Date: 2019-12-25 20:54:03 CET, cola version: 1.3.2
Document is loading...
All available functions which can be applied to this res_list object:
res_list
#> A 'ConsensusPartitionList' object with 24 methods.
#> On a matrix with 15497 rows and 84 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] 15497 84
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 | ||
|---|---|---|---|---|---|---|
| ATC:kmeans | 2 | 1.000 | 0.950 | 0.980 | ** | |
| ATC:skmeans | 2 | 1.000 | 0.997 | 0.998 | ** | |
| ATC:mclust | 4 | 0.934 | 0.934 | 0.967 | * | 2 |
| CV:kmeans | 2 | 0.927 | 0.939 | 0.965 | * | |
| ATC:pam | 5 | 0.927 | 0.851 | 0.940 | * | 2 |
| CV:skmeans | 2 | 0.926 | 0.945 | 0.977 | * | |
| ATC:NMF | 3 | 0.920 | 0.911 | 0.949 | * | 2 |
| ATC:hclust | 2 | 0.904 | 0.944 | 0.970 | * | |
| SD:skmeans | 2 | 0.903 | 0.916 | 0.963 | * | |
| MAD:mclust | 4 | 0.895 | 0.902 | 0.947 | ||
| MAD:skmeans | 2 | 0.862 | 0.956 | 0.978 | ||
| SD:mclust | 4 | 0.852 | 0.885 | 0.922 | ||
| MAD:kmeans | 2 | 0.798 | 0.931 | 0.964 | ||
| MAD:NMF | 2 | 0.786 | 0.853 | 0.943 | ||
| CV:mclust | 5 | 0.770 | 0.881 | 0.886 | ||
| CV:NMF | 2 | 0.745 | 0.814 | 0.927 | ||
| SD:kmeans | 2 | 0.736 | 0.889 | 0.945 | ||
| SD:NMF | 2 | 0.702 | 0.835 | 0.933 | ||
| CV:pam | 5 | 0.668 | 0.661 | 0.825 | ||
| MAD:pam | 2 | 0.560 | 0.823 | 0.916 | ||
| SD:hclust | 3 | 0.506 | 0.783 | 0.856 | ||
| MAD:hclust | 3 | 0.435 | 0.721 | 0.830 | ||
| SD:pam | 2 | 0.401 | 0.772 | 0.890 | ||
| CV:hclust | 2 | 0.378 | 0.622 | 0.820 |
**: 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 0.702 0.835 0.933 0.503 0.499 0.499
#> CV:NMF 2 0.745 0.814 0.927 0.505 0.494 0.494
#> MAD:NMF 2 0.786 0.853 0.943 0.502 0.497 0.497
#> ATC:NMF 2 1.000 0.964 0.984 0.496 0.501 0.501
#> SD:skmeans 2 0.903 0.916 0.963 0.505 0.497 0.497
#> CV:skmeans 2 0.926 0.945 0.977 0.505 0.497 0.497
#> MAD:skmeans 2 0.862 0.956 0.978 0.504 0.497 0.497
#> ATC:skmeans 2 1.000 0.997 0.998 0.504 0.497 0.497
#> SD:mclust 2 0.533 0.618 0.843 0.458 0.501 0.501
#> CV:mclust 2 0.485 0.853 0.900 0.447 0.535 0.535
#> MAD:mclust 2 0.323 0.257 0.691 0.416 0.826 0.826
#> ATC:mclust 2 1.000 0.979 0.987 0.437 0.567 0.567
#> SD:kmeans 2 0.736 0.889 0.945 0.502 0.497 0.497
#> CV:kmeans 2 0.927 0.939 0.965 0.504 0.497 0.497
#> MAD:kmeans 2 0.798 0.931 0.964 0.502 0.497 0.497
#> ATC:kmeans 2 1.000 0.950 0.980 0.493 0.501 0.501
#> SD:pam 2 0.401 0.772 0.890 0.496 0.501 0.501
#> CV:pam 2 0.290 0.658 0.790 0.495 0.495 0.495
#> MAD:pam 2 0.560 0.823 0.916 0.495 0.504 0.504
#> ATC:pam 2 1.000 0.999 0.999 0.502 0.499 0.499
#> SD:hclust 2 0.625 0.837 0.921 0.447 0.523 0.523
#> CV:hclust 2 0.378 0.622 0.820 0.457 0.512 0.512
#> MAD:hclust 2 0.374 0.736 0.875 0.445 0.523 0.523
#> ATC:hclust 2 0.904 0.944 0.970 0.496 0.497 0.497
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 0.640 0.748 0.869 0.324 0.768 0.563
#> CV:NMF 3 0.517 0.462 0.724 0.320 0.794 0.607
#> MAD:NMF 3 0.716 0.823 0.891 0.325 0.777 0.577
#> ATC:NMF 3 0.920 0.911 0.949 0.328 0.752 0.543
#> SD:skmeans 3 0.789 0.863 0.924 0.315 0.762 0.554
#> CV:skmeans 3 0.709 0.756 0.892 0.319 0.742 0.526
#> MAD:skmeans 3 0.773 0.894 0.932 0.313 0.787 0.594
#> ATC:skmeans 3 0.894 0.850 0.937 0.231 0.893 0.786
#> SD:mclust 3 0.679 0.853 0.888 0.386 0.799 0.614
#> CV:mclust 3 0.445 0.655 0.813 0.354 0.627 0.416
#> MAD:mclust 3 0.549 0.848 0.877 0.490 0.429 0.343
#> ATC:mclust 3 0.781 0.876 0.929 0.397 0.715 0.536
#> SD:kmeans 3 0.646 0.750 0.863 0.294 0.748 0.534
#> CV:kmeans 3 0.604 0.689 0.828 0.288 0.755 0.544
#> MAD:kmeans 3 0.636 0.819 0.865 0.293 0.762 0.554
#> ATC:kmeans 3 0.662 0.740 0.883 0.323 0.741 0.526
#> SD:pam 3 0.488 0.687 0.796 0.323 0.765 0.561
#> CV:pam 3 0.484 0.606 0.805 0.317 0.724 0.507
#> MAD:pam 3 0.525 0.736 0.827 0.331 0.770 0.568
#> ATC:pam 3 0.659 0.781 0.853 0.293 0.802 0.623
#> SD:hclust 3 0.506 0.783 0.856 0.464 0.806 0.629
#> CV:hclust 3 0.298 0.500 0.727 0.370 0.789 0.599
#> MAD:hclust 3 0.435 0.721 0.830 0.468 0.806 0.629
#> ATC:hclust 3 0.698 0.867 0.909 0.233 0.907 0.813
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.693 0.726 0.860 0.1166 0.825 0.541
#> CV:NMF 4 0.595 0.670 0.808 0.1164 0.784 0.471
#> MAD:NMF 4 0.703 0.717 0.859 0.1178 0.845 0.587
#> ATC:NMF 4 0.838 0.809 0.906 0.0951 0.896 0.708
#> SD:skmeans 4 0.721 0.858 0.874 0.1005 0.919 0.765
#> CV:skmeans 4 0.654 0.678 0.785 0.1062 0.913 0.751
#> MAD:skmeans 4 0.733 0.864 0.880 0.1041 0.922 0.774
#> ATC:skmeans 4 0.803 0.898 0.915 0.1231 0.893 0.734
#> SD:mclust 4 0.852 0.885 0.922 0.0971 0.869 0.662
#> CV:mclust 4 0.706 0.837 0.864 0.1194 0.768 0.502
#> MAD:mclust 4 0.895 0.902 0.947 0.1225 0.869 0.662
#> ATC:mclust 4 0.934 0.934 0.967 0.1399 0.784 0.515
#> SD:kmeans 4 0.601 0.762 0.756 0.1199 0.927 0.788
#> CV:kmeans 4 0.548 0.689 0.733 0.1195 0.915 0.765
#> MAD:kmeans 4 0.615 0.734 0.710 0.1239 0.937 0.815
#> ATC:kmeans 4 0.681 0.726 0.789 0.1221 0.811 0.515
#> SD:pam 4 0.606 0.783 0.843 0.1356 0.809 0.504
#> CV:pam 4 0.555 0.432 0.684 0.0978 0.772 0.472
#> MAD:pam 4 0.679 0.807 0.867 0.1416 0.824 0.531
#> ATC:pam 4 0.717 0.750 0.860 0.1341 0.899 0.719
#> SD:hclust 4 0.580 0.620 0.779 0.1241 0.863 0.620
#> CV:hclust 4 0.436 0.409 0.631 0.1569 0.888 0.683
#> MAD:hclust 4 0.567 0.603 0.729 0.1294 0.900 0.707
#> ATC:hclust 4 0.639 0.804 0.840 0.1648 0.856 0.646
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.605 0.472 0.693 0.0610 0.847 0.507
#> CV:NMF 5 0.549 0.414 0.670 0.0640 0.874 0.572
#> MAD:NMF 5 0.651 0.481 0.739 0.0594 0.859 0.538
#> ATC:NMF 5 0.730 0.602 0.828 0.0616 0.966 0.878
#> SD:skmeans 5 0.716 0.670 0.803 0.0746 0.950 0.822
#> CV:skmeans 5 0.642 0.557 0.715 0.0695 0.880 0.610
#> MAD:skmeans 5 0.699 0.659 0.798 0.0729 0.969 0.887
#> ATC:skmeans 5 0.752 0.763 0.867 0.0686 0.983 0.942
#> SD:mclust 5 0.679 0.780 0.834 0.0611 0.989 0.964
#> CV:mclust 5 0.770 0.881 0.886 0.1197 0.852 0.590
#> MAD:mclust 5 0.719 0.791 0.853 0.0663 0.989 0.964
#> ATC:mclust 5 0.807 0.755 0.878 0.1175 0.812 0.484
#> SD:kmeans 5 0.585 0.603 0.697 0.0694 0.908 0.678
#> CV:kmeans 5 0.589 0.493 0.651 0.0675 0.982 0.940
#> MAD:kmeans 5 0.598 0.631 0.702 0.0677 0.892 0.632
#> ATC:kmeans 5 0.680 0.670 0.715 0.0688 0.922 0.727
#> SD:pam 5 0.665 0.742 0.842 0.0587 0.948 0.790
#> CV:pam 5 0.668 0.661 0.825 0.0842 0.760 0.352
#> MAD:pam 5 0.675 0.721 0.819 0.0547 0.930 0.725
#> ATC:pam 5 0.927 0.851 0.940 0.0648 0.904 0.666
#> SD:hclust 5 0.622 0.695 0.778 0.0669 0.903 0.649
#> CV:hclust 5 0.556 0.478 0.688 0.0704 0.820 0.439
#> MAD:hclust 5 0.591 0.696 0.751 0.0674 0.900 0.638
#> ATC:hclust 5 0.687 0.642 0.807 0.0797 0.960 0.852
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.653 0.574 0.741 0.0410 0.913 0.640
#> CV:NMF 6 0.612 0.340 0.604 0.0459 0.822 0.358
#> MAD:NMF 6 0.669 0.602 0.761 0.0406 0.878 0.532
#> ATC:NMF 6 0.722 0.630 0.816 0.0409 0.903 0.649
#> SD:skmeans 6 0.731 0.685 0.770 0.0446 0.939 0.745
#> CV:skmeans 6 0.650 0.530 0.671 0.0453 0.944 0.761
#> MAD:skmeans 6 0.756 0.715 0.805 0.0467 0.910 0.647
#> ATC:skmeans 6 0.748 0.567 0.732 0.0506 0.877 0.598
#> SD:mclust 6 0.715 0.758 0.801 0.0566 0.916 0.722
#> CV:mclust 6 0.766 0.706 0.805 0.0578 0.958 0.829
#> MAD:mclust 6 0.714 0.707 0.802 0.0494 0.974 0.911
#> ATC:mclust 6 0.730 0.712 0.823 0.0241 0.958 0.835
#> SD:kmeans 6 0.616 0.521 0.674 0.0418 0.919 0.662
#> CV:kmeans 6 0.611 0.389 0.571 0.0461 0.859 0.541
#> MAD:kmeans 6 0.639 0.566 0.689 0.0453 0.951 0.777
#> ATC:kmeans 6 0.720 0.762 0.772 0.0452 0.923 0.681
#> SD:pam 6 0.736 0.749 0.843 0.0415 0.897 0.572
#> CV:pam 6 0.669 0.613 0.764 0.0507 0.905 0.605
#> MAD:pam 6 0.740 0.749 0.843 0.0387 0.911 0.614
#> ATC:pam 6 0.846 0.799 0.873 0.0574 0.923 0.662
#> SD:hclust 6 0.785 0.780 0.847 0.0501 0.972 0.862
#> CV:hclust 6 0.628 0.465 0.680 0.0504 0.935 0.701
#> MAD:hclust 6 0.749 0.762 0.845 0.0469 0.972 0.862
#> ATC:hclust 6 0.703 0.581 0.743 0.0544 0.894 0.577
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 protocol(p) agent(p) individual(p) k
#> SD:NMF 75 0.919 0.925 0.004135 2
#> CV:NMF 72 1.000 0.846 0.004521 2
#> MAD:NMF 76 1.000 0.789 0.005067 2
#> ATC:NMF 83 0.900 0.446 0.004258 2
#> SD:skmeans 81 1.000 0.726 0.001838 2
#> CV:skmeans 81 1.000 0.726 0.001838 2
#> MAD:skmeans 84 1.000 0.769 0.001220 2
#> ATC:skmeans 84 1.000 0.550 0.003233 2
#> SD:mclust 59 0.891 0.864 0.003568 2
#> CV:mclust 80 0.767 0.798 0.001673 2
#> MAD:mclust 39 1.000 0.990 0.019841 2
#> ATC:mclust 84 1.000 0.606 0.001026 2
#> SD:kmeans 83 1.000 0.703 0.001570 2
#> CV:kmeans 83 1.000 0.703 0.001570 2
#> MAD:kmeans 83 1.000 0.703 0.001570 2
#> ATC:kmeans 81 0.896 0.405 0.004325 2
#> SD:pam 78 1.000 0.893 0.003281 2
#> CV:pam 69 0.952 0.502 0.013791 2
#> MAD:pam 79 1.000 0.859 0.003100 2
#> ATC:pam 84 1.000 0.421 0.005233 2
#> SD:hclust 78 1.000 0.886 0.000481 2
#> CV:hclust 64 1.000 0.966 0.001157 2
#> MAD:hclust 70 1.000 0.871 0.000970 2
#> ATC:hclust 84 1.000 0.769 0.001220 2
test_to_known_factors(res_list, k = 3)
#> n protocol(p) agent(p) individual(p) k
#> SD:NMF 80 0.964 0.957 4.46e-05 3
#> CV:NMF 48 1.000 0.744 2.26e-02 3
#> MAD:NMF 81 0.991 0.928 2.93e-05 3
#> ATC:NMF 82 0.904 0.778 4.41e-05 3
#> SD:skmeans 83 0.988 0.963 3.05e-05 3
#> CV:skmeans 79 0.985 0.995 2.05e-05 3
#> MAD:skmeans 83 0.895 0.973 6.95e-06 3
#> ATC:skmeans 71 0.361 0.513 1.45e-04 3
#> SD:mclust 82 0.982 0.784 1.10e-04 3
#> CV:mclust 69 0.495 0.739 7.74e-05 3
#> MAD:mclust 81 0.939 0.815 8.53e-05 3
#> ATC:mclust 83 0.986 0.996 1.26e-05 3
#> SD:kmeans 75 0.985 0.993 3.72e-05 3
#> CV:kmeans 76 0.953 0.846 4.54e-05 3
#> MAD:kmeans 84 0.961 0.957 3.97e-05 3
#> ATC:kmeans 72 0.948 0.886 6.99e-04 3
#> SD:pam 75 0.724 0.879 1.65e-05 3
#> CV:pam 60 0.846 0.862 8.09e-04 3
#> MAD:pam 77 0.557 0.794 2.27e-05 3
#> ATC:pam 82 0.527 0.839 1.28e-03 3
#> SD:hclust 82 0.697 0.958 4.59e-07 3
#> CV:hclust 58 0.916 0.995 3.57e-05 3
#> MAD:hclust 78 0.698 0.956 8.95e-07 3
#> ATC:hclust 83 0.780 0.854 2.57e-04 3
test_to_known_factors(res_list, k = 4)
#> n protocol(p) agent(p) individual(p) k
#> SD:NMF 71 0.239 0.723 7.00e-07 4
#> CV:NMF 71 0.317 0.977 1.90e-06 4
#> MAD:NMF 71 0.148 0.716 1.63e-06 4
#> ATC:NMF 76 0.781 0.969 7.92e-06 4
#> SD:skmeans 82 0.917 0.997 3.41e-08 4
#> CV:skmeans 71 0.995 1.000 8.77e-08 4
#> MAD:skmeans 81 0.868 0.997 3.28e-08 4
#> ATC:skmeans 83 0.936 0.874 2.70e-05 4
#> SD:mclust 81 0.889 0.956 4.96e-08 4
#> CV:mclust 82 0.713 0.985 3.88e-09 4
#> MAD:mclust 82 0.827 0.899 6.82e-08 4
#> ATC:mclust 83 0.733 0.928 2.02e-07 4
#> SD:kmeans 81 0.996 0.990 7.14e-08 4
#> CV:kmeans 75 0.984 0.986 6.91e-08 4
#> MAD:kmeans 80 0.995 0.990 4.69e-08 4
#> ATC:kmeans 77 0.700 0.635 5.21e-04 4
#> SD:pam 81 0.639 0.970 5.50e-07 4
#> CV:pam 39 1.000 0.713 5.36e-02 4
#> MAD:pam 80 0.769 0.976 1.20e-06 4
#> ATC:pam 76 0.251 0.654 6.85e-04 4
#> SD:hclust 62 0.658 0.946 9.45e-06 4
#> CV:hclust 35 0.993 1.000 5.86e-04 4
#> MAD:hclust 72 0.939 0.996 8.45e-09 4
#> ATC:hclust 80 0.810 0.872 2.07e-05 4
test_to_known_factors(res_list, k = 5)
#> n protocol(p) agent(p) individual(p) k
#> SD:NMF 46 0.585 0.556 5.01e-03 5
#> CV:NMF 33 0.396 0.650 5.33e-03 5
#> MAD:NMF 40 0.145 0.668 1.25e-03 5
#> ATC:NMF 63 0.756 0.523 6.56e-07 5
#> SD:skmeans 72 0.903 0.998 7.90e-10 5
#> CV:skmeans 57 0.950 0.989 6.44e-06 5
#> MAD:skmeans 71 0.850 0.979 8.45e-10 5
#> ATC:skmeans 75 0.927 0.955 7.03e-05 5
#> SD:mclust 80 0.837 0.873 3.48e-07 5
#> CV:mclust 84 0.936 0.962 4.66e-09 5
#> MAD:mclust 81 0.889 0.934 1.70e-07 5
#> ATC:mclust 75 0.693 0.787 1.72e-07 5
#> SD:kmeans 70 0.941 0.985 3.16e-09 5
#> CV:kmeans 46 0.377 0.854 7.15e-06 5
#> MAD:kmeans 70 0.849 0.986 2.77e-09 5
#> ATC:kmeans 66 0.640 0.692 3.64e-05 5
#> SD:pam 76 0.620 0.728 3.78e-08 5
#> CV:pam 70 0.745 0.926 1.03e-06 5
#> MAD:pam 74 0.426 0.703 3.71e-08 5
#> ATC:pam 77 0.495 0.861 6.55e-06 5
#> SD:hclust 70 0.928 0.999 3.64e-11 5
#> CV:hclust 46 1.000 0.999 4.30e-06 5
#> MAD:hclust 67 0.922 0.998 1.89e-10 5
#> ATC:hclust 63 0.888 0.955 4.61e-05 5
test_to_known_factors(res_list, k = 6)
#> n protocol(p) agent(p) individual(p) k
#> SD:NMF 61 0.852 0.842 1.06e-04 6
#> CV:NMF 25 0.981 0.890 2.23e-02 6
#> MAD:NMF 66 0.772 0.889 7.34e-08 6
#> ATC:NMF 60 0.636 0.743 1.34e-05 6
#> SD:skmeans 72 0.860 0.994 3.78e-12 6
#> CV:skmeans 57 0.975 1.000 1.38e-07 6
#> MAD:skmeans 72 0.775 0.994 2.58e-12 6
#> ATC:skmeans 55 0.473 0.832 1.31e-05 6
#> SD:mclust 78 0.798 0.941 9.61e-10 6
#> CV:mclust 71 0.933 0.996 1.02e-09 6
#> MAD:mclust 68 0.625 0.854 8.79e-08 6
#> ATC:mclust 70 0.690 0.902 2.72e-05 6
#> SD:kmeans 56 0.747 0.965 7.75e-08 6
#> CV:kmeans 33 0.483 0.889 1.90e-04 6
#> MAD:kmeans 56 0.951 0.997 9.73e-08 6
#> ATC:kmeans 76 0.759 0.774 2.84e-07 6
#> SD:pam 75 0.709 0.842 1.40e-08 6
#> CV:pam 66 0.463 0.956 5.30e-09 6
#> MAD:pam 78 0.474 0.723 5.92e-10 6
#> ATC:pam 75 0.320 0.430 1.33e-06 6
#> SD:hclust 76 0.946 1.000 1.68e-14 6
#> CV:hclust 43 0.989 1.000 6.16e-06 6
#> MAD:hclust 79 0.964 1.000 1.14e-14 6
#> ATC:hclust 60 0.914 0.953 4.75e-07 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 15497 rows and 84 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 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 0.625 0.837 0.921 0.4474 0.523 0.523
#> 3 3 0.506 0.783 0.856 0.4639 0.806 0.629
#> 4 4 0.580 0.620 0.779 0.1241 0.863 0.620
#> 5 5 0.622 0.695 0.778 0.0669 0.903 0.649
#> 6 6 0.785 0.780 0.847 0.0501 0.972 0.862
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
#> GSM339455 1 0.0376 0.946 0.996 0.004
#> GSM339456 2 0.4298 0.798 0.088 0.912
#> GSM339457 1 0.3274 0.917 0.940 0.060
#> GSM339458 2 0.9358 0.544 0.352 0.648
#> GSM339459 1 0.4690 0.885 0.900 0.100
#> GSM339460 2 0.2236 0.837 0.036 0.964
#> GSM339461 2 0.0000 0.841 0.000 1.000
#> GSM339462 1 0.0376 0.946 0.996 0.004
#> GSM339463 1 0.0000 0.946 1.000 0.000
#> GSM339464 1 0.1184 0.943 0.984 0.016
#> GSM339465 1 0.0000 0.946 1.000 0.000
#> GSM339466 2 0.9944 0.288 0.456 0.544
#> GSM339467 2 0.0000 0.841 0.000 1.000
#> GSM339468 1 0.7528 0.732 0.784 0.216
#> GSM339469 1 0.3274 0.915 0.940 0.060
#> GSM339470 2 0.9866 0.396 0.432 0.568
#> GSM339471 1 0.0000 0.946 1.000 0.000
#> GSM339472 2 0.0000 0.841 0.000 1.000
#> GSM339473 1 0.0000 0.946 1.000 0.000
#> GSM339474 2 0.0000 0.841 0.000 1.000
#> GSM339475 1 0.0000 0.946 1.000 0.000
#> GSM339476 1 0.0376 0.946 0.996 0.004
#> GSM339477 2 0.0000 0.841 0.000 1.000
#> GSM339478 1 0.3274 0.917 0.940 0.060
#> GSM339479 2 0.9358 0.544 0.352 0.648
#> GSM339480 1 0.4690 0.885 0.900 0.100
#> GSM339481 2 0.2236 0.837 0.036 0.964
#> GSM339482 1 0.0000 0.946 1.000 0.000
#> GSM339483 1 0.0376 0.946 0.996 0.004
#> GSM339484 1 0.0000 0.946 1.000 0.000
#> GSM339485 1 0.1184 0.943 0.984 0.016
#> GSM339486 1 0.0000 0.946 1.000 0.000
#> GSM339487 2 0.9944 0.288 0.456 0.544
#> GSM339488 2 0.0000 0.841 0.000 1.000
#> GSM339489 1 0.7528 0.732 0.784 0.216
#> GSM339490 1 0.3274 0.915 0.940 0.060
#> GSM339491 2 0.9866 0.396 0.432 0.568
#> GSM339492 1 0.0000 0.946 1.000 0.000
#> GSM339493 2 0.1184 0.840 0.016 0.984
#> GSM339494 1 0.0000 0.946 1.000 0.000
#> GSM339495 2 0.0000 0.841 0.000 1.000
#> GSM339496 1 0.0000 0.946 1.000 0.000
#> GSM339497 2 0.2043 0.838 0.032 0.968
#> GSM339498 1 0.6623 0.796 0.828 0.172
#> GSM339499 1 0.3274 0.917 0.940 0.060
#> GSM339500 2 0.9358 0.544 0.352 0.648
#> GSM339501 1 0.5946 0.838 0.856 0.144
#> GSM339502 2 0.2236 0.837 0.036 0.964
#> GSM339503 1 0.0000 0.946 1.000 0.000
#> GSM339504 1 0.0376 0.946 0.996 0.004
#> GSM339505 1 0.0938 0.944 0.988 0.012
#> GSM339506 1 0.1184 0.943 0.984 0.016
#> GSM339507 1 0.0000 0.946 1.000 0.000
#> GSM339508 2 0.0000 0.841 0.000 1.000
#> GSM339509 2 0.0000 0.841 0.000 1.000
#> GSM339510 1 0.7528 0.732 0.784 0.216
#> GSM339511 1 0.3274 0.915 0.940 0.060
#> GSM339512 2 0.9866 0.396 0.432 0.568
#> GSM339513 1 0.0000 0.946 1.000 0.000
#> GSM339514 2 0.0000 0.841 0.000 1.000
#> GSM339515 1 0.0000 0.946 1.000 0.000
#> GSM339516 2 0.0000 0.841 0.000 1.000
#> GSM339517 1 0.0000 0.946 1.000 0.000
#> GSM339518 2 0.2043 0.838 0.032 0.968
#> GSM339519 1 0.4690 0.877 0.900 0.100
#> GSM339520 1 0.3274 0.917 0.940 0.060
#> GSM339521 2 0.9358 0.544 0.352 0.648
#> GSM339522 1 0.5946 0.838 0.856 0.144
#> GSM339523 2 0.2236 0.837 0.036 0.964
#> GSM339524 1 0.0000 0.946 1.000 0.000
#> GSM339525 1 0.0376 0.946 0.996 0.004
#> GSM339526 1 0.0000 0.946 1.000 0.000
#> GSM339527 1 0.1184 0.943 0.984 0.016
#> GSM339528 1 0.0000 0.946 1.000 0.000
#> GSM339529 2 0.0000 0.841 0.000 1.000
#> GSM339530 1 0.3274 0.917 0.940 0.060
#> GSM339531 1 0.7528 0.732 0.784 0.216
#> GSM339532 1 0.3274 0.915 0.940 0.060
#> GSM339533 2 0.9866 0.396 0.432 0.568
#> GSM339534 1 0.0000 0.946 1.000 0.000
#> GSM339535 2 0.1184 0.840 0.016 0.984
#> GSM339536 1 0.0000 0.946 1.000 0.000
#> GSM339537 2 0.0000 0.841 0.000 1.000
#> GSM339538 1 0.0000 0.946 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM339455 1 0.5690 0.783 0.708 0.004 0.288
#> GSM339456 2 0.3293 0.778 0.012 0.900 0.088
#> GSM339457 3 0.2743 0.849 0.020 0.052 0.928
#> GSM339458 2 0.7562 0.585 0.308 0.628 0.064
#> GSM339459 3 0.5344 0.830 0.092 0.084 0.824
#> GSM339460 2 0.2063 0.831 0.044 0.948 0.008
#> GSM339461 2 0.0592 0.837 0.012 0.988 0.000
#> GSM339462 1 0.1643 0.881 0.956 0.000 0.044
#> GSM339463 3 0.1964 0.829 0.056 0.000 0.944
#> GSM339464 1 0.0592 0.870 0.988 0.000 0.012
#> GSM339465 1 0.4178 0.861 0.828 0.000 0.172
#> GSM339466 2 0.7353 0.107 0.032 0.532 0.436
#> GSM339467 2 0.0000 0.837 0.000 1.000 0.000
#> GSM339468 3 0.7437 0.724 0.108 0.200 0.692
#> GSM339469 1 0.2063 0.859 0.948 0.044 0.008
#> GSM339470 2 0.8842 0.518 0.308 0.548 0.144
#> GSM339471 1 0.5529 0.777 0.704 0.000 0.296
#> GSM339472 2 0.0000 0.837 0.000 1.000 0.000
#> GSM339473 1 0.3412 0.873 0.876 0.000 0.124
#> GSM339474 2 0.0000 0.837 0.000 1.000 0.000
#> GSM339475 3 0.2959 0.805 0.100 0.000 0.900
#> GSM339476 1 0.5690 0.783 0.708 0.004 0.288
#> GSM339477 2 0.0592 0.837 0.012 0.988 0.000
#> GSM339478 3 0.2743 0.849 0.020 0.052 0.928
#> GSM339479 2 0.7562 0.585 0.308 0.628 0.064
#> GSM339480 3 0.5344 0.830 0.092 0.084 0.824
#> GSM339481 2 0.2063 0.831 0.044 0.948 0.008
#> GSM339482 3 0.3340 0.794 0.120 0.000 0.880
#> GSM339483 1 0.1643 0.881 0.956 0.000 0.044
#> GSM339484 3 0.1964 0.829 0.056 0.000 0.944
#> GSM339485 1 0.0592 0.870 0.988 0.000 0.012
#> GSM339486 1 0.4178 0.861 0.828 0.000 0.172
#> GSM339487 2 0.7353 0.107 0.032 0.532 0.436
#> GSM339488 2 0.0000 0.837 0.000 1.000 0.000
#> GSM339489 3 0.7437 0.724 0.108 0.200 0.692
#> GSM339490 1 0.2063 0.859 0.948 0.044 0.008
#> GSM339491 2 0.8842 0.518 0.308 0.548 0.144
#> GSM339492 1 0.5529 0.777 0.704 0.000 0.296
#> GSM339493 2 0.0747 0.833 0.000 0.984 0.016
#> GSM339494 1 0.3412 0.873 0.876 0.000 0.124
#> GSM339495 2 0.0000 0.837 0.000 1.000 0.000
#> GSM339496 3 0.2959 0.805 0.100 0.000 0.900
#> GSM339497 2 0.1832 0.833 0.036 0.956 0.008
#> GSM339498 3 0.6880 0.766 0.108 0.156 0.736
#> GSM339499 3 0.2743 0.849 0.020 0.052 0.928
#> GSM339500 2 0.7562 0.585 0.308 0.628 0.064
#> GSM339501 3 0.6309 0.806 0.100 0.128 0.772
#> GSM339502 2 0.2063 0.831 0.044 0.948 0.008
#> GSM339503 3 0.3340 0.794 0.120 0.000 0.880
#> GSM339504 1 0.1643 0.881 0.956 0.000 0.044
#> GSM339505 3 0.1751 0.838 0.028 0.012 0.960
#> GSM339506 1 0.0592 0.870 0.988 0.000 0.012
#> GSM339507 1 0.4178 0.861 0.828 0.000 0.172
#> GSM339508 2 0.0424 0.837 0.008 0.992 0.000
#> GSM339509 2 0.0000 0.837 0.000 1.000 0.000
#> GSM339510 3 0.7437 0.724 0.108 0.200 0.692
#> GSM339511 1 0.2063 0.859 0.948 0.044 0.008
#> GSM339512 2 0.8842 0.518 0.308 0.548 0.144
#> GSM339513 1 0.5529 0.777 0.704 0.000 0.296
#> GSM339514 2 0.0000 0.837 0.000 1.000 0.000
#> GSM339515 1 0.3412 0.873 0.876 0.000 0.124
#> GSM339516 2 0.0000 0.837 0.000 1.000 0.000
#> GSM339517 3 0.2959 0.805 0.100 0.000 0.900
#> GSM339518 2 0.1832 0.833 0.036 0.956 0.008
#> GSM339519 3 0.7383 0.710 0.236 0.084 0.680
#> GSM339520 3 0.2743 0.849 0.020 0.052 0.928
#> GSM339521 2 0.7562 0.585 0.308 0.628 0.064
#> GSM339522 3 0.6309 0.806 0.100 0.128 0.772
#> GSM339523 2 0.2063 0.831 0.044 0.948 0.008
#> GSM339524 3 0.3340 0.794 0.120 0.000 0.880
#> GSM339525 1 0.1643 0.881 0.956 0.000 0.044
#> GSM339526 3 0.1964 0.829 0.056 0.000 0.944
#> GSM339527 1 0.0592 0.870 0.988 0.000 0.012
#> GSM339528 1 0.4178 0.861 0.828 0.000 0.172
#> GSM339529 2 0.0424 0.837 0.008 0.992 0.000
#> GSM339530 3 0.2743 0.849 0.020 0.052 0.928
#> GSM339531 3 0.7437 0.724 0.108 0.200 0.692
#> GSM339532 1 0.2063 0.859 0.948 0.044 0.008
#> GSM339533 2 0.8842 0.518 0.308 0.548 0.144
#> GSM339534 1 0.5529 0.777 0.704 0.000 0.296
#> GSM339535 2 0.0747 0.833 0.000 0.984 0.016
#> GSM339536 1 0.3412 0.873 0.876 0.000 0.124
#> GSM339537 2 0.0000 0.837 0.000 1.000 0.000
#> GSM339538 3 0.2959 0.805 0.100 0.000 0.900
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM339455 1 0.4579 0.66637 0.720 0.004 0.272 0.004
#> GSM339456 2 0.4488 0.78254 0.008 0.820 0.076 0.096
#> GSM339457 3 0.2342 0.78037 0.008 0.000 0.912 0.080
#> GSM339458 4 0.4898 0.41593 0.000 0.260 0.024 0.716
#> GSM339459 3 0.3688 0.75880 0.000 0.000 0.792 0.208
#> GSM339460 2 0.3895 0.79214 0.000 0.804 0.012 0.184
#> GSM339461 2 0.2222 0.88522 0.008 0.928 0.008 0.056
#> GSM339462 1 0.5220 0.20663 0.568 0.000 0.008 0.424
#> GSM339463 3 0.2053 0.75537 0.072 0.000 0.924 0.004
#> GSM339464 4 0.5290 -0.02531 0.476 0.000 0.008 0.516
#> GSM339465 1 0.1867 0.70212 0.928 0.000 0.072 0.000
#> GSM339466 3 0.7841 0.20597 0.000 0.324 0.400 0.276
#> GSM339467 2 0.0000 0.89661 0.000 1.000 0.000 0.000
#> GSM339468 3 0.5110 0.68721 0.000 0.016 0.656 0.328
#> GSM339469 1 0.5697 -0.11669 0.488 0.024 0.000 0.488
#> GSM339470 4 0.5355 0.47442 0.000 0.180 0.084 0.736
#> GSM339471 1 0.4277 0.66632 0.720 0.000 0.280 0.000
#> GSM339472 2 0.1109 0.89232 0.000 0.968 0.004 0.028
#> GSM339473 1 0.0469 0.69530 0.988 0.000 0.012 0.000
#> GSM339474 2 0.0336 0.89538 0.008 0.992 0.000 0.000
#> GSM339475 3 0.3969 0.71858 0.180 0.000 0.804 0.016
#> GSM339476 1 0.4579 0.66637 0.720 0.004 0.272 0.004
#> GSM339477 2 0.0804 0.89574 0.008 0.980 0.000 0.012
#> GSM339478 3 0.2342 0.78037 0.008 0.000 0.912 0.080
#> GSM339479 4 0.4898 0.41593 0.000 0.260 0.024 0.716
#> GSM339480 3 0.3688 0.75880 0.000 0.000 0.792 0.208
#> GSM339481 2 0.3895 0.79214 0.000 0.804 0.012 0.184
#> GSM339482 3 0.3791 0.71021 0.200 0.000 0.796 0.004
#> GSM339483 1 0.5220 0.20663 0.568 0.000 0.008 0.424
#> GSM339484 3 0.2053 0.75537 0.072 0.000 0.924 0.004
#> GSM339485 4 0.5290 -0.02531 0.476 0.000 0.008 0.516
#> GSM339486 1 0.1867 0.70212 0.928 0.000 0.072 0.000
#> GSM339487 3 0.7841 0.20597 0.000 0.324 0.400 0.276
#> GSM339488 2 0.0000 0.89661 0.000 1.000 0.000 0.000
#> GSM339489 3 0.5110 0.68721 0.000 0.016 0.656 0.328
#> GSM339490 4 0.5697 0.00102 0.488 0.024 0.000 0.488
#> GSM339491 4 0.5355 0.47442 0.000 0.180 0.084 0.736
#> GSM339492 1 0.4277 0.66632 0.720 0.000 0.280 0.000
#> GSM339493 2 0.1798 0.88525 0.000 0.944 0.016 0.040
#> GSM339494 1 0.0469 0.69530 0.988 0.000 0.012 0.000
#> GSM339495 2 0.0336 0.89538 0.008 0.992 0.000 0.000
#> GSM339496 3 0.3969 0.71858 0.180 0.000 0.804 0.016
#> GSM339497 2 0.4323 0.77541 0.000 0.776 0.020 0.204
#> GSM339498 3 0.4673 0.71121 0.000 0.008 0.700 0.292
#> GSM339499 3 0.2342 0.78037 0.008 0.000 0.912 0.080
#> GSM339500 4 0.4898 0.41593 0.000 0.260 0.024 0.716
#> GSM339501 3 0.4452 0.73933 0.000 0.008 0.732 0.260
#> GSM339502 2 0.3895 0.79214 0.000 0.804 0.012 0.184
#> GSM339503 3 0.3791 0.71021 0.200 0.000 0.796 0.004
#> GSM339504 1 0.5220 0.20663 0.568 0.000 0.008 0.424
#> GSM339505 3 0.1489 0.76726 0.044 0.000 0.952 0.004
#> GSM339506 4 0.5290 -0.02531 0.476 0.000 0.008 0.516
#> GSM339507 1 0.1867 0.70212 0.928 0.000 0.072 0.000
#> GSM339508 2 0.1059 0.89597 0.012 0.972 0.000 0.016
#> GSM339509 2 0.0000 0.89661 0.000 1.000 0.000 0.000
#> GSM339510 3 0.5110 0.68721 0.000 0.016 0.656 0.328
#> GSM339511 4 0.5697 0.00102 0.488 0.024 0.000 0.488
#> GSM339512 4 0.5355 0.47442 0.000 0.180 0.084 0.736
#> GSM339513 1 0.4277 0.66632 0.720 0.000 0.280 0.000
#> GSM339514 2 0.1109 0.89232 0.000 0.968 0.004 0.028
#> GSM339515 1 0.0469 0.69530 0.988 0.000 0.012 0.000
#> GSM339516 2 0.2302 0.88132 0.008 0.924 0.008 0.060
#> GSM339517 3 0.3969 0.71858 0.180 0.000 0.804 0.016
#> GSM339518 2 0.4323 0.77541 0.000 0.776 0.020 0.204
#> GSM339519 3 0.6528 0.64229 0.128 0.008 0.656 0.208
#> GSM339520 3 0.2342 0.78037 0.008 0.000 0.912 0.080
#> GSM339521 4 0.4898 0.41593 0.000 0.260 0.024 0.716
#> GSM339522 3 0.4452 0.73933 0.000 0.008 0.732 0.260
#> GSM339523 2 0.3895 0.79214 0.000 0.804 0.012 0.184
#> GSM339524 3 0.3791 0.71021 0.200 0.000 0.796 0.004
#> GSM339525 1 0.5220 0.20663 0.568 0.000 0.008 0.424
#> GSM339526 3 0.2053 0.75537 0.072 0.000 0.924 0.004
#> GSM339527 4 0.5290 -0.02531 0.476 0.000 0.008 0.516
#> GSM339528 1 0.1867 0.70212 0.928 0.000 0.072 0.000
#> GSM339529 2 0.1059 0.89597 0.012 0.972 0.000 0.016
#> GSM339530 3 0.2342 0.78037 0.008 0.000 0.912 0.080
#> GSM339531 3 0.5110 0.68721 0.000 0.016 0.656 0.328
#> GSM339532 4 0.5697 0.00102 0.488 0.024 0.000 0.488
#> GSM339533 4 0.5355 0.47442 0.000 0.180 0.084 0.736
#> GSM339534 1 0.4277 0.66632 0.720 0.000 0.280 0.000
#> GSM339535 2 0.1798 0.88525 0.000 0.944 0.016 0.040
#> GSM339536 1 0.0469 0.69530 0.988 0.000 0.012 0.000
#> GSM339537 2 0.2302 0.88132 0.008 0.924 0.008 0.060
#> GSM339538 3 0.3969 0.71858 0.180 0.000 0.804 0.016
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM339455 1 0.2915 0.798 0.860 0.000 0.116 0.000 0.024
#> GSM339456 2 0.4007 0.765 0.004 0.816 0.008 0.068 0.104
#> GSM339457 3 0.5792 0.748 0.144 0.000 0.696 0.064 0.096
#> GSM339458 4 0.6573 0.331 0.000 0.192 0.004 0.476 0.328
#> GSM339459 5 0.5165 0.706 0.012 0.000 0.240 0.064 0.684
#> GSM339460 2 0.4096 0.743 0.000 0.744 0.004 0.020 0.232
#> GSM339461 2 0.2054 0.862 0.004 0.916 0.000 0.008 0.072
#> GSM339462 4 0.5111 0.275 0.464 0.000 0.000 0.500 0.036
#> GSM339463 3 0.3590 0.814 0.148 0.000 0.820 0.016 0.016
#> GSM339464 4 0.4573 0.509 0.256 0.000 0.000 0.700 0.044
#> GSM339465 1 0.3074 0.835 0.804 0.000 0.196 0.000 0.000
#> GSM339466 5 0.4583 0.366 0.000 0.272 0.012 0.020 0.696
#> GSM339467 2 0.0000 0.879 0.000 1.000 0.000 0.000 0.000
#> GSM339468 5 0.2864 0.806 0.000 0.000 0.136 0.012 0.852
#> GSM339469 4 0.3715 0.514 0.260 0.000 0.000 0.736 0.004
#> GSM339470 4 0.6364 0.320 0.000 0.120 0.016 0.528 0.336
#> GSM339471 1 0.2825 0.799 0.860 0.000 0.124 0.000 0.016
#> GSM339472 2 0.0880 0.874 0.000 0.968 0.000 0.000 0.032
#> GSM339473 1 0.2848 0.813 0.840 0.000 0.156 0.004 0.000
#> GSM339474 2 0.0290 0.878 0.000 0.992 0.000 0.008 0.000
#> GSM339475 3 0.1124 0.799 0.036 0.000 0.960 0.000 0.004
#> GSM339476 1 0.2915 0.798 0.860 0.000 0.116 0.000 0.024
#> GSM339477 2 0.0854 0.876 0.004 0.976 0.000 0.008 0.012
#> GSM339478 3 0.5792 0.748 0.144 0.000 0.696 0.064 0.096
#> GSM339479 4 0.6573 0.331 0.000 0.192 0.004 0.476 0.328
#> GSM339480 5 0.5165 0.706 0.012 0.000 0.240 0.064 0.684
#> GSM339481 2 0.4096 0.743 0.000 0.744 0.004 0.020 0.232
#> GSM339482 3 0.1628 0.801 0.056 0.000 0.936 0.000 0.008
#> GSM339483 4 0.5111 0.275 0.464 0.000 0.000 0.500 0.036
#> GSM339484 3 0.3590 0.814 0.148 0.000 0.820 0.016 0.016
#> GSM339485 4 0.4573 0.509 0.256 0.000 0.000 0.700 0.044
#> GSM339486 1 0.3074 0.835 0.804 0.000 0.196 0.000 0.000
#> GSM339487 5 0.4583 0.366 0.000 0.272 0.012 0.020 0.696
#> GSM339488 2 0.0000 0.879 0.000 1.000 0.000 0.000 0.000
#> GSM339489 5 0.2864 0.806 0.000 0.000 0.136 0.012 0.852
#> GSM339490 4 0.3715 0.514 0.260 0.000 0.000 0.736 0.004
#> GSM339491 4 0.6364 0.320 0.000 0.120 0.016 0.528 0.336
#> GSM339492 1 0.2825 0.799 0.860 0.000 0.124 0.000 0.016
#> GSM339493 2 0.1341 0.867 0.000 0.944 0.000 0.000 0.056
#> GSM339494 1 0.2848 0.813 0.840 0.000 0.156 0.004 0.000
#> GSM339495 2 0.0290 0.878 0.000 0.992 0.000 0.008 0.000
#> GSM339496 3 0.1124 0.799 0.036 0.000 0.960 0.000 0.004
#> GSM339497 2 0.4260 0.728 0.000 0.720 0.004 0.020 0.256
#> GSM339498 5 0.4138 0.781 0.000 0.000 0.148 0.072 0.780
#> GSM339499 3 0.5792 0.748 0.144 0.000 0.696 0.064 0.096
#> GSM339500 4 0.6573 0.331 0.000 0.192 0.004 0.476 0.328
#> GSM339501 5 0.4012 0.761 0.012 0.000 0.216 0.012 0.760
#> GSM339502 2 0.4096 0.743 0.000 0.744 0.004 0.020 0.232
#> GSM339503 3 0.1628 0.801 0.056 0.000 0.936 0.000 0.008
#> GSM339504 4 0.5111 0.275 0.464 0.000 0.000 0.500 0.036
#> GSM339505 3 0.3783 0.809 0.120 0.000 0.824 0.016 0.040
#> GSM339506 4 0.4573 0.509 0.256 0.000 0.000 0.700 0.044
#> GSM339507 1 0.3074 0.835 0.804 0.000 0.196 0.000 0.000
#> GSM339508 2 0.1443 0.874 0.004 0.948 0.000 0.044 0.004
#> GSM339509 2 0.0000 0.879 0.000 1.000 0.000 0.000 0.000
#> GSM339510 5 0.2864 0.806 0.000 0.000 0.136 0.012 0.852
#> GSM339511 4 0.3715 0.514 0.260 0.000 0.000 0.736 0.004
#> GSM339512 4 0.6364 0.320 0.000 0.120 0.016 0.528 0.336
#> GSM339513 1 0.2825 0.799 0.860 0.000 0.124 0.000 0.016
#> GSM339514 2 0.0880 0.874 0.000 0.968 0.000 0.000 0.032
#> GSM339515 1 0.2848 0.813 0.840 0.000 0.156 0.004 0.000
#> GSM339516 2 0.1956 0.859 0.000 0.916 0.000 0.008 0.076
#> GSM339517 3 0.1124 0.799 0.036 0.000 0.960 0.000 0.004
#> GSM339518 2 0.4260 0.728 0.000 0.720 0.004 0.020 0.256
#> GSM339519 5 0.5451 0.681 0.132 0.000 0.168 0.012 0.688
#> GSM339520 3 0.5792 0.748 0.144 0.000 0.696 0.064 0.096
#> GSM339521 4 0.6573 0.331 0.000 0.192 0.004 0.476 0.328
#> GSM339522 5 0.4012 0.761 0.012 0.000 0.216 0.012 0.760
#> GSM339523 2 0.4096 0.743 0.000 0.744 0.004 0.020 0.232
#> GSM339524 3 0.1628 0.801 0.056 0.000 0.936 0.000 0.008
#> GSM339525 4 0.5111 0.275 0.464 0.000 0.000 0.500 0.036
#> GSM339526 3 0.3590 0.814 0.148 0.000 0.820 0.016 0.016
#> GSM339527 4 0.4573 0.509 0.256 0.000 0.000 0.700 0.044
#> GSM339528 1 0.3074 0.835 0.804 0.000 0.196 0.000 0.000
#> GSM339529 2 0.1443 0.874 0.004 0.948 0.000 0.044 0.004
#> GSM339530 3 0.5792 0.748 0.144 0.000 0.696 0.064 0.096
#> GSM339531 5 0.2864 0.806 0.000 0.000 0.136 0.012 0.852
#> GSM339532 4 0.3715 0.514 0.260 0.000 0.000 0.736 0.004
#> GSM339533 4 0.6364 0.320 0.000 0.120 0.016 0.528 0.336
#> GSM339534 1 0.2825 0.799 0.860 0.000 0.124 0.000 0.016
#> GSM339535 2 0.1341 0.867 0.000 0.944 0.000 0.000 0.056
#> GSM339536 1 0.2848 0.813 0.840 0.000 0.156 0.004 0.000
#> GSM339537 2 0.1956 0.859 0.000 0.916 0.000 0.008 0.076
#> GSM339538 3 0.1124 0.799 0.036 0.000 0.960 0.000 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM339455 1 0.3855 0.789 0.704 0.000 0.272 0.000 0.000 0.024
#> GSM339456 2 0.3426 0.724 0.000 0.816 0.000 0.004 0.116 0.064
#> GSM339457 3 0.2852 0.781 0.000 0.000 0.856 0.000 0.064 0.080
#> GSM339458 6 0.2585 0.890 0.000 0.048 0.000 0.016 0.048 0.888
#> GSM339459 5 0.1141 0.754 0.000 0.000 0.000 0.000 0.948 0.052
#> GSM339460 2 0.3727 0.478 0.000 0.612 0.000 0.000 0.000 0.388
#> GSM339461 2 0.2263 0.802 0.000 0.900 0.000 0.004 0.060 0.036
#> GSM339462 4 0.3867 0.784 0.216 0.000 0.000 0.744 0.036 0.004
#> GSM339463 3 0.1951 0.809 0.076 0.000 0.908 0.000 0.000 0.016
#> GSM339464 4 0.1296 0.887 0.004 0.000 0.000 0.948 0.044 0.004
#> GSM339465 1 0.0937 0.839 0.960 0.000 0.040 0.000 0.000 0.000
#> GSM339466 5 0.5576 0.208 0.000 0.144 0.000 0.000 0.480 0.376
#> GSM339467 2 0.0458 0.829 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM339468 5 0.2513 0.804 0.000 0.000 0.000 0.008 0.852 0.140
#> GSM339469 4 0.0291 0.884 0.004 0.000 0.000 0.992 0.000 0.004
#> GSM339470 6 0.2076 0.887 0.000 0.000 0.012 0.016 0.060 0.912
#> GSM339471 1 0.3738 0.788 0.704 0.000 0.280 0.000 0.000 0.016
#> GSM339472 2 0.1261 0.826 0.000 0.952 0.000 0.000 0.024 0.024
#> GSM339473 1 0.0603 0.829 0.980 0.000 0.000 0.016 0.000 0.004
#> GSM339474 2 0.0000 0.827 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM339475 3 0.3788 0.798 0.188 0.000 0.772 0.004 0.024 0.012
#> GSM339476 1 0.3855 0.789 0.704 0.000 0.272 0.000 0.000 0.024
#> GSM339477 2 0.0767 0.824 0.000 0.976 0.000 0.004 0.012 0.008
#> GSM339478 3 0.2852 0.781 0.000 0.000 0.856 0.000 0.064 0.080
#> GSM339479 6 0.2585 0.890 0.000 0.048 0.000 0.016 0.048 0.888
#> GSM339480 5 0.1141 0.754 0.000 0.000 0.000 0.000 0.948 0.052
#> GSM339481 2 0.3727 0.478 0.000 0.612 0.000 0.000 0.000 0.388
#> GSM339482 3 0.3549 0.800 0.192 0.000 0.776 0.004 0.028 0.000
#> GSM339483 4 0.3867 0.784 0.216 0.000 0.000 0.744 0.036 0.004
#> GSM339484 3 0.1951 0.809 0.076 0.000 0.908 0.000 0.000 0.016
#> GSM339485 4 0.1296 0.887 0.004 0.000 0.000 0.948 0.044 0.004
#> GSM339486 1 0.0937 0.839 0.960 0.000 0.040 0.000 0.000 0.000
#> GSM339487 5 0.5576 0.208 0.000 0.144 0.000 0.000 0.480 0.376
#> GSM339488 2 0.0458 0.829 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM339489 5 0.2513 0.804 0.000 0.000 0.000 0.008 0.852 0.140
#> GSM339490 4 0.0291 0.884 0.004 0.000 0.000 0.992 0.000 0.004
#> GSM339491 6 0.2076 0.887 0.000 0.000 0.012 0.016 0.060 0.912
#> GSM339492 1 0.3738 0.788 0.704 0.000 0.280 0.000 0.000 0.016
#> GSM339493 2 0.1713 0.819 0.000 0.928 0.000 0.000 0.044 0.028
#> GSM339494 1 0.0603 0.829 0.980 0.000 0.000 0.016 0.000 0.004
#> GSM339495 2 0.0000 0.827 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM339496 3 0.3788 0.798 0.188 0.000 0.772 0.004 0.024 0.012
#> GSM339497 2 0.4598 0.472 0.000 0.592 0.000 0.000 0.048 0.360
#> GSM339498 5 0.3030 0.779 0.000 0.000 0.008 0.008 0.816 0.168
#> GSM339499 3 0.2852 0.781 0.000 0.000 0.856 0.000 0.064 0.080
#> GSM339500 6 0.2585 0.890 0.000 0.048 0.000 0.016 0.048 0.888
#> GSM339501 5 0.1265 0.790 0.000 0.000 0.000 0.008 0.948 0.044
#> GSM339502 2 0.3727 0.478 0.000 0.612 0.000 0.000 0.000 0.388
#> GSM339503 3 0.3549 0.800 0.192 0.000 0.776 0.004 0.028 0.000
#> GSM339504 4 0.3867 0.784 0.216 0.000 0.000 0.744 0.036 0.004
#> GSM339505 3 0.2462 0.814 0.064 0.000 0.892 0.000 0.012 0.032
#> GSM339506 4 0.1296 0.887 0.004 0.000 0.000 0.948 0.044 0.004
#> GSM339507 1 0.0937 0.839 0.960 0.000 0.040 0.000 0.000 0.000
#> GSM339508 2 0.1528 0.818 0.000 0.936 0.000 0.048 0.000 0.016
#> GSM339509 2 0.0458 0.829 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM339510 5 0.2513 0.804 0.000 0.000 0.000 0.008 0.852 0.140
#> GSM339511 4 0.0291 0.884 0.004 0.000 0.000 0.992 0.000 0.004
#> GSM339512 6 0.2076 0.887 0.000 0.000 0.012 0.016 0.060 0.912
#> GSM339513 1 0.3738 0.788 0.704 0.000 0.280 0.000 0.000 0.016
#> GSM339514 2 0.1261 0.826 0.000 0.952 0.000 0.000 0.024 0.024
#> GSM339515 1 0.0603 0.829 0.980 0.000 0.000 0.016 0.000 0.004
#> GSM339516 2 0.2070 0.799 0.000 0.908 0.000 0.000 0.048 0.044
#> GSM339517 3 0.3788 0.798 0.188 0.000 0.772 0.004 0.024 0.012
#> GSM339518 2 0.4598 0.472 0.000 0.592 0.000 0.000 0.048 0.360
#> GSM339519 5 0.5125 0.704 0.124 0.000 0.032 0.012 0.712 0.120
#> GSM339520 3 0.2852 0.781 0.000 0.000 0.856 0.000 0.064 0.080
#> GSM339521 6 0.2585 0.890 0.000 0.048 0.000 0.016 0.048 0.888
#> GSM339522 5 0.1265 0.790 0.000 0.000 0.000 0.008 0.948 0.044
#> GSM339523 2 0.3727 0.478 0.000 0.612 0.000 0.000 0.000 0.388
#> GSM339524 3 0.3549 0.800 0.192 0.000 0.776 0.004 0.028 0.000
#> GSM339525 4 0.3867 0.784 0.216 0.000 0.000 0.744 0.036 0.004
#> GSM339526 3 0.1951 0.809 0.076 0.000 0.908 0.000 0.000 0.016
#> GSM339527 4 0.1296 0.887 0.004 0.000 0.000 0.948 0.044 0.004
#> GSM339528 1 0.0937 0.839 0.960 0.000 0.040 0.000 0.000 0.000
#> GSM339529 2 0.1528 0.818 0.000 0.936 0.000 0.048 0.000 0.016
#> GSM339530 3 0.2852 0.781 0.000 0.000 0.856 0.000 0.064 0.080
#> GSM339531 5 0.2513 0.804 0.000 0.000 0.000 0.008 0.852 0.140
#> GSM339532 4 0.0291 0.884 0.004 0.000 0.000 0.992 0.000 0.004
#> GSM339533 6 0.2076 0.887 0.000 0.000 0.012 0.016 0.060 0.912
#> GSM339534 1 0.3738 0.788 0.704 0.000 0.280 0.000 0.000 0.016
#> GSM339535 2 0.1713 0.819 0.000 0.928 0.000 0.000 0.044 0.028
#> GSM339536 1 0.0603 0.829 0.980 0.000 0.000 0.016 0.000 0.004
#> GSM339537 2 0.2070 0.799 0.000 0.908 0.000 0.000 0.048 0.044
#> GSM339538 3 0.3788 0.798 0.188 0.000 0.772 0.004 0.024 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 protocol(p) agent(p) individual(p) k
#> SD:hclust 78 1.000 0.886 4.81e-04 2
#> SD:hclust 82 0.697 0.958 4.59e-07 3
#> SD:hclust 62 0.658 0.946 9.45e-06 4
#> SD:hclust 70 0.928 0.999 3.64e-11 5
#> SD:hclust 76 0.946 1.000 1.68e-14 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 15497 rows and 84 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 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 0.736 0.889 0.945 0.5022 0.497 0.497
#> 3 3 0.646 0.750 0.863 0.2944 0.748 0.534
#> 4 4 0.601 0.762 0.756 0.1199 0.927 0.788
#> 5 5 0.585 0.603 0.697 0.0694 0.908 0.678
#> 6 6 0.616 0.521 0.674 0.0418 0.919 0.662
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
#> GSM339455 1 0.0000 0.955 1.000 0.000
#> GSM339456 2 0.0000 0.927 0.000 1.000
#> GSM339457 2 0.9087 0.622 0.324 0.676
#> GSM339458 2 0.0000 0.927 0.000 1.000
#> GSM339459 2 0.9460 0.549 0.364 0.636
#> GSM339460 2 0.0000 0.927 0.000 1.000
#> GSM339461 2 0.0000 0.927 0.000 1.000
#> GSM339462 1 0.2948 0.930 0.948 0.052
#> GSM339463 1 0.0000 0.955 1.000 0.000
#> GSM339464 1 0.4939 0.885 0.892 0.108
#> GSM339465 1 0.0000 0.955 1.000 0.000
#> GSM339466 2 0.0000 0.927 0.000 1.000
#> GSM339467 2 0.0000 0.927 0.000 1.000
#> GSM339468 2 0.0672 0.923 0.008 0.992
#> GSM339469 1 0.4939 0.885 0.892 0.108
#> GSM339470 2 0.7056 0.776 0.192 0.808
#> GSM339471 1 0.0000 0.955 1.000 0.000
#> GSM339472 2 0.0000 0.927 0.000 1.000
#> GSM339473 1 0.0000 0.955 1.000 0.000
#> GSM339474 2 0.0000 0.927 0.000 1.000
#> GSM339475 1 0.0000 0.955 1.000 0.000
#> GSM339476 1 0.0000 0.955 1.000 0.000
#> GSM339477 2 0.0000 0.927 0.000 1.000
#> GSM339478 2 0.6247 0.819 0.156 0.844
#> GSM339479 2 0.0000 0.927 0.000 1.000
#> GSM339480 2 0.9460 0.549 0.364 0.636
#> GSM339481 2 0.0000 0.927 0.000 1.000
#> GSM339482 1 0.0000 0.955 1.000 0.000
#> GSM339483 1 0.3274 0.926 0.940 0.060
#> GSM339484 1 0.0000 0.955 1.000 0.000
#> GSM339485 1 0.4939 0.885 0.892 0.108
#> GSM339486 1 0.0000 0.955 1.000 0.000
#> GSM339487 2 0.0000 0.927 0.000 1.000
#> GSM339488 2 0.0000 0.927 0.000 1.000
#> GSM339489 2 0.0672 0.923 0.008 0.992
#> GSM339490 1 0.4939 0.885 0.892 0.108
#> GSM339491 2 0.6438 0.803 0.164 0.836
#> GSM339492 1 0.0000 0.955 1.000 0.000
#> GSM339493 2 0.0000 0.927 0.000 1.000
#> GSM339494 1 0.0000 0.955 1.000 0.000
#> GSM339495 2 0.0000 0.927 0.000 1.000
#> GSM339496 1 0.0000 0.955 1.000 0.000
#> GSM339497 2 0.0000 0.927 0.000 1.000
#> GSM339498 2 0.8081 0.709 0.248 0.752
#> GSM339499 2 0.9087 0.622 0.324 0.676
#> GSM339500 2 0.0000 0.927 0.000 1.000
#> GSM339501 1 0.3274 0.926 0.940 0.060
#> GSM339502 2 0.0000 0.927 0.000 1.000
#> GSM339503 1 0.0000 0.955 1.000 0.000
#> GSM339504 1 0.3274 0.926 0.940 0.060
#> GSM339505 2 0.9248 0.595 0.340 0.660
#> GSM339506 1 0.3274 0.926 0.940 0.060
#> GSM339507 1 0.0000 0.955 1.000 0.000
#> GSM339508 2 0.0000 0.927 0.000 1.000
#> GSM339509 2 0.0000 0.927 0.000 1.000
#> GSM339510 2 0.0672 0.923 0.008 0.992
#> GSM339511 1 0.9710 0.402 0.600 0.400
#> GSM339512 2 0.0000 0.927 0.000 1.000
#> GSM339513 1 0.0000 0.955 1.000 0.000
#> GSM339514 2 0.0000 0.927 0.000 1.000
#> GSM339515 1 0.0000 0.955 1.000 0.000
#> GSM339516 2 0.0000 0.927 0.000 1.000
#> GSM339517 1 0.0000 0.955 1.000 0.000
#> GSM339518 2 0.0000 0.927 0.000 1.000
#> GSM339519 1 0.0000 0.955 1.000 0.000
#> GSM339520 2 0.7883 0.741 0.236 0.764
#> GSM339521 2 0.0000 0.927 0.000 1.000
#> GSM339522 2 0.0000 0.927 0.000 1.000
#> GSM339523 2 0.0000 0.927 0.000 1.000
#> GSM339524 1 0.0000 0.955 1.000 0.000
#> GSM339525 1 0.3274 0.926 0.940 0.060
#> GSM339526 1 0.0000 0.955 1.000 0.000
#> GSM339527 1 0.3274 0.926 0.940 0.060
#> GSM339528 1 0.0000 0.955 1.000 0.000
#> GSM339529 2 0.0000 0.927 0.000 1.000
#> GSM339530 2 0.9087 0.622 0.324 0.676
#> GSM339531 2 0.0672 0.923 0.008 0.992
#> GSM339532 1 0.9209 0.542 0.664 0.336
#> GSM339533 1 0.0000 0.955 1.000 0.000
#> GSM339534 1 0.0000 0.955 1.000 0.000
#> GSM339535 2 0.0000 0.927 0.000 1.000
#> GSM339536 1 0.0000 0.955 1.000 0.000
#> GSM339537 2 0.0000 0.927 0.000 1.000
#> GSM339538 1 0.0000 0.955 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM339455 3 0.1964 0.744 0.056 0.000 0.944
#> GSM339456 2 0.1964 0.943 0.056 0.944 0.000
#> GSM339457 3 0.3816 0.739 0.000 0.148 0.852
#> GSM339458 2 0.1643 0.950 0.000 0.956 0.044
#> GSM339459 3 0.7319 0.645 0.128 0.164 0.708
#> GSM339460 2 0.1129 0.960 0.004 0.976 0.020
#> GSM339461 2 0.2165 0.937 0.064 0.936 0.000
#> GSM339462 1 0.1163 0.716 0.972 0.000 0.028
#> GSM339463 3 0.2165 0.740 0.064 0.000 0.936
#> GSM339464 1 0.0237 0.709 0.996 0.000 0.004
#> GSM339465 3 0.2165 0.740 0.064 0.000 0.936
#> GSM339466 2 0.1015 0.960 0.012 0.980 0.008
#> GSM339467 2 0.1399 0.956 0.004 0.968 0.028
#> GSM339468 2 0.4291 0.858 0.152 0.840 0.008
#> GSM339469 1 0.0237 0.709 0.996 0.000 0.004
#> GSM339470 3 0.5061 0.690 0.008 0.208 0.784
#> GSM339471 1 0.6307 0.477 0.512 0.000 0.488
#> GSM339472 2 0.0592 0.961 0.012 0.988 0.000
#> GSM339473 1 0.6252 0.532 0.556 0.000 0.444
#> GSM339474 2 0.1031 0.958 0.024 0.976 0.000
#> GSM339475 3 0.1529 0.752 0.040 0.000 0.960
#> GSM339476 1 0.5016 0.639 0.760 0.000 0.240
#> GSM339477 2 0.2066 0.941 0.060 0.940 0.000
#> GSM339478 3 0.4399 0.710 0.000 0.188 0.812
#> GSM339479 2 0.1643 0.950 0.000 0.956 0.044
#> GSM339480 3 0.7319 0.645 0.128 0.164 0.708
#> GSM339481 2 0.0424 0.961 0.008 0.992 0.000
#> GSM339482 3 0.1964 0.749 0.056 0.000 0.944
#> GSM339483 1 0.1163 0.716 0.972 0.000 0.028
#> GSM339484 3 0.6299 -0.429 0.476 0.000 0.524
#> GSM339485 1 0.0237 0.709 0.996 0.000 0.004
#> GSM339486 1 0.6309 0.453 0.504 0.000 0.496
#> GSM339487 2 0.1015 0.960 0.012 0.980 0.008
#> GSM339488 2 0.1399 0.956 0.004 0.968 0.028
#> GSM339489 2 0.3755 0.889 0.120 0.872 0.008
#> GSM339490 1 0.0237 0.709 0.996 0.000 0.004
#> GSM339491 3 0.5461 0.651 0.008 0.244 0.748
#> GSM339492 1 0.6307 0.477 0.512 0.000 0.488
#> GSM339493 2 0.0424 0.961 0.008 0.992 0.000
#> GSM339494 1 0.6252 0.532 0.556 0.000 0.444
#> GSM339495 2 0.1031 0.958 0.024 0.976 0.000
#> GSM339496 3 0.1529 0.752 0.040 0.000 0.960
#> GSM339497 2 0.0592 0.961 0.000 0.988 0.012
#> GSM339498 3 0.8623 0.517 0.176 0.224 0.600
#> GSM339499 3 0.3816 0.739 0.000 0.148 0.852
#> GSM339500 2 0.1643 0.950 0.000 0.956 0.044
#> GSM339501 1 0.1643 0.708 0.956 0.000 0.044
#> GSM339502 2 0.1399 0.956 0.004 0.968 0.028
#> GSM339503 3 0.2356 0.743 0.072 0.000 0.928
#> GSM339504 1 0.1163 0.716 0.972 0.000 0.028
#> GSM339505 3 0.3412 0.745 0.000 0.124 0.876
#> GSM339506 1 0.0892 0.715 0.980 0.000 0.020
#> GSM339507 3 0.6309 -0.491 0.500 0.000 0.500
#> GSM339508 2 0.1031 0.958 0.024 0.976 0.000
#> GSM339509 2 0.1399 0.956 0.004 0.968 0.028
#> GSM339510 2 0.4291 0.858 0.152 0.840 0.008
#> GSM339511 1 0.2165 0.662 0.936 0.064 0.000
#> GSM339512 2 0.1411 0.955 0.000 0.964 0.036
#> GSM339513 1 0.6295 0.492 0.528 0.000 0.472
#> GSM339514 2 0.1399 0.956 0.004 0.968 0.028
#> GSM339515 1 0.6252 0.532 0.556 0.000 0.444
#> GSM339516 2 0.1031 0.958 0.024 0.976 0.000
#> GSM339517 3 0.2066 0.748 0.060 0.000 0.940
#> GSM339518 2 0.0592 0.961 0.000 0.988 0.012
#> GSM339519 3 0.2066 0.748 0.060 0.000 0.940
#> GSM339520 3 0.4002 0.732 0.000 0.160 0.840
#> GSM339521 2 0.1163 0.957 0.000 0.972 0.028
#> GSM339522 2 0.1170 0.960 0.016 0.976 0.008
#> GSM339523 2 0.1399 0.956 0.004 0.968 0.028
#> GSM339524 1 0.6299 0.477 0.524 0.000 0.476
#> GSM339525 1 0.1163 0.716 0.972 0.000 0.028
#> GSM339526 3 0.1529 0.752 0.040 0.000 0.960
#> GSM339527 1 0.0892 0.715 0.980 0.000 0.020
#> GSM339528 1 0.6309 0.453 0.504 0.000 0.496
#> GSM339529 2 0.1031 0.958 0.024 0.976 0.000
#> GSM339530 3 0.3983 0.739 0.004 0.144 0.852
#> GSM339531 2 0.3755 0.889 0.120 0.872 0.008
#> GSM339532 1 0.1753 0.676 0.952 0.048 0.000
#> GSM339533 3 0.1411 0.754 0.036 0.000 0.964
#> GSM339534 1 0.6307 0.477 0.512 0.000 0.488
#> GSM339535 2 0.0661 0.960 0.004 0.988 0.008
#> GSM339536 1 0.6252 0.532 0.556 0.000 0.444
#> GSM339537 2 0.1031 0.958 0.024 0.976 0.000
#> GSM339538 3 0.2066 0.748 0.060 0.000 0.940
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM339455 3 0.5772 0.680 0.176 0.000 0.708 0.116
#> GSM339456 2 0.2256 0.812 0.000 0.924 0.020 0.056
#> GSM339457 3 0.3606 0.752 0.080 0.028 0.872 0.020
#> GSM339458 2 0.7466 0.695 0.020 0.572 0.252 0.156
#> GSM339459 3 0.5945 0.701 0.152 0.032 0.736 0.080
#> GSM339460 2 0.5861 0.797 0.000 0.704 0.144 0.152
#> GSM339461 2 0.4789 0.805 0.000 0.772 0.056 0.172
#> GSM339462 4 0.4748 0.850 0.268 0.000 0.016 0.716
#> GSM339463 3 0.5535 0.669 0.304 0.000 0.656 0.040
#> GSM339464 4 0.4137 0.874 0.208 0.000 0.012 0.780
#> GSM339465 1 0.4933 0.390 0.688 0.000 0.296 0.016
#> GSM339466 2 0.5175 0.800 0.000 0.760 0.120 0.120
#> GSM339467 2 0.3424 0.806 0.012 0.880 0.072 0.036
#> GSM339468 2 0.6828 0.703 0.000 0.588 0.148 0.264
#> GSM339469 4 0.3908 0.875 0.212 0.000 0.004 0.784
#> GSM339470 3 0.5697 0.676 0.104 0.068 0.768 0.060
#> GSM339471 1 0.4568 0.815 0.800 0.000 0.076 0.124
#> GSM339472 2 0.0657 0.828 0.000 0.984 0.004 0.012
#> GSM339473 1 0.3172 0.771 0.840 0.000 0.000 0.160
#> GSM339474 2 0.0895 0.826 0.000 0.976 0.004 0.020
#> GSM339475 3 0.4585 0.711 0.332 0.000 0.668 0.000
#> GSM339476 4 0.6575 0.325 0.412 0.000 0.080 0.508
#> GSM339477 2 0.1824 0.816 0.000 0.936 0.004 0.060
#> GSM339478 3 0.3881 0.740 0.068 0.028 0.864 0.040
#> GSM339479 2 0.7559 0.691 0.024 0.568 0.252 0.156
#> GSM339480 3 0.5945 0.701 0.152 0.032 0.736 0.080
#> GSM339481 2 0.0657 0.829 0.000 0.984 0.004 0.012
#> GSM339482 3 0.4999 0.705 0.328 0.000 0.660 0.012
#> GSM339483 4 0.4748 0.850 0.268 0.000 0.016 0.716
#> GSM339484 1 0.4015 0.805 0.832 0.000 0.116 0.052
#> GSM339485 4 0.4137 0.874 0.208 0.000 0.012 0.780
#> GSM339486 1 0.3716 0.811 0.852 0.000 0.096 0.052
#> GSM339487 2 0.5175 0.800 0.000 0.760 0.120 0.120
#> GSM339488 2 0.3424 0.806 0.012 0.880 0.072 0.036
#> GSM339489 2 0.6609 0.731 0.000 0.620 0.144 0.236
#> GSM339490 4 0.3908 0.875 0.212 0.000 0.004 0.784
#> GSM339491 3 0.5697 0.676 0.104 0.068 0.768 0.060
#> GSM339492 1 0.4568 0.815 0.800 0.000 0.076 0.124
#> GSM339493 2 0.0895 0.831 0.000 0.976 0.004 0.020
#> GSM339494 1 0.3172 0.771 0.840 0.000 0.000 0.160
#> GSM339495 2 0.0895 0.826 0.000 0.976 0.004 0.020
#> GSM339496 3 0.4522 0.712 0.320 0.000 0.680 0.000
#> GSM339497 2 0.6155 0.773 0.000 0.676 0.176 0.148
#> GSM339498 3 0.6212 0.621 0.040 0.092 0.724 0.144
#> GSM339499 3 0.3606 0.752 0.080 0.028 0.872 0.020
#> GSM339500 2 0.7244 0.699 0.012 0.580 0.256 0.152
#> GSM339501 4 0.5708 0.435 0.076 0.004 0.212 0.708
#> GSM339502 2 0.3424 0.806 0.012 0.880 0.072 0.036
#> GSM339503 3 0.5152 0.711 0.316 0.000 0.664 0.020
#> GSM339504 4 0.4748 0.850 0.268 0.000 0.016 0.716
#> GSM339505 3 0.3870 0.751 0.164 0.008 0.820 0.008
#> GSM339506 4 0.4361 0.874 0.208 0.000 0.020 0.772
#> GSM339507 1 0.3716 0.813 0.852 0.000 0.096 0.052
#> GSM339508 2 0.2057 0.818 0.008 0.940 0.020 0.032
#> GSM339509 2 0.3424 0.806 0.012 0.880 0.072 0.036
#> GSM339510 2 0.6868 0.698 0.000 0.584 0.152 0.264
#> GSM339511 4 0.4104 0.823 0.164 0.028 0.000 0.808
#> GSM339512 2 0.5021 0.797 0.000 0.756 0.180 0.064
#> GSM339513 1 0.4282 0.811 0.816 0.000 0.060 0.124
#> GSM339514 2 0.3351 0.807 0.012 0.884 0.068 0.036
#> GSM339515 1 0.3172 0.771 0.840 0.000 0.000 0.160
#> GSM339516 2 0.2197 0.831 0.000 0.916 0.004 0.080
#> GSM339517 3 0.5090 0.709 0.324 0.000 0.660 0.016
#> GSM339518 2 0.5990 0.785 0.000 0.692 0.164 0.144
#> GSM339519 3 0.4936 0.717 0.316 0.000 0.672 0.012
#> GSM339520 3 0.3536 0.751 0.076 0.028 0.876 0.020
#> GSM339521 2 0.6025 0.782 0.000 0.688 0.172 0.140
#> GSM339522 2 0.5993 0.777 0.000 0.692 0.148 0.160
#> GSM339523 2 0.3351 0.807 0.012 0.884 0.068 0.036
#> GSM339524 1 0.4761 0.607 0.764 0.000 0.192 0.044
#> GSM339525 4 0.4748 0.850 0.268 0.000 0.016 0.716
#> GSM339526 3 0.4605 0.707 0.336 0.000 0.664 0.000
#> GSM339527 4 0.4361 0.874 0.208 0.000 0.020 0.772
#> GSM339528 1 0.3716 0.811 0.852 0.000 0.096 0.052
#> GSM339529 2 0.2057 0.818 0.008 0.940 0.020 0.032
#> GSM339530 3 0.3536 0.745 0.076 0.028 0.876 0.020
#> GSM339531 2 0.6609 0.731 0.000 0.620 0.144 0.236
#> GSM339532 4 0.4323 0.861 0.204 0.020 0.000 0.776
#> GSM339533 3 0.5282 0.695 0.276 0.000 0.688 0.036
#> GSM339534 1 0.4931 0.805 0.776 0.000 0.092 0.132
#> GSM339535 2 0.2115 0.829 0.004 0.936 0.036 0.024
#> GSM339536 1 0.3172 0.771 0.840 0.000 0.000 0.160
#> GSM339537 2 0.2197 0.831 0.000 0.916 0.004 0.080
#> GSM339538 3 0.5110 0.705 0.328 0.000 0.656 0.016
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM339455 3 0.7673 0.3347 0.172 0.056 0.416 0.008 0.348
#> GSM339456 2 0.5058 0.6553 0.008 0.492 0.012 0.004 0.484
#> GSM339457 3 0.5695 0.6268 0.092 0.100 0.712 0.000 0.096
#> GSM339458 5 0.6996 0.4908 0.112 0.160 0.140 0.000 0.588
#> GSM339459 3 0.6354 0.5435 0.064 0.020 0.640 0.048 0.228
#> GSM339460 5 0.4877 0.4705 0.032 0.236 0.024 0.000 0.708
#> GSM339461 5 0.4437 0.3413 0.024 0.188 0.008 0.016 0.764
#> GSM339462 4 0.3625 0.8327 0.076 0.020 0.016 0.856 0.032
#> GSM339463 3 0.6524 0.4516 0.344 0.040 0.540 0.008 0.068
#> GSM339464 4 0.2235 0.8649 0.012 0.040 0.008 0.924 0.016
#> GSM339465 1 0.3854 0.5726 0.792 0.016 0.180 0.008 0.004
#> GSM339466 5 0.3578 0.5117 0.000 0.132 0.048 0.000 0.820
#> GSM339467 2 0.4237 0.7464 0.008 0.752 0.028 0.000 0.212
#> GSM339468 5 0.3139 0.5484 0.004 0.024 0.036 0.056 0.880
#> GSM339469 4 0.0854 0.8785 0.004 0.008 0.000 0.976 0.012
#> GSM339470 3 0.7255 0.5405 0.140 0.108 0.568 0.004 0.180
#> GSM339471 1 0.6451 0.7359 0.612 0.020 0.120 0.232 0.016
#> GSM339472 2 0.4686 0.7343 0.004 0.588 0.012 0.000 0.396
#> GSM339473 1 0.5206 0.6989 0.672 0.060 0.012 0.256 0.000
#> GSM339474 2 0.5385 0.6885 0.028 0.528 0.016 0.000 0.428
#> GSM339475 3 0.3728 0.5712 0.244 0.008 0.748 0.000 0.000
#> GSM339476 4 0.6338 0.4382 0.180 0.028 0.112 0.656 0.024
#> GSM339477 2 0.5551 0.6699 0.028 0.504 0.016 0.004 0.448
#> GSM339478 3 0.5978 0.6176 0.092 0.104 0.688 0.000 0.116
#> GSM339479 5 0.7280 0.4718 0.132 0.172 0.140 0.000 0.556
#> GSM339480 3 0.6354 0.5435 0.064 0.020 0.640 0.048 0.228
#> GSM339481 2 0.4723 0.7380 0.008 0.612 0.012 0.000 0.368
#> GSM339482 3 0.4687 0.5568 0.244 0.016 0.716 0.016 0.008
#> GSM339483 4 0.3625 0.8327 0.076 0.020 0.016 0.856 0.032
#> GSM339484 1 0.5249 0.6918 0.712 0.016 0.164 0.108 0.000
#> GSM339485 4 0.2235 0.8649 0.012 0.040 0.008 0.924 0.016
#> GSM339486 1 0.4454 0.7333 0.784 0.016 0.092 0.108 0.000
#> GSM339487 5 0.3578 0.5117 0.000 0.132 0.048 0.000 0.820
#> GSM339488 2 0.4268 0.7464 0.008 0.748 0.028 0.000 0.216
#> GSM339489 5 0.2727 0.5536 0.004 0.016 0.032 0.048 0.900
#> GSM339490 4 0.0854 0.8785 0.004 0.008 0.000 0.976 0.012
#> GSM339491 3 0.7255 0.5405 0.140 0.108 0.568 0.004 0.180
#> GSM339492 1 0.6530 0.7346 0.604 0.020 0.128 0.232 0.016
#> GSM339493 2 0.4617 0.6728 0.000 0.552 0.012 0.000 0.436
#> GSM339494 1 0.5206 0.6989 0.672 0.060 0.012 0.256 0.000
#> GSM339495 2 0.5390 0.6843 0.028 0.524 0.016 0.000 0.432
#> GSM339496 3 0.3662 0.5678 0.252 0.004 0.744 0.000 0.000
#> GSM339497 5 0.4871 0.5579 0.032 0.128 0.080 0.000 0.760
#> GSM339498 3 0.5981 0.4796 0.004 0.020 0.572 0.064 0.340
#> GSM339499 3 0.5695 0.6268 0.092 0.100 0.712 0.000 0.096
#> GSM339500 5 0.6800 0.4979 0.088 0.160 0.148 0.000 0.604
#> GSM339501 5 0.6940 -0.1430 0.020 0.024 0.096 0.404 0.456
#> GSM339502 2 0.4376 0.7442 0.012 0.744 0.028 0.000 0.216
#> GSM339503 3 0.4902 0.5724 0.208 0.016 0.732 0.024 0.020
#> GSM339504 4 0.3625 0.8327 0.076 0.020 0.016 0.856 0.032
#> GSM339505 3 0.5143 0.6326 0.156 0.032 0.740 0.004 0.068
#> GSM339506 4 0.2268 0.8662 0.012 0.036 0.016 0.924 0.012
#> GSM339507 1 0.4454 0.7339 0.784 0.016 0.092 0.108 0.000
#> GSM339508 2 0.5588 0.7192 0.036 0.620 0.016 0.012 0.316
#> GSM339509 2 0.4237 0.7464 0.008 0.752 0.028 0.000 0.212
#> GSM339510 5 0.3018 0.5488 0.004 0.016 0.036 0.060 0.884
#> GSM339511 4 0.1538 0.8682 0.008 0.008 0.000 0.948 0.036
#> GSM339512 5 0.6498 0.0923 0.012 0.408 0.132 0.000 0.448
#> GSM339513 1 0.5907 0.7334 0.628 0.016 0.116 0.240 0.000
#> GSM339514 2 0.4024 0.7516 0.000 0.752 0.028 0.000 0.220
#> GSM339515 1 0.5206 0.6989 0.672 0.060 0.012 0.256 0.000
#> GSM339516 5 0.5285 -0.4779 0.024 0.412 0.016 0.000 0.548
#> GSM339517 3 0.4407 0.5747 0.232 0.012 0.736 0.012 0.008
#> GSM339518 5 0.4927 0.5452 0.032 0.144 0.072 0.000 0.752
#> GSM339519 3 0.4593 0.5758 0.216 0.012 0.740 0.016 0.016
#> GSM339520 3 0.5743 0.6253 0.092 0.104 0.708 0.000 0.096
#> GSM339521 5 0.5583 0.5277 0.032 0.180 0.096 0.000 0.692
#> GSM339522 5 0.1901 0.5429 0.004 0.056 0.012 0.000 0.928
#> GSM339523 2 0.4323 0.7488 0.012 0.744 0.024 0.000 0.220
#> GSM339524 1 0.6994 0.3217 0.472 0.036 0.372 0.112 0.008
#> GSM339525 4 0.3625 0.8327 0.076 0.020 0.016 0.856 0.032
#> GSM339526 3 0.3756 0.5698 0.248 0.008 0.744 0.000 0.000
#> GSM339527 4 0.2268 0.8662 0.012 0.036 0.016 0.924 0.012
#> GSM339528 1 0.4454 0.7333 0.784 0.016 0.092 0.108 0.000
#> GSM339529 2 0.5588 0.7192 0.036 0.620 0.016 0.012 0.316
#> GSM339530 3 0.5478 0.6164 0.088 0.148 0.716 0.000 0.048
#> GSM339531 5 0.2917 0.5509 0.004 0.024 0.032 0.048 0.892
#> GSM339532 4 0.0968 0.8772 0.004 0.012 0.000 0.972 0.012
#> GSM339533 3 0.5853 0.5809 0.248 0.032 0.648 0.004 0.068
#> GSM339534 1 0.7020 0.7080 0.576 0.020 0.144 0.224 0.036
#> GSM339535 2 0.4640 0.7030 0.000 0.584 0.016 0.000 0.400
#> GSM339536 1 0.5206 0.6989 0.672 0.060 0.012 0.256 0.000
#> GSM339537 5 0.5292 -0.4896 0.024 0.416 0.016 0.000 0.544
#> GSM339538 3 0.4316 0.5719 0.236 0.012 0.736 0.012 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM339455 6 0.5823 0.1643 0.168 0.000 0.160 0.008 NA 0.628
#> GSM339456 2 0.3078 0.5965 0.000 0.852 0.004 0.004 NA 0.060
#> GSM339457 3 0.6844 0.4956 0.112 0.000 0.468 0.000 NA 0.288
#> GSM339458 6 0.4348 0.5335 0.064 0.140 0.004 0.000 NA 0.764
#> GSM339459 3 0.6349 0.4101 0.048 0.012 0.592 0.008 NA 0.216
#> GSM339460 6 0.4616 0.3924 0.000 0.316 0.000 0.000 NA 0.624
#> GSM339461 2 0.5504 -0.1346 0.000 0.540 0.020 0.008 NA 0.372
#> GSM339462 4 0.4802 0.7526 0.132 0.000 0.024 0.736 NA 0.012
#> GSM339463 3 0.6732 0.2732 0.348 0.000 0.352 0.000 NA 0.264
#> GSM339464 4 0.2044 0.8278 0.012 0.008 0.004 0.920 NA 0.004
#> GSM339465 1 0.3670 0.6195 0.788 0.000 0.152 0.004 NA 0.056
#> GSM339466 2 0.5210 -0.2917 0.008 0.476 0.008 0.000 NA 0.460
#> GSM339467 2 0.4720 0.6168 0.000 0.560 0.000 0.000 NA 0.052
#> GSM339468 6 0.6749 0.4186 0.020 0.328 0.020 0.020 NA 0.488
#> GSM339469 4 0.0881 0.8373 0.008 0.008 0.000 0.972 NA 0.000
#> GSM339470 6 0.7021 -0.1845 0.160 0.016 0.292 0.000 NA 0.464
#> GSM339471 1 0.7016 0.7028 0.556 0.000 0.116 0.156 NA 0.036
#> GSM339472 2 0.3319 0.6469 0.000 0.800 0.000 0.000 NA 0.036
#> GSM339473 1 0.5566 0.6823 0.652 0.000 0.028 0.156 NA 0.008
#> GSM339474 2 0.1605 0.6007 0.012 0.940 0.000 0.000 NA 0.016
#> GSM339475 3 0.1812 0.5886 0.080 0.000 0.912 0.000 NA 0.000
#> GSM339476 4 0.6552 0.4014 0.232 0.000 0.072 0.580 NA 0.064
#> GSM339477 2 0.2145 0.5856 0.008 0.912 0.000 0.004 NA 0.020
#> GSM339478 3 0.6915 0.4572 0.112 0.000 0.436 0.000 NA 0.320
#> GSM339479 6 0.4339 0.5318 0.072 0.128 0.004 0.000 NA 0.768
#> GSM339480 3 0.6349 0.4101 0.048 0.012 0.592 0.008 NA 0.216
#> GSM339481 2 0.3796 0.6398 0.000 0.764 0.000 0.000 NA 0.060
#> GSM339482 3 0.2501 0.5754 0.072 0.000 0.888 0.000 NA 0.028
#> GSM339483 4 0.4802 0.7526 0.132 0.000 0.024 0.736 NA 0.012
#> GSM339484 1 0.4752 0.6113 0.728 0.000 0.172 0.032 NA 0.060
#> GSM339485 4 0.2044 0.8278 0.012 0.008 0.004 0.920 NA 0.004
#> GSM339486 1 0.3968 0.6617 0.788 0.000 0.132 0.032 NA 0.048
#> GSM339487 2 0.5210 -0.2917 0.008 0.476 0.008 0.000 NA 0.460
#> GSM339488 2 0.4823 0.6152 0.000 0.552 0.000 0.000 NA 0.060
#> GSM339489 6 0.6636 0.4317 0.020 0.312 0.020 0.016 NA 0.508
#> GSM339490 4 0.0881 0.8373 0.008 0.008 0.000 0.972 NA 0.000
#> GSM339491 6 0.7021 -0.1845 0.160 0.016 0.292 0.000 NA 0.464
#> GSM339492 1 0.7102 0.6988 0.552 0.000 0.116 0.156 NA 0.044
#> GSM339493 2 0.3691 0.6355 0.004 0.780 0.000 0.000 NA 0.048
#> GSM339494 1 0.5566 0.6823 0.652 0.000 0.028 0.156 NA 0.008
#> GSM339495 2 0.1605 0.6007 0.012 0.940 0.000 0.000 NA 0.016
#> GSM339496 3 0.2566 0.5793 0.112 0.000 0.868 0.000 NA 0.012
#> GSM339497 6 0.4045 0.4909 0.004 0.268 0.000 0.000 NA 0.700
#> GSM339498 3 0.7748 0.1446 0.028 0.080 0.400 0.020 NA 0.332
#> GSM339499 3 0.6844 0.4956 0.112 0.000 0.468 0.000 NA 0.288
#> GSM339500 6 0.4011 0.5355 0.044 0.136 0.004 0.000 NA 0.788
#> GSM339501 6 0.7746 0.2380 0.080 0.004 0.064 0.236 NA 0.460
#> GSM339502 2 0.4957 0.6120 0.000 0.544 0.000 0.000 NA 0.072
#> GSM339503 3 0.2278 0.5894 0.052 0.000 0.904 0.000 NA 0.032
#> GSM339504 4 0.4802 0.7526 0.132 0.000 0.024 0.736 NA 0.012
#> GSM339505 3 0.6173 0.5138 0.144 0.000 0.536 0.000 NA 0.276
#> GSM339506 4 0.2687 0.8259 0.020 0.000 0.016 0.884 NA 0.008
#> GSM339507 1 0.3829 0.6677 0.804 0.000 0.124 0.032 NA 0.036
#> GSM339508 2 0.4055 0.6091 0.004 0.744 0.000 0.024 NA 0.016
#> GSM339509 2 0.4720 0.6168 0.000 0.560 0.000 0.000 NA 0.052
#> GSM339510 6 0.6758 0.4344 0.020 0.304 0.024 0.020 NA 0.508
#> GSM339511 4 0.1086 0.8355 0.012 0.012 0.000 0.964 NA 0.000
#> GSM339512 6 0.6112 -0.0239 0.004 0.412 0.012 0.000 NA 0.416
#> GSM339513 1 0.6816 0.6948 0.552 0.000 0.144 0.156 NA 0.012
#> GSM339514 2 0.4799 0.6251 0.000 0.592 0.000 0.000 NA 0.068
#> GSM339515 1 0.5566 0.6823 0.652 0.000 0.028 0.156 NA 0.008
#> GSM339516 2 0.2978 0.5350 0.012 0.860 0.000 0.000 NA 0.072
#> GSM339517 3 0.1588 0.5878 0.072 0.000 0.924 0.000 NA 0.000
#> GSM339518 6 0.4074 0.4712 0.004 0.288 0.000 0.000 NA 0.684
#> GSM339519 3 0.2945 0.5915 0.064 0.000 0.868 0.000 NA 0.040
#> GSM339520 3 0.6844 0.4956 0.112 0.000 0.468 0.000 NA 0.288
#> GSM339521 6 0.4306 0.4462 0.000 0.308 0.004 0.000 NA 0.656
#> GSM339522 6 0.6184 0.3944 0.020 0.356 0.012 0.004 NA 0.500
#> GSM339523 2 0.4949 0.6137 0.000 0.548 0.000 0.000 NA 0.072
#> GSM339524 3 0.5463 -0.0342 0.332 0.000 0.584 0.024 NA 0.036
#> GSM339525 4 0.4802 0.7526 0.132 0.000 0.024 0.736 NA 0.012
#> GSM339526 3 0.1806 0.5869 0.088 0.000 0.908 0.000 NA 0.000
#> GSM339527 4 0.2687 0.8259 0.020 0.000 0.016 0.884 NA 0.008
#> GSM339528 1 0.3968 0.6617 0.788 0.000 0.132 0.032 NA 0.048
#> GSM339529 2 0.4055 0.6091 0.004 0.744 0.000 0.024 NA 0.016
#> GSM339530 3 0.6898 0.5109 0.104 0.000 0.484 0.000 NA 0.224
#> GSM339531 6 0.6684 0.4161 0.020 0.332 0.020 0.016 NA 0.488
#> GSM339532 4 0.0881 0.8373 0.008 0.008 0.000 0.972 NA 0.000
#> GSM339533 3 0.6694 0.4044 0.256 0.000 0.420 0.000 NA 0.284
#> GSM339534 1 0.7300 0.6899 0.540 0.000 0.104 0.156 NA 0.068
#> GSM339535 2 0.4443 0.6334 0.004 0.704 0.000 0.000 NA 0.076
#> GSM339536 1 0.5566 0.6823 0.652 0.000 0.028 0.156 NA 0.008
#> GSM339537 2 0.2922 0.5381 0.012 0.864 0.000 0.000 NA 0.068
#> GSM339538 3 0.1701 0.5862 0.072 0.000 0.920 0.000 NA 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 protocol(p) agent(p) individual(p) k
#> SD:kmeans 83 1.000 0.703 1.57e-03 2
#> SD:kmeans 75 0.985 0.993 3.72e-05 3
#> SD:kmeans 81 0.996 0.990 7.14e-08 4
#> SD:kmeans 70 0.941 0.985 3.16e-09 5
#> SD:kmeans 56 0.747 0.965 7.75e-08 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 15497 rows and 84 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 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 0.903 0.916 0.963 0.5046 0.497 0.497
#> 3 3 0.789 0.863 0.924 0.3149 0.762 0.554
#> 4 4 0.721 0.858 0.874 0.1005 0.919 0.765
#> 5 5 0.716 0.670 0.803 0.0746 0.950 0.822
#> 6 6 0.731 0.685 0.770 0.0446 0.939 0.745
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
#> GSM339455 1 0.000 0.977 1.000 0.000
#> GSM339456 2 0.000 0.945 0.000 1.000
#> GSM339457 2 0.886 0.615 0.304 0.696
#> GSM339458 2 0.000 0.945 0.000 1.000
#> GSM339459 2 0.969 0.429 0.396 0.604
#> GSM339460 2 0.000 0.945 0.000 1.000
#> GSM339461 2 0.000 0.945 0.000 1.000
#> GSM339462 1 0.000 0.977 1.000 0.000
#> GSM339463 1 0.000 0.977 1.000 0.000
#> GSM339464 1 0.204 0.951 0.968 0.032
#> GSM339465 1 0.000 0.977 1.000 0.000
#> GSM339466 2 0.000 0.945 0.000 1.000
#> GSM339467 2 0.000 0.945 0.000 1.000
#> GSM339468 2 0.000 0.945 0.000 1.000
#> GSM339469 1 0.204 0.951 0.968 0.032
#> GSM339470 2 0.204 0.924 0.032 0.968
#> GSM339471 1 0.000 0.977 1.000 0.000
#> GSM339472 2 0.000 0.945 0.000 1.000
#> GSM339473 1 0.000 0.977 1.000 0.000
#> GSM339474 2 0.000 0.945 0.000 1.000
#> GSM339475 1 0.000 0.977 1.000 0.000
#> GSM339476 1 0.000 0.977 1.000 0.000
#> GSM339477 2 0.000 0.945 0.000 1.000
#> GSM339478 2 0.204 0.924 0.032 0.968
#> GSM339479 2 0.000 0.945 0.000 1.000
#> GSM339480 2 0.971 0.419 0.400 0.600
#> GSM339481 2 0.000 0.945 0.000 1.000
#> GSM339482 1 0.000 0.977 1.000 0.000
#> GSM339483 1 0.000 0.977 1.000 0.000
#> GSM339484 1 0.000 0.977 1.000 0.000
#> GSM339485 1 0.204 0.951 0.968 0.032
#> GSM339486 1 0.000 0.977 1.000 0.000
#> GSM339487 2 0.000 0.945 0.000 1.000
#> GSM339488 2 0.000 0.945 0.000 1.000
#> GSM339489 2 0.000 0.945 0.000 1.000
#> GSM339490 1 0.204 0.951 0.968 0.032
#> GSM339491 2 0.184 0.926 0.028 0.972
#> GSM339492 1 0.000 0.977 1.000 0.000
#> GSM339493 2 0.000 0.945 0.000 1.000
#> GSM339494 1 0.000 0.977 1.000 0.000
#> GSM339495 2 0.000 0.945 0.000 1.000
#> GSM339496 1 0.000 0.977 1.000 0.000
#> GSM339497 2 0.000 0.945 0.000 1.000
#> GSM339498 2 0.753 0.740 0.216 0.784
#> GSM339499 2 0.876 0.629 0.296 0.704
#> GSM339500 2 0.000 0.945 0.000 1.000
#> GSM339501 1 0.000 0.977 1.000 0.000
#> GSM339502 2 0.000 0.945 0.000 1.000
#> GSM339503 1 0.000 0.977 1.000 0.000
#> GSM339504 1 0.000 0.977 1.000 0.000
#> GSM339505 2 0.881 0.622 0.300 0.700
#> GSM339506 1 0.000 0.977 1.000 0.000
#> GSM339507 1 0.000 0.977 1.000 0.000
#> GSM339508 2 0.000 0.945 0.000 1.000
#> GSM339509 2 0.000 0.945 0.000 1.000
#> GSM339510 2 0.000 0.945 0.000 1.000
#> GSM339511 1 0.958 0.395 0.620 0.380
#> GSM339512 2 0.000 0.945 0.000 1.000
#> GSM339513 1 0.000 0.977 1.000 0.000
#> GSM339514 2 0.000 0.945 0.000 1.000
#> GSM339515 1 0.000 0.977 1.000 0.000
#> GSM339516 2 0.000 0.945 0.000 1.000
#> GSM339517 1 0.000 0.977 1.000 0.000
#> GSM339518 2 0.000 0.945 0.000 1.000
#> GSM339519 1 0.000 0.977 1.000 0.000
#> GSM339520 2 0.224 0.921 0.036 0.964
#> GSM339521 2 0.000 0.945 0.000 1.000
#> GSM339522 2 0.000 0.945 0.000 1.000
#> GSM339523 2 0.000 0.945 0.000 1.000
#> GSM339524 1 0.000 0.977 1.000 0.000
#> GSM339525 1 0.000 0.977 1.000 0.000
#> GSM339526 1 0.000 0.977 1.000 0.000
#> GSM339527 1 0.000 0.977 1.000 0.000
#> GSM339528 1 0.000 0.977 1.000 0.000
#> GSM339529 2 0.000 0.945 0.000 1.000
#> GSM339530 2 0.876 0.629 0.296 0.704
#> GSM339531 2 0.000 0.945 0.000 1.000
#> GSM339532 1 0.876 0.576 0.704 0.296
#> GSM339533 1 0.000 0.977 1.000 0.000
#> GSM339534 1 0.000 0.977 1.000 0.000
#> GSM339535 2 0.000 0.945 0.000 1.000
#> GSM339536 1 0.000 0.977 1.000 0.000
#> GSM339537 2 0.000 0.945 0.000 1.000
#> GSM339538 1 0.000 0.977 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM339455 3 0.6252 -0.152 0.444 0.000 0.556
#> GSM339456 2 0.2165 0.930 0.064 0.936 0.000
#> GSM339457 3 0.0000 0.907 0.000 0.000 1.000
#> GSM339458 2 0.0237 0.967 0.000 0.996 0.004
#> GSM339459 3 0.5016 0.676 0.240 0.000 0.760
#> GSM339460 2 0.0000 0.970 0.000 1.000 0.000
#> GSM339461 2 0.2165 0.930 0.064 0.936 0.000
#> GSM339462 1 0.0000 0.825 1.000 0.000 0.000
#> GSM339463 3 0.3192 0.795 0.112 0.000 0.888
#> GSM339464 1 0.0000 0.825 1.000 0.000 0.000
#> GSM339465 3 0.3192 0.795 0.112 0.000 0.888
#> GSM339466 2 0.0000 0.970 0.000 1.000 0.000
#> GSM339467 2 0.0000 0.970 0.000 1.000 0.000
#> GSM339468 2 0.4504 0.813 0.196 0.804 0.000
#> GSM339469 1 0.0000 0.825 1.000 0.000 0.000
#> GSM339470 3 0.2261 0.853 0.000 0.068 0.932
#> GSM339471 1 0.5138 0.795 0.748 0.000 0.252
#> GSM339472 2 0.0000 0.970 0.000 1.000 0.000
#> GSM339473 1 0.5058 0.799 0.756 0.000 0.244
#> GSM339474 2 0.0000 0.970 0.000 1.000 0.000
#> GSM339475 3 0.0000 0.907 0.000 0.000 1.000
#> GSM339476 1 0.4504 0.808 0.804 0.000 0.196
#> GSM339477 2 0.2066 0.933 0.060 0.940 0.000
#> GSM339478 3 0.0237 0.905 0.000 0.004 0.996
#> GSM339479 2 0.1267 0.950 0.024 0.972 0.004
#> GSM339480 3 0.5016 0.676 0.240 0.000 0.760
#> GSM339481 2 0.0000 0.970 0.000 1.000 0.000
#> GSM339482 3 0.0237 0.906 0.004 0.000 0.996
#> GSM339483 1 0.0000 0.825 1.000 0.000 0.000
#> GSM339484 1 0.6045 0.624 0.620 0.000 0.380
#> GSM339485 1 0.0000 0.825 1.000 0.000 0.000
#> GSM339486 1 0.5706 0.725 0.680 0.000 0.320
#> GSM339487 2 0.0000 0.970 0.000 1.000 0.000
#> GSM339488 2 0.0000 0.970 0.000 1.000 0.000
#> GSM339489 2 0.4504 0.813 0.196 0.804 0.000
#> GSM339490 1 0.0000 0.825 1.000 0.000 0.000
#> GSM339491 3 0.2537 0.841 0.000 0.080 0.920
#> GSM339492 1 0.5138 0.795 0.748 0.000 0.252
#> GSM339493 2 0.0000 0.970 0.000 1.000 0.000
#> GSM339494 1 0.5058 0.799 0.756 0.000 0.244
#> GSM339495 2 0.0000 0.970 0.000 1.000 0.000
#> GSM339496 3 0.0000 0.907 0.000 0.000 1.000
#> GSM339497 2 0.0000 0.970 0.000 1.000 0.000
#> GSM339498 3 0.6208 0.675 0.200 0.048 0.752
#> GSM339499 3 0.0000 0.907 0.000 0.000 1.000
#> GSM339500 2 0.0237 0.967 0.000 0.996 0.004
#> GSM339501 1 0.0000 0.825 1.000 0.000 0.000
#> GSM339502 2 0.0000 0.970 0.000 1.000 0.000
#> GSM339503 3 0.0237 0.906 0.004 0.000 0.996
#> GSM339504 1 0.0000 0.825 1.000 0.000 0.000
#> GSM339505 3 0.0000 0.907 0.000 0.000 1.000
#> GSM339506 1 0.0000 0.825 1.000 0.000 0.000
#> GSM339507 1 0.5706 0.725 0.680 0.000 0.320
#> GSM339508 2 0.0000 0.970 0.000 1.000 0.000
#> GSM339509 2 0.0000 0.970 0.000 1.000 0.000
#> GSM339510 2 0.4504 0.813 0.196 0.804 0.000
#> GSM339511 1 0.0237 0.823 0.996 0.004 0.000
#> GSM339512 2 0.0000 0.970 0.000 1.000 0.000
#> GSM339513 1 0.5098 0.797 0.752 0.000 0.248
#> GSM339514 2 0.0000 0.970 0.000 1.000 0.000
#> GSM339515 1 0.5058 0.799 0.756 0.000 0.244
#> GSM339516 2 0.0000 0.970 0.000 1.000 0.000
#> GSM339517 3 0.0237 0.906 0.004 0.000 0.996
#> GSM339518 2 0.0000 0.970 0.000 1.000 0.000
#> GSM339519 3 0.0237 0.906 0.004 0.000 0.996
#> GSM339520 3 0.0000 0.907 0.000 0.000 1.000
#> GSM339521 2 0.0000 0.970 0.000 1.000 0.000
#> GSM339522 2 0.0424 0.966 0.008 0.992 0.000
#> GSM339523 2 0.0000 0.970 0.000 1.000 0.000
#> GSM339524 1 0.5178 0.791 0.744 0.000 0.256
#> GSM339525 1 0.0000 0.825 1.000 0.000 0.000
#> GSM339526 3 0.0000 0.907 0.000 0.000 1.000
#> GSM339527 1 0.0000 0.825 1.000 0.000 0.000
#> GSM339528 1 0.5706 0.725 0.680 0.000 0.320
#> GSM339529 2 0.0000 0.970 0.000 1.000 0.000
#> GSM339530 3 0.0000 0.907 0.000 0.000 1.000
#> GSM339531 2 0.4504 0.813 0.196 0.804 0.000
#> GSM339532 1 0.0237 0.823 0.996 0.004 0.000
#> GSM339533 3 0.0000 0.907 0.000 0.000 1.000
#> GSM339534 1 0.5138 0.795 0.748 0.000 0.252
#> GSM339535 2 0.0000 0.970 0.000 1.000 0.000
#> GSM339536 1 0.5058 0.799 0.756 0.000 0.244
#> GSM339537 2 0.0000 0.970 0.000 1.000 0.000
#> GSM339538 3 0.0237 0.906 0.004 0.000 0.996
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM339455 1 0.5008 0.692 0.732 0.000 0.228 0.040
#> GSM339456 2 0.0804 0.914 0.000 0.980 0.008 0.012
#> GSM339457 3 0.0592 0.819 0.016 0.000 0.984 0.000
#> GSM339458 2 0.5768 0.801 0.060 0.752 0.144 0.044
#> GSM339459 3 0.5149 0.790 0.084 0.012 0.780 0.124
#> GSM339460 2 0.3266 0.892 0.000 0.876 0.084 0.040
#> GSM339461 2 0.0927 0.915 0.000 0.976 0.008 0.016
#> GSM339462 4 0.2216 0.993 0.092 0.000 0.000 0.908
#> GSM339463 1 0.2704 0.769 0.876 0.000 0.124 0.000
#> GSM339464 4 0.2216 0.993 0.092 0.000 0.000 0.908
#> GSM339465 1 0.2011 0.801 0.920 0.000 0.080 0.000
#> GSM339466 2 0.0376 0.917 0.000 0.992 0.004 0.004
#> GSM339467 2 0.1978 0.909 0.000 0.928 0.068 0.004
#> GSM339468 2 0.3710 0.790 0.000 0.804 0.004 0.192
#> GSM339469 4 0.2216 0.993 0.092 0.000 0.000 0.908
#> GSM339470 3 0.3852 0.740 0.192 0.008 0.800 0.000
#> GSM339471 1 0.3533 0.861 0.864 0.000 0.080 0.056
#> GSM339472 2 0.0000 0.918 0.000 1.000 0.000 0.000
#> GSM339473 1 0.2048 0.876 0.928 0.000 0.008 0.064
#> GSM339474 2 0.0188 0.918 0.000 0.996 0.004 0.000
#> GSM339475 3 0.3610 0.829 0.200 0.000 0.800 0.000
#> GSM339476 1 0.6805 0.230 0.500 0.000 0.100 0.400
#> GSM339477 2 0.0804 0.914 0.000 0.980 0.008 0.012
#> GSM339478 3 0.0592 0.819 0.016 0.000 0.984 0.000
#> GSM339479 2 0.8500 0.218 0.060 0.432 0.144 0.364
#> GSM339480 3 0.5149 0.790 0.084 0.012 0.780 0.124
#> GSM339481 2 0.0188 0.918 0.000 0.996 0.000 0.004
#> GSM339482 3 0.4040 0.792 0.248 0.000 0.752 0.000
#> GSM339483 4 0.2216 0.993 0.092 0.000 0.000 0.908
#> GSM339484 1 0.1284 0.865 0.964 0.000 0.024 0.012
#> GSM339485 4 0.2216 0.993 0.092 0.000 0.000 0.908
#> GSM339486 1 0.1174 0.866 0.968 0.000 0.020 0.012
#> GSM339487 2 0.0376 0.917 0.000 0.992 0.004 0.004
#> GSM339488 2 0.2053 0.909 0.000 0.924 0.072 0.004
#> GSM339489 2 0.3448 0.812 0.000 0.828 0.004 0.168
#> GSM339490 4 0.2216 0.993 0.092 0.000 0.000 0.908
#> GSM339491 3 0.4276 0.736 0.192 0.016 0.788 0.004
#> GSM339492 1 0.3667 0.858 0.856 0.000 0.088 0.056
#> GSM339493 2 0.0188 0.918 0.000 0.996 0.000 0.004
#> GSM339494 1 0.2048 0.876 0.928 0.000 0.008 0.064
#> GSM339495 2 0.0188 0.918 0.000 0.996 0.004 0.000
#> GSM339496 3 0.3610 0.829 0.200 0.000 0.800 0.000
#> GSM339497 2 0.3216 0.893 0.000 0.880 0.076 0.044
#> GSM339498 3 0.5752 0.688 0.008 0.084 0.720 0.188
#> GSM339499 3 0.0592 0.819 0.016 0.000 0.984 0.000
#> GSM339500 2 0.5451 0.795 0.024 0.748 0.184 0.044
#> GSM339501 4 0.1576 0.931 0.048 0.000 0.004 0.948
#> GSM339502 2 0.1978 0.909 0.000 0.928 0.068 0.004
#> GSM339503 3 0.3908 0.824 0.212 0.000 0.784 0.004
#> GSM339504 4 0.2216 0.993 0.092 0.000 0.000 0.908
#> GSM339505 3 0.3569 0.814 0.196 0.000 0.804 0.000
#> GSM339506 4 0.2216 0.993 0.092 0.000 0.000 0.908
#> GSM339507 1 0.1174 0.866 0.968 0.000 0.020 0.012
#> GSM339508 2 0.0188 0.918 0.000 0.996 0.004 0.000
#> GSM339509 2 0.2053 0.909 0.000 0.924 0.072 0.004
#> GSM339510 2 0.3751 0.785 0.000 0.800 0.004 0.196
#> GSM339511 4 0.2401 0.990 0.092 0.000 0.004 0.904
#> GSM339512 2 0.3380 0.871 0.008 0.852 0.136 0.004
#> GSM339513 1 0.3392 0.861 0.872 0.000 0.072 0.056
#> GSM339514 2 0.1978 0.909 0.000 0.928 0.068 0.004
#> GSM339515 1 0.2048 0.876 0.928 0.000 0.008 0.064
#> GSM339516 2 0.0376 0.917 0.000 0.992 0.004 0.004
#> GSM339517 3 0.3688 0.827 0.208 0.000 0.792 0.000
#> GSM339518 2 0.3286 0.892 0.000 0.876 0.080 0.044
#> GSM339519 3 0.3726 0.824 0.212 0.000 0.788 0.000
#> GSM339520 3 0.0592 0.819 0.016 0.000 0.984 0.000
#> GSM339521 2 0.3457 0.891 0.008 0.876 0.076 0.040
#> GSM339522 2 0.1722 0.900 0.000 0.944 0.008 0.048
#> GSM339523 2 0.1902 0.910 0.000 0.932 0.064 0.004
#> GSM339524 1 0.4094 0.825 0.828 0.000 0.116 0.056
#> GSM339525 4 0.2216 0.993 0.092 0.000 0.000 0.908
#> GSM339526 3 0.3688 0.826 0.208 0.000 0.792 0.000
#> GSM339527 4 0.2216 0.993 0.092 0.000 0.000 0.908
#> GSM339528 1 0.1174 0.866 0.968 0.000 0.020 0.012
#> GSM339529 2 0.0188 0.918 0.000 0.996 0.004 0.000
#> GSM339530 3 0.0592 0.819 0.016 0.000 0.984 0.000
#> GSM339531 2 0.3402 0.815 0.000 0.832 0.004 0.164
#> GSM339532 4 0.2401 0.990 0.092 0.000 0.004 0.904
#> GSM339533 3 0.4304 0.740 0.284 0.000 0.716 0.000
#> GSM339534 1 0.3919 0.850 0.840 0.000 0.104 0.056
#> GSM339535 2 0.1661 0.914 0.000 0.944 0.052 0.004
#> GSM339536 1 0.2048 0.876 0.928 0.000 0.008 0.064
#> GSM339537 2 0.0376 0.917 0.000 0.992 0.004 0.004
#> GSM339538 3 0.3764 0.822 0.216 0.000 0.784 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM339455 1 0.7249 0.1525 0.384 0.000 0.312 0.020 0.284
#> GSM339456 2 0.2339 0.6526 0.000 0.892 0.004 0.004 0.100
#> GSM339457 3 0.3399 0.7342 0.020 0.000 0.812 0.000 0.168
#> GSM339458 5 0.5110 0.7481 0.028 0.288 0.024 0.000 0.660
#> GSM339459 3 0.5138 0.6207 0.024 0.012 0.688 0.020 0.256
#> GSM339460 2 0.4449 -0.5243 0.000 0.512 0.004 0.000 0.484
#> GSM339461 2 0.3461 0.6127 0.000 0.812 0.004 0.016 0.168
#> GSM339462 4 0.0162 0.9411 0.000 0.000 0.000 0.996 0.004
#> GSM339463 1 0.3130 0.7270 0.856 0.000 0.096 0.000 0.048
#> GSM339464 4 0.0324 0.9402 0.004 0.004 0.000 0.992 0.000
#> GSM339465 1 0.1168 0.8179 0.960 0.000 0.032 0.000 0.008
#> GSM339466 2 0.1121 0.6980 0.000 0.956 0.000 0.000 0.044
#> GSM339467 2 0.3039 0.6030 0.000 0.836 0.012 0.000 0.152
#> GSM339468 2 0.5594 0.4217 0.020 0.636 0.004 0.052 0.288
#> GSM339469 4 0.0162 0.9409 0.000 0.004 0.000 0.996 0.000
#> GSM339470 3 0.6303 0.5011 0.196 0.000 0.524 0.000 0.280
#> GSM339471 1 0.5020 0.8038 0.752 0.000 0.120 0.092 0.036
#> GSM339472 2 0.1638 0.6803 0.000 0.932 0.004 0.000 0.064
#> GSM339473 1 0.2793 0.8465 0.876 0.000 0.036 0.088 0.000
#> GSM339474 2 0.0794 0.6955 0.000 0.972 0.000 0.000 0.028
#> GSM339475 3 0.2377 0.7573 0.128 0.000 0.872 0.000 0.000
#> GSM339476 4 0.6498 0.3424 0.240 0.000 0.136 0.588 0.036
#> GSM339477 2 0.1731 0.6802 0.000 0.932 0.004 0.004 0.060
#> GSM339478 3 0.3399 0.7342 0.020 0.000 0.812 0.000 0.168
#> GSM339479 5 0.6359 0.6666 0.040 0.184 0.024 0.092 0.660
#> GSM339480 3 0.5138 0.6207 0.024 0.012 0.688 0.020 0.256
#> GSM339481 2 0.2338 0.6476 0.000 0.884 0.004 0.000 0.112
#> GSM339482 3 0.3048 0.7112 0.176 0.000 0.820 0.000 0.004
#> GSM339483 4 0.0162 0.9411 0.000 0.000 0.000 0.996 0.004
#> GSM339484 1 0.1503 0.8280 0.952 0.000 0.020 0.020 0.008
#> GSM339485 4 0.0162 0.9409 0.000 0.004 0.000 0.996 0.000
#> GSM339486 1 0.1299 0.8312 0.960 0.000 0.012 0.020 0.008
#> GSM339487 2 0.1197 0.6972 0.000 0.952 0.000 0.000 0.048
#> GSM339488 2 0.3039 0.6030 0.000 0.836 0.012 0.000 0.152
#> GSM339489 2 0.5523 0.4193 0.020 0.632 0.004 0.044 0.300
#> GSM339490 4 0.0162 0.9409 0.000 0.004 0.000 0.996 0.000
#> GSM339491 3 0.6682 0.4835 0.200 0.012 0.508 0.000 0.280
#> GSM339492 1 0.5065 0.8022 0.748 0.000 0.124 0.092 0.036
#> GSM339493 2 0.2011 0.6838 0.000 0.908 0.004 0.000 0.088
#> GSM339494 1 0.2793 0.8465 0.876 0.000 0.036 0.088 0.000
#> GSM339495 2 0.0703 0.6961 0.000 0.976 0.000 0.000 0.024
#> GSM339496 3 0.2377 0.7573 0.128 0.000 0.872 0.000 0.000
#> GSM339497 2 0.4562 -0.5778 0.000 0.496 0.008 0.000 0.496
#> GSM339498 3 0.6440 0.5947 0.016 0.080 0.640 0.052 0.212
#> GSM339499 3 0.3399 0.7342 0.020 0.000 0.812 0.000 0.168
#> GSM339500 5 0.4599 0.7368 0.000 0.272 0.040 0.000 0.688
#> GSM339501 4 0.4301 0.6879 0.020 0.000 0.008 0.728 0.244
#> GSM339502 2 0.3039 0.6030 0.000 0.836 0.012 0.000 0.152
#> GSM339503 3 0.3005 0.7529 0.124 0.000 0.856 0.012 0.008
#> GSM339504 4 0.0162 0.9411 0.000 0.000 0.000 0.996 0.004
#> GSM339505 3 0.4168 0.7125 0.200 0.000 0.756 0.000 0.044
#> GSM339506 4 0.0451 0.9384 0.008 0.000 0.000 0.988 0.004
#> GSM339507 1 0.1280 0.8328 0.960 0.000 0.008 0.024 0.008
#> GSM339508 2 0.0671 0.7000 0.000 0.980 0.000 0.004 0.016
#> GSM339509 2 0.3039 0.6030 0.000 0.836 0.012 0.000 0.152
#> GSM339510 2 0.6173 0.3349 0.020 0.560 0.004 0.080 0.336
#> GSM339511 4 0.0451 0.9374 0.000 0.008 0.000 0.988 0.004
#> GSM339512 2 0.5446 -0.0705 0.012 0.592 0.048 0.000 0.348
#> GSM339513 1 0.4403 0.8059 0.772 0.000 0.132 0.092 0.004
#> GSM339514 2 0.2997 0.6070 0.000 0.840 0.012 0.000 0.148
#> GSM339515 1 0.2793 0.8465 0.876 0.000 0.036 0.088 0.000
#> GSM339516 2 0.1270 0.6938 0.000 0.948 0.000 0.000 0.052
#> GSM339517 3 0.2329 0.7575 0.124 0.000 0.876 0.000 0.000
#> GSM339518 5 0.4451 0.4753 0.000 0.492 0.004 0.000 0.504
#> GSM339519 3 0.2935 0.7552 0.120 0.000 0.860 0.004 0.016
#> GSM339520 3 0.3399 0.7342 0.020 0.000 0.812 0.000 0.168
#> GSM339521 5 0.4283 0.5743 0.000 0.456 0.000 0.000 0.544
#> GSM339522 2 0.4552 0.4547 0.020 0.668 0.004 0.000 0.308
#> GSM339523 2 0.3039 0.6030 0.000 0.836 0.012 0.000 0.152
#> GSM339524 1 0.5032 0.7034 0.692 0.000 0.228 0.076 0.004
#> GSM339525 4 0.0162 0.9411 0.000 0.000 0.000 0.996 0.004
#> GSM339526 3 0.2605 0.7517 0.148 0.000 0.852 0.000 0.000
#> GSM339527 4 0.0451 0.9384 0.008 0.000 0.000 0.988 0.004
#> GSM339528 1 0.1280 0.8328 0.960 0.000 0.008 0.024 0.008
#> GSM339529 2 0.0671 0.7000 0.000 0.980 0.000 0.004 0.016
#> GSM339530 3 0.3449 0.7353 0.024 0.000 0.812 0.000 0.164
#> GSM339531 2 0.5466 0.4304 0.020 0.644 0.004 0.044 0.288
#> GSM339532 4 0.0290 0.9392 0.000 0.008 0.000 0.992 0.000
#> GSM339533 3 0.6152 0.5036 0.324 0.000 0.524 0.000 0.152
#> GSM339534 1 0.5235 0.7959 0.740 0.000 0.120 0.092 0.048
#> GSM339535 2 0.2304 0.6760 0.000 0.892 0.008 0.000 0.100
#> GSM339536 1 0.2793 0.8465 0.876 0.000 0.036 0.088 0.000
#> GSM339537 2 0.1270 0.6938 0.000 0.948 0.000 0.000 0.052
#> GSM339538 3 0.2424 0.7542 0.132 0.000 0.868 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM339455 6 0.7380 0.0401 0.288 0.000 0.172 0.020 0.092 0.428
#> GSM339456 2 0.2597 0.6049 0.000 0.824 0.000 0.000 0.176 0.000
#> GSM339457 3 0.5687 0.5716 0.020 0.000 0.592 0.000 0.228 0.160
#> GSM339458 6 0.2356 0.7422 0.016 0.096 0.000 0.000 0.004 0.884
#> GSM339459 3 0.3961 0.2993 0.000 0.000 0.556 0.004 0.440 0.000
#> GSM339460 6 0.3756 0.5651 0.000 0.352 0.000 0.000 0.004 0.644
#> GSM339461 2 0.4792 0.4384 0.000 0.672 0.000 0.000 0.180 0.148
#> GSM339462 4 0.0984 0.9416 0.012 0.000 0.000 0.968 0.012 0.008
#> GSM339463 1 0.5087 0.5995 0.712 0.000 0.100 0.000 0.116 0.072
#> GSM339464 4 0.0291 0.9471 0.000 0.000 0.000 0.992 0.004 0.004
#> GSM339465 1 0.1434 0.8206 0.940 0.000 0.000 0.000 0.048 0.012
#> GSM339466 2 0.2263 0.7310 0.000 0.884 0.000 0.000 0.100 0.016
#> GSM339467 2 0.3042 0.7556 0.000 0.836 0.004 0.000 0.032 0.128
#> GSM339468 5 0.4076 0.7498 0.000 0.364 0.000 0.016 0.620 0.000
#> GSM339469 4 0.0000 0.9482 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM339470 3 0.7699 0.4074 0.148 0.012 0.380 0.000 0.236 0.224
#> GSM339471 1 0.4568 0.7792 0.780 0.000 0.080 0.060 0.052 0.028
#> GSM339472 2 0.1643 0.7804 0.000 0.924 0.000 0.000 0.008 0.068
#> GSM339473 1 0.2152 0.8332 0.904 0.000 0.024 0.068 0.000 0.004
#> GSM339474 2 0.2145 0.7529 0.000 0.900 0.000 0.000 0.072 0.028
#> GSM339475 3 0.1908 0.6537 0.096 0.000 0.900 0.000 0.004 0.000
#> GSM339476 4 0.6308 0.3823 0.224 0.000 0.132 0.580 0.048 0.016
#> GSM339477 2 0.2320 0.6859 0.000 0.864 0.000 0.000 0.132 0.004
#> GSM339478 3 0.5708 0.5692 0.020 0.000 0.588 0.000 0.232 0.160
#> GSM339479 6 0.2658 0.7290 0.016 0.072 0.000 0.024 0.004 0.884
#> GSM339480 3 0.3966 0.2927 0.000 0.000 0.552 0.004 0.444 0.000
#> GSM339481 2 0.2302 0.7675 0.000 0.872 0.000 0.000 0.008 0.120
#> GSM339482 3 0.3490 0.5631 0.176 0.000 0.784 0.000 0.040 0.000
#> GSM339483 4 0.0984 0.9416 0.012 0.000 0.000 0.968 0.012 0.008
#> GSM339484 1 0.2400 0.8021 0.896 0.000 0.024 0.000 0.064 0.016
#> GSM339485 4 0.0291 0.9471 0.000 0.000 0.000 0.992 0.004 0.004
#> GSM339486 1 0.1434 0.8206 0.940 0.000 0.000 0.000 0.048 0.012
#> GSM339487 2 0.2350 0.7288 0.000 0.880 0.000 0.000 0.100 0.020
#> GSM339488 2 0.3042 0.7556 0.000 0.836 0.004 0.000 0.032 0.128
#> GSM339489 5 0.4046 0.7491 0.000 0.368 0.000 0.008 0.620 0.004
#> GSM339490 4 0.0000 0.9482 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM339491 3 0.7962 0.3878 0.148 0.028 0.364 0.000 0.236 0.224
#> GSM339492 1 0.4618 0.7771 0.776 0.000 0.084 0.060 0.052 0.028
#> GSM339493 2 0.1686 0.7793 0.000 0.924 0.000 0.000 0.012 0.064
#> GSM339494 1 0.2152 0.8332 0.904 0.000 0.024 0.068 0.000 0.004
#> GSM339495 2 0.2039 0.7462 0.000 0.904 0.000 0.000 0.076 0.020
#> GSM339496 3 0.1908 0.6537 0.096 0.000 0.900 0.000 0.004 0.000
#> GSM339497 6 0.3790 0.6973 0.004 0.264 0.000 0.000 0.016 0.716
#> GSM339498 3 0.4748 0.3450 0.000 0.028 0.564 0.004 0.396 0.008
#> GSM339499 3 0.5687 0.5716 0.020 0.000 0.592 0.000 0.228 0.160
#> GSM339500 6 0.1779 0.7069 0.000 0.064 0.000 0.000 0.016 0.920
#> GSM339501 5 0.4635 -0.1883 0.008 0.000 0.024 0.480 0.488 0.000
#> GSM339502 2 0.3084 0.7533 0.000 0.832 0.004 0.000 0.032 0.132
#> GSM339503 3 0.2999 0.6297 0.112 0.000 0.840 0.000 0.048 0.000
#> GSM339504 4 0.0984 0.9416 0.012 0.000 0.000 0.968 0.012 0.008
#> GSM339505 3 0.5764 0.6007 0.152 0.000 0.640 0.000 0.136 0.072
#> GSM339506 4 0.0405 0.9476 0.000 0.000 0.000 0.988 0.008 0.004
#> GSM339507 1 0.1434 0.8206 0.940 0.000 0.000 0.000 0.048 0.012
#> GSM339508 2 0.1812 0.7567 0.000 0.912 0.000 0.000 0.080 0.008
#> GSM339509 2 0.3042 0.7556 0.000 0.836 0.004 0.000 0.032 0.128
#> GSM339510 5 0.4780 0.7338 0.000 0.324 0.000 0.016 0.620 0.040
#> GSM339511 4 0.0260 0.9459 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM339512 2 0.6609 0.1241 0.004 0.488 0.044 0.000 0.204 0.260
#> GSM339513 1 0.4497 0.7754 0.768 0.000 0.116 0.060 0.048 0.008
#> GSM339514 2 0.2826 0.7588 0.000 0.844 0.000 0.000 0.028 0.128
#> GSM339515 1 0.2152 0.8332 0.904 0.000 0.024 0.068 0.000 0.004
#> GSM339516 2 0.2581 0.7091 0.000 0.860 0.000 0.000 0.120 0.020
#> GSM339517 3 0.1970 0.6537 0.092 0.000 0.900 0.000 0.008 0.000
#> GSM339518 6 0.3586 0.6939 0.000 0.268 0.000 0.000 0.012 0.720
#> GSM339519 3 0.2826 0.6438 0.092 0.000 0.856 0.000 0.052 0.000
#> GSM339520 3 0.5687 0.5716 0.020 0.000 0.592 0.000 0.228 0.160
#> GSM339521 6 0.2994 0.7331 0.000 0.208 0.000 0.000 0.004 0.788
#> GSM339522 5 0.4646 0.5690 0.000 0.460 0.000 0.000 0.500 0.040
#> GSM339523 2 0.2909 0.7554 0.000 0.836 0.000 0.000 0.028 0.136
#> GSM339524 1 0.5326 0.3465 0.540 0.000 0.384 0.020 0.052 0.004
#> GSM339525 4 0.0984 0.9416 0.012 0.000 0.000 0.968 0.012 0.008
#> GSM339526 3 0.2092 0.6459 0.124 0.000 0.876 0.000 0.000 0.000
#> GSM339527 4 0.0405 0.9476 0.000 0.000 0.000 0.988 0.008 0.004
#> GSM339528 1 0.1434 0.8206 0.940 0.000 0.000 0.000 0.048 0.012
#> GSM339529 2 0.1812 0.7567 0.000 0.912 0.000 0.000 0.080 0.008
#> GSM339530 3 0.5772 0.5710 0.020 0.004 0.592 0.000 0.236 0.148
#> GSM339531 5 0.4046 0.7491 0.000 0.368 0.000 0.008 0.620 0.004
#> GSM339532 4 0.0260 0.9459 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM339533 3 0.7476 0.4185 0.220 0.000 0.384 0.000 0.220 0.176
#> GSM339534 1 0.4778 0.7737 0.768 0.000 0.080 0.060 0.052 0.040
#> GSM339535 2 0.1951 0.7787 0.000 0.908 0.000 0.000 0.016 0.076
#> GSM339536 1 0.2152 0.8332 0.904 0.000 0.024 0.068 0.000 0.004
#> GSM339537 2 0.2581 0.7096 0.000 0.860 0.000 0.000 0.120 0.020
#> GSM339538 3 0.2312 0.6423 0.112 0.000 0.876 0.000 0.012 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 protocol(p) agent(p) individual(p) k
#> SD:skmeans 81 1.000 0.726 1.84e-03 2
#> SD:skmeans 83 0.988 0.963 3.05e-05 3
#> SD:skmeans 82 0.917 0.997 3.41e-08 4
#> SD:skmeans 72 0.903 0.998 7.90e-10 5
#> SD:skmeans 72 0.860 0.994 3.78e-12 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 15497 rows and 84 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 0.401 0.772 0.890 0.4965 0.501 0.501
#> 3 3 0.488 0.687 0.796 0.3235 0.765 0.561
#> 4 4 0.606 0.783 0.843 0.1356 0.809 0.504
#> 5 5 0.665 0.742 0.842 0.0587 0.948 0.790
#> 6 6 0.736 0.749 0.843 0.0415 0.897 0.572
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
#> GSM339455 1 0.8144 0.727 0.748 0.252
#> GSM339456 2 0.7056 0.748 0.192 0.808
#> GSM339457 1 0.9209 0.552 0.664 0.336
#> GSM339458 1 0.9710 0.486 0.600 0.400
#> GSM339459 2 0.7139 0.744 0.196 0.804
#> GSM339460 2 0.0672 0.893 0.008 0.992
#> GSM339461 2 0.0000 0.897 0.000 1.000
#> GSM339462 1 0.0376 0.842 0.996 0.004
#> GSM339463 1 0.6048 0.797 0.852 0.148
#> GSM339464 1 0.7745 0.729 0.772 0.228
#> GSM339465 1 0.3733 0.835 0.928 0.072
#> GSM339466 2 0.0000 0.897 0.000 1.000
#> GSM339467 2 0.0000 0.897 0.000 1.000
#> GSM339468 2 0.6801 0.760 0.180 0.820
#> GSM339469 1 0.5294 0.804 0.880 0.120
#> GSM339470 1 0.9248 0.590 0.660 0.340
#> GSM339471 1 0.0000 0.841 1.000 0.000
#> GSM339472 2 0.0000 0.897 0.000 1.000
#> GSM339473 1 0.0376 0.842 0.996 0.004
#> GSM339474 2 0.0000 0.897 0.000 1.000
#> GSM339475 1 0.2236 0.841 0.964 0.036
#> GSM339476 1 0.6887 0.765 0.816 0.184
#> GSM339477 2 0.4298 0.842 0.088 0.912
#> GSM339478 2 0.9044 0.386 0.320 0.680
#> GSM339479 1 0.7139 0.739 0.804 0.196
#> GSM339480 2 0.7219 0.739 0.200 0.800
#> GSM339481 2 0.0000 0.897 0.000 1.000
#> GSM339482 1 0.1843 0.842 0.972 0.028
#> GSM339483 1 0.6247 0.772 0.844 0.156
#> GSM339484 1 0.0000 0.841 1.000 0.000
#> GSM339485 1 0.7056 0.751 0.808 0.192
#> GSM339486 1 0.0376 0.842 0.996 0.004
#> GSM339487 2 0.0938 0.892 0.012 0.988
#> GSM339488 2 0.0000 0.897 0.000 1.000
#> GSM339489 2 0.7056 0.749 0.192 0.808
#> GSM339490 1 0.6623 0.762 0.828 0.172
#> GSM339491 1 0.7745 0.726 0.772 0.228
#> GSM339492 1 0.0000 0.841 1.000 0.000
#> GSM339493 2 0.0000 0.897 0.000 1.000
#> GSM339494 1 0.0000 0.841 1.000 0.000
#> GSM339495 2 0.0000 0.897 0.000 1.000
#> GSM339496 1 0.1843 0.842 0.972 0.028
#> GSM339497 2 0.4161 0.830 0.084 0.916
#> GSM339498 1 0.9970 0.235 0.532 0.468
#> GSM339499 1 0.8443 0.667 0.728 0.272
#> GSM339500 2 0.9996 -0.191 0.488 0.512
#> GSM339501 1 0.8955 0.589 0.688 0.312
#> GSM339502 2 0.0000 0.897 0.000 1.000
#> GSM339503 1 0.7139 0.735 0.804 0.196
#> GSM339504 1 0.0376 0.842 0.996 0.004
#> GSM339505 1 0.9248 0.590 0.660 0.340
#> GSM339506 1 0.0000 0.841 1.000 0.000
#> GSM339507 1 0.2043 0.839 0.968 0.032
#> GSM339508 2 0.0000 0.897 0.000 1.000
#> GSM339509 2 0.0000 0.897 0.000 1.000
#> GSM339510 2 0.2603 0.873 0.044 0.956
#> GSM339511 2 0.6887 0.701 0.184 0.816
#> GSM339512 2 0.6048 0.744 0.148 0.852
#> GSM339513 1 0.0000 0.841 1.000 0.000
#> GSM339514 2 0.0000 0.897 0.000 1.000
#> GSM339515 1 0.0000 0.841 1.000 0.000
#> GSM339516 2 0.0000 0.897 0.000 1.000
#> GSM339517 1 0.7299 0.727 0.796 0.204
#> GSM339518 2 0.0376 0.895 0.004 0.996
#> GSM339519 1 0.6531 0.774 0.832 0.168
#> GSM339520 1 0.9881 0.366 0.564 0.436
#> GSM339521 2 0.0000 0.897 0.000 1.000
#> GSM339522 2 0.0000 0.897 0.000 1.000
#> GSM339523 2 0.0000 0.897 0.000 1.000
#> GSM339524 1 0.0000 0.841 1.000 0.000
#> GSM339525 1 0.5946 0.778 0.856 0.144
#> GSM339526 1 0.1843 0.842 0.972 0.028
#> GSM339527 1 0.5946 0.778 0.856 0.144
#> GSM339528 1 0.2236 0.838 0.964 0.036
#> GSM339529 2 0.0000 0.897 0.000 1.000
#> GSM339530 1 0.8861 0.604 0.696 0.304
#> GSM339531 2 0.6973 0.753 0.188 0.812
#> GSM339532 2 0.9754 0.198 0.408 0.592
#> GSM339533 1 0.1843 0.842 0.972 0.028
#> GSM339534 1 0.4431 0.817 0.908 0.092
#> GSM339535 2 0.0000 0.897 0.000 1.000
#> GSM339536 1 0.0000 0.841 1.000 0.000
#> GSM339537 2 0.0000 0.897 0.000 1.000
#> GSM339538 1 0.0000 0.841 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM339455 3 0.4921 0.6536 0.164 0.020 0.816
#> GSM339456 2 0.4676 0.7892 0.040 0.848 0.112
#> GSM339457 3 0.3043 0.7155 0.008 0.084 0.908
#> GSM339458 3 0.9172 0.2464 0.148 0.396 0.456
#> GSM339459 2 0.8221 0.6884 0.248 0.624 0.128
#> GSM339460 2 0.2434 0.8406 0.036 0.940 0.024
#> GSM339461 2 0.4178 0.8493 0.172 0.828 0.000
#> GSM339462 1 0.4654 0.7321 0.792 0.000 0.208
#> GSM339463 3 0.3272 0.7038 0.104 0.004 0.892
#> GSM339464 1 0.1289 0.7162 0.968 0.032 0.000
#> GSM339465 3 0.1170 0.7412 0.016 0.008 0.976
#> GSM339466 2 0.4978 0.8271 0.216 0.780 0.004
#> GSM339467 2 0.0237 0.8556 0.000 0.996 0.004
#> GSM339468 2 0.7501 0.7529 0.212 0.684 0.104
#> GSM339469 1 0.5305 0.7293 0.788 0.020 0.192
#> GSM339470 3 0.2050 0.7406 0.028 0.020 0.952
#> GSM339471 1 0.5926 0.6826 0.644 0.000 0.356
#> GSM339472 2 0.0000 0.8572 0.000 1.000 0.000
#> GSM339473 1 0.5678 0.7002 0.684 0.000 0.316
#> GSM339474 2 0.0892 0.8588 0.020 0.980 0.000
#> GSM339475 3 0.1163 0.7387 0.028 0.000 0.972
#> GSM339476 1 0.3120 0.7299 0.908 0.012 0.080
#> GSM339477 2 0.1999 0.8575 0.036 0.952 0.012
#> GSM339478 3 0.9399 0.1034 0.176 0.372 0.452
#> GSM339479 3 0.7601 -0.0381 0.416 0.044 0.540
#> GSM339480 2 0.8278 0.6841 0.248 0.620 0.132
#> GSM339481 2 0.0000 0.8572 0.000 1.000 0.000
#> GSM339482 3 0.2625 0.7223 0.084 0.000 0.916
#> GSM339483 1 0.1999 0.7284 0.952 0.012 0.036
#> GSM339484 3 0.1647 0.7404 0.036 0.004 0.960
#> GSM339485 1 0.1877 0.7208 0.956 0.032 0.012
#> GSM339486 3 0.2537 0.7100 0.080 0.000 0.920
#> GSM339487 2 0.5461 0.8229 0.216 0.768 0.016
#> GSM339488 2 0.0424 0.8545 0.000 0.992 0.008
#> GSM339489 2 0.7782 0.7146 0.256 0.648 0.096
#> GSM339490 1 0.2031 0.7216 0.952 0.032 0.016
#> GSM339491 3 0.1453 0.7447 0.024 0.008 0.968
#> GSM339492 1 0.5948 0.6804 0.640 0.000 0.360
#> GSM339493 2 0.0237 0.8579 0.004 0.996 0.000
#> GSM339494 1 0.5810 0.6925 0.664 0.000 0.336
#> GSM339495 2 0.0892 0.8588 0.020 0.980 0.000
#> GSM339496 3 0.1289 0.7415 0.032 0.000 0.968
#> GSM339497 2 0.6541 0.8064 0.212 0.732 0.056
#> GSM339498 3 0.9617 0.2237 0.248 0.280 0.472
#> GSM339499 3 0.1453 0.7456 0.008 0.024 0.968
#> GSM339500 3 0.6836 0.3505 0.016 0.412 0.572
#> GSM339501 1 0.8408 0.2390 0.596 0.280 0.124
#> GSM339502 2 0.0237 0.8562 0.000 0.996 0.004
#> GSM339503 3 0.2625 0.7221 0.084 0.000 0.916
#> GSM339504 1 0.4702 0.7322 0.788 0.000 0.212
#> GSM339505 3 0.6441 0.5146 0.028 0.276 0.696
#> GSM339506 3 0.6505 -0.0801 0.468 0.004 0.528
#> GSM339507 3 0.0848 0.7432 0.008 0.008 0.984
#> GSM339508 2 0.1031 0.8585 0.024 0.976 0.000
#> GSM339509 2 0.0237 0.8556 0.000 0.996 0.004
#> GSM339510 2 0.6539 0.7634 0.288 0.684 0.028
#> GSM339511 1 0.1711 0.7175 0.960 0.032 0.008
#> GSM339512 3 0.6678 0.2782 0.008 0.480 0.512
#> GSM339513 1 0.6126 0.5683 0.600 0.000 0.400
#> GSM339514 2 0.0000 0.8572 0.000 1.000 0.000
#> GSM339515 1 0.5733 0.7013 0.676 0.000 0.324
#> GSM339516 2 0.4654 0.8320 0.208 0.792 0.000
#> GSM339517 3 0.1529 0.7372 0.040 0.000 0.960
#> GSM339518 2 0.4645 0.8386 0.176 0.816 0.008
#> GSM339519 3 0.5016 0.5828 0.240 0.000 0.760
#> GSM339520 3 0.5254 0.6010 0.000 0.264 0.736
#> GSM339521 2 0.0237 0.8556 0.000 0.996 0.004
#> GSM339522 2 0.5098 0.8116 0.248 0.752 0.000
#> GSM339523 2 0.0000 0.8572 0.000 1.000 0.000
#> GSM339524 3 0.3192 0.7073 0.112 0.000 0.888
#> GSM339525 1 0.2682 0.7375 0.920 0.004 0.076
#> GSM339526 3 0.0747 0.7387 0.016 0.000 0.984
#> GSM339527 1 0.6520 -0.0631 0.508 0.004 0.488
#> GSM339528 3 0.3213 0.7174 0.092 0.008 0.900
#> GSM339529 2 0.4346 0.8397 0.184 0.816 0.000
#> GSM339530 3 0.5785 0.5651 0.004 0.300 0.696
#> GSM339531 2 0.7568 0.7464 0.212 0.680 0.108
#> GSM339532 1 0.2939 0.7012 0.916 0.072 0.012
#> GSM339533 3 0.0592 0.7424 0.012 0.000 0.988
#> GSM339534 1 0.5692 0.7020 0.724 0.008 0.268
#> GSM339535 2 0.3295 0.8577 0.096 0.896 0.008
#> GSM339536 1 0.5859 0.6788 0.656 0.000 0.344
#> GSM339537 2 0.4605 0.8328 0.204 0.796 0.000
#> GSM339538 3 0.2537 0.7240 0.080 0.000 0.920
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM339455 4 0.4673 0.7338 0.012 0.008 0.232 0.748
#> GSM339456 2 0.5375 0.7167 0.028 0.776 0.124 0.072
#> GSM339457 3 0.1118 0.8583 0.000 0.000 0.964 0.036
#> GSM339458 4 0.7093 0.5688 0.000 0.212 0.220 0.568
#> GSM339459 4 0.4691 0.8132 0.044 0.016 0.136 0.804
#> GSM339460 2 0.1648 0.8727 0.012 0.956 0.016 0.016
#> GSM339461 2 0.4722 0.6203 0.008 0.692 0.000 0.300
#> GSM339462 1 0.2670 0.8397 0.904 0.000 0.072 0.024
#> GSM339463 3 0.2915 0.8208 0.088 0.004 0.892 0.016
#> GSM339464 1 0.3479 0.8149 0.840 0.012 0.000 0.148
#> GSM339465 3 0.2457 0.8378 0.004 0.008 0.912 0.076
#> GSM339466 4 0.2281 0.8319 0.000 0.096 0.000 0.904
#> GSM339467 2 0.0000 0.8814 0.000 1.000 0.000 0.000
#> GSM339468 4 0.3965 0.8333 0.008 0.032 0.120 0.840
#> GSM339469 1 0.4152 0.8199 0.840 0.012 0.100 0.048
#> GSM339470 3 0.2179 0.8408 0.000 0.012 0.924 0.064
#> GSM339471 1 0.4225 0.7820 0.792 0.000 0.184 0.024
#> GSM339472 2 0.0921 0.8787 0.000 0.972 0.000 0.028
#> GSM339473 1 0.3764 0.8127 0.852 0.000 0.076 0.072
#> GSM339474 2 0.1716 0.8681 0.000 0.936 0.000 0.064
#> GSM339475 3 0.1576 0.8553 0.048 0.000 0.948 0.004
#> GSM339476 1 0.4419 0.8276 0.820 0.008 0.056 0.116
#> GSM339477 2 0.2441 0.8627 0.004 0.916 0.012 0.068
#> GSM339478 4 0.4487 0.8095 0.000 0.100 0.092 0.808
#> GSM339479 4 0.7780 0.5417 0.144 0.044 0.240 0.572
#> GSM339480 4 0.4749 0.8143 0.044 0.020 0.132 0.804
#> GSM339481 2 0.0188 0.8807 0.000 0.996 0.000 0.004
#> GSM339482 3 0.3653 0.8081 0.128 0.000 0.844 0.028
#> GSM339483 1 0.3435 0.8288 0.864 0.000 0.036 0.100
#> GSM339484 3 0.1109 0.8595 0.028 0.000 0.968 0.004
#> GSM339485 1 0.3612 0.8165 0.840 0.012 0.004 0.144
#> GSM339486 3 0.2408 0.8218 0.104 0.000 0.896 0.000
#> GSM339487 4 0.2593 0.8398 0.000 0.080 0.016 0.904
#> GSM339488 2 0.0188 0.8804 0.000 0.996 0.004 0.000
#> GSM339489 4 0.4660 0.8225 0.056 0.020 0.108 0.816
#> GSM339490 1 0.3612 0.8165 0.840 0.012 0.004 0.144
#> GSM339491 3 0.1492 0.8572 0.004 0.004 0.956 0.036
#> GSM339492 1 0.4139 0.7878 0.800 0.000 0.176 0.024
#> GSM339493 2 0.4040 0.6595 0.000 0.752 0.000 0.248
#> GSM339494 1 0.3471 0.8102 0.868 0.000 0.060 0.072
#> GSM339495 2 0.2081 0.8627 0.000 0.916 0.000 0.084
#> GSM339496 3 0.0921 0.8574 0.028 0.000 0.972 0.000
#> GSM339497 4 0.3266 0.8381 0.004 0.064 0.048 0.884
#> GSM339498 4 0.4504 0.8058 0.044 0.004 0.152 0.800
#> GSM339499 3 0.0657 0.8603 0.000 0.004 0.984 0.012
#> GSM339500 3 0.6229 0.5589 0.000 0.228 0.656 0.116
#> GSM339501 4 0.5082 0.7928 0.108 0.004 0.112 0.776
#> GSM339502 2 0.0376 0.8799 0.000 0.992 0.004 0.004
#> GSM339503 3 0.2908 0.8395 0.064 0.000 0.896 0.040
#> GSM339504 1 0.3497 0.8240 0.852 0.000 0.124 0.024
#> GSM339505 3 0.2255 0.8416 0.000 0.012 0.920 0.068
#> GSM339506 1 0.5602 0.2685 0.568 0.000 0.408 0.024
#> GSM339507 3 0.3037 0.8321 0.036 0.000 0.888 0.076
#> GSM339508 2 0.2593 0.8502 0.004 0.892 0.000 0.104
#> GSM339509 2 0.0000 0.8814 0.000 1.000 0.000 0.000
#> GSM339510 4 0.2719 0.8416 0.024 0.040 0.020 0.916
#> GSM339511 1 0.3479 0.8149 0.840 0.012 0.000 0.148
#> GSM339512 3 0.6028 0.5165 0.000 0.280 0.644 0.076
#> GSM339513 1 0.5277 0.5845 0.668 0.000 0.304 0.028
#> GSM339514 2 0.0000 0.8814 0.000 1.000 0.000 0.000
#> GSM339515 1 0.3471 0.8163 0.868 0.000 0.060 0.072
#> GSM339516 4 0.2401 0.8323 0.004 0.092 0.000 0.904
#> GSM339517 3 0.3105 0.8199 0.120 0.000 0.868 0.012
#> GSM339518 4 0.3895 0.7996 0.000 0.184 0.012 0.804
#> GSM339519 3 0.5000 0.7586 0.128 0.000 0.772 0.100
#> GSM339520 2 0.4891 0.5543 0.000 0.680 0.308 0.012
#> GSM339521 2 0.1792 0.8640 0.000 0.932 0.000 0.068
#> GSM339522 4 0.2271 0.8376 0.008 0.076 0.000 0.916
#> GSM339523 2 0.0000 0.8814 0.000 1.000 0.000 0.000
#> GSM339524 3 0.4741 0.7081 0.228 0.000 0.744 0.028
#> GSM339525 1 0.3834 0.8373 0.848 0.000 0.076 0.076
#> GSM339526 3 0.0779 0.8591 0.016 0.000 0.980 0.004
#> GSM339527 3 0.7052 0.0862 0.372 0.000 0.500 0.128
#> GSM339528 3 0.3127 0.8416 0.068 0.008 0.892 0.032
#> GSM339529 4 0.3668 0.7764 0.004 0.188 0.000 0.808
#> GSM339530 2 0.5099 0.3500 0.000 0.612 0.380 0.008
#> GSM339531 4 0.4440 0.8252 0.024 0.028 0.128 0.820
#> GSM339532 1 0.3994 0.8090 0.828 0.028 0.004 0.140
#> GSM339533 3 0.0336 0.8599 0.008 0.000 0.992 0.000
#> GSM339534 1 0.4431 0.8171 0.824 0.008 0.084 0.084
#> GSM339535 4 0.4456 0.7071 0.000 0.280 0.004 0.716
#> GSM339536 1 0.3764 0.8024 0.852 0.000 0.076 0.072
#> GSM339537 4 0.2281 0.8319 0.000 0.096 0.000 0.904
#> GSM339538 3 0.3606 0.8088 0.132 0.000 0.844 0.024
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM339455 5 0.4025 0.59052 0.000 0.000 0.292 0.008 0.700
#> GSM339456 2 0.5498 0.65831 0.000 0.708 0.124 0.032 0.136
#> GSM339457 3 0.2170 0.76308 0.004 0.000 0.904 0.004 0.088
#> GSM339458 5 0.6438 0.32831 0.000 0.212 0.292 0.000 0.496
#> GSM339459 5 0.3619 0.78049 0.008 0.000 0.124 0.040 0.828
#> GSM339460 2 0.1653 0.84827 0.000 0.944 0.004 0.024 0.028
#> GSM339461 2 0.4765 0.42027 0.008 0.556 0.000 0.008 0.428
#> GSM339462 4 0.1310 0.88493 0.000 0.000 0.020 0.956 0.024
#> GSM339463 3 0.2570 0.77171 0.000 0.000 0.888 0.084 0.028
#> GSM339464 4 0.0955 0.89732 0.000 0.004 0.000 0.968 0.028
#> GSM339465 3 0.2720 0.76603 0.020 0.000 0.880 0.004 0.096
#> GSM339466 5 0.1082 0.80743 0.000 0.028 0.000 0.008 0.964
#> GSM339467 2 0.0000 0.85715 0.000 1.000 0.000 0.000 0.000
#> GSM339468 5 0.2722 0.79556 0.000 0.004 0.120 0.008 0.868
#> GSM339469 4 0.0794 0.89896 0.000 0.000 0.000 0.972 0.028
#> GSM339470 3 0.2286 0.76555 0.000 0.000 0.888 0.004 0.108
#> GSM339471 1 0.4049 0.84798 0.780 0.000 0.164 0.056 0.000
#> GSM339472 2 0.1168 0.85416 0.000 0.960 0.000 0.008 0.032
#> GSM339473 1 0.0451 0.83501 0.988 0.000 0.008 0.004 0.000
#> GSM339474 2 0.1956 0.84371 0.000 0.916 0.000 0.008 0.076
#> GSM339475 3 0.1399 0.78393 0.028 0.000 0.952 0.020 0.000
#> GSM339476 4 0.3248 0.81991 0.020 0.000 0.048 0.868 0.064
#> GSM339477 2 0.2177 0.84240 0.000 0.908 0.004 0.008 0.080
#> GSM339478 5 0.4738 0.67751 0.004 0.064 0.192 0.004 0.736
#> GSM339479 5 0.6979 0.28064 0.000 0.044 0.316 0.140 0.500
#> GSM339480 5 0.3619 0.78049 0.008 0.000 0.124 0.040 0.828
#> GSM339481 2 0.0162 0.85742 0.000 0.996 0.000 0.000 0.004
#> GSM339482 3 0.5163 0.23756 0.368 0.000 0.588 0.040 0.004
#> GSM339483 4 0.1211 0.88716 0.000 0.000 0.016 0.960 0.024
#> GSM339484 3 0.3033 0.74807 0.000 0.000 0.864 0.052 0.084
#> GSM339485 4 0.0794 0.89896 0.000 0.000 0.000 0.972 0.028
#> GSM339486 3 0.2280 0.77499 0.000 0.000 0.880 0.120 0.000
#> GSM339487 5 0.1386 0.80608 0.000 0.032 0.000 0.016 0.952
#> GSM339488 2 0.0000 0.85715 0.000 1.000 0.000 0.000 0.000
#> GSM339489 5 0.3506 0.79079 0.000 0.000 0.104 0.064 0.832
#> GSM339490 4 0.0794 0.89896 0.000 0.000 0.000 0.972 0.028
#> GSM339491 3 0.2124 0.79415 0.000 0.000 0.916 0.028 0.056
#> GSM339492 1 0.4138 0.84657 0.776 0.000 0.160 0.064 0.000
#> GSM339493 2 0.4298 0.50462 0.000 0.640 0.000 0.008 0.352
#> GSM339494 1 0.0451 0.83501 0.988 0.000 0.008 0.004 0.000
#> GSM339495 2 0.2358 0.83552 0.000 0.888 0.000 0.008 0.104
#> GSM339496 3 0.0703 0.78809 0.000 0.000 0.976 0.024 0.000
#> GSM339497 5 0.2166 0.79784 0.000 0.012 0.072 0.004 0.912
#> GSM339498 5 0.3578 0.77872 0.000 0.000 0.132 0.048 0.820
#> GSM339499 3 0.1365 0.79033 0.004 0.000 0.952 0.004 0.040
#> GSM339500 3 0.5880 0.51421 0.000 0.172 0.600 0.000 0.228
#> GSM339501 5 0.4630 0.73345 0.000 0.000 0.088 0.176 0.736
#> GSM339502 2 0.0510 0.85356 0.000 0.984 0.000 0.000 0.016
#> GSM339503 3 0.3928 0.67504 0.152 0.000 0.800 0.040 0.008
#> GSM339504 4 0.1403 0.88254 0.000 0.000 0.024 0.952 0.024
#> GSM339505 3 0.2304 0.77497 0.000 0.000 0.892 0.008 0.100
#> GSM339506 4 0.4841 0.10338 0.000 0.000 0.416 0.560 0.024
#> GSM339507 3 0.3480 0.67541 0.248 0.000 0.752 0.000 0.000
#> GSM339508 2 0.3724 0.75638 0.000 0.776 0.000 0.020 0.204
#> GSM339509 2 0.0000 0.85715 0.000 1.000 0.000 0.000 0.000
#> GSM339510 5 0.1365 0.81168 0.000 0.004 0.004 0.040 0.952
#> GSM339511 4 0.1341 0.88840 0.000 0.000 0.000 0.944 0.056
#> GSM339512 3 0.6426 0.36726 0.000 0.260 0.544 0.008 0.188
#> GSM339513 1 0.4088 0.84689 0.792 0.000 0.140 0.064 0.004
#> GSM339514 2 0.0000 0.85715 0.000 1.000 0.000 0.000 0.000
#> GSM339515 1 0.0451 0.83501 0.988 0.000 0.008 0.004 0.000
#> GSM339516 5 0.1300 0.80696 0.000 0.028 0.000 0.016 0.956
#> GSM339517 3 0.3606 0.67651 0.164 0.000 0.808 0.024 0.004
#> GSM339518 5 0.3264 0.75384 0.000 0.164 0.016 0.000 0.820
#> GSM339519 1 0.5101 0.65331 0.652 0.000 0.296 0.040 0.012
#> GSM339520 2 0.4871 0.46824 0.004 0.624 0.348 0.004 0.020
#> GSM339521 2 0.3342 0.78784 0.000 0.836 0.020 0.008 0.136
#> GSM339522 5 0.0912 0.81211 0.000 0.012 0.000 0.016 0.972
#> GSM339523 2 0.0000 0.85715 0.000 1.000 0.000 0.000 0.000
#> GSM339524 1 0.4087 0.82791 0.784 0.000 0.168 0.040 0.008
#> GSM339525 4 0.0880 0.88606 0.000 0.000 0.032 0.968 0.000
#> GSM339526 3 0.1267 0.78564 0.012 0.000 0.960 0.024 0.004
#> GSM339527 3 0.5933 0.00153 0.000 0.000 0.452 0.444 0.104
#> GSM339528 3 0.4125 0.73048 0.000 0.000 0.772 0.172 0.056
#> GSM339529 5 0.3278 0.72783 0.000 0.156 0.000 0.020 0.824
#> GSM339530 2 0.4193 0.58977 0.004 0.716 0.268 0.004 0.008
#> GSM339531 5 0.3080 0.78997 0.000 0.004 0.124 0.020 0.852
#> GSM339532 4 0.1764 0.87171 0.000 0.008 0.000 0.928 0.064
#> GSM339533 3 0.0794 0.78819 0.000 0.000 0.972 0.028 0.000
#> GSM339534 1 0.4813 0.78992 0.776 0.000 0.072 0.060 0.092
#> GSM339535 5 0.3480 0.68726 0.000 0.248 0.000 0.000 0.752
#> GSM339536 1 0.0451 0.83501 0.988 0.000 0.008 0.004 0.000
#> GSM339537 5 0.1386 0.80608 0.000 0.032 0.000 0.016 0.952
#> GSM339538 1 0.3645 0.83486 0.804 0.000 0.168 0.024 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM339455 3 0.5774 0.293 0.000 0.000 0.456 0.000 0.364 0.180
#> GSM339456 2 0.5252 0.375 0.000 0.580 0.108 0.004 0.308 0.000
#> GSM339457 6 0.1267 0.880 0.000 0.000 0.060 0.000 0.000 0.940
#> GSM339458 3 0.4001 0.707 0.000 0.128 0.760 0.000 0.112 0.000
#> GSM339459 5 0.3777 0.716 0.000 0.000 0.124 0.004 0.788 0.084
#> GSM339460 2 0.1934 0.839 0.000 0.916 0.044 0.000 0.040 0.000
#> GSM339461 5 0.5661 0.140 0.000 0.392 0.020 0.016 0.516 0.056
#> GSM339462 4 0.0993 0.931 0.000 0.000 0.012 0.964 0.024 0.000
#> GSM339463 3 0.2358 0.761 0.000 0.000 0.876 0.016 0.000 0.108
#> GSM339464 4 0.0260 0.937 0.000 0.000 0.000 0.992 0.008 0.000
#> GSM339465 3 0.2703 0.771 0.008 0.000 0.876 0.000 0.052 0.064
#> GSM339466 5 0.1010 0.777 0.000 0.036 0.004 0.000 0.960 0.000
#> GSM339467 2 0.0146 0.867 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM339468 5 0.1700 0.770 0.000 0.000 0.080 0.000 0.916 0.004
#> GSM339469 4 0.0260 0.938 0.000 0.000 0.000 0.992 0.008 0.000
#> GSM339470 3 0.2568 0.769 0.000 0.000 0.876 0.000 0.056 0.068
#> GSM339471 1 0.3706 0.846 0.796 0.000 0.148 0.024 0.000 0.032
#> GSM339472 2 0.1141 0.858 0.000 0.948 0.000 0.000 0.052 0.000
#> GSM339473 1 0.0000 0.835 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM339474 2 0.2135 0.828 0.000 0.872 0.000 0.000 0.128 0.000
#> GSM339475 6 0.2531 0.786 0.008 0.000 0.128 0.004 0.000 0.860
#> GSM339476 4 0.3186 0.811 0.008 0.000 0.108 0.844 0.032 0.008
#> GSM339477 2 0.2219 0.824 0.000 0.864 0.000 0.000 0.136 0.000
#> GSM339478 6 0.1327 0.878 0.000 0.000 0.064 0.000 0.000 0.936
#> GSM339479 3 0.4251 0.747 0.000 0.060 0.780 0.060 0.100 0.000
#> GSM339480 5 0.3454 0.727 0.000 0.000 0.124 0.004 0.812 0.060
#> GSM339481 2 0.0405 0.868 0.000 0.988 0.004 0.000 0.008 0.000
#> GSM339482 3 0.4415 0.468 0.236 0.000 0.696 0.004 0.000 0.064
#> GSM339483 4 0.0993 0.931 0.000 0.000 0.012 0.964 0.024 0.000
#> GSM339484 3 0.1010 0.780 0.000 0.000 0.960 0.036 0.000 0.004
#> GSM339485 4 0.0146 0.937 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM339486 3 0.2176 0.781 0.000 0.000 0.896 0.080 0.000 0.024
#> GSM339487 5 0.1440 0.775 0.000 0.044 0.004 0.004 0.944 0.004
#> GSM339488 2 0.0146 0.867 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM339489 5 0.2747 0.755 0.000 0.000 0.108 0.028 0.860 0.004
#> GSM339490 4 0.0146 0.937 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM339491 3 0.1296 0.791 0.000 0.012 0.952 0.004 0.032 0.000
#> GSM339492 1 0.3670 0.846 0.796 0.000 0.152 0.024 0.000 0.028
#> GSM339493 5 0.3838 0.154 0.000 0.448 0.000 0.000 0.552 0.000
#> GSM339494 1 0.0000 0.835 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM339495 2 0.3464 0.595 0.000 0.688 0.000 0.000 0.312 0.000
#> GSM339496 3 0.2009 0.756 0.000 0.000 0.904 0.004 0.008 0.084
#> GSM339497 5 0.2631 0.657 0.000 0.000 0.180 0.000 0.820 0.000
#> GSM339498 5 0.5298 0.543 0.000 0.000 0.124 0.020 0.644 0.212
#> GSM339499 6 0.1267 0.880 0.000 0.000 0.060 0.000 0.000 0.940
#> GSM339500 3 0.6322 0.361 0.000 0.052 0.516 0.000 0.288 0.144
#> GSM339501 5 0.4607 0.501 0.000 0.000 0.056 0.328 0.616 0.000
#> GSM339502 2 0.0777 0.859 0.000 0.972 0.000 0.000 0.024 0.004
#> GSM339503 3 0.2113 0.742 0.028 0.000 0.908 0.004 0.000 0.060
#> GSM339504 4 0.0993 0.931 0.000 0.000 0.012 0.964 0.024 0.000
#> GSM339505 3 0.1984 0.784 0.000 0.000 0.912 0.000 0.056 0.032
#> GSM339506 3 0.4408 0.535 0.000 0.000 0.636 0.320 0.044 0.000
#> GSM339507 3 0.2340 0.753 0.148 0.000 0.852 0.000 0.000 0.000
#> GSM339508 2 0.3073 0.780 0.000 0.788 0.000 0.008 0.204 0.000
#> GSM339509 2 0.0146 0.867 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM339510 5 0.1765 0.751 0.000 0.000 0.000 0.096 0.904 0.000
#> GSM339511 4 0.1863 0.871 0.000 0.000 0.000 0.896 0.104 0.000
#> GSM339512 2 0.4074 0.737 0.000 0.752 0.108 0.000 0.140 0.000
#> GSM339513 1 0.3550 0.856 0.800 0.000 0.156 0.020 0.000 0.024
#> GSM339514 2 0.0146 0.867 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM339515 1 0.0000 0.835 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM339516 5 0.1124 0.777 0.000 0.036 0.000 0.008 0.956 0.000
#> GSM339517 6 0.5462 0.372 0.200 0.000 0.204 0.004 0.000 0.592
#> GSM339518 5 0.4076 0.484 0.000 0.348 0.012 0.000 0.636 0.004
#> GSM339519 1 0.3691 0.847 0.788 0.000 0.148 0.004 0.000 0.060
#> GSM339520 6 0.1327 0.878 0.000 0.000 0.064 0.000 0.000 0.936
#> GSM339521 2 0.2994 0.716 0.000 0.788 0.004 0.000 0.208 0.000
#> GSM339522 5 0.0146 0.774 0.000 0.000 0.004 0.000 0.996 0.000
#> GSM339523 2 0.0146 0.867 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM339524 1 0.3615 0.851 0.796 0.000 0.140 0.004 0.000 0.060
#> GSM339525 4 0.0508 0.934 0.000 0.000 0.012 0.984 0.004 0.000
#> GSM339526 3 0.0837 0.775 0.004 0.000 0.972 0.004 0.000 0.020
#> GSM339527 3 0.5926 0.266 0.000 0.000 0.460 0.296 0.244 0.000
#> GSM339528 3 0.2128 0.791 0.004 0.000 0.908 0.056 0.032 0.000
#> GSM339529 5 0.3161 0.636 0.000 0.216 0.000 0.008 0.776 0.000
#> GSM339530 6 0.1267 0.830 0.000 0.060 0.000 0.000 0.000 0.940
#> GSM339531 5 0.2196 0.759 0.000 0.000 0.108 0.004 0.884 0.004
#> GSM339532 4 0.2092 0.849 0.000 0.000 0.000 0.876 0.124 0.000
#> GSM339533 3 0.0622 0.782 0.000 0.000 0.980 0.012 0.000 0.008
#> GSM339534 1 0.4310 0.804 0.796 0.000 0.084 0.040 0.052 0.028
#> GSM339535 5 0.3337 0.668 0.000 0.260 0.000 0.000 0.736 0.004
#> GSM339536 1 0.0000 0.835 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM339537 5 0.1265 0.774 0.000 0.044 0.000 0.008 0.948 0.000
#> GSM339538 1 0.3615 0.851 0.796 0.000 0.140 0.004 0.000 0.060
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 protocol(p) agent(p) individual(p) k
#> SD:pam 78 1.000 0.893 3.28e-03 2
#> SD:pam 75 0.724 0.879 1.65e-05 3
#> SD:pam 81 0.639 0.970 5.50e-07 4
#> SD:pam 76 0.620 0.728 3.78e-08 5
#> SD:pam 75 0.709 0.842 1.40e-08 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 15497 rows and 84 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 0.533 0.618 0.843 0.4577 0.501 0.501
#> 3 3 0.679 0.853 0.888 0.3861 0.799 0.614
#> 4 4 0.852 0.885 0.922 0.0971 0.869 0.662
#> 5 5 0.679 0.780 0.834 0.0611 0.989 0.964
#> 6 6 0.715 0.758 0.801 0.0566 0.916 0.722
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
#> GSM339455 1 0.9983 0.3132 0.524 0.476
#> GSM339456 2 0.3274 0.8271 0.060 0.940
#> GSM339457 1 0.9983 0.3132 0.524 0.476
#> GSM339458 2 0.2236 0.8469 0.036 0.964
#> GSM339459 1 0.9983 0.3132 0.524 0.476
#> GSM339460 2 0.0000 0.8715 0.000 1.000
#> GSM339461 2 0.4815 0.7768 0.104 0.896
#> GSM339462 1 0.3274 0.7114 0.940 0.060
#> GSM339463 1 0.3114 0.7101 0.944 0.056
#> GSM339464 1 0.3584 0.7073 0.932 0.068
#> GSM339465 1 0.0376 0.7181 0.996 0.004
#> GSM339466 2 0.0000 0.8715 0.000 1.000
#> GSM339467 2 0.0000 0.8715 0.000 1.000
#> GSM339468 2 0.9710 0.0501 0.400 0.600
#> GSM339469 1 0.3431 0.7096 0.936 0.064
#> GSM339470 2 0.9970 -0.2023 0.468 0.532
#> GSM339471 1 0.0376 0.7181 0.996 0.004
#> GSM339472 2 0.0000 0.8715 0.000 1.000
#> GSM339473 1 0.0376 0.7181 0.996 0.004
#> GSM339474 2 0.0000 0.8715 0.000 1.000
#> GSM339475 1 0.9983 0.3132 0.524 0.476
#> GSM339476 1 0.0938 0.7197 0.988 0.012
#> GSM339477 2 0.0672 0.8669 0.008 0.992
#> GSM339478 1 0.9993 0.2925 0.516 0.484
#> GSM339479 2 0.9775 -0.0105 0.412 0.588
#> GSM339480 1 0.9983 0.3132 0.524 0.476
#> GSM339481 2 0.0000 0.8715 0.000 1.000
#> GSM339482 1 0.9983 0.3132 0.524 0.476
#> GSM339483 1 0.3274 0.7114 0.940 0.060
#> GSM339484 1 0.0938 0.7197 0.988 0.012
#> GSM339485 1 0.3584 0.7073 0.932 0.068
#> GSM339486 1 0.0376 0.7181 0.996 0.004
#> GSM339487 2 0.0000 0.8715 0.000 1.000
#> GSM339488 2 0.0000 0.8715 0.000 1.000
#> GSM339489 2 0.4298 0.7966 0.088 0.912
#> GSM339490 1 0.3431 0.7096 0.936 0.064
#> GSM339491 2 0.9970 -0.2023 0.468 0.532
#> GSM339492 1 0.0376 0.7181 0.996 0.004
#> GSM339493 2 0.0000 0.8715 0.000 1.000
#> GSM339494 1 0.0376 0.7181 0.996 0.004
#> GSM339495 2 0.0000 0.8715 0.000 1.000
#> GSM339496 1 0.9983 0.3132 0.524 0.476
#> GSM339497 2 0.0000 0.8715 0.000 1.000
#> GSM339498 2 0.9977 -0.2145 0.472 0.528
#> GSM339499 1 0.9983 0.3132 0.524 0.476
#> GSM339500 2 0.3274 0.8273 0.060 0.940
#> GSM339501 1 0.9866 0.3766 0.568 0.432
#> GSM339502 2 0.0000 0.8715 0.000 1.000
#> GSM339503 1 0.9983 0.3132 0.524 0.476
#> GSM339504 1 0.3274 0.7114 0.940 0.060
#> GSM339505 1 0.9988 0.3042 0.520 0.480
#> GSM339506 1 0.3431 0.7118 0.936 0.064
#> GSM339507 1 0.0376 0.7181 0.996 0.004
#> GSM339508 2 0.0000 0.8715 0.000 1.000
#> GSM339509 2 0.0000 0.8715 0.000 1.000
#> GSM339510 2 0.9881 -0.0938 0.436 0.564
#> GSM339511 1 0.4939 0.6755 0.892 0.108
#> GSM339512 2 0.0000 0.8715 0.000 1.000
#> GSM339513 1 0.0938 0.7197 0.988 0.012
#> GSM339514 2 0.0000 0.8715 0.000 1.000
#> GSM339515 1 0.0376 0.7181 0.996 0.004
#> GSM339516 2 0.0000 0.8715 0.000 1.000
#> GSM339517 1 0.9983 0.3132 0.524 0.476
#> GSM339518 2 0.0000 0.8715 0.000 1.000
#> GSM339519 1 0.9983 0.3132 0.524 0.476
#> GSM339520 1 0.9983 0.3132 0.524 0.476
#> GSM339521 2 0.0000 0.8715 0.000 1.000
#> GSM339522 2 0.2603 0.8403 0.044 0.956
#> GSM339523 2 0.0000 0.8715 0.000 1.000
#> GSM339524 1 0.0938 0.7197 0.988 0.012
#> GSM339525 1 0.3274 0.7114 0.940 0.060
#> GSM339526 1 0.9983 0.3132 0.524 0.476
#> GSM339527 1 0.3431 0.7118 0.936 0.064
#> GSM339528 1 0.0376 0.7181 0.996 0.004
#> GSM339529 2 0.0000 0.8715 0.000 1.000
#> GSM339530 1 0.9983 0.3132 0.524 0.476
#> GSM339531 2 0.4690 0.7819 0.100 0.900
#> GSM339532 1 0.3431 0.7096 0.936 0.064
#> GSM339533 1 0.9983 0.3132 0.524 0.476
#> GSM339534 1 0.0938 0.7197 0.988 0.012
#> GSM339535 2 0.0000 0.8715 0.000 1.000
#> GSM339536 1 0.0376 0.7181 0.996 0.004
#> GSM339537 2 0.0000 0.8715 0.000 1.000
#> GSM339538 1 0.9983 0.3132 0.524 0.476
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM339455 3 0.5581 0.734 0.168 0.040 0.792
#> GSM339456 2 0.1015 0.958 0.012 0.980 0.008
#> GSM339457 3 0.3532 0.870 0.008 0.108 0.884
#> GSM339458 2 0.0661 0.959 0.008 0.988 0.004
#> GSM339459 3 0.1919 0.885 0.024 0.020 0.956
#> GSM339460 2 0.0424 0.959 0.008 0.992 0.000
#> GSM339461 2 0.1482 0.956 0.020 0.968 0.012
#> GSM339462 1 0.1751 0.746 0.960 0.012 0.028
#> GSM339463 3 0.4228 0.764 0.148 0.008 0.844
#> GSM339464 1 0.1751 0.746 0.960 0.012 0.028
#> GSM339465 3 0.3425 0.810 0.112 0.004 0.884
#> GSM339466 2 0.0237 0.960 0.004 0.996 0.000
#> GSM339467 2 0.0424 0.959 0.008 0.992 0.000
#> GSM339468 2 0.2434 0.933 0.024 0.940 0.036
#> GSM339469 1 0.2527 0.754 0.936 0.020 0.044
#> GSM339470 3 0.4062 0.824 0.000 0.164 0.836
#> GSM339471 1 0.5873 0.777 0.684 0.004 0.312
#> GSM339472 2 0.1015 0.958 0.012 0.980 0.008
#> GSM339473 1 0.5650 0.776 0.688 0.000 0.312
#> GSM339474 2 0.1015 0.958 0.012 0.980 0.008
#> GSM339475 3 0.0475 0.890 0.004 0.004 0.992
#> GSM339476 1 0.6715 0.764 0.660 0.028 0.312
#> GSM339477 2 0.1015 0.958 0.012 0.980 0.008
#> GSM339478 2 0.6229 0.414 0.008 0.652 0.340
#> GSM339479 2 0.4892 0.806 0.112 0.840 0.048
#> GSM339480 3 0.1620 0.886 0.024 0.012 0.964
#> GSM339481 2 0.0592 0.958 0.012 0.988 0.000
#> GSM339482 3 0.0892 0.897 0.000 0.020 0.980
#> GSM339483 1 0.1877 0.748 0.956 0.012 0.032
#> GSM339484 1 0.6155 0.768 0.664 0.008 0.328
#> GSM339485 1 0.1751 0.746 0.960 0.012 0.028
#> GSM339486 1 0.5873 0.777 0.684 0.004 0.312
#> GSM339487 2 0.0237 0.960 0.004 0.996 0.000
#> GSM339488 2 0.0424 0.959 0.008 0.992 0.000
#> GSM339489 2 0.1267 0.953 0.004 0.972 0.024
#> GSM339490 1 0.1751 0.746 0.960 0.012 0.028
#> GSM339491 2 0.5733 0.450 0.000 0.676 0.324
#> GSM339492 1 0.5982 0.771 0.668 0.004 0.328
#> GSM339493 2 0.0237 0.960 0.004 0.996 0.000
#> GSM339494 1 0.5650 0.776 0.688 0.000 0.312
#> GSM339495 2 0.1015 0.958 0.012 0.980 0.008
#> GSM339496 3 0.0661 0.888 0.008 0.004 0.988
#> GSM339497 2 0.0424 0.958 0.000 0.992 0.008
#> GSM339498 3 0.3028 0.860 0.032 0.048 0.920
#> GSM339499 3 0.3532 0.870 0.008 0.108 0.884
#> GSM339500 2 0.0892 0.951 0.000 0.980 0.020
#> GSM339501 1 0.7141 0.679 0.600 0.032 0.368
#> GSM339502 2 0.0424 0.959 0.008 0.992 0.000
#> GSM339503 3 0.0892 0.897 0.000 0.020 0.980
#> GSM339504 1 0.1751 0.746 0.960 0.012 0.028
#> GSM339505 3 0.3896 0.861 0.008 0.128 0.864
#> GSM339506 1 0.3618 0.770 0.884 0.012 0.104
#> GSM339507 1 0.5785 0.770 0.668 0.000 0.332
#> GSM339508 2 0.1015 0.958 0.012 0.980 0.008
#> GSM339509 2 0.0424 0.959 0.008 0.992 0.000
#> GSM339510 2 0.2681 0.925 0.040 0.932 0.028
#> GSM339511 1 0.4979 0.677 0.812 0.168 0.020
#> GSM339512 2 0.0424 0.959 0.008 0.992 0.000
#> GSM339513 1 0.6396 0.767 0.664 0.016 0.320
#> GSM339514 2 0.0424 0.959 0.008 0.992 0.000
#> GSM339515 1 0.5650 0.776 0.688 0.000 0.312
#> GSM339516 2 0.0892 0.955 0.020 0.980 0.000
#> GSM339517 3 0.0892 0.897 0.000 0.020 0.980
#> GSM339518 2 0.0424 0.959 0.008 0.992 0.000
#> GSM339519 3 0.1031 0.897 0.000 0.024 0.976
#> GSM339520 3 0.3607 0.868 0.008 0.112 0.880
#> GSM339521 2 0.0237 0.960 0.004 0.996 0.000
#> GSM339522 2 0.1337 0.954 0.012 0.972 0.016
#> GSM339523 2 0.0424 0.959 0.008 0.992 0.000
#> GSM339524 1 0.7021 0.628 0.544 0.020 0.436
#> GSM339525 1 0.4411 0.776 0.844 0.016 0.140
#> GSM339526 3 0.0829 0.895 0.004 0.012 0.984
#> GSM339527 1 0.5220 0.742 0.780 0.012 0.208
#> GSM339528 1 0.5873 0.777 0.684 0.004 0.312
#> GSM339529 2 0.1015 0.958 0.012 0.980 0.008
#> GSM339530 3 0.3532 0.870 0.008 0.108 0.884
#> GSM339531 2 0.1482 0.956 0.012 0.968 0.020
#> GSM339532 1 0.4799 0.703 0.836 0.132 0.032
#> GSM339533 3 0.3682 0.867 0.008 0.116 0.876
#> GSM339534 1 0.6501 0.768 0.664 0.020 0.316
#> GSM339535 2 0.0424 0.959 0.008 0.992 0.000
#> GSM339536 1 0.5650 0.776 0.688 0.000 0.312
#> GSM339537 2 0.1015 0.958 0.012 0.980 0.008
#> GSM339538 3 0.0892 0.897 0.000 0.020 0.980
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM339455 3 0.2706 0.864 0.080 0.020 0.900 0.000
#> GSM339456 2 0.1191 0.974 0.024 0.968 0.004 0.004
#> GSM339457 3 0.1867 0.872 0.072 0.000 0.928 0.000
#> GSM339458 2 0.0592 0.970 0.000 0.984 0.016 0.000
#> GSM339459 3 0.0859 0.871 0.008 0.008 0.980 0.004
#> GSM339460 2 0.0188 0.971 0.000 0.996 0.004 0.000
#> GSM339461 2 0.1543 0.971 0.032 0.956 0.004 0.008
#> GSM339462 4 0.0000 0.914 0.000 0.000 0.000 1.000
#> GSM339463 3 0.3894 0.811 0.140 0.004 0.832 0.024
#> GSM339464 4 0.0000 0.914 0.000 0.000 0.000 1.000
#> GSM339465 3 0.5610 0.476 0.356 0.004 0.616 0.024
#> GSM339466 2 0.1396 0.973 0.032 0.960 0.004 0.004
#> GSM339467 2 0.1284 0.964 0.024 0.964 0.012 0.000
#> GSM339468 2 0.1543 0.971 0.032 0.956 0.004 0.008
#> GSM339469 4 0.0000 0.914 0.000 0.000 0.000 1.000
#> GSM339470 3 0.3598 0.792 0.028 0.124 0.848 0.000
#> GSM339471 1 0.3328 0.922 0.872 0.004 0.100 0.024
#> GSM339472 2 0.0895 0.974 0.020 0.976 0.000 0.004
#> GSM339473 1 0.1920 0.908 0.944 0.004 0.028 0.024
#> GSM339474 2 0.1211 0.954 0.000 0.960 0.000 0.040
#> GSM339475 3 0.0592 0.872 0.016 0.000 0.984 0.000
#> GSM339476 3 0.5867 0.724 0.092 0.016 0.728 0.164
#> GSM339477 2 0.1489 0.951 0.000 0.952 0.004 0.044
#> GSM339478 3 0.5288 0.665 0.068 0.200 0.732 0.000
#> GSM339479 2 0.1118 0.959 0.000 0.964 0.036 0.000
#> GSM339480 3 0.0859 0.871 0.008 0.008 0.980 0.004
#> GSM339481 2 0.0376 0.972 0.000 0.992 0.004 0.004
#> GSM339482 3 0.0000 0.870 0.000 0.000 1.000 0.000
#> GSM339483 4 0.0000 0.914 0.000 0.000 0.000 1.000
#> GSM339484 1 0.3264 0.924 0.876 0.004 0.096 0.024
#> GSM339485 4 0.0000 0.914 0.000 0.000 0.000 1.000
#> GSM339486 1 0.3067 0.928 0.888 0.004 0.084 0.024
#> GSM339487 2 0.1396 0.973 0.032 0.960 0.004 0.004
#> GSM339488 2 0.1151 0.965 0.024 0.968 0.008 0.000
#> GSM339489 2 0.1396 0.973 0.032 0.960 0.004 0.004
#> GSM339490 4 0.0000 0.914 0.000 0.000 0.000 1.000
#> GSM339491 3 0.5291 0.516 0.024 0.324 0.652 0.000
#> GSM339492 1 0.3945 0.890 0.828 0.004 0.144 0.024
#> GSM339493 2 0.1296 0.973 0.028 0.964 0.004 0.004
#> GSM339494 1 0.1920 0.908 0.944 0.004 0.028 0.024
#> GSM339495 2 0.1302 0.952 0.000 0.956 0.000 0.044
#> GSM339496 3 0.1474 0.872 0.052 0.000 0.948 0.000
#> GSM339497 2 0.1356 0.972 0.032 0.960 0.008 0.000
#> GSM339498 3 0.2673 0.841 0.008 0.080 0.904 0.008
#> GSM339499 3 0.1867 0.872 0.072 0.000 0.928 0.000
#> GSM339500 2 0.1488 0.971 0.032 0.956 0.012 0.000
#> GSM339501 3 0.4469 0.789 0.000 0.080 0.808 0.112
#> GSM339502 2 0.1284 0.964 0.024 0.964 0.012 0.000
#> GSM339503 3 0.0336 0.871 0.008 0.000 0.992 0.000
#> GSM339504 4 0.0000 0.914 0.000 0.000 0.000 1.000
#> GSM339505 3 0.2125 0.871 0.076 0.004 0.920 0.000
#> GSM339506 4 0.4817 0.256 0.000 0.000 0.388 0.612
#> GSM339507 1 0.3067 0.928 0.888 0.004 0.084 0.024
#> GSM339508 2 0.0336 0.971 0.000 0.992 0.000 0.008
#> GSM339509 2 0.1151 0.965 0.024 0.968 0.008 0.000
#> GSM339510 2 0.1943 0.967 0.032 0.944 0.008 0.016
#> GSM339511 4 0.2469 0.808 0.000 0.108 0.000 0.892
#> GSM339512 2 0.1109 0.973 0.028 0.968 0.004 0.000
#> GSM339513 1 0.5426 0.608 0.656 0.004 0.316 0.024
#> GSM339514 2 0.1284 0.964 0.024 0.964 0.012 0.000
#> GSM339515 1 0.1920 0.908 0.944 0.004 0.028 0.024
#> GSM339516 2 0.1211 0.954 0.000 0.960 0.000 0.040
#> GSM339517 3 0.0000 0.870 0.000 0.000 1.000 0.000
#> GSM339518 2 0.0336 0.971 0.000 0.992 0.008 0.000
#> GSM339519 3 0.1118 0.873 0.036 0.000 0.964 0.000
#> GSM339520 3 0.1867 0.872 0.072 0.000 0.928 0.000
#> GSM339521 2 0.1396 0.973 0.032 0.960 0.004 0.004
#> GSM339522 2 0.1396 0.972 0.032 0.960 0.004 0.004
#> GSM339523 2 0.0895 0.968 0.020 0.976 0.004 0.000
#> GSM339524 3 0.2469 0.819 0.108 0.000 0.892 0.000
#> GSM339525 4 0.0336 0.907 0.000 0.000 0.008 0.992
#> GSM339526 3 0.0592 0.872 0.016 0.000 0.984 0.000
#> GSM339527 3 0.4990 0.499 0.000 0.008 0.640 0.352
#> GSM339528 1 0.3067 0.928 0.888 0.004 0.084 0.024
#> GSM339529 2 0.0188 0.971 0.000 0.996 0.000 0.004
#> GSM339530 3 0.1867 0.872 0.072 0.000 0.928 0.000
#> GSM339531 2 0.1690 0.972 0.032 0.952 0.008 0.008
#> GSM339532 4 0.2281 0.822 0.000 0.096 0.000 0.904
#> GSM339533 3 0.3052 0.843 0.136 0.004 0.860 0.000
#> GSM339534 3 0.4489 0.748 0.192 0.004 0.780 0.024
#> GSM339535 2 0.1356 0.973 0.032 0.960 0.008 0.000
#> GSM339536 1 0.1920 0.908 0.944 0.004 0.028 0.024
#> GSM339537 2 0.2021 0.956 0.024 0.936 0.000 0.040
#> GSM339538 3 0.0000 0.870 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
#> GSM339455 3 0.3587 0.7929 0.096 0.024 0.844 0.000 NA
#> GSM339456 2 0.0771 0.8576 0.000 0.976 0.004 0.000 NA
#> GSM339457 3 0.3700 0.7231 0.008 0.000 0.752 0.000 NA
#> GSM339458 2 0.1757 0.8519 0.012 0.936 0.004 0.000 NA
#> GSM339459 3 0.3010 0.7687 0.000 0.004 0.824 0.000 NA
#> GSM339460 2 0.1121 0.8547 0.000 0.956 0.000 0.000 NA
#> GSM339461 2 0.3160 0.8273 0.000 0.808 0.004 0.000 NA
#> GSM339462 4 0.0000 0.8507 0.000 0.000 0.000 1.000 NA
#> GSM339463 3 0.3366 0.7055 0.232 0.000 0.768 0.000 NA
#> GSM339464 4 0.0000 0.8507 0.000 0.000 0.000 1.000 NA
#> GSM339465 3 0.3684 0.6554 0.280 0.000 0.720 0.000 NA
#> GSM339466 2 0.3177 0.8291 0.000 0.792 0.000 0.000 NA
#> GSM339467 2 0.4066 0.6962 0.000 0.672 0.004 0.000 NA
#> GSM339468 2 0.3596 0.8161 0.000 0.784 0.016 0.000 NA
#> GSM339469 4 0.0000 0.8507 0.000 0.000 0.000 1.000 NA
#> GSM339470 3 0.3933 0.7641 0.012 0.112 0.816 0.000 NA
#> GSM339471 1 0.2074 0.9123 0.896 0.000 0.104 0.000 NA
#> GSM339472 2 0.0794 0.8542 0.000 0.972 0.000 0.000 NA
#> GSM339473 1 0.0000 0.8828 1.000 0.000 0.000 0.000 NA
#> GSM339474 2 0.1732 0.8422 0.000 0.920 0.000 0.000 NA
#> GSM339475 3 0.1205 0.8123 0.004 0.000 0.956 0.000 NA
#> GSM339476 3 0.5086 0.6790 0.156 0.000 0.700 0.144 NA
#> GSM339477 2 0.1892 0.8418 0.000 0.916 0.000 0.004 NA
#> GSM339478 3 0.5645 0.3737 0.008 0.352 0.572 0.000 NA
#> GSM339479 2 0.3730 0.7961 0.012 0.828 0.112 0.000 NA
#> GSM339480 3 0.3242 0.7665 0.000 0.012 0.816 0.000 NA
#> GSM339481 2 0.0703 0.8545 0.000 0.976 0.000 0.000 NA
#> GSM339482 3 0.1121 0.8110 0.000 0.000 0.956 0.000 NA
#> GSM339483 4 0.0000 0.8507 0.000 0.000 0.000 1.000 NA
#> GSM339484 1 0.2377 0.8944 0.872 0.000 0.128 0.000 NA
#> GSM339485 4 0.0000 0.8507 0.000 0.000 0.000 1.000 NA
#> GSM339486 1 0.1908 0.9161 0.908 0.000 0.092 0.000 NA
#> GSM339487 2 0.3074 0.8278 0.000 0.804 0.000 0.000 NA
#> GSM339488 2 0.4066 0.6962 0.000 0.672 0.004 0.000 NA
#> GSM339489 2 0.3039 0.8273 0.000 0.808 0.000 0.000 NA
#> GSM339490 4 0.0000 0.8507 0.000 0.000 0.000 1.000 NA
#> GSM339491 3 0.5664 0.3288 0.012 0.384 0.548 0.000 NA
#> GSM339492 1 0.2471 0.8922 0.864 0.000 0.136 0.000 NA
#> GSM339493 2 0.2561 0.8410 0.000 0.856 0.000 0.000 NA
#> GSM339494 1 0.0000 0.8828 1.000 0.000 0.000 0.000 NA
#> GSM339495 2 0.1732 0.8422 0.000 0.920 0.000 0.000 NA
#> GSM339496 3 0.1300 0.8115 0.028 0.000 0.956 0.000 NA
#> GSM339497 2 0.3196 0.8368 0.004 0.804 0.000 0.000 NA
#> GSM339498 3 0.4143 0.7740 0.000 0.084 0.804 0.012 NA
#> GSM339499 3 0.3728 0.7218 0.008 0.000 0.748 0.000 NA
#> GSM339500 2 0.4822 0.7905 0.008 0.728 0.072 0.000 NA
#> GSM339501 3 0.4801 0.7394 0.000 0.092 0.768 0.108 NA
#> GSM339502 2 0.4047 0.6975 0.000 0.676 0.004 0.000 NA
#> GSM339503 3 0.0290 0.8119 0.000 0.000 0.992 0.000 NA
#> GSM339504 4 0.0000 0.8507 0.000 0.000 0.000 1.000 NA
#> GSM339505 3 0.3165 0.7940 0.036 0.000 0.848 0.000 NA
#> GSM339506 4 0.4622 0.1312 0.000 0.000 0.440 0.548 NA
#> GSM339507 1 0.2074 0.9126 0.896 0.000 0.104 0.000 NA
#> GSM339508 2 0.1121 0.8524 0.000 0.956 0.000 0.000 NA
#> GSM339509 2 0.4066 0.6962 0.000 0.672 0.004 0.000 NA
#> GSM339510 2 0.3596 0.8190 0.000 0.784 0.000 0.016 NA
#> GSM339511 4 0.2329 0.7608 0.000 0.124 0.000 0.876 NA
#> GSM339512 2 0.1502 0.8563 0.004 0.940 0.000 0.000 NA
#> GSM339513 1 0.3336 0.7522 0.772 0.000 0.228 0.000 NA
#> GSM339514 2 0.4066 0.6962 0.000 0.672 0.004 0.000 NA
#> GSM339515 1 0.0000 0.8828 1.000 0.000 0.000 0.000 NA
#> GSM339516 2 0.1341 0.8486 0.000 0.944 0.000 0.000 NA
#> GSM339517 3 0.1121 0.8110 0.000 0.000 0.956 0.000 NA
#> GSM339518 2 0.1205 0.8548 0.004 0.956 0.000 0.000 NA
#> GSM339519 3 0.0451 0.8126 0.000 0.004 0.988 0.000 NA
#> GSM339520 3 0.3728 0.7218 0.008 0.000 0.748 0.000 NA
#> GSM339521 2 0.3074 0.8278 0.000 0.804 0.000 0.000 NA
#> GSM339522 2 0.3266 0.8242 0.000 0.796 0.004 0.000 NA
#> GSM339523 2 0.3521 0.7675 0.004 0.764 0.000 0.000 NA
#> GSM339524 3 0.2719 0.7647 0.144 0.000 0.852 0.000 NA
#> GSM339525 4 0.1671 0.7881 0.000 0.000 0.076 0.924 NA
#> GSM339526 3 0.1205 0.8123 0.004 0.000 0.956 0.000 NA
#> GSM339527 4 0.4656 -0.0169 0.000 0.000 0.480 0.508 NA
#> GSM339528 1 0.1908 0.9161 0.908 0.000 0.092 0.000 NA
#> GSM339529 2 0.0880 0.8539 0.000 0.968 0.000 0.000 NA
#> GSM339530 3 0.3635 0.7212 0.004 0.000 0.748 0.000 NA
#> GSM339531 2 0.3074 0.8240 0.000 0.804 0.000 0.000 NA
#> GSM339532 4 0.2127 0.7733 0.000 0.108 0.000 0.892 NA
#> GSM339533 3 0.2597 0.7978 0.092 0.000 0.884 0.000 NA
#> GSM339534 3 0.3636 0.6593 0.272 0.000 0.728 0.000 NA
#> GSM339535 2 0.2890 0.8502 0.000 0.836 0.004 0.000 NA
#> GSM339536 1 0.0000 0.8828 1.000 0.000 0.000 0.000 NA
#> GSM339537 2 0.1671 0.8432 0.000 0.924 0.000 0.000 NA
#> GSM339538 3 0.1121 0.8110 0.000 0.000 0.956 0.000 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM339455 3 0.5531 0.630 0.104 0.028 0.680 0.000 0.028 0.160
#> GSM339456 2 0.2981 0.792 0.000 0.820 0.000 0.000 0.160 0.020
#> GSM339457 6 0.2664 1.000 0.000 0.000 0.184 0.000 0.000 0.816
#> GSM339458 2 0.3672 0.736 0.004 0.744 0.012 0.000 0.236 0.004
#> GSM339459 3 0.4117 0.635 0.000 0.012 0.760 0.000 0.160 0.068
#> GSM339460 2 0.3161 0.762 0.000 0.776 0.000 0.000 0.216 0.008
#> GSM339461 2 0.1982 0.766 0.000 0.924 0.004 0.012 0.040 0.020
#> GSM339462 4 0.0000 0.908 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM339463 3 0.4263 0.540 0.376 0.000 0.600 0.000 0.000 0.024
#> GSM339464 4 0.0000 0.908 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM339465 3 0.3923 0.493 0.416 0.000 0.580 0.000 0.000 0.004
#> GSM339466 2 0.1753 0.781 0.000 0.912 0.000 0.000 0.084 0.004
#> GSM339467 5 0.3240 0.968 0.000 0.244 0.000 0.000 0.752 0.004
#> GSM339468 2 0.3103 0.680 0.000 0.864 0.024 0.016 0.076 0.020
#> GSM339469 4 0.0000 0.908 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM339470 3 0.6500 0.547 0.044 0.080 0.608 0.000 0.088 0.180
#> GSM339471 1 0.1462 0.931 0.936 0.000 0.056 0.000 0.000 0.008
#> GSM339472 2 0.2513 0.802 0.000 0.852 0.000 0.000 0.140 0.008
#> GSM339473 1 0.1007 0.917 0.956 0.000 0.000 0.000 0.000 0.044
#> GSM339474 2 0.3351 0.769 0.000 0.800 0.000 0.000 0.160 0.040
#> GSM339475 3 0.1745 0.668 0.000 0.000 0.924 0.000 0.020 0.056
#> GSM339476 3 0.5418 0.573 0.252 0.000 0.616 0.116 0.012 0.004
#> GSM339477 2 0.3562 0.765 0.000 0.788 0.004 0.000 0.168 0.040
#> GSM339478 3 0.5316 0.422 0.000 0.092 0.580 0.000 0.012 0.316
#> GSM339479 2 0.3887 0.743 0.012 0.744 0.016 0.000 0.224 0.004
#> GSM339480 3 0.4117 0.635 0.000 0.012 0.760 0.000 0.160 0.068
#> GSM339481 2 0.2320 0.803 0.000 0.864 0.000 0.000 0.132 0.004
#> GSM339482 3 0.0547 0.676 0.000 0.000 0.980 0.000 0.020 0.000
#> GSM339483 4 0.0000 0.908 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM339484 1 0.1584 0.924 0.928 0.000 0.064 0.000 0.000 0.008
#> GSM339485 4 0.0000 0.908 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM339486 1 0.1219 0.934 0.948 0.000 0.048 0.000 0.000 0.004
#> GSM339487 2 0.1866 0.780 0.000 0.908 0.000 0.000 0.084 0.008
#> GSM339488 5 0.3240 0.968 0.000 0.244 0.000 0.000 0.752 0.004
#> GSM339489 2 0.0922 0.796 0.000 0.968 0.004 0.000 0.024 0.004
#> GSM339490 4 0.0000 0.908 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM339491 3 0.6904 0.476 0.036 0.140 0.564 0.000 0.092 0.168
#> GSM339492 1 0.2020 0.906 0.896 0.000 0.096 0.000 0.000 0.008
#> GSM339493 2 0.1141 0.808 0.000 0.948 0.000 0.000 0.052 0.000
#> GSM339494 1 0.1007 0.917 0.956 0.000 0.000 0.000 0.000 0.044
#> GSM339495 2 0.3351 0.769 0.000 0.800 0.000 0.000 0.160 0.040
#> GSM339496 3 0.3713 0.609 0.032 0.000 0.744 0.000 0.000 0.224
#> GSM339497 2 0.2278 0.771 0.000 0.868 0.000 0.000 0.128 0.004
#> GSM339498 3 0.5465 0.604 0.000 0.092 0.684 0.028 0.168 0.028
#> GSM339499 6 0.2664 1.000 0.000 0.000 0.184 0.000 0.000 0.816
#> GSM339500 2 0.2420 0.765 0.004 0.864 0.000 0.000 0.128 0.004
#> GSM339501 3 0.5985 0.588 0.000 0.108 0.648 0.068 0.156 0.020
#> GSM339502 5 0.3290 0.962 0.000 0.252 0.000 0.000 0.744 0.004
#> GSM339503 3 0.0146 0.683 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM339504 4 0.0000 0.908 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM339505 3 0.5511 0.229 0.060 0.000 0.516 0.000 0.032 0.392
#> GSM339506 4 0.4534 -0.243 0.000 0.000 0.476 0.492 0.000 0.032
#> GSM339507 1 0.1049 0.934 0.960 0.000 0.032 0.000 0.000 0.008
#> GSM339508 2 0.2768 0.793 0.000 0.832 0.000 0.000 0.156 0.012
#> GSM339509 5 0.3240 0.968 0.000 0.244 0.000 0.000 0.752 0.004
#> GSM339510 2 0.2725 0.719 0.000 0.884 0.004 0.032 0.060 0.020
#> GSM339511 4 0.2146 0.774 0.000 0.116 0.004 0.880 0.000 0.000
#> GSM339512 2 0.3240 0.733 0.000 0.752 0.000 0.000 0.244 0.004
#> GSM339513 1 0.2191 0.876 0.876 0.000 0.120 0.000 0.000 0.004
#> GSM339514 5 0.3240 0.968 0.000 0.244 0.000 0.000 0.752 0.004
#> GSM339515 1 0.1007 0.917 0.956 0.000 0.000 0.000 0.000 0.044
#> GSM339516 2 0.2982 0.790 0.000 0.820 0.004 0.000 0.164 0.012
#> GSM339517 3 0.0692 0.676 0.000 0.000 0.976 0.000 0.020 0.004
#> GSM339518 2 0.3163 0.747 0.000 0.764 0.000 0.000 0.232 0.004
#> GSM339519 3 0.0820 0.687 0.012 0.000 0.972 0.000 0.000 0.016
#> GSM339520 6 0.2664 1.000 0.000 0.000 0.184 0.000 0.000 0.816
#> GSM339521 2 0.1918 0.779 0.000 0.904 0.000 0.000 0.088 0.008
#> GSM339522 2 0.0976 0.787 0.000 0.968 0.016 0.000 0.008 0.008
#> GSM339523 5 0.3531 0.834 0.000 0.328 0.000 0.000 0.672 0.000
#> GSM339524 3 0.1714 0.686 0.092 0.000 0.908 0.000 0.000 0.000
#> GSM339525 4 0.0146 0.904 0.000 0.000 0.004 0.996 0.000 0.000
#> GSM339526 3 0.1682 0.668 0.000 0.000 0.928 0.000 0.020 0.052
#> GSM339527 3 0.4535 0.172 0.000 0.000 0.488 0.480 0.000 0.032
#> GSM339528 1 0.1219 0.934 0.948 0.000 0.048 0.000 0.000 0.004
#> GSM339529 2 0.2653 0.799 0.000 0.844 0.000 0.000 0.144 0.012
#> GSM339530 6 0.2664 1.000 0.000 0.000 0.184 0.000 0.000 0.816
#> GSM339531 2 0.1592 0.770 0.000 0.944 0.004 0.012 0.024 0.016
#> GSM339532 4 0.0632 0.886 0.000 0.024 0.000 0.976 0.000 0.000
#> GSM339533 3 0.5113 0.602 0.164 0.000 0.644 0.000 0.004 0.188
#> GSM339534 3 0.4138 0.548 0.364 0.000 0.620 0.000 0.008 0.008
#> GSM339535 2 0.3323 0.710 0.000 0.752 0.000 0.000 0.240 0.008
#> GSM339536 1 0.1007 0.917 0.956 0.000 0.000 0.000 0.000 0.044
#> GSM339537 2 0.3098 0.782 0.000 0.812 0.000 0.000 0.164 0.024
#> GSM339538 3 0.0692 0.676 0.000 0.000 0.976 0.000 0.020 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 protocol(p) agent(p) individual(p) k
#> SD:mclust 59 0.891 0.864 3.57e-03 2
#> SD:mclust 82 0.982 0.784 1.10e-04 3
#> SD:mclust 81 0.889 0.956 4.96e-08 4
#> SD:mclust 80 0.837 0.873 3.48e-07 5
#> SD:mclust 78 0.798 0.941 9.61e-10 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 15497 rows and 84 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 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 0.702 0.835 0.933 0.503 0.499 0.499
#> 3 3 0.640 0.748 0.869 0.324 0.768 0.563
#> 4 4 0.693 0.726 0.860 0.117 0.825 0.541
#> 5 5 0.605 0.472 0.693 0.061 0.847 0.507
#> 6 6 0.653 0.574 0.741 0.041 0.913 0.640
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
#> GSM339455 1 0.000 0.8984 1.000 0.000
#> GSM339456 2 0.000 0.9508 0.000 1.000
#> GSM339457 1 0.886 0.5616 0.696 0.304
#> GSM339458 2 0.000 0.9508 0.000 1.000
#> GSM339459 2 0.981 0.2291 0.420 0.580
#> GSM339460 2 0.000 0.9508 0.000 1.000
#> GSM339461 2 0.000 0.9508 0.000 1.000
#> GSM339462 1 0.000 0.8984 1.000 0.000
#> GSM339463 1 0.000 0.8984 1.000 0.000
#> GSM339464 1 0.722 0.7239 0.800 0.200
#> GSM339465 1 0.000 0.8984 1.000 0.000
#> GSM339466 2 0.000 0.9508 0.000 1.000
#> GSM339467 2 0.000 0.9508 0.000 1.000
#> GSM339468 2 0.000 0.9508 0.000 1.000
#> GSM339469 1 0.625 0.7713 0.844 0.156
#> GSM339470 1 0.760 0.6897 0.780 0.220
#> GSM339471 1 0.000 0.8984 1.000 0.000
#> GSM339472 2 0.000 0.9508 0.000 1.000
#> GSM339473 1 0.000 0.8984 1.000 0.000
#> GSM339474 2 0.000 0.9508 0.000 1.000
#> GSM339475 1 0.000 0.8984 1.000 0.000
#> GSM339476 1 0.000 0.8984 1.000 0.000
#> GSM339477 2 0.000 0.9508 0.000 1.000
#> GSM339478 2 0.802 0.6469 0.244 0.756
#> GSM339479 2 0.821 0.6149 0.256 0.744
#> GSM339480 1 0.929 0.4865 0.656 0.344
#> GSM339481 2 0.000 0.9508 0.000 1.000
#> GSM339482 1 0.000 0.8984 1.000 0.000
#> GSM339483 1 0.000 0.8984 1.000 0.000
#> GSM339484 1 0.000 0.8984 1.000 0.000
#> GSM339485 1 0.722 0.7240 0.800 0.200
#> GSM339486 1 0.000 0.8984 1.000 0.000
#> GSM339487 2 0.000 0.9508 0.000 1.000
#> GSM339488 2 0.000 0.9508 0.000 1.000
#> GSM339489 2 0.000 0.9508 0.000 1.000
#> GSM339490 1 0.714 0.7285 0.804 0.196
#> GSM339491 1 0.969 0.3690 0.604 0.396
#> GSM339492 1 0.000 0.8984 1.000 0.000
#> GSM339493 2 0.000 0.9508 0.000 1.000
#> GSM339494 1 0.000 0.8984 1.000 0.000
#> GSM339495 2 0.000 0.9508 0.000 1.000
#> GSM339496 1 0.000 0.8984 1.000 0.000
#> GSM339497 2 0.000 0.9508 0.000 1.000
#> GSM339498 2 0.714 0.7254 0.196 0.804
#> GSM339499 1 0.978 0.3255 0.588 0.412
#> GSM339500 2 0.373 0.8814 0.072 0.928
#> GSM339501 1 0.000 0.8984 1.000 0.000
#> GSM339502 2 0.000 0.9508 0.000 1.000
#> GSM339503 1 0.000 0.8984 1.000 0.000
#> GSM339504 1 0.000 0.8984 1.000 0.000
#> GSM339505 1 0.943 0.4529 0.640 0.360
#> GSM339506 1 0.000 0.8984 1.000 0.000
#> GSM339507 1 0.000 0.8984 1.000 0.000
#> GSM339508 2 0.000 0.9508 0.000 1.000
#> GSM339509 2 0.000 0.9508 0.000 1.000
#> GSM339510 2 0.000 0.9508 0.000 1.000
#> GSM339511 1 0.978 0.3420 0.588 0.412
#> GSM339512 2 0.000 0.9508 0.000 1.000
#> GSM339513 1 0.000 0.8984 1.000 0.000
#> GSM339514 2 0.000 0.9508 0.000 1.000
#> GSM339515 1 0.000 0.8984 1.000 0.000
#> GSM339516 2 0.000 0.9508 0.000 1.000
#> GSM339517 1 0.000 0.8984 1.000 0.000
#> GSM339518 2 0.000 0.9508 0.000 1.000
#> GSM339519 1 0.000 0.8984 1.000 0.000
#> GSM339520 2 0.966 0.3136 0.392 0.608
#> GSM339521 2 0.000 0.9508 0.000 1.000
#> GSM339522 2 0.000 0.9508 0.000 1.000
#> GSM339523 2 0.000 0.9508 0.000 1.000
#> GSM339524 1 0.000 0.8984 1.000 0.000
#> GSM339525 1 0.000 0.8984 1.000 0.000
#> GSM339526 1 0.000 0.8984 1.000 0.000
#> GSM339527 1 0.000 0.8984 1.000 0.000
#> GSM339528 1 0.000 0.8984 1.000 0.000
#> GSM339529 2 0.000 0.9508 0.000 1.000
#> GSM339530 1 0.999 0.0917 0.516 0.484
#> GSM339531 2 0.000 0.9508 0.000 1.000
#> GSM339532 1 0.971 0.3707 0.600 0.400
#> GSM339533 1 0.000 0.8984 1.000 0.000
#> GSM339534 1 0.000 0.8984 1.000 0.000
#> GSM339535 2 0.000 0.9508 0.000 1.000
#> GSM339536 1 0.000 0.8984 1.000 0.000
#> GSM339537 2 0.000 0.9508 0.000 1.000
#> GSM339538 1 0.000 0.8984 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM339455 3 0.4002 0.625 0.160 0.000 0.840
#> GSM339456 2 0.4346 0.822 0.184 0.816 0.000
#> GSM339457 3 0.2959 0.774 0.000 0.100 0.900
#> GSM339458 2 0.2229 0.914 0.044 0.944 0.012
#> GSM339459 3 0.6054 0.662 0.180 0.052 0.768
#> GSM339460 2 0.2200 0.914 0.056 0.940 0.004
#> GSM339461 2 0.5058 0.784 0.244 0.756 0.000
#> GSM339462 1 0.1643 0.762 0.956 0.000 0.044
#> GSM339463 3 0.0592 0.801 0.012 0.000 0.988
#> GSM339464 1 0.0424 0.760 0.992 0.008 0.000
#> GSM339465 3 0.0237 0.804 0.004 0.000 0.996
#> GSM339466 2 0.0000 0.920 0.000 1.000 0.000
#> GSM339467 2 0.0424 0.918 0.000 0.992 0.008
#> GSM339468 2 0.5497 0.736 0.292 0.708 0.000
#> GSM339469 1 0.0237 0.762 0.996 0.004 0.000
#> GSM339470 3 0.1529 0.800 0.000 0.040 0.960
#> GSM339471 1 0.6026 0.622 0.624 0.000 0.376
#> GSM339472 2 0.0592 0.920 0.012 0.988 0.000
#> GSM339473 1 0.5760 0.668 0.672 0.000 0.328
#> GSM339474 2 0.2066 0.913 0.060 0.940 0.000
#> GSM339475 3 0.0237 0.805 0.004 0.000 0.996
#> GSM339476 1 0.5560 0.681 0.700 0.000 0.300
#> GSM339477 2 0.5016 0.797 0.240 0.760 0.000
#> GSM339478 3 0.5810 0.524 0.000 0.336 0.664
#> GSM339479 1 0.5956 0.554 0.720 0.264 0.016
#> GSM339480 3 0.5384 0.668 0.188 0.024 0.788
#> GSM339481 2 0.0000 0.920 0.000 1.000 0.000
#> GSM339482 3 0.0592 0.805 0.012 0.000 0.988
#> GSM339483 1 0.0237 0.762 0.996 0.004 0.000
#> GSM339484 3 0.6309 -0.386 0.496 0.000 0.504
#> GSM339485 1 0.0237 0.762 0.996 0.004 0.000
#> GSM339486 3 0.6299 -0.337 0.476 0.000 0.524
#> GSM339487 2 0.0424 0.920 0.008 0.992 0.000
#> GSM339488 2 0.0592 0.917 0.000 0.988 0.012
#> GSM339489 2 0.4063 0.884 0.112 0.868 0.020
#> GSM339490 1 0.0237 0.762 0.996 0.004 0.000
#> GSM339491 3 0.2796 0.779 0.000 0.092 0.908
#> GSM339492 1 0.6180 0.557 0.584 0.000 0.416
#> GSM339493 2 0.0000 0.920 0.000 1.000 0.000
#> GSM339494 1 0.5733 0.669 0.676 0.000 0.324
#> GSM339495 2 0.2356 0.909 0.072 0.928 0.000
#> GSM339496 3 0.0000 0.805 0.000 0.000 1.000
#> GSM339497 2 0.1315 0.920 0.020 0.972 0.008
#> GSM339498 3 0.6537 0.634 0.196 0.064 0.740
#> GSM339499 3 0.3619 0.749 0.000 0.136 0.864
#> GSM339500 2 0.1529 0.901 0.000 0.960 0.040
#> GSM339501 1 0.1163 0.764 0.972 0.000 0.028
#> GSM339502 2 0.0424 0.918 0.000 0.992 0.008
#> GSM339503 3 0.1031 0.802 0.024 0.000 0.976
#> GSM339504 1 0.0424 0.764 0.992 0.000 0.008
#> GSM339505 3 0.1163 0.803 0.000 0.028 0.972
#> GSM339506 1 0.0237 0.763 0.996 0.000 0.004
#> GSM339507 1 0.6280 0.468 0.540 0.000 0.460
#> GSM339508 2 0.1860 0.915 0.052 0.948 0.000
#> GSM339509 2 0.0424 0.918 0.000 0.992 0.008
#> GSM339510 2 0.5968 0.649 0.364 0.636 0.000
#> GSM339511 1 0.0424 0.760 0.992 0.008 0.000
#> GSM339512 2 0.0424 0.918 0.000 0.992 0.008
#> GSM339513 1 0.6192 0.541 0.580 0.000 0.420
#> GSM339514 2 0.0424 0.918 0.000 0.992 0.008
#> GSM339515 1 0.5785 0.664 0.668 0.000 0.332
#> GSM339516 2 0.4399 0.837 0.188 0.812 0.000
#> GSM339517 3 0.0592 0.805 0.012 0.000 0.988
#> GSM339518 2 0.1015 0.920 0.012 0.980 0.008
#> GSM339519 3 0.0592 0.805 0.012 0.000 0.988
#> GSM339520 3 0.5497 0.602 0.000 0.292 0.708
#> GSM339521 2 0.0000 0.920 0.000 1.000 0.000
#> GSM339522 2 0.4178 0.852 0.172 0.828 0.000
#> GSM339523 2 0.0237 0.919 0.000 0.996 0.004
#> GSM339524 3 0.5948 0.165 0.360 0.000 0.640
#> GSM339525 1 0.3619 0.742 0.864 0.000 0.136
#> GSM339526 3 0.0424 0.804 0.008 0.000 0.992
#> GSM339527 1 0.0892 0.764 0.980 0.000 0.020
#> GSM339528 1 0.6062 0.608 0.616 0.000 0.384
#> GSM339529 2 0.2165 0.911 0.064 0.936 0.000
#> GSM339530 3 0.4555 0.695 0.000 0.200 0.800
#> GSM339531 2 0.4887 0.797 0.228 0.772 0.000
#> GSM339532 1 0.0424 0.760 0.992 0.008 0.000
#> GSM339533 3 0.0000 0.805 0.000 0.000 1.000
#> GSM339534 1 0.6154 0.576 0.592 0.000 0.408
#> GSM339535 2 0.0592 0.917 0.000 0.988 0.012
#> GSM339536 1 0.5785 0.664 0.668 0.000 0.332
#> GSM339537 2 0.3879 0.865 0.152 0.848 0.000
#> GSM339538 3 0.0592 0.805 0.012 0.000 0.988
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM339455 3 0.4817 0.30703 0.388 0.000 0.612 0.000
#> GSM339456 2 0.5245 0.46902 0.004 0.660 0.016 0.320
#> GSM339457 3 0.1042 0.86984 0.020 0.008 0.972 0.000
#> GSM339458 2 0.2644 0.82789 0.060 0.908 0.000 0.032
#> GSM339459 3 0.2737 0.83000 0.000 0.008 0.888 0.104
#> GSM339460 2 0.1629 0.85989 0.024 0.952 0.000 0.024
#> GSM339461 2 0.5857 -0.00609 0.004 0.508 0.024 0.464
#> GSM339462 1 0.3024 0.75745 0.852 0.000 0.000 0.148
#> GSM339463 1 0.3271 0.79993 0.856 0.000 0.132 0.012
#> GSM339464 4 0.4164 0.53675 0.264 0.000 0.000 0.736
#> GSM339465 1 0.3508 0.79375 0.848 0.004 0.136 0.012
#> GSM339466 2 0.0895 0.87567 0.004 0.976 0.000 0.020
#> GSM339467 2 0.0000 0.87757 0.000 1.000 0.000 0.000
#> GSM339468 4 0.3366 0.70920 0.004 0.028 0.096 0.872
#> GSM339469 1 0.4164 0.63369 0.736 0.000 0.000 0.264
#> GSM339470 3 0.7092 0.54472 0.216 0.164 0.608 0.012
#> GSM339471 1 0.2654 0.83032 0.888 0.000 0.108 0.004
#> GSM339472 2 0.0336 0.87760 0.000 0.992 0.000 0.008
#> GSM339473 1 0.0927 0.83806 0.976 0.000 0.016 0.008
#> GSM339474 2 0.1022 0.87139 0.000 0.968 0.000 0.032
#> GSM339475 3 0.0657 0.87160 0.012 0.000 0.984 0.004
#> GSM339476 1 0.4907 0.73987 0.764 0.000 0.176 0.060
#> GSM339477 4 0.4843 0.33043 0.000 0.396 0.000 0.604
#> GSM339478 2 0.5653 0.16168 0.016 0.532 0.448 0.004
#> GSM339479 1 0.4375 0.66768 0.788 0.180 0.000 0.032
#> GSM339480 3 0.3074 0.80096 0.000 0.000 0.848 0.152
#> GSM339481 2 0.0188 0.87778 0.000 0.996 0.000 0.004
#> GSM339482 3 0.0817 0.87062 0.000 0.000 0.976 0.024
#> GSM339483 1 0.2149 0.80404 0.912 0.000 0.000 0.088
#> GSM339484 1 0.2730 0.82587 0.896 0.000 0.088 0.016
#> GSM339485 4 0.3024 0.68045 0.148 0.000 0.000 0.852
#> GSM339486 1 0.2473 0.83003 0.908 0.000 0.080 0.012
#> GSM339487 2 0.1716 0.84945 0.000 0.936 0.000 0.064
#> GSM339488 2 0.0188 0.87663 0.000 0.996 0.000 0.004
#> GSM339489 2 0.5472 0.07472 0.000 0.544 0.016 0.440
#> GSM339490 4 0.5000 -0.13517 0.500 0.000 0.000 0.500
#> GSM339491 2 0.6785 0.48361 0.208 0.640 0.140 0.012
#> GSM339492 1 0.3945 0.75281 0.780 0.000 0.216 0.004
#> GSM339493 2 0.0592 0.87627 0.000 0.984 0.000 0.016
#> GSM339494 1 0.1059 0.83719 0.972 0.000 0.016 0.012
#> GSM339495 2 0.3486 0.71152 0.000 0.812 0.000 0.188
#> GSM339496 3 0.0779 0.87114 0.016 0.000 0.980 0.004
#> GSM339497 2 0.1624 0.86930 0.020 0.952 0.000 0.028
#> GSM339498 3 0.4434 0.70419 0.004 0.016 0.772 0.208
#> GSM339499 3 0.1297 0.86824 0.020 0.016 0.964 0.000
#> GSM339500 2 0.3927 0.78346 0.060 0.856 0.072 0.012
#> GSM339501 4 0.2546 0.71520 0.008 0.000 0.092 0.900
#> GSM339502 2 0.0336 0.87510 0.000 0.992 0.000 0.008
#> GSM339503 3 0.2101 0.85851 0.012 0.000 0.928 0.060
#> GSM339504 1 0.4746 0.41594 0.632 0.000 0.000 0.368
#> GSM339505 3 0.2334 0.83685 0.088 0.004 0.908 0.000
#> GSM339506 4 0.2053 0.72275 0.072 0.000 0.004 0.924
#> GSM339507 1 0.2222 0.83414 0.924 0.000 0.060 0.016
#> GSM339508 2 0.0707 0.87568 0.000 0.980 0.000 0.020
#> GSM339509 2 0.0000 0.87757 0.000 1.000 0.000 0.000
#> GSM339510 4 0.2189 0.74275 0.004 0.044 0.020 0.932
#> GSM339511 4 0.3610 0.64012 0.200 0.000 0.000 0.800
#> GSM339512 2 0.0188 0.87725 0.004 0.996 0.000 0.000
#> GSM339513 1 0.2480 0.83553 0.904 0.000 0.088 0.008
#> GSM339514 2 0.0000 0.87757 0.000 1.000 0.000 0.000
#> GSM339515 1 0.1042 0.83850 0.972 0.000 0.020 0.008
#> GSM339516 4 0.4746 0.42901 0.000 0.368 0.000 0.632
#> GSM339517 3 0.1389 0.86548 0.000 0.000 0.952 0.048
#> GSM339518 2 0.0895 0.87602 0.004 0.976 0.000 0.020
#> GSM339519 3 0.1677 0.86662 0.012 0.000 0.948 0.040
#> GSM339520 3 0.1610 0.86316 0.016 0.032 0.952 0.000
#> GSM339521 2 0.0804 0.87755 0.008 0.980 0.000 0.012
#> GSM339522 4 0.5173 0.70472 0.004 0.132 0.096 0.768
#> GSM339523 2 0.0000 0.87757 0.000 1.000 0.000 0.000
#> GSM339524 3 0.2483 0.85958 0.032 0.000 0.916 0.052
#> GSM339525 1 0.2053 0.81582 0.924 0.000 0.004 0.072
#> GSM339526 3 0.0592 0.87143 0.016 0.000 0.984 0.000
#> GSM339527 4 0.1798 0.73029 0.040 0.000 0.016 0.944
#> GSM339528 1 0.2101 0.83548 0.928 0.000 0.060 0.012
#> GSM339529 2 0.0817 0.87460 0.000 0.976 0.000 0.024
#> GSM339530 3 0.3130 0.83205 0.024 0.072 0.892 0.012
#> GSM339531 4 0.4388 0.71523 0.004 0.124 0.056 0.816
#> GSM339532 1 0.4992 0.12116 0.524 0.000 0.000 0.476
#> GSM339533 3 0.5363 0.42311 0.372 0.004 0.612 0.012
#> GSM339534 1 0.3852 0.78483 0.808 0.000 0.180 0.012
#> GSM339535 2 0.0336 0.87760 0.000 0.992 0.000 0.008
#> GSM339536 1 0.1151 0.83902 0.968 0.000 0.024 0.008
#> GSM339537 4 0.4843 0.36468 0.000 0.396 0.000 0.604
#> GSM339538 3 0.1488 0.87027 0.012 0.000 0.956 0.032
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM339455 3 0.7054 -0.01437 0.032 0.000 0.416 0.160 0.392
#> GSM339456 2 0.5571 0.45215 0.000 0.620 0.028 0.044 0.308
#> GSM339457 3 0.3132 0.66208 0.000 0.000 0.820 0.008 0.172
#> GSM339458 5 0.7382 0.08387 0.020 0.156 0.024 0.368 0.432
#> GSM339459 3 0.3387 0.63570 0.004 0.004 0.796 0.000 0.196
#> GSM339460 4 0.6632 -0.12821 0.000 0.228 0.000 0.428 0.344
#> GSM339461 2 0.7431 0.09099 0.000 0.380 0.032 0.272 0.316
#> GSM339462 1 0.5322 0.36731 0.660 0.000 0.000 0.228 0.112
#> GSM339463 5 0.7102 -0.13388 0.328 0.000 0.208 0.024 0.440
#> GSM339464 4 0.3862 0.46478 0.088 0.000 0.000 0.808 0.104
#> GSM339465 1 0.5513 0.29729 0.524 0.000 0.068 0.000 0.408
#> GSM339466 2 0.2447 0.78960 0.000 0.912 0.024 0.032 0.032
#> GSM339467 2 0.0798 0.80514 0.000 0.976 0.000 0.008 0.016
#> GSM339468 5 0.7043 0.02923 0.000 0.032 0.284 0.192 0.492
#> GSM339469 4 0.4789 0.32058 0.392 0.000 0.000 0.584 0.024
#> GSM339470 5 0.8497 0.13023 0.212 0.196 0.276 0.000 0.316
#> GSM339471 1 0.5782 0.51100 0.704 0.000 0.084 0.100 0.112
#> GSM339472 2 0.0000 0.80598 0.000 1.000 0.000 0.000 0.000
#> GSM339473 1 0.0324 0.65504 0.992 0.000 0.004 0.000 0.004
#> GSM339474 2 0.1725 0.79552 0.000 0.936 0.000 0.044 0.020
#> GSM339475 3 0.0324 0.73565 0.004 0.000 0.992 0.000 0.004
#> GSM339476 1 0.6600 0.09362 0.544 0.000 0.100 0.312 0.044
#> GSM339477 2 0.5322 0.58279 0.000 0.660 0.000 0.228 0.112
#> GSM339478 3 0.6296 0.36504 0.000 0.204 0.584 0.012 0.200
#> GSM339479 5 0.7330 0.01015 0.116 0.032 0.024 0.408 0.420
#> GSM339480 3 0.4060 0.58777 0.004 0.004 0.748 0.012 0.232
#> GSM339481 2 0.0000 0.80598 0.000 1.000 0.000 0.000 0.000
#> GSM339482 3 0.1408 0.73328 0.008 0.000 0.948 0.000 0.044
#> GSM339483 1 0.2685 0.59986 0.880 0.000 0.000 0.092 0.028
#> GSM339484 1 0.2519 0.64508 0.884 0.000 0.016 0.000 0.100
#> GSM339485 4 0.4069 0.46519 0.096 0.000 0.000 0.792 0.112
#> GSM339486 1 0.5324 0.33591 0.536 0.000 0.036 0.008 0.420
#> GSM339487 2 0.2012 0.79222 0.000 0.920 0.000 0.060 0.020
#> GSM339488 2 0.0833 0.80507 0.004 0.976 0.000 0.004 0.016
#> GSM339489 2 0.5123 0.50786 0.004 0.600 0.008 0.364 0.024
#> GSM339490 4 0.4505 0.35254 0.384 0.000 0.000 0.604 0.012
#> GSM339491 2 0.6497 0.25571 0.272 0.540 0.012 0.000 0.176
#> GSM339492 3 0.8216 -0.17168 0.332 0.000 0.340 0.140 0.188
#> GSM339493 2 0.0671 0.80409 0.000 0.980 0.000 0.004 0.016
#> GSM339494 1 0.0960 0.65170 0.972 0.000 0.004 0.008 0.016
#> GSM339495 2 0.3151 0.73965 0.000 0.836 0.000 0.144 0.020
#> GSM339496 3 0.0566 0.73590 0.004 0.000 0.984 0.000 0.012
#> GSM339497 5 0.7236 0.10300 0.004 0.308 0.016 0.256 0.416
#> GSM339498 3 0.4735 0.46799 0.000 0.012 0.668 0.020 0.300
#> GSM339499 3 0.3461 0.61080 0.000 0.000 0.772 0.004 0.224
#> GSM339500 5 0.8353 0.22389 0.016 0.108 0.240 0.216 0.420
#> GSM339501 4 0.6008 0.19291 0.012 0.008 0.276 0.612 0.092
#> GSM339502 2 0.0955 0.80240 0.000 0.968 0.000 0.004 0.028
#> GSM339503 3 0.2513 0.70503 0.008 0.000 0.876 0.000 0.116
#> GSM339504 4 0.5811 0.36798 0.340 0.000 0.000 0.552 0.108
#> GSM339505 3 0.3617 0.66715 0.044 0.004 0.824 0.000 0.128
#> GSM339506 5 0.6162 -0.14438 0.044 0.000 0.048 0.392 0.516
#> GSM339507 1 0.2722 0.63192 0.868 0.000 0.008 0.004 0.120
#> GSM339508 2 0.1408 0.80070 0.000 0.948 0.000 0.044 0.008
#> GSM339509 2 0.0898 0.80433 0.000 0.972 0.000 0.008 0.020
#> GSM339510 4 0.5325 0.07417 0.000 0.024 0.016 0.520 0.440
#> GSM339511 4 0.2740 0.47724 0.096 0.000 0.000 0.876 0.028
#> GSM339512 2 0.1124 0.79961 0.004 0.960 0.000 0.000 0.036
#> GSM339513 1 0.2199 0.63437 0.916 0.000 0.060 0.016 0.008
#> GSM339514 2 0.0671 0.80509 0.000 0.980 0.000 0.004 0.016
#> GSM339515 1 0.0451 0.65409 0.988 0.000 0.004 0.000 0.008
#> GSM339516 2 0.5012 0.50091 0.016 0.600 0.000 0.368 0.016
#> GSM339517 3 0.2249 0.71442 0.008 0.000 0.896 0.000 0.096
#> GSM339518 2 0.6795 0.07365 0.000 0.460 0.016 0.172 0.352
#> GSM339519 3 0.1628 0.72694 0.008 0.000 0.936 0.000 0.056
#> GSM339520 3 0.3852 0.64799 0.000 0.028 0.796 0.008 0.168
#> GSM339521 2 0.2597 0.77516 0.004 0.896 0.000 0.040 0.060
#> GSM339522 4 0.4272 0.32737 0.000 0.124 0.020 0.796 0.060
#> GSM339523 2 0.0671 0.80563 0.000 0.980 0.000 0.004 0.016
#> GSM339524 3 0.2473 0.71895 0.032 0.000 0.896 0.000 0.072
#> GSM339525 1 0.4863 0.30636 0.656 0.000 0.000 0.296 0.048
#> GSM339526 3 0.1211 0.73402 0.016 0.000 0.960 0.000 0.024
#> GSM339527 5 0.6513 -0.09733 0.036 0.000 0.092 0.356 0.516
#> GSM339528 1 0.5283 0.36446 0.552 0.000 0.020 0.020 0.408
#> GSM339529 2 0.2358 0.77223 0.000 0.888 0.000 0.104 0.008
#> GSM339530 3 0.4562 0.61193 0.000 0.128 0.760 0.004 0.108
#> GSM339531 5 0.8248 0.03609 0.000 0.244 0.192 0.168 0.396
#> GSM339532 4 0.4434 0.21178 0.460 0.000 0.000 0.536 0.004
#> GSM339533 1 0.6752 0.01618 0.384 0.000 0.352 0.000 0.264
#> GSM339534 5 0.8602 0.00894 0.232 0.000 0.256 0.240 0.272
#> GSM339535 2 0.0290 0.80611 0.000 0.992 0.000 0.000 0.008
#> GSM339536 1 0.0566 0.65456 0.984 0.000 0.004 0.000 0.012
#> GSM339537 2 0.4917 0.43584 0.000 0.556 0.000 0.416 0.028
#> GSM339538 3 0.1764 0.72615 0.008 0.000 0.928 0.000 0.064
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM339455 4 0.6551 0.0421 0.004 0.000 0.336 0.404 0.020 0.236
#> GSM339456 2 0.4394 0.4718 0.000 0.656 0.032 0.008 0.304 0.000
#> GSM339457 3 0.3257 0.7075 0.000 0.000 0.816 0.012 0.020 0.152
#> GSM339458 6 0.2207 0.7018 0.004 0.008 0.000 0.060 0.020 0.908
#> GSM339459 3 0.2257 0.7170 0.000 0.008 0.876 0.000 0.116 0.000
#> GSM339460 6 0.4998 0.5653 0.004 0.048 0.000 0.152 0.080 0.716
#> GSM339461 5 0.5374 0.4128 0.000 0.244 0.016 0.012 0.640 0.088
#> GSM339462 1 0.7143 0.3574 0.472 0.000 0.004 0.212 0.128 0.184
#> GSM339463 6 0.4138 0.6984 0.116 0.000 0.092 0.004 0.012 0.776
#> GSM339464 4 0.4575 0.4170 0.044 0.000 0.000 0.704 0.224 0.028
#> GSM339465 6 0.3865 0.6773 0.216 0.000 0.020 0.000 0.016 0.748
#> GSM339466 2 0.4822 0.6893 0.000 0.752 0.028 0.032 0.116 0.072
#> GSM339467 2 0.2018 0.7275 0.016 0.924 0.000 0.004 0.028 0.028
#> GSM339468 5 0.5588 0.5312 0.000 0.060 0.176 0.100 0.660 0.004
#> GSM339469 4 0.3268 0.5551 0.144 0.000 0.000 0.812 0.000 0.044
#> GSM339470 6 0.6486 0.6456 0.112 0.056 0.128 0.012 0.052 0.640
#> GSM339471 1 0.5950 0.5486 0.632 0.000 0.108 0.168 0.004 0.088
#> GSM339472 2 0.1245 0.7470 0.000 0.952 0.000 0.000 0.032 0.016
#> GSM339473 1 0.0862 0.7727 0.972 0.000 0.008 0.016 0.000 0.004
#> GSM339474 2 0.4070 0.6932 0.000 0.776 0.000 0.020 0.136 0.068
#> GSM339475 3 0.1261 0.7542 0.000 0.000 0.952 0.000 0.024 0.024
#> GSM339476 4 0.4611 0.4617 0.240 0.000 0.020 0.700 0.016 0.024
#> GSM339477 2 0.4912 0.5534 0.000 0.632 0.000 0.028 0.300 0.040
#> GSM339478 3 0.5537 0.6354 0.000 0.064 0.696 0.056 0.036 0.148
#> GSM339479 6 0.2125 0.6974 0.004 0.004 0.000 0.068 0.016 0.908
#> GSM339480 3 0.2673 0.7033 0.000 0.012 0.852 0.000 0.132 0.004
#> GSM339481 2 0.1720 0.7467 0.000 0.928 0.000 0.000 0.040 0.032
#> GSM339482 3 0.2050 0.7544 0.008 0.000 0.920 0.004 0.032 0.036
#> GSM339483 1 0.4979 0.6396 0.712 0.000 0.004 0.168 0.048 0.068
#> GSM339484 1 0.2890 0.7077 0.852 0.000 0.004 0.008 0.016 0.120
#> GSM339485 4 0.4885 0.4381 0.060 0.000 0.000 0.700 0.196 0.044
#> GSM339486 6 0.3510 0.6818 0.212 0.000 0.012 0.004 0.004 0.768
#> GSM339487 2 0.4596 0.6718 0.000 0.736 0.000 0.128 0.112 0.024
#> GSM339488 2 0.2001 0.7279 0.012 0.924 0.004 0.000 0.032 0.028
#> GSM339489 2 0.5801 0.5072 0.000 0.592 0.000 0.120 0.248 0.040
#> GSM339490 4 0.3111 0.5755 0.120 0.000 0.000 0.840 0.020 0.020
#> GSM339491 6 0.6993 0.4529 0.224 0.240 0.004 0.012 0.048 0.472
#> GSM339492 3 0.7303 0.1819 0.160 0.000 0.460 0.220 0.008 0.152
#> GSM339493 2 0.1801 0.7425 0.000 0.924 0.000 0.004 0.056 0.016
#> GSM339494 1 0.0520 0.7692 0.984 0.000 0.008 0.008 0.000 0.000
#> GSM339495 2 0.4492 0.6581 0.000 0.724 0.000 0.020 0.192 0.064
#> GSM339496 3 0.1629 0.7545 0.004 0.000 0.940 0.004 0.028 0.024
#> GSM339497 6 0.4008 0.6483 0.004 0.080 0.004 0.032 0.072 0.808
#> GSM339498 3 0.4366 0.1757 0.000 0.016 0.540 0.000 0.440 0.004
#> GSM339499 3 0.3421 0.6794 0.004 0.000 0.780 0.004 0.012 0.200
#> GSM339500 6 0.2817 0.7126 0.004 0.016 0.060 0.028 0.008 0.884
#> GSM339501 4 0.6824 0.0596 0.000 0.012 0.364 0.388 0.204 0.032
#> GSM339502 2 0.2100 0.7266 0.016 0.916 0.000 0.000 0.032 0.036
#> GSM339503 3 0.2773 0.7006 0.000 0.000 0.828 0.004 0.164 0.004
#> GSM339504 4 0.7281 0.1968 0.224 0.000 0.004 0.448 0.144 0.180
#> GSM339505 3 0.4618 0.4850 0.020 0.000 0.640 0.000 0.028 0.312
#> GSM339506 5 0.4828 0.4558 0.012 0.000 0.052 0.204 0.708 0.024
#> GSM339507 1 0.1956 0.7293 0.908 0.004 0.000 0.000 0.008 0.080
#> GSM339508 2 0.4949 0.5084 0.000 0.656 0.004 0.268 0.048 0.024
#> GSM339509 2 0.1965 0.7290 0.008 0.924 0.000 0.004 0.040 0.024
#> GSM339510 5 0.4781 0.4762 0.000 0.076 0.004 0.116 0.744 0.060
#> GSM339511 4 0.2725 0.5574 0.020 0.000 0.000 0.880 0.040 0.060
#> GSM339512 2 0.1901 0.7246 0.004 0.912 0.000 0.000 0.008 0.076
#> GSM339513 1 0.3086 0.7350 0.852 0.000 0.056 0.080 0.000 0.012
#> GSM339514 2 0.0622 0.7436 0.012 0.980 0.000 0.000 0.000 0.008
#> GSM339515 1 0.1007 0.7730 0.968 0.000 0.008 0.016 0.004 0.004
#> GSM339516 2 0.5506 0.5692 0.004 0.632 0.000 0.132 0.212 0.020
#> GSM339517 3 0.3309 0.6951 0.004 0.000 0.816 0.028 0.148 0.004
#> GSM339518 6 0.4989 0.5375 0.000 0.156 0.000 0.048 0.088 0.708
#> GSM339519 3 0.1477 0.7465 0.004 0.000 0.940 0.008 0.048 0.000
#> GSM339520 3 0.4029 0.6963 0.000 0.024 0.780 0.008 0.032 0.156
#> GSM339521 2 0.5245 0.0345 0.004 0.468 0.000 0.020 0.040 0.468
#> GSM339522 4 0.7665 -0.0872 0.000 0.160 0.032 0.416 0.276 0.116
#> GSM339523 2 0.1485 0.7367 0.004 0.944 0.000 0.000 0.028 0.024
#> GSM339524 3 0.3406 0.7101 0.056 0.000 0.824 0.004 0.112 0.004
#> GSM339525 1 0.6057 0.3367 0.496 0.000 0.000 0.308 0.016 0.180
#> GSM339526 3 0.1863 0.7549 0.004 0.000 0.928 0.004 0.032 0.032
#> GSM339527 5 0.4961 0.4847 0.012 0.000 0.088 0.180 0.704 0.016
#> GSM339528 6 0.3463 0.6561 0.240 0.000 0.004 0.008 0.000 0.748
#> GSM339529 2 0.5260 0.3983 0.000 0.576 0.004 0.348 0.048 0.024
#> GSM339530 3 0.5329 0.6027 0.000 0.156 0.696 0.012 0.048 0.088
#> GSM339531 5 0.6299 0.2944 0.000 0.368 0.136 0.032 0.460 0.004
#> GSM339532 4 0.3702 0.5119 0.208 0.000 0.000 0.760 0.008 0.024
#> GSM339533 6 0.6421 0.4529 0.312 0.004 0.120 0.004 0.048 0.512
#> GSM339534 3 0.7494 -0.0438 0.092 0.000 0.368 0.280 0.012 0.248
#> GSM339535 2 0.0881 0.7472 0.008 0.972 0.000 0.000 0.012 0.008
#> GSM339536 1 0.0912 0.7724 0.972 0.000 0.008 0.012 0.004 0.004
#> GSM339537 2 0.5986 0.5204 0.000 0.592 0.000 0.108 0.232 0.068
#> GSM339538 3 0.2469 0.7377 0.012 0.000 0.896 0.028 0.060 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 protocol(p) agent(p) individual(p) k
#> SD:NMF 75 0.919 0.925 4.13e-03 2
#> SD:NMF 80 0.964 0.957 4.46e-05 3
#> SD:NMF 71 0.239 0.723 7.00e-07 4
#> SD:NMF 46 0.585 0.556 5.01e-03 5
#> SD:NMF 61 0.852 0.842 1.06e-04 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 15497 rows and 84 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 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 0.378 0.622 0.820 0.4572 0.512 0.512
#> 3 3 0.298 0.500 0.727 0.3698 0.789 0.599
#> 4 4 0.436 0.409 0.631 0.1569 0.888 0.683
#> 5 5 0.556 0.478 0.688 0.0704 0.820 0.439
#> 6 6 0.628 0.465 0.680 0.0504 0.935 0.701
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
#> GSM339455 1 0.4431 0.7305 0.908 0.092
#> GSM339456 2 0.9608 0.3272 0.384 0.616
#> GSM339457 1 0.9358 0.4086 0.648 0.352
#> GSM339458 2 0.9286 0.4847 0.344 0.656
#> GSM339459 1 0.9977 0.1698 0.528 0.472
#> GSM339460 2 0.3431 0.7987 0.064 0.936
#> GSM339461 2 0.0672 0.8035 0.008 0.992
#> GSM339462 1 0.1184 0.7624 0.984 0.016
#> GSM339463 1 0.0000 0.7663 1.000 0.000
#> GSM339464 1 0.9170 0.5132 0.668 0.332
#> GSM339465 1 0.0000 0.7663 1.000 0.000
#> GSM339466 2 0.6247 0.7384 0.156 0.844
#> GSM339467 2 0.0376 0.8038 0.004 0.996
#> GSM339468 1 0.9963 0.2165 0.536 0.464
#> GSM339469 1 0.9129 0.5188 0.672 0.328
#> GSM339470 2 0.9087 0.5374 0.324 0.676
#> GSM339471 1 0.0000 0.7663 1.000 0.000
#> GSM339472 2 0.0938 0.8047 0.012 0.988
#> GSM339473 1 0.0000 0.7663 1.000 0.000
#> GSM339474 2 0.0000 0.8008 0.000 1.000
#> GSM339475 1 0.0000 0.7663 1.000 0.000
#> GSM339476 1 0.4431 0.7305 0.908 0.092
#> GSM339477 2 0.0376 0.8029 0.004 0.996
#> GSM339478 1 0.9358 0.4086 0.648 0.352
#> GSM339479 2 0.9286 0.4847 0.344 0.656
#> GSM339480 1 0.9977 0.1698 0.528 0.472
#> GSM339481 2 0.2948 0.8034 0.052 0.948
#> GSM339482 1 0.0000 0.7663 1.000 0.000
#> GSM339483 1 0.1184 0.7624 0.984 0.016
#> GSM339484 1 0.0000 0.7663 1.000 0.000
#> GSM339485 1 0.9170 0.5132 0.668 0.332
#> GSM339486 1 0.0000 0.7663 1.000 0.000
#> GSM339487 2 0.6247 0.7384 0.156 0.844
#> GSM339488 2 0.6247 0.7359 0.156 0.844
#> GSM339489 1 0.9963 0.2165 0.536 0.464
#> GSM339490 1 0.9129 0.5188 0.672 0.328
#> GSM339491 2 0.9087 0.5374 0.324 0.676
#> GSM339492 1 0.0000 0.7663 1.000 0.000
#> GSM339493 2 0.0938 0.8047 0.012 0.988
#> GSM339494 1 0.0000 0.7663 1.000 0.000
#> GSM339495 2 0.0000 0.8008 0.000 1.000
#> GSM339496 1 0.0000 0.7663 1.000 0.000
#> GSM339497 2 0.2778 0.8044 0.048 0.952
#> GSM339498 2 1.0000 -0.1106 0.500 0.500
#> GSM339499 1 0.9358 0.4086 0.648 0.352
#> GSM339500 2 0.9286 0.4847 0.344 0.656
#> GSM339501 1 0.9881 0.2930 0.564 0.436
#> GSM339502 2 0.2948 0.8034 0.052 0.948
#> GSM339503 1 0.0000 0.7663 1.000 0.000
#> GSM339504 1 0.1184 0.7624 0.984 0.016
#> GSM339505 1 0.7674 0.6014 0.776 0.224
#> GSM339506 1 0.9170 0.5132 0.668 0.332
#> GSM339507 1 0.0000 0.7663 1.000 0.000
#> GSM339508 2 0.0672 0.8048 0.008 0.992
#> GSM339509 2 0.0376 0.8038 0.004 0.996
#> GSM339510 1 0.9963 0.2165 0.536 0.464
#> GSM339511 1 0.9129 0.5188 0.672 0.328
#> GSM339512 2 0.9087 0.5374 0.324 0.676
#> GSM339513 1 0.0000 0.7663 1.000 0.000
#> GSM339514 2 0.0938 0.8047 0.012 0.988
#> GSM339515 1 0.0000 0.7663 1.000 0.000
#> GSM339516 2 0.0376 0.8039 0.004 0.996
#> GSM339517 1 0.0000 0.7663 1.000 0.000
#> GSM339518 2 0.2778 0.8044 0.048 0.952
#> GSM339519 1 0.9996 0.1102 0.512 0.488
#> GSM339520 1 0.9358 0.4086 0.648 0.352
#> GSM339521 2 0.9286 0.4847 0.344 0.656
#> GSM339522 1 0.9881 0.2930 0.564 0.436
#> GSM339523 2 0.2948 0.8034 0.052 0.948
#> GSM339524 1 0.0000 0.7663 1.000 0.000
#> GSM339525 1 0.1184 0.7624 0.984 0.016
#> GSM339526 1 0.0000 0.7663 1.000 0.000
#> GSM339527 1 0.9170 0.5132 0.668 0.332
#> GSM339528 1 0.0000 0.7663 1.000 0.000
#> GSM339529 2 0.0672 0.8048 0.008 0.992
#> GSM339530 2 1.0000 0.0386 0.496 0.504
#> GSM339531 1 0.9963 0.2165 0.536 0.464
#> GSM339532 1 0.9129 0.5188 0.672 0.328
#> GSM339533 2 0.9087 0.5374 0.324 0.676
#> GSM339534 1 0.0000 0.7663 1.000 0.000
#> GSM339535 2 0.0938 0.8047 0.012 0.988
#> GSM339536 1 0.0000 0.7663 1.000 0.000
#> GSM339537 2 0.0376 0.8039 0.004 0.996
#> GSM339538 1 0.0000 0.7663 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM339455 1 0.8454 0.2625 0.480 0.088 0.432
#> GSM339456 2 0.9342 0.1021 0.168 0.452 0.380
#> GSM339457 3 0.7825 0.4207 0.080 0.300 0.620
#> GSM339458 2 0.8643 0.5291 0.188 0.600 0.212
#> GSM339459 3 0.9457 0.2370 0.236 0.264 0.500
#> GSM339460 2 0.3983 0.7902 0.068 0.884 0.048
#> GSM339461 2 0.4291 0.7072 0.152 0.840 0.008
#> GSM339462 1 0.4605 0.5562 0.796 0.000 0.204
#> GSM339463 3 0.4062 0.4482 0.164 0.000 0.836
#> GSM339464 1 0.5677 0.5078 0.804 0.124 0.072
#> GSM339465 3 0.5621 0.2338 0.308 0.000 0.692
#> GSM339466 2 0.5507 0.7451 0.056 0.808 0.136
#> GSM339467 2 0.0424 0.7900 0.000 0.992 0.008
#> GSM339468 1 0.9866 -0.1481 0.388 0.256 0.356
#> GSM339469 1 0.5307 0.5193 0.820 0.124 0.056
#> GSM339470 2 0.7670 0.5378 0.068 0.620 0.312
#> GSM339471 1 0.5678 0.5104 0.684 0.000 0.316
#> GSM339472 2 0.0983 0.7889 0.004 0.980 0.016
#> GSM339473 1 0.5138 0.5329 0.748 0.000 0.252
#> GSM339474 2 0.0475 0.7871 0.004 0.992 0.004
#> GSM339475 3 0.1529 0.5408 0.040 0.000 0.960
#> GSM339476 1 0.8454 0.2625 0.480 0.088 0.432
#> GSM339477 2 0.4110 0.7076 0.152 0.844 0.004
#> GSM339478 3 0.7825 0.4207 0.080 0.300 0.620
#> GSM339479 2 0.8643 0.5291 0.188 0.600 0.212
#> GSM339480 3 0.9457 0.2370 0.236 0.264 0.500
#> GSM339481 2 0.3692 0.7937 0.056 0.896 0.048
#> GSM339482 3 0.1643 0.5392 0.044 0.000 0.956
#> GSM339483 1 0.4605 0.5562 0.796 0.000 0.204
#> GSM339484 3 0.4062 0.4482 0.164 0.000 0.836
#> GSM339485 1 0.5677 0.5078 0.804 0.124 0.072
#> GSM339486 3 0.5621 0.2338 0.308 0.000 0.692
#> GSM339487 2 0.5507 0.7451 0.056 0.808 0.136
#> GSM339488 2 0.4172 0.7294 0.004 0.840 0.156
#> GSM339489 1 0.9866 -0.1481 0.388 0.256 0.356
#> GSM339490 1 0.5307 0.5193 0.820 0.124 0.056
#> GSM339491 2 0.7670 0.5378 0.068 0.620 0.312
#> GSM339492 1 0.5678 0.5104 0.684 0.000 0.316
#> GSM339493 2 0.0983 0.7889 0.004 0.980 0.016
#> GSM339494 1 0.5138 0.5329 0.748 0.000 0.252
#> GSM339495 2 0.0475 0.7871 0.004 0.992 0.004
#> GSM339496 3 0.1529 0.5408 0.040 0.000 0.960
#> GSM339497 2 0.3155 0.7977 0.044 0.916 0.040
#> GSM339498 3 0.9624 0.1867 0.240 0.292 0.468
#> GSM339499 3 0.7825 0.4207 0.080 0.300 0.620
#> GSM339500 2 0.8643 0.5291 0.188 0.600 0.212
#> GSM339501 3 0.9757 0.1142 0.384 0.228 0.388
#> GSM339502 2 0.3692 0.7937 0.056 0.896 0.048
#> GSM339503 3 0.1643 0.5392 0.044 0.000 0.956
#> GSM339504 1 0.4605 0.5562 0.796 0.000 0.204
#> GSM339505 3 0.7339 0.4782 0.088 0.224 0.688
#> GSM339506 1 0.5677 0.5078 0.804 0.124 0.072
#> GSM339507 3 0.5621 0.2338 0.308 0.000 0.692
#> GSM339508 2 0.3995 0.7738 0.116 0.868 0.016
#> GSM339509 2 0.0424 0.7900 0.000 0.992 0.008
#> GSM339510 1 0.9866 -0.1481 0.388 0.256 0.356
#> GSM339511 1 0.5307 0.5193 0.820 0.124 0.056
#> GSM339512 2 0.7670 0.5378 0.068 0.620 0.312
#> GSM339513 1 0.5678 0.5104 0.684 0.000 0.316
#> GSM339514 2 0.0983 0.7889 0.004 0.980 0.016
#> GSM339515 1 0.5138 0.5329 0.748 0.000 0.252
#> GSM339516 2 0.0661 0.7885 0.008 0.988 0.004
#> GSM339517 3 0.1529 0.5408 0.040 0.000 0.960
#> GSM339518 2 0.3155 0.7977 0.044 0.916 0.040
#> GSM339519 3 0.9569 0.2087 0.240 0.280 0.480
#> GSM339520 3 0.7825 0.4207 0.080 0.300 0.620
#> GSM339521 2 0.8643 0.5291 0.188 0.600 0.212
#> GSM339522 3 0.9757 0.1142 0.384 0.228 0.388
#> GSM339523 2 0.3692 0.7937 0.056 0.896 0.048
#> GSM339524 3 0.1643 0.5392 0.044 0.000 0.956
#> GSM339525 1 0.4605 0.5562 0.796 0.000 0.204
#> GSM339526 3 0.4062 0.4482 0.164 0.000 0.836
#> GSM339527 1 0.5677 0.5078 0.804 0.124 0.072
#> GSM339528 3 0.5621 0.2338 0.308 0.000 0.692
#> GSM339529 2 0.3995 0.7738 0.116 0.868 0.016
#> GSM339530 3 0.8341 0.0342 0.080 0.452 0.468
#> GSM339531 1 0.9866 -0.1481 0.388 0.256 0.356
#> GSM339532 1 0.5307 0.5193 0.820 0.124 0.056
#> GSM339533 2 0.7670 0.5378 0.068 0.620 0.312
#> GSM339534 1 0.5678 0.5104 0.684 0.000 0.316
#> GSM339535 2 0.0983 0.7889 0.004 0.980 0.016
#> GSM339536 1 0.5138 0.5329 0.748 0.000 0.252
#> GSM339537 2 0.0661 0.7885 0.008 0.988 0.004
#> GSM339538 3 0.1529 0.5408 0.040 0.000 0.960
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM339455 4 0.7895 -0.0824 0.232 0.004 0.356 0.408
#> GSM339456 3 0.8517 0.1511 0.032 0.304 0.420 0.244
#> GSM339457 3 0.5972 0.4727 0.112 0.148 0.724 0.016
#> GSM339458 2 0.9209 0.3712 0.080 0.380 0.276 0.264
#> GSM339459 3 0.7990 0.2377 0.060 0.112 0.536 0.292
#> GSM339460 2 0.3945 0.7206 0.008 0.852 0.064 0.076
#> GSM339461 2 0.3831 0.5745 0.000 0.792 0.004 0.204
#> GSM339462 1 0.5590 0.5170 0.524 0.000 0.020 0.456
#> GSM339463 3 0.5558 0.2320 0.364 0.000 0.608 0.028
#> GSM339464 4 0.0336 0.4595 0.000 0.000 0.008 0.992
#> GSM339465 1 0.6607 0.1375 0.476 0.000 0.444 0.080
#> GSM339466 2 0.5885 0.6608 0.028 0.728 0.180 0.064
#> GSM339467 2 0.4469 0.6900 0.112 0.808 0.080 0.000
#> GSM339468 4 0.6634 0.2135 0.020 0.044 0.412 0.524
#> GSM339469 4 0.0895 0.4477 0.020 0.000 0.004 0.976
#> GSM339470 2 0.8546 0.3757 0.112 0.424 0.380 0.084
#> GSM339471 4 0.7732 -0.4130 0.384 0.000 0.228 0.388
#> GSM339472 2 0.0992 0.7112 0.008 0.976 0.012 0.004
#> GSM339473 1 0.5548 0.5780 0.628 0.000 0.032 0.340
#> GSM339474 2 0.0524 0.7095 0.008 0.988 0.000 0.004
#> GSM339475 3 0.5022 0.5024 0.264 0.000 0.708 0.028
#> GSM339476 4 0.7895 -0.0824 0.232 0.004 0.356 0.408
#> GSM339477 2 0.3688 0.5727 0.000 0.792 0.000 0.208
#> GSM339478 3 0.5972 0.4727 0.112 0.148 0.724 0.016
#> GSM339479 2 0.9209 0.3712 0.080 0.380 0.276 0.264
#> GSM339480 3 0.7990 0.2377 0.060 0.112 0.536 0.292
#> GSM339481 2 0.3728 0.7230 0.008 0.864 0.064 0.064
#> GSM339482 3 0.5050 0.4984 0.268 0.000 0.704 0.028
#> GSM339483 1 0.5590 0.5170 0.524 0.000 0.020 0.456
#> GSM339484 3 0.5558 0.2320 0.364 0.000 0.608 0.028
#> GSM339485 4 0.0336 0.4595 0.000 0.000 0.008 0.992
#> GSM339486 1 0.6607 0.1375 0.476 0.000 0.444 0.080
#> GSM339487 2 0.5885 0.6608 0.028 0.728 0.180 0.064
#> GSM339488 2 0.6617 0.5644 0.124 0.628 0.244 0.004
#> GSM339489 4 0.6634 0.2135 0.020 0.044 0.412 0.524
#> GSM339490 4 0.0895 0.4477 0.020 0.000 0.004 0.976
#> GSM339491 2 0.8546 0.3757 0.112 0.424 0.380 0.084
#> GSM339492 4 0.7732 -0.4130 0.384 0.000 0.228 0.388
#> GSM339493 2 0.0992 0.7112 0.008 0.976 0.012 0.004
#> GSM339494 1 0.5548 0.5780 0.628 0.000 0.032 0.340
#> GSM339495 2 0.0524 0.7095 0.008 0.988 0.000 0.004
#> GSM339496 3 0.5022 0.5024 0.264 0.000 0.708 0.028
#> GSM339497 2 0.2830 0.7245 0.000 0.900 0.040 0.060
#> GSM339498 3 0.7955 0.2023 0.040 0.132 0.512 0.316
#> GSM339499 3 0.5972 0.4727 0.112 0.148 0.724 0.016
#> GSM339500 2 0.9209 0.3712 0.080 0.380 0.276 0.264
#> GSM339501 4 0.6205 0.1671 0.020 0.020 0.460 0.500
#> GSM339502 2 0.3728 0.7230 0.008 0.864 0.064 0.064
#> GSM339503 3 0.5050 0.4984 0.268 0.000 0.704 0.028
#> GSM339504 1 0.5590 0.5170 0.524 0.000 0.020 0.456
#> GSM339505 3 0.7117 0.4452 0.236 0.152 0.600 0.012
#> GSM339506 4 0.0336 0.4595 0.000 0.000 0.008 0.992
#> GSM339507 1 0.6607 0.1375 0.476 0.000 0.444 0.080
#> GSM339508 2 0.7646 0.6027 0.104 0.632 0.132 0.132
#> GSM339509 2 0.4469 0.6900 0.112 0.808 0.080 0.000
#> GSM339510 4 0.6634 0.2135 0.020 0.044 0.412 0.524
#> GSM339511 4 0.0895 0.4477 0.020 0.000 0.004 0.976
#> GSM339512 2 0.8546 0.3757 0.112 0.424 0.380 0.084
#> GSM339513 4 0.7732 -0.4130 0.384 0.000 0.228 0.388
#> GSM339514 2 0.0992 0.7112 0.008 0.976 0.012 0.004
#> GSM339515 1 0.5548 0.5780 0.628 0.000 0.032 0.340
#> GSM339516 2 0.1042 0.7145 0.008 0.972 0.000 0.020
#> GSM339517 3 0.5022 0.5024 0.264 0.000 0.708 0.028
#> GSM339518 2 0.2830 0.7245 0.000 0.900 0.040 0.060
#> GSM339519 3 0.7833 0.2043 0.040 0.120 0.524 0.316
#> GSM339520 3 0.5972 0.4727 0.112 0.148 0.724 0.016
#> GSM339521 2 0.9209 0.3712 0.080 0.380 0.276 0.264
#> GSM339522 4 0.6205 0.1671 0.020 0.020 0.460 0.500
#> GSM339523 2 0.3728 0.7230 0.008 0.864 0.064 0.064
#> GSM339524 3 0.5050 0.4984 0.268 0.000 0.704 0.028
#> GSM339525 1 0.5590 0.5170 0.524 0.000 0.020 0.456
#> GSM339526 3 0.5558 0.2320 0.364 0.000 0.608 0.028
#> GSM339527 4 0.0336 0.4595 0.000 0.000 0.008 0.992
#> GSM339528 1 0.6607 0.1375 0.476 0.000 0.444 0.080
#> GSM339529 2 0.7646 0.6027 0.104 0.632 0.132 0.132
#> GSM339530 3 0.7406 0.2579 0.184 0.220 0.580 0.016
#> GSM339531 4 0.6634 0.2135 0.020 0.044 0.412 0.524
#> GSM339532 4 0.0895 0.4477 0.020 0.000 0.004 0.976
#> GSM339533 2 0.8546 0.3757 0.112 0.424 0.380 0.084
#> GSM339534 4 0.7732 -0.4130 0.384 0.000 0.228 0.388
#> GSM339535 2 0.0992 0.7112 0.008 0.976 0.012 0.004
#> GSM339536 1 0.5548 0.5780 0.628 0.000 0.032 0.340
#> GSM339537 2 0.1042 0.7145 0.008 0.972 0.000 0.020
#> GSM339538 3 0.5022 0.5024 0.264 0.000 0.708 0.028
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM339455 1 0.8460 0.23713 0.328 0.000 0.220 0.272 0.180
#> GSM339456 5 0.8381 0.12737 0.000 0.196 0.280 0.176 0.348
#> GSM339457 5 0.4088 0.18032 0.000 0.000 0.368 0.000 0.632
#> GSM339458 5 0.6665 0.32602 0.000 0.312 0.000 0.252 0.436
#> GSM339459 3 0.6738 -0.11331 0.000 0.008 0.440 0.192 0.360
#> GSM339460 2 0.3375 0.73353 0.000 0.840 0.000 0.056 0.104
#> GSM339461 2 0.4210 0.57979 0.000 0.788 0.008 0.140 0.064
#> GSM339462 1 0.2329 0.73642 0.876 0.000 0.000 0.124 0.000
#> GSM339463 3 0.5983 0.54138 0.140 0.000 0.652 0.028 0.180
#> GSM339464 4 0.1788 0.60693 0.056 0.000 0.008 0.932 0.004
#> GSM339465 3 0.6901 0.36391 0.300 0.000 0.500 0.028 0.172
#> GSM339466 2 0.5196 0.24306 0.000 0.576 0.004 0.040 0.380
#> GSM339467 2 0.4768 0.26842 0.000 0.592 0.000 0.024 0.384
#> GSM339468 4 0.7235 0.34931 0.000 0.036 0.216 0.464 0.284
#> GSM339469 4 0.3946 0.54130 0.080 0.000 0.000 0.800 0.120
#> GSM339470 5 0.5807 0.46798 0.004 0.236 0.060 0.040 0.660
#> GSM339471 1 0.6201 0.63074 0.648 0.000 0.196 0.072 0.084
#> GSM339472 2 0.0451 0.78403 0.000 0.988 0.008 0.000 0.004
#> GSM339473 1 0.0451 0.72439 0.988 0.000 0.008 0.000 0.004
#> GSM339474 2 0.0000 0.78178 0.000 1.000 0.000 0.000 0.000
#> GSM339475 3 0.1121 0.62890 0.044 0.000 0.956 0.000 0.000
#> GSM339476 1 0.8460 0.23713 0.328 0.000 0.220 0.272 0.180
#> GSM339477 2 0.4082 0.58081 0.000 0.796 0.008 0.140 0.056
#> GSM339478 5 0.4088 0.18032 0.000 0.000 0.368 0.000 0.632
#> GSM339479 5 0.6665 0.32602 0.000 0.312 0.000 0.252 0.436
#> GSM339480 3 0.6738 -0.11331 0.000 0.008 0.440 0.192 0.360
#> GSM339481 2 0.3164 0.74318 0.000 0.852 0.000 0.044 0.104
#> GSM339482 3 0.1197 0.63006 0.048 0.000 0.952 0.000 0.000
#> GSM339483 1 0.2329 0.73642 0.876 0.000 0.000 0.124 0.000
#> GSM339484 3 0.5983 0.54138 0.140 0.000 0.652 0.028 0.180
#> GSM339485 4 0.1788 0.60693 0.056 0.000 0.008 0.932 0.004
#> GSM339486 3 0.6901 0.36391 0.300 0.000 0.500 0.028 0.172
#> GSM339487 2 0.5196 0.24306 0.000 0.576 0.004 0.040 0.380
#> GSM339488 5 0.4973 0.20446 0.000 0.408 0.004 0.024 0.564
#> GSM339489 4 0.7235 0.34931 0.000 0.036 0.216 0.464 0.284
#> GSM339490 4 0.3946 0.54130 0.080 0.000 0.000 0.800 0.120
#> GSM339491 5 0.5807 0.46798 0.004 0.236 0.060 0.040 0.660
#> GSM339492 1 0.6201 0.63074 0.648 0.000 0.196 0.072 0.084
#> GSM339493 2 0.0451 0.78403 0.000 0.988 0.008 0.000 0.004
#> GSM339494 1 0.0451 0.72439 0.988 0.000 0.008 0.000 0.004
#> GSM339495 2 0.0000 0.78178 0.000 1.000 0.000 0.000 0.000
#> GSM339496 3 0.1121 0.62890 0.044 0.000 0.956 0.000 0.000
#> GSM339497 2 0.2813 0.75820 0.000 0.876 0.000 0.040 0.084
#> GSM339498 5 0.7202 0.00402 0.000 0.024 0.356 0.224 0.396
#> GSM339499 5 0.4088 0.18032 0.000 0.000 0.368 0.000 0.632
#> GSM339500 5 0.6665 0.32602 0.000 0.312 0.000 0.252 0.436
#> GSM339501 4 0.7013 0.32599 0.000 0.012 0.268 0.428 0.292
#> GSM339502 2 0.3164 0.74318 0.000 0.852 0.000 0.044 0.104
#> GSM339503 3 0.1197 0.63006 0.048 0.000 0.952 0.000 0.000
#> GSM339504 1 0.2329 0.73642 0.876 0.000 0.000 0.124 0.000
#> GSM339505 3 0.5897 0.15583 0.048 0.012 0.472 0.008 0.460
#> GSM339506 4 0.1788 0.60693 0.056 0.000 0.008 0.932 0.004
#> GSM339507 3 0.6901 0.36391 0.300 0.000 0.500 0.028 0.172
#> GSM339508 5 0.5190 -0.09104 0.008 0.424 0.000 0.028 0.540
#> GSM339509 2 0.4768 0.26842 0.000 0.592 0.000 0.024 0.384
#> GSM339510 4 0.7235 0.34931 0.000 0.036 0.216 0.464 0.284
#> GSM339511 4 0.3946 0.54130 0.080 0.000 0.000 0.800 0.120
#> GSM339512 5 0.5807 0.46798 0.004 0.236 0.060 0.040 0.660
#> GSM339513 1 0.6201 0.63074 0.648 0.000 0.196 0.072 0.084
#> GSM339514 2 0.0451 0.78403 0.000 0.988 0.008 0.000 0.004
#> GSM339515 1 0.0451 0.72439 0.988 0.000 0.008 0.000 0.004
#> GSM339516 2 0.0693 0.78394 0.000 0.980 0.000 0.012 0.008
#> GSM339517 3 0.1121 0.62890 0.044 0.000 0.956 0.000 0.000
#> GSM339518 2 0.2813 0.75820 0.000 0.876 0.000 0.040 0.084
#> GSM339519 5 0.6969 0.00495 0.000 0.012 0.356 0.224 0.408
#> GSM339520 5 0.4088 0.18032 0.000 0.000 0.368 0.000 0.632
#> GSM339521 5 0.6665 0.32602 0.000 0.312 0.000 0.252 0.436
#> GSM339522 4 0.7013 0.32599 0.000 0.012 0.268 0.428 0.292
#> GSM339523 2 0.3164 0.74318 0.000 0.852 0.000 0.044 0.104
#> GSM339524 3 0.1197 0.63006 0.048 0.000 0.952 0.000 0.000
#> GSM339525 1 0.2329 0.73642 0.876 0.000 0.000 0.124 0.000
#> GSM339526 3 0.5983 0.54138 0.140 0.000 0.652 0.028 0.180
#> GSM339527 4 0.1788 0.60693 0.056 0.000 0.008 0.932 0.004
#> GSM339528 3 0.6901 0.36391 0.300 0.000 0.500 0.028 0.172
#> GSM339529 5 0.5190 -0.09104 0.008 0.424 0.000 0.028 0.540
#> GSM339530 5 0.4058 0.29792 0.000 0.000 0.236 0.024 0.740
#> GSM339531 4 0.7235 0.34931 0.000 0.036 0.216 0.464 0.284
#> GSM339532 4 0.3946 0.54130 0.080 0.000 0.000 0.800 0.120
#> GSM339533 5 0.5807 0.46798 0.004 0.236 0.060 0.040 0.660
#> GSM339534 1 0.6201 0.63074 0.648 0.000 0.196 0.072 0.084
#> GSM339535 2 0.0451 0.78403 0.000 0.988 0.008 0.000 0.004
#> GSM339536 1 0.0451 0.72439 0.988 0.000 0.008 0.000 0.004
#> GSM339537 2 0.0693 0.78394 0.000 0.980 0.000 0.012 0.008
#> GSM339538 3 0.1121 0.62890 0.044 0.000 0.956 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM339455 5 0.7254 -0.0792 0.312 0.000 0.080 0.080 0.464 0.064
#> GSM339456 6 0.7669 -0.1358 0.000 0.188 0.184 0.004 0.300 0.324
#> GSM339457 6 0.5774 0.3075 0.004 0.000 0.216 0.000 0.248 0.532
#> GSM339458 6 0.6048 0.3023 0.000 0.236 0.000 0.020 0.212 0.532
#> GSM339459 5 0.6086 0.2078 0.000 0.000 0.328 0.000 0.388 0.284
#> GSM339460 2 0.3507 0.6819 0.000 0.764 0.000 0.012 0.008 0.216
#> GSM339461 2 0.3858 0.5689 0.000 0.780 0.000 0.004 0.084 0.132
#> GSM339462 1 0.2261 0.7767 0.884 0.000 0.000 0.104 0.004 0.008
#> GSM339463 3 0.5394 0.3955 0.036 0.000 0.508 0.000 0.412 0.044
#> GSM339464 4 0.4697 0.7586 0.004 0.000 0.000 0.688 0.200 0.108
#> GSM339465 5 0.6458 -0.2557 0.176 0.000 0.364 0.000 0.424 0.036
#> GSM339466 2 0.4399 0.2210 0.000 0.516 0.000 0.000 0.024 0.460
#> GSM339467 2 0.4150 0.2854 0.000 0.592 0.000 0.000 0.016 0.392
#> GSM339468 5 0.6613 0.3569 0.004 0.024 0.112 0.044 0.536 0.280
#> GSM339469 4 0.0547 0.7856 0.020 0.000 0.000 0.980 0.000 0.000
#> GSM339470 6 0.4034 0.4363 0.000 0.160 0.036 0.000 0.032 0.772
#> GSM339471 1 0.5696 0.6577 0.640 0.000 0.064 0.072 0.216 0.008
#> GSM339472 2 0.0458 0.7572 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM339473 1 0.1643 0.7653 0.924 0.000 0.008 0.000 0.068 0.000
#> GSM339474 2 0.0000 0.7540 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM339475 3 0.0146 0.7708 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM339476 5 0.7254 -0.0792 0.312 0.000 0.080 0.080 0.464 0.064
#> GSM339477 2 0.3777 0.5700 0.000 0.788 0.000 0.004 0.084 0.124
#> GSM339478 6 0.5774 0.3075 0.004 0.000 0.216 0.000 0.248 0.532
#> GSM339479 6 0.6048 0.3023 0.000 0.236 0.000 0.020 0.212 0.532
#> GSM339480 5 0.6086 0.2078 0.000 0.000 0.328 0.000 0.388 0.284
#> GSM339481 2 0.3161 0.6881 0.000 0.776 0.000 0.000 0.008 0.216
#> GSM339482 3 0.0291 0.7711 0.004 0.000 0.992 0.000 0.004 0.000
#> GSM339483 1 0.2261 0.7767 0.884 0.000 0.000 0.104 0.004 0.008
#> GSM339484 3 0.5394 0.3955 0.036 0.000 0.508 0.000 0.412 0.044
#> GSM339485 4 0.4697 0.7586 0.004 0.000 0.000 0.688 0.200 0.108
#> GSM339486 5 0.6458 -0.2557 0.176 0.000 0.364 0.000 0.424 0.036
#> GSM339487 2 0.4399 0.2210 0.000 0.516 0.000 0.000 0.024 0.460
#> GSM339488 6 0.4261 0.1232 0.000 0.408 0.000 0.000 0.020 0.572
#> GSM339489 5 0.6613 0.3569 0.004 0.024 0.112 0.044 0.536 0.280
#> GSM339490 4 0.0547 0.7856 0.020 0.000 0.000 0.980 0.000 0.000
#> GSM339491 6 0.4034 0.4363 0.000 0.160 0.036 0.000 0.032 0.772
#> GSM339492 1 0.5696 0.6577 0.640 0.000 0.064 0.072 0.216 0.008
#> GSM339493 2 0.0458 0.7572 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM339494 1 0.1643 0.7653 0.924 0.000 0.008 0.000 0.068 0.000
#> GSM339495 2 0.0000 0.7540 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM339496 3 0.0146 0.7708 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM339497 2 0.2912 0.7113 0.000 0.816 0.000 0.000 0.012 0.172
#> GSM339498 6 0.6439 -0.2357 0.004 0.012 0.244 0.000 0.348 0.392
#> GSM339499 6 0.5774 0.3075 0.004 0.000 0.216 0.000 0.248 0.532
#> GSM339500 6 0.6048 0.3023 0.000 0.236 0.000 0.020 0.212 0.532
#> GSM339501 5 0.6079 0.3538 0.000 0.004 0.160 0.044 0.588 0.204
#> GSM339502 2 0.3161 0.6881 0.000 0.776 0.000 0.000 0.008 0.216
#> GSM339503 3 0.0291 0.7711 0.004 0.000 0.992 0.000 0.004 0.000
#> GSM339504 1 0.2261 0.7767 0.884 0.000 0.000 0.104 0.004 0.008
#> GSM339505 6 0.6362 -0.0571 0.004 0.004 0.324 0.000 0.308 0.360
#> GSM339506 4 0.4697 0.7586 0.004 0.000 0.000 0.688 0.200 0.108
#> GSM339507 5 0.6458 -0.2557 0.176 0.000 0.364 0.000 0.424 0.036
#> GSM339508 6 0.5919 -0.1278 0.000 0.424 0.000 0.132 0.016 0.428
#> GSM339509 2 0.4150 0.2854 0.000 0.592 0.000 0.000 0.016 0.392
#> GSM339510 5 0.6613 0.3569 0.004 0.024 0.112 0.044 0.536 0.280
#> GSM339511 4 0.0547 0.7856 0.020 0.000 0.000 0.980 0.000 0.000
#> GSM339512 6 0.4034 0.4363 0.000 0.160 0.036 0.000 0.032 0.772
#> GSM339513 1 0.5696 0.6577 0.640 0.000 0.064 0.072 0.216 0.008
#> GSM339514 2 0.0458 0.7572 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM339515 1 0.1643 0.7653 0.924 0.000 0.008 0.000 0.068 0.000
#> GSM339516 2 0.0622 0.7557 0.000 0.980 0.000 0.000 0.008 0.012
#> GSM339517 3 0.0146 0.7708 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM339518 2 0.2912 0.7113 0.000 0.816 0.000 0.000 0.012 0.172
#> GSM339519 6 0.6146 -0.2385 0.004 0.000 0.244 0.000 0.360 0.392
#> GSM339520 6 0.5774 0.3075 0.004 0.000 0.216 0.000 0.248 0.532
#> GSM339521 6 0.6048 0.3023 0.000 0.236 0.000 0.020 0.212 0.532
#> GSM339522 5 0.6079 0.3538 0.000 0.004 0.160 0.044 0.588 0.204
#> GSM339523 2 0.3161 0.6881 0.000 0.776 0.000 0.000 0.008 0.216
#> GSM339524 3 0.0291 0.7711 0.004 0.000 0.992 0.000 0.004 0.000
#> GSM339525 1 0.2261 0.7767 0.884 0.000 0.000 0.104 0.004 0.008
#> GSM339526 3 0.5394 0.3955 0.036 0.000 0.508 0.000 0.412 0.044
#> GSM339527 4 0.4697 0.7586 0.004 0.000 0.000 0.688 0.200 0.108
#> GSM339528 5 0.6458 -0.2557 0.176 0.000 0.364 0.000 0.424 0.036
#> GSM339529 6 0.5919 -0.1278 0.000 0.424 0.000 0.132 0.016 0.428
#> GSM339530 6 0.4707 0.3628 0.004 0.000 0.092 0.000 0.228 0.676
#> GSM339531 5 0.6613 0.3569 0.004 0.024 0.112 0.044 0.536 0.280
#> GSM339532 4 0.0547 0.7856 0.020 0.000 0.000 0.980 0.000 0.000
#> GSM339533 6 0.4034 0.4363 0.000 0.160 0.036 0.000 0.032 0.772
#> GSM339534 1 0.5696 0.6577 0.640 0.000 0.064 0.072 0.216 0.008
#> GSM339535 2 0.0458 0.7572 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM339536 1 0.1643 0.7653 0.924 0.000 0.008 0.000 0.068 0.000
#> GSM339537 2 0.0622 0.7557 0.000 0.980 0.000 0.000 0.008 0.012
#> GSM339538 3 0.0146 0.7708 0.004 0.000 0.996 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 protocol(p) agent(p) individual(p) k
#> CV:hclust 64 1.000 0.966 1.16e-03 2
#> CV:hclust 58 0.916 0.995 3.57e-05 3
#> CV:hclust 35 0.993 1.000 5.86e-04 4
#> CV:hclust 46 1.000 0.999 4.30e-06 5
#> CV:hclust 43 0.989 1.000 6.16e-06 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 15497 rows and 84 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 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 0.927 0.939 0.965 0.5038 0.497 0.497
#> 3 3 0.604 0.689 0.828 0.2877 0.755 0.544
#> 4 4 0.548 0.689 0.733 0.1195 0.915 0.765
#> 5 5 0.589 0.493 0.651 0.0675 0.982 0.940
#> 6 6 0.611 0.389 0.571 0.0461 0.859 0.541
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
#> GSM339455 1 0.0000 0.974 1.000 0.000
#> GSM339456 2 0.0000 0.956 0.000 1.000
#> GSM339457 2 0.6887 0.817 0.184 0.816
#> GSM339458 2 0.1414 0.957 0.020 0.980
#> GSM339459 2 0.8661 0.617 0.288 0.712
#> GSM339460 2 0.0672 0.957 0.008 0.992
#> GSM339461 2 0.0000 0.956 0.000 1.000
#> GSM339462 1 0.2236 0.965 0.964 0.036
#> GSM339463 1 0.0672 0.971 0.992 0.008
#> GSM339464 1 0.2423 0.963 0.960 0.040
#> GSM339465 1 0.0000 0.974 1.000 0.000
#> GSM339466 2 0.0672 0.957 0.008 0.992
#> GSM339467 2 0.1843 0.955 0.028 0.972
#> GSM339468 2 0.2043 0.941 0.032 0.968
#> GSM339469 1 0.2236 0.965 0.964 0.036
#> GSM339470 2 0.2043 0.953 0.032 0.968
#> GSM339471 1 0.0000 0.974 1.000 0.000
#> GSM339472 2 0.0000 0.956 0.000 1.000
#> GSM339473 1 0.0000 0.974 1.000 0.000
#> GSM339474 2 0.0000 0.956 0.000 1.000
#> GSM339475 1 0.0672 0.971 0.992 0.008
#> GSM339476 1 0.0000 0.974 1.000 0.000
#> GSM339477 2 0.0000 0.956 0.000 1.000
#> GSM339478 2 0.2423 0.948 0.040 0.960
#> GSM339479 2 0.1414 0.957 0.020 0.980
#> GSM339480 2 0.8661 0.617 0.288 0.712
#> GSM339481 2 0.0000 0.956 0.000 1.000
#> GSM339482 1 0.0000 0.974 1.000 0.000
#> GSM339483 1 0.2236 0.965 0.964 0.036
#> GSM339484 1 0.0000 0.974 1.000 0.000
#> GSM339485 1 0.2423 0.963 0.960 0.040
#> GSM339486 1 0.0000 0.974 1.000 0.000
#> GSM339487 2 0.0672 0.957 0.008 0.992
#> GSM339488 2 0.1843 0.955 0.028 0.972
#> GSM339489 2 0.2043 0.941 0.032 0.968
#> GSM339490 1 0.2236 0.965 0.964 0.036
#> GSM339491 2 0.1843 0.955 0.028 0.972
#> GSM339492 1 0.0000 0.974 1.000 0.000
#> GSM339493 2 0.0000 0.956 0.000 1.000
#> GSM339494 1 0.0000 0.974 1.000 0.000
#> GSM339495 2 0.0000 0.956 0.000 1.000
#> GSM339496 1 0.0672 0.971 0.992 0.008
#> GSM339497 2 0.1414 0.957 0.020 0.980
#> GSM339498 2 0.6623 0.801 0.172 0.828
#> GSM339499 2 0.6887 0.817 0.184 0.816
#> GSM339500 2 0.1414 0.957 0.020 0.980
#> GSM339501 1 0.2236 0.965 0.964 0.036
#> GSM339502 2 0.1843 0.955 0.028 0.972
#> GSM339503 1 0.2948 0.944 0.948 0.052
#> GSM339504 1 0.2236 0.965 0.964 0.036
#> GSM339505 2 0.2236 0.950 0.036 0.964
#> GSM339506 1 0.2423 0.963 0.960 0.040
#> GSM339507 1 0.0000 0.974 1.000 0.000
#> GSM339508 2 0.0000 0.956 0.000 1.000
#> GSM339509 2 0.1843 0.955 0.028 0.972
#> GSM339510 2 0.2043 0.941 0.032 0.968
#> GSM339511 1 0.9710 0.382 0.600 0.400
#> GSM339512 2 0.1843 0.955 0.028 0.972
#> GSM339513 1 0.0000 0.974 1.000 0.000
#> GSM339514 2 0.1843 0.955 0.028 0.972
#> GSM339515 1 0.0000 0.974 1.000 0.000
#> GSM339516 2 0.0000 0.956 0.000 1.000
#> GSM339517 1 0.2948 0.944 0.948 0.052
#> GSM339518 2 0.1414 0.957 0.020 0.980
#> GSM339519 1 0.0672 0.972 0.992 0.008
#> GSM339520 2 0.2423 0.948 0.040 0.960
#> GSM339521 2 0.0672 0.957 0.008 0.992
#> GSM339522 2 0.0000 0.956 0.000 1.000
#> GSM339523 2 0.0672 0.957 0.008 0.992
#> GSM339524 1 0.0672 0.972 0.992 0.008
#> GSM339525 1 0.2236 0.965 0.964 0.036
#> GSM339526 1 0.0000 0.974 1.000 0.000
#> GSM339527 1 0.2423 0.963 0.960 0.040
#> GSM339528 1 0.0000 0.974 1.000 0.000
#> GSM339529 2 0.0000 0.956 0.000 1.000
#> GSM339530 2 0.6887 0.817 0.184 0.816
#> GSM339531 2 0.2043 0.941 0.032 0.968
#> GSM339532 1 0.2778 0.958 0.952 0.048
#> GSM339533 1 0.0672 0.971 0.992 0.008
#> GSM339534 1 0.0000 0.974 1.000 0.000
#> GSM339535 2 0.1843 0.955 0.028 0.972
#> GSM339536 1 0.0000 0.974 1.000 0.000
#> GSM339537 2 0.0000 0.956 0.000 1.000
#> GSM339538 1 0.0672 0.972 0.992 0.008
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM339455 3 0.6359 0.694 0.404 0.004 0.592
#> GSM339456 2 0.3116 0.892 0.000 0.892 0.108
#> GSM339457 3 0.8576 0.693 0.240 0.160 0.600
#> GSM339458 2 0.1765 0.936 0.004 0.956 0.040
#> GSM339459 3 0.7192 0.538 0.120 0.164 0.716
#> GSM339460 2 0.0747 0.949 0.000 0.984 0.016
#> GSM339461 2 0.1964 0.927 0.000 0.944 0.056
#> GSM339462 1 0.6081 0.668 0.652 0.004 0.344
#> GSM339463 3 0.6398 0.693 0.416 0.004 0.580
#> GSM339464 1 0.6701 0.652 0.576 0.012 0.412
#> GSM339465 3 0.6244 0.672 0.440 0.000 0.560
#> GSM339466 2 0.0237 0.950 0.000 0.996 0.004
#> GSM339467 2 0.1765 0.942 0.004 0.956 0.040
#> GSM339468 2 0.5223 0.800 0.024 0.800 0.176
#> GSM339469 1 0.6434 0.662 0.612 0.008 0.380
#> GSM339470 3 0.6633 0.340 0.008 0.444 0.548
#> GSM339471 1 0.2537 0.502 0.920 0.000 0.080
#> GSM339472 2 0.0237 0.950 0.000 0.996 0.004
#> GSM339473 1 0.0747 0.554 0.984 0.000 0.016
#> GSM339474 2 0.0000 0.950 0.000 1.000 0.000
#> GSM339475 3 0.6386 0.695 0.412 0.004 0.584
#> GSM339476 1 0.2711 0.554 0.912 0.000 0.088
#> GSM339477 2 0.2625 0.907 0.000 0.916 0.084
#> GSM339478 3 0.8675 0.661 0.184 0.220 0.596
#> GSM339479 2 0.1765 0.936 0.004 0.956 0.040
#> GSM339480 3 0.7192 0.538 0.120 0.164 0.716
#> GSM339481 2 0.0000 0.950 0.000 1.000 0.000
#> GSM339482 3 0.6192 0.687 0.420 0.000 0.580
#> GSM339483 1 0.6081 0.668 0.652 0.004 0.344
#> GSM339484 1 0.6252 -0.501 0.556 0.000 0.444
#> GSM339485 1 0.6701 0.652 0.576 0.012 0.412
#> GSM339486 1 0.6252 -0.498 0.556 0.000 0.444
#> GSM339487 2 0.0000 0.950 0.000 1.000 0.000
#> GSM339488 2 0.1765 0.942 0.004 0.956 0.040
#> GSM339489 2 0.4602 0.836 0.016 0.832 0.152
#> GSM339490 1 0.6483 0.661 0.600 0.008 0.392
#> GSM339491 3 0.6664 0.289 0.008 0.464 0.528
#> GSM339492 1 0.2537 0.502 0.920 0.000 0.080
#> GSM339493 2 0.0237 0.950 0.000 0.996 0.004
#> GSM339494 1 0.0747 0.554 0.984 0.000 0.016
#> GSM339495 2 0.0892 0.946 0.000 0.980 0.020
#> GSM339496 3 0.6373 0.697 0.408 0.004 0.588
#> GSM339497 2 0.0592 0.949 0.000 0.988 0.012
#> GSM339498 3 0.6684 0.449 0.032 0.292 0.676
#> GSM339499 3 0.8576 0.693 0.240 0.160 0.600
#> GSM339500 2 0.1765 0.936 0.004 0.956 0.040
#> GSM339501 1 0.6540 0.657 0.584 0.008 0.408
#> GSM339502 2 0.1647 0.944 0.004 0.960 0.036
#> GSM339503 3 0.6737 0.673 0.384 0.016 0.600
#> GSM339504 1 0.6081 0.668 0.652 0.004 0.344
#> GSM339505 3 0.8872 0.612 0.152 0.296 0.552
#> GSM339506 1 0.6724 0.651 0.568 0.012 0.420
#> GSM339507 1 0.6252 -0.503 0.556 0.000 0.444
#> GSM339508 2 0.2066 0.940 0.000 0.940 0.060
#> GSM339509 2 0.1765 0.942 0.004 0.956 0.040
#> GSM339510 2 0.4934 0.819 0.024 0.820 0.156
#> GSM339511 1 0.8649 0.589 0.528 0.112 0.360
#> GSM339512 2 0.1399 0.946 0.004 0.968 0.028
#> GSM339513 1 0.1643 0.528 0.956 0.000 0.044
#> GSM339514 2 0.1647 0.944 0.004 0.960 0.036
#> GSM339515 1 0.0747 0.554 0.984 0.000 0.016
#> GSM339516 2 0.0892 0.946 0.000 0.980 0.020
#> GSM339517 3 0.6701 0.688 0.412 0.012 0.576
#> GSM339518 2 0.0592 0.949 0.000 0.988 0.012
#> GSM339519 3 0.6398 0.665 0.416 0.004 0.580
#> GSM339520 3 0.8675 0.661 0.184 0.220 0.596
#> GSM339521 2 0.0424 0.950 0.000 0.992 0.008
#> GSM339522 2 0.1031 0.945 0.000 0.976 0.024
#> GSM339523 2 0.1411 0.945 0.000 0.964 0.036
#> GSM339524 3 0.6386 0.662 0.412 0.004 0.584
#> GSM339525 1 0.6081 0.668 0.652 0.004 0.344
#> GSM339526 3 0.6215 0.685 0.428 0.000 0.572
#> GSM339527 1 0.6724 0.651 0.568 0.012 0.420
#> GSM339528 1 0.6252 -0.498 0.556 0.000 0.444
#> GSM339529 2 0.2066 0.940 0.000 0.940 0.060
#> GSM339530 3 0.8544 0.694 0.248 0.152 0.600
#> GSM339531 2 0.4602 0.836 0.016 0.832 0.152
#> GSM339532 1 0.6832 0.658 0.604 0.020 0.376
#> GSM339533 3 0.6553 0.696 0.412 0.008 0.580
#> GSM339534 1 0.2625 0.497 0.916 0.000 0.084
#> GSM339535 2 0.0829 0.949 0.004 0.984 0.012
#> GSM339536 1 0.0747 0.554 0.984 0.000 0.016
#> GSM339537 2 0.0892 0.946 0.000 0.980 0.020
#> GSM339538 3 0.6235 0.672 0.436 0.000 0.564
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM339455 3 0.5674 0.602 0.132 0.000 0.720 0.148
#> GSM339456 2 0.3245 0.817 0.028 0.884 0.008 0.080
#> GSM339457 3 0.2441 0.633 0.056 0.020 0.920 0.004
#> GSM339458 2 0.8120 0.585 0.116 0.564 0.232 0.088
#> GSM339459 3 0.8837 0.445 0.160 0.108 0.492 0.240
#> GSM339460 2 0.4889 0.827 0.088 0.808 0.080 0.024
#> GSM339461 2 0.2896 0.840 0.056 0.904 0.008 0.032
#> GSM339462 4 0.4594 0.652 0.280 0.000 0.008 0.712
#> GSM339463 3 0.5442 0.614 0.164 0.008 0.748 0.080
#> GSM339464 4 0.0657 0.697 0.012 0.004 0.000 0.984
#> GSM339465 3 0.6625 0.381 0.380 0.004 0.540 0.076
#> GSM339466 2 0.2385 0.846 0.052 0.920 0.028 0.000
#> GSM339467 2 0.4568 0.802 0.076 0.800 0.124 0.000
#> GSM339468 2 0.6983 0.635 0.076 0.640 0.048 0.236
#> GSM339469 4 0.4012 0.715 0.184 0.000 0.016 0.800
#> GSM339470 3 0.6256 0.521 0.072 0.216 0.688 0.024
#> GSM339471 1 0.6651 0.853 0.616 0.000 0.148 0.236
#> GSM339472 2 0.0592 0.848 0.016 0.984 0.000 0.000
#> GSM339473 1 0.5444 0.863 0.688 0.000 0.048 0.264
#> GSM339474 2 0.1151 0.848 0.024 0.968 0.000 0.008
#> GSM339475 3 0.4955 0.629 0.268 0.000 0.708 0.024
#> GSM339476 4 0.6025 0.291 0.172 0.000 0.140 0.688
#> GSM339477 2 0.2635 0.823 0.016 0.908 0.004 0.072
#> GSM339478 3 0.2706 0.628 0.064 0.024 0.908 0.004
#> GSM339479 2 0.8120 0.585 0.116 0.564 0.232 0.088
#> GSM339480 3 0.8837 0.445 0.160 0.108 0.492 0.240
#> GSM339481 2 0.0817 0.850 0.024 0.976 0.000 0.000
#> GSM339482 3 0.5366 0.624 0.276 0.000 0.684 0.040
#> GSM339483 4 0.4594 0.652 0.280 0.000 0.008 0.712
#> GSM339484 3 0.7002 0.328 0.352 0.000 0.520 0.128
#> GSM339485 4 0.0657 0.697 0.012 0.004 0.000 0.984
#> GSM339486 3 0.6894 0.305 0.376 0.000 0.512 0.112
#> GSM339487 2 0.2385 0.846 0.052 0.920 0.028 0.000
#> GSM339488 2 0.4568 0.802 0.076 0.800 0.124 0.000
#> GSM339489 2 0.6830 0.655 0.072 0.656 0.048 0.224
#> GSM339490 4 0.3725 0.720 0.180 0.000 0.008 0.812
#> GSM339491 3 0.6321 0.513 0.072 0.224 0.680 0.024
#> GSM339492 1 0.6651 0.853 0.616 0.000 0.148 0.236
#> GSM339493 2 0.0592 0.848 0.016 0.984 0.000 0.000
#> GSM339494 1 0.5444 0.863 0.688 0.000 0.048 0.264
#> GSM339495 2 0.1151 0.847 0.024 0.968 0.000 0.008
#> GSM339496 3 0.4955 0.629 0.268 0.000 0.708 0.024
#> GSM339497 2 0.4983 0.822 0.088 0.808 0.064 0.040
#> GSM339498 3 0.8943 0.434 0.132 0.172 0.496 0.200
#> GSM339499 3 0.2441 0.633 0.056 0.020 0.920 0.004
#> GSM339500 2 0.7162 0.662 0.100 0.632 0.224 0.044
#> GSM339501 4 0.4786 0.620 0.132 0.008 0.064 0.796
#> GSM339502 2 0.4426 0.813 0.096 0.812 0.092 0.000
#> GSM339503 3 0.6326 0.609 0.256 0.000 0.636 0.108
#> GSM339504 4 0.4594 0.652 0.280 0.000 0.008 0.712
#> GSM339505 3 0.4050 0.611 0.036 0.144 0.820 0.000
#> GSM339506 4 0.3110 0.638 0.056 0.004 0.048 0.892
#> GSM339507 3 0.6840 0.316 0.372 0.000 0.520 0.108
#> GSM339508 2 0.5424 0.791 0.076 0.784 0.092 0.048
#> GSM339509 2 0.4621 0.800 0.076 0.796 0.128 0.000
#> GSM339510 2 0.6967 0.636 0.080 0.640 0.044 0.236
#> GSM339511 4 0.4999 0.699 0.172 0.044 0.012 0.772
#> GSM339512 2 0.4083 0.830 0.068 0.832 0.100 0.000
#> GSM339513 1 0.6400 0.857 0.632 0.000 0.116 0.252
#> GSM339514 2 0.3679 0.827 0.060 0.856 0.084 0.000
#> GSM339515 1 0.5444 0.863 0.688 0.000 0.048 0.264
#> GSM339516 2 0.1256 0.847 0.028 0.964 0.000 0.008
#> GSM339517 3 0.5835 0.618 0.280 0.000 0.656 0.064
#> GSM339518 2 0.3754 0.837 0.084 0.852 0.064 0.000
#> GSM339519 3 0.6245 0.606 0.268 0.000 0.636 0.096
#> GSM339520 3 0.2706 0.628 0.064 0.024 0.908 0.004
#> GSM339521 2 0.3617 0.838 0.076 0.860 0.064 0.000
#> GSM339522 2 0.4041 0.827 0.060 0.856 0.024 0.060
#> GSM339523 2 0.4297 0.816 0.096 0.820 0.084 0.000
#> GSM339524 3 0.6664 0.593 0.272 0.000 0.600 0.128
#> GSM339525 4 0.4594 0.652 0.280 0.000 0.008 0.712
#> GSM339526 3 0.4776 0.628 0.272 0.000 0.712 0.016
#> GSM339527 4 0.3110 0.638 0.056 0.004 0.048 0.892
#> GSM339528 3 0.6979 0.291 0.376 0.000 0.504 0.120
#> GSM339529 2 0.5424 0.791 0.076 0.784 0.092 0.048
#> GSM339530 3 0.2821 0.626 0.076 0.020 0.900 0.004
#> GSM339531 2 0.6893 0.650 0.076 0.652 0.048 0.224
#> GSM339532 4 0.4132 0.718 0.176 0.008 0.012 0.804
#> GSM339533 3 0.4512 0.636 0.148 0.008 0.804 0.040
#> GSM339534 1 0.6651 0.853 0.616 0.000 0.148 0.236
#> GSM339535 2 0.1624 0.848 0.020 0.952 0.028 0.000
#> GSM339536 1 0.5444 0.863 0.688 0.000 0.048 0.264
#> GSM339537 2 0.1256 0.847 0.028 0.964 0.000 0.008
#> GSM339538 3 0.5859 0.613 0.284 0.000 0.652 0.064
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM339455 3 0.774 0.449 0.112 0.004 0.436 0.116 0.332
#> GSM339456 2 0.550 0.471 0.028 0.740 0.040 0.056 0.136
#> GSM339457 3 0.552 0.516 0.052 0.000 0.552 0.008 0.388
#> GSM339458 5 0.729 1.000 0.044 0.412 0.036 0.072 0.436
#> GSM339459 3 0.753 0.345 0.056 0.072 0.580 0.196 0.096
#> GSM339460 2 0.554 0.194 0.028 0.688 0.012 0.048 0.224
#> GSM339461 2 0.320 0.488 0.020 0.876 0.012 0.020 0.072
#> GSM339462 4 0.556 0.622 0.320 0.000 0.036 0.612 0.032
#> GSM339463 3 0.618 0.547 0.104 0.000 0.588 0.024 0.284
#> GSM339464 4 0.207 0.676 0.016 0.004 0.008 0.928 0.044
#> GSM339465 3 0.705 0.268 0.380 0.000 0.412 0.024 0.184
#> GSM339466 2 0.247 0.495 0.000 0.896 0.008 0.012 0.084
#> GSM339467 2 0.508 0.261 0.020 0.508 0.008 0.000 0.464
#> GSM339468 2 0.738 0.188 0.036 0.584 0.068 0.192 0.120
#> GSM339469 4 0.432 0.696 0.208 0.000 0.004 0.748 0.040
#> GSM339470 3 0.703 0.310 0.028 0.124 0.484 0.012 0.352
#> GSM339471 1 0.533 0.848 0.724 0.000 0.124 0.120 0.032
#> GSM339472 2 0.252 0.545 0.012 0.880 0.000 0.000 0.108
#> GSM339473 1 0.327 0.864 0.848 0.000 0.056 0.096 0.000
#> GSM339474 2 0.146 0.543 0.016 0.952 0.000 0.004 0.028
#> GSM339475 3 0.268 0.582 0.100 0.000 0.880 0.004 0.016
#> GSM339476 4 0.727 0.243 0.208 0.000 0.148 0.544 0.100
#> GSM339477 2 0.414 0.520 0.024 0.820 0.008 0.048 0.100
#> GSM339478 3 0.555 0.499 0.052 0.000 0.532 0.008 0.408
#> GSM339479 5 0.729 1.000 0.044 0.412 0.036 0.072 0.436
#> GSM339480 3 0.753 0.345 0.056 0.072 0.580 0.196 0.096
#> GSM339481 2 0.230 0.525 0.008 0.892 0.000 0.000 0.100
#> GSM339482 3 0.251 0.578 0.088 0.000 0.892 0.016 0.004
#> GSM339483 4 0.556 0.622 0.320 0.000 0.036 0.612 0.032
#> GSM339484 3 0.694 0.338 0.320 0.000 0.476 0.024 0.180
#> GSM339485 4 0.217 0.678 0.020 0.004 0.008 0.924 0.044
#> GSM339486 3 0.703 0.256 0.384 0.000 0.412 0.024 0.180
#> GSM339487 2 0.247 0.495 0.000 0.896 0.008 0.012 0.084
#> GSM339488 2 0.490 0.260 0.012 0.516 0.008 0.000 0.464
#> GSM339489 2 0.737 0.188 0.036 0.584 0.068 0.196 0.116
#> GSM339490 4 0.432 0.696 0.208 0.000 0.004 0.748 0.040
#> GSM339491 3 0.708 0.291 0.028 0.132 0.480 0.012 0.348
#> GSM339492 1 0.537 0.846 0.720 0.000 0.128 0.120 0.032
#> GSM339493 2 0.256 0.540 0.008 0.872 0.000 0.000 0.120
#> GSM339494 1 0.327 0.864 0.848 0.000 0.056 0.096 0.000
#> GSM339495 2 0.146 0.542 0.016 0.952 0.000 0.004 0.028
#> GSM339496 3 0.262 0.583 0.096 0.000 0.884 0.004 0.016
#> GSM339497 2 0.508 0.287 0.024 0.740 0.012 0.048 0.176
#> GSM339498 3 0.796 0.268 0.036 0.148 0.536 0.168 0.112
#> GSM339499 3 0.552 0.512 0.052 0.000 0.548 0.008 0.392
#> GSM339500 2 0.645 -0.633 0.024 0.540 0.032 0.044 0.360
#> GSM339501 4 0.589 0.531 0.044 0.020 0.120 0.712 0.104
#> GSM339502 2 0.469 0.302 0.016 0.560 0.000 0.000 0.424
#> GSM339503 3 0.348 0.558 0.052 0.004 0.860 0.064 0.020
#> GSM339504 4 0.554 0.625 0.316 0.000 0.036 0.616 0.032
#> GSM339505 3 0.596 0.503 0.024 0.072 0.632 0.008 0.264
#> GSM339506 4 0.315 0.647 0.012 0.004 0.056 0.876 0.052
#> GSM339507 3 0.703 0.254 0.380 0.000 0.416 0.024 0.180
#> GSM339508 2 0.585 0.348 0.020 0.584 0.012 0.040 0.344
#> GSM339509 2 0.508 0.261 0.020 0.508 0.008 0.000 0.464
#> GSM339510 2 0.724 0.193 0.032 0.592 0.064 0.196 0.116
#> GSM339511 4 0.471 0.694 0.188 0.020 0.000 0.744 0.048
#> GSM339512 2 0.487 0.255 0.004 0.624 0.020 0.004 0.348
#> GSM339513 1 0.525 0.849 0.724 0.000 0.128 0.124 0.024
#> GSM339514 2 0.411 0.421 0.008 0.684 0.000 0.000 0.308
#> GSM339515 1 0.327 0.864 0.848 0.000 0.056 0.096 0.000
#> GSM339516 2 0.170 0.532 0.016 0.944 0.000 0.012 0.028
#> GSM339517 3 0.262 0.578 0.052 0.000 0.900 0.036 0.012
#> GSM339518 2 0.455 0.337 0.024 0.772 0.012 0.024 0.168
#> GSM339519 3 0.354 0.564 0.088 0.000 0.848 0.044 0.020
#> GSM339520 3 0.555 0.499 0.052 0.000 0.532 0.008 0.408
#> GSM339521 2 0.391 0.386 0.012 0.796 0.008 0.012 0.172
#> GSM339522 2 0.435 0.404 0.020 0.800 0.004 0.064 0.112
#> GSM339523 2 0.467 0.313 0.016 0.572 0.000 0.000 0.412
#> GSM339524 3 0.401 0.550 0.096 0.000 0.820 0.060 0.024
#> GSM339525 4 0.550 0.617 0.324 0.000 0.032 0.612 0.032
#> GSM339526 3 0.252 0.583 0.100 0.000 0.884 0.000 0.016
#> GSM339527 4 0.315 0.647 0.012 0.004 0.056 0.876 0.052
#> GSM339528 3 0.703 0.256 0.384 0.000 0.412 0.024 0.180
#> GSM339529 2 0.585 0.348 0.020 0.584 0.012 0.040 0.344
#> GSM339530 3 0.555 0.460 0.056 0.000 0.476 0.004 0.464
#> GSM339531 2 0.738 0.188 0.036 0.584 0.068 0.192 0.120
#> GSM339532 4 0.444 0.697 0.204 0.004 0.004 0.748 0.040
#> GSM339533 3 0.577 0.567 0.088 0.000 0.624 0.016 0.272
#> GSM339534 1 0.543 0.829 0.720 0.000 0.120 0.120 0.040
#> GSM339535 2 0.281 0.527 0.004 0.844 0.000 0.000 0.152
#> GSM339536 1 0.327 0.864 0.848 0.000 0.056 0.096 0.000
#> GSM339537 2 0.118 0.538 0.016 0.964 0.000 0.004 0.016
#> GSM339538 3 0.281 0.574 0.084 0.000 0.880 0.032 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM339455 5 0.7674 -0.30112 0.156 0.000 0.268 0.012 0.380 0.184
#> GSM339456 2 0.4466 0.38792 0.004 0.716 0.000 0.000 0.180 0.100
#> GSM339457 3 0.6962 0.46718 0.064 0.004 0.464 0.008 0.160 0.300
#> GSM339458 5 0.7366 0.09697 0.096 0.244 0.008 0.000 0.404 0.248
#> GSM339459 3 0.5796 0.14657 0.016 0.048 0.520 0.012 0.388 0.016
#> GSM339460 2 0.6293 0.38411 0.036 0.520 0.000 0.000 0.232 0.212
#> GSM339461 2 0.3134 0.50240 0.000 0.808 0.000 0.000 0.168 0.024
#> GSM339462 4 0.5121 0.60408 0.192 0.000 0.028 0.700 0.056 0.024
#> GSM339463 3 0.7097 0.24192 0.152 0.000 0.452 0.000 0.252 0.144
#> GSM339464 4 0.4319 0.64805 0.040 0.000 0.000 0.736 0.196 0.028
#> GSM339465 1 0.7173 0.29414 0.412 0.000 0.276 0.000 0.204 0.108
#> GSM339466 2 0.3563 0.55837 0.012 0.808 0.000 0.000 0.132 0.048
#> GSM339467 6 0.3881 0.60138 0.004 0.396 0.000 0.000 0.000 0.600
#> GSM339468 5 0.5287 0.29943 0.000 0.420 0.032 0.012 0.516 0.020
#> GSM339469 4 0.0405 0.70637 0.000 0.000 0.000 0.988 0.008 0.004
#> GSM339470 3 0.7930 0.30905 0.052 0.088 0.356 0.000 0.204 0.300
#> GSM339471 1 0.6897 0.48679 0.532 0.000 0.112 0.248 0.036 0.072
#> GSM339472 2 0.3580 0.39477 0.004 0.772 0.000 0.000 0.028 0.196
#> GSM339473 1 0.3915 0.49072 0.756 0.000 0.052 0.188 0.000 0.004
#> GSM339474 2 0.0951 0.55285 0.008 0.968 0.000 0.000 0.004 0.020
#> GSM339475 3 0.1390 0.57830 0.032 0.000 0.948 0.000 0.004 0.016
#> GSM339476 4 0.8220 0.03199 0.188 0.000 0.108 0.404 0.200 0.100
#> GSM339477 2 0.3260 0.48863 0.004 0.832 0.000 0.000 0.092 0.072
#> GSM339478 3 0.6962 0.46718 0.064 0.004 0.464 0.008 0.160 0.300
#> GSM339479 5 0.7366 0.09697 0.096 0.244 0.008 0.000 0.404 0.248
#> GSM339480 3 0.5796 0.14657 0.016 0.048 0.520 0.012 0.388 0.016
#> GSM339481 2 0.3091 0.48822 0.004 0.824 0.000 0.000 0.024 0.148
#> GSM339482 3 0.2034 0.58129 0.024 0.000 0.912 0.000 0.060 0.004
#> GSM339483 4 0.5121 0.60408 0.192 0.000 0.028 0.700 0.056 0.024
#> GSM339484 1 0.7284 0.19260 0.360 0.000 0.356 0.008 0.184 0.092
#> GSM339485 4 0.4289 0.65035 0.040 0.000 0.000 0.740 0.192 0.028
#> GSM339486 1 0.7343 0.32200 0.420 0.000 0.268 0.008 0.196 0.108
#> GSM339487 2 0.3563 0.55837 0.012 0.808 0.000 0.000 0.132 0.048
#> GSM339488 6 0.3890 0.60095 0.004 0.400 0.000 0.000 0.000 0.596
#> GSM339489 5 0.5232 0.29186 0.000 0.428 0.028 0.012 0.512 0.020
#> GSM339490 4 0.0405 0.70637 0.000 0.000 0.000 0.988 0.008 0.004
#> GSM339491 3 0.7930 0.30905 0.052 0.088 0.356 0.000 0.204 0.300
#> GSM339492 1 0.6897 0.48679 0.532 0.000 0.112 0.248 0.036 0.072
#> GSM339493 2 0.3187 0.41491 0.004 0.796 0.000 0.000 0.012 0.188
#> GSM339494 1 0.3915 0.49072 0.756 0.000 0.052 0.188 0.000 0.004
#> GSM339495 2 0.0951 0.55285 0.008 0.968 0.000 0.000 0.004 0.020
#> GSM339496 3 0.1390 0.57830 0.032 0.000 0.948 0.000 0.004 0.016
#> GSM339497 2 0.5979 0.33837 0.036 0.560 0.000 0.000 0.264 0.140
#> GSM339498 5 0.6015 -0.02256 0.000 0.116 0.396 0.008 0.464 0.016
#> GSM339499 3 0.6962 0.46718 0.064 0.004 0.464 0.008 0.160 0.300
#> GSM339500 2 0.7027 -0.00327 0.048 0.376 0.008 0.000 0.332 0.236
#> GSM339501 5 0.6906 -0.18057 0.020 0.040 0.108 0.352 0.464 0.016
#> GSM339502 6 0.4433 0.53735 0.008 0.416 0.000 0.000 0.016 0.560
#> GSM339503 3 0.2312 0.57684 0.012 0.000 0.876 0.000 0.112 0.000
#> GSM339504 4 0.5121 0.60408 0.192 0.000 0.028 0.700 0.056 0.024
#> GSM339505 3 0.7302 0.44695 0.048 0.084 0.512 0.000 0.156 0.200
#> GSM339506 4 0.5720 0.57772 0.052 0.000 0.024 0.592 0.300 0.032
#> GSM339507 1 0.7327 0.30993 0.416 0.000 0.284 0.008 0.184 0.108
#> GSM339508 2 0.5597 -0.23559 0.016 0.508 0.000 0.044 0.024 0.408
#> GSM339509 6 0.3881 0.60138 0.004 0.396 0.000 0.000 0.000 0.600
#> GSM339510 5 0.5084 0.28083 0.000 0.436 0.028 0.012 0.512 0.012
#> GSM339511 4 0.1262 0.70006 0.000 0.020 0.000 0.956 0.016 0.008
#> GSM339512 2 0.5555 -0.03750 0.004 0.492 0.008 0.000 0.092 0.404
#> GSM339513 1 0.6860 0.47642 0.532 0.000 0.128 0.244 0.032 0.064
#> GSM339514 2 0.4070 -0.27498 0.004 0.568 0.000 0.000 0.004 0.424
#> GSM339515 1 0.3915 0.49072 0.756 0.000 0.052 0.188 0.000 0.004
#> GSM339516 2 0.1230 0.56607 0.008 0.956 0.000 0.000 0.028 0.008
#> GSM339517 3 0.1624 0.58656 0.012 0.000 0.936 0.000 0.044 0.008
#> GSM339518 2 0.5719 0.40410 0.032 0.600 0.000 0.000 0.236 0.132
#> GSM339519 3 0.3463 0.55917 0.032 0.000 0.800 0.000 0.160 0.008
#> GSM339520 3 0.6962 0.46718 0.064 0.004 0.464 0.008 0.160 0.300
#> GSM339521 2 0.5584 0.44394 0.028 0.620 0.000 0.000 0.212 0.140
#> GSM339522 2 0.4538 0.26788 0.020 0.660 0.004 0.000 0.296 0.020
#> GSM339523 6 0.4457 0.50686 0.008 0.432 0.000 0.000 0.016 0.544
#> GSM339524 3 0.2939 0.55770 0.044 0.000 0.864 0.004 0.080 0.008
#> GSM339525 4 0.5076 0.60311 0.196 0.000 0.024 0.700 0.056 0.024
#> GSM339526 3 0.1974 0.56827 0.048 0.000 0.920 0.000 0.020 0.012
#> GSM339527 4 0.5720 0.57772 0.052 0.000 0.024 0.592 0.300 0.032
#> GSM339528 1 0.7343 0.32200 0.420 0.000 0.268 0.008 0.196 0.108
#> GSM339529 2 0.5597 -0.23559 0.016 0.508 0.000 0.044 0.024 0.408
#> GSM339530 6 0.6387 -0.50739 0.060 0.000 0.412 0.004 0.096 0.428
#> GSM339531 5 0.5235 0.28825 0.000 0.432 0.028 0.012 0.508 0.020
#> GSM339532 4 0.0551 0.70625 0.000 0.004 0.000 0.984 0.008 0.004
#> GSM339533 3 0.6841 0.34392 0.128 0.000 0.504 0.000 0.216 0.152
#> GSM339534 1 0.6996 0.48065 0.528 0.000 0.104 0.248 0.048 0.072
#> GSM339535 2 0.3481 0.36744 0.004 0.756 0.000 0.000 0.012 0.228
#> GSM339536 1 0.3915 0.49072 0.756 0.000 0.052 0.188 0.000 0.004
#> GSM339537 2 0.0976 0.56383 0.008 0.968 0.000 0.000 0.016 0.008
#> GSM339538 3 0.1930 0.57928 0.028 0.000 0.924 0.000 0.036 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 protocol(p) agent(p) individual(p) k
#> CV:kmeans 83 1.000 0.703 1.57e-03 2
#> CV:kmeans 76 0.953 0.846 4.54e-05 3
#> CV:kmeans 75 0.984 0.986 6.91e-08 4
#> CV:kmeans 46 0.377 0.854 7.15e-06 5
#> CV:kmeans 33 0.483 0.889 1.90e-04 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 15497 rows and 84 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 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 0.926 0.945 0.977 0.5047 0.497 0.497
#> 3 3 0.709 0.756 0.892 0.3192 0.742 0.526
#> 4 4 0.654 0.678 0.785 0.1062 0.913 0.751
#> 5 5 0.642 0.557 0.715 0.0695 0.880 0.610
#> 6 6 0.650 0.530 0.671 0.0453 0.944 0.761
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
#> GSM339455 1 0.0000 0.988 1.000 0.000
#> GSM339456 2 0.0000 0.965 0.000 1.000
#> GSM339457 2 0.7219 0.761 0.200 0.800
#> GSM339458 2 0.0000 0.965 0.000 1.000
#> GSM339459 2 0.9686 0.393 0.396 0.604
#> GSM339460 2 0.0000 0.965 0.000 1.000
#> GSM339461 2 0.0000 0.965 0.000 1.000
#> GSM339462 1 0.0000 0.988 1.000 0.000
#> GSM339463 1 0.0000 0.988 1.000 0.000
#> GSM339464 1 0.0000 0.988 1.000 0.000
#> GSM339465 1 0.0000 0.988 1.000 0.000
#> GSM339466 2 0.0000 0.965 0.000 1.000
#> GSM339467 2 0.0000 0.965 0.000 1.000
#> GSM339468 2 0.0376 0.962 0.004 0.996
#> GSM339469 1 0.0000 0.988 1.000 0.000
#> GSM339470 2 0.0000 0.965 0.000 1.000
#> GSM339471 1 0.0000 0.988 1.000 0.000
#> GSM339472 2 0.0000 0.965 0.000 1.000
#> GSM339473 1 0.0000 0.988 1.000 0.000
#> GSM339474 2 0.0000 0.965 0.000 1.000
#> GSM339475 1 0.0000 0.988 1.000 0.000
#> GSM339476 1 0.0000 0.988 1.000 0.000
#> GSM339477 2 0.0000 0.965 0.000 1.000
#> GSM339478 2 0.0000 0.965 0.000 1.000
#> GSM339479 2 0.0000 0.965 0.000 1.000
#> GSM339480 2 0.9686 0.393 0.396 0.604
#> GSM339481 2 0.0000 0.965 0.000 1.000
#> GSM339482 1 0.0000 0.988 1.000 0.000
#> GSM339483 1 0.0000 0.988 1.000 0.000
#> GSM339484 1 0.0000 0.988 1.000 0.000
#> GSM339485 1 0.0000 0.988 1.000 0.000
#> GSM339486 1 0.0000 0.988 1.000 0.000
#> GSM339487 2 0.0000 0.965 0.000 1.000
#> GSM339488 2 0.0000 0.965 0.000 1.000
#> GSM339489 2 0.0376 0.962 0.004 0.996
#> GSM339490 1 0.0000 0.988 1.000 0.000
#> GSM339491 2 0.0000 0.965 0.000 1.000
#> GSM339492 1 0.0000 0.988 1.000 0.000
#> GSM339493 2 0.0000 0.965 0.000 1.000
#> GSM339494 1 0.0000 0.988 1.000 0.000
#> GSM339495 2 0.0000 0.965 0.000 1.000
#> GSM339496 1 0.0000 0.988 1.000 0.000
#> GSM339497 2 0.0000 0.965 0.000 1.000
#> GSM339498 2 0.6343 0.812 0.160 0.840
#> GSM339499 2 0.6712 0.793 0.176 0.824
#> GSM339500 2 0.0000 0.965 0.000 1.000
#> GSM339501 1 0.0000 0.988 1.000 0.000
#> GSM339502 2 0.0000 0.965 0.000 1.000
#> GSM339503 1 0.0000 0.988 1.000 0.000
#> GSM339504 1 0.0000 0.988 1.000 0.000
#> GSM339505 2 0.0000 0.965 0.000 1.000
#> GSM339506 1 0.0000 0.988 1.000 0.000
#> GSM339507 1 0.0000 0.988 1.000 0.000
#> GSM339508 2 0.0000 0.965 0.000 1.000
#> GSM339509 2 0.0000 0.965 0.000 1.000
#> GSM339510 2 0.0376 0.962 0.004 0.996
#> GSM339511 1 0.9710 0.322 0.600 0.400
#> GSM339512 2 0.0000 0.965 0.000 1.000
#> GSM339513 1 0.0000 0.988 1.000 0.000
#> GSM339514 2 0.0000 0.965 0.000 1.000
#> GSM339515 1 0.0000 0.988 1.000 0.000
#> GSM339516 2 0.0000 0.965 0.000 1.000
#> GSM339517 1 0.0000 0.988 1.000 0.000
#> GSM339518 2 0.0000 0.965 0.000 1.000
#> GSM339519 1 0.0000 0.988 1.000 0.000
#> GSM339520 2 0.0000 0.965 0.000 1.000
#> GSM339521 2 0.0000 0.965 0.000 1.000
#> GSM339522 2 0.0000 0.965 0.000 1.000
#> GSM339523 2 0.0000 0.965 0.000 1.000
#> GSM339524 1 0.0000 0.988 1.000 0.000
#> GSM339525 1 0.0000 0.988 1.000 0.000
#> GSM339526 1 0.0000 0.988 1.000 0.000
#> GSM339527 1 0.0000 0.988 1.000 0.000
#> GSM339528 1 0.0000 0.988 1.000 0.000
#> GSM339529 2 0.0000 0.965 0.000 1.000
#> GSM339530 2 0.6712 0.793 0.176 0.824
#> GSM339531 2 0.0376 0.962 0.004 0.996
#> GSM339532 1 0.1414 0.968 0.980 0.020
#> GSM339533 1 0.0000 0.988 1.000 0.000
#> GSM339534 1 0.0000 0.988 1.000 0.000
#> GSM339535 2 0.0000 0.965 0.000 1.000
#> GSM339536 1 0.0000 0.988 1.000 0.000
#> GSM339537 2 0.0000 0.965 0.000 1.000
#> GSM339538 1 0.0000 0.988 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM339455 1 0.6299 0.3275 0.524 0.000 0.476
#> GSM339456 2 0.4399 0.8017 0.188 0.812 0.000
#> GSM339457 3 0.0000 0.7878 0.000 0.000 1.000
#> GSM339458 2 0.0237 0.9448 0.000 0.996 0.004
#> GSM339459 3 0.6307 0.5117 0.328 0.012 0.660
#> GSM339460 2 0.0000 0.9475 0.000 1.000 0.000
#> GSM339461 2 0.3340 0.8614 0.120 0.880 0.000
#> GSM339462 1 0.0000 0.7958 1.000 0.000 0.000
#> GSM339463 3 0.0000 0.7878 0.000 0.000 1.000
#> GSM339464 1 0.0000 0.7958 1.000 0.000 0.000
#> GSM339465 3 0.2165 0.7385 0.064 0.000 0.936
#> GSM339466 2 0.0000 0.9475 0.000 1.000 0.000
#> GSM339467 2 0.0000 0.9475 0.000 1.000 0.000
#> GSM339468 2 0.5529 0.6824 0.296 0.704 0.000
#> GSM339469 1 0.0000 0.7958 1.000 0.000 0.000
#> GSM339470 3 0.5363 0.5703 0.000 0.276 0.724
#> GSM339471 1 0.5591 0.6859 0.696 0.000 0.304
#> GSM339472 2 0.0000 0.9475 0.000 1.000 0.000
#> GSM339473 1 0.5560 0.6899 0.700 0.000 0.300
#> GSM339474 2 0.0000 0.9475 0.000 1.000 0.000
#> GSM339475 3 0.0000 0.7878 0.000 0.000 1.000
#> GSM339476 1 0.5254 0.7087 0.736 0.000 0.264
#> GSM339477 2 0.4178 0.8170 0.172 0.828 0.000
#> GSM339478 3 0.0000 0.7878 0.000 0.000 1.000
#> GSM339479 2 0.0424 0.9417 0.000 0.992 0.008
#> GSM339480 3 0.6307 0.5117 0.328 0.012 0.660
#> GSM339481 2 0.0000 0.9475 0.000 1.000 0.000
#> GSM339482 3 0.0000 0.7878 0.000 0.000 1.000
#> GSM339483 1 0.0000 0.7958 1.000 0.000 0.000
#> GSM339484 3 0.6252 -0.1131 0.444 0.000 0.556
#> GSM339485 1 0.0000 0.7958 1.000 0.000 0.000
#> GSM339486 3 0.6252 -0.1131 0.444 0.000 0.556
#> GSM339487 2 0.0000 0.9475 0.000 1.000 0.000
#> GSM339488 2 0.0000 0.9475 0.000 1.000 0.000
#> GSM339489 2 0.5497 0.6873 0.292 0.708 0.000
#> GSM339490 1 0.0000 0.7958 1.000 0.000 0.000
#> GSM339491 3 0.5431 0.5624 0.000 0.284 0.716
#> GSM339492 1 0.5591 0.6859 0.696 0.000 0.304
#> GSM339493 2 0.0000 0.9475 0.000 1.000 0.000
#> GSM339494 1 0.5560 0.6899 0.700 0.000 0.300
#> GSM339495 2 0.0000 0.9475 0.000 1.000 0.000
#> GSM339496 3 0.0000 0.7878 0.000 0.000 1.000
#> GSM339497 2 0.0000 0.9475 0.000 1.000 0.000
#> GSM339498 3 0.6357 0.5389 0.296 0.020 0.684
#> GSM339499 3 0.0000 0.7878 0.000 0.000 1.000
#> GSM339500 2 0.0237 0.9448 0.000 0.996 0.004
#> GSM339501 1 0.0000 0.7958 1.000 0.000 0.000
#> GSM339502 2 0.0000 0.9475 0.000 1.000 0.000
#> GSM339503 3 0.3941 0.6917 0.156 0.000 0.844
#> GSM339504 1 0.0000 0.7958 1.000 0.000 0.000
#> GSM339505 3 0.2878 0.7303 0.000 0.096 0.904
#> GSM339506 1 0.0000 0.7958 1.000 0.000 0.000
#> GSM339507 3 0.6244 -0.0997 0.440 0.000 0.560
#> GSM339508 2 0.0000 0.9475 0.000 1.000 0.000
#> GSM339509 2 0.0000 0.9475 0.000 1.000 0.000
#> GSM339510 2 0.5529 0.6824 0.296 0.704 0.000
#> GSM339511 1 0.2356 0.7524 0.928 0.072 0.000
#> GSM339512 2 0.0000 0.9475 0.000 1.000 0.000
#> GSM339513 1 0.5560 0.6899 0.700 0.000 0.300
#> GSM339514 2 0.0000 0.9475 0.000 1.000 0.000
#> GSM339515 1 0.5560 0.6899 0.700 0.000 0.300
#> GSM339516 2 0.0000 0.9475 0.000 1.000 0.000
#> GSM339517 3 0.0592 0.7842 0.012 0.000 0.988
#> GSM339518 2 0.0000 0.9475 0.000 1.000 0.000
#> GSM339519 3 0.4399 0.6674 0.188 0.000 0.812
#> GSM339520 3 0.0000 0.7878 0.000 0.000 1.000
#> GSM339521 2 0.0000 0.9475 0.000 1.000 0.000
#> GSM339522 2 0.0237 0.9453 0.004 0.996 0.000
#> GSM339523 2 0.0000 0.9475 0.000 1.000 0.000
#> GSM339524 1 0.5650 0.5609 0.688 0.000 0.312
#> GSM339525 1 0.0000 0.7958 1.000 0.000 0.000
#> GSM339526 3 0.0000 0.7878 0.000 0.000 1.000
#> GSM339527 1 0.0000 0.7958 1.000 0.000 0.000
#> GSM339528 3 0.6260 -0.1281 0.448 0.000 0.552
#> GSM339529 2 0.0000 0.9475 0.000 1.000 0.000
#> GSM339530 3 0.0000 0.7878 0.000 0.000 1.000
#> GSM339531 2 0.5497 0.6873 0.292 0.708 0.000
#> GSM339532 1 0.0000 0.7958 1.000 0.000 0.000
#> GSM339533 3 0.0000 0.7878 0.000 0.000 1.000
#> GSM339534 1 0.5591 0.6859 0.696 0.000 0.304
#> GSM339535 2 0.0000 0.9475 0.000 1.000 0.000
#> GSM339536 1 0.5560 0.6899 0.700 0.000 0.300
#> GSM339537 2 0.0000 0.9475 0.000 1.000 0.000
#> GSM339538 3 0.0424 0.7855 0.008 0.000 0.992
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM339455 1 0.7595 0.275 0.428 0.000 0.372 0.200
#> GSM339456 2 0.4079 0.759 0.000 0.800 0.020 0.180
#> GSM339457 3 0.0895 0.687 0.020 0.000 0.976 0.004
#> GSM339458 2 0.7649 0.385 0.004 0.496 0.224 0.276
#> GSM339459 3 0.7403 0.553 0.064 0.060 0.572 0.304
#> GSM339460 2 0.3286 0.842 0.000 0.876 0.080 0.044
#> GSM339461 2 0.2662 0.830 0.000 0.900 0.016 0.084
#> GSM339462 4 0.4989 0.878 0.472 0.000 0.000 0.528
#> GSM339463 3 0.7513 0.173 0.284 0.000 0.492 0.224
#> GSM339464 4 0.4830 0.869 0.392 0.000 0.000 0.608
#> GSM339465 1 0.7491 0.353 0.500 0.000 0.268 0.232
#> GSM339466 2 0.0657 0.863 0.000 0.984 0.004 0.012
#> GSM339467 2 0.2610 0.849 0.000 0.900 0.088 0.012
#> GSM339468 2 0.5193 0.607 0.000 0.656 0.020 0.324
#> GSM339469 4 0.6071 0.869 0.452 0.000 0.044 0.504
#> GSM339470 3 0.6526 0.540 0.072 0.080 0.712 0.136
#> GSM339471 1 0.1474 0.571 0.948 0.000 0.052 0.000
#> GSM339472 2 0.0000 0.863 0.000 1.000 0.000 0.000
#> GSM339473 1 0.0000 0.564 1.000 0.000 0.000 0.000
#> GSM339474 2 0.0188 0.863 0.000 0.996 0.000 0.004
#> GSM339475 3 0.5394 0.665 0.228 0.000 0.712 0.060
#> GSM339476 1 0.5723 -0.173 0.696 0.000 0.084 0.220
#> GSM339477 2 0.2859 0.817 0.000 0.880 0.008 0.112
#> GSM339478 3 0.0895 0.687 0.020 0.000 0.976 0.004
#> GSM339479 2 0.8064 0.332 0.016 0.464 0.224 0.296
#> GSM339480 3 0.7403 0.553 0.064 0.060 0.572 0.304
#> GSM339481 2 0.0188 0.863 0.000 0.996 0.000 0.004
#> GSM339482 3 0.6084 0.664 0.204 0.000 0.676 0.120
#> GSM339483 4 0.4989 0.878 0.472 0.000 0.000 0.528
#> GSM339484 1 0.6973 0.441 0.584 0.000 0.220 0.196
#> GSM339485 4 0.4855 0.872 0.400 0.000 0.000 0.600
#> GSM339486 1 0.7301 0.419 0.536 0.000 0.236 0.228
#> GSM339487 2 0.0657 0.863 0.000 0.984 0.004 0.012
#> GSM339488 2 0.2610 0.849 0.000 0.900 0.088 0.012
#> GSM339489 2 0.5193 0.611 0.000 0.656 0.020 0.324
#> GSM339490 4 0.6071 0.869 0.452 0.000 0.044 0.504
#> GSM339491 3 0.6746 0.529 0.068 0.096 0.696 0.140
#> GSM339492 1 0.1474 0.571 0.948 0.000 0.052 0.000
#> GSM339493 2 0.0000 0.863 0.000 1.000 0.000 0.000
#> GSM339494 1 0.0000 0.564 1.000 0.000 0.000 0.000
#> GSM339495 2 0.0469 0.862 0.000 0.988 0.000 0.012
#> GSM339496 3 0.5361 0.666 0.224 0.000 0.716 0.060
#> GSM339497 2 0.2816 0.846 0.000 0.900 0.036 0.064
#> GSM339498 3 0.6878 0.507 0.008 0.092 0.552 0.348
#> GSM339499 3 0.0895 0.687 0.020 0.000 0.976 0.004
#> GSM339500 2 0.7036 0.507 0.000 0.576 0.216 0.208
#> GSM339501 4 0.4406 0.787 0.300 0.000 0.000 0.700
#> GSM339502 2 0.2610 0.849 0.000 0.900 0.088 0.012
#> GSM339503 3 0.6352 0.645 0.156 0.000 0.656 0.188
#> GSM339504 4 0.4985 0.880 0.468 0.000 0.000 0.532
#> GSM339505 3 0.4773 0.658 0.100 0.036 0.816 0.048
#> GSM339506 4 0.4277 0.776 0.280 0.000 0.000 0.720
#> GSM339507 1 0.7347 0.407 0.528 0.000 0.244 0.228
#> GSM339508 2 0.2300 0.852 0.000 0.920 0.064 0.016
#> GSM339509 2 0.2610 0.849 0.000 0.900 0.088 0.012
#> GSM339510 2 0.5233 0.600 0.000 0.648 0.020 0.332
#> GSM339511 4 0.6546 0.857 0.448 0.012 0.048 0.492
#> GSM339512 2 0.3161 0.828 0.000 0.864 0.124 0.012
#> GSM339513 1 0.0707 0.556 0.980 0.000 0.020 0.000
#> GSM339514 2 0.2473 0.850 0.000 0.908 0.080 0.012
#> GSM339515 1 0.0000 0.564 1.000 0.000 0.000 0.000
#> GSM339516 2 0.0469 0.862 0.000 0.988 0.000 0.012
#> GSM339517 3 0.6027 0.667 0.192 0.000 0.684 0.124
#> GSM339518 2 0.2399 0.857 0.000 0.920 0.048 0.032
#> GSM339519 3 0.7315 0.475 0.308 0.000 0.512 0.180
#> GSM339520 3 0.0895 0.687 0.020 0.000 0.976 0.004
#> GSM339521 2 0.2450 0.852 0.000 0.912 0.072 0.016
#> GSM339522 2 0.2271 0.842 0.000 0.916 0.008 0.076
#> GSM339523 2 0.2610 0.849 0.000 0.900 0.088 0.012
#> GSM339524 1 0.7170 0.132 0.540 0.000 0.288 0.172
#> GSM339525 4 0.4998 0.865 0.488 0.000 0.000 0.512
#> GSM339526 3 0.5520 0.660 0.244 0.000 0.696 0.060
#> GSM339527 4 0.4277 0.776 0.280 0.000 0.000 0.720
#> GSM339528 1 0.7301 0.419 0.536 0.000 0.236 0.228
#> GSM339529 2 0.2300 0.852 0.000 0.920 0.064 0.016
#> GSM339530 3 0.1004 0.687 0.024 0.000 0.972 0.004
#> GSM339531 2 0.5173 0.613 0.000 0.660 0.020 0.320
#> GSM339532 4 0.6071 0.869 0.452 0.000 0.044 0.504
#> GSM339533 3 0.6463 0.484 0.196 0.000 0.644 0.160
#> GSM339534 1 0.1743 0.570 0.940 0.000 0.056 0.004
#> GSM339535 2 0.0895 0.863 0.000 0.976 0.020 0.004
#> GSM339536 1 0.0000 0.564 1.000 0.000 0.000 0.000
#> GSM339537 2 0.0469 0.862 0.000 0.988 0.000 0.012
#> GSM339538 3 0.6167 0.657 0.220 0.000 0.664 0.116
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM339455 1 0.7565 0.21293 0.440 0.000 0.336 0.104 0.120
#> GSM339456 2 0.4675 0.31237 0.000 0.640 0.004 0.020 0.336
#> GSM339457 3 0.0290 0.52105 0.008 0.000 0.992 0.000 0.000
#> GSM339458 3 0.8520 0.11591 0.196 0.256 0.316 0.000 0.232
#> GSM339459 5 0.6074 0.26983 0.052 0.016 0.260 0.036 0.636
#> GSM339460 2 0.5587 0.68955 0.012 0.712 0.096 0.024 0.156
#> GSM339461 2 0.3768 0.62709 0.004 0.760 0.000 0.008 0.228
#> GSM339462 4 0.2124 0.82915 0.056 0.000 0.000 0.916 0.028
#> GSM339463 1 0.6121 -0.22896 0.464 0.000 0.408 0.000 0.128
#> GSM339464 4 0.2390 0.81674 0.020 0.000 0.000 0.896 0.084
#> GSM339465 1 0.3055 0.53085 0.864 0.000 0.064 0.000 0.072
#> GSM339466 2 0.1952 0.79026 0.004 0.912 0.000 0.000 0.084
#> GSM339467 2 0.3639 0.75771 0.000 0.812 0.144 0.000 0.044
#> GSM339468 5 0.4958 0.38909 0.000 0.400 0.000 0.032 0.568
#> GSM339469 4 0.0451 0.84425 0.004 0.000 0.008 0.988 0.000
#> GSM339470 3 0.6730 0.47307 0.172 0.072 0.604 0.000 0.152
#> GSM339471 1 0.5563 0.61558 0.640 0.000 0.072 0.272 0.016
#> GSM339472 2 0.1168 0.79637 0.000 0.960 0.008 0.000 0.032
#> GSM339473 1 0.4114 0.63232 0.712 0.000 0.000 0.272 0.016
#> GSM339474 2 0.1571 0.79195 0.004 0.936 0.000 0.000 0.060
#> GSM339475 3 0.6423 0.39886 0.276 0.000 0.504 0.000 0.220
#> GSM339476 4 0.5847 0.18004 0.308 0.000 0.108 0.580 0.004
#> GSM339477 2 0.3224 0.68554 0.000 0.824 0.000 0.016 0.160
#> GSM339478 3 0.0162 0.51927 0.004 0.000 0.996 0.000 0.000
#> GSM339479 3 0.8537 0.12779 0.204 0.252 0.312 0.000 0.232
#> GSM339480 5 0.6029 0.27942 0.052 0.016 0.252 0.036 0.644
#> GSM339481 2 0.1285 0.80042 0.004 0.956 0.004 0.000 0.036
#> GSM339482 3 0.6835 0.30192 0.276 0.000 0.428 0.004 0.292
#> GSM339483 4 0.2124 0.82915 0.056 0.000 0.000 0.916 0.028
#> GSM339484 1 0.3240 0.57003 0.868 0.000 0.072 0.036 0.024
#> GSM339485 4 0.2069 0.82391 0.012 0.000 0.000 0.912 0.076
#> GSM339486 1 0.2954 0.54684 0.876 0.000 0.064 0.004 0.056
#> GSM339487 2 0.2011 0.78892 0.004 0.908 0.000 0.000 0.088
#> GSM339488 2 0.3639 0.75771 0.000 0.812 0.144 0.000 0.044
#> GSM339489 5 0.4940 0.39357 0.000 0.392 0.000 0.032 0.576
#> GSM339490 4 0.0451 0.84425 0.004 0.000 0.008 0.988 0.000
#> GSM339491 3 0.6957 0.45953 0.168 0.096 0.588 0.000 0.148
#> GSM339492 1 0.5563 0.61558 0.640 0.000 0.072 0.272 0.016
#> GSM339493 2 0.0693 0.79857 0.000 0.980 0.008 0.000 0.012
#> GSM339494 1 0.4114 0.63232 0.712 0.000 0.000 0.272 0.016
#> GSM339495 2 0.1704 0.78755 0.004 0.928 0.000 0.000 0.068
#> GSM339496 3 0.6438 0.39650 0.280 0.000 0.500 0.000 0.220
#> GSM339497 2 0.5144 0.66686 0.040 0.720 0.048 0.000 0.192
#> GSM339498 5 0.5701 0.33963 0.012 0.064 0.236 0.020 0.668
#> GSM339499 3 0.0404 0.52198 0.012 0.000 0.988 0.000 0.000
#> GSM339500 3 0.8216 -0.00666 0.120 0.324 0.328 0.000 0.228
#> GSM339501 4 0.3934 0.66483 0.008 0.000 0.000 0.716 0.276
#> GSM339502 2 0.3647 0.76080 0.000 0.816 0.132 0.000 0.052
#> GSM339503 5 0.6798 -0.26773 0.180 0.000 0.404 0.012 0.404
#> GSM339504 4 0.2054 0.83122 0.052 0.000 0.000 0.920 0.028
#> GSM339505 3 0.6451 0.49470 0.204 0.036 0.604 0.000 0.156
#> GSM339506 4 0.3944 0.73197 0.032 0.000 0.000 0.768 0.200
#> GSM339507 1 0.2878 0.55082 0.880 0.000 0.068 0.004 0.048
#> GSM339508 2 0.4411 0.74672 0.000 0.796 0.104 0.032 0.068
#> GSM339509 2 0.3565 0.75921 0.000 0.816 0.144 0.000 0.040
#> GSM339510 5 0.5002 0.40103 0.000 0.364 0.000 0.040 0.596
#> GSM339511 4 0.0486 0.84397 0.004 0.000 0.004 0.988 0.004
#> GSM339512 2 0.5815 0.51749 0.020 0.628 0.264 0.000 0.088
#> GSM339513 1 0.5175 0.62071 0.668 0.000 0.036 0.272 0.024
#> GSM339514 2 0.2754 0.78422 0.000 0.880 0.080 0.000 0.040
#> GSM339515 1 0.4114 0.63232 0.712 0.000 0.000 0.272 0.016
#> GSM339516 2 0.1991 0.78316 0.004 0.916 0.000 0.004 0.076
#> GSM339517 3 0.6666 0.33126 0.232 0.000 0.476 0.004 0.288
#> GSM339518 2 0.4814 0.70389 0.032 0.752 0.052 0.000 0.164
#> GSM339519 1 0.7330 -0.19073 0.352 0.000 0.276 0.024 0.348
#> GSM339520 3 0.0290 0.52105 0.008 0.000 0.992 0.000 0.000
#> GSM339521 2 0.4697 0.72117 0.020 0.760 0.068 0.000 0.152
#> GSM339522 2 0.4037 0.56103 0.004 0.704 0.004 0.000 0.288
#> GSM339523 2 0.3622 0.76246 0.000 0.820 0.124 0.000 0.056
#> GSM339524 1 0.7189 0.23040 0.512 0.000 0.132 0.072 0.284
#> GSM339525 4 0.2236 0.82036 0.068 0.000 0.000 0.908 0.024
#> GSM339526 3 0.6515 0.37502 0.328 0.000 0.464 0.000 0.208
#> GSM339527 4 0.3877 0.72409 0.024 0.000 0.000 0.764 0.212
#> GSM339528 1 0.2888 0.54983 0.880 0.000 0.060 0.004 0.056
#> GSM339529 2 0.4330 0.74993 0.000 0.800 0.104 0.028 0.068
#> GSM339530 3 0.0960 0.52120 0.016 0.004 0.972 0.000 0.008
#> GSM339531 5 0.4966 0.37971 0.000 0.404 0.000 0.032 0.564
#> GSM339532 4 0.0451 0.84425 0.004 0.000 0.008 0.988 0.000
#> GSM339533 3 0.6062 0.38919 0.324 0.004 0.548 0.000 0.124
#> GSM339534 1 0.5919 0.60348 0.620 0.000 0.080 0.272 0.028
#> GSM339535 2 0.1012 0.79992 0.000 0.968 0.012 0.000 0.020
#> GSM339536 1 0.4114 0.63232 0.712 0.000 0.000 0.272 0.016
#> GSM339537 2 0.1892 0.78441 0.004 0.916 0.000 0.000 0.080
#> GSM339538 3 0.6739 0.29443 0.336 0.000 0.400 0.000 0.264
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM339455 6 0.8394 0.104 0.268 0.004 0.152 0.116 0.096 0.364
#> GSM339456 2 0.4277 0.205 0.000 0.576 0.004 0.004 0.408 0.008
#> GSM339457 3 0.5596 -0.366 0.024 0.004 0.464 0.004 0.052 0.452
#> GSM339458 6 0.6212 0.291 0.108 0.176 0.000 0.004 0.108 0.604
#> GSM339459 3 0.4545 0.276 0.004 0.000 0.568 0.016 0.404 0.008
#> GSM339460 2 0.5721 0.460 0.008 0.560 0.000 0.036 0.064 0.332
#> GSM339461 2 0.4892 0.508 0.000 0.628 0.000 0.000 0.272 0.100
#> GSM339462 4 0.2790 0.792 0.132 0.000 0.000 0.844 0.024 0.000
#> GSM339463 1 0.7362 -0.148 0.344 0.000 0.252 0.000 0.112 0.292
#> GSM339464 4 0.2123 0.807 0.020 0.000 0.008 0.908 0.064 0.000
#> GSM339465 1 0.4938 0.536 0.720 0.000 0.060 0.000 0.084 0.136
#> GSM339466 2 0.2930 0.662 0.000 0.840 0.000 0.000 0.124 0.036
#> GSM339467 2 0.3725 0.631 0.000 0.776 0.004 0.000 0.048 0.172
#> GSM339468 5 0.3641 0.812 0.000 0.224 0.000 0.028 0.748 0.000
#> GSM339469 4 0.0146 0.831 0.004 0.000 0.000 0.996 0.000 0.000
#> GSM339470 6 0.7529 0.290 0.096 0.072 0.316 0.000 0.084 0.432
#> GSM339471 1 0.5021 0.662 0.700 0.000 0.056 0.176 0.000 0.068
#> GSM339472 2 0.2383 0.674 0.000 0.880 0.000 0.000 0.096 0.024
#> GSM339473 1 0.3385 0.687 0.788 0.000 0.032 0.180 0.000 0.000
#> GSM339474 2 0.2983 0.656 0.000 0.832 0.000 0.000 0.136 0.032
#> GSM339475 3 0.1701 0.616 0.072 0.000 0.920 0.000 0.000 0.008
#> GSM339476 4 0.6547 0.247 0.292 0.000 0.044 0.532 0.032 0.100
#> GSM339477 2 0.3584 0.549 0.000 0.740 0.000 0.004 0.244 0.012
#> GSM339478 6 0.5739 0.278 0.024 0.008 0.440 0.004 0.056 0.468
#> GSM339479 6 0.6165 0.304 0.112 0.164 0.000 0.004 0.108 0.612
#> GSM339480 3 0.4566 0.250 0.004 0.000 0.556 0.016 0.416 0.008
#> GSM339481 2 0.2672 0.678 0.000 0.868 0.000 0.000 0.052 0.080
#> GSM339482 3 0.3078 0.637 0.108 0.000 0.836 0.000 0.056 0.000
#> GSM339483 4 0.2790 0.792 0.132 0.000 0.000 0.844 0.024 0.000
#> GSM339484 1 0.5638 0.534 0.688 0.000 0.116 0.020 0.072 0.104
#> GSM339485 4 0.1655 0.818 0.008 0.000 0.008 0.932 0.052 0.000
#> GSM339486 1 0.4775 0.547 0.732 0.000 0.052 0.000 0.080 0.136
#> GSM339487 2 0.3083 0.657 0.000 0.828 0.000 0.000 0.132 0.040
#> GSM339488 2 0.3819 0.628 0.000 0.768 0.004 0.000 0.052 0.176
#> GSM339489 5 0.3586 0.812 0.000 0.216 0.000 0.028 0.756 0.000
#> GSM339490 4 0.0146 0.831 0.004 0.000 0.000 0.996 0.000 0.000
#> GSM339491 6 0.7618 0.293 0.096 0.076 0.304 0.000 0.092 0.432
#> GSM339492 1 0.5021 0.662 0.700 0.000 0.056 0.176 0.000 0.068
#> GSM339493 2 0.1686 0.681 0.000 0.924 0.000 0.000 0.064 0.012
#> GSM339494 1 0.3385 0.687 0.788 0.000 0.032 0.180 0.000 0.000
#> GSM339495 2 0.3027 0.645 0.000 0.824 0.000 0.000 0.148 0.028
#> GSM339496 3 0.1802 0.614 0.072 0.000 0.916 0.000 0.000 0.012
#> GSM339497 2 0.6093 0.382 0.036 0.512 0.004 0.000 0.108 0.340
#> GSM339498 5 0.4804 0.025 0.000 0.012 0.392 0.016 0.568 0.012
#> GSM339499 6 0.5689 0.272 0.024 0.004 0.448 0.004 0.060 0.460
#> GSM339500 6 0.5895 0.111 0.052 0.280 0.004 0.000 0.084 0.580
#> GSM339501 4 0.5054 0.586 0.036 0.000 0.044 0.632 0.288 0.000
#> GSM339502 2 0.4147 0.627 0.000 0.736 0.004 0.000 0.064 0.196
#> GSM339503 3 0.3486 0.600 0.024 0.000 0.788 0.008 0.180 0.000
#> GSM339504 4 0.2748 0.795 0.128 0.000 0.000 0.848 0.024 0.000
#> GSM339505 3 0.7368 -0.141 0.124 0.060 0.472 0.000 0.068 0.276
#> GSM339506 4 0.3821 0.714 0.020 0.000 0.024 0.768 0.188 0.000
#> GSM339507 1 0.4812 0.547 0.728 0.000 0.052 0.000 0.080 0.140
#> GSM339508 2 0.5349 0.586 0.000 0.692 0.012 0.056 0.168 0.072
#> GSM339509 2 0.3662 0.632 0.000 0.780 0.004 0.000 0.044 0.172
#> GSM339510 5 0.3630 0.809 0.000 0.212 0.000 0.032 0.756 0.000
#> GSM339511 4 0.0551 0.829 0.004 0.004 0.000 0.984 0.008 0.000
#> GSM339512 2 0.6087 0.273 0.012 0.516 0.048 0.000 0.068 0.356
#> GSM339513 1 0.4683 0.668 0.724 0.000 0.068 0.172 0.000 0.036
#> GSM339514 2 0.2404 0.673 0.000 0.884 0.000 0.000 0.036 0.080
#> GSM339515 1 0.3385 0.687 0.788 0.000 0.032 0.180 0.000 0.000
#> GSM339516 2 0.3799 0.606 0.000 0.764 0.000 0.016 0.196 0.024
#> GSM339517 3 0.1924 0.622 0.048 0.000 0.920 0.000 0.028 0.004
#> GSM339518 2 0.5408 0.473 0.012 0.580 0.004 0.000 0.088 0.316
#> GSM339519 3 0.5849 0.496 0.256 0.000 0.588 0.024 0.124 0.008
#> GSM339520 6 0.5642 0.279 0.024 0.004 0.444 0.004 0.056 0.468
#> GSM339521 2 0.4972 0.476 0.008 0.580 0.000 0.000 0.060 0.352
#> GSM339522 2 0.5338 0.133 0.000 0.508 0.004 0.004 0.404 0.080
#> GSM339523 2 0.3953 0.634 0.000 0.744 0.000 0.000 0.060 0.196
#> GSM339524 3 0.5307 0.439 0.312 0.000 0.592 0.012 0.080 0.004
#> GSM339525 4 0.2790 0.792 0.132 0.000 0.000 0.844 0.024 0.000
#> GSM339526 3 0.3429 0.561 0.144 0.000 0.812 0.000 0.028 0.016
#> GSM339527 4 0.4022 0.700 0.016 0.000 0.040 0.756 0.188 0.000
#> GSM339528 1 0.4823 0.545 0.728 0.000 0.052 0.000 0.084 0.136
#> GSM339529 2 0.5349 0.586 0.000 0.692 0.012 0.056 0.168 0.072
#> GSM339530 6 0.5872 0.278 0.024 0.008 0.436 0.004 0.068 0.460
#> GSM339531 5 0.3645 0.798 0.000 0.236 0.000 0.024 0.740 0.000
#> GSM339532 4 0.0436 0.829 0.004 0.004 0.000 0.988 0.004 0.000
#> GSM339533 6 0.7289 0.175 0.232 0.000 0.320 0.000 0.104 0.344
#> GSM339534 1 0.5290 0.650 0.684 0.000 0.056 0.180 0.004 0.076
#> GSM339535 2 0.1341 0.686 0.000 0.948 0.000 0.000 0.024 0.028
#> GSM339536 1 0.3385 0.687 0.788 0.000 0.032 0.180 0.000 0.000
#> GSM339537 2 0.3175 0.636 0.000 0.808 0.000 0.000 0.164 0.028
#> GSM339538 3 0.2869 0.627 0.148 0.000 0.832 0.000 0.020 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 protocol(p) agent(p) individual(p) k
#> CV:skmeans 81 1.000 0.726 1.84e-03 2
#> CV:skmeans 79 0.985 0.995 2.05e-05 3
#> CV:skmeans 71 0.995 1.000 8.77e-08 4
#> CV:skmeans 57 0.950 0.989 6.44e-06 5
#> CV:skmeans 57 0.975 1.000 1.38e-07 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 15497 rows and 84 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 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 0.290 0.658 0.790 0.4952 0.495 0.495
#> 3 3 0.484 0.606 0.805 0.3173 0.724 0.507
#> 4 4 0.555 0.432 0.684 0.0978 0.772 0.472
#> 5 5 0.668 0.661 0.825 0.0842 0.760 0.352
#> 6 6 0.669 0.613 0.764 0.0507 0.905 0.605
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
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
#> GSM339455 1 0.9896 0.3250 0.560 0.440
#> GSM339456 2 0.8661 0.4581 0.288 0.712
#> GSM339457 1 0.9580 0.3223 0.620 0.380
#> GSM339458 2 0.8813 0.5634 0.300 0.700
#> GSM339459 1 1.0000 0.2256 0.504 0.496
#> GSM339460 2 0.2423 0.8070 0.040 0.960
#> GSM339461 2 0.0000 0.8180 0.000 1.000
#> GSM339462 1 0.0672 0.7842 0.992 0.008
#> GSM339463 2 0.9850 0.3264 0.428 0.572
#> GSM339464 1 0.9661 0.4763 0.608 0.392
#> GSM339465 1 0.8443 0.5502 0.728 0.272
#> GSM339466 2 0.0938 0.8169 0.012 0.988
#> GSM339467 2 0.0938 0.8158 0.012 0.988
#> GSM339468 2 0.7219 0.6410 0.200 0.800
#> GSM339469 1 0.4815 0.7691 0.896 0.104
#> GSM339470 2 0.9044 0.5392 0.320 0.680
#> GSM339471 1 0.0000 0.7819 1.000 0.000
#> GSM339472 2 0.0000 0.8180 0.000 1.000
#> GSM339473 1 0.0000 0.7819 1.000 0.000
#> GSM339474 2 0.0000 0.8180 0.000 1.000
#> GSM339475 1 0.0938 0.7845 0.988 0.012
#> GSM339476 1 0.6973 0.7207 0.812 0.188
#> GSM339477 2 0.6048 0.6986 0.148 0.852
#> GSM339478 2 0.4431 0.7804 0.092 0.908
#> GSM339479 2 0.9491 0.4557 0.368 0.632
#> GSM339480 2 0.9988 -0.1814 0.480 0.520
#> GSM339481 2 0.0000 0.8180 0.000 1.000
#> GSM339482 1 0.5178 0.7512 0.884 0.116
#> GSM339483 1 0.8016 0.6709 0.756 0.244
#> GSM339484 1 0.1184 0.7846 0.984 0.016
#> GSM339485 1 0.9944 0.3452 0.544 0.456
#> GSM339486 1 0.1184 0.7846 0.984 0.016
#> GSM339487 2 0.0376 0.8175 0.004 0.996
#> GSM339488 2 0.2043 0.8099 0.032 0.968
#> GSM339489 2 0.9393 0.3272 0.356 0.644
#> GSM339490 1 0.7815 0.6724 0.768 0.232
#> GSM339491 1 0.9954 0.0267 0.540 0.460
#> GSM339492 1 0.0376 0.7833 0.996 0.004
#> GSM339493 2 0.0000 0.8180 0.000 1.000
#> GSM339494 1 0.4562 0.7719 0.904 0.096
#> GSM339495 2 0.0000 0.8180 0.000 1.000
#> GSM339496 1 0.8327 0.6402 0.736 0.264
#> GSM339497 2 0.1184 0.8149 0.016 0.984
#> GSM339498 2 0.9933 -0.0248 0.452 0.548
#> GSM339499 2 0.9996 0.1383 0.488 0.512
#> GSM339500 2 0.8207 0.6175 0.256 0.744
#> GSM339501 1 0.9833 0.4108 0.576 0.424
#> GSM339502 2 0.2948 0.8008 0.052 0.948
#> GSM339503 1 0.8555 0.5482 0.720 0.280
#> GSM339504 1 0.4161 0.7770 0.916 0.084
#> GSM339505 2 0.8955 0.5485 0.312 0.688
#> GSM339506 1 0.5519 0.7589 0.872 0.128
#> GSM339507 1 0.1414 0.7845 0.980 0.020
#> GSM339508 2 0.0000 0.8180 0.000 1.000
#> GSM339509 2 0.0000 0.8180 0.000 1.000
#> GSM339510 2 0.6531 0.6961 0.168 0.832
#> GSM339511 2 0.0938 0.8158 0.012 0.988
#> GSM339512 2 0.7528 0.6594 0.216 0.784
#> GSM339513 1 0.0000 0.7819 1.000 0.000
#> GSM339514 2 0.0000 0.8180 0.000 1.000
#> GSM339515 1 0.0000 0.7819 1.000 0.000
#> GSM339516 2 0.0000 0.8180 0.000 1.000
#> GSM339517 1 0.4690 0.7543 0.900 0.100
#> GSM339518 2 0.0000 0.8180 0.000 1.000
#> GSM339519 1 0.7528 0.6897 0.784 0.216
#> GSM339520 2 0.8955 0.5469 0.312 0.688
#> GSM339521 2 0.6623 0.6975 0.172 0.828
#> GSM339522 2 0.0000 0.8180 0.000 1.000
#> GSM339523 2 0.0000 0.8180 0.000 1.000
#> GSM339524 1 0.0376 0.7833 0.996 0.004
#> GSM339525 1 0.6801 0.7223 0.820 0.180
#> GSM339526 1 0.0938 0.7846 0.988 0.012
#> GSM339527 1 0.7815 0.6839 0.768 0.232
#> GSM339528 1 0.1184 0.7846 0.984 0.016
#> GSM339529 2 0.0000 0.8180 0.000 1.000
#> GSM339530 1 0.8909 0.5037 0.692 0.308
#> GSM339531 2 0.6887 0.6565 0.184 0.816
#> GSM339532 2 0.7056 0.6497 0.192 0.808
#> GSM339533 1 0.6887 0.6696 0.816 0.184
#> GSM339534 1 0.9552 0.3572 0.624 0.376
#> GSM339535 2 0.0000 0.8180 0.000 1.000
#> GSM339536 1 0.2603 0.7838 0.956 0.044
#> GSM339537 2 0.0000 0.8180 0.000 1.000
#> GSM339538 1 0.0000 0.7819 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM339455 3 0.5939 0.5911 0.224 0.028 0.748
#> GSM339456 2 0.3752 0.7490 0.096 0.884 0.020
#> GSM339457 3 0.7471 -0.1253 0.036 0.448 0.516
#> GSM339458 3 0.6045 0.4053 0.000 0.380 0.620
#> GSM339459 2 0.7289 0.3331 0.468 0.504 0.028
#> GSM339460 2 0.2492 0.7849 0.016 0.936 0.048
#> GSM339461 2 0.2063 0.7870 0.044 0.948 0.008
#> GSM339462 1 0.1289 0.7299 0.968 0.000 0.032
#> GSM339463 3 0.2550 0.7277 0.012 0.056 0.932
#> GSM339464 1 0.6051 0.4526 0.696 0.012 0.292
#> GSM339465 3 0.2200 0.7279 0.004 0.056 0.940
#> GSM339466 2 0.6646 0.6190 0.048 0.712 0.240
#> GSM339467 2 0.1643 0.7854 0.000 0.956 0.044
#> GSM339468 2 0.7178 0.3481 0.464 0.512 0.024
#> GSM339469 1 0.2066 0.7269 0.940 0.000 0.060
#> GSM339470 3 0.2703 0.7268 0.016 0.056 0.928
#> GSM339471 1 0.6111 0.3781 0.604 0.000 0.396
#> GSM339472 2 0.1411 0.7863 0.000 0.964 0.036
#> GSM339473 1 0.6079 0.3801 0.612 0.000 0.388
#> GSM339474 2 0.0829 0.7879 0.012 0.984 0.004
#> GSM339475 3 0.2959 0.7198 0.100 0.000 0.900
#> GSM339476 1 0.4912 0.6140 0.796 0.008 0.196
#> GSM339477 2 0.3375 0.7614 0.100 0.892 0.008
#> GSM339478 2 0.3183 0.7776 0.016 0.908 0.076
#> GSM339479 3 0.4411 0.6594 0.016 0.140 0.844
#> GSM339480 2 0.7072 0.3380 0.476 0.504 0.020
#> GSM339481 2 0.1411 0.7863 0.000 0.964 0.036
#> GSM339482 3 0.6421 0.2417 0.424 0.004 0.572
#> GSM339483 1 0.1453 0.7257 0.968 0.008 0.024
#> GSM339484 3 0.2200 0.7421 0.056 0.004 0.940
#> GSM339485 1 0.6522 0.4779 0.696 0.032 0.272
#> GSM339486 3 0.2384 0.7445 0.056 0.008 0.936
#> GSM339487 2 0.7978 0.6045 0.176 0.660 0.164
#> GSM339488 2 0.1643 0.7861 0.000 0.956 0.044
#> GSM339489 2 0.8268 0.3168 0.440 0.484 0.076
#> GSM339490 1 0.1289 0.7299 0.968 0.000 0.032
#> GSM339491 3 0.1950 0.7380 0.040 0.008 0.952
#> GSM339492 1 0.4605 0.6555 0.796 0.000 0.204
#> GSM339493 2 0.0829 0.7879 0.012 0.984 0.004
#> GSM339494 1 0.6548 0.3992 0.616 0.012 0.372
#> GSM339495 2 0.0829 0.7879 0.012 0.984 0.004
#> GSM339496 3 0.3030 0.7310 0.092 0.004 0.904
#> GSM339497 2 0.7360 0.6165 0.096 0.692 0.212
#> GSM339498 2 0.9301 0.3082 0.360 0.472 0.168
#> GSM339499 3 0.2443 0.7371 0.028 0.032 0.940
#> GSM339500 2 0.4235 0.6903 0.000 0.824 0.176
#> GSM339501 2 0.7074 0.3297 0.480 0.500 0.020
#> GSM339502 2 0.1860 0.7847 0.000 0.948 0.052
#> GSM339503 3 0.5536 0.5927 0.236 0.012 0.752
#> GSM339504 1 0.1289 0.7299 0.968 0.000 0.032
#> GSM339505 3 0.3129 0.7151 0.008 0.088 0.904
#> GSM339506 3 0.6500 0.1575 0.464 0.004 0.532
#> GSM339507 3 0.2261 0.7432 0.068 0.000 0.932
#> GSM339508 2 0.0237 0.7883 0.000 0.996 0.004
#> GSM339509 2 0.2066 0.7824 0.000 0.940 0.060
#> GSM339510 2 0.7049 0.3760 0.452 0.528 0.020
#> GSM339511 1 0.7023 0.2059 0.624 0.344 0.032
#> GSM339512 2 0.2625 0.7712 0.000 0.916 0.084
#> GSM339513 1 0.1289 0.7299 0.968 0.000 0.032
#> GSM339514 2 0.1411 0.7863 0.000 0.964 0.036
#> GSM339515 1 0.3192 0.7125 0.888 0.000 0.112
#> GSM339516 2 0.6255 0.5626 0.320 0.668 0.012
#> GSM339517 3 0.3038 0.7171 0.104 0.000 0.896
#> GSM339518 2 0.1170 0.7885 0.016 0.976 0.008
#> GSM339519 1 0.5291 0.5054 0.732 0.000 0.268
#> GSM339520 2 0.6235 0.2498 0.000 0.564 0.436
#> GSM339521 2 0.1643 0.7854 0.000 0.956 0.044
#> GSM339522 2 0.6617 0.4730 0.388 0.600 0.012
#> GSM339523 2 0.1411 0.7863 0.000 0.964 0.036
#> GSM339524 3 0.6309 0.0658 0.496 0.000 0.504
#> GSM339525 1 0.2774 0.7262 0.920 0.008 0.072
#> GSM339526 3 0.2066 0.7392 0.060 0.000 0.940
#> GSM339527 3 0.6659 0.1420 0.460 0.008 0.532
#> GSM339528 3 0.2486 0.7445 0.060 0.008 0.932
#> GSM339529 2 0.1636 0.7887 0.020 0.964 0.016
#> GSM339530 3 0.5968 0.4036 0.000 0.364 0.636
#> GSM339531 2 0.8091 0.5068 0.320 0.592 0.088
#> GSM339532 1 0.3690 0.6786 0.884 0.100 0.016
#> GSM339533 3 0.2066 0.7422 0.060 0.000 0.940
#> GSM339534 1 0.4281 0.7031 0.872 0.072 0.056
#> GSM339535 2 0.1620 0.7877 0.024 0.964 0.012
#> GSM339536 1 0.6008 0.4114 0.628 0.000 0.372
#> GSM339537 2 0.1877 0.7868 0.032 0.956 0.012
#> GSM339538 1 0.5733 0.4442 0.676 0.000 0.324
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM339455 4 0.7786 -0.0043 0.224 0.004 0.316 0.456
#> GSM339456 2 0.2928 0.7267 0.056 0.904 0.012 0.028
#> GSM339457 4 0.7890 -0.3709 0.008 0.220 0.316 0.456
#> GSM339458 2 0.7001 -0.1604 0.000 0.464 0.420 0.116
#> GSM339459 1 0.7881 0.0391 0.492 0.232 0.012 0.264
#> GSM339460 2 0.1297 0.7646 0.016 0.964 0.000 0.020
#> GSM339461 2 0.3312 0.7275 0.052 0.876 0.000 0.072
#> GSM339462 1 0.3907 0.3889 0.768 0.000 0.000 0.232
#> GSM339463 3 0.5273 0.8699 0.000 0.008 0.536 0.456
#> GSM339464 4 0.5861 -0.3288 0.480 0.000 0.032 0.488
#> GSM339465 3 0.5273 0.8699 0.000 0.008 0.536 0.456
#> GSM339466 4 0.6615 0.2199 0.052 0.384 0.016 0.548
#> GSM339467 2 0.0000 0.7722 0.000 1.000 0.000 0.000
#> GSM339468 1 0.8045 0.0212 0.476 0.244 0.016 0.264
#> GSM339469 1 0.4838 0.3774 0.724 0.000 0.024 0.252
#> GSM339470 3 0.5273 0.8699 0.000 0.008 0.536 0.456
#> GSM339471 1 0.7176 0.1763 0.552 0.000 0.196 0.252
#> GSM339472 2 0.0707 0.7680 0.000 0.980 0.000 0.020
#> GSM339473 1 0.4972 0.2934 0.544 0.000 0.456 0.000
#> GSM339474 2 0.1389 0.7652 0.000 0.952 0.000 0.048
#> GSM339475 3 0.6252 0.8506 0.056 0.000 0.512 0.432
#> GSM339476 1 0.5673 0.2501 0.528 0.000 0.024 0.448
#> GSM339477 2 0.2961 0.7355 0.044 0.904 0.012 0.040
#> GSM339478 2 0.4769 0.4891 0.000 0.684 0.008 0.308
#> GSM339479 3 0.6983 0.7445 0.000 0.124 0.516 0.360
#> GSM339480 1 0.7899 0.0377 0.488 0.232 0.012 0.268
#> GSM339481 2 0.0000 0.7722 0.000 1.000 0.000 0.000
#> GSM339482 3 0.6445 0.0517 0.444 0.000 0.488 0.068
#> GSM339483 1 0.5060 0.3057 0.584 0.000 0.004 0.412
#> GSM339484 3 0.5650 0.8816 0.024 0.000 0.544 0.432
#> GSM339485 1 0.5478 0.2901 0.540 0.016 0.000 0.444
#> GSM339486 3 0.5908 0.8801 0.028 0.004 0.536 0.432
#> GSM339487 4 0.7962 0.2799 0.224 0.340 0.008 0.428
#> GSM339488 2 0.0376 0.7714 0.000 0.992 0.004 0.004
#> GSM339489 1 0.8154 -0.0337 0.444 0.240 0.016 0.300
#> GSM339490 1 0.4103 0.3860 0.744 0.000 0.000 0.256
#> GSM339491 3 0.6079 0.8769 0.016 0.020 0.532 0.432
#> GSM339492 1 0.6469 0.2592 0.644 0.000 0.192 0.164
#> GSM339493 2 0.1637 0.7628 0.000 0.940 0.000 0.060
#> GSM339494 1 0.4977 0.2928 0.540 0.000 0.460 0.000
#> GSM339495 2 0.1474 0.7644 0.000 0.948 0.000 0.052
#> GSM339496 4 0.5903 -0.5350 0.052 0.000 0.332 0.616
#> GSM339497 4 0.7714 0.3103 0.160 0.360 0.012 0.468
#> GSM339498 4 0.8233 0.1625 0.316 0.228 0.020 0.436
#> GSM339499 3 0.5268 0.8760 0.008 0.000 0.540 0.452
#> GSM339500 2 0.7093 0.1528 0.000 0.568 0.216 0.216
#> GSM339501 1 0.7881 0.0402 0.492 0.232 0.012 0.264
#> GSM339502 2 0.0524 0.7716 0.000 0.988 0.008 0.004
#> GSM339503 3 0.7527 0.5468 0.216 0.000 0.484 0.300
#> GSM339504 1 0.4134 0.3849 0.740 0.000 0.000 0.260
#> GSM339505 3 0.5388 0.8676 0.000 0.012 0.532 0.456
#> GSM339506 1 0.6010 -0.0822 0.488 0.000 0.472 0.040
#> GSM339507 3 0.5650 0.8816 0.024 0.000 0.544 0.432
#> GSM339508 2 0.1209 0.7705 0.000 0.964 0.004 0.032
#> GSM339509 2 0.0376 0.7710 0.000 0.992 0.004 0.004
#> GSM339510 1 0.7714 0.0260 0.484 0.236 0.004 0.276
#> GSM339511 1 0.5937 0.2747 0.512 0.028 0.004 0.456
#> GSM339512 2 0.2965 0.7248 0.000 0.892 0.036 0.072
#> GSM339513 1 0.3356 0.3637 0.824 0.000 0.176 0.000
#> GSM339514 2 0.0000 0.7722 0.000 1.000 0.000 0.000
#> GSM339515 1 0.4961 0.2931 0.552 0.000 0.448 0.000
#> GSM339516 2 0.7889 -0.2810 0.348 0.364 0.000 0.288
#> GSM339517 3 0.6552 0.8256 0.076 0.000 0.484 0.440
#> GSM339518 2 0.2760 0.7229 0.000 0.872 0.000 0.128
#> GSM339519 1 0.5032 0.3456 0.764 0.000 0.156 0.080
#> GSM339520 2 0.5383 0.5149 0.000 0.744 0.128 0.128
#> GSM339521 2 0.0188 0.7725 0.000 0.996 0.000 0.004
#> GSM339522 1 0.7773 -0.0630 0.432 0.284 0.000 0.284
#> GSM339523 2 0.0000 0.7722 0.000 1.000 0.000 0.000
#> GSM339524 1 0.4948 -0.0166 0.560 0.000 0.440 0.000
#> GSM339525 1 0.5839 0.3236 0.604 0.000 0.044 0.352
#> GSM339526 3 0.5650 0.8816 0.024 0.000 0.544 0.432
#> GSM339527 1 0.7557 0.0166 0.488 0.000 0.252 0.260
#> GSM339528 3 0.5908 0.8822 0.028 0.004 0.536 0.432
#> GSM339529 2 0.4343 0.5413 0.000 0.732 0.004 0.264
#> GSM339530 2 0.5365 0.3834 0.000 0.692 0.264 0.044
#> GSM339531 2 0.8298 -0.3461 0.324 0.336 0.012 0.328
#> GSM339532 1 0.5769 0.3296 0.588 0.036 0.000 0.376
#> GSM339533 3 0.5650 0.8816 0.024 0.000 0.544 0.432
#> GSM339534 1 0.5394 0.3384 0.748 0.012 0.180 0.060
#> GSM339535 2 0.3942 0.5988 0.000 0.764 0.000 0.236
#> GSM339536 1 0.4972 0.2934 0.544 0.000 0.456 0.000
#> GSM339537 2 0.4456 0.5251 0.004 0.716 0.000 0.280
#> GSM339538 1 0.5292 0.2671 0.512 0.000 0.480 0.008
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM339455 3 0.5383 0.5475 0.000 0.004 0.644 0.084 0.268
#> GSM339456 2 0.4752 0.4471 0.000 0.648 0.036 0.000 0.316
#> GSM339457 3 0.4920 0.1430 0.000 0.008 0.568 0.016 0.408
#> GSM339458 3 0.4452 0.0580 0.000 0.496 0.500 0.000 0.004
#> GSM339459 5 0.3323 0.6649 0.004 0.000 0.036 0.116 0.844
#> GSM339460 2 0.1498 0.7798 0.000 0.952 0.008 0.024 0.016
#> GSM339461 5 0.4972 0.3673 0.000 0.336 0.000 0.044 0.620
#> GSM339462 4 0.4737 0.7153 0.156 0.000 0.020 0.756 0.068
#> GSM339463 3 0.1082 0.8339 0.000 0.008 0.964 0.000 0.028
#> GSM339464 4 0.3919 0.7378 0.000 0.000 0.036 0.776 0.188
#> GSM339465 3 0.1082 0.8339 0.000 0.008 0.964 0.000 0.028
#> GSM339466 5 0.2722 0.6960 0.000 0.060 0.040 0.008 0.892
#> GSM339467 2 0.0290 0.7953 0.000 0.992 0.000 0.000 0.008
#> GSM339468 5 0.3623 0.6768 0.004 0.004 0.052 0.104 0.836
#> GSM339469 4 0.0898 0.8281 0.020 0.000 0.008 0.972 0.000
#> GSM339470 3 0.1082 0.8339 0.000 0.008 0.964 0.000 0.028
#> GSM339471 1 0.3280 0.8043 0.808 0.000 0.184 0.004 0.004
#> GSM339472 2 0.0703 0.7938 0.000 0.976 0.000 0.000 0.024
#> GSM339473 1 0.0000 0.8677 1.000 0.000 0.000 0.000 0.000
#> GSM339474 2 0.4464 0.2933 0.000 0.584 0.000 0.008 0.408
#> GSM339475 3 0.0609 0.8351 0.000 0.000 0.980 0.000 0.020
#> GSM339476 4 0.5892 0.5856 0.040 0.000 0.068 0.636 0.256
#> GSM339477 2 0.3262 0.7120 0.000 0.840 0.036 0.000 0.124
#> GSM339478 5 0.4905 0.5462 0.000 0.256 0.036 0.016 0.692
#> GSM339479 3 0.2233 0.7921 0.000 0.104 0.892 0.000 0.004
#> GSM339480 5 0.3165 0.6651 0.000 0.000 0.036 0.116 0.848
#> GSM339481 2 0.0404 0.7950 0.000 0.988 0.000 0.000 0.012
#> GSM339482 3 0.3548 0.7412 0.008 0.000 0.836 0.112 0.044
#> GSM339483 4 0.3516 0.7847 0.004 0.000 0.020 0.812 0.164
#> GSM339484 3 0.0000 0.8392 0.000 0.000 1.000 0.000 0.000
#> GSM339485 4 0.0740 0.8343 0.000 0.008 0.008 0.980 0.004
#> GSM339486 3 0.0451 0.8398 0.000 0.000 0.988 0.008 0.004
#> GSM339487 5 0.3483 0.6783 0.000 0.088 0.052 0.012 0.848
#> GSM339488 2 0.0162 0.7951 0.000 0.996 0.000 0.000 0.004
#> GSM339489 5 0.3693 0.6857 0.000 0.012 0.072 0.080 0.836
#> GSM339490 4 0.0798 0.8299 0.016 0.000 0.008 0.976 0.000
#> GSM339491 3 0.0609 0.8378 0.000 0.020 0.980 0.000 0.000
#> GSM339492 1 0.4059 0.8201 0.804 0.008 0.148 0.020 0.020
#> GSM339493 5 0.4549 0.0174 0.000 0.464 0.000 0.008 0.528
#> GSM339494 1 0.0000 0.8677 1.000 0.000 0.000 0.000 0.000
#> GSM339495 5 0.4533 0.0658 0.000 0.448 0.000 0.008 0.544
#> GSM339496 3 0.3003 0.7072 0.000 0.000 0.812 0.000 0.188
#> GSM339497 5 0.3924 0.6879 0.000 0.096 0.080 0.008 0.816
#> GSM339498 5 0.3527 0.6537 0.000 0.000 0.056 0.116 0.828
#> GSM339499 3 0.1836 0.8255 0.000 0.008 0.936 0.016 0.040
#> GSM339500 5 0.6756 0.1708 0.000 0.308 0.288 0.000 0.404
#> GSM339501 5 0.3565 0.6387 0.000 0.000 0.024 0.176 0.800
#> GSM339502 2 0.0807 0.7930 0.000 0.976 0.012 0.000 0.012
#> GSM339503 3 0.4013 0.7153 0.004 0.000 0.804 0.108 0.084
#> GSM339504 4 0.4206 0.7814 0.048 0.000 0.024 0.800 0.128
#> GSM339505 3 0.1082 0.8339 0.000 0.008 0.964 0.000 0.028
#> GSM339506 3 0.5572 0.5215 0.000 0.000 0.644 0.164 0.192
#> GSM339507 3 0.0162 0.8394 0.004 0.000 0.996 0.000 0.000
#> GSM339508 2 0.4517 0.1324 0.000 0.556 0.000 0.008 0.436
#> GSM339509 2 0.0693 0.7871 0.000 0.980 0.000 0.008 0.012
#> GSM339510 5 0.3106 0.6651 0.000 0.000 0.020 0.140 0.840
#> GSM339511 4 0.2172 0.8020 0.000 0.016 0.000 0.908 0.076
#> GSM339512 2 0.4989 0.1250 0.000 0.552 0.032 0.000 0.416
#> GSM339513 1 0.3849 0.8004 0.820 0.000 0.036 0.124 0.020
#> GSM339514 2 0.0510 0.7940 0.000 0.984 0.000 0.000 0.016
#> GSM339515 1 0.0000 0.8677 1.000 0.000 0.000 0.000 0.000
#> GSM339516 5 0.1845 0.6997 0.000 0.056 0.000 0.016 0.928
#> GSM339517 3 0.1525 0.8247 0.012 0.000 0.948 0.004 0.036
#> GSM339518 5 0.4415 0.2932 0.000 0.388 0.000 0.008 0.604
#> GSM339519 1 0.4387 0.7835 0.796 0.000 0.040 0.116 0.048
#> GSM339520 2 0.3860 0.6555 0.000 0.808 0.148 0.016 0.028
#> GSM339521 2 0.4150 0.2332 0.000 0.612 0.000 0.000 0.388
#> GSM339522 5 0.3413 0.6932 0.000 0.044 0.000 0.124 0.832
#> GSM339523 2 0.0290 0.7953 0.000 0.992 0.000 0.000 0.008
#> GSM339524 3 0.6548 0.3314 0.288 0.000 0.556 0.124 0.032
#> GSM339525 4 0.1282 0.8310 0.000 0.000 0.044 0.952 0.004
#> GSM339526 3 0.0000 0.8392 0.000 0.000 1.000 0.000 0.000
#> GSM339527 5 0.6373 -0.1212 0.000 0.000 0.412 0.164 0.424
#> GSM339528 3 0.0324 0.8401 0.000 0.000 0.992 0.004 0.004
#> GSM339529 5 0.4003 0.5388 0.000 0.288 0.000 0.008 0.704
#> GSM339530 2 0.1904 0.7681 0.000 0.936 0.020 0.016 0.028
#> GSM339531 5 0.1996 0.7057 0.000 0.032 0.036 0.004 0.928
#> GSM339532 4 0.2616 0.7706 0.000 0.020 0.000 0.880 0.100
#> GSM339533 3 0.0000 0.8392 0.000 0.000 1.000 0.000 0.000
#> GSM339534 1 0.4626 0.8292 0.804 0.016 0.056 0.076 0.048
#> GSM339535 5 0.3910 0.5230 0.000 0.272 0.000 0.008 0.720
#> GSM339536 1 0.0000 0.8677 1.000 0.000 0.000 0.000 0.000
#> GSM339537 5 0.1956 0.6943 0.000 0.076 0.000 0.008 0.916
#> GSM339538 1 0.2607 0.8638 0.904 0.000 0.040 0.032 0.024
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM339455 6 0.3919 0.1815 0.000 0.016 0.020 0.004 0.204 0.756
#> GSM339456 2 0.4512 0.5275 0.000 0.708 0.096 0.004 0.192 0.000
#> GSM339457 6 0.3877 0.1887 0.000 0.016 0.024 0.004 0.188 0.768
#> GSM339458 2 0.5708 0.0564 0.000 0.520 0.216 0.000 0.000 0.264
#> GSM339459 3 0.5303 0.4757 0.000 0.000 0.644 0.060 0.052 0.244
#> GSM339460 2 0.0653 0.7955 0.000 0.980 0.004 0.004 0.012 0.000
#> GSM339461 3 0.5385 0.1562 0.000 0.060 0.572 0.032 0.336 0.000
#> GSM339462 4 0.3325 0.7798 0.092 0.000 0.032 0.840 0.036 0.000
#> GSM339463 6 0.4249 0.7584 0.000 0.000 0.328 0.000 0.032 0.640
#> GSM339464 4 0.3825 0.7286 0.000 0.000 0.076 0.788 0.128 0.008
#> GSM339465 6 0.4249 0.7584 0.000 0.000 0.328 0.000 0.032 0.640
#> GSM339466 5 0.1088 0.7148 0.000 0.016 0.000 0.000 0.960 0.024
#> GSM339467 2 0.0458 0.7976 0.000 0.984 0.000 0.000 0.016 0.000
#> GSM339468 5 0.4400 0.6315 0.000 0.008 0.120 0.064 0.772 0.036
#> GSM339469 4 0.0547 0.8320 0.000 0.000 0.000 0.980 0.000 0.020
#> GSM339470 6 0.4249 0.7584 0.000 0.000 0.328 0.000 0.032 0.640
#> GSM339471 1 0.5215 0.7192 0.696 0.000 0.120 0.060 0.000 0.124
#> GSM339472 2 0.0748 0.7925 0.000 0.976 0.004 0.004 0.016 0.000
#> GSM339473 1 0.0000 0.8046 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM339474 5 0.3789 0.3031 0.000 0.416 0.000 0.000 0.584 0.000
#> GSM339475 3 0.3737 -0.3255 0.000 0.000 0.608 0.000 0.000 0.392
#> GSM339476 4 0.6656 0.5438 0.028 0.016 0.092 0.588 0.220 0.056
#> GSM339477 2 0.3477 0.6727 0.000 0.808 0.056 0.004 0.132 0.000
#> GSM339478 5 0.6001 0.3537 0.000 0.140 0.012 0.004 0.460 0.384
#> GSM339479 6 0.5405 0.6665 0.000 0.112 0.312 0.000 0.008 0.568
#> GSM339480 3 0.5500 0.4809 0.000 0.000 0.640 0.060 0.076 0.224
#> GSM339481 2 0.0458 0.7976 0.000 0.984 0.000 0.000 0.016 0.000
#> GSM339482 3 0.2325 0.6191 0.000 0.000 0.892 0.060 0.000 0.048
#> GSM339483 4 0.2633 0.8050 0.000 0.000 0.032 0.864 0.104 0.000
#> GSM339484 6 0.3930 0.7542 0.000 0.000 0.364 0.004 0.004 0.628
#> GSM339485 4 0.0520 0.8339 0.000 0.000 0.008 0.984 0.008 0.000
#> GSM339486 6 0.4102 0.7568 0.000 0.000 0.356 0.012 0.004 0.628
#> GSM339487 5 0.1418 0.7156 0.000 0.024 0.000 0.000 0.944 0.032
#> GSM339488 2 0.0363 0.7975 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM339489 5 0.4726 0.5969 0.000 0.000 0.124 0.044 0.736 0.096
#> GSM339490 4 0.0146 0.8324 0.000 0.000 0.004 0.996 0.000 0.000
#> GSM339491 6 0.4196 0.7534 0.000 0.028 0.332 0.000 0.000 0.640
#> GSM339492 1 0.5680 0.7276 0.680 0.016 0.092 0.056 0.004 0.152
#> GSM339493 5 0.3266 0.5580 0.000 0.272 0.000 0.000 0.728 0.000
#> GSM339494 1 0.0000 0.8046 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM339495 5 0.3244 0.5622 0.000 0.268 0.000 0.000 0.732 0.000
#> GSM339496 6 0.4175 0.3223 0.000 0.000 0.136 0.004 0.108 0.752
#> GSM339497 5 0.3957 0.6887 0.000 0.072 0.056 0.000 0.804 0.068
#> GSM339498 5 0.4897 0.3242 0.000 0.000 0.344 0.064 0.588 0.004
#> GSM339499 6 0.0862 0.4230 0.000 0.016 0.000 0.004 0.008 0.972
#> GSM339500 5 0.6178 0.3865 0.000 0.308 0.024 0.000 0.492 0.176
#> GSM339501 5 0.4524 0.5608 0.000 0.000 0.092 0.200 0.704 0.004
#> GSM339502 2 0.0603 0.7978 0.000 0.980 0.000 0.000 0.016 0.004
#> GSM339503 3 0.2714 0.6131 0.000 0.000 0.872 0.060 0.004 0.064
#> GSM339504 4 0.2986 0.8161 0.032 0.000 0.032 0.876 0.048 0.012
#> GSM339505 6 0.4438 0.7512 0.000 0.000 0.328 0.000 0.044 0.628
#> GSM339506 3 0.6553 0.0213 0.000 0.000 0.460 0.156 0.056 0.328
#> GSM339507 6 0.3861 0.7593 0.008 0.000 0.352 0.000 0.000 0.640
#> GSM339508 5 0.4350 0.3648 0.000 0.428 0.000 0.004 0.552 0.016
#> GSM339509 2 0.0000 0.7934 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM339510 5 0.4721 0.6079 0.000 0.000 0.092 0.116 0.740 0.052
#> GSM339511 4 0.3109 0.7078 0.000 0.004 0.000 0.772 0.224 0.000
#> GSM339512 5 0.4875 0.2726 0.000 0.460 0.008 0.000 0.492 0.040
#> GSM339513 1 0.4252 0.7549 0.752 0.000 0.120 0.120 0.000 0.008
#> GSM339514 2 0.0632 0.7936 0.000 0.976 0.000 0.000 0.024 0.000
#> GSM339515 1 0.0000 0.8046 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM339516 5 0.0993 0.7156 0.000 0.024 0.012 0.000 0.964 0.000
#> GSM339517 3 0.1219 0.5469 0.000 0.000 0.948 0.004 0.000 0.048
#> GSM339518 5 0.2902 0.6502 0.000 0.196 0.000 0.000 0.800 0.004
#> GSM339519 1 0.5509 0.6895 0.676 0.000 0.184 0.060 0.064 0.016
#> GSM339520 2 0.4222 0.3971 0.000 0.516 0.000 0.004 0.008 0.472
#> GSM339521 2 0.3868 -0.3025 0.000 0.504 0.000 0.000 0.496 0.000
#> GSM339522 5 0.1863 0.7025 0.000 0.016 0.004 0.060 0.920 0.000
#> GSM339523 2 0.0458 0.7976 0.000 0.984 0.000 0.000 0.016 0.000
#> GSM339524 3 0.3450 0.6188 0.060 0.000 0.836 0.072 0.000 0.032
#> GSM339525 4 0.1523 0.8290 0.000 0.000 0.008 0.940 0.008 0.044
#> GSM339526 6 0.3737 0.7409 0.000 0.000 0.392 0.000 0.000 0.608
#> GSM339527 3 0.4123 0.5974 0.000 0.000 0.772 0.124 0.088 0.016
#> GSM339528 6 0.4022 0.7563 0.000 0.000 0.360 0.008 0.004 0.628
#> GSM339529 5 0.4105 0.6695 0.000 0.152 0.000 0.008 0.760 0.080
#> GSM339530 2 0.3940 0.5539 0.000 0.652 0.000 0.004 0.008 0.336
#> GSM339531 5 0.2196 0.6841 0.000 0.004 0.108 0.004 0.884 0.000
#> GSM339532 4 0.2300 0.7702 0.000 0.000 0.000 0.856 0.144 0.000
#> GSM339533 6 0.3769 0.7578 0.000 0.000 0.356 0.004 0.000 0.640
#> GSM339534 1 0.6016 0.7414 0.680 0.012 0.040 0.116 0.052 0.100
#> GSM339535 5 0.2378 0.6778 0.000 0.152 0.000 0.000 0.848 0.000
#> GSM339536 1 0.0000 0.8046 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM339537 5 0.0790 0.7173 0.000 0.032 0.000 0.000 0.968 0.000
#> GSM339538 1 0.3652 0.7066 0.720 0.000 0.264 0.016 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 protocol(p) agent(p) individual(p) k
#> CV:pam 69 0.952 0.502 1.38e-02 2
#> CV:pam 60 0.846 0.862 8.09e-04 3
#> CV:pam 39 1.000 0.713 5.36e-02 4
#> CV:pam 70 0.745 0.926 1.03e-06 5
#> CV:pam 66 0.463 0.956 5.30e-09 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 15497 rows and 84 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 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 0.485 0.853 0.900 0.4470 0.535 0.535
#> 3 3 0.445 0.655 0.813 0.3543 0.627 0.416
#> 4 4 0.706 0.837 0.864 0.1194 0.768 0.502
#> 5 5 0.770 0.881 0.886 0.1197 0.852 0.590
#> 6 6 0.766 0.706 0.805 0.0578 0.958 0.829
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
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
#> GSM339455 1 0.5294 0.866 0.880 0.120
#> GSM339456 2 0.8861 0.647 0.304 0.696
#> GSM339457 1 0.5408 0.863 0.876 0.124
#> GSM339458 1 0.9988 0.241 0.520 0.480
#> GSM339459 1 0.1843 0.902 0.972 0.028
#> GSM339460 2 0.2236 0.921 0.036 0.964
#> GSM339461 2 0.4815 0.908 0.104 0.896
#> GSM339462 1 0.2778 0.898 0.952 0.048
#> GSM339463 1 0.6438 0.849 0.836 0.164
#> GSM339464 1 0.0376 0.896 0.996 0.004
#> GSM339465 1 0.6438 0.849 0.836 0.164
#> GSM339466 2 0.2236 0.921 0.036 0.964
#> GSM339467 2 0.4298 0.919 0.088 0.912
#> GSM339468 1 0.9795 0.315 0.584 0.416
#> GSM339469 1 0.0376 0.896 0.996 0.004
#> GSM339470 1 0.7528 0.803 0.784 0.216
#> GSM339471 1 0.2043 0.874 0.968 0.032
#> GSM339472 2 0.4022 0.922 0.080 0.920
#> GSM339473 1 0.3733 0.886 0.928 0.072
#> GSM339474 2 0.4161 0.921 0.084 0.916
#> GSM339475 1 0.1843 0.903 0.972 0.028
#> GSM339476 1 0.0376 0.896 0.996 0.004
#> GSM339477 2 0.5737 0.886 0.136 0.864
#> GSM339478 1 0.5519 0.861 0.872 0.128
#> GSM339479 1 0.8267 0.764 0.740 0.260
#> GSM339480 1 0.1843 0.902 0.972 0.028
#> GSM339481 2 0.3879 0.923 0.076 0.924
#> GSM339482 1 0.1843 0.903 0.972 0.028
#> GSM339483 1 0.2778 0.898 0.952 0.048
#> GSM339484 1 0.5946 0.859 0.856 0.144
#> GSM339485 1 0.0376 0.896 0.996 0.004
#> GSM339486 1 0.6623 0.859 0.828 0.172
#> GSM339487 2 0.2043 0.920 0.032 0.968
#> GSM339488 2 0.4022 0.922 0.080 0.920
#> GSM339489 2 0.9850 0.218 0.428 0.572
#> GSM339490 1 0.0376 0.896 0.996 0.004
#> GSM339491 1 0.9000 0.645 0.684 0.316
#> GSM339492 1 0.2236 0.876 0.964 0.036
#> GSM339493 2 0.2423 0.922 0.040 0.960
#> GSM339494 1 0.3733 0.886 0.928 0.072
#> GSM339495 2 0.4161 0.921 0.084 0.916
#> GSM339496 1 0.2948 0.900 0.948 0.052
#> GSM339497 2 0.2043 0.920 0.032 0.968
#> GSM339498 1 0.5737 0.862 0.864 0.136
#> GSM339499 1 0.5294 0.866 0.880 0.120
#> GSM339500 2 0.2043 0.920 0.032 0.968
#> GSM339501 1 0.1184 0.900 0.984 0.016
#> GSM339502 2 0.2043 0.920 0.032 0.968
#> GSM339503 1 0.2043 0.902 0.968 0.032
#> GSM339504 1 0.2778 0.898 0.952 0.048
#> GSM339505 1 0.7453 0.808 0.788 0.212
#> GSM339506 1 0.1184 0.900 0.984 0.016
#> GSM339507 1 0.5946 0.859 0.856 0.144
#> GSM339508 2 0.6531 0.870 0.168 0.832
#> GSM339509 2 0.6247 0.880 0.156 0.844
#> GSM339510 1 0.9866 0.312 0.568 0.432
#> GSM339511 1 0.1843 0.899 0.972 0.028
#> GSM339512 2 0.2043 0.920 0.032 0.968
#> GSM339513 1 0.1414 0.896 0.980 0.020
#> GSM339514 2 0.2423 0.922 0.040 0.960
#> GSM339515 1 0.3733 0.886 0.928 0.072
#> GSM339516 2 0.4022 0.922 0.080 0.920
#> GSM339517 1 0.1843 0.903 0.972 0.028
#> GSM339518 2 0.2043 0.920 0.032 0.968
#> GSM339519 1 0.2043 0.902 0.968 0.032
#> GSM339520 1 0.5519 0.861 0.872 0.128
#> GSM339521 2 0.2043 0.920 0.032 0.968
#> GSM339522 2 0.5519 0.893 0.128 0.872
#> GSM339523 2 0.2043 0.920 0.032 0.968
#> GSM339524 1 0.1843 0.903 0.972 0.028
#> GSM339525 1 0.2778 0.898 0.952 0.048
#> GSM339526 1 0.2043 0.903 0.968 0.032
#> GSM339527 1 0.1184 0.900 0.984 0.016
#> GSM339528 1 0.6531 0.863 0.832 0.168
#> GSM339529 2 0.6531 0.870 0.168 0.832
#> GSM339530 1 0.5408 0.863 0.876 0.124
#> GSM339531 2 0.8813 0.605 0.300 0.700
#> GSM339532 1 0.0672 0.898 0.992 0.008
#> GSM339533 1 0.6438 0.849 0.836 0.164
#> GSM339534 1 0.2423 0.900 0.960 0.040
#> GSM339535 2 0.2043 0.920 0.032 0.968
#> GSM339536 1 0.3733 0.886 0.928 0.072
#> GSM339537 2 0.4022 0.922 0.080 0.920
#> GSM339538 1 0.1843 0.903 0.972 0.028
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM339455 3 0.7389 -0.121 0.032 0.464 0.504
#> GSM339456 2 0.6096 0.646 0.016 0.704 0.280
#> GSM339457 3 0.7394 -0.140 0.032 0.472 0.496
#> GSM339458 2 0.3030 0.799 0.004 0.904 0.092
#> GSM339459 3 0.2339 0.686 0.048 0.012 0.940
#> GSM339460 2 0.0424 0.825 0.000 0.992 0.008
#> GSM339461 2 0.3532 0.806 0.008 0.884 0.108
#> GSM339462 1 0.5012 0.759 0.788 0.008 0.204
#> GSM339463 2 0.8382 0.144 0.084 0.492 0.424
#> GSM339464 1 0.5216 0.735 0.740 0.000 0.260
#> GSM339465 2 0.8820 0.119 0.116 0.476 0.408
#> GSM339466 2 0.0000 0.823 0.000 1.000 0.000
#> GSM339467 2 0.1765 0.828 0.004 0.956 0.040
#> GSM339468 2 0.7230 0.497 0.040 0.616 0.344
#> GSM339469 1 0.5016 0.743 0.760 0.000 0.240
#> GSM339470 2 0.6057 0.490 0.004 0.656 0.340
#> GSM339471 1 0.4796 0.735 0.780 0.000 0.220
#> GSM339472 2 0.2269 0.826 0.016 0.944 0.040
#> GSM339473 1 0.4589 0.727 0.820 0.008 0.172
#> GSM339474 2 0.2383 0.826 0.016 0.940 0.044
#> GSM339475 3 0.1163 0.679 0.028 0.000 0.972
#> GSM339476 1 0.6026 0.709 0.624 0.000 0.376
#> GSM339477 2 0.4749 0.760 0.012 0.816 0.172
#> GSM339478 2 0.6952 0.442 0.024 0.600 0.376
#> GSM339479 2 0.4172 0.750 0.004 0.840 0.156
#> GSM339480 3 0.2599 0.682 0.052 0.016 0.932
#> GSM339481 2 0.1751 0.826 0.012 0.960 0.028
#> GSM339482 3 0.1031 0.688 0.024 0.000 0.976
#> GSM339483 1 0.5012 0.759 0.788 0.008 0.204
#> GSM339484 1 0.6661 0.604 0.588 0.012 0.400
#> GSM339485 1 0.5291 0.735 0.732 0.000 0.268
#> GSM339486 1 0.6180 0.640 0.660 0.008 0.332
#> GSM339487 2 0.0237 0.823 0.004 0.996 0.000
#> GSM339488 2 0.1129 0.828 0.004 0.976 0.020
#> GSM339489 2 0.4121 0.761 0.000 0.832 0.168
#> GSM339490 1 0.4931 0.738 0.768 0.000 0.232
#> GSM339491 2 0.5291 0.633 0.000 0.732 0.268
#> GSM339492 1 0.4974 0.739 0.764 0.000 0.236
#> GSM339493 2 0.0829 0.823 0.012 0.984 0.004
#> GSM339494 1 0.4700 0.731 0.812 0.008 0.180
#> GSM339495 2 0.2383 0.826 0.016 0.940 0.044
#> GSM339496 3 0.0747 0.691 0.016 0.000 0.984
#> GSM339497 2 0.0000 0.823 0.000 1.000 0.000
#> GSM339498 3 0.3356 0.670 0.056 0.036 0.908
#> GSM339499 3 0.7394 -0.140 0.032 0.472 0.496
#> GSM339500 2 0.0000 0.823 0.000 1.000 0.000
#> GSM339501 3 0.4883 0.477 0.208 0.004 0.788
#> GSM339502 2 0.0237 0.823 0.004 0.996 0.000
#> GSM339503 3 0.0747 0.700 0.016 0.000 0.984
#> GSM339504 1 0.5012 0.759 0.788 0.008 0.204
#> GSM339505 2 0.6104 0.480 0.004 0.648 0.348
#> GSM339506 3 0.4834 0.478 0.204 0.004 0.792
#> GSM339507 1 0.9520 0.227 0.416 0.188 0.396
#> GSM339508 2 0.4413 0.790 0.036 0.860 0.104
#> GSM339509 2 0.3445 0.808 0.016 0.896 0.088
#> GSM339510 2 0.6276 0.680 0.040 0.736 0.224
#> GSM339511 1 0.7062 0.710 0.696 0.068 0.236
#> GSM339512 2 0.0000 0.823 0.000 1.000 0.000
#> GSM339513 1 0.6104 0.728 0.648 0.004 0.348
#> GSM339514 2 0.0475 0.825 0.004 0.992 0.004
#> GSM339515 1 0.4645 0.729 0.816 0.008 0.176
#> GSM339516 2 0.2229 0.827 0.012 0.944 0.044
#> GSM339517 3 0.0237 0.701 0.004 0.000 0.996
#> GSM339518 2 0.0000 0.823 0.000 1.000 0.000
#> GSM339519 3 0.0424 0.701 0.008 0.000 0.992
#> GSM339520 2 0.7164 0.244 0.024 0.524 0.452
#> GSM339521 2 0.0000 0.823 0.000 1.000 0.000
#> GSM339522 2 0.3637 0.810 0.024 0.892 0.084
#> GSM339523 2 0.0000 0.823 0.000 1.000 0.000
#> GSM339524 3 0.0000 0.700 0.000 0.000 1.000
#> GSM339525 1 0.5012 0.759 0.788 0.008 0.204
#> GSM339526 3 0.2165 0.645 0.064 0.000 0.936
#> GSM339527 3 0.4465 0.527 0.176 0.004 0.820
#> GSM339528 1 0.5420 0.706 0.752 0.008 0.240
#> GSM339529 2 0.4413 0.790 0.036 0.860 0.104
#> GSM339530 3 0.7186 -0.150 0.024 0.476 0.500
#> GSM339531 2 0.4755 0.747 0.008 0.808 0.184
#> GSM339532 1 0.5315 0.739 0.772 0.012 0.216
#> GSM339533 2 0.8113 0.171 0.068 0.504 0.428
#> GSM339534 1 0.6673 0.728 0.636 0.020 0.344
#> GSM339535 2 0.0000 0.823 0.000 1.000 0.000
#> GSM339536 1 0.4700 0.731 0.812 0.008 0.180
#> GSM339537 2 0.2269 0.826 0.016 0.944 0.040
#> GSM339538 3 0.0424 0.700 0.008 0.000 0.992
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM339455 3 0.4814 0.783 0.172 0.004 0.776 0.048
#> GSM339456 2 0.4343 0.883 0.040 0.844 0.060 0.056
#> GSM339457 3 0.4573 0.783 0.124 0.024 0.816 0.036
#> GSM339458 2 0.0524 0.947 0.008 0.988 0.004 0.000
#> GSM339459 3 0.2207 0.790 0.012 0.004 0.928 0.056
#> GSM339460 2 0.0188 0.949 0.000 0.996 0.000 0.004
#> GSM339461 2 0.2505 0.942 0.036 0.920 0.004 0.040
#> GSM339462 4 0.2222 0.912 0.060 0.000 0.016 0.924
#> GSM339463 3 0.5021 0.756 0.180 0.064 0.756 0.000
#> GSM339464 4 0.2125 0.906 0.004 0.000 0.076 0.920
#> GSM339465 3 0.4690 0.723 0.260 0.016 0.724 0.000
#> GSM339466 2 0.1356 0.947 0.032 0.960 0.000 0.008
#> GSM339467 2 0.0712 0.951 0.004 0.984 0.008 0.004
#> GSM339468 3 0.7470 0.401 0.036 0.360 0.520 0.084
#> GSM339469 4 0.1890 0.916 0.008 0.000 0.056 0.936
#> GSM339470 3 0.5417 0.638 0.040 0.284 0.676 0.000
#> GSM339471 1 0.4188 0.841 0.824 0.000 0.112 0.064
#> GSM339472 2 0.1489 0.947 0.004 0.952 0.000 0.044
#> GSM339473 1 0.2945 0.880 0.904 0.012 0.052 0.032
#> GSM339474 2 0.1489 0.947 0.004 0.952 0.000 0.044
#> GSM339475 3 0.0592 0.792 0.016 0.000 0.984 0.000
#> GSM339476 3 0.5257 0.756 0.144 0.000 0.752 0.104
#> GSM339477 2 0.2170 0.942 0.012 0.936 0.016 0.036
#> GSM339478 3 0.5908 0.725 0.084 0.136 0.744 0.036
#> GSM339479 2 0.1356 0.937 0.008 0.960 0.032 0.000
#> GSM339480 3 0.2186 0.789 0.012 0.008 0.932 0.048
#> GSM339481 2 0.1211 0.949 0.000 0.960 0.000 0.040
#> GSM339482 3 0.1510 0.790 0.016 0.000 0.956 0.028
#> GSM339483 4 0.2222 0.912 0.060 0.000 0.016 0.924
#> GSM339484 3 0.5795 0.717 0.212 0.048 0.716 0.024
#> GSM339485 4 0.2125 0.906 0.004 0.000 0.076 0.920
#> GSM339486 3 0.5718 0.567 0.344 0.012 0.624 0.020
#> GSM339487 2 0.1452 0.947 0.036 0.956 0.000 0.008
#> GSM339488 2 0.0376 0.950 0.004 0.992 0.004 0.000
#> GSM339489 2 0.3410 0.925 0.036 0.888 0.032 0.044
#> GSM339490 4 0.1890 0.916 0.008 0.000 0.056 0.936
#> GSM339491 3 0.5828 0.589 0.036 0.316 0.640 0.008
#> GSM339492 1 0.4336 0.837 0.812 0.000 0.128 0.060
#> GSM339493 2 0.1724 0.947 0.032 0.948 0.000 0.020
#> GSM339494 1 0.2945 0.880 0.904 0.012 0.052 0.032
#> GSM339495 2 0.1635 0.946 0.008 0.948 0.000 0.044
#> GSM339496 3 0.1576 0.793 0.048 0.000 0.948 0.004
#> GSM339497 2 0.0817 0.948 0.024 0.976 0.000 0.000
#> GSM339498 3 0.3657 0.788 0.016 0.024 0.864 0.096
#> GSM339499 3 0.4672 0.782 0.124 0.028 0.812 0.036
#> GSM339500 2 0.1022 0.945 0.032 0.968 0.000 0.000
#> GSM339501 3 0.4313 0.699 0.004 0.000 0.736 0.260
#> GSM339502 2 0.0188 0.948 0.004 0.996 0.000 0.000
#> GSM339503 3 0.2300 0.788 0.016 0.000 0.920 0.064
#> GSM339504 4 0.2222 0.912 0.060 0.000 0.016 0.924
#> GSM339505 3 0.5137 0.681 0.040 0.244 0.716 0.000
#> GSM339506 3 0.4535 0.673 0.000 0.004 0.704 0.292
#> GSM339507 3 0.5658 0.725 0.208 0.048 0.724 0.020
#> GSM339508 2 0.3641 0.889 0.008 0.868 0.052 0.072
#> GSM339509 2 0.3272 0.904 0.004 0.884 0.052 0.060
#> GSM339510 2 0.5109 0.831 0.036 0.800 0.080 0.084
#> GSM339511 4 0.3828 0.832 0.000 0.084 0.068 0.848
#> GSM339512 2 0.1118 0.945 0.036 0.964 0.000 0.000
#> GSM339513 1 0.6058 0.486 0.604 0.000 0.336 0.060
#> GSM339514 2 0.0376 0.950 0.004 0.992 0.004 0.000
#> GSM339515 1 0.2945 0.880 0.904 0.012 0.052 0.032
#> GSM339516 2 0.1635 0.948 0.008 0.948 0.000 0.044
#> GSM339517 3 0.0937 0.792 0.012 0.000 0.976 0.012
#> GSM339518 2 0.0000 0.948 0.000 1.000 0.000 0.000
#> GSM339519 3 0.1854 0.790 0.012 0.000 0.940 0.048
#> GSM339520 3 0.5174 0.764 0.088 0.080 0.796 0.036
#> GSM339521 2 0.0707 0.949 0.020 0.980 0.000 0.000
#> GSM339522 2 0.3116 0.933 0.032 0.900 0.024 0.044
#> GSM339523 2 0.0000 0.948 0.000 1.000 0.000 0.000
#> GSM339524 3 0.1635 0.790 0.008 0.000 0.948 0.044
#> GSM339525 4 0.2837 0.895 0.068 0.012 0.016 0.904
#> GSM339526 3 0.3084 0.793 0.064 0.012 0.896 0.028
#> GSM339527 3 0.4164 0.703 0.000 0.000 0.736 0.264
#> GSM339528 3 0.5993 0.528 0.344 0.012 0.612 0.032
#> GSM339529 2 0.3769 0.885 0.012 0.864 0.052 0.072
#> GSM339530 3 0.4859 0.781 0.124 0.036 0.804 0.036
#> GSM339531 2 0.3843 0.900 0.036 0.868 0.056 0.040
#> GSM339532 4 0.2300 0.914 0.000 0.028 0.048 0.924
#> GSM339533 3 0.4636 0.773 0.140 0.068 0.792 0.000
#> GSM339534 3 0.5259 0.744 0.164 0.032 0.768 0.036
#> GSM339535 2 0.0469 0.949 0.012 0.988 0.000 0.000
#> GSM339536 1 0.2945 0.880 0.904 0.012 0.052 0.032
#> GSM339537 2 0.1489 0.947 0.004 0.952 0.000 0.044
#> GSM339538 3 0.0804 0.792 0.012 0.000 0.980 0.008
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM339455 3 0.4899 0.768 0.088 0.008 0.776 0.036 0.092
#> GSM339456 2 0.2729 0.854 0.000 0.884 0.000 0.056 0.060
#> GSM339457 3 0.0703 0.856 0.000 0.000 0.976 0.000 0.024
#> GSM339458 2 0.2877 0.870 0.004 0.848 0.144 0.000 0.004
#> GSM339459 5 0.1764 0.924 0.000 0.000 0.008 0.064 0.928
#> GSM339460 2 0.1341 0.895 0.000 0.944 0.056 0.000 0.000
#> GSM339461 2 0.1403 0.890 0.000 0.952 0.000 0.024 0.024
#> GSM339462 4 0.2131 0.915 0.056 0.008 0.000 0.920 0.016
#> GSM339463 3 0.4735 0.764 0.196 0.036 0.740 0.000 0.028
#> GSM339464 4 0.1872 0.934 0.000 0.000 0.020 0.928 0.052
#> GSM339465 3 0.4867 0.674 0.260 0.020 0.692 0.000 0.028
#> GSM339466 2 0.1732 0.892 0.000 0.920 0.080 0.000 0.000
#> GSM339467 2 0.2877 0.874 0.004 0.848 0.144 0.000 0.004
#> GSM339468 2 0.3234 0.817 0.000 0.852 0.000 0.064 0.084
#> GSM339469 4 0.1484 0.934 0.000 0.000 0.008 0.944 0.048
#> GSM339470 3 0.3308 0.804 0.004 0.144 0.832 0.000 0.020
#> GSM339471 1 0.2727 0.899 0.888 0.000 0.020 0.012 0.080
#> GSM339472 2 0.1469 0.889 0.000 0.948 0.000 0.016 0.036
#> GSM339473 1 0.0880 0.914 0.968 0.000 0.000 0.032 0.000
#> GSM339474 2 0.1386 0.890 0.000 0.952 0.000 0.016 0.032
#> GSM339475 5 0.2011 0.927 0.044 0.000 0.020 0.008 0.928
#> GSM339476 1 0.5137 0.757 0.724 0.000 0.016 0.152 0.108
#> GSM339477 2 0.1668 0.888 0.000 0.940 0.000 0.032 0.028
#> GSM339478 3 0.0771 0.855 0.000 0.004 0.976 0.000 0.020
#> GSM339479 2 0.2877 0.870 0.004 0.848 0.144 0.000 0.004
#> GSM339480 5 0.1764 0.924 0.000 0.000 0.008 0.064 0.928
#> GSM339481 2 0.1106 0.892 0.000 0.964 0.000 0.012 0.024
#> GSM339482 5 0.1682 0.929 0.044 0.000 0.012 0.004 0.940
#> GSM339483 4 0.2131 0.915 0.056 0.008 0.000 0.920 0.016
#> GSM339484 1 0.1399 0.908 0.952 0.020 0.000 0.000 0.028
#> GSM339485 4 0.1872 0.934 0.000 0.000 0.020 0.928 0.052
#> GSM339486 1 0.1082 0.915 0.964 0.000 0.008 0.000 0.028
#> GSM339487 2 0.0880 0.897 0.000 0.968 0.032 0.000 0.000
#> GSM339488 2 0.2719 0.872 0.004 0.852 0.144 0.000 0.000
#> GSM339489 2 0.2372 0.893 0.016 0.920 0.028 0.028 0.008
#> GSM339490 4 0.1557 0.934 0.000 0.000 0.008 0.940 0.052
#> GSM339491 3 0.4342 0.750 0.024 0.188 0.764 0.000 0.024
#> GSM339492 1 0.2727 0.899 0.888 0.000 0.020 0.012 0.080
#> GSM339493 2 0.1267 0.893 0.004 0.960 0.000 0.012 0.024
#> GSM339494 1 0.1041 0.915 0.964 0.000 0.000 0.032 0.004
#> GSM339495 2 0.1485 0.890 0.000 0.948 0.000 0.020 0.032
#> GSM339496 5 0.3885 0.763 0.040 0.000 0.176 0.000 0.784
#> GSM339497 2 0.2629 0.876 0.004 0.860 0.136 0.000 0.000
#> GSM339498 5 0.2869 0.899 0.008 0.036 0.004 0.064 0.888
#> GSM339499 3 0.0703 0.856 0.000 0.000 0.976 0.000 0.024
#> GSM339500 2 0.2516 0.875 0.000 0.860 0.140 0.000 0.000
#> GSM339501 4 0.2575 0.922 0.004 0.000 0.012 0.884 0.100
#> GSM339502 2 0.2719 0.872 0.004 0.852 0.144 0.000 0.000
#> GSM339503 5 0.1547 0.941 0.016 0.000 0.004 0.032 0.948
#> GSM339504 4 0.2131 0.915 0.056 0.008 0.000 0.920 0.016
#> GSM339505 3 0.3308 0.804 0.004 0.144 0.832 0.000 0.020
#> GSM339506 4 0.2589 0.925 0.008 0.000 0.012 0.888 0.092
#> GSM339507 1 0.2599 0.880 0.904 0.024 0.044 0.000 0.028
#> GSM339508 2 0.3188 0.839 0.000 0.860 0.100 0.028 0.012
#> GSM339509 2 0.4273 0.811 0.000 0.732 0.240 0.020 0.008
#> GSM339510 2 0.2856 0.863 0.032 0.892 0.000 0.044 0.032
#> GSM339511 4 0.3423 0.882 0.000 0.068 0.016 0.856 0.060
#> GSM339512 2 0.2833 0.875 0.004 0.852 0.140 0.004 0.000
#> GSM339513 1 0.2629 0.889 0.880 0.000 0.004 0.012 0.104
#> GSM339514 2 0.2719 0.872 0.004 0.852 0.144 0.000 0.000
#> GSM339515 1 0.0880 0.914 0.968 0.000 0.000 0.032 0.000
#> GSM339516 2 0.1195 0.891 0.000 0.960 0.000 0.012 0.028
#> GSM339517 5 0.1806 0.941 0.016 0.000 0.016 0.028 0.940
#> GSM339518 2 0.2629 0.876 0.004 0.860 0.136 0.000 0.000
#> GSM339519 5 0.1710 0.940 0.016 0.000 0.004 0.040 0.940
#> GSM339520 3 0.0703 0.856 0.000 0.000 0.976 0.000 0.024
#> GSM339521 2 0.0880 0.897 0.000 0.968 0.032 0.000 0.000
#> GSM339522 2 0.1653 0.888 0.000 0.944 0.004 0.028 0.024
#> GSM339523 2 0.2516 0.876 0.000 0.860 0.140 0.000 0.000
#> GSM339524 5 0.1630 0.941 0.016 0.000 0.004 0.036 0.944
#> GSM339525 4 0.2199 0.912 0.060 0.008 0.000 0.916 0.016
#> GSM339526 5 0.2859 0.894 0.096 0.000 0.016 0.012 0.876
#> GSM339527 4 0.2520 0.924 0.004 0.000 0.012 0.888 0.096
#> GSM339528 1 0.1243 0.916 0.960 0.000 0.008 0.004 0.028
#> GSM339529 2 0.3188 0.839 0.000 0.860 0.100 0.028 0.012
#> GSM339530 3 0.0703 0.856 0.000 0.000 0.976 0.000 0.024
#> GSM339531 2 0.2362 0.872 0.028 0.916 0.000 0.032 0.024
#> GSM339532 4 0.1956 0.934 0.000 0.012 0.008 0.928 0.052
#> GSM339533 3 0.4293 0.804 0.156 0.032 0.784 0.000 0.028
#> GSM339534 1 0.2604 0.903 0.896 0.020 0.012 0.000 0.072
#> GSM339535 2 0.2674 0.873 0.004 0.856 0.140 0.000 0.000
#> GSM339536 1 0.0880 0.914 0.968 0.000 0.000 0.032 0.000
#> GSM339537 2 0.1300 0.890 0.000 0.956 0.000 0.016 0.028
#> GSM339538 5 0.1701 0.941 0.016 0.000 0.012 0.028 0.944
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM339455 6 0.5659 0.0794 0.072 0.000 0.400 0.032 0.000 0.496
#> GSM339456 2 0.3926 0.6013 0.000 0.796 0.024 0.080 0.100 0.000
#> GSM339457 6 0.0260 0.8133 0.000 0.000 0.008 0.000 0.000 0.992
#> GSM339458 2 0.3979 0.3701 0.000 0.628 0.000 0.000 0.360 0.012
#> GSM339459 3 0.4512 0.7311 0.000 0.000 0.708 0.096 0.192 0.004
#> GSM339460 2 0.3221 0.5738 0.000 0.736 0.000 0.000 0.264 0.000
#> GSM339461 2 0.1708 0.7033 0.000 0.932 0.004 0.024 0.040 0.000
#> GSM339462 4 0.2372 0.8005 0.036 0.000 0.024 0.908 0.024 0.008
#> GSM339463 6 0.4878 0.7075 0.156 0.024 0.092 0.000 0.008 0.720
#> GSM339464 4 0.0146 0.8077 0.000 0.000 0.004 0.996 0.000 0.000
#> GSM339465 6 0.5798 0.4728 0.312 0.004 0.144 0.000 0.008 0.532
#> GSM339466 2 0.3271 0.5995 0.000 0.760 0.000 0.000 0.232 0.008
#> GSM339467 5 0.4049 0.9632 0.000 0.256 0.000 0.004 0.708 0.032
#> GSM339468 2 0.5310 0.4571 0.000 0.668 0.044 0.100 0.188 0.000
#> GSM339469 4 0.0458 0.8053 0.000 0.000 0.016 0.984 0.000 0.000
#> GSM339470 6 0.3045 0.7329 0.000 0.060 0.000 0.000 0.100 0.840
#> GSM339471 1 0.2425 0.9102 0.884 0.000 0.088 0.000 0.004 0.024
#> GSM339472 2 0.0405 0.7139 0.000 0.988 0.004 0.000 0.008 0.000
#> GSM339473 1 0.0260 0.9380 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM339474 2 0.0713 0.7075 0.000 0.972 0.000 0.000 0.028 0.000
#> GSM339475 3 0.1616 0.8351 0.028 0.000 0.940 0.012 0.000 0.020
#> GSM339476 1 0.3782 0.8432 0.808 0.000 0.080 0.088 0.000 0.024
#> GSM339477 2 0.2007 0.7024 0.000 0.916 0.004 0.036 0.044 0.000
#> GSM339478 6 0.0520 0.8128 0.000 0.000 0.008 0.000 0.008 0.984
#> GSM339479 2 0.4102 0.3730 0.000 0.628 0.004 0.000 0.356 0.012
#> GSM339480 3 0.4556 0.7269 0.000 0.000 0.704 0.100 0.192 0.004
#> GSM339481 2 0.1007 0.7118 0.000 0.956 0.000 0.000 0.044 0.000
#> GSM339482 3 0.1649 0.8611 0.032 0.000 0.932 0.036 0.000 0.000
#> GSM339483 4 0.2372 0.8005 0.036 0.000 0.024 0.908 0.024 0.008
#> GSM339484 1 0.0551 0.9362 0.984 0.004 0.004 0.000 0.008 0.000
#> GSM339485 4 0.0146 0.8077 0.000 0.000 0.004 0.996 0.000 0.000
#> GSM339486 1 0.0551 0.9366 0.984 0.000 0.004 0.000 0.004 0.008
#> GSM339487 2 0.2805 0.6431 0.000 0.812 0.000 0.000 0.184 0.004
#> GSM339488 5 0.4071 0.9616 0.000 0.248 0.000 0.004 0.712 0.036
#> GSM339489 2 0.2144 0.7120 0.000 0.908 0.000 0.040 0.048 0.004
#> GSM339490 4 0.0260 0.8073 0.000 0.000 0.008 0.992 0.000 0.000
#> GSM339491 6 0.3616 0.6774 0.000 0.076 0.000 0.000 0.132 0.792
#> GSM339492 1 0.2476 0.9080 0.880 0.000 0.092 0.000 0.004 0.024
#> GSM339493 2 0.0260 0.7150 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM339494 1 0.0260 0.9380 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM339495 2 0.0790 0.7065 0.000 0.968 0.000 0.000 0.032 0.000
#> GSM339496 3 0.5011 0.5122 0.036 0.000 0.632 0.040 0.000 0.292
#> GSM339497 2 0.3729 0.5078 0.000 0.692 0.000 0.000 0.296 0.012
#> GSM339498 3 0.4876 0.6952 0.000 0.020 0.688 0.088 0.204 0.000
#> GSM339499 6 0.0405 0.8131 0.000 0.000 0.008 0.004 0.000 0.988
#> GSM339500 2 0.3905 0.4667 0.000 0.668 0.000 0.000 0.316 0.016
#> GSM339501 4 0.5781 0.0109 0.000 0.000 0.396 0.428 0.176 0.000
#> GSM339502 5 0.3711 0.9606 0.000 0.260 0.000 0.000 0.720 0.020
#> GSM339503 3 0.1624 0.8559 0.008 0.000 0.936 0.044 0.012 0.000
#> GSM339504 4 0.2372 0.8005 0.036 0.000 0.024 0.908 0.024 0.008
#> GSM339505 6 0.2948 0.7398 0.000 0.060 0.000 0.000 0.092 0.848
#> GSM339506 4 0.5829 0.0467 0.000 0.000 0.380 0.432 0.188 0.000
#> GSM339507 1 0.1836 0.9056 0.928 0.012 0.004 0.000 0.008 0.048
#> GSM339508 2 0.2929 0.6785 0.000 0.868 0.008 0.040 0.008 0.076
#> GSM339509 2 0.5951 -0.1576 0.000 0.472 0.008 0.016 0.396 0.108
#> GSM339510 2 0.4142 0.5478 0.000 0.752 0.008 0.072 0.168 0.000
#> GSM339511 4 0.2252 0.7606 0.000 0.072 0.016 0.900 0.012 0.000
#> GSM339512 2 0.3969 0.4643 0.000 0.668 0.000 0.000 0.312 0.020
#> GSM339513 1 0.2457 0.8853 0.880 0.000 0.084 0.036 0.000 0.000
#> GSM339514 5 0.3888 0.9651 0.000 0.252 0.000 0.000 0.716 0.032
#> GSM339515 1 0.0260 0.9380 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM339516 2 0.0000 0.7142 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM339517 3 0.1780 0.8610 0.028 0.000 0.924 0.048 0.000 0.000
#> GSM339518 2 0.3871 0.4825 0.000 0.676 0.000 0.000 0.308 0.016
#> GSM339519 3 0.1511 0.8589 0.012 0.000 0.940 0.044 0.000 0.004
#> GSM339520 6 0.0405 0.8134 0.000 0.000 0.008 0.000 0.004 0.988
#> GSM339521 2 0.3050 0.6042 0.000 0.764 0.000 0.000 0.236 0.000
#> GSM339522 2 0.1922 0.7129 0.000 0.924 0.012 0.040 0.024 0.000
#> GSM339523 5 0.3816 0.9095 0.000 0.296 0.000 0.000 0.688 0.016
#> GSM339524 3 0.1572 0.8615 0.028 0.000 0.936 0.036 0.000 0.000
#> GSM339525 4 0.2272 0.7996 0.040 0.000 0.016 0.912 0.024 0.008
#> GSM339526 3 0.2358 0.8093 0.108 0.000 0.876 0.000 0.000 0.016
#> GSM339527 4 0.5848 0.0390 0.000 0.000 0.380 0.428 0.192 0.000
#> GSM339528 1 0.0405 0.9372 0.988 0.000 0.004 0.000 0.000 0.008
#> GSM339529 2 0.3191 0.6783 0.000 0.856 0.008 0.036 0.020 0.080
#> GSM339530 6 0.0260 0.8133 0.000 0.000 0.008 0.000 0.000 0.992
#> GSM339531 2 0.3314 0.6322 0.000 0.828 0.008 0.052 0.112 0.000
#> GSM339532 4 0.1059 0.8035 0.000 0.016 0.016 0.964 0.004 0.000
#> GSM339533 6 0.3490 0.7622 0.152 0.024 0.008 0.000 0.008 0.808
#> GSM339534 1 0.2731 0.9069 0.892 0.008 0.044 0.036 0.008 0.012
#> GSM339535 2 0.3986 0.4552 0.000 0.664 0.000 0.000 0.316 0.020
#> GSM339536 1 0.0260 0.9380 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM339537 2 0.0363 0.7126 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM339538 3 0.1780 0.8610 0.028 0.000 0.924 0.048 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 protocol(p) agent(p) individual(p) k
#> CV:mclust 80 0.767 0.798 1.67e-03 2
#> CV:mclust 69 0.495 0.739 7.74e-05 3
#> CV:mclust 82 0.713 0.985 3.88e-09 4
#> CV:mclust 84 0.936 0.962 4.66e-09 5
#> CV:mclust 71 0.933 0.996 1.02e-09 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 15497 rows and 84 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 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 0.745 0.814 0.927 0.5045 0.494 0.494
#> 3 3 0.517 0.462 0.724 0.3200 0.794 0.607
#> 4 4 0.595 0.670 0.808 0.1164 0.784 0.471
#> 5 5 0.549 0.414 0.670 0.0640 0.874 0.572
#> 6 6 0.612 0.340 0.604 0.0459 0.822 0.358
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
#> GSM339455 1 0.0376 0.90425 0.996 0.004
#> GSM339456 2 0.0376 0.92516 0.004 0.996
#> GSM339457 1 0.5294 0.80015 0.880 0.120
#> GSM339458 2 0.1184 0.91683 0.016 0.984
#> GSM339459 2 0.9881 0.26732 0.436 0.564
#> GSM339460 2 0.0000 0.92587 0.000 1.000
#> GSM339461 2 0.0376 0.92516 0.004 0.996
#> GSM339462 1 0.0000 0.90497 1.000 0.000
#> GSM339463 1 0.0376 0.90425 0.996 0.004
#> GSM339464 1 0.9552 0.42756 0.624 0.376
#> GSM339465 1 0.0376 0.90425 0.996 0.004
#> GSM339466 2 0.0000 0.92587 0.000 1.000
#> GSM339467 2 0.0000 0.92587 0.000 1.000
#> GSM339468 2 0.0376 0.92516 0.004 0.996
#> GSM339469 1 0.2423 0.87994 0.960 0.040
#> GSM339470 1 0.9988 -0.00977 0.520 0.480
#> GSM339471 1 0.0376 0.90425 0.996 0.004
#> GSM339472 2 0.0376 0.92516 0.004 0.996
#> GSM339473 1 0.0000 0.90497 1.000 0.000
#> GSM339474 2 0.0000 0.92587 0.000 1.000
#> GSM339475 1 0.0000 0.90497 1.000 0.000
#> GSM339476 1 0.0000 0.90497 1.000 0.000
#> GSM339477 2 0.0376 0.92516 0.004 0.996
#> GSM339478 2 0.9170 0.51009 0.332 0.668
#> GSM339479 2 0.4161 0.85831 0.084 0.916
#> GSM339480 2 0.9710 0.36073 0.400 0.600
#> GSM339481 2 0.0000 0.92587 0.000 1.000
#> GSM339482 1 0.0000 0.90497 1.000 0.000
#> GSM339483 1 0.0376 0.90330 0.996 0.004
#> GSM339484 1 0.0000 0.90497 1.000 0.000
#> GSM339485 1 0.9661 0.39369 0.608 0.392
#> GSM339486 1 0.0376 0.90425 0.996 0.004
#> GSM339487 2 0.0000 0.92587 0.000 1.000
#> GSM339488 2 0.0376 0.92423 0.004 0.996
#> GSM339489 2 0.0672 0.92348 0.008 0.992
#> GSM339490 1 0.6343 0.76717 0.840 0.160
#> GSM339491 2 0.9427 0.45535 0.360 0.640
#> GSM339492 1 0.0376 0.90425 0.996 0.004
#> GSM339493 2 0.0000 0.92587 0.000 1.000
#> GSM339494 1 0.0000 0.90497 1.000 0.000
#> GSM339495 2 0.0376 0.92516 0.004 0.996
#> GSM339496 1 0.0376 0.90425 0.996 0.004
#> GSM339497 2 0.0376 0.92423 0.004 0.996
#> GSM339498 2 0.3114 0.88550 0.056 0.944
#> GSM339499 1 0.9393 0.38850 0.644 0.356
#> GSM339500 2 0.2948 0.88796 0.052 0.948
#> GSM339501 1 0.0938 0.89929 0.988 0.012
#> GSM339502 2 0.0000 0.92587 0.000 1.000
#> GSM339503 1 0.0000 0.90497 1.000 0.000
#> GSM339504 1 0.0376 0.90330 0.996 0.004
#> GSM339505 2 0.9815 0.31074 0.420 0.580
#> GSM339506 1 0.4690 0.83052 0.900 0.100
#> GSM339507 1 0.0376 0.90425 0.996 0.004
#> GSM339508 2 0.0000 0.92587 0.000 1.000
#> GSM339509 2 0.0000 0.92587 0.000 1.000
#> GSM339510 2 0.0376 0.92516 0.004 0.996
#> GSM339511 1 0.9993 0.15030 0.516 0.484
#> GSM339512 2 0.0000 0.92587 0.000 1.000
#> GSM339513 1 0.0000 0.90497 1.000 0.000
#> GSM339514 2 0.0000 0.92587 0.000 1.000
#> GSM339515 1 0.0000 0.90497 1.000 0.000
#> GSM339516 2 0.0376 0.92516 0.004 0.996
#> GSM339517 1 0.0000 0.90497 1.000 0.000
#> GSM339518 2 0.0376 0.92423 0.004 0.996
#> GSM339519 1 0.0000 0.90497 1.000 0.000
#> GSM339520 2 0.9608 0.39962 0.384 0.616
#> GSM339521 2 0.0000 0.92587 0.000 1.000
#> GSM339522 2 0.0376 0.92516 0.004 0.996
#> GSM339523 2 0.0000 0.92587 0.000 1.000
#> GSM339524 1 0.0000 0.90497 1.000 0.000
#> GSM339525 1 0.0000 0.90497 1.000 0.000
#> GSM339526 1 0.0000 0.90497 1.000 0.000
#> GSM339527 1 0.4022 0.84864 0.920 0.080
#> GSM339528 1 0.0376 0.90425 0.996 0.004
#> GSM339529 2 0.0000 0.92587 0.000 1.000
#> GSM339530 1 0.9998 -0.05696 0.508 0.492
#> GSM339531 2 0.0376 0.92516 0.004 0.996
#> GSM339532 1 0.9608 0.41106 0.616 0.384
#> GSM339533 1 0.0376 0.90425 0.996 0.004
#> GSM339534 1 0.0376 0.90425 0.996 0.004
#> GSM339535 2 0.0000 0.92587 0.000 1.000
#> GSM339536 1 0.0000 0.90497 1.000 0.000
#> GSM339537 2 0.0376 0.92516 0.004 0.996
#> GSM339538 1 0.0000 0.90497 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM339455 1 0.7640 0.5616 0.576 0.052 0.372
#> GSM339456 2 0.5621 0.5796 0.000 0.692 0.308
#> GSM339457 3 0.9510 -0.0940 0.196 0.348 0.456
#> GSM339458 2 0.3482 0.7519 0.000 0.872 0.128
#> GSM339459 3 0.6699 0.1574 0.092 0.164 0.744
#> GSM339460 2 0.4654 0.7033 0.000 0.792 0.208
#> GSM339461 2 0.5810 0.5600 0.000 0.664 0.336
#> GSM339462 1 0.5926 -0.1937 0.644 0.000 0.356
#> GSM339463 1 0.7049 0.5567 0.528 0.020 0.452
#> GSM339464 3 0.6641 0.4127 0.448 0.008 0.544
#> GSM339465 1 0.7661 0.5351 0.504 0.044 0.452
#> GSM339466 2 0.0000 0.7682 0.000 1.000 0.000
#> GSM339467 2 0.0747 0.7643 0.000 0.984 0.016
#> GSM339468 2 0.6008 0.5046 0.000 0.628 0.372
#> GSM339469 3 0.6309 0.3743 0.496 0.000 0.504
#> GSM339470 3 0.9706 -0.2008 0.276 0.268 0.456
#> GSM339471 1 0.1765 0.4919 0.956 0.004 0.040
#> GSM339472 2 0.2261 0.7660 0.000 0.932 0.068
#> GSM339473 1 0.0424 0.4669 0.992 0.000 0.008
#> GSM339474 2 0.4121 0.7394 0.000 0.832 0.168
#> GSM339475 1 0.6654 0.5600 0.536 0.008 0.456
#> GSM339476 1 0.1399 0.4398 0.968 0.004 0.028
#> GSM339477 2 0.6302 0.4044 0.000 0.520 0.480
#> GSM339478 2 0.6925 0.0728 0.016 0.532 0.452
#> GSM339479 2 0.4589 0.7249 0.008 0.820 0.172
#> GSM339480 3 0.6463 0.1945 0.080 0.164 0.756
#> GSM339481 2 0.1643 0.7724 0.000 0.956 0.044
#> GSM339482 1 0.6225 0.5741 0.568 0.000 0.432
#> GSM339483 1 0.6309 -0.4193 0.500 0.000 0.500
#> GSM339484 1 0.5859 0.5838 0.656 0.000 0.344
#> GSM339485 3 0.6641 0.4127 0.448 0.008 0.544
#> GSM339486 1 0.6832 0.5815 0.604 0.020 0.376
#> GSM339487 2 0.1411 0.7734 0.000 0.964 0.036
#> GSM339488 2 0.1860 0.7434 0.000 0.948 0.052
#> GSM339489 2 0.6416 0.5539 0.008 0.616 0.376
#> GSM339490 3 0.6286 0.4046 0.464 0.000 0.536
#> GSM339491 3 0.9730 -0.1592 0.256 0.296 0.448
#> GSM339492 1 0.1525 0.4895 0.964 0.004 0.032
#> GSM339493 2 0.1643 0.7724 0.000 0.956 0.044
#> GSM339494 1 0.0592 0.4567 0.988 0.000 0.012
#> GSM339495 2 0.5058 0.6925 0.000 0.756 0.244
#> GSM339496 1 0.6654 0.5610 0.536 0.008 0.456
#> GSM339497 2 0.2711 0.7630 0.000 0.912 0.088
#> GSM339498 3 0.6523 0.2040 0.048 0.228 0.724
#> GSM339499 3 0.9550 -0.1000 0.204 0.340 0.456
#> GSM339500 2 0.1163 0.7593 0.000 0.972 0.028
#> GSM339501 3 0.6295 0.3992 0.472 0.000 0.528
#> GSM339502 2 0.0892 0.7630 0.000 0.980 0.020
#> GSM339503 1 0.6521 0.5167 0.504 0.004 0.492
#> GSM339504 1 0.6295 -0.3831 0.528 0.000 0.472
#> GSM339505 3 0.9701 -0.2153 0.284 0.260 0.456
#> GSM339506 3 0.6305 0.3911 0.484 0.000 0.516
#> GSM339507 1 0.7112 0.5699 0.552 0.024 0.424
#> GSM339508 2 0.3686 0.7526 0.000 0.860 0.140
#> GSM339509 2 0.0592 0.7657 0.000 0.988 0.012
#> GSM339510 3 0.6952 -0.3786 0.016 0.480 0.504
#> GSM339511 3 0.7256 0.4112 0.440 0.028 0.532
#> GSM339512 2 0.1031 0.7614 0.000 0.976 0.024
#> GSM339513 1 0.1163 0.4835 0.972 0.000 0.028
#> GSM339514 2 0.1031 0.7614 0.000 0.976 0.024
#> GSM339515 1 0.0592 0.4567 0.988 0.000 0.012
#> GSM339516 2 0.6869 0.4740 0.016 0.560 0.424
#> GSM339517 1 0.7493 0.5219 0.484 0.036 0.480
#> GSM339518 2 0.2165 0.7695 0.000 0.936 0.064
#> GSM339519 1 0.6215 0.5673 0.572 0.000 0.428
#> GSM339520 2 0.7169 0.0483 0.024 0.520 0.456
#> GSM339521 2 0.0892 0.7716 0.000 0.980 0.020
#> GSM339522 2 0.6008 0.5673 0.000 0.628 0.372
#> GSM339523 2 0.0237 0.7674 0.000 0.996 0.004
#> GSM339524 1 0.6062 0.5728 0.616 0.000 0.384
#> GSM339525 1 0.4887 0.0919 0.772 0.000 0.228
#> GSM339526 1 0.6267 0.5664 0.548 0.000 0.452
#> GSM339527 3 0.6520 0.3880 0.488 0.004 0.508
#> GSM339528 1 0.5072 0.5444 0.792 0.012 0.196
#> GSM339529 2 0.3551 0.7539 0.000 0.868 0.132
#> GSM339530 2 0.8209 -0.0522 0.072 0.472 0.456
#> GSM339531 2 0.6026 0.5049 0.000 0.624 0.376
#> GSM339532 3 0.6912 0.4132 0.444 0.016 0.540
#> GSM339533 1 0.7278 0.5468 0.516 0.028 0.456
#> GSM339534 1 0.1781 0.4704 0.960 0.020 0.020
#> GSM339535 2 0.0592 0.7656 0.000 0.988 0.012
#> GSM339536 1 0.0747 0.4807 0.984 0.000 0.016
#> GSM339537 2 0.5465 0.6561 0.000 0.712 0.288
#> GSM339538 1 0.6192 0.5772 0.580 0.000 0.420
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM339455 1 0.5522 0.613745 0.648 0.012 0.324 0.016
#> GSM339456 4 0.6501 0.447821 0.000 0.316 0.096 0.588
#> GSM339457 3 0.4640 0.673752 0.076 0.116 0.804 0.004
#> GSM339458 2 0.2563 0.832736 0.060 0.916 0.012 0.012
#> GSM339459 3 0.4429 0.594199 0.012 0.004 0.764 0.220
#> GSM339460 2 0.3266 0.821743 0.064 0.884 0.004 0.048
#> GSM339461 4 0.5678 0.494332 0.000 0.316 0.044 0.640
#> GSM339462 1 0.3933 0.688682 0.792 0.000 0.008 0.200
#> GSM339463 1 0.5832 0.452694 0.640 0.044 0.312 0.004
#> GSM339464 4 0.2805 0.680910 0.100 0.000 0.012 0.888
#> GSM339465 1 0.4805 0.715410 0.780 0.052 0.164 0.004
#> GSM339466 2 0.1398 0.852793 0.000 0.956 0.004 0.040
#> GSM339467 2 0.0188 0.859905 0.000 0.996 0.000 0.004
#> GSM339468 4 0.5990 0.311917 0.008 0.036 0.352 0.604
#> GSM339469 1 0.5977 0.594645 0.688 0.000 0.120 0.192
#> GSM339470 3 0.7594 0.260818 0.152 0.400 0.440 0.008
#> GSM339471 1 0.1617 0.831156 0.956 0.008 0.024 0.012
#> GSM339472 2 0.1489 0.851498 0.000 0.952 0.004 0.044
#> GSM339473 1 0.1452 0.831639 0.956 0.000 0.036 0.008
#> GSM339474 2 0.2654 0.803473 0.000 0.888 0.004 0.108
#> GSM339475 3 0.2216 0.757743 0.092 0.000 0.908 0.000
#> GSM339476 1 0.4711 0.727072 0.784 0.000 0.152 0.064
#> GSM339477 4 0.3751 0.668361 0.000 0.196 0.004 0.800
#> GSM339478 2 0.5430 0.644166 0.036 0.716 0.236 0.012
#> GSM339479 2 0.5124 0.618171 0.244 0.724 0.016 0.016
#> GSM339480 3 0.5034 0.501351 0.012 0.008 0.700 0.280
#> GSM339481 2 0.0921 0.856199 0.000 0.972 0.000 0.028
#> GSM339482 3 0.3333 0.758869 0.088 0.000 0.872 0.040
#> GSM339483 1 0.4086 0.674489 0.776 0.000 0.008 0.216
#> GSM339484 1 0.3575 0.780371 0.852 0.020 0.124 0.004
#> GSM339485 4 0.2924 0.680592 0.100 0.000 0.016 0.884
#> GSM339486 1 0.3681 0.781049 0.848 0.024 0.124 0.004
#> GSM339487 2 0.1489 0.851337 0.000 0.952 0.004 0.044
#> GSM339488 2 0.1771 0.839728 0.012 0.948 0.036 0.004
#> GSM339489 4 0.4647 0.566512 0.008 0.288 0.000 0.704
#> GSM339490 4 0.6532 0.138986 0.420 0.000 0.076 0.504
#> GSM339491 2 0.6480 0.478708 0.124 0.660 0.208 0.008
#> GSM339492 1 0.1739 0.831377 0.952 0.008 0.024 0.016
#> GSM339493 2 0.1302 0.850406 0.000 0.956 0.000 0.044
#> GSM339494 1 0.1724 0.831163 0.948 0.000 0.032 0.020
#> GSM339495 2 0.4964 0.317236 0.000 0.616 0.004 0.380
#> GSM339496 3 0.2675 0.753906 0.100 0.008 0.892 0.000
#> GSM339497 2 0.1362 0.858998 0.020 0.964 0.004 0.012
#> GSM339498 3 0.4933 0.518998 0.000 0.016 0.688 0.296
#> GSM339499 3 0.5271 0.657918 0.068 0.180 0.748 0.004
#> GSM339500 2 0.1854 0.847780 0.020 0.948 0.024 0.008
#> GSM339501 4 0.2586 0.674511 0.040 0.000 0.048 0.912
#> GSM339502 2 0.0992 0.853951 0.008 0.976 0.012 0.004
#> GSM339503 3 0.3796 0.731608 0.056 0.000 0.848 0.096
#> GSM339504 1 0.5039 0.325078 0.592 0.000 0.004 0.404
#> GSM339505 3 0.6471 0.633899 0.144 0.196 0.656 0.004
#> GSM339506 4 0.2882 0.661144 0.024 0.000 0.084 0.892
#> GSM339507 1 0.3914 0.774551 0.840 0.036 0.120 0.004
#> GSM339508 2 0.4372 0.780845 0.012 0.828 0.104 0.056
#> GSM339509 2 0.1082 0.856950 0.004 0.972 0.020 0.004
#> GSM339510 4 0.2840 0.679236 0.000 0.044 0.056 0.900
#> GSM339511 4 0.5363 0.576092 0.212 0.004 0.056 0.728
#> GSM339512 2 0.0992 0.860514 0.004 0.976 0.008 0.012
#> GSM339513 1 0.2443 0.825369 0.916 0.000 0.060 0.024
#> GSM339514 2 0.0712 0.856689 0.004 0.984 0.008 0.004
#> GSM339515 1 0.1929 0.830576 0.940 0.000 0.036 0.024
#> GSM339516 4 0.5498 0.510408 0.028 0.312 0.004 0.656
#> GSM339517 3 0.3164 0.753028 0.064 0.000 0.884 0.052
#> GSM339518 2 0.0844 0.859906 0.004 0.980 0.004 0.012
#> GSM339519 3 0.4477 0.741281 0.108 0.000 0.808 0.084
#> GSM339520 3 0.5964 0.240598 0.028 0.396 0.568 0.008
#> GSM339521 2 0.0817 0.857226 0.000 0.976 0.000 0.024
#> GSM339522 4 0.5585 0.649325 0.020 0.200 0.048 0.732
#> GSM339523 2 0.0844 0.860071 0.004 0.980 0.004 0.012
#> GSM339524 3 0.4037 0.752212 0.112 0.000 0.832 0.056
#> GSM339525 1 0.2466 0.783106 0.900 0.000 0.004 0.096
#> GSM339526 3 0.3450 0.723151 0.156 0.008 0.836 0.000
#> GSM339527 4 0.3658 0.624242 0.020 0.000 0.144 0.836
#> GSM339528 1 0.2861 0.805939 0.892 0.012 0.092 0.004
#> GSM339529 2 0.4449 0.778075 0.012 0.824 0.104 0.060
#> GSM339530 2 0.6673 -0.101325 0.072 0.464 0.460 0.004
#> GSM339531 4 0.5179 0.548475 0.000 0.052 0.220 0.728
#> GSM339532 4 0.6380 -0.000352 0.464 0.004 0.052 0.480
#> GSM339533 3 0.5888 0.517254 0.308 0.048 0.640 0.004
#> GSM339534 1 0.1509 0.826112 0.960 0.012 0.008 0.020
#> GSM339535 2 0.0524 0.859629 0.004 0.988 0.000 0.008
#> GSM339536 1 0.2111 0.829480 0.932 0.000 0.044 0.024
#> GSM339537 2 0.5105 0.154628 0.000 0.564 0.004 0.432
#> GSM339538 3 0.3453 0.756971 0.080 0.000 0.868 0.052
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM339455 1 0.7235 -0.05759 0.392 0.000 0.308 0.280 0.020
#> GSM339456 5 0.5599 0.40507 0.000 0.328 0.092 0.000 0.580
#> GSM339457 3 0.7420 0.44019 0.212 0.056 0.560 0.144 0.028
#> GSM339458 1 0.6572 -0.27583 0.460 0.392 0.000 0.132 0.016
#> GSM339459 3 0.4429 0.45467 0.004 0.000 0.712 0.028 0.256
#> GSM339460 2 0.7906 0.35562 0.216 0.460 0.000 0.192 0.132
#> GSM339461 5 0.4848 0.40037 0.028 0.272 0.016 0.000 0.684
#> GSM339462 4 0.5488 0.40733 0.404 0.000 0.008 0.540 0.048
#> GSM339463 1 0.4217 0.33907 0.704 0.004 0.280 0.000 0.012
#> GSM339464 5 0.4549 0.22682 0.008 0.000 0.000 0.464 0.528
#> GSM339465 1 0.2848 0.40538 0.840 0.004 0.156 0.000 0.000
#> GSM339466 2 0.2930 0.73447 0.048 0.888 0.000 0.032 0.032
#> GSM339467 2 0.1256 0.73490 0.012 0.964 0.004 0.008 0.012
#> GSM339468 5 0.4449 0.25922 0.000 0.004 0.352 0.008 0.636
#> GSM339469 4 0.3081 0.55777 0.072 0.000 0.004 0.868 0.056
#> GSM339470 2 0.6740 0.29394 0.260 0.512 0.216 0.004 0.008
#> GSM339471 1 0.5406 -0.27504 0.476 0.000 0.056 0.468 0.000
#> GSM339472 2 0.0703 0.74207 0.000 0.976 0.000 0.000 0.024
#> GSM339473 1 0.4841 -0.11574 0.560 0.000 0.024 0.416 0.000
#> GSM339474 2 0.4485 0.66798 0.040 0.772 0.000 0.028 0.160
#> GSM339475 3 0.1357 0.66531 0.048 0.000 0.948 0.000 0.004
#> GSM339476 4 0.5076 0.48888 0.188 0.000 0.060 0.724 0.028
#> GSM339477 5 0.5636 0.19762 0.012 0.372 0.000 0.056 0.560
#> GSM339478 3 0.8582 0.29773 0.128 0.276 0.404 0.164 0.028
#> GSM339479 1 0.6878 0.00357 0.528 0.280 0.008 0.164 0.020
#> GSM339480 3 0.4822 0.27807 0.000 0.000 0.616 0.032 0.352
#> GSM339481 2 0.3063 0.72232 0.036 0.864 0.000 0.004 0.096
#> GSM339482 3 0.1281 0.66509 0.032 0.000 0.956 0.000 0.012
#> GSM339483 4 0.5376 0.40094 0.404 0.000 0.004 0.544 0.048
#> GSM339484 1 0.5010 0.32965 0.708 0.000 0.144 0.148 0.000
#> GSM339485 5 0.4294 0.23162 0.000 0.000 0.000 0.468 0.532
#> GSM339486 1 0.3413 0.39690 0.832 0.000 0.124 0.044 0.000
#> GSM339487 2 0.3372 0.72391 0.044 0.864 0.000 0.032 0.060
#> GSM339488 2 0.1362 0.73512 0.016 0.960 0.004 0.008 0.012
#> GSM339489 5 0.6046 0.12383 0.020 0.360 0.000 0.076 0.544
#> GSM339490 4 0.3802 0.53138 0.036 0.000 0.020 0.824 0.120
#> GSM339491 2 0.4399 0.62684 0.168 0.768 0.056 0.004 0.004
#> GSM339492 4 0.6257 0.20494 0.392 0.000 0.148 0.460 0.000
#> GSM339493 2 0.1393 0.74136 0.008 0.956 0.000 0.012 0.024
#> GSM339494 1 0.5347 -0.11830 0.528 0.004 0.044 0.424 0.000
#> GSM339495 2 0.5587 0.52201 0.036 0.640 0.000 0.044 0.280
#> GSM339496 3 0.1478 0.66271 0.064 0.000 0.936 0.000 0.000
#> GSM339497 2 0.6327 0.48117 0.348 0.540 0.000 0.040 0.072
#> GSM339498 3 0.4437 0.11784 0.004 0.000 0.532 0.000 0.464
#> GSM339499 3 0.6220 0.36135 0.324 0.028 0.580 0.052 0.016
#> GSM339500 2 0.7658 0.25475 0.404 0.412 0.068 0.084 0.032
#> GSM339501 5 0.6838 0.46735 0.016 0.000 0.200 0.300 0.484
#> GSM339502 2 0.1243 0.74201 0.028 0.960 0.000 0.008 0.004
#> GSM339503 3 0.3224 0.59742 0.016 0.000 0.824 0.000 0.160
#> GSM339504 4 0.5656 0.50361 0.308 0.000 0.000 0.588 0.104
#> GSM339505 3 0.6427 0.36011 0.244 0.200 0.548 0.000 0.008
#> GSM339506 5 0.3504 0.50465 0.008 0.000 0.160 0.016 0.816
#> GSM339507 1 0.4195 0.36539 0.796 0.008 0.092 0.104 0.000
#> GSM339508 2 0.5961 0.41345 0.032 0.628 0.032 0.284 0.024
#> GSM339509 2 0.1362 0.73094 0.008 0.960 0.004 0.012 0.016
#> GSM339510 5 0.2549 0.55730 0.008 0.024 0.060 0.004 0.904
#> GSM339511 4 0.4642 0.37110 0.060 0.008 0.000 0.740 0.192
#> GSM339512 2 0.0451 0.74179 0.008 0.988 0.000 0.004 0.000
#> GSM339513 1 0.5733 -0.14918 0.476 0.000 0.084 0.440 0.000
#> GSM339514 2 0.0290 0.74254 0.008 0.992 0.000 0.000 0.000
#> GSM339515 1 0.5206 -0.12609 0.528 0.000 0.044 0.428 0.000
#> GSM339516 2 0.6979 0.13261 0.020 0.476 0.000 0.224 0.280
#> GSM339517 3 0.2825 0.62206 0.016 0.000 0.860 0.000 0.124
#> GSM339518 2 0.5809 0.60746 0.216 0.660 0.000 0.032 0.092
#> GSM339519 3 0.3005 0.65034 0.032 0.000 0.880 0.020 0.068
#> GSM339520 3 0.8047 0.40450 0.188 0.176 0.504 0.108 0.024
#> GSM339521 2 0.4400 0.69264 0.108 0.780 0.000 0.008 0.104
#> GSM339522 5 0.6832 0.34604 0.052 0.084 0.004 0.364 0.496
#> GSM339523 2 0.0833 0.74314 0.016 0.976 0.000 0.004 0.004
#> GSM339524 3 0.3209 0.64083 0.060 0.000 0.860 0.004 0.076
#> GSM339525 4 0.4470 0.42433 0.396 0.000 0.004 0.596 0.004
#> GSM339526 3 0.2818 0.62865 0.132 0.000 0.856 0.000 0.012
#> GSM339527 5 0.3455 0.46851 0.000 0.000 0.208 0.008 0.784
#> GSM339528 1 0.3409 0.38650 0.836 0.000 0.112 0.052 0.000
#> GSM339529 2 0.6052 0.35261 0.032 0.592 0.032 0.324 0.020
#> GSM339530 3 0.7553 0.35892 0.108 0.316 0.488 0.068 0.020
#> GSM339531 5 0.4973 0.39919 0.004 0.044 0.272 0.004 0.676
#> GSM339532 4 0.3176 0.57218 0.080 0.000 0.000 0.856 0.064
#> GSM339533 1 0.4688 0.16448 0.616 0.004 0.364 0.000 0.016
#> GSM339534 4 0.5896 0.30349 0.396 0.008 0.080 0.516 0.000
#> GSM339535 2 0.0727 0.74283 0.004 0.980 0.000 0.004 0.012
#> GSM339536 1 0.5345 -0.08038 0.540 0.000 0.056 0.404 0.000
#> GSM339537 2 0.6041 0.42633 0.044 0.580 0.000 0.052 0.324
#> GSM339538 3 0.1828 0.66057 0.032 0.000 0.936 0.004 0.028
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM339455 4 0.5489 0.0825 0.008 0.000 0.000 0.496 0.100 0.396
#> GSM339456 3 0.5324 -0.1078 0.004 0.428 0.500 0.008 0.056 0.004
#> GSM339457 4 0.4543 0.1739 0.004 0.008 0.036 0.660 0.000 0.292
#> GSM339458 6 0.5349 0.3283 0.016 0.044 0.000 0.024 0.308 0.608
#> GSM339459 3 0.4524 0.4919 0.000 0.000 0.616 0.336 0.000 0.048
#> GSM339460 5 0.5672 0.2150 0.004 0.088 0.000 0.056 0.636 0.216
#> GSM339461 5 0.6092 0.2966 0.000 0.196 0.352 0.004 0.444 0.004
#> GSM339462 1 0.5438 0.6397 0.704 0.000 0.036 0.068 0.144 0.048
#> GSM339463 6 0.1124 0.4753 0.036 0.000 0.008 0.000 0.000 0.956
#> GSM339464 5 0.6811 0.1833 0.064 0.000 0.172 0.268 0.488 0.008
#> GSM339465 6 0.1788 0.4795 0.076 0.000 0.000 0.004 0.004 0.916
#> GSM339466 2 0.4371 0.5174 0.000 0.664 0.000 0.000 0.284 0.052
#> GSM339467 2 0.1542 0.6666 0.004 0.936 0.000 0.052 0.000 0.008
#> GSM339468 3 0.2238 0.4683 0.004 0.004 0.908 0.020 0.060 0.004
#> GSM339469 4 0.6097 0.0169 0.244 0.000 0.000 0.472 0.276 0.008
#> GSM339470 2 0.5874 0.1827 0.024 0.516 0.052 0.020 0.004 0.384
#> GSM339471 1 0.4930 0.6408 0.716 0.000 0.000 0.136 0.044 0.104
#> GSM339472 2 0.1267 0.6845 0.000 0.940 0.000 0.000 0.060 0.000
#> GSM339473 1 0.0937 0.7225 0.960 0.000 0.000 0.000 0.000 0.040
#> GSM339474 2 0.3937 0.3825 0.000 0.572 0.000 0.000 0.424 0.004
#> GSM339475 3 0.6129 0.2381 0.000 0.000 0.340 0.320 0.000 0.340
#> GSM339476 4 0.6659 0.0186 0.244 0.000 0.004 0.480 0.228 0.044
#> GSM339477 5 0.6465 0.1210 0.008 0.356 0.236 0.004 0.392 0.004
#> GSM339478 4 0.4269 0.2970 0.000 0.080 0.004 0.760 0.012 0.144
#> GSM339479 6 0.5221 0.3191 0.016 0.032 0.000 0.024 0.324 0.604
#> GSM339480 3 0.4593 0.5156 0.000 0.000 0.660 0.280 0.008 0.052
#> GSM339481 2 0.3488 0.5825 0.000 0.744 0.000 0.004 0.244 0.008
#> GSM339482 6 0.6228 -0.2675 0.004 0.000 0.312 0.308 0.000 0.376
#> GSM339483 1 0.2865 0.7061 0.868 0.000 0.000 0.032 0.080 0.020
#> GSM339484 1 0.4372 0.2475 0.544 0.000 0.024 0.000 0.000 0.432
#> GSM339485 5 0.6685 0.2048 0.080 0.000 0.184 0.232 0.504 0.000
#> GSM339486 6 0.2398 0.4739 0.104 0.000 0.000 0.000 0.020 0.876
#> GSM339487 2 0.3758 0.5132 0.000 0.668 0.000 0.000 0.324 0.008
#> GSM339488 2 0.1410 0.6710 0.004 0.944 0.000 0.044 0.000 0.008
#> GSM339489 5 0.6753 0.2359 0.004 0.312 0.152 0.036 0.480 0.016
#> GSM339490 4 0.6268 0.0522 0.216 0.000 0.020 0.472 0.292 0.000
#> GSM339491 2 0.4648 0.5329 0.072 0.756 0.024 0.012 0.004 0.132
#> GSM339492 6 0.7020 -0.0551 0.308 0.000 0.000 0.292 0.060 0.340
#> GSM339493 2 0.2003 0.6680 0.000 0.884 0.000 0.000 0.116 0.000
#> GSM339494 1 0.1096 0.7216 0.964 0.008 0.000 0.004 0.004 0.020
#> GSM339495 2 0.3950 0.3584 0.000 0.564 0.004 0.000 0.432 0.000
#> GSM339496 4 0.6713 -0.3136 0.032 0.000 0.292 0.344 0.000 0.332
#> GSM339497 6 0.5397 0.1311 0.000 0.092 0.000 0.008 0.384 0.516
#> GSM339498 3 0.2053 0.5382 0.000 0.004 0.916 0.052 0.004 0.024
#> GSM339499 6 0.4450 0.1762 0.000 0.024 0.016 0.308 0.000 0.652
#> GSM339500 6 0.4810 0.2833 0.000 0.040 0.000 0.012 0.360 0.588
#> GSM339501 5 0.6615 0.0396 0.024 0.000 0.300 0.204 0.460 0.012
#> GSM339502 2 0.1225 0.6793 0.000 0.952 0.000 0.036 0.000 0.012
#> GSM339503 3 0.5357 0.4787 0.000 0.000 0.588 0.180 0.000 0.232
#> GSM339504 1 0.6520 0.4284 0.504 0.000 0.040 0.084 0.336 0.036
#> GSM339505 6 0.4787 0.3250 0.000 0.044 0.140 0.088 0.000 0.728
#> GSM339506 3 0.3938 0.3367 0.020 0.000 0.788 0.028 0.152 0.012
#> GSM339507 1 0.4349 0.3928 0.632 0.020 0.000 0.004 0.004 0.340
#> GSM339508 2 0.4753 0.1642 0.000 0.496 0.000 0.456 0.048 0.000
#> GSM339509 2 0.1812 0.6535 0.000 0.912 0.000 0.080 0.000 0.008
#> GSM339510 3 0.4407 0.0875 0.004 0.008 0.640 0.008 0.332 0.008
#> GSM339511 5 0.5493 -0.0333 0.120 0.000 0.004 0.356 0.520 0.000
#> GSM339512 2 0.0551 0.6856 0.008 0.984 0.000 0.004 0.000 0.004
#> GSM339513 1 0.2461 0.7193 0.900 0.000 0.004 0.048 0.020 0.028
#> GSM339514 2 0.1116 0.6881 0.008 0.960 0.000 0.004 0.028 0.000
#> GSM339515 1 0.1003 0.7231 0.964 0.004 0.000 0.004 0.000 0.028
#> GSM339516 2 0.5416 0.2119 0.060 0.528 0.004 0.012 0.392 0.004
#> GSM339517 3 0.5388 0.4994 0.004 0.000 0.600 0.228 0.000 0.168
#> GSM339518 5 0.6102 0.0897 0.000 0.256 0.000 0.004 0.440 0.300
#> GSM339519 3 0.6325 0.4246 0.036 0.000 0.472 0.332 0.000 0.160
#> GSM339520 4 0.5800 -0.0176 0.000 0.072 0.040 0.448 0.000 0.440
#> GSM339521 2 0.6171 0.0989 0.000 0.416 0.004 0.004 0.364 0.212
#> GSM339522 5 0.3060 0.4343 0.000 0.084 0.020 0.032 0.860 0.004
#> GSM339523 2 0.1232 0.6871 0.000 0.956 0.000 0.024 0.016 0.004
#> GSM339524 3 0.6101 0.4204 0.016 0.000 0.504 0.212 0.000 0.268
#> GSM339525 1 0.4735 0.6451 0.720 0.000 0.000 0.072 0.172 0.036
#> GSM339526 6 0.6125 -0.2123 0.004 0.000 0.312 0.256 0.000 0.428
#> GSM339527 3 0.2926 0.4105 0.012 0.000 0.852 0.024 0.112 0.000
#> GSM339528 6 0.3023 0.4577 0.140 0.000 0.000 0.000 0.032 0.828
#> GSM339529 4 0.4787 -0.1500 0.000 0.432 0.000 0.516 0.052 0.000
#> GSM339530 4 0.6305 0.1515 0.000 0.276 0.020 0.468 0.000 0.236
#> GSM339531 3 0.2670 0.4335 0.000 0.040 0.872 0.000 0.084 0.004
#> GSM339532 1 0.5992 0.1369 0.412 0.000 0.000 0.352 0.236 0.000
#> GSM339533 6 0.3656 0.4427 0.060 0.020 0.060 0.024 0.000 0.836
#> GSM339534 6 0.7590 -0.0400 0.224 0.000 0.000 0.284 0.172 0.320
#> GSM339535 2 0.1908 0.6768 0.004 0.900 0.000 0.000 0.096 0.000
#> GSM339536 1 0.1443 0.7200 0.948 0.004 0.004 0.004 0.004 0.036
#> GSM339537 5 0.3955 -0.1884 0.000 0.436 0.004 0.000 0.560 0.000
#> GSM339538 3 0.6563 0.3802 0.036 0.000 0.436 0.312 0.000 0.216
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 protocol(p) agent(p) individual(p) k
#> CV:NMF 72 1.000 0.846 4.52e-03 2
#> CV:NMF 48 1.000 0.744 2.26e-02 3
#> CV:NMF 71 0.317 0.977 1.90e-06 4
#> CV:NMF 33 0.396 0.650 5.33e-03 5
#> CV:NMF 25 0.981 0.890 2.23e-02 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 15497 rows and 84 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 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 0.374 0.736 0.875 0.4451 0.523 0.523
#> 3 3 0.435 0.721 0.830 0.4682 0.806 0.629
#> 4 4 0.567 0.603 0.729 0.1294 0.900 0.707
#> 5 5 0.591 0.696 0.751 0.0674 0.900 0.638
#> 6 6 0.749 0.762 0.845 0.0469 0.972 0.862
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
#> GSM339455 1 0.4939 0.842 0.892 0.108
#> GSM339456 2 0.6048 0.718 0.148 0.852
#> GSM339457 1 0.4022 0.835 0.920 0.080
#> GSM339458 2 0.9460 0.480 0.364 0.636
#> GSM339459 1 0.7745 0.742 0.772 0.228
#> GSM339460 2 0.4431 0.784 0.092 0.908
#> GSM339461 2 0.0376 0.808 0.004 0.996
#> GSM339462 1 0.5842 0.831 0.860 0.140
#> GSM339463 1 0.0000 0.862 1.000 0.000
#> GSM339464 1 0.5842 0.831 0.860 0.140
#> GSM339465 1 0.0000 0.862 1.000 0.000
#> GSM339466 2 0.9850 0.214 0.428 0.572
#> GSM339467 2 0.0000 0.808 0.000 1.000
#> GSM339468 1 0.9775 0.365 0.588 0.412
#> GSM339469 1 0.5842 0.831 0.860 0.140
#> GSM339470 2 0.9970 0.202 0.468 0.532
#> GSM339471 1 0.0000 0.862 1.000 0.000
#> GSM339472 2 0.0000 0.808 0.000 1.000
#> GSM339473 1 0.0000 0.862 1.000 0.000
#> GSM339474 2 0.0000 0.808 0.000 1.000
#> GSM339475 1 0.0000 0.862 1.000 0.000
#> GSM339476 1 0.4939 0.842 0.892 0.108
#> GSM339477 2 0.0000 0.808 0.000 1.000
#> GSM339478 1 0.4022 0.835 0.920 0.080
#> GSM339479 2 0.9460 0.480 0.364 0.636
#> GSM339480 1 0.7745 0.742 0.772 0.228
#> GSM339481 2 0.3274 0.798 0.060 0.940
#> GSM339482 1 0.0000 0.862 1.000 0.000
#> GSM339483 1 0.5842 0.831 0.860 0.140
#> GSM339484 1 0.0000 0.862 1.000 0.000
#> GSM339485 1 0.5842 0.831 0.860 0.140
#> GSM339486 1 0.0000 0.862 1.000 0.000
#> GSM339487 2 0.9850 0.214 0.428 0.572
#> GSM339488 2 0.0000 0.808 0.000 1.000
#> GSM339489 1 0.9775 0.365 0.588 0.412
#> GSM339490 1 0.5842 0.831 0.860 0.140
#> GSM339491 2 0.9970 0.202 0.468 0.532
#> GSM339492 1 0.0000 0.862 1.000 0.000
#> GSM339493 2 0.0000 0.808 0.000 1.000
#> GSM339494 1 0.0000 0.862 1.000 0.000
#> GSM339495 2 0.0000 0.808 0.000 1.000
#> GSM339496 1 0.0000 0.862 1.000 0.000
#> GSM339497 2 0.5408 0.768 0.124 0.876
#> GSM339498 1 0.8955 0.608 0.688 0.312
#> GSM339499 1 0.4022 0.835 0.920 0.080
#> GSM339500 2 0.9460 0.480 0.364 0.636
#> GSM339501 1 0.8813 0.632 0.700 0.300
#> GSM339502 2 0.3274 0.798 0.060 0.940
#> GSM339503 1 0.0000 0.862 1.000 0.000
#> GSM339504 1 0.5842 0.831 0.860 0.140
#> GSM339505 1 0.0000 0.862 1.000 0.000
#> GSM339506 1 0.5842 0.831 0.860 0.140
#> GSM339507 1 0.0000 0.862 1.000 0.000
#> GSM339508 2 0.0000 0.808 0.000 1.000
#> GSM339509 2 0.0000 0.808 0.000 1.000
#> GSM339510 1 0.9775 0.365 0.588 0.412
#> GSM339511 1 0.5842 0.831 0.860 0.140
#> GSM339512 2 0.9970 0.202 0.468 0.532
#> GSM339513 1 0.0000 0.862 1.000 0.000
#> GSM339514 2 0.0000 0.808 0.000 1.000
#> GSM339515 1 0.0000 0.862 1.000 0.000
#> GSM339516 2 0.1184 0.807 0.016 0.984
#> GSM339517 1 0.0000 0.862 1.000 0.000
#> GSM339518 2 0.5408 0.768 0.124 0.876
#> GSM339519 1 0.8661 0.653 0.712 0.288
#> GSM339520 1 0.4022 0.835 0.920 0.080
#> GSM339521 2 0.9460 0.480 0.364 0.636
#> GSM339522 1 0.8813 0.632 0.700 0.300
#> GSM339523 2 0.3274 0.798 0.060 0.940
#> GSM339524 1 0.0000 0.862 1.000 0.000
#> GSM339525 1 0.5842 0.831 0.860 0.140
#> GSM339526 1 0.0000 0.862 1.000 0.000
#> GSM339527 1 0.5842 0.831 0.860 0.140
#> GSM339528 1 0.0000 0.862 1.000 0.000
#> GSM339529 2 0.0000 0.808 0.000 1.000
#> GSM339530 1 0.4022 0.835 0.920 0.080
#> GSM339531 1 0.9775 0.365 0.588 0.412
#> GSM339532 1 0.5842 0.831 0.860 0.140
#> GSM339533 2 0.9983 0.171 0.476 0.524
#> GSM339534 1 0.0000 0.862 1.000 0.000
#> GSM339535 2 0.0000 0.808 0.000 1.000
#> GSM339536 1 0.0000 0.862 1.000 0.000
#> GSM339537 2 0.1184 0.807 0.016 0.984
#> GSM339538 1 0.0000 0.862 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM339455 1 0.6435 0.7676 0.756 0.076 0.168
#> GSM339456 2 0.7281 0.6017 0.140 0.712 0.148
#> GSM339457 3 0.1647 0.7942 0.004 0.036 0.960
#> GSM339458 2 0.8752 0.5483 0.284 0.568 0.148
#> GSM339459 3 0.5835 0.7258 0.164 0.052 0.784
#> GSM339460 2 0.4443 0.7564 0.052 0.864 0.084
#> GSM339461 2 0.3918 0.7229 0.140 0.856 0.004
#> GSM339462 1 0.0592 0.8464 0.988 0.000 0.012
#> GSM339463 3 0.2878 0.7685 0.096 0.000 0.904
#> GSM339464 1 0.0237 0.8441 0.996 0.000 0.004
#> GSM339465 1 0.4842 0.8199 0.776 0.000 0.224
#> GSM339466 2 0.7159 0.0787 0.024 0.528 0.448
#> GSM339467 2 0.0000 0.7795 0.000 1.000 0.000
#> GSM339468 3 0.8868 0.5211 0.196 0.228 0.576
#> GSM339469 1 0.0237 0.8441 0.996 0.000 0.004
#> GSM339470 2 0.9725 0.3853 0.276 0.452 0.272
#> GSM339471 1 0.5497 0.7703 0.708 0.000 0.292
#> GSM339472 2 0.0000 0.7795 0.000 1.000 0.000
#> GSM339473 1 0.4346 0.8318 0.816 0.000 0.184
#> GSM339474 2 0.0000 0.7795 0.000 1.000 0.000
#> GSM339475 3 0.2356 0.7847 0.072 0.000 0.928
#> GSM339476 1 0.6435 0.7676 0.756 0.076 0.168
#> GSM339477 2 0.3686 0.7239 0.140 0.860 0.000
#> GSM339478 3 0.1647 0.7942 0.004 0.036 0.960
#> GSM339479 2 0.8752 0.5483 0.284 0.568 0.148
#> GSM339480 3 0.5835 0.7258 0.164 0.052 0.784
#> GSM339481 2 0.3370 0.7683 0.024 0.904 0.072
#> GSM339482 3 0.3192 0.7617 0.112 0.000 0.888
#> GSM339483 1 0.0592 0.8464 0.988 0.000 0.012
#> GSM339484 3 0.2878 0.7685 0.096 0.000 0.904
#> GSM339485 1 0.0237 0.8441 0.996 0.000 0.004
#> GSM339486 1 0.4842 0.8199 0.776 0.000 0.224
#> GSM339487 2 0.7159 0.0787 0.024 0.528 0.448
#> GSM339488 2 0.0000 0.7795 0.000 1.000 0.000
#> GSM339489 3 0.8868 0.5211 0.196 0.228 0.576
#> GSM339490 1 0.0237 0.8441 0.996 0.000 0.004
#> GSM339491 2 0.9725 0.3853 0.276 0.452 0.272
#> GSM339492 1 0.5497 0.7703 0.708 0.000 0.292
#> GSM339493 2 0.0000 0.7795 0.000 1.000 0.000
#> GSM339494 1 0.4346 0.8318 0.816 0.000 0.184
#> GSM339495 2 0.0000 0.7795 0.000 1.000 0.000
#> GSM339496 3 0.2356 0.7847 0.072 0.000 0.928
#> GSM339497 2 0.5582 0.7370 0.088 0.812 0.100
#> GSM339498 3 0.7572 0.6555 0.184 0.128 0.688
#> GSM339499 3 0.1647 0.7942 0.004 0.036 0.960
#> GSM339500 2 0.8752 0.5483 0.284 0.568 0.148
#> GSM339501 3 0.7412 0.6777 0.176 0.124 0.700
#> GSM339502 2 0.3370 0.7683 0.024 0.904 0.072
#> GSM339503 3 0.3192 0.7617 0.112 0.000 0.888
#> GSM339504 1 0.0592 0.8464 0.988 0.000 0.012
#> GSM339505 3 0.1964 0.7851 0.056 0.000 0.944
#> GSM339506 1 0.0237 0.8441 0.996 0.000 0.004
#> GSM339507 1 0.4842 0.8199 0.776 0.000 0.224
#> GSM339508 2 0.0000 0.7795 0.000 1.000 0.000
#> GSM339509 2 0.0000 0.7795 0.000 1.000 0.000
#> GSM339510 3 0.8868 0.5211 0.196 0.228 0.576
#> GSM339511 1 0.0237 0.8441 0.996 0.000 0.004
#> GSM339512 2 0.9725 0.3853 0.276 0.452 0.272
#> GSM339513 1 0.5497 0.7703 0.708 0.000 0.292
#> GSM339514 2 0.0000 0.7795 0.000 1.000 0.000
#> GSM339515 1 0.4346 0.8318 0.816 0.000 0.184
#> GSM339516 2 0.0829 0.7793 0.012 0.984 0.004
#> GSM339517 3 0.2356 0.7847 0.072 0.000 0.928
#> GSM339518 2 0.5582 0.7370 0.088 0.812 0.100
#> GSM339519 3 0.8395 0.5830 0.328 0.104 0.568
#> GSM339520 3 0.1647 0.7942 0.004 0.036 0.960
#> GSM339521 2 0.8752 0.5483 0.284 0.568 0.148
#> GSM339522 3 0.7412 0.6777 0.176 0.124 0.700
#> GSM339523 2 0.3370 0.7683 0.024 0.904 0.072
#> GSM339524 3 0.3192 0.7617 0.112 0.000 0.888
#> GSM339525 1 0.0592 0.8464 0.988 0.000 0.012
#> GSM339526 3 0.2878 0.7685 0.096 0.000 0.904
#> GSM339527 1 0.0237 0.8441 0.996 0.000 0.004
#> GSM339528 1 0.4842 0.8199 0.776 0.000 0.224
#> GSM339529 2 0.0000 0.7795 0.000 1.000 0.000
#> GSM339530 3 0.1647 0.7942 0.004 0.036 0.960
#> GSM339531 3 0.8868 0.5211 0.196 0.228 0.576
#> GSM339532 1 0.0237 0.8441 0.996 0.000 0.004
#> GSM339533 2 0.9760 0.3702 0.276 0.444 0.280
#> GSM339534 1 0.5497 0.7703 0.708 0.000 0.292
#> GSM339535 2 0.0000 0.7795 0.000 1.000 0.000
#> GSM339536 1 0.4346 0.8318 0.816 0.000 0.184
#> GSM339537 2 0.0829 0.7793 0.012 0.984 0.004
#> GSM339538 3 0.2356 0.7847 0.072 0.000 0.928
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM339455 1 0.6833 0.6049 0.668 0.052 0.200 0.080
#> GSM339456 2 0.6170 0.5541 0.008 0.696 0.136 0.160
#> GSM339457 3 0.3725 0.6196 0.008 0.000 0.812 0.180
#> GSM339458 4 0.5031 0.5553 0.000 0.212 0.048 0.740
#> GSM339459 3 0.5159 0.4309 0.012 0.000 0.624 0.364
#> GSM339460 2 0.5249 0.6064 0.000 0.708 0.044 0.248
#> GSM339461 2 0.3870 0.7196 0.008 0.820 0.008 0.164
#> GSM339462 1 0.4898 0.6537 0.584 0.000 0.000 0.416
#> GSM339463 3 0.1824 0.6626 0.060 0.000 0.936 0.004
#> GSM339464 1 0.4961 0.6404 0.552 0.000 0.000 0.448
#> GSM339465 1 0.2408 0.6383 0.896 0.000 0.104 0.000
#> GSM339466 4 0.7892 0.3001 0.000 0.340 0.292 0.368
#> GSM339467 2 0.0000 0.8417 0.000 1.000 0.000 0.000
#> GSM339468 4 0.6773 0.0734 0.008 0.072 0.420 0.500
#> GSM339469 1 0.4961 0.6404 0.552 0.000 0.000 0.448
#> GSM339470 4 0.4610 0.6260 0.000 0.100 0.100 0.800
#> GSM339471 1 0.4632 0.5881 0.688 0.000 0.308 0.004
#> GSM339472 2 0.0469 0.8412 0.000 0.988 0.000 0.012
#> GSM339473 1 0.1209 0.6708 0.964 0.000 0.032 0.004
#> GSM339474 2 0.0000 0.8417 0.000 1.000 0.000 0.000
#> GSM339475 3 0.3486 0.6648 0.188 0.000 0.812 0.000
#> GSM339476 1 0.6833 0.6049 0.668 0.052 0.200 0.080
#> GSM339477 2 0.3360 0.7353 0.008 0.860 0.008 0.124
#> GSM339478 3 0.3725 0.6196 0.008 0.000 0.812 0.180
#> GSM339479 4 0.5031 0.5553 0.000 0.212 0.048 0.740
#> GSM339480 3 0.5159 0.4309 0.012 0.000 0.624 0.364
#> GSM339481 2 0.4914 0.6648 0.000 0.748 0.044 0.208
#> GSM339482 3 0.3873 0.6504 0.228 0.000 0.772 0.000
#> GSM339483 1 0.4898 0.6537 0.584 0.000 0.000 0.416
#> GSM339484 3 0.1824 0.6626 0.060 0.000 0.936 0.004
#> GSM339485 1 0.4961 0.6404 0.552 0.000 0.000 0.448
#> GSM339486 1 0.2408 0.6383 0.896 0.000 0.104 0.000
#> GSM339487 4 0.7892 0.3001 0.000 0.340 0.292 0.368
#> GSM339488 2 0.0000 0.8417 0.000 1.000 0.000 0.000
#> GSM339489 4 0.6773 0.0734 0.008 0.072 0.420 0.500
#> GSM339490 1 0.4961 0.6404 0.552 0.000 0.000 0.448
#> GSM339491 4 0.4610 0.6260 0.000 0.100 0.100 0.800
#> GSM339492 1 0.4632 0.5881 0.688 0.000 0.308 0.004
#> GSM339493 2 0.0469 0.8412 0.000 0.988 0.000 0.012
#> GSM339494 1 0.1209 0.6708 0.964 0.000 0.032 0.004
#> GSM339495 2 0.0000 0.8417 0.000 1.000 0.000 0.000
#> GSM339496 3 0.3486 0.6648 0.188 0.000 0.812 0.000
#> GSM339497 2 0.5898 0.5037 0.000 0.628 0.056 0.316
#> GSM339498 3 0.6032 0.1992 0.008 0.028 0.536 0.428
#> GSM339499 3 0.3725 0.6196 0.008 0.000 0.812 0.180
#> GSM339500 4 0.5031 0.5553 0.000 0.212 0.048 0.740
#> GSM339501 3 0.5673 0.2712 0.012 0.008 0.536 0.444
#> GSM339502 2 0.4914 0.6648 0.000 0.748 0.044 0.208
#> GSM339503 3 0.3873 0.6504 0.228 0.000 0.772 0.000
#> GSM339504 1 0.4898 0.6537 0.584 0.000 0.000 0.416
#> GSM339505 3 0.1174 0.6661 0.020 0.000 0.968 0.012
#> GSM339506 1 0.4961 0.6404 0.552 0.000 0.000 0.448
#> GSM339507 1 0.2408 0.6383 0.896 0.000 0.104 0.000
#> GSM339508 2 0.0000 0.8417 0.000 1.000 0.000 0.000
#> GSM339509 2 0.0000 0.8417 0.000 1.000 0.000 0.000
#> GSM339510 4 0.6773 0.0734 0.008 0.072 0.420 0.500
#> GSM339511 1 0.4961 0.6404 0.552 0.000 0.000 0.448
#> GSM339512 4 0.4610 0.6260 0.000 0.100 0.100 0.800
#> GSM339513 1 0.4632 0.5881 0.688 0.000 0.308 0.004
#> GSM339514 2 0.0469 0.8412 0.000 0.988 0.000 0.012
#> GSM339515 1 0.1209 0.6708 0.964 0.000 0.032 0.004
#> GSM339516 2 0.2149 0.7995 0.000 0.912 0.000 0.088
#> GSM339517 3 0.3486 0.6648 0.188 0.000 0.812 0.000
#> GSM339518 2 0.5898 0.5037 0.000 0.628 0.056 0.316
#> GSM339519 3 0.7889 0.1072 0.152 0.020 0.436 0.392
#> GSM339520 3 0.3725 0.6196 0.008 0.000 0.812 0.180
#> GSM339521 4 0.5031 0.5553 0.000 0.212 0.048 0.740
#> GSM339522 3 0.5673 0.2712 0.012 0.008 0.536 0.444
#> GSM339523 2 0.4914 0.6648 0.000 0.748 0.044 0.208
#> GSM339524 3 0.3873 0.6504 0.228 0.000 0.772 0.000
#> GSM339525 1 0.4898 0.6537 0.584 0.000 0.000 0.416
#> GSM339526 3 0.1824 0.6626 0.060 0.000 0.936 0.004
#> GSM339527 1 0.4961 0.6404 0.552 0.000 0.000 0.448
#> GSM339528 1 0.2408 0.6383 0.896 0.000 0.104 0.000
#> GSM339529 2 0.0000 0.8417 0.000 1.000 0.000 0.000
#> GSM339530 3 0.3725 0.6196 0.008 0.000 0.812 0.180
#> GSM339531 4 0.6773 0.0734 0.008 0.072 0.420 0.500
#> GSM339532 1 0.4961 0.6404 0.552 0.000 0.000 0.448
#> GSM339533 4 0.4718 0.6171 0.000 0.092 0.116 0.792
#> GSM339534 1 0.4632 0.5881 0.688 0.000 0.308 0.004
#> GSM339535 2 0.0469 0.8412 0.000 0.988 0.000 0.012
#> GSM339536 1 0.1209 0.6708 0.964 0.000 0.032 0.004
#> GSM339537 2 0.2149 0.7995 0.000 0.912 0.000 0.088
#> GSM339538 3 0.3486 0.6648 0.188 0.000 0.812 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM339455 1 0.7579 0.694 0.496 0.000 0.132 0.248 0.124
#> GSM339456 2 0.6443 0.581 0.044 0.684 0.056 0.092 0.124
#> GSM339457 3 0.3236 0.686 0.020 0.000 0.828 0.000 0.152
#> GSM339458 5 0.8757 0.389 0.176 0.124 0.044 0.240 0.416
#> GSM339459 5 0.6383 0.409 0.060 0.000 0.212 0.104 0.624
#> GSM339460 2 0.5868 0.558 0.024 0.624 0.028 0.028 0.296
#> GSM339461 2 0.3865 0.721 0.000 0.808 0.000 0.092 0.100
#> GSM339462 4 0.2127 0.873 0.108 0.000 0.000 0.892 0.000
#> GSM339463 3 0.1851 0.762 0.088 0.000 0.912 0.000 0.000
#> GSM339464 4 0.0000 0.943 0.000 0.000 0.000 1.000 0.000
#> GSM339465 1 0.4646 0.817 0.712 0.000 0.060 0.228 0.000
#> GSM339466 5 0.5275 0.317 0.008 0.324 0.040 0.004 0.624
#> GSM339467 2 0.0000 0.827 0.000 1.000 0.000 0.000 0.000
#> GSM339468 5 0.5222 0.558 0.000 0.044 0.100 0.116 0.740
#> GSM339469 4 0.0000 0.943 0.000 0.000 0.000 1.000 0.000
#> GSM339470 5 0.7870 0.422 0.176 0.016 0.080 0.240 0.488
#> GSM339471 1 0.6410 0.747 0.504 0.000 0.284 0.212 0.000
#> GSM339472 2 0.0404 0.827 0.000 0.988 0.000 0.000 0.012
#> GSM339473 1 0.3534 0.797 0.744 0.000 0.000 0.256 0.000
#> GSM339474 2 0.0000 0.827 0.000 1.000 0.000 0.000 0.000
#> GSM339475 3 0.3550 0.758 0.236 0.000 0.760 0.000 0.004
#> GSM339476 1 0.7579 0.694 0.496 0.000 0.132 0.248 0.124
#> GSM339477 2 0.3281 0.737 0.000 0.848 0.000 0.092 0.060
#> GSM339478 3 0.3236 0.686 0.020 0.000 0.828 0.000 0.152
#> GSM339479 5 0.8757 0.389 0.176 0.124 0.044 0.240 0.416
#> GSM339480 5 0.6383 0.409 0.060 0.000 0.212 0.104 0.624
#> GSM339481 2 0.4880 0.611 0.012 0.664 0.028 0.000 0.296
#> GSM339482 3 0.3661 0.739 0.276 0.000 0.724 0.000 0.000
#> GSM339483 4 0.2127 0.873 0.108 0.000 0.000 0.892 0.000
#> GSM339484 3 0.1851 0.762 0.088 0.000 0.912 0.000 0.000
#> GSM339485 4 0.0000 0.943 0.000 0.000 0.000 1.000 0.000
#> GSM339486 1 0.4646 0.817 0.712 0.000 0.060 0.228 0.000
#> GSM339487 5 0.5275 0.317 0.008 0.324 0.040 0.004 0.624
#> GSM339488 2 0.0000 0.827 0.000 1.000 0.000 0.000 0.000
#> GSM339489 5 0.5222 0.558 0.000 0.044 0.100 0.116 0.740
#> GSM339490 4 0.0000 0.943 0.000 0.000 0.000 1.000 0.000
#> GSM339491 5 0.7870 0.422 0.176 0.016 0.080 0.240 0.488
#> GSM339492 1 0.6410 0.747 0.504 0.000 0.284 0.212 0.000
#> GSM339493 2 0.0404 0.827 0.000 0.988 0.000 0.000 0.012
#> GSM339494 1 0.3534 0.797 0.744 0.000 0.000 0.256 0.000
#> GSM339495 2 0.0000 0.827 0.000 1.000 0.000 0.000 0.000
#> GSM339496 3 0.3550 0.758 0.236 0.000 0.760 0.000 0.004
#> GSM339497 2 0.6683 0.488 0.020 0.564 0.040 0.068 0.308
#> GSM339498 5 0.6048 0.502 0.044 0.008 0.156 0.112 0.680
#> GSM339499 3 0.3236 0.686 0.020 0.000 0.828 0.000 0.152
#> GSM339500 5 0.8757 0.389 0.176 0.124 0.044 0.240 0.416
#> GSM339501 5 0.5223 0.477 0.012 0.000 0.172 0.108 0.708
#> GSM339502 2 0.4880 0.611 0.012 0.664 0.028 0.000 0.296
#> GSM339503 3 0.3661 0.739 0.276 0.000 0.724 0.000 0.000
#> GSM339504 4 0.2127 0.873 0.108 0.000 0.000 0.892 0.000
#> GSM339505 3 0.1800 0.769 0.048 0.000 0.932 0.000 0.020
#> GSM339506 4 0.0000 0.943 0.000 0.000 0.000 1.000 0.000
#> GSM339507 1 0.4646 0.817 0.712 0.000 0.060 0.228 0.000
#> GSM339508 2 0.0000 0.827 0.000 1.000 0.000 0.000 0.000
#> GSM339509 2 0.0000 0.827 0.000 1.000 0.000 0.000 0.000
#> GSM339510 5 0.5222 0.558 0.000 0.044 0.100 0.116 0.740
#> GSM339511 4 0.0000 0.943 0.000 0.000 0.000 1.000 0.000
#> GSM339512 5 0.7870 0.422 0.176 0.016 0.080 0.240 0.488
#> GSM339513 1 0.6410 0.747 0.504 0.000 0.284 0.212 0.000
#> GSM339514 2 0.0404 0.827 0.000 0.988 0.000 0.000 0.012
#> GSM339515 1 0.3534 0.797 0.744 0.000 0.000 0.256 0.000
#> GSM339516 2 0.2068 0.782 0.000 0.904 0.000 0.004 0.092
#> GSM339517 3 0.3550 0.758 0.236 0.000 0.760 0.000 0.004
#> GSM339518 2 0.6683 0.488 0.020 0.564 0.040 0.068 0.308
#> GSM339519 5 0.6655 0.453 0.084 0.000 0.124 0.176 0.616
#> GSM339520 3 0.3236 0.686 0.020 0.000 0.828 0.000 0.152
#> GSM339521 5 0.8757 0.389 0.176 0.124 0.044 0.240 0.416
#> GSM339522 5 0.5223 0.477 0.012 0.000 0.172 0.108 0.708
#> GSM339523 2 0.4880 0.611 0.012 0.664 0.028 0.000 0.296
#> GSM339524 3 0.3661 0.739 0.276 0.000 0.724 0.000 0.000
#> GSM339525 4 0.2127 0.873 0.108 0.000 0.000 0.892 0.000
#> GSM339526 3 0.1851 0.762 0.088 0.000 0.912 0.000 0.000
#> GSM339527 4 0.0000 0.943 0.000 0.000 0.000 1.000 0.000
#> GSM339528 1 0.4646 0.817 0.712 0.000 0.060 0.228 0.000
#> GSM339529 2 0.0000 0.827 0.000 1.000 0.000 0.000 0.000
#> GSM339530 3 0.3236 0.686 0.020 0.000 0.828 0.000 0.152
#> GSM339531 5 0.5222 0.558 0.000 0.044 0.100 0.116 0.740
#> GSM339532 4 0.0000 0.943 0.000 0.000 0.000 1.000 0.000
#> GSM339533 5 0.7855 0.414 0.176 0.008 0.096 0.240 0.480
#> GSM339534 1 0.6410 0.747 0.504 0.000 0.284 0.212 0.000
#> GSM339535 2 0.0404 0.827 0.000 0.988 0.000 0.000 0.012
#> GSM339536 1 0.3534 0.797 0.744 0.000 0.000 0.256 0.000
#> GSM339537 2 0.2068 0.782 0.000 0.904 0.000 0.004 0.092
#> GSM339538 3 0.3550 0.758 0.236 0.000 0.760 0.000 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM339455 1 0.5060 0.723 0.688 0.000 0.108 0.004 0.020 0.180
#> GSM339456 2 0.4308 0.572 0.000 0.676 0.000 0.004 0.280 0.040
#> GSM339457 3 0.4095 0.696 0.000 0.000 0.748 0.000 0.152 0.100
#> GSM339458 6 0.1901 0.876 0.000 0.076 0.004 0.000 0.008 0.912
#> GSM339459 5 0.0551 0.731 0.000 0.000 0.004 0.004 0.984 0.008
#> GSM339460 2 0.3756 0.444 0.000 0.600 0.000 0.000 0.000 0.400
#> GSM339461 2 0.3897 0.710 0.000 0.776 0.000 0.004 0.136 0.084
#> GSM339462 4 0.2048 0.893 0.120 0.000 0.000 0.880 0.000 0.000
#> GSM339463 3 0.2106 0.730 0.064 0.000 0.904 0.000 0.000 0.032
#> GSM339464 4 0.0000 0.950 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM339465 1 0.1007 0.824 0.956 0.000 0.044 0.000 0.000 0.000
#> GSM339466 5 0.5978 0.383 0.000 0.296 0.000 0.000 0.444 0.260
#> GSM339467 2 0.0000 0.816 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM339468 5 0.3781 0.768 0.000 0.036 0.000 0.004 0.756 0.204
#> GSM339469 4 0.0000 0.950 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM339470 6 0.2266 0.864 0.000 0.000 0.012 0.000 0.108 0.880
#> GSM339471 1 0.3897 0.731 0.696 0.000 0.280 0.000 0.000 0.024
#> GSM339472 2 0.0363 0.816 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM339473 1 0.0972 0.815 0.964 0.000 0.000 0.008 0.000 0.028
#> GSM339474 2 0.0000 0.816 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM339475 3 0.3577 0.732 0.200 0.000 0.772 0.000 0.012 0.016
#> GSM339476 1 0.5060 0.723 0.688 0.000 0.108 0.004 0.020 0.180
#> GSM339477 2 0.2714 0.735 0.000 0.848 0.000 0.004 0.136 0.012
#> GSM339478 3 0.4095 0.696 0.000 0.000 0.748 0.000 0.152 0.100
#> GSM339479 6 0.1901 0.876 0.000 0.076 0.004 0.000 0.008 0.912
#> GSM339480 5 0.0551 0.731 0.000 0.000 0.004 0.004 0.984 0.008
#> GSM339481 2 0.3647 0.520 0.000 0.640 0.000 0.000 0.000 0.360
#> GSM339482 3 0.3314 0.726 0.224 0.000 0.764 0.000 0.012 0.000
#> GSM339483 4 0.2048 0.893 0.120 0.000 0.000 0.880 0.000 0.000
#> GSM339484 3 0.2106 0.730 0.064 0.000 0.904 0.000 0.000 0.032
#> GSM339485 4 0.0000 0.950 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM339486 1 0.1007 0.824 0.956 0.000 0.044 0.000 0.000 0.000
#> GSM339487 5 0.5978 0.383 0.000 0.296 0.000 0.000 0.444 0.260
#> GSM339488 2 0.0000 0.816 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM339489 5 0.3781 0.768 0.000 0.036 0.000 0.004 0.756 0.204
#> GSM339490 4 0.0000 0.950 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM339491 6 0.2266 0.864 0.000 0.000 0.012 0.000 0.108 0.880
#> GSM339492 1 0.3897 0.731 0.696 0.000 0.280 0.000 0.000 0.024
#> GSM339493 2 0.0458 0.815 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM339494 1 0.0972 0.815 0.964 0.000 0.000 0.008 0.000 0.028
#> GSM339495 2 0.0000 0.816 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM339496 3 0.3577 0.732 0.200 0.000 0.772 0.000 0.012 0.016
#> GSM339497 2 0.4581 0.326 0.000 0.524 0.004 0.004 0.020 0.448
#> GSM339498 5 0.2504 0.754 0.000 0.000 0.004 0.004 0.856 0.136
#> GSM339499 3 0.4095 0.696 0.000 0.000 0.748 0.000 0.152 0.100
#> GSM339500 6 0.1901 0.876 0.000 0.076 0.004 0.000 0.008 0.912
#> GSM339501 5 0.1897 0.766 0.000 0.000 0.004 0.004 0.908 0.084
#> GSM339502 2 0.3647 0.520 0.000 0.640 0.000 0.000 0.000 0.360
#> GSM339503 3 0.3314 0.726 0.224 0.000 0.764 0.000 0.012 0.000
#> GSM339504 4 0.2048 0.893 0.120 0.000 0.000 0.880 0.000 0.000
#> GSM339505 3 0.2620 0.739 0.040 0.000 0.888 0.000 0.024 0.048
#> GSM339506 4 0.0000 0.950 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM339507 1 0.1007 0.824 0.956 0.000 0.044 0.000 0.000 0.000
#> GSM339508 2 0.0000 0.816 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM339509 2 0.0000 0.816 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM339510 5 0.3781 0.768 0.000 0.036 0.000 0.004 0.756 0.204
#> GSM339511 4 0.0000 0.950 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM339512 6 0.2266 0.864 0.000 0.000 0.012 0.000 0.108 0.880
#> GSM339513 1 0.3897 0.731 0.696 0.000 0.280 0.000 0.000 0.024
#> GSM339514 2 0.0363 0.816 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM339515 1 0.0972 0.815 0.964 0.000 0.000 0.008 0.000 0.028
#> GSM339516 2 0.2212 0.756 0.000 0.880 0.000 0.000 0.008 0.112
#> GSM339517 3 0.3577 0.732 0.200 0.000 0.772 0.000 0.012 0.016
#> GSM339518 2 0.4581 0.326 0.000 0.524 0.004 0.004 0.020 0.448
#> GSM339519 5 0.4982 0.682 0.136 0.000 0.036 0.004 0.716 0.108
#> GSM339520 3 0.4095 0.696 0.000 0.000 0.748 0.000 0.152 0.100
#> GSM339521 6 0.1901 0.876 0.000 0.076 0.004 0.000 0.008 0.912
#> GSM339522 5 0.1897 0.766 0.000 0.000 0.004 0.004 0.908 0.084
#> GSM339523 2 0.3647 0.520 0.000 0.640 0.000 0.000 0.000 0.360
#> GSM339524 3 0.3314 0.726 0.224 0.000 0.764 0.000 0.012 0.000
#> GSM339525 4 0.2048 0.893 0.120 0.000 0.000 0.880 0.000 0.000
#> GSM339526 3 0.2106 0.730 0.064 0.000 0.904 0.000 0.000 0.032
#> GSM339527 4 0.0000 0.950 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM339528 1 0.1007 0.824 0.956 0.000 0.044 0.000 0.000 0.000
#> GSM339529 2 0.0000 0.816 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM339530 3 0.4095 0.696 0.000 0.000 0.748 0.000 0.152 0.100
#> GSM339531 5 0.3781 0.768 0.000 0.036 0.000 0.004 0.756 0.204
#> GSM339532 4 0.0000 0.950 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM339533 6 0.2510 0.857 0.000 0.000 0.028 0.000 0.100 0.872
#> GSM339534 1 0.3897 0.731 0.696 0.000 0.280 0.000 0.000 0.024
#> GSM339535 2 0.0458 0.815 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM339536 1 0.0972 0.815 0.964 0.000 0.000 0.008 0.000 0.028
#> GSM339537 2 0.2212 0.756 0.000 0.880 0.000 0.000 0.008 0.112
#> GSM339538 3 0.3577 0.732 0.200 0.000 0.772 0.000 0.012 0.016
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 protocol(p) agent(p) individual(p) k
#> MAD:hclust 70 1.000 0.871 9.70e-04 2
#> MAD:hclust 78 0.698 0.956 8.95e-07 3
#> MAD:hclust 72 0.939 0.996 8.45e-09 4
#> MAD:hclust 67 0.922 0.998 1.89e-10 5
#> MAD:hclust 79 0.964 1.000 1.14e-14 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 15497 rows and 84 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 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 0.798 0.931 0.964 0.5025 0.497 0.497
#> 3 3 0.636 0.819 0.865 0.2931 0.762 0.554
#> 4 4 0.615 0.734 0.710 0.1239 0.937 0.815
#> 5 5 0.598 0.631 0.702 0.0677 0.892 0.632
#> 6 6 0.639 0.566 0.689 0.0453 0.951 0.777
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
#> GSM339455 1 0.0000 0.978 1.000 0.000
#> GSM339456 2 0.0000 0.947 0.000 1.000
#> GSM339457 2 0.7528 0.786 0.216 0.784
#> GSM339458 2 0.0000 0.947 0.000 1.000
#> GSM339459 2 0.7602 0.778 0.220 0.780
#> GSM339460 2 0.0000 0.947 0.000 1.000
#> GSM339461 2 0.0000 0.947 0.000 1.000
#> GSM339462 1 0.0672 0.975 0.992 0.008
#> GSM339463 1 0.0000 0.978 1.000 0.000
#> GSM339464 1 0.2423 0.949 0.960 0.040
#> GSM339465 1 0.0000 0.978 1.000 0.000
#> GSM339466 2 0.0000 0.947 0.000 1.000
#> GSM339467 2 0.0000 0.947 0.000 1.000
#> GSM339468 2 0.0000 0.947 0.000 1.000
#> GSM339469 1 0.2423 0.949 0.960 0.040
#> GSM339470 2 0.7139 0.807 0.196 0.804
#> GSM339471 1 0.0000 0.978 1.000 0.000
#> GSM339472 2 0.0000 0.947 0.000 1.000
#> GSM339473 1 0.0000 0.978 1.000 0.000
#> GSM339474 2 0.0000 0.947 0.000 1.000
#> GSM339475 1 0.0000 0.978 1.000 0.000
#> GSM339476 1 0.0000 0.978 1.000 0.000
#> GSM339477 2 0.0000 0.947 0.000 1.000
#> GSM339478 2 0.6712 0.826 0.176 0.824
#> GSM339479 2 0.0000 0.947 0.000 1.000
#> GSM339480 2 0.7602 0.778 0.220 0.780
#> GSM339481 2 0.0000 0.947 0.000 1.000
#> GSM339482 1 0.0000 0.978 1.000 0.000
#> GSM339483 1 0.0672 0.975 0.992 0.008
#> GSM339484 1 0.0000 0.978 1.000 0.000
#> GSM339485 1 0.2423 0.949 0.960 0.040
#> GSM339486 1 0.0000 0.978 1.000 0.000
#> GSM339487 2 0.0000 0.947 0.000 1.000
#> GSM339488 2 0.0000 0.947 0.000 1.000
#> GSM339489 2 0.0000 0.947 0.000 1.000
#> GSM339490 1 0.2423 0.949 0.960 0.040
#> GSM339491 2 0.6801 0.819 0.180 0.820
#> GSM339492 1 0.0000 0.978 1.000 0.000
#> GSM339493 2 0.0000 0.947 0.000 1.000
#> GSM339494 1 0.0000 0.978 1.000 0.000
#> GSM339495 2 0.0000 0.947 0.000 1.000
#> GSM339496 1 0.0000 0.978 1.000 0.000
#> GSM339497 2 0.0000 0.947 0.000 1.000
#> GSM339498 2 0.7299 0.796 0.204 0.796
#> GSM339499 2 0.7528 0.786 0.216 0.784
#> GSM339500 2 0.0000 0.947 0.000 1.000
#> GSM339501 1 0.0672 0.975 0.992 0.008
#> GSM339502 2 0.0000 0.947 0.000 1.000
#> GSM339503 1 0.0000 0.978 1.000 0.000
#> GSM339504 1 0.0672 0.975 0.992 0.008
#> GSM339505 2 0.7528 0.786 0.216 0.784
#> GSM339506 1 0.0672 0.975 0.992 0.008
#> GSM339507 1 0.0000 0.978 1.000 0.000
#> GSM339508 2 0.0000 0.947 0.000 1.000
#> GSM339509 2 0.0000 0.947 0.000 1.000
#> GSM339510 2 0.0000 0.947 0.000 1.000
#> GSM339511 1 0.9393 0.486 0.644 0.356
#> GSM339512 2 0.0000 0.947 0.000 1.000
#> GSM339513 1 0.0000 0.978 1.000 0.000
#> GSM339514 2 0.0000 0.947 0.000 1.000
#> GSM339515 1 0.0000 0.978 1.000 0.000
#> GSM339516 2 0.0000 0.947 0.000 1.000
#> GSM339517 1 0.0000 0.978 1.000 0.000
#> GSM339518 2 0.0000 0.947 0.000 1.000
#> GSM339519 1 0.0000 0.978 1.000 0.000
#> GSM339520 2 0.7056 0.811 0.192 0.808
#> GSM339521 2 0.0000 0.947 0.000 1.000
#> GSM339522 2 0.0000 0.947 0.000 1.000
#> GSM339523 2 0.0000 0.947 0.000 1.000
#> GSM339524 1 0.0000 0.978 1.000 0.000
#> GSM339525 1 0.0672 0.975 0.992 0.008
#> GSM339526 1 0.0000 0.978 1.000 0.000
#> GSM339527 1 0.0672 0.975 0.992 0.008
#> GSM339528 1 0.0000 0.978 1.000 0.000
#> GSM339529 2 0.0000 0.947 0.000 1.000
#> GSM339530 2 0.7299 0.799 0.204 0.796
#> GSM339531 2 0.0000 0.947 0.000 1.000
#> GSM339532 1 0.7745 0.714 0.772 0.228
#> GSM339533 1 0.0000 0.978 1.000 0.000
#> GSM339534 1 0.0000 0.978 1.000 0.000
#> GSM339535 2 0.0000 0.947 0.000 1.000
#> GSM339536 1 0.0000 0.978 1.000 0.000
#> GSM339537 2 0.0000 0.947 0.000 1.000
#> GSM339538 1 0.0000 0.978 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM339455 3 0.2796 0.761 0.092 0.000 0.908
#> GSM339456 2 0.0661 0.950 0.004 0.988 0.008
#> GSM339457 3 0.3192 0.783 0.000 0.112 0.888
#> GSM339458 2 0.3193 0.931 0.004 0.896 0.100
#> GSM339459 3 0.7036 0.677 0.096 0.184 0.720
#> GSM339460 2 0.2860 0.939 0.004 0.912 0.084
#> GSM339461 2 0.2280 0.947 0.008 0.940 0.052
#> GSM339462 1 0.1129 0.766 0.976 0.004 0.020
#> GSM339463 3 0.4002 0.723 0.160 0.000 0.840
#> GSM339464 1 0.1453 0.761 0.968 0.008 0.024
#> GSM339465 3 0.4002 0.722 0.160 0.000 0.840
#> GSM339466 2 0.2165 0.943 0.000 0.936 0.064
#> GSM339467 2 0.1525 0.945 0.004 0.964 0.032
#> GSM339468 2 0.4914 0.882 0.088 0.844 0.068
#> GSM339469 1 0.1453 0.761 0.968 0.008 0.024
#> GSM339470 3 0.4033 0.770 0.008 0.136 0.856
#> GSM339471 1 0.5968 0.693 0.636 0.000 0.364
#> GSM339472 2 0.0661 0.950 0.004 0.988 0.008
#> GSM339473 1 0.5706 0.719 0.680 0.000 0.320
#> GSM339474 2 0.0475 0.949 0.004 0.992 0.004
#> GSM339475 3 0.3267 0.770 0.116 0.000 0.884
#> GSM339476 1 0.4002 0.752 0.840 0.000 0.160
#> GSM339477 2 0.0661 0.949 0.004 0.988 0.008
#> GSM339478 3 0.3941 0.754 0.000 0.156 0.844
#> GSM339479 2 0.3375 0.930 0.008 0.892 0.100
#> GSM339480 3 0.7036 0.677 0.096 0.184 0.720
#> GSM339481 2 0.0237 0.950 0.004 0.996 0.000
#> GSM339482 3 0.3482 0.767 0.128 0.000 0.872
#> GSM339483 1 0.1129 0.766 0.976 0.004 0.020
#> GSM339484 1 0.5968 0.689 0.636 0.000 0.364
#> GSM339485 1 0.1453 0.761 0.968 0.008 0.024
#> GSM339486 1 0.5968 0.691 0.636 0.000 0.364
#> GSM339487 2 0.2165 0.943 0.000 0.936 0.064
#> GSM339488 2 0.1525 0.945 0.004 0.964 0.032
#> GSM339489 2 0.4189 0.911 0.056 0.876 0.068
#> GSM339490 1 0.1453 0.761 0.968 0.008 0.024
#> GSM339491 3 0.4575 0.752 0.012 0.160 0.828
#> GSM339492 1 0.5968 0.693 0.636 0.000 0.364
#> GSM339493 2 0.0237 0.950 0.004 0.996 0.000
#> GSM339494 1 0.5706 0.719 0.680 0.000 0.320
#> GSM339495 2 0.0475 0.949 0.004 0.992 0.004
#> GSM339496 3 0.3267 0.770 0.116 0.000 0.884
#> GSM339497 2 0.2682 0.940 0.004 0.920 0.076
#> GSM339498 3 0.7741 0.602 0.104 0.236 0.660
#> GSM339499 3 0.3192 0.783 0.000 0.112 0.888
#> GSM339500 2 0.3193 0.931 0.004 0.896 0.100
#> GSM339501 1 0.3193 0.717 0.896 0.004 0.100
#> GSM339502 2 0.1525 0.945 0.004 0.964 0.032
#> GSM339503 3 0.3551 0.766 0.132 0.000 0.868
#> GSM339504 1 0.1129 0.766 0.976 0.004 0.020
#> GSM339505 3 0.3532 0.784 0.008 0.108 0.884
#> GSM339506 1 0.1399 0.765 0.968 0.004 0.028
#> GSM339507 1 0.5948 0.691 0.640 0.000 0.360
#> GSM339508 2 0.0475 0.949 0.004 0.992 0.004
#> GSM339509 2 0.1525 0.945 0.004 0.964 0.032
#> GSM339510 2 0.4995 0.878 0.092 0.840 0.068
#> GSM339511 1 0.4189 0.673 0.876 0.056 0.068
#> GSM339512 2 0.2590 0.945 0.004 0.924 0.072
#> GSM339513 1 0.5926 0.697 0.644 0.000 0.356
#> GSM339514 2 0.1525 0.945 0.004 0.964 0.032
#> GSM339515 1 0.5706 0.719 0.680 0.000 0.320
#> GSM339516 2 0.0475 0.949 0.004 0.992 0.004
#> GSM339517 3 0.3412 0.769 0.124 0.000 0.876
#> GSM339518 2 0.2448 0.941 0.000 0.924 0.076
#> GSM339519 3 0.3412 0.769 0.124 0.000 0.876
#> GSM339520 3 0.3551 0.773 0.000 0.132 0.868
#> GSM339521 2 0.2356 0.945 0.000 0.928 0.072
#> GSM339522 2 0.2680 0.940 0.008 0.924 0.068
#> GSM339523 2 0.1399 0.946 0.004 0.968 0.028
#> GSM339524 1 0.5926 0.694 0.644 0.000 0.356
#> GSM339525 1 0.1129 0.766 0.976 0.004 0.020
#> GSM339526 3 0.3340 0.769 0.120 0.000 0.880
#> GSM339527 1 0.1399 0.765 0.968 0.004 0.028
#> GSM339528 1 0.5968 0.691 0.636 0.000 0.364
#> GSM339529 2 0.0475 0.949 0.004 0.992 0.004
#> GSM339530 3 0.3425 0.782 0.004 0.112 0.884
#> GSM339531 2 0.4189 0.911 0.056 0.876 0.068
#> GSM339532 1 0.2743 0.723 0.928 0.052 0.020
#> GSM339533 3 0.3412 0.767 0.124 0.000 0.876
#> GSM339534 1 0.6045 0.682 0.620 0.000 0.380
#> GSM339535 2 0.0983 0.949 0.004 0.980 0.016
#> GSM339536 1 0.5706 0.719 0.680 0.000 0.320
#> GSM339537 2 0.0475 0.949 0.004 0.992 0.004
#> GSM339538 3 0.3482 0.767 0.128 0.000 0.872
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM339455 3 0.5977 0.622 0.120 0.000 0.688 0.192
#> GSM339456 2 0.1042 0.800 0.000 0.972 0.008 0.020
#> GSM339457 3 0.2870 0.759 0.036 0.012 0.908 0.044
#> GSM339458 2 0.7410 0.688 0.004 0.540 0.208 0.248
#> GSM339459 3 0.6059 0.666 0.044 0.036 0.700 0.220
#> GSM339460 2 0.6589 0.755 0.004 0.632 0.124 0.240
#> GSM339461 2 0.5433 0.780 0.004 0.720 0.056 0.220
#> GSM339462 4 0.5285 0.870 0.468 0.000 0.008 0.524
#> GSM339463 3 0.5436 0.462 0.356 0.000 0.620 0.024
#> GSM339464 4 0.5284 0.881 0.436 0.004 0.004 0.556
#> GSM339465 1 0.5560 0.213 0.584 0.000 0.392 0.024
#> GSM339466 2 0.6229 0.755 0.000 0.656 0.116 0.228
#> GSM339467 2 0.2909 0.785 0.008 0.904 0.036 0.052
#> GSM339468 2 0.7008 0.684 0.004 0.540 0.116 0.340
#> GSM339469 4 0.5126 0.881 0.444 0.004 0.000 0.552
#> GSM339470 3 0.4597 0.722 0.060 0.024 0.824 0.092
#> GSM339471 1 0.2611 0.783 0.896 0.000 0.096 0.008
#> GSM339472 2 0.0524 0.800 0.004 0.988 0.008 0.000
#> GSM339473 1 0.2494 0.725 0.916 0.000 0.036 0.048
#> GSM339474 2 0.0817 0.799 0.000 0.976 0.000 0.024
#> GSM339475 3 0.5073 0.718 0.200 0.000 0.744 0.056
#> GSM339476 1 0.6367 -0.299 0.584 0.000 0.080 0.336
#> GSM339477 2 0.1022 0.799 0.000 0.968 0.000 0.032
#> GSM339478 3 0.3026 0.753 0.032 0.012 0.900 0.056
#> GSM339479 2 0.7718 0.671 0.012 0.520 0.208 0.260
#> GSM339480 3 0.6059 0.666 0.044 0.036 0.700 0.220
#> GSM339481 2 0.0859 0.800 0.004 0.980 0.008 0.008
#> GSM339482 3 0.5363 0.704 0.216 0.000 0.720 0.064
#> GSM339483 4 0.5285 0.870 0.468 0.000 0.008 0.524
#> GSM339484 1 0.3991 0.763 0.808 0.000 0.172 0.020
#> GSM339485 4 0.5284 0.881 0.436 0.004 0.004 0.556
#> GSM339486 1 0.3853 0.768 0.820 0.000 0.160 0.020
#> GSM339487 2 0.6229 0.755 0.000 0.656 0.116 0.228
#> GSM339488 2 0.2909 0.785 0.008 0.904 0.036 0.052
#> GSM339489 2 0.6920 0.701 0.004 0.556 0.112 0.328
#> GSM339490 4 0.5126 0.881 0.444 0.004 0.000 0.552
#> GSM339491 3 0.4867 0.717 0.064 0.032 0.812 0.092
#> GSM339492 1 0.2611 0.783 0.896 0.000 0.096 0.008
#> GSM339493 2 0.1296 0.806 0.004 0.964 0.004 0.028
#> GSM339494 1 0.2494 0.725 0.916 0.000 0.036 0.048
#> GSM339495 2 0.0817 0.799 0.000 0.976 0.000 0.024
#> GSM339496 3 0.5144 0.714 0.216 0.000 0.732 0.052
#> GSM339497 2 0.6878 0.740 0.004 0.604 0.148 0.244
#> GSM339498 3 0.5607 0.640 0.004 0.072 0.716 0.208
#> GSM339499 3 0.2870 0.759 0.036 0.012 0.908 0.044
#> GSM339500 2 0.7444 0.680 0.004 0.536 0.220 0.240
#> GSM339501 4 0.5946 0.298 0.136 0.004 0.152 0.708
#> GSM339502 2 0.2909 0.785 0.008 0.904 0.036 0.052
#> GSM339503 3 0.5594 0.707 0.192 0.000 0.716 0.092
#> GSM339504 4 0.5285 0.870 0.468 0.000 0.008 0.524
#> GSM339505 3 0.3070 0.764 0.068 0.016 0.896 0.020
#> GSM339506 4 0.5236 0.879 0.432 0.000 0.008 0.560
#> GSM339507 1 0.3910 0.767 0.820 0.000 0.156 0.024
#> GSM339508 2 0.1909 0.791 0.004 0.940 0.008 0.048
#> GSM339509 2 0.2909 0.785 0.008 0.904 0.036 0.052
#> GSM339510 2 0.7089 0.673 0.004 0.524 0.120 0.352
#> GSM339511 4 0.5437 0.758 0.356 0.012 0.008 0.624
#> GSM339512 2 0.5379 0.774 0.004 0.752 0.144 0.100
#> GSM339513 1 0.2610 0.779 0.900 0.000 0.088 0.012
#> GSM339514 2 0.2909 0.785 0.008 0.904 0.036 0.052
#> GSM339515 1 0.2494 0.725 0.916 0.000 0.036 0.048
#> GSM339516 2 0.2868 0.802 0.000 0.864 0.000 0.136
#> GSM339517 3 0.5184 0.717 0.204 0.000 0.736 0.060
#> GSM339518 2 0.6669 0.751 0.004 0.628 0.136 0.232
#> GSM339519 3 0.5109 0.718 0.196 0.000 0.744 0.060
#> GSM339520 3 0.2870 0.759 0.036 0.012 0.908 0.044
#> GSM339521 2 0.6905 0.737 0.004 0.604 0.156 0.236
#> GSM339522 2 0.6765 0.718 0.000 0.576 0.124 0.300
#> GSM339523 2 0.2814 0.786 0.008 0.908 0.032 0.052
#> GSM339524 1 0.5412 0.664 0.736 0.000 0.168 0.096
#> GSM339525 4 0.5285 0.870 0.468 0.000 0.008 0.524
#> GSM339526 3 0.5148 0.711 0.208 0.000 0.736 0.056
#> GSM339527 4 0.5236 0.879 0.432 0.000 0.008 0.560
#> GSM339528 1 0.3853 0.768 0.820 0.000 0.160 0.020
#> GSM339529 2 0.1909 0.791 0.004 0.940 0.008 0.048
#> GSM339530 3 0.2961 0.759 0.044 0.012 0.904 0.040
#> GSM339531 2 0.6904 0.701 0.004 0.560 0.112 0.324
#> GSM339532 4 0.5452 0.867 0.428 0.016 0.000 0.556
#> GSM339533 3 0.4361 0.707 0.208 0.000 0.772 0.020
#> GSM339534 1 0.3032 0.774 0.868 0.000 0.124 0.008
#> GSM339535 2 0.2555 0.803 0.008 0.920 0.032 0.040
#> GSM339536 1 0.2494 0.725 0.916 0.000 0.036 0.048
#> GSM339537 2 0.2760 0.803 0.000 0.872 0.000 0.128
#> GSM339538 3 0.5257 0.709 0.212 0.000 0.728 0.060
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM339455 5 0.6606 -0.2735 0.192 0.000 0.344 0.004 0.460
#> GSM339456 2 0.3724 0.7024 0.028 0.788 0.000 0.000 0.184
#> GSM339457 3 0.5128 0.6607 0.064 0.020 0.708 0.000 0.208
#> GSM339458 5 0.6368 0.5220 0.072 0.228 0.080 0.000 0.620
#> GSM339459 3 0.6081 0.4479 0.032 0.020 0.584 0.032 0.332
#> GSM339460 5 0.5870 0.4779 0.032 0.408 0.040 0.000 0.520
#> GSM339461 5 0.5192 0.1898 0.032 0.476 0.000 0.004 0.488
#> GSM339462 4 0.2610 0.8599 0.076 0.000 0.004 0.892 0.028
#> GSM339463 3 0.6658 0.2327 0.388 0.000 0.452 0.016 0.144
#> GSM339464 4 0.1978 0.8799 0.032 0.000 0.012 0.932 0.024
#> GSM339465 1 0.4818 0.6189 0.732 0.000 0.196 0.016 0.056
#> GSM339466 5 0.4798 0.4988 0.000 0.396 0.024 0.000 0.580
#> GSM339467 2 0.2445 0.7187 0.020 0.908 0.016 0.000 0.056
#> GSM339468 5 0.5086 0.5541 0.004 0.304 0.016 0.024 0.652
#> GSM339469 4 0.0613 0.8855 0.004 0.000 0.004 0.984 0.008
#> GSM339470 3 0.6775 0.5043 0.104 0.052 0.528 0.000 0.316
#> GSM339471 1 0.5620 0.7965 0.664 0.000 0.104 0.216 0.016
#> GSM339472 2 0.2519 0.7415 0.016 0.884 0.000 0.000 0.100
#> GSM339473 1 0.4986 0.7545 0.700 0.000 0.032 0.240 0.028
#> GSM339474 2 0.4318 0.6917 0.056 0.764 0.004 0.000 0.176
#> GSM339475 3 0.3003 0.6068 0.188 0.000 0.812 0.000 0.000
#> GSM339476 4 0.5726 0.2806 0.276 0.000 0.076 0.628 0.020
#> GSM339477 2 0.4177 0.7002 0.052 0.776 0.004 0.000 0.168
#> GSM339478 3 0.5303 0.6477 0.068 0.020 0.688 0.000 0.224
#> GSM339479 5 0.6482 0.5070 0.096 0.200 0.080 0.000 0.624
#> GSM339480 3 0.6081 0.4479 0.032 0.020 0.584 0.032 0.332
#> GSM339481 2 0.1908 0.7384 0.000 0.908 0.000 0.000 0.092
#> GSM339482 3 0.3421 0.5843 0.204 0.000 0.788 0.000 0.008
#> GSM339483 4 0.2610 0.8599 0.076 0.000 0.004 0.892 0.028
#> GSM339484 1 0.5663 0.7677 0.700 0.000 0.144 0.112 0.044
#> GSM339485 4 0.1978 0.8799 0.032 0.000 0.012 0.932 0.024
#> GSM339486 1 0.5480 0.7786 0.720 0.000 0.120 0.112 0.048
#> GSM339487 5 0.4798 0.4988 0.000 0.396 0.024 0.000 0.580
#> GSM339488 2 0.2445 0.7187 0.020 0.908 0.016 0.000 0.056
#> GSM339489 5 0.5027 0.5603 0.004 0.292 0.016 0.024 0.664
#> GSM339490 4 0.0613 0.8855 0.004 0.000 0.004 0.984 0.008
#> GSM339491 3 0.6775 0.5043 0.104 0.052 0.528 0.000 0.316
#> GSM339492 1 0.5755 0.7965 0.656 0.000 0.108 0.216 0.020
#> GSM339493 2 0.2966 0.7198 0.016 0.848 0.000 0.000 0.136
#> GSM339494 1 0.4986 0.7545 0.700 0.000 0.032 0.240 0.028
#> GSM339495 2 0.4318 0.6917 0.056 0.764 0.004 0.000 0.176
#> GSM339496 3 0.3563 0.6001 0.208 0.000 0.780 0.000 0.012
#> GSM339497 5 0.6287 0.5602 0.044 0.348 0.064 0.000 0.544
#> GSM339498 3 0.6344 0.4117 0.012 0.048 0.556 0.040 0.344
#> GSM339499 3 0.5128 0.6607 0.064 0.020 0.708 0.000 0.208
#> GSM339500 5 0.6358 0.5249 0.064 0.228 0.088 0.000 0.620
#> GSM339501 5 0.7038 0.0546 0.056 0.004 0.100 0.356 0.484
#> GSM339502 2 0.2445 0.7187 0.020 0.908 0.016 0.000 0.056
#> GSM339503 3 0.4030 0.6143 0.140 0.000 0.804 0.020 0.036
#> GSM339504 4 0.2610 0.8599 0.076 0.000 0.004 0.892 0.028
#> GSM339505 3 0.5285 0.6599 0.108 0.008 0.692 0.000 0.192
#> GSM339506 4 0.2060 0.8780 0.036 0.000 0.012 0.928 0.024
#> GSM339507 1 0.5320 0.7811 0.732 0.000 0.112 0.112 0.044
#> GSM339508 2 0.3548 0.7227 0.044 0.836 0.008 0.000 0.112
#> GSM339509 2 0.2445 0.7187 0.020 0.908 0.016 0.000 0.056
#> GSM339510 5 0.5012 0.5609 0.004 0.292 0.012 0.028 0.664
#> GSM339511 4 0.1924 0.8464 0.008 0.000 0.004 0.924 0.064
#> GSM339512 2 0.6578 -0.0614 0.044 0.520 0.088 0.000 0.348
#> GSM339513 1 0.5657 0.7938 0.656 0.000 0.116 0.216 0.012
#> GSM339514 2 0.2445 0.7187 0.020 0.908 0.016 0.000 0.056
#> GSM339515 1 0.4986 0.7545 0.700 0.000 0.032 0.240 0.028
#> GSM339516 2 0.5196 0.4748 0.056 0.632 0.004 0.000 0.308
#> GSM339517 3 0.2966 0.6067 0.184 0.000 0.816 0.000 0.000
#> GSM339518 5 0.6218 0.5418 0.036 0.372 0.064 0.000 0.528
#> GSM339519 3 0.3516 0.6189 0.152 0.000 0.820 0.008 0.020
#> GSM339520 3 0.5128 0.6607 0.064 0.020 0.708 0.000 0.208
#> GSM339521 5 0.6063 0.5329 0.032 0.324 0.068 0.000 0.576
#> GSM339522 5 0.4568 0.5601 0.012 0.304 0.012 0.000 0.672
#> GSM339523 2 0.2341 0.7195 0.020 0.912 0.012 0.000 0.056
#> GSM339524 1 0.6273 0.6092 0.556 0.000 0.308 0.120 0.016
#> GSM339525 4 0.2610 0.8599 0.076 0.000 0.004 0.892 0.028
#> GSM339526 3 0.3003 0.6054 0.188 0.000 0.812 0.000 0.000
#> GSM339527 4 0.2060 0.8780 0.036 0.000 0.012 0.928 0.024
#> GSM339528 1 0.5480 0.7786 0.720 0.000 0.120 0.112 0.048
#> GSM339529 2 0.3548 0.7227 0.044 0.836 0.008 0.000 0.112
#> GSM339530 3 0.5435 0.6541 0.064 0.044 0.704 0.000 0.188
#> GSM339531 5 0.5086 0.5541 0.004 0.304 0.016 0.024 0.652
#> GSM339532 4 0.0932 0.8820 0.004 0.000 0.004 0.972 0.020
#> GSM339533 3 0.5530 0.5829 0.228 0.000 0.640 0.000 0.132
#> GSM339534 1 0.6155 0.7823 0.636 0.000 0.124 0.204 0.036
#> GSM339535 2 0.2833 0.7252 0.012 0.864 0.004 0.000 0.120
#> GSM339536 1 0.4986 0.7545 0.700 0.000 0.032 0.240 0.028
#> GSM339537 2 0.5159 0.4953 0.056 0.640 0.004 0.000 0.300
#> GSM339538 3 0.2966 0.6067 0.184 0.000 0.816 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM339455 6 0.534 0.2182 0.096 0.000 0.160 0.000 NA 0.680
#> GSM339456 2 0.401 0.6746 0.012 0.764 0.004 0.000 NA 0.040
#> GSM339457 3 0.664 0.4930 0.060 0.004 0.500 0.000 NA 0.268
#> GSM339458 6 0.297 0.5311 0.008 0.096 0.008 0.000 NA 0.860
#> GSM339459 3 0.595 0.3346 0.012 0.000 0.540 0.008 NA 0.148
#> GSM339460 6 0.348 0.4082 0.000 0.316 0.000 0.000 NA 0.684
#> GSM339461 2 0.643 -0.1418 0.012 0.448 0.028 0.000 NA 0.376
#> GSM339462 4 0.342 0.8323 0.084 0.000 0.016 0.840 NA 0.008
#> GSM339463 3 0.742 0.2328 0.300 0.000 0.376 0.008 NA 0.216
#> GSM339464 4 0.204 0.8526 0.008 0.000 0.004 0.908 NA 0.004
#> GSM339465 1 0.493 0.6527 0.732 0.000 0.136 0.008 NA 0.068
#> GSM339466 6 0.630 0.3361 0.004 0.376 0.016 0.000 NA 0.424
#> GSM339467 2 0.369 0.7137 0.004 0.804 0.008 0.000 NA 0.056
#> GSM339468 6 0.686 0.4683 0.000 0.248 0.036 0.008 NA 0.416
#> GSM339469 4 0.125 0.8663 0.012 0.000 0.000 0.956 NA 0.008
#> GSM339470 6 0.642 -0.2903 0.084 0.000 0.352 0.000 NA 0.472
#> GSM339471 1 0.532 0.7506 0.696 0.000 0.096 0.156 NA 0.016
#> GSM339472 2 0.193 0.7339 0.012 0.924 0.000 0.000 NA 0.032
#> GSM339473 1 0.407 0.7352 0.756 0.000 0.008 0.172 NA 0.000
#> GSM339474 2 0.420 0.6901 0.028 0.768 0.004 0.000 NA 0.044
#> GSM339475 3 0.249 0.5897 0.124 0.000 0.864 0.000 NA 0.008
#> GSM339476 4 0.614 0.3247 0.280 0.000 0.076 0.576 NA 0.032
#> GSM339477 2 0.430 0.6830 0.028 0.748 0.004 0.000 NA 0.036
#> GSM339478 3 0.667 0.4850 0.060 0.004 0.492 0.000 NA 0.276
#> GSM339479 6 0.294 0.5311 0.008 0.088 0.008 0.000 NA 0.864
#> GSM339480 3 0.595 0.3346 0.012 0.000 0.540 0.008 NA 0.148
#> GSM339481 2 0.158 0.7355 0.000 0.928 0.000 0.000 NA 0.064
#> GSM339482 3 0.336 0.5491 0.140 0.000 0.808 0.000 NA 0.000
#> GSM339483 4 0.342 0.8323 0.084 0.000 0.016 0.840 NA 0.008
#> GSM339484 1 0.566 0.6755 0.680 0.000 0.164 0.044 NA 0.040
#> GSM339485 4 0.204 0.8526 0.008 0.000 0.004 0.908 NA 0.004
#> GSM339486 1 0.515 0.7088 0.736 0.000 0.112 0.044 NA 0.052
#> GSM339487 6 0.630 0.3361 0.004 0.376 0.016 0.000 NA 0.424
#> GSM339488 2 0.365 0.7133 0.004 0.808 0.008 0.000 NA 0.056
#> GSM339489 6 0.682 0.4721 0.000 0.240 0.036 0.008 NA 0.428
#> GSM339490 4 0.114 0.8671 0.012 0.000 0.000 0.960 NA 0.004
#> GSM339491 6 0.642 -0.2903 0.084 0.000 0.352 0.000 NA 0.472
#> GSM339492 1 0.540 0.7492 0.692 0.000 0.096 0.156 NA 0.020
#> GSM339493 2 0.282 0.7184 0.008 0.868 0.000 0.000 NA 0.056
#> GSM339494 1 0.407 0.7352 0.756 0.000 0.008 0.172 NA 0.000
#> GSM339495 2 0.423 0.6882 0.028 0.764 0.004 0.000 NA 0.044
#> GSM339496 3 0.266 0.5841 0.140 0.000 0.848 0.000 NA 0.008
#> GSM339497 6 0.335 0.5302 0.000 0.176 0.000 0.000 NA 0.792
#> GSM339498 3 0.693 0.1764 0.000 0.052 0.440 0.008 NA 0.212
#> GSM339499 3 0.664 0.4930 0.060 0.004 0.500 0.000 NA 0.268
#> GSM339500 6 0.240 0.5238 0.004 0.072 0.012 0.000 NA 0.896
#> GSM339501 6 0.748 0.2524 0.008 0.000 0.100 0.244 NA 0.352
#> GSM339502 2 0.370 0.7108 0.004 0.804 0.008 0.000 NA 0.060
#> GSM339503 3 0.301 0.5876 0.076 0.000 0.860 0.004 NA 0.008
#> GSM339504 4 0.342 0.8323 0.084 0.000 0.016 0.840 NA 0.008
#> GSM339505 3 0.616 0.4962 0.084 0.000 0.540 0.000 NA 0.296
#> GSM339506 4 0.242 0.8524 0.008 0.000 0.012 0.888 NA 0.004
#> GSM339507 1 0.490 0.7132 0.756 0.000 0.100 0.040 NA 0.048
#> GSM339508 2 0.379 0.7185 0.008 0.756 0.004 0.000 NA 0.020
#> GSM339509 2 0.369 0.7137 0.004 0.804 0.008 0.000 NA 0.056
#> GSM339510 6 0.685 0.4733 0.000 0.236 0.040 0.008 NA 0.432
#> GSM339511 4 0.170 0.8586 0.012 0.000 0.000 0.936 NA 0.028
#> GSM339512 6 0.603 0.0177 0.008 0.428 0.032 0.000 NA 0.448
#> GSM339513 1 0.520 0.7495 0.696 0.000 0.108 0.156 NA 0.008
#> GSM339514 2 0.347 0.7163 0.004 0.824 0.008 0.000 NA 0.056
#> GSM339515 1 0.407 0.7352 0.756 0.000 0.008 0.172 NA 0.000
#> GSM339516 2 0.563 0.5279 0.024 0.624 0.004 0.000 NA 0.144
#> GSM339517 3 0.244 0.5884 0.120 0.000 0.868 0.000 NA 0.004
#> GSM339518 6 0.331 0.4886 0.000 0.224 0.000 0.000 NA 0.764
#> GSM339519 3 0.252 0.5959 0.068 0.000 0.884 0.000 NA 0.004
#> GSM339520 3 0.666 0.4889 0.060 0.004 0.496 0.000 NA 0.272
#> GSM339521 6 0.329 0.5086 0.000 0.200 0.008 0.000 NA 0.784
#> GSM339522 6 0.661 0.4541 0.004 0.268 0.024 0.000 NA 0.424
#> GSM339523 2 0.359 0.7124 0.004 0.808 0.004 0.000 NA 0.060
#> GSM339524 3 0.596 -0.2462 0.400 0.000 0.480 0.044 NA 0.004
#> GSM339525 4 0.342 0.8323 0.084 0.000 0.016 0.840 NA 0.008
#> GSM339526 3 0.228 0.5892 0.128 0.000 0.868 0.000 NA 0.004
#> GSM339527 4 0.242 0.8524 0.008 0.000 0.012 0.888 NA 0.004
#> GSM339528 1 0.515 0.7088 0.736 0.000 0.112 0.044 NA 0.052
#> GSM339529 2 0.379 0.7185 0.008 0.756 0.004 0.000 NA 0.020
#> GSM339530 3 0.691 0.4891 0.056 0.020 0.504 0.000 NA 0.232
#> GSM339531 6 0.686 0.4683 0.000 0.248 0.036 0.008 NA 0.416
#> GSM339532 4 0.125 0.8663 0.012 0.000 0.000 0.956 NA 0.008
#> GSM339533 3 0.664 0.4661 0.156 0.000 0.484 0.000 NA 0.288
#> GSM339534 1 0.582 0.7424 0.672 0.000 0.084 0.152 NA 0.056
#> GSM339535 2 0.331 0.7166 0.000 0.828 0.004 0.000 NA 0.072
#> GSM339536 1 0.407 0.7352 0.756 0.000 0.008 0.172 NA 0.000
#> GSM339537 2 0.542 0.5620 0.024 0.648 0.004 0.000 NA 0.120
#> GSM339538 3 0.244 0.5884 0.120 0.000 0.868 0.000 NA 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 protocol(p) agent(p) individual(p) k
#> MAD:kmeans 83 1.000 0.703 1.57e-03 2
#> MAD:kmeans 84 0.961 0.957 3.97e-05 3
#> MAD:kmeans 80 0.995 0.990 4.69e-08 4
#> MAD:kmeans 70 0.849 0.986 2.77e-09 5
#> MAD:kmeans 56 0.951 0.997 9.73e-08 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 15497 rows and 84 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 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 0.862 0.956 0.978 0.5042 0.497 0.497
#> 3 3 0.773 0.894 0.932 0.3126 0.787 0.594
#> 4 4 0.733 0.864 0.880 0.1041 0.922 0.774
#> 5 5 0.699 0.659 0.798 0.0729 0.969 0.887
#> 6 6 0.756 0.715 0.805 0.0467 0.910 0.647
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
#> GSM339455 1 0.0000 0.989 1.000 0.000
#> GSM339456 2 0.0000 0.966 0.000 1.000
#> GSM339457 2 0.7219 0.785 0.200 0.800
#> GSM339458 2 0.0000 0.966 0.000 1.000
#> GSM339459 2 0.7219 0.785 0.200 0.800
#> GSM339460 2 0.0000 0.966 0.000 1.000
#> GSM339461 2 0.0000 0.966 0.000 1.000
#> GSM339462 1 0.0000 0.989 1.000 0.000
#> GSM339463 1 0.0000 0.989 1.000 0.000
#> GSM339464 1 0.0000 0.989 1.000 0.000
#> GSM339465 1 0.0000 0.989 1.000 0.000
#> GSM339466 2 0.0000 0.966 0.000 1.000
#> GSM339467 2 0.0000 0.966 0.000 1.000
#> GSM339468 2 0.0000 0.966 0.000 1.000
#> GSM339469 1 0.0000 0.989 1.000 0.000
#> GSM339470 2 0.3114 0.927 0.056 0.944
#> GSM339471 1 0.0000 0.989 1.000 0.000
#> GSM339472 2 0.0000 0.966 0.000 1.000
#> GSM339473 1 0.0000 0.989 1.000 0.000
#> GSM339474 2 0.0000 0.966 0.000 1.000
#> GSM339475 1 0.0000 0.989 1.000 0.000
#> GSM339476 1 0.0000 0.989 1.000 0.000
#> GSM339477 2 0.0000 0.966 0.000 1.000
#> GSM339478 2 0.0000 0.966 0.000 1.000
#> GSM339479 2 0.0000 0.966 0.000 1.000
#> GSM339480 2 0.7602 0.759 0.220 0.780
#> GSM339481 2 0.0000 0.966 0.000 1.000
#> GSM339482 1 0.0000 0.989 1.000 0.000
#> GSM339483 1 0.0000 0.989 1.000 0.000
#> GSM339484 1 0.0000 0.989 1.000 0.000
#> GSM339485 1 0.0000 0.989 1.000 0.000
#> GSM339486 1 0.0000 0.989 1.000 0.000
#> GSM339487 2 0.0000 0.966 0.000 1.000
#> GSM339488 2 0.0000 0.966 0.000 1.000
#> GSM339489 2 0.0000 0.966 0.000 1.000
#> GSM339490 1 0.0000 0.989 1.000 0.000
#> GSM339491 2 0.2778 0.934 0.048 0.952
#> GSM339492 1 0.0000 0.989 1.000 0.000
#> GSM339493 2 0.0000 0.966 0.000 1.000
#> GSM339494 1 0.0000 0.989 1.000 0.000
#> GSM339495 2 0.0000 0.966 0.000 1.000
#> GSM339496 1 0.0000 0.989 1.000 0.000
#> GSM339497 2 0.0000 0.966 0.000 1.000
#> GSM339498 2 0.7056 0.795 0.192 0.808
#> GSM339499 2 0.7219 0.785 0.200 0.800
#> GSM339500 2 0.0000 0.966 0.000 1.000
#> GSM339501 1 0.0000 0.989 1.000 0.000
#> GSM339502 2 0.0000 0.966 0.000 1.000
#> GSM339503 1 0.0000 0.989 1.000 0.000
#> GSM339504 1 0.0000 0.989 1.000 0.000
#> GSM339505 2 0.7219 0.785 0.200 0.800
#> GSM339506 1 0.0000 0.989 1.000 0.000
#> GSM339507 1 0.0000 0.989 1.000 0.000
#> GSM339508 2 0.0000 0.966 0.000 1.000
#> GSM339509 2 0.0000 0.966 0.000 1.000
#> GSM339510 2 0.0000 0.966 0.000 1.000
#> GSM339511 1 0.7219 0.753 0.800 0.200
#> GSM339512 2 0.0000 0.966 0.000 1.000
#> GSM339513 1 0.0000 0.989 1.000 0.000
#> GSM339514 2 0.0000 0.966 0.000 1.000
#> GSM339515 1 0.0000 0.989 1.000 0.000
#> GSM339516 2 0.0000 0.966 0.000 1.000
#> GSM339517 1 0.0000 0.989 1.000 0.000
#> GSM339518 2 0.0000 0.966 0.000 1.000
#> GSM339519 1 0.0000 0.989 1.000 0.000
#> GSM339520 2 0.0938 0.959 0.012 0.988
#> GSM339521 2 0.0000 0.966 0.000 1.000
#> GSM339522 2 0.0000 0.966 0.000 1.000
#> GSM339523 2 0.0000 0.966 0.000 1.000
#> GSM339524 1 0.0000 0.989 1.000 0.000
#> GSM339525 1 0.0000 0.989 1.000 0.000
#> GSM339526 1 0.0000 0.989 1.000 0.000
#> GSM339527 1 0.0000 0.989 1.000 0.000
#> GSM339528 1 0.0000 0.989 1.000 0.000
#> GSM339529 2 0.0000 0.966 0.000 1.000
#> GSM339530 2 0.4939 0.882 0.108 0.892
#> GSM339531 2 0.0000 0.966 0.000 1.000
#> GSM339532 1 0.7219 0.753 0.800 0.200
#> GSM339533 1 0.0000 0.989 1.000 0.000
#> GSM339534 1 0.0000 0.989 1.000 0.000
#> GSM339535 2 0.0000 0.966 0.000 1.000
#> GSM339536 1 0.0000 0.989 1.000 0.000
#> GSM339537 2 0.0000 0.966 0.000 1.000
#> GSM339538 1 0.0000 0.989 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM339455 1 0.5968 0.653 0.636 0.000 0.364
#> GSM339456 2 0.0000 0.970 0.000 1.000 0.000
#> GSM339457 3 0.0000 0.957 0.000 0.000 1.000
#> GSM339458 2 0.0000 0.970 0.000 1.000 0.000
#> GSM339459 3 0.4912 0.751 0.196 0.008 0.796
#> GSM339460 2 0.0000 0.970 0.000 1.000 0.000
#> GSM339461 2 0.0592 0.961 0.012 0.988 0.000
#> GSM339462 1 0.0000 0.839 1.000 0.000 0.000
#> GSM339463 1 0.5968 0.653 0.636 0.000 0.364
#> GSM339464 1 0.0000 0.839 1.000 0.000 0.000
#> GSM339465 1 0.6309 0.346 0.504 0.000 0.496
#> GSM339466 2 0.0000 0.970 0.000 1.000 0.000
#> GSM339467 2 0.0000 0.970 0.000 1.000 0.000
#> GSM339468 2 0.4504 0.806 0.196 0.804 0.000
#> GSM339469 1 0.0000 0.839 1.000 0.000 0.000
#> GSM339470 3 0.0000 0.957 0.000 0.000 1.000
#> GSM339471 1 0.4605 0.850 0.796 0.000 0.204
#> GSM339472 2 0.0000 0.970 0.000 1.000 0.000
#> GSM339473 1 0.4605 0.850 0.796 0.000 0.204
#> GSM339474 2 0.0000 0.970 0.000 1.000 0.000
#> GSM339475 3 0.0000 0.957 0.000 0.000 1.000
#> GSM339476 1 0.4452 0.851 0.808 0.000 0.192
#> GSM339477 2 0.0000 0.970 0.000 1.000 0.000
#> GSM339478 3 0.0000 0.957 0.000 0.000 1.000
#> GSM339479 2 0.4399 0.759 0.188 0.812 0.000
#> GSM339480 3 0.4654 0.745 0.208 0.000 0.792
#> GSM339481 2 0.0000 0.970 0.000 1.000 0.000
#> GSM339482 3 0.0000 0.957 0.000 0.000 1.000
#> GSM339483 1 0.0000 0.839 1.000 0.000 0.000
#> GSM339484 1 0.4654 0.848 0.792 0.000 0.208
#> GSM339485 1 0.0000 0.839 1.000 0.000 0.000
#> GSM339486 1 0.4654 0.848 0.792 0.000 0.208
#> GSM339487 2 0.0000 0.970 0.000 1.000 0.000
#> GSM339488 2 0.0000 0.970 0.000 1.000 0.000
#> GSM339489 2 0.4504 0.806 0.196 0.804 0.000
#> GSM339490 1 0.0000 0.839 1.000 0.000 0.000
#> GSM339491 3 0.0592 0.945 0.000 0.012 0.988
#> GSM339492 1 0.4605 0.850 0.796 0.000 0.204
#> GSM339493 2 0.0000 0.970 0.000 1.000 0.000
#> GSM339494 1 0.4605 0.850 0.796 0.000 0.204
#> GSM339495 2 0.0000 0.970 0.000 1.000 0.000
#> GSM339496 3 0.0000 0.957 0.000 0.000 1.000
#> GSM339497 2 0.0000 0.970 0.000 1.000 0.000
#> GSM339498 3 0.4912 0.751 0.196 0.008 0.796
#> GSM339499 3 0.0000 0.957 0.000 0.000 1.000
#> GSM339500 2 0.0000 0.970 0.000 1.000 0.000
#> GSM339501 1 0.0000 0.839 1.000 0.000 0.000
#> GSM339502 2 0.0000 0.970 0.000 1.000 0.000
#> GSM339503 3 0.0424 0.950 0.008 0.000 0.992
#> GSM339504 1 0.0000 0.839 1.000 0.000 0.000
#> GSM339505 3 0.0000 0.957 0.000 0.000 1.000
#> GSM339506 1 0.0000 0.839 1.000 0.000 0.000
#> GSM339507 1 0.4654 0.848 0.792 0.000 0.208
#> GSM339508 2 0.0000 0.970 0.000 1.000 0.000
#> GSM339509 2 0.0000 0.970 0.000 1.000 0.000
#> GSM339510 2 0.4504 0.806 0.196 0.804 0.000
#> GSM339511 1 0.0000 0.839 1.000 0.000 0.000
#> GSM339512 2 0.0000 0.970 0.000 1.000 0.000
#> GSM339513 1 0.4605 0.850 0.796 0.000 0.204
#> GSM339514 2 0.0000 0.970 0.000 1.000 0.000
#> GSM339515 1 0.4605 0.850 0.796 0.000 0.204
#> GSM339516 2 0.0000 0.970 0.000 1.000 0.000
#> GSM339517 3 0.0000 0.957 0.000 0.000 1.000
#> GSM339518 2 0.0000 0.970 0.000 1.000 0.000
#> GSM339519 3 0.0000 0.957 0.000 0.000 1.000
#> GSM339520 3 0.0000 0.957 0.000 0.000 1.000
#> GSM339521 2 0.0000 0.970 0.000 1.000 0.000
#> GSM339522 2 0.0000 0.970 0.000 1.000 0.000
#> GSM339523 2 0.0000 0.970 0.000 1.000 0.000
#> GSM339524 1 0.4504 0.851 0.804 0.000 0.196
#> GSM339525 1 0.0000 0.839 1.000 0.000 0.000
#> GSM339526 3 0.0000 0.957 0.000 0.000 1.000
#> GSM339527 1 0.0000 0.839 1.000 0.000 0.000
#> GSM339528 1 0.4605 0.850 0.796 0.000 0.204
#> GSM339529 2 0.0000 0.970 0.000 1.000 0.000
#> GSM339530 3 0.0000 0.957 0.000 0.000 1.000
#> GSM339531 2 0.4504 0.806 0.196 0.804 0.000
#> GSM339532 1 0.0000 0.839 1.000 0.000 0.000
#> GSM339533 3 0.0000 0.957 0.000 0.000 1.000
#> GSM339534 1 0.4605 0.850 0.796 0.000 0.204
#> GSM339535 2 0.0000 0.970 0.000 1.000 0.000
#> GSM339536 1 0.4605 0.850 0.796 0.000 0.204
#> GSM339537 2 0.0000 0.970 0.000 1.000 0.000
#> GSM339538 3 0.0000 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
#> GSM339455 1 0.4312 0.81448 0.812 0.000 0.132 0.056
#> GSM339456 2 0.1118 0.91860 0.000 0.964 0.036 0.000
#> GSM339457 3 0.1557 0.84547 0.056 0.000 0.944 0.000
#> GSM339458 2 0.5280 0.80731 0.096 0.748 0.156 0.000
#> GSM339459 3 0.5267 0.75618 0.056 0.052 0.792 0.100
#> GSM339460 2 0.3149 0.90709 0.032 0.880 0.088 0.000
#> GSM339461 2 0.1452 0.91897 0.008 0.956 0.036 0.000
#> GSM339462 4 0.0000 0.92008 0.000 0.000 0.000 1.000
#> GSM339463 1 0.3107 0.84068 0.884 0.000 0.080 0.036
#> GSM339464 4 0.0000 0.92008 0.000 0.000 0.000 1.000
#> GSM339465 1 0.2483 0.86100 0.916 0.000 0.052 0.032
#> GSM339466 2 0.0188 0.92927 0.004 0.996 0.000 0.000
#> GSM339467 2 0.2011 0.92067 0.000 0.920 0.080 0.000
#> GSM339468 2 0.4608 0.82420 0.048 0.828 0.040 0.084
#> GSM339469 4 0.0000 0.92008 0.000 0.000 0.000 1.000
#> GSM339470 3 0.3172 0.80074 0.160 0.000 0.840 0.000
#> GSM339471 1 0.4322 0.92221 0.804 0.000 0.044 0.152
#> GSM339472 2 0.0188 0.92979 0.000 0.996 0.004 0.000
#> GSM339473 1 0.3172 0.92411 0.840 0.000 0.000 0.160
#> GSM339474 2 0.0000 0.92953 0.000 1.000 0.000 0.000
#> GSM339475 3 0.3610 0.83463 0.200 0.000 0.800 0.000
#> GSM339476 4 0.5894 0.00671 0.392 0.000 0.040 0.568
#> GSM339477 2 0.0817 0.92337 0.000 0.976 0.024 0.000
#> GSM339478 3 0.1557 0.84547 0.056 0.000 0.944 0.000
#> GSM339479 4 0.8442 0.45750 0.096 0.204 0.156 0.544
#> GSM339480 3 0.5267 0.75618 0.056 0.052 0.792 0.100
#> GSM339481 2 0.0469 0.92971 0.000 0.988 0.012 0.000
#> GSM339482 3 0.4972 0.36309 0.456 0.000 0.544 0.000
#> GSM339483 4 0.0000 0.92008 0.000 0.000 0.000 1.000
#> GSM339484 1 0.2611 0.92053 0.896 0.000 0.008 0.096
#> GSM339485 4 0.0000 0.92008 0.000 0.000 0.000 1.000
#> GSM339486 1 0.2530 0.92261 0.896 0.000 0.004 0.100
#> GSM339487 2 0.0188 0.92927 0.004 0.996 0.000 0.000
#> GSM339488 2 0.2011 0.92067 0.000 0.920 0.080 0.000
#> GSM339489 2 0.3943 0.85691 0.048 0.864 0.040 0.048
#> GSM339490 4 0.0000 0.92008 0.000 0.000 0.000 1.000
#> GSM339491 3 0.3172 0.80074 0.160 0.000 0.840 0.000
#> GSM339492 1 0.4322 0.92221 0.804 0.000 0.044 0.152
#> GSM339493 2 0.0524 0.93014 0.004 0.988 0.008 0.000
#> GSM339494 1 0.3172 0.92411 0.840 0.000 0.000 0.160
#> GSM339495 2 0.0000 0.92953 0.000 1.000 0.000 0.000
#> GSM339496 3 0.3610 0.83463 0.200 0.000 0.800 0.000
#> GSM339497 2 0.2871 0.91445 0.032 0.896 0.072 0.000
#> GSM339498 3 0.5780 0.71833 0.044 0.100 0.760 0.096
#> GSM339499 3 0.1557 0.84547 0.056 0.000 0.944 0.000
#> GSM339500 2 0.4731 0.83596 0.060 0.780 0.160 0.000
#> GSM339501 4 0.2759 0.83772 0.052 0.000 0.044 0.904
#> GSM339502 2 0.2011 0.92067 0.000 0.920 0.080 0.000
#> GSM339503 3 0.3448 0.83734 0.168 0.000 0.828 0.004
#> GSM339504 4 0.0000 0.92008 0.000 0.000 0.000 1.000
#> GSM339505 3 0.3074 0.84808 0.152 0.000 0.848 0.000
#> GSM339506 4 0.0000 0.92008 0.000 0.000 0.000 1.000
#> GSM339507 1 0.2408 0.92377 0.896 0.000 0.000 0.104
#> GSM339508 2 0.0000 0.92953 0.000 1.000 0.000 0.000
#> GSM339509 2 0.2011 0.92067 0.000 0.920 0.080 0.000
#> GSM339510 2 0.4941 0.80673 0.052 0.808 0.040 0.100
#> GSM339511 4 0.0000 0.92008 0.000 0.000 0.000 1.000
#> GSM339512 2 0.3554 0.88034 0.020 0.844 0.136 0.000
#> GSM339513 1 0.4237 0.92257 0.808 0.000 0.040 0.152
#> GSM339514 2 0.2011 0.92067 0.000 0.920 0.080 0.000
#> GSM339515 1 0.3172 0.92411 0.840 0.000 0.000 0.160
#> GSM339516 2 0.0188 0.92927 0.004 0.996 0.000 0.000
#> GSM339517 3 0.3610 0.83463 0.200 0.000 0.800 0.000
#> GSM339518 2 0.3082 0.90917 0.032 0.884 0.084 0.000
#> GSM339519 3 0.3219 0.83618 0.164 0.000 0.836 0.000
#> GSM339520 3 0.1557 0.84547 0.056 0.000 0.944 0.000
#> GSM339521 2 0.3634 0.89347 0.048 0.856 0.096 0.000
#> GSM339522 2 0.2586 0.89155 0.048 0.912 0.040 0.000
#> GSM339523 2 0.2011 0.92067 0.000 0.920 0.080 0.000
#> GSM339524 1 0.4436 0.91429 0.800 0.000 0.052 0.148
#> GSM339525 4 0.0000 0.92008 0.000 0.000 0.000 1.000
#> GSM339526 3 0.3649 0.83288 0.204 0.000 0.796 0.000
#> GSM339527 4 0.0000 0.92008 0.000 0.000 0.000 1.000
#> GSM339528 1 0.2408 0.92377 0.896 0.000 0.000 0.104
#> GSM339529 2 0.0000 0.92953 0.000 1.000 0.000 0.000
#> GSM339530 3 0.1557 0.84547 0.056 0.000 0.944 0.000
#> GSM339531 2 0.3943 0.85691 0.048 0.864 0.040 0.048
#> GSM339532 4 0.0000 0.92008 0.000 0.000 0.000 1.000
#> GSM339533 3 0.3975 0.80791 0.240 0.000 0.760 0.000
#> GSM339534 1 0.4485 0.91910 0.796 0.000 0.052 0.152
#> GSM339535 2 0.1978 0.92388 0.004 0.928 0.068 0.000
#> GSM339536 1 0.3172 0.92411 0.840 0.000 0.000 0.160
#> GSM339537 2 0.0188 0.92927 0.004 0.996 0.000 0.000
#> GSM339538 3 0.3610 0.83463 0.200 0.000 0.800 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM339455 1 0.6831 0.425 0.508 0.000 0.160 0.028 0.304
#> GSM339456 2 0.2068 0.634 0.000 0.904 0.004 0.000 0.092
#> GSM339457 3 0.2513 0.741 0.008 0.000 0.876 0.000 0.116
#> GSM339458 5 0.5667 0.731 0.024 0.336 0.048 0.000 0.592
#> GSM339459 3 0.6368 0.536 0.068 0.024 0.568 0.016 0.324
#> GSM339460 2 0.4449 -0.477 0.000 0.512 0.004 0.000 0.484
#> GSM339461 2 0.2798 0.618 0.000 0.852 0.008 0.000 0.140
#> GSM339462 4 0.0162 0.932 0.004 0.000 0.000 0.996 0.000
#> GSM339463 1 0.2959 0.793 0.864 0.000 0.112 0.008 0.016
#> GSM339464 4 0.0000 0.934 0.000 0.000 0.000 1.000 0.000
#> GSM339465 1 0.2331 0.831 0.908 0.000 0.068 0.008 0.016
#> GSM339466 2 0.1484 0.663 0.008 0.944 0.000 0.000 0.048
#> GSM339467 2 0.3236 0.568 0.000 0.828 0.020 0.000 0.152
#> GSM339468 2 0.6098 0.333 0.060 0.552 0.008 0.020 0.360
#> GSM339469 4 0.0000 0.934 0.000 0.000 0.000 1.000 0.000
#> GSM339470 3 0.5341 0.608 0.124 0.000 0.664 0.000 0.212
#> GSM339471 1 0.3608 0.881 0.824 0.000 0.064 0.112 0.000
#> GSM339472 2 0.1121 0.657 0.000 0.956 0.000 0.000 0.044
#> GSM339473 1 0.2439 0.893 0.876 0.000 0.004 0.120 0.000
#> GSM339474 2 0.0404 0.667 0.000 0.988 0.000 0.000 0.012
#> GSM339475 3 0.2732 0.757 0.160 0.000 0.840 0.000 0.000
#> GSM339476 4 0.4957 0.290 0.332 0.000 0.044 0.624 0.000
#> GSM339477 2 0.1410 0.656 0.000 0.940 0.000 0.000 0.060
#> GSM339478 3 0.2563 0.739 0.008 0.000 0.872 0.000 0.120
#> GSM339479 5 0.7238 0.645 0.036 0.172 0.048 0.152 0.592
#> GSM339480 3 0.6454 0.535 0.068 0.020 0.564 0.024 0.324
#> GSM339481 2 0.2179 0.623 0.000 0.896 0.004 0.000 0.100
#> GSM339482 3 0.4182 0.492 0.352 0.000 0.644 0.000 0.004
#> GSM339483 4 0.0162 0.932 0.004 0.000 0.000 0.996 0.000
#> GSM339484 1 0.2800 0.884 0.888 0.000 0.024 0.072 0.016
#> GSM339485 4 0.0000 0.934 0.000 0.000 0.000 1.000 0.000
#> GSM339486 1 0.2507 0.887 0.900 0.000 0.012 0.072 0.016
#> GSM339487 2 0.1484 0.663 0.008 0.944 0.000 0.000 0.048
#> GSM339488 2 0.3236 0.568 0.000 0.828 0.020 0.000 0.152
#> GSM339489 2 0.6034 0.329 0.060 0.548 0.008 0.016 0.368
#> GSM339490 4 0.0000 0.934 0.000 0.000 0.000 1.000 0.000
#> GSM339491 3 0.5396 0.597 0.124 0.000 0.656 0.000 0.220
#> GSM339492 1 0.3608 0.881 0.824 0.000 0.064 0.112 0.000
#> GSM339493 2 0.1952 0.658 0.000 0.912 0.004 0.000 0.084
#> GSM339494 1 0.2439 0.893 0.876 0.000 0.004 0.120 0.000
#> GSM339495 2 0.0404 0.669 0.000 0.988 0.000 0.000 0.012
#> GSM339496 3 0.2773 0.756 0.164 0.000 0.836 0.000 0.000
#> GSM339497 2 0.4450 -0.491 0.000 0.508 0.004 0.000 0.488
#> GSM339498 3 0.6822 0.540 0.040 0.080 0.584 0.028 0.268
#> GSM339499 3 0.2513 0.741 0.008 0.000 0.876 0.000 0.116
#> GSM339500 5 0.5582 0.733 0.008 0.284 0.084 0.000 0.624
#> GSM339501 4 0.5673 0.508 0.060 0.000 0.020 0.608 0.312
#> GSM339502 2 0.3236 0.568 0.000 0.828 0.020 0.000 0.152
#> GSM339503 3 0.3319 0.750 0.160 0.000 0.820 0.000 0.020
#> GSM339504 4 0.0162 0.932 0.004 0.000 0.000 0.996 0.000
#> GSM339505 3 0.3164 0.764 0.104 0.000 0.852 0.000 0.044
#> GSM339506 4 0.0000 0.934 0.000 0.000 0.000 1.000 0.000
#> GSM339507 1 0.2507 0.887 0.900 0.000 0.012 0.072 0.016
#> GSM339508 2 0.0510 0.670 0.000 0.984 0.000 0.000 0.016
#> GSM339509 2 0.3236 0.568 0.000 0.828 0.020 0.000 0.152
#> GSM339510 2 0.6495 0.292 0.060 0.516 0.008 0.040 0.376
#> GSM339511 4 0.0162 0.931 0.000 0.000 0.000 0.996 0.004
#> GSM339512 2 0.5328 0.195 0.008 0.660 0.076 0.000 0.256
#> GSM339513 1 0.3608 0.880 0.824 0.000 0.064 0.112 0.000
#> GSM339514 2 0.3194 0.572 0.000 0.832 0.020 0.000 0.148
#> GSM339515 1 0.2439 0.893 0.876 0.000 0.004 0.120 0.000
#> GSM339516 2 0.1557 0.662 0.008 0.940 0.000 0.000 0.052
#> GSM339517 3 0.2732 0.757 0.160 0.000 0.840 0.000 0.000
#> GSM339518 2 0.4450 -0.502 0.000 0.508 0.004 0.000 0.488
#> GSM339519 3 0.3527 0.758 0.116 0.000 0.828 0.000 0.056
#> GSM339520 3 0.2563 0.739 0.008 0.000 0.872 0.000 0.120
#> GSM339521 5 0.4705 0.469 0.008 0.484 0.004 0.000 0.504
#> GSM339522 2 0.5592 0.338 0.060 0.560 0.008 0.000 0.372
#> GSM339523 2 0.3141 0.568 0.000 0.832 0.016 0.000 0.152
#> GSM339524 1 0.4499 0.818 0.764 0.000 0.136 0.096 0.004
#> GSM339525 4 0.0162 0.932 0.004 0.000 0.000 0.996 0.000
#> GSM339526 3 0.2929 0.748 0.180 0.000 0.820 0.000 0.000
#> GSM339527 4 0.0000 0.934 0.000 0.000 0.000 1.000 0.000
#> GSM339528 1 0.2395 0.888 0.904 0.000 0.008 0.072 0.016
#> GSM339529 2 0.0609 0.670 0.000 0.980 0.000 0.000 0.020
#> GSM339530 3 0.2677 0.743 0.016 0.000 0.872 0.000 0.112
#> GSM339531 2 0.6013 0.337 0.060 0.556 0.008 0.016 0.360
#> GSM339532 4 0.0000 0.934 0.000 0.000 0.000 1.000 0.000
#> GSM339533 3 0.5354 0.638 0.240 0.000 0.652 0.000 0.108
#> GSM339534 1 0.4255 0.871 0.800 0.000 0.068 0.112 0.020
#> GSM339535 2 0.2574 0.641 0.000 0.876 0.012 0.000 0.112
#> GSM339536 1 0.2439 0.893 0.876 0.000 0.004 0.120 0.000
#> GSM339537 2 0.1557 0.662 0.008 0.940 0.000 0.000 0.052
#> GSM339538 3 0.3010 0.749 0.172 0.000 0.824 0.000 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM339455 6 0.6515 0.2866 0.260 0.000 0.140 0.024 0.036 0.540
#> GSM339456 2 0.2772 0.7327 0.000 0.816 0.000 0.000 0.180 0.004
#> GSM339457 3 0.2755 0.6587 0.004 0.000 0.844 0.000 0.012 0.140
#> GSM339458 6 0.2118 0.7786 0.008 0.104 0.000 0.000 0.000 0.888
#> GSM339459 5 0.3844 0.1663 0.004 0.000 0.312 0.000 0.676 0.008
#> GSM339460 6 0.3714 0.6272 0.000 0.340 0.000 0.000 0.004 0.656
#> GSM339461 2 0.4585 0.6559 0.000 0.692 0.000 0.000 0.192 0.116
#> GSM339462 4 0.0508 0.9522 0.012 0.000 0.000 0.984 0.000 0.004
#> GSM339463 1 0.2838 0.8376 0.872 0.000 0.032 0.000 0.072 0.024
#> GSM339464 4 0.0260 0.9535 0.000 0.000 0.000 0.992 0.008 0.000
#> GSM339465 1 0.1514 0.8885 0.944 0.000 0.004 0.004 0.036 0.012
#> GSM339466 2 0.3062 0.7577 0.000 0.816 0.000 0.000 0.160 0.024
#> GSM339467 2 0.2554 0.7791 0.000 0.876 0.028 0.000 0.004 0.092
#> GSM339468 5 0.3707 0.5324 0.000 0.312 0.000 0.008 0.680 0.000
#> GSM339469 4 0.0000 0.9562 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM339470 3 0.6879 0.4646 0.120 0.028 0.548 0.000 0.092 0.212
#> GSM339471 1 0.3562 0.8604 0.840 0.000 0.068 0.048 0.012 0.032
#> GSM339472 2 0.1464 0.8132 0.000 0.944 0.004 0.000 0.016 0.036
#> GSM339473 1 0.1267 0.8955 0.940 0.000 0.000 0.060 0.000 0.000
#> GSM339474 2 0.2384 0.8037 0.000 0.884 0.000 0.000 0.084 0.032
#> GSM339475 3 0.4187 0.6756 0.096 0.000 0.736 0.000 0.168 0.000
#> GSM339476 4 0.5107 0.4399 0.288 0.000 0.044 0.636 0.012 0.020
#> GSM339477 2 0.2692 0.7658 0.000 0.840 0.000 0.000 0.148 0.012
#> GSM339478 3 0.2755 0.6587 0.004 0.000 0.844 0.000 0.012 0.140
#> GSM339479 6 0.2535 0.7512 0.012 0.064 0.000 0.036 0.000 0.888
#> GSM339480 5 0.3827 0.1753 0.004 0.000 0.308 0.000 0.680 0.008
#> GSM339481 2 0.1644 0.7981 0.000 0.920 0.004 0.000 0.000 0.076
#> GSM339482 3 0.6004 0.4905 0.276 0.000 0.520 0.000 0.188 0.016
#> GSM339483 4 0.0508 0.9522 0.012 0.000 0.000 0.984 0.000 0.004
#> GSM339484 1 0.2164 0.8819 0.916 0.000 0.020 0.008 0.044 0.012
#> GSM339485 4 0.0260 0.9535 0.000 0.000 0.000 0.992 0.008 0.000
#> GSM339486 1 0.1483 0.8902 0.944 0.000 0.000 0.008 0.036 0.012
#> GSM339487 2 0.3098 0.7537 0.000 0.812 0.000 0.000 0.164 0.024
#> GSM339488 2 0.2554 0.7791 0.000 0.876 0.028 0.000 0.004 0.092
#> GSM339489 5 0.3738 0.5320 0.000 0.312 0.000 0.004 0.680 0.004
#> GSM339490 4 0.0000 0.9562 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM339491 3 0.7142 0.4417 0.116 0.048 0.532 0.000 0.092 0.212
#> GSM339492 1 0.3562 0.8604 0.840 0.000 0.068 0.048 0.012 0.032
#> GSM339493 2 0.2113 0.8103 0.000 0.908 0.004 0.000 0.060 0.028
#> GSM339494 1 0.1267 0.8955 0.940 0.000 0.000 0.060 0.000 0.000
#> GSM339495 2 0.2282 0.8022 0.000 0.888 0.000 0.000 0.088 0.024
#> GSM339496 3 0.4304 0.6780 0.100 0.000 0.736 0.000 0.160 0.004
#> GSM339497 6 0.3534 0.7503 0.000 0.244 0.000 0.000 0.016 0.740
#> GSM339498 5 0.4505 0.0668 0.004 0.020 0.356 0.000 0.612 0.008
#> GSM339499 3 0.2755 0.6587 0.004 0.000 0.844 0.000 0.012 0.140
#> GSM339500 6 0.1843 0.7581 0.000 0.080 0.004 0.000 0.004 0.912
#> GSM339501 5 0.4766 -0.0161 0.004 0.000 0.020 0.444 0.520 0.012
#> GSM339502 2 0.2554 0.7791 0.000 0.876 0.028 0.000 0.004 0.092
#> GSM339503 3 0.5153 0.6227 0.112 0.000 0.652 0.000 0.220 0.016
#> GSM339504 4 0.0508 0.9522 0.012 0.000 0.000 0.984 0.000 0.004
#> GSM339505 3 0.4095 0.6782 0.088 0.000 0.792 0.000 0.072 0.048
#> GSM339506 4 0.0405 0.9524 0.004 0.000 0.000 0.988 0.008 0.000
#> GSM339507 1 0.1483 0.8902 0.944 0.000 0.000 0.008 0.036 0.012
#> GSM339508 2 0.1967 0.8061 0.000 0.904 0.000 0.000 0.084 0.012
#> GSM339509 2 0.2554 0.7791 0.000 0.876 0.028 0.000 0.004 0.092
#> GSM339510 5 0.4375 0.5467 0.000 0.276 0.000 0.016 0.680 0.028
#> GSM339511 4 0.0000 0.9562 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM339512 2 0.6765 0.1061 0.004 0.500 0.184 0.000 0.072 0.240
#> GSM339513 1 0.3550 0.8562 0.844 0.000 0.056 0.048 0.036 0.016
#> GSM339514 2 0.2554 0.7791 0.000 0.876 0.028 0.000 0.004 0.092
#> GSM339515 1 0.1267 0.8955 0.940 0.000 0.000 0.060 0.000 0.000
#> GSM339516 2 0.3062 0.7579 0.000 0.816 0.000 0.000 0.160 0.024
#> GSM339517 3 0.4299 0.6667 0.092 0.000 0.720 0.000 0.188 0.000
#> GSM339518 6 0.3420 0.7572 0.000 0.240 0.000 0.000 0.012 0.748
#> GSM339519 3 0.4720 0.6235 0.076 0.000 0.672 0.000 0.244 0.008
#> GSM339520 3 0.2755 0.6587 0.004 0.000 0.844 0.000 0.012 0.140
#> GSM339521 6 0.3109 0.7510 0.000 0.224 0.000 0.000 0.004 0.772
#> GSM339522 5 0.4514 0.3942 0.000 0.372 0.000 0.000 0.588 0.040
#> GSM339523 2 0.2554 0.7791 0.000 0.876 0.028 0.000 0.004 0.092
#> GSM339524 1 0.5249 0.6470 0.700 0.000 0.108 0.024 0.148 0.020
#> GSM339525 4 0.0508 0.9522 0.012 0.000 0.000 0.984 0.000 0.004
#> GSM339526 3 0.4513 0.6671 0.124 0.000 0.704 0.000 0.172 0.000
#> GSM339527 4 0.0405 0.9524 0.004 0.000 0.000 0.988 0.008 0.000
#> GSM339528 1 0.1483 0.8902 0.944 0.000 0.000 0.008 0.036 0.012
#> GSM339529 2 0.2112 0.8041 0.000 0.896 0.000 0.000 0.088 0.016
#> GSM339530 3 0.2983 0.6560 0.004 0.012 0.844 0.000 0.012 0.128
#> GSM339531 5 0.3619 0.5275 0.000 0.316 0.000 0.004 0.680 0.000
#> GSM339532 4 0.0000 0.9562 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM339533 3 0.6659 0.4904 0.188 0.000 0.532 0.000 0.108 0.172
#> GSM339534 1 0.3634 0.8584 0.836 0.000 0.068 0.048 0.012 0.036
#> GSM339535 2 0.3125 0.7948 0.000 0.856 0.024 0.000 0.056 0.064
#> GSM339536 1 0.1267 0.8955 0.940 0.000 0.000 0.060 0.000 0.000
#> GSM339537 2 0.3062 0.7579 0.000 0.816 0.000 0.000 0.160 0.024
#> GSM339538 3 0.4693 0.6566 0.116 0.000 0.692 0.000 0.188 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 protocol(p) agent(p) individual(p) k
#> MAD:skmeans 84 1.000 0.769 1.22e-03 2
#> MAD:skmeans 83 0.895 0.973 6.95e-06 3
#> MAD:skmeans 81 0.868 0.997 3.28e-08 4
#> MAD:skmeans 71 0.850 0.979 8.45e-10 5
#> MAD:skmeans 72 0.775 0.994 2.58e-12 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 15497 rows and 84 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 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 0.560 0.823 0.916 0.4953 0.504 0.504
#> 3 3 0.525 0.736 0.827 0.3312 0.770 0.568
#> 4 4 0.679 0.807 0.867 0.1416 0.824 0.531
#> 5 5 0.675 0.721 0.819 0.0547 0.930 0.725
#> 6 6 0.740 0.749 0.843 0.0387 0.911 0.614
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
#> GSM339455 1 0.3274 0.879 0.940 0.060
#> GSM339456 2 0.5059 0.852 0.112 0.888
#> GSM339457 1 0.9427 0.493 0.640 0.360
#> GSM339458 1 0.9209 0.611 0.664 0.336
#> GSM339459 2 0.5519 0.837 0.128 0.872
#> GSM339460 2 0.3274 0.886 0.060 0.940
#> GSM339461 2 0.0376 0.926 0.004 0.996
#> GSM339462 1 0.0000 0.886 1.000 0.000
#> GSM339463 1 0.3114 0.880 0.944 0.056
#> GSM339464 1 0.5519 0.828 0.872 0.128
#> GSM339465 1 0.2043 0.883 0.968 0.032
#> GSM339466 2 0.0000 0.928 0.000 1.000
#> GSM339467 2 0.0000 0.928 0.000 1.000
#> GSM339468 2 0.4161 0.875 0.084 0.916
#> GSM339469 1 0.5059 0.838 0.888 0.112
#> GSM339470 1 0.8713 0.670 0.708 0.292
#> GSM339471 1 0.0000 0.886 1.000 0.000
#> GSM339472 2 0.0000 0.928 0.000 1.000
#> GSM339473 1 0.1184 0.885 0.984 0.016
#> GSM339474 2 0.0000 0.928 0.000 1.000
#> GSM339475 1 0.1633 0.885 0.976 0.024
#> GSM339476 1 0.1843 0.882 0.972 0.028
#> GSM339477 2 0.2043 0.910 0.032 0.968
#> GSM339478 2 0.9710 0.215 0.400 0.600
#> GSM339479 1 0.5294 0.833 0.880 0.120
#> GSM339480 2 0.6343 0.804 0.160 0.840
#> GSM339481 2 0.0000 0.928 0.000 1.000
#> GSM339482 1 0.1633 0.885 0.976 0.024
#> GSM339483 1 0.3431 0.861 0.936 0.064
#> GSM339484 1 0.0000 0.886 1.000 0.000
#> GSM339485 1 0.6343 0.802 0.840 0.160
#> GSM339486 1 0.0376 0.886 0.996 0.004
#> GSM339487 2 0.0000 0.928 0.000 1.000
#> GSM339488 2 0.0000 0.928 0.000 1.000
#> GSM339489 2 0.5519 0.837 0.128 0.872
#> GSM339490 1 0.4690 0.841 0.900 0.100
#> GSM339491 1 0.7453 0.738 0.788 0.212
#> GSM339492 1 0.0000 0.886 1.000 0.000
#> GSM339493 2 0.0000 0.928 0.000 1.000
#> GSM339494 1 0.0000 0.886 1.000 0.000
#> GSM339495 2 0.0000 0.928 0.000 1.000
#> GSM339496 1 0.1633 0.885 0.976 0.024
#> GSM339497 2 0.6247 0.764 0.156 0.844
#> GSM339498 1 0.9922 0.265 0.552 0.448
#> GSM339499 1 0.7883 0.711 0.764 0.236
#> GSM339500 2 0.9998 -0.194 0.492 0.508
#> GSM339501 1 0.7376 0.732 0.792 0.208
#> GSM339502 2 0.0000 0.928 0.000 1.000
#> GSM339503 1 0.5629 0.820 0.868 0.132
#> GSM339504 1 0.0000 0.886 1.000 0.000
#> GSM339505 1 0.8713 0.670 0.708 0.292
#> GSM339506 1 0.0000 0.886 1.000 0.000
#> GSM339507 1 0.1843 0.882 0.972 0.028
#> GSM339508 2 0.0000 0.928 0.000 1.000
#> GSM339509 2 0.0000 0.928 0.000 1.000
#> GSM339510 2 0.2236 0.909 0.036 0.964
#> GSM339511 2 0.8763 0.542 0.296 0.704
#> GSM339512 2 0.0000 0.928 0.000 1.000
#> GSM339513 1 0.0000 0.886 1.000 0.000
#> GSM339514 2 0.0000 0.928 0.000 1.000
#> GSM339515 1 0.0000 0.886 1.000 0.000
#> GSM339516 2 0.0000 0.928 0.000 1.000
#> GSM339517 1 0.7528 0.733 0.784 0.216
#> GSM339518 2 0.0000 0.928 0.000 1.000
#> GSM339519 1 0.2043 0.883 0.968 0.032
#> GSM339520 1 0.9815 0.358 0.580 0.420
#> GSM339521 2 0.0000 0.928 0.000 1.000
#> GSM339522 2 0.0000 0.928 0.000 1.000
#> GSM339523 2 0.0000 0.928 0.000 1.000
#> GSM339524 1 0.0000 0.886 1.000 0.000
#> GSM339525 1 0.0000 0.886 1.000 0.000
#> GSM339526 1 0.1633 0.885 0.976 0.024
#> GSM339527 1 0.0000 0.886 1.000 0.000
#> GSM339528 1 0.1843 0.882 0.972 0.028
#> GSM339529 2 0.0000 0.928 0.000 1.000
#> GSM339530 1 0.9248 0.538 0.660 0.340
#> GSM339531 2 0.3274 0.895 0.060 0.940
#> GSM339532 1 0.8016 0.711 0.756 0.244
#> GSM339533 1 0.1633 0.885 0.976 0.024
#> GSM339534 1 0.2778 0.876 0.952 0.048
#> GSM339535 2 0.0000 0.928 0.000 1.000
#> GSM339536 1 0.0000 0.886 1.000 0.000
#> GSM339537 2 0.0000 0.928 0.000 1.000
#> GSM339538 1 0.0000 0.886 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM339455 3 0.5435 0.768 0.192 0.024 0.784
#> GSM339456 2 0.4859 0.798 0.044 0.840 0.116
#> GSM339457 3 0.6437 0.778 0.220 0.048 0.732
#> GSM339458 3 0.9674 0.387 0.392 0.212 0.396
#> GSM339459 2 0.7481 0.696 0.048 0.596 0.356
#> GSM339460 2 0.2173 0.840 0.048 0.944 0.008
#> GSM339461 2 0.2689 0.855 0.036 0.932 0.032
#> GSM339462 1 0.0424 0.785 0.992 0.000 0.008
#> GSM339463 3 0.5835 0.694 0.340 0.000 0.660
#> GSM339464 1 0.2663 0.772 0.932 0.044 0.024
#> GSM339465 3 0.4842 0.786 0.224 0.000 0.776
#> GSM339466 2 0.5627 0.828 0.032 0.780 0.188
#> GSM339467 2 0.0000 0.865 0.000 1.000 0.000
#> GSM339468 2 0.6744 0.762 0.032 0.668 0.300
#> GSM339469 1 0.1999 0.778 0.952 0.012 0.036
#> GSM339470 3 0.5406 0.786 0.224 0.012 0.764
#> GSM339471 1 0.4062 0.694 0.836 0.000 0.164
#> GSM339472 2 0.0000 0.865 0.000 1.000 0.000
#> GSM339473 1 0.2165 0.773 0.936 0.000 0.064
#> GSM339474 2 0.0000 0.865 0.000 1.000 0.000
#> GSM339475 3 0.4555 0.782 0.200 0.000 0.800
#> GSM339476 1 0.4974 0.718 0.764 0.000 0.236
#> GSM339477 2 0.1453 0.864 0.024 0.968 0.008
#> GSM339478 3 0.7208 0.109 0.040 0.340 0.620
#> GSM339479 1 0.4062 0.656 0.836 0.000 0.164
#> GSM339480 2 0.7499 0.691 0.048 0.592 0.360
#> GSM339481 2 0.0000 0.865 0.000 1.000 0.000
#> GSM339482 3 0.4555 0.782 0.200 0.000 0.800
#> GSM339483 1 0.5627 0.690 0.780 0.032 0.188
#> GSM339484 3 0.5497 0.748 0.292 0.000 0.708
#> GSM339485 1 0.4146 0.752 0.876 0.044 0.080
#> GSM339486 3 0.5968 0.664 0.364 0.000 0.636
#> GSM339487 2 0.5536 0.828 0.024 0.776 0.200
#> GSM339488 2 0.0592 0.860 0.000 0.988 0.012
#> GSM339489 2 0.7246 0.746 0.052 0.648 0.300
#> GSM339490 1 0.5743 0.700 0.784 0.044 0.172
#> GSM339491 3 0.4796 0.786 0.220 0.000 0.780
#> GSM339492 1 0.3340 0.742 0.880 0.000 0.120
#> GSM339493 2 0.0000 0.865 0.000 1.000 0.000
#> GSM339494 1 0.2878 0.764 0.904 0.000 0.096
#> GSM339495 2 0.0000 0.865 0.000 1.000 0.000
#> GSM339496 3 0.4931 0.784 0.232 0.000 0.768
#> GSM339497 2 0.6756 0.798 0.056 0.712 0.232
#> GSM339498 3 0.5497 0.457 0.048 0.148 0.804
#> GSM339499 3 0.5506 0.787 0.220 0.016 0.764
#> GSM339500 3 0.9587 0.537 0.224 0.308 0.468
#> GSM339501 1 0.8825 0.472 0.532 0.132 0.336
#> GSM339502 2 0.0000 0.865 0.000 1.000 0.000
#> GSM339503 3 0.4750 0.776 0.216 0.000 0.784
#> GSM339504 1 0.0424 0.785 0.992 0.000 0.008
#> GSM339505 3 0.8063 0.708 0.224 0.132 0.644
#> GSM339506 1 0.5138 0.492 0.748 0.000 0.252
#> GSM339507 3 0.4842 0.786 0.224 0.000 0.776
#> GSM339508 2 0.0000 0.865 0.000 1.000 0.000
#> GSM339509 2 0.0000 0.865 0.000 1.000 0.000
#> GSM339510 2 0.6867 0.766 0.040 0.672 0.288
#> GSM339511 1 0.5791 0.697 0.784 0.048 0.168
#> GSM339512 3 0.6274 0.332 0.000 0.456 0.544
#> GSM339513 1 0.5098 0.621 0.752 0.000 0.248
#> GSM339514 2 0.0000 0.865 0.000 1.000 0.000
#> GSM339515 1 0.2066 0.774 0.940 0.000 0.060
#> GSM339516 2 0.5741 0.827 0.036 0.776 0.188
#> GSM339517 3 0.4605 0.780 0.204 0.000 0.796
#> GSM339518 2 0.4912 0.836 0.008 0.796 0.196
#> GSM339519 3 0.1753 0.587 0.048 0.000 0.952
#> GSM339520 3 0.6416 0.617 0.032 0.260 0.708
#> GSM339521 2 0.0000 0.865 0.000 1.000 0.000
#> GSM339522 2 0.5842 0.824 0.036 0.768 0.196
#> GSM339523 2 0.0000 0.865 0.000 1.000 0.000
#> GSM339524 3 0.6062 0.555 0.384 0.000 0.616
#> GSM339525 1 0.1529 0.777 0.960 0.000 0.040
#> GSM339526 3 0.4931 0.784 0.232 0.000 0.768
#> GSM339527 1 0.6260 0.301 0.552 0.000 0.448
#> GSM339528 3 0.6140 0.629 0.404 0.000 0.596
#> GSM339529 2 0.4399 0.837 0.000 0.812 0.188
#> GSM339530 3 0.6621 0.591 0.032 0.284 0.684
#> GSM339531 2 0.6823 0.762 0.036 0.668 0.296
#> GSM339532 1 0.6354 0.682 0.748 0.056 0.196
#> GSM339533 3 0.4796 0.786 0.220 0.000 0.780
#> GSM339534 1 0.1753 0.776 0.952 0.000 0.048
#> GSM339535 2 0.2537 0.862 0.000 0.920 0.080
#> GSM339536 1 0.2711 0.766 0.912 0.000 0.088
#> GSM339537 2 0.5508 0.829 0.028 0.784 0.188
#> GSM339538 3 0.4605 0.780 0.204 0.000 0.796
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM339455 4 0.5050 0.633 0.028 0.000 0.268 0.704
#> GSM339456 2 0.4824 0.749 0.000 0.780 0.076 0.144
#> GSM339457 3 0.2111 0.882 0.024 0.000 0.932 0.044
#> GSM339458 4 0.7844 0.535 0.028 0.216 0.208 0.548
#> GSM339459 4 0.2831 0.810 0.004 0.000 0.120 0.876
#> GSM339460 2 0.2075 0.855 0.044 0.936 0.016 0.004
#> GSM339461 2 0.4644 0.734 0.000 0.748 0.024 0.228
#> GSM339462 1 0.0376 0.889 0.992 0.000 0.004 0.004
#> GSM339463 3 0.2996 0.867 0.064 0.000 0.892 0.044
#> GSM339464 1 0.1109 0.883 0.968 0.004 0.000 0.028
#> GSM339465 3 0.2845 0.864 0.028 0.000 0.896 0.076
#> GSM339466 4 0.2635 0.834 0.000 0.076 0.020 0.904
#> GSM339467 2 0.0000 0.875 0.000 1.000 0.000 0.000
#> GSM339468 4 0.3229 0.831 0.000 0.048 0.072 0.880
#> GSM339469 1 0.0564 0.890 0.988 0.004 0.004 0.004
#> GSM339470 3 0.2521 0.868 0.024 0.000 0.912 0.064
#> GSM339471 1 0.4281 0.794 0.792 0.000 0.180 0.028
#> GSM339472 2 0.0921 0.872 0.000 0.972 0.000 0.028
#> GSM339473 1 0.3497 0.845 0.860 0.000 0.104 0.036
#> GSM339474 2 0.1302 0.870 0.000 0.956 0.000 0.044
#> GSM339475 3 0.1978 0.874 0.004 0.000 0.928 0.068
#> GSM339476 1 0.2313 0.888 0.924 0.000 0.032 0.044
#> GSM339477 2 0.1302 0.870 0.000 0.956 0.000 0.044
#> GSM339478 4 0.4622 0.796 0.004 0.060 0.136 0.800
#> GSM339479 4 0.7491 0.447 0.260 0.008 0.192 0.540
#> GSM339480 4 0.3161 0.811 0.012 0.000 0.124 0.864
#> GSM339481 2 0.0000 0.875 0.000 1.000 0.000 0.000
#> GSM339482 3 0.2125 0.873 0.004 0.000 0.920 0.076
#> GSM339483 1 0.1109 0.884 0.968 0.000 0.004 0.028
#> GSM339484 3 0.2142 0.888 0.056 0.000 0.928 0.016
#> GSM339485 1 0.1109 0.883 0.968 0.004 0.000 0.028
#> GSM339486 3 0.3032 0.852 0.124 0.000 0.868 0.008
#> GSM339487 4 0.2473 0.834 0.000 0.080 0.012 0.908
#> GSM339488 2 0.0895 0.867 0.000 0.976 0.020 0.004
#> GSM339489 4 0.3659 0.830 0.032 0.016 0.084 0.868
#> GSM339490 1 0.1109 0.883 0.968 0.004 0.000 0.028
#> GSM339491 3 0.1406 0.891 0.024 0.000 0.960 0.016
#> GSM339492 1 0.3279 0.865 0.872 0.000 0.096 0.032
#> GSM339493 2 0.3356 0.771 0.000 0.824 0.000 0.176
#> GSM339494 1 0.3009 0.878 0.892 0.000 0.056 0.052
#> GSM339495 2 0.2149 0.854 0.000 0.912 0.000 0.088
#> GSM339496 3 0.1929 0.889 0.024 0.000 0.940 0.036
#> GSM339497 4 0.3571 0.826 0.008 0.036 0.088 0.868
#> GSM339498 4 0.3547 0.795 0.016 0.000 0.144 0.840
#> GSM339499 3 0.1151 0.891 0.024 0.000 0.968 0.008
#> GSM339500 2 0.7838 0.443 0.024 0.528 0.272 0.176
#> GSM339501 4 0.4879 0.785 0.128 0.000 0.092 0.780
#> GSM339502 2 0.0188 0.875 0.000 0.996 0.004 0.000
#> GSM339503 3 0.2329 0.870 0.012 0.000 0.916 0.072
#> GSM339504 1 0.0524 0.889 0.988 0.000 0.008 0.004
#> GSM339505 3 0.2949 0.859 0.024 0.000 0.888 0.088
#> GSM339506 1 0.4606 0.644 0.724 0.000 0.264 0.012
#> GSM339507 3 0.2797 0.876 0.032 0.000 0.900 0.068
#> GSM339508 2 0.2530 0.838 0.000 0.888 0.000 0.112
#> GSM339509 2 0.0188 0.875 0.000 0.996 0.004 0.000
#> GSM339510 4 0.2484 0.840 0.040 0.024 0.012 0.924
#> GSM339511 1 0.1610 0.880 0.952 0.016 0.000 0.032
#> GSM339512 3 0.5416 0.555 0.000 0.260 0.692 0.048
#> GSM339513 1 0.6249 0.509 0.592 0.000 0.336 0.072
#> GSM339514 2 0.0000 0.875 0.000 1.000 0.000 0.000
#> GSM339515 1 0.2670 0.878 0.904 0.000 0.072 0.024
#> GSM339516 4 0.2281 0.830 0.000 0.096 0.000 0.904
#> GSM339517 3 0.2053 0.872 0.004 0.000 0.924 0.072
#> GSM339518 4 0.4139 0.801 0.000 0.144 0.040 0.816
#> GSM339519 3 0.3831 0.745 0.004 0.000 0.792 0.204
#> GSM339520 2 0.4434 0.721 0.016 0.772 0.208 0.004
#> GSM339521 2 0.2011 0.856 0.000 0.920 0.000 0.080
#> GSM339522 4 0.2281 0.830 0.000 0.096 0.000 0.904
#> GSM339523 2 0.0000 0.875 0.000 1.000 0.000 0.000
#> GSM339524 3 0.5966 0.488 0.280 0.000 0.648 0.072
#> GSM339525 1 0.0895 0.890 0.976 0.000 0.020 0.004
#> GSM339526 3 0.2124 0.889 0.028 0.000 0.932 0.040
#> GSM339527 1 0.5250 0.564 0.660 0.000 0.316 0.024
#> GSM339528 3 0.3876 0.847 0.124 0.000 0.836 0.040
#> GSM339529 4 0.3219 0.789 0.000 0.164 0.000 0.836
#> GSM339530 2 0.5360 0.223 0.000 0.552 0.436 0.012
#> GSM339531 4 0.3216 0.830 0.000 0.044 0.076 0.880
#> GSM339532 1 0.2408 0.861 0.920 0.036 0.000 0.044
#> GSM339533 3 0.1004 0.891 0.024 0.000 0.972 0.004
#> GSM339534 1 0.3383 0.858 0.872 0.000 0.052 0.076
#> GSM339535 4 0.4456 0.688 0.000 0.280 0.004 0.716
#> GSM339536 1 0.2844 0.879 0.900 0.000 0.048 0.052
#> GSM339537 4 0.2281 0.830 0.000 0.096 0.000 0.904
#> GSM339538 3 0.2053 0.872 0.004 0.000 0.924 0.072
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM339455 5 0.4714 0.421 0.004 0.000 0.372 0.016 0.608
#> GSM339456 2 0.4785 0.745 0.004 0.732 0.088 0.000 0.176
#> GSM339457 3 0.2983 0.706 0.056 0.000 0.868 0.000 0.076
#> GSM339458 5 0.6146 0.217 0.000 0.116 0.392 0.004 0.488
#> GSM339459 5 0.3791 0.754 0.076 0.000 0.112 0.000 0.812
#> GSM339460 2 0.2316 0.847 0.000 0.916 0.036 0.036 0.012
#> GSM339461 2 0.5124 0.637 0.068 0.644 0.000 0.000 0.288
#> GSM339462 4 0.0290 0.905 0.000 0.000 0.000 0.992 0.008
#> GSM339463 3 0.2504 0.732 0.004 0.000 0.900 0.032 0.064
#> GSM339464 4 0.0000 0.905 0.000 0.000 0.000 1.000 0.000
#> GSM339465 3 0.2409 0.730 0.032 0.000 0.900 0.000 0.068
#> GSM339466 5 0.0404 0.806 0.000 0.012 0.000 0.000 0.988
#> GSM339467 2 0.0000 0.866 0.000 1.000 0.000 0.000 0.000
#> GSM339468 5 0.1704 0.794 0.000 0.004 0.068 0.000 0.928
#> GSM339469 4 0.0162 0.905 0.000 0.000 0.004 0.996 0.000
#> GSM339470 3 0.1544 0.740 0.000 0.000 0.932 0.000 0.068
#> GSM339471 1 0.5396 0.785 0.688 0.000 0.156 0.148 0.008
#> GSM339472 2 0.1792 0.859 0.000 0.916 0.000 0.000 0.084
#> GSM339473 1 0.2927 0.785 0.872 0.000 0.060 0.068 0.000
#> GSM339474 2 0.2179 0.852 0.000 0.888 0.000 0.000 0.112
#> GSM339475 3 0.2707 0.708 0.132 0.000 0.860 0.000 0.008
#> GSM339476 4 0.3183 0.814 0.020 0.000 0.048 0.872 0.060
#> GSM339477 2 0.2280 0.851 0.000 0.880 0.000 0.000 0.120
#> GSM339478 5 0.6098 0.351 0.020 0.084 0.344 0.000 0.552
#> GSM339479 5 0.6718 0.169 0.004 0.012 0.368 0.148 0.468
#> GSM339480 5 0.3839 0.757 0.072 0.000 0.108 0.004 0.816
#> GSM339481 2 0.0162 0.866 0.000 0.996 0.000 0.000 0.004
#> GSM339482 1 0.4533 0.305 0.544 0.000 0.448 0.000 0.008
#> GSM339483 4 0.0290 0.905 0.000 0.000 0.000 0.992 0.008
#> GSM339484 3 0.4040 0.533 0.000 0.000 0.712 0.276 0.012
#> GSM339485 4 0.0000 0.905 0.000 0.000 0.000 1.000 0.000
#> GSM339486 3 0.4779 0.508 0.024 0.000 0.672 0.292 0.012
#> GSM339487 5 0.0510 0.806 0.000 0.016 0.000 0.000 0.984
#> GSM339488 2 0.0000 0.866 0.000 1.000 0.000 0.000 0.000
#> GSM339489 5 0.3117 0.783 0.004 0.000 0.100 0.036 0.860
#> GSM339490 4 0.0000 0.905 0.000 0.000 0.000 1.000 0.000
#> GSM339491 3 0.0703 0.750 0.000 0.000 0.976 0.000 0.024
#> GSM339492 1 0.5533 0.776 0.672 0.000 0.144 0.176 0.008
#> GSM339493 2 0.3586 0.723 0.000 0.736 0.000 0.000 0.264
#> GSM339494 1 0.2830 0.785 0.876 0.000 0.044 0.080 0.000
#> GSM339495 2 0.2773 0.833 0.000 0.836 0.000 0.000 0.164
#> GSM339496 3 0.1670 0.744 0.052 0.000 0.936 0.000 0.012
#> GSM339497 5 0.1956 0.789 0.000 0.008 0.076 0.000 0.916
#> GSM339498 5 0.4275 0.747 0.076 0.000 0.120 0.012 0.792
#> GSM339499 3 0.1502 0.743 0.056 0.000 0.940 0.000 0.004
#> GSM339500 3 0.6398 0.407 0.012 0.204 0.568 0.000 0.216
#> GSM339501 5 0.4583 0.709 0.004 0.000 0.064 0.192 0.740
#> GSM339502 2 0.0000 0.866 0.000 1.000 0.000 0.000 0.000
#> GSM339503 3 0.2796 0.698 0.116 0.000 0.868 0.008 0.008
#> GSM339504 4 0.0290 0.905 0.000 0.000 0.000 0.992 0.008
#> GSM339505 3 0.1671 0.741 0.000 0.000 0.924 0.000 0.076
#> GSM339506 4 0.4217 0.551 0.012 0.000 0.280 0.704 0.004
#> GSM339507 3 0.4126 0.307 0.380 0.000 0.620 0.000 0.000
#> GSM339508 2 0.3242 0.789 0.000 0.784 0.000 0.000 0.216
#> GSM339509 2 0.0000 0.866 0.000 1.000 0.000 0.000 0.000
#> GSM339510 5 0.1341 0.800 0.000 0.000 0.000 0.056 0.944
#> GSM339511 4 0.1478 0.870 0.000 0.000 0.000 0.936 0.064
#> GSM339512 3 0.6290 0.138 0.000 0.332 0.500 0.000 0.168
#> GSM339513 1 0.4233 0.779 0.792 0.000 0.116 0.084 0.008
#> GSM339514 2 0.0000 0.866 0.000 1.000 0.000 0.000 0.000
#> GSM339515 1 0.2914 0.785 0.872 0.000 0.052 0.076 0.000
#> GSM339516 5 0.0404 0.806 0.000 0.012 0.000 0.000 0.988
#> GSM339517 3 0.3980 0.512 0.284 0.000 0.708 0.000 0.008
#> GSM339518 5 0.3639 0.759 0.000 0.144 0.044 0.000 0.812
#> GSM339519 1 0.4197 0.668 0.728 0.000 0.244 0.000 0.028
#> GSM339520 2 0.4970 0.329 0.020 0.580 0.392 0.000 0.008
#> GSM339521 2 0.4098 0.804 0.000 0.780 0.064 0.000 0.156
#> GSM339522 5 0.0404 0.806 0.000 0.012 0.000 0.000 0.988
#> GSM339523 2 0.0000 0.866 0.000 1.000 0.000 0.000 0.000
#> GSM339524 1 0.4153 0.721 0.740 0.000 0.236 0.016 0.008
#> GSM339525 4 0.0162 0.905 0.000 0.000 0.004 0.996 0.000
#> GSM339526 3 0.1894 0.736 0.072 0.000 0.920 0.000 0.008
#> GSM339527 4 0.4133 0.640 0.012 0.000 0.232 0.744 0.012
#> GSM339528 3 0.5548 0.450 0.012 0.000 0.612 0.312 0.064
#> GSM339529 5 0.1965 0.763 0.000 0.096 0.000 0.000 0.904
#> GSM339530 2 0.3110 0.776 0.028 0.856 0.112 0.000 0.004
#> GSM339531 5 0.1928 0.793 0.004 0.004 0.072 0.000 0.920
#> GSM339532 4 0.2488 0.807 0.000 0.004 0.000 0.872 0.124
#> GSM339533 3 0.0290 0.747 0.000 0.000 0.992 0.000 0.008
#> GSM339534 1 0.5925 0.727 0.672 0.000 0.072 0.188 0.068
#> GSM339535 5 0.3612 0.657 0.000 0.268 0.000 0.000 0.732
#> GSM339536 1 0.2793 0.785 0.876 0.000 0.036 0.088 0.000
#> GSM339537 5 0.0510 0.806 0.000 0.016 0.000 0.000 0.984
#> GSM339538 1 0.3487 0.720 0.780 0.000 0.212 0.000 0.008
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM339455 3 0.5460 0.219 0.000 0.000 0.492 0.004 0.396 0.108
#> GSM339456 2 0.4784 0.593 0.000 0.624 0.048 0.000 0.316 0.012
#> GSM339457 6 0.1910 0.831 0.000 0.000 0.108 0.000 0.000 0.892
#> GSM339458 3 0.3045 0.737 0.000 0.060 0.840 0.000 0.100 0.000
#> GSM339459 5 0.4307 0.663 0.000 0.000 0.072 0.000 0.704 0.224
#> GSM339460 2 0.2577 0.798 0.000 0.884 0.072 0.032 0.012 0.000
#> GSM339461 2 0.5640 0.540 0.000 0.580 0.032 0.000 0.292 0.096
#> GSM339462 4 0.0146 0.917 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM339463 3 0.1801 0.773 0.000 0.000 0.924 0.016 0.004 0.056
#> GSM339464 4 0.0000 0.917 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM339465 3 0.1829 0.777 0.036 0.000 0.928 0.000 0.028 0.008
#> GSM339466 5 0.0405 0.842 0.000 0.004 0.008 0.000 0.988 0.000
#> GSM339467 2 0.0146 0.833 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM339468 5 0.1010 0.837 0.000 0.004 0.036 0.000 0.960 0.000
#> GSM339469 4 0.0146 0.916 0.000 0.000 0.004 0.996 0.000 0.000
#> GSM339470 3 0.1713 0.772 0.000 0.000 0.928 0.000 0.028 0.044
#> GSM339471 1 0.4427 0.788 0.764 0.000 0.108 0.100 0.008 0.020
#> GSM339472 2 0.1910 0.834 0.000 0.892 0.000 0.000 0.108 0.000
#> GSM339473 1 0.0000 0.804 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM339474 2 0.2378 0.824 0.000 0.848 0.000 0.000 0.152 0.000
#> GSM339475 6 0.1219 0.749 0.004 0.000 0.048 0.000 0.000 0.948
#> GSM339476 4 0.2657 0.820 0.000 0.000 0.076 0.880 0.024 0.020
#> GSM339477 2 0.2416 0.823 0.000 0.844 0.000 0.000 0.156 0.000
#> GSM339478 6 0.3124 0.831 0.000 0.028 0.100 0.000 0.024 0.848
#> GSM339479 3 0.3626 0.749 0.000 0.012 0.812 0.092 0.084 0.000
#> GSM339480 5 0.3352 0.752 0.000 0.000 0.072 0.000 0.816 0.112
#> GSM339481 2 0.0363 0.836 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM339482 3 0.5607 0.170 0.304 0.000 0.556 0.000 0.012 0.128
#> GSM339483 4 0.0146 0.917 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM339484 3 0.2274 0.764 0.000 0.000 0.892 0.088 0.008 0.012
#> GSM339485 4 0.0000 0.917 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM339486 3 0.2468 0.771 0.000 0.000 0.880 0.096 0.008 0.016
#> GSM339487 5 0.0508 0.843 0.000 0.012 0.004 0.000 0.984 0.000
#> GSM339488 2 0.0146 0.833 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM339489 5 0.2744 0.807 0.000 0.000 0.052 0.060 0.876 0.012
#> GSM339490 4 0.0000 0.917 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM339491 3 0.0837 0.779 0.000 0.020 0.972 0.000 0.004 0.004
#> GSM339492 1 0.4753 0.757 0.720 0.000 0.100 0.160 0.008 0.012
#> GSM339493 2 0.3672 0.580 0.000 0.632 0.000 0.000 0.368 0.000
#> GSM339494 1 0.0000 0.804 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM339495 2 0.3482 0.685 0.000 0.684 0.000 0.000 0.316 0.000
#> GSM339496 3 0.3403 0.634 0.000 0.000 0.768 0.000 0.020 0.212
#> GSM339497 5 0.2793 0.702 0.000 0.000 0.200 0.000 0.800 0.000
#> GSM339498 5 0.4616 0.560 0.000 0.000 0.072 0.000 0.648 0.280
#> GSM339499 6 0.2092 0.829 0.000 0.000 0.124 0.000 0.000 0.876
#> GSM339500 3 0.6655 0.186 0.000 0.072 0.504 0.000 0.216 0.208
#> GSM339501 5 0.4234 0.555 0.000 0.000 0.032 0.324 0.644 0.000
#> GSM339502 2 0.0146 0.833 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM339503 3 0.2520 0.709 0.008 0.000 0.872 0.000 0.012 0.108
#> GSM339504 4 0.0146 0.917 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM339505 3 0.1341 0.780 0.000 0.000 0.948 0.000 0.028 0.024
#> GSM339506 3 0.4141 0.249 0.000 0.000 0.556 0.432 0.000 0.012
#> GSM339507 3 0.2300 0.752 0.144 0.000 0.856 0.000 0.000 0.000
#> GSM339508 2 0.2838 0.814 0.000 0.808 0.000 0.004 0.188 0.000
#> GSM339509 2 0.0146 0.833 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM339510 5 0.1462 0.830 0.000 0.000 0.008 0.056 0.936 0.000
#> GSM339511 4 0.1556 0.858 0.000 0.000 0.000 0.920 0.080 0.000
#> GSM339512 2 0.3828 0.777 0.000 0.776 0.124 0.000 0.100 0.000
#> GSM339513 1 0.4349 0.805 0.780 0.000 0.080 0.028 0.012 0.100
#> GSM339514 2 0.0146 0.833 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM339515 1 0.0000 0.804 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM339516 5 0.0508 0.843 0.000 0.012 0.004 0.000 0.984 0.000
#> GSM339517 6 0.5549 0.323 0.176 0.000 0.212 0.000 0.012 0.600
#> GSM339518 5 0.4663 0.591 0.000 0.272 0.068 0.000 0.656 0.004
#> GSM339519 1 0.4744 0.775 0.716 0.000 0.116 0.000 0.020 0.148
#> GSM339520 6 0.2948 0.831 0.000 0.060 0.092 0.000 0.000 0.848
#> GSM339521 2 0.3141 0.794 0.000 0.788 0.012 0.000 0.200 0.000
#> GSM339522 5 0.0405 0.842 0.000 0.004 0.008 0.000 0.988 0.000
#> GSM339523 2 0.0146 0.833 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM339524 1 0.4701 0.782 0.728 0.000 0.144 0.008 0.012 0.108
#> GSM339525 4 0.0146 0.916 0.000 0.000 0.004 0.996 0.000 0.000
#> GSM339526 3 0.2163 0.745 0.004 0.000 0.892 0.000 0.008 0.096
#> GSM339527 4 0.4238 0.401 0.000 0.000 0.340 0.636 0.016 0.008
#> GSM339528 3 0.3020 0.768 0.016 0.000 0.856 0.100 0.024 0.004
#> GSM339529 5 0.1471 0.820 0.000 0.064 0.004 0.000 0.932 0.000
#> GSM339530 6 0.2260 0.777 0.000 0.140 0.000 0.000 0.000 0.860
#> GSM339531 5 0.1226 0.835 0.000 0.004 0.040 0.000 0.952 0.004
#> GSM339532 4 0.2558 0.768 0.000 0.004 0.000 0.840 0.156 0.000
#> GSM339533 3 0.0976 0.780 0.000 0.000 0.968 0.016 0.008 0.008
#> GSM339534 1 0.4993 0.741 0.720 0.000 0.080 0.156 0.028 0.016
#> GSM339535 5 0.3215 0.715 0.000 0.240 0.000 0.000 0.756 0.004
#> GSM339536 1 0.0000 0.804 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM339537 5 0.0603 0.842 0.000 0.016 0.004 0.000 0.980 0.000
#> GSM339538 1 0.4533 0.780 0.728 0.000 0.112 0.000 0.012 0.148
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 protocol(p) agent(p) individual(p) k
#> MAD:pam 79 1.000 0.859 3.10e-03 2
#> MAD:pam 77 0.557 0.794 2.27e-05 3
#> MAD:pam 80 0.769 0.976 1.20e-06 4
#> MAD:pam 74 0.426 0.703 3.71e-08 5
#> MAD:pam 78 0.474 0.723 5.92e-10 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 15497 rows and 84 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 0.323 0.257 0.691 0.4162 0.826 0.826
#> 3 3 0.549 0.848 0.877 0.4897 0.429 0.343
#> 4 4 0.895 0.902 0.947 0.1225 0.869 0.662
#> 5 5 0.719 0.791 0.853 0.0663 0.989 0.964
#> 6 6 0.714 0.707 0.802 0.0494 0.974 0.911
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
#> GSM339455 2 0.0000 0.439 0.000 1.000
#> GSM339456 2 0.9795 0.549 0.416 0.584
#> GSM339457 2 0.0000 0.439 0.000 1.000
#> GSM339458 2 0.8861 0.538 0.304 0.696
#> GSM339459 2 0.0000 0.439 0.000 1.000
#> GSM339460 2 0.9881 0.550 0.436 0.564
#> GSM339461 2 0.9209 0.543 0.336 0.664
#> GSM339462 2 0.9815 -0.692 0.420 0.580
#> GSM339463 2 0.9775 -0.682 0.412 0.588
#> GSM339464 2 0.9815 -0.692 0.420 0.580
#> GSM339465 2 0.9996 -0.868 0.488 0.512
#> GSM339466 2 0.9881 0.550 0.436 0.564
#> GSM339467 2 0.9881 0.550 0.436 0.564
#> GSM339468 2 0.3733 0.467 0.072 0.928
#> GSM339469 2 0.9795 -0.686 0.416 0.584
#> GSM339470 2 0.0000 0.439 0.000 1.000
#> GSM339471 1 0.9944 0.972 0.544 0.456
#> GSM339472 2 0.9881 0.550 0.436 0.564
#> GSM339473 1 0.9909 0.986 0.556 0.444
#> GSM339474 2 0.9881 0.550 0.436 0.564
#> GSM339475 2 0.0376 0.435 0.004 0.996
#> GSM339476 2 0.9775 -0.680 0.412 0.588
#> GSM339477 2 0.9881 0.550 0.436 0.564
#> GSM339478 2 0.0376 0.441 0.004 0.996
#> GSM339479 2 0.1184 0.417 0.016 0.984
#> GSM339480 2 0.0000 0.439 0.000 1.000
#> GSM339481 2 0.9881 0.550 0.436 0.564
#> GSM339482 2 0.0376 0.435 0.004 0.996
#> GSM339483 2 0.9815 -0.692 0.420 0.580
#> GSM339484 2 0.9909 -0.761 0.444 0.556
#> GSM339485 2 0.9815 -0.692 0.420 0.580
#> GSM339486 1 0.9909 0.986 0.556 0.444
#> GSM339487 2 0.9881 0.550 0.436 0.564
#> GSM339488 2 0.9881 0.550 0.436 0.564
#> GSM339489 2 0.8861 0.538 0.304 0.696
#> GSM339490 2 0.9815 -0.692 0.420 0.580
#> GSM339491 2 0.0000 0.439 0.000 1.000
#> GSM339492 2 0.9977 -0.830 0.472 0.528
#> GSM339493 2 0.9881 0.550 0.436 0.564
#> GSM339494 1 0.9909 0.986 0.556 0.444
#> GSM339495 2 0.9881 0.550 0.436 0.564
#> GSM339496 2 0.0376 0.435 0.004 0.996
#> GSM339497 2 0.9522 0.546 0.372 0.628
#> GSM339498 2 0.0000 0.439 0.000 1.000
#> GSM339499 2 0.0000 0.439 0.000 1.000
#> GSM339500 2 0.8909 0.539 0.308 0.692
#> GSM339501 2 0.1184 0.417 0.016 0.984
#> GSM339502 2 0.9881 0.550 0.436 0.564
#> GSM339503 2 0.0376 0.435 0.004 0.996
#> GSM339504 2 0.9815 -0.692 0.420 0.580
#> GSM339505 2 0.0000 0.439 0.000 1.000
#> GSM339506 2 0.9795 -0.686 0.416 0.584
#> GSM339507 1 0.9988 0.929 0.520 0.480
#> GSM339508 2 0.9881 0.550 0.436 0.564
#> GSM339509 2 0.9881 0.550 0.436 0.564
#> GSM339510 2 0.1633 0.449 0.024 0.976
#> GSM339511 2 0.9795 -0.686 0.416 0.584
#> GSM339512 2 0.9881 0.550 0.436 0.564
#> GSM339513 2 0.9775 -0.680 0.412 0.588
#> GSM339514 2 0.9881 0.550 0.436 0.564
#> GSM339515 1 0.9909 0.986 0.556 0.444
#> GSM339516 2 0.9881 0.550 0.436 0.564
#> GSM339517 2 0.0376 0.435 0.004 0.996
#> GSM339518 2 0.9881 0.550 0.436 0.564
#> GSM339519 2 0.0376 0.435 0.004 0.996
#> GSM339520 2 0.0000 0.439 0.000 1.000
#> GSM339521 2 0.9881 0.550 0.436 0.564
#> GSM339522 2 0.9881 0.550 0.436 0.564
#> GSM339523 2 0.9881 0.550 0.436 0.564
#> GSM339524 2 0.9775 -0.680 0.412 0.588
#> GSM339525 2 0.9795 -0.686 0.416 0.584
#> GSM339526 2 0.0376 0.435 0.004 0.996
#> GSM339527 2 0.9795 -0.686 0.416 0.584
#> GSM339528 1 0.9909 0.986 0.556 0.444
#> GSM339529 2 0.9881 0.550 0.436 0.564
#> GSM339530 2 0.0000 0.439 0.000 1.000
#> GSM339531 2 0.9248 0.544 0.340 0.660
#> GSM339532 2 0.9795 -0.686 0.416 0.584
#> GSM339533 2 0.0376 0.435 0.004 0.996
#> GSM339534 2 0.9815 -0.700 0.420 0.580
#> GSM339535 2 0.9881 0.550 0.436 0.564
#> GSM339536 1 0.9909 0.986 0.556 0.444
#> GSM339537 2 0.9881 0.550 0.436 0.564
#> GSM339538 2 0.0376 0.435 0.004 0.996
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM339455 3 0.6719 0.599 0.204 0.068 0.728
#> GSM339456 2 0.1163 0.933 0.000 0.972 0.028
#> GSM339457 3 0.3038 0.916 0.000 0.104 0.896
#> GSM339458 2 0.2152 0.920 0.016 0.948 0.036
#> GSM339459 3 0.3038 0.905 0.000 0.104 0.896
#> GSM339460 2 0.0237 0.945 0.000 0.996 0.004
#> GSM339461 2 0.1163 0.933 0.000 0.972 0.028
#> GSM339462 1 0.3532 0.793 0.884 0.008 0.108
#> GSM339463 3 0.7284 0.125 0.336 0.044 0.620
#> GSM339464 1 0.3532 0.793 0.884 0.008 0.108
#> GSM339465 3 0.3550 0.800 0.080 0.024 0.896
#> GSM339466 2 0.0000 0.947 0.000 1.000 0.000
#> GSM339467 2 0.0000 0.947 0.000 1.000 0.000
#> GSM339468 2 0.3116 0.854 0.000 0.892 0.108
#> GSM339469 1 0.4799 0.803 0.836 0.032 0.132
#> GSM339470 3 0.3607 0.906 0.008 0.112 0.880
#> GSM339471 1 0.5578 0.779 0.748 0.012 0.240
#> GSM339472 2 0.0237 0.946 0.000 0.996 0.004
#> GSM339473 1 0.5138 0.779 0.748 0.000 0.252
#> GSM339474 2 0.0000 0.947 0.000 1.000 0.000
#> GSM339475 3 0.2356 0.920 0.000 0.072 0.928
#> GSM339476 1 0.7391 0.746 0.636 0.056 0.308
#> GSM339477 2 0.0892 0.938 0.000 0.980 0.020
#> GSM339478 2 0.5760 0.473 0.000 0.672 0.328
#> GSM339479 2 0.5850 0.710 0.040 0.772 0.188
#> GSM339480 3 0.3038 0.905 0.000 0.104 0.896
#> GSM339481 2 0.0000 0.947 0.000 1.000 0.000
#> GSM339482 3 0.2356 0.920 0.000 0.072 0.928
#> GSM339483 1 0.3532 0.793 0.884 0.008 0.108
#> GSM339484 1 0.6867 0.778 0.672 0.040 0.288
#> GSM339485 1 0.3532 0.793 0.884 0.008 0.108
#> GSM339486 1 0.5138 0.779 0.748 0.000 0.252
#> GSM339487 2 0.0000 0.947 0.000 1.000 0.000
#> GSM339488 2 0.0000 0.947 0.000 1.000 0.000
#> GSM339489 2 0.2959 0.864 0.000 0.900 0.100
#> GSM339490 1 0.3532 0.793 0.884 0.008 0.108
#> GSM339491 2 0.6434 0.321 0.008 0.612 0.380
#> GSM339492 1 0.6217 0.785 0.712 0.024 0.264
#> GSM339493 2 0.0000 0.947 0.000 1.000 0.000
#> GSM339494 1 0.5138 0.779 0.748 0.000 0.252
#> GSM339495 2 0.0000 0.947 0.000 1.000 0.000
#> GSM339496 3 0.2537 0.920 0.000 0.080 0.920
#> GSM339497 2 0.0829 0.942 0.004 0.984 0.012
#> GSM339498 3 0.4047 0.852 0.004 0.148 0.848
#> GSM339499 3 0.3038 0.916 0.000 0.104 0.896
#> GSM339500 2 0.3038 0.863 0.000 0.896 0.104
#> GSM339501 1 0.7418 0.741 0.672 0.080 0.248
#> GSM339502 2 0.0000 0.947 0.000 1.000 0.000
#> GSM339503 3 0.2356 0.920 0.000 0.072 0.928
#> GSM339504 1 0.3532 0.793 0.884 0.008 0.108
#> GSM339505 3 0.3116 0.914 0.000 0.108 0.892
#> GSM339506 1 0.4802 0.808 0.824 0.020 0.156
#> GSM339507 1 0.5988 0.786 0.688 0.008 0.304
#> GSM339508 2 0.0000 0.947 0.000 1.000 0.000
#> GSM339509 2 0.0000 0.947 0.000 1.000 0.000
#> GSM339510 2 0.3846 0.843 0.016 0.876 0.108
#> GSM339511 1 0.6254 0.759 0.776 0.116 0.108
#> GSM339512 2 0.0000 0.947 0.000 1.000 0.000
#> GSM339513 1 0.7478 0.742 0.632 0.060 0.308
#> GSM339514 2 0.0000 0.947 0.000 1.000 0.000
#> GSM339515 1 0.5138 0.779 0.748 0.000 0.252
#> GSM339516 2 0.0000 0.947 0.000 1.000 0.000
#> GSM339517 3 0.2356 0.920 0.000 0.072 0.928
#> GSM339518 2 0.0237 0.945 0.000 0.996 0.004
#> GSM339519 3 0.2356 0.920 0.000 0.072 0.928
#> GSM339520 3 0.3340 0.904 0.000 0.120 0.880
#> GSM339521 2 0.0000 0.947 0.000 1.000 0.000
#> GSM339522 2 0.0237 0.946 0.000 0.996 0.004
#> GSM339523 2 0.0000 0.947 0.000 1.000 0.000
#> GSM339524 1 0.7749 0.709 0.616 0.072 0.312
#> GSM339525 1 0.5119 0.806 0.816 0.032 0.152
#> GSM339526 3 0.2356 0.920 0.000 0.072 0.928
#> GSM339527 1 0.5355 0.805 0.804 0.036 0.160
#> GSM339528 1 0.5138 0.779 0.748 0.000 0.252
#> GSM339529 2 0.0000 0.947 0.000 1.000 0.000
#> GSM339530 3 0.3038 0.916 0.000 0.104 0.896
#> GSM339531 2 0.1529 0.924 0.000 0.960 0.040
#> GSM339532 1 0.5650 0.779 0.808 0.084 0.108
#> GSM339533 3 0.3370 0.892 0.024 0.072 0.904
#> GSM339534 1 0.7181 0.761 0.648 0.048 0.304
#> GSM339535 2 0.0000 0.947 0.000 1.000 0.000
#> GSM339536 1 0.5138 0.779 0.748 0.000 0.252
#> GSM339537 2 0.0000 0.947 0.000 1.000 0.000
#> GSM339538 3 0.2356 0.920 0.000 0.072 0.928
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM339455 3 0.1745 0.904 0.020 0.008 0.952 0.020
#> GSM339456 2 0.0927 0.986 0.000 0.976 0.008 0.016
#> GSM339457 3 0.1369 0.907 0.004 0.016 0.964 0.016
#> GSM339458 2 0.0188 0.987 0.004 0.996 0.000 0.000
#> GSM339459 3 0.0188 0.909 0.000 0.000 0.996 0.004
#> GSM339460 2 0.0188 0.987 0.004 0.996 0.000 0.000
#> GSM339461 2 0.1114 0.985 0.004 0.972 0.008 0.016
#> GSM339462 4 0.0707 0.882 0.020 0.000 0.000 0.980
#> GSM339463 3 0.4018 0.746 0.224 0.004 0.772 0.000
#> GSM339464 4 0.0707 0.882 0.020 0.000 0.000 0.980
#> GSM339465 3 0.4313 0.699 0.260 0.004 0.736 0.000
#> GSM339466 2 0.0779 0.986 0.004 0.980 0.000 0.016
#> GSM339467 2 0.0336 0.984 0.008 0.992 0.000 0.000
#> GSM339468 2 0.1229 0.983 0.004 0.968 0.008 0.020
#> GSM339469 4 0.1229 0.877 0.020 0.008 0.004 0.968
#> GSM339470 3 0.4082 0.763 0.004 0.164 0.812 0.020
#> GSM339471 1 0.0524 0.945 0.988 0.004 0.008 0.000
#> GSM339472 2 0.0779 0.987 0.004 0.980 0.000 0.016
#> GSM339473 1 0.0524 0.945 0.988 0.004 0.008 0.000
#> GSM339474 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM339475 3 0.0376 0.909 0.004 0.004 0.992 0.000
#> GSM339476 3 0.5144 0.721 0.068 0.004 0.760 0.168
#> GSM339477 2 0.0336 0.985 0.000 0.992 0.008 0.000
#> GSM339478 3 0.3988 0.776 0.004 0.156 0.820 0.020
#> GSM339479 2 0.0524 0.984 0.004 0.988 0.008 0.000
#> GSM339480 3 0.0188 0.909 0.000 0.000 0.996 0.004
#> GSM339481 2 0.0188 0.987 0.004 0.996 0.000 0.000
#> GSM339482 3 0.0000 0.909 0.000 0.000 1.000 0.000
#> GSM339483 4 0.0707 0.882 0.020 0.000 0.000 0.980
#> GSM339484 1 0.0657 0.942 0.984 0.004 0.012 0.000
#> GSM339485 4 0.0707 0.882 0.020 0.000 0.000 0.980
#> GSM339486 1 0.0524 0.945 0.988 0.004 0.008 0.000
#> GSM339487 2 0.1042 0.985 0.008 0.972 0.000 0.020
#> GSM339488 2 0.0336 0.984 0.008 0.992 0.000 0.000
#> GSM339489 2 0.1042 0.985 0.008 0.972 0.000 0.020
#> GSM339490 4 0.0707 0.882 0.020 0.000 0.000 0.980
#> GSM339491 3 0.4504 0.707 0.004 0.204 0.772 0.020
#> GSM339492 1 0.1109 0.927 0.968 0.004 0.028 0.000
#> GSM339493 2 0.0927 0.986 0.008 0.976 0.000 0.016
#> GSM339494 1 0.0524 0.945 0.988 0.004 0.008 0.000
#> GSM339495 2 0.0188 0.987 0.004 0.996 0.000 0.000
#> GSM339496 3 0.0376 0.909 0.004 0.004 0.992 0.000
#> GSM339497 2 0.1042 0.985 0.008 0.972 0.000 0.020
#> GSM339498 3 0.0779 0.909 0.000 0.016 0.980 0.004
#> GSM339499 3 0.1369 0.907 0.004 0.016 0.964 0.016
#> GSM339500 2 0.1042 0.985 0.008 0.972 0.000 0.020
#> GSM339501 3 0.1510 0.902 0.000 0.016 0.956 0.028
#> GSM339502 2 0.0336 0.984 0.008 0.992 0.000 0.000
#> GSM339503 3 0.0000 0.909 0.000 0.000 1.000 0.000
#> GSM339504 4 0.0707 0.882 0.020 0.000 0.000 0.980
#> GSM339505 3 0.1369 0.907 0.004 0.016 0.964 0.016
#> GSM339506 4 0.5028 0.228 0.004 0.000 0.400 0.596
#> GSM339507 1 0.0524 0.945 0.988 0.004 0.008 0.000
#> GSM339508 2 0.0188 0.987 0.004 0.996 0.000 0.000
#> GSM339509 2 0.0336 0.984 0.008 0.992 0.000 0.000
#> GSM339510 2 0.1229 0.983 0.004 0.968 0.008 0.020
#> GSM339511 4 0.4163 0.697 0.020 0.188 0.000 0.792
#> GSM339512 2 0.0592 0.987 0.000 0.984 0.000 0.016
#> GSM339513 1 0.5060 0.320 0.584 0.004 0.412 0.000
#> GSM339514 2 0.0336 0.984 0.008 0.992 0.000 0.000
#> GSM339515 1 0.0524 0.945 0.988 0.004 0.008 0.000
#> GSM339516 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM339517 3 0.0000 0.909 0.000 0.000 1.000 0.000
#> GSM339518 2 0.0188 0.987 0.004 0.996 0.000 0.000
#> GSM339519 3 0.0000 0.909 0.000 0.000 1.000 0.000
#> GSM339520 3 0.1369 0.907 0.004 0.016 0.964 0.016
#> GSM339521 2 0.0927 0.986 0.008 0.976 0.000 0.016
#> GSM339522 2 0.1042 0.985 0.008 0.972 0.000 0.020
#> GSM339523 2 0.0336 0.984 0.008 0.992 0.000 0.000
#> GSM339524 3 0.0921 0.901 0.028 0.000 0.972 0.000
#> GSM339525 4 0.1174 0.875 0.020 0.000 0.012 0.968
#> GSM339526 3 0.0376 0.909 0.004 0.004 0.992 0.000
#> GSM339527 3 0.4832 0.577 0.004 0.004 0.680 0.312
#> GSM339528 1 0.0524 0.945 0.988 0.004 0.008 0.000
#> GSM339529 2 0.0188 0.987 0.004 0.996 0.000 0.000
#> GSM339530 3 0.1369 0.907 0.004 0.016 0.964 0.016
#> GSM339531 2 0.1229 0.984 0.008 0.968 0.004 0.020
#> GSM339532 4 0.4163 0.697 0.020 0.188 0.000 0.792
#> GSM339533 3 0.3232 0.852 0.108 0.004 0.872 0.016
#> GSM339534 3 0.3870 0.767 0.208 0.004 0.788 0.000
#> GSM339535 2 0.0779 0.986 0.004 0.980 0.000 0.016
#> GSM339536 1 0.0524 0.945 0.988 0.004 0.008 0.000
#> GSM339537 2 0.0592 0.987 0.000 0.984 0.000 0.016
#> GSM339538 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
#> GSM339455 3 0.3022 0.8028 0.136 0.004 0.848 0.000 NA
#> GSM339456 2 0.1364 0.8569 0.000 0.952 0.012 0.000 NA
#> GSM339457 3 0.3109 0.7742 0.000 0.000 0.800 0.000 NA
#> GSM339458 2 0.1525 0.8527 0.036 0.948 0.000 0.004 NA
#> GSM339459 3 0.3661 0.7195 0.000 0.000 0.724 0.000 NA
#> GSM339460 2 0.0693 0.8580 0.012 0.980 0.000 0.000 NA
#> GSM339461 2 0.3890 0.7939 0.000 0.736 0.012 0.000 NA
#> GSM339462 4 0.0000 0.8613 0.000 0.000 0.000 1.000 NA
#> GSM339463 3 0.3774 0.6675 0.296 0.000 0.704 0.000 NA
#> GSM339464 4 0.0000 0.8613 0.000 0.000 0.000 1.000 NA
#> GSM339465 3 0.4015 0.5962 0.348 0.000 0.652 0.000 NA
#> GSM339466 2 0.3727 0.8102 0.016 0.768 0.000 0.000 NA
#> GSM339467 2 0.3838 0.7143 0.000 0.716 0.004 0.000 NA
#> GSM339468 2 0.4152 0.7647 0.000 0.692 0.012 0.000 NA
#> GSM339469 4 0.0000 0.8613 0.000 0.000 0.000 1.000 NA
#> GSM339470 3 0.3365 0.8121 0.052 0.056 0.864 0.000 NA
#> GSM339471 1 0.0162 0.9551 0.996 0.000 0.004 0.000 NA
#> GSM339472 2 0.0912 0.8593 0.016 0.972 0.000 0.000 NA
#> GSM339473 1 0.0000 0.9543 1.000 0.000 0.000 0.000 NA
#> GSM339474 2 0.0671 0.8581 0.004 0.980 0.000 0.000 NA
#> GSM339475 3 0.0510 0.8291 0.000 0.000 0.984 0.000 NA
#> GSM339476 3 0.5798 0.5633 0.156 0.000 0.608 0.236 NA
#> GSM339477 2 0.1281 0.8558 0.000 0.956 0.012 0.000 NA
#> GSM339478 3 0.4847 0.6154 0.000 0.240 0.692 0.000 NA
#> GSM339479 2 0.4428 0.7397 0.040 0.780 0.156 0.004 NA
#> GSM339480 3 0.3814 0.7181 0.000 0.004 0.720 0.000 NA
#> GSM339481 2 0.0451 0.8582 0.008 0.988 0.000 0.000 NA
#> GSM339482 3 0.0162 0.8295 0.000 0.000 0.996 0.000 NA
#> GSM339483 4 0.0000 0.8613 0.000 0.000 0.000 1.000 NA
#> GSM339484 1 0.0794 0.9391 0.972 0.000 0.028 0.000 NA
#> GSM339485 4 0.0000 0.8613 0.000 0.000 0.000 1.000 NA
#> GSM339486 1 0.0162 0.9551 0.996 0.000 0.004 0.000 NA
#> GSM339487 2 0.3789 0.8018 0.016 0.760 0.000 0.000 NA
#> GSM339488 2 0.3838 0.7143 0.000 0.716 0.004 0.000 NA
#> GSM339489 2 0.3970 0.8010 0.024 0.752 0.000 0.000 NA
#> GSM339490 4 0.0000 0.8613 0.000 0.000 0.000 1.000 NA
#> GSM339491 3 0.5555 0.4850 0.040 0.320 0.612 0.000 NA
#> GSM339492 1 0.0963 0.9325 0.964 0.000 0.036 0.000 NA
#> GSM339493 2 0.2818 0.8384 0.012 0.856 0.000 0.000 NA
#> GSM339494 1 0.0000 0.9543 1.000 0.000 0.000 0.000 NA
#> GSM339495 2 0.0566 0.8577 0.004 0.984 0.000 0.000 NA
#> GSM339496 3 0.1300 0.8306 0.028 0.000 0.956 0.000 NA
#> GSM339497 2 0.3236 0.8375 0.020 0.828 0.000 0.000 NA
#> GSM339498 3 0.3819 0.7545 0.000 0.016 0.756 0.000 NA
#> GSM339499 3 0.3109 0.7742 0.000 0.000 0.800 0.000 NA
#> GSM339500 2 0.5081 0.7938 0.036 0.736 0.064 0.000 NA
#> GSM339501 3 0.3902 0.7839 0.000 0.016 0.824 0.092 NA
#> GSM339502 2 0.3838 0.7143 0.000 0.716 0.004 0.000 NA
#> GSM339503 3 0.0510 0.8292 0.000 0.000 0.984 0.000 NA
#> GSM339504 4 0.0000 0.8613 0.000 0.000 0.000 1.000 NA
#> GSM339505 3 0.2012 0.8224 0.000 0.020 0.920 0.000 NA
#> GSM339506 4 0.4697 0.2427 0.000 0.000 0.388 0.592 NA
#> GSM339507 1 0.0324 0.9532 0.992 0.004 0.004 0.000 NA
#> GSM339508 2 0.0324 0.8578 0.004 0.992 0.000 0.000 NA
#> GSM339509 2 0.3838 0.7143 0.000 0.716 0.004 0.000 NA
#> GSM339510 2 0.4152 0.7647 0.000 0.692 0.012 0.000 NA
#> GSM339511 4 0.2377 0.7576 0.000 0.128 0.000 0.872 NA
#> GSM339512 2 0.1267 0.8588 0.012 0.960 0.004 0.000 NA
#> GSM339513 1 0.3774 0.5461 0.704 0.000 0.296 0.000 NA
#> GSM339514 2 0.3838 0.7143 0.000 0.716 0.004 0.000 NA
#> GSM339515 1 0.0000 0.9543 1.000 0.000 0.000 0.000 NA
#> GSM339516 2 0.0324 0.8585 0.004 0.992 0.000 0.000 NA
#> GSM339517 3 0.0609 0.8291 0.000 0.000 0.980 0.000 NA
#> GSM339518 2 0.1216 0.8556 0.020 0.960 0.000 0.000 NA
#> GSM339519 3 0.0510 0.8292 0.000 0.000 0.984 0.000 NA
#> GSM339520 3 0.3109 0.7742 0.000 0.000 0.800 0.000 NA
#> GSM339521 2 0.3496 0.8148 0.012 0.788 0.000 0.000 NA
#> GSM339522 2 0.3890 0.7893 0.012 0.736 0.000 0.000 NA
#> GSM339523 2 0.3333 0.7669 0.000 0.788 0.004 0.000 NA
#> GSM339524 3 0.2707 0.7948 0.132 0.000 0.860 0.000 NA
#> GSM339525 4 0.0162 0.8587 0.000 0.000 0.004 0.996 NA
#> GSM339526 3 0.0510 0.8291 0.000 0.000 0.984 0.000 NA
#> GSM339527 4 0.4829 -0.0839 0.000 0.000 0.480 0.500 NA
#> GSM339528 1 0.0162 0.9551 0.996 0.000 0.004 0.000 NA
#> GSM339529 2 0.0324 0.8578 0.004 0.992 0.000 0.000 NA
#> GSM339530 3 0.3109 0.7742 0.000 0.000 0.800 0.000 NA
#> GSM339531 2 0.4130 0.7659 0.000 0.696 0.012 0.000 NA
#> GSM339532 4 0.2377 0.7576 0.000 0.128 0.000 0.872 NA
#> GSM339533 3 0.2488 0.8084 0.124 0.000 0.872 0.000 NA
#> GSM339534 3 0.3661 0.6913 0.276 0.000 0.724 0.000 NA
#> GSM339535 2 0.2719 0.8308 0.000 0.852 0.004 0.000 NA
#> GSM339536 1 0.0000 0.9543 1.000 0.000 0.000 0.000 NA
#> GSM339537 2 0.0451 0.8582 0.004 0.988 0.000 0.000 NA
#> GSM339538 3 0.0609 0.8291 0.000 0.000 0.980 0.000 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM339455 3 0.5251 0.5259 0.344 0.020 0.572 0.000 NA 0.064
#> GSM339456 2 0.1542 0.8062 0.000 0.936 0.004 0.000 NA 0.008
#> GSM339457 6 0.2631 1.0000 0.000 0.000 0.180 0.000 NA 0.820
#> GSM339458 2 0.2251 0.7929 0.052 0.904 0.008 0.000 NA 0.000
#> GSM339459 3 0.4549 0.5519 0.000 0.008 0.692 0.000 NA 0.068
#> GSM339460 2 0.0935 0.8071 0.000 0.964 0.000 0.000 NA 0.004
#> GSM339461 2 0.3215 0.7416 0.000 0.756 0.004 0.000 NA 0.000
#> GSM339462 4 0.0000 0.8633 0.000 0.000 0.000 1.000 NA 0.000
#> GSM339463 3 0.3851 0.4397 0.460 0.000 0.540 0.000 NA 0.000
#> GSM339464 4 0.0000 0.8633 0.000 0.000 0.000 1.000 NA 0.000
#> GSM339465 3 0.3868 0.3742 0.496 0.000 0.504 0.000 NA 0.000
#> GSM339466 2 0.2941 0.7715 0.000 0.780 0.000 0.000 NA 0.000
#> GSM339467 2 0.3991 0.4882 0.000 0.524 0.000 0.000 NA 0.004
#> GSM339468 2 0.4105 0.6281 0.000 0.632 0.020 0.000 NA 0.000
#> GSM339469 4 0.0146 0.8607 0.000 0.004 0.000 0.996 NA 0.000
#> GSM339470 3 0.6934 0.4392 0.068 0.152 0.564 0.000 NA 0.164
#> GSM339471 1 0.0000 0.9815 1.000 0.000 0.000 0.000 NA 0.000
#> GSM339472 2 0.2095 0.8059 0.004 0.904 0.000 0.000 NA 0.016
#> GSM339473 1 0.0260 0.9814 0.992 0.000 0.000 0.000 NA 0.008
#> GSM339474 2 0.1644 0.8011 0.000 0.932 0.000 0.000 NA 0.040
#> GSM339475 3 0.2618 0.5601 0.000 0.000 0.860 0.000 NA 0.116
#> GSM339476 3 0.5884 0.4121 0.380 0.000 0.456 0.156 NA 0.008
#> GSM339477 2 0.2451 0.7925 0.000 0.888 0.004 0.000 NA 0.040
#> GSM339478 3 0.5723 0.3508 0.000 0.096 0.556 0.000 NA 0.316
#> GSM339479 2 0.2633 0.7637 0.112 0.864 0.020 0.000 NA 0.000
#> GSM339480 3 0.4601 0.5498 0.000 0.008 0.688 0.000 NA 0.072
#> GSM339481 2 0.0717 0.8090 0.000 0.976 0.000 0.000 NA 0.008
#> GSM339482 3 0.0891 0.6019 0.000 0.000 0.968 0.000 NA 0.008
#> GSM339483 4 0.0000 0.8633 0.000 0.000 0.000 1.000 NA 0.000
#> GSM339484 1 0.0146 0.9796 0.996 0.000 0.004 0.000 NA 0.000
#> GSM339485 4 0.0000 0.8633 0.000 0.000 0.000 1.000 NA 0.000
#> GSM339486 1 0.0000 0.9815 1.000 0.000 0.000 0.000 NA 0.000
#> GSM339487 2 0.2823 0.7691 0.000 0.796 0.000 0.000 NA 0.000
#> GSM339488 2 0.3991 0.4882 0.000 0.524 0.000 0.000 NA 0.004
#> GSM339489 2 0.2762 0.7646 0.000 0.804 0.000 0.000 NA 0.000
#> GSM339490 4 0.0000 0.8633 0.000 0.000 0.000 1.000 NA 0.000
#> GSM339491 3 0.6971 0.4130 0.052 0.180 0.552 0.000 NA 0.156
#> GSM339492 1 0.0146 0.9796 0.996 0.000 0.004 0.000 NA 0.000
#> GSM339493 2 0.2135 0.7916 0.000 0.872 0.000 0.000 NA 0.000
#> GSM339494 1 0.0260 0.9814 0.992 0.000 0.000 0.000 NA 0.008
#> GSM339495 2 0.2066 0.7974 0.000 0.908 0.000 0.000 NA 0.040
#> GSM339496 3 0.4190 0.4943 0.048 0.000 0.692 0.000 NA 0.260
#> GSM339497 2 0.2950 0.7925 0.024 0.828 0.000 0.000 NA 0.000
#> GSM339498 3 0.4837 0.5505 0.000 0.036 0.668 0.000 NA 0.040
#> GSM339499 6 0.2631 1.0000 0.000 0.000 0.180 0.000 NA 0.820
#> GSM339500 2 0.3488 0.7801 0.036 0.780 0.000 0.000 NA 0.000
#> GSM339501 3 0.5968 0.5304 0.000 0.088 0.616 0.052 NA 0.016
#> GSM339502 2 0.3989 0.4926 0.000 0.528 0.000 0.000 NA 0.004
#> GSM339503 3 0.0146 0.6119 0.000 0.000 0.996 0.000 NA 0.004
#> GSM339504 4 0.0000 0.8633 0.000 0.000 0.000 1.000 NA 0.000
#> GSM339505 3 0.5253 0.0299 0.000 0.072 0.484 0.000 NA 0.436
#> GSM339506 4 0.4855 0.1594 0.000 0.000 0.380 0.556 NA 0.064
#> GSM339507 1 0.0146 0.9800 0.996 0.004 0.000 0.000 NA 0.000
#> GSM339508 2 0.0993 0.8074 0.000 0.964 0.000 0.000 NA 0.024
#> GSM339509 2 0.3991 0.4882 0.000 0.524 0.000 0.000 NA 0.004
#> GSM339510 2 0.3592 0.6564 0.000 0.656 0.000 0.000 NA 0.000
#> GSM339511 4 0.1444 0.7936 0.000 0.072 0.000 0.928 NA 0.000
#> GSM339512 2 0.1765 0.7938 0.000 0.904 0.000 0.000 NA 0.000
#> GSM339513 1 0.1958 0.8584 0.896 0.000 0.100 0.000 NA 0.004
#> GSM339514 2 0.3991 0.4882 0.000 0.524 0.000 0.000 NA 0.004
#> GSM339515 1 0.0260 0.9814 0.992 0.000 0.000 0.000 NA 0.008
#> GSM339516 2 0.0603 0.8083 0.000 0.980 0.000 0.000 NA 0.016
#> GSM339517 3 0.1341 0.5981 0.000 0.000 0.948 0.000 NA 0.028
#> GSM339518 2 0.1461 0.8035 0.016 0.940 0.000 0.000 NA 0.000
#> GSM339519 3 0.0632 0.6131 0.000 0.000 0.976 0.000 NA 0.000
#> GSM339520 6 0.2631 1.0000 0.000 0.000 0.180 0.000 NA 0.820
#> GSM339521 2 0.2730 0.7706 0.000 0.808 0.000 0.000 NA 0.000
#> GSM339522 2 0.3151 0.7369 0.000 0.748 0.000 0.000 NA 0.000
#> GSM339523 2 0.3961 0.5214 0.000 0.556 0.000 0.000 NA 0.004
#> GSM339524 3 0.2653 0.6147 0.144 0.000 0.844 0.000 NA 0.012
#> GSM339525 4 0.0000 0.8633 0.000 0.000 0.000 1.000 NA 0.000
#> GSM339526 3 0.2618 0.5601 0.000 0.000 0.860 0.000 NA 0.116
#> GSM339527 4 0.4978 -0.0309 0.000 0.000 0.432 0.500 NA 0.068
#> GSM339528 1 0.0146 0.9820 0.996 0.000 0.000 0.000 NA 0.004
#> GSM339529 2 0.1003 0.8078 0.000 0.964 0.000 0.000 NA 0.020
#> GSM339530 6 0.2631 1.0000 0.000 0.000 0.180 0.000 NA 0.820
#> GSM339531 2 0.3244 0.7256 0.000 0.732 0.000 0.000 NA 0.000
#> GSM339532 4 0.1444 0.7936 0.000 0.072 0.000 0.928 NA 0.000
#> GSM339533 3 0.5252 0.5197 0.264 0.000 0.592 0.000 NA 0.144
#> GSM339534 3 0.3975 0.4524 0.452 0.000 0.544 0.000 NA 0.004
#> GSM339535 2 0.2260 0.7890 0.000 0.860 0.000 0.000 NA 0.000
#> GSM339536 1 0.0260 0.9814 0.992 0.000 0.000 0.000 NA 0.008
#> GSM339537 2 0.0972 0.8078 0.000 0.964 0.000 0.000 NA 0.028
#> GSM339538 3 0.1341 0.5981 0.000 0.000 0.948 0.000 NA 0.028
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 protocol(p) agent(p) individual(p) k
#> MAD:mclust 39 1.000 0.990 1.98e-02 2
#> MAD:mclust 81 0.939 0.815 8.53e-05 3
#> MAD:mclust 82 0.827 0.899 6.82e-08 4
#> MAD:mclust 81 0.889 0.934 1.70e-07 5
#> MAD:mclust 68 0.625 0.854 8.79e-08 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 15497 rows and 84 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 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 0.786 0.853 0.943 0.5016 0.497 0.497
#> 3 3 0.716 0.823 0.891 0.3246 0.777 0.577
#> 4 4 0.703 0.717 0.859 0.1178 0.845 0.587
#> 5 5 0.651 0.481 0.739 0.0594 0.859 0.538
#> 6 6 0.669 0.602 0.761 0.0406 0.878 0.532
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
#> GSM339455 1 0.0000 0.9267 1.000 0.000
#> GSM339456 2 0.0000 0.9461 0.000 1.000
#> GSM339457 1 0.9323 0.4530 0.652 0.348
#> GSM339458 2 0.0000 0.9461 0.000 1.000
#> GSM339459 2 0.8443 0.6199 0.272 0.728
#> GSM339460 2 0.0000 0.9461 0.000 1.000
#> GSM339461 2 0.0000 0.9461 0.000 1.000
#> GSM339462 1 0.0000 0.9267 1.000 0.000
#> GSM339463 1 0.0000 0.9267 1.000 0.000
#> GSM339464 1 0.1184 0.9148 0.984 0.016
#> GSM339465 1 0.0000 0.9267 1.000 0.000
#> GSM339466 2 0.0000 0.9461 0.000 1.000
#> GSM339467 2 0.0000 0.9461 0.000 1.000
#> GSM339468 2 0.0000 0.9461 0.000 1.000
#> GSM339469 1 0.0000 0.9267 1.000 0.000
#> GSM339470 1 0.7674 0.6802 0.776 0.224
#> GSM339471 1 0.0000 0.9267 1.000 0.000
#> GSM339472 2 0.0000 0.9461 0.000 1.000
#> GSM339473 1 0.0000 0.9267 1.000 0.000
#> GSM339474 2 0.0000 0.9461 0.000 1.000
#> GSM339475 1 0.0000 0.9267 1.000 0.000
#> GSM339476 1 0.0000 0.9267 1.000 0.000
#> GSM339477 2 0.0000 0.9461 0.000 1.000
#> GSM339478 2 0.7602 0.7042 0.220 0.780
#> GSM339479 1 0.9881 0.2463 0.564 0.436
#> GSM339480 1 0.9983 0.0774 0.524 0.476
#> GSM339481 2 0.0000 0.9461 0.000 1.000
#> GSM339482 1 0.0000 0.9267 1.000 0.000
#> GSM339483 1 0.0000 0.9267 1.000 0.000
#> GSM339484 1 0.0000 0.9267 1.000 0.000
#> GSM339485 1 0.0376 0.9238 0.996 0.004
#> GSM339486 1 0.0000 0.9267 1.000 0.000
#> GSM339487 2 0.0000 0.9461 0.000 1.000
#> GSM339488 2 0.0000 0.9461 0.000 1.000
#> GSM339489 2 0.0376 0.9431 0.004 0.996
#> GSM339490 1 0.1414 0.9115 0.980 0.020
#> GSM339491 1 0.9922 0.1807 0.552 0.448
#> GSM339492 1 0.0000 0.9267 1.000 0.000
#> GSM339493 2 0.0000 0.9461 0.000 1.000
#> GSM339494 1 0.0000 0.9267 1.000 0.000
#> GSM339495 2 0.0000 0.9461 0.000 1.000
#> GSM339496 1 0.0000 0.9267 1.000 0.000
#> GSM339497 2 0.0000 0.9461 0.000 1.000
#> GSM339498 2 0.5629 0.8194 0.132 0.868
#> GSM339499 2 0.9993 0.0414 0.484 0.516
#> GSM339500 2 0.3114 0.8981 0.056 0.944
#> GSM339501 1 0.0000 0.9267 1.000 0.000
#> GSM339502 2 0.0000 0.9461 0.000 1.000
#> GSM339503 1 0.0000 0.9267 1.000 0.000
#> GSM339504 1 0.0000 0.9267 1.000 0.000
#> GSM339505 1 0.9661 0.3458 0.608 0.392
#> GSM339506 1 0.0000 0.9267 1.000 0.000
#> GSM339507 1 0.0000 0.9267 1.000 0.000
#> GSM339508 2 0.0000 0.9461 0.000 1.000
#> GSM339509 2 0.0000 0.9461 0.000 1.000
#> GSM339510 2 0.0000 0.9461 0.000 1.000
#> GSM339511 1 0.9323 0.4687 0.652 0.348
#> GSM339512 2 0.0000 0.9461 0.000 1.000
#> GSM339513 1 0.0000 0.9267 1.000 0.000
#> GSM339514 2 0.0000 0.9461 0.000 1.000
#> GSM339515 1 0.0000 0.9267 1.000 0.000
#> GSM339516 2 0.0000 0.9461 0.000 1.000
#> GSM339517 1 0.0000 0.9267 1.000 0.000
#> GSM339518 2 0.0000 0.9461 0.000 1.000
#> GSM339519 1 0.0000 0.9267 1.000 0.000
#> GSM339520 2 0.8267 0.6411 0.260 0.740
#> GSM339521 2 0.0000 0.9461 0.000 1.000
#> GSM339522 2 0.0000 0.9461 0.000 1.000
#> GSM339523 2 0.0000 0.9461 0.000 1.000
#> GSM339524 1 0.0000 0.9267 1.000 0.000
#> GSM339525 1 0.0000 0.9267 1.000 0.000
#> GSM339526 1 0.0000 0.9267 1.000 0.000
#> GSM339527 1 0.0000 0.9267 1.000 0.000
#> GSM339528 1 0.0000 0.9267 1.000 0.000
#> GSM339529 2 0.0000 0.9461 0.000 1.000
#> GSM339530 2 0.9775 0.2903 0.412 0.588
#> GSM339531 2 0.0000 0.9461 0.000 1.000
#> GSM339532 1 0.7674 0.6855 0.776 0.224
#> GSM339533 1 0.0000 0.9267 1.000 0.000
#> GSM339534 1 0.0000 0.9267 1.000 0.000
#> GSM339535 2 0.0000 0.9461 0.000 1.000
#> GSM339536 1 0.0000 0.9267 1.000 0.000
#> GSM339537 2 0.0000 0.9461 0.000 1.000
#> GSM339538 1 0.0000 0.9267 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM339455 3 0.5138 0.444 0.252 0.000 0.748
#> GSM339456 2 0.2711 0.908 0.088 0.912 0.000
#> GSM339457 3 0.1643 0.880 0.000 0.044 0.956
#> GSM339458 2 0.2066 0.932 0.060 0.940 0.000
#> GSM339459 3 0.5657 0.779 0.104 0.088 0.808
#> GSM339460 2 0.1411 0.940 0.036 0.964 0.000
#> GSM339461 2 0.4750 0.805 0.216 0.784 0.000
#> GSM339462 1 0.0592 0.776 0.988 0.000 0.012
#> GSM339463 3 0.2066 0.829 0.060 0.000 0.940
#> GSM339464 1 0.0000 0.774 1.000 0.000 0.000
#> GSM339465 3 0.0237 0.884 0.004 0.000 0.996
#> GSM339466 2 0.0000 0.944 0.000 1.000 0.000
#> GSM339467 2 0.0000 0.944 0.000 1.000 0.000
#> GSM339468 2 0.5254 0.766 0.264 0.736 0.000
#> GSM339469 1 0.0000 0.774 1.000 0.000 0.000
#> GSM339470 3 0.0892 0.886 0.000 0.020 0.980
#> GSM339471 1 0.5760 0.716 0.672 0.000 0.328
#> GSM339472 2 0.0000 0.944 0.000 1.000 0.000
#> GSM339473 1 0.5621 0.730 0.692 0.000 0.308
#> GSM339474 2 0.1163 0.941 0.028 0.972 0.000
#> GSM339475 3 0.0000 0.886 0.000 0.000 1.000
#> GSM339476 1 0.5216 0.745 0.740 0.000 0.260
#> GSM339477 2 0.3482 0.895 0.128 0.872 0.000
#> GSM339478 3 0.5621 0.603 0.000 0.308 0.692
#> GSM339479 1 0.5635 0.671 0.784 0.180 0.036
#> GSM339480 3 0.4349 0.792 0.128 0.020 0.852
#> GSM339481 2 0.0000 0.944 0.000 1.000 0.000
#> GSM339482 3 0.0000 0.886 0.000 0.000 1.000
#> GSM339483 1 0.0000 0.774 1.000 0.000 0.000
#> GSM339484 1 0.6280 0.532 0.540 0.000 0.460
#> GSM339485 1 0.0000 0.774 1.000 0.000 0.000
#> GSM339486 1 0.6299 0.497 0.524 0.000 0.476
#> GSM339487 2 0.0000 0.944 0.000 1.000 0.000
#> GSM339488 2 0.0000 0.944 0.000 1.000 0.000
#> GSM339489 2 0.2774 0.927 0.072 0.920 0.008
#> GSM339490 1 0.0000 0.774 1.000 0.000 0.000
#> GSM339491 3 0.2537 0.862 0.000 0.080 0.920
#> GSM339492 1 0.6008 0.676 0.628 0.000 0.372
#> GSM339493 2 0.0000 0.944 0.000 1.000 0.000
#> GSM339494 1 0.5465 0.737 0.712 0.000 0.288
#> GSM339495 2 0.1031 0.943 0.024 0.976 0.000
#> GSM339496 3 0.0000 0.886 0.000 0.000 1.000
#> GSM339497 2 0.2063 0.937 0.044 0.948 0.008
#> GSM339498 3 0.7153 0.652 0.200 0.092 0.708
#> GSM339499 3 0.2625 0.859 0.000 0.084 0.916
#> GSM339500 2 0.1643 0.917 0.000 0.956 0.044
#> GSM339501 1 0.0424 0.776 0.992 0.000 0.008
#> GSM339502 2 0.0000 0.944 0.000 1.000 0.000
#> GSM339503 3 0.1031 0.880 0.024 0.000 0.976
#> GSM339504 1 0.0424 0.776 0.992 0.000 0.008
#> GSM339505 3 0.1163 0.884 0.000 0.028 0.972
#> GSM339506 1 0.0237 0.775 0.996 0.000 0.004
#> GSM339507 1 0.5926 0.694 0.644 0.000 0.356
#> GSM339508 2 0.1529 0.939 0.040 0.960 0.000
#> GSM339509 2 0.0000 0.944 0.000 1.000 0.000
#> GSM339510 2 0.5591 0.719 0.304 0.696 0.000
#> GSM339511 1 0.0000 0.774 1.000 0.000 0.000
#> GSM339512 2 0.0000 0.944 0.000 1.000 0.000
#> GSM339513 1 0.6045 0.666 0.620 0.000 0.380
#> GSM339514 2 0.0000 0.944 0.000 1.000 0.000
#> GSM339515 1 0.5621 0.730 0.692 0.000 0.308
#> GSM339516 2 0.4178 0.854 0.172 0.828 0.000
#> GSM339517 3 0.0237 0.885 0.004 0.000 0.996
#> GSM339518 2 0.0424 0.943 0.008 0.992 0.000
#> GSM339519 3 0.0747 0.883 0.016 0.000 0.984
#> GSM339520 3 0.4002 0.792 0.000 0.160 0.840
#> GSM339521 2 0.0000 0.944 0.000 1.000 0.000
#> GSM339522 2 0.2165 0.933 0.064 0.936 0.000
#> GSM339523 2 0.0000 0.944 0.000 1.000 0.000
#> GSM339524 1 0.6286 0.488 0.536 0.000 0.464
#> GSM339525 1 0.2711 0.773 0.912 0.000 0.088
#> GSM339526 3 0.0000 0.886 0.000 0.000 1.000
#> GSM339527 1 0.0424 0.776 0.992 0.000 0.008
#> GSM339528 1 0.5859 0.704 0.656 0.000 0.344
#> GSM339529 2 0.2165 0.930 0.064 0.936 0.000
#> GSM339530 3 0.3551 0.820 0.000 0.132 0.868
#> GSM339531 2 0.4346 0.836 0.184 0.816 0.000
#> GSM339532 1 0.0000 0.774 1.000 0.000 0.000
#> GSM339533 3 0.0000 0.886 0.000 0.000 1.000
#> GSM339534 1 0.6111 0.643 0.604 0.000 0.396
#> GSM339535 2 0.0000 0.944 0.000 1.000 0.000
#> GSM339536 1 0.5621 0.730 0.692 0.000 0.308
#> GSM339537 2 0.2625 0.920 0.084 0.916 0.000
#> GSM339538 3 0.0000 0.886 0.000 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM339455 1 0.5404 0.159983 0.512 0.000 0.476 0.012
#> GSM339456 2 0.4635 0.587514 0.000 0.720 0.012 0.268
#> GSM339457 3 0.0859 0.857650 0.008 0.008 0.980 0.004
#> GSM339458 2 0.4305 0.721245 0.136 0.816 0.004 0.044
#> GSM339459 3 0.3695 0.789082 0.000 0.016 0.828 0.156
#> GSM339460 2 0.1510 0.857790 0.028 0.956 0.000 0.016
#> GSM339461 2 0.5257 0.147996 0.000 0.548 0.008 0.444
#> GSM339462 1 0.2868 0.772988 0.864 0.000 0.000 0.136
#> GSM339463 1 0.3962 0.770674 0.820 0.000 0.152 0.028
#> GSM339464 4 0.4790 0.294387 0.380 0.000 0.000 0.620
#> GSM339465 1 0.4281 0.746082 0.792 0.000 0.180 0.028
#> GSM339466 2 0.0657 0.875397 0.000 0.984 0.004 0.012
#> GSM339467 2 0.0188 0.876540 0.000 0.996 0.004 0.000
#> GSM339468 4 0.3320 0.713488 0.000 0.056 0.068 0.876
#> GSM339469 1 0.3105 0.768776 0.856 0.004 0.000 0.140
#> GSM339470 3 0.6925 0.549984 0.204 0.120 0.648 0.028
#> GSM339471 1 0.2124 0.834613 0.924 0.000 0.068 0.008
#> GSM339472 2 0.0524 0.875966 0.000 0.988 0.004 0.008
#> GSM339473 1 0.0895 0.834034 0.976 0.000 0.020 0.004
#> GSM339474 2 0.0592 0.873609 0.000 0.984 0.000 0.016
#> GSM339475 3 0.0657 0.858760 0.012 0.000 0.984 0.004
#> GSM339476 1 0.2376 0.820294 0.916 0.000 0.016 0.068
#> GSM339477 2 0.4994 0.000446 0.000 0.520 0.000 0.480
#> GSM339478 3 0.5427 0.233214 0.000 0.416 0.568 0.016
#> GSM339479 1 0.2297 0.820066 0.928 0.024 0.004 0.044
#> GSM339480 3 0.3768 0.773597 0.000 0.008 0.808 0.184
#> GSM339481 2 0.0188 0.876540 0.000 0.996 0.004 0.000
#> GSM339482 3 0.1545 0.857253 0.008 0.000 0.952 0.040
#> GSM339483 1 0.1940 0.810051 0.924 0.000 0.000 0.076
#> GSM339484 1 0.3182 0.810022 0.876 0.000 0.096 0.028
#> GSM339485 4 0.3942 0.600510 0.236 0.000 0.000 0.764
#> GSM339486 1 0.3307 0.805211 0.868 0.000 0.104 0.028
#> GSM339487 2 0.1716 0.844089 0.000 0.936 0.000 0.064
#> GSM339488 2 0.0672 0.872999 0.000 0.984 0.008 0.008
#> GSM339489 4 0.5000 0.058858 0.000 0.500 0.000 0.500
#> GSM339490 1 0.4916 0.288095 0.576 0.000 0.000 0.424
#> GSM339491 2 0.7540 0.387310 0.204 0.588 0.180 0.028
#> GSM339492 1 0.3946 0.777267 0.812 0.000 0.168 0.020
#> GSM339493 2 0.0657 0.875397 0.000 0.984 0.004 0.012
#> GSM339494 1 0.0804 0.833164 0.980 0.000 0.012 0.008
#> GSM339495 2 0.2345 0.811617 0.000 0.900 0.000 0.100
#> GSM339496 3 0.0657 0.858760 0.012 0.000 0.984 0.004
#> GSM339497 2 0.2124 0.852274 0.040 0.932 0.000 0.028
#> GSM339498 3 0.4290 0.729865 0.000 0.016 0.772 0.212
#> GSM339499 3 0.1139 0.855897 0.008 0.008 0.972 0.012
#> GSM339500 2 0.2764 0.822932 0.052 0.908 0.036 0.004
#> GSM339501 4 0.2489 0.709531 0.020 0.000 0.068 0.912
#> GSM339502 2 0.0895 0.868878 0.000 0.976 0.004 0.020
#> GSM339503 3 0.3037 0.828959 0.020 0.000 0.880 0.100
#> GSM339504 1 0.4730 0.445639 0.636 0.000 0.000 0.364
#> GSM339505 3 0.0927 0.855204 0.008 0.000 0.976 0.016
#> GSM339506 4 0.2530 0.703135 0.112 0.000 0.000 0.888
#> GSM339507 1 0.2596 0.820972 0.908 0.000 0.068 0.024
#> GSM339508 2 0.0469 0.875208 0.000 0.988 0.000 0.012
#> GSM339509 2 0.0188 0.876540 0.000 0.996 0.004 0.000
#> GSM339510 4 0.2124 0.743380 0.000 0.068 0.008 0.924
#> GSM339511 4 0.4283 0.583989 0.256 0.004 0.000 0.740
#> GSM339512 2 0.0376 0.875972 0.000 0.992 0.004 0.004
#> GSM339513 1 0.3219 0.807862 0.868 0.000 0.112 0.020
#> GSM339514 2 0.0376 0.875972 0.000 0.992 0.004 0.004
#> GSM339515 1 0.1182 0.832667 0.968 0.000 0.016 0.016
#> GSM339516 4 0.4877 0.346527 0.000 0.408 0.000 0.592
#> GSM339517 3 0.2197 0.844009 0.004 0.000 0.916 0.080
#> GSM339518 2 0.1174 0.869581 0.012 0.968 0.000 0.020
#> GSM339519 3 0.2256 0.849716 0.020 0.000 0.924 0.056
#> GSM339520 3 0.1484 0.851416 0.004 0.020 0.960 0.016
#> GSM339521 2 0.0376 0.876280 0.004 0.992 0.000 0.004
#> GSM339522 4 0.5433 0.642328 0.004 0.220 0.056 0.720
#> GSM339523 2 0.0376 0.875972 0.000 0.992 0.004 0.004
#> GSM339524 3 0.3542 0.827169 0.060 0.000 0.864 0.076
#> GSM339525 1 0.1940 0.810825 0.924 0.000 0.000 0.076
#> GSM339526 3 0.0469 0.858109 0.012 0.000 0.988 0.000
#> GSM339527 4 0.1743 0.722569 0.056 0.000 0.004 0.940
#> GSM339528 1 0.2197 0.829243 0.928 0.000 0.048 0.024
#> GSM339529 2 0.0592 0.873726 0.000 0.984 0.000 0.016
#> GSM339530 3 0.2700 0.830595 0.020 0.044 0.916 0.020
#> GSM339531 4 0.4182 0.675013 0.000 0.180 0.024 0.796
#> GSM339532 1 0.4964 0.388461 0.616 0.004 0.000 0.380
#> GSM339533 3 0.5786 0.285357 0.380 0.004 0.588 0.028
#> GSM339534 1 0.2987 0.827860 0.880 0.000 0.104 0.016
#> GSM339535 2 0.0188 0.876540 0.000 0.996 0.004 0.000
#> GSM339536 1 0.1042 0.833864 0.972 0.000 0.020 0.008
#> GSM339537 2 0.5000 -0.149194 0.000 0.504 0.000 0.496
#> GSM339538 3 0.1677 0.856166 0.012 0.000 0.948 0.040
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM339455 1 0.6600 -0.05641 0.408 0.000 0.380 0.212 0.000
#> GSM339456 2 0.3355 0.67583 0.000 0.804 0.012 0.000 0.184
#> GSM339457 3 0.1704 0.85863 0.068 0.000 0.928 0.004 0.000
#> GSM339458 4 0.5961 0.16540 0.448 0.092 0.004 0.456 0.000
#> GSM339459 3 0.2280 0.81841 0.000 0.000 0.880 0.000 0.120
#> GSM339460 4 0.6933 0.16274 0.344 0.160 0.000 0.468 0.028
#> GSM339461 5 0.5506 0.14877 0.016 0.392 0.024 0.008 0.560
#> GSM339462 4 0.5928 0.01417 0.392 0.000 0.000 0.500 0.108
#> GSM339463 1 0.3184 0.34057 0.852 0.000 0.100 0.048 0.000
#> GSM339464 5 0.5106 0.20363 0.036 0.000 0.000 0.456 0.508
#> GSM339465 1 0.1818 0.37970 0.932 0.000 0.044 0.024 0.000
#> GSM339466 2 0.2507 0.80998 0.004 0.908 0.016 0.056 0.016
#> GSM339467 2 0.0162 0.83536 0.004 0.996 0.000 0.000 0.000
#> GSM339468 5 0.3835 0.44912 0.000 0.012 0.244 0.000 0.744
#> GSM339469 4 0.2903 0.39420 0.080 0.000 0.000 0.872 0.048
#> GSM339470 1 0.6841 0.16241 0.492 0.240 0.256 0.008 0.004
#> GSM339471 4 0.5922 -0.17998 0.420 0.000 0.104 0.476 0.000
#> GSM339472 2 0.0162 0.83599 0.000 0.996 0.000 0.004 0.000
#> GSM339473 1 0.4219 0.33533 0.584 0.000 0.000 0.416 0.000
#> GSM339474 2 0.1564 0.82539 0.004 0.948 0.000 0.024 0.024
#> GSM339475 3 0.0290 0.87539 0.008 0.000 0.992 0.000 0.000
#> GSM339476 4 0.3883 0.22472 0.244 0.000 0.008 0.744 0.004
#> GSM339477 2 0.3355 0.70487 0.000 0.804 0.000 0.012 0.184
#> GSM339478 3 0.5836 0.49901 0.116 0.244 0.628 0.012 0.000
#> GSM339479 1 0.5045 -0.23188 0.508 0.024 0.004 0.464 0.000
#> GSM339480 3 0.2966 0.75235 0.000 0.000 0.816 0.000 0.184
#> GSM339481 2 0.0162 0.83599 0.000 0.996 0.000 0.004 0.000
#> GSM339482 3 0.1205 0.87082 0.040 0.000 0.956 0.004 0.000
#> GSM339483 4 0.4449 -0.25804 0.484 0.000 0.000 0.512 0.004
#> GSM339484 1 0.4251 0.35935 0.624 0.000 0.004 0.372 0.000
#> GSM339485 5 0.5044 0.21145 0.032 0.000 0.000 0.464 0.504
#> GSM339486 1 0.1741 0.37824 0.936 0.000 0.024 0.040 0.000
#> GSM339487 2 0.2824 0.77208 0.000 0.864 0.000 0.116 0.020
#> GSM339488 2 0.0162 0.83536 0.004 0.996 0.000 0.000 0.000
#> GSM339489 2 0.6562 0.14178 0.000 0.496 0.032 0.100 0.372
#> GSM339490 4 0.3019 0.40573 0.048 0.000 0.000 0.864 0.088
#> GSM339491 2 0.4850 0.14774 0.484 0.500 0.004 0.008 0.004
#> GSM339492 4 0.6344 0.04590 0.160 0.000 0.400 0.440 0.000
#> GSM339493 2 0.0807 0.83207 0.000 0.976 0.000 0.012 0.012
#> GSM339494 1 0.4359 0.33692 0.584 0.000 0.000 0.412 0.004
#> GSM339495 2 0.1725 0.82063 0.000 0.936 0.000 0.020 0.044
#> GSM339496 3 0.0566 0.87609 0.012 0.000 0.984 0.004 0.000
#> GSM339497 4 0.7152 0.15965 0.392 0.164 0.004 0.412 0.028
#> GSM339498 3 0.3895 0.53726 0.000 0.000 0.680 0.000 0.320
#> GSM339499 3 0.2583 0.81415 0.132 0.000 0.864 0.004 0.000
#> GSM339500 1 0.8006 -0.11107 0.400 0.068 0.244 0.280 0.008
#> GSM339501 5 0.6682 0.25957 0.000 0.000 0.236 0.368 0.396
#> GSM339502 2 0.0162 0.83536 0.004 0.996 0.000 0.000 0.000
#> GSM339503 3 0.1121 0.86493 0.000 0.000 0.956 0.000 0.044
#> GSM339504 4 0.5398 0.31620 0.112 0.000 0.000 0.648 0.240
#> GSM339505 3 0.2387 0.85265 0.092 0.004 0.896 0.004 0.004
#> GSM339506 5 0.2338 0.54638 0.016 0.000 0.036 0.032 0.916
#> GSM339507 1 0.3949 0.36930 0.668 0.000 0.000 0.332 0.000
#> GSM339508 2 0.0290 0.83583 0.000 0.992 0.000 0.008 0.000
#> GSM339509 2 0.0000 0.83571 0.000 1.000 0.000 0.000 0.000
#> GSM339510 5 0.3081 0.52714 0.000 0.000 0.012 0.156 0.832
#> GSM339511 4 0.4592 -0.04730 0.024 0.000 0.000 0.644 0.332
#> GSM339512 2 0.0290 0.83494 0.008 0.992 0.000 0.000 0.000
#> GSM339513 1 0.5548 0.25070 0.492 0.000 0.068 0.440 0.000
#> GSM339514 2 0.0000 0.83571 0.000 1.000 0.000 0.000 0.000
#> GSM339515 1 0.4219 0.33597 0.584 0.000 0.000 0.416 0.000
#> GSM339516 2 0.5700 0.39165 0.000 0.600 0.000 0.120 0.280
#> GSM339517 3 0.1557 0.86196 0.008 0.000 0.940 0.000 0.052
#> GSM339518 2 0.7358 -0.00162 0.364 0.380 0.004 0.228 0.024
#> GSM339519 3 0.0771 0.87126 0.004 0.000 0.976 0.000 0.020
#> GSM339520 3 0.2582 0.84591 0.080 0.024 0.892 0.004 0.000
#> GSM339521 2 0.2758 0.78220 0.076 0.888 0.000 0.012 0.024
#> GSM339522 4 0.6073 -0.29924 0.016 0.048 0.012 0.484 0.440
#> GSM339523 2 0.0162 0.83599 0.000 0.996 0.000 0.004 0.000
#> GSM339524 3 0.2546 0.84490 0.048 0.000 0.904 0.012 0.036
#> GSM339525 4 0.3816 0.16833 0.304 0.000 0.000 0.696 0.000
#> GSM339526 3 0.0880 0.87507 0.032 0.000 0.968 0.000 0.000
#> GSM339527 5 0.2467 0.54856 0.016 0.000 0.052 0.024 0.908
#> GSM339528 1 0.1981 0.37333 0.920 0.000 0.016 0.064 0.000
#> GSM339529 2 0.1478 0.81451 0.000 0.936 0.000 0.064 0.000
#> GSM339530 3 0.3317 0.81228 0.056 0.088 0.852 0.004 0.000
#> GSM339531 5 0.6372 0.15375 0.004 0.404 0.124 0.004 0.464
#> GSM339532 4 0.2376 0.39430 0.052 0.000 0.000 0.904 0.044
#> GSM339533 1 0.4956 0.28902 0.644 0.000 0.312 0.040 0.004
#> GSM339534 4 0.6598 0.11128 0.228 0.000 0.324 0.448 0.000
#> GSM339535 2 0.0162 0.83571 0.000 0.996 0.000 0.004 0.000
#> GSM339536 1 0.4201 0.33990 0.592 0.000 0.000 0.408 0.000
#> GSM339537 2 0.5894 0.24038 0.000 0.532 0.000 0.112 0.356
#> GSM339538 3 0.1195 0.86889 0.012 0.000 0.960 0.000 0.028
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM339455 3 0.6180 0.2240 0.004 0.000 0.460 0.324 0.008 0.204
#> GSM339456 2 0.3171 0.6966 0.000 0.784 0.012 0.000 0.204 0.000
#> GSM339457 3 0.2253 0.7793 0.000 0.004 0.896 0.004 0.012 0.084
#> GSM339458 6 0.2853 0.6596 0.008 0.008 0.000 0.124 0.008 0.852
#> GSM339459 3 0.2432 0.7642 0.000 0.024 0.888 0.008 0.080 0.000
#> GSM339460 6 0.4671 0.5500 0.000 0.044 0.000 0.228 0.032 0.696
#> GSM339461 5 0.5949 0.2900 0.000 0.332 0.004 0.028 0.528 0.108
#> GSM339462 1 0.6839 0.0258 0.444 0.000 0.000 0.320 0.096 0.140
#> GSM339463 6 0.5256 0.6603 0.144 0.000 0.064 0.044 0.032 0.716
#> GSM339464 4 0.4919 0.2037 0.020 0.000 0.000 0.612 0.324 0.044
#> GSM339465 6 0.4561 0.6051 0.268 0.000 0.024 0.000 0.032 0.676
#> GSM339466 2 0.3682 0.7631 0.000 0.828 0.020 0.096 0.028 0.028
#> GSM339467 2 0.2364 0.7916 0.004 0.892 0.000 0.000 0.032 0.072
#> GSM339468 5 0.5662 0.5927 0.000 0.160 0.108 0.080 0.652 0.000
#> GSM339469 4 0.3549 0.5684 0.192 0.000 0.000 0.776 0.004 0.028
#> GSM339470 6 0.6277 0.6009 0.116 0.060 0.104 0.000 0.072 0.648
#> GSM339471 1 0.5223 0.4750 0.652 0.000 0.116 0.212 0.000 0.020
#> GSM339472 2 0.1296 0.8072 0.000 0.948 0.000 0.004 0.004 0.044
#> GSM339473 1 0.0291 0.7870 0.992 0.000 0.000 0.004 0.000 0.004
#> GSM339474 2 0.3361 0.7659 0.000 0.844 0.000 0.048 0.044 0.064
#> GSM339475 3 0.0603 0.7909 0.004 0.000 0.980 0.000 0.016 0.000
#> GSM339476 4 0.4956 0.2482 0.412 0.000 0.024 0.540 0.004 0.020
#> GSM339477 2 0.3988 0.7242 0.000 0.784 0.000 0.040 0.140 0.036
#> GSM339478 3 0.3665 0.7602 0.000 0.028 0.832 0.024 0.028 0.088
#> GSM339479 6 0.2742 0.6571 0.012 0.000 0.000 0.128 0.008 0.852
#> GSM339480 3 0.2367 0.7655 0.000 0.016 0.888 0.008 0.088 0.000
#> GSM339481 2 0.2159 0.8061 0.000 0.904 0.000 0.012 0.012 0.072
#> GSM339482 3 0.2101 0.7923 0.008 0.000 0.920 0.016 0.016 0.040
#> GSM339483 1 0.3868 0.6330 0.772 0.000 0.000 0.172 0.012 0.044
#> GSM339484 1 0.2611 0.7298 0.880 0.000 0.012 0.000 0.028 0.080
#> GSM339485 4 0.4792 0.2599 0.020 0.000 0.000 0.644 0.292 0.044
#> GSM339486 6 0.4228 0.6250 0.248 0.000 0.020 0.008 0.012 0.712
#> GSM339487 2 0.4624 0.5541 0.000 0.652 0.004 0.300 0.028 0.016
#> GSM339488 2 0.2344 0.7915 0.000 0.892 0.004 0.000 0.028 0.076
#> GSM339489 2 0.5679 0.5521 0.000 0.636 0.016 0.212 0.112 0.024
#> GSM339490 4 0.3992 0.5691 0.200 0.000 0.000 0.752 0.024 0.024
#> GSM339491 6 0.7046 0.4806 0.228 0.172 0.012 0.004 0.080 0.504
#> GSM339492 3 0.6813 0.1785 0.188 0.000 0.472 0.272 0.004 0.064
#> GSM339493 2 0.1452 0.8033 0.000 0.948 0.000 0.020 0.020 0.012
#> GSM339494 1 0.0146 0.7867 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM339495 2 0.3023 0.7733 0.000 0.864 0.000 0.028 0.052 0.056
#> GSM339496 3 0.0508 0.7918 0.000 0.000 0.984 0.000 0.012 0.004
#> GSM339497 6 0.4035 0.6264 0.012 0.100 0.000 0.068 0.020 0.800
#> GSM339498 3 0.4319 0.3405 0.000 0.024 0.576 0.000 0.400 0.000
#> GSM339499 3 0.2425 0.7751 0.000 0.008 0.880 0.000 0.012 0.100
#> GSM339500 6 0.3257 0.6672 0.004 0.016 0.040 0.084 0.004 0.852
#> GSM339501 4 0.5582 0.1863 0.000 0.024 0.324 0.568 0.080 0.004
#> GSM339502 2 0.2615 0.7853 0.008 0.876 0.000 0.000 0.028 0.088
#> GSM339503 3 0.2951 0.7305 0.004 0.000 0.820 0.004 0.168 0.004
#> GSM339504 4 0.5881 0.4549 0.224 0.000 0.000 0.608 0.084 0.084
#> GSM339505 3 0.3827 0.7040 0.000 0.012 0.764 0.000 0.032 0.192
#> GSM339506 5 0.3363 0.5465 0.008 0.000 0.008 0.124 0.828 0.032
#> GSM339507 1 0.1807 0.7393 0.920 0.000 0.000 0.000 0.020 0.060
#> GSM339508 2 0.2743 0.7922 0.000 0.880 0.000 0.060 0.028 0.032
#> GSM339509 2 0.2164 0.7946 0.000 0.900 0.000 0.000 0.032 0.068
#> GSM339510 5 0.5705 0.5306 0.000 0.096 0.016 0.220 0.636 0.032
#> GSM339511 4 0.1708 0.5389 0.024 0.000 0.000 0.932 0.004 0.040
#> GSM339512 2 0.3121 0.7672 0.008 0.844 0.004 0.000 0.032 0.112
#> GSM339513 1 0.3867 0.6624 0.788 0.000 0.080 0.124 0.004 0.004
#> GSM339514 2 0.1760 0.8019 0.004 0.928 0.000 0.000 0.020 0.048
#> GSM339515 1 0.0146 0.7867 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM339516 2 0.4580 0.6258 0.004 0.692 0.000 0.232 0.068 0.004
#> GSM339517 3 0.3269 0.7291 0.004 0.000 0.808 0.008 0.168 0.012
#> GSM339518 6 0.4425 0.5838 0.000 0.136 0.000 0.104 0.016 0.744
#> GSM339519 3 0.1736 0.7885 0.016 0.004 0.940 0.012 0.024 0.004
#> GSM339520 3 0.2833 0.7699 0.000 0.012 0.860 0.000 0.024 0.104
#> GSM339521 6 0.5328 0.0942 0.000 0.404 0.000 0.040 0.036 0.520
#> GSM339522 4 0.6072 0.0389 0.000 0.176 0.012 0.620 0.136 0.056
#> GSM339523 2 0.2066 0.7987 0.000 0.904 0.000 0.000 0.024 0.072
#> GSM339524 3 0.4322 0.6995 0.128 0.000 0.764 0.008 0.088 0.012
#> GSM339525 4 0.5075 0.0222 0.460 0.000 0.000 0.464 0.000 0.076
#> GSM339526 3 0.1296 0.7919 0.004 0.000 0.952 0.000 0.012 0.032
#> GSM339527 5 0.3191 0.5772 0.008 0.000 0.036 0.080 0.856 0.020
#> GSM339528 6 0.4576 0.5763 0.296 0.000 0.016 0.012 0.016 0.660
#> GSM339529 2 0.4020 0.7086 0.004 0.768 0.000 0.176 0.028 0.024
#> GSM339530 3 0.4474 0.6920 0.000 0.088 0.764 0.004 0.036 0.108
#> GSM339531 2 0.5849 0.1437 0.000 0.548 0.064 0.044 0.336 0.008
#> GSM339532 4 0.4099 0.5161 0.272 0.000 0.000 0.696 0.008 0.024
#> GSM339533 6 0.6417 0.3890 0.352 0.004 0.096 0.000 0.068 0.480
#> GSM339534 3 0.6655 0.1000 0.072 0.000 0.440 0.376 0.008 0.104
#> GSM339535 2 0.1036 0.8084 0.000 0.964 0.004 0.008 0.000 0.024
#> GSM339536 1 0.0291 0.7870 0.992 0.000 0.000 0.004 0.000 0.004
#> GSM339537 2 0.4710 0.6663 0.000 0.716 0.000 0.180 0.076 0.028
#> GSM339538 3 0.1686 0.7810 0.004 0.000 0.932 0.004 0.052 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 protocol(p) agent(p) individual(p) k
#> MAD:NMF 76 1.000 0.789 5.07e-03 2
#> MAD:NMF 81 0.991 0.928 2.93e-05 3
#> MAD:NMF 71 0.148 0.716 1.63e-06 4
#> MAD:NMF 40 0.145 0.668 1.25e-03 5
#> MAD:NMF 66 0.772 0.889 7.34e-08 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 15497 rows and 84 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 0.904 0.944 0.970 0.4965 0.497 0.497
#> 3 3 0.698 0.867 0.909 0.2326 0.907 0.813
#> 4 4 0.639 0.804 0.840 0.1648 0.856 0.646
#> 5 5 0.687 0.642 0.807 0.0797 0.960 0.852
#> 6 6 0.703 0.581 0.743 0.0544 0.894 0.577
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
#> GSM339455 1 0.6801 0.813 0.820 0.180
#> GSM339456 2 0.0000 0.985 0.000 1.000
#> GSM339457 2 0.3274 0.943 0.060 0.940
#> GSM339458 2 0.2236 0.961 0.036 0.964
#> GSM339459 2 0.3274 0.943 0.060 0.940
#> GSM339460 2 0.1843 0.967 0.028 0.972
#> GSM339461 2 0.0000 0.985 0.000 1.000
#> GSM339462 1 0.0000 0.949 1.000 0.000
#> GSM339463 1 0.4690 0.890 0.900 0.100
#> GSM339464 1 0.0000 0.949 1.000 0.000
#> GSM339465 1 0.3431 0.914 0.936 0.064
#> GSM339466 2 0.0000 0.985 0.000 1.000
#> GSM339467 2 0.0000 0.985 0.000 1.000
#> GSM339468 2 0.0000 0.985 0.000 1.000
#> GSM339469 1 0.0000 0.949 1.000 0.000
#> GSM339470 2 0.1414 0.973 0.020 0.980
#> GSM339471 1 0.0000 0.949 1.000 0.000
#> GSM339472 2 0.0000 0.985 0.000 1.000
#> GSM339473 1 0.0000 0.949 1.000 0.000
#> GSM339474 2 0.0000 0.985 0.000 1.000
#> GSM339475 1 0.8207 0.712 0.744 0.256
#> GSM339476 1 0.0000 0.949 1.000 0.000
#> GSM339477 2 0.0000 0.985 0.000 1.000
#> GSM339478 2 0.3274 0.943 0.060 0.940
#> GSM339479 2 0.2236 0.961 0.036 0.964
#> GSM339480 2 0.3274 0.943 0.060 0.940
#> GSM339481 2 0.0000 0.985 0.000 1.000
#> GSM339482 1 0.1633 0.939 0.976 0.024
#> GSM339483 1 0.0000 0.949 1.000 0.000
#> GSM339484 1 0.0000 0.949 1.000 0.000
#> GSM339485 1 0.0000 0.949 1.000 0.000
#> GSM339486 1 0.0000 0.949 1.000 0.000
#> GSM339487 2 0.0000 0.985 0.000 1.000
#> GSM339488 2 0.0000 0.985 0.000 1.000
#> GSM339489 2 0.0000 0.985 0.000 1.000
#> GSM339490 1 0.0000 0.949 1.000 0.000
#> GSM339491 2 0.1414 0.973 0.020 0.980
#> GSM339492 1 0.0000 0.949 1.000 0.000
#> GSM339493 2 0.0000 0.985 0.000 1.000
#> GSM339494 1 0.0000 0.949 1.000 0.000
#> GSM339495 2 0.0000 0.985 0.000 1.000
#> GSM339496 1 0.8144 0.718 0.748 0.252
#> GSM339497 2 0.0000 0.985 0.000 1.000
#> GSM339498 2 0.3274 0.943 0.060 0.940
#> GSM339499 2 0.3274 0.943 0.060 0.940
#> GSM339500 2 0.0000 0.985 0.000 1.000
#> GSM339501 1 0.7883 0.750 0.764 0.236
#> GSM339502 2 0.0000 0.985 0.000 1.000
#> GSM339503 1 0.4815 0.886 0.896 0.104
#> GSM339504 1 0.0000 0.949 1.000 0.000
#> GSM339505 2 0.0000 0.985 0.000 1.000
#> GSM339506 1 0.0000 0.949 1.000 0.000
#> GSM339507 1 0.0000 0.949 1.000 0.000
#> GSM339508 2 0.0000 0.985 0.000 1.000
#> GSM339509 2 0.0000 0.985 0.000 1.000
#> GSM339510 2 0.0000 0.985 0.000 1.000
#> GSM339511 1 0.0000 0.949 1.000 0.000
#> GSM339512 2 0.0000 0.985 0.000 1.000
#> GSM339513 1 0.0000 0.949 1.000 0.000
#> GSM339514 2 0.0000 0.985 0.000 1.000
#> GSM339515 1 0.0000 0.949 1.000 0.000
#> GSM339516 2 0.0000 0.985 0.000 1.000
#> GSM339517 1 0.8661 0.657 0.712 0.288
#> GSM339518 2 0.0000 0.985 0.000 1.000
#> GSM339519 1 0.2236 0.933 0.964 0.036
#> GSM339520 2 0.3274 0.943 0.060 0.940
#> GSM339521 2 0.0000 0.985 0.000 1.000
#> GSM339522 2 0.0000 0.985 0.000 1.000
#> GSM339523 2 0.0000 0.985 0.000 1.000
#> GSM339524 1 0.0376 0.947 0.996 0.004
#> GSM339525 1 0.0000 0.949 1.000 0.000
#> GSM339526 1 0.7674 0.757 0.776 0.224
#> GSM339527 1 0.0000 0.949 1.000 0.000
#> GSM339528 1 0.0000 0.949 1.000 0.000
#> GSM339529 2 0.0000 0.985 0.000 1.000
#> GSM339530 2 0.3274 0.943 0.060 0.940
#> GSM339531 2 0.0000 0.985 0.000 1.000
#> GSM339532 1 0.0000 0.949 1.000 0.000
#> GSM339533 1 0.5178 0.876 0.884 0.116
#> GSM339534 1 0.1184 0.943 0.984 0.016
#> GSM339535 2 0.0000 0.985 0.000 1.000
#> GSM339536 1 0.0000 0.949 1.000 0.000
#> GSM339537 2 0.0000 0.985 0.000 1.000
#> GSM339538 1 0.1633 0.939 0.976 0.024
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM339455 3 0.7606 0.747 0.244 0.092 0.664
#> GSM339456 2 0.1753 0.894 0.000 0.952 0.048
#> GSM339457 2 0.5098 0.794 0.000 0.752 0.248
#> GSM339458 2 0.4235 0.851 0.000 0.824 0.176
#> GSM339459 2 0.5098 0.794 0.000 0.752 0.248
#> GSM339460 2 0.3412 0.880 0.000 0.876 0.124
#> GSM339461 2 0.2711 0.899 0.000 0.912 0.088
#> GSM339462 1 0.0000 0.959 1.000 0.000 0.000
#> GSM339463 3 0.5167 0.806 0.192 0.016 0.792
#> GSM339464 1 0.0000 0.959 1.000 0.000 0.000
#> GSM339465 1 0.4702 0.657 0.788 0.000 0.212
#> GSM339466 2 0.0747 0.905 0.000 0.984 0.016
#> GSM339467 2 0.1753 0.894 0.000 0.952 0.048
#> GSM339468 2 0.0592 0.905 0.000 0.988 0.012
#> GSM339469 1 0.0000 0.959 1.000 0.000 0.000
#> GSM339470 2 0.3941 0.866 0.000 0.844 0.156
#> GSM339471 1 0.0000 0.959 1.000 0.000 0.000
#> GSM339472 2 0.1753 0.894 0.000 0.952 0.048
#> GSM339473 1 0.0000 0.959 1.000 0.000 0.000
#> GSM339474 2 0.1753 0.894 0.000 0.952 0.048
#> GSM339475 3 0.1753 0.781 0.000 0.048 0.952
#> GSM339476 1 0.0424 0.953 0.992 0.000 0.008
#> GSM339477 2 0.1753 0.894 0.000 0.952 0.048
#> GSM339478 2 0.5098 0.794 0.000 0.752 0.248
#> GSM339479 2 0.4235 0.851 0.000 0.824 0.176
#> GSM339480 2 0.5098 0.794 0.000 0.752 0.248
#> GSM339481 2 0.1753 0.894 0.000 0.952 0.048
#> GSM339482 3 0.6172 0.695 0.308 0.012 0.680
#> GSM339483 1 0.0000 0.959 1.000 0.000 0.000
#> GSM339484 1 0.0424 0.953 0.992 0.000 0.008
#> GSM339485 1 0.0000 0.959 1.000 0.000 0.000
#> GSM339486 1 0.0424 0.953 0.992 0.000 0.008
#> GSM339487 2 0.0747 0.905 0.000 0.984 0.016
#> GSM339488 2 0.1753 0.894 0.000 0.952 0.048
#> GSM339489 2 0.0592 0.905 0.000 0.988 0.012
#> GSM339490 1 0.0000 0.959 1.000 0.000 0.000
#> GSM339491 2 0.3941 0.866 0.000 0.844 0.156
#> GSM339492 1 0.0000 0.959 1.000 0.000 0.000
#> GSM339493 2 0.0000 0.903 0.000 1.000 0.000
#> GSM339494 1 0.0000 0.959 1.000 0.000 0.000
#> GSM339495 2 0.1753 0.894 0.000 0.952 0.048
#> GSM339496 3 0.1878 0.784 0.004 0.044 0.952
#> GSM339497 2 0.2261 0.897 0.000 0.932 0.068
#> GSM339498 2 0.5098 0.794 0.000 0.752 0.248
#> GSM339499 2 0.5098 0.794 0.000 0.752 0.248
#> GSM339500 2 0.3116 0.886 0.000 0.892 0.108
#> GSM339501 3 0.7860 0.729 0.228 0.116 0.656
#> GSM339502 2 0.1753 0.894 0.000 0.952 0.048
#> GSM339503 3 0.4840 0.813 0.168 0.016 0.816
#> GSM339504 1 0.0000 0.959 1.000 0.000 0.000
#> GSM339505 2 0.3619 0.874 0.000 0.864 0.136
#> GSM339506 1 0.0000 0.959 1.000 0.000 0.000
#> GSM339507 1 0.0424 0.953 0.992 0.000 0.008
#> GSM339508 2 0.1753 0.894 0.000 0.952 0.048
#> GSM339509 2 0.1753 0.894 0.000 0.952 0.048
#> GSM339510 2 0.0592 0.905 0.000 0.988 0.012
#> GSM339511 1 0.0000 0.959 1.000 0.000 0.000
#> GSM339512 2 0.3192 0.888 0.000 0.888 0.112
#> GSM339513 1 0.0000 0.959 1.000 0.000 0.000
#> GSM339514 2 0.1753 0.894 0.000 0.952 0.048
#> GSM339515 1 0.0000 0.959 1.000 0.000 0.000
#> GSM339516 2 0.0592 0.905 0.000 0.988 0.012
#> GSM339517 3 0.2537 0.766 0.000 0.080 0.920
#> GSM339518 2 0.2261 0.897 0.000 0.932 0.068
#> GSM339519 3 0.6600 0.575 0.384 0.012 0.604
#> GSM339520 2 0.5098 0.794 0.000 0.752 0.248
#> GSM339521 2 0.3116 0.886 0.000 0.892 0.108
#> GSM339522 2 0.3038 0.887 0.000 0.896 0.104
#> GSM339523 2 0.1753 0.894 0.000 0.952 0.048
#> GSM339524 1 0.6104 0.267 0.648 0.004 0.348
#> GSM339525 1 0.0000 0.959 1.000 0.000 0.000
#> GSM339526 3 0.2313 0.795 0.032 0.024 0.944
#> GSM339527 1 0.0000 0.959 1.000 0.000 0.000
#> GSM339528 1 0.0424 0.953 0.992 0.000 0.008
#> GSM339529 2 0.1753 0.894 0.000 0.952 0.048
#> GSM339530 2 0.5098 0.794 0.000 0.752 0.248
#> GSM339531 2 0.0592 0.905 0.000 0.988 0.012
#> GSM339532 1 0.0000 0.959 1.000 0.000 0.000
#> GSM339533 3 0.4663 0.815 0.156 0.016 0.828
#> GSM339534 1 0.5244 0.582 0.756 0.004 0.240
#> GSM339535 2 0.0000 0.903 0.000 1.000 0.000
#> GSM339536 1 0.0000 0.959 1.000 0.000 0.000
#> GSM339537 2 0.0592 0.905 0.000 0.988 0.012
#> GSM339538 3 0.6051 0.713 0.292 0.012 0.696
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM339455 3 0.6500 0.778 0.100 0.152 0.704 0.044
#> GSM339456 4 0.2760 0.888 0.000 0.128 0.000 0.872
#> GSM339457 2 0.1557 0.790 0.000 0.944 0.056 0.000
#> GSM339458 2 0.3464 0.809 0.000 0.860 0.032 0.108
#> GSM339459 2 0.1389 0.793 0.000 0.952 0.048 0.000
#> GSM339460 2 0.4095 0.794 0.000 0.792 0.016 0.192
#> GSM339461 2 0.4522 0.539 0.000 0.680 0.000 0.320
#> GSM339462 1 0.1716 0.908 0.936 0.000 0.000 0.064
#> GSM339463 3 0.2759 0.828 0.044 0.052 0.904 0.000
#> GSM339464 1 0.0707 0.917 0.980 0.000 0.020 0.000
#> GSM339465 1 0.5463 0.556 0.692 0.052 0.256 0.000
#> GSM339466 2 0.3688 0.778 0.000 0.792 0.000 0.208
#> GSM339467 4 0.2760 0.888 0.000 0.128 0.000 0.872
#> GSM339468 2 0.3726 0.776 0.000 0.788 0.000 0.212
#> GSM339469 1 0.1406 0.913 0.960 0.000 0.024 0.016
#> GSM339470 2 0.2796 0.822 0.000 0.892 0.016 0.092
#> GSM339471 1 0.3471 0.878 0.868 0.000 0.060 0.072
#> GSM339472 4 0.2760 0.888 0.000 0.128 0.000 0.872
#> GSM339473 1 0.1716 0.908 0.936 0.000 0.000 0.064
#> GSM339474 4 0.2760 0.888 0.000 0.128 0.000 0.872
#> GSM339475 3 0.3972 0.789 0.000 0.204 0.788 0.008
#> GSM339476 1 0.1211 0.913 0.960 0.000 0.040 0.000
#> GSM339477 4 0.2760 0.888 0.000 0.128 0.000 0.872
#> GSM339478 2 0.1557 0.790 0.000 0.944 0.056 0.000
#> GSM339479 2 0.3464 0.809 0.000 0.860 0.032 0.108
#> GSM339480 2 0.1389 0.793 0.000 0.952 0.048 0.000
#> GSM339481 4 0.3123 0.882 0.000 0.156 0.000 0.844
#> GSM339482 3 0.2805 0.783 0.100 0.000 0.888 0.012
#> GSM339483 1 0.1716 0.908 0.936 0.000 0.000 0.064
#> GSM339484 1 0.1211 0.913 0.960 0.000 0.040 0.000
#> GSM339485 1 0.0707 0.917 0.980 0.000 0.020 0.000
#> GSM339486 1 0.1211 0.913 0.960 0.000 0.040 0.000
#> GSM339487 2 0.3688 0.778 0.000 0.792 0.000 0.208
#> GSM339488 4 0.2760 0.888 0.000 0.128 0.000 0.872
#> GSM339489 2 0.3726 0.776 0.000 0.788 0.000 0.212
#> GSM339490 1 0.1406 0.913 0.960 0.000 0.024 0.016
#> GSM339491 2 0.2796 0.822 0.000 0.892 0.016 0.092
#> GSM339492 1 0.3471 0.878 0.868 0.000 0.060 0.072
#> GSM339493 4 0.4843 0.467 0.000 0.396 0.000 0.604
#> GSM339494 1 0.1716 0.908 0.936 0.000 0.000 0.064
#> GSM339495 4 0.2760 0.888 0.000 0.128 0.000 0.872
#> GSM339496 3 0.3972 0.790 0.000 0.204 0.788 0.008
#> GSM339497 2 0.4134 0.672 0.000 0.740 0.000 0.260
#> GSM339498 2 0.1557 0.790 0.000 0.944 0.056 0.000
#> GSM339499 2 0.1557 0.790 0.000 0.944 0.056 0.000
#> GSM339500 2 0.2469 0.825 0.000 0.892 0.000 0.108
#> GSM339501 3 0.6901 0.750 0.088 0.212 0.656 0.044
#> GSM339502 4 0.3172 0.880 0.000 0.160 0.000 0.840
#> GSM339503 3 0.2174 0.826 0.020 0.052 0.928 0.000
#> GSM339504 1 0.1716 0.908 0.936 0.000 0.000 0.064
#> GSM339505 2 0.1978 0.826 0.000 0.928 0.004 0.068
#> GSM339506 1 0.0707 0.917 0.980 0.000 0.020 0.000
#> GSM339507 1 0.1211 0.913 0.960 0.000 0.040 0.000
#> GSM339508 4 0.4661 0.616 0.000 0.348 0.000 0.652
#> GSM339509 4 0.2868 0.888 0.000 0.136 0.000 0.864
#> GSM339510 2 0.3726 0.776 0.000 0.788 0.000 0.212
#> GSM339511 1 0.1406 0.913 0.960 0.000 0.024 0.016
#> GSM339512 2 0.2647 0.823 0.000 0.880 0.000 0.120
#> GSM339513 1 0.3471 0.878 0.868 0.000 0.060 0.072
#> GSM339514 4 0.3311 0.869 0.000 0.172 0.000 0.828
#> GSM339515 1 0.1716 0.908 0.936 0.000 0.000 0.064
#> GSM339516 2 0.3726 0.776 0.000 0.788 0.000 0.212
#> GSM339517 3 0.4422 0.751 0.000 0.256 0.736 0.008
#> GSM339518 2 0.4134 0.672 0.000 0.740 0.000 0.260
#> GSM339519 3 0.5142 0.733 0.160 0.016 0.772 0.052
#> GSM339520 2 0.1557 0.790 0.000 0.944 0.056 0.000
#> GSM339521 2 0.2469 0.825 0.000 0.892 0.000 0.108
#> GSM339522 2 0.3945 0.725 0.000 0.780 0.004 0.216
#> GSM339523 4 0.3074 0.884 0.000 0.152 0.000 0.848
#> GSM339524 3 0.5383 0.151 0.452 0.000 0.536 0.012
#> GSM339525 1 0.1716 0.908 0.936 0.000 0.000 0.064
#> GSM339526 3 0.3863 0.804 0.004 0.176 0.812 0.008
#> GSM339527 1 0.0707 0.917 0.980 0.000 0.020 0.000
#> GSM339528 1 0.1211 0.913 0.960 0.000 0.040 0.000
#> GSM339529 4 0.4661 0.616 0.000 0.348 0.000 0.652
#> GSM339530 2 0.1557 0.790 0.000 0.944 0.056 0.000
#> GSM339531 2 0.3726 0.776 0.000 0.788 0.000 0.212
#> GSM339532 1 0.1406 0.913 0.960 0.000 0.024 0.016
#> GSM339533 3 0.2376 0.827 0.016 0.068 0.916 0.000
#> GSM339534 1 0.6450 0.284 0.572 0.012 0.364 0.052
#> GSM339535 4 0.4843 0.467 0.000 0.396 0.000 0.604
#> GSM339536 1 0.1716 0.908 0.936 0.000 0.000 0.064
#> GSM339537 2 0.3726 0.776 0.000 0.788 0.000 0.212
#> GSM339538 3 0.3614 0.788 0.100 0.016 0.864 0.020
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM339455 3 0.5722 0.6894 0.000 0.008 0.600 0.304 0.088
#> GSM339456 2 0.0404 0.8623 0.000 0.988 0.000 0.000 0.012
#> GSM339457 5 0.2886 0.8099 0.000 0.000 0.148 0.008 0.844
#> GSM339458 5 0.2910 0.8248 0.000 0.012 0.044 0.060 0.884
#> GSM339459 5 0.2798 0.8122 0.000 0.000 0.140 0.008 0.852
#> GSM339460 5 0.3948 0.8186 0.000 0.096 0.024 0.056 0.824
#> GSM339461 5 0.3561 0.6344 0.000 0.260 0.000 0.000 0.740
#> GSM339462 1 0.0609 0.5119 0.980 0.000 0.000 0.020 0.000
#> GSM339463 3 0.3143 0.7786 0.000 0.000 0.796 0.204 0.000
#> GSM339464 1 0.4291 0.2295 0.536 0.000 0.000 0.464 0.000
#> GSM339465 4 0.6166 0.2049 0.272 0.000 0.180 0.548 0.000
#> GSM339466 5 0.3016 0.8236 0.000 0.132 0.000 0.020 0.848
#> GSM339467 2 0.0404 0.8623 0.000 0.988 0.000 0.000 0.012
#> GSM339468 5 0.3193 0.8221 0.000 0.132 0.000 0.028 0.840
#> GSM339469 4 0.4434 0.3979 0.460 0.000 0.004 0.536 0.000
#> GSM339470 5 0.1524 0.8429 0.000 0.016 0.016 0.016 0.952
#> GSM339471 1 0.2852 0.3713 0.828 0.000 0.000 0.172 0.000
#> GSM339472 2 0.0404 0.8623 0.000 0.988 0.000 0.000 0.012
#> GSM339473 1 0.1270 0.5336 0.948 0.000 0.000 0.052 0.000
#> GSM339474 2 0.0404 0.8623 0.000 0.988 0.000 0.000 0.012
#> GSM339475 3 0.1341 0.7545 0.000 0.000 0.944 0.000 0.056
#> GSM339476 1 0.4434 0.2451 0.536 0.000 0.004 0.460 0.000
#> GSM339477 2 0.0404 0.8623 0.000 0.988 0.000 0.000 0.012
#> GSM339478 5 0.2886 0.8099 0.000 0.000 0.148 0.008 0.844
#> GSM339479 5 0.2910 0.8248 0.000 0.012 0.044 0.060 0.884
#> GSM339480 5 0.2798 0.8122 0.000 0.000 0.140 0.008 0.852
#> GSM339481 2 0.1478 0.8571 0.000 0.936 0.000 0.000 0.064
#> GSM339482 3 0.3913 0.7399 0.000 0.000 0.676 0.324 0.000
#> GSM339483 1 0.0609 0.5119 0.980 0.000 0.000 0.020 0.000
#> GSM339484 1 0.4434 0.2451 0.536 0.000 0.004 0.460 0.000
#> GSM339485 1 0.4291 0.2295 0.536 0.000 0.000 0.464 0.000
#> GSM339486 1 0.4297 0.2395 0.528 0.000 0.000 0.472 0.000
#> GSM339487 5 0.3016 0.8236 0.000 0.132 0.000 0.020 0.848
#> GSM339488 2 0.0404 0.8623 0.000 0.988 0.000 0.000 0.012
#> GSM339489 5 0.3193 0.8221 0.000 0.132 0.000 0.028 0.840
#> GSM339490 4 0.4434 0.3979 0.460 0.000 0.004 0.536 0.000
#> GSM339491 5 0.1524 0.8429 0.000 0.016 0.016 0.016 0.952
#> GSM339492 1 0.2852 0.3713 0.828 0.000 0.000 0.172 0.000
#> GSM339493 2 0.4088 0.4352 0.000 0.632 0.000 0.000 0.368
#> GSM339494 1 0.1270 0.5336 0.948 0.000 0.000 0.052 0.000
#> GSM339495 2 0.0404 0.8623 0.000 0.988 0.000 0.000 0.012
#> GSM339496 3 0.1341 0.7561 0.000 0.000 0.944 0.000 0.056
#> GSM339497 5 0.3109 0.7286 0.000 0.200 0.000 0.000 0.800
#> GSM339498 5 0.2886 0.8099 0.000 0.000 0.148 0.008 0.844
#> GSM339499 5 0.2886 0.8099 0.000 0.000 0.148 0.008 0.844
#> GSM339500 5 0.1205 0.8475 0.000 0.040 0.000 0.004 0.956
#> GSM339501 3 0.6261 0.6099 0.000 0.008 0.576 0.228 0.188
#> GSM339502 2 0.1608 0.8545 0.000 0.928 0.000 0.000 0.072
#> GSM339503 3 0.2929 0.7843 0.000 0.000 0.820 0.180 0.000
#> GSM339504 1 0.0609 0.5119 0.980 0.000 0.000 0.020 0.000
#> GSM339505 5 0.0693 0.8458 0.000 0.000 0.008 0.012 0.980
#> GSM339506 1 0.4291 0.2295 0.536 0.000 0.000 0.464 0.000
#> GSM339507 1 0.4297 0.2395 0.528 0.000 0.000 0.472 0.000
#> GSM339508 2 0.4047 0.5539 0.000 0.676 0.000 0.004 0.320
#> GSM339509 2 0.0703 0.8625 0.000 0.976 0.000 0.000 0.024
#> GSM339510 5 0.3193 0.8221 0.000 0.132 0.000 0.028 0.840
#> GSM339511 4 0.4430 0.3999 0.456 0.000 0.004 0.540 0.000
#> GSM339512 5 0.1430 0.8478 0.000 0.052 0.000 0.004 0.944
#> GSM339513 1 0.2852 0.3713 0.828 0.000 0.000 0.172 0.000
#> GSM339514 2 0.1732 0.8455 0.000 0.920 0.000 0.000 0.080
#> GSM339515 1 0.1270 0.5336 0.948 0.000 0.000 0.052 0.000
#> GSM339516 5 0.3193 0.8221 0.000 0.132 0.000 0.028 0.840
#> GSM339517 3 0.2304 0.7205 0.000 0.000 0.892 0.008 0.100
#> GSM339518 5 0.3109 0.7286 0.000 0.200 0.000 0.000 0.800
#> GSM339519 3 0.4651 0.6594 0.000 0.008 0.560 0.428 0.004
#> GSM339520 5 0.2886 0.8099 0.000 0.000 0.148 0.008 0.844
#> GSM339521 5 0.1205 0.8475 0.000 0.040 0.000 0.004 0.956
#> GSM339522 5 0.3340 0.7602 0.000 0.156 0.016 0.004 0.824
#> GSM339523 2 0.1410 0.8580 0.000 0.940 0.000 0.000 0.060
#> GSM339524 4 0.5338 -0.0987 0.072 0.000 0.324 0.604 0.000
#> GSM339525 1 0.0880 0.5103 0.968 0.000 0.000 0.032 0.000
#> GSM339526 3 0.1168 0.7616 0.000 0.000 0.960 0.008 0.032
#> GSM339527 1 0.4291 0.2295 0.536 0.000 0.000 0.464 0.000
#> GSM339528 1 0.4297 0.2395 0.528 0.000 0.000 0.472 0.000
#> GSM339529 2 0.4047 0.5539 0.000 0.676 0.000 0.004 0.320
#> GSM339530 5 0.2886 0.8099 0.000 0.000 0.148 0.008 0.844
#> GSM339531 5 0.3193 0.8221 0.000 0.132 0.000 0.028 0.840
#> GSM339532 4 0.4430 0.3999 0.456 0.000 0.004 0.540 0.000
#> GSM339533 3 0.3304 0.7898 0.000 0.000 0.816 0.168 0.016
#> GSM339534 4 0.6209 0.2585 0.184 0.008 0.224 0.584 0.000
#> GSM339535 2 0.4088 0.4352 0.000 0.632 0.000 0.000 0.368
#> GSM339536 1 0.1270 0.5336 0.948 0.000 0.000 0.052 0.000
#> GSM339537 5 0.3193 0.8221 0.000 0.132 0.000 0.028 0.840
#> GSM339538 3 0.3796 0.7482 0.000 0.000 0.700 0.300 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM339455 3 0.4049 0.746 0.004 0.000 0.768 0.036 0.020 0.172
#> GSM339456 2 0.0000 0.864 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM339457 6 0.3515 0.865 0.000 0.000 0.000 0.000 0.324 0.676
#> GSM339458 5 0.3568 0.364 0.008 0.000 0.016 0.000 0.764 0.212
#> GSM339459 6 0.3547 0.859 0.000 0.000 0.000 0.000 0.332 0.668
#> GSM339460 5 0.4464 0.430 0.008 0.084 0.004 0.000 0.732 0.172
#> GSM339461 5 0.5889 0.165 0.000 0.260 0.000 0.000 0.476 0.264
#> GSM339462 1 0.3684 0.706 0.628 0.000 0.000 0.372 0.000 0.000
#> GSM339463 3 0.0790 0.798 0.000 0.000 0.968 0.032 0.000 0.000
#> GSM339464 4 0.0260 0.674 0.008 0.000 0.000 0.992 0.000 0.000
#> GSM339465 4 0.3409 0.421 0.000 0.000 0.300 0.700 0.000 0.000
#> GSM339466 5 0.4650 0.429 0.000 0.132 0.000 0.000 0.688 0.180
#> GSM339467 2 0.0000 0.864 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM339468 5 0.2178 0.554 0.000 0.132 0.000 0.000 0.868 0.000
#> GSM339469 4 0.5007 0.415 0.416 0.000 0.000 0.512 0.000 0.072
#> GSM339470 6 0.4226 0.223 0.000 0.008 0.004 0.000 0.484 0.504
#> GSM339471 1 0.3361 0.608 0.788 0.000 0.020 0.188 0.000 0.004
#> GSM339472 2 0.0000 0.864 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM339473 1 0.3862 0.664 0.524 0.000 0.000 0.476 0.000 0.000
#> GSM339474 2 0.0000 0.864 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM339475 3 0.3109 0.758 0.004 0.000 0.772 0.000 0.000 0.224
#> GSM339476 4 0.2265 0.633 0.076 0.000 0.024 0.896 0.000 0.004
#> GSM339477 2 0.0000 0.864 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM339478 6 0.3515 0.865 0.000 0.000 0.000 0.000 0.324 0.676
#> GSM339479 5 0.3568 0.364 0.008 0.000 0.016 0.000 0.764 0.212
#> GSM339480 6 0.3547 0.859 0.000 0.000 0.000 0.000 0.332 0.668
#> GSM339481 2 0.1219 0.852 0.000 0.948 0.000 0.000 0.048 0.004
#> GSM339482 3 0.2981 0.774 0.116 0.000 0.848 0.020 0.000 0.016
#> GSM339483 1 0.3684 0.706 0.628 0.000 0.000 0.372 0.000 0.000
#> GSM339484 4 0.2265 0.633 0.076 0.000 0.024 0.896 0.000 0.004
#> GSM339485 4 0.0260 0.674 0.008 0.000 0.000 0.992 0.000 0.000
#> GSM339486 4 0.1867 0.650 0.064 0.000 0.020 0.916 0.000 0.000
#> GSM339487 5 0.4650 0.429 0.000 0.132 0.000 0.000 0.688 0.180
#> GSM339488 2 0.0000 0.864 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM339489 5 0.2178 0.554 0.000 0.132 0.000 0.000 0.868 0.000
#> GSM339490 4 0.5007 0.415 0.416 0.000 0.000 0.512 0.000 0.072
#> GSM339491 6 0.4226 0.223 0.000 0.008 0.004 0.000 0.484 0.504
#> GSM339492 1 0.3361 0.608 0.788 0.000 0.020 0.188 0.000 0.004
#> GSM339493 2 0.3874 0.355 0.000 0.636 0.000 0.000 0.356 0.008
#> GSM339494 1 0.3862 0.664 0.524 0.000 0.000 0.476 0.000 0.000
#> GSM339495 2 0.0000 0.864 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM339496 3 0.3109 0.760 0.004 0.000 0.772 0.000 0.000 0.224
#> GSM339497 5 0.5710 0.169 0.000 0.200 0.000 0.000 0.512 0.288
#> GSM339498 6 0.3515 0.865 0.000 0.000 0.000 0.000 0.324 0.676
#> GSM339499 6 0.3515 0.865 0.000 0.000 0.000 0.000 0.324 0.676
#> GSM339500 5 0.4603 -0.252 0.000 0.040 0.000 0.000 0.544 0.416
#> GSM339501 3 0.5628 0.688 0.012 0.000 0.648 0.036 0.204 0.100
#> GSM339502 2 0.1411 0.847 0.000 0.936 0.000 0.000 0.060 0.004
#> GSM339503 3 0.0260 0.800 0.000 0.000 0.992 0.008 0.000 0.000
#> GSM339504 1 0.3684 0.706 0.628 0.000 0.000 0.372 0.000 0.000
#> GSM339505 5 0.3998 -0.473 0.000 0.000 0.004 0.000 0.504 0.492
#> GSM339506 4 0.0260 0.674 0.008 0.000 0.000 0.992 0.000 0.000
#> GSM339507 4 0.1867 0.650 0.064 0.000 0.020 0.916 0.000 0.000
#> GSM339508 2 0.3784 0.545 0.000 0.680 0.000 0.000 0.308 0.012
#> GSM339509 2 0.0458 0.862 0.000 0.984 0.000 0.000 0.016 0.000
#> GSM339510 5 0.2178 0.554 0.000 0.132 0.000 0.000 0.868 0.000
#> GSM339511 4 0.5040 0.419 0.408 0.000 0.000 0.516 0.000 0.076
#> GSM339512 5 0.4768 -0.269 0.000 0.052 0.000 0.000 0.532 0.416
#> GSM339513 1 0.3361 0.608 0.788 0.000 0.020 0.188 0.000 0.004
#> GSM339514 2 0.1643 0.830 0.000 0.924 0.000 0.000 0.068 0.008
#> GSM339515 1 0.3862 0.664 0.524 0.000 0.000 0.476 0.000 0.000
#> GSM339516 5 0.2320 0.552 0.000 0.132 0.000 0.000 0.864 0.004
#> GSM339517 3 0.3543 0.727 0.004 0.000 0.720 0.000 0.004 0.272
#> GSM339518 5 0.5710 0.169 0.000 0.200 0.000 0.000 0.512 0.288
#> GSM339519 3 0.4944 0.732 0.120 0.000 0.732 0.036 0.012 0.100
#> GSM339520 6 0.3515 0.865 0.000 0.000 0.000 0.000 0.324 0.676
#> GSM339521 5 0.4603 -0.252 0.000 0.040 0.000 0.000 0.544 0.416
#> GSM339522 5 0.4881 0.339 0.008 0.156 0.000 0.000 0.684 0.152
#> GSM339523 2 0.1152 0.853 0.000 0.952 0.000 0.000 0.044 0.004
#> GSM339524 3 0.5845 0.272 0.128 0.000 0.488 0.368 0.000 0.016
#> GSM339525 1 0.3717 0.696 0.616 0.000 0.000 0.384 0.000 0.000
#> GSM339526 3 0.3043 0.766 0.004 0.000 0.796 0.004 0.000 0.196
#> GSM339527 4 0.0260 0.674 0.008 0.000 0.000 0.992 0.000 0.000
#> GSM339528 4 0.1867 0.650 0.064 0.000 0.020 0.916 0.000 0.000
#> GSM339529 2 0.3784 0.545 0.000 0.680 0.000 0.000 0.308 0.012
#> GSM339530 6 0.3515 0.865 0.000 0.000 0.000 0.000 0.324 0.676
#> GSM339531 5 0.2178 0.554 0.000 0.132 0.000 0.000 0.868 0.000
#> GSM339532 4 0.5040 0.419 0.408 0.000 0.000 0.516 0.000 0.076
#> GSM339533 3 0.0717 0.803 0.000 0.000 0.976 0.008 0.000 0.016
#> GSM339534 1 0.7509 -0.294 0.376 0.000 0.296 0.212 0.012 0.104
#> GSM339535 2 0.3874 0.355 0.000 0.636 0.000 0.000 0.356 0.008
#> GSM339536 1 0.3862 0.664 0.524 0.000 0.000 0.476 0.000 0.000
#> GSM339537 5 0.2178 0.554 0.000 0.132 0.000 0.000 0.868 0.000
#> GSM339538 3 0.3307 0.780 0.120 0.000 0.828 0.012 0.000 0.040
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 protocol(p) agent(p) individual(p) k
#> ATC:hclust 84 1.000 0.769 1.22e-03 2
#> ATC:hclust 83 0.780 0.854 2.57e-04 3
#> ATC:hclust 80 0.810 0.872 2.07e-05 4
#> ATC:hclust 63 0.888 0.955 4.61e-05 5
#> ATC:hclust 60 0.914 0.953 4.75e-07 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 15497 rows and 84 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 0.950 0.980 0.4932 0.501 0.501
#> 3 3 0.662 0.740 0.883 0.3225 0.741 0.526
#> 4 4 0.681 0.726 0.789 0.1221 0.811 0.515
#> 5 5 0.680 0.670 0.715 0.0688 0.922 0.727
#> 6 6 0.720 0.762 0.772 0.0452 0.923 0.681
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
#> GSM339455 1 0.995 0.210 0.540 0.460
#> GSM339456 2 0.000 0.999 0.000 1.000
#> GSM339457 2 0.000 0.999 0.000 1.000
#> GSM339458 2 0.000 0.999 0.000 1.000
#> GSM339459 2 0.000 0.999 0.000 1.000
#> GSM339460 2 0.000 0.999 0.000 1.000
#> GSM339461 2 0.000 0.999 0.000 1.000
#> GSM339462 1 0.000 0.954 1.000 0.000
#> GSM339463 1 0.000 0.954 1.000 0.000
#> GSM339464 1 0.000 0.954 1.000 0.000
#> GSM339465 1 0.000 0.954 1.000 0.000
#> GSM339466 2 0.000 0.999 0.000 1.000
#> GSM339467 2 0.000 0.999 0.000 1.000
#> GSM339468 2 0.000 0.999 0.000 1.000
#> GSM339469 1 0.000 0.954 1.000 0.000
#> GSM339470 2 0.000 0.999 0.000 1.000
#> GSM339471 1 0.000 0.954 1.000 0.000
#> GSM339472 2 0.000 0.999 0.000 1.000
#> GSM339473 1 0.000 0.954 1.000 0.000
#> GSM339474 2 0.000 0.999 0.000 1.000
#> GSM339475 2 0.000 0.999 0.000 1.000
#> GSM339476 1 0.000 0.954 1.000 0.000
#> GSM339477 2 0.000 0.999 0.000 1.000
#> GSM339478 2 0.000 0.999 0.000 1.000
#> GSM339479 2 0.278 0.946 0.048 0.952
#> GSM339480 2 0.000 0.999 0.000 1.000
#> GSM339481 2 0.000 0.999 0.000 1.000
#> GSM339482 1 0.000 0.954 1.000 0.000
#> GSM339483 1 0.000 0.954 1.000 0.000
#> GSM339484 1 0.000 0.954 1.000 0.000
#> GSM339485 1 0.000 0.954 1.000 0.000
#> GSM339486 1 0.000 0.954 1.000 0.000
#> GSM339487 2 0.000 0.999 0.000 1.000
#> GSM339488 2 0.000 0.999 0.000 1.000
#> GSM339489 2 0.000 0.999 0.000 1.000
#> GSM339490 1 0.000 0.954 1.000 0.000
#> GSM339491 2 0.000 0.999 0.000 1.000
#> GSM339492 1 0.000 0.954 1.000 0.000
#> GSM339493 2 0.000 0.999 0.000 1.000
#> GSM339494 1 0.000 0.954 1.000 0.000
#> GSM339495 2 0.000 0.999 0.000 1.000
#> GSM339496 1 0.998 0.171 0.528 0.472
#> GSM339497 2 0.000 0.999 0.000 1.000
#> GSM339498 2 0.000 0.999 0.000 1.000
#> GSM339499 2 0.000 0.999 0.000 1.000
#> GSM339500 2 0.000 0.999 0.000 1.000
#> GSM339501 1 0.000 0.954 1.000 0.000
#> GSM339502 2 0.000 0.999 0.000 1.000
#> GSM339503 1 0.943 0.470 0.640 0.360
#> GSM339504 1 0.000 0.954 1.000 0.000
#> GSM339505 2 0.000 0.999 0.000 1.000
#> GSM339506 1 0.000 0.954 1.000 0.000
#> GSM339507 1 0.000 0.954 1.000 0.000
#> GSM339508 2 0.000 0.999 0.000 1.000
#> GSM339509 2 0.000 0.999 0.000 1.000
#> GSM339510 2 0.000 0.999 0.000 1.000
#> GSM339511 1 0.000 0.954 1.000 0.000
#> GSM339512 2 0.000 0.999 0.000 1.000
#> GSM339513 1 0.000 0.954 1.000 0.000
#> GSM339514 2 0.000 0.999 0.000 1.000
#> GSM339515 1 0.000 0.954 1.000 0.000
#> GSM339516 2 0.000 0.999 0.000 1.000
#> GSM339517 2 0.000 0.999 0.000 1.000
#> GSM339518 2 0.000 0.999 0.000 1.000
#> GSM339519 1 0.000 0.954 1.000 0.000
#> GSM339520 2 0.000 0.999 0.000 1.000
#> GSM339521 2 0.000 0.999 0.000 1.000
#> GSM339522 2 0.000 0.999 0.000 1.000
#> GSM339523 2 0.000 0.999 0.000 1.000
#> GSM339524 1 0.000 0.954 1.000 0.000
#> GSM339525 1 0.000 0.954 1.000 0.000
#> GSM339526 1 0.000 0.954 1.000 0.000
#> GSM339527 1 0.000 0.954 1.000 0.000
#> GSM339528 1 0.000 0.954 1.000 0.000
#> GSM339529 2 0.000 0.999 0.000 1.000
#> GSM339530 2 0.000 0.999 0.000 1.000
#> GSM339531 2 0.000 0.999 0.000 1.000
#> GSM339532 1 0.000 0.954 1.000 0.000
#> GSM339533 1 0.909 0.542 0.676 0.324
#> GSM339534 1 0.000 0.954 1.000 0.000
#> GSM339535 2 0.000 0.999 0.000 1.000
#> GSM339536 1 0.000 0.954 1.000 0.000
#> GSM339537 2 0.000 0.999 0.000 1.000
#> GSM339538 1 0.000 0.954 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM339455 3 0.0000 0.719 0.000 0.000 1.000
#> GSM339456 2 0.0000 0.846 0.000 1.000 0.000
#> GSM339457 3 0.5785 0.456 0.000 0.332 0.668
#> GSM339458 2 0.5905 0.538 0.000 0.648 0.352
#> GSM339459 3 0.6308 0.138 0.000 0.492 0.508
#> GSM339460 2 0.5016 0.704 0.000 0.760 0.240
#> GSM339461 2 0.0000 0.846 0.000 1.000 0.000
#> GSM339462 1 0.0000 0.958 1.000 0.000 0.000
#> GSM339463 3 0.4887 0.481 0.228 0.000 0.772
#> GSM339464 1 0.0000 0.958 1.000 0.000 0.000
#> GSM339465 3 0.5178 0.433 0.256 0.000 0.744
#> GSM339466 2 0.0000 0.846 0.000 1.000 0.000
#> GSM339467 2 0.0000 0.846 0.000 1.000 0.000
#> GSM339468 2 0.5835 0.560 0.000 0.660 0.340
#> GSM339469 1 0.0000 0.958 1.000 0.000 0.000
#> GSM339470 3 0.3192 0.677 0.000 0.112 0.888
#> GSM339471 1 0.0000 0.958 1.000 0.000 0.000
#> GSM339472 2 0.0000 0.846 0.000 1.000 0.000
#> GSM339473 1 0.0000 0.958 1.000 0.000 0.000
#> GSM339474 2 0.0000 0.846 0.000 1.000 0.000
#> GSM339475 3 0.0000 0.719 0.000 0.000 1.000
#> GSM339476 1 0.0000 0.958 1.000 0.000 0.000
#> GSM339477 2 0.0000 0.846 0.000 1.000 0.000
#> GSM339478 3 0.6126 0.318 0.000 0.400 0.600
#> GSM339479 3 0.4974 0.519 0.000 0.236 0.764
#> GSM339480 3 0.5560 0.503 0.000 0.300 0.700
#> GSM339481 2 0.0000 0.846 0.000 1.000 0.000
#> GSM339482 3 0.5098 0.448 0.248 0.000 0.752
#> GSM339483 1 0.0000 0.958 1.000 0.000 0.000
#> GSM339484 1 0.3192 0.893 0.888 0.000 0.112
#> GSM339485 1 0.0000 0.958 1.000 0.000 0.000
#> GSM339486 1 0.3192 0.893 0.888 0.000 0.112
#> GSM339487 2 0.5138 0.691 0.000 0.748 0.252
#> GSM339488 2 0.0000 0.846 0.000 1.000 0.000
#> GSM339489 2 0.5835 0.560 0.000 0.660 0.340
#> GSM339490 1 0.0000 0.958 1.000 0.000 0.000
#> GSM339491 3 0.3192 0.677 0.000 0.112 0.888
#> GSM339492 1 0.0000 0.958 1.000 0.000 0.000
#> GSM339493 2 0.0000 0.846 0.000 1.000 0.000
#> GSM339494 1 0.0000 0.958 1.000 0.000 0.000
#> GSM339495 2 0.0000 0.846 0.000 1.000 0.000
#> GSM339496 3 0.0000 0.719 0.000 0.000 1.000
#> GSM339497 2 0.5835 0.560 0.000 0.660 0.340
#> GSM339498 3 0.6168 0.297 0.000 0.412 0.588
#> GSM339499 3 0.6168 0.297 0.000 0.412 0.588
#> GSM339500 2 0.5650 0.603 0.000 0.688 0.312
#> GSM339501 3 0.0000 0.719 0.000 0.000 1.000
#> GSM339502 2 0.0000 0.846 0.000 1.000 0.000
#> GSM339503 3 0.0000 0.719 0.000 0.000 1.000
#> GSM339504 1 0.0000 0.958 1.000 0.000 0.000
#> GSM339505 3 0.5810 0.450 0.000 0.336 0.664
#> GSM339506 1 0.2878 0.904 0.904 0.000 0.096
#> GSM339507 1 0.0892 0.948 0.980 0.000 0.020
#> GSM339508 2 0.0000 0.846 0.000 1.000 0.000
#> GSM339509 2 0.0000 0.846 0.000 1.000 0.000
#> GSM339510 2 0.5835 0.560 0.000 0.660 0.340
#> GSM339511 1 0.0000 0.958 1.000 0.000 0.000
#> GSM339512 2 0.0000 0.846 0.000 1.000 0.000
#> GSM339513 1 0.0000 0.958 1.000 0.000 0.000
#> GSM339514 2 0.0000 0.846 0.000 1.000 0.000
#> GSM339515 1 0.0000 0.958 1.000 0.000 0.000
#> GSM339516 2 0.5178 0.688 0.000 0.744 0.256
#> GSM339517 3 0.0000 0.719 0.000 0.000 1.000
#> GSM339518 2 0.4235 0.753 0.000 0.824 0.176
#> GSM339519 3 0.0000 0.719 0.000 0.000 1.000
#> GSM339520 3 0.6309 0.128 0.000 0.496 0.504
#> GSM339521 2 0.4974 0.706 0.000 0.764 0.236
#> GSM339522 2 0.4504 0.737 0.000 0.804 0.196
#> GSM339523 2 0.0000 0.846 0.000 1.000 0.000
#> GSM339524 1 0.3192 0.893 0.888 0.000 0.112
#> GSM339525 1 0.0000 0.958 1.000 0.000 0.000
#> GSM339526 3 0.0747 0.712 0.016 0.000 0.984
#> GSM339527 1 0.5760 0.619 0.672 0.000 0.328
#> GSM339528 1 0.2356 0.919 0.928 0.000 0.072
#> GSM339529 2 0.0000 0.846 0.000 1.000 0.000
#> GSM339530 3 0.6302 0.171 0.000 0.480 0.520
#> GSM339531 2 0.5465 0.642 0.000 0.712 0.288
#> GSM339532 1 0.0000 0.958 1.000 0.000 0.000
#> GSM339533 3 0.0000 0.719 0.000 0.000 1.000
#> GSM339534 1 0.4842 0.749 0.776 0.000 0.224
#> GSM339535 2 0.0000 0.846 0.000 1.000 0.000
#> GSM339536 1 0.0000 0.958 1.000 0.000 0.000
#> GSM339537 2 0.0000 0.846 0.000 1.000 0.000
#> GSM339538 3 0.5138 0.441 0.252 0.000 0.748
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM339455 4 0.3444 0.7699 0.000 0.000 0.184 0.816
#> GSM339456 2 0.0000 0.8862 0.000 1.000 0.000 0.000
#> GSM339457 3 0.5764 0.6164 0.000 0.052 0.644 0.304
#> GSM339458 3 0.4542 0.7326 0.000 0.228 0.752 0.020
#> GSM339459 3 0.6474 0.6672 0.000 0.120 0.624 0.256
#> GSM339460 3 0.4331 0.6904 0.000 0.288 0.712 0.000
#> GSM339461 2 0.0469 0.8837 0.000 0.988 0.012 0.000
#> GSM339462 1 0.0188 0.8599 0.996 0.000 0.004 0.000
#> GSM339463 4 0.3557 0.7556 0.036 0.000 0.108 0.856
#> GSM339464 1 0.5279 0.8018 0.736 0.000 0.192 0.072
#> GSM339465 4 0.3958 0.7132 0.032 0.000 0.144 0.824
#> GSM339466 3 0.4761 0.5648 0.000 0.372 0.628 0.000
#> GSM339467 2 0.0000 0.8862 0.000 1.000 0.000 0.000
#> GSM339468 3 0.4434 0.7336 0.000 0.228 0.756 0.016
#> GSM339469 1 0.0817 0.8576 0.976 0.000 0.024 0.000
#> GSM339470 3 0.4720 0.5559 0.000 0.004 0.672 0.324
#> GSM339471 1 0.0895 0.8576 0.976 0.000 0.020 0.004
#> GSM339472 2 0.0000 0.8862 0.000 1.000 0.000 0.000
#> GSM339473 1 0.1890 0.8603 0.936 0.000 0.056 0.008
#> GSM339474 2 0.0469 0.8837 0.000 0.988 0.012 0.000
#> GSM339475 4 0.2647 0.8316 0.000 0.000 0.120 0.880
#> GSM339476 1 0.5412 0.7933 0.736 0.000 0.168 0.096
#> GSM339477 2 0.0469 0.8837 0.000 0.988 0.012 0.000
#> GSM339478 3 0.5842 0.6849 0.000 0.092 0.688 0.220
#> GSM339479 3 0.6130 -0.0926 0.004 0.044 0.564 0.388
#> GSM339480 3 0.5720 0.6221 0.000 0.052 0.652 0.296
#> GSM339481 2 0.0188 0.8855 0.000 0.996 0.004 0.000
#> GSM339482 4 0.1724 0.8199 0.032 0.000 0.020 0.948
#> GSM339483 1 0.0336 0.8597 0.992 0.000 0.008 0.000
#> GSM339484 1 0.6473 0.7283 0.644 0.000 0.168 0.188
#> GSM339485 1 0.4677 0.8154 0.768 0.000 0.192 0.040
#> GSM339486 1 0.6511 0.7268 0.640 0.000 0.172 0.188
#> GSM339487 3 0.4277 0.6985 0.000 0.280 0.720 0.000
#> GSM339488 2 0.0000 0.8862 0.000 1.000 0.000 0.000
#> GSM339489 3 0.4434 0.7336 0.000 0.228 0.756 0.016
#> GSM339490 1 0.0921 0.8567 0.972 0.000 0.028 0.000
#> GSM339491 3 0.4655 0.5714 0.000 0.004 0.684 0.312
#> GSM339492 1 0.0895 0.8576 0.976 0.000 0.020 0.004
#> GSM339493 2 0.4948 -0.0262 0.000 0.560 0.440 0.000
#> GSM339494 1 0.1890 0.8603 0.936 0.000 0.056 0.008
#> GSM339495 2 0.0469 0.8837 0.000 0.988 0.012 0.000
#> GSM339496 4 0.2589 0.8329 0.000 0.000 0.116 0.884
#> GSM339497 3 0.4387 0.7309 0.000 0.236 0.752 0.012
#> GSM339498 3 0.6138 0.6644 0.000 0.092 0.648 0.260
#> GSM339499 3 0.6133 0.6578 0.000 0.088 0.644 0.268
#> GSM339500 3 0.4137 0.7344 0.000 0.208 0.780 0.012
#> GSM339501 4 0.3870 0.7550 0.004 0.000 0.208 0.788
#> GSM339502 2 0.0000 0.8862 0.000 1.000 0.000 0.000
#> GSM339503 4 0.2216 0.8433 0.000 0.000 0.092 0.908
#> GSM339504 1 0.0336 0.8597 0.992 0.000 0.008 0.000
#> GSM339505 3 0.5764 0.6164 0.000 0.052 0.644 0.304
#> GSM339506 1 0.6511 0.7330 0.640 0.000 0.188 0.172
#> GSM339507 1 0.5979 0.7699 0.692 0.000 0.172 0.136
#> GSM339508 2 0.0469 0.8837 0.000 0.988 0.012 0.000
#> GSM339509 2 0.0000 0.8862 0.000 1.000 0.000 0.000
#> GSM339510 3 0.4468 0.7323 0.000 0.232 0.752 0.016
#> GSM339511 1 0.2224 0.8543 0.928 0.000 0.032 0.040
#> GSM339512 3 0.4981 0.3873 0.000 0.464 0.536 0.000
#> GSM339513 1 0.0895 0.8576 0.976 0.000 0.020 0.004
#> GSM339514 2 0.0000 0.8862 0.000 1.000 0.000 0.000
#> GSM339515 1 0.1890 0.8603 0.936 0.000 0.056 0.008
#> GSM339516 3 0.4331 0.6904 0.000 0.288 0.712 0.000
#> GSM339517 4 0.2760 0.8240 0.000 0.000 0.128 0.872
#> GSM339518 3 0.4356 0.6851 0.000 0.292 0.708 0.000
#> GSM339519 4 0.2216 0.8436 0.000 0.000 0.092 0.908
#> GSM339520 3 0.6524 0.6628 0.000 0.120 0.616 0.264
#> GSM339521 3 0.4277 0.6985 0.000 0.280 0.720 0.000
#> GSM339522 3 0.4304 0.6954 0.000 0.284 0.716 0.000
#> GSM339523 2 0.0000 0.8862 0.000 1.000 0.000 0.000
#> GSM339524 1 0.6576 0.7157 0.632 0.000 0.168 0.200
#> GSM339525 1 0.0469 0.8593 0.988 0.000 0.012 0.000
#> GSM339526 4 0.0336 0.8335 0.000 0.000 0.008 0.992
#> GSM339527 4 0.7105 0.1830 0.256 0.000 0.184 0.560
#> GSM339528 1 0.6401 0.7383 0.652 0.000 0.172 0.176
#> GSM339529 2 0.4830 0.1626 0.000 0.608 0.392 0.000
#> GSM339530 3 0.6378 0.6640 0.000 0.108 0.628 0.264
#> GSM339531 3 0.4262 0.7307 0.000 0.236 0.756 0.008
#> GSM339532 1 0.0921 0.8567 0.972 0.000 0.028 0.000
#> GSM339533 4 0.2216 0.8433 0.000 0.000 0.092 0.908
#> GSM339534 1 0.5231 0.3923 0.604 0.000 0.012 0.384
#> GSM339535 3 0.4817 0.5414 0.000 0.388 0.612 0.000
#> GSM339536 1 0.1890 0.8603 0.936 0.000 0.056 0.008
#> GSM339537 2 0.4948 -0.0262 0.000 0.560 0.440 0.000
#> GSM339538 4 0.1256 0.8258 0.028 0.000 0.008 0.964
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM339455 3 0.5066 0.5929 0.084 0.000 0.676 0.000 0.240
#> GSM339456 2 0.1300 0.9847 0.016 0.956 0.000 0.000 0.028
#> GSM339457 5 0.6585 0.4487 0.268 0.000 0.264 0.000 0.468
#> GSM339458 5 0.4202 0.6815 0.124 0.068 0.012 0.000 0.796
#> GSM339459 5 0.6795 0.4721 0.252 0.012 0.244 0.000 0.492
#> GSM339460 5 0.3888 0.6898 0.120 0.076 0.000 0.000 0.804
#> GSM339461 2 0.1774 0.9680 0.016 0.932 0.000 0.000 0.052
#> GSM339462 4 0.0510 0.7510 0.016 0.000 0.000 0.984 0.000
#> GSM339463 3 0.4353 0.4738 0.328 0.000 0.660 0.008 0.004
#> GSM339464 4 0.4747 -0.6029 0.484 0.000 0.000 0.500 0.016
#> GSM339465 3 0.4706 0.0814 0.488 0.000 0.500 0.008 0.004
#> GSM339466 5 0.3993 0.6199 0.028 0.216 0.000 0.000 0.756
#> GSM339467 2 0.1082 0.9869 0.008 0.964 0.000 0.000 0.028
#> GSM339468 5 0.2046 0.6998 0.016 0.068 0.000 0.000 0.916
#> GSM339469 4 0.0324 0.7484 0.004 0.000 0.000 0.992 0.004
#> GSM339470 5 0.5848 0.5302 0.192 0.000 0.200 0.000 0.608
#> GSM339471 4 0.3721 0.7255 0.088 0.024 0.024 0.848 0.016
#> GSM339472 2 0.1300 0.9847 0.016 0.956 0.000 0.000 0.028
#> GSM339473 4 0.4715 0.6851 0.140 0.028 0.024 0.780 0.028
#> GSM339474 2 0.1668 0.9819 0.028 0.940 0.000 0.000 0.032
#> GSM339475 3 0.2450 0.7749 0.048 0.000 0.900 0.000 0.052
#> GSM339476 1 0.5389 0.7901 0.508 0.000 0.056 0.436 0.000
#> GSM339477 2 0.1668 0.9819 0.028 0.940 0.000 0.000 0.032
#> GSM339478 5 0.6249 0.5289 0.284 0.004 0.164 0.000 0.548
#> GSM339479 5 0.5941 0.3153 0.168 0.000 0.244 0.000 0.588
#> GSM339480 5 0.6510 0.4584 0.252 0.000 0.260 0.000 0.488
#> GSM339481 2 0.0794 0.9874 0.000 0.972 0.000 0.000 0.028
#> GSM339482 3 0.2605 0.7329 0.148 0.000 0.852 0.000 0.000
#> GSM339483 4 0.0000 0.7508 0.000 0.000 0.000 1.000 0.000
#> GSM339484 1 0.5707 0.8717 0.544 0.000 0.092 0.364 0.000
#> GSM339485 4 0.4738 -0.5445 0.464 0.000 0.000 0.520 0.016
#> GSM339486 1 0.5595 0.8730 0.560 0.000 0.084 0.356 0.000
#> GSM339487 5 0.2362 0.6995 0.024 0.076 0.000 0.000 0.900
#> GSM339488 2 0.0955 0.9871 0.004 0.968 0.000 0.000 0.028
#> GSM339489 5 0.3056 0.6896 0.068 0.068 0.000 0.000 0.864
#> GSM339490 4 0.0324 0.7484 0.004 0.000 0.000 0.992 0.004
#> GSM339491 5 0.5702 0.5482 0.192 0.000 0.180 0.000 0.628
#> GSM339492 4 0.3244 0.7330 0.088 0.012 0.016 0.868 0.016
#> GSM339493 5 0.4761 0.4091 0.028 0.356 0.000 0.000 0.616
#> GSM339494 4 0.4715 0.6851 0.140 0.028 0.024 0.780 0.028
#> GSM339495 2 0.1668 0.9819 0.028 0.940 0.000 0.000 0.032
#> GSM339496 3 0.1282 0.8023 0.004 0.000 0.952 0.000 0.044
#> GSM339497 5 0.3719 0.6882 0.116 0.068 0.000 0.000 0.816
#> GSM339498 5 0.6637 0.4692 0.260 0.004 0.248 0.000 0.488
#> GSM339499 5 0.6637 0.4692 0.260 0.004 0.248 0.000 0.488
#> GSM339500 5 0.3578 0.6903 0.132 0.048 0.000 0.000 0.820
#> GSM339501 3 0.4714 0.5343 0.032 0.000 0.644 0.000 0.324
#> GSM339502 2 0.0955 0.9871 0.004 0.968 0.000 0.000 0.028
#> GSM339503 3 0.1168 0.8073 0.008 0.000 0.960 0.000 0.032
#> GSM339504 4 0.0000 0.7508 0.000 0.000 0.000 1.000 0.000
#> GSM339505 5 0.6556 0.4493 0.260 0.000 0.264 0.000 0.476
#> GSM339506 1 0.5850 0.8372 0.544 0.000 0.072 0.372 0.012
#> GSM339507 1 0.5439 0.8613 0.560 0.000 0.068 0.372 0.000
#> GSM339508 2 0.1386 0.9835 0.016 0.952 0.000 0.000 0.032
#> GSM339509 2 0.1082 0.9869 0.008 0.964 0.000 0.000 0.028
#> GSM339510 5 0.3056 0.6896 0.068 0.068 0.000 0.000 0.864
#> GSM339511 4 0.2228 0.6517 0.092 0.000 0.004 0.900 0.004
#> GSM339512 5 0.5812 0.4034 0.100 0.372 0.000 0.000 0.528
#> GSM339513 4 0.3244 0.7330 0.088 0.012 0.016 0.868 0.016
#> GSM339514 2 0.0955 0.9871 0.004 0.968 0.000 0.000 0.028
#> GSM339515 4 0.4715 0.6851 0.140 0.028 0.024 0.780 0.028
#> GSM339516 5 0.3362 0.6859 0.080 0.076 0.000 0.000 0.844
#> GSM339517 3 0.2927 0.7506 0.068 0.000 0.872 0.000 0.060
#> GSM339518 5 0.3849 0.6902 0.112 0.080 0.000 0.000 0.808
#> GSM339519 3 0.0880 0.8065 0.000 0.000 0.968 0.000 0.032
#> GSM339520 5 0.6931 0.4665 0.260 0.016 0.248 0.000 0.476
#> GSM339521 5 0.2983 0.7027 0.056 0.076 0.000 0.000 0.868
#> GSM339522 5 0.2388 0.6995 0.028 0.072 0.000 0.000 0.900
#> GSM339523 2 0.0794 0.9874 0.000 0.972 0.000 0.000 0.028
#> GSM339524 1 0.5822 0.8552 0.548 0.000 0.108 0.344 0.000
#> GSM339525 4 0.0000 0.7508 0.000 0.000 0.000 1.000 0.000
#> GSM339526 3 0.1270 0.7960 0.052 0.000 0.948 0.000 0.000
#> GSM339527 1 0.6535 0.5604 0.536 0.000 0.268 0.184 0.012
#> GSM339528 1 0.5520 0.8700 0.560 0.000 0.076 0.364 0.000
#> GSM339529 5 0.4886 0.3455 0.032 0.372 0.000 0.000 0.596
#> GSM339530 5 0.6843 0.4674 0.260 0.012 0.248 0.000 0.480
#> GSM339531 5 0.1704 0.6997 0.004 0.068 0.000 0.000 0.928
#> GSM339532 4 0.0451 0.7460 0.008 0.000 0.000 0.988 0.004
#> GSM339533 3 0.2209 0.8014 0.056 0.000 0.912 0.000 0.032
#> GSM339534 4 0.5274 0.1016 0.064 0.000 0.336 0.600 0.000
#> GSM339535 5 0.4083 0.6135 0.028 0.228 0.000 0.000 0.744
#> GSM339536 4 0.4715 0.6851 0.140 0.028 0.024 0.780 0.028
#> GSM339537 5 0.4339 0.4240 0.012 0.336 0.000 0.000 0.652
#> GSM339538 3 0.1544 0.7888 0.068 0.000 0.932 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM339455 3 0.5902 0.514 0.000 0.004 0.612 0.056 0.220 0.108
#> GSM339456 2 0.1675 0.960 0.000 0.936 0.000 0.024 0.008 0.032
#> GSM339457 6 0.5451 0.959 0.000 0.000 0.148 0.000 0.308 0.544
#> GSM339458 5 0.5581 0.598 0.000 0.024 0.024 0.108 0.664 0.180
#> GSM339459 6 0.5694 0.935 0.000 0.000 0.124 0.016 0.316 0.544
#> GSM339460 5 0.5084 0.631 0.000 0.028 0.016 0.100 0.716 0.140
#> GSM339461 2 0.3116 0.924 0.000 0.860 0.000 0.044 0.044 0.052
#> GSM339462 1 0.0547 0.833 0.980 0.000 0.000 0.020 0.000 0.000
#> GSM339463 3 0.4597 0.304 0.000 0.004 0.584 0.376 0.000 0.036
#> GSM339464 4 0.4626 0.789 0.228 0.000 0.000 0.688 0.008 0.076
#> GSM339465 4 0.3766 0.471 0.000 0.000 0.304 0.684 0.000 0.012
#> GSM339466 5 0.4024 0.578 0.000 0.128 0.000 0.012 0.776 0.084
#> GSM339467 2 0.0405 0.965 0.000 0.988 0.000 0.000 0.008 0.004
#> GSM339468 5 0.1743 0.667 0.000 0.024 0.008 0.004 0.936 0.028
#> GSM339469 1 0.0951 0.827 0.968 0.000 0.000 0.020 0.008 0.004
#> GSM339470 5 0.6645 0.328 0.000 0.000 0.128 0.108 0.516 0.248
#> GSM339471 1 0.3249 0.812 0.836 0.000 0.000 0.060 0.008 0.096
#> GSM339472 2 0.1515 0.962 0.000 0.944 0.000 0.020 0.008 0.028
#> GSM339473 1 0.4502 0.760 0.732 0.000 0.000 0.116 0.012 0.140
#> GSM339474 2 0.2113 0.956 0.000 0.912 0.000 0.032 0.008 0.048
#> GSM339475 3 0.2048 0.757 0.000 0.000 0.880 0.000 0.000 0.120
#> GSM339476 4 0.4268 0.814 0.264 0.004 0.028 0.696 0.000 0.008
#> GSM339477 2 0.2113 0.956 0.000 0.912 0.000 0.032 0.008 0.048
#> GSM339478 6 0.5193 0.905 0.000 0.000 0.104 0.000 0.344 0.552
#> GSM339479 5 0.6768 0.444 0.000 0.004 0.160 0.120 0.536 0.180
#> GSM339480 6 0.5739 0.924 0.000 0.000 0.124 0.016 0.332 0.528
#> GSM339481 2 0.0779 0.966 0.000 0.976 0.000 0.008 0.008 0.008
#> GSM339482 3 0.2266 0.773 0.000 0.000 0.880 0.108 0.000 0.012
#> GSM339483 1 0.0363 0.833 0.988 0.000 0.000 0.012 0.000 0.000
#> GSM339484 4 0.4325 0.844 0.180 0.004 0.068 0.740 0.000 0.008
#> GSM339485 4 0.4827 0.742 0.264 0.000 0.000 0.652 0.008 0.076
#> GSM339486 4 0.3487 0.856 0.168 0.000 0.044 0.788 0.000 0.000
#> GSM339487 5 0.2146 0.644 0.000 0.024 0.000 0.008 0.908 0.060
#> GSM339488 2 0.0260 0.965 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM339489 5 0.2720 0.675 0.000 0.024 0.016 0.032 0.892 0.036
#> GSM339490 1 0.0951 0.827 0.968 0.000 0.000 0.020 0.008 0.004
#> GSM339491 5 0.6614 0.331 0.000 0.000 0.124 0.108 0.520 0.248
#> GSM339492 1 0.2994 0.818 0.856 0.000 0.000 0.060 0.008 0.076
#> GSM339493 5 0.4620 0.518 0.000 0.228 0.000 0.012 0.692 0.068
#> GSM339494 1 0.4502 0.760 0.732 0.000 0.000 0.116 0.012 0.140
#> GSM339495 2 0.2113 0.956 0.000 0.912 0.000 0.032 0.008 0.048
#> GSM339496 3 0.1152 0.813 0.000 0.000 0.952 0.004 0.000 0.044
#> GSM339497 5 0.4902 0.634 0.000 0.024 0.016 0.104 0.732 0.124
#> GSM339498 6 0.5463 0.961 0.000 0.000 0.148 0.000 0.312 0.540
#> GSM339499 6 0.5463 0.961 0.000 0.000 0.148 0.000 0.312 0.540
#> GSM339500 5 0.4411 0.529 0.000 0.004 0.000 0.080 0.712 0.204
#> GSM339501 3 0.5167 0.504 0.000 0.004 0.616 0.024 0.304 0.052
#> GSM339502 2 0.0976 0.961 0.000 0.968 0.000 0.008 0.008 0.016
#> GSM339503 3 0.1088 0.821 0.000 0.000 0.960 0.016 0.000 0.024
#> GSM339504 1 0.0363 0.833 0.988 0.000 0.000 0.012 0.000 0.000
#> GSM339505 6 0.5719 0.949 0.000 0.000 0.148 0.008 0.320 0.524
#> GSM339506 4 0.4596 0.831 0.172 0.000 0.028 0.728 0.000 0.072
#> GSM339507 4 0.3318 0.854 0.172 0.000 0.032 0.796 0.000 0.000
#> GSM339508 2 0.1577 0.959 0.000 0.940 0.000 0.016 0.008 0.036
#> GSM339509 2 0.1065 0.961 0.000 0.964 0.000 0.008 0.008 0.020
#> GSM339510 5 0.2720 0.675 0.000 0.024 0.016 0.032 0.892 0.036
#> GSM339511 1 0.4109 0.682 0.800 0.004 0.028 0.104 0.008 0.056
#> GSM339512 5 0.6697 0.432 0.000 0.216 0.000 0.084 0.508 0.192
#> GSM339513 1 0.2994 0.818 0.856 0.000 0.000 0.060 0.008 0.076
#> GSM339514 2 0.0976 0.961 0.000 0.968 0.000 0.008 0.008 0.016
#> GSM339515 1 0.4502 0.760 0.732 0.000 0.000 0.116 0.012 0.140
#> GSM339516 5 0.3067 0.676 0.000 0.028 0.016 0.032 0.872 0.052
#> GSM339517 3 0.2135 0.749 0.000 0.000 0.872 0.000 0.000 0.128
#> GSM339518 5 0.4320 0.654 0.000 0.028 0.000 0.088 0.764 0.120
#> GSM339519 3 0.0692 0.819 0.000 0.000 0.976 0.004 0.000 0.020
#> GSM339520 6 0.5438 0.958 0.000 0.000 0.148 0.000 0.304 0.548
#> GSM339521 5 0.4052 0.639 0.000 0.024 0.000 0.076 0.784 0.116
#> GSM339522 5 0.1909 0.648 0.000 0.024 0.000 0.004 0.920 0.052
#> GSM339523 2 0.0260 0.965 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM339524 4 0.4249 0.844 0.184 0.004 0.068 0.740 0.000 0.004
#> GSM339525 1 0.0363 0.833 0.988 0.000 0.000 0.012 0.000 0.000
#> GSM339526 3 0.1398 0.810 0.000 0.000 0.940 0.052 0.000 0.008
#> GSM339527 4 0.5088 0.760 0.092 0.000 0.120 0.712 0.000 0.076
#> GSM339528 4 0.3487 0.856 0.168 0.000 0.044 0.788 0.000 0.000
#> GSM339529 5 0.4492 0.499 0.000 0.260 0.000 0.016 0.684 0.040
#> GSM339530 6 0.5557 0.955 0.000 0.004 0.148 0.000 0.300 0.548
#> GSM339531 5 0.1341 0.663 0.000 0.024 0.000 0.000 0.948 0.028
#> GSM339532 1 0.1647 0.815 0.940 0.004 0.000 0.032 0.008 0.016
#> GSM339533 3 0.2007 0.813 0.000 0.004 0.916 0.044 0.000 0.036
#> GSM339534 1 0.5600 0.363 0.616 0.008 0.268 0.064 0.000 0.044
#> GSM339535 5 0.4191 0.564 0.000 0.156 0.000 0.008 0.752 0.084
#> GSM339536 1 0.4502 0.760 0.732 0.000 0.000 0.116 0.012 0.140
#> GSM339537 5 0.4348 0.545 0.000 0.200 0.000 0.028 0.732 0.040
#> GSM339538 3 0.1913 0.795 0.000 0.000 0.908 0.080 0.000 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 protocol(p) agent(p) individual(p) k
#> ATC:kmeans 81 0.896 0.405 4.32e-03 2
#> ATC:kmeans 72 0.948 0.886 6.99e-04 3
#> ATC:kmeans 77 0.700 0.635 5.21e-04 4
#> ATC:kmeans 66 0.640 0.692 3.64e-05 5
#> ATC:kmeans 76 0.759 0.774 2.84e-07 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 15497 rows and 84 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 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 0.997 0.998 0.5037 0.497 0.497
#> 3 3 0.894 0.850 0.937 0.2309 0.893 0.786
#> 4 4 0.803 0.898 0.915 0.1231 0.893 0.734
#> 5 5 0.752 0.763 0.867 0.0686 0.983 0.942
#> 6 6 0.748 0.567 0.732 0.0506 0.877 0.598
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
#> GSM339455 1 0.000 0.997 1.000 0.000
#> GSM339456 2 0.000 1.000 0.000 1.000
#> GSM339457 2 0.000 1.000 0.000 1.000
#> GSM339458 2 0.000 1.000 0.000 1.000
#> GSM339459 2 0.000 1.000 0.000 1.000
#> GSM339460 2 0.000 1.000 0.000 1.000
#> GSM339461 2 0.000 1.000 0.000 1.000
#> GSM339462 1 0.000 0.997 1.000 0.000
#> GSM339463 1 0.000 0.997 1.000 0.000
#> GSM339464 1 0.000 0.997 1.000 0.000
#> GSM339465 1 0.000 0.997 1.000 0.000
#> GSM339466 2 0.000 1.000 0.000 1.000
#> GSM339467 2 0.000 1.000 0.000 1.000
#> GSM339468 2 0.000 1.000 0.000 1.000
#> GSM339469 1 0.000 0.997 1.000 0.000
#> GSM339470 2 0.000 1.000 0.000 1.000
#> GSM339471 1 0.000 0.997 1.000 0.000
#> GSM339472 2 0.000 1.000 0.000 1.000
#> GSM339473 1 0.000 0.997 1.000 0.000
#> GSM339474 2 0.000 1.000 0.000 1.000
#> GSM339475 1 0.552 0.853 0.872 0.128
#> GSM339476 1 0.000 0.997 1.000 0.000
#> GSM339477 2 0.000 1.000 0.000 1.000
#> GSM339478 2 0.000 1.000 0.000 1.000
#> GSM339479 1 0.000 0.997 1.000 0.000
#> GSM339480 2 0.000 1.000 0.000 1.000
#> GSM339481 2 0.000 1.000 0.000 1.000
#> GSM339482 1 0.000 0.997 1.000 0.000
#> GSM339483 1 0.000 0.997 1.000 0.000
#> GSM339484 1 0.000 0.997 1.000 0.000
#> GSM339485 1 0.000 0.997 1.000 0.000
#> GSM339486 1 0.000 0.997 1.000 0.000
#> GSM339487 2 0.000 1.000 0.000 1.000
#> GSM339488 2 0.000 1.000 0.000 1.000
#> GSM339489 2 0.000 1.000 0.000 1.000
#> GSM339490 1 0.000 0.997 1.000 0.000
#> GSM339491 2 0.000 1.000 0.000 1.000
#> GSM339492 1 0.000 0.997 1.000 0.000
#> GSM339493 2 0.000 1.000 0.000 1.000
#> GSM339494 1 0.000 0.997 1.000 0.000
#> GSM339495 2 0.000 1.000 0.000 1.000
#> GSM339496 1 0.000 0.997 1.000 0.000
#> GSM339497 2 0.000 1.000 0.000 1.000
#> GSM339498 2 0.000 1.000 0.000 1.000
#> GSM339499 2 0.000 1.000 0.000 1.000
#> GSM339500 2 0.000 1.000 0.000 1.000
#> GSM339501 1 0.000 0.997 1.000 0.000
#> GSM339502 2 0.000 1.000 0.000 1.000
#> GSM339503 1 0.000 0.997 1.000 0.000
#> GSM339504 1 0.000 0.997 1.000 0.000
#> GSM339505 2 0.000 1.000 0.000 1.000
#> GSM339506 1 0.000 0.997 1.000 0.000
#> GSM339507 1 0.000 0.997 1.000 0.000
#> GSM339508 2 0.000 1.000 0.000 1.000
#> GSM339509 2 0.000 1.000 0.000 1.000
#> GSM339510 2 0.000 1.000 0.000 1.000
#> GSM339511 1 0.000 0.997 1.000 0.000
#> GSM339512 2 0.000 1.000 0.000 1.000
#> GSM339513 1 0.000 0.997 1.000 0.000
#> GSM339514 2 0.000 1.000 0.000 1.000
#> GSM339515 1 0.000 0.997 1.000 0.000
#> GSM339516 2 0.000 1.000 0.000 1.000
#> GSM339517 2 0.000 1.000 0.000 1.000
#> GSM339518 2 0.000 1.000 0.000 1.000
#> GSM339519 1 0.000 0.997 1.000 0.000
#> GSM339520 2 0.000 1.000 0.000 1.000
#> GSM339521 2 0.000 1.000 0.000 1.000
#> GSM339522 2 0.000 1.000 0.000 1.000
#> GSM339523 2 0.000 1.000 0.000 1.000
#> GSM339524 1 0.000 0.997 1.000 0.000
#> GSM339525 1 0.000 0.997 1.000 0.000
#> GSM339526 1 0.000 0.997 1.000 0.000
#> GSM339527 1 0.000 0.997 1.000 0.000
#> GSM339528 1 0.000 0.997 1.000 0.000
#> GSM339529 2 0.000 1.000 0.000 1.000
#> GSM339530 2 0.000 1.000 0.000 1.000
#> GSM339531 2 0.000 1.000 0.000 1.000
#> GSM339532 1 0.000 0.997 1.000 0.000
#> GSM339533 1 0.000 0.997 1.000 0.000
#> GSM339534 1 0.000 0.997 1.000 0.000
#> GSM339535 2 0.000 1.000 0.000 1.000
#> GSM339536 1 0.000 0.997 1.000 0.000
#> GSM339537 2 0.000 1.000 0.000 1.000
#> GSM339538 1 0.000 0.997 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM339455 3 0.5968 0.3646 0.364 0.000 0.636
#> GSM339456 2 0.0000 0.8898 0.000 1.000 0.000
#> GSM339457 2 0.6192 0.4154 0.000 0.580 0.420
#> GSM339458 2 0.0000 0.8898 0.000 1.000 0.000
#> GSM339459 2 0.6126 0.4578 0.000 0.600 0.400
#> GSM339460 2 0.0000 0.8898 0.000 1.000 0.000
#> GSM339461 2 0.0000 0.8898 0.000 1.000 0.000
#> GSM339462 1 0.0000 0.9975 1.000 0.000 0.000
#> GSM339463 1 0.0237 0.9936 0.996 0.000 0.004
#> GSM339464 1 0.0000 0.9975 1.000 0.000 0.000
#> GSM339465 1 0.2165 0.9270 0.936 0.000 0.064
#> GSM339466 2 0.0000 0.8898 0.000 1.000 0.000
#> GSM339467 2 0.0000 0.8898 0.000 1.000 0.000
#> GSM339468 2 0.0000 0.8898 0.000 1.000 0.000
#> GSM339469 1 0.0000 0.9975 1.000 0.000 0.000
#> GSM339470 3 0.6111 0.0828 0.000 0.396 0.604
#> GSM339471 1 0.0000 0.9975 1.000 0.000 0.000
#> GSM339472 2 0.0000 0.8898 0.000 1.000 0.000
#> GSM339473 1 0.0000 0.9975 1.000 0.000 0.000
#> GSM339474 2 0.0000 0.8898 0.000 1.000 0.000
#> GSM339475 3 0.0000 0.8644 0.000 0.000 1.000
#> GSM339476 1 0.0000 0.9975 1.000 0.000 0.000
#> GSM339477 2 0.0000 0.8898 0.000 1.000 0.000
#> GSM339478 2 0.6126 0.4578 0.000 0.600 0.400
#> GSM339479 1 0.0000 0.9975 1.000 0.000 0.000
#> GSM339480 2 0.6126 0.4578 0.000 0.600 0.400
#> GSM339481 2 0.0000 0.8898 0.000 1.000 0.000
#> GSM339482 3 0.6062 0.3742 0.384 0.000 0.616
#> GSM339483 1 0.0000 0.9975 1.000 0.000 0.000
#> GSM339484 1 0.0000 0.9975 1.000 0.000 0.000
#> GSM339485 1 0.0000 0.9975 1.000 0.000 0.000
#> GSM339486 1 0.0000 0.9975 1.000 0.000 0.000
#> GSM339487 2 0.0000 0.8898 0.000 1.000 0.000
#> GSM339488 2 0.0000 0.8898 0.000 1.000 0.000
#> GSM339489 2 0.0000 0.8898 0.000 1.000 0.000
#> GSM339490 1 0.0000 0.9975 1.000 0.000 0.000
#> GSM339491 2 0.6192 0.4172 0.000 0.580 0.420
#> GSM339492 1 0.0000 0.9975 1.000 0.000 0.000
#> GSM339493 2 0.0000 0.8898 0.000 1.000 0.000
#> GSM339494 1 0.0000 0.9975 1.000 0.000 0.000
#> GSM339495 2 0.0000 0.8898 0.000 1.000 0.000
#> GSM339496 3 0.0000 0.8644 0.000 0.000 1.000
#> GSM339497 2 0.0000 0.8898 0.000 1.000 0.000
#> GSM339498 2 0.6126 0.4578 0.000 0.600 0.400
#> GSM339499 2 0.6126 0.4578 0.000 0.600 0.400
#> GSM339500 2 0.0000 0.8898 0.000 1.000 0.000
#> GSM339501 1 0.0000 0.9975 1.000 0.000 0.000
#> GSM339502 2 0.0000 0.8898 0.000 1.000 0.000
#> GSM339503 3 0.0000 0.8644 0.000 0.000 1.000
#> GSM339504 1 0.0000 0.9975 1.000 0.000 0.000
#> GSM339505 2 0.6126 0.4578 0.000 0.600 0.400
#> GSM339506 1 0.0000 0.9975 1.000 0.000 0.000
#> GSM339507 1 0.0000 0.9975 1.000 0.000 0.000
#> GSM339508 2 0.0000 0.8898 0.000 1.000 0.000
#> GSM339509 2 0.0000 0.8898 0.000 1.000 0.000
#> GSM339510 2 0.0000 0.8898 0.000 1.000 0.000
#> GSM339511 1 0.0000 0.9975 1.000 0.000 0.000
#> GSM339512 2 0.0000 0.8898 0.000 1.000 0.000
#> GSM339513 1 0.0000 0.9975 1.000 0.000 0.000
#> GSM339514 2 0.0000 0.8898 0.000 1.000 0.000
#> GSM339515 1 0.0000 0.9975 1.000 0.000 0.000
#> GSM339516 2 0.0000 0.8898 0.000 1.000 0.000
#> GSM339517 3 0.0000 0.8644 0.000 0.000 1.000
#> GSM339518 2 0.0000 0.8898 0.000 1.000 0.000
#> GSM339519 3 0.0592 0.8613 0.012 0.000 0.988
#> GSM339520 2 0.6126 0.4578 0.000 0.600 0.400
#> GSM339521 2 0.0000 0.8898 0.000 1.000 0.000
#> GSM339522 2 0.0000 0.8898 0.000 1.000 0.000
#> GSM339523 2 0.0000 0.8898 0.000 1.000 0.000
#> GSM339524 1 0.0000 0.9975 1.000 0.000 0.000
#> GSM339525 1 0.0000 0.9975 1.000 0.000 0.000
#> GSM339526 3 0.0000 0.8644 0.000 0.000 1.000
#> GSM339527 1 0.0000 0.9975 1.000 0.000 0.000
#> GSM339528 1 0.0000 0.9975 1.000 0.000 0.000
#> GSM339529 2 0.0000 0.8898 0.000 1.000 0.000
#> GSM339530 2 0.6126 0.4578 0.000 0.600 0.400
#> GSM339531 2 0.0000 0.8898 0.000 1.000 0.000
#> GSM339532 1 0.0000 0.9975 1.000 0.000 0.000
#> GSM339533 3 0.0000 0.8644 0.000 0.000 1.000
#> GSM339534 1 0.0000 0.9975 1.000 0.000 0.000
#> GSM339535 2 0.0000 0.8898 0.000 1.000 0.000
#> GSM339536 1 0.0000 0.9975 1.000 0.000 0.000
#> GSM339537 2 0.0000 0.8898 0.000 1.000 0.000
#> GSM339538 3 0.0592 0.8613 0.012 0.000 0.988
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM339455 4 0.2256 0.807 0.056 0.000 0.020 0.924
#> GSM339456 2 0.0000 0.960 0.000 1.000 0.000 0.000
#> GSM339457 3 0.4678 0.913 0.000 0.232 0.744 0.024
#> GSM339458 2 0.3852 0.757 0.000 0.808 0.180 0.012
#> GSM339459 3 0.4711 0.910 0.000 0.236 0.740 0.024
#> GSM339460 2 0.0336 0.957 0.000 0.992 0.000 0.008
#> GSM339461 2 0.0188 0.958 0.000 0.996 0.004 0.000
#> GSM339462 1 0.0000 0.933 1.000 0.000 0.000 0.000
#> GSM339463 1 0.5322 0.619 0.660 0.000 0.028 0.312
#> GSM339464 1 0.2773 0.899 0.900 0.000 0.028 0.072
#> GSM339465 1 0.5750 0.319 0.532 0.000 0.028 0.440
#> GSM339466 2 0.0469 0.958 0.000 0.988 0.012 0.000
#> GSM339467 2 0.0000 0.960 0.000 1.000 0.000 0.000
#> GSM339468 2 0.2222 0.926 0.000 0.924 0.060 0.016
#> GSM339469 1 0.0000 0.933 1.000 0.000 0.000 0.000
#> GSM339470 3 0.2282 0.693 0.000 0.052 0.924 0.024
#> GSM339471 1 0.0000 0.933 1.000 0.000 0.000 0.000
#> GSM339472 2 0.0000 0.960 0.000 1.000 0.000 0.000
#> GSM339473 1 0.0000 0.933 1.000 0.000 0.000 0.000
#> GSM339474 2 0.0000 0.960 0.000 1.000 0.000 0.000
#> GSM339475 4 0.2814 0.900 0.000 0.000 0.132 0.868
#> GSM339476 1 0.0188 0.932 0.996 0.000 0.000 0.004
#> GSM339477 2 0.0000 0.960 0.000 1.000 0.000 0.000
#> GSM339478 3 0.4610 0.910 0.000 0.236 0.744 0.020
#> GSM339479 1 0.6312 0.696 0.680 0.012 0.204 0.104
#> GSM339480 3 0.4446 0.875 0.000 0.196 0.776 0.028
#> GSM339481 2 0.0000 0.960 0.000 1.000 0.000 0.000
#> GSM339482 4 0.4633 0.681 0.172 0.000 0.048 0.780
#> GSM339483 1 0.0000 0.933 1.000 0.000 0.000 0.000
#> GSM339484 1 0.2011 0.906 0.920 0.000 0.000 0.080
#> GSM339485 1 0.1256 0.922 0.964 0.000 0.028 0.008
#> GSM339486 1 0.3427 0.876 0.860 0.000 0.028 0.112
#> GSM339487 2 0.1398 0.944 0.000 0.956 0.040 0.004
#> GSM339488 2 0.0000 0.960 0.000 1.000 0.000 0.000
#> GSM339489 2 0.2300 0.923 0.000 0.920 0.064 0.016
#> GSM339490 1 0.0000 0.933 1.000 0.000 0.000 0.000
#> GSM339491 3 0.2256 0.699 0.000 0.056 0.924 0.020
#> GSM339492 1 0.0000 0.933 1.000 0.000 0.000 0.000
#> GSM339493 2 0.0592 0.957 0.000 0.984 0.016 0.000
#> GSM339494 1 0.0000 0.933 1.000 0.000 0.000 0.000
#> GSM339495 2 0.0000 0.960 0.000 1.000 0.000 0.000
#> GSM339496 4 0.2589 0.909 0.000 0.000 0.116 0.884
#> GSM339497 2 0.2048 0.910 0.000 0.928 0.064 0.008
#> GSM339498 3 0.4678 0.913 0.000 0.232 0.744 0.024
#> GSM339499 3 0.4678 0.913 0.000 0.232 0.744 0.024
#> GSM339500 3 0.5007 0.657 0.000 0.356 0.636 0.008
#> GSM339501 1 0.0336 0.928 0.992 0.000 0.000 0.008
#> GSM339502 2 0.0000 0.960 0.000 1.000 0.000 0.000
#> GSM339503 4 0.2469 0.912 0.000 0.000 0.108 0.892
#> GSM339504 1 0.0000 0.933 1.000 0.000 0.000 0.000
#> GSM339505 3 0.4775 0.908 0.000 0.232 0.740 0.028
#> GSM339506 1 0.3182 0.886 0.876 0.000 0.028 0.096
#> GSM339507 1 0.3182 0.886 0.876 0.000 0.028 0.096
#> GSM339508 2 0.0000 0.960 0.000 1.000 0.000 0.000
#> GSM339509 2 0.0000 0.960 0.000 1.000 0.000 0.000
#> GSM339510 2 0.2222 0.925 0.000 0.924 0.060 0.016
#> GSM339511 1 0.0000 0.933 1.000 0.000 0.000 0.000
#> GSM339512 2 0.1211 0.937 0.000 0.960 0.040 0.000
#> GSM339513 1 0.0000 0.933 1.000 0.000 0.000 0.000
#> GSM339514 2 0.0000 0.960 0.000 1.000 0.000 0.000
#> GSM339515 1 0.0000 0.933 1.000 0.000 0.000 0.000
#> GSM339516 2 0.2060 0.930 0.000 0.932 0.052 0.016
#> GSM339517 4 0.3024 0.886 0.000 0.000 0.148 0.852
#> GSM339518 2 0.2342 0.893 0.000 0.912 0.080 0.008
#> GSM339519 4 0.3325 0.905 0.024 0.000 0.112 0.864
#> GSM339520 3 0.4678 0.913 0.000 0.232 0.744 0.024
#> GSM339521 2 0.2011 0.900 0.000 0.920 0.080 0.000
#> GSM339522 2 0.1109 0.951 0.000 0.968 0.028 0.004
#> GSM339523 2 0.0000 0.960 0.000 1.000 0.000 0.000
#> GSM339524 1 0.2654 0.891 0.888 0.000 0.004 0.108
#> GSM339525 1 0.0000 0.933 1.000 0.000 0.000 0.000
#> GSM339526 4 0.2469 0.912 0.000 0.000 0.108 0.892
#> GSM339527 1 0.3182 0.886 0.876 0.000 0.028 0.096
#> GSM339528 1 0.3367 0.879 0.864 0.000 0.028 0.108
#> GSM339529 2 0.0921 0.952 0.000 0.972 0.028 0.000
#> GSM339530 3 0.4678 0.913 0.000 0.232 0.744 0.024
#> GSM339531 2 0.2222 0.926 0.000 0.924 0.060 0.016
#> GSM339532 1 0.0000 0.933 1.000 0.000 0.000 0.000
#> GSM339533 4 0.1118 0.873 0.000 0.000 0.036 0.964
#> GSM339534 1 0.0000 0.933 1.000 0.000 0.000 0.000
#> GSM339535 2 0.0707 0.955 0.000 0.980 0.020 0.000
#> GSM339536 1 0.0000 0.933 1.000 0.000 0.000 0.000
#> GSM339537 2 0.1635 0.940 0.000 0.948 0.044 0.008
#> GSM339538 4 0.2928 0.911 0.012 0.000 0.108 0.880
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM339455 3 0.4001 0.7316 0.024 0.000 0.764 0.004 0.208
#> GSM339456 2 0.0510 0.8542 0.000 0.984 0.000 0.016 0.000
#> GSM339457 4 0.2763 0.8370 0.000 0.148 0.004 0.848 0.000
#> GSM339458 5 0.4808 0.1658 0.000 0.400 0.000 0.024 0.576
#> GSM339459 4 0.2806 0.8336 0.000 0.152 0.004 0.844 0.000
#> GSM339460 2 0.2677 0.7645 0.000 0.872 0.000 0.016 0.112
#> GSM339461 2 0.0955 0.8425 0.000 0.968 0.000 0.028 0.004
#> GSM339462 1 0.0162 0.8638 0.996 0.000 0.000 0.000 0.004
#> GSM339463 1 0.6428 0.4672 0.504 0.000 0.224 0.000 0.272
#> GSM339464 1 0.4016 0.7370 0.716 0.000 0.012 0.000 0.272
#> GSM339465 1 0.6734 0.2791 0.408 0.000 0.324 0.000 0.268
#> GSM339466 2 0.1082 0.8489 0.000 0.964 0.000 0.008 0.028
#> GSM339467 2 0.0510 0.8542 0.000 0.984 0.000 0.016 0.000
#> GSM339468 2 0.5032 0.6147 0.000 0.704 0.000 0.128 0.168
#> GSM339469 1 0.0162 0.8638 0.996 0.000 0.000 0.000 0.004
#> GSM339470 4 0.5302 0.4106 0.000 0.016 0.028 0.572 0.384
#> GSM339471 1 0.0162 0.8646 0.996 0.000 0.000 0.000 0.004
#> GSM339472 2 0.0510 0.8542 0.000 0.984 0.000 0.016 0.000
#> GSM339473 1 0.0404 0.8646 0.988 0.000 0.000 0.000 0.012
#> GSM339474 2 0.0290 0.8540 0.000 0.992 0.000 0.008 0.000
#> GSM339475 3 0.1341 0.9156 0.000 0.000 0.944 0.056 0.000
#> GSM339476 1 0.0404 0.8646 0.988 0.000 0.000 0.000 0.012
#> GSM339477 2 0.0290 0.8540 0.000 0.992 0.000 0.008 0.000
#> GSM339478 4 0.2763 0.8370 0.000 0.148 0.004 0.848 0.000
#> GSM339479 5 0.3686 0.2688 0.104 0.036 0.008 0.012 0.840
#> GSM339480 4 0.2492 0.7238 0.000 0.072 0.008 0.900 0.020
#> GSM339481 2 0.0510 0.8542 0.000 0.984 0.000 0.016 0.000
#> GSM339482 3 0.3291 0.7256 0.120 0.000 0.840 0.000 0.040
#> GSM339483 1 0.0162 0.8638 0.996 0.000 0.000 0.000 0.004
#> GSM339484 1 0.3752 0.7930 0.804 0.000 0.048 0.000 0.148
#> GSM339485 1 0.3662 0.7549 0.744 0.000 0.004 0.000 0.252
#> GSM339486 1 0.4777 0.7115 0.680 0.000 0.052 0.000 0.268
#> GSM339487 2 0.2616 0.8025 0.000 0.888 0.000 0.036 0.076
#> GSM339488 2 0.0510 0.8542 0.000 0.984 0.000 0.016 0.000
#> GSM339489 2 0.5136 0.5996 0.000 0.692 0.000 0.128 0.180
#> GSM339490 1 0.0290 0.8633 0.992 0.000 0.000 0.000 0.008
#> GSM339491 4 0.5181 0.3968 0.000 0.016 0.020 0.564 0.400
#> GSM339492 1 0.0162 0.8646 0.996 0.000 0.000 0.000 0.004
#> GSM339493 2 0.1082 0.8475 0.000 0.964 0.000 0.008 0.028
#> GSM339494 1 0.0404 0.8646 0.988 0.000 0.000 0.000 0.012
#> GSM339495 2 0.0000 0.8539 0.000 1.000 0.000 0.000 0.000
#> GSM339496 3 0.1121 0.9219 0.000 0.000 0.956 0.044 0.000
#> GSM339497 2 0.4485 0.4079 0.000 0.680 0.000 0.028 0.292
#> GSM339498 4 0.2763 0.8370 0.000 0.148 0.004 0.848 0.000
#> GSM339499 4 0.2763 0.8370 0.000 0.148 0.004 0.848 0.000
#> GSM339500 4 0.6714 0.0685 0.000 0.344 0.000 0.404 0.252
#> GSM339501 1 0.0162 0.8638 0.996 0.000 0.000 0.000 0.004
#> GSM339502 2 0.0510 0.8542 0.000 0.984 0.000 0.016 0.000
#> GSM339503 3 0.0865 0.9260 0.000 0.000 0.972 0.024 0.004
#> GSM339504 1 0.0162 0.8638 0.996 0.000 0.000 0.000 0.004
#> GSM339505 4 0.2763 0.8139 0.000 0.148 0.004 0.848 0.000
#> GSM339506 1 0.4475 0.7227 0.692 0.000 0.032 0.000 0.276
#> GSM339507 1 0.4503 0.7246 0.696 0.000 0.036 0.000 0.268
#> GSM339508 2 0.0000 0.8539 0.000 1.000 0.000 0.000 0.000
#> GSM339509 2 0.0510 0.8542 0.000 0.984 0.000 0.016 0.000
#> GSM339510 2 0.5093 0.6050 0.000 0.696 0.000 0.124 0.180
#> GSM339511 1 0.0404 0.8624 0.988 0.000 0.000 0.000 0.012
#> GSM339512 2 0.3532 0.6904 0.000 0.824 0.000 0.048 0.128
#> GSM339513 1 0.0162 0.8646 0.996 0.000 0.000 0.000 0.004
#> GSM339514 2 0.0510 0.8542 0.000 0.984 0.000 0.016 0.000
#> GSM339515 1 0.0404 0.8646 0.988 0.000 0.000 0.000 0.012
#> GSM339516 2 0.4827 0.6405 0.000 0.724 0.000 0.116 0.160
#> GSM339517 3 0.1410 0.9129 0.000 0.000 0.940 0.060 0.000
#> GSM339518 2 0.4268 0.4601 0.000 0.708 0.000 0.024 0.268
#> GSM339519 3 0.1386 0.9234 0.016 0.000 0.952 0.032 0.000
#> GSM339520 4 0.2763 0.8370 0.000 0.148 0.004 0.848 0.000
#> GSM339521 2 0.4104 0.5415 0.000 0.748 0.000 0.032 0.220
#> GSM339522 2 0.1522 0.8363 0.000 0.944 0.000 0.012 0.044
#> GSM339523 2 0.0510 0.8542 0.000 0.984 0.000 0.016 0.000
#> GSM339524 1 0.3863 0.7889 0.796 0.000 0.052 0.000 0.152
#> GSM339525 1 0.0162 0.8638 0.996 0.000 0.000 0.000 0.004
#> GSM339526 3 0.0865 0.9260 0.000 0.000 0.972 0.024 0.004
#> GSM339527 1 0.4475 0.7227 0.692 0.000 0.032 0.000 0.276
#> GSM339528 1 0.4777 0.7115 0.680 0.000 0.052 0.000 0.268
#> GSM339529 2 0.0794 0.8459 0.000 0.972 0.000 0.028 0.000
#> GSM339530 4 0.2763 0.8370 0.000 0.148 0.004 0.848 0.000
#> GSM339531 2 0.4989 0.6192 0.000 0.708 0.000 0.124 0.168
#> GSM339532 1 0.0290 0.8633 0.992 0.000 0.000 0.000 0.008
#> GSM339533 3 0.0162 0.9127 0.000 0.000 0.996 0.004 0.000
#> GSM339534 1 0.0162 0.8638 0.996 0.000 0.000 0.000 0.004
#> GSM339535 2 0.1281 0.8463 0.000 0.956 0.000 0.012 0.032
#> GSM339536 1 0.0404 0.8646 0.988 0.000 0.000 0.000 0.012
#> GSM339537 2 0.4172 0.7011 0.000 0.784 0.000 0.108 0.108
#> GSM339538 3 0.1106 0.9247 0.012 0.000 0.964 0.024 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM339455 3 0.5224 0.6113 0.096 0.000 0.668 0.036 0.200 0.000
#> GSM339456 2 0.0260 0.8589 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM339457 6 0.2312 0.9495 0.000 0.112 0.012 0.000 0.000 0.876
#> GSM339458 5 0.3073 0.5097 0.000 0.204 0.000 0.008 0.788 0.000
#> GSM339459 6 0.2377 0.9296 0.000 0.124 0.004 0.004 0.000 0.868
#> GSM339460 2 0.2416 0.7540 0.000 0.844 0.000 0.000 0.156 0.000
#> GSM339461 2 0.0951 0.8512 0.000 0.968 0.000 0.004 0.020 0.008
#> GSM339462 4 0.3828 0.3076 0.440 0.000 0.000 0.560 0.000 0.000
#> GSM339463 1 0.2454 0.5019 0.840 0.000 0.160 0.000 0.000 0.000
#> GSM339464 1 0.0603 0.6258 0.980 0.000 0.000 0.016 0.004 0.000
#> GSM339465 1 0.2697 0.4520 0.812 0.000 0.188 0.000 0.000 0.000
#> GSM339466 2 0.1293 0.8491 0.000 0.956 0.004 0.016 0.020 0.004
#> GSM339467 2 0.0146 0.8603 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM339468 4 0.7597 -0.2638 0.000 0.272 0.020 0.396 0.208 0.104
#> GSM339469 4 0.3828 0.3076 0.440 0.000 0.000 0.560 0.000 0.000
#> GSM339470 5 0.5493 0.4750 0.000 0.004 0.056 0.028 0.540 0.372
#> GSM339471 4 0.3843 0.2888 0.452 0.000 0.000 0.548 0.000 0.000
#> GSM339472 2 0.0146 0.8603 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM339473 1 0.3867 -0.1527 0.512 0.000 0.000 0.488 0.000 0.000
#> GSM339474 2 0.0146 0.8602 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM339475 3 0.1692 0.8932 0.000 0.000 0.932 0.012 0.008 0.048
#> GSM339476 1 0.3851 -0.0680 0.540 0.000 0.000 0.460 0.000 0.000
#> GSM339477 2 0.0146 0.8602 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM339478 6 0.2312 0.9495 0.000 0.112 0.012 0.000 0.000 0.876
#> GSM339479 5 0.3483 0.5208 0.236 0.000 0.000 0.016 0.748 0.000
#> GSM339480 6 0.2924 0.7217 0.000 0.032 0.004 0.068 0.024 0.872
#> GSM339481 2 0.0146 0.8603 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM339482 3 0.3161 0.6854 0.216 0.000 0.776 0.008 0.000 0.000
#> GSM339483 4 0.3828 0.3076 0.440 0.000 0.000 0.560 0.000 0.000
#> GSM339484 1 0.3349 0.4473 0.748 0.000 0.008 0.244 0.000 0.000
#> GSM339485 1 0.1753 0.5952 0.912 0.000 0.000 0.084 0.004 0.000
#> GSM339486 1 0.0717 0.6249 0.976 0.000 0.016 0.008 0.000 0.000
#> GSM339487 2 0.3967 0.7240 0.000 0.800 0.008 0.092 0.084 0.016
#> GSM339488 2 0.0146 0.8603 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM339489 4 0.7612 -0.2679 0.000 0.260 0.020 0.396 0.220 0.104
#> GSM339490 4 0.3828 0.3076 0.440 0.000 0.000 0.560 0.000 0.000
#> GSM339491 5 0.5496 0.5020 0.000 0.008 0.052 0.028 0.560 0.352
#> GSM339492 4 0.3843 0.2888 0.452 0.000 0.000 0.548 0.000 0.000
#> GSM339493 2 0.1377 0.8448 0.000 0.952 0.004 0.016 0.024 0.004
#> GSM339494 1 0.3867 -0.1527 0.512 0.000 0.000 0.488 0.000 0.000
#> GSM339495 2 0.0260 0.8601 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM339496 3 0.1453 0.8975 0.000 0.000 0.944 0.008 0.008 0.040
#> GSM339497 2 0.4321 0.5252 0.000 0.652 0.000 0.012 0.316 0.020
#> GSM339498 6 0.2312 0.9495 0.000 0.112 0.012 0.000 0.000 0.876
#> GSM339499 6 0.2312 0.9495 0.000 0.112 0.012 0.000 0.000 0.876
#> GSM339500 2 0.6041 -0.0225 0.000 0.464 0.000 0.008 0.328 0.200
#> GSM339501 4 0.4002 0.2604 0.404 0.000 0.000 0.588 0.000 0.008
#> GSM339502 2 0.0146 0.8603 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM339503 3 0.0777 0.9011 0.004 0.000 0.972 0.000 0.000 0.024
#> GSM339504 4 0.3828 0.3076 0.440 0.000 0.000 0.560 0.000 0.000
#> GSM339505 6 0.3338 0.8551 0.000 0.152 0.012 0.000 0.024 0.812
#> GSM339506 1 0.0291 0.6276 0.992 0.000 0.000 0.004 0.004 0.000
#> GSM339507 1 0.0260 0.6282 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM339508 2 0.0260 0.8601 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM339509 2 0.0000 0.8603 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM339510 4 0.7590 -0.2668 0.000 0.264 0.020 0.396 0.220 0.100
#> GSM339511 4 0.3833 0.3026 0.444 0.000 0.000 0.556 0.000 0.000
#> GSM339512 2 0.2944 0.7413 0.000 0.832 0.000 0.008 0.148 0.012
#> GSM339513 4 0.3843 0.2888 0.452 0.000 0.000 0.548 0.000 0.000
#> GSM339514 2 0.0146 0.8603 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM339515 1 0.3867 -0.1527 0.512 0.000 0.000 0.488 0.000 0.000
#> GSM339516 2 0.7448 0.0596 0.000 0.360 0.020 0.344 0.196 0.080
#> GSM339517 3 0.1757 0.8908 0.000 0.000 0.928 0.012 0.008 0.052
#> GSM339518 2 0.3684 0.5715 0.000 0.692 0.000 0.004 0.300 0.004
#> GSM339519 3 0.1401 0.8945 0.004 0.000 0.948 0.020 0.000 0.028
#> GSM339520 6 0.2312 0.9495 0.000 0.112 0.012 0.000 0.000 0.876
#> GSM339521 2 0.3973 0.5411 0.000 0.684 0.000 0.012 0.296 0.008
#> GSM339522 2 0.2808 0.8069 0.000 0.884 0.012 0.044 0.044 0.016
#> GSM339523 2 0.0146 0.8603 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM339524 1 0.3511 0.4929 0.760 0.000 0.024 0.216 0.000 0.000
#> GSM339525 4 0.3828 0.3076 0.440 0.000 0.000 0.560 0.000 0.000
#> GSM339526 3 0.0891 0.8998 0.008 0.000 0.968 0.000 0.000 0.024
#> GSM339527 1 0.0291 0.6276 0.992 0.000 0.000 0.004 0.004 0.000
#> GSM339528 1 0.0717 0.6249 0.976 0.000 0.016 0.008 0.000 0.000
#> GSM339529 2 0.0551 0.8583 0.000 0.984 0.000 0.008 0.004 0.004
#> GSM339530 6 0.2312 0.9495 0.000 0.112 0.012 0.000 0.000 0.876
#> GSM339531 4 0.7597 -0.2638 0.000 0.272 0.020 0.396 0.208 0.104
#> GSM339532 4 0.3833 0.3026 0.444 0.000 0.000 0.556 0.000 0.000
#> GSM339533 3 0.2219 0.8839 0.036 0.000 0.916 0.012 0.016 0.020
#> GSM339534 4 0.3838 0.2970 0.448 0.000 0.000 0.552 0.000 0.000
#> GSM339535 2 0.1647 0.8414 0.000 0.940 0.004 0.016 0.032 0.008
#> GSM339536 1 0.3867 -0.1527 0.512 0.000 0.000 0.488 0.000 0.000
#> GSM339537 2 0.6524 0.4297 0.000 0.576 0.016 0.200 0.132 0.076
#> GSM339538 3 0.1332 0.8969 0.012 0.000 0.952 0.008 0.000 0.028
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 protocol(p) agent(p) individual(p) k
#> ATC:skmeans 84 1.000 0.550 3.23e-03 2
#> ATC:skmeans 71 0.361 0.513 1.45e-04 3
#> ATC:skmeans 83 0.936 0.874 2.70e-05 4
#> ATC:skmeans 75 0.927 0.955 7.03e-05 5
#> ATC:skmeans 55 0.473 0.832 1.31e-05 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 15497 rows and 84 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 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 0.999 0.999 0.5018 0.499 0.499
#> 3 3 0.659 0.781 0.853 0.2926 0.802 0.623
#> 4 4 0.717 0.750 0.860 0.1341 0.899 0.719
#> 5 5 0.927 0.851 0.940 0.0648 0.904 0.666
#> 6 6 0.846 0.799 0.873 0.0574 0.923 0.662
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
#> GSM339455 1 0.000 0.999 1.000 0.000
#> GSM339456 2 0.000 1.000 0.000 1.000
#> GSM339457 2 0.000 1.000 0.000 1.000
#> GSM339458 2 0.000 1.000 0.000 1.000
#> GSM339459 2 0.000 1.000 0.000 1.000
#> GSM339460 2 0.000 1.000 0.000 1.000
#> GSM339461 2 0.000 1.000 0.000 1.000
#> GSM339462 1 0.000 0.999 1.000 0.000
#> GSM339463 1 0.000 0.999 1.000 0.000
#> GSM339464 1 0.000 0.999 1.000 0.000
#> GSM339465 1 0.000 0.999 1.000 0.000
#> GSM339466 2 0.000 1.000 0.000 1.000
#> GSM339467 2 0.000 1.000 0.000 1.000
#> GSM339468 2 0.000 1.000 0.000 1.000
#> GSM339469 1 0.000 0.999 1.000 0.000
#> GSM339470 2 0.000 1.000 0.000 1.000
#> GSM339471 1 0.000 0.999 1.000 0.000
#> GSM339472 2 0.000 1.000 0.000 1.000
#> GSM339473 1 0.000 0.999 1.000 0.000
#> GSM339474 2 0.000 1.000 0.000 1.000
#> GSM339475 2 0.000 1.000 0.000 1.000
#> GSM339476 1 0.000 0.999 1.000 0.000
#> GSM339477 2 0.000 1.000 0.000 1.000
#> GSM339478 2 0.000 1.000 0.000 1.000
#> GSM339479 1 0.000 0.999 1.000 0.000
#> GSM339480 2 0.000 1.000 0.000 1.000
#> GSM339481 2 0.000 1.000 0.000 1.000
#> GSM339482 1 0.000 0.999 1.000 0.000
#> GSM339483 1 0.000 0.999 1.000 0.000
#> GSM339484 1 0.000 0.999 1.000 0.000
#> GSM339485 1 0.000 0.999 1.000 0.000
#> GSM339486 1 0.000 0.999 1.000 0.000
#> GSM339487 2 0.000 1.000 0.000 1.000
#> GSM339488 2 0.000 1.000 0.000 1.000
#> GSM339489 2 0.000 1.000 0.000 1.000
#> GSM339490 1 0.000 0.999 1.000 0.000
#> GSM339491 2 0.000 1.000 0.000 1.000
#> GSM339492 1 0.000 0.999 1.000 0.000
#> GSM339493 2 0.000 1.000 0.000 1.000
#> GSM339494 1 0.000 0.999 1.000 0.000
#> GSM339495 2 0.000 1.000 0.000 1.000
#> GSM339496 1 0.000 0.999 1.000 0.000
#> GSM339497 2 0.000 1.000 0.000 1.000
#> GSM339498 2 0.000 1.000 0.000 1.000
#> GSM339499 2 0.000 1.000 0.000 1.000
#> GSM339500 2 0.000 1.000 0.000 1.000
#> GSM339501 1 0.000 0.999 1.000 0.000
#> GSM339502 2 0.000 1.000 0.000 1.000
#> GSM339503 1 0.278 0.950 0.952 0.048
#> GSM339504 1 0.000 0.999 1.000 0.000
#> GSM339505 2 0.000 1.000 0.000 1.000
#> GSM339506 1 0.000 0.999 1.000 0.000
#> GSM339507 1 0.000 0.999 1.000 0.000
#> GSM339508 2 0.000 1.000 0.000 1.000
#> GSM339509 2 0.000 1.000 0.000 1.000
#> GSM339510 2 0.000 1.000 0.000 1.000
#> GSM339511 1 0.000 0.999 1.000 0.000
#> GSM339512 2 0.000 1.000 0.000 1.000
#> GSM339513 1 0.000 0.999 1.000 0.000
#> GSM339514 2 0.000 1.000 0.000 1.000
#> GSM339515 1 0.000 0.999 1.000 0.000
#> GSM339516 2 0.000 1.000 0.000 1.000
#> GSM339517 2 0.000 1.000 0.000 1.000
#> GSM339518 2 0.000 1.000 0.000 1.000
#> GSM339519 1 0.000 0.999 1.000 0.000
#> GSM339520 2 0.000 1.000 0.000 1.000
#> GSM339521 2 0.000 1.000 0.000 1.000
#> GSM339522 2 0.000 1.000 0.000 1.000
#> GSM339523 2 0.000 1.000 0.000 1.000
#> GSM339524 1 0.000 0.999 1.000 0.000
#> GSM339525 1 0.000 0.999 1.000 0.000
#> GSM339526 1 0.000 0.999 1.000 0.000
#> GSM339527 1 0.000 0.999 1.000 0.000
#> GSM339528 1 0.000 0.999 1.000 0.000
#> GSM339529 2 0.000 1.000 0.000 1.000
#> GSM339530 2 0.000 1.000 0.000 1.000
#> GSM339531 2 0.000 1.000 0.000 1.000
#> GSM339532 1 0.000 0.999 1.000 0.000
#> GSM339533 1 0.000 0.999 1.000 0.000
#> GSM339534 1 0.000 0.999 1.000 0.000
#> GSM339535 2 0.000 1.000 0.000 1.000
#> GSM339536 1 0.000 0.999 1.000 0.000
#> GSM339537 2 0.000 1.000 0.000 1.000
#> GSM339538 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
#> GSM339455 3 0.0000 0.877 0.000 0.000 1.000
#> GSM339456 2 0.0000 0.773 0.000 1.000 0.000
#> GSM339457 3 0.4346 0.625 0.000 0.184 0.816
#> GSM339458 3 0.5327 0.399 0.000 0.272 0.728
#> GSM339459 2 0.5178 0.700 0.000 0.744 0.256
#> GSM339460 2 0.5098 0.702 0.000 0.752 0.248
#> GSM339461 2 0.0000 0.773 0.000 1.000 0.000
#> GSM339462 1 0.0000 0.943 1.000 0.000 0.000
#> GSM339463 3 0.1860 0.864 0.052 0.000 0.948
#> GSM339464 1 0.0000 0.943 1.000 0.000 0.000
#> GSM339465 3 0.2261 0.856 0.068 0.000 0.932
#> GSM339466 2 0.0237 0.773 0.000 0.996 0.004
#> GSM339467 2 0.0000 0.773 0.000 1.000 0.000
#> GSM339468 2 0.6140 0.625 0.000 0.596 0.404
#> GSM339469 1 0.0000 0.943 1.000 0.000 0.000
#> GSM339470 3 0.0000 0.877 0.000 0.000 1.000
#> GSM339471 1 0.0000 0.943 1.000 0.000 0.000
#> GSM339472 2 0.0000 0.773 0.000 1.000 0.000
#> GSM339473 1 0.0000 0.943 1.000 0.000 0.000
#> GSM339474 2 0.0000 0.773 0.000 1.000 0.000
#> GSM339475 3 0.0000 0.877 0.000 0.000 1.000
#> GSM339476 1 0.0000 0.943 1.000 0.000 0.000
#> GSM339477 2 0.0000 0.773 0.000 1.000 0.000
#> GSM339478 2 0.6140 0.625 0.000 0.596 0.404
#> GSM339479 3 0.2711 0.791 0.000 0.088 0.912
#> GSM339480 3 0.3941 0.678 0.000 0.156 0.844
#> GSM339481 2 0.0000 0.773 0.000 1.000 0.000
#> GSM339482 3 0.4750 0.671 0.216 0.000 0.784
#> GSM339483 1 0.0000 0.943 1.000 0.000 0.000
#> GSM339484 1 0.3941 0.824 0.844 0.000 0.156
#> GSM339485 1 0.0000 0.943 1.000 0.000 0.000
#> GSM339486 1 0.4452 0.785 0.808 0.000 0.192
#> GSM339487 2 0.6126 0.628 0.000 0.600 0.400
#> GSM339488 2 0.0000 0.773 0.000 1.000 0.000
#> GSM339489 2 0.6204 0.589 0.000 0.576 0.424
#> GSM339490 1 0.0000 0.943 1.000 0.000 0.000
#> GSM339491 3 0.0000 0.877 0.000 0.000 1.000
#> GSM339492 1 0.0000 0.943 1.000 0.000 0.000
#> GSM339493 2 0.0237 0.773 0.000 0.996 0.004
#> GSM339494 1 0.0000 0.943 1.000 0.000 0.000
#> GSM339495 2 0.0000 0.773 0.000 1.000 0.000
#> GSM339496 3 0.0000 0.877 0.000 0.000 1.000
#> GSM339497 2 0.6140 0.625 0.000 0.596 0.404
#> GSM339498 2 0.6140 0.625 0.000 0.596 0.404
#> GSM339499 2 0.6140 0.625 0.000 0.596 0.404
#> GSM339500 2 0.6140 0.625 0.000 0.596 0.404
#> GSM339501 3 0.2165 0.858 0.064 0.000 0.936
#> GSM339502 2 0.0000 0.773 0.000 1.000 0.000
#> GSM339503 3 0.0000 0.877 0.000 0.000 1.000
#> GSM339504 1 0.0000 0.943 1.000 0.000 0.000
#> GSM339505 2 0.6140 0.625 0.000 0.596 0.404
#> GSM339506 1 0.6299 0.200 0.524 0.000 0.476
#> GSM339507 1 0.3482 0.851 0.872 0.000 0.128
#> GSM339508 2 0.0000 0.773 0.000 1.000 0.000
#> GSM339509 2 0.0000 0.773 0.000 1.000 0.000
#> GSM339510 2 0.6140 0.625 0.000 0.596 0.404
#> GSM339511 1 0.0000 0.943 1.000 0.000 0.000
#> GSM339512 2 0.6126 0.626 0.000 0.600 0.400
#> GSM339513 1 0.0000 0.943 1.000 0.000 0.000
#> GSM339514 2 0.0000 0.773 0.000 1.000 0.000
#> GSM339515 1 0.0000 0.943 1.000 0.000 0.000
#> GSM339516 2 0.6140 0.625 0.000 0.596 0.404
#> GSM339517 3 0.0000 0.877 0.000 0.000 1.000
#> GSM339518 2 0.6140 0.625 0.000 0.596 0.404
#> GSM339519 3 0.2261 0.856 0.068 0.000 0.932
#> GSM339520 2 0.2625 0.756 0.000 0.916 0.084
#> GSM339521 2 0.6140 0.625 0.000 0.596 0.404
#> GSM339522 2 0.5810 0.666 0.000 0.664 0.336
#> GSM339523 2 0.0000 0.773 0.000 1.000 0.000
#> GSM339524 1 0.4842 0.744 0.776 0.000 0.224
#> GSM339525 1 0.0000 0.943 1.000 0.000 0.000
#> GSM339526 3 0.0237 0.877 0.004 0.000 0.996
#> GSM339527 3 0.4887 0.648 0.228 0.000 0.772
#> GSM339528 1 0.3412 0.854 0.876 0.000 0.124
#> GSM339529 2 0.0237 0.773 0.000 0.996 0.004
#> GSM339530 2 0.0000 0.773 0.000 1.000 0.000
#> GSM339531 2 0.6140 0.625 0.000 0.596 0.404
#> GSM339532 1 0.0000 0.943 1.000 0.000 0.000
#> GSM339533 3 0.0000 0.877 0.000 0.000 1.000
#> GSM339534 1 0.0000 0.943 1.000 0.000 0.000
#> GSM339535 2 0.0237 0.773 0.000 0.996 0.004
#> GSM339536 1 0.0000 0.943 1.000 0.000 0.000
#> GSM339537 2 0.3686 0.740 0.000 0.860 0.140
#> GSM339538 3 0.4750 0.671 0.216 0.000 0.784
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM339455 3 0.0000 0.830 0.000 0.000 1.000 0.000
#> GSM339456 2 0.4941 -0.418 0.000 0.564 0.000 0.436
#> GSM339457 3 0.3356 0.616 0.000 0.176 0.824 0.000
#> GSM339458 3 0.4933 -0.117 0.000 0.432 0.568 0.000
#> GSM339459 2 0.3528 0.801 0.000 0.808 0.192 0.000
#> GSM339460 2 0.6826 -0.135 0.000 0.484 0.100 0.416
#> GSM339461 2 0.0188 0.673 0.000 0.996 0.000 0.004
#> GSM339462 1 0.0000 0.905 1.000 0.000 0.000 0.000
#> GSM339463 3 0.2704 0.783 0.000 0.000 0.876 0.124
#> GSM339464 1 0.3610 0.784 0.800 0.000 0.000 0.200
#> GSM339465 3 0.4072 0.694 0.000 0.000 0.748 0.252
#> GSM339466 2 0.0000 0.677 0.000 1.000 0.000 0.000
#> GSM339467 4 0.4072 0.970 0.000 0.252 0.000 0.748
#> GSM339468 2 0.3907 0.807 0.000 0.768 0.232 0.000
#> GSM339469 1 0.0000 0.905 1.000 0.000 0.000 0.000
#> GSM339470 3 0.0000 0.830 0.000 0.000 1.000 0.000
#> GSM339471 1 0.0000 0.905 1.000 0.000 0.000 0.000
#> GSM339472 4 0.4072 0.970 0.000 0.252 0.000 0.748
#> GSM339473 1 0.0000 0.905 1.000 0.000 0.000 0.000
#> GSM339474 4 0.4072 0.970 0.000 0.252 0.000 0.748
#> GSM339475 3 0.0000 0.830 0.000 0.000 1.000 0.000
#> GSM339476 1 0.0000 0.905 1.000 0.000 0.000 0.000
#> GSM339477 4 0.4072 0.970 0.000 0.252 0.000 0.748
#> GSM339478 2 0.4008 0.802 0.000 0.756 0.244 0.000
#> GSM339479 3 0.2859 0.723 0.000 0.112 0.880 0.008
#> GSM339480 3 0.4477 0.330 0.000 0.312 0.688 0.000
#> GSM339481 4 0.4072 0.970 0.000 0.252 0.000 0.748
#> GSM339482 3 0.4008 0.698 0.000 0.000 0.756 0.244
#> GSM339483 1 0.0000 0.905 1.000 0.000 0.000 0.000
#> GSM339484 1 0.6873 0.572 0.588 0.000 0.160 0.252
#> GSM339485 1 0.0000 0.905 1.000 0.000 0.000 0.000
#> GSM339486 1 0.7145 0.520 0.556 0.000 0.192 0.252
#> GSM339487 2 0.3873 0.807 0.000 0.772 0.228 0.000
#> GSM339488 4 0.4072 0.970 0.000 0.252 0.000 0.748
#> GSM339489 2 0.4103 0.792 0.000 0.744 0.256 0.000
#> GSM339490 1 0.0000 0.905 1.000 0.000 0.000 0.000
#> GSM339491 3 0.0000 0.830 0.000 0.000 1.000 0.000
#> GSM339492 1 0.0000 0.905 1.000 0.000 0.000 0.000
#> GSM339493 2 0.0000 0.677 0.000 1.000 0.000 0.000
#> GSM339494 1 0.0000 0.905 1.000 0.000 0.000 0.000
#> GSM339495 4 0.4072 0.970 0.000 0.252 0.000 0.748
#> GSM339496 3 0.0000 0.830 0.000 0.000 1.000 0.000
#> GSM339497 2 0.4008 0.802 0.000 0.756 0.244 0.000
#> GSM339498 2 0.4008 0.802 0.000 0.756 0.244 0.000
#> GSM339499 2 0.4193 0.784 0.000 0.732 0.268 0.000
#> GSM339500 2 0.4008 0.802 0.000 0.756 0.244 0.000
#> GSM339501 3 0.1474 0.792 0.000 0.052 0.948 0.000
#> GSM339502 4 0.4072 0.970 0.000 0.252 0.000 0.748
#> GSM339503 3 0.0000 0.830 0.000 0.000 1.000 0.000
#> GSM339504 1 0.0000 0.905 1.000 0.000 0.000 0.000
#> GSM339505 2 0.4222 0.780 0.000 0.728 0.272 0.000
#> GSM339506 3 0.7436 0.328 0.236 0.000 0.512 0.252
#> GSM339507 1 0.6587 0.612 0.616 0.000 0.132 0.252
#> GSM339508 2 0.3801 0.285 0.000 0.780 0.000 0.220
#> GSM339509 4 0.4072 0.970 0.000 0.252 0.000 0.748
#> GSM339510 2 0.3907 0.807 0.000 0.768 0.232 0.000
#> GSM339511 1 0.0000 0.905 1.000 0.000 0.000 0.000
#> GSM339512 2 0.4008 0.802 0.000 0.756 0.244 0.000
#> GSM339513 1 0.0000 0.905 1.000 0.000 0.000 0.000
#> GSM339514 4 0.4996 0.601 0.000 0.484 0.000 0.516
#> GSM339515 1 0.0000 0.905 1.000 0.000 0.000 0.000
#> GSM339516 2 0.3907 0.807 0.000 0.768 0.232 0.000
#> GSM339517 3 0.0000 0.830 0.000 0.000 1.000 0.000
#> GSM339518 2 0.4008 0.802 0.000 0.756 0.244 0.000
#> GSM339519 3 0.0000 0.830 0.000 0.000 1.000 0.000
#> GSM339520 2 0.6141 0.178 0.000 0.616 0.072 0.312
#> GSM339521 2 0.4008 0.802 0.000 0.756 0.244 0.000
#> GSM339522 2 0.3649 0.805 0.000 0.796 0.204 0.000
#> GSM339523 4 0.4072 0.970 0.000 0.252 0.000 0.748
#> GSM339524 1 0.7390 0.451 0.520 0.000 0.228 0.252
#> GSM339525 1 0.0000 0.905 1.000 0.000 0.000 0.000
#> GSM339526 3 0.0469 0.827 0.000 0.000 0.988 0.012
#> GSM339527 3 0.4008 0.698 0.000 0.000 0.756 0.244
#> GSM339528 1 0.6542 0.617 0.620 0.000 0.128 0.252
#> GSM339529 2 0.0000 0.677 0.000 1.000 0.000 0.000
#> GSM339530 2 0.1389 0.620 0.000 0.952 0.000 0.048
#> GSM339531 2 0.3907 0.807 0.000 0.768 0.232 0.000
#> GSM339532 1 0.0000 0.905 1.000 0.000 0.000 0.000
#> GSM339533 3 0.0000 0.830 0.000 0.000 1.000 0.000
#> GSM339534 1 0.0000 0.905 1.000 0.000 0.000 0.000
#> GSM339535 2 0.0000 0.677 0.000 1.000 0.000 0.000
#> GSM339536 1 0.0000 0.905 1.000 0.000 0.000 0.000
#> GSM339537 2 0.2647 0.774 0.000 0.880 0.120 0.000
#> GSM339538 3 0.4008 0.698 0.000 0.000 0.756 0.244
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM339455 3 0.0000 0.9267 0.000 0.000 1.000 0.000 0.000
#> GSM339456 2 0.3966 0.4677 0.000 0.664 0.000 0.000 0.336
#> GSM339457 3 0.1364 0.8890 0.012 0.000 0.952 0.000 0.036
#> GSM339458 5 0.4063 0.5986 0.012 0.000 0.280 0.000 0.708
#> GSM339459 5 0.0000 0.9400 0.000 0.000 0.000 0.000 1.000
#> GSM339460 2 0.4658 0.0523 0.012 0.504 0.000 0.000 0.484
#> GSM339461 5 0.0880 0.9284 0.000 0.032 0.000 0.000 0.968
#> GSM339462 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000
#> GSM339463 1 0.3074 0.6606 0.804 0.000 0.196 0.000 0.000
#> GSM339464 1 0.4297 0.1095 0.528 0.000 0.000 0.472 0.000
#> GSM339465 1 0.0404 0.8187 0.988 0.000 0.012 0.000 0.000
#> GSM339466 5 0.0000 0.9400 0.000 0.000 0.000 0.000 1.000
#> GSM339467 2 0.0000 0.8689 0.000 1.000 0.000 0.000 0.000
#> GSM339468 5 0.0566 0.9387 0.012 0.000 0.004 0.000 0.984
#> GSM339469 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000
#> GSM339470 3 0.0000 0.9267 0.000 0.000 1.000 0.000 0.000
#> GSM339471 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000
#> GSM339472 2 0.0000 0.8689 0.000 1.000 0.000 0.000 0.000
#> GSM339473 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000
#> GSM339474 2 0.0000 0.8689 0.000 1.000 0.000 0.000 0.000
#> GSM339475 3 0.0000 0.9267 0.000 0.000 1.000 0.000 0.000
#> GSM339476 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000
#> GSM339477 2 0.0000 0.8689 0.000 1.000 0.000 0.000 0.000
#> GSM339478 5 0.1281 0.9328 0.012 0.000 0.032 0.000 0.956
#> GSM339479 3 0.4876 0.2518 0.396 0.000 0.576 0.000 0.028
#> GSM339480 3 0.3659 0.6485 0.012 0.000 0.768 0.000 0.220
#> GSM339481 2 0.0000 0.8689 0.000 1.000 0.000 0.000 0.000
#> GSM339482 1 0.4287 0.2007 0.540 0.000 0.460 0.000 0.000
#> GSM339483 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000
#> GSM339484 1 0.0404 0.8269 0.988 0.000 0.000 0.012 0.000
#> GSM339485 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000
#> GSM339486 1 0.0404 0.8269 0.988 0.000 0.000 0.012 0.000
#> GSM339487 5 0.0000 0.9400 0.000 0.000 0.000 0.000 1.000
#> GSM339488 2 0.0000 0.8689 0.000 1.000 0.000 0.000 0.000
#> GSM339489 5 0.0912 0.9345 0.012 0.000 0.016 0.000 0.972
#> GSM339490 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000
#> GSM339491 3 0.0162 0.9244 0.004 0.000 0.996 0.000 0.000
#> GSM339492 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000
#> GSM339493 5 0.0000 0.9400 0.000 0.000 0.000 0.000 1.000
#> GSM339494 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000
#> GSM339495 2 0.0000 0.8689 0.000 1.000 0.000 0.000 0.000
#> GSM339496 3 0.0000 0.9267 0.000 0.000 1.000 0.000 0.000
#> GSM339497 5 0.1281 0.9328 0.012 0.000 0.032 0.000 0.956
#> GSM339498 5 0.0510 0.9398 0.000 0.000 0.016 0.000 0.984
#> GSM339499 5 0.0794 0.9359 0.000 0.000 0.028 0.000 0.972
#> GSM339500 5 0.0880 0.9356 0.000 0.000 0.032 0.000 0.968
#> GSM339501 3 0.1608 0.8607 0.000 0.000 0.928 0.000 0.072
#> GSM339502 2 0.0000 0.8689 0.000 1.000 0.000 0.000 0.000
#> GSM339503 3 0.0000 0.9267 0.000 0.000 1.000 0.000 0.000
#> GSM339504 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000
#> GSM339505 5 0.0880 0.9352 0.000 0.000 0.032 0.000 0.968
#> GSM339506 1 0.0404 0.8269 0.988 0.000 0.000 0.012 0.000
#> GSM339507 1 0.0404 0.8269 0.988 0.000 0.000 0.012 0.000
#> GSM339508 5 0.3707 0.5685 0.000 0.284 0.000 0.000 0.716
#> GSM339509 2 0.0000 0.8689 0.000 1.000 0.000 0.000 0.000
#> GSM339510 5 0.0693 0.9392 0.012 0.000 0.008 0.000 0.980
#> GSM339511 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000
#> GSM339512 5 0.0794 0.9364 0.000 0.000 0.028 0.000 0.972
#> GSM339513 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000
#> GSM339514 2 0.3876 0.5485 0.000 0.684 0.000 0.000 0.316
#> GSM339515 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000
#> GSM339516 5 0.0566 0.9387 0.012 0.000 0.004 0.000 0.984
#> GSM339517 3 0.0000 0.9267 0.000 0.000 1.000 0.000 0.000
#> GSM339518 5 0.1082 0.9359 0.008 0.000 0.028 0.000 0.964
#> GSM339519 3 0.0000 0.9267 0.000 0.000 1.000 0.000 0.000
#> GSM339520 5 0.4464 0.2191 0.000 0.408 0.008 0.000 0.584
#> GSM339521 5 0.0880 0.9356 0.000 0.000 0.032 0.000 0.968
#> GSM339522 5 0.0000 0.9400 0.000 0.000 0.000 0.000 1.000
#> GSM339523 2 0.0000 0.8689 0.000 1.000 0.000 0.000 0.000
#> GSM339524 1 0.0404 0.8269 0.988 0.000 0.000 0.012 0.000
#> GSM339525 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000
#> GSM339526 3 0.0000 0.9267 0.000 0.000 1.000 0.000 0.000
#> GSM339527 1 0.4227 0.3014 0.580 0.000 0.420 0.000 0.000
#> GSM339528 1 0.0404 0.8269 0.988 0.000 0.000 0.012 0.000
#> GSM339529 5 0.0000 0.9400 0.000 0.000 0.000 0.000 1.000
#> GSM339530 5 0.1168 0.9197 0.000 0.032 0.008 0.000 0.960
#> GSM339531 5 0.0404 0.9388 0.012 0.000 0.000 0.000 0.988
#> GSM339532 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000
#> GSM339533 3 0.0000 0.9267 0.000 0.000 1.000 0.000 0.000
#> GSM339534 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000
#> GSM339535 5 0.0000 0.9400 0.000 0.000 0.000 0.000 1.000
#> GSM339536 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000
#> GSM339537 5 0.0000 0.9400 0.000 0.000 0.000 0.000 1.000
#> GSM339538 3 0.0880 0.8956 0.032 0.000 0.968 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM339455 3 0.1910 0.828 0.000 0.000 0.892 0.000 0.108 0.000
#> GSM339456 2 0.3126 0.633 0.000 0.752 0.000 0.000 0.000 0.248
#> GSM339457 3 0.4561 0.412 0.000 0.000 0.568 0.000 0.392 0.040
#> GSM339458 5 0.3349 0.777 0.000 0.000 0.008 0.000 0.748 0.244
#> GSM339459 6 0.0260 0.837 0.000 0.000 0.000 0.000 0.008 0.992
#> GSM339460 5 0.4165 0.726 0.000 0.100 0.000 0.000 0.740 0.160
#> GSM339461 6 0.0865 0.836 0.000 0.036 0.000 0.000 0.000 0.964
#> GSM339462 4 0.0000 0.991 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM339463 1 0.2527 0.693 0.832 0.000 0.168 0.000 0.000 0.000
#> GSM339464 1 0.3851 0.139 0.540 0.000 0.000 0.460 0.000 0.000
#> GSM339465 1 0.0000 0.831 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM339466 6 0.0713 0.837 0.000 0.000 0.000 0.000 0.028 0.972
#> GSM339467 2 0.0000 0.929 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM339468 5 0.3337 0.778 0.000 0.000 0.004 0.000 0.736 0.260
#> GSM339469 4 0.0000 0.991 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM339470 3 0.0146 0.938 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM339471 4 0.0790 0.977 0.000 0.000 0.000 0.968 0.032 0.000
#> GSM339472 2 0.0000 0.929 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM339473 4 0.0865 0.976 0.000 0.000 0.000 0.964 0.036 0.000
#> GSM339474 2 0.0000 0.929 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM339475 3 0.0000 0.940 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM339476 4 0.0000 0.991 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM339477 2 0.0000 0.929 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM339478 5 0.3448 0.370 0.000 0.000 0.004 0.000 0.716 0.280
#> GSM339479 5 0.4447 0.620 0.096 0.000 0.148 0.000 0.740 0.016
#> GSM339480 5 0.5999 0.509 0.000 0.000 0.312 0.000 0.432 0.256
#> GSM339481 2 0.0000 0.929 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM339482 1 0.3843 0.237 0.548 0.000 0.452 0.000 0.000 0.000
#> GSM339483 4 0.0000 0.991 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM339484 1 0.0000 0.831 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM339485 4 0.0000 0.991 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM339486 1 0.0000 0.831 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM339487 6 0.0713 0.837 0.000 0.000 0.000 0.000 0.028 0.972
#> GSM339488 2 0.0000 0.929 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM339489 5 0.3337 0.778 0.000 0.000 0.004 0.000 0.736 0.260
#> GSM339490 4 0.0000 0.991 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM339491 5 0.3847 0.163 0.000 0.000 0.456 0.000 0.544 0.000
#> GSM339492 4 0.0000 0.991 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM339493 6 0.0713 0.838 0.000 0.028 0.000 0.000 0.000 0.972
#> GSM339494 4 0.0865 0.976 0.000 0.000 0.000 0.964 0.036 0.000
#> GSM339495 2 0.0000 0.929 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM339496 3 0.0000 0.940 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM339497 5 0.3337 0.778 0.000 0.000 0.004 0.000 0.736 0.260
#> GSM339498 5 0.3607 0.210 0.000 0.000 0.000 0.000 0.652 0.348
#> GSM339499 6 0.2996 0.691 0.000 0.000 0.000 0.000 0.228 0.772
#> GSM339500 6 0.0508 0.836 0.000 0.000 0.004 0.000 0.012 0.984
#> GSM339501 5 0.5504 0.646 0.000 0.000 0.232 0.000 0.564 0.204
#> GSM339502 2 0.0000 0.929 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM339503 3 0.0000 0.940 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM339504 4 0.0000 0.991 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM339505 6 0.2883 0.704 0.000 0.000 0.000 0.000 0.212 0.788
#> GSM339506 1 0.0000 0.831 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM339507 1 0.0000 0.831 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM339508 6 0.3647 0.405 0.000 0.360 0.000 0.000 0.000 0.640
#> GSM339509 2 0.0000 0.929 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM339510 5 0.3337 0.778 0.000 0.000 0.004 0.000 0.736 0.260
#> GSM339511 4 0.0000 0.991 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM339512 6 0.0858 0.839 0.000 0.028 0.000 0.000 0.004 0.968
#> GSM339513 4 0.0000 0.991 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM339514 2 0.3727 0.302 0.000 0.612 0.000 0.000 0.000 0.388
#> GSM339515 4 0.0865 0.976 0.000 0.000 0.000 0.964 0.036 0.000
#> GSM339516 5 0.3337 0.778 0.000 0.000 0.004 0.000 0.736 0.260
#> GSM339517 3 0.0000 0.940 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM339518 6 0.2300 0.696 0.000 0.000 0.000 0.000 0.144 0.856
#> GSM339519 3 0.0000 0.940 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM339520 6 0.5224 0.543 0.000 0.164 0.000 0.000 0.228 0.608
#> GSM339521 6 0.1053 0.840 0.000 0.012 0.004 0.000 0.020 0.964
#> GSM339522 6 0.1075 0.824 0.000 0.000 0.000 0.000 0.048 0.952
#> GSM339523 2 0.0000 0.929 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM339524 1 0.0000 0.831 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM339525 4 0.0000 0.991 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM339526 3 0.0000 0.940 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM339527 1 0.3810 0.295 0.572 0.000 0.428 0.000 0.000 0.000
#> GSM339528 1 0.0000 0.831 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM339529 6 0.2416 0.677 0.000 0.000 0.000 0.000 0.156 0.844
#> GSM339530 6 0.2969 0.694 0.000 0.000 0.000 0.000 0.224 0.776
#> GSM339531 5 0.3221 0.775 0.000 0.000 0.000 0.000 0.736 0.264
#> GSM339532 4 0.0000 0.991 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM339533 3 0.0146 0.938 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM339534 4 0.0000 0.991 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM339535 6 0.0713 0.837 0.000 0.000 0.000 0.000 0.028 0.972
#> GSM339536 4 0.0865 0.976 0.000 0.000 0.000 0.964 0.036 0.000
#> GSM339537 6 0.0713 0.837 0.000 0.000 0.000 0.000 0.028 0.972
#> GSM339538 3 0.0146 0.936 0.004 0.000 0.996 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 protocol(p) agent(p) individual(p) k
#> ATC:pam 84 1.000 0.421 5.23e-03 2
#> ATC:pam 82 0.527 0.839 1.28e-03 3
#> ATC:pam 76 0.251 0.654 6.85e-04 4
#> ATC:pam 77 0.495 0.861 6.55e-06 5
#> ATC:pam 75 0.320 0.430 1.33e-06 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 15497 rows and 84 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 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 0.979 0.987 0.4366 0.567 0.567
#> 3 3 0.781 0.876 0.929 0.3965 0.715 0.536
#> 4 4 0.934 0.934 0.967 0.1399 0.784 0.515
#> 5 5 0.807 0.755 0.878 0.1175 0.812 0.484
#> 6 6 0.730 0.712 0.823 0.0241 0.958 0.835
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
#> GSM339455 2 0.1843 0.968 0.028 0.972
#> GSM339456 2 0.0000 0.985 0.000 1.000
#> GSM339457 2 0.0000 0.985 0.000 1.000
#> GSM339458 2 0.0000 0.985 0.000 1.000
#> GSM339459 2 0.0000 0.985 0.000 1.000
#> GSM339460 2 0.0000 0.985 0.000 1.000
#> GSM339461 2 0.0000 0.985 0.000 1.000
#> GSM339462 1 0.0000 0.993 1.000 0.000
#> GSM339463 2 0.3274 0.947 0.060 0.940
#> GSM339464 1 0.1184 0.989 0.984 0.016
#> GSM339465 2 0.5294 0.885 0.120 0.880
#> GSM339466 2 0.0000 0.985 0.000 1.000
#> GSM339467 2 0.0000 0.985 0.000 1.000
#> GSM339468 2 0.0000 0.985 0.000 1.000
#> GSM339469 1 0.0000 0.993 1.000 0.000
#> GSM339470 2 0.0000 0.985 0.000 1.000
#> GSM339471 1 0.0000 0.993 1.000 0.000
#> GSM339472 2 0.0000 0.985 0.000 1.000
#> GSM339473 1 0.0000 0.993 1.000 0.000
#> GSM339474 2 0.0000 0.985 0.000 1.000
#> GSM339475 2 0.3114 0.950 0.056 0.944
#> GSM339476 1 0.1184 0.989 0.984 0.016
#> GSM339477 2 0.0000 0.985 0.000 1.000
#> GSM339478 2 0.0000 0.985 0.000 1.000
#> GSM339479 2 0.1843 0.968 0.028 0.972
#> GSM339480 2 0.0000 0.985 0.000 1.000
#> GSM339481 2 0.0000 0.985 0.000 1.000
#> GSM339482 2 0.3274 0.946 0.060 0.940
#> GSM339483 1 0.0000 0.993 1.000 0.000
#> GSM339484 1 0.1184 0.989 0.984 0.016
#> GSM339485 1 0.1184 0.989 0.984 0.016
#> GSM339486 1 0.1184 0.989 0.984 0.016
#> GSM339487 2 0.0000 0.985 0.000 1.000
#> GSM339488 2 0.0000 0.985 0.000 1.000
#> GSM339489 2 0.0000 0.985 0.000 1.000
#> GSM339490 1 0.0000 0.993 1.000 0.000
#> GSM339491 2 0.0000 0.985 0.000 1.000
#> GSM339492 1 0.0000 0.993 1.000 0.000
#> GSM339493 2 0.0000 0.985 0.000 1.000
#> GSM339494 1 0.0000 0.993 1.000 0.000
#> GSM339495 2 0.0000 0.985 0.000 1.000
#> GSM339496 2 0.3114 0.950 0.056 0.944
#> GSM339497 2 0.0000 0.985 0.000 1.000
#> GSM339498 2 0.0000 0.985 0.000 1.000
#> GSM339499 2 0.0000 0.985 0.000 1.000
#> GSM339500 2 0.0000 0.985 0.000 1.000
#> GSM339501 2 0.6148 0.844 0.152 0.848
#> GSM339502 2 0.0000 0.985 0.000 1.000
#> GSM339503 2 0.3114 0.950 0.056 0.944
#> GSM339504 1 0.0000 0.993 1.000 0.000
#> GSM339505 2 0.0000 0.985 0.000 1.000
#> GSM339506 1 0.1184 0.989 0.984 0.016
#> GSM339507 1 0.1184 0.989 0.984 0.016
#> GSM339508 2 0.0000 0.985 0.000 1.000
#> GSM339509 2 0.0000 0.985 0.000 1.000
#> GSM339510 2 0.0000 0.985 0.000 1.000
#> GSM339511 1 0.0000 0.993 1.000 0.000
#> GSM339512 2 0.0000 0.985 0.000 1.000
#> GSM339513 1 0.0000 0.993 1.000 0.000
#> GSM339514 2 0.0000 0.985 0.000 1.000
#> GSM339515 1 0.0000 0.993 1.000 0.000
#> GSM339516 2 0.0000 0.985 0.000 1.000
#> GSM339517 2 0.3114 0.950 0.056 0.944
#> GSM339518 2 0.0000 0.985 0.000 1.000
#> GSM339519 2 0.3274 0.946 0.060 0.940
#> GSM339520 2 0.0000 0.985 0.000 1.000
#> GSM339521 2 0.0000 0.985 0.000 1.000
#> GSM339522 2 0.0000 0.985 0.000 1.000
#> GSM339523 2 0.0000 0.985 0.000 1.000
#> GSM339524 1 0.1184 0.989 0.984 0.016
#> GSM339525 1 0.0000 0.993 1.000 0.000
#> GSM339526 2 0.3114 0.950 0.056 0.944
#> GSM339527 1 0.1184 0.989 0.984 0.016
#> GSM339528 1 0.1184 0.989 0.984 0.016
#> GSM339529 2 0.0000 0.985 0.000 1.000
#> GSM339530 2 0.0000 0.985 0.000 1.000
#> GSM339531 2 0.0000 0.985 0.000 1.000
#> GSM339532 1 0.0000 0.993 1.000 0.000
#> GSM339533 2 0.2236 0.963 0.036 0.964
#> GSM339534 1 0.0938 0.988 0.988 0.012
#> GSM339535 2 0.0000 0.985 0.000 1.000
#> GSM339536 1 0.0000 0.993 1.000 0.000
#> GSM339537 2 0.0000 0.985 0.000 1.000
#> GSM339538 2 0.3274 0.946 0.060 0.940
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM339455 3 0.5621 0.616 0.000 0.308 0.692
#> GSM339456 2 0.0237 0.980 0.000 0.996 0.004
#> GSM339457 2 0.2261 0.930 0.000 0.932 0.068
#> GSM339458 2 0.0237 0.980 0.000 0.996 0.004
#> GSM339459 2 0.0237 0.980 0.000 0.996 0.004
#> GSM339460 3 0.7839 0.517 0.060 0.380 0.560
#> GSM339461 2 0.0237 0.980 0.000 0.996 0.004
#> GSM339462 1 0.0000 0.973 1.000 0.000 0.000
#> GSM339463 3 0.0424 0.768 0.000 0.008 0.992
#> GSM339464 3 0.3375 0.763 0.100 0.008 0.892
#> GSM339465 3 0.0424 0.768 0.000 0.008 0.992
#> GSM339466 2 0.0424 0.974 0.000 0.992 0.008
#> GSM339467 2 0.0237 0.980 0.000 0.996 0.004
#> GSM339468 2 0.0237 0.980 0.000 0.996 0.004
#> GSM339469 1 0.0000 0.973 1.000 0.000 0.000
#> GSM339470 2 0.4002 0.816 0.000 0.840 0.160
#> GSM339471 1 0.0000 0.973 1.000 0.000 0.000
#> GSM339472 2 0.0237 0.980 0.000 0.996 0.004
#> GSM339473 1 0.0000 0.973 1.000 0.000 0.000
#> GSM339474 2 0.0237 0.980 0.000 0.996 0.004
#> GSM339475 3 0.4121 0.710 0.000 0.168 0.832
#> GSM339476 3 0.5541 0.641 0.252 0.008 0.740
#> GSM339477 2 0.0000 0.979 0.000 1.000 0.000
#> GSM339478 2 0.0237 0.980 0.000 0.996 0.004
#> GSM339479 3 0.6008 0.553 0.000 0.372 0.628
#> GSM339480 2 0.2261 0.930 0.000 0.932 0.068
#> GSM339481 2 0.0424 0.974 0.000 0.992 0.008
#> GSM339482 3 0.0424 0.768 0.000 0.008 0.992
#> GSM339483 1 0.0000 0.973 1.000 0.000 0.000
#> GSM339484 3 0.5247 0.674 0.224 0.008 0.768
#> GSM339485 3 0.3375 0.763 0.100 0.008 0.892
#> GSM339486 3 0.3375 0.763 0.100 0.008 0.892
#> GSM339487 2 0.0237 0.980 0.000 0.996 0.004
#> GSM339488 2 0.0237 0.977 0.000 0.996 0.004
#> GSM339489 2 0.0237 0.980 0.000 0.996 0.004
#> GSM339490 1 0.0000 0.973 1.000 0.000 0.000
#> GSM339491 2 0.1031 0.968 0.000 0.976 0.024
#> GSM339492 1 0.0000 0.973 1.000 0.000 0.000
#> GSM339493 2 0.0424 0.974 0.000 0.992 0.008
#> GSM339494 1 0.0000 0.973 1.000 0.000 0.000
#> GSM339495 2 0.0237 0.980 0.000 0.996 0.004
#> GSM339496 3 0.5291 0.657 0.000 0.268 0.732
#> GSM339497 2 0.0237 0.980 0.000 0.996 0.004
#> GSM339498 2 0.0592 0.976 0.000 0.988 0.012
#> GSM339499 2 0.2261 0.930 0.000 0.932 0.068
#> GSM339500 2 0.0237 0.980 0.000 0.996 0.004
#> GSM339501 3 0.7860 0.588 0.228 0.116 0.656
#> GSM339502 2 0.0424 0.974 0.000 0.992 0.008
#> GSM339503 3 0.5591 0.613 0.000 0.304 0.696
#> GSM339504 1 0.0000 0.973 1.000 0.000 0.000
#> GSM339505 2 0.2261 0.930 0.000 0.932 0.068
#> GSM339506 3 0.3375 0.763 0.100 0.008 0.892
#> GSM339507 3 0.3375 0.763 0.100 0.008 0.892
#> GSM339508 2 0.0000 0.979 0.000 1.000 0.000
#> GSM339509 2 0.0000 0.979 0.000 1.000 0.000
#> GSM339510 2 0.0237 0.980 0.000 0.996 0.004
#> GSM339511 1 0.4002 0.793 0.840 0.000 0.160
#> GSM339512 2 0.0237 0.980 0.000 0.996 0.004
#> GSM339513 1 0.0000 0.973 1.000 0.000 0.000
#> GSM339514 2 0.0424 0.974 0.000 0.992 0.008
#> GSM339515 1 0.0000 0.973 1.000 0.000 0.000
#> GSM339516 3 0.7839 0.517 0.060 0.380 0.560
#> GSM339517 3 0.4235 0.707 0.000 0.176 0.824
#> GSM339518 2 0.0237 0.980 0.000 0.996 0.004
#> GSM339519 3 0.4291 0.707 0.152 0.008 0.840
#> GSM339520 2 0.2066 0.938 0.000 0.940 0.060
#> GSM339521 2 0.0237 0.980 0.000 0.996 0.004
#> GSM339522 2 0.0000 0.979 0.000 1.000 0.000
#> GSM339523 2 0.0424 0.974 0.000 0.992 0.008
#> GSM339524 3 0.4164 0.738 0.144 0.008 0.848
#> GSM339525 1 0.0000 0.973 1.000 0.000 0.000
#> GSM339526 3 0.0424 0.768 0.000 0.008 0.992
#> GSM339527 3 0.3375 0.763 0.100 0.008 0.892
#> GSM339528 3 0.3375 0.763 0.100 0.008 0.892
#> GSM339529 2 0.0237 0.980 0.000 0.996 0.004
#> GSM339530 2 0.3267 0.875 0.000 0.884 0.116
#> GSM339531 2 0.0237 0.980 0.000 0.996 0.004
#> GSM339532 1 0.0000 0.973 1.000 0.000 0.000
#> GSM339533 3 0.6154 0.414 0.000 0.408 0.592
#> GSM339534 1 0.4399 0.750 0.812 0.000 0.188
#> GSM339535 2 0.0424 0.974 0.000 0.992 0.008
#> GSM339536 1 0.0000 0.973 1.000 0.000 0.000
#> GSM339537 2 0.0237 0.980 0.000 0.996 0.004
#> GSM339538 3 0.0424 0.768 0.000 0.008 0.992
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM339455 3 0.1940 0.874 0.000 0.076 0.924 0.000
#> GSM339456 2 0.0469 0.977 0.000 0.988 0.000 0.012
#> GSM339457 3 0.1557 0.881 0.000 0.056 0.944 0.000
#> GSM339458 2 0.0000 0.979 0.000 1.000 0.000 0.000
#> GSM339459 3 0.3907 0.754 0.000 0.232 0.768 0.000
#> GSM339460 2 0.0000 0.979 0.000 1.000 0.000 0.000
#> GSM339461 2 0.0000 0.979 0.000 1.000 0.000 0.000
#> GSM339462 1 0.0000 0.980 1.000 0.000 0.000 0.000
#> GSM339463 4 0.3528 0.791 0.000 0.000 0.192 0.808
#> GSM339464 4 0.0469 0.976 0.012 0.000 0.000 0.988
#> GSM339465 4 0.0469 0.965 0.000 0.000 0.012 0.988
#> GSM339466 2 0.0000 0.979 0.000 1.000 0.000 0.000
#> GSM339467 2 0.0469 0.977 0.000 0.988 0.000 0.012
#> GSM339468 2 0.0000 0.979 0.000 1.000 0.000 0.000
#> GSM339469 1 0.0000 0.980 1.000 0.000 0.000 0.000
#> GSM339470 2 0.3942 0.657 0.000 0.764 0.236 0.000
#> GSM339471 1 0.0000 0.980 1.000 0.000 0.000 0.000
#> GSM339472 2 0.0469 0.977 0.000 0.988 0.000 0.012
#> GSM339473 1 0.0000 0.980 1.000 0.000 0.000 0.000
#> GSM339474 2 0.0469 0.977 0.000 0.988 0.000 0.012
#> GSM339475 3 0.0000 0.884 0.000 0.000 1.000 0.000
#> GSM339476 1 0.0000 0.980 1.000 0.000 0.000 0.000
#> GSM339477 2 0.0469 0.977 0.000 0.988 0.000 0.012
#> GSM339478 2 0.0000 0.979 0.000 1.000 0.000 0.000
#> GSM339479 2 0.4560 0.571 0.000 0.700 0.004 0.296
#> GSM339480 3 0.3907 0.755 0.000 0.232 0.768 0.000
#> GSM339481 2 0.0469 0.977 0.000 0.988 0.000 0.012
#> GSM339482 3 0.0000 0.884 0.000 0.000 1.000 0.000
#> GSM339483 1 0.0000 0.980 1.000 0.000 0.000 0.000
#> GSM339484 1 0.0000 0.980 1.000 0.000 0.000 0.000
#> GSM339485 4 0.0469 0.976 0.012 0.000 0.000 0.988
#> GSM339486 4 0.0469 0.976 0.012 0.000 0.000 0.988
#> GSM339487 2 0.0000 0.979 0.000 1.000 0.000 0.000
#> GSM339488 2 0.0469 0.977 0.000 0.988 0.000 0.012
#> GSM339489 2 0.0000 0.979 0.000 1.000 0.000 0.000
#> GSM339490 1 0.0000 0.980 1.000 0.000 0.000 0.000
#> GSM339491 2 0.0336 0.974 0.000 0.992 0.008 0.000
#> GSM339492 1 0.0000 0.980 1.000 0.000 0.000 0.000
#> GSM339493 2 0.0000 0.979 0.000 1.000 0.000 0.000
#> GSM339494 1 0.0000 0.980 1.000 0.000 0.000 0.000
#> GSM339495 2 0.0469 0.977 0.000 0.988 0.000 0.012
#> GSM339496 3 0.0000 0.884 0.000 0.000 1.000 0.000
#> GSM339497 2 0.0000 0.979 0.000 1.000 0.000 0.000
#> GSM339498 3 0.4134 0.717 0.000 0.260 0.740 0.000
#> GSM339499 3 0.2973 0.840 0.000 0.144 0.856 0.000
#> GSM339500 2 0.0000 0.979 0.000 1.000 0.000 0.000
#> GSM339501 1 0.5966 0.496 0.648 0.072 0.280 0.000
#> GSM339502 2 0.0469 0.977 0.000 0.988 0.000 0.012
#> GSM339503 3 0.0000 0.884 0.000 0.000 1.000 0.000
#> GSM339504 1 0.0000 0.980 1.000 0.000 0.000 0.000
#> GSM339505 3 0.1940 0.876 0.000 0.076 0.924 0.000
#> GSM339506 4 0.0469 0.976 0.012 0.000 0.000 0.988
#> GSM339507 4 0.0469 0.976 0.012 0.000 0.000 0.988
#> GSM339508 2 0.0469 0.977 0.000 0.988 0.000 0.012
#> GSM339509 2 0.0469 0.977 0.000 0.988 0.000 0.012
#> GSM339510 2 0.0000 0.979 0.000 1.000 0.000 0.000
#> GSM339511 1 0.0000 0.980 1.000 0.000 0.000 0.000
#> GSM339512 2 0.0000 0.979 0.000 1.000 0.000 0.000
#> GSM339513 1 0.0000 0.980 1.000 0.000 0.000 0.000
#> GSM339514 2 0.0336 0.978 0.000 0.992 0.000 0.008
#> GSM339515 1 0.0000 0.980 1.000 0.000 0.000 0.000
#> GSM339516 2 0.0000 0.979 0.000 1.000 0.000 0.000
#> GSM339517 3 0.0000 0.884 0.000 0.000 1.000 0.000
#> GSM339518 2 0.0000 0.979 0.000 1.000 0.000 0.000
#> GSM339519 3 0.0000 0.884 0.000 0.000 1.000 0.000
#> GSM339520 3 0.3219 0.824 0.000 0.164 0.836 0.000
#> GSM339521 2 0.0000 0.979 0.000 1.000 0.000 0.000
#> GSM339522 2 0.0000 0.979 0.000 1.000 0.000 0.000
#> GSM339523 2 0.0469 0.977 0.000 0.988 0.000 0.012
#> GSM339524 1 0.0188 0.976 0.996 0.000 0.000 0.004
#> GSM339525 1 0.0000 0.980 1.000 0.000 0.000 0.000
#> GSM339526 3 0.0000 0.884 0.000 0.000 1.000 0.000
#> GSM339527 4 0.0469 0.976 0.012 0.000 0.000 0.988
#> GSM339528 4 0.0469 0.976 0.012 0.000 0.000 0.988
#> GSM339529 2 0.0336 0.978 0.000 0.992 0.000 0.008
#> GSM339530 3 0.2868 0.846 0.000 0.136 0.864 0.000
#> GSM339531 2 0.0000 0.979 0.000 1.000 0.000 0.000
#> GSM339532 1 0.0000 0.980 1.000 0.000 0.000 0.000
#> GSM339533 3 0.0000 0.884 0.000 0.000 1.000 0.000
#> GSM339534 1 0.0000 0.980 1.000 0.000 0.000 0.000
#> GSM339535 2 0.0000 0.979 0.000 1.000 0.000 0.000
#> GSM339536 1 0.0000 0.980 1.000 0.000 0.000 0.000
#> GSM339537 2 0.0336 0.978 0.000 0.992 0.000 0.008
#> GSM339538 3 0.0000 0.884 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
#> GSM339455 5 0.4242 -0.0261 0.000 0.000 0.428 0.000 0.572
#> GSM339456 2 0.0000 0.9500 0.000 1.000 0.000 0.000 0.000
#> GSM339457 5 0.5791 0.5072 0.000 0.052 0.388 0.020 0.540
#> GSM339458 5 0.0000 0.7418 0.000 0.000 0.000 0.000 1.000
#> GSM339459 5 0.5791 0.5072 0.000 0.052 0.388 0.020 0.540
#> GSM339460 5 0.4262 0.3976 0.000 0.440 0.000 0.000 0.560
#> GSM339461 5 0.1671 0.7352 0.000 0.076 0.000 0.000 0.924
#> GSM339462 1 0.0000 0.9292 1.000 0.000 0.000 0.000 0.000
#> GSM339463 3 0.4989 0.1358 0.000 0.000 0.552 0.416 0.032
#> GSM339464 4 0.0609 0.9784 0.020 0.000 0.000 0.980 0.000
#> GSM339465 4 0.2471 0.8271 0.000 0.000 0.136 0.864 0.000
#> GSM339466 5 0.4262 0.3976 0.000 0.440 0.000 0.000 0.560
#> GSM339467 2 0.0000 0.9500 0.000 1.000 0.000 0.000 0.000
#> GSM339468 5 0.0000 0.7418 0.000 0.000 0.000 0.000 1.000
#> GSM339469 1 0.0000 0.9292 1.000 0.000 0.000 0.000 0.000
#> GSM339470 5 0.0000 0.7418 0.000 0.000 0.000 0.000 1.000
#> GSM339471 1 0.0000 0.9292 1.000 0.000 0.000 0.000 0.000
#> GSM339472 2 0.0000 0.9500 0.000 1.000 0.000 0.000 0.000
#> GSM339473 1 0.0000 0.9292 1.000 0.000 0.000 0.000 0.000
#> GSM339474 2 0.0000 0.9500 0.000 1.000 0.000 0.000 0.000
#> GSM339475 3 0.0000 0.8823 0.000 0.000 1.000 0.000 0.000
#> GSM339476 1 0.3424 0.7040 0.760 0.000 0.000 0.240 0.000
#> GSM339477 2 0.0000 0.9500 0.000 1.000 0.000 0.000 0.000
#> GSM339478 5 0.5480 0.5359 0.000 0.072 0.368 0.000 0.560
#> GSM339479 5 0.1043 0.7177 0.000 0.000 0.040 0.000 0.960
#> GSM339480 5 0.3636 0.6248 0.000 0.000 0.272 0.000 0.728
#> GSM339481 2 0.0000 0.9500 0.000 1.000 0.000 0.000 0.000
#> GSM339482 3 0.0000 0.8823 0.000 0.000 1.000 0.000 0.000
#> GSM339483 1 0.0000 0.9292 1.000 0.000 0.000 0.000 0.000
#> GSM339484 1 0.3857 0.5973 0.688 0.000 0.000 0.312 0.000
#> GSM339485 4 0.0609 0.9784 0.020 0.000 0.000 0.980 0.000
#> GSM339486 4 0.0609 0.9784 0.020 0.000 0.000 0.980 0.000
#> GSM339487 5 0.3274 0.6638 0.000 0.220 0.000 0.000 0.780
#> GSM339488 2 0.0000 0.9500 0.000 1.000 0.000 0.000 0.000
#> GSM339489 5 0.0794 0.7406 0.000 0.028 0.000 0.000 0.972
#> GSM339490 1 0.0000 0.9292 1.000 0.000 0.000 0.000 0.000
#> GSM339491 5 0.0000 0.7418 0.000 0.000 0.000 0.000 1.000
#> GSM339492 1 0.0000 0.9292 1.000 0.000 0.000 0.000 0.000
#> GSM339493 5 0.4302 0.3005 0.000 0.480 0.000 0.000 0.520
#> GSM339494 1 0.0000 0.9292 1.000 0.000 0.000 0.000 0.000
#> GSM339495 2 0.0000 0.9500 0.000 1.000 0.000 0.000 0.000
#> GSM339496 3 0.0000 0.8823 0.000 0.000 1.000 0.000 0.000
#> GSM339497 5 0.0000 0.7418 0.000 0.000 0.000 0.000 1.000
#> GSM339498 5 0.5123 0.5236 0.000 0.016 0.376 0.020 0.588
#> GSM339499 5 0.5791 0.5072 0.000 0.052 0.388 0.020 0.540
#> GSM339500 5 0.0000 0.7418 0.000 0.000 0.000 0.000 1.000
#> GSM339501 3 0.6792 0.2222 0.360 0.036 0.484 0.000 0.120
#> GSM339502 2 0.0000 0.9500 0.000 1.000 0.000 0.000 0.000
#> GSM339503 3 0.0000 0.8823 0.000 0.000 1.000 0.000 0.000
#> GSM339504 1 0.0000 0.9292 1.000 0.000 0.000 0.000 0.000
#> GSM339505 5 0.4610 0.5152 0.000 0.000 0.388 0.016 0.596
#> GSM339506 4 0.0609 0.9784 0.020 0.000 0.000 0.980 0.000
#> GSM339507 4 0.0609 0.9784 0.020 0.000 0.000 0.980 0.000
#> GSM339508 2 0.0000 0.9500 0.000 1.000 0.000 0.000 0.000
#> GSM339509 2 0.0000 0.9500 0.000 1.000 0.000 0.000 0.000
#> GSM339510 5 0.0000 0.7418 0.000 0.000 0.000 0.000 1.000
#> GSM339511 1 0.1043 0.9028 0.960 0.000 0.000 0.040 0.000
#> GSM339512 5 0.0000 0.7418 0.000 0.000 0.000 0.000 1.000
#> GSM339513 1 0.0000 0.9292 1.000 0.000 0.000 0.000 0.000
#> GSM339514 2 0.0162 0.9456 0.000 0.996 0.000 0.000 0.004
#> GSM339515 1 0.0000 0.9292 1.000 0.000 0.000 0.000 0.000
#> GSM339516 5 0.3305 0.6605 0.000 0.224 0.000 0.000 0.776
#> GSM339517 3 0.0000 0.8823 0.000 0.000 1.000 0.000 0.000
#> GSM339518 5 0.0000 0.7418 0.000 0.000 0.000 0.000 1.000
#> GSM339519 3 0.0963 0.8501 0.000 0.036 0.964 0.000 0.000
#> GSM339520 5 0.5791 0.5072 0.000 0.052 0.388 0.020 0.540
#> GSM339521 5 0.0000 0.7418 0.000 0.000 0.000 0.000 1.000
#> GSM339522 5 0.4088 0.5092 0.000 0.368 0.000 0.000 0.632
#> GSM339523 2 0.0000 0.9500 0.000 1.000 0.000 0.000 0.000
#> GSM339524 1 0.4150 0.4475 0.612 0.000 0.000 0.388 0.000
#> GSM339525 1 0.0000 0.9292 1.000 0.000 0.000 0.000 0.000
#> GSM339526 3 0.0000 0.8823 0.000 0.000 1.000 0.000 0.000
#> GSM339527 4 0.0609 0.9784 0.020 0.000 0.000 0.980 0.000
#> GSM339528 4 0.0609 0.9784 0.020 0.000 0.000 0.980 0.000
#> GSM339529 2 0.4287 -0.1959 0.000 0.540 0.000 0.000 0.460
#> GSM339530 5 0.5791 0.5072 0.000 0.052 0.388 0.020 0.540
#> GSM339531 5 0.0000 0.7418 0.000 0.000 0.000 0.000 1.000
#> GSM339532 1 0.0000 0.9292 1.000 0.000 0.000 0.000 0.000
#> GSM339533 3 0.1197 0.8495 0.000 0.000 0.952 0.000 0.048
#> GSM339534 1 0.3395 0.6793 0.764 0.000 0.236 0.000 0.000
#> GSM339535 5 0.4262 0.3976 0.000 0.440 0.000 0.000 0.560
#> GSM339536 1 0.0000 0.9292 1.000 0.000 0.000 0.000 0.000
#> GSM339537 5 0.3109 0.6604 0.000 0.200 0.000 0.000 0.800
#> GSM339538 3 0.0000 0.8823 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
#> GSM339455 3 0.3950 0.404 0.000 0.000 0.564 0.000 0.004 0.432
#> GSM339456 2 0.0000 0.938 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM339457 6 0.6533 0.472 0.000 0.000 0.196 0.312 0.040 0.452
#> GSM339458 6 0.0000 0.752 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM339459 6 0.6533 0.472 0.000 0.000 0.196 0.312 0.040 0.452
#> GSM339460 6 0.4265 0.593 0.000 0.300 0.000 0.040 0.000 0.660
#> GSM339461 6 0.0937 0.751 0.000 0.040 0.000 0.000 0.000 0.960
#> GSM339462 1 0.1745 0.681 0.920 0.000 0.000 0.068 0.012 0.000
#> GSM339463 3 0.3533 0.557 0.004 0.000 0.748 0.000 0.236 0.012
#> GSM339464 5 0.1390 0.865 0.016 0.000 0.032 0.004 0.948 0.000
#> GSM339465 5 0.3838 0.198 0.000 0.000 0.448 0.000 0.552 0.000
#> GSM339466 6 0.4552 0.586 0.000 0.300 0.000 0.060 0.000 0.640
#> GSM339467 2 0.0146 0.938 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM339468 6 0.0000 0.752 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM339469 4 0.3857 1.000 0.468 0.000 0.000 0.532 0.000 0.000
#> GSM339470 6 0.0937 0.740 0.000 0.000 0.040 0.000 0.000 0.960
#> GSM339471 1 0.1176 0.724 0.956 0.000 0.000 0.024 0.020 0.000
#> GSM339472 2 0.0146 0.938 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM339473 1 0.0653 0.709 0.980 0.000 0.004 0.012 0.004 0.000
#> GSM339474 2 0.2320 0.835 0.000 0.864 0.000 0.132 0.004 0.000
#> GSM339475 3 0.0363 0.843 0.000 0.000 0.988 0.012 0.000 0.000
#> GSM339476 1 0.3579 0.617 0.804 0.000 0.072 0.004 0.120 0.000
#> GSM339477 2 0.0146 0.938 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM339478 6 0.6321 0.603 0.000 0.152 0.064 0.236 0.000 0.548
#> GSM339479 6 0.3652 0.228 0.000 0.000 0.324 0.000 0.004 0.672
#> GSM339480 6 0.2786 0.715 0.000 0.000 0.084 0.056 0.000 0.860
#> GSM339481 2 0.0000 0.938 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM339482 3 0.0146 0.847 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM339483 4 0.3857 1.000 0.468 0.000 0.000 0.532 0.000 0.000
#> GSM339484 1 0.4264 0.539 0.744 0.000 0.128 0.004 0.124 0.000
#> GSM339485 5 0.1390 0.865 0.016 0.000 0.032 0.004 0.948 0.000
#> GSM339486 5 0.3112 0.854 0.104 0.000 0.052 0.004 0.840 0.000
#> GSM339487 6 0.3858 0.670 0.000 0.216 0.000 0.044 0.000 0.740
#> GSM339488 2 0.0000 0.938 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM339489 6 0.0146 0.752 0.000 0.004 0.000 0.000 0.000 0.996
#> GSM339490 4 0.3857 1.000 0.468 0.000 0.000 0.532 0.000 0.000
#> GSM339491 6 0.0146 0.751 0.000 0.000 0.004 0.000 0.000 0.996
#> GSM339492 1 0.1148 0.725 0.960 0.000 0.004 0.016 0.020 0.000
#> GSM339493 6 0.4569 0.452 0.000 0.396 0.000 0.040 0.000 0.564
#> GSM339494 1 0.0508 0.713 0.984 0.000 0.004 0.012 0.000 0.000
#> GSM339495 2 0.2462 0.831 0.000 0.860 0.000 0.132 0.004 0.004
#> GSM339496 3 0.0291 0.848 0.000 0.000 0.992 0.000 0.004 0.004
#> GSM339497 6 0.0000 0.752 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM339498 6 0.6515 0.477 0.000 0.000 0.196 0.304 0.040 0.460
#> GSM339499 6 0.6533 0.472 0.000 0.000 0.196 0.312 0.040 0.452
#> GSM339500 6 0.0000 0.752 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM339501 3 0.5572 0.470 0.248 0.000 0.624 0.028 0.008 0.092
#> GSM339502 2 0.0146 0.935 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM339503 3 0.0291 0.848 0.000 0.000 0.992 0.000 0.004 0.004
#> GSM339504 1 0.2912 0.612 0.844 0.000 0.000 0.116 0.040 0.000
#> GSM339505 6 0.5994 0.540 0.000 0.000 0.196 0.228 0.024 0.552
#> GSM339506 5 0.1708 0.870 0.024 0.000 0.040 0.004 0.932 0.000
#> GSM339507 5 0.2721 0.863 0.088 0.000 0.040 0.004 0.868 0.000
#> GSM339508 2 0.0146 0.938 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM339509 2 0.0000 0.938 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM339510 6 0.0000 0.752 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM339511 1 0.5175 0.419 0.696 0.000 0.116 0.136 0.052 0.000
#> GSM339512 6 0.0000 0.752 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM339513 1 0.1148 0.725 0.960 0.000 0.004 0.016 0.020 0.000
#> GSM339514 2 0.4087 0.374 0.000 0.688 0.000 0.036 0.000 0.276
#> GSM339515 1 0.0748 0.709 0.976 0.000 0.004 0.016 0.004 0.000
#> GSM339516 6 0.2854 0.676 0.000 0.208 0.000 0.000 0.000 0.792
#> GSM339517 3 0.0363 0.843 0.000 0.000 0.988 0.012 0.000 0.000
#> GSM339518 6 0.0000 0.752 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM339519 3 0.2794 0.771 0.004 0.000 0.868 0.088 0.004 0.036
#> GSM339520 6 0.6533 0.472 0.000 0.000 0.196 0.312 0.040 0.452
#> GSM339521 6 0.0000 0.752 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM339522 6 0.4060 0.614 0.000 0.284 0.000 0.032 0.000 0.684
#> GSM339523 2 0.0000 0.938 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM339524 1 0.4199 0.531 0.748 0.000 0.100 0.004 0.148 0.000
#> GSM339525 4 0.3857 1.000 0.468 0.000 0.000 0.532 0.000 0.000
#> GSM339526 3 0.0291 0.848 0.000 0.000 0.992 0.000 0.004 0.004
#> GSM339527 5 0.2586 0.852 0.032 0.000 0.100 0.000 0.868 0.000
#> GSM339528 5 0.3164 0.839 0.120 0.000 0.044 0.004 0.832 0.000
#> GSM339529 6 0.3499 0.577 0.000 0.320 0.000 0.000 0.000 0.680
#> GSM339530 6 0.6919 0.467 0.000 0.016 0.196 0.312 0.040 0.436
#> GSM339531 6 0.0000 0.752 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM339532 1 0.3897 0.550 0.788 0.000 0.024 0.140 0.048 0.000
#> GSM339533 3 0.2020 0.776 0.000 0.000 0.896 0.000 0.008 0.096
#> GSM339534 1 0.5791 0.150 0.580 0.000 0.280 0.092 0.048 0.000
#> GSM339535 6 0.4532 0.577 0.000 0.308 0.000 0.056 0.000 0.636
#> GSM339536 1 0.0748 0.709 0.976 0.000 0.004 0.016 0.004 0.000
#> GSM339537 6 0.2003 0.717 0.000 0.116 0.000 0.000 0.000 0.884
#> GSM339538 3 0.0146 0.847 0.000 0.000 0.996 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 protocol(p) agent(p) individual(p) k
#> ATC:mclust 84 1.000 0.606 1.03e-03 2
#> ATC:mclust 83 0.986 0.996 1.26e-05 3
#> ATC:mclust 83 0.733 0.928 2.02e-07 4
#> ATC:mclust 75 0.693 0.787 1.72e-07 5
#> ATC:mclust 70 0.690 0.902 2.72e-05 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 15497 rows and 84 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 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 0.964 0.984 0.4956 0.501 0.501
#> 3 3 0.920 0.911 0.949 0.3281 0.752 0.543
#> 4 4 0.838 0.809 0.906 0.0951 0.896 0.708
#> 5 5 0.730 0.602 0.828 0.0616 0.966 0.878
#> 6 6 0.722 0.630 0.816 0.0409 0.903 0.649
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
#> GSM339455 1 0.955 0.432 0.624 0.376
#> GSM339456 2 0.000 0.995 0.000 1.000
#> GSM339457 2 0.000 0.995 0.000 1.000
#> GSM339458 2 0.000 0.995 0.000 1.000
#> GSM339459 2 0.000 0.995 0.000 1.000
#> GSM339460 2 0.000 0.995 0.000 1.000
#> GSM339461 2 0.000 0.995 0.000 1.000
#> GSM339462 1 0.000 0.968 1.000 0.000
#> GSM339463 1 0.000 0.968 1.000 0.000
#> GSM339464 1 0.000 0.968 1.000 0.000
#> GSM339465 1 0.000 0.968 1.000 0.000
#> GSM339466 2 0.000 0.995 0.000 1.000
#> GSM339467 2 0.000 0.995 0.000 1.000
#> GSM339468 2 0.000 0.995 0.000 1.000
#> GSM339469 1 0.000 0.968 1.000 0.000
#> GSM339470 2 0.000 0.995 0.000 1.000
#> GSM339471 1 0.000 0.968 1.000 0.000
#> GSM339472 2 0.000 0.995 0.000 1.000
#> GSM339473 1 0.000 0.968 1.000 0.000
#> GSM339474 2 0.000 0.995 0.000 1.000
#> GSM339475 2 0.388 0.914 0.076 0.924
#> GSM339476 1 0.000 0.968 1.000 0.000
#> GSM339477 2 0.000 0.995 0.000 1.000
#> GSM339478 2 0.000 0.995 0.000 1.000
#> GSM339479 2 0.563 0.842 0.132 0.868
#> GSM339480 2 0.000 0.995 0.000 1.000
#> GSM339481 2 0.000 0.995 0.000 1.000
#> GSM339482 1 0.000 0.968 1.000 0.000
#> GSM339483 1 0.000 0.968 1.000 0.000
#> GSM339484 1 0.000 0.968 1.000 0.000
#> GSM339485 1 0.000 0.968 1.000 0.000
#> GSM339486 1 0.000 0.968 1.000 0.000
#> GSM339487 2 0.000 0.995 0.000 1.000
#> GSM339488 2 0.000 0.995 0.000 1.000
#> GSM339489 2 0.000 0.995 0.000 1.000
#> GSM339490 1 0.000 0.968 1.000 0.000
#> GSM339491 2 0.000 0.995 0.000 1.000
#> GSM339492 1 0.000 0.968 1.000 0.000
#> GSM339493 2 0.000 0.995 0.000 1.000
#> GSM339494 1 0.000 0.968 1.000 0.000
#> GSM339495 2 0.000 0.995 0.000 1.000
#> GSM339496 1 0.917 0.532 0.668 0.332
#> GSM339497 2 0.000 0.995 0.000 1.000
#> GSM339498 2 0.000 0.995 0.000 1.000
#> GSM339499 2 0.000 0.995 0.000 1.000
#> GSM339500 2 0.000 0.995 0.000 1.000
#> GSM339501 1 0.224 0.940 0.964 0.036
#> GSM339502 2 0.000 0.995 0.000 1.000
#> GSM339503 1 0.802 0.692 0.756 0.244
#> GSM339504 1 0.000 0.968 1.000 0.000
#> GSM339505 2 0.000 0.995 0.000 1.000
#> GSM339506 1 0.000 0.968 1.000 0.000
#> GSM339507 1 0.000 0.968 1.000 0.000
#> GSM339508 2 0.000 0.995 0.000 1.000
#> GSM339509 2 0.000 0.995 0.000 1.000
#> GSM339510 2 0.000 0.995 0.000 1.000
#> GSM339511 1 0.000 0.968 1.000 0.000
#> GSM339512 2 0.000 0.995 0.000 1.000
#> GSM339513 1 0.000 0.968 1.000 0.000
#> GSM339514 2 0.000 0.995 0.000 1.000
#> GSM339515 1 0.000 0.968 1.000 0.000
#> GSM339516 2 0.000 0.995 0.000 1.000
#> GSM339517 2 0.000 0.995 0.000 1.000
#> GSM339518 2 0.000 0.995 0.000 1.000
#> GSM339519 1 0.141 0.953 0.980 0.020
#> GSM339520 2 0.000 0.995 0.000 1.000
#> GSM339521 2 0.000 0.995 0.000 1.000
#> GSM339522 2 0.000 0.995 0.000 1.000
#> GSM339523 2 0.000 0.995 0.000 1.000
#> GSM339524 1 0.000 0.968 1.000 0.000
#> GSM339525 1 0.000 0.968 1.000 0.000
#> GSM339526 1 0.000 0.968 1.000 0.000
#> GSM339527 1 0.000 0.968 1.000 0.000
#> GSM339528 1 0.000 0.968 1.000 0.000
#> GSM339529 2 0.000 0.995 0.000 1.000
#> GSM339530 2 0.000 0.995 0.000 1.000
#> GSM339531 2 0.000 0.995 0.000 1.000
#> GSM339532 1 0.000 0.968 1.000 0.000
#> GSM339533 1 0.518 0.861 0.884 0.116
#> GSM339534 1 0.000 0.968 1.000 0.000
#> GSM339535 2 0.000 0.995 0.000 1.000
#> GSM339536 1 0.000 0.968 1.000 0.000
#> GSM339537 2 0.000 0.995 0.000 1.000
#> GSM339538 1 0.000 0.968 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM339455 3 0.3155 0.884 0.044 0.040 0.916
#> GSM339456 2 0.0237 0.980 0.000 0.996 0.004
#> GSM339457 3 0.2165 0.893 0.000 0.064 0.936
#> GSM339458 2 0.0237 0.978 0.004 0.996 0.000
#> GSM339459 3 0.3879 0.836 0.000 0.152 0.848
#> GSM339460 2 0.1315 0.960 0.008 0.972 0.020
#> GSM339461 2 0.0237 0.980 0.000 0.996 0.004
#> GSM339462 1 0.0237 0.949 0.996 0.000 0.004
#> GSM339463 3 0.1289 0.888 0.032 0.000 0.968
#> GSM339464 1 0.1163 0.955 0.972 0.000 0.028
#> GSM339465 3 0.1031 0.892 0.024 0.000 0.976
#> GSM339466 2 0.0237 0.980 0.000 0.996 0.004
#> GSM339467 2 0.0000 0.980 0.000 1.000 0.000
#> GSM339468 2 0.0237 0.980 0.000 0.996 0.004
#> GSM339469 1 0.0892 0.940 0.980 0.000 0.020
#> GSM339470 3 0.2448 0.891 0.000 0.076 0.924
#> GSM339471 1 0.1529 0.955 0.960 0.000 0.040
#> GSM339472 2 0.0237 0.980 0.000 0.996 0.004
#> GSM339473 1 0.1411 0.955 0.964 0.000 0.036
#> GSM339474 2 0.0000 0.980 0.000 1.000 0.000
#> GSM339475 3 0.1163 0.897 0.000 0.028 0.972
#> GSM339476 1 0.1289 0.956 0.968 0.000 0.032
#> GSM339477 2 0.0000 0.980 0.000 1.000 0.000
#> GSM339478 2 0.4399 0.747 0.000 0.812 0.188
#> GSM339479 2 0.5201 0.697 0.236 0.760 0.004
#> GSM339480 3 0.3340 0.865 0.000 0.120 0.880
#> GSM339481 2 0.0000 0.980 0.000 1.000 0.000
#> GSM339482 3 0.1031 0.892 0.024 0.000 0.976
#> GSM339483 1 0.0892 0.940 0.980 0.000 0.020
#> GSM339484 1 0.1860 0.950 0.948 0.000 0.052
#> GSM339485 1 0.1163 0.955 0.972 0.000 0.028
#> GSM339486 3 0.6274 0.107 0.456 0.000 0.544
#> GSM339487 2 0.0237 0.980 0.000 0.996 0.004
#> GSM339488 2 0.0237 0.980 0.000 0.996 0.004
#> GSM339489 2 0.0237 0.980 0.000 0.996 0.004
#> GSM339490 1 0.0892 0.940 0.980 0.000 0.020
#> GSM339491 3 0.6154 0.375 0.000 0.408 0.592
#> GSM339492 1 0.1643 0.953 0.956 0.000 0.044
#> GSM339493 2 0.0000 0.980 0.000 1.000 0.000
#> GSM339494 1 0.1289 0.956 0.968 0.000 0.032
#> GSM339495 2 0.0000 0.980 0.000 1.000 0.000
#> GSM339496 3 0.0892 0.893 0.020 0.000 0.980
#> GSM339497 2 0.0237 0.980 0.000 0.996 0.004
#> GSM339498 3 0.2959 0.879 0.000 0.100 0.900
#> GSM339499 3 0.2537 0.890 0.000 0.080 0.920
#> GSM339500 2 0.0592 0.974 0.000 0.988 0.012
#> GSM339501 1 0.2269 0.947 0.944 0.016 0.040
#> GSM339502 2 0.0000 0.980 0.000 1.000 0.000
#> GSM339503 3 0.0892 0.893 0.020 0.000 0.980
#> GSM339504 1 0.0000 0.948 1.000 0.000 0.000
#> GSM339505 3 0.2261 0.892 0.000 0.068 0.932
#> GSM339506 1 0.5760 0.568 0.672 0.000 0.328
#> GSM339507 1 0.1753 0.952 0.952 0.000 0.048
#> GSM339508 2 0.0000 0.980 0.000 1.000 0.000
#> GSM339509 2 0.0000 0.980 0.000 1.000 0.000
#> GSM339510 2 0.0237 0.980 0.000 0.996 0.004
#> GSM339511 1 0.0892 0.940 0.980 0.000 0.020
#> GSM339512 2 0.0237 0.980 0.000 0.996 0.004
#> GSM339513 1 0.1753 0.952 0.952 0.000 0.048
#> GSM339514 2 0.0000 0.980 0.000 1.000 0.000
#> GSM339515 1 0.1529 0.955 0.960 0.000 0.040
#> GSM339516 2 0.2636 0.923 0.048 0.932 0.020
#> GSM339517 3 0.1411 0.897 0.000 0.036 0.964
#> GSM339518 2 0.0000 0.980 0.000 1.000 0.000
#> GSM339519 3 0.1163 0.891 0.028 0.000 0.972
#> GSM339520 3 0.2711 0.886 0.000 0.088 0.912
#> GSM339521 2 0.0237 0.980 0.000 0.996 0.004
#> GSM339522 2 0.0000 0.980 0.000 1.000 0.000
#> GSM339523 2 0.0000 0.980 0.000 1.000 0.000
#> GSM339524 3 0.5431 0.584 0.284 0.000 0.716
#> GSM339525 1 0.0892 0.940 0.980 0.000 0.020
#> GSM339526 3 0.1031 0.892 0.024 0.000 0.976
#> GSM339527 1 0.4887 0.751 0.772 0.000 0.228
#> GSM339528 1 0.2625 0.926 0.916 0.000 0.084
#> GSM339529 2 0.1315 0.960 0.008 0.972 0.020
#> GSM339530 3 0.2711 0.886 0.000 0.088 0.912
#> GSM339531 2 0.0237 0.980 0.000 0.996 0.004
#> GSM339532 1 0.0892 0.940 0.980 0.000 0.020
#> GSM339533 3 0.0892 0.893 0.020 0.000 0.980
#> GSM339534 1 0.1163 0.956 0.972 0.000 0.028
#> GSM339535 2 0.0000 0.980 0.000 1.000 0.000
#> GSM339536 1 0.1529 0.955 0.960 0.000 0.040
#> GSM339537 2 0.0829 0.969 0.004 0.984 0.012
#> GSM339538 3 0.1031 0.892 0.024 0.000 0.976
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM339455 3 0.6050 0.6339 0.140 0.096 0.732 0.032
#> GSM339456 2 0.0000 0.9614 0.000 1.000 0.000 0.000
#> GSM339457 3 0.0188 0.8990 0.000 0.004 0.996 0.000
#> GSM339458 2 0.2704 0.8628 0.000 0.876 0.000 0.124
#> GSM339459 3 0.1792 0.8617 0.000 0.068 0.932 0.000
#> GSM339460 2 0.1510 0.9407 0.016 0.956 0.000 0.028
#> GSM339461 2 0.2149 0.9126 0.000 0.912 0.000 0.088
#> GSM339462 1 0.0336 0.8774 0.992 0.000 0.000 0.008
#> GSM339463 4 0.5221 0.6934 0.208 0.000 0.060 0.732
#> GSM339464 4 0.4730 0.4975 0.364 0.000 0.000 0.636
#> GSM339465 4 0.5480 0.6925 0.124 0.000 0.140 0.736
#> GSM339466 2 0.0000 0.9614 0.000 1.000 0.000 0.000
#> GSM339467 2 0.0000 0.9614 0.000 1.000 0.000 0.000
#> GSM339468 2 0.2466 0.9034 0.000 0.900 0.004 0.096
#> GSM339469 1 0.0592 0.8738 0.984 0.000 0.000 0.016
#> GSM339470 4 0.3894 0.6509 0.000 0.068 0.088 0.844
#> GSM339471 1 0.0592 0.8768 0.984 0.000 0.000 0.016
#> GSM339472 2 0.0000 0.9614 0.000 1.000 0.000 0.000
#> GSM339473 1 0.0921 0.8740 0.972 0.000 0.000 0.028
#> GSM339474 2 0.0000 0.9614 0.000 1.000 0.000 0.000
#> GSM339475 3 0.0817 0.8953 0.000 0.000 0.976 0.024
#> GSM339476 1 0.1022 0.8733 0.968 0.000 0.000 0.032
#> GSM339477 2 0.0188 0.9609 0.000 0.996 0.000 0.004
#> GSM339478 3 0.4981 0.1405 0.000 0.464 0.536 0.000
#> GSM339479 4 0.5073 0.6758 0.200 0.056 0.000 0.744
#> GSM339480 3 0.1854 0.8815 0.000 0.048 0.940 0.012
#> GSM339481 2 0.0188 0.9609 0.000 0.996 0.000 0.004
#> GSM339482 3 0.0469 0.8977 0.000 0.000 0.988 0.012
#> GSM339483 1 0.0000 0.8774 1.000 0.000 0.000 0.000
#> GSM339484 1 0.1389 0.8619 0.952 0.000 0.000 0.048
#> GSM339485 1 0.4907 0.1237 0.580 0.000 0.000 0.420
#> GSM339486 4 0.5850 0.2504 0.456 0.000 0.032 0.512
#> GSM339487 2 0.1411 0.9419 0.020 0.960 0.000 0.020
#> GSM339488 2 0.0000 0.9614 0.000 1.000 0.000 0.000
#> GSM339489 2 0.1256 0.9456 0.008 0.964 0.000 0.028
#> GSM339490 1 0.0592 0.8738 0.984 0.000 0.000 0.016
#> GSM339491 4 0.2797 0.6615 0.000 0.068 0.032 0.900
#> GSM339492 1 0.0672 0.8774 0.984 0.000 0.008 0.008
#> GSM339493 2 0.0188 0.9607 0.000 0.996 0.000 0.004
#> GSM339494 1 0.0921 0.8740 0.972 0.000 0.000 0.028
#> GSM339495 2 0.0188 0.9607 0.000 0.996 0.000 0.004
#> GSM339496 3 0.1022 0.8922 0.000 0.000 0.968 0.032
#> GSM339497 2 0.0707 0.9554 0.000 0.980 0.000 0.020
#> GSM339498 3 0.1118 0.8904 0.000 0.036 0.964 0.000
#> GSM339499 3 0.0336 0.8992 0.000 0.008 0.992 0.000
#> GSM339500 2 0.4328 0.7190 0.000 0.748 0.008 0.244
#> GSM339501 1 0.3199 0.8028 0.892 0.012 0.060 0.036
#> GSM339502 2 0.0000 0.9614 0.000 1.000 0.000 0.000
#> GSM339503 3 0.3764 0.6961 0.000 0.000 0.784 0.216
#> GSM339504 1 0.0188 0.8769 0.996 0.000 0.000 0.004
#> GSM339505 3 0.1820 0.8890 0.000 0.020 0.944 0.036
#> GSM339506 4 0.3801 0.6871 0.220 0.000 0.000 0.780
#> GSM339507 1 0.4999 -0.1764 0.508 0.000 0.000 0.492
#> GSM339508 2 0.0000 0.9614 0.000 1.000 0.000 0.000
#> GSM339509 2 0.0000 0.9614 0.000 1.000 0.000 0.000
#> GSM339510 2 0.1118 0.9482 0.000 0.964 0.000 0.036
#> GSM339511 1 0.1022 0.8691 0.968 0.000 0.000 0.032
#> GSM339512 2 0.4356 0.6669 0.000 0.708 0.000 0.292
#> GSM339513 1 0.1722 0.8551 0.944 0.000 0.048 0.008
#> GSM339514 2 0.0188 0.9609 0.000 0.996 0.000 0.004
#> GSM339515 1 0.0921 0.8740 0.972 0.000 0.000 0.028
#> GSM339516 2 0.2411 0.9101 0.040 0.920 0.000 0.040
#> GSM339517 3 0.1867 0.8678 0.000 0.000 0.928 0.072
#> GSM339518 2 0.1211 0.9473 0.000 0.960 0.000 0.040
#> GSM339519 3 0.0592 0.8918 0.016 0.000 0.984 0.000
#> GSM339520 3 0.0707 0.8977 0.000 0.020 0.980 0.000
#> GSM339521 4 0.4103 0.5004 0.000 0.256 0.000 0.744
#> GSM339522 2 0.0469 0.9580 0.000 0.988 0.000 0.012
#> GSM339523 2 0.0000 0.9614 0.000 1.000 0.000 0.000
#> GSM339524 1 0.5624 0.4482 0.668 0.000 0.280 0.052
#> GSM339525 1 0.0592 0.8738 0.984 0.000 0.000 0.016
#> GSM339526 3 0.0336 0.8980 0.000 0.000 0.992 0.008
#> GSM339527 4 0.3837 0.6846 0.224 0.000 0.000 0.776
#> GSM339528 1 0.5090 0.3777 0.660 0.000 0.016 0.324
#> GSM339529 2 0.0000 0.9614 0.000 1.000 0.000 0.000
#> GSM339530 3 0.0592 0.8979 0.000 0.016 0.984 0.000
#> GSM339531 2 0.0524 0.9593 0.000 0.988 0.004 0.008
#> GSM339532 1 0.0921 0.8696 0.972 0.000 0.000 0.028
#> GSM339533 4 0.5290 0.0245 0.008 0.000 0.476 0.516
#> GSM339534 1 0.1833 0.8536 0.944 0.000 0.024 0.032
#> GSM339535 2 0.0921 0.9513 0.000 0.972 0.000 0.028
#> GSM339536 1 0.1211 0.8676 0.960 0.000 0.000 0.040
#> GSM339537 2 0.0707 0.9558 0.000 0.980 0.000 0.020
#> GSM339538 3 0.0000 0.8976 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
#> GSM339455 3 0.7544 0.36798 0.084 0.020 0.548 0.132 0.216
#> GSM339456 2 0.0609 0.80272 0.000 0.980 0.000 0.000 0.020
#> GSM339457 3 0.0000 0.86685 0.000 0.000 1.000 0.000 0.000
#> GSM339458 2 0.6106 0.14837 0.000 0.568 0.000 0.204 0.228
#> GSM339459 3 0.2141 0.83728 0.000 0.064 0.916 0.004 0.016
#> GSM339460 2 0.2233 0.71811 0.004 0.892 0.000 0.000 0.104
#> GSM339461 2 0.1403 0.78821 0.000 0.952 0.000 0.024 0.024
#> GSM339462 1 0.0451 0.75912 0.988 0.000 0.000 0.008 0.004
#> GSM339463 4 0.4645 0.48427 0.268 0.000 0.000 0.688 0.044
#> GSM339464 4 0.5107 0.36578 0.356 0.000 0.000 0.596 0.048
#> GSM339465 4 0.3289 0.63635 0.108 0.000 0.000 0.844 0.048
#> GSM339466 2 0.0510 0.80272 0.000 0.984 0.000 0.000 0.016
#> GSM339467 2 0.0693 0.80188 0.000 0.980 0.000 0.012 0.008
#> GSM339468 5 0.6015 0.75867 0.000 0.276 0.080 0.032 0.612
#> GSM339469 1 0.3039 0.67329 0.808 0.000 0.000 0.000 0.192
#> GSM339470 4 0.3336 0.62032 0.000 0.000 0.096 0.844 0.060
#> GSM339471 1 0.0451 0.75924 0.988 0.000 0.000 0.008 0.004
#> GSM339472 2 0.0510 0.80393 0.000 0.984 0.000 0.000 0.016
#> GSM339473 1 0.1106 0.75160 0.964 0.000 0.000 0.024 0.012
#> GSM339474 2 0.0290 0.80444 0.000 0.992 0.000 0.000 0.008
#> GSM339475 3 0.0404 0.86652 0.000 0.000 0.988 0.012 0.000
#> GSM339476 1 0.2179 0.72887 0.888 0.000 0.000 0.000 0.112
#> GSM339477 2 0.0290 0.80444 0.000 0.992 0.000 0.000 0.008
#> GSM339478 3 0.4420 0.01775 0.000 0.448 0.548 0.000 0.004
#> GSM339479 4 0.7797 0.41454 0.232 0.124 0.000 0.472 0.172
#> GSM339480 3 0.2002 0.85483 0.000 0.028 0.932 0.020 0.020
#> GSM339481 2 0.0162 0.80419 0.000 0.996 0.000 0.000 0.004
#> GSM339482 3 0.2291 0.82971 0.000 0.000 0.908 0.056 0.036
#> GSM339483 1 0.0162 0.75880 0.996 0.000 0.000 0.000 0.004
#> GSM339484 1 0.3691 0.65441 0.820 0.000 0.000 0.076 0.104
#> GSM339485 1 0.5815 0.00177 0.508 0.000 0.000 0.396 0.096
#> GSM339486 1 0.6367 -0.02454 0.460 0.000 0.000 0.372 0.168
#> GSM339487 2 0.3934 0.21147 0.008 0.716 0.000 0.000 0.276
#> GSM339488 2 0.0451 0.80418 0.000 0.988 0.000 0.004 0.008
#> GSM339489 2 0.4437 -0.54256 0.004 0.532 0.000 0.000 0.464
#> GSM339490 1 0.3039 0.67351 0.808 0.000 0.000 0.000 0.192
#> GSM339491 4 0.4550 0.41187 0.000 0.276 0.000 0.688 0.036
#> GSM339492 1 0.0000 0.75873 1.000 0.000 0.000 0.000 0.000
#> GSM339493 2 0.0880 0.79405 0.000 0.968 0.000 0.000 0.032
#> GSM339494 1 0.0579 0.75803 0.984 0.000 0.000 0.008 0.008
#> GSM339495 2 0.0510 0.80380 0.000 0.984 0.000 0.000 0.016
#> GSM339496 3 0.0703 0.86482 0.000 0.000 0.976 0.024 0.000
#> GSM339497 2 0.1809 0.76709 0.000 0.928 0.000 0.012 0.060
#> GSM339498 3 0.1124 0.86185 0.000 0.036 0.960 0.004 0.000
#> GSM339499 3 0.0000 0.86685 0.000 0.000 1.000 0.000 0.000
#> GSM339500 2 0.3753 0.62735 0.000 0.828 0.020 0.116 0.036
#> GSM339501 1 0.6692 0.15134 0.408 0.004 0.200 0.000 0.388
#> GSM339502 2 0.1741 0.77192 0.000 0.936 0.000 0.024 0.040
#> GSM339503 3 0.4066 0.51382 0.000 0.000 0.672 0.324 0.004
#> GSM339504 1 0.0963 0.75519 0.964 0.000 0.000 0.000 0.036
#> GSM339505 3 0.4402 0.70885 0.000 0.148 0.780 0.052 0.020
#> GSM339506 4 0.3752 0.63354 0.064 0.000 0.000 0.812 0.124
#> GSM339507 1 0.5314 0.07171 0.528 0.000 0.000 0.420 0.052
#> GSM339508 2 0.0000 0.80461 0.000 1.000 0.000 0.000 0.000
#> GSM339509 2 0.0579 0.80457 0.000 0.984 0.000 0.008 0.008
#> GSM339510 2 0.4420 -0.51071 0.000 0.548 0.000 0.004 0.448
#> GSM339511 1 0.4451 0.30144 0.504 0.000 0.000 0.004 0.492
#> GSM339512 2 0.3409 0.64392 0.000 0.836 0.000 0.052 0.112
#> GSM339513 1 0.0510 0.75831 0.984 0.000 0.016 0.000 0.000
#> GSM339514 2 0.0324 0.80451 0.000 0.992 0.000 0.004 0.004
#> GSM339515 1 0.0451 0.75854 0.988 0.000 0.000 0.008 0.004
#> GSM339516 2 0.5019 -0.55098 0.032 0.532 0.000 0.000 0.436
#> GSM339517 3 0.1544 0.84802 0.000 0.000 0.932 0.068 0.000
#> GSM339518 2 0.1251 0.78818 0.000 0.956 0.000 0.008 0.036
#> GSM339519 3 0.0000 0.86685 0.000 0.000 1.000 0.000 0.000
#> GSM339520 3 0.1430 0.85288 0.000 0.052 0.944 0.000 0.004
#> GSM339521 4 0.6279 0.19880 0.000 0.280 0.000 0.528 0.192
#> GSM339522 2 0.4114 -0.22275 0.000 0.624 0.000 0.000 0.376
#> GSM339523 2 0.0290 0.80483 0.000 0.992 0.000 0.000 0.008
#> GSM339524 1 0.3115 0.70252 0.876 0.000 0.056 0.048 0.020
#> GSM339525 1 0.1732 0.74089 0.920 0.000 0.000 0.000 0.080
#> GSM339526 3 0.0290 0.86674 0.000 0.000 0.992 0.008 0.000
#> GSM339527 4 0.4038 0.62700 0.080 0.000 0.000 0.792 0.128
#> GSM339528 1 0.6175 0.10565 0.508 0.000 0.000 0.344 0.148
#> GSM339529 2 0.0162 0.80543 0.000 0.996 0.000 0.000 0.004
#> GSM339530 3 0.1569 0.86000 0.000 0.032 0.948 0.008 0.012
#> GSM339531 5 0.5215 0.82174 0.000 0.380 0.024 0.016 0.580
#> GSM339532 1 0.4294 0.34903 0.532 0.000 0.000 0.000 0.468
#> GSM339533 4 0.4015 0.31684 0.000 0.000 0.348 0.652 0.000
#> GSM339534 1 0.1741 0.74680 0.936 0.000 0.040 0.000 0.024
#> GSM339535 2 0.0703 0.79964 0.000 0.976 0.000 0.000 0.024
#> GSM339536 1 0.1195 0.74977 0.960 0.000 0.000 0.028 0.012
#> GSM339537 5 0.4510 0.75361 0.000 0.432 0.000 0.008 0.560
#> GSM339538 3 0.0162 0.86679 0.000 0.000 0.996 0.004 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM339455 6 0.4962 0.5271 0.056 0.004 0.100 0.020 0.068 0.752
#> GSM339456 2 0.0767 0.8458 0.000 0.976 0.000 0.004 0.012 0.008
#> GSM339457 3 0.0696 0.8256 0.000 0.004 0.980 0.004 0.004 0.008
#> GSM339458 6 0.3267 0.5414 0.004 0.076 0.000 0.056 0.016 0.848
#> GSM339459 3 0.2151 0.8027 0.000 0.072 0.904 0.000 0.008 0.016
#> GSM339460 2 0.5455 0.0212 0.004 0.456 0.000 0.000 0.104 0.436
#> GSM339461 2 0.1577 0.8418 0.000 0.940 0.000 0.008 0.016 0.036
#> GSM339462 1 0.1003 0.8775 0.964 0.000 0.000 0.000 0.020 0.016
#> GSM339463 4 0.4975 0.3937 0.044 0.000 0.024 0.660 0.008 0.264
#> GSM339464 4 0.5099 0.3234 0.284 0.000 0.000 0.632 0.040 0.044
#> GSM339465 4 0.4470 0.4128 0.036 0.000 0.016 0.680 0.000 0.268
#> GSM339466 2 0.1232 0.8378 0.000 0.956 0.004 0.000 0.024 0.016
#> GSM339467 2 0.1232 0.8435 0.000 0.956 0.000 0.004 0.016 0.024
#> GSM339468 5 0.7816 0.2500 0.000 0.144 0.296 0.212 0.332 0.016
#> GSM339469 1 0.3171 0.7578 0.784 0.000 0.000 0.000 0.204 0.012
#> GSM339470 4 0.2905 0.5204 0.000 0.000 0.064 0.852 0.000 0.084
#> GSM339471 1 0.0291 0.8764 0.992 0.000 0.000 0.000 0.004 0.004
#> GSM339472 2 0.0551 0.8458 0.000 0.984 0.000 0.004 0.008 0.004
#> GSM339473 1 0.0725 0.8732 0.976 0.000 0.000 0.000 0.012 0.012
#> GSM339474 2 0.0717 0.8445 0.000 0.976 0.000 0.000 0.016 0.008
#> GSM339475 3 0.1074 0.8238 0.000 0.000 0.960 0.028 0.000 0.012
#> GSM339476 1 0.2845 0.7993 0.820 0.000 0.000 0.004 0.172 0.004
#> GSM339477 2 0.1151 0.8415 0.000 0.956 0.000 0.000 0.032 0.012
#> GSM339478 3 0.3497 0.6046 0.000 0.224 0.760 0.004 0.008 0.004
#> GSM339479 6 0.3893 0.4788 0.016 0.016 0.000 0.212 0.004 0.752
#> GSM339480 3 0.2632 0.8025 0.000 0.020 0.896 0.028 0.040 0.016
#> GSM339481 2 0.1341 0.8394 0.000 0.948 0.000 0.000 0.024 0.028
#> GSM339482 3 0.5059 0.6368 0.016 0.000 0.704 0.032 0.060 0.188
#> GSM339483 1 0.1480 0.8739 0.940 0.000 0.000 0.000 0.040 0.020
#> GSM339484 1 0.3168 0.7506 0.820 0.000 0.000 0.004 0.028 0.148
#> GSM339485 4 0.5462 0.0817 0.440 0.000 0.000 0.468 0.076 0.016
#> GSM339486 6 0.5472 0.4796 0.180 0.000 0.004 0.144 0.024 0.648
#> GSM339487 2 0.2407 0.8009 0.000 0.896 0.008 0.008 0.072 0.016
#> GSM339488 2 0.0748 0.8453 0.000 0.976 0.000 0.004 0.004 0.016
#> GSM339489 5 0.3242 0.3639 0.004 0.120 0.012 0.008 0.840 0.016
#> GSM339490 1 0.2501 0.8333 0.872 0.000 0.000 0.004 0.108 0.016
#> GSM339491 4 0.5172 0.4104 0.000 0.108 0.032 0.676 0.000 0.184
#> GSM339492 1 0.0622 0.8777 0.980 0.000 0.008 0.000 0.012 0.000
#> GSM339493 2 0.1138 0.8409 0.000 0.960 0.004 0.000 0.024 0.012
#> GSM339494 1 0.0725 0.8732 0.976 0.000 0.000 0.000 0.012 0.012
#> GSM339495 2 0.0922 0.8451 0.000 0.968 0.000 0.004 0.024 0.004
#> GSM339496 3 0.1049 0.8244 0.000 0.000 0.960 0.032 0.000 0.008
#> GSM339497 6 0.7399 0.0724 0.000 0.268 0.000 0.116 0.280 0.336
#> GSM339498 3 0.1757 0.8163 0.000 0.052 0.928 0.000 0.012 0.008
#> GSM339499 3 0.0810 0.8261 0.000 0.004 0.976 0.004 0.008 0.008
#> GSM339500 2 0.5025 0.5174 0.000 0.680 0.048 0.216 0.000 0.056
#> GSM339501 5 0.5088 0.0804 0.068 0.004 0.412 0.000 0.516 0.000
#> GSM339502 2 0.1858 0.8220 0.000 0.912 0.000 0.000 0.012 0.076
#> GSM339503 3 0.5606 0.3348 0.000 0.000 0.556 0.336 0.040 0.068
#> GSM339504 1 0.1010 0.8739 0.960 0.000 0.000 0.000 0.036 0.004
#> GSM339505 3 0.6182 0.1812 0.000 0.376 0.500 0.032 0.044 0.048
#> GSM339506 4 0.1364 0.5204 0.012 0.000 0.000 0.952 0.020 0.016
#> GSM339507 1 0.6118 0.0184 0.504 0.000 0.000 0.288 0.020 0.188
#> GSM339508 2 0.0405 0.8459 0.000 0.988 0.000 0.000 0.004 0.008
#> GSM339509 2 0.1148 0.8450 0.000 0.960 0.000 0.004 0.020 0.016
#> GSM339510 5 0.5304 0.3935 0.000 0.264 0.000 0.112 0.612 0.012
#> GSM339511 5 0.4371 0.0541 0.352 0.000 0.000 0.012 0.620 0.016
#> GSM339512 2 0.2326 0.8163 0.000 0.908 0.004 0.040 0.028 0.020
#> GSM339513 1 0.0508 0.8777 0.984 0.000 0.012 0.000 0.004 0.000
#> GSM339514 2 0.0665 0.8457 0.000 0.980 0.000 0.004 0.008 0.008
#> GSM339515 1 0.0508 0.8752 0.984 0.000 0.000 0.000 0.004 0.012
#> GSM339516 2 0.4532 0.3627 0.020 0.628 0.000 0.012 0.336 0.004
#> GSM339517 3 0.2213 0.7984 0.000 0.000 0.888 0.100 0.004 0.008
#> GSM339518 2 0.4726 0.6364 0.000 0.740 0.000 0.056 0.120 0.084
#> GSM339519 3 0.0458 0.8222 0.000 0.000 0.984 0.000 0.016 0.000
#> GSM339520 3 0.3123 0.7200 0.000 0.152 0.824 0.008 0.004 0.012
#> GSM339521 4 0.4225 0.1661 0.000 0.352 0.004 0.628 0.012 0.004
#> GSM339522 5 0.4103 0.0906 0.000 0.448 0.004 0.000 0.544 0.004
#> GSM339523 2 0.0632 0.8448 0.000 0.976 0.000 0.000 0.000 0.024
#> GSM339524 1 0.2961 0.8089 0.872 0.000 0.016 0.008 0.044 0.060
#> GSM339525 1 0.1701 0.8620 0.920 0.000 0.000 0.000 0.072 0.008
#> GSM339526 3 0.0984 0.8249 0.000 0.000 0.968 0.012 0.008 0.012
#> GSM339527 4 0.1785 0.5086 0.016 0.000 0.000 0.928 0.048 0.008
#> GSM339528 6 0.5825 0.4457 0.224 0.000 0.008 0.132 0.028 0.608
#> GSM339529 2 0.1983 0.8186 0.000 0.908 0.000 0.000 0.072 0.020
#> GSM339530 3 0.3145 0.7631 0.000 0.104 0.848 0.004 0.028 0.016
#> GSM339531 2 0.7924 -0.4205 0.000 0.316 0.192 0.188 0.288 0.016
#> GSM339532 1 0.4317 0.5238 0.636 0.000 0.000 0.012 0.336 0.016
#> GSM339533 4 0.5127 0.3268 0.000 0.000 0.268 0.616 0.004 0.112
#> GSM339534 1 0.1901 0.8609 0.924 0.000 0.040 0.000 0.028 0.008
#> GSM339535 2 0.1194 0.8377 0.000 0.956 0.004 0.000 0.032 0.008
#> GSM339536 1 0.0820 0.8717 0.972 0.000 0.000 0.000 0.016 0.012
#> GSM339537 2 0.5251 0.4222 0.000 0.636 0.000 0.180 0.176 0.008
#> GSM339538 3 0.0665 0.8240 0.000 0.000 0.980 0.008 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 protocol(p) agent(p) individual(p) k
#> ATC:NMF 83 0.900 0.446 4.26e-03 2
#> ATC:NMF 82 0.904 0.778 4.41e-05 3
#> ATC:NMF 76 0.781 0.969 7.92e-06 4
#> ATC:NMF 63 0.756 0.523 6.56e-07 5
#> ATC:NMF 60 0.636 0.743 1.34e-05 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