> GSM711959 4 0.4697 0.2379 0.000 0.356 0.000 0.644
#> GSM711961 2 0.4817 0.5820 0.000 0.612 0.000 0.388
#> GSM711965 3 0.1305 0.6775 0.000 0.004 0.960 0.036
#> GSM711967 1 0.0336 0.8617 0.992 0.008 0.000 0.000
#> GSM711969 2 0.4804 0.5857 0.000 0.616 0.000 0.384
#> GSM711973 3 0.5769 0.7187 0.036 0.376 0.588 0.000
#> GSM711977 3 0.5085 0.7309 0.008 0.376 0.616 0.000
#> GSM711981 2 0.4837 -0.4099 0.004 0.648 0.348 0.000
#> GSM711987 2 0.4804 0.5857 0.000 0.616 0.000 0.384
#> GSM711905 4 0.4454 0.3082 0.000 0.308 0.000 0.692
#> GSM711907 4 0.3583 0.3306 0.000 0.180 0.004 0.816
#> GSM711909 3 0.2814 0.6249 0.000 0.000 0.868 0.132
#> GSM711911 3 0.4103 0.7496 0.000 0.256 0.744 0.000
#> GSM711915 4 0.4866 -0.0631 0.000 0.000 0.404 0.596
#> GSM711917 2 0.4817 0.5820 0.000 0.612 0.000 0.388
#> GSM711923 3 0.5204 0.7305 0.012 0.376 0.612 0.000
#> GSM711925 2 0.4948 0.4531 0.000 0.560 0.000 0.440
#> GSM711927 3 0.2469 0.6410 0.000 0.000 0.892 0.108
#> GSM711929 2 0.4817 0.5820 0.000 0.612 0.000 0.388
#> GSM711931 2 0.1792 0.2035 0.000 0.932 0.000 0.068
#> GSM711933 1 0.0188 0.8632 0.996 0.000 0.004 0.000
#> GSM711935 4 0.4948 -0.1036 0.000 0.440 0.000 0.560
#> GSM711941 3 0.6804 0.6669 0.104 0.376 0.520 0.000
#> GSM711943 3 0.5143 0.7376 0.012 0.360 0.628 0.000
#> GSM711945 3 0.4737 0.7472 0.004 0.296 0.696 0.004
#> GSM711947 4 0.6498 -0.0189 0.000 0.072 0.440 0.488
#> GSM711949 4 0.4643 0.2720 0.000 0.344 0.000 0.656
#> GSM711953 2 0.4804 0.5857 0.000 0.616 0.000 0.384
#> GSM711955 3 0.6189 0.7240 0.092 0.268 0.640 0.000
#> GSM711963 2 0.4817 0.5820 0.000 0.612 0.000 0.388
#> GSM711971 3 0.3448 0.7373 0.004 0.168 0.828 0.000
#> GSM711975 2 0.4679 0.5486 0.000 0.648 0.000 0.352
#> GSM711979 1 0.7466 0.0802 0.436 0.388 0.176 0.000
#> GSM711989 2 0.4790 0.5826 0.000 0.620 0.000 0.380
#> GSM711991 3 0.2647 0.6356 0.000 0.000 0.880 0.120
#> GSM711993 2 0.4764 -0.1596 0.032 0.748 0.220 0.000
#> GSM711983 3 0.5186 0.7412 0.016 0.344 0.640 0.000
#> GSM711985 2 0.4804 0.5857 0.000 0.616 0.000 0.384
#> GSM711913 3 0.4800 0.7438 0.004 0.340 0.656 0.000
#> GSM711919 3 0.2814 0.6249 0.000 0.000 0.868 0.132
#> GSM711921 3 0.1004 0.6962 0.000 0.024 0.972 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM711936 2 0.0162 0.8969 0.000 0.996 0.000 0.000 0.004
#> GSM711938 2 0.0000 0.8972 0.000 1.000 0.000 0.000 0.000
#> GSM711950 1 0.6994 0.0367 0.440 0.000 0.220 0.324 0.016
#> GSM711956 1 0.0566 0.8050 0.984 0.000 0.012 0.000 0.004
#> GSM711958 1 0.3069 0.7653 0.864 0.000 0.104 0.016 0.016
#> GSM711960 3 0.5532 0.4573 0.224 0.000 0.664 0.012 0.100
#> GSM711964 1 0.1772 0.7990 0.940 0.000 0.020 0.008 0.032
#> GSM711966 1 0.2403 0.7877 0.904 0.000 0.072 0.012 0.012
#> GSM711968 1 0.1012 0.7995 0.968 0.000 0.000 0.012 0.020
#> GSM711972 1 0.0451 0.8048 0.988 0.000 0.004 0.000 0.008
#> GSM711976 1 0.2321 0.7900 0.912 0.000 0.024 0.056 0.008
#> GSM711980 1 0.1808 0.7978 0.936 0.000 0.044 0.008 0.012
#> GSM711986 1 0.0404 0.8032 0.988 0.000 0.000 0.000 0.012
#> GSM711904 1 0.4422 0.5283 0.680 0.000 0.016 0.004 0.300
#> GSM711906 1 0.0404 0.8026 0.988 0.000 0.000 0.000 0.012
#> GSM711908 1 0.4166 0.4213 0.648 0.000 0.000 0.004 0.348
#> GSM711910 3 0.2305 0.7322 0.000 0.000 0.896 0.012 0.092
#> GSM711914 1 0.0693 0.8037 0.980 0.000 0.000 0.008 0.012
#> GSM711916 1 0.4912 0.5499 0.688 0.000 0.048 0.008 0.256
#> GSM711922 1 0.0771 0.8011 0.976 0.000 0.000 0.004 0.020
#> GSM711924 1 0.2464 0.7588 0.892 0.000 0.004 0.092 0.012
#> GSM711926 4 0.5476 0.0754 0.032 0.448 0.000 0.504 0.016
#> GSM711928 1 0.1280 0.8028 0.960 0.000 0.008 0.008 0.024
#> GSM711930 1 0.5076 0.3528 0.592 0.000 0.028 0.008 0.372
#> GSM711932 4 0.4921 0.2144 0.360 0.000 0.000 0.604 0.036
#> GSM711934 1 0.2747 0.7756 0.884 0.000 0.088 0.016 0.012
#> GSM711940 1 0.4275 0.7186 0.796 0.000 0.128 0.052 0.024
#> GSM711942 1 0.0898 0.8016 0.972 0.000 0.000 0.008 0.020
#> GSM711944 3 0.6315 0.3439 0.148 0.000 0.608 0.216 0.028
#> GSM711946 3 0.2234 0.7230 0.032 0.000 0.920 0.036 0.012
#> GSM711948 1 0.7011 -0.0158 0.436 0.000 0.224 0.324 0.016
#> GSM711952 1 0.1469 0.7928 0.948 0.000 0.000 0.016 0.036
#> GSM711954 1 0.2158 0.7920 0.920 0.000 0.020 0.008 0.052
#> GSM711962 1 0.0955 0.8047 0.968 0.000 0.028 0.000 0.004
#> GSM711970 5 0.4737 0.0569 0.380 0.000 0.016 0.004 0.600
#> GSM711974 1 0.4617 0.5080 0.660 0.000 0.316 0.008 0.016
#> GSM711978 1 0.7037 0.2030 0.512 0.096 0.048 0.332 0.012
#> GSM711988 1 0.5328 0.6348 0.716 0.000 0.096 0.160 0.028
#> GSM711990 3 0.2456 0.7366 0.024 0.000 0.904 0.008 0.064
#> GSM711992 1 0.8279 -0.1760 0.348 0.236 0.060 0.332 0.024
#> GSM711982 1 0.2291 0.7892 0.908 0.000 0.072 0.008 0.012
#> GSM711984 2 0.3530 0.7501 0.000 0.784 0.000 0.012 0.204
#> GSM711912 1 0.0865 0.8003 0.972 0.000 0.000 0.004 0.024
#> GSM711918 1 0.1018 0.7983 0.968 0.000 0.000 0.016 0.016
#> GSM711920 1 0.4295 0.5953 0.740 0.000 0.000 0.216 0.044
#> GSM711937 2 0.0000 0.8972 0.000 1.000 0.000 0.000 0.000
#> GSM711939 2 0.0000 0.8972 0.000 1.000 0.000 0.000 0.000
#> GSM711951 2 0.3969 0.4853 0.000 0.692 0.000 0.304 0.004
#> GSM711957 4 0.4851 0.2243 0.340 0.000 0.000 0.624 0.036
#> GSM711959 2 0.3355 0.7721 0.000 0.804 0.000 0.012 0.184
#> GSM711961 2 0.0290 0.8961 0.000 0.992 0.000 0.008 0.000
#> GSM711965 3 0.3421 0.7129 0.000 0.000 0.840 0.080 0.080
#> GSM711967 1 0.0566 0.8030 0.984 0.000 0.000 0.012 0.004
#> GSM711969 2 0.0000 0.8972 0.000 1.000 0.000 0.000 0.000
#> GSM711973 4 0.3154 0.4688 0.012 0.000 0.104 0.860 0.024
#> GSM711977 4 0.4920 0.1666 0.000 0.000 0.384 0.584 0.032
#> GSM711981 4 0.6827 0.4036 0.012 0.228 0.204 0.544 0.012
#> GSM711987 2 0.0000 0.8972 0.000 1.000 0.000 0.000 0.000
#> GSM711905 2 0.3720 0.7189 0.000 0.760 0.000 0.012 0.228
#> GSM711907 5 0.4653 0.1357 0.000 0.324 0.008 0.016 0.652
#> GSM711909 3 0.1894 0.7377 0.000 0.000 0.920 0.008 0.072
#> GSM711911 3 0.3012 0.7006 0.000 0.000 0.860 0.104 0.036
#> GSM711915 5 0.2929 0.2979 0.000 0.000 0.152 0.008 0.840
#> GSM711917 2 0.0510 0.8902 0.000 0.984 0.000 0.016 0.000
#> GSM711923 3 0.5955 0.2765 0.088 0.000 0.560 0.340 0.012
#> GSM711925 2 0.0771 0.8912 0.000 0.976 0.000 0.004 0.020
#> GSM711927 3 0.2473 0.7318 0.000 0.000 0.896 0.032 0.072
#> GSM711929 2 0.1012 0.8875 0.000 0.968 0.000 0.012 0.020
#> GSM711931 4 0.3690 0.4216 0.000 0.200 0.000 0.780 0.020
#> GSM711933 1 0.1442 0.8025 0.952 0.000 0.032 0.004 0.012
#> GSM711935 2 0.2522 0.8345 0.000 0.880 0.000 0.012 0.108
#> GSM711941 4 0.6609 0.0730 0.136 0.000 0.400 0.448 0.016
#> GSM711943 3 0.5924 0.3284 0.080 0.004 0.588 0.316 0.012
#> GSM711945 3 0.5508 0.3516 0.000 0.048 0.616 0.316 0.020
#> GSM711947 3 0.6977 0.0220 0.000 0.324 0.444 0.016 0.216
#> GSM711949 2 0.3355 0.7710 0.000 0.804 0.000 0.012 0.184
#> GSM711953 2 0.0000 0.8972 0.000 1.000 0.000 0.000 0.000
#> GSM711955 3 0.2906 0.6889 0.080 0.000 0.880 0.028 0.012
#> GSM711963 2 0.0162 0.8967 0.000 0.996 0.000 0.004 0.000
#> GSM711971 3 0.1074 0.7406 0.012 0.000 0.968 0.016 0.004
#> GSM711975 2 0.3491 0.6351 0.000 0.768 0.000 0.228 0.004
#> GSM711979 4 0.3326 0.4280 0.152 0.000 0.024 0.824 0.000
#> GSM711989 2 0.2338 0.8012 0.000 0.884 0.000 0.112 0.004
#> GSM711991 3 0.2171 0.7330 0.008 0.020 0.928 0.012 0.032
#> GSM711993 4 0.5758 0.3968 0.016 0.304 0.064 0.612 0.004
#> GSM711983 3 0.2494 0.7210 0.032 0.000 0.908 0.044 0.016
#> GSM711985 2 0.0000 0.8972 0.000 1.000 0.000 0.000 0.000
#> GSM711913 4 0.4902 0.1154 0.000 0.000 0.408 0.564 0.028
#> GSM711919 3 0.2228 0.7428 0.008 0.000 0.916 0.020 0.056
#> GSM711921 3 0.2992 0.7197 0.000 0.000 0.868 0.064 0.068
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM711936 2 0.0146 0.9441 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM711938 2 0.0146 0.9441 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM711950 4 0.5932 0.3424 0.272 0.000 0.096 0.580 0.048 0.004
#> GSM711956 1 0.1088 0.8867 0.960 0.000 0.024 0.000 0.016 0.000
#> GSM711958 1 0.2976 0.8289 0.844 0.000 0.128 0.008 0.016 0.004
#> GSM711960 3 0.4650 0.5038 0.232 0.000 0.696 0.052 0.004 0.016
#> GSM711964 1 0.0806 0.8852 0.972 0.000 0.000 0.008 0.000 0.020
#> GSM711966 1 0.1608 0.8798 0.940 0.000 0.036 0.016 0.004 0.004
#> GSM711968 1 0.2136 0.8740 0.908 0.000 0.000 0.016 0.064 0.012
#> GSM711972 1 0.0837 0.8852 0.972 0.000 0.004 0.004 0.020 0.000
#> GSM711976 1 0.1857 0.8814 0.928 0.000 0.012 0.028 0.032 0.000
#> GSM711980 1 0.1985 0.8780 0.916 0.000 0.008 0.064 0.004 0.008
#> GSM711986 1 0.0862 0.8854 0.972 0.000 0.000 0.004 0.008 0.016
#> GSM711904 1 0.3584 0.7266 0.740 0.000 0.000 0.012 0.004 0.244
#> GSM711906 1 0.0692 0.8847 0.976 0.000 0.000 0.004 0.020 0.000
#> GSM711908 1 0.3489 0.6577 0.708 0.000 0.000 0.000 0.004 0.288
#> GSM711910 3 0.1779 0.7710 0.000 0.000 0.920 0.000 0.016 0.064
#> GSM711914 1 0.1226 0.8841 0.952 0.000 0.004 0.004 0.040 0.000
#> GSM711916 1 0.2841 0.8534 0.864 0.000 0.012 0.032 0.000 0.092
#> GSM711922 1 0.1262 0.8863 0.956 0.000 0.000 0.020 0.016 0.008
#> GSM711924 1 0.3512 0.6963 0.740 0.000 0.008 0.004 0.248 0.000
#> GSM711926 4 0.6093 0.1951 0.012 0.312 0.000 0.476 0.200 0.000
#> GSM711928 1 0.1649 0.8829 0.932 0.000 0.000 0.036 0.000 0.032
#> GSM711930 1 0.3073 0.7831 0.788 0.000 0.000 0.008 0.000 0.204
#> GSM711932 5 0.2612 0.3739 0.108 0.000 0.016 0.008 0.868 0.000
#> GSM711934 1 0.2747 0.8545 0.876 0.000 0.036 0.076 0.004 0.008
#> GSM711940 1 0.4460 0.6516 0.716 0.000 0.052 0.216 0.004 0.012
#> GSM711942 1 0.1956 0.8725 0.908 0.000 0.000 0.004 0.080 0.008
#> GSM711944 3 0.6402 0.1910 0.160 0.000 0.496 0.048 0.296 0.000
#> GSM711946 3 0.3530 0.6509 0.012 0.000 0.776 0.200 0.004 0.008
#> GSM711948 4 0.6829 0.1435 0.380 0.000 0.100 0.396 0.124 0.000
#> GSM711952 1 0.3149 0.8442 0.852 0.000 0.000 0.020 0.052 0.076
#> GSM711954 1 0.2817 0.8638 0.872 0.000 0.004 0.076 0.008 0.040
#> GSM711962 1 0.1149 0.8841 0.960 0.000 0.024 0.008 0.008 0.000
#> GSM711970 6 0.3852 0.6577 0.108 0.000 0.012 0.068 0.008 0.804
#> GSM711974 1 0.3938 0.5777 0.672 0.000 0.312 0.012 0.004 0.000
#> GSM711978 4 0.3832 0.4787 0.180 0.024 0.000 0.776 0.012 0.008
#> GSM711988 1 0.2968 0.8590 0.868 0.000 0.044 0.032 0.056 0.000
#> GSM711990 3 0.1894 0.7815 0.016 0.000 0.928 0.040 0.004 0.012
#> GSM711992 4 0.4556 0.4475 0.184 0.076 0.004 0.724 0.000 0.012
#> GSM711982 1 0.1586 0.8789 0.940 0.000 0.040 0.012 0.004 0.004
#> GSM711984 2 0.2706 0.8570 0.000 0.832 0.000 0.000 0.008 0.160
#> GSM711912 1 0.1738 0.8799 0.928 0.000 0.000 0.004 0.052 0.016
#> GSM711918 1 0.2408 0.8527 0.876 0.000 0.000 0.004 0.108 0.012
#> GSM711920 5 0.4300 -0.0796 0.456 0.000 0.012 0.004 0.528 0.000
#> GSM711937 2 0.0405 0.9431 0.000 0.988 0.000 0.008 0.004 0.000
#> GSM711939 2 0.0146 0.9441 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM711951 4 0.3937 0.2693 0.000 0.424 0.000 0.572 0.004 0.000
#> GSM711957 5 0.1672 0.3904 0.048 0.000 0.004 0.016 0.932 0.000
#> GSM711959 2 0.2146 0.8929 0.000 0.880 0.000 0.000 0.004 0.116
#> GSM711961 2 0.0806 0.9401 0.000 0.972 0.000 0.020 0.000 0.008
#> GSM711965 4 0.5405 -0.0676 0.000 0.000 0.436 0.480 0.020 0.064
#> GSM711967 1 0.1349 0.8806 0.940 0.000 0.000 0.004 0.056 0.000
#> GSM711969 2 0.0508 0.9419 0.000 0.984 0.000 0.012 0.004 0.000
#> GSM711973 5 0.4950 0.2993 0.000 0.000 0.080 0.344 0.576 0.000
#> GSM711977 5 0.5528 0.3916 0.000 0.000 0.252 0.192 0.556 0.000
#> GSM711981 4 0.3659 0.4557 0.000 0.060 0.032 0.820 0.088 0.000
#> GSM711987 2 0.0291 0.9438 0.000 0.992 0.000 0.004 0.004 0.000
#> GSM711905 2 0.3222 0.8482 0.000 0.824 0.000 0.024 0.012 0.140
#> GSM711907 6 0.4586 0.6732 0.000 0.036 0.024 0.236 0.004 0.700
#> GSM711909 3 0.0717 0.7930 0.000 0.000 0.976 0.000 0.008 0.016
#> GSM711911 3 0.2666 0.7405 0.000 0.000 0.872 0.028 0.092 0.008
#> GSM711915 6 0.2937 0.6983 0.000 0.000 0.100 0.044 0.004 0.852
#> GSM711917 2 0.0547 0.9389 0.000 0.980 0.000 0.020 0.000 0.000
#> GSM711923 4 0.3478 0.5171 0.064 0.000 0.108 0.820 0.004 0.004
#> GSM711925 2 0.0458 0.9427 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM711927 3 0.0914 0.7927 0.000 0.000 0.968 0.000 0.016 0.016
#> GSM711929 2 0.1480 0.9286 0.000 0.940 0.000 0.020 0.000 0.040
#> GSM711931 5 0.5004 0.1136 0.000 0.084 0.000 0.348 0.568 0.000
#> GSM711933 1 0.2693 0.8729 0.884 0.000 0.036 0.052 0.028 0.000
#> GSM711935 2 0.2020 0.9050 0.000 0.896 0.000 0.000 0.008 0.096
#> GSM711941 4 0.6067 0.3722 0.120 0.000 0.124 0.616 0.140 0.000
#> GSM711943 4 0.4354 0.4650 0.052 0.000 0.236 0.704 0.008 0.000
#> GSM711945 4 0.3369 0.4855 0.008 0.012 0.140 0.824 0.008 0.008
#> GSM711947 3 0.5030 0.4712 0.000 0.200 0.696 0.036 0.008 0.060
#> GSM711949 2 0.2846 0.8650 0.000 0.840 0.000 0.016 0.004 0.140
#> GSM711953 2 0.0260 0.9441 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM711955 3 0.5158 0.4177 0.276 0.000 0.624 0.088 0.008 0.004
#> GSM711963 2 0.0653 0.9435 0.000 0.980 0.000 0.004 0.004 0.012
#> GSM711971 3 0.0862 0.7941 0.008 0.000 0.972 0.016 0.004 0.000
#> GSM711975 2 0.2201 0.8737 0.000 0.896 0.000 0.076 0.028 0.000
#> GSM711979 4 0.5008 0.3164 0.108 0.000 0.000 0.612 0.280 0.000
#> GSM711989 2 0.1556 0.8921 0.000 0.920 0.000 0.080 0.000 0.000
#> GSM711991 3 0.2128 0.7669 0.000 0.004 0.908 0.056 0.000 0.032
#> GSM711993 4 0.4156 0.4430 0.004 0.160 0.004 0.756 0.076 0.000
#> GSM711983 3 0.1457 0.7870 0.028 0.000 0.948 0.016 0.004 0.004
#> GSM711985 2 0.0146 0.9441 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM711913 5 0.6289 0.2550 0.000 0.000 0.320 0.280 0.392 0.008
#> GSM711919 3 0.0964 0.7953 0.004 0.000 0.968 0.016 0.012 0.000
#> GSM711921 3 0.2136 0.7652 0.000 0.000 0.908 0.016 0.064 0.012
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) disease.state(p) individual(p) k
#> ATC:NMF 89 1.62e-05 0.236 0.559 2
#> ATC:NMF 84 9.89e-05 0.232 0.142 3
#> ATC:NMF 70 1.13e-08 0.197 0.526 4
#> ATC:NMF 63 1.58e-08 0.185 0.506 5
#> ATC:NMF 67 3.43e-07 0.363 0.782 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
sessionInfo()
#> R version 3.6.0 (2019-04-26)
#> Platform: x86_64-pc-linux-gnu (64-bit)
#> Running under: CentOS Linux 7 (Core)
#>
#> Matrix products: default
#> BLAS: /usr/lib64/libblas.so.3.4.2
#> LAPACK: /usr/lib64/liblapack.so.3.4.2
#>
#> locale:
#> [1] LC_CTYPE=en_GB.UTF-8 LC_NUMERIC=C LC_TIME=en_GB.UTF-8
#> [4] LC_COLLATE=en_GB.UTF-8 LC_MONETARY=en_GB.UTF-8 LC_MESSAGES=en_GB.UTF-8
#> [7] LC_PAPER=en_GB.UTF-8 LC_NAME=C LC_ADDRESS=C
#> [10] LC_TELEPHONE=C LC_MEASUREMENT=en_GB.UTF-8 LC_IDENTIFICATION=C
#>
#> attached base packages:
#> [1] grid stats graphics grDevices utils datasets methods base
#>
#> other attached packages:
#> [1] genefilter_1.66.0 ComplexHeatmap_2.3.1 markdown_1.1 knitr_1.26
#> [5] GetoptLong_0.1.7 cola_1.3.2
#>
#> loaded via a namespace (and not attached):
#> [1] circlize_0.4.8 shape_1.4.4 xfun_0.11 slam_0.1-46
#> [5] lattice_0.20-38 splines_3.6.0 colorspace_1.4-1 vctrs_0.2.0
#> [9] stats4_3.6.0 blob_1.2.0 XML_3.98-1.20 survival_2.44-1.1
#> [13] rlang_0.4.2 pillar_1.4.2 DBI_1.0.0 BiocGenerics_0.30.0
#> [17] bit64_0.9-7 RColorBrewer_1.1-2 matrixStats_0.55.0 stringr_1.4.0
#> [21] GlobalOptions_0.1.1 evaluate_0.14 memoise_1.1.0 Biobase_2.44.0
#> [25] IRanges_2.18.3 parallel_3.6.0 AnnotationDbi_1.46.1 highr_0.8
#> [29] Rcpp_1.0.3 xtable_1.8-4 backports_1.1.5 S4Vectors_0.22.1
#> [33] annotate_1.62.0 skmeans_0.2-11 bit_1.1-14 microbenchmark_1.4-7
#> [37] brew_1.0-6 impute_1.58.0 rjson_0.2.20 png_0.1-7
#> [41] digest_0.6.23 stringi_1.4.3 polyclip_1.10-0 clue_0.3-57
#> [45] tools_3.6.0 bitops_1.0-6 magrittr_1.5 eulerr_6.0.0
#> [49] RCurl_1.95-4.12 RSQLite_2.1.4 tibble_2.1.3 cluster_2.1.0
#> [53] crayon_1.3.4 pkgconfig_2.0.3 zeallot_0.1.0 Matrix_1.2-17
#> [57] xml2_1.2.2 httr_1.4.1 R6_2.4.1 mclust_5.4.5
#> [61] compiler_3.6.0