Date: 2019-12-25 21:04:46 CET, cola version: 1.3.2
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All available functions which can be applied to this res_list object:
res_list
#> A 'ConsensusPartitionList' object with 24 methods.
#> On a matrix with 19175 rows and 81 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] 19175 81
The density distribution for each sample is visualized as in one column in the following heatmap. The clustering is based on the distance which is the Kolmogorov-Smirnov statistic between two distributions.
library(ComplexHeatmap)
densityHeatmap(mat, top_annotation = HeatmapAnnotation(df = get_anno(res_list),
col = get_anno_col(res_list)), ylab = "value", cluster_columns = TRUE, show_column_names = FALSE,
mc.cores = 4)
Folowing table shows the best k (number of partitions) for each combination
of top-value methods and partition methods. Clicking on the method name in
the table goes to the section for a single combination of methods.
The cola vignette explains the definition of the metrics used for determining the best number of partitions.
suggest_best_k(res_list)
| The best k | 1-PAC | Mean silhouette | Concordance | Optional k | ||
|---|---|---|---|---|---|---|
| SD:kmeans | 2 | 1.000 | 0.999 | 1.000 | ** | |
| CV:kmeans | 2 | 1.000 | 0.990 | 0.996 | ** | |
| CV:skmeans | 2 | 1.000 | 0.984 | 0.994 | ** | |
| CV:NMF | 2 | 1.000 | 0.998 | 0.999 | ** | |
| MAD:kmeans | 2 | 1.000 | 0.974 | 0.990 | ** | |
| MAD:skmeans | 2 | 1.000 | 0.987 | 0.995 | ** | |
| ATC:kmeans | 2 | 1.000 | 1.000 | 1.000 | ** | |
| SD:skmeans | 4 | 0.989 | 0.962 | 0.979 | ** | 2,3 |
| MAD:mclust | 4 | 0.988 | 0.958 | 0.971 | ** | 2,3 |
| ATC:NMF | 3 | 0.953 | 0.942 | 0.976 | ** | 2 |
| SD:pam | 2 | 0.948 | 0.943 | 0.978 | * | |
| ATC:mclust | 3 | 0.928 | 0.962 | 0.979 | * | 2 |
| MAD:pam | 2 | 0.924 | 0.960 | 0.982 | * | |
| ATC:skmeans | 4 | 0.920 | 0.922 | 0.957 | * | 2,3 |
| SD:mclust | 4 | 0.920 | 0.899 | 0.952 | * | 2 |
| ATC:hclust | 3 | 0.908 | 0.928 | 0.960 | * | |
| SD:NMF | 4 | 0.907 | 0.876 | 0.941 | * | 2 |
| ATC:pam | 6 | 0.905 | 0.811 | 0.909 | * | 2 |
| MAD:NMF | 4 | 0.904 | 0.902 | 0.945 | * | 2 |
| MAD:hclust | 6 | 0.887 | 0.844 | 0.905 | ||
| CV:mclust | 2 | 0.860 | 0.978 | 0.988 | ||
| CV:pam | 2 | 0.737 | 0.848 | 0.938 | ||
| SD:hclust | 4 | 0.685 | 0.836 | 0.854 | ||
| CV:hclust | 2 | 0.547 | 0.863 | 0.927 |
**: 1-PAC > 0.95, *: 1-PAC > 0.9
Cumulative distribution function curves of consensus matrix for all methods.
collect_plots(res_list, fun = plot_ecdf)
Consensus heatmaps for all methods. (What is a consensus heatmap?)
collect_plots(res_list, k = 2, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 3, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 4, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 5, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 6, fun = consensus_heatmap, mc.cores = 4)
Membership heatmaps for all methods. (What is a membership heatmap?)
collect_plots(res_list, k = 2, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 3, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 4, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 5, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 6, fun = membership_heatmap, mc.cores = 4)
Signature heatmaps for all methods. (What is a signature heatmap?)
Note in following heatmaps, rows are scaled.
collect_plots(res_list, k = 2, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 3, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 4, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 5, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 6, fun = get_signatures, mc.cores = 4)
The statistics used for measuring the stability of consensus partitioning. (How are they defined?)
get_stats(res_list, k = 2)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 2 1.000 0.9999 1.000 0.507 0.494 0.494
#> CV:NMF 2 1.000 0.9977 0.999 0.506 0.494 0.494
#> MAD:NMF 2 1.000 0.9953 0.998 0.507 0.494 0.494
#> ATC:NMF 2 1.000 0.9697 0.987 0.503 0.496 0.496
#> SD:skmeans 2 1.000 0.9973 0.999 0.507 0.494 0.494
#> CV:skmeans 2 1.000 0.9844 0.994 0.506 0.494 0.494
#> MAD:skmeans 2 1.000 0.9870 0.995 0.507 0.494 0.494
#> ATC:skmeans 2 1.000 1.0000 1.000 0.507 0.494 0.494
#> SD:mclust 2 1.000 1.0000 1.000 0.501 0.500 0.500
#> CV:mclust 2 0.860 0.9780 0.988 0.494 0.503 0.503
#> MAD:mclust 2 1.000 1.0000 1.000 0.501 0.500 0.500
#> ATC:mclust 2 1.000 1.0000 1.000 0.501 0.500 0.500
#> SD:kmeans 2 1.000 0.9992 1.000 0.507 0.494 0.494
#> CV:kmeans 2 1.000 0.9896 0.996 0.506 0.494 0.494
#> MAD:kmeans 2 1.000 0.9744 0.990 0.506 0.494 0.494
#> ATC:kmeans 2 1.000 1.0000 1.000 0.507 0.494 0.494
#> SD:pam 2 0.948 0.9434 0.978 0.505 0.494 0.494
#> CV:pam 2 0.737 0.8476 0.938 0.497 0.498 0.498
#> MAD:pam 2 0.924 0.9602 0.982 0.505 0.494 0.494
#> ATC:pam 2 1.000 0.9989 0.999 0.507 0.494 0.494
#> SD:hclust 2 0.502 0.6191 0.829 0.443 0.650 0.650
#> CV:hclust 2 0.547 0.8627 0.927 0.485 0.494 0.494
#> MAD:hclust 2 0.497 0.0676 0.621 0.453 0.568 0.568
#> ATC:hclust 2 0.664 0.8963 0.932 0.482 0.494 0.494
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 0.830 0.860 0.939 0.289 0.797 0.609
#> CV:NMF 3 0.718 0.814 0.903 0.253 0.819 0.649
#> MAD:NMF 3 0.764 0.822 0.916 0.286 0.800 0.615
#> ATC:NMF 3 0.953 0.942 0.976 0.279 0.811 0.635
#> SD:skmeans 3 0.975 0.956 0.970 0.264 0.805 0.627
#> CV:skmeans 3 0.866 0.863 0.939 0.277 0.805 0.625
#> MAD:skmeans 3 0.859 0.923 0.932 0.261 0.800 0.618
#> ATC:skmeans 3 1.000 0.970 0.986 0.210 0.898 0.794
#> SD:mclust 3 0.822 0.778 0.905 0.299 0.861 0.722
#> CV:mclust 3 0.621 0.812 0.879 0.300 0.832 0.673
#> MAD:mclust 3 0.901 0.973 0.983 0.287 0.857 0.714
#> ATC:mclust 3 0.928 0.962 0.979 0.301 0.844 0.689
#> SD:kmeans 3 0.725 0.563 0.727 0.244 0.794 0.606
#> CV:kmeans 3 0.708 0.821 0.846 0.264 0.810 0.637
#> MAD:kmeans 3 0.652 0.457 0.765 0.247 0.966 0.931
#> ATC:kmeans 3 0.695 0.792 0.828 0.234 0.880 0.756
#> SD:pam 3 0.646 0.730 0.840 0.259 0.863 0.729
#> CV:pam 3 0.563 0.542 0.768 0.311 0.765 0.560
#> MAD:pam 3 0.785 0.828 0.886 0.290 0.794 0.606
#> ATC:pam 3 0.867 0.852 0.905 0.235 0.809 0.638
#> SD:hclust 3 0.535 0.569 0.760 0.437 0.666 0.495
#> CV:hclust 3 0.447 0.778 0.840 0.255 0.883 0.763
#> MAD:hclust 3 0.549 0.550 0.760 0.411 0.514 0.300
#> ATC:hclust 3 0.908 0.928 0.960 0.254 0.896 0.790
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.907 0.876 0.941 0.1331 0.771 0.447
#> CV:NMF 4 0.741 0.803 0.888 0.1750 0.799 0.498
#> MAD:NMF 4 0.904 0.902 0.945 0.1382 0.760 0.430
#> ATC:NMF 4 0.733 0.738 0.854 0.1256 0.822 0.571
#> SD:skmeans 4 0.989 0.962 0.979 0.1643 0.870 0.647
#> CV:skmeans 4 0.754 0.855 0.917 0.1587 0.845 0.587
#> MAD:skmeans 4 0.883 0.928 0.957 0.1509 0.864 0.635
#> ATC:skmeans 4 0.920 0.922 0.957 0.1299 0.895 0.735
#> SD:mclust 4 0.920 0.899 0.952 0.0944 0.921 0.786
#> CV:mclust 4 0.782 0.851 0.908 0.0938 0.941 0.837
#> MAD:mclust 4 0.988 0.958 0.971 0.0864 0.934 0.817
#> ATC:mclust 4 0.789 0.839 0.889 0.0894 0.911 0.748
#> SD:kmeans 4 0.701 0.773 0.797 0.1469 0.858 0.626
#> CV:kmeans 4 0.815 0.805 0.871 0.1403 0.859 0.625
#> MAD:kmeans 4 0.710 0.716 0.783 0.1457 0.767 0.508
#> ATC:kmeans 4 0.808 0.681 0.839 0.1397 0.819 0.558
#> SD:pam 4 0.688 0.571 0.723 0.1388 0.956 0.883
#> CV:pam 4 0.564 0.569 0.776 0.1248 0.853 0.600
#> MAD:pam 4 0.669 0.771 0.852 0.1450 0.903 0.717
#> ATC:pam 4 0.894 0.870 0.939 0.0989 0.862 0.668
#> SD:hclust 4 0.685 0.836 0.854 0.1485 0.815 0.521
#> CV:hclust 4 0.600 0.656 0.787 0.1680 0.841 0.591
#> MAD:hclust 4 0.768 0.842 0.850 0.1603 0.868 0.628
#> ATC:hclust 4 0.809 0.843 0.898 0.1441 0.944 0.858
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.809 0.788 0.884 0.0598 0.921 0.714
#> CV:NMF 5 0.717 0.642 0.797 0.0566 0.976 0.901
#> MAD:NMF 5 0.866 0.844 0.917 0.0572 0.919 0.707
#> ATC:NMF 5 0.864 0.868 0.922 0.0861 0.881 0.625
#> SD:skmeans 5 0.846 0.815 0.893 0.0564 0.921 0.708
#> CV:skmeans 5 0.740 0.717 0.849 0.0588 0.923 0.708
#> MAD:skmeans 5 0.846 0.818 0.899 0.0704 0.914 0.691
#> ATC:skmeans 5 0.857 0.876 0.925 0.1137 0.869 0.590
#> SD:mclust 5 0.835 0.894 0.923 0.0876 0.920 0.733
#> CV:mclust 5 0.681 0.701 0.798 0.0763 0.917 0.735
#> MAD:mclust 5 0.837 0.822 0.893 0.0821 0.905 0.699
#> ATC:mclust 5 0.776 0.799 0.864 0.0716 0.922 0.724
#> SD:kmeans 5 0.665 0.735 0.816 0.0684 0.930 0.749
#> CV:kmeans 5 0.788 0.792 0.838 0.0631 0.911 0.677
#> MAD:kmeans 5 0.680 0.777 0.833 0.0663 0.931 0.743
#> ATC:kmeans 5 0.725 0.668 0.751 0.0779 0.885 0.625
#> SD:pam 5 0.834 0.791 0.904 0.0961 0.814 0.489
#> CV:pam 5 0.734 0.663 0.796 0.0827 0.899 0.635
#> MAD:pam 5 0.827 0.832 0.917 0.0667 0.867 0.540
#> ATC:pam 5 0.862 0.925 0.935 0.1419 0.868 0.596
#> SD:hclust 5 0.813 0.790 0.875 0.0803 0.963 0.853
#> CV:hclust 5 0.686 0.630 0.819 0.0753 0.909 0.671
#> MAD:hclust 5 0.815 0.789 0.851 0.0635 0.972 0.886
#> ATC:hclust 5 0.857 0.403 0.681 0.0754 0.821 0.498
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.857 0.830 0.909 0.0357 0.959 0.815
#> CV:NMF 6 0.756 0.716 0.841 0.0364 0.932 0.707
#> MAD:NMF 6 0.851 0.785 0.893 0.0330 0.949 0.776
#> ATC:NMF 6 0.771 0.768 0.859 0.0194 0.954 0.794
#> SD:skmeans 6 0.824 0.748 0.852 0.0341 0.965 0.840
#> CV:skmeans 6 0.721 0.630 0.807 0.0340 0.968 0.852
#> MAD:skmeans 6 0.825 0.744 0.850 0.0350 0.974 0.876
#> ATC:skmeans 6 0.849 0.874 0.914 0.0428 0.965 0.840
#> SD:mclust 6 0.759 0.779 0.834 0.0296 0.961 0.827
#> CV:mclust 6 0.667 0.715 0.765 0.0434 0.958 0.827
#> MAD:mclust 6 0.781 0.757 0.817 0.0439 0.952 0.808
#> ATC:mclust 6 0.880 0.861 0.906 0.0396 0.962 0.838
#> SD:kmeans 6 0.717 0.666 0.759 0.0478 1.000 1.000
#> CV:kmeans 6 0.759 0.689 0.816 0.0430 0.966 0.844
#> MAD:kmeans 6 0.780 0.714 0.790 0.0470 0.982 0.919
#> ATC:kmeans 6 0.701 0.652 0.778 0.0458 0.940 0.751
#> SD:pam 6 0.869 0.799 0.902 0.0391 0.952 0.775
#> CV:pam 6 0.791 0.690 0.837 0.0325 0.945 0.746
#> MAD:pam 6 0.865 0.834 0.920 0.0312 0.973 0.864
#> ATC:pam 6 0.905 0.811 0.909 0.0543 0.887 0.529
#> SD:hclust 6 0.834 0.767 0.825 0.0327 0.967 0.844
#> CV:hclust 6 0.766 0.701 0.834 0.0339 0.963 0.836
#> MAD:hclust 6 0.887 0.844 0.905 0.0325 0.943 0.752
#> ATC:hclust 6 0.801 0.769 0.879 0.0442 0.841 0.448
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 disease.state(p) time(p) k
#> SD:NMF 81 8.31e-15 6.68e-12 2
#> CV:NMF 81 2.66e-14 3.66e-11 2
#> MAD:NMF 81 8.31e-15 6.68e-12 2
#> ATC:NMF 81 3.67e-13 7.52e-11 2
#> SD:skmeans 81 8.31e-15 6.68e-12 2
#> CV:skmeans 80 1.27e-14 1.07e-11 2
#> MAD:skmeans 80 3.52e-15 2.80e-12 2
#> ATC:skmeans 81 2.25e-15 1.79e-12 2
#> SD:mclust 81 2.58e-18 2.22e-15 2
#> CV:mclust 81 1.87e-17 1.38e-14 2
#> MAD:mclust 81 2.58e-18 2.22e-15 2
#> ATC:mclust 81 2.58e-18 2.22e-15 2
#> SD:kmeans 81 8.31e-15 6.68e-12 2
#> CV:kmeans 80 1.27e-14 1.07e-11 2
#> MAD:kmeans 80 3.52e-15 2.80e-12 2
#> ATC:kmeans 81 2.25e-15 1.79e-12 2
#> SD:pam 79 1.34e-15 8.94e-13 2
#> CV:pam 74 3.66e-13 6.07e-10 2
#> MAD:pam 80 3.52e-15 2.13e-12 2
#> ATC:pam 81 2.25e-15 1.79e-12 2
#> SD:hclust 57 9.39e-10 2.44e-07 2
#> CV:hclust 79 5.88e-14 9.17e-11 2
#> MAD:hclust 0 NA NA 2
#> ATC:hclust 81 8.31e-15 6.68e-12 2
test_to_known_factors(res_list, k = 3)
#> n disease.state(p) time(p) k
#> SD:NMF 74 1.13e-14 2.50e-06 3
#> CV:NMF 73 9.31e-17 1.77e-07 3
#> MAD:NMF 75 7.19e-11 5.22e-07 3
#> ATC:NMF 79 1.35e-17 1.03e-07 3
#> SD:skmeans 81 3.60e-27 5.71e-12 3
#> CV:skmeans 75 2.83e-28 3.27e-12 3
#> MAD:skmeans 80 2.62e-29 2.47e-12 3
#> ATC:skmeans 79 2.34e-21 2.10e-09 3
#> SD:mclust 64 2.57e-22 2.07e-09 3
#> CV:mclust 74 6.00e-28 2.93e-11 3
#> MAD:mclust 81 3.91e-20 4.99e-13 3
#> ATC:mclust 81 2.64e-23 5.91e-13 3
#> SD:kmeans 53 3.10e-12 1.17e-09 3
#> CV:kmeans 76 3.75e-26 3.41e-11 3
#> MAD:kmeans 50 2.49e-15 1.53e-10 3
#> ATC:kmeans 71 3.57e-20 1.36e-08 3
#> SD:pam 70 1.75e-20 1.23e-10 3
#> CV:pam 49 2.29e-11 7.46e-09 3
#> MAD:pam 80 1.31e-16 5.09e-13 3
#> ATC:pam 77 9.00e-19 3.70e-12 3
#> SD:hclust 70 1.89e-11 4.80e-03 3
#> CV:hclust 75 1.31e-21 3.11e-08 3
#> MAD:hclust 52 1.47e-14 5.95e-05 3
#> ATC:hclust 81 1.14e-20 2.30e-09 3
test_to_known_factors(res_list, k = 4)
#> n disease.state(p) time(p) k
#> SD:NMF 75 1.29e-22 1.20e-07 4
#> CV:NMF 75 6.77e-23 6.06e-07 4
#> MAD:NMF 78 2.10e-23 5.21e-08 4
#> ATC:NMF 70 7.81e-25 5.24e-09 4
#> SD:skmeans 80 7.58e-24 3.57e-08 4
#> CV:skmeans 77 1.32e-22 1.20e-07 4
#> MAD:skmeans 80 2.81e-24 4.12e-08 4
#> ATC:skmeans 79 5.71e-21 3.22e-08 4
#> SD:mclust 79 4.89e-26 5.11e-10 4
#> CV:mclust 78 2.73e-28 7.14e-10 4
#> MAD:mclust 81 7.80e-27 1.38e-10 4
#> ATC:mclust 78 9.56e-22 1.24e-10 4
#> SD:kmeans 74 7.74e-25 4.80e-09 4
#> CV:kmeans 74 5.68e-25 3.30e-09 4
#> MAD:kmeans 68 8.55e-24 5.14e-08 4
#> ATC:kmeans 60 6.88e-22 6.36e-09 4
#> SD:pam 63 1.66e-21 3.09e-08 4
#> CV:pam 58 6.50e-21 1.04e-06 4
#> MAD:pam 77 7.44e-15 4.55e-10 4
#> ATC:pam 76 8.89e-23 1.89e-10 4
#> SD:hclust 75 7.84e-23 6.00e-07 4
#> CV:hclust 64 9.97e-20 2.41e-07 4
#> MAD:hclust 80 7.11e-22 1.39e-07 4
#> ATC:hclust 76 1.33e-22 6.02e-10 4
test_to_known_factors(res_list, k = 5)
#> n disease.state(p) time(p) k
#> SD:NMF 76 1.35e-20 2.64e-07 5
#> CV:NMF 66 2.10e-19 1.51e-06 5
#> MAD:NMF 78 5.39e-22 4.75e-09 5
#> ATC:NMF 78 9.09e-22 1.39e-08 5
#> SD:skmeans 77 5.28e-24 3.07e-08 5
#> CV:skmeans 70 2.73e-22 2.97e-07 5
#> MAD:skmeans 75 1.82e-24 5.75e-08 5
#> ATC:skmeans 74 1.51e-23 7.66e-08 5
#> SD:mclust 80 4.92e-25 2.60e-08 5
#> CV:mclust 67 3.26e-22 1.19e-06 5
#> MAD:mclust 74 1.01e-23 6.87e-08 5
#> ATC:mclust 70 1.20e-21 1.07e-09 5
#> SD:kmeans 68 1.52e-19 5.08e-07 5
#> CV:kmeans 74 1.78e-25 1.10e-07 5
#> MAD:kmeans 71 1.83e-22 3.13e-07 5
#> ATC:kmeans 61 4.93e-17 7.00e-06 5
#> SD:pam 71 2.84e-22 2.95e-08 5
#> CV:pam 63 7.92e-21 1.07e-06 5
#> MAD:pam 74 1.78e-25 1.42e-07 5
#> ATC:pam 79 2.36e-19 7.35e-07 5
#> SD:hclust 75 3.58e-20 1.09e-07 5
#> CV:hclust 58 1.31e-15 7.82e-07 5
#> MAD:hclust 74 4.64e-18 1.27e-07 5
#> ATC:hclust 42 9.88e-06 7.67e-01 5
test_to_known_factors(res_list, k = 6)
#> n disease.state(p) time(p) k
#> SD:NMF 78 2.64e-21 4.13e-07 6
#> CV:NMF 70 6.40e-19 3.29e-06 6
#> MAD:NMF 72 4.21e-20 1.81e-06 6
#> ATC:NMF 75 2.99e-20 1.72e-06 6
#> SD:skmeans 74 3.62e-24 3.66e-06 6
#> CV:skmeans 67 2.20e-22 1.81e-06 6
#> MAD:skmeans 72 2.18e-23 5.08e-06 6
#> ATC:skmeans 78 2.39e-23 3.26e-08 6
#> SD:mclust 75 4.06e-22 4.91e-08 6
#> CV:mclust 71 1.15e-22 4.08e-07 6
#> MAD:mclust 73 4.00e-22 1.78e-08 6
#> ATC:mclust 77 1.48e-22 1.54e-08 6
#> SD:kmeans 69 3.74e-20 4.80e-07 6
#> CV:kmeans 68 7.82e-23 6.70e-07 6
#> MAD:kmeans 71 1.83e-22 3.13e-07 6
#> ATC:kmeans 64 7.33e-19 6.72e-06 6
#> SD:pam 73 5.87e-20 4.16e-08 6
#> CV:pam 69 1.30e-23 5.06e-05 6
#> MAD:pam 75 1.15e-24 2.15e-06 6
#> ATC:pam 69 1.16e-19 3.70e-07 6
#> SD:hclust 79 5.29e-24 2.24e-08 6
#> CV:hclust 69 7.90e-20 6.23e-06 6
#> MAD:hclust 77 1.36e-22 3.65e-08 6
#> ATC:hclust 69 1.28e-19 8.02e-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 19175 rows and 81 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 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 0.502 0.619 0.829 0.4433 0.650 0.650
#> 3 3 0.535 0.569 0.760 0.4368 0.666 0.495
#> 4 4 0.685 0.836 0.854 0.1485 0.815 0.521
#> 5 5 0.813 0.790 0.875 0.0803 0.963 0.853
#> 6 6 0.834 0.767 0.825 0.0327 0.967 0.844
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
#> GSM509706 1 0.9922 0.754 0.552 0.448
#> GSM509711 1 0.9286 0.713 0.656 0.344
#> GSM509714 1 0.7528 0.165 0.784 0.216
#> GSM509719 1 0.9922 0.754 0.552 0.448
#> GSM509724 1 0.9922 0.754 0.552 0.448
#> GSM509729 1 0.9909 0.755 0.556 0.444
#> GSM509707 1 0.9922 0.754 0.552 0.448
#> GSM509712 1 0.9286 0.713 0.656 0.344
#> GSM509715 2 0.9933 0.955 0.452 0.548
#> GSM509720 1 0.9922 0.754 0.552 0.448
#> GSM509725 1 0.9922 0.754 0.552 0.448
#> GSM509730 1 0.9909 0.755 0.556 0.444
#> GSM509708 1 0.9922 0.754 0.552 0.448
#> GSM509713 1 0.9286 0.713 0.656 0.344
#> GSM509716 2 0.9933 0.955 0.452 0.548
#> GSM509721 1 0.9922 0.754 0.552 0.448
#> GSM509726 1 0.9922 0.754 0.552 0.448
#> GSM509731 2 1.0000 0.901 0.496 0.504
#> GSM509709 1 0.9922 0.754 0.552 0.448
#> GSM509717 2 0.9933 0.955 0.452 0.548
#> GSM509722 1 0.9922 0.754 0.552 0.448
#> GSM509727 1 0.9909 0.755 0.556 0.444
#> GSM509710 1 0.9922 0.754 0.552 0.448
#> GSM509718 1 0.9993 -0.876 0.516 0.484
#> GSM509723 1 0.9922 0.754 0.552 0.448
#> GSM509728 1 0.9909 0.755 0.556 0.444
#> GSM509732 1 0.9922 0.754 0.552 0.448
#> GSM509736 1 0.9896 0.754 0.560 0.440
#> GSM509741 1 0.9922 0.754 0.552 0.448
#> GSM509746 1 0.9922 0.754 0.552 0.448
#> GSM509733 1 0.9922 0.754 0.552 0.448
#> GSM509737 1 0.9896 0.754 0.560 0.440
#> GSM509742 1 0.9922 0.754 0.552 0.448
#> GSM509747 1 0.9922 0.754 0.552 0.448
#> GSM509734 1 0.9922 0.754 0.552 0.448
#> GSM509738 1 0.9896 0.754 0.560 0.440
#> GSM509743 1 0.9909 0.755 0.556 0.444
#> GSM509748 1 0.9909 0.755 0.556 0.444
#> GSM509735 1 0.9922 0.754 0.552 0.448
#> GSM509739 1 0.9922 0.754 0.552 0.448
#> GSM509744 1 0.9909 0.755 0.556 0.444
#> GSM509749 1 0.9909 0.755 0.556 0.444
#> GSM509740 1 0.9552 0.710 0.624 0.376
#> GSM509745 1 0.9491 0.714 0.632 0.368
#> GSM509750 1 0.9896 0.754 0.560 0.440
#> GSM509751 1 0.0000 0.417 1.000 0.000
#> GSM509753 1 0.0000 0.417 1.000 0.000
#> GSM509755 1 0.0000 0.417 1.000 0.000
#> GSM509757 1 0.0000 0.417 1.000 0.000
#> GSM509759 1 0.0000 0.417 1.000 0.000
#> GSM509761 1 0.0376 0.410 0.996 0.004
#> GSM509763 2 0.9993 0.951 0.484 0.516
#> GSM509765 2 0.9998 0.941 0.492 0.508
#> GSM509767 1 0.0376 0.409 0.996 0.004
#> GSM509769 1 0.6887 -0.162 0.816 0.184
#> GSM509771 1 0.0000 0.417 1.000 0.000
#> GSM509773 1 0.8955 -0.559 0.688 0.312
#> GSM509775 1 0.9209 -0.619 0.664 0.336
#> GSM509777 2 0.9922 0.975 0.448 0.552
#> GSM509779 2 0.9922 0.975 0.448 0.552
#> GSM509781 2 0.9922 0.975 0.448 0.552
#> GSM509783 2 0.9922 0.975 0.448 0.552
#> GSM509785 2 0.9922 0.975 0.448 0.552
#> GSM509752 1 0.0000 0.417 1.000 0.000
#> GSM509754 1 0.0000 0.417 1.000 0.000
#> GSM509756 1 0.0000 0.417 1.000 0.000
#> GSM509758 1 0.0376 0.409 0.996 0.004
#> GSM509760 1 0.0000 0.417 1.000 0.000
#> GSM509762 1 0.0376 0.410 0.996 0.004
#> GSM509764 1 0.0000 0.417 1.000 0.000
#> GSM509766 2 0.9998 0.941 0.492 0.508
#> GSM509768 1 0.9815 -0.801 0.580 0.420
#> GSM509770 1 0.0000 0.417 1.000 0.000
#> GSM509772 1 0.0000 0.417 1.000 0.000
#> GSM509774 2 0.9922 0.975 0.448 0.552
#> GSM509776 1 0.9087 -0.589 0.676 0.324
#> GSM509778 2 0.9922 0.975 0.448 0.552
#> GSM509780 2 0.9922 0.975 0.448 0.552
#> GSM509782 2 0.9922 0.975 0.448 0.552
#> GSM509784 2 0.9922 0.975 0.448 0.552
#> GSM509786 2 0.9922 0.975 0.448 0.552
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM509706 1 0.8494 0.7387 0.556 0.336 0.108
#> GSM509711 1 0.6476 0.6858 0.548 0.448 0.004
#> GSM509714 1 0.5929 -0.0493 0.676 0.320 0.004
#> GSM509719 1 0.8683 0.7365 0.540 0.340 0.120
#> GSM509724 1 0.8494 0.7387 0.556 0.336 0.108
#> GSM509729 1 0.8666 0.7363 0.544 0.336 0.120
#> GSM509707 1 0.8494 0.7387 0.556 0.336 0.108
#> GSM509712 1 0.6476 0.6858 0.548 0.448 0.004
#> GSM509715 2 0.6104 0.7926 0.348 0.648 0.004
#> GSM509720 1 0.8683 0.7365 0.540 0.340 0.120
#> GSM509725 1 0.8610 0.7367 0.548 0.336 0.116
#> GSM509730 1 0.8666 0.7363 0.544 0.336 0.120
#> GSM509708 1 0.8494 0.7387 0.556 0.336 0.108
#> GSM509713 1 0.6476 0.6858 0.548 0.448 0.004
#> GSM509716 2 0.6104 0.7926 0.348 0.648 0.004
#> GSM509721 1 0.8683 0.7365 0.540 0.340 0.120
#> GSM509726 1 0.8610 0.7367 0.548 0.336 0.116
#> GSM509731 2 0.6298 0.7534 0.388 0.608 0.004
#> GSM509709 1 0.8494 0.7387 0.556 0.336 0.108
#> GSM509717 2 0.6104 0.7926 0.348 0.648 0.004
#> GSM509722 1 0.8683 0.7365 0.540 0.340 0.120
#> GSM509727 1 0.9961 0.5011 0.372 0.296 0.332
#> GSM509710 1 0.8494 0.7387 0.556 0.336 0.108
#> GSM509718 2 0.7459 0.7497 0.372 0.584 0.044
#> GSM509723 1 0.8683 0.7365 0.540 0.340 0.120
#> GSM509728 1 0.9961 0.5011 0.372 0.296 0.332
#> GSM509732 3 0.0237 0.6296 0.004 0.000 0.996
#> GSM509736 3 0.4609 0.4798 0.128 0.028 0.844
#> GSM509741 3 0.0424 0.6276 0.008 0.000 0.992
#> GSM509746 3 0.0237 0.6296 0.004 0.000 0.996
#> GSM509733 3 0.0237 0.6296 0.004 0.000 0.996
#> GSM509737 3 0.4609 0.4798 0.128 0.028 0.844
#> GSM509742 3 0.0424 0.6276 0.008 0.000 0.992
#> GSM509747 3 0.0237 0.6296 0.004 0.000 0.996
#> GSM509734 3 0.0237 0.6296 0.004 0.000 0.996
#> GSM509738 3 0.4609 0.4798 0.128 0.028 0.844
#> GSM509743 3 0.0475 0.6295 0.004 0.004 0.992
#> GSM509748 3 0.0237 0.6297 0.004 0.000 0.996
#> GSM509735 1 0.8494 0.7387 0.556 0.336 0.108
#> GSM509739 1 0.8494 0.7387 0.556 0.336 0.108
#> GSM509744 3 0.0829 0.6272 0.004 0.012 0.984
#> GSM509749 3 0.0237 0.6297 0.004 0.000 0.996
#> GSM509740 2 0.9894 -0.5401 0.324 0.400 0.276
#> GSM509745 3 0.9757 -0.2276 0.228 0.380 0.392
#> GSM509750 3 0.0848 0.6299 0.008 0.008 0.984
#> GSM509751 3 0.6252 0.5624 0.444 0.000 0.556
#> GSM509753 3 0.6252 0.5624 0.444 0.000 0.556
#> GSM509755 3 0.6252 0.5624 0.444 0.000 0.556
#> GSM509757 3 0.6252 0.5624 0.444 0.000 0.556
#> GSM509759 3 0.6252 0.5624 0.444 0.000 0.556
#> GSM509761 3 0.6468 0.5558 0.444 0.004 0.552
#> GSM509763 2 0.7466 0.8435 0.444 0.520 0.036
#> GSM509765 2 0.7652 0.8325 0.444 0.512 0.044
#> GSM509767 3 0.6468 0.5555 0.444 0.004 0.552
#> GSM509769 1 0.9465 -0.5205 0.444 0.184 0.372
#> GSM509771 3 0.6252 0.5624 0.444 0.000 0.556
#> GSM509773 1 0.9713 -0.6470 0.444 0.316 0.240
#> GSM509775 1 0.9633 -0.6737 0.444 0.340 0.216
#> GSM509777 2 0.6252 0.8759 0.444 0.556 0.000
#> GSM509779 2 0.6252 0.8759 0.444 0.556 0.000
#> GSM509781 2 0.6252 0.8759 0.444 0.556 0.000
#> GSM509783 2 0.6252 0.8759 0.444 0.556 0.000
#> GSM509785 2 0.6252 0.8759 0.444 0.556 0.000
#> GSM509752 3 0.6252 0.5624 0.444 0.000 0.556
#> GSM509754 3 0.6252 0.5624 0.444 0.000 0.556
#> GSM509756 3 0.6252 0.5624 0.444 0.000 0.556
#> GSM509758 3 0.6468 0.5556 0.444 0.004 0.552
#> GSM509760 3 0.6252 0.5624 0.444 0.000 0.556
#> GSM509762 3 0.6468 0.5558 0.444 0.004 0.552
#> GSM509764 3 0.6252 0.5624 0.444 0.000 0.556
#> GSM509766 2 0.7652 0.8325 0.444 0.512 0.044
#> GSM509768 1 0.9068 -0.7736 0.444 0.420 0.136
#> GSM509770 3 0.6252 0.5624 0.444 0.000 0.556
#> GSM509772 3 0.6252 0.5624 0.444 0.000 0.556
#> GSM509774 2 0.6252 0.8759 0.444 0.556 0.000
#> GSM509776 1 0.9678 -0.6592 0.444 0.328 0.228
#> GSM509778 2 0.6252 0.8759 0.444 0.556 0.000
#> GSM509780 2 0.6252 0.8759 0.444 0.556 0.000
#> GSM509782 2 0.6252 0.8759 0.444 0.556 0.000
#> GSM509784 2 0.6252 0.8759 0.444 0.556 0.000
#> GSM509786 2 0.6252 0.8759 0.444 0.556 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM509706 1 0.0000 0.8801 1.000 0.000 0.000 0.000
#> GSM509711 1 0.5897 0.7996 0.756 0.068 0.068 0.108
#> GSM509714 4 0.6537 -0.0212 0.392 0.004 0.068 0.536
#> GSM509719 1 0.2652 0.8769 0.912 0.028 0.056 0.004
#> GSM509724 1 0.0000 0.8801 1.000 0.000 0.000 0.000
#> GSM509729 1 0.2652 0.8769 0.912 0.028 0.056 0.004
#> GSM509707 1 0.0000 0.8801 1.000 0.000 0.000 0.000
#> GSM509712 1 0.5897 0.7996 0.756 0.068 0.068 0.108
#> GSM509715 4 0.1356 0.7753 0.000 0.008 0.032 0.960
#> GSM509720 1 0.2652 0.8769 0.912 0.028 0.056 0.004
#> GSM509725 1 0.0336 0.8788 0.992 0.000 0.008 0.000
#> GSM509730 1 0.2652 0.8769 0.912 0.028 0.056 0.004
#> GSM509708 1 0.0000 0.8801 1.000 0.000 0.000 0.000
#> GSM509713 1 0.5897 0.7996 0.756 0.068 0.068 0.108
#> GSM509716 4 0.1356 0.7753 0.000 0.008 0.032 0.960
#> GSM509721 1 0.2652 0.8769 0.912 0.028 0.056 0.004
#> GSM509726 1 0.0336 0.8788 0.992 0.000 0.008 0.000
#> GSM509731 4 0.2125 0.7497 0.000 0.004 0.076 0.920
#> GSM509709 1 0.0000 0.8801 1.000 0.000 0.000 0.000
#> GSM509717 4 0.1356 0.7753 0.000 0.008 0.032 0.960
#> GSM509722 1 0.2652 0.8769 0.912 0.028 0.056 0.004
#> GSM509727 1 0.6560 0.5656 0.616 0.088 0.288 0.008
#> GSM509710 1 0.0000 0.8801 1.000 0.000 0.000 0.000
#> GSM509718 4 0.2908 0.7496 0.000 0.040 0.064 0.896
#> GSM509723 1 0.2652 0.8769 0.912 0.028 0.056 0.004
#> GSM509728 1 0.6560 0.5656 0.616 0.088 0.288 0.008
#> GSM509732 3 0.2654 0.9357 0.004 0.108 0.888 0.000
#> GSM509736 3 0.5186 0.8454 0.076 0.128 0.780 0.016
#> GSM509741 3 0.2831 0.9409 0.004 0.120 0.876 0.000
#> GSM509746 3 0.2654 0.9357 0.004 0.108 0.888 0.000
#> GSM509733 3 0.2654 0.9357 0.004 0.108 0.888 0.000
#> GSM509737 3 0.5186 0.8454 0.076 0.128 0.780 0.016
#> GSM509742 3 0.2831 0.9409 0.004 0.120 0.876 0.000
#> GSM509747 3 0.2654 0.9357 0.004 0.108 0.888 0.000
#> GSM509734 3 0.2654 0.9357 0.004 0.108 0.888 0.000
#> GSM509738 3 0.5186 0.8454 0.076 0.128 0.780 0.016
#> GSM509743 3 0.3105 0.9375 0.000 0.140 0.856 0.004
#> GSM509748 3 0.2921 0.9379 0.000 0.140 0.860 0.000
#> GSM509735 1 0.0188 0.8800 0.996 0.000 0.004 0.000
#> GSM509739 1 0.0000 0.8801 1.000 0.000 0.000 0.000
#> GSM509744 3 0.3208 0.9360 0.000 0.148 0.848 0.004
#> GSM509749 3 0.2921 0.9379 0.000 0.140 0.860 0.000
#> GSM509740 1 0.9093 0.4143 0.452 0.156 0.268 0.124
#> GSM509745 1 0.9221 0.2223 0.408 0.192 0.296 0.104
#> GSM509750 3 0.3208 0.9348 0.000 0.148 0.848 0.004
#> GSM509751 2 0.1867 0.9836 0.000 0.928 0.000 0.072
#> GSM509753 2 0.1867 0.9836 0.000 0.928 0.000 0.072
#> GSM509755 2 0.1867 0.9836 0.000 0.928 0.000 0.072
#> GSM509757 2 0.1867 0.9836 0.000 0.928 0.000 0.072
#> GSM509759 2 0.1867 0.9836 0.000 0.928 0.000 0.072
#> GSM509761 2 0.1940 0.9803 0.000 0.924 0.000 0.076
#> GSM509763 4 0.3219 0.8271 0.000 0.164 0.000 0.836
#> GSM509765 4 0.3649 0.7942 0.000 0.204 0.000 0.796
#> GSM509767 2 0.1940 0.9796 0.000 0.924 0.000 0.076
#> GSM509769 2 0.4103 0.6690 0.000 0.744 0.000 0.256
#> GSM509771 2 0.1867 0.9836 0.000 0.928 0.000 0.072
#> GSM509773 4 0.4916 0.4298 0.000 0.424 0.000 0.576
#> GSM509775 4 0.4907 0.4470 0.000 0.420 0.000 0.580
#> GSM509777 4 0.2647 0.8504 0.000 0.120 0.000 0.880
#> GSM509779 4 0.2647 0.8504 0.000 0.120 0.000 0.880
#> GSM509781 4 0.2647 0.8504 0.000 0.120 0.000 0.880
#> GSM509783 4 0.2647 0.8504 0.000 0.120 0.000 0.880
#> GSM509785 4 0.2647 0.8504 0.000 0.120 0.000 0.880
#> GSM509752 2 0.1867 0.9836 0.000 0.928 0.000 0.072
#> GSM509754 2 0.1867 0.9836 0.000 0.928 0.000 0.072
#> GSM509756 2 0.1867 0.9836 0.000 0.928 0.000 0.072
#> GSM509758 2 0.1940 0.9802 0.000 0.924 0.000 0.076
#> GSM509760 2 0.1867 0.9836 0.000 0.928 0.000 0.072
#> GSM509762 2 0.1940 0.9803 0.000 0.924 0.000 0.076
#> GSM509764 2 0.1867 0.9836 0.000 0.928 0.000 0.072
#> GSM509766 4 0.3649 0.7942 0.000 0.204 0.000 0.796
#> GSM509768 4 0.4585 0.6323 0.000 0.332 0.000 0.668
#> GSM509770 2 0.1867 0.9836 0.000 0.928 0.000 0.072
#> GSM509772 2 0.1867 0.9836 0.000 0.928 0.000 0.072
#> GSM509774 4 0.2647 0.8504 0.000 0.120 0.000 0.880
#> GSM509776 4 0.4941 0.4022 0.000 0.436 0.000 0.564
#> GSM509778 4 0.2647 0.8504 0.000 0.120 0.000 0.880
#> GSM509780 4 0.2647 0.8504 0.000 0.120 0.000 0.880
#> GSM509782 4 0.2647 0.8504 0.000 0.120 0.000 0.880
#> GSM509784 4 0.2647 0.8504 0.000 0.120 0.000 0.880
#> GSM509786 4 0.2647 0.8504 0.000 0.120 0.000 0.880
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM509706 1 0.0000 0.8166 1.000 0.000 0.000 0.000 0.000
#> GSM509711 5 0.4264 0.4931 0.376 0.000 0.000 0.004 0.620
#> GSM509714 4 0.6749 -0.0717 0.268 0.000 0.000 0.396 0.336
#> GSM509719 1 0.3774 0.6739 0.704 0.000 0.000 0.000 0.296
#> GSM509724 1 0.0000 0.8166 1.000 0.000 0.000 0.000 0.000
#> GSM509729 1 0.3684 0.6859 0.720 0.000 0.000 0.000 0.280
#> GSM509707 1 0.0000 0.8166 1.000 0.000 0.000 0.000 0.000
#> GSM509712 5 0.4264 0.4931 0.376 0.000 0.000 0.004 0.620
#> GSM509715 4 0.2929 0.7627 0.000 0.000 0.000 0.820 0.180
#> GSM509720 1 0.3774 0.6739 0.704 0.000 0.000 0.000 0.296
#> GSM509725 1 0.0290 0.8106 0.992 0.000 0.008 0.000 0.000
#> GSM509730 1 0.3684 0.6859 0.720 0.000 0.000 0.000 0.280
#> GSM509708 1 0.0000 0.8166 1.000 0.000 0.000 0.000 0.000
#> GSM509713 5 0.4264 0.4931 0.376 0.000 0.000 0.004 0.620
#> GSM509716 4 0.2929 0.7627 0.000 0.000 0.000 0.820 0.180
#> GSM509721 1 0.3774 0.6739 0.704 0.000 0.000 0.000 0.296
#> GSM509726 1 0.0290 0.8106 0.992 0.000 0.008 0.000 0.000
#> GSM509731 4 0.3336 0.7271 0.000 0.000 0.000 0.772 0.228
#> GSM509709 1 0.0000 0.8166 1.000 0.000 0.000 0.000 0.000
#> GSM509717 4 0.2929 0.7627 0.000 0.000 0.000 0.820 0.180
#> GSM509722 1 0.3774 0.6739 0.704 0.000 0.000 0.000 0.296
#> GSM509727 5 0.5918 0.6492 0.168 0.000 0.240 0.000 0.592
#> GSM509710 1 0.0000 0.8166 1.000 0.000 0.000 0.000 0.000
#> GSM509718 4 0.3993 0.7153 0.000 0.000 0.028 0.756 0.216
#> GSM509723 1 0.3774 0.6739 0.704 0.000 0.000 0.000 0.296
#> GSM509728 5 0.5918 0.6492 0.168 0.000 0.240 0.000 0.592
#> GSM509732 3 0.2930 0.8167 0.000 0.004 0.832 0.000 0.164
#> GSM509736 3 0.3398 0.7174 0.000 0.004 0.780 0.000 0.216
#> GSM509741 3 0.0609 0.8588 0.000 0.000 0.980 0.000 0.020
#> GSM509746 3 0.2930 0.8167 0.000 0.004 0.832 0.000 0.164
#> GSM509733 3 0.2930 0.8167 0.000 0.004 0.832 0.000 0.164
#> GSM509737 3 0.3398 0.7174 0.000 0.004 0.780 0.000 0.216
#> GSM509742 3 0.0609 0.8588 0.000 0.000 0.980 0.000 0.020
#> GSM509747 3 0.2930 0.8167 0.000 0.004 0.832 0.000 0.164
#> GSM509734 3 0.2930 0.8167 0.000 0.004 0.832 0.000 0.164
#> GSM509738 3 0.3398 0.7174 0.000 0.004 0.780 0.000 0.216
#> GSM509743 3 0.0955 0.8583 0.000 0.004 0.968 0.000 0.028
#> GSM509748 3 0.0955 0.8582 0.000 0.004 0.968 0.000 0.028
#> GSM509735 1 0.0162 0.8139 0.996 0.000 0.004 0.000 0.000
#> GSM509739 1 0.0000 0.8166 1.000 0.000 0.000 0.000 0.000
#> GSM509744 3 0.1357 0.8509 0.000 0.004 0.948 0.000 0.048
#> GSM509749 3 0.0955 0.8582 0.000 0.004 0.968 0.000 0.028
#> GSM509740 5 0.3366 0.5841 0.000 0.004 0.212 0.000 0.784
#> GSM509745 5 0.4151 0.4706 0.000 0.004 0.344 0.000 0.652
#> GSM509750 3 0.1282 0.8531 0.000 0.004 0.952 0.000 0.044
#> GSM509751 2 0.0000 0.9839 0.000 1.000 0.000 0.000 0.000
#> GSM509753 2 0.0000 0.9839 0.000 1.000 0.000 0.000 0.000
#> GSM509755 2 0.0000 0.9839 0.000 1.000 0.000 0.000 0.000
#> GSM509757 2 0.0000 0.9839 0.000 1.000 0.000 0.000 0.000
#> GSM509759 2 0.0000 0.9839 0.000 1.000 0.000 0.000 0.000
#> GSM509761 2 0.0162 0.9811 0.000 0.996 0.000 0.004 0.000
#> GSM509763 4 0.1197 0.8332 0.000 0.048 0.000 0.952 0.000
#> GSM509765 4 0.2020 0.8055 0.000 0.100 0.000 0.900 0.000
#> GSM509767 2 0.0404 0.9729 0.000 0.988 0.000 0.012 0.000
#> GSM509769 2 0.3074 0.7191 0.000 0.804 0.000 0.196 0.000
#> GSM509771 2 0.0000 0.9839 0.000 1.000 0.000 0.000 0.000
#> GSM509773 4 0.3857 0.5927 0.000 0.312 0.000 0.688 0.000
#> GSM509775 4 0.3966 0.5585 0.000 0.336 0.000 0.664 0.000
#> GSM509777 4 0.0162 0.8466 0.000 0.004 0.000 0.996 0.000
#> GSM509779 4 0.0162 0.8466 0.000 0.004 0.000 0.996 0.000
#> GSM509781 4 0.0162 0.8466 0.000 0.004 0.000 0.996 0.000
#> GSM509783 4 0.0162 0.8466 0.000 0.004 0.000 0.996 0.000
#> GSM509785 4 0.0162 0.8466 0.000 0.004 0.000 0.996 0.000
#> GSM509752 2 0.0000 0.9839 0.000 1.000 0.000 0.000 0.000
#> GSM509754 2 0.0000 0.9839 0.000 1.000 0.000 0.000 0.000
#> GSM509756 2 0.0000 0.9839 0.000 1.000 0.000 0.000 0.000
#> GSM509758 2 0.0162 0.9810 0.000 0.996 0.000 0.004 0.000
#> GSM509760 2 0.0000 0.9839 0.000 1.000 0.000 0.000 0.000
#> GSM509762 2 0.0162 0.9811 0.000 0.996 0.000 0.004 0.000
#> GSM509764 2 0.0000 0.9839 0.000 1.000 0.000 0.000 0.000
#> GSM509766 4 0.2020 0.8055 0.000 0.100 0.000 0.900 0.000
#> GSM509768 4 0.4101 0.4920 0.000 0.372 0.000 0.628 0.000
#> GSM509770 2 0.0000 0.9839 0.000 1.000 0.000 0.000 0.000
#> GSM509772 2 0.0000 0.9839 0.000 1.000 0.000 0.000 0.000
#> GSM509774 4 0.0162 0.8466 0.000 0.004 0.000 0.996 0.000
#> GSM509776 4 0.4030 0.5275 0.000 0.352 0.000 0.648 0.000
#> GSM509778 4 0.0162 0.8466 0.000 0.004 0.000 0.996 0.000
#> GSM509780 4 0.0162 0.8466 0.000 0.004 0.000 0.996 0.000
#> GSM509782 4 0.0162 0.8466 0.000 0.004 0.000 0.996 0.000
#> GSM509784 4 0.0162 0.8466 0.000 0.004 0.000 0.996 0.000
#> GSM509786 4 0.0162 0.8466 0.000 0.004 0.000 0.996 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM509706 1 0.0000 0.733 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509711 6 0.5471 0.553 0.336 0.000 0.000 0.000 0.140 0.524
#> GSM509714 5 0.6573 0.219 0.224 0.000 0.000 0.128 0.536 0.112
#> GSM509719 1 0.5672 0.542 0.528 0.000 0.000 0.000 0.212 0.260
#> GSM509724 1 0.0146 0.730 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM509729 1 0.5611 0.554 0.544 0.000 0.000 0.000 0.232 0.224
#> GSM509707 1 0.0000 0.733 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509712 6 0.5471 0.553 0.336 0.000 0.000 0.000 0.140 0.524
#> GSM509715 5 0.3244 0.853 0.000 0.000 0.000 0.268 0.732 0.000
#> GSM509720 1 0.5672 0.542 0.528 0.000 0.000 0.000 0.212 0.260
#> GSM509725 1 0.0692 0.716 0.976 0.000 0.000 0.000 0.004 0.020
#> GSM509730 1 0.5611 0.554 0.544 0.000 0.000 0.000 0.232 0.224
#> GSM509708 1 0.0000 0.733 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509713 6 0.5471 0.553 0.336 0.000 0.000 0.000 0.140 0.524
#> GSM509716 5 0.3244 0.853 0.000 0.000 0.000 0.268 0.732 0.000
#> GSM509721 1 0.5672 0.542 0.528 0.000 0.000 0.000 0.212 0.260
#> GSM509726 1 0.0692 0.716 0.976 0.000 0.000 0.000 0.004 0.020
#> GSM509731 5 0.2883 0.819 0.000 0.000 0.000 0.212 0.788 0.000
#> GSM509709 1 0.0000 0.733 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509717 5 0.3244 0.853 0.000 0.000 0.000 0.268 0.732 0.000
#> GSM509722 1 0.5672 0.542 0.528 0.000 0.000 0.000 0.212 0.260
#> GSM509727 6 0.2377 0.664 0.124 0.000 0.004 0.000 0.004 0.868
#> GSM509710 1 0.0000 0.733 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509718 5 0.4215 0.812 0.000 0.000 0.000 0.244 0.700 0.056
#> GSM509723 1 0.5672 0.542 0.528 0.000 0.000 0.000 0.212 0.260
#> GSM509728 6 0.2377 0.664 0.124 0.000 0.004 0.000 0.004 0.868
#> GSM509732 3 0.0000 0.744 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509736 3 0.4685 0.665 0.000 0.000 0.520 0.000 0.044 0.436
#> GSM509741 3 0.2883 0.804 0.000 0.000 0.788 0.000 0.000 0.212
#> GSM509746 3 0.0000 0.744 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509733 3 0.0000 0.744 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509737 3 0.4685 0.665 0.000 0.000 0.520 0.000 0.044 0.436
#> GSM509742 3 0.2883 0.804 0.000 0.000 0.788 0.000 0.000 0.212
#> GSM509747 3 0.0000 0.744 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509734 3 0.0000 0.744 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509738 3 0.4685 0.665 0.000 0.000 0.520 0.000 0.044 0.436
#> GSM509743 3 0.3409 0.805 0.000 0.000 0.700 0.000 0.000 0.300
#> GSM509748 3 0.3428 0.804 0.000 0.000 0.696 0.000 0.000 0.304
#> GSM509735 1 0.0146 0.730 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM509739 1 0.0000 0.733 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509744 3 0.3515 0.796 0.000 0.000 0.676 0.000 0.000 0.324
#> GSM509749 3 0.3428 0.804 0.000 0.000 0.696 0.000 0.000 0.304
#> GSM509740 6 0.2491 0.576 0.000 0.000 0.000 0.000 0.164 0.836
#> GSM509745 6 0.3792 0.515 0.000 0.000 0.108 0.000 0.112 0.780
#> GSM509750 3 0.3619 0.798 0.000 0.000 0.680 0.000 0.004 0.316
#> GSM509751 2 0.0000 0.984 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509753 2 0.0000 0.984 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509755 2 0.0000 0.984 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509757 2 0.0000 0.984 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509759 2 0.0000 0.984 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509761 2 0.0146 0.981 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM509763 4 0.1007 0.824 0.000 0.044 0.000 0.956 0.000 0.000
#> GSM509765 4 0.1765 0.788 0.000 0.096 0.000 0.904 0.000 0.000
#> GSM509767 2 0.0363 0.973 0.000 0.988 0.000 0.012 0.000 0.000
#> GSM509769 2 0.2762 0.716 0.000 0.804 0.000 0.196 0.000 0.000
#> GSM509771 2 0.0000 0.984 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509773 4 0.3446 0.558 0.000 0.308 0.000 0.692 0.000 0.000
#> GSM509775 4 0.3547 0.539 0.000 0.332 0.000 0.668 0.000 0.000
#> GSM509777 4 0.0000 0.846 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM509779 4 0.0000 0.846 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM509781 4 0.0000 0.846 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM509783 4 0.0000 0.846 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM509785 4 0.0000 0.846 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM509752 2 0.0000 0.984 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509754 2 0.0000 0.984 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509756 2 0.0000 0.984 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509758 2 0.0146 0.981 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM509760 2 0.0000 0.984 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509762 2 0.0146 0.981 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM509764 2 0.0000 0.984 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509766 4 0.1765 0.788 0.000 0.096 0.000 0.904 0.000 0.000
#> GSM509768 4 0.3684 0.461 0.000 0.372 0.000 0.628 0.000 0.000
#> GSM509770 2 0.0000 0.984 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509772 2 0.0000 0.984 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509774 4 0.0000 0.846 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM509776 4 0.3607 0.516 0.000 0.348 0.000 0.652 0.000 0.000
#> GSM509778 4 0.0000 0.846 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM509780 4 0.0000 0.846 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM509782 4 0.0000 0.846 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM509784 4 0.0000 0.846 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM509786 4 0.0000 0.846 0.000 0.000 0.000 1.000 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 disease.state(p) time(p) k
#> SD:hclust 57 9.39e-10 2.44e-07 2
#> SD:hclust 70 1.89e-11 4.80e-03 3
#> SD:hclust 75 7.84e-23 6.00e-07 4
#> SD:hclust 75 3.58e-20 1.09e-07 5
#> SD:hclust 79 5.29e-24 2.24e-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", "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 19175 rows and 81 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 1.000 0.999 1.000 0.5067 0.494 0.494
#> 3 3 0.725 0.563 0.727 0.2440 0.794 0.606
#> 4 4 0.701 0.773 0.797 0.1469 0.858 0.626
#> 5 5 0.665 0.735 0.816 0.0684 0.930 0.749
#> 6 6 0.717 0.666 0.759 0.0478 1.000 1.000
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
#> GSM509706 1 0.000 1.000 1.000 0.000
#> GSM509711 1 0.000 1.000 1.000 0.000
#> GSM509714 1 0.000 1.000 1.000 0.000
#> GSM509719 1 0.000 1.000 1.000 0.000
#> GSM509724 1 0.000 1.000 1.000 0.000
#> GSM509729 1 0.000 1.000 1.000 0.000
#> GSM509707 1 0.000 1.000 1.000 0.000
#> GSM509712 1 0.000 1.000 1.000 0.000
#> GSM509715 2 0.000 0.999 0.000 1.000
#> GSM509720 1 0.000 1.000 1.000 0.000
#> GSM509725 1 0.000 1.000 1.000 0.000
#> GSM509730 1 0.000 1.000 1.000 0.000
#> GSM509708 1 0.000 1.000 1.000 0.000
#> GSM509713 1 0.000 1.000 1.000 0.000
#> GSM509716 2 0.000 0.999 0.000 1.000
#> GSM509721 1 0.000 1.000 1.000 0.000
#> GSM509726 1 0.000 1.000 1.000 0.000
#> GSM509731 2 0.204 0.967 0.032 0.968
#> GSM509709 1 0.000 1.000 1.000 0.000
#> GSM509717 2 0.000 0.999 0.000 1.000
#> GSM509722 1 0.000 1.000 1.000 0.000
#> GSM509727 1 0.000 1.000 1.000 0.000
#> GSM509710 1 0.000 1.000 1.000 0.000
#> GSM509718 2 0.000 0.999 0.000 1.000
#> GSM509723 1 0.000 1.000 1.000 0.000
#> GSM509728 1 0.000 1.000 1.000 0.000
#> GSM509732 1 0.000 1.000 1.000 0.000
#> GSM509736 1 0.000 1.000 1.000 0.000
#> GSM509741 1 0.000 1.000 1.000 0.000
#> GSM509746 1 0.000 1.000 1.000 0.000
#> GSM509733 1 0.000 1.000 1.000 0.000
#> GSM509737 1 0.000 1.000 1.000 0.000
#> GSM509742 1 0.000 1.000 1.000 0.000
#> GSM509747 1 0.000 1.000 1.000 0.000
#> GSM509734 1 0.000 1.000 1.000 0.000
#> GSM509738 1 0.000 1.000 1.000 0.000
#> GSM509743 1 0.000 1.000 1.000 0.000
#> GSM509748 1 0.000 1.000 1.000 0.000
#> GSM509735 1 0.000 1.000 1.000 0.000
#> GSM509739 1 0.000 1.000 1.000 0.000
#> GSM509744 1 0.000 1.000 1.000 0.000
#> GSM509749 1 0.000 1.000 1.000 0.000
#> GSM509740 1 0.000 1.000 1.000 0.000
#> GSM509745 1 0.000 1.000 1.000 0.000
#> GSM509750 1 0.000 1.000 1.000 0.000
#> GSM509751 2 0.000 0.999 0.000 1.000
#> GSM509753 2 0.000 0.999 0.000 1.000
#> GSM509755 2 0.000 0.999 0.000 1.000
#> GSM509757 2 0.000 0.999 0.000 1.000
#> GSM509759 2 0.000 0.999 0.000 1.000
#> GSM509761 2 0.000 0.999 0.000 1.000
#> GSM509763 2 0.000 0.999 0.000 1.000
#> GSM509765 2 0.000 0.999 0.000 1.000
#> GSM509767 2 0.000 0.999 0.000 1.000
#> GSM509769 2 0.000 0.999 0.000 1.000
#> GSM509771 2 0.000 0.999 0.000 1.000
#> GSM509773 2 0.000 0.999 0.000 1.000
#> GSM509775 2 0.000 0.999 0.000 1.000
#> GSM509777 2 0.000 0.999 0.000 1.000
#> GSM509779 2 0.000 0.999 0.000 1.000
#> GSM509781 2 0.000 0.999 0.000 1.000
#> GSM509783 2 0.000 0.999 0.000 1.000
#> GSM509785 2 0.000 0.999 0.000 1.000
#> GSM509752 2 0.000 0.999 0.000 1.000
#> GSM509754 2 0.000 0.999 0.000 1.000
#> GSM509756 2 0.000 0.999 0.000 1.000
#> GSM509758 2 0.000 0.999 0.000 1.000
#> GSM509760 2 0.000 0.999 0.000 1.000
#> GSM509762 2 0.000 0.999 0.000 1.000
#> GSM509764 2 0.000 0.999 0.000 1.000
#> GSM509766 2 0.000 0.999 0.000 1.000
#> GSM509768 2 0.000 0.999 0.000 1.000
#> GSM509770 2 0.000 0.999 0.000 1.000
#> GSM509772 2 0.000 0.999 0.000 1.000
#> GSM509774 2 0.000 0.999 0.000 1.000
#> GSM509776 2 0.000 0.999 0.000 1.000
#> GSM509778 2 0.000 0.999 0.000 1.000
#> GSM509780 2 0.000 0.999 0.000 1.000
#> GSM509782 2 0.000 0.999 0.000 1.000
#> GSM509784 2 0.000 0.999 0.000 1.000
#> GSM509786 2 0.000 0.999 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM509706 1 0.6308 0.361 0.508 0.000 0.492
#> GSM509711 1 0.6154 0.355 0.592 0.000 0.408
#> GSM509714 1 0.5497 0.265 0.708 0.000 0.292
#> GSM509719 3 0.6309 -0.317 0.496 0.000 0.504
#> GSM509724 1 0.6308 0.361 0.508 0.000 0.492
#> GSM509729 1 0.6299 0.361 0.524 0.000 0.476
#> GSM509707 1 0.6308 0.361 0.508 0.000 0.492
#> GSM509712 1 0.6192 0.343 0.580 0.000 0.420
#> GSM509715 1 0.7292 -0.513 0.500 0.472 0.028
#> GSM509720 3 0.6309 -0.317 0.496 0.000 0.504
#> GSM509725 1 0.6308 0.361 0.508 0.000 0.492
#> GSM509730 3 0.6299 -0.320 0.476 0.000 0.524
#> GSM509708 1 0.6308 0.361 0.508 0.000 0.492
#> GSM509713 1 0.6140 0.357 0.596 0.000 0.404
#> GSM509716 1 0.7292 -0.513 0.500 0.472 0.028
#> GSM509721 3 0.6309 -0.317 0.496 0.000 0.504
#> GSM509726 1 0.6308 0.361 0.508 0.000 0.492
#> GSM509731 1 0.4677 0.176 0.840 0.132 0.028
#> GSM509709 1 0.6308 0.361 0.508 0.000 0.492
#> GSM509717 1 0.7292 -0.513 0.500 0.472 0.028
#> GSM509722 1 0.6274 0.289 0.544 0.000 0.456
#> GSM509727 1 0.6295 0.316 0.528 0.000 0.472
#> GSM509710 1 0.6308 0.361 0.508 0.000 0.492
#> GSM509718 1 0.7292 -0.513 0.500 0.472 0.028
#> GSM509723 3 0.6309 -0.317 0.496 0.000 0.504
#> GSM509728 3 0.2066 0.737 0.060 0.000 0.940
#> GSM509732 3 0.0237 0.782 0.004 0.000 0.996
#> GSM509736 3 0.0747 0.778 0.016 0.000 0.984
#> GSM509741 3 0.0000 0.783 0.000 0.000 1.000
#> GSM509746 3 0.0237 0.782 0.004 0.000 0.996
#> GSM509733 3 0.0237 0.782 0.004 0.000 0.996
#> GSM509737 3 0.1163 0.770 0.028 0.000 0.972
#> GSM509742 3 0.0000 0.783 0.000 0.000 1.000
#> GSM509747 3 0.0237 0.782 0.004 0.000 0.996
#> GSM509734 3 0.0237 0.782 0.004 0.000 0.996
#> GSM509738 3 0.2537 0.731 0.080 0.000 0.920
#> GSM509743 3 0.0000 0.783 0.000 0.000 1.000
#> GSM509748 3 0.0000 0.783 0.000 0.000 1.000
#> GSM509735 1 0.6308 0.361 0.508 0.000 0.492
#> GSM509739 1 0.6308 0.361 0.508 0.000 0.492
#> GSM509744 3 0.0237 0.781 0.004 0.000 0.996
#> GSM509749 3 0.0000 0.783 0.000 0.000 1.000
#> GSM509740 1 0.6305 0.231 0.516 0.000 0.484
#> GSM509745 3 0.3116 0.697 0.108 0.000 0.892
#> GSM509750 3 0.1529 0.753 0.040 0.000 0.960
#> GSM509751 2 0.0000 0.892 0.000 1.000 0.000
#> GSM509753 2 0.0000 0.892 0.000 1.000 0.000
#> GSM509755 2 0.0000 0.892 0.000 1.000 0.000
#> GSM509757 2 0.0000 0.892 0.000 1.000 0.000
#> GSM509759 2 0.0000 0.892 0.000 1.000 0.000
#> GSM509761 2 0.0000 0.892 0.000 1.000 0.000
#> GSM509763 2 0.0000 0.892 0.000 1.000 0.000
#> GSM509765 2 0.0000 0.892 0.000 1.000 0.000
#> GSM509767 2 0.0000 0.892 0.000 1.000 0.000
#> GSM509769 2 0.0000 0.892 0.000 1.000 0.000
#> GSM509771 2 0.0000 0.892 0.000 1.000 0.000
#> GSM509773 2 0.0000 0.892 0.000 1.000 0.000
#> GSM509775 2 0.0000 0.892 0.000 1.000 0.000
#> GSM509777 2 0.5431 0.733 0.284 0.716 0.000
#> GSM509779 2 0.6140 0.652 0.404 0.596 0.000
#> GSM509781 2 0.6140 0.652 0.404 0.596 0.000
#> GSM509783 2 0.6140 0.652 0.404 0.596 0.000
#> GSM509785 2 0.6140 0.652 0.404 0.596 0.000
#> GSM509752 2 0.0000 0.892 0.000 1.000 0.000
#> GSM509754 2 0.0000 0.892 0.000 1.000 0.000
#> GSM509756 2 0.0000 0.892 0.000 1.000 0.000
#> GSM509758 2 0.0000 0.892 0.000 1.000 0.000
#> GSM509760 2 0.0000 0.892 0.000 1.000 0.000
#> GSM509762 2 0.0000 0.892 0.000 1.000 0.000
#> GSM509764 2 0.0000 0.892 0.000 1.000 0.000
#> GSM509766 2 0.0000 0.892 0.000 1.000 0.000
#> GSM509768 2 0.0000 0.892 0.000 1.000 0.000
#> GSM509770 2 0.0000 0.892 0.000 1.000 0.000
#> GSM509772 2 0.0000 0.892 0.000 1.000 0.000
#> GSM509774 2 0.5948 0.683 0.360 0.640 0.000
#> GSM509776 2 0.0000 0.892 0.000 1.000 0.000
#> GSM509778 2 0.6140 0.652 0.404 0.596 0.000
#> GSM509780 2 0.0000 0.892 0.000 1.000 0.000
#> GSM509782 2 0.6140 0.652 0.404 0.596 0.000
#> GSM509784 2 0.6126 0.655 0.400 0.600 0.000
#> GSM509786 2 0.6140 0.652 0.404 0.596 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM509706 1 0.7293 0.5766 0.536 0.248 0.216 0.000
#> GSM509711 1 0.2611 0.5704 0.896 0.096 0.008 0.000
#> GSM509714 1 0.3581 0.5346 0.852 0.116 0.000 0.032
#> GSM509719 1 0.3311 0.5898 0.828 0.000 0.172 0.000
#> GSM509724 1 0.7315 0.5751 0.532 0.252 0.216 0.000
#> GSM509729 1 0.6049 0.5969 0.684 0.132 0.184 0.000
#> GSM509707 1 0.7293 0.5766 0.536 0.248 0.216 0.000
#> GSM509712 1 0.2342 0.5653 0.912 0.080 0.008 0.000
#> GSM509715 1 0.7003 0.0537 0.460 0.116 0.000 0.424
#> GSM509720 1 0.3311 0.5898 0.828 0.000 0.172 0.000
#> GSM509725 1 0.7315 0.5751 0.532 0.252 0.216 0.000
#> GSM509730 1 0.5432 0.5798 0.716 0.068 0.216 0.000
#> GSM509708 1 0.7293 0.5766 0.536 0.248 0.216 0.000
#> GSM509713 1 0.4228 0.6034 0.760 0.232 0.008 0.000
#> GSM509716 1 0.7003 0.0537 0.460 0.116 0.000 0.424
#> GSM509721 1 0.3311 0.5898 0.828 0.000 0.172 0.000
#> GSM509726 1 0.7315 0.5751 0.532 0.252 0.216 0.000
#> GSM509731 1 0.6998 0.0741 0.468 0.116 0.000 0.416
#> GSM509709 1 0.7293 0.5766 0.536 0.248 0.216 0.000
#> GSM509717 1 0.7003 0.0537 0.460 0.116 0.000 0.424
#> GSM509722 1 0.1389 0.5844 0.952 0.000 0.048 0.000
#> GSM509727 1 0.5874 0.5570 0.700 0.176 0.124 0.000
#> GSM509710 1 0.7293 0.5766 0.536 0.248 0.216 0.000
#> GSM509718 1 0.7040 0.0608 0.460 0.120 0.000 0.420
#> GSM509723 1 0.3311 0.5898 0.828 0.000 0.172 0.000
#> GSM509728 3 0.3820 0.8024 0.064 0.088 0.848 0.000
#> GSM509732 3 0.0000 0.9055 0.000 0.000 1.000 0.000
#> GSM509736 3 0.3128 0.8487 0.076 0.040 0.884 0.000
#> GSM509741 3 0.0000 0.9055 0.000 0.000 1.000 0.000
#> GSM509746 3 0.0000 0.9055 0.000 0.000 1.000 0.000
#> GSM509733 3 0.0000 0.9055 0.000 0.000 1.000 0.000
#> GSM509737 3 0.3463 0.8304 0.096 0.040 0.864 0.000
#> GSM509742 3 0.0000 0.9055 0.000 0.000 1.000 0.000
#> GSM509747 3 0.0000 0.9055 0.000 0.000 1.000 0.000
#> GSM509734 3 0.0000 0.9055 0.000 0.000 1.000 0.000
#> GSM509738 3 0.5949 0.5490 0.288 0.068 0.644 0.000
#> GSM509743 3 0.0469 0.9031 0.000 0.012 0.988 0.000
#> GSM509748 3 0.0000 0.9055 0.000 0.000 1.000 0.000
#> GSM509735 1 0.7293 0.5766 0.536 0.248 0.216 0.000
#> GSM509739 1 0.7267 0.5784 0.540 0.248 0.212 0.000
#> GSM509744 3 0.1452 0.8924 0.008 0.036 0.956 0.000
#> GSM509749 3 0.0336 0.9041 0.000 0.008 0.992 0.000
#> GSM509740 1 0.5714 0.3886 0.716 0.128 0.156 0.000
#> GSM509745 3 0.6554 0.3972 0.376 0.084 0.540 0.000
#> GSM509750 3 0.3056 0.8456 0.072 0.040 0.888 0.000
#> GSM509751 2 0.4804 0.9862 0.000 0.616 0.000 0.384
#> GSM509753 2 0.4804 0.9862 0.000 0.616 0.000 0.384
#> GSM509755 2 0.4804 0.9862 0.000 0.616 0.000 0.384
#> GSM509757 2 0.4804 0.9862 0.000 0.616 0.000 0.384
#> GSM509759 2 0.4804 0.9862 0.000 0.616 0.000 0.384
#> GSM509761 2 0.4804 0.9862 0.000 0.616 0.000 0.384
#> GSM509763 2 0.4916 0.9426 0.000 0.576 0.000 0.424
#> GSM509765 2 0.4916 0.9426 0.000 0.576 0.000 0.424
#> GSM509767 2 0.4804 0.9862 0.000 0.616 0.000 0.384
#> GSM509769 2 0.4804 0.9862 0.000 0.616 0.000 0.384
#> GSM509771 2 0.4804 0.9862 0.000 0.616 0.000 0.384
#> GSM509773 2 0.4830 0.9807 0.000 0.608 0.000 0.392
#> GSM509775 2 0.4830 0.9807 0.000 0.608 0.000 0.392
#> GSM509777 4 0.2011 0.8367 0.000 0.080 0.000 0.920
#> GSM509779 4 0.0000 0.9758 0.000 0.000 0.000 1.000
#> GSM509781 4 0.0336 0.9791 0.008 0.000 0.000 0.992
#> GSM509783 4 0.0336 0.9791 0.008 0.000 0.000 0.992
#> GSM509785 4 0.0336 0.9791 0.008 0.000 0.000 0.992
#> GSM509752 2 0.4804 0.9862 0.000 0.616 0.000 0.384
#> GSM509754 2 0.4804 0.9862 0.000 0.616 0.000 0.384
#> GSM509756 2 0.4804 0.9862 0.000 0.616 0.000 0.384
#> GSM509758 2 0.4804 0.9862 0.000 0.616 0.000 0.384
#> GSM509760 2 0.4804 0.9862 0.000 0.616 0.000 0.384
#> GSM509762 2 0.4804 0.9862 0.000 0.616 0.000 0.384
#> GSM509764 2 0.4804 0.9862 0.000 0.616 0.000 0.384
#> GSM509766 2 0.4916 0.9426 0.000 0.576 0.000 0.424
#> GSM509768 2 0.4830 0.9807 0.000 0.608 0.000 0.392
#> GSM509770 2 0.4804 0.9862 0.000 0.616 0.000 0.384
#> GSM509772 2 0.4804 0.9862 0.000 0.616 0.000 0.384
#> GSM509774 4 0.0336 0.9675 0.000 0.008 0.000 0.992
#> GSM509776 2 0.4830 0.9807 0.000 0.608 0.000 0.392
#> GSM509778 4 0.0336 0.9791 0.008 0.000 0.000 0.992
#> GSM509780 2 0.4977 0.8818 0.000 0.540 0.000 0.460
#> GSM509782 4 0.0336 0.9791 0.008 0.000 0.000 0.992
#> GSM509784 4 0.0000 0.9758 0.000 0.000 0.000 1.000
#> GSM509786 4 0.0336 0.9791 0.008 0.000 0.000 0.992
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM509706 1 0.2471 0.8748 0.864 0.000 0.136 0.000 0.000
#> GSM509711 5 0.4747 0.4636 0.284 0.000 0.004 0.036 0.676
#> GSM509714 5 0.2624 0.5645 0.116 0.000 0.000 0.012 0.872
#> GSM509719 5 0.7235 -0.0116 0.408 0.000 0.092 0.088 0.412
#> GSM509724 1 0.2753 0.8700 0.856 0.000 0.136 0.000 0.008
#> GSM509729 1 0.7096 0.3686 0.536 0.000 0.104 0.092 0.268
#> GSM509707 1 0.2471 0.8748 0.864 0.000 0.136 0.000 0.000
#> GSM509712 5 0.4451 0.4958 0.236 0.000 0.004 0.036 0.724
#> GSM509715 5 0.2891 0.5290 0.000 0.000 0.000 0.176 0.824
#> GSM509720 5 0.7235 -0.0116 0.408 0.000 0.092 0.088 0.412
#> GSM509725 1 0.2753 0.8700 0.856 0.000 0.136 0.000 0.008
#> GSM509730 1 0.7351 0.1630 0.464 0.000 0.104 0.096 0.336
#> GSM509708 1 0.2471 0.8748 0.864 0.000 0.136 0.000 0.000
#> GSM509713 1 0.4506 0.4880 0.716 0.000 0.004 0.036 0.244
#> GSM509716 5 0.2891 0.5290 0.000 0.000 0.000 0.176 0.824
#> GSM509721 5 0.7235 -0.0116 0.408 0.000 0.092 0.088 0.412
#> GSM509726 1 0.3681 0.8492 0.820 0.000 0.136 0.036 0.008
#> GSM509731 5 0.2690 0.5396 0.000 0.000 0.000 0.156 0.844
#> GSM509709 1 0.2471 0.8748 0.864 0.000 0.136 0.000 0.000
#> GSM509717 5 0.2891 0.5290 0.000 0.000 0.000 0.176 0.824
#> GSM509722 5 0.6095 0.1746 0.404 0.000 0.012 0.088 0.496
#> GSM509727 5 0.6793 0.3903 0.160 0.000 0.132 0.100 0.608
#> GSM509710 1 0.2471 0.8748 0.864 0.000 0.136 0.000 0.000
#> GSM509718 5 0.2891 0.5290 0.000 0.000 0.000 0.176 0.824
#> GSM509723 5 0.7235 -0.0116 0.408 0.000 0.092 0.088 0.412
#> GSM509728 3 0.4733 0.8093 0.040 0.000 0.776 0.108 0.076
#> GSM509732 3 0.0290 0.9034 0.000 0.000 0.992 0.000 0.008
#> GSM509736 3 0.3898 0.8241 0.000 0.000 0.804 0.080 0.116
#> GSM509741 3 0.0000 0.9035 0.000 0.000 1.000 0.000 0.000
#> GSM509746 3 0.0290 0.9034 0.000 0.000 0.992 0.000 0.008
#> GSM509733 3 0.0290 0.9034 0.000 0.000 0.992 0.000 0.008
#> GSM509737 3 0.3898 0.8241 0.000 0.000 0.804 0.080 0.116
#> GSM509742 3 0.0000 0.9035 0.000 0.000 1.000 0.000 0.000
#> GSM509747 3 0.0290 0.9034 0.000 0.000 0.992 0.000 0.008
#> GSM509734 3 0.0290 0.9034 0.000 0.000 0.992 0.000 0.008
#> GSM509738 3 0.5576 0.3459 0.000 0.000 0.536 0.076 0.388
#> GSM509743 3 0.1907 0.8936 0.000 0.000 0.928 0.044 0.028
#> GSM509748 3 0.0290 0.9034 0.000 0.000 0.992 0.000 0.008
#> GSM509735 1 0.2629 0.8732 0.860 0.000 0.136 0.004 0.000
#> GSM509739 1 0.2471 0.8748 0.864 0.000 0.136 0.000 0.000
#> GSM509744 3 0.2438 0.8843 0.000 0.000 0.900 0.060 0.040
#> GSM509749 3 0.1741 0.8955 0.000 0.000 0.936 0.040 0.024
#> GSM509740 5 0.3999 0.5530 0.048 0.000 0.048 0.076 0.828
#> GSM509745 5 0.5854 -0.1880 0.000 0.000 0.436 0.096 0.468
#> GSM509750 3 0.3119 0.8668 0.000 0.000 0.860 0.072 0.068
#> GSM509751 2 0.0000 0.8952 0.000 1.000 0.000 0.000 0.000
#> GSM509753 2 0.0000 0.8952 0.000 1.000 0.000 0.000 0.000
#> GSM509755 2 0.0000 0.8952 0.000 1.000 0.000 0.000 0.000
#> GSM509757 2 0.0000 0.8952 0.000 1.000 0.000 0.000 0.000
#> GSM509759 2 0.0324 0.8936 0.004 0.992 0.000 0.000 0.004
#> GSM509761 2 0.0162 0.8951 0.004 0.996 0.000 0.000 0.000
#> GSM509763 2 0.4926 0.7175 0.132 0.716 0.000 0.152 0.000
#> GSM509765 2 0.4926 0.7175 0.132 0.716 0.000 0.152 0.000
#> GSM509767 2 0.1831 0.8792 0.076 0.920 0.000 0.000 0.004
#> GSM509769 2 0.2069 0.8755 0.076 0.912 0.000 0.012 0.000
#> GSM509771 2 0.1952 0.8771 0.084 0.912 0.000 0.000 0.004
#> GSM509773 2 0.3966 0.8082 0.132 0.796 0.000 0.072 0.000
#> GSM509775 2 0.3966 0.8082 0.132 0.796 0.000 0.072 0.000
#> GSM509777 4 0.4613 0.8769 0.072 0.200 0.000 0.728 0.000
#> GSM509779 4 0.4136 0.9009 0.048 0.188 0.000 0.764 0.000
#> GSM509781 4 0.4514 0.9326 0.000 0.188 0.000 0.740 0.072
#> GSM509783 4 0.4514 0.9326 0.000 0.188 0.000 0.740 0.072
#> GSM509785 4 0.4514 0.9326 0.000 0.188 0.000 0.740 0.072
#> GSM509752 2 0.0000 0.8952 0.000 1.000 0.000 0.000 0.000
#> GSM509754 2 0.0000 0.8952 0.000 1.000 0.000 0.000 0.000
#> GSM509756 2 0.0000 0.8952 0.000 1.000 0.000 0.000 0.000
#> GSM509758 2 0.0000 0.8952 0.000 1.000 0.000 0.000 0.000
#> GSM509760 2 0.0162 0.8941 0.000 0.996 0.000 0.000 0.004
#> GSM509762 2 0.0000 0.8952 0.000 1.000 0.000 0.000 0.000
#> GSM509764 2 0.0000 0.8952 0.000 1.000 0.000 0.000 0.000
#> GSM509766 2 0.4926 0.7175 0.132 0.716 0.000 0.152 0.000
#> GSM509768 2 0.4123 0.8072 0.132 0.792 0.000 0.072 0.004
#> GSM509770 2 0.1831 0.8793 0.076 0.920 0.000 0.000 0.004
#> GSM509772 2 0.0324 0.8936 0.004 0.992 0.000 0.000 0.004
#> GSM509774 4 0.4571 0.8873 0.076 0.188 0.000 0.736 0.000
#> GSM509776 2 0.3966 0.8082 0.132 0.796 0.000 0.072 0.000
#> GSM509778 4 0.4514 0.9326 0.000 0.188 0.000 0.740 0.072
#> GSM509780 2 0.5602 0.5981 0.132 0.648 0.000 0.216 0.004
#> GSM509782 4 0.4514 0.9326 0.000 0.188 0.000 0.740 0.072
#> GSM509784 4 0.4514 0.8898 0.072 0.188 0.000 0.740 0.000
#> GSM509786 4 0.4514 0.9326 0.000 0.188 0.000 0.740 0.072
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM509706 1 0.1141 0.84216 0.948 0.000 0.052 0.000 0.000 NA
#> GSM509711 5 0.5096 0.47904 0.204 0.000 0.000 0.032 0.676 NA
#> GSM509714 5 0.1536 0.59099 0.016 0.000 0.000 0.004 0.940 NA
#> GSM509719 5 0.7160 0.25181 0.288 0.000 0.028 0.028 0.376 NA
#> GSM509724 1 0.1686 0.83584 0.932 0.000 0.052 0.004 0.004 NA
#> GSM509729 1 0.7299 -0.00363 0.412 0.000 0.028 0.048 0.240 NA
#> GSM509707 1 0.1141 0.84216 0.948 0.000 0.052 0.000 0.000 NA
#> GSM509712 5 0.4744 0.53569 0.124 0.000 0.000 0.032 0.728 NA
#> GSM509715 5 0.2669 0.55570 0.000 0.000 0.000 0.156 0.836 NA
#> GSM509720 5 0.7160 0.25181 0.288 0.000 0.028 0.028 0.376 NA
#> GSM509725 1 0.1799 0.83573 0.928 0.000 0.052 0.008 0.004 NA
#> GSM509730 1 0.7438 -0.20916 0.332 0.000 0.028 0.048 0.296 NA
#> GSM509708 1 0.1141 0.84216 0.948 0.000 0.052 0.000 0.000 NA
#> GSM509713 1 0.4970 0.54981 0.696 0.000 0.000 0.032 0.180 NA
#> GSM509716 5 0.2669 0.55570 0.000 0.000 0.000 0.156 0.836 NA
#> GSM509721 5 0.7160 0.25181 0.288 0.000 0.028 0.028 0.376 NA
#> GSM509726 1 0.3734 0.77240 0.836 0.000 0.052 0.036 0.028 NA
#> GSM509731 5 0.2859 0.55361 0.000 0.000 0.000 0.156 0.828 NA
#> GSM509709 1 0.1141 0.84216 0.948 0.000 0.052 0.000 0.000 NA
#> GSM509717 5 0.2669 0.55570 0.000 0.000 0.000 0.156 0.836 NA
#> GSM509722 5 0.6812 0.27582 0.288 0.000 0.008 0.028 0.396 NA
#> GSM509727 5 0.6742 0.42511 0.112 0.000 0.040 0.040 0.508 NA
#> GSM509710 1 0.1141 0.84216 0.948 0.000 0.052 0.000 0.000 NA
#> GSM509718 5 0.2859 0.55355 0.000 0.000 0.000 0.156 0.828 NA
#> GSM509723 5 0.7160 0.25181 0.288 0.000 0.028 0.028 0.376 NA
#> GSM509728 3 0.6252 0.59538 0.052 0.000 0.548 0.036 0.052 NA
#> GSM509732 3 0.0146 0.83195 0.000 0.000 0.996 0.000 0.004 NA
#> GSM509736 3 0.4817 0.65968 0.004 0.000 0.612 0.000 0.064 NA
#> GSM509741 3 0.0000 0.83269 0.000 0.000 1.000 0.000 0.000 NA
#> GSM509746 3 0.0405 0.83208 0.000 0.000 0.988 0.008 0.004 NA
#> GSM509733 3 0.0146 0.83195 0.000 0.000 0.996 0.000 0.004 NA
#> GSM509737 3 0.4817 0.65968 0.004 0.000 0.612 0.000 0.064 NA
#> GSM509742 3 0.0000 0.83269 0.000 0.000 1.000 0.000 0.000 NA
#> GSM509747 3 0.0405 0.83208 0.000 0.000 0.988 0.008 0.004 NA
#> GSM509734 3 0.0405 0.83208 0.000 0.000 0.988 0.008 0.004 NA
#> GSM509738 3 0.6220 0.19088 0.004 0.000 0.376 0.000 0.288 NA
#> GSM509743 3 0.2488 0.81073 0.000 0.000 0.864 0.008 0.004 NA
#> GSM509748 3 0.0508 0.83218 0.000 0.000 0.984 0.012 0.004 NA
#> GSM509735 1 0.1285 0.84153 0.944 0.000 0.052 0.004 0.000 NA
#> GSM509739 1 0.1285 0.84153 0.944 0.000 0.052 0.004 0.000 NA
#> GSM509744 3 0.3507 0.77156 0.000 0.000 0.764 0.008 0.012 NA
#> GSM509749 3 0.2203 0.82056 0.000 0.000 0.896 0.016 0.004 NA
#> GSM509740 5 0.3894 0.51406 0.008 0.000 0.004 0.000 0.664 NA
#> GSM509745 5 0.6114 -0.10113 0.000 0.000 0.304 0.000 0.368 NA
#> GSM509750 3 0.4273 0.73604 0.000 0.000 0.696 0.012 0.032 NA
#> GSM509751 2 0.0000 0.80422 0.000 1.000 0.000 0.000 0.000 NA
#> GSM509753 2 0.0146 0.80399 0.000 0.996 0.000 0.000 0.004 NA
#> GSM509755 2 0.0405 0.80334 0.008 0.988 0.000 0.000 0.004 NA
#> GSM509757 2 0.0146 0.80399 0.000 0.996 0.000 0.000 0.004 NA
#> GSM509759 2 0.0862 0.79904 0.016 0.972 0.000 0.000 0.004 NA
#> GSM509761 2 0.0146 0.80457 0.000 0.996 0.000 0.000 0.000 NA
#> GSM509763 2 0.5197 0.51272 0.008 0.504 0.000 0.068 0.000 NA
#> GSM509765 2 0.4975 0.51661 0.000 0.504 0.000 0.068 0.000 NA
#> GSM509767 2 0.2809 0.76607 0.004 0.824 0.000 0.000 0.004 NA
#> GSM509769 2 0.3281 0.74826 0.012 0.784 0.000 0.000 0.004 NA
#> GSM509771 2 0.2879 0.76382 0.004 0.816 0.000 0.000 0.004 NA
#> GSM509773 2 0.4063 0.60894 0.004 0.572 0.000 0.000 0.004 NA
#> GSM509775 2 0.3810 0.60801 0.000 0.572 0.000 0.000 0.000 NA
#> GSM509777 4 0.5405 0.73108 0.008 0.112 0.000 0.568 0.000 NA
#> GSM509779 4 0.4845 0.80883 0.016 0.100 0.000 0.692 0.000 NA
#> GSM509781 4 0.1958 0.85941 0.004 0.100 0.000 0.896 0.000 NA
#> GSM509783 4 0.2070 0.85878 0.008 0.100 0.000 0.892 0.000 NA
#> GSM509785 4 0.1958 0.85941 0.004 0.100 0.000 0.896 0.000 NA
#> GSM509752 2 0.0000 0.80422 0.000 1.000 0.000 0.000 0.000 NA
#> GSM509754 2 0.0000 0.80422 0.000 1.000 0.000 0.000 0.000 NA
#> GSM509756 2 0.0260 0.80328 0.008 0.992 0.000 0.000 0.000 NA
#> GSM509758 2 0.0000 0.80422 0.000 1.000 0.000 0.000 0.000 NA
#> GSM509760 2 0.0603 0.80059 0.016 0.980 0.000 0.000 0.000 NA
#> GSM509762 2 0.0000 0.80422 0.000 1.000 0.000 0.000 0.000 NA
#> GSM509764 2 0.0000 0.80422 0.000 1.000 0.000 0.000 0.000 NA
#> GSM509766 2 0.4975 0.51661 0.000 0.504 0.000 0.068 0.000 NA
#> GSM509768 2 0.3810 0.60801 0.000 0.572 0.000 0.000 0.000 NA
#> GSM509770 2 0.3343 0.75739 0.024 0.796 0.000 0.000 0.004 NA
#> GSM509772 2 0.0436 0.80216 0.004 0.988 0.000 0.000 0.004 NA
#> GSM509774 4 0.5278 0.75181 0.008 0.100 0.000 0.584 0.000 NA
#> GSM509776 2 0.3810 0.60801 0.000 0.572 0.000 0.000 0.000 NA
#> GSM509778 4 0.2070 0.85878 0.008 0.100 0.000 0.892 0.000 NA
#> GSM509780 2 0.5613 0.42116 0.008 0.456 0.000 0.112 0.000 NA
#> GSM509782 4 0.1958 0.85941 0.004 0.100 0.000 0.896 0.000 NA
#> GSM509784 4 0.5360 0.76738 0.016 0.100 0.000 0.600 0.000 NA
#> GSM509786 4 0.1958 0.85941 0.004 0.100 0.000 0.896 0.000 NA
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 disease.state(p) time(p) k
#> SD:kmeans 81 8.31e-15 6.68e-12 2
#> SD:kmeans 53 3.10e-12 1.17e-09 3
#> SD:kmeans 74 7.74e-25 4.80e-09 4
#> SD:kmeans 68 1.52e-19 5.08e-07 5
#> SD:kmeans 69 3.74e-20 4.80e-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["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 19175 rows and 81 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.997 0.999 0.5067 0.494 0.494
#> 3 3 0.975 0.956 0.970 0.2641 0.805 0.627
#> 4 4 0.989 0.962 0.979 0.1643 0.870 0.647
#> 5 5 0.846 0.815 0.893 0.0564 0.921 0.708
#> 6 6 0.824 0.748 0.852 0.0341 0.965 0.840
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 2 3
There is also optional best \(k\) = 2 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM509706 1 0.000 1.000 1.000 0.000
#> GSM509711 1 0.000 1.000 1.000 0.000
#> GSM509714 1 0.000 1.000 1.000 0.000
#> GSM509719 1 0.000 1.000 1.000 0.000
#> GSM509724 1 0.000 1.000 1.000 0.000
#> GSM509729 1 0.000 1.000 1.000 0.000
#> GSM509707 1 0.000 1.000 1.000 0.000
#> GSM509712 1 0.000 1.000 1.000 0.000
#> GSM509715 2 0.000 0.997 0.000 1.000
#> GSM509720 1 0.000 1.000 1.000 0.000
#> GSM509725 1 0.000 1.000 1.000 0.000
#> GSM509730 1 0.000 1.000 1.000 0.000
#> GSM509708 1 0.000 1.000 1.000 0.000
#> GSM509713 1 0.000 1.000 1.000 0.000
#> GSM509716 2 0.000 0.997 0.000 1.000
#> GSM509721 1 0.000 1.000 1.000 0.000
#> GSM509726 1 0.000 1.000 1.000 0.000
#> GSM509731 2 0.482 0.884 0.104 0.896
#> GSM509709 1 0.000 1.000 1.000 0.000
#> GSM509717 2 0.000 0.997 0.000 1.000
#> GSM509722 1 0.000 1.000 1.000 0.000
#> GSM509727 1 0.000 1.000 1.000 0.000
#> GSM509710 1 0.000 1.000 1.000 0.000
#> GSM509718 2 0.000 0.997 0.000 1.000
#> GSM509723 1 0.000 1.000 1.000 0.000
#> GSM509728 1 0.000 1.000 1.000 0.000
#> GSM509732 1 0.000 1.000 1.000 0.000
#> GSM509736 1 0.000 1.000 1.000 0.000
#> GSM509741 1 0.000 1.000 1.000 0.000
#> GSM509746 1 0.000 1.000 1.000 0.000
#> GSM509733 1 0.000 1.000 1.000 0.000
#> GSM509737 1 0.000 1.000 1.000 0.000
#> GSM509742 1 0.000 1.000 1.000 0.000
#> GSM509747 1 0.000 1.000 1.000 0.000
#> GSM509734 1 0.000 1.000 1.000 0.000
#> GSM509738 1 0.000 1.000 1.000 0.000
#> GSM509743 1 0.000 1.000 1.000 0.000
#> GSM509748 1 0.000 1.000 1.000 0.000
#> GSM509735 1 0.000 1.000 1.000 0.000
#> GSM509739 1 0.000 1.000 1.000 0.000
#> GSM509744 1 0.000 1.000 1.000 0.000
#> GSM509749 1 0.000 1.000 1.000 0.000
#> GSM509740 1 0.000 1.000 1.000 0.000
#> GSM509745 1 0.000 1.000 1.000 0.000
#> GSM509750 1 0.000 1.000 1.000 0.000
#> GSM509751 2 0.000 0.997 0.000 1.000
#> GSM509753 2 0.000 0.997 0.000 1.000
#> GSM509755 2 0.000 0.997 0.000 1.000
#> GSM509757 2 0.000 0.997 0.000 1.000
#> GSM509759 2 0.000 0.997 0.000 1.000
#> GSM509761 2 0.000 0.997 0.000 1.000
#> GSM509763 2 0.000 0.997 0.000 1.000
#> GSM509765 2 0.000 0.997 0.000 1.000
#> GSM509767 2 0.000 0.997 0.000 1.000
#> GSM509769 2 0.000 0.997 0.000 1.000
#> GSM509771 2 0.000 0.997 0.000 1.000
#> GSM509773 2 0.000 0.997 0.000 1.000
#> GSM509775 2 0.000 0.997 0.000 1.000
#> GSM509777 2 0.000 0.997 0.000 1.000
#> GSM509779 2 0.000 0.997 0.000 1.000
#> GSM509781 2 0.000 0.997 0.000 1.000
#> GSM509783 2 0.000 0.997 0.000 1.000
#> GSM509785 2 0.000 0.997 0.000 1.000
#> GSM509752 2 0.000 0.997 0.000 1.000
#> GSM509754 2 0.000 0.997 0.000 1.000
#> GSM509756 2 0.000 0.997 0.000 1.000
#> GSM509758 2 0.000 0.997 0.000 1.000
#> GSM509760 2 0.000 0.997 0.000 1.000
#> GSM509762 2 0.000 0.997 0.000 1.000
#> GSM509764 2 0.000 0.997 0.000 1.000
#> GSM509766 2 0.000 0.997 0.000 1.000
#> GSM509768 2 0.000 0.997 0.000 1.000
#> GSM509770 2 0.000 0.997 0.000 1.000
#> GSM509772 2 0.000 0.997 0.000 1.000
#> GSM509774 2 0.000 0.997 0.000 1.000
#> GSM509776 2 0.000 0.997 0.000 1.000
#> GSM509778 2 0.000 0.997 0.000 1.000
#> GSM509780 2 0.000 0.997 0.000 1.000
#> GSM509782 2 0.000 0.997 0.000 1.000
#> GSM509784 2 0.000 0.997 0.000 1.000
#> GSM509786 2 0.000 0.997 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM509706 1 0.1964 0.937 0.944 0.000 0.056
#> GSM509711 1 0.0747 0.920 0.984 0.000 0.016
#> GSM509714 1 0.0000 0.910 1.000 0.000 0.000
#> GSM509719 1 0.1860 0.937 0.948 0.000 0.052
#> GSM509724 1 0.1964 0.937 0.944 0.000 0.056
#> GSM509729 1 0.1964 0.937 0.944 0.000 0.056
#> GSM509707 1 0.1964 0.937 0.944 0.000 0.056
#> GSM509712 1 0.0747 0.920 0.984 0.000 0.016
#> GSM509715 1 0.5560 0.570 0.700 0.300 0.000
#> GSM509720 1 0.1860 0.937 0.948 0.000 0.052
#> GSM509725 1 0.1964 0.937 0.944 0.000 0.056
#> GSM509730 1 0.1964 0.937 0.944 0.000 0.056
#> GSM509708 1 0.1964 0.937 0.944 0.000 0.056
#> GSM509713 1 0.0892 0.922 0.980 0.000 0.020
#> GSM509716 1 0.5216 0.644 0.740 0.260 0.000
#> GSM509721 1 0.1860 0.937 0.948 0.000 0.052
#> GSM509726 1 0.1964 0.937 0.944 0.000 0.056
#> GSM509731 1 0.1643 0.881 0.956 0.044 0.000
#> GSM509709 1 0.1964 0.937 0.944 0.000 0.056
#> GSM509717 1 0.5138 0.656 0.748 0.252 0.000
#> GSM509722 1 0.1753 0.936 0.952 0.000 0.048
#> GSM509727 1 0.2711 0.915 0.912 0.000 0.088
#> GSM509710 1 0.1964 0.937 0.944 0.000 0.056
#> GSM509718 2 0.4235 0.802 0.176 0.824 0.000
#> GSM509723 1 0.1860 0.937 0.948 0.000 0.052
#> GSM509728 3 0.0237 0.994 0.004 0.000 0.996
#> GSM509732 3 0.0000 0.997 0.000 0.000 1.000
#> GSM509736 3 0.0000 0.997 0.000 0.000 1.000
#> GSM509741 3 0.0000 0.997 0.000 0.000 1.000
#> GSM509746 3 0.0000 0.997 0.000 0.000 1.000
#> GSM509733 3 0.0000 0.997 0.000 0.000 1.000
#> GSM509737 3 0.0000 0.997 0.000 0.000 1.000
#> GSM509742 3 0.0000 0.997 0.000 0.000 1.000
#> GSM509747 3 0.0000 0.997 0.000 0.000 1.000
#> GSM509734 3 0.0000 0.997 0.000 0.000 1.000
#> GSM509738 3 0.0000 0.997 0.000 0.000 1.000
#> GSM509743 3 0.0000 0.997 0.000 0.000 1.000
#> GSM509748 3 0.0000 0.997 0.000 0.000 1.000
#> GSM509735 1 0.1964 0.937 0.944 0.000 0.056
#> GSM509739 1 0.1964 0.937 0.944 0.000 0.056
#> GSM509744 3 0.0000 0.997 0.000 0.000 1.000
#> GSM509749 3 0.0000 0.997 0.000 0.000 1.000
#> GSM509740 1 0.4062 0.795 0.836 0.000 0.164
#> GSM509745 3 0.1411 0.960 0.036 0.000 0.964
#> GSM509750 3 0.0000 0.997 0.000 0.000 1.000
#> GSM509751 2 0.0000 0.992 0.000 1.000 0.000
#> GSM509753 2 0.0000 0.992 0.000 1.000 0.000
#> GSM509755 2 0.0000 0.992 0.000 1.000 0.000
#> GSM509757 2 0.0000 0.992 0.000 1.000 0.000
#> GSM509759 2 0.0000 0.992 0.000 1.000 0.000
#> GSM509761 2 0.0000 0.992 0.000 1.000 0.000
#> GSM509763 2 0.0000 0.992 0.000 1.000 0.000
#> GSM509765 2 0.0000 0.992 0.000 1.000 0.000
#> GSM509767 2 0.0000 0.992 0.000 1.000 0.000
#> GSM509769 2 0.0000 0.992 0.000 1.000 0.000
#> GSM509771 2 0.0000 0.992 0.000 1.000 0.000
#> GSM509773 2 0.0000 0.992 0.000 1.000 0.000
#> GSM509775 2 0.0000 0.992 0.000 1.000 0.000
#> GSM509777 2 0.0592 0.987 0.012 0.988 0.000
#> GSM509779 2 0.0747 0.985 0.016 0.984 0.000
#> GSM509781 2 0.0747 0.985 0.016 0.984 0.000
#> GSM509783 2 0.0747 0.985 0.016 0.984 0.000
#> GSM509785 2 0.0747 0.985 0.016 0.984 0.000
#> GSM509752 2 0.0000 0.992 0.000 1.000 0.000
#> GSM509754 2 0.0000 0.992 0.000 1.000 0.000
#> GSM509756 2 0.0000 0.992 0.000 1.000 0.000
#> GSM509758 2 0.0000 0.992 0.000 1.000 0.000
#> GSM509760 2 0.0000 0.992 0.000 1.000 0.000
#> GSM509762 2 0.0000 0.992 0.000 1.000 0.000
#> GSM509764 2 0.0000 0.992 0.000 1.000 0.000
#> GSM509766 2 0.0000 0.992 0.000 1.000 0.000
#> GSM509768 2 0.0000 0.992 0.000 1.000 0.000
#> GSM509770 2 0.0000 0.992 0.000 1.000 0.000
#> GSM509772 2 0.0000 0.992 0.000 1.000 0.000
#> GSM509774 2 0.0592 0.987 0.012 0.988 0.000
#> GSM509776 2 0.0000 0.992 0.000 1.000 0.000
#> GSM509778 2 0.0747 0.985 0.016 0.984 0.000
#> GSM509780 2 0.0000 0.992 0.000 1.000 0.000
#> GSM509782 2 0.0747 0.985 0.016 0.984 0.000
#> GSM509784 2 0.0747 0.985 0.016 0.984 0.000
#> GSM509786 2 0.0747 0.985 0.016 0.984 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM509706 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM509711 1 0.0921 0.955 0.972 0.000 0.000 0.028
#> GSM509714 1 0.1637 0.934 0.940 0.000 0.000 0.060
#> GSM509719 1 0.0336 0.967 0.992 0.000 0.000 0.008
#> GSM509724 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM509729 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM509707 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM509712 1 0.0921 0.955 0.972 0.000 0.000 0.028
#> GSM509715 4 0.0000 0.947 0.000 0.000 0.000 1.000
#> GSM509720 1 0.0336 0.967 0.992 0.000 0.000 0.008
#> GSM509725 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM509730 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM509708 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM509713 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM509716 4 0.0000 0.947 0.000 0.000 0.000 1.000
#> GSM509721 1 0.0336 0.967 0.992 0.000 0.000 0.008
#> GSM509726 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM509731 4 0.0000 0.947 0.000 0.000 0.000 1.000
#> GSM509709 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM509717 4 0.0000 0.947 0.000 0.000 0.000 1.000
#> GSM509722 1 0.0336 0.967 0.992 0.000 0.000 0.008
#> GSM509727 1 0.1890 0.920 0.936 0.000 0.056 0.008
#> GSM509710 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM509718 4 0.0000 0.947 0.000 0.000 0.000 1.000
#> GSM509723 1 0.0336 0.967 0.992 0.000 0.000 0.008
#> GSM509728 3 0.2011 0.908 0.080 0.000 0.920 0.000
#> GSM509732 3 0.0000 0.994 0.000 0.000 1.000 0.000
#> GSM509736 3 0.0000 0.994 0.000 0.000 1.000 0.000
#> GSM509741 3 0.0000 0.994 0.000 0.000 1.000 0.000
#> GSM509746 3 0.0000 0.994 0.000 0.000 1.000 0.000
#> GSM509733 3 0.0000 0.994 0.000 0.000 1.000 0.000
#> GSM509737 3 0.0000 0.994 0.000 0.000 1.000 0.000
#> GSM509742 3 0.0000 0.994 0.000 0.000 1.000 0.000
#> GSM509747 3 0.0000 0.994 0.000 0.000 1.000 0.000
#> GSM509734 3 0.0000 0.994 0.000 0.000 1.000 0.000
#> GSM509738 3 0.0000 0.994 0.000 0.000 1.000 0.000
#> GSM509743 3 0.0000 0.994 0.000 0.000 1.000 0.000
#> GSM509748 3 0.0000 0.994 0.000 0.000 1.000 0.000
#> GSM509735 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM509739 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM509744 3 0.0000 0.994 0.000 0.000 1.000 0.000
#> GSM509749 3 0.0000 0.994 0.000 0.000 1.000 0.000
#> GSM509740 1 0.6265 0.114 0.500 0.000 0.444 0.056
#> GSM509745 3 0.0000 0.994 0.000 0.000 1.000 0.000
#> GSM509750 3 0.0000 0.994 0.000 0.000 1.000 0.000
#> GSM509751 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM509753 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM509755 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM509757 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM509759 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM509761 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM509763 2 0.0188 0.987 0.000 0.996 0.000 0.004
#> GSM509765 2 0.0817 0.968 0.000 0.976 0.000 0.024
#> GSM509767 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM509769 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM509771 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM509773 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM509775 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM509777 4 0.2345 0.934 0.000 0.100 0.000 0.900
#> GSM509779 4 0.1637 0.968 0.000 0.060 0.000 0.940
#> GSM509781 4 0.1557 0.970 0.000 0.056 0.000 0.944
#> GSM509783 4 0.1557 0.970 0.000 0.056 0.000 0.944
#> GSM509785 4 0.1557 0.970 0.000 0.056 0.000 0.944
#> GSM509752 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM509754 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM509756 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM509758 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM509760 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM509762 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM509764 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM509766 2 0.0188 0.987 0.000 0.996 0.000 0.004
#> GSM509768 2 0.0188 0.987 0.000 0.996 0.000 0.004
#> GSM509770 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM509772 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM509774 4 0.1940 0.957 0.000 0.076 0.000 0.924
#> GSM509776 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM509778 4 0.1557 0.970 0.000 0.056 0.000 0.944
#> GSM509780 2 0.3610 0.736 0.000 0.800 0.000 0.200
#> GSM509782 4 0.1557 0.970 0.000 0.056 0.000 0.944
#> GSM509784 4 0.1867 0.960 0.000 0.072 0.000 0.928
#> GSM509786 4 0.1557 0.970 0.000 0.056 0.000 0.944
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM509706 1 0.0000 0.872 1.000 0.000 0.000 0.000 0.000
#> GSM509711 1 0.3684 0.573 0.720 0.000 0.000 0.000 0.280
#> GSM509714 5 0.2763 0.610 0.148 0.000 0.000 0.004 0.848
#> GSM509719 1 0.3897 0.791 0.768 0.000 0.000 0.028 0.204
#> GSM509724 1 0.0000 0.872 1.000 0.000 0.000 0.000 0.000
#> GSM509729 1 0.2900 0.834 0.864 0.000 0.000 0.028 0.108
#> GSM509707 1 0.0000 0.872 1.000 0.000 0.000 0.000 0.000
#> GSM509712 1 0.3752 0.559 0.708 0.000 0.000 0.000 0.292
#> GSM509715 5 0.3707 0.849 0.000 0.000 0.000 0.284 0.716
#> GSM509720 1 0.3897 0.791 0.768 0.000 0.000 0.028 0.204
#> GSM509725 1 0.0000 0.872 1.000 0.000 0.000 0.000 0.000
#> GSM509730 1 0.3454 0.814 0.816 0.000 0.000 0.028 0.156
#> GSM509708 1 0.0000 0.872 1.000 0.000 0.000 0.000 0.000
#> GSM509713 1 0.0703 0.862 0.976 0.000 0.000 0.000 0.024
#> GSM509716 5 0.3636 0.849 0.000 0.000 0.000 0.272 0.728
#> GSM509721 1 0.3897 0.791 0.768 0.000 0.000 0.028 0.204
#> GSM509726 1 0.0510 0.866 0.984 0.000 0.000 0.000 0.016
#> GSM509731 5 0.3684 0.850 0.000 0.000 0.000 0.280 0.720
#> GSM509709 1 0.0000 0.872 1.000 0.000 0.000 0.000 0.000
#> GSM509717 5 0.3707 0.849 0.000 0.000 0.000 0.284 0.716
#> GSM509722 1 0.3897 0.791 0.768 0.000 0.000 0.028 0.204
#> GSM509727 1 0.5387 0.553 0.688 0.000 0.136 0.008 0.168
#> GSM509710 1 0.0000 0.872 1.000 0.000 0.000 0.000 0.000
#> GSM509718 5 0.3707 0.847 0.000 0.000 0.000 0.284 0.716
#> GSM509723 1 0.3897 0.791 0.768 0.000 0.000 0.028 0.204
#> GSM509728 3 0.5297 0.581 0.260 0.000 0.660 0.008 0.072
#> GSM509732 3 0.0000 0.953 0.000 0.000 1.000 0.000 0.000
#> GSM509736 3 0.1697 0.937 0.000 0.000 0.932 0.008 0.060
#> GSM509741 3 0.0000 0.953 0.000 0.000 1.000 0.000 0.000
#> GSM509746 3 0.0000 0.953 0.000 0.000 1.000 0.000 0.000
#> GSM509733 3 0.0000 0.953 0.000 0.000 1.000 0.000 0.000
#> GSM509737 3 0.1697 0.937 0.000 0.000 0.932 0.008 0.060
#> GSM509742 3 0.0000 0.953 0.000 0.000 1.000 0.000 0.000
#> GSM509747 3 0.0000 0.953 0.000 0.000 1.000 0.000 0.000
#> GSM509734 3 0.0000 0.953 0.000 0.000 1.000 0.000 0.000
#> GSM509738 3 0.1956 0.930 0.000 0.000 0.916 0.008 0.076
#> GSM509743 3 0.0609 0.950 0.000 0.000 0.980 0.000 0.020
#> GSM509748 3 0.0000 0.953 0.000 0.000 1.000 0.000 0.000
#> GSM509735 1 0.0000 0.872 1.000 0.000 0.000 0.000 0.000
#> GSM509739 1 0.0000 0.872 1.000 0.000 0.000 0.000 0.000
#> GSM509744 3 0.1697 0.937 0.000 0.000 0.932 0.008 0.060
#> GSM509749 3 0.0000 0.953 0.000 0.000 1.000 0.000 0.000
#> GSM509740 5 0.4439 0.608 0.176 0.000 0.056 0.008 0.760
#> GSM509745 3 0.2358 0.910 0.000 0.000 0.888 0.008 0.104
#> GSM509750 3 0.1408 0.943 0.000 0.000 0.948 0.008 0.044
#> GSM509751 2 0.0290 0.934 0.000 0.992 0.000 0.000 0.008
#> GSM509753 2 0.0290 0.934 0.000 0.992 0.000 0.000 0.008
#> GSM509755 2 0.0290 0.934 0.000 0.992 0.000 0.000 0.008
#> GSM509757 2 0.0290 0.934 0.000 0.992 0.000 0.000 0.008
#> GSM509759 2 0.0290 0.934 0.000 0.992 0.000 0.000 0.008
#> GSM509761 2 0.0609 0.925 0.000 0.980 0.000 0.020 0.000
#> GSM509763 4 0.4088 0.525 0.000 0.368 0.000 0.632 0.000
#> GSM509765 4 0.4060 0.541 0.000 0.360 0.000 0.640 0.000
#> GSM509767 2 0.0671 0.929 0.000 0.980 0.000 0.016 0.004
#> GSM509769 2 0.0609 0.924 0.000 0.980 0.000 0.020 0.000
#> GSM509771 2 0.0771 0.926 0.000 0.976 0.000 0.020 0.004
#> GSM509773 2 0.2929 0.728 0.000 0.820 0.000 0.180 0.000
#> GSM509775 2 0.4182 0.158 0.000 0.600 0.000 0.400 0.000
#> GSM509777 4 0.2127 0.754 0.000 0.108 0.000 0.892 0.000
#> GSM509779 4 0.1124 0.758 0.000 0.036 0.000 0.960 0.004
#> GSM509781 4 0.1836 0.754 0.000 0.036 0.000 0.932 0.032
#> GSM509783 4 0.1918 0.752 0.000 0.036 0.000 0.928 0.036
#> GSM509785 4 0.1918 0.752 0.000 0.036 0.000 0.928 0.036
#> GSM509752 2 0.0000 0.934 0.000 1.000 0.000 0.000 0.000
#> GSM509754 2 0.0162 0.934 0.000 0.996 0.000 0.000 0.004
#> GSM509756 2 0.0000 0.934 0.000 1.000 0.000 0.000 0.000
#> GSM509758 2 0.0000 0.934 0.000 1.000 0.000 0.000 0.000
#> GSM509760 2 0.0290 0.932 0.000 0.992 0.000 0.008 0.000
#> GSM509762 2 0.0162 0.934 0.000 0.996 0.000 0.000 0.004
#> GSM509764 2 0.0290 0.934 0.000 0.992 0.000 0.000 0.008
#> GSM509766 4 0.4219 0.425 0.000 0.416 0.000 0.584 0.000
#> GSM509768 2 0.3999 0.358 0.000 0.656 0.000 0.344 0.000
#> GSM509770 2 0.0290 0.932 0.000 0.992 0.000 0.008 0.000
#> GSM509772 2 0.0290 0.934 0.000 0.992 0.000 0.000 0.008
#> GSM509774 4 0.1952 0.761 0.000 0.084 0.000 0.912 0.004
#> GSM509776 4 0.4302 0.240 0.000 0.480 0.000 0.520 0.000
#> GSM509778 4 0.1918 0.752 0.000 0.036 0.000 0.928 0.036
#> GSM509780 4 0.3430 0.696 0.000 0.220 0.000 0.776 0.004
#> GSM509782 4 0.1836 0.754 0.000 0.036 0.000 0.932 0.032
#> GSM509784 4 0.1197 0.762 0.000 0.048 0.000 0.952 0.000
#> GSM509786 4 0.1918 0.752 0.000 0.036 0.000 0.928 0.036
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM509706 1 0.0000 0.7842 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509711 1 0.3513 0.6330 0.796 0.000 0.000 0.000 0.144 0.060
#> GSM509714 5 0.3994 0.6430 0.048 0.000 0.000 0.008 0.752 0.192
#> GSM509719 6 0.4037 0.9937 0.380 0.000 0.000 0.000 0.012 0.608
#> GSM509724 1 0.0260 0.7831 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM509729 1 0.3769 -0.3073 0.640 0.000 0.000 0.000 0.004 0.356
#> GSM509707 1 0.0000 0.7842 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509712 1 0.3928 0.5986 0.760 0.000 0.000 0.000 0.160 0.080
#> GSM509715 5 0.2135 0.8597 0.000 0.000 0.000 0.128 0.872 0.000
#> GSM509720 6 0.4037 0.9937 0.380 0.000 0.000 0.000 0.012 0.608
#> GSM509725 1 0.0260 0.7831 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM509730 1 0.4222 -0.7039 0.516 0.000 0.008 0.000 0.004 0.472
#> GSM509708 1 0.0000 0.7842 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509713 1 0.1829 0.7458 0.920 0.000 0.000 0.000 0.024 0.056
#> GSM509716 5 0.2092 0.8608 0.000 0.000 0.000 0.124 0.876 0.000
#> GSM509721 6 0.4037 0.9937 0.380 0.000 0.000 0.000 0.012 0.608
#> GSM509726 1 0.0935 0.7710 0.964 0.000 0.000 0.000 0.004 0.032
#> GSM509731 5 0.2821 0.8440 0.000 0.000 0.000 0.152 0.832 0.016
#> GSM509709 1 0.0000 0.7842 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509717 5 0.2048 0.8606 0.000 0.000 0.000 0.120 0.880 0.000
#> GSM509722 6 0.4312 0.9751 0.368 0.000 0.000 0.000 0.028 0.604
#> GSM509727 1 0.4491 0.5673 0.744 0.000 0.048 0.000 0.048 0.160
#> GSM509710 1 0.0000 0.7842 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509718 5 0.2404 0.8545 0.000 0.000 0.000 0.112 0.872 0.016
#> GSM509723 6 0.4037 0.9937 0.380 0.000 0.000 0.000 0.012 0.608
#> GSM509728 1 0.5859 0.3288 0.576 0.000 0.216 0.000 0.024 0.184
#> GSM509732 3 0.0000 0.8639 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509736 3 0.5205 0.7403 0.000 0.000 0.644 0.020 0.100 0.236
#> GSM509741 3 0.0000 0.8639 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509746 3 0.0000 0.8639 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509733 3 0.0000 0.8639 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509737 3 0.5205 0.7403 0.000 0.000 0.644 0.020 0.100 0.236
#> GSM509742 3 0.0000 0.8639 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509747 3 0.0000 0.8639 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509734 3 0.0000 0.8639 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509738 3 0.5371 0.7204 0.000 0.000 0.616 0.020 0.104 0.260
#> GSM509743 3 0.2201 0.8432 0.000 0.000 0.904 0.004 0.036 0.056
#> GSM509748 3 0.0000 0.8639 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509735 1 0.0000 0.7842 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509739 1 0.0000 0.7842 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509744 3 0.4948 0.7547 0.000 0.000 0.668 0.016 0.088 0.228
#> GSM509749 3 0.0291 0.8630 0.000 0.000 0.992 0.004 0.004 0.000
#> GSM509740 5 0.6210 0.4432 0.080 0.000 0.048 0.020 0.556 0.296
#> GSM509745 3 0.5811 0.6743 0.004 0.000 0.572 0.020 0.132 0.272
#> GSM509750 3 0.3958 0.7978 0.000 0.000 0.768 0.012 0.052 0.168
#> GSM509751 2 0.0260 0.8996 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM509753 2 0.0547 0.8988 0.000 0.980 0.000 0.000 0.000 0.020
#> GSM509755 2 0.0603 0.8975 0.000 0.980 0.000 0.000 0.004 0.016
#> GSM509757 2 0.0508 0.8977 0.000 0.984 0.000 0.000 0.004 0.012
#> GSM509759 2 0.0891 0.8976 0.000 0.968 0.000 0.000 0.008 0.024
#> GSM509761 2 0.1769 0.8778 0.000 0.924 0.000 0.060 0.004 0.012
#> GSM509763 4 0.4002 0.6391 0.000 0.260 0.000 0.704 0.000 0.036
#> GSM509765 4 0.4024 0.6293 0.000 0.264 0.000 0.700 0.000 0.036
#> GSM509767 2 0.2000 0.8840 0.000 0.916 0.000 0.048 0.004 0.032
#> GSM509769 2 0.2279 0.8705 0.000 0.900 0.000 0.048 0.004 0.048
#> GSM509771 2 0.2384 0.8766 0.000 0.896 0.000 0.056 0.008 0.040
#> GSM509773 2 0.4131 0.5526 0.000 0.688 0.000 0.272 0.000 0.040
#> GSM509775 2 0.4780 -0.0925 0.000 0.484 0.000 0.472 0.004 0.040
#> GSM509777 4 0.2094 0.7939 0.000 0.068 0.000 0.908 0.008 0.016
#> GSM509779 4 0.1408 0.8001 0.000 0.020 0.000 0.944 0.036 0.000
#> GSM509781 4 0.2069 0.7929 0.000 0.020 0.000 0.908 0.068 0.004
#> GSM509783 4 0.2126 0.7902 0.000 0.020 0.000 0.904 0.072 0.004
#> GSM509785 4 0.2126 0.7902 0.000 0.020 0.000 0.904 0.072 0.004
#> GSM509752 2 0.0000 0.9001 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509754 2 0.0508 0.9004 0.000 0.984 0.000 0.012 0.000 0.004
#> GSM509756 2 0.0363 0.9006 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM509758 2 0.1168 0.8970 0.000 0.956 0.000 0.016 0.000 0.028
#> GSM509760 2 0.1478 0.8943 0.000 0.944 0.000 0.020 0.004 0.032
#> GSM509762 2 0.0508 0.9005 0.000 0.984 0.000 0.004 0.000 0.012
#> GSM509764 2 0.0260 0.9007 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM509766 4 0.4302 0.5222 0.000 0.324 0.000 0.644 0.004 0.028
#> GSM509768 2 0.4759 0.2262 0.000 0.556 0.000 0.396 0.004 0.044
#> GSM509770 2 0.2209 0.8760 0.000 0.904 0.000 0.040 0.004 0.052
#> GSM509772 2 0.0806 0.8978 0.000 0.972 0.000 0.000 0.008 0.020
#> GSM509774 4 0.1542 0.8005 0.000 0.052 0.000 0.936 0.008 0.004
#> GSM509776 4 0.4508 0.3286 0.000 0.396 0.000 0.568 0.000 0.036
#> GSM509778 4 0.2011 0.7946 0.000 0.020 0.000 0.912 0.064 0.004
#> GSM509780 4 0.3053 0.7511 0.000 0.144 0.000 0.828 0.004 0.024
#> GSM509782 4 0.2069 0.7929 0.000 0.020 0.000 0.908 0.068 0.004
#> GSM509784 4 0.1478 0.8028 0.000 0.032 0.000 0.944 0.020 0.004
#> GSM509786 4 0.2011 0.7940 0.000 0.020 0.000 0.912 0.064 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 disease.state(p) time(p) k
#> SD:skmeans 81 8.31e-15 6.68e-12 2
#> SD:skmeans 81 3.60e-27 5.71e-12 3
#> SD:skmeans 80 7.58e-24 3.57e-08 4
#> SD:skmeans 77 5.28e-24 3.07e-08 5
#> SD:skmeans 74 3.62e-24 3.66e-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["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 19175 rows and 81 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 0.948 0.943 0.978 0.5048 0.494 0.494
#> 3 3 0.646 0.730 0.840 0.2593 0.863 0.729
#> 4 4 0.688 0.571 0.723 0.1388 0.956 0.883
#> 5 5 0.834 0.791 0.904 0.0961 0.814 0.489
#> 6 6 0.869 0.799 0.902 0.0391 0.952 0.775
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
#> GSM509706 1 0.000 0.976 1.000 0.000
#> GSM509711 1 0.000 0.976 1.000 0.000
#> GSM509714 1 0.552 0.837 0.872 0.128
#> GSM509719 1 0.000 0.976 1.000 0.000
#> GSM509724 1 0.000 0.976 1.000 0.000
#> GSM509729 1 0.000 0.976 1.000 0.000
#> GSM509707 1 0.000 0.976 1.000 0.000
#> GSM509712 1 0.000 0.976 1.000 0.000
#> GSM509715 2 0.839 0.634 0.268 0.732
#> GSM509720 1 0.000 0.976 1.000 0.000
#> GSM509725 1 0.000 0.976 1.000 0.000
#> GSM509730 1 0.000 0.976 1.000 0.000
#> GSM509708 1 0.000 0.976 1.000 0.000
#> GSM509713 1 0.000 0.976 1.000 0.000
#> GSM509716 2 0.850 0.620 0.276 0.724
#> GSM509721 1 0.000 0.976 1.000 0.000
#> GSM509726 1 0.000 0.976 1.000 0.000
#> GSM509731 1 0.971 0.321 0.600 0.400
#> GSM509709 1 0.000 0.976 1.000 0.000
#> GSM509717 2 0.904 0.532 0.320 0.680
#> GSM509722 1 0.000 0.976 1.000 0.000
#> GSM509727 1 0.000 0.976 1.000 0.000
#> GSM509710 1 0.000 0.976 1.000 0.000
#> GSM509718 1 0.980 0.270 0.584 0.416
#> GSM509723 1 0.000 0.976 1.000 0.000
#> GSM509728 1 0.000 0.976 1.000 0.000
#> GSM509732 1 0.000 0.976 1.000 0.000
#> GSM509736 1 0.000 0.976 1.000 0.000
#> GSM509741 1 0.000 0.976 1.000 0.000
#> GSM509746 1 0.000 0.976 1.000 0.000
#> GSM509733 1 0.000 0.976 1.000 0.000
#> GSM509737 1 0.000 0.976 1.000 0.000
#> GSM509742 1 0.000 0.976 1.000 0.000
#> GSM509747 1 0.000 0.976 1.000 0.000
#> GSM509734 1 0.000 0.976 1.000 0.000
#> GSM509738 1 0.000 0.976 1.000 0.000
#> GSM509743 1 0.000 0.976 1.000 0.000
#> GSM509748 1 0.000 0.976 1.000 0.000
#> GSM509735 1 0.000 0.976 1.000 0.000
#> GSM509739 1 0.000 0.976 1.000 0.000
#> GSM509744 1 0.000 0.976 1.000 0.000
#> GSM509749 1 0.000 0.976 1.000 0.000
#> GSM509740 1 0.000 0.976 1.000 0.000
#> GSM509745 1 0.000 0.976 1.000 0.000
#> GSM509750 1 0.000 0.976 1.000 0.000
#> GSM509751 2 0.000 0.976 0.000 1.000
#> GSM509753 2 0.000 0.976 0.000 1.000
#> GSM509755 2 0.000 0.976 0.000 1.000
#> GSM509757 2 0.000 0.976 0.000 1.000
#> GSM509759 2 0.000 0.976 0.000 1.000
#> GSM509761 2 0.000 0.976 0.000 1.000
#> GSM509763 2 0.000 0.976 0.000 1.000
#> GSM509765 2 0.000 0.976 0.000 1.000
#> GSM509767 2 0.000 0.976 0.000 1.000
#> GSM509769 2 0.000 0.976 0.000 1.000
#> GSM509771 2 0.000 0.976 0.000 1.000
#> GSM509773 2 0.000 0.976 0.000 1.000
#> GSM509775 2 0.000 0.976 0.000 1.000
#> GSM509777 2 0.000 0.976 0.000 1.000
#> GSM509779 2 0.000 0.976 0.000 1.000
#> GSM509781 2 0.000 0.976 0.000 1.000
#> GSM509783 2 0.000 0.976 0.000 1.000
#> GSM509785 2 0.000 0.976 0.000 1.000
#> GSM509752 2 0.000 0.976 0.000 1.000
#> GSM509754 2 0.000 0.976 0.000 1.000
#> GSM509756 2 0.000 0.976 0.000 1.000
#> GSM509758 2 0.000 0.976 0.000 1.000
#> GSM509760 2 0.000 0.976 0.000 1.000
#> GSM509762 2 0.000 0.976 0.000 1.000
#> GSM509764 2 0.000 0.976 0.000 1.000
#> GSM509766 2 0.000 0.976 0.000 1.000
#> GSM509768 2 0.000 0.976 0.000 1.000
#> GSM509770 2 0.000 0.976 0.000 1.000
#> GSM509772 2 0.000 0.976 0.000 1.000
#> GSM509774 2 0.000 0.976 0.000 1.000
#> GSM509776 2 0.000 0.976 0.000 1.000
#> GSM509778 2 0.000 0.976 0.000 1.000
#> GSM509780 2 0.000 0.976 0.000 1.000
#> GSM509782 2 0.000 0.976 0.000 1.000
#> GSM509784 2 0.000 0.976 0.000 1.000
#> GSM509786 2 0.000 0.976 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM509706 1 0.4178 0.93361 0.828 0.000 0.172
#> GSM509711 1 0.5926 0.62209 0.644 0.000 0.356
#> GSM509714 3 0.8606 0.12069 0.364 0.108 0.528
#> GSM509719 3 0.5397 0.50142 0.280 0.000 0.720
#> GSM509724 1 0.4178 0.93361 0.828 0.000 0.172
#> GSM509729 1 0.4235 0.93200 0.824 0.000 0.176
#> GSM509707 1 0.4178 0.93361 0.828 0.000 0.172
#> GSM509712 3 0.6154 0.16611 0.408 0.000 0.592
#> GSM509715 2 0.8312 0.30909 0.100 0.576 0.324
#> GSM509720 3 0.5363 0.50196 0.276 0.000 0.724
#> GSM509725 1 0.4931 0.86275 0.768 0.000 0.232
#> GSM509730 3 0.5706 0.46230 0.320 0.000 0.680
#> GSM509708 1 0.4178 0.93361 0.828 0.000 0.172
#> GSM509713 1 0.4346 0.92505 0.816 0.000 0.184
#> GSM509716 2 0.9836 -0.07054 0.252 0.404 0.344
#> GSM509721 3 0.5588 0.50374 0.276 0.004 0.720
#> GSM509726 1 0.5810 0.67665 0.664 0.000 0.336
#> GSM509731 2 0.9776 -0.06216 0.244 0.424 0.332
#> GSM509709 1 0.4178 0.93361 0.828 0.000 0.172
#> GSM509717 2 0.9690 0.00592 0.232 0.444 0.324
#> GSM509722 3 0.5588 0.49934 0.276 0.004 0.720
#> GSM509727 3 0.4750 0.55757 0.216 0.000 0.784
#> GSM509710 1 0.4235 0.93127 0.824 0.000 0.176
#> GSM509718 3 0.6941 0.05858 0.016 0.464 0.520
#> GSM509723 3 0.5497 0.48170 0.292 0.000 0.708
#> GSM509728 3 0.5591 0.45988 0.304 0.000 0.696
#> GSM509732 3 0.3551 0.67769 0.132 0.000 0.868
#> GSM509736 3 0.0000 0.73071 0.000 0.000 1.000
#> GSM509741 3 0.3340 0.68795 0.120 0.000 0.880
#> GSM509746 3 0.3340 0.68795 0.120 0.000 0.880
#> GSM509733 3 0.3551 0.67784 0.132 0.000 0.868
#> GSM509737 3 0.0000 0.73071 0.000 0.000 1.000
#> GSM509742 3 0.3340 0.68795 0.120 0.000 0.880
#> GSM509747 3 0.4605 0.58352 0.204 0.000 0.796
#> GSM509734 3 0.4974 0.52524 0.236 0.000 0.764
#> GSM509738 3 0.0000 0.73071 0.000 0.000 1.000
#> GSM509743 3 0.0000 0.73071 0.000 0.000 1.000
#> GSM509748 3 0.3340 0.68795 0.120 0.000 0.880
#> GSM509735 1 0.4750 0.89404 0.784 0.000 0.216
#> GSM509739 1 0.4178 0.93361 0.828 0.000 0.172
#> GSM509744 3 0.0000 0.73071 0.000 0.000 1.000
#> GSM509749 3 0.0000 0.73071 0.000 0.000 1.000
#> GSM509740 3 0.0000 0.73071 0.000 0.000 1.000
#> GSM509745 3 0.0000 0.73071 0.000 0.000 1.000
#> GSM509750 3 0.0000 0.73071 0.000 0.000 1.000
#> GSM509751 2 0.3551 0.87835 0.132 0.868 0.000
#> GSM509753 2 0.3551 0.87835 0.132 0.868 0.000
#> GSM509755 2 0.3551 0.87835 0.132 0.868 0.000
#> GSM509757 2 0.3551 0.87835 0.132 0.868 0.000
#> GSM509759 2 0.3551 0.87835 0.132 0.868 0.000
#> GSM509761 2 0.3551 0.87835 0.132 0.868 0.000
#> GSM509763 2 0.0892 0.86834 0.020 0.980 0.000
#> GSM509765 2 0.1411 0.86510 0.036 0.964 0.000
#> GSM509767 2 0.3551 0.87835 0.132 0.868 0.000
#> GSM509769 2 0.3551 0.87835 0.132 0.868 0.000
#> GSM509771 2 0.3551 0.87835 0.132 0.868 0.000
#> GSM509773 2 0.3551 0.87835 0.132 0.868 0.000
#> GSM509775 2 0.1411 0.87432 0.036 0.964 0.000
#> GSM509777 2 0.1529 0.86414 0.040 0.960 0.000
#> GSM509779 2 0.1529 0.86414 0.040 0.960 0.000
#> GSM509781 2 0.1529 0.86414 0.040 0.960 0.000
#> GSM509783 2 0.1529 0.86414 0.040 0.960 0.000
#> GSM509785 2 0.1529 0.86414 0.040 0.960 0.000
#> GSM509752 2 0.3551 0.87835 0.132 0.868 0.000
#> GSM509754 2 0.3551 0.87835 0.132 0.868 0.000
#> GSM509756 2 0.3551 0.87835 0.132 0.868 0.000
#> GSM509758 2 0.3551 0.87835 0.132 0.868 0.000
#> GSM509760 2 0.3551 0.87835 0.132 0.868 0.000
#> GSM509762 2 0.3551 0.87835 0.132 0.868 0.000
#> GSM509764 2 0.3551 0.87835 0.132 0.868 0.000
#> GSM509766 2 0.0892 0.86831 0.020 0.980 0.000
#> GSM509768 2 0.2066 0.87448 0.060 0.940 0.000
#> GSM509770 2 0.3551 0.87835 0.132 0.868 0.000
#> GSM509772 2 0.3551 0.87835 0.132 0.868 0.000
#> GSM509774 2 0.1529 0.86414 0.040 0.960 0.000
#> GSM509776 2 0.1031 0.86779 0.024 0.976 0.000
#> GSM509778 2 0.1529 0.86414 0.040 0.960 0.000
#> GSM509780 2 0.1411 0.86510 0.036 0.964 0.000
#> GSM509782 2 0.1529 0.86414 0.040 0.960 0.000
#> GSM509784 2 0.1529 0.86414 0.040 0.960 0.000
#> GSM509786 2 0.1529 0.86414 0.040 0.960 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM509706 1 0.0000 0.894586 1.000 0.000 0.000 0.000
#> GSM509711 1 0.7241 0.166668 0.536 0.000 0.188 0.276
#> GSM509714 3 0.8175 -0.304900 0.272 0.012 0.416 0.300
#> GSM509719 3 0.7239 -0.087231 0.128 0.016 0.576 0.280
#> GSM509724 1 0.0000 0.894586 1.000 0.000 0.000 0.000
#> GSM509729 1 0.4313 0.636935 0.736 0.000 0.004 0.260
#> GSM509707 1 0.0000 0.894586 1.000 0.000 0.000 0.000
#> GSM509712 3 0.7784 -0.252009 0.292 0.000 0.428 0.280
#> GSM509715 4 0.6136 0.796085 0.000 0.060 0.356 0.584
#> GSM509720 3 0.6876 -0.079702 0.144 0.000 0.576 0.280
#> GSM509725 1 0.0336 0.888940 0.992 0.000 0.008 0.000
#> GSM509730 3 0.7289 -0.018207 0.212 0.000 0.536 0.252
#> GSM509708 1 0.0000 0.894586 1.000 0.000 0.000 0.000
#> GSM509713 1 0.3495 0.780072 0.844 0.000 0.016 0.140
#> GSM509716 4 0.7156 0.818952 0.080 0.024 0.356 0.540
#> GSM509721 3 0.7295 -0.089977 0.124 0.020 0.576 0.280
#> GSM509726 1 0.3219 0.802833 0.868 0.000 0.112 0.020
#> GSM509731 4 0.6054 0.859562 0.056 0.000 0.352 0.592
#> GSM509709 1 0.0000 0.894586 1.000 0.000 0.000 0.000
#> GSM509717 4 0.5182 0.862667 0.004 0.008 0.356 0.632
#> GSM509722 3 0.7174 -0.085306 0.132 0.012 0.576 0.280
#> GSM509727 3 0.6305 0.000977 0.424 0.000 0.516 0.060
#> GSM509710 1 0.0000 0.894586 1.000 0.000 0.000 0.000
#> GSM509718 3 0.5924 -0.555310 0.000 0.040 0.556 0.404
#> GSM509723 3 0.7064 -0.108405 0.164 0.000 0.556 0.280
#> GSM509728 3 0.4999 -0.019334 0.492 0.000 0.508 0.000
#> GSM509732 3 0.6025 0.529934 0.096 0.000 0.668 0.236
#> GSM509736 3 0.0000 0.496247 0.000 0.000 1.000 0.000
#> GSM509741 3 0.6025 0.529934 0.096 0.000 0.668 0.236
#> GSM509746 3 0.6025 0.529934 0.096 0.000 0.668 0.236
#> GSM509733 3 0.6025 0.529934 0.096 0.000 0.668 0.236
#> GSM509737 3 0.0000 0.496247 0.000 0.000 1.000 0.000
#> GSM509742 3 0.6025 0.529934 0.096 0.000 0.668 0.236
#> GSM509747 3 0.6025 0.529934 0.096 0.000 0.668 0.236
#> GSM509734 3 0.6025 0.529934 0.096 0.000 0.668 0.236
#> GSM509738 3 0.0000 0.496247 0.000 0.000 1.000 0.000
#> GSM509743 3 0.3726 0.522211 0.000 0.000 0.788 0.212
#> GSM509748 3 0.6025 0.529934 0.096 0.000 0.668 0.236
#> GSM509735 1 0.1716 0.855120 0.936 0.000 0.064 0.000
#> GSM509739 1 0.0000 0.894586 1.000 0.000 0.000 0.000
#> GSM509744 3 0.2921 0.521715 0.000 0.000 0.860 0.140
#> GSM509749 3 0.1211 0.507760 0.000 0.000 0.960 0.040
#> GSM509740 3 0.1716 0.438740 0.000 0.000 0.936 0.064
#> GSM509745 3 0.0000 0.496247 0.000 0.000 1.000 0.000
#> GSM509750 3 0.0000 0.496247 0.000 0.000 1.000 0.000
#> GSM509751 2 0.0000 0.768958 0.000 1.000 0.000 0.000
#> GSM509753 2 0.0000 0.768958 0.000 1.000 0.000 0.000
#> GSM509755 2 0.0000 0.768958 0.000 1.000 0.000 0.000
#> GSM509757 2 0.0000 0.768958 0.000 1.000 0.000 0.000
#> GSM509759 2 0.0000 0.768958 0.000 1.000 0.000 0.000
#> GSM509761 2 0.0000 0.768958 0.000 1.000 0.000 0.000
#> GSM509763 2 0.4877 0.655177 0.000 0.592 0.000 0.408
#> GSM509765 2 0.4948 0.638622 0.000 0.560 0.000 0.440
#> GSM509767 2 0.0000 0.768958 0.000 1.000 0.000 0.000
#> GSM509769 2 0.0000 0.768958 0.000 1.000 0.000 0.000
#> GSM509771 2 0.0000 0.768958 0.000 1.000 0.000 0.000
#> GSM509773 2 0.0921 0.763546 0.000 0.972 0.000 0.028
#> GSM509775 2 0.3486 0.727145 0.000 0.812 0.000 0.188
#> GSM509777 2 0.4992 0.615891 0.000 0.524 0.000 0.476
#> GSM509779 2 0.4996 0.610206 0.000 0.516 0.000 0.484
#> GSM509781 2 0.4996 0.610206 0.000 0.516 0.000 0.484
#> GSM509783 2 0.4999 0.599534 0.000 0.508 0.000 0.492
#> GSM509785 2 0.4996 0.610206 0.000 0.516 0.000 0.484
#> GSM509752 2 0.0000 0.768958 0.000 1.000 0.000 0.000
#> GSM509754 2 0.0000 0.768958 0.000 1.000 0.000 0.000
#> GSM509756 2 0.0000 0.768958 0.000 1.000 0.000 0.000
#> GSM509758 2 0.0000 0.768958 0.000 1.000 0.000 0.000
#> GSM509760 2 0.0000 0.768958 0.000 1.000 0.000 0.000
#> GSM509762 2 0.0000 0.768958 0.000 1.000 0.000 0.000
#> GSM509764 2 0.0000 0.768958 0.000 1.000 0.000 0.000
#> GSM509766 2 0.4746 0.672048 0.000 0.632 0.000 0.368
#> GSM509768 2 0.4164 0.706846 0.000 0.736 0.000 0.264
#> GSM509770 2 0.0000 0.768958 0.000 1.000 0.000 0.000
#> GSM509772 2 0.0000 0.768958 0.000 1.000 0.000 0.000
#> GSM509774 2 0.4996 0.610206 0.000 0.516 0.000 0.484
#> GSM509776 2 0.4843 0.659830 0.000 0.604 0.000 0.396
#> GSM509778 2 0.4996 0.610206 0.000 0.516 0.000 0.484
#> GSM509780 2 0.4955 0.636165 0.000 0.556 0.000 0.444
#> GSM509782 2 0.4996 0.610206 0.000 0.516 0.000 0.484
#> GSM509784 2 0.4996 0.610206 0.000 0.516 0.000 0.484
#> GSM509786 2 0.4996 0.610206 0.000 0.516 0.000 0.484
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM509706 1 0.0000 0.9137 1.000 0.000 0.000 0.000 0.000
#> GSM509711 5 0.4350 -0.0174 0.408 0.000 0.000 0.004 0.588
#> GSM509714 5 0.0162 0.7563 0.000 0.000 0.000 0.004 0.996
#> GSM509719 5 0.0162 0.7563 0.000 0.000 0.000 0.004 0.996
#> GSM509724 1 0.0000 0.9137 1.000 0.000 0.000 0.000 0.000
#> GSM509729 1 0.4538 0.4105 0.564 0.000 0.004 0.004 0.428
#> GSM509707 1 0.0000 0.9137 1.000 0.000 0.000 0.000 0.000
#> GSM509712 5 0.0162 0.7563 0.000 0.000 0.000 0.004 0.996
#> GSM509715 5 0.3003 0.6823 0.000 0.000 0.000 0.188 0.812
#> GSM509720 5 0.0162 0.7563 0.000 0.000 0.000 0.004 0.996
#> GSM509725 1 0.0162 0.9118 0.996 0.000 0.004 0.000 0.000
#> GSM509730 5 0.0854 0.7525 0.008 0.000 0.012 0.004 0.976
#> GSM509708 1 0.0000 0.9137 1.000 0.000 0.000 0.000 0.000
#> GSM509713 1 0.3456 0.7475 0.788 0.000 0.004 0.004 0.204
#> GSM509716 5 0.0290 0.7555 0.000 0.000 0.000 0.008 0.992
#> GSM509721 5 0.0162 0.7563 0.000 0.000 0.000 0.004 0.996
#> GSM509726 1 0.2843 0.8065 0.848 0.000 0.008 0.000 0.144
#> GSM509731 5 0.1851 0.7342 0.000 0.000 0.000 0.088 0.912
#> GSM509709 1 0.0000 0.9137 1.000 0.000 0.000 0.000 0.000
#> GSM509717 5 0.2690 0.7029 0.000 0.000 0.000 0.156 0.844
#> GSM509722 5 0.0162 0.7563 0.000 0.000 0.000 0.004 0.996
#> GSM509727 5 0.5156 0.5018 0.320 0.000 0.060 0.000 0.620
#> GSM509710 1 0.0000 0.9137 1.000 0.000 0.000 0.000 0.000
#> GSM509718 5 0.4400 0.6500 0.000 0.000 0.196 0.060 0.744
#> GSM509723 5 0.0162 0.7563 0.000 0.000 0.000 0.004 0.996
#> GSM509728 5 0.6023 0.5094 0.260 0.000 0.168 0.000 0.572
#> GSM509732 3 0.0000 0.9013 0.000 0.000 1.000 0.000 0.000
#> GSM509736 5 0.4219 0.4206 0.000 0.000 0.416 0.000 0.584
#> GSM509741 3 0.0000 0.9013 0.000 0.000 1.000 0.000 0.000
#> GSM509746 3 0.0000 0.9013 0.000 0.000 1.000 0.000 0.000
#> GSM509733 3 0.0000 0.9013 0.000 0.000 1.000 0.000 0.000
#> GSM509737 5 0.4219 0.4206 0.000 0.000 0.416 0.000 0.584
#> GSM509742 3 0.0000 0.9013 0.000 0.000 1.000 0.000 0.000
#> GSM509747 3 0.0000 0.9013 0.000 0.000 1.000 0.000 0.000
#> GSM509734 3 0.0000 0.9013 0.000 0.000 1.000 0.000 0.000
#> GSM509738 5 0.4219 0.4206 0.000 0.000 0.416 0.000 0.584
#> GSM509743 3 0.0963 0.8720 0.000 0.000 0.964 0.000 0.036
#> GSM509748 3 0.0000 0.9013 0.000 0.000 1.000 0.000 0.000
#> GSM509735 1 0.2124 0.8477 0.900 0.000 0.004 0.000 0.096
#> GSM509739 1 0.0000 0.9137 1.000 0.000 0.000 0.000 0.000
#> GSM509744 3 0.3561 0.5243 0.000 0.000 0.740 0.000 0.260
#> GSM509749 3 0.4262 -0.0771 0.000 0.000 0.560 0.000 0.440
#> GSM509740 5 0.3932 0.5458 0.000 0.000 0.328 0.000 0.672
#> GSM509745 5 0.4219 0.4206 0.000 0.000 0.416 0.000 0.584
#> GSM509750 5 0.4219 0.4206 0.000 0.000 0.416 0.000 0.584
#> GSM509751 2 0.0000 0.9558 0.000 1.000 0.000 0.000 0.000
#> GSM509753 2 0.0000 0.9558 0.000 1.000 0.000 0.000 0.000
#> GSM509755 2 0.0000 0.9558 0.000 1.000 0.000 0.000 0.000
#> GSM509757 2 0.0000 0.9558 0.000 1.000 0.000 0.000 0.000
#> GSM509759 2 0.0000 0.9558 0.000 1.000 0.000 0.000 0.000
#> GSM509761 2 0.0000 0.9558 0.000 1.000 0.000 0.000 0.000
#> GSM509763 4 0.2929 0.8211 0.000 0.180 0.000 0.820 0.000
#> GSM509765 4 0.1908 0.8979 0.000 0.092 0.000 0.908 0.000
#> GSM509767 2 0.0000 0.9558 0.000 1.000 0.000 0.000 0.000
#> GSM509769 2 0.0000 0.9558 0.000 1.000 0.000 0.000 0.000
#> GSM509771 2 0.0162 0.9525 0.000 0.996 0.000 0.004 0.000
#> GSM509773 2 0.1043 0.9197 0.000 0.960 0.000 0.040 0.000
#> GSM509775 2 0.3913 0.4702 0.000 0.676 0.000 0.324 0.000
#> GSM509777 4 0.1197 0.9189 0.000 0.048 0.000 0.952 0.000
#> GSM509779 4 0.0162 0.9308 0.000 0.004 0.000 0.996 0.000
#> GSM509781 4 0.0162 0.9308 0.000 0.004 0.000 0.996 0.000
#> GSM509783 4 0.0162 0.9308 0.000 0.004 0.000 0.996 0.000
#> GSM509785 4 0.0162 0.9308 0.000 0.004 0.000 0.996 0.000
#> GSM509752 2 0.0000 0.9558 0.000 1.000 0.000 0.000 0.000
#> GSM509754 2 0.0000 0.9558 0.000 1.000 0.000 0.000 0.000
#> GSM509756 2 0.0000 0.9558 0.000 1.000 0.000 0.000 0.000
#> GSM509758 2 0.0000 0.9558 0.000 1.000 0.000 0.000 0.000
#> GSM509760 2 0.0000 0.9558 0.000 1.000 0.000 0.000 0.000
#> GSM509762 2 0.0000 0.9558 0.000 1.000 0.000 0.000 0.000
#> GSM509764 2 0.0000 0.9558 0.000 1.000 0.000 0.000 0.000
#> GSM509766 4 0.3336 0.7551 0.000 0.228 0.000 0.772 0.000
#> GSM509768 2 0.4249 0.1582 0.000 0.568 0.000 0.432 0.000
#> GSM509770 2 0.0000 0.9558 0.000 1.000 0.000 0.000 0.000
#> GSM509772 2 0.0000 0.9558 0.000 1.000 0.000 0.000 0.000
#> GSM509774 4 0.0404 0.9302 0.000 0.012 0.000 0.988 0.000
#> GSM509776 4 0.3210 0.7802 0.000 0.212 0.000 0.788 0.000
#> GSM509778 4 0.0162 0.9308 0.000 0.004 0.000 0.996 0.000
#> GSM509780 4 0.1792 0.9021 0.000 0.084 0.000 0.916 0.000
#> GSM509782 4 0.0162 0.9308 0.000 0.004 0.000 0.996 0.000
#> GSM509784 4 0.0290 0.9308 0.000 0.008 0.000 0.992 0.000
#> GSM509786 4 0.0162 0.9308 0.000 0.004 0.000 0.996 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM509706 1 0.0000 0.8378 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509711 5 0.5803 0.2948 0.184 0.000 0.000 0.000 0.444 0.372
#> GSM509714 5 0.3515 0.5897 0.000 0.000 0.000 0.000 0.676 0.324
#> GSM509719 5 0.1075 0.8531 0.000 0.000 0.000 0.000 0.952 0.048
#> GSM509724 1 0.0000 0.8378 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509729 5 0.0000 0.8602 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM509707 1 0.0000 0.8378 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509712 6 0.3961 0.0608 0.004 0.000 0.000 0.000 0.440 0.556
#> GSM509715 6 0.1644 0.6734 0.000 0.000 0.000 0.004 0.076 0.920
#> GSM509720 5 0.0937 0.8577 0.000 0.000 0.000 0.000 0.960 0.040
#> GSM509725 1 0.0000 0.8378 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509730 5 0.1387 0.8357 0.000 0.000 0.000 0.000 0.932 0.068
#> GSM509708 1 0.0000 0.8378 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509713 1 0.5871 0.1534 0.468 0.000 0.000 0.000 0.312 0.220
#> GSM509716 6 0.1644 0.6734 0.000 0.000 0.000 0.004 0.076 0.920
#> GSM509721 5 0.0713 0.8609 0.000 0.000 0.000 0.000 0.972 0.028
#> GSM509726 1 0.3995 0.0815 0.516 0.000 0.004 0.000 0.000 0.480
#> GSM509731 6 0.2214 0.6512 0.000 0.000 0.000 0.016 0.096 0.888
#> GSM509709 1 0.0000 0.8378 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509717 6 0.1644 0.6734 0.000 0.000 0.000 0.004 0.076 0.920
#> GSM509722 5 0.0000 0.8602 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM509727 6 0.4307 0.6467 0.172 0.000 0.068 0.000 0.016 0.744
#> GSM509710 1 0.0000 0.8378 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509718 6 0.1296 0.6902 0.000 0.000 0.004 0.004 0.044 0.948
#> GSM509723 5 0.0000 0.8602 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM509728 6 0.4605 0.6760 0.124 0.000 0.184 0.000 0.000 0.692
#> GSM509732 3 0.0000 0.9548 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509736 6 0.3528 0.6773 0.000 0.000 0.296 0.000 0.004 0.700
#> GSM509741 3 0.0000 0.9548 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509746 3 0.0000 0.9548 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509733 3 0.0000 0.9548 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509737 6 0.3528 0.6773 0.000 0.000 0.296 0.000 0.004 0.700
#> GSM509742 3 0.0000 0.9548 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509747 3 0.0000 0.9548 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509734 3 0.0000 0.9548 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509738 6 0.3528 0.6773 0.000 0.000 0.296 0.000 0.004 0.700
#> GSM509743 3 0.1267 0.9050 0.000 0.000 0.940 0.000 0.000 0.060
#> GSM509748 3 0.0632 0.9394 0.000 0.000 0.976 0.000 0.000 0.024
#> GSM509735 1 0.5605 0.2010 0.488 0.000 0.000 0.000 0.360 0.152
#> GSM509739 1 0.0000 0.8378 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509744 3 0.3050 0.6044 0.000 0.000 0.764 0.000 0.000 0.236
#> GSM509749 6 0.3847 0.4169 0.000 0.000 0.456 0.000 0.000 0.544
#> GSM509740 6 0.2416 0.7254 0.000 0.000 0.156 0.000 0.000 0.844
#> GSM509745 6 0.3390 0.6781 0.000 0.000 0.296 0.000 0.000 0.704
#> GSM509750 6 0.3409 0.6742 0.000 0.000 0.300 0.000 0.000 0.700
#> GSM509751 2 0.0000 0.9525 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509753 2 0.0000 0.9525 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509755 2 0.0000 0.9525 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509757 2 0.0000 0.9525 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509759 2 0.0000 0.9525 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509761 2 0.0000 0.9525 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509763 4 0.2454 0.8245 0.000 0.160 0.000 0.840 0.000 0.000
#> GSM509765 4 0.1267 0.9119 0.000 0.060 0.000 0.940 0.000 0.000
#> GSM509767 2 0.0000 0.9525 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509769 2 0.0000 0.9525 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509771 2 0.0146 0.9493 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM509773 2 0.0937 0.9168 0.000 0.960 0.000 0.040 0.000 0.000
#> GSM509775 2 0.3607 0.4276 0.000 0.652 0.000 0.348 0.000 0.000
#> GSM509777 4 0.0260 0.9406 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM509779 4 0.0000 0.9433 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM509781 4 0.0000 0.9433 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM509783 4 0.0000 0.9433 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM509785 4 0.0000 0.9433 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM509752 2 0.0000 0.9525 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509754 2 0.0000 0.9525 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509756 2 0.0000 0.9525 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509758 2 0.0000 0.9525 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509760 2 0.0000 0.9525 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509762 2 0.0000 0.9525 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509764 2 0.0000 0.9525 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509766 4 0.2762 0.7809 0.000 0.196 0.000 0.804 0.000 0.000
#> GSM509768 2 0.3838 0.1331 0.000 0.552 0.000 0.448 0.000 0.000
#> GSM509770 2 0.0000 0.9525 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509772 2 0.0000 0.9525 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509774 4 0.0000 0.9433 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM509776 4 0.2664 0.7969 0.000 0.184 0.000 0.816 0.000 0.000
#> GSM509778 4 0.0000 0.9433 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM509780 4 0.0937 0.9245 0.000 0.040 0.000 0.960 0.000 0.000
#> GSM509782 4 0.0000 0.9433 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM509784 4 0.0000 0.9433 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM509786 4 0.0000 0.9433 0.000 0.000 0.000 1.000 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 disease.state(p) time(p) k
#> SD:pam 79 1.34e-15 8.94e-13 2
#> SD:pam 70 1.75e-20 1.23e-10 3
#> SD:pam 63 1.66e-21 3.09e-08 4
#> SD:pam 71 2.84e-22 2.95e-08 5
#> SD:pam 73 5.87e-20 4.16e-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 19175 rows and 81 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 1.000 1.000 1.000 0.5005 0.500 0.500
#> 3 3 0.822 0.778 0.905 0.2994 0.861 0.722
#> 4 4 0.920 0.899 0.952 0.0944 0.921 0.786
#> 5 5 0.835 0.894 0.923 0.0876 0.920 0.733
#> 6 6 0.759 0.779 0.834 0.0296 0.961 0.827
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
#> GSM509706 1 0 1 1 0
#> GSM509711 1 0 1 1 0
#> GSM509714 1 0 1 1 0
#> GSM509719 1 0 1 1 0
#> GSM509724 1 0 1 1 0
#> GSM509729 1 0 1 1 0
#> GSM509707 1 0 1 1 0
#> GSM509712 1 0 1 1 0
#> GSM509715 1 0 1 1 0
#> GSM509720 1 0 1 1 0
#> GSM509725 1 0 1 1 0
#> GSM509730 1 0 1 1 0
#> GSM509708 1 0 1 1 0
#> GSM509713 1 0 1 1 0
#> GSM509716 1 0 1 1 0
#> GSM509721 1 0 1 1 0
#> GSM509726 1 0 1 1 0
#> GSM509731 1 0 1 1 0
#> GSM509709 1 0 1 1 0
#> GSM509717 1 0 1 1 0
#> GSM509722 1 0 1 1 0
#> GSM509727 1 0 1 1 0
#> GSM509710 1 0 1 1 0
#> GSM509718 1 0 1 1 0
#> GSM509723 1 0 1 1 0
#> GSM509728 1 0 1 1 0
#> GSM509732 1 0 1 1 0
#> GSM509736 1 0 1 1 0
#> GSM509741 1 0 1 1 0
#> GSM509746 1 0 1 1 0
#> GSM509733 1 0 1 1 0
#> GSM509737 1 0 1 1 0
#> GSM509742 1 0 1 1 0
#> GSM509747 1 0 1 1 0
#> GSM509734 1 0 1 1 0
#> GSM509738 1 0 1 1 0
#> GSM509743 1 0 1 1 0
#> GSM509748 1 0 1 1 0
#> GSM509735 1 0 1 1 0
#> GSM509739 1 0 1 1 0
#> GSM509744 1 0 1 1 0
#> GSM509749 1 0 1 1 0
#> GSM509740 1 0 1 1 0
#> GSM509745 1 0 1 1 0
#> GSM509750 1 0 1 1 0
#> GSM509751 2 0 1 0 1
#> GSM509753 2 0 1 0 1
#> GSM509755 2 0 1 0 1
#> GSM509757 2 0 1 0 1
#> GSM509759 2 0 1 0 1
#> GSM509761 2 0 1 0 1
#> GSM509763 2 0 1 0 1
#> GSM509765 2 0 1 0 1
#> GSM509767 2 0 1 0 1
#> GSM509769 2 0 1 0 1
#> GSM509771 2 0 1 0 1
#> GSM509773 2 0 1 0 1
#> GSM509775 2 0 1 0 1
#> GSM509777 2 0 1 0 1
#> GSM509779 2 0 1 0 1
#> GSM509781 2 0 1 0 1
#> GSM509783 2 0 1 0 1
#> GSM509785 2 0 1 0 1
#> GSM509752 2 0 1 0 1
#> GSM509754 2 0 1 0 1
#> GSM509756 2 0 1 0 1
#> GSM509758 2 0 1 0 1
#> GSM509760 2 0 1 0 1
#> GSM509762 2 0 1 0 1
#> GSM509764 2 0 1 0 1
#> GSM509766 2 0 1 0 1
#> GSM509768 2 0 1 0 1
#> GSM509770 2 0 1 0 1
#> GSM509772 2 0 1 0 1
#> GSM509774 2 0 1 0 1
#> GSM509776 2 0 1 0 1
#> GSM509778 2 0 1 0 1
#> GSM509780 2 0 1 0 1
#> GSM509782 2 0 1 0 1
#> GSM509784 2 0 1 0 1
#> GSM509786 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM509706 1 0.6215 1.000 0.572 0.000 0.428
#> GSM509711 3 0.0000 0.439 0.000 0.000 1.000
#> GSM509714 3 0.0000 0.439 0.000 0.000 1.000
#> GSM509719 1 0.6215 1.000 0.572 0.000 0.428
#> GSM509724 1 0.6215 1.000 0.572 0.000 0.428
#> GSM509729 1 0.6215 1.000 0.572 0.000 0.428
#> GSM509707 1 0.6215 1.000 0.572 0.000 0.428
#> GSM509712 3 0.0000 0.439 0.000 0.000 1.000
#> GSM509715 3 0.0000 0.439 0.000 0.000 1.000
#> GSM509720 1 0.6215 1.000 0.572 0.000 0.428
#> GSM509725 1 0.6215 1.000 0.572 0.000 0.428
#> GSM509730 1 0.6215 1.000 0.572 0.000 0.428
#> GSM509708 1 0.6215 1.000 0.572 0.000 0.428
#> GSM509713 3 0.0424 0.423 0.008 0.000 0.992
#> GSM509716 3 0.0000 0.439 0.000 0.000 1.000
#> GSM509721 1 0.6215 1.000 0.572 0.000 0.428
#> GSM509726 3 0.3267 0.132 0.116 0.000 0.884
#> GSM509731 3 0.0000 0.439 0.000 0.000 1.000
#> GSM509709 1 0.6215 1.000 0.572 0.000 0.428
#> GSM509717 3 0.0000 0.439 0.000 0.000 1.000
#> GSM509722 1 0.6225 0.995 0.568 0.000 0.432
#> GSM509727 3 0.6215 0.792 0.428 0.000 0.572
#> GSM509710 1 0.6215 1.000 0.572 0.000 0.428
#> GSM509718 3 0.0000 0.439 0.000 0.000 1.000
#> GSM509723 1 0.6215 1.000 0.572 0.000 0.428
#> GSM509728 3 0.6215 0.792 0.428 0.000 0.572
#> GSM509732 3 0.6215 0.792 0.428 0.000 0.572
#> GSM509736 3 0.6215 0.792 0.428 0.000 0.572
#> GSM509741 3 0.6215 0.792 0.428 0.000 0.572
#> GSM509746 3 0.6215 0.792 0.428 0.000 0.572
#> GSM509733 3 0.6215 0.792 0.428 0.000 0.572
#> GSM509737 3 0.6215 0.792 0.428 0.000 0.572
#> GSM509742 3 0.6215 0.792 0.428 0.000 0.572
#> GSM509747 3 0.6215 0.792 0.428 0.000 0.572
#> GSM509734 3 0.6215 0.792 0.428 0.000 0.572
#> GSM509738 3 0.6215 0.792 0.428 0.000 0.572
#> GSM509743 3 0.6215 0.792 0.428 0.000 0.572
#> GSM509748 3 0.6215 0.792 0.428 0.000 0.572
#> GSM509735 3 0.6168 -0.748 0.412 0.000 0.588
#> GSM509739 1 0.6215 1.000 0.572 0.000 0.428
#> GSM509744 3 0.6215 0.792 0.428 0.000 0.572
#> GSM509749 3 0.6215 0.792 0.428 0.000 0.572
#> GSM509740 3 0.6215 0.792 0.428 0.000 0.572
#> GSM509745 3 0.6215 0.792 0.428 0.000 0.572
#> GSM509750 3 0.6215 0.792 0.428 0.000 0.572
#> GSM509751 2 0.0000 0.920 0.000 1.000 0.000
#> GSM509753 2 0.0000 0.920 0.000 1.000 0.000
#> GSM509755 2 0.0000 0.920 0.000 1.000 0.000
#> GSM509757 2 0.0000 0.920 0.000 1.000 0.000
#> GSM509759 2 0.0000 0.920 0.000 1.000 0.000
#> GSM509761 2 0.0000 0.920 0.000 1.000 0.000
#> GSM509763 2 0.0000 0.920 0.000 1.000 0.000
#> GSM509765 2 0.0000 0.920 0.000 1.000 0.000
#> GSM509767 2 0.0000 0.920 0.000 1.000 0.000
#> GSM509769 2 0.0000 0.920 0.000 1.000 0.000
#> GSM509771 2 0.0000 0.920 0.000 1.000 0.000
#> GSM509773 2 0.0000 0.920 0.000 1.000 0.000
#> GSM509775 2 0.0000 0.920 0.000 1.000 0.000
#> GSM509777 2 0.0000 0.920 0.000 1.000 0.000
#> GSM509779 2 0.0000 0.920 0.000 1.000 0.000
#> GSM509781 2 0.6168 0.341 0.000 0.588 0.412
#> GSM509783 2 0.6180 0.330 0.000 0.584 0.416
#> GSM509785 2 0.6168 0.341 0.000 0.588 0.412
#> GSM509752 2 0.0000 0.920 0.000 1.000 0.000
#> GSM509754 2 0.0000 0.920 0.000 1.000 0.000
#> GSM509756 2 0.0000 0.920 0.000 1.000 0.000
#> GSM509758 2 0.0000 0.920 0.000 1.000 0.000
#> GSM509760 2 0.0000 0.920 0.000 1.000 0.000
#> GSM509762 2 0.0000 0.920 0.000 1.000 0.000
#> GSM509764 2 0.0000 0.920 0.000 1.000 0.000
#> GSM509766 2 0.0000 0.920 0.000 1.000 0.000
#> GSM509768 2 0.0000 0.920 0.000 1.000 0.000
#> GSM509770 2 0.0000 0.920 0.000 1.000 0.000
#> GSM509772 2 0.0000 0.920 0.000 1.000 0.000
#> GSM509774 2 0.0000 0.920 0.000 1.000 0.000
#> GSM509776 2 0.0000 0.920 0.000 1.000 0.000
#> GSM509778 2 0.6126 0.367 0.000 0.600 0.400
#> GSM509780 2 0.0000 0.920 0.000 1.000 0.000
#> GSM509782 2 0.6180 0.330 0.000 0.584 0.416
#> GSM509784 2 0.0000 0.920 0.000 1.000 0.000
#> GSM509786 2 0.6168 0.341 0.000 0.588 0.412
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM509706 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> GSM509711 4 0.2197 0.859 0.080 0.000 0.004 0.916
#> GSM509714 4 0.0817 0.888 0.024 0.000 0.000 0.976
#> GSM509719 1 0.0336 0.980 0.992 0.000 0.000 0.008
#> GSM509724 1 0.1022 0.959 0.968 0.000 0.000 0.032
#> GSM509729 1 0.0336 0.980 0.992 0.000 0.000 0.008
#> GSM509707 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> GSM509712 4 0.4304 0.646 0.284 0.000 0.000 0.716
#> GSM509715 4 0.0188 0.893 0.004 0.000 0.000 0.996
#> GSM509720 1 0.0336 0.980 0.992 0.000 0.000 0.008
#> GSM509725 1 0.0592 0.972 0.984 0.000 0.000 0.016
#> GSM509730 1 0.0336 0.980 0.992 0.000 0.000 0.008
#> GSM509708 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> GSM509713 4 0.5147 0.268 0.460 0.000 0.004 0.536
#> GSM509716 4 0.0188 0.893 0.004 0.000 0.000 0.996
#> GSM509721 1 0.0336 0.980 0.992 0.000 0.000 0.008
#> GSM509726 1 0.2197 0.903 0.916 0.000 0.004 0.080
#> GSM509731 4 0.0188 0.893 0.004 0.000 0.000 0.996
#> GSM509709 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> GSM509717 4 0.0188 0.893 0.004 0.000 0.000 0.996
#> GSM509722 1 0.0336 0.980 0.992 0.000 0.000 0.008
#> GSM509727 3 0.3858 0.852 0.056 0.000 0.844 0.100
#> GSM509710 1 0.0592 0.972 0.984 0.000 0.000 0.016
#> GSM509718 4 0.0188 0.893 0.004 0.000 0.000 0.996
#> GSM509723 1 0.0336 0.980 0.992 0.000 0.000 0.008
#> GSM509728 3 0.2675 0.904 0.008 0.000 0.892 0.100
#> GSM509732 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM509736 3 0.0469 0.965 0.000 0.000 0.988 0.012
#> GSM509741 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM509746 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM509733 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM509737 3 0.1940 0.928 0.000 0.000 0.924 0.076
#> GSM509742 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM509747 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM509734 3 0.2197 0.923 0.004 0.000 0.916 0.080
#> GSM509738 3 0.0469 0.965 0.000 0.000 0.988 0.012
#> GSM509743 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM509748 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM509735 1 0.1940 0.912 0.924 0.000 0.000 0.076
#> GSM509739 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> GSM509744 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM509749 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM509740 3 0.2675 0.903 0.008 0.000 0.892 0.100
#> GSM509745 3 0.0469 0.965 0.000 0.000 0.988 0.012
#> GSM509750 3 0.0592 0.964 0.000 0.000 0.984 0.016
#> GSM509751 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM509753 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM509755 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM509757 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM509759 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM509761 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM509763 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM509765 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM509767 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM509769 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM509771 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM509773 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM509775 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM509777 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM509779 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM509781 2 0.4679 0.527 0.000 0.648 0.000 0.352
#> GSM509783 2 0.4713 0.512 0.000 0.640 0.000 0.360
#> GSM509785 2 0.4679 0.527 0.000 0.648 0.000 0.352
#> GSM509752 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM509754 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM509756 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM509758 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM509760 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM509762 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM509764 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM509766 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM509768 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM509770 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM509772 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM509774 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM509776 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM509778 2 0.4564 0.567 0.000 0.672 0.000 0.328
#> GSM509780 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM509782 2 0.4804 0.464 0.000 0.616 0.000 0.384
#> GSM509784 2 0.0188 0.932 0.000 0.996 0.000 0.004
#> GSM509786 2 0.4679 0.527 0.000 0.648 0.000 0.352
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM509706 1 0.0000 0.974 1.000 0.000 0.000 0.000 0.000
#> GSM509711 5 0.1522 0.855 0.044 0.000 0.012 0.000 0.944
#> GSM509714 5 0.0703 0.867 0.024 0.000 0.000 0.000 0.976
#> GSM509719 1 0.0609 0.973 0.980 0.000 0.000 0.000 0.020
#> GSM509724 1 0.0000 0.974 1.000 0.000 0.000 0.000 0.000
#> GSM509729 1 0.0609 0.973 0.980 0.000 0.000 0.000 0.020
#> GSM509707 1 0.0000 0.974 1.000 0.000 0.000 0.000 0.000
#> GSM509712 5 0.4046 0.596 0.296 0.000 0.008 0.000 0.696
#> GSM509715 5 0.0162 0.870 0.004 0.000 0.000 0.000 0.996
#> GSM509720 1 0.0609 0.973 0.980 0.000 0.000 0.000 0.020
#> GSM509725 1 0.0000 0.974 1.000 0.000 0.000 0.000 0.000
#> GSM509730 1 0.0609 0.973 0.980 0.000 0.000 0.000 0.020
#> GSM509708 1 0.0000 0.974 1.000 0.000 0.000 0.000 0.000
#> GSM509713 5 0.4656 0.165 0.480 0.000 0.012 0.000 0.508
#> GSM509716 5 0.0162 0.870 0.004 0.000 0.000 0.000 0.996
#> GSM509721 1 0.0609 0.973 0.980 0.000 0.000 0.000 0.020
#> GSM509726 1 0.2470 0.839 0.884 0.000 0.012 0.000 0.104
#> GSM509731 5 0.0404 0.871 0.012 0.000 0.000 0.000 0.988
#> GSM509709 1 0.0000 0.974 1.000 0.000 0.000 0.000 0.000
#> GSM509717 5 0.0162 0.870 0.004 0.000 0.000 0.000 0.996
#> GSM509722 1 0.0609 0.973 0.980 0.000 0.000 0.000 0.020
#> GSM509727 3 0.4252 0.856 0.020 0.000 0.796 0.056 0.128
#> GSM509710 1 0.0000 0.974 1.000 0.000 0.000 0.000 0.000
#> GSM509718 5 0.0162 0.870 0.004 0.000 0.000 0.000 0.996
#> GSM509723 1 0.0609 0.973 0.980 0.000 0.000 0.000 0.020
#> GSM509728 3 0.3948 0.867 0.008 0.000 0.808 0.056 0.128
#> GSM509732 3 0.0880 0.897 0.000 0.000 0.968 0.032 0.000
#> GSM509736 3 0.3375 0.884 0.000 0.000 0.840 0.056 0.104
#> GSM509741 3 0.0963 0.896 0.000 0.000 0.964 0.036 0.000
#> GSM509746 3 0.0880 0.897 0.000 0.000 0.968 0.032 0.000
#> GSM509733 3 0.0880 0.897 0.000 0.000 0.968 0.032 0.000
#> GSM509737 3 0.3622 0.874 0.000 0.000 0.820 0.056 0.124
#> GSM509742 3 0.0963 0.896 0.000 0.000 0.964 0.036 0.000
#> GSM509747 3 0.0290 0.900 0.000 0.000 0.992 0.008 0.000
#> GSM509734 3 0.3575 0.877 0.000 0.000 0.824 0.056 0.120
#> GSM509738 3 0.3527 0.879 0.000 0.000 0.828 0.056 0.116
#> GSM509743 3 0.0963 0.896 0.000 0.000 0.964 0.036 0.000
#> GSM509748 3 0.0510 0.900 0.000 0.000 0.984 0.016 0.000
#> GSM509735 1 0.1608 0.901 0.928 0.000 0.000 0.000 0.072
#> GSM509739 1 0.0000 0.974 1.000 0.000 0.000 0.000 0.000
#> GSM509744 3 0.0963 0.896 0.000 0.000 0.964 0.036 0.000
#> GSM509749 3 0.0510 0.899 0.000 0.000 0.984 0.016 0.000
#> GSM509740 3 0.4057 0.863 0.012 0.000 0.804 0.056 0.128
#> GSM509745 3 0.3323 0.885 0.000 0.000 0.844 0.056 0.100
#> GSM509750 3 0.3090 0.889 0.000 0.000 0.860 0.052 0.088
#> GSM509751 2 0.0510 0.943 0.000 0.984 0.000 0.016 0.000
#> GSM509753 2 0.0162 0.943 0.000 0.996 0.000 0.004 0.000
#> GSM509755 2 0.0404 0.940 0.000 0.988 0.000 0.012 0.000
#> GSM509757 2 0.0404 0.940 0.000 0.988 0.000 0.012 0.000
#> GSM509759 2 0.0404 0.940 0.000 0.988 0.000 0.012 0.000
#> GSM509761 2 0.0609 0.943 0.000 0.980 0.000 0.020 0.000
#> GSM509763 2 0.3480 0.672 0.000 0.752 0.000 0.248 0.000
#> GSM509765 2 0.3274 0.718 0.000 0.780 0.000 0.220 0.000
#> GSM509767 2 0.0404 0.943 0.000 0.988 0.000 0.012 0.000
#> GSM509769 2 0.0609 0.943 0.000 0.980 0.000 0.020 0.000
#> GSM509771 2 0.0000 0.942 0.000 1.000 0.000 0.000 0.000
#> GSM509773 2 0.2127 0.879 0.000 0.892 0.000 0.108 0.000
#> GSM509775 2 0.0703 0.942 0.000 0.976 0.000 0.024 0.000
#> GSM509777 4 0.3884 0.752 0.000 0.288 0.000 0.708 0.004
#> GSM509779 4 0.2970 0.906 0.000 0.168 0.000 0.828 0.004
#> GSM509781 4 0.2612 0.916 0.000 0.124 0.000 0.868 0.008
#> GSM509783 4 0.4219 0.867 0.000 0.116 0.000 0.780 0.104
#> GSM509785 4 0.3012 0.915 0.000 0.124 0.000 0.852 0.024
#> GSM509752 2 0.1410 0.923 0.000 0.940 0.000 0.060 0.000
#> GSM509754 2 0.0609 0.943 0.000 0.980 0.000 0.020 0.000
#> GSM509756 2 0.0404 0.940 0.000 0.988 0.000 0.012 0.000
#> GSM509758 2 0.0963 0.937 0.000 0.964 0.000 0.036 0.000
#> GSM509760 2 0.0404 0.940 0.000 0.988 0.000 0.012 0.000
#> GSM509762 2 0.0404 0.940 0.000 0.988 0.000 0.012 0.000
#> GSM509764 2 0.2966 0.784 0.000 0.816 0.000 0.184 0.000
#> GSM509766 2 0.2020 0.896 0.000 0.900 0.000 0.100 0.000
#> GSM509768 2 0.1671 0.913 0.000 0.924 0.000 0.076 0.000
#> GSM509770 2 0.0404 0.940 0.000 0.988 0.000 0.012 0.000
#> GSM509772 2 0.0404 0.940 0.000 0.988 0.000 0.012 0.000
#> GSM509774 4 0.3048 0.901 0.000 0.176 0.000 0.820 0.004
#> GSM509776 2 0.1270 0.931 0.000 0.948 0.000 0.052 0.000
#> GSM509778 4 0.2612 0.916 0.000 0.124 0.000 0.868 0.008
#> GSM509780 2 0.0609 0.943 0.000 0.980 0.000 0.020 0.000
#> GSM509782 4 0.4768 0.768 0.000 0.096 0.000 0.724 0.180
#> GSM509784 4 0.2848 0.914 0.000 0.156 0.000 0.840 0.004
#> GSM509786 4 0.3002 0.912 0.000 0.116 0.000 0.856 0.028
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM509706 1 0.0000 0.9442 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509711 5 0.3967 0.7943 0.148 0.000 0.000 0.000 0.760 0.092
#> GSM509714 5 0.2482 0.8325 0.148 0.000 0.000 0.000 0.848 0.004
#> GSM509719 1 0.0632 0.9509 0.976 0.000 0.000 0.000 0.024 0.000
#> GSM509724 1 0.1714 0.9005 0.908 0.000 0.000 0.000 0.000 0.092
#> GSM509729 1 0.0632 0.9509 0.976 0.000 0.000 0.000 0.024 0.000
#> GSM509707 1 0.0000 0.9442 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509712 5 0.4705 0.7067 0.260 0.000 0.000 0.000 0.652 0.088
#> GSM509715 5 0.1152 0.8435 0.044 0.000 0.000 0.000 0.952 0.004
#> GSM509720 1 0.0632 0.9509 0.976 0.000 0.000 0.000 0.024 0.000
#> GSM509725 1 0.2060 0.9056 0.900 0.000 0.000 0.000 0.016 0.084
#> GSM509730 1 0.0632 0.9509 0.976 0.000 0.000 0.000 0.024 0.000
#> GSM509708 1 0.0000 0.9442 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509713 5 0.5307 0.4514 0.380 0.000 0.000 0.000 0.512 0.108
#> GSM509716 5 0.1152 0.8435 0.044 0.000 0.000 0.000 0.952 0.004
#> GSM509721 1 0.0632 0.9509 0.976 0.000 0.000 0.000 0.024 0.000
#> GSM509726 1 0.3269 0.7794 0.792 0.000 0.000 0.000 0.024 0.184
#> GSM509731 5 0.1908 0.8469 0.096 0.000 0.000 0.000 0.900 0.004
#> GSM509709 1 0.0000 0.9442 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509717 5 0.1152 0.8435 0.044 0.000 0.000 0.000 0.952 0.004
#> GSM509722 1 0.0632 0.9509 0.976 0.000 0.000 0.000 0.024 0.000
#> GSM509727 6 0.1749 0.8026 0.036 0.000 0.008 0.000 0.024 0.932
#> GSM509710 1 0.1327 0.9201 0.936 0.000 0.000 0.000 0.000 0.064
#> GSM509718 5 0.1152 0.8435 0.044 0.000 0.000 0.000 0.952 0.004
#> GSM509723 1 0.0632 0.9509 0.976 0.000 0.000 0.000 0.024 0.000
#> GSM509728 6 0.2333 0.8200 0.000 0.000 0.092 0.000 0.024 0.884
#> GSM509732 3 0.1007 0.8459 0.000 0.000 0.956 0.000 0.000 0.044
#> GSM509736 6 0.3789 0.6861 0.000 0.000 0.260 0.000 0.024 0.716
#> GSM509741 3 0.0713 0.8372 0.000 0.000 0.972 0.000 0.000 0.028
#> GSM509746 3 0.1007 0.8459 0.000 0.000 0.956 0.000 0.000 0.044
#> GSM509733 3 0.1007 0.8459 0.000 0.000 0.956 0.000 0.000 0.044
#> GSM509737 6 0.3719 0.6978 0.000 0.000 0.248 0.000 0.024 0.728
#> GSM509742 3 0.0713 0.8372 0.000 0.000 0.972 0.000 0.000 0.028
#> GSM509747 3 0.3531 0.4961 0.000 0.000 0.672 0.000 0.000 0.328
#> GSM509734 6 0.3668 0.5774 0.000 0.000 0.328 0.000 0.004 0.668
#> GSM509738 6 0.1261 0.8237 0.000 0.000 0.024 0.000 0.024 0.952
#> GSM509743 3 0.0713 0.8372 0.000 0.000 0.972 0.000 0.000 0.028
#> GSM509748 3 0.3620 0.4474 0.000 0.000 0.648 0.000 0.000 0.352
#> GSM509735 1 0.2432 0.8882 0.876 0.000 0.000 0.000 0.024 0.100
#> GSM509739 1 0.0146 0.9459 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM509744 3 0.2121 0.7903 0.000 0.000 0.892 0.000 0.012 0.096
#> GSM509749 3 0.2697 0.7434 0.000 0.000 0.812 0.000 0.000 0.188
#> GSM509740 6 0.1700 0.8113 0.028 0.000 0.012 0.000 0.024 0.936
#> GSM509745 6 0.1176 0.8217 0.000 0.000 0.020 0.000 0.024 0.956
#> GSM509750 6 0.2613 0.7772 0.000 0.000 0.140 0.000 0.012 0.848
#> GSM509751 2 0.0865 0.8139 0.000 0.964 0.000 0.036 0.000 0.000
#> GSM509753 2 0.1003 0.7987 0.000 0.964 0.000 0.004 0.004 0.028
#> GSM509755 2 0.1642 0.7813 0.000 0.936 0.000 0.032 0.004 0.028
#> GSM509757 2 0.1408 0.7865 0.000 0.944 0.000 0.036 0.000 0.020
#> GSM509759 2 0.1788 0.7757 0.000 0.928 0.000 0.040 0.004 0.028
#> GSM509761 2 0.2454 0.7563 0.000 0.840 0.000 0.160 0.000 0.000
#> GSM509763 2 0.3695 0.4416 0.000 0.624 0.000 0.376 0.000 0.000
#> GSM509765 4 0.3838 -0.0191 0.000 0.448 0.000 0.552 0.000 0.000
#> GSM509767 2 0.0713 0.8133 0.000 0.972 0.000 0.028 0.000 0.000
#> GSM509769 2 0.1267 0.8064 0.000 0.940 0.000 0.060 0.000 0.000
#> GSM509771 2 0.0000 0.8090 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509773 2 0.3428 0.5730 0.000 0.696 0.000 0.304 0.000 0.000
#> GSM509775 2 0.2664 0.7533 0.000 0.816 0.000 0.184 0.000 0.000
#> GSM509777 4 0.3727 0.6251 0.000 0.388 0.000 0.612 0.000 0.000
#> GSM509779 4 0.3330 0.8019 0.000 0.284 0.000 0.716 0.000 0.000
#> GSM509781 4 0.4497 0.8284 0.000 0.260 0.000 0.676 0.060 0.004
#> GSM509783 4 0.4653 0.8235 0.000 0.260 0.000 0.664 0.072 0.004
#> GSM509785 4 0.4454 0.8272 0.000 0.252 0.000 0.684 0.060 0.004
#> GSM509752 2 0.2378 0.7589 0.000 0.848 0.000 0.152 0.000 0.000
#> GSM509754 2 0.1556 0.8015 0.000 0.920 0.000 0.080 0.000 0.000
#> GSM509756 2 0.1387 0.8010 0.000 0.932 0.000 0.068 0.000 0.000
#> GSM509758 2 0.3198 0.6901 0.000 0.740 0.000 0.260 0.000 0.000
#> GSM509760 2 0.1387 0.8017 0.000 0.932 0.000 0.068 0.000 0.000
#> GSM509762 2 0.0146 0.8097 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM509764 2 0.3967 0.4548 0.012 0.632 0.000 0.356 0.000 0.000
#> GSM509766 2 0.3634 0.5539 0.000 0.644 0.000 0.356 0.000 0.000
#> GSM509768 2 0.3023 0.6825 0.000 0.768 0.000 0.232 0.000 0.000
#> GSM509770 2 0.0622 0.8100 0.000 0.980 0.000 0.012 0.000 0.008
#> GSM509772 2 0.2113 0.7586 0.000 0.908 0.000 0.060 0.004 0.028
#> GSM509774 4 0.3309 0.7579 0.000 0.280 0.000 0.720 0.000 0.000
#> GSM509776 2 0.3371 0.6435 0.000 0.708 0.000 0.292 0.000 0.000
#> GSM509778 4 0.4497 0.8284 0.000 0.260 0.000 0.676 0.060 0.004
#> GSM509780 2 0.2219 0.7787 0.000 0.864 0.000 0.136 0.000 0.000
#> GSM509782 4 0.3767 0.6367 0.000 0.080 0.000 0.788 0.128 0.004
#> GSM509784 4 0.3371 0.8016 0.000 0.292 0.000 0.708 0.000 0.000
#> GSM509786 4 0.4497 0.8284 0.000 0.260 0.000 0.676 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 disease.state(p) time(p) k
#> SD:mclust 81 2.58e-18 2.22e-15 2
#> SD:mclust 64 2.57e-22 2.07e-09 3
#> SD:mclust 79 4.89e-26 5.11e-10 4
#> SD:mclust 80 4.92e-25 2.60e-08 5
#> SD:mclust 75 4.06e-22 4.91e-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", "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 19175 rows and 81 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 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.5067 0.494 0.494
#> 3 3 0.830 0.860 0.939 0.2887 0.797 0.609
#> 4 4 0.907 0.876 0.941 0.1331 0.771 0.447
#> 5 5 0.809 0.788 0.884 0.0598 0.921 0.714
#> 6 6 0.857 0.830 0.909 0.0357 0.959 0.815
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
#> GSM509706 1 0.0000 1.000 1.000 0.000
#> GSM509711 1 0.0000 1.000 1.000 0.000
#> GSM509714 1 0.0376 0.996 0.996 0.004
#> GSM509719 1 0.0000 1.000 1.000 0.000
#> GSM509724 1 0.0000 1.000 1.000 0.000
#> GSM509729 1 0.0000 1.000 1.000 0.000
#> GSM509707 1 0.0000 1.000 1.000 0.000
#> GSM509712 1 0.0000 1.000 1.000 0.000
#> GSM509715 2 0.0000 1.000 0.000 1.000
#> GSM509720 1 0.0000 1.000 1.000 0.000
#> GSM509725 1 0.0000 1.000 1.000 0.000
#> GSM509730 1 0.0000 1.000 1.000 0.000
#> GSM509708 1 0.0000 1.000 1.000 0.000
#> GSM509713 1 0.0000 1.000 1.000 0.000
#> GSM509716 2 0.0000 1.000 0.000 1.000
#> GSM509721 1 0.0000 1.000 1.000 0.000
#> GSM509726 1 0.0000 1.000 1.000 0.000
#> GSM509731 2 0.0000 1.000 0.000 1.000
#> GSM509709 1 0.0000 1.000 1.000 0.000
#> GSM509717 2 0.0000 1.000 0.000 1.000
#> GSM509722 1 0.0000 1.000 1.000 0.000
#> GSM509727 1 0.0000 1.000 1.000 0.000
#> GSM509710 1 0.0000 1.000 1.000 0.000
#> GSM509718 2 0.0000 1.000 0.000 1.000
#> GSM509723 1 0.0000 1.000 1.000 0.000
#> GSM509728 1 0.0000 1.000 1.000 0.000
#> GSM509732 1 0.0000 1.000 1.000 0.000
#> GSM509736 1 0.0000 1.000 1.000 0.000
#> GSM509741 1 0.0000 1.000 1.000 0.000
#> GSM509746 1 0.0000 1.000 1.000 0.000
#> GSM509733 1 0.0000 1.000 1.000 0.000
#> GSM509737 1 0.0000 1.000 1.000 0.000
#> GSM509742 1 0.0000 1.000 1.000 0.000
#> GSM509747 1 0.0000 1.000 1.000 0.000
#> GSM509734 1 0.0000 1.000 1.000 0.000
#> GSM509738 1 0.0000 1.000 1.000 0.000
#> GSM509743 1 0.0000 1.000 1.000 0.000
#> GSM509748 1 0.0000 1.000 1.000 0.000
#> GSM509735 1 0.0000 1.000 1.000 0.000
#> GSM509739 1 0.0000 1.000 1.000 0.000
#> GSM509744 1 0.0000 1.000 1.000 0.000
#> GSM509749 1 0.0000 1.000 1.000 0.000
#> GSM509740 1 0.0000 1.000 1.000 0.000
#> GSM509745 1 0.0000 1.000 1.000 0.000
#> GSM509750 1 0.0000 1.000 1.000 0.000
#> GSM509751 2 0.0000 1.000 0.000 1.000
#> GSM509753 2 0.0000 1.000 0.000 1.000
#> GSM509755 2 0.0000 1.000 0.000 1.000
#> GSM509757 2 0.0000 1.000 0.000 1.000
#> GSM509759 2 0.0000 1.000 0.000 1.000
#> GSM509761 2 0.0000 1.000 0.000 1.000
#> GSM509763 2 0.0000 1.000 0.000 1.000
#> GSM509765 2 0.0000 1.000 0.000 1.000
#> GSM509767 2 0.0000 1.000 0.000 1.000
#> GSM509769 2 0.0000 1.000 0.000 1.000
#> GSM509771 2 0.0000 1.000 0.000 1.000
#> GSM509773 2 0.0000 1.000 0.000 1.000
#> GSM509775 2 0.0000 1.000 0.000 1.000
#> GSM509777 2 0.0000 1.000 0.000 1.000
#> GSM509779 2 0.0000 1.000 0.000 1.000
#> GSM509781 2 0.0000 1.000 0.000 1.000
#> GSM509783 2 0.0000 1.000 0.000 1.000
#> GSM509785 2 0.0000 1.000 0.000 1.000
#> GSM509752 2 0.0000 1.000 0.000 1.000
#> GSM509754 2 0.0000 1.000 0.000 1.000
#> GSM509756 2 0.0000 1.000 0.000 1.000
#> GSM509758 2 0.0000 1.000 0.000 1.000
#> GSM509760 2 0.0000 1.000 0.000 1.000
#> GSM509762 2 0.0000 1.000 0.000 1.000
#> GSM509764 2 0.0000 1.000 0.000 1.000
#> GSM509766 2 0.0000 1.000 0.000 1.000
#> GSM509768 2 0.0000 1.000 0.000 1.000
#> GSM509770 2 0.0000 1.000 0.000 1.000
#> GSM509772 2 0.0000 1.000 0.000 1.000
#> GSM509774 2 0.0000 1.000 0.000 1.000
#> GSM509776 2 0.0000 1.000 0.000 1.000
#> GSM509778 2 0.0000 1.000 0.000 1.000
#> GSM509780 2 0.0000 1.000 0.000 1.000
#> GSM509782 2 0.0000 1.000 0.000 1.000
#> GSM509784 2 0.0000 1.000 0.000 1.000
#> GSM509786 2 0.0000 1.000 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM509706 1 0.0000 0.9807 1.000 0.000 0.000
#> GSM509711 1 0.0000 0.9807 1.000 0.000 0.000
#> GSM509714 1 0.1031 0.9541 0.976 0.024 0.000
#> GSM509719 1 0.0000 0.9807 1.000 0.000 0.000
#> GSM509724 1 0.0000 0.9807 1.000 0.000 0.000
#> GSM509729 1 0.0000 0.9807 1.000 0.000 0.000
#> GSM509707 1 0.0000 0.9807 1.000 0.000 0.000
#> GSM509712 1 0.0000 0.9807 1.000 0.000 0.000
#> GSM509715 2 0.0000 0.9369 0.000 1.000 0.000
#> GSM509720 1 0.0000 0.9807 1.000 0.000 0.000
#> GSM509725 1 0.0000 0.9807 1.000 0.000 0.000
#> GSM509730 1 0.0000 0.9807 1.000 0.000 0.000
#> GSM509708 1 0.0000 0.9807 1.000 0.000 0.000
#> GSM509713 1 0.0000 0.9807 1.000 0.000 0.000
#> GSM509716 2 0.1031 0.9182 0.024 0.976 0.000
#> GSM509721 1 0.0000 0.9807 1.000 0.000 0.000
#> GSM509726 1 0.0000 0.9807 1.000 0.000 0.000
#> GSM509731 2 0.5098 0.6244 0.248 0.752 0.000
#> GSM509709 1 0.0000 0.9807 1.000 0.000 0.000
#> GSM509717 2 0.0237 0.9344 0.004 0.996 0.000
#> GSM509722 1 0.0000 0.9807 1.000 0.000 0.000
#> GSM509727 1 0.0000 0.9807 1.000 0.000 0.000
#> GSM509710 1 0.0000 0.9807 1.000 0.000 0.000
#> GSM509718 2 0.0000 0.9369 0.000 1.000 0.000
#> GSM509723 1 0.0000 0.9807 1.000 0.000 0.000
#> GSM509728 1 0.0237 0.9775 0.996 0.000 0.004
#> GSM509732 3 0.0000 0.8411 0.000 0.000 1.000
#> GSM509736 3 0.6309 0.0214 0.496 0.000 0.504
#> GSM509741 3 0.1753 0.8264 0.048 0.000 0.952
#> GSM509746 3 0.0000 0.8411 0.000 0.000 1.000
#> GSM509733 3 0.0000 0.8411 0.000 0.000 1.000
#> GSM509737 1 0.1411 0.9453 0.964 0.000 0.036
#> GSM509742 3 0.0592 0.8412 0.012 0.000 0.988
#> GSM509747 3 0.0424 0.8416 0.008 0.000 0.992
#> GSM509734 1 0.6140 0.2781 0.596 0.000 0.404
#> GSM509738 1 0.0424 0.9741 0.992 0.000 0.008
#> GSM509743 3 0.0237 0.8416 0.004 0.000 0.996
#> GSM509748 3 0.2356 0.8127 0.072 0.000 0.928
#> GSM509735 1 0.0000 0.9807 1.000 0.000 0.000
#> GSM509739 1 0.0000 0.9807 1.000 0.000 0.000
#> GSM509744 3 0.5733 0.4826 0.324 0.000 0.676
#> GSM509749 3 0.2625 0.8042 0.084 0.000 0.916
#> GSM509740 1 0.0000 0.9807 1.000 0.000 0.000
#> GSM509745 1 0.0000 0.9807 1.000 0.000 0.000
#> GSM509750 3 0.3267 0.7762 0.116 0.000 0.884
#> GSM509751 3 0.6168 0.2568 0.000 0.412 0.588
#> GSM509753 3 0.2165 0.8066 0.000 0.064 0.936
#> GSM509755 3 0.4504 0.6785 0.000 0.196 0.804
#> GSM509757 3 0.5785 0.4602 0.000 0.332 0.668
#> GSM509759 3 0.0000 0.8411 0.000 0.000 1.000
#> GSM509761 2 0.0237 0.9361 0.000 0.996 0.004
#> GSM509763 2 0.0237 0.9361 0.000 0.996 0.004
#> GSM509765 2 0.0000 0.9369 0.000 1.000 0.000
#> GSM509767 2 0.5905 0.4888 0.000 0.648 0.352
#> GSM509769 2 0.2959 0.8771 0.000 0.900 0.100
#> GSM509771 2 0.5785 0.5328 0.000 0.668 0.332
#> GSM509773 2 0.2356 0.8985 0.000 0.928 0.072
#> GSM509775 2 0.0237 0.9361 0.000 0.996 0.004
#> GSM509777 2 0.0000 0.9369 0.000 1.000 0.000
#> GSM509779 2 0.0000 0.9369 0.000 1.000 0.000
#> GSM509781 2 0.0000 0.9369 0.000 1.000 0.000
#> GSM509783 2 0.0000 0.9369 0.000 1.000 0.000
#> GSM509785 2 0.0000 0.9369 0.000 1.000 0.000
#> GSM509752 2 0.3879 0.8263 0.000 0.848 0.152
#> GSM509754 2 0.4346 0.7892 0.000 0.816 0.184
#> GSM509756 2 0.1643 0.9166 0.000 0.956 0.044
#> GSM509758 2 0.1411 0.9212 0.000 0.964 0.036
#> GSM509760 2 0.0747 0.9312 0.000 0.984 0.016
#> GSM509762 2 0.3038 0.8731 0.000 0.896 0.104
#> GSM509764 3 0.6126 0.2970 0.000 0.400 0.600
#> GSM509766 2 0.0000 0.9369 0.000 1.000 0.000
#> GSM509768 2 0.0237 0.9361 0.000 0.996 0.004
#> GSM509770 2 0.4452 0.7818 0.000 0.808 0.192
#> GSM509772 3 0.0000 0.8411 0.000 0.000 1.000
#> GSM509774 2 0.0000 0.9369 0.000 1.000 0.000
#> GSM509776 2 0.0000 0.9369 0.000 1.000 0.000
#> GSM509778 2 0.0000 0.9369 0.000 1.000 0.000
#> GSM509780 2 0.0000 0.9369 0.000 1.000 0.000
#> GSM509782 2 0.0000 0.9369 0.000 1.000 0.000
#> GSM509784 2 0.0000 0.9369 0.000 1.000 0.000
#> GSM509786 2 0.0000 0.9369 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM509706 1 0.0000 0.994 1.000 0.000 0.000 0.000
#> GSM509711 1 0.0336 0.990 0.992 0.000 0.000 0.008
#> GSM509714 1 0.1637 0.943 0.940 0.000 0.000 0.060
#> GSM509719 1 0.0188 0.992 0.996 0.000 0.004 0.000
#> GSM509724 1 0.0188 0.992 0.996 0.000 0.004 0.000
#> GSM509729 1 0.0000 0.994 1.000 0.000 0.000 0.000
#> GSM509707 1 0.0000 0.994 1.000 0.000 0.000 0.000
#> GSM509712 1 0.0524 0.988 0.988 0.000 0.004 0.008
#> GSM509715 4 0.0000 0.835 0.000 0.000 0.000 1.000
#> GSM509720 1 0.0000 0.994 1.000 0.000 0.000 0.000
#> GSM509725 1 0.0000 0.994 1.000 0.000 0.000 0.000
#> GSM509730 1 0.0000 0.994 1.000 0.000 0.000 0.000
#> GSM509708 1 0.0000 0.994 1.000 0.000 0.000 0.000
#> GSM509713 1 0.0188 0.992 0.996 0.000 0.004 0.000
#> GSM509716 4 0.0188 0.837 0.000 0.004 0.000 0.996
#> GSM509721 1 0.0188 0.992 0.996 0.000 0.004 0.000
#> GSM509726 1 0.0469 0.987 0.988 0.000 0.012 0.000
#> GSM509731 4 0.0469 0.841 0.000 0.012 0.000 0.988
#> GSM509709 1 0.0000 0.994 1.000 0.000 0.000 0.000
#> GSM509717 4 0.0188 0.837 0.000 0.004 0.000 0.996
#> GSM509722 1 0.0188 0.992 0.996 0.000 0.004 0.000
#> GSM509727 3 0.5987 0.198 0.440 0.000 0.520 0.040
#> GSM509710 1 0.0000 0.994 1.000 0.000 0.000 0.000
#> GSM509718 4 0.0188 0.832 0.000 0.000 0.004 0.996
#> GSM509723 1 0.0188 0.992 0.996 0.000 0.004 0.000
#> GSM509728 3 0.2623 0.891 0.064 0.000 0.908 0.028
#> GSM509732 3 0.0921 0.933 0.000 0.028 0.972 0.000
#> GSM509736 3 0.0657 0.941 0.004 0.000 0.984 0.012
#> GSM509741 3 0.0188 0.943 0.000 0.004 0.996 0.000
#> GSM509746 3 0.0817 0.935 0.000 0.024 0.976 0.000
#> GSM509733 3 0.0592 0.939 0.000 0.016 0.984 0.000
#> GSM509737 3 0.0927 0.940 0.008 0.000 0.976 0.016
#> GSM509742 3 0.0188 0.943 0.000 0.004 0.996 0.000
#> GSM509747 3 0.1022 0.930 0.000 0.032 0.968 0.000
#> GSM509734 3 0.0592 0.940 0.016 0.000 0.984 0.000
#> GSM509738 3 0.1807 0.922 0.008 0.000 0.940 0.052
#> GSM509743 3 0.0376 0.943 0.000 0.004 0.992 0.004
#> GSM509748 3 0.0469 0.941 0.000 0.012 0.988 0.000
#> GSM509735 1 0.0469 0.987 0.988 0.000 0.012 0.000
#> GSM509739 1 0.0000 0.994 1.000 0.000 0.000 0.000
#> GSM509744 3 0.1004 0.938 0.004 0.000 0.972 0.024
#> GSM509749 3 0.0188 0.943 0.000 0.004 0.996 0.000
#> GSM509740 4 0.5604 -0.152 0.020 0.000 0.476 0.504
#> GSM509745 3 0.2480 0.896 0.008 0.000 0.904 0.088
#> GSM509750 3 0.0779 0.941 0.004 0.000 0.980 0.016
#> GSM509751 2 0.0469 0.920 0.000 0.988 0.012 0.000
#> GSM509753 2 0.0817 0.913 0.000 0.976 0.024 0.000
#> GSM509755 2 0.0592 0.920 0.000 0.984 0.016 0.000
#> GSM509757 2 0.0336 0.922 0.000 0.992 0.008 0.000
#> GSM509759 2 0.1867 0.870 0.000 0.928 0.072 0.000
#> GSM509761 2 0.1743 0.907 0.000 0.940 0.004 0.056
#> GSM509763 2 0.2530 0.869 0.000 0.888 0.000 0.112
#> GSM509765 2 0.3024 0.831 0.000 0.852 0.000 0.148
#> GSM509767 2 0.0188 0.923 0.000 0.996 0.004 0.000
#> GSM509769 2 0.0469 0.925 0.000 0.988 0.000 0.012
#> GSM509771 2 0.0188 0.923 0.000 0.996 0.004 0.000
#> GSM509773 2 0.0469 0.925 0.000 0.988 0.000 0.012
#> GSM509775 2 0.1211 0.915 0.000 0.960 0.000 0.040
#> GSM509777 2 0.4624 0.492 0.000 0.660 0.000 0.340
#> GSM509779 4 0.4746 0.422 0.000 0.368 0.000 0.632
#> GSM509781 4 0.2281 0.846 0.000 0.096 0.000 0.904
#> GSM509783 4 0.1940 0.852 0.000 0.076 0.000 0.924
#> GSM509785 4 0.1867 0.853 0.000 0.072 0.000 0.928
#> GSM509752 2 0.0188 0.925 0.000 0.996 0.000 0.004
#> GSM509754 2 0.0000 0.924 0.000 1.000 0.000 0.000
#> GSM509756 2 0.0524 0.925 0.000 0.988 0.004 0.008
#> GSM509758 2 0.0469 0.925 0.000 0.988 0.000 0.012
#> GSM509760 2 0.0657 0.924 0.000 0.984 0.004 0.012
#> GSM509762 2 0.0336 0.925 0.000 0.992 0.000 0.008
#> GSM509764 2 0.0707 0.916 0.000 0.980 0.020 0.000
#> GSM509766 2 0.2345 0.879 0.000 0.900 0.000 0.100
#> GSM509768 2 0.1940 0.895 0.000 0.924 0.000 0.076
#> GSM509770 2 0.0000 0.924 0.000 1.000 0.000 0.000
#> GSM509772 2 0.1118 0.903 0.000 0.964 0.036 0.000
#> GSM509774 2 0.4877 0.302 0.000 0.592 0.000 0.408
#> GSM509776 2 0.2408 0.876 0.000 0.896 0.000 0.104
#> GSM509778 4 0.2281 0.846 0.000 0.096 0.000 0.904
#> GSM509780 2 0.3024 0.831 0.000 0.852 0.000 0.148
#> GSM509782 4 0.2149 0.849 0.000 0.088 0.000 0.912
#> GSM509784 4 0.4916 0.263 0.000 0.424 0.000 0.576
#> GSM509786 4 0.2345 0.843 0.000 0.100 0.000 0.900
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM509706 1 0.0000 0.8580 1.000 0.000 0.000 0.000 0.000
#> GSM509711 1 0.0162 0.8576 0.996 0.000 0.000 0.000 0.004
#> GSM509714 1 0.5954 0.4962 0.576 0.000 0.000 0.152 0.272
#> GSM509719 1 0.4731 0.6606 0.640 0.032 0.000 0.000 0.328
#> GSM509724 1 0.0000 0.8580 1.000 0.000 0.000 0.000 0.000
#> GSM509729 1 0.1697 0.8376 0.932 0.000 0.008 0.000 0.060
#> GSM509707 1 0.0000 0.8580 1.000 0.000 0.000 0.000 0.000
#> GSM509712 1 0.0000 0.8580 1.000 0.000 0.000 0.000 0.000
#> GSM509715 5 0.3816 0.6917 0.000 0.000 0.000 0.304 0.696
#> GSM509720 1 0.4310 0.6093 0.604 0.004 0.000 0.000 0.392
#> GSM509725 1 0.0000 0.8580 1.000 0.000 0.000 0.000 0.000
#> GSM509730 1 0.3988 0.7624 0.768 0.000 0.036 0.000 0.196
#> GSM509708 1 0.0000 0.8580 1.000 0.000 0.000 0.000 0.000
#> GSM509713 1 0.0000 0.8580 1.000 0.000 0.000 0.000 0.000
#> GSM509716 5 0.3816 0.6852 0.000 0.000 0.000 0.304 0.696
#> GSM509721 1 0.5658 0.5847 0.572 0.096 0.000 0.000 0.332
#> GSM509726 1 0.0162 0.8576 0.996 0.000 0.000 0.000 0.004
#> GSM509731 4 0.1478 0.7563 0.000 0.000 0.000 0.936 0.064
#> GSM509709 1 0.0000 0.8580 1.000 0.000 0.000 0.000 0.000
#> GSM509717 5 0.4375 0.5391 0.000 0.000 0.004 0.420 0.576
#> GSM509722 1 0.4135 0.6690 0.656 0.004 0.000 0.000 0.340
#> GSM509727 1 0.5968 -0.1329 0.452 0.000 0.108 0.000 0.440
#> GSM509710 1 0.0162 0.8576 0.996 0.000 0.000 0.000 0.004
#> GSM509718 5 0.3885 0.7161 0.000 0.000 0.008 0.268 0.724
#> GSM509723 1 0.3910 0.7245 0.720 0.008 0.000 0.000 0.272
#> GSM509728 3 0.4378 0.6070 0.036 0.000 0.716 0.000 0.248
#> GSM509732 3 0.0865 0.9264 0.000 0.004 0.972 0.000 0.024
#> GSM509736 5 0.2966 0.7038 0.000 0.000 0.184 0.000 0.816
#> GSM509741 3 0.0510 0.9315 0.000 0.000 0.984 0.000 0.016
#> GSM509746 3 0.0671 0.9297 0.000 0.004 0.980 0.000 0.016
#> GSM509733 3 0.0566 0.9313 0.000 0.004 0.984 0.000 0.012
#> GSM509737 5 0.2929 0.7043 0.000 0.000 0.180 0.000 0.820
#> GSM509742 3 0.0404 0.9325 0.000 0.000 0.988 0.000 0.012
#> GSM509747 3 0.0865 0.9264 0.000 0.004 0.972 0.000 0.024
#> GSM509734 3 0.0290 0.9323 0.008 0.000 0.992 0.000 0.000
#> GSM509738 5 0.2648 0.7200 0.000 0.000 0.152 0.000 0.848
#> GSM509743 3 0.1671 0.8956 0.000 0.000 0.924 0.000 0.076
#> GSM509748 3 0.0566 0.9318 0.000 0.004 0.984 0.000 0.012
#> GSM509735 1 0.0451 0.8528 0.988 0.000 0.008 0.000 0.004
#> GSM509739 1 0.0162 0.8576 0.996 0.000 0.000 0.000 0.004
#> GSM509744 3 0.2471 0.8313 0.000 0.000 0.864 0.000 0.136
#> GSM509749 3 0.0510 0.9333 0.000 0.000 0.984 0.000 0.016
#> GSM509740 5 0.3002 0.7431 0.008 0.000 0.048 0.068 0.876
#> GSM509745 5 0.4561 0.0765 0.000 0.000 0.488 0.008 0.504
#> GSM509750 3 0.1341 0.9108 0.000 0.000 0.944 0.000 0.056
#> GSM509751 2 0.0000 0.9118 0.000 1.000 0.000 0.000 0.000
#> GSM509753 2 0.0000 0.9118 0.000 1.000 0.000 0.000 0.000
#> GSM509755 2 0.0162 0.9100 0.000 0.996 0.000 0.000 0.004
#> GSM509757 2 0.0000 0.9118 0.000 1.000 0.000 0.000 0.000
#> GSM509759 2 0.0290 0.9078 0.000 0.992 0.000 0.000 0.008
#> GSM509761 2 0.1341 0.8964 0.000 0.944 0.000 0.056 0.000
#> GSM509763 2 0.4210 0.3142 0.000 0.588 0.000 0.412 0.000
#> GSM509765 2 0.3876 0.5716 0.000 0.684 0.000 0.316 0.000
#> GSM509767 2 0.1205 0.9026 0.000 0.956 0.004 0.040 0.000
#> GSM509769 2 0.0609 0.9105 0.000 0.980 0.000 0.020 0.000
#> GSM509771 2 0.1956 0.8824 0.000 0.916 0.008 0.076 0.000
#> GSM509773 2 0.1965 0.8714 0.000 0.904 0.000 0.096 0.000
#> GSM509775 2 0.2852 0.8029 0.000 0.828 0.000 0.172 0.000
#> GSM509777 4 0.3480 0.6967 0.000 0.248 0.000 0.752 0.000
#> GSM509779 4 0.2280 0.7999 0.000 0.120 0.000 0.880 0.000
#> GSM509781 4 0.0510 0.8228 0.000 0.016 0.000 0.984 0.000
#> GSM509783 4 0.0000 0.8060 0.000 0.000 0.000 1.000 0.000
#> GSM509785 4 0.0290 0.8167 0.000 0.008 0.000 0.992 0.000
#> GSM509752 2 0.0162 0.9124 0.000 0.996 0.000 0.004 0.000
#> GSM509754 2 0.0290 0.9126 0.000 0.992 0.000 0.008 0.000
#> GSM509756 2 0.0000 0.9118 0.000 1.000 0.000 0.000 0.000
#> GSM509758 2 0.0404 0.9124 0.000 0.988 0.000 0.012 0.000
#> GSM509760 2 0.0404 0.9123 0.000 0.988 0.000 0.012 0.000
#> GSM509762 2 0.0000 0.9118 0.000 1.000 0.000 0.000 0.000
#> GSM509764 2 0.0000 0.9118 0.000 1.000 0.000 0.000 0.000
#> GSM509766 2 0.3508 0.6922 0.000 0.748 0.000 0.252 0.000
#> GSM509768 2 0.3039 0.7789 0.000 0.808 0.000 0.192 0.000
#> GSM509770 2 0.0290 0.9126 0.000 0.992 0.000 0.008 0.000
#> GSM509772 2 0.0162 0.9101 0.000 0.996 0.000 0.000 0.004
#> GSM509774 4 0.3424 0.7086 0.000 0.240 0.000 0.760 0.000
#> GSM509776 2 0.2605 0.8272 0.000 0.852 0.000 0.148 0.000
#> GSM509778 4 0.0703 0.8240 0.000 0.024 0.000 0.976 0.000
#> GSM509780 4 0.4299 0.3778 0.000 0.388 0.000 0.608 0.004
#> GSM509782 4 0.0404 0.8205 0.000 0.012 0.000 0.988 0.000
#> GSM509784 4 0.2424 0.7939 0.000 0.132 0.000 0.868 0.000
#> GSM509786 4 0.0510 0.8230 0.000 0.016 0.000 0.984 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM509706 1 0.0146 0.971 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM509711 1 0.0260 0.970 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM509714 5 0.6014 0.352 0.028 0.000 0.000 0.144 0.528 0.300
#> GSM509719 5 0.1401 0.820 0.004 0.020 0.000 0.000 0.948 0.028
#> GSM509724 1 0.0000 0.970 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509729 5 0.4303 0.357 0.392 0.000 0.012 0.000 0.588 0.008
#> GSM509707 1 0.0146 0.971 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM509712 1 0.0858 0.954 0.968 0.000 0.000 0.000 0.028 0.004
#> GSM509715 6 0.2301 0.752 0.000 0.000 0.000 0.096 0.020 0.884
#> GSM509720 5 0.1719 0.817 0.008 0.008 0.000 0.000 0.928 0.056
#> GSM509725 1 0.0000 0.970 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509730 5 0.3513 0.729 0.072 0.000 0.104 0.000 0.816 0.008
#> GSM509708 1 0.0260 0.969 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM509713 1 0.0146 0.971 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM509716 6 0.3472 0.699 0.000 0.000 0.000 0.100 0.092 0.808
#> GSM509721 5 0.1977 0.817 0.008 0.032 0.000 0.000 0.920 0.040
#> GSM509726 1 0.0260 0.966 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM509731 4 0.3925 0.532 0.000 0.000 0.000 0.724 0.236 0.040
#> GSM509709 1 0.0146 0.971 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM509717 6 0.3709 0.651 0.000 0.000 0.000 0.204 0.040 0.756
#> GSM509722 5 0.1542 0.818 0.008 0.004 0.000 0.000 0.936 0.052
#> GSM509727 1 0.3368 0.658 0.756 0.000 0.012 0.000 0.000 0.232
#> GSM509710 1 0.0146 0.969 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM509718 6 0.1010 0.776 0.000 0.000 0.000 0.036 0.004 0.960
#> GSM509723 5 0.1353 0.821 0.012 0.012 0.000 0.000 0.952 0.024
#> GSM509728 6 0.6059 0.227 0.312 0.000 0.280 0.000 0.000 0.408
#> GSM509732 3 0.0146 0.924 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM509736 6 0.2905 0.756 0.008 0.000 0.088 0.004 0.036 0.864
#> GSM509741 3 0.0713 0.922 0.000 0.000 0.972 0.000 0.000 0.028
#> GSM509746 3 0.0000 0.925 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509733 3 0.0146 0.924 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM509737 6 0.3232 0.750 0.008 0.000 0.088 0.004 0.056 0.844
#> GSM509742 3 0.0632 0.923 0.000 0.000 0.976 0.000 0.000 0.024
#> GSM509747 3 0.0790 0.909 0.000 0.000 0.968 0.000 0.032 0.000
#> GSM509734 3 0.0363 0.926 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM509738 6 0.1485 0.778 0.000 0.000 0.028 0.004 0.024 0.944
#> GSM509743 3 0.3250 0.747 0.000 0.000 0.788 0.004 0.012 0.196
#> GSM509748 3 0.0458 0.921 0.000 0.000 0.984 0.000 0.016 0.000
#> GSM509735 1 0.0777 0.955 0.972 0.000 0.004 0.000 0.024 0.000
#> GSM509739 1 0.0146 0.971 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM509744 3 0.3563 0.503 0.000 0.000 0.664 0.000 0.000 0.336
#> GSM509749 3 0.0260 0.926 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM509740 6 0.1080 0.773 0.004 0.000 0.004 0.000 0.032 0.960
#> GSM509745 6 0.3595 0.540 0.000 0.000 0.288 0.000 0.008 0.704
#> GSM509750 3 0.1556 0.888 0.000 0.000 0.920 0.000 0.000 0.080
#> GSM509751 2 0.0146 0.921 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM509753 2 0.0146 0.919 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM509755 2 0.0146 0.920 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM509757 2 0.0000 0.921 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509759 2 0.0922 0.911 0.000 0.968 0.000 0.004 0.024 0.004
#> GSM509761 2 0.0790 0.922 0.000 0.968 0.000 0.032 0.000 0.000
#> GSM509763 2 0.3584 0.624 0.000 0.688 0.000 0.308 0.000 0.004
#> GSM509765 2 0.3309 0.681 0.000 0.720 0.000 0.280 0.000 0.000
#> GSM509767 2 0.1226 0.919 0.000 0.952 0.000 0.040 0.004 0.004
#> GSM509769 2 0.1194 0.920 0.000 0.956 0.000 0.032 0.008 0.004
#> GSM509771 2 0.1732 0.904 0.000 0.920 0.000 0.072 0.004 0.004
#> GSM509773 2 0.2051 0.888 0.000 0.896 0.000 0.096 0.004 0.004
#> GSM509775 2 0.2632 0.834 0.000 0.832 0.000 0.164 0.000 0.004
#> GSM509777 4 0.2631 0.744 0.000 0.180 0.000 0.820 0.000 0.000
#> GSM509779 4 0.0713 0.859 0.000 0.028 0.000 0.972 0.000 0.000
#> GSM509781 4 0.0405 0.862 0.000 0.008 0.000 0.988 0.004 0.000
#> GSM509783 4 0.0436 0.858 0.000 0.004 0.000 0.988 0.004 0.004
#> GSM509785 4 0.0436 0.858 0.000 0.004 0.000 0.988 0.004 0.004
#> GSM509752 2 0.0260 0.923 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM509754 2 0.0363 0.923 0.000 0.988 0.000 0.012 0.000 0.000
#> GSM509756 2 0.0000 0.921 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509758 2 0.0632 0.923 0.000 0.976 0.000 0.024 0.000 0.000
#> GSM509760 2 0.1088 0.922 0.000 0.960 0.000 0.024 0.016 0.000
#> GSM509762 2 0.0146 0.922 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM509764 2 0.0291 0.919 0.000 0.992 0.000 0.004 0.004 0.000
#> GSM509766 2 0.2996 0.759 0.000 0.772 0.000 0.228 0.000 0.000
#> GSM509768 2 0.2838 0.808 0.000 0.808 0.000 0.188 0.000 0.004
#> GSM509770 2 0.0508 0.924 0.000 0.984 0.000 0.012 0.004 0.000
#> GSM509772 2 0.0665 0.921 0.000 0.980 0.000 0.008 0.008 0.004
#> GSM509774 4 0.3290 0.662 0.000 0.252 0.000 0.744 0.004 0.000
#> GSM509776 2 0.2416 0.843 0.000 0.844 0.000 0.156 0.000 0.000
#> GSM509778 4 0.0260 0.862 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM509780 4 0.3531 0.500 0.000 0.328 0.000 0.672 0.000 0.000
#> GSM509782 4 0.0363 0.862 0.000 0.012 0.000 0.988 0.000 0.000
#> GSM509784 4 0.0865 0.855 0.000 0.036 0.000 0.964 0.000 0.000
#> GSM509786 4 0.0405 0.862 0.000 0.008 0.000 0.988 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 disease.state(p) time(p) k
#> SD:NMF 81 8.31e-15 6.68e-12 2
#> SD:NMF 74 1.13e-14 2.50e-06 3
#> SD:NMF 75 1.29e-22 1.20e-07 4
#> SD:NMF 76 1.35e-20 2.64e-07 5
#> SD:NMF 78 2.64e-21 4.13e-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", "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 19175 rows and 81 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 0.547 0.863 0.927 0.4845 0.494 0.494
#> 3 3 0.447 0.778 0.840 0.2546 0.883 0.763
#> 4 4 0.600 0.656 0.787 0.1680 0.841 0.591
#> 5 5 0.686 0.630 0.819 0.0753 0.909 0.671
#> 6 6 0.766 0.701 0.834 0.0339 0.963 0.836
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
#> GSM509706 1 0.0000 0.901 1.000 0.000
#> GSM509711 1 0.8386 0.647 0.732 0.268
#> GSM509714 2 0.7950 0.635 0.240 0.760
#> GSM509719 1 0.9129 0.551 0.672 0.328
#> GSM509724 1 0.0000 0.901 1.000 0.000
#> GSM509729 1 0.9795 0.324 0.584 0.416
#> GSM509707 1 0.0000 0.901 1.000 0.000
#> GSM509712 1 0.8386 0.647 0.732 0.268
#> GSM509715 2 0.1843 0.924 0.028 0.972
#> GSM509720 1 0.9129 0.551 0.672 0.328
#> GSM509725 1 0.0000 0.901 1.000 0.000
#> GSM509730 1 0.9795 0.324 0.584 0.416
#> GSM509708 1 0.0000 0.901 1.000 0.000
#> GSM509713 1 0.8386 0.647 0.732 0.268
#> GSM509716 2 0.2043 0.922 0.032 0.968
#> GSM509721 1 0.9129 0.551 0.672 0.328
#> GSM509726 1 0.0000 0.901 1.000 0.000
#> GSM509731 2 0.0672 0.927 0.008 0.992
#> GSM509709 1 0.0000 0.901 1.000 0.000
#> GSM509717 2 0.2236 0.920 0.036 0.964
#> GSM509722 1 0.9129 0.551 0.672 0.328
#> GSM509727 1 0.0000 0.901 1.000 0.000
#> GSM509710 1 0.0000 0.901 1.000 0.000
#> GSM509718 2 0.1633 0.933 0.024 0.976
#> GSM509723 1 0.9129 0.551 0.672 0.328
#> GSM509728 1 0.0000 0.901 1.000 0.000
#> GSM509732 1 0.0000 0.901 1.000 0.000
#> GSM509736 1 0.0000 0.901 1.000 0.000
#> GSM509741 1 0.0000 0.901 1.000 0.000
#> GSM509746 1 0.0000 0.901 1.000 0.000
#> GSM509733 1 0.0000 0.901 1.000 0.000
#> GSM509737 1 0.0000 0.901 1.000 0.000
#> GSM509742 1 0.0000 0.901 1.000 0.000
#> GSM509747 1 0.0000 0.901 1.000 0.000
#> GSM509734 1 0.0000 0.901 1.000 0.000
#> GSM509738 1 0.0376 0.899 0.996 0.004
#> GSM509743 1 0.0000 0.901 1.000 0.000
#> GSM509748 1 0.0000 0.901 1.000 0.000
#> GSM509735 1 0.0000 0.901 1.000 0.000
#> GSM509739 1 0.0000 0.901 1.000 0.000
#> GSM509744 1 0.0000 0.901 1.000 0.000
#> GSM509749 1 0.0000 0.901 1.000 0.000
#> GSM509740 1 0.1843 0.885 0.972 0.028
#> GSM509745 1 0.0938 0.895 0.988 0.012
#> GSM509750 1 0.0376 0.899 0.996 0.004
#> GSM509751 2 0.5408 0.908 0.124 0.876
#> GSM509753 2 0.5408 0.908 0.124 0.876
#> GSM509755 2 0.5408 0.908 0.124 0.876
#> GSM509757 2 0.5408 0.908 0.124 0.876
#> GSM509759 2 0.5408 0.908 0.124 0.876
#> GSM509761 2 0.5178 0.913 0.116 0.884
#> GSM509763 2 0.0938 0.931 0.012 0.988
#> GSM509765 2 0.0672 0.930 0.008 0.992
#> GSM509767 2 0.4022 0.926 0.080 0.920
#> GSM509769 2 0.2948 0.933 0.052 0.948
#> GSM509771 2 0.4298 0.924 0.088 0.912
#> GSM509773 2 0.2778 0.933 0.048 0.952
#> GSM509775 2 0.2948 0.932 0.052 0.948
#> GSM509777 2 0.0672 0.930 0.008 0.992
#> GSM509779 2 0.0000 0.926 0.000 1.000
#> GSM509781 2 0.0000 0.926 0.000 1.000
#> GSM509783 2 0.0000 0.926 0.000 1.000
#> GSM509785 2 0.0000 0.926 0.000 1.000
#> GSM509752 2 0.5408 0.908 0.124 0.876
#> GSM509754 2 0.5178 0.913 0.116 0.884
#> GSM509756 2 0.5408 0.908 0.124 0.876
#> GSM509758 2 0.4939 0.917 0.108 0.892
#> GSM509760 2 0.5294 0.911 0.120 0.880
#> GSM509762 2 0.5178 0.913 0.116 0.884
#> GSM509764 2 0.5408 0.908 0.124 0.876
#> GSM509766 2 0.1633 0.933 0.024 0.976
#> GSM509768 2 0.1414 0.933 0.020 0.980
#> GSM509770 2 0.5294 0.911 0.120 0.880
#> GSM509772 2 0.5408 0.908 0.124 0.876
#> GSM509774 2 0.0376 0.928 0.004 0.996
#> GSM509776 2 0.1633 0.934 0.024 0.976
#> GSM509778 2 0.0000 0.926 0.000 1.000
#> GSM509780 2 0.0672 0.930 0.008 0.992
#> GSM509782 2 0.0000 0.926 0.000 1.000
#> GSM509784 2 0.0672 0.930 0.008 0.992
#> GSM509786 2 0.0000 0.926 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM509706 1 0.5291 0.610 0.732 0.000 0.268
#> GSM509711 1 0.4195 0.612 0.852 0.136 0.012
#> GSM509714 2 0.6026 0.349 0.376 0.624 0.000
#> GSM509719 1 0.8940 0.573 0.568 0.232 0.200
#> GSM509724 1 0.5397 0.601 0.720 0.000 0.280
#> GSM509729 1 0.9713 0.437 0.444 0.316 0.240
#> GSM509707 1 0.5291 0.610 0.732 0.000 0.268
#> GSM509712 1 0.4195 0.612 0.852 0.136 0.012
#> GSM509715 2 0.3619 0.810 0.136 0.864 0.000
#> GSM509720 1 0.8940 0.573 0.568 0.232 0.200
#> GSM509725 1 0.6260 0.316 0.552 0.000 0.448
#> GSM509730 1 0.9713 0.437 0.444 0.316 0.240
#> GSM509708 1 0.5291 0.610 0.732 0.000 0.268
#> GSM509713 1 0.4195 0.612 0.852 0.136 0.012
#> GSM509716 2 0.3816 0.799 0.148 0.852 0.000
#> GSM509721 1 0.8940 0.573 0.568 0.232 0.200
#> GSM509726 1 0.6305 0.208 0.516 0.000 0.484
#> GSM509731 2 0.4842 0.759 0.224 0.776 0.000
#> GSM509709 1 0.5291 0.610 0.732 0.000 0.268
#> GSM509717 2 0.4178 0.773 0.172 0.828 0.000
#> GSM509722 1 0.8940 0.573 0.568 0.232 0.200
#> GSM509727 3 0.3941 0.806 0.156 0.000 0.844
#> GSM509710 1 0.5291 0.610 0.732 0.000 0.268
#> GSM509718 2 0.2383 0.869 0.044 0.940 0.016
#> GSM509723 1 0.8940 0.573 0.568 0.232 0.200
#> GSM509728 3 0.3941 0.806 0.156 0.000 0.844
#> GSM509732 3 0.0000 0.928 0.000 0.000 1.000
#> GSM509736 3 0.0829 0.925 0.012 0.004 0.984
#> GSM509741 3 0.0000 0.928 0.000 0.000 1.000
#> GSM509746 3 0.0000 0.928 0.000 0.000 1.000
#> GSM509733 3 0.0000 0.928 0.000 0.000 1.000
#> GSM509737 3 0.0829 0.925 0.012 0.004 0.984
#> GSM509742 3 0.0000 0.928 0.000 0.000 1.000
#> GSM509747 3 0.0000 0.928 0.000 0.000 1.000
#> GSM509734 3 0.0000 0.928 0.000 0.000 1.000
#> GSM509738 3 0.3607 0.859 0.112 0.008 0.880
#> GSM509743 3 0.0237 0.925 0.000 0.004 0.996
#> GSM509748 3 0.0892 0.924 0.020 0.000 0.980
#> GSM509735 1 0.6111 0.463 0.604 0.000 0.396
#> GSM509739 1 0.5397 0.601 0.720 0.000 0.280
#> GSM509744 3 0.0983 0.926 0.016 0.004 0.980
#> GSM509749 3 0.0892 0.924 0.020 0.000 0.980
#> GSM509740 3 0.4799 0.810 0.132 0.032 0.836
#> GSM509745 3 0.4059 0.834 0.128 0.012 0.860
#> GSM509750 3 0.3573 0.850 0.120 0.004 0.876
#> GSM509751 2 0.4270 0.857 0.024 0.860 0.116
#> GSM509753 2 0.4270 0.857 0.024 0.860 0.116
#> GSM509755 2 0.4270 0.857 0.024 0.860 0.116
#> GSM509757 2 0.4270 0.857 0.024 0.860 0.116
#> GSM509759 2 0.4270 0.857 0.024 0.860 0.116
#> GSM509761 2 0.4121 0.862 0.024 0.868 0.108
#> GSM509763 2 0.2229 0.869 0.044 0.944 0.012
#> GSM509765 2 0.2280 0.863 0.052 0.940 0.008
#> GSM509767 2 0.2939 0.873 0.012 0.916 0.072
#> GSM509769 2 0.2063 0.877 0.008 0.948 0.044
#> GSM509771 2 0.2955 0.872 0.008 0.912 0.080
#> GSM509773 2 0.1950 0.876 0.008 0.952 0.040
#> GSM509775 2 0.2527 0.877 0.020 0.936 0.044
#> GSM509777 2 0.2774 0.857 0.072 0.920 0.008
#> GSM509779 2 0.3619 0.823 0.136 0.864 0.000
#> GSM509781 2 0.3619 0.823 0.136 0.864 0.000
#> GSM509783 2 0.3619 0.823 0.136 0.864 0.000
#> GSM509785 2 0.3619 0.823 0.136 0.864 0.000
#> GSM509752 2 0.4270 0.857 0.024 0.860 0.116
#> GSM509754 2 0.4121 0.862 0.024 0.868 0.108
#> GSM509756 2 0.4270 0.857 0.024 0.860 0.116
#> GSM509758 2 0.3966 0.865 0.024 0.876 0.100
#> GSM509760 2 0.4196 0.860 0.024 0.864 0.112
#> GSM509762 2 0.4121 0.862 0.024 0.868 0.108
#> GSM509764 2 0.4270 0.857 0.024 0.860 0.116
#> GSM509766 2 0.2297 0.871 0.036 0.944 0.020
#> GSM509768 2 0.1774 0.872 0.024 0.960 0.016
#> GSM509770 2 0.3771 0.862 0.012 0.876 0.112
#> GSM509772 2 0.4270 0.857 0.024 0.860 0.116
#> GSM509774 2 0.2590 0.856 0.072 0.924 0.004
#> GSM509776 2 0.2414 0.874 0.040 0.940 0.020
#> GSM509778 2 0.3619 0.823 0.136 0.864 0.000
#> GSM509780 2 0.2774 0.858 0.072 0.920 0.008
#> GSM509782 2 0.3619 0.823 0.136 0.864 0.000
#> GSM509784 2 0.2866 0.856 0.076 0.916 0.008
#> GSM509786 2 0.3619 0.823 0.136 0.864 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM509706 1 0.2011 0.747 0.920 0.000 0.080 0.000
#> GSM509711 1 0.3764 0.699 0.784 0.216 0.000 0.000
#> GSM509714 4 0.7853 0.245 0.292 0.308 0.000 0.400
#> GSM509719 1 0.5751 0.564 0.592 0.380 0.016 0.012
#> GSM509724 1 0.2281 0.741 0.904 0.000 0.096 0.000
#> GSM509729 2 0.6010 -0.542 0.472 0.488 0.040 0.000
#> GSM509707 1 0.2011 0.747 0.920 0.000 0.080 0.000
#> GSM509712 1 0.3764 0.699 0.784 0.216 0.000 0.000
#> GSM509715 4 0.6443 0.439 0.076 0.376 0.000 0.548
#> GSM509720 1 0.5751 0.564 0.592 0.380 0.016 0.012
#> GSM509725 1 0.4643 0.426 0.656 0.000 0.344 0.000
#> GSM509730 2 0.6010 -0.542 0.472 0.488 0.040 0.000
#> GSM509708 1 0.2011 0.747 0.920 0.000 0.080 0.000
#> GSM509713 1 0.3764 0.699 0.784 0.216 0.000 0.000
#> GSM509716 4 0.6532 0.444 0.084 0.368 0.000 0.548
#> GSM509721 1 0.5751 0.564 0.592 0.380 0.016 0.012
#> GSM509726 1 0.4866 0.278 0.596 0.000 0.404 0.000
#> GSM509731 4 0.5720 0.464 0.052 0.296 0.000 0.652
#> GSM509709 1 0.2011 0.747 0.920 0.000 0.080 0.000
#> GSM509717 4 0.6617 0.440 0.088 0.380 0.000 0.532
#> GSM509722 1 0.5751 0.564 0.592 0.380 0.016 0.012
#> GSM509727 3 0.3311 0.821 0.172 0.000 0.828 0.000
#> GSM509710 1 0.2011 0.747 0.920 0.000 0.080 0.000
#> GSM509718 4 0.5526 0.293 0.020 0.416 0.000 0.564
#> GSM509723 1 0.5751 0.564 0.592 0.380 0.016 0.012
#> GSM509728 3 0.3311 0.821 0.172 0.000 0.828 0.000
#> GSM509732 3 0.0000 0.930 0.000 0.000 1.000 0.000
#> GSM509736 3 0.1042 0.926 0.008 0.020 0.972 0.000
#> GSM509741 3 0.0000 0.930 0.000 0.000 1.000 0.000
#> GSM509746 3 0.0000 0.930 0.000 0.000 1.000 0.000
#> GSM509733 3 0.0000 0.930 0.000 0.000 1.000 0.000
#> GSM509737 3 0.1042 0.926 0.008 0.020 0.972 0.000
#> GSM509742 3 0.0000 0.930 0.000 0.000 1.000 0.000
#> GSM509747 3 0.0000 0.930 0.000 0.000 1.000 0.000
#> GSM509734 3 0.0000 0.930 0.000 0.000 1.000 0.000
#> GSM509738 3 0.3335 0.865 0.120 0.020 0.860 0.000
#> GSM509743 3 0.0469 0.926 0.000 0.012 0.988 0.000
#> GSM509748 3 0.0817 0.927 0.024 0.000 0.976 0.000
#> GSM509735 1 0.4008 0.609 0.756 0.000 0.244 0.000
#> GSM509739 1 0.2216 0.742 0.908 0.000 0.092 0.000
#> GSM509744 3 0.1059 0.928 0.016 0.012 0.972 0.000
#> GSM509749 3 0.0817 0.927 0.024 0.000 0.976 0.000
#> GSM509740 3 0.4324 0.824 0.140 0.036 0.816 0.008
#> GSM509745 3 0.3659 0.844 0.136 0.024 0.840 0.000
#> GSM509750 3 0.3280 0.862 0.124 0.016 0.860 0.000
#> GSM509751 2 0.4040 0.802 0.000 0.752 0.000 0.248
#> GSM509753 2 0.4040 0.802 0.000 0.752 0.000 0.248
#> GSM509755 2 0.4040 0.802 0.000 0.752 0.000 0.248
#> GSM509757 2 0.4040 0.802 0.000 0.752 0.000 0.248
#> GSM509759 2 0.4040 0.802 0.000 0.752 0.000 0.248
#> GSM509761 2 0.4134 0.795 0.000 0.740 0.000 0.260
#> GSM509763 4 0.4761 0.341 0.000 0.372 0.000 0.628
#> GSM509765 4 0.4382 0.494 0.000 0.296 0.000 0.704
#> GSM509767 2 0.4564 0.702 0.000 0.672 0.000 0.328
#> GSM509769 2 0.4817 0.573 0.000 0.612 0.000 0.388
#> GSM509771 2 0.4543 0.712 0.000 0.676 0.000 0.324
#> GSM509773 2 0.4948 0.411 0.000 0.560 0.000 0.440
#> GSM509775 2 0.4941 0.433 0.000 0.564 0.000 0.436
#> GSM509777 4 0.3688 0.607 0.000 0.208 0.000 0.792
#> GSM509779 4 0.0921 0.655 0.000 0.028 0.000 0.972
#> GSM509781 4 0.0000 0.655 0.000 0.000 0.000 1.000
#> GSM509783 4 0.0000 0.655 0.000 0.000 0.000 1.000
#> GSM509785 4 0.0000 0.655 0.000 0.000 0.000 1.000
#> GSM509752 2 0.4040 0.802 0.000 0.752 0.000 0.248
#> GSM509754 2 0.4103 0.798 0.000 0.744 0.000 0.256
#> GSM509756 2 0.4040 0.802 0.000 0.752 0.000 0.248
#> GSM509758 2 0.4222 0.781 0.000 0.728 0.000 0.272
#> GSM509760 2 0.4072 0.800 0.000 0.748 0.000 0.252
#> GSM509762 2 0.4103 0.798 0.000 0.744 0.000 0.256
#> GSM509764 2 0.4040 0.802 0.000 0.752 0.000 0.248
#> GSM509766 4 0.4776 0.326 0.000 0.376 0.000 0.624
#> GSM509768 4 0.4877 0.229 0.000 0.408 0.000 0.592
#> GSM509770 2 0.4193 0.788 0.000 0.732 0.000 0.268
#> GSM509772 2 0.4040 0.802 0.000 0.752 0.000 0.248
#> GSM509774 4 0.3528 0.618 0.000 0.192 0.000 0.808
#> GSM509776 4 0.4916 0.124 0.000 0.424 0.000 0.576
#> GSM509778 4 0.0000 0.655 0.000 0.000 0.000 1.000
#> GSM509780 4 0.3837 0.593 0.000 0.224 0.000 0.776
#> GSM509782 4 0.0000 0.655 0.000 0.000 0.000 1.000
#> GSM509784 4 0.3528 0.619 0.000 0.192 0.000 0.808
#> GSM509786 4 0.0000 0.655 0.000 0.000 0.000 1.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM509706 1 0.0000 0.6518 1.000 0.000 0.000 0.000 0.000
#> GSM509711 1 0.4419 0.4997 0.668 0.020 0.000 0.000 0.312
#> GSM509714 5 0.7858 0.3824 0.188 0.116 0.000 0.240 0.456
#> GSM509719 1 0.6504 0.2786 0.448 0.196 0.000 0.000 0.356
#> GSM509724 1 0.0510 0.6487 0.984 0.000 0.016 0.000 0.000
#> GSM509729 5 0.6170 -0.1771 0.336 0.132 0.004 0.000 0.528
#> GSM509707 1 0.0000 0.6518 1.000 0.000 0.000 0.000 0.000
#> GSM509712 1 0.4419 0.4997 0.668 0.020 0.000 0.000 0.312
#> GSM509715 5 0.7001 0.3700 0.008 0.320 0.000 0.280 0.392
#> GSM509720 1 0.6504 0.2786 0.448 0.196 0.000 0.000 0.356
#> GSM509725 1 0.4046 0.4402 0.696 0.000 0.296 0.000 0.008
#> GSM509730 5 0.6170 -0.1771 0.336 0.132 0.004 0.000 0.528
#> GSM509708 1 0.0000 0.6518 1.000 0.000 0.000 0.000 0.000
#> GSM509713 1 0.4419 0.4997 0.668 0.020 0.000 0.000 0.312
#> GSM509716 5 0.6976 0.3937 0.008 0.304 0.000 0.280 0.408
#> GSM509721 1 0.6504 0.2786 0.448 0.196 0.000 0.000 0.356
#> GSM509726 1 0.4313 0.3121 0.636 0.000 0.356 0.000 0.008
#> GSM509731 5 0.4192 0.1294 0.000 0.000 0.000 0.404 0.596
#> GSM509709 1 0.0000 0.6518 1.000 0.000 0.000 0.000 0.000
#> GSM509717 5 0.6898 0.4157 0.008 0.284 0.000 0.268 0.440
#> GSM509722 1 0.6504 0.2786 0.448 0.196 0.000 0.000 0.356
#> GSM509727 3 0.3667 0.8370 0.140 0.000 0.812 0.000 0.048
#> GSM509710 1 0.0000 0.6518 1.000 0.000 0.000 0.000 0.000
#> GSM509718 2 0.6578 -0.0206 0.000 0.500 0.004 0.228 0.268
#> GSM509723 1 0.6504 0.2786 0.448 0.196 0.000 0.000 0.356
#> GSM509728 3 0.3667 0.8370 0.140 0.000 0.812 0.000 0.048
#> GSM509732 3 0.0162 0.9350 0.004 0.000 0.996 0.000 0.000
#> GSM509736 3 0.0794 0.9311 0.000 0.000 0.972 0.000 0.028
#> GSM509741 3 0.0162 0.9350 0.004 0.000 0.996 0.000 0.000
#> GSM509746 3 0.0162 0.9350 0.004 0.000 0.996 0.000 0.000
#> GSM509733 3 0.0162 0.9350 0.004 0.000 0.996 0.000 0.000
#> GSM509737 3 0.0794 0.9311 0.000 0.000 0.972 0.000 0.028
#> GSM509742 3 0.0162 0.9350 0.004 0.000 0.996 0.000 0.000
#> GSM509747 3 0.0162 0.9350 0.004 0.000 0.996 0.000 0.000
#> GSM509734 3 0.0162 0.9350 0.004 0.000 0.996 0.000 0.000
#> GSM509738 3 0.3176 0.8829 0.064 0.000 0.856 0.000 0.080
#> GSM509743 3 0.0404 0.9318 0.000 0.000 0.988 0.000 0.012
#> GSM509748 3 0.1168 0.9291 0.032 0.000 0.960 0.000 0.008
#> GSM509735 1 0.3209 0.5536 0.812 0.000 0.180 0.000 0.008
#> GSM509739 1 0.0404 0.6495 0.988 0.000 0.012 0.000 0.000
#> GSM509744 3 0.0898 0.9330 0.008 0.000 0.972 0.000 0.020
#> GSM509749 3 0.1168 0.9291 0.032 0.000 0.960 0.000 0.008
#> GSM509740 3 0.4187 0.8469 0.080 0.016 0.804 0.000 0.100
#> GSM509745 3 0.3805 0.8622 0.084 0.004 0.820 0.000 0.092
#> GSM509750 3 0.3420 0.8762 0.076 0.000 0.840 0.000 0.084
#> GSM509751 2 0.0000 0.8209 0.000 1.000 0.000 0.000 0.000
#> GSM509753 2 0.0000 0.8209 0.000 1.000 0.000 0.000 0.000
#> GSM509755 2 0.0000 0.8209 0.000 1.000 0.000 0.000 0.000
#> GSM509757 2 0.0000 0.8209 0.000 1.000 0.000 0.000 0.000
#> GSM509759 2 0.0000 0.8209 0.000 1.000 0.000 0.000 0.000
#> GSM509761 2 0.0404 0.8214 0.000 0.988 0.000 0.012 0.000
#> GSM509763 2 0.4304 -0.0544 0.000 0.516 0.000 0.484 0.000
#> GSM509765 4 0.4256 0.2647 0.000 0.436 0.000 0.564 0.000
#> GSM509767 2 0.1732 0.7912 0.000 0.920 0.000 0.080 0.000
#> GSM509769 2 0.2852 0.7185 0.000 0.828 0.000 0.172 0.000
#> GSM509771 2 0.1671 0.7941 0.000 0.924 0.000 0.076 0.000
#> GSM509773 2 0.3305 0.6557 0.000 0.776 0.000 0.224 0.000
#> GSM509775 2 0.3366 0.6422 0.000 0.768 0.000 0.232 0.000
#> GSM509777 4 0.3932 0.5560 0.000 0.328 0.000 0.672 0.000
#> GSM509779 4 0.1197 0.6904 0.000 0.048 0.000 0.952 0.000
#> GSM509781 4 0.0000 0.6979 0.000 0.000 0.000 1.000 0.000
#> GSM509783 4 0.0000 0.6979 0.000 0.000 0.000 1.000 0.000
#> GSM509785 4 0.0000 0.6979 0.000 0.000 0.000 1.000 0.000
#> GSM509752 2 0.0000 0.8209 0.000 1.000 0.000 0.000 0.000
#> GSM509754 2 0.0290 0.8219 0.000 0.992 0.000 0.008 0.000
#> GSM509756 2 0.0000 0.8209 0.000 1.000 0.000 0.000 0.000
#> GSM509758 2 0.0703 0.8180 0.000 0.976 0.000 0.024 0.000
#> GSM509760 2 0.0290 0.8217 0.000 0.992 0.000 0.008 0.000
#> GSM509762 2 0.0290 0.8219 0.000 0.992 0.000 0.008 0.000
#> GSM509764 2 0.0162 0.8201 0.000 0.996 0.000 0.000 0.004
#> GSM509766 2 0.4294 0.0241 0.000 0.532 0.000 0.468 0.000
#> GSM509768 2 0.4262 0.1280 0.000 0.560 0.000 0.440 0.000
#> GSM509770 2 0.0703 0.8180 0.000 0.976 0.000 0.024 0.000
#> GSM509772 2 0.0000 0.8209 0.000 1.000 0.000 0.000 0.000
#> GSM509774 4 0.3752 0.5962 0.000 0.292 0.000 0.708 0.000
#> GSM509776 2 0.4182 0.2742 0.000 0.600 0.000 0.400 0.000
#> GSM509778 4 0.0000 0.6979 0.000 0.000 0.000 1.000 0.000
#> GSM509780 4 0.4030 0.5073 0.000 0.352 0.000 0.648 0.000
#> GSM509782 4 0.0000 0.6979 0.000 0.000 0.000 1.000 0.000
#> GSM509784 4 0.3796 0.5910 0.000 0.300 0.000 0.700 0.000
#> GSM509786 4 0.0000 0.6979 0.000 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM509706 1 0.0000 0.7183 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509711 1 0.4493 0.4097 0.612 0.000 0.000 0.000 0.044 0.344
#> GSM509714 6 0.5444 0.3961 0.144 0.036 0.000 0.064 0.052 0.704
#> GSM509719 5 0.6677 0.6909 0.316 0.044 0.000 0.000 0.424 0.216
#> GSM509724 1 0.0547 0.7139 0.980 0.000 0.020 0.000 0.000 0.000
#> GSM509729 5 0.3888 0.5347 0.204 0.028 0.004 0.000 0.756 0.008
#> GSM509707 1 0.0000 0.7183 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509712 1 0.4493 0.4097 0.612 0.000 0.000 0.000 0.044 0.344
#> GSM509715 6 0.3886 0.7636 0.000 0.140 0.000 0.080 0.004 0.776
#> GSM509720 5 0.6677 0.6909 0.316 0.044 0.000 0.000 0.424 0.216
#> GSM509725 1 0.4202 0.4366 0.668 0.000 0.300 0.000 0.028 0.004
#> GSM509730 5 0.3888 0.5347 0.204 0.028 0.004 0.000 0.756 0.008
#> GSM509708 1 0.0260 0.7151 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM509713 1 0.4493 0.4097 0.612 0.000 0.000 0.000 0.044 0.344
#> GSM509716 6 0.3726 0.7675 0.000 0.124 0.000 0.080 0.004 0.792
#> GSM509721 5 0.6677 0.6909 0.316 0.044 0.000 0.000 0.424 0.216
#> GSM509726 1 0.4490 0.3670 0.604 0.000 0.360 0.000 0.032 0.004
#> GSM509731 5 0.4936 -0.3537 0.000 0.000 0.000 0.064 0.500 0.436
#> GSM509709 1 0.0000 0.7183 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509717 6 0.3118 0.7403 0.000 0.092 0.000 0.072 0.000 0.836
#> GSM509722 5 0.6677 0.6909 0.316 0.044 0.000 0.000 0.424 0.216
#> GSM509727 3 0.3782 0.8453 0.088 0.000 0.808 0.000 0.080 0.024
#> GSM509710 1 0.0000 0.7183 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509718 6 0.4800 0.5526 0.000 0.304 0.000 0.032 0.028 0.636
#> GSM509723 5 0.6677 0.6909 0.316 0.044 0.000 0.000 0.424 0.216
#> GSM509728 3 0.3782 0.8453 0.088 0.000 0.808 0.000 0.080 0.024
#> GSM509732 3 0.0146 0.9339 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM509736 3 0.1049 0.9304 0.000 0.000 0.960 0.000 0.032 0.008
#> GSM509741 3 0.0146 0.9339 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM509746 3 0.0146 0.9339 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM509733 3 0.0146 0.9339 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM509737 3 0.1049 0.9304 0.000 0.000 0.960 0.000 0.032 0.008
#> GSM509742 3 0.0146 0.9339 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM509747 3 0.0146 0.9339 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM509734 3 0.0000 0.9341 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509738 3 0.3140 0.8854 0.024 0.000 0.844 0.000 0.108 0.024
#> GSM509743 3 0.0458 0.9318 0.000 0.000 0.984 0.000 0.016 0.000
#> GSM509748 3 0.1074 0.9299 0.012 0.000 0.960 0.000 0.028 0.000
#> GSM509735 1 0.3667 0.5473 0.776 0.000 0.184 0.000 0.032 0.008
#> GSM509739 1 0.0363 0.7166 0.988 0.000 0.012 0.000 0.000 0.000
#> GSM509744 3 0.1074 0.9313 0.000 0.000 0.960 0.000 0.028 0.012
#> GSM509749 3 0.1074 0.9299 0.012 0.000 0.960 0.000 0.028 0.000
#> GSM509740 3 0.3934 0.8522 0.036 0.000 0.792 0.000 0.128 0.044
#> GSM509745 3 0.3573 0.8668 0.036 0.000 0.816 0.000 0.120 0.028
#> GSM509750 3 0.3226 0.8804 0.028 0.000 0.836 0.000 0.116 0.020
#> GSM509751 2 0.0000 0.8498 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509753 2 0.0000 0.8498 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509755 2 0.0000 0.8498 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509757 2 0.0000 0.8498 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509759 2 0.0000 0.8498 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509761 2 0.0363 0.8505 0.000 0.988 0.000 0.012 0.000 0.000
#> GSM509763 2 0.3866 -0.0561 0.000 0.516 0.000 0.484 0.000 0.000
#> GSM509765 4 0.3823 0.2668 0.000 0.436 0.000 0.564 0.000 0.000
#> GSM509767 2 0.1556 0.8177 0.000 0.920 0.000 0.080 0.000 0.000
#> GSM509769 2 0.2562 0.7319 0.000 0.828 0.000 0.172 0.000 0.000
#> GSM509771 2 0.1501 0.8210 0.000 0.924 0.000 0.076 0.000 0.000
#> GSM509773 2 0.2969 0.6685 0.000 0.776 0.000 0.224 0.000 0.000
#> GSM509775 2 0.3023 0.6537 0.000 0.768 0.000 0.232 0.000 0.000
#> GSM509777 4 0.3531 0.5596 0.000 0.328 0.000 0.672 0.000 0.000
#> GSM509779 4 0.1075 0.7278 0.000 0.048 0.000 0.952 0.000 0.000
#> GSM509781 4 0.0000 0.7327 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM509783 4 0.0000 0.7327 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM509785 4 0.0000 0.7327 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM509752 2 0.0000 0.8498 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509754 2 0.0260 0.8508 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM509756 2 0.0000 0.8498 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509758 2 0.0632 0.8474 0.000 0.976 0.000 0.024 0.000 0.000
#> GSM509760 2 0.0260 0.8508 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM509762 2 0.0260 0.8508 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM509764 2 0.0146 0.8490 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM509766 2 0.3857 0.0239 0.000 0.532 0.000 0.468 0.000 0.000
#> GSM509768 2 0.3828 0.1278 0.000 0.560 0.000 0.440 0.000 0.000
#> GSM509770 2 0.0632 0.8475 0.000 0.976 0.000 0.024 0.000 0.000
#> GSM509772 2 0.0000 0.8498 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509774 4 0.3371 0.6127 0.000 0.292 0.000 0.708 0.000 0.000
#> GSM509776 2 0.3756 0.2747 0.000 0.600 0.000 0.400 0.000 0.000
#> GSM509778 4 0.0000 0.7327 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM509780 4 0.3620 0.5113 0.000 0.352 0.000 0.648 0.000 0.000
#> GSM509782 4 0.0000 0.7327 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM509784 4 0.3409 0.6036 0.000 0.300 0.000 0.700 0.000 0.000
#> GSM509786 4 0.0000 0.7327 0.000 0.000 0.000 1.000 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 disease.state(p) time(p) k
#> CV:hclust 79 5.88e-14 9.17e-11 2
#> CV:hclust 75 1.31e-21 3.11e-08 3
#> CV:hclust 64 9.97e-20 2.41e-07 4
#> CV:hclust 58 1.31e-15 7.82e-07 5
#> CV:hclust 69 7.90e-20 6.23e-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 19175 rows and 81 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 1.000 0.990 0.996 0.5063 0.494 0.494
#> 3 3 0.708 0.821 0.846 0.2644 0.810 0.637
#> 4 4 0.815 0.805 0.871 0.1403 0.859 0.625
#> 5 5 0.788 0.792 0.838 0.0631 0.911 0.677
#> 6 6 0.759 0.689 0.816 0.0430 0.966 0.844
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
#> GSM509706 1 0.000 1.000 1.000 0.000
#> GSM509711 1 0.000 1.000 1.000 0.000
#> GSM509714 2 0.921 0.494 0.336 0.664
#> GSM509719 1 0.000 1.000 1.000 0.000
#> GSM509724 1 0.000 1.000 1.000 0.000
#> GSM509729 1 0.000 1.000 1.000 0.000
#> GSM509707 1 0.000 1.000 1.000 0.000
#> GSM509712 1 0.000 1.000 1.000 0.000
#> GSM509715 2 0.000 0.992 0.000 1.000
#> GSM509720 1 0.000 1.000 1.000 0.000
#> GSM509725 1 0.000 1.000 1.000 0.000
#> GSM509730 1 0.000 1.000 1.000 0.000
#> GSM509708 1 0.000 1.000 1.000 0.000
#> GSM509713 1 0.000 1.000 1.000 0.000
#> GSM509716 2 0.000 0.992 0.000 1.000
#> GSM509721 1 0.000 1.000 1.000 0.000
#> GSM509726 1 0.000 1.000 1.000 0.000
#> GSM509731 2 0.000 0.992 0.000 1.000
#> GSM509709 1 0.000 1.000 1.000 0.000
#> GSM509717 2 0.000 0.992 0.000 1.000
#> GSM509722 1 0.000 1.000 1.000 0.000
#> GSM509727 1 0.000 1.000 1.000 0.000
#> GSM509710 1 0.000 1.000 1.000 0.000
#> GSM509718 2 0.000 0.992 0.000 1.000
#> GSM509723 1 0.000 1.000 1.000 0.000
#> GSM509728 1 0.000 1.000 1.000 0.000
#> GSM509732 1 0.000 1.000 1.000 0.000
#> GSM509736 1 0.000 1.000 1.000 0.000
#> GSM509741 1 0.000 1.000 1.000 0.000
#> GSM509746 1 0.000 1.000 1.000 0.000
#> GSM509733 1 0.000 1.000 1.000 0.000
#> GSM509737 1 0.000 1.000 1.000 0.000
#> GSM509742 1 0.000 1.000 1.000 0.000
#> GSM509747 1 0.000 1.000 1.000 0.000
#> GSM509734 1 0.000 1.000 1.000 0.000
#> GSM509738 1 0.000 1.000 1.000 0.000
#> GSM509743 1 0.000 1.000 1.000 0.000
#> GSM509748 1 0.000 1.000 1.000 0.000
#> GSM509735 1 0.000 1.000 1.000 0.000
#> GSM509739 1 0.000 1.000 1.000 0.000
#> GSM509744 1 0.000 1.000 1.000 0.000
#> GSM509749 1 0.000 1.000 1.000 0.000
#> GSM509740 1 0.000 1.000 1.000 0.000
#> GSM509745 1 0.000 1.000 1.000 0.000
#> GSM509750 1 0.000 1.000 1.000 0.000
#> GSM509751 2 0.000 0.992 0.000 1.000
#> GSM509753 2 0.000 0.992 0.000 1.000
#> GSM509755 2 0.000 0.992 0.000 1.000
#> GSM509757 2 0.000 0.992 0.000 1.000
#> GSM509759 2 0.000 0.992 0.000 1.000
#> GSM509761 2 0.000 0.992 0.000 1.000
#> GSM509763 2 0.000 0.992 0.000 1.000
#> GSM509765 2 0.000 0.992 0.000 1.000
#> GSM509767 2 0.000 0.992 0.000 1.000
#> GSM509769 2 0.000 0.992 0.000 1.000
#> GSM509771 2 0.000 0.992 0.000 1.000
#> GSM509773 2 0.000 0.992 0.000 1.000
#> GSM509775 2 0.000 0.992 0.000 1.000
#> GSM509777 2 0.000 0.992 0.000 1.000
#> GSM509779 2 0.000 0.992 0.000 1.000
#> GSM509781 2 0.000 0.992 0.000 1.000
#> GSM509783 2 0.000 0.992 0.000 1.000
#> GSM509785 2 0.000 0.992 0.000 1.000
#> GSM509752 2 0.000 0.992 0.000 1.000
#> GSM509754 2 0.000 0.992 0.000 1.000
#> GSM509756 2 0.000 0.992 0.000 1.000
#> GSM509758 2 0.000 0.992 0.000 1.000
#> GSM509760 2 0.000 0.992 0.000 1.000
#> GSM509762 2 0.000 0.992 0.000 1.000
#> GSM509764 2 0.000 0.992 0.000 1.000
#> GSM509766 2 0.000 0.992 0.000 1.000
#> GSM509768 2 0.000 0.992 0.000 1.000
#> GSM509770 2 0.000 0.992 0.000 1.000
#> GSM509772 2 0.000 0.992 0.000 1.000
#> GSM509774 2 0.000 0.992 0.000 1.000
#> GSM509776 2 0.000 0.992 0.000 1.000
#> GSM509778 2 0.000 0.992 0.000 1.000
#> GSM509780 2 0.000 0.992 0.000 1.000
#> GSM509782 2 0.000 0.992 0.000 1.000
#> GSM509784 2 0.000 0.992 0.000 1.000
#> GSM509786 2 0.000 0.992 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM509706 1 0.2261 0.781 0.932 0.000 0.068
#> GSM509711 1 0.0424 0.789 0.992 0.000 0.008
#> GSM509714 1 0.6143 0.562 0.720 0.024 0.256
#> GSM509719 1 0.1753 0.774 0.952 0.048 0.000
#> GSM509724 1 0.3412 0.735 0.876 0.000 0.124
#> GSM509729 1 0.0424 0.788 0.992 0.008 0.000
#> GSM509707 1 0.2261 0.781 0.932 0.000 0.068
#> GSM509712 1 0.0237 0.789 0.996 0.000 0.004
#> GSM509715 2 0.9884 0.135 0.364 0.376 0.260
#> GSM509720 1 0.1753 0.774 0.952 0.048 0.000
#> GSM509725 1 0.3482 0.731 0.872 0.000 0.128
#> GSM509730 1 0.0424 0.788 0.992 0.008 0.000
#> GSM509708 1 0.2261 0.781 0.932 0.000 0.068
#> GSM509713 1 0.1529 0.787 0.960 0.000 0.040
#> GSM509716 1 0.9560 0.216 0.484 0.260 0.256
#> GSM509721 1 0.1753 0.774 0.952 0.048 0.000
#> GSM509726 1 0.3482 0.731 0.872 0.000 0.128
#> GSM509731 1 0.9150 0.355 0.536 0.192 0.272
#> GSM509709 1 0.2261 0.781 0.932 0.000 0.068
#> GSM509717 1 0.9182 0.356 0.536 0.204 0.260
#> GSM509722 1 0.1753 0.774 0.952 0.048 0.000
#> GSM509727 1 0.3482 0.731 0.872 0.000 0.128
#> GSM509710 1 0.3482 0.731 0.872 0.000 0.128
#> GSM509718 2 0.9072 0.564 0.192 0.548 0.260
#> GSM509723 1 0.1753 0.774 0.952 0.048 0.000
#> GSM509728 3 0.6111 0.781 0.396 0.000 0.604
#> GSM509732 3 0.5397 0.989 0.280 0.000 0.720
#> GSM509736 3 0.5397 0.989 0.280 0.000 0.720
#> GSM509741 3 0.5397 0.989 0.280 0.000 0.720
#> GSM509746 3 0.5397 0.989 0.280 0.000 0.720
#> GSM509733 3 0.5397 0.989 0.280 0.000 0.720
#> GSM509737 3 0.5397 0.989 0.280 0.000 0.720
#> GSM509742 3 0.5397 0.989 0.280 0.000 0.720
#> GSM509747 3 0.5397 0.989 0.280 0.000 0.720
#> GSM509734 3 0.5397 0.989 0.280 0.000 0.720
#> GSM509738 3 0.5397 0.989 0.280 0.000 0.720
#> GSM509743 3 0.5397 0.989 0.280 0.000 0.720
#> GSM509748 3 0.5397 0.989 0.280 0.000 0.720
#> GSM509735 1 0.3482 0.731 0.872 0.000 0.128
#> GSM509739 1 0.2448 0.776 0.924 0.000 0.076
#> GSM509744 3 0.5397 0.989 0.280 0.000 0.720
#> GSM509749 3 0.5397 0.989 0.280 0.000 0.720
#> GSM509740 1 0.5098 0.485 0.752 0.000 0.248
#> GSM509745 3 0.5397 0.989 0.280 0.000 0.720
#> GSM509750 3 0.5397 0.989 0.280 0.000 0.720
#> GSM509751 2 0.0424 0.895 0.008 0.992 0.000
#> GSM509753 2 0.0424 0.895 0.008 0.992 0.000
#> GSM509755 2 0.0424 0.895 0.008 0.992 0.000
#> GSM509757 2 0.0424 0.895 0.008 0.992 0.000
#> GSM509759 2 0.0424 0.895 0.008 0.992 0.000
#> GSM509761 2 0.0000 0.895 0.000 1.000 0.000
#> GSM509763 2 0.1163 0.891 0.000 0.972 0.028
#> GSM509765 2 0.2711 0.877 0.000 0.912 0.088
#> GSM509767 2 0.0237 0.895 0.004 0.996 0.000
#> GSM509769 2 0.0424 0.894 0.000 0.992 0.008
#> GSM509771 2 0.0237 0.895 0.004 0.996 0.000
#> GSM509773 2 0.0747 0.893 0.000 0.984 0.016
#> GSM509775 2 0.0592 0.894 0.000 0.988 0.012
#> GSM509777 2 0.5291 0.803 0.000 0.732 0.268
#> GSM509779 2 0.5397 0.797 0.000 0.720 0.280
#> GSM509781 2 0.5797 0.792 0.008 0.712 0.280
#> GSM509783 2 0.5797 0.792 0.008 0.712 0.280
#> GSM509785 2 0.5797 0.792 0.008 0.712 0.280
#> GSM509752 2 0.0424 0.895 0.008 0.992 0.000
#> GSM509754 2 0.0424 0.895 0.008 0.992 0.000
#> GSM509756 2 0.0424 0.895 0.008 0.992 0.000
#> GSM509758 2 0.0424 0.895 0.008 0.992 0.000
#> GSM509760 2 0.0424 0.895 0.008 0.992 0.000
#> GSM509762 2 0.0424 0.895 0.008 0.992 0.000
#> GSM509764 2 0.0424 0.895 0.008 0.992 0.000
#> GSM509766 2 0.1860 0.886 0.000 0.948 0.052
#> GSM509768 2 0.1163 0.891 0.000 0.972 0.028
#> GSM509770 2 0.0424 0.895 0.008 0.992 0.000
#> GSM509772 2 0.0424 0.895 0.008 0.992 0.000
#> GSM509774 2 0.5397 0.797 0.000 0.720 0.280
#> GSM509776 2 0.1031 0.892 0.000 0.976 0.024
#> GSM509778 2 0.5797 0.792 0.008 0.712 0.280
#> GSM509780 2 0.3192 0.869 0.000 0.888 0.112
#> GSM509782 2 0.5797 0.792 0.008 0.712 0.280
#> GSM509784 2 0.5397 0.797 0.000 0.720 0.280
#> GSM509786 2 0.5797 0.792 0.008 0.712 0.280
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM509706 1 0.1022 0.80810 0.968 0.000 0.032 0.000
#> GSM509711 1 0.3801 0.77702 0.780 0.000 0.000 0.220
#> GSM509714 1 0.4950 0.71530 0.620 0.004 0.000 0.376
#> GSM509719 1 0.5148 0.73468 0.640 0.008 0.004 0.348
#> GSM509724 1 0.2149 0.78575 0.912 0.000 0.088 0.000
#> GSM509729 1 0.4995 0.73947 0.648 0.004 0.004 0.344
#> GSM509707 1 0.1022 0.80810 0.968 0.000 0.032 0.000
#> GSM509712 1 0.3942 0.77338 0.764 0.000 0.000 0.236
#> GSM509715 4 0.3495 0.35550 0.140 0.016 0.000 0.844
#> GSM509720 1 0.5148 0.73468 0.640 0.008 0.004 0.348
#> GSM509725 1 0.2149 0.78575 0.912 0.000 0.088 0.000
#> GSM509730 1 0.4995 0.73947 0.648 0.004 0.004 0.344
#> GSM509708 1 0.1022 0.80810 0.968 0.000 0.032 0.000
#> GSM509713 1 0.1452 0.80415 0.956 0.000 0.008 0.036
#> GSM509716 4 0.3495 0.35550 0.140 0.016 0.000 0.844
#> GSM509721 1 0.5148 0.73468 0.640 0.008 0.004 0.348
#> GSM509726 1 0.2149 0.78575 0.912 0.000 0.088 0.000
#> GSM509731 4 0.2546 0.41234 0.092 0.008 0.000 0.900
#> GSM509709 1 0.1022 0.80810 0.968 0.000 0.032 0.000
#> GSM509717 4 0.3428 0.34528 0.144 0.012 0.000 0.844
#> GSM509722 1 0.5148 0.73468 0.640 0.008 0.004 0.348
#> GSM509727 1 0.2401 0.78139 0.904 0.000 0.092 0.004
#> GSM509710 1 0.2149 0.78575 0.912 0.000 0.088 0.000
#> GSM509718 4 0.4017 0.40264 0.128 0.044 0.000 0.828
#> GSM509723 1 0.5148 0.73468 0.640 0.008 0.004 0.348
#> GSM509728 3 0.4313 0.63536 0.260 0.000 0.736 0.004
#> GSM509732 3 0.0000 0.94516 0.000 0.000 1.000 0.000
#> GSM509736 3 0.0817 0.94170 0.000 0.000 0.976 0.024
#> GSM509741 3 0.0188 0.94489 0.000 0.000 0.996 0.004
#> GSM509746 3 0.0000 0.94516 0.000 0.000 1.000 0.000
#> GSM509733 3 0.0000 0.94516 0.000 0.000 1.000 0.000
#> GSM509737 3 0.1004 0.94068 0.004 0.000 0.972 0.024
#> GSM509742 3 0.0188 0.94489 0.000 0.000 0.996 0.004
#> GSM509747 3 0.0000 0.94516 0.000 0.000 1.000 0.000
#> GSM509734 3 0.0000 0.94516 0.000 0.000 1.000 0.000
#> GSM509738 3 0.1004 0.94068 0.004 0.000 0.972 0.024
#> GSM509743 3 0.0817 0.94170 0.000 0.000 0.976 0.024
#> GSM509748 3 0.0000 0.94516 0.000 0.000 1.000 0.000
#> GSM509735 1 0.2149 0.78575 0.912 0.000 0.088 0.000
#> GSM509739 1 0.1118 0.80734 0.964 0.000 0.036 0.000
#> GSM509744 3 0.0817 0.94170 0.000 0.000 0.976 0.024
#> GSM509749 3 0.0000 0.94516 0.000 0.000 1.000 0.000
#> GSM509740 3 0.7531 0.00794 0.316 0.000 0.476 0.208
#> GSM509745 3 0.1004 0.94068 0.004 0.000 0.972 0.024
#> GSM509750 3 0.0188 0.94494 0.000 0.000 0.996 0.004
#> GSM509751 2 0.0188 0.95995 0.000 0.996 0.000 0.004
#> GSM509753 2 0.0188 0.95995 0.000 0.996 0.000 0.004
#> GSM509755 2 0.0188 0.95995 0.000 0.996 0.000 0.004
#> GSM509757 2 0.0188 0.95995 0.000 0.996 0.000 0.004
#> GSM509759 2 0.0188 0.95995 0.000 0.996 0.000 0.004
#> GSM509761 2 0.0000 0.95880 0.000 1.000 0.000 0.000
#> GSM509763 2 0.0469 0.95154 0.000 0.988 0.000 0.012
#> GSM509765 2 0.3837 0.58770 0.000 0.776 0.000 0.224
#> GSM509767 2 0.0000 0.95880 0.000 1.000 0.000 0.000
#> GSM509769 2 0.0188 0.95650 0.000 0.996 0.000 0.004
#> GSM509771 2 0.0000 0.95880 0.000 1.000 0.000 0.000
#> GSM509773 2 0.0336 0.95431 0.000 0.992 0.000 0.008
#> GSM509775 2 0.0336 0.95431 0.000 0.992 0.000 0.008
#> GSM509777 4 0.4888 0.65702 0.000 0.412 0.000 0.588
#> GSM509779 4 0.4855 0.68007 0.000 0.400 0.000 0.600
#> GSM509781 4 0.4855 0.68007 0.000 0.400 0.000 0.600
#> GSM509783 4 0.4855 0.68007 0.000 0.400 0.000 0.600
#> GSM509785 4 0.4855 0.68007 0.000 0.400 0.000 0.600
#> GSM509752 2 0.0188 0.95995 0.000 0.996 0.000 0.004
#> GSM509754 2 0.0188 0.95995 0.000 0.996 0.000 0.004
#> GSM509756 2 0.0188 0.95995 0.000 0.996 0.000 0.004
#> GSM509758 2 0.0188 0.95995 0.000 0.996 0.000 0.004
#> GSM509760 2 0.0188 0.95995 0.000 0.996 0.000 0.004
#> GSM509762 2 0.0188 0.95995 0.000 0.996 0.000 0.004
#> GSM509764 2 0.0469 0.95167 0.000 0.988 0.000 0.012
#> GSM509766 2 0.2149 0.85516 0.000 0.912 0.000 0.088
#> GSM509768 2 0.0469 0.95154 0.000 0.988 0.000 0.012
#> GSM509770 2 0.0188 0.95995 0.000 0.996 0.000 0.004
#> GSM509772 2 0.0188 0.95995 0.000 0.996 0.000 0.004
#> GSM509774 4 0.4855 0.68007 0.000 0.400 0.000 0.600
#> GSM509776 2 0.0469 0.95154 0.000 0.988 0.000 0.012
#> GSM509778 4 0.4855 0.68007 0.000 0.400 0.000 0.600
#> GSM509780 2 0.4356 0.38677 0.000 0.708 0.000 0.292
#> GSM509782 4 0.4855 0.68007 0.000 0.400 0.000 0.600
#> GSM509784 4 0.4855 0.68007 0.000 0.400 0.000 0.600
#> GSM509786 4 0.4855 0.68007 0.000 0.400 0.000 0.600
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM509706 1 0.4666 0.9354 0.596 0.000 0.012 0.004 0.388
#> GSM509711 5 0.4907 -0.1740 0.292 0.000 0.000 0.052 0.656
#> GSM509714 5 0.4599 0.5848 0.272 0.000 0.000 0.040 0.688
#> GSM509719 5 0.0000 0.5640 0.000 0.000 0.000 0.000 1.000
#> GSM509724 1 0.5203 0.9331 0.600 0.000 0.032 0.012 0.356
#> GSM509729 5 0.1117 0.5341 0.020 0.000 0.000 0.016 0.964
#> GSM509707 1 0.4666 0.9354 0.596 0.000 0.012 0.004 0.388
#> GSM509712 5 0.4689 -0.0617 0.264 0.000 0.000 0.048 0.688
#> GSM509715 5 0.6374 0.5508 0.300 0.000 0.000 0.196 0.504
#> GSM509720 5 0.0000 0.5640 0.000 0.000 0.000 0.000 1.000
#> GSM509725 1 0.5203 0.9330 0.600 0.000 0.032 0.012 0.356
#> GSM509730 5 0.1117 0.5341 0.020 0.000 0.000 0.016 0.964
#> GSM509708 1 0.4666 0.9354 0.596 0.000 0.012 0.004 0.388
#> GSM509713 1 0.5103 0.8069 0.512 0.000 0.000 0.036 0.452
#> GSM509716 5 0.6374 0.5508 0.300 0.000 0.000 0.196 0.504
#> GSM509721 5 0.0000 0.5640 0.000 0.000 0.000 0.000 1.000
#> GSM509726 1 0.6033 0.9015 0.560 0.000 0.032 0.060 0.348
#> GSM509731 5 0.6597 0.5126 0.296 0.000 0.000 0.244 0.460
#> GSM509709 1 0.4666 0.9354 0.596 0.000 0.012 0.004 0.388
#> GSM509717 5 0.6374 0.5508 0.300 0.000 0.000 0.196 0.504
#> GSM509722 5 0.0290 0.5670 0.008 0.000 0.000 0.000 0.992
#> GSM509727 1 0.6273 0.8778 0.532 0.000 0.032 0.076 0.360
#> GSM509710 1 0.4986 0.9341 0.608 0.000 0.032 0.004 0.356
#> GSM509718 5 0.7161 0.5004 0.332 0.024 0.000 0.220 0.424
#> GSM509723 5 0.0000 0.5640 0.000 0.000 0.000 0.000 1.000
#> GSM509728 3 0.6770 0.4435 0.248 0.000 0.576 0.076 0.100
#> GSM509732 3 0.0162 0.9265 0.004 0.000 0.996 0.000 0.000
#> GSM509736 3 0.2645 0.9081 0.044 0.000 0.888 0.068 0.000
#> GSM509741 3 0.0000 0.9262 0.000 0.000 1.000 0.000 0.000
#> GSM509746 3 0.0162 0.9265 0.004 0.000 0.996 0.000 0.000
#> GSM509733 3 0.0162 0.9265 0.004 0.000 0.996 0.000 0.000
#> GSM509737 3 0.2645 0.9081 0.044 0.000 0.888 0.068 0.000
#> GSM509742 3 0.0000 0.9262 0.000 0.000 1.000 0.000 0.000
#> GSM509747 3 0.0162 0.9265 0.004 0.000 0.996 0.000 0.000
#> GSM509734 3 0.0162 0.9265 0.004 0.000 0.996 0.000 0.000
#> GSM509738 3 0.3714 0.8831 0.056 0.000 0.832 0.100 0.012
#> GSM509743 3 0.2438 0.9106 0.040 0.000 0.900 0.060 0.000
#> GSM509748 3 0.0162 0.9265 0.004 0.000 0.996 0.000 0.000
#> GSM509735 1 0.5616 0.9270 0.580 0.000 0.032 0.032 0.356
#> GSM509739 1 0.4655 0.9364 0.600 0.000 0.012 0.004 0.384
#> GSM509744 3 0.2843 0.9046 0.048 0.000 0.876 0.076 0.000
#> GSM509749 3 0.0451 0.9255 0.004 0.000 0.988 0.008 0.000
#> GSM509740 5 0.7780 -0.0318 0.112 0.000 0.372 0.136 0.380
#> GSM509745 3 0.3867 0.8756 0.056 0.000 0.820 0.112 0.012
#> GSM509750 3 0.3089 0.8988 0.040 0.000 0.872 0.076 0.012
#> GSM509751 2 0.0451 0.9311 0.008 0.988 0.000 0.000 0.004
#> GSM509753 2 0.0451 0.9311 0.008 0.988 0.000 0.000 0.004
#> GSM509755 2 0.0451 0.9311 0.008 0.988 0.000 0.000 0.004
#> GSM509757 2 0.0451 0.9311 0.008 0.988 0.000 0.000 0.004
#> GSM509759 2 0.0451 0.9311 0.008 0.988 0.000 0.000 0.004
#> GSM509761 2 0.0404 0.9314 0.012 0.988 0.000 0.000 0.000
#> GSM509763 2 0.1997 0.8966 0.036 0.924 0.000 0.040 0.000
#> GSM509765 2 0.5103 -0.2371 0.036 0.512 0.000 0.452 0.000
#> GSM509767 2 0.0451 0.9299 0.008 0.988 0.000 0.004 0.000
#> GSM509769 2 0.1493 0.9125 0.028 0.948 0.000 0.024 0.000
#> GSM509771 2 0.0451 0.9299 0.008 0.988 0.000 0.004 0.000
#> GSM509773 2 0.1836 0.9025 0.032 0.932 0.000 0.036 0.000
#> GSM509775 2 0.1753 0.9052 0.032 0.936 0.000 0.032 0.000
#> GSM509777 4 0.3795 0.9116 0.028 0.192 0.000 0.780 0.000
#> GSM509779 4 0.3280 0.9279 0.012 0.176 0.000 0.812 0.000
#> GSM509781 4 0.3732 0.9347 0.032 0.176 0.000 0.792 0.000
#> GSM509783 4 0.3732 0.9347 0.032 0.176 0.000 0.792 0.000
#> GSM509785 4 0.3732 0.9347 0.032 0.176 0.000 0.792 0.000
#> GSM509752 2 0.0290 0.9316 0.008 0.992 0.000 0.000 0.000
#> GSM509754 2 0.0290 0.9316 0.008 0.992 0.000 0.000 0.000
#> GSM509756 2 0.0451 0.9311 0.008 0.988 0.000 0.000 0.004
#> GSM509758 2 0.0162 0.9320 0.004 0.996 0.000 0.000 0.000
#> GSM509760 2 0.0451 0.9316 0.008 0.988 0.000 0.004 0.000
#> GSM509762 2 0.0162 0.9320 0.004 0.996 0.000 0.000 0.000
#> GSM509764 2 0.0854 0.9216 0.008 0.976 0.000 0.012 0.004
#> GSM509766 2 0.4479 0.4943 0.036 0.700 0.000 0.264 0.000
#> GSM509768 2 0.1997 0.8966 0.036 0.924 0.000 0.040 0.000
#> GSM509770 2 0.0912 0.9242 0.012 0.972 0.000 0.016 0.000
#> GSM509772 2 0.0451 0.9311 0.008 0.988 0.000 0.000 0.004
#> GSM509774 4 0.3687 0.9212 0.028 0.180 0.000 0.792 0.000
#> GSM509776 2 0.1997 0.8966 0.036 0.924 0.000 0.040 0.000
#> GSM509778 4 0.3732 0.9347 0.032 0.176 0.000 0.792 0.000
#> GSM509780 4 0.5088 0.4227 0.036 0.436 0.000 0.528 0.000
#> GSM509782 4 0.3732 0.9347 0.032 0.176 0.000 0.792 0.000
#> GSM509784 4 0.3565 0.9249 0.024 0.176 0.000 0.800 0.000
#> GSM509786 4 0.3650 0.9347 0.028 0.176 0.000 0.796 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM509706 1 0.1053 0.8594 0.964 0.000 0.012 0.004 0.020 0.000
#> GSM509711 1 0.5967 0.3801 0.568 0.000 0.000 0.044 0.264 0.124
#> GSM509714 5 0.3593 0.3936 0.016 0.000 0.000 0.020 0.784 0.180
#> GSM509719 5 0.2597 0.6376 0.176 0.000 0.000 0.000 0.824 0.000
#> GSM509724 1 0.1078 0.8579 0.964 0.000 0.012 0.008 0.000 0.016
#> GSM509729 5 0.5343 0.5390 0.184 0.000 0.000 0.040 0.664 0.112
#> GSM509707 1 0.1053 0.8594 0.964 0.000 0.012 0.004 0.020 0.000
#> GSM509712 1 0.6094 0.3025 0.540 0.000 0.000 0.044 0.288 0.128
#> GSM509715 5 0.4812 0.2778 0.008 0.000 0.000 0.080 0.660 0.252
#> GSM509720 5 0.2597 0.6376 0.176 0.000 0.000 0.000 0.824 0.000
#> GSM509725 1 0.1448 0.8560 0.948 0.000 0.012 0.016 0.000 0.024
#> GSM509730 5 0.5284 0.5464 0.176 0.000 0.000 0.040 0.672 0.112
#> GSM509708 1 0.1053 0.8594 0.964 0.000 0.012 0.004 0.020 0.000
#> GSM509713 1 0.3988 0.7786 0.804 0.000 0.004 0.040 0.060 0.092
#> GSM509716 5 0.4812 0.2778 0.008 0.000 0.000 0.080 0.660 0.252
#> GSM509721 5 0.2597 0.6376 0.176 0.000 0.000 0.000 0.824 0.000
#> GSM509726 1 0.3444 0.7959 0.812 0.000 0.012 0.036 0.000 0.140
#> GSM509731 5 0.5749 0.1341 0.008 0.000 0.000 0.144 0.504 0.344
#> GSM509709 1 0.1053 0.8594 0.964 0.000 0.012 0.004 0.020 0.000
#> GSM509717 5 0.4812 0.2778 0.008 0.000 0.000 0.080 0.660 0.252
#> GSM509722 5 0.2562 0.6367 0.172 0.000 0.000 0.000 0.828 0.000
#> GSM509727 1 0.3943 0.7654 0.772 0.000 0.012 0.040 0.004 0.172
#> GSM509710 1 0.0798 0.8600 0.976 0.000 0.012 0.004 0.004 0.004
#> GSM509718 6 0.5218 -0.2433 0.008 0.000 0.000 0.068 0.460 0.464
#> GSM509723 5 0.2597 0.6376 0.176 0.000 0.000 0.000 0.824 0.000
#> GSM509728 3 0.6521 0.0857 0.320 0.000 0.464 0.036 0.004 0.176
#> GSM509732 3 0.0000 0.8099 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509736 3 0.3524 0.7130 0.008 0.000 0.756 0.004 0.004 0.228
#> GSM509741 3 0.0146 0.8097 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM509746 3 0.0000 0.8099 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509733 3 0.0000 0.8099 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509737 3 0.3524 0.7130 0.008 0.000 0.756 0.004 0.004 0.228
#> GSM509742 3 0.0146 0.8097 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM509747 3 0.0000 0.8099 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509734 3 0.0000 0.8099 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509738 3 0.4315 0.5701 0.024 0.000 0.624 0.000 0.004 0.348
#> GSM509743 3 0.3104 0.7282 0.000 0.000 0.788 0.004 0.004 0.204
#> GSM509748 3 0.0000 0.8099 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509735 1 0.2644 0.8373 0.884 0.000 0.012 0.028 0.004 0.072
#> GSM509739 1 0.0508 0.8613 0.984 0.000 0.012 0.000 0.000 0.004
#> GSM509744 3 0.3290 0.7069 0.000 0.000 0.744 0.000 0.004 0.252
#> GSM509749 3 0.0547 0.8043 0.000 0.000 0.980 0.000 0.000 0.020
#> GSM509740 6 0.6931 -0.0196 0.100 0.000 0.312 0.000 0.152 0.436
#> GSM509745 3 0.4341 0.5572 0.024 0.000 0.616 0.000 0.004 0.356
#> GSM509750 3 0.3430 0.6854 0.016 0.000 0.772 0.000 0.004 0.208
#> GSM509751 2 0.0291 0.8573 0.004 0.992 0.000 0.000 0.004 0.000
#> GSM509753 2 0.0291 0.8573 0.004 0.992 0.000 0.000 0.004 0.000
#> GSM509755 2 0.0291 0.8573 0.004 0.992 0.000 0.000 0.004 0.000
#> GSM509757 2 0.0291 0.8573 0.004 0.992 0.000 0.000 0.004 0.000
#> GSM509759 2 0.0551 0.8549 0.004 0.984 0.000 0.000 0.004 0.008
#> GSM509761 2 0.1531 0.8511 0.000 0.928 0.000 0.004 0.000 0.068
#> GSM509763 2 0.4614 0.7082 0.000 0.684 0.000 0.208 0.000 0.108
#> GSM509765 4 0.5173 0.2817 0.000 0.324 0.000 0.568 0.000 0.108
#> GSM509767 2 0.1895 0.8469 0.000 0.912 0.000 0.016 0.000 0.072
#> GSM509769 2 0.4209 0.7535 0.000 0.736 0.000 0.160 0.000 0.104
#> GSM509771 2 0.2060 0.8433 0.000 0.900 0.000 0.016 0.000 0.084
#> GSM509773 2 0.4518 0.7208 0.000 0.696 0.000 0.200 0.000 0.104
#> GSM509775 2 0.4490 0.7245 0.000 0.700 0.000 0.196 0.000 0.104
#> GSM509777 4 0.3045 0.7396 0.000 0.100 0.000 0.840 0.000 0.060
#> GSM509779 4 0.4338 0.8117 0.000 0.100 0.000 0.732 0.004 0.164
#> GSM509781 4 0.4584 0.8148 0.000 0.100 0.000 0.700 0.004 0.196
#> GSM509783 4 0.4584 0.8148 0.000 0.100 0.000 0.700 0.004 0.196
#> GSM509785 4 0.4584 0.8148 0.000 0.100 0.000 0.700 0.004 0.196
#> GSM509752 2 0.0000 0.8581 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509754 2 0.0000 0.8581 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509756 2 0.0000 0.8581 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509758 2 0.0508 0.8591 0.000 0.984 0.000 0.004 0.000 0.012
#> GSM509760 2 0.1845 0.8483 0.000 0.920 0.000 0.052 0.000 0.028
#> GSM509762 2 0.0260 0.8591 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM509764 2 0.0982 0.8398 0.004 0.968 0.000 0.004 0.004 0.020
#> GSM509766 2 0.5355 0.1959 0.000 0.468 0.000 0.424 0.000 0.108
#> GSM509768 2 0.4614 0.7082 0.000 0.684 0.000 0.208 0.000 0.108
#> GSM509770 2 0.3686 0.7905 0.000 0.788 0.000 0.124 0.000 0.088
#> GSM509772 2 0.0291 0.8573 0.004 0.992 0.000 0.000 0.004 0.000
#> GSM509774 4 0.2728 0.7556 0.000 0.100 0.000 0.860 0.000 0.040
#> GSM509776 2 0.4614 0.7082 0.000 0.684 0.000 0.208 0.000 0.108
#> GSM509778 4 0.4584 0.8148 0.000 0.100 0.000 0.700 0.004 0.196
#> GSM509780 4 0.4972 0.4297 0.000 0.272 0.000 0.620 0.000 0.108
#> GSM509782 4 0.4584 0.8148 0.000 0.100 0.000 0.700 0.004 0.196
#> GSM509784 4 0.2350 0.7615 0.000 0.100 0.000 0.880 0.000 0.020
#> GSM509786 4 0.4584 0.8148 0.000 0.100 0.000 0.700 0.004 0.196
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 disease.state(p) time(p) k
#> CV:kmeans 80 1.27e-14 1.07e-11 2
#> CV:kmeans 76 3.75e-26 3.41e-11 3
#> CV:kmeans 74 5.68e-25 3.30e-09 4
#> CV:kmeans 74 1.78e-25 1.10e-07 5
#> CV:kmeans 68 7.82e-23 6.70e-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", "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 19175 rows and 81 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 1.000 0.984 0.994 0.5064 0.494 0.494
#> 3 3 0.866 0.863 0.939 0.2773 0.805 0.625
#> 4 4 0.754 0.855 0.917 0.1587 0.845 0.587
#> 5 5 0.740 0.717 0.849 0.0588 0.923 0.708
#> 6 6 0.721 0.630 0.807 0.0340 0.968 0.852
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
#> GSM509706 1 0.000 0.988 1.000 0.000
#> GSM509711 1 0.000 0.988 1.000 0.000
#> GSM509714 1 0.992 0.188 0.552 0.448
#> GSM509719 1 0.000 0.988 1.000 0.000
#> GSM509724 1 0.000 0.988 1.000 0.000
#> GSM509729 1 0.000 0.988 1.000 0.000
#> GSM509707 1 0.000 0.988 1.000 0.000
#> GSM509712 1 0.000 0.988 1.000 0.000
#> GSM509715 2 0.000 1.000 0.000 1.000
#> GSM509720 1 0.000 0.988 1.000 0.000
#> GSM509725 1 0.000 0.988 1.000 0.000
#> GSM509730 1 0.000 0.988 1.000 0.000
#> GSM509708 1 0.000 0.988 1.000 0.000
#> GSM509713 1 0.000 0.988 1.000 0.000
#> GSM509716 2 0.000 1.000 0.000 1.000
#> GSM509721 1 0.000 0.988 1.000 0.000
#> GSM509726 1 0.000 0.988 1.000 0.000
#> GSM509731 2 0.000 1.000 0.000 1.000
#> GSM509709 1 0.000 0.988 1.000 0.000
#> GSM509717 2 0.000 1.000 0.000 1.000
#> GSM509722 1 0.000 0.988 1.000 0.000
#> GSM509727 1 0.000 0.988 1.000 0.000
#> GSM509710 1 0.000 0.988 1.000 0.000
#> GSM509718 2 0.000 1.000 0.000 1.000
#> GSM509723 1 0.000 0.988 1.000 0.000
#> GSM509728 1 0.000 0.988 1.000 0.000
#> GSM509732 1 0.000 0.988 1.000 0.000
#> GSM509736 1 0.000 0.988 1.000 0.000
#> GSM509741 1 0.000 0.988 1.000 0.000
#> GSM509746 1 0.000 0.988 1.000 0.000
#> GSM509733 1 0.000 0.988 1.000 0.000
#> GSM509737 1 0.000 0.988 1.000 0.000
#> GSM509742 1 0.000 0.988 1.000 0.000
#> GSM509747 1 0.000 0.988 1.000 0.000
#> GSM509734 1 0.000 0.988 1.000 0.000
#> GSM509738 1 0.000 0.988 1.000 0.000
#> GSM509743 1 0.000 0.988 1.000 0.000
#> GSM509748 1 0.000 0.988 1.000 0.000
#> GSM509735 1 0.000 0.988 1.000 0.000
#> GSM509739 1 0.000 0.988 1.000 0.000
#> GSM509744 1 0.000 0.988 1.000 0.000
#> GSM509749 1 0.000 0.988 1.000 0.000
#> GSM509740 1 0.000 0.988 1.000 0.000
#> GSM509745 1 0.000 0.988 1.000 0.000
#> GSM509750 1 0.000 0.988 1.000 0.000
#> GSM509751 2 0.000 1.000 0.000 1.000
#> GSM509753 2 0.000 1.000 0.000 1.000
#> GSM509755 2 0.000 1.000 0.000 1.000
#> GSM509757 2 0.000 1.000 0.000 1.000
#> GSM509759 2 0.000 1.000 0.000 1.000
#> GSM509761 2 0.000 1.000 0.000 1.000
#> GSM509763 2 0.000 1.000 0.000 1.000
#> GSM509765 2 0.000 1.000 0.000 1.000
#> GSM509767 2 0.000 1.000 0.000 1.000
#> GSM509769 2 0.000 1.000 0.000 1.000
#> GSM509771 2 0.000 1.000 0.000 1.000
#> GSM509773 2 0.000 1.000 0.000 1.000
#> GSM509775 2 0.000 1.000 0.000 1.000
#> GSM509777 2 0.000 1.000 0.000 1.000
#> GSM509779 2 0.000 1.000 0.000 1.000
#> GSM509781 2 0.000 1.000 0.000 1.000
#> GSM509783 2 0.000 1.000 0.000 1.000
#> GSM509785 2 0.000 1.000 0.000 1.000
#> GSM509752 2 0.000 1.000 0.000 1.000
#> GSM509754 2 0.000 1.000 0.000 1.000
#> GSM509756 2 0.000 1.000 0.000 1.000
#> GSM509758 2 0.000 1.000 0.000 1.000
#> GSM509760 2 0.000 1.000 0.000 1.000
#> GSM509762 2 0.000 1.000 0.000 1.000
#> GSM509764 2 0.000 1.000 0.000 1.000
#> GSM509766 2 0.000 1.000 0.000 1.000
#> GSM509768 2 0.000 1.000 0.000 1.000
#> GSM509770 2 0.000 1.000 0.000 1.000
#> GSM509772 2 0.000 1.000 0.000 1.000
#> GSM509774 2 0.000 1.000 0.000 1.000
#> GSM509776 2 0.000 1.000 0.000 1.000
#> GSM509778 2 0.000 1.000 0.000 1.000
#> GSM509780 2 0.000 1.000 0.000 1.000
#> GSM509782 2 0.000 1.000 0.000 1.000
#> GSM509784 2 0.000 1.000 0.000 1.000
#> GSM509786 2 0.000 1.000 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM509706 1 0.1643 0.8263 0.956 0.000 0.044
#> GSM509711 1 0.0424 0.8261 0.992 0.000 0.008
#> GSM509714 1 0.0000 0.8215 1.000 0.000 0.000
#> GSM509719 1 0.0892 0.8301 0.980 0.000 0.020
#> GSM509724 1 0.5650 0.5647 0.688 0.000 0.312
#> GSM509729 1 0.0892 0.8301 0.980 0.000 0.020
#> GSM509707 1 0.1753 0.8244 0.952 0.000 0.048
#> GSM509712 1 0.1163 0.8299 0.972 0.000 0.028
#> GSM509715 1 0.5431 0.5559 0.716 0.284 0.000
#> GSM509720 1 0.0747 0.8294 0.984 0.000 0.016
#> GSM509725 1 0.6309 0.1454 0.500 0.000 0.500
#> GSM509730 1 0.1031 0.8303 0.976 0.000 0.024
#> GSM509708 1 0.1529 0.8276 0.960 0.000 0.040
#> GSM509713 1 0.1411 0.8286 0.964 0.000 0.036
#> GSM509716 1 0.4605 0.6716 0.796 0.204 0.000
#> GSM509721 1 0.0892 0.8301 0.980 0.000 0.020
#> GSM509726 1 0.6309 0.1452 0.500 0.000 0.500
#> GSM509731 1 0.4452 0.6837 0.808 0.192 0.000
#> GSM509709 1 0.1643 0.8263 0.956 0.000 0.044
#> GSM509717 1 0.4346 0.6909 0.816 0.184 0.000
#> GSM509722 1 0.0592 0.8280 0.988 0.000 0.012
#> GSM509727 3 0.6280 -0.0947 0.460 0.000 0.540
#> GSM509710 1 0.6307 0.1826 0.512 0.000 0.488
#> GSM509718 2 0.8610 0.2749 0.336 0.548 0.116
#> GSM509723 1 0.0747 0.8294 0.984 0.000 0.016
#> GSM509728 3 0.1163 0.9360 0.028 0.000 0.972
#> GSM509732 3 0.0000 0.9671 0.000 0.000 1.000
#> GSM509736 3 0.0000 0.9671 0.000 0.000 1.000
#> GSM509741 3 0.0000 0.9671 0.000 0.000 1.000
#> GSM509746 3 0.0000 0.9671 0.000 0.000 1.000
#> GSM509733 3 0.0000 0.9671 0.000 0.000 1.000
#> GSM509737 3 0.0000 0.9671 0.000 0.000 1.000
#> GSM509742 3 0.0000 0.9671 0.000 0.000 1.000
#> GSM509747 3 0.0000 0.9671 0.000 0.000 1.000
#> GSM509734 3 0.0000 0.9671 0.000 0.000 1.000
#> GSM509738 3 0.0000 0.9671 0.000 0.000 1.000
#> GSM509743 3 0.0000 0.9671 0.000 0.000 1.000
#> GSM509748 3 0.0000 0.9671 0.000 0.000 1.000
#> GSM509735 1 0.6204 0.3563 0.576 0.000 0.424
#> GSM509739 1 0.5178 0.6422 0.744 0.000 0.256
#> GSM509744 3 0.0000 0.9671 0.000 0.000 1.000
#> GSM509749 3 0.0000 0.9671 0.000 0.000 1.000
#> GSM509740 3 0.0237 0.9632 0.004 0.000 0.996
#> GSM509745 3 0.0000 0.9671 0.000 0.000 1.000
#> GSM509750 3 0.0000 0.9671 0.000 0.000 1.000
#> GSM509751 2 0.0000 0.9822 0.000 1.000 0.000
#> GSM509753 2 0.0000 0.9822 0.000 1.000 0.000
#> GSM509755 2 0.0000 0.9822 0.000 1.000 0.000
#> GSM509757 2 0.0000 0.9822 0.000 1.000 0.000
#> GSM509759 2 0.0000 0.9822 0.000 1.000 0.000
#> GSM509761 2 0.0000 0.9822 0.000 1.000 0.000
#> GSM509763 2 0.0000 0.9822 0.000 1.000 0.000
#> GSM509765 2 0.0237 0.9813 0.004 0.996 0.000
#> GSM509767 2 0.0000 0.9822 0.000 1.000 0.000
#> GSM509769 2 0.0000 0.9822 0.000 1.000 0.000
#> GSM509771 2 0.0000 0.9822 0.000 1.000 0.000
#> GSM509773 2 0.0000 0.9822 0.000 1.000 0.000
#> GSM509775 2 0.0000 0.9822 0.000 1.000 0.000
#> GSM509777 2 0.0747 0.9770 0.016 0.984 0.000
#> GSM509779 2 0.0892 0.9754 0.020 0.980 0.000
#> GSM509781 2 0.0892 0.9754 0.020 0.980 0.000
#> GSM509783 2 0.0892 0.9754 0.020 0.980 0.000
#> GSM509785 2 0.0892 0.9754 0.020 0.980 0.000
#> GSM509752 2 0.0000 0.9822 0.000 1.000 0.000
#> GSM509754 2 0.0000 0.9822 0.000 1.000 0.000
#> GSM509756 2 0.0000 0.9822 0.000 1.000 0.000
#> GSM509758 2 0.0000 0.9822 0.000 1.000 0.000
#> GSM509760 2 0.0000 0.9822 0.000 1.000 0.000
#> GSM509762 2 0.0000 0.9822 0.000 1.000 0.000
#> GSM509764 2 0.0592 0.9739 0.000 0.988 0.012
#> GSM509766 2 0.0237 0.9813 0.004 0.996 0.000
#> GSM509768 2 0.0000 0.9822 0.000 1.000 0.000
#> GSM509770 2 0.0000 0.9822 0.000 1.000 0.000
#> GSM509772 2 0.0000 0.9822 0.000 1.000 0.000
#> GSM509774 2 0.0892 0.9754 0.020 0.980 0.000
#> GSM509776 2 0.0237 0.9813 0.004 0.996 0.000
#> GSM509778 2 0.0892 0.9754 0.020 0.980 0.000
#> GSM509780 2 0.0424 0.9801 0.008 0.992 0.000
#> GSM509782 2 0.0892 0.9754 0.020 0.980 0.000
#> GSM509784 2 0.0892 0.9754 0.020 0.980 0.000
#> GSM509786 2 0.0892 0.9754 0.020 0.980 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM509706 1 0.1022 0.8994 0.968 0.000 0.032 0.000
#> GSM509711 1 0.0921 0.8979 0.972 0.000 0.000 0.028
#> GSM509714 1 0.4304 0.6798 0.716 0.000 0.000 0.284
#> GSM509719 1 0.2011 0.8855 0.920 0.000 0.000 0.080
#> GSM509724 1 0.2469 0.8707 0.892 0.000 0.108 0.000
#> GSM509729 1 0.1584 0.9008 0.952 0.000 0.012 0.036
#> GSM509707 1 0.1022 0.8994 0.968 0.000 0.032 0.000
#> GSM509712 1 0.0804 0.9009 0.980 0.000 0.008 0.012
#> GSM509715 4 0.1118 0.8274 0.036 0.000 0.000 0.964
#> GSM509720 1 0.2216 0.8807 0.908 0.000 0.000 0.092
#> GSM509725 1 0.3649 0.7921 0.796 0.000 0.204 0.000
#> GSM509730 1 0.1820 0.9010 0.944 0.000 0.020 0.036
#> GSM509708 1 0.0895 0.9016 0.976 0.000 0.020 0.004
#> GSM509713 1 0.0895 0.9020 0.976 0.000 0.020 0.004
#> GSM509716 4 0.1389 0.8207 0.048 0.000 0.000 0.952
#> GSM509721 1 0.2081 0.8839 0.916 0.000 0.000 0.084
#> GSM509726 1 0.3837 0.7681 0.776 0.000 0.224 0.000
#> GSM509731 4 0.1302 0.8256 0.044 0.000 0.000 0.956
#> GSM509709 1 0.0817 0.9004 0.976 0.000 0.024 0.000
#> GSM509717 4 0.1557 0.8153 0.056 0.000 0.000 0.944
#> GSM509722 1 0.2081 0.8839 0.916 0.000 0.000 0.084
#> GSM509727 1 0.4605 0.5791 0.664 0.000 0.336 0.000
#> GSM509710 1 0.3074 0.8438 0.848 0.000 0.152 0.000
#> GSM509718 4 0.2901 0.8275 0.016 0.040 0.036 0.908
#> GSM509723 1 0.2011 0.8855 0.920 0.000 0.000 0.080
#> GSM509728 3 0.2647 0.8545 0.120 0.000 0.880 0.000
#> GSM509732 3 0.0000 0.9867 0.000 0.000 1.000 0.000
#> GSM509736 3 0.0000 0.9867 0.000 0.000 1.000 0.000
#> GSM509741 3 0.0000 0.9867 0.000 0.000 1.000 0.000
#> GSM509746 3 0.0000 0.9867 0.000 0.000 1.000 0.000
#> GSM509733 3 0.0000 0.9867 0.000 0.000 1.000 0.000
#> GSM509737 3 0.0000 0.9867 0.000 0.000 1.000 0.000
#> GSM509742 3 0.0000 0.9867 0.000 0.000 1.000 0.000
#> GSM509747 3 0.0000 0.9867 0.000 0.000 1.000 0.000
#> GSM509734 3 0.0000 0.9867 0.000 0.000 1.000 0.000
#> GSM509738 3 0.0188 0.9841 0.004 0.000 0.996 0.000
#> GSM509743 3 0.0000 0.9867 0.000 0.000 1.000 0.000
#> GSM509748 3 0.0000 0.9867 0.000 0.000 1.000 0.000
#> GSM509735 1 0.3486 0.8108 0.812 0.000 0.188 0.000
#> GSM509739 1 0.2469 0.8713 0.892 0.000 0.108 0.000
#> GSM509744 3 0.0000 0.9867 0.000 0.000 1.000 0.000
#> GSM509749 3 0.0000 0.9867 0.000 0.000 1.000 0.000
#> GSM509740 3 0.2053 0.9155 0.072 0.000 0.924 0.004
#> GSM509745 3 0.0188 0.9841 0.004 0.000 0.996 0.000
#> GSM509750 3 0.0188 0.9841 0.004 0.000 0.996 0.000
#> GSM509751 2 0.0000 0.8988 0.000 1.000 0.000 0.000
#> GSM509753 2 0.0000 0.8988 0.000 1.000 0.000 0.000
#> GSM509755 2 0.0000 0.8988 0.000 1.000 0.000 0.000
#> GSM509757 2 0.0000 0.8988 0.000 1.000 0.000 0.000
#> GSM509759 2 0.0000 0.8988 0.000 1.000 0.000 0.000
#> GSM509761 2 0.1389 0.8809 0.000 0.952 0.000 0.048
#> GSM509763 2 0.4713 0.4007 0.000 0.640 0.000 0.360
#> GSM509765 4 0.4222 0.7035 0.000 0.272 0.000 0.728
#> GSM509767 2 0.0188 0.8981 0.000 0.996 0.000 0.004
#> GSM509769 2 0.1716 0.8722 0.000 0.936 0.000 0.064
#> GSM509771 2 0.0707 0.8934 0.000 0.980 0.000 0.020
#> GSM509773 2 0.2973 0.7995 0.000 0.856 0.000 0.144
#> GSM509775 2 0.2469 0.8366 0.000 0.892 0.000 0.108
#> GSM509777 4 0.2973 0.8704 0.000 0.144 0.000 0.856
#> GSM509779 4 0.2469 0.8948 0.000 0.108 0.000 0.892
#> GSM509781 4 0.2408 0.8961 0.000 0.104 0.000 0.896
#> GSM509783 4 0.2408 0.8961 0.000 0.104 0.000 0.896
#> GSM509785 4 0.2408 0.8961 0.000 0.104 0.000 0.896
#> GSM509752 2 0.0000 0.8988 0.000 1.000 0.000 0.000
#> GSM509754 2 0.0000 0.8988 0.000 1.000 0.000 0.000
#> GSM509756 2 0.0000 0.8988 0.000 1.000 0.000 0.000
#> GSM509758 2 0.0188 0.8981 0.000 0.996 0.000 0.004
#> GSM509760 2 0.3172 0.7775 0.000 0.840 0.000 0.160
#> GSM509762 2 0.0000 0.8988 0.000 1.000 0.000 0.000
#> GSM509764 2 0.0188 0.8965 0.000 0.996 0.004 0.000
#> GSM509766 4 0.4933 0.3060 0.000 0.432 0.000 0.568
#> GSM509768 2 0.4967 0.0935 0.000 0.548 0.000 0.452
#> GSM509770 2 0.1940 0.8649 0.000 0.924 0.000 0.076
#> GSM509772 2 0.0000 0.8988 0.000 1.000 0.000 0.000
#> GSM509774 4 0.2530 0.8930 0.000 0.112 0.000 0.888
#> GSM509776 2 0.4992 -0.0125 0.000 0.524 0.000 0.476
#> GSM509778 4 0.2408 0.8961 0.000 0.104 0.000 0.896
#> GSM509780 4 0.3610 0.8125 0.000 0.200 0.000 0.800
#> GSM509782 4 0.2408 0.8961 0.000 0.104 0.000 0.896
#> GSM509784 4 0.2589 0.8908 0.000 0.116 0.000 0.884
#> GSM509786 4 0.2408 0.8961 0.000 0.104 0.000 0.896
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM509706 1 0.0290 0.7934 0.992 0.000 0.000 0.000 0.008
#> GSM509711 1 0.3109 0.6779 0.800 0.000 0.000 0.000 0.200
#> GSM509714 5 0.4238 0.5994 0.164 0.000 0.000 0.068 0.768
#> GSM509719 5 0.3999 0.6286 0.344 0.000 0.000 0.000 0.656
#> GSM509724 1 0.1211 0.7980 0.960 0.000 0.024 0.000 0.016
#> GSM509729 1 0.4074 0.1737 0.636 0.000 0.000 0.000 0.364
#> GSM509707 1 0.0162 0.7926 0.996 0.000 0.000 0.000 0.004
#> GSM509712 1 0.2966 0.6883 0.816 0.000 0.000 0.000 0.184
#> GSM509715 4 0.4748 -0.0749 0.016 0.000 0.000 0.492 0.492
#> GSM509720 5 0.3966 0.6365 0.336 0.000 0.000 0.000 0.664
#> GSM509725 1 0.2573 0.7681 0.880 0.000 0.104 0.000 0.016
#> GSM509730 1 0.5250 -0.0840 0.536 0.000 0.048 0.000 0.416
#> GSM509708 1 0.0880 0.7861 0.968 0.000 0.000 0.000 0.032
#> GSM509713 1 0.1544 0.7808 0.932 0.000 0.000 0.000 0.068
#> GSM509716 5 0.4658 0.1836 0.016 0.000 0.000 0.408 0.576
#> GSM509721 5 0.4166 0.6225 0.348 0.000 0.004 0.000 0.648
#> GSM509726 1 0.2712 0.7730 0.880 0.000 0.088 0.000 0.032
#> GSM509731 4 0.5006 0.3155 0.048 0.000 0.000 0.624 0.328
#> GSM509709 1 0.0609 0.7895 0.980 0.000 0.000 0.000 0.020
#> GSM509717 5 0.4808 0.1980 0.024 0.000 0.000 0.400 0.576
#> GSM509722 5 0.3895 0.6399 0.320 0.000 0.000 0.000 0.680
#> GSM509727 1 0.4647 0.6289 0.732 0.000 0.184 0.000 0.084
#> GSM509710 1 0.2540 0.7747 0.888 0.000 0.088 0.000 0.024
#> GSM509718 4 0.6847 0.1132 0.072 0.044 0.012 0.464 0.408
#> GSM509723 5 0.4060 0.6083 0.360 0.000 0.000 0.000 0.640
#> GSM509728 3 0.4276 0.6310 0.244 0.000 0.724 0.000 0.032
#> GSM509732 3 0.0000 0.9371 0.000 0.000 1.000 0.000 0.000
#> GSM509736 3 0.1924 0.9245 0.008 0.000 0.924 0.004 0.064
#> GSM509741 3 0.0290 0.9373 0.000 0.000 0.992 0.000 0.008
#> GSM509746 3 0.0000 0.9371 0.000 0.000 1.000 0.000 0.000
#> GSM509733 3 0.0000 0.9371 0.000 0.000 1.000 0.000 0.000
#> GSM509737 3 0.1990 0.9230 0.008 0.000 0.920 0.004 0.068
#> GSM509742 3 0.0162 0.9374 0.000 0.000 0.996 0.000 0.004
#> GSM509747 3 0.0000 0.9371 0.000 0.000 1.000 0.000 0.000
#> GSM509734 3 0.0000 0.9371 0.000 0.000 1.000 0.000 0.000
#> GSM509738 3 0.2464 0.9148 0.012 0.000 0.892 0.004 0.092
#> GSM509743 3 0.1571 0.9277 0.004 0.000 0.936 0.000 0.060
#> GSM509748 3 0.0162 0.9376 0.000 0.000 0.996 0.000 0.004
#> GSM509735 1 0.3527 0.6809 0.792 0.000 0.192 0.000 0.016
#> GSM509739 1 0.1668 0.7967 0.940 0.000 0.028 0.000 0.032
#> GSM509744 3 0.1864 0.9255 0.004 0.000 0.924 0.004 0.068
#> GSM509749 3 0.0404 0.9366 0.000 0.000 0.988 0.000 0.012
#> GSM509740 3 0.5587 0.6554 0.188 0.000 0.656 0.004 0.152
#> GSM509745 3 0.2729 0.9085 0.028 0.000 0.884 0.004 0.084
#> GSM509750 3 0.1638 0.9149 0.004 0.000 0.932 0.000 0.064
#> GSM509751 2 0.0510 0.8613 0.000 0.984 0.000 0.000 0.016
#> GSM509753 2 0.0609 0.8616 0.000 0.980 0.000 0.000 0.020
#> GSM509755 2 0.0609 0.8623 0.000 0.980 0.000 0.000 0.020
#> GSM509757 2 0.0290 0.8618 0.000 0.992 0.000 0.000 0.008
#> GSM509759 2 0.0609 0.8613 0.000 0.980 0.000 0.000 0.020
#> GSM509761 2 0.3639 0.7482 0.000 0.792 0.000 0.184 0.024
#> GSM509763 4 0.4682 0.3846 0.000 0.356 0.000 0.620 0.024
#> GSM509765 4 0.3106 0.7430 0.000 0.140 0.000 0.840 0.020
#> GSM509767 2 0.2300 0.8393 0.000 0.904 0.000 0.072 0.024
#> GSM509769 2 0.4428 0.6349 0.000 0.700 0.000 0.268 0.032
#> GSM509771 2 0.2795 0.8218 0.000 0.872 0.000 0.100 0.028
#> GSM509773 2 0.5071 0.2556 0.000 0.540 0.000 0.424 0.036
#> GSM509775 2 0.5077 0.3644 0.000 0.568 0.000 0.392 0.040
#> GSM509777 4 0.1697 0.7942 0.000 0.060 0.000 0.932 0.008
#> GSM509779 4 0.1012 0.8010 0.000 0.020 0.000 0.968 0.012
#> GSM509781 4 0.1012 0.8007 0.000 0.020 0.000 0.968 0.012
#> GSM509783 4 0.1117 0.7992 0.000 0.020 0.000 0.964 0.016
#> GSM509785 4 0.1012 0.8007 0.000 0.020 0.000 0.968 0.012
#> GSM509752 2 0.0566 0.8630 0.000 0.984 0.000 0.004 0.012
#> GSM509754 2 0.0798 0.8633 0.000 0.976 0.000 0.016 0.008
#> GSM509756 2 0.0912 0.8628 0.000 0.972 0.000 0.016 0.012
#> GSM509758 2 0.1725 0.8523 0.000 0.936 0.000 0.044 0.020
#> GSM509760 2 0.4758 0.5819 0.000 0.676 0.000 0.276 0.048
#> GSM509762 2 0.0566 0.8636 0.000 0.984 0.000 0.004 0.012
#> GSM509764 2 0.0880 0.8604 0.000 0.968 0.000 0.000 0.032
#> GSM509766 4 0.4248 0.6272 0.000 0.240 0.000 0.728 0.032
#> GSM509768 4 0.4354 0.5946 0.000 0.256 0.000 0.712 0.032
#> GSM509770 2 0.4404 0.6435 0.000 0.704 0.000 0.264 0.032
#> GSM509772 2 0.0404 0.8617 0.000 0.988 0.000 0.000 0.012
#> GSM509774 4 0.1041 0.8022 0.000 0.032 0.000 0.964 0.004
#> GSM509776 4 0.4642 0.4806 0.000 0.308 0.000 0.660 0.032
#> GSM509778 4 0.0898 0.8010 0.000 0.020 0.000 0.972 0.008
#> GSM509780 4 0.2795 0.7773 0.000 0.100 0.000 0.872 0.028
#> GSM509782 4 0.1012 0.8007 0.000 0.020 0.000 0.968 0.012
#> GSM509784 4 0.1300 0.8020 0.000 0.028 0.000 0.956 0.016
#> GSM509786 4 0.0898 0.8012 0.000 0.020 0.000 0.972 0.008
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM509706 1 0.0405 0.8476 0.988 0.000 0.000 0.000 0.004 0.008
#> GSM509711 1 0.4585 0.6252 0.692 0.000 0.000 0.000 0.192 0.116
#> GSM509714 5 0.4657 0.3392 0.040 0.000 0.000 0.032 0.692 0.236
#> GSM509719 5 0.2572 0.5860 0.136 0.000 0.000 0.000 0.852 0.012
#> GSM509724 1 0.0405 0.8478 0.988 0.000 0.000 0.000 0.008 0.004
#> GSM509729 1 0.4666 0.1648 0.536 0.000 0.000 0.000 0.420 0.044
#> GSM509707 1 0.0291 0.8478 0.992 0.000 0.000 0.000 0.004 0.004
#> GSM509712 1 0.4506 0.6641 0.704 0.000 0.000 0.000 0.176 0.120
#> GSM509715 5 0.6414 -0.5335 0.012 0.000 0.000 0.332 0.348 0.308
#> GSM509720 5 0.2357 0.5868 0.116 0.000 0.000 0.000 0.872 0.012
#> GSM509725 1 0.1369 0.8469 0.952 0.000 0.016 0.000 0.016 0.016
#> GSM509730 5 0.5293 0.1873 0.372 0.000 0.024 0.000 0.548 0.056
#> GSM509708 1 0.1563 0.8383 0.932 0.000 0.000 0.000 0.056 0.012
#> GSM509713 1 0.2966 0.7977 0.848 0.000 0.000 0.000 0.076 0.076
#> GSM509716 5 0.6125 -0.3678 0.004 0.000 0.000 0.264 0.432 0.300
#> GSM509721 5 0.2680 0.5834 0.124 0.000 0.004 0.000 0.856 0.016
#> GSM509726 1 0.2295 0.8266 0.904 0.000 0.028 0.000 0.016 0.052
#> GSM509731 4 0.6756 -0.5207 0.060 0.000 0.000 0.460 0.228 0.252
#> GSM509709 1 0.1151 0.8460 0.956 0.000 0.000 0.000 0.032 0.012
#> GSM509717 5 0.6276 -0.4050 0.008 0.000 0.000 0.276 0.400 0.316
#> GSM509722 5 0.2383 0.5729 0.096 0.000 0.000 0.000 0.880 0.024
#> GSM509727 1 0.5227 0.6308 0.688 0.000 0.144 0.000 0.048 0.120
#> GSM509710 1 0.0951 0.8492 0.968 0.000 0.008 0.000 0.004 0.020
#> GSM509718 6 0.7595 0.0000 0.024 0.040 0.040 0.304 0.156 0.436
#> GSM509723 5 0.2790 0.5823 0.140 0.000 0.000 0.000 0.840 0.020
#> GSM509728 3 0.5245 0.4990 0.268 0.000 0.616 0.000 0.012 0.104
#> GSM509732 3 0.0603 0.8681 0.004 0.000 0.980 0.000 0.000 0.016
#> GSM509736 3 0.3133 0.8156 0.008 0.000 0.804 0.000 0.008 0.180
#> GSM509741 3 0.1296 0.8662 0.004 0.000 0.948 0.000 0.004 0.044
#> GSM509746 3 0.0603 0.8681 0.004 0.000 0.980 0.000 0.000 0.016
#> GSM509733 3 0.0603 0.8681 0.004 0.000 0.980 0.000 0.000 0.016
#> GSM509737 3 0.3065 0.8189 0.008 0.000 0.812 0.000 0.008 0.172
#> GSM509742 3 0.0692 0.8692 0.004 0.000 0.976 0.000 0.000 0.020
#> GSM509747 3 0.0653 0.8684 0.004 0.000 0.980 0.000 0.004 0.012
#> GSM509734 3 0.0717 0.8685 0.008 0.000 0.976 0.000 0.000 0.016
#> GSM509738 3 0.3693 0.7973 0.012 0.000 0.756 0.000 0.016 0.216
#> GSM509743 3 0.2473 0.8385 0.000 0.000 0.856 0.000 0.008 0.136
#> GSM509748 3 0.0508 0.8694 0.004 0.000 0.984 0.000 0.000 0.012
#> GSM509735 1 0.2975 0.7500 0.840 0.000 0.132 0.000 0.012 0.016
#> GSM509739 1 0.0964 0.8488 0.968 0.000 0.004 0.000 0.012 0.016
#> GSM509744 3 0.2234 0.8483 0.000 0.000 0.872 0.000 0.004 0.124
#> GSM509749 3 0.1010 0.8679 0.004 0.000 0.960 0.000 0.000 0.036
#> GSM509740 3 0.6866 0.3564 0.168 0.000 0.456 0.000 0.088 0.288
#> GSM509745 3 0.4112 0.7695 0.048 0.000 0.724 0.000 0.004 0.224
#> GSM509750 3 0.2275 0.8416 0.008 0.000 0.888 0.000 0.008 0.096
#> GSM509751 2 0.1152 0.7922 0.000 0.952 0.000 0.000 0.004 0.044
#> GSM509753 2 0.1152 0.7929 0.000 0.952 0.000 0.000 0.004 0.044
#> GSM509755 2 0.1010 0.7888 0.000 0.960 0.000 0.000 0.004 0.036
#> GSM509757 2 0.1082 0.7945 0.000 0.956 0.000 0.000 0.004 0.040
#> GSM509759 2 0.1686 0.7830 0.000 0.924 0.000 0.000 0.012 0.064
#> GSM509761 2 0.5031 0.6358 0.000 0.644 0.000 0.228 0.004 0.124
#> GSM509763 4 0.4923 0.5387 0.000 0.236 0.000 0.652 0.004 0.108
#> GSM509765 4 0.3611 0.6692 0.000 0.096 0.000 0.796 0.000 0.108
#> GSM509767 2 0.4196 0.7384 0.000 0.740 0.000 0.116 0.000 0.144
#> GSM509769 2 0.5775 0.4020 0.000 0.496 0.000 0.296 0.000 0.208
#> GSM509771 2 0.3962 0.7480 0.000 0.764 0.000 0.120 0.000 0.116
#> GSM509773 4 0.5722 -0.0675 0.000 0.404 0.000 0.432 0.000 0.164
#> GSM509775 2 0.5782 0.1138 0.000 0.424 0.000 0.400 0.000 0.176
#> GSM509777 4 0.1984 0.7229 0.000 0.032 0.000 0.912 0.000 0.056
#> GSM509779 4 0.0806 0.7294 0.000 0.008 0.000 0.972 0.000 0.020
#> GSM509781 4 0.1036 0.7185 0.000 0.008 0.000 0.964 0.004 0.024
#> GSM509783 4 0.0951 0.7210 0.000 0.008 0.000 0.968 0.004 0.020
#> GSM509785 4 0.0922 0.7180 0.000 0.004 0.000 0.968 0.004 0.024
#> GSM509752 2 0.1524 0.7959 0.000 0.932 0.000 0.008 0.000 0.060
#> GSM509754 2 0.2309 0.7977 0.000 0.888 0.000 0.028 0.000 0.084
#> GSM509756 2 0.2971 0.7827 0.000 0.844 0.000 0.052 0.000 0.104
#> GSM509758 2 0.4013 0.7611 0.000 0.768 0.000 0.104 0.004 0.124
#> GSM509760 2 0.6099 0.4292 0.000 0.520 0.000 0.292 0.028 0.160
#> GSM509762 2 0.2452 0.7942 0.000 0.884 0.000 0.028 0.004 0.084
#> GSM509764 2 0.1644 0.7870 0.000 0.920 0.000 0.000 0.004 0.076
#> GSM509766 4 0.4736 0.5879 0.000 0.164 0.000 0.692 0.004 0.140
#> GSM509768 4 0.4902 0.5716 0.000 0.172 0.000 0.672 0.004 0.152
#> GSM509770 2 0.5932 0.5430 0.000 0.532 0.000 0.232 0.012 0.224
#> GSM509772 2 0.1285 0.7953 0.000 0.944 0.000 0.004 0.000 0.052
#> GSM509774 4 0.1168 0.7303 0.000 0.016 0.000 0.956 0.000 0.028
#> GSM509776 4 0.5227 0.5006 0.000 0.232 0.000 0.620 0.004 0.144
#> GSM509778 4 0.0951 0.7210 0.000 0.008 0.000 0.968 0.004 0.020
#> GSM509780 4 0.2994 0.6980 0.000 0.080 0.000 0.852 0.004 0.064
#> GSM509782 4 0.1194 0.7212 0.000 0.008 0.000 0.956 0.004 0.032
#> GSM509784 4 0.1453 0.7291 0.000 0.008 0.000 0.944 0.008 0.040
#> GSM509786 4 0.0862 0.7247 0.000 0.008 0.000 0.972 0.004 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 disease.state(p) time(p) k
#> CV:skmeans 80 1.27e-14 1.07e-11 2
#> CV:skmeans 75 2.83e-28 3.27e-12 3
#> CV:skmeans 77 1.32e-22 1.20e-07 4
#> CV:skmeans 70 2.73e-22 2.97e-07 5
#> CV:skmeans 67 2.20e-22 1.81e-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", "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 19175 rows and 81 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 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 0.737 0.848 0.938 0.4973 0.498 0.498
#> 3 3 0.563 0.542 0.768 0.3106 0.765 0.560
#> 4 4 0.564 0.569 0.776 0.1248 0.853 0.600
#> 5 5 0.734 0.663 0.796 0.0827 0.899 0.635
#> 6 6 0.791 0.690 0.837 0.0325 0.945 0.746
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
#> GSM509706 1 0.0376 0.9261 0.996 0.004
#> GSM509711 1 0.9323 0.4603 0.652 0.348
#> GSM509714 2 0.8016 0.6744 0.244 0.756
#> GSM509719 1 0.9661 0.3573 0.608 0.392
#> GSM509724 1 0.0000 0.9277 1.000 0.000
#> GSM509729 1 0.4431 0.8503 0.908 0.092
#> GSM509707 1 0.0376 0.9261 0.996 0.004
#> GSM509712 1 0.9286 0.4761 0.656 0.344
#> GSM509715 2 0.8081 0.6734 0.248 0.752
#> GSM509720 2 0.9754 0.3170 0.408 0.592
#> GSM509725 1 0.0000 0.9277 1.000 0.000
#> GSM509730 1 0.9087 0.5189 0.676 0.324
#> GSM509708 1 0.1184 0.9185 0.984 0.016
#> GSM509713 1 0.1184 0.9184 0.984 0.016
#> GSM509716 2 0.7453 0.7194 0.212 0.788
#> GSM509721 1 0.9552 0.4012 0.624 0.376
#> GSM509726 1 0.0000 0.9277 1.000 0.000
#> GSM509731 2 0.7950 0.6823 0.240 0.760
#> GSM509709 1 0.0938 0.9211 0.988 0.012
#> GSM509717 2 0.8016 0.6744 0.244 0.756
#> GSM509722 2 0.9087 0.5284 0.324 0.676
#> GSM509727 1 0.0376 0.9261 0.996 0.004
#> GSM509710 1 0.0000 0.9277 1.000 0.000
#> GSM509718 1 0.9815 0.2622 0.580 0.420
#> GSM509723 2 1.0000 -0.0194 0.500 0.500
#> GSM509728 1 0.0000 0.9277 1.000 0.000
#> GSM509732 1 0.0000 0.9277 1.000 0.000
#> GSM509736 1 0.0000 0.9277 1.000 0.000
#> GSM509741 1 0.0000 0.9277 1.000 0.000
#> GSM509746 1 0.0000 0.9277 1.000 0.000
#> GSM509733 1 0.0000 0.9277 1.000 0.000
#> GSM509737 1 0.0000 0.9277 1.000 0.000
#> GSM509742 1 0.0000 0.9277 1.000 0.000
#> GSM509747 1 0.0000 0.9277 1.000 0.000
#> GSM509734 1 0.0000 0.9277 1.000 0.000
#> GSM509738 1 0.0000 0.9277 1.000 0.000
#> GSM509743 1 0.0000 0.9277 1.000 0.000
#> GSM509748 1 0.0000 0.9277 1.000 0.000
#> GSM509735 1 0.0000 0.9277 1.000 0.000
#> GSM509739 1 0.0000 0.9277 1.000 0.000
#> GSM509744 1 0.0000 0.9277 1.000 0.000
#> GSM509749 1 0.0000 0.9277 1.000 0.000
#> GSM509740 1 0.0376 0.9260 0.996 0.004
#> GSM509745 1 0.0000 0.9277 1.000 0.000
#> GSM509750 1 0.0376 0.9261 0.996 0.004
#> GSM509751 2 0.0000 0.9312 0.000 1.000
#> GSM509753 2 0.0000 0.9312 0.000 1.000
#> GSM509755 2 0.0000 0.9312 0.000 1.000
#> GSM509757 2 0.0000 0.9312 0.000 1.000
#> GSM509759 2 0.0000 0.9312 0.000 1.000
#> GSM509761 2 0.0000 0.9312 0.000 1.000
#> GSM509763 2 0.0000 0.9312 0.000 1.000
#> GSM509765 2 0.0000 0.9312 0.000 1.000
#> GSM509767 2 0.0000 0.9312 0.000 1.000
#> GSM509769 2 0.0000 0.9312 0.000 1.000
#> GSM509771 2 0.0000 0.9312 0.000 1.000
#> GSM509773 2 0.0000 0.9312 0.000 1.000
#> GSM509775 2 0.0000 0.9312 0.000 1.000
#> GSM509777 2 0.0000 0.9312 0.000 1.000
#> GSM509779 2 0.0000 0.9312 0.000 1.000
#> GSM509781 2 0.0000 0.9312 0.000 1.000
#> GSM509783 2 0.0000 0.9312 0.000 1.000
#> GSM509785 2 0.0000 0.9312 0.000 1.000
#> GSM509752 2 0.0000 0.9312 0.000 1.000
#> GSM509754 2 0.0000 0.9312 0.000 1.000
#> GSM509756 2 0.0000 0.9312 0.000 1.000
#> GSM509758 2 0.0000 0.9312 0.000 1.000
#> GSM509760 2 0.0000 0.9312 0.000 1.000
#> GSM509762 2 0.0000 0.9312 0.000 1.000
#> GSM509764 2 0.7528 0.6923 0.216 0.784
#> GSM509766 2 0.0000 0.9312 0.000 1.000
#> GSM509768 2 0.0000 0.9312 0.000 1.000
#> GSM509770 2 0.0000 0.9312 0.000 1.000
#> GSM509772 2 0.0000 0.9312 0.000 1.000
#> GSM509774 2 0.0000 0.9312 0.000 1.000
#> GSM509776 2 0.0000 0.9312 0.000 1.000
#> GSM509778 2 0.0000 0.9312 0.000 1.000
#> GSM509780 2 0.0000 0.9312 0.000 1.000
#> GSM509782 2 0.0000 0.9312 0.000 1.000
#> GSM509784 2 0.0000 0.9312 0.000 1.000
#> GSM509786 2 0.0000 0.9312 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM509706 3 0.7236 0.6081 0.392 0.032 0.576
#> GSM509711 1 0.9257 -0.1049 0.520 0.196 0.284
#> GSM509714 1 0.6955 0.0721 0.636 0.332 0.032
#> GSM509719 2 0.7690 0.1762 0.416 0.536 0.048
#> GSM509724 3 0.4346 0.8043 0.184 0.000 0.816
#> GSM509729 1 0.9541 -0.2602 0.452 0.200 0.348
#> GSM509707 3 0.6264 0.6480 0.380 0.004 0.616
#> GSM509712 1 0.9098 -0.0664 0.456 0.404 0.140
#> GSM509715 1 0.4811 0.3984 0.828 0.148 0.024
#> GSM509720 2 0.7353 0.1702 0.436 0.532 0.032
#> GSM509725 3 0.2356 0.8493 0.072 0.000 0.928
#> GSM509730 1 0.9836 -0.0562 0.420 0.312 0.268
#> GSM509708 3 0.7181 0.5222 0.468 0.024 0.508
#> GSM509713 3 0.6669 0.5449 0.468 0.008 0.524
#> GSM509716 1 0.4897 0.3382 0.812 0.172 0.016
#> GSM509721 2 0.7652 0.1494 0.444 0.512 0.044
#> GSM509726 3 0.3192 0.8404 0.112 0.000 0.888
#> GSM509731 1 0.5098 0.4205 0.752 0.248 0.000
#> GSM509709 3 0.7054 0.5441 0.456 0.020 0.524
#> GSM509717 1 0.4799 0.3509 0.836 0.132 0.032
#> GSM509722 2 0.7619 0.1680 0.424 0.532 0.044
#> GSM509727 3 0.6247 0.6480 0.376 0.004 0.620
#> GSM509710 3 0.1643 0.8496 0.044 0.000 0.956
#> GSM509718 3 0.8902 0.0946 0.320 0.144 0.536
#> GSM509723 2 0.7647 0.1539 0.440 0.516 0.044
#> GSM509728 3 0.3038 0.8432 0.104 0.000 0.896
#> GSM509732 3 0.0237 0.8499 0.004 0.000 0.996
#> GSM509736 3 0.0000 0.8493 0.000 0.000 1.000
#> GSM509741 3 0.0000 0.8493 0.000 0.000 1.000
#> GSM509746 3 0.0237 0.8499 0.004 0.000 0.996
#> GSM509733 3 0.0237 0.8499 0.004 0.000 0.996
#> GSM509737 3 0.0000 0.8493 0.000 0.000 1.000
#> GSM509742 3 0.0237 0.8499 0.004 0.000 0.996
#> GSM509747 3 0.0237 0.8499 0.004 0.000 0.996
#> GSM509734 3 0.0237 0.8499 0.004 0.000 0.996
#> GSM509738 3 0.2165 0.8494 0.064 0.000 0.936
#> GSM509743 3 0.0000 0.8493 0.000 0.000 1.000
#> GSM509748 3 0.0000 0.8493 0.000 0.000 1.000
#> GSM509735 3 0.5905 0.6739 0.352 0.000 0.648
#> GSM509739 3 0.3412 0.8371 0.124 0.000 0.876
#> GSM509744 3 0.0000 0.8493 0.000 0.000 1.000
#> GSM509749 3 0.2165 0.8496 0.064 0.000 0.936
#> GSM509740 3 0.3370 0.8413 0.072 0.024 0.904
#> GSM509745 3 0.2066 0.8496 0.060 0.000 0.940
#> GSM509750 3 0.4068 0.8272 0.120 0.016 0.864
#> GSM509751 2 0.0000 0.7138 0.000 1.000 0.000
#> GSM509753 2 0.0000 0.7138 0.000 1.000 0.000
#> GSM509755 2 0.0000 0.7138 0.000 1.000 0.000
#> GSM509757 2 0.0000 0.7138 0.000 1.000 0.000
#> GSM509759 2 0.0000 0.7138 0.000 1.000 0.000
#> GSM509761 2 0.0237 0.7119 0.004 0.996 0.000
#> GSM509763 2 0.4346 0.4556 0.184 0.816 0.000
#> GSM509765 1 0.6309 0.3697 0.504 0.496 0.000
#> GSM509767 2 0.0000 0.7138 0.000 1.000 0.000
#> GSM509769 2 0.0237 0.7118 0.004 0.996 0.000
#> GSM509771 2 0.0000 0.7138 0.000 1.000 0.000
#> GSM509773 2 0.1643 0.6748 0.044 0.956 0.000
#> GSM509775 2 0.0892 0.7002 0.020 0.980 0.000
#> GSM509777 1 0.6302 0.3966 0.520 0.480 0.000
#> GSM509779 1 0.6291 0.4147 0.532 0.468 0.000
#> GSM509781 1 0.6225 0.4471 0.568 0.432 0.000
#> GSM509783 1 0.6215 0.4483 0.572 0.428 0.000
#> GSM509785 1 0.6225 0.4473 0.568 0.432 0.000
#> GSM509752 2 0.0000 0.7138 0.000 1.000 0.000
#> GSM509754 2 0.0000 0.7138 0.000 1.000 0.000
#> GSM509756 2 0.0592 0.7056 0.012 0.988 0.000
#> GSM509758 2 0.0000 0.7138 0.000 1.000 0.000
#> GSM509760 2 0.2796 0.6071 0.092 0.908 0.000
#> GSM509762 2 0.0237 0.7119 0.004 0.996 0.000
#> GSM509764 2 0.5465 0.3387 0.000 0.712 0.288
#> GSM509766 2 0.6252 -0.2835 0.444 0.556 0.000
#> GSM509768 2 0.5098 0.3029 0.248 0.752 0.000
#> GSM509770 2 0.0237 0.7120 0.004 0.996 0.000
#> GSM509772 2 0.0000 0.7138 0.000 1.000 0.000
#> GSM509774 1 0.6291 0.4147 0.532 0.468 0.000
#> GSM509776 2 0.6280 -0.3251 0.460 0.540 0.000
#> GSM509778 1 0.6215 0.4483 0.572 0.428 0.000
#> GSM509780 2 0.6260 -0.3016 0.448 0.552 0.000
#> GSM509782 1 0.6235 0.4450 0.564 0.436 0.000
#> GSM509784 1 0.6291 0.4147 0.532 0.468 0.000
#> GSM509786 1 0.6274 0.4278 0.544 0.456 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM509706 1 0.2530 0.5417 0.896 0.000 0.100 0.004
#> GSM509711 1 0.5922 0.5689 0.736 0.056 0.044 0.164
#> GSM509714 1 0.7816 0.1850 0.412 0.272 0.000 0.316
#> GSM509719 2 0.7665 0.0235 0.380 0.448 0.008 0.164
#> GSM509724 1 0.4428 0.2246 0.720 0.000 0.276 0.004
#> GSM509729 1 0.7734 0.4397 0.580 0.216 0.040 0.164
#> GSM509707 1 0.3105 0.5397 0.856 0.000 0.140 0.004
#> GSM509712 1 0.7919 0.2557 0.496 0.316 0.024 0.164
#> GSM509715 4 0.5559 0.4830 0.240 0.064 0.000 0.696
#> GSM509720 2 0.7450 -0.0382 0.404 0.424 0.000 0.172
#> GSM509725 1 0.5028 -0.1106 0.596 0.000 0.400 0.004
#> GSM509730 1 0.8254 0.2256 0.472 0.332 0.044 0.152
#> GSM509708 1 0.3557 0.5857 0.856 0.000 0.036 0.108
#> GSM509713 1 0.4297 0.5846 0.820 0.000 0.096 0.084
#> GSM509716 4 0.7220 -0.0138 0.384 0.144 0.000 0.472
#> GSM509721 2 0.7728 -0.0156 0.388 0.432 0.008 0.172
#> GSM509726 3 0.5296 0.0886 0.492 0.000 0.500 0.008
#> GSM509731 4 0.4542 0.7138 0.088 0.108 0.000 0.804
#> GSM509709 1 0.2335 0.5913 0.920 0.000 0.020 0.060
#> GSM509717 4 0.6637 0.1133 0.368 0.092 0.000 0.540
#> GSM509722 2 0.7736 -0.0578 0.404 0.416 0.008 0.172
#> GSM509727 1 0.2973 0.5238 0.856 0.000 0.144 0.000
#> GSM509710 3 0.5126 0.1616 0.444 0.000 0.552 0.004
#> GSM509718 3 0.6858 0.2666 0.008 0.100 0.576 0.316
#> GSM509723 2 0.7609 -0.0258 0.396 0.428 0.004 0.172
#> GSM509728 1 0.4981 -0.2072 0.536 0.000 0.464 0.000
#> GSM509732 3 0.3311 0.7506 0.172 0.000 0.828 0.000
#> GSM509736 3 0.1389 0.7680 0.048 0.000 0.952 0.000
#> GSM509741 3 0.1211 0.7754 0.040 0.000 0.960 0.000
#> GSM509746 3 0.3356 0.7498 0.176 0.000 0.824 0.000
#> GSM509733 3 0.3311 0.7506 0.172 0.000 0.828 0.000
#> GSM509737 3 0.1389 0.7680 0.048 0.000 0.952 0.000
#> GSM509742 3 0.1022 0.7737 0.032 0.000 0.968 0.000
#> GSM509747 3 0.3311 0.7506 0.172 0.000 0.828 0.000
#> GSM509734 3 0.3311 0.7506 0.172 0.000 0.828 0.000
#> GSM509738 3 0.3142 0.7264 0.132 0.000 0.860 0.008
#> GSM509743 3 0.1389 0.7680 0.048 0.000 0.952 0.000
#> GSM509748 3 0.1940 0.7734 0.076 0.000 0.924 0.000
#> GSM509735 1 0.3494 0.4886 0.824 0.000 0.172 0.004
#> GSM509739 1 0.5000 -0.0986 0.504 0.000 0.496 0.000
#> GSM509744 3 0.1389 0.7680 0.048 0.000 0.952 0.000
#> GSM509749 3 0.4072 0.7000 0.252 0.000 0.748 0.000
#> GSM509740 3 0.3142 0.7222 0.132 0.000 0.860 0.008
#> GSM509745 3 0.2760 0.7313 0.128 0.000 0.872 0.000
#> GSM509750 3 0.5252 0.6158 0.336 0.020 0.644 0.000
#> GSM509751 2 0.0000 0.7890 0.000 1.000 0.000 0.000
#> GSM509753 2 0.0000 0.7890 0.000 1.000 0.000 0.000
#> GSM509755 2 0.0000 0.7890 0.000 1.000 0.000 0.000
#> GSM509757 2 0.0000 0.7890 0.000 1.000 0.000 0.000
#> GSM509759 2 0.0000 0.7890 0.000 1.000 0.000 0.000
#> GSM509761 2 0.0336 0.7849 0.000 0.992 0.000 0.008
#> GSM509763 2 0.4331 0.3417 0.000 0.712 0.000 0.288
#> GSM509765 4 0.4134 0.7683 0.000 0.260 0.000 0.740
#> GSM509767 2 0.0000 0.7890 0.000 1.000 0.000 0.000
#> GSM509769 2 0.0336 0.7856 0.000 0.992 0.000 0.008
#> GSM509771 2 0.0000 0.7890 0.000 1.000 0.000 0.000
#> GSM509773 2 0.1716 0.7327 0.000 0.936 0.000 0.064
#> GSM509775 2 0.1118 0.7653 0.000 0.964 0.000 0.036
#> GSM509777 4 0.3649 0.8074 0.000 0.204 0.000 0.796
#> GSM509779 4 0.3356 0.8186 0.000 0.176 0.000 0.824
#> GSM509781 4 0.3172 0.8193 0.000 0.160 0.000 0.840
#> GSM509783 4 0.3172 0.8193 0.000 0.160 0.000 0.840
#> GSM509785 4 0.3172 0.8193 0.000 0.160 0.000 0.840
#> GSM509752 2 0.0000 0.7890 0.000 1.000 0.000 0.000
#> GSM509754 2 0.0000 0.7890 0.000 1.000 0.000 0.000
#> GSM509756 2 0.0469 0.7815 0.000 0.988 0.000 0.012
#> GSM509758 2 0.0000 0.7890 0.000 1.000 0.000 0.000
#> GSM509760 2 0.2530 0.6632 0.000 0.888 0.000 0.112
#> GSM509762 2 0.0188 0.7870 0.000 0.996 0.000 0.004
#> GSM509764 2 0.4500 0.4436 0.000 0.684 0.316 0.000
#> GSM509766 4 0.4855 0.5950 0.000 0.400 0.000 0.600
#> GSM509768 2 0.4643 0.1504 0.000 0.656 0.000 0.344
#> GSM509770 2 0.0336 0.7857 0.000 0.992 0.000 0.008
#> GSM509772 2 0.0000 0.7890 0.000 1.000 0.000 0.000
#> GSM509774 4 0.3356 0.8186 0.000 0.176 0.000 0.824
#> GSM509776 4 0.4855 0.5981 0.000 0.400 0.000 0.600
#> GSM509778 4 0.3172 0.8193 0.000 0.160 0.000 0.840
#> GSM509780 4 0.4866 0.5934 0.000 0.404 0.000 0.596
#> GSM509782 4 0.3219 0.8196 0.000 0.164 0.000 0.836
#> GSM509784 4 0.3486 0.8150 0.000 0.188 0.000 0.812
#> GSM509786 4 0.3356 0.8186 0.000 0.176 0.000 0.824
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM509706 1 0.0798 0.59070 0.976 0.000 0.016 0.000 0.008
#> GSM509711 5 0.3388 0.69889 0.200 0.000 0.000 0.008 0.792
#> GSM509714 5 0.1822 0.86256 0.004 0.024 0.000 0.036 0.936
#> GSM509719 5 0.2230 0.86831 0.000 0.116 0.000 0.000 0.884
#> GSM509724 1 0.0404 0.58821 0.988 0.000 0.012 0.000 0.000
#> GSM509729 5 0.2945 0.86605 0.056 0.056 0.008 0.000 0.880
#> GSM509707 1 0.2707 0.56494 0.860 0.000 0.132 0.000 0.008
#> GSM509712 5 0.3142 0.85150 0.056 0.068 0.000 0.008 0.868
#> GSM509715 4 0.4744 0.24815 0.000 0.020 0.000 0.572 0.408
#> GSM509720 5 0.1671 0.88780 0.000 0.076 0.000 0.000 0.924
#> GSM509725 1 0.0290 0.58278 0.992 0.000 0.008 0.000 0.000
#> GSM509730 5 0.2604 0.88082 0.020 0.072 0.012 0.000 0.896
#> GSM509708 1 0.4294 -0.00366 0.532 0.000 0.000 0.000 0.468
#> GSM509713 1 0.5345 0.27113 0.540 0.000 0.056 0.000 0.404
#> GSM509716 5 0.2773 0.81226 0.000 0.020 0.000 0.112 0.868
#> GSM509721 5 0.2179 0.87217 0.000 0.112 0.000 0.000 0.888
#> GSM509726 1 0.5382 0.40746 0.592 0.000 0.336 0.000 0.072
#> GSM509731 4 0.3612 0.57323 0.000 0.000 0.000 0.732 0.268
#> GSM509709 1 0.4310 0.21589 0.604 0.000 0.004 0.000 0.392
#> GSM509717 5 0.4284 0.66451 0.000 0.040 0.000 0.224 0.736
#> GSM509722 5 0.1608 0.88775 0.000 0.072 0.000 0.000 0.928
#> GSM509727 1 0.3669 0.54522 0.816 0.000 0.056 0.000 0.128
#> GSM509710 1 0.4305 0.18869 0.512 0.000 0.488 0.000 0.000
#> GSM509718 3 0.6289 0.24963 0.020 0.056 0.592 0.304 0.028
#> GSM509723 5 0.1908 0.88469 0.000 0.092 0.000 0.000 0.908
#> GSM509728 1 0.4036 0.48689 0.788 0.000 0.144 0.000 0.068
#> GSM509732 3 0.5250 0.44473 0.416 0.000 0.536 0.000 0.048
#> GSM509736 3 0.1478 0.60743 0.064 0.000 0.936 0.000 0.000
#> GSM509741 3 0.3289 0.60914 0.108 0.000 0.844 0.000 0.048
#> GSM509746 3 0.5365 0.43792 0.416 0.000 0.528 0.000 0.056
#> GSM509733 3 0.5250 0.44473 0.416 0.000 0.536 0.000 0.048
#> GSM509737 3 0.1478 0.60743 0.064 0.000 0.936 0.000 0.000
#> GSM509742 3 0.2645 0.61477 0.068 0.000 0.888 0.000 0.044
#> GSM509747 3 0.5250 0.44473 0.416 0.000 0.536 0.000 0.048
#> GSM509734 3 0.5250 0.44473 0.416 0.000 0.536 0.000 0.048
#> GSM509738 3 0.3569 0.54009 0.068 0.000 0.828 0.000 0.104
#> GSM509743 3 0.1478 0.60743 0.064 0.000 0.936 0.000 0.000
#> GSM509748 3 0.3835 0.59409 0.156 0.000 0.796 0.000 0.048
#> GSM509735 1 0.2770 0.56785 0.880 0.000 0.044 0.000 0.076
#> GSM509739 1 0.5452 0.26646 0.492 0.000 0.448 0.000 0.060
#> GSM509744 3 0.1478 0.60743 0.064 0.000 0.936 0.000 0.000
#> GSM509749 3 0.6028 0.36281 0.416 0.000 0.468 0.000 0.116
#> GSM509740 3 0.3861 0.51031 0.068 0.000 0.804 0.000 0.128
#> GSM509745 3 0.3056 0.56374 0.068 0.000 0.864 0.000 0.068
#> GSM509750 1 0.5985 -0.32552 0.480 0.000 0.408 0.000 0.112
#> GSM509751 2 0.0000 0.91439 0.000 1.000 0.000 0.000 0.000
#> GSM509753 2 0.0000 0.91439 0.000 1.000 0.000 0.000 0.000
#> GSM509755 2 0.0000 0.91439 0.000 1.000 0.000 0.000 0.000
#> GSM509757 2 0.0290 0.91477 0.000 0.992 0.000 0.008 0.000
#> GSM509759 2 0.0000 0.91439 0.000 1.000 0.000 0.000 0.000
#> GSM509761 2 0.0880 0.90649 0.000 0.968 0.000 0.032 0.000
#> GSM509763 2 0.4161 0.30792 0.000 0.608 0.000 0.392 0.000
#> GSM509765 4 0.2852 0.77042 0.000 0.172 0.000 0.828 0.000
#> GSM509767 2 0.0000 0.91439 0.000 1.000 0.000 0.000 0.000
#> GSM509769 2 0.1608 0.88297 0.000 0.928 0.000 0.072 0.000
#> GSM509771 2 0.0404 0.91413 0.000 0.988 0.000 0.012 0.000
#> GSM509773 2 0.2280 0.84278 0.000 0.880 0.000 0.120 0.000
#> GSM509775 2 0.2377 0.83024 0.000 0.872 0.000 0.128 0.000
#> GSM509777 4 0.1792 0.83275 0.000 0.084 0.000 0.916 0.000
#> GSM509779 4 0.0510 0.85693 0.000 0.016 0.000 0.984 0.000
#> GSM509781 4 0.0404 0.85430 0.000 0.012 0.000 0.988 0.000
#> GSM509783 4 0.0510 0.85693 0.000 0.016 0.000 0.984 0.000
#> GSM509785 4 0.0290 0.85091 0.000 0.008 0.000 0.992 0.000
#> GSM509752 2 0.0162 0.91511 0.000 0.996 0.000 0.004 0.000
#> GSM509754 2 0.0162 0.91490 0.000 0.996 0.000 0.004 0.000
#> GSM509756 2 0.0290 0.91482 0.000 0.992 0.000 0.008 0.000
#> GSM509758 2 0.0290 0.91488 0.000 0.992 0.000 0.008 0.000
#> GSM509760 2 0.1732 0.87035 0.000 0.920 0.000 0.080 0.000
#> GSM509762 2 0.0162 0.91511 0.000 0.996 0.000 0.004 0.000
#> GSM509764 2 0.3039 0.73068 0.000 0.808 0.192 0.000 0.000
#> GSM509766 4 0.3932 0.54764 0.000 0.328 0.000 0.672 0.000
#> GSM509768 2 0.4294 0.04307 0.000 0.532 0.000 0.468 0.000
#> GSM509770 2 0.1270 0.89568 0.000 0.948 0.000 0.052 0.000
#> GSM509772 2 0.0000 0.91439 0.000 1.000 0.000 0.000 0.000
#> GSM509774 4 0.0609 0.85671 0.000 0.020 0.000 0.980 0.000
#> GSM509776 4 0.3816 0.59985 0.000 0.304 0.000 0.696 0.000
#> GSM509778 4 0.0510 0.85693 0.000 0.016 0.000 0.984 0.000
#> GSM509780 4 0.3857 0.57466 0.000 0.312 0.000 0.688 0.000
#> GSM509782 4 0.0510 0.85693 0.000 0.016 0.000 0.984 0.000
#> GSM509784 4 0.0794 0.85509 0.000 0.028 0.000 0.972 0.000
#> GSM509786 4 0.0510 0.85693 0.000 0.016 0.000 0.984 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM509706 1 0.0260 0.819514 0.992 0.000 0.008 0.000 0.000 0.000
#> GSM509711 5 0.4281 0.742393 0.132 0.000 0.000 0.000 0.732 0.136
#> GSM509714 5 0.3023 0.809700 0.008 0.000 0.000 0.004 0.808 0.180
#> GSM509719 5 0.0632 0.867763 0.000 0.024 0.000 0.000 0.976 0.000
#> GSM509724 1 0.1124 0.794958 0.956 0.000 0.036 0.000 0.000 0.008
#> GSM509729 5 0.0767 0.869139 0.008 0.004 0.012 0.000 0.976 0.000
#> GSM509707 1 0.0260 0.819514 0.992 0.000 0.008 0.000 0.000 0.000
#> GSM509712 5 0.4619 0.749795 0.048 0.052 0.000 0.000 0.732 0.168
#> GSM509715 4 0.6776 -0.033460 0.008 0.028 0.000 0.404 0.312 0.248
#> GSM509720 5 0.0405 0.872801 0.000 0.008 0.000 0.000 0.988 0.004
#> GSM509725 3 0.4407 0.129005 0.484 0.000 0.492 0.000 0.000 0.024
#> GSM509730 5 0.1053 0.864298 0.000 0.012 0.020 0.000 0.964 0.004
#> GSM509708 1 0.0000 0.817161 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509713 1 0.6963 0.104783 0.396 0.000 0.116 0.000 0.360 0.128
#> GSM509716 5 0.3900 0.787884 0.008 0.004 0.000 0.032 0.760 0.196
#> GSM509721 5 0.0692 0.869410 0.000 0.020 0.000 0.000 0.976 0.004
#> GSM509726 3 0.6112 0.250806 0.300 0.000 0.368 0.000 0.000 0.332
#> GSM509731 4 0.4851 0.552177 0.008 0.000 0.000 0.672 0.100 0.220
#> GSM509709 1 0.0291 0.819019 0.992 0.000 0.004 0.000 0.004 0.000
#> GSM509717 5 0.5932 0.631055 0.008 0.032 0.000 0.120 0.588 0.252
#> GSM509722 5 0.0260 0.873059 0.000 0.008 0.000 0.000 0.992 0.000
#> GSM509727 3 0.5796 0.417746 0.296 0.000 0.564 0.000 0.036 0.104
#> GSM509710 1 0.3468 0.527643 0.712 0.000 0.004 0.000 0.000 0.284
#> GSM509718 6 0.4783 0.445610 0.000 0.020 0.072 0.184 0.008 0.716
#> GSM509723 5 0.0260 0.873059 0.000 0.008 0.000 0.000 0.992 0.000
#> GSM509728 3 0.5348 0.471251 0.272 0.000 0.576 0.000 0.000 0.152
#> GSM509732 3 0.0458 0.612013 0.000 0.000 0.984 0.000 0.000 0.016
#> GSM509736 6 0.3266 0.761810 0.000 0.000 0.272 0.000 0.000 0.728
#> GSM509741 6 0.3860 0.566013 0.000 0.000 0.472 0.000 0.000 0.528
#> GSM509746 3 0.0146 0.621648 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM509733 3 0.0713 0.603009 0.000 0.000 0.972 0.000 0.000 0.028
#> GSM509737 6 0.3266 0.761810 0.000 0.000 0.272 0.000 0.000 0.728
#> GSM509742 6 0.3864 0.553712 0.000 0.000 0.480 0.000 0.000 0.520
#> GSM509747 3 0.0000 0.620599 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509734 3 0.0000 0.620599 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509738 6 0.3602 0.716073 0.000 0.000 0.208 0.000 0.032 0.760
#> GSM509743 6 0.3330 0.759131 0.000 0.000 0.284 0.000 0.000 0.716
#> GSM509748 3 0.3737 -0.397811 0.000 0.000 0.608 0.000 0.000 0.392
#> GSM509735 3 0.5766 0.401853 0.292 0.000 0.520 0.000 0.004 0.184
#> GSM509739 6 0.4084 0.060472 0.400 0.000 0.012 0.000 0.000 0.588
#> GSM509744 6 0.3330 0.759131 0.000 0.000 0.284 0.000 0.000 0.716
#> GSM509749 3 0.1501 0.615054 0.000 0.000 0.924 0.000 0.000 0.076
#> GSM509740 6 0.3377 0.726292 0.000 0.000 0.188 0.000 0.028 0.784
#> GSM509745 6 0.3109 0.724766 0.004 0.000 0.224 0.000 0.000 0.772
#> GSM509750 3 0.3384 0.519374 0.004 0.000 0.760 0.000 0.008 0.228
#> GSM509751 2 0.0000 0.908524 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509753 2 0.0000 0.908524 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509755 2 0.0000 0.908524 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509757 2 0.0260 0.907041 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM509759 2 0.0000 0.908524 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509761 2 0.0865 0.896735 0.000 0.964 0.000 0.036 0.000 0.000
#> GSM509763 2 0.3804 0.221560 0.000 0.576 0.000 0.424 0.000 0.000
#> GSM509765 4 0.2597 0.746622 0.000 0.176 0.000 0.824 0.000 0.000
#> GSM509767 2 0.0000 0.908524 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509769 2 0.1610 0.866964 0.000 0.916 0.000 0.084 0.000 0.000
#> GSM509771 2 0.0547 0.903499 0.000 0.980 0.000 0.020 0.000 0.000
#> GSM509773 2 0.2092 0.832524 0.000 0.876 0.000 0.124 0.000 0.000
#> GSM509775 2 0.2178 0.819866 0.000 0.868 0.000 0.132 0.000 0.000
#> GSM509777 4 0.1556 0.808109 0.000 0.080 0.000 0.920 0.000 0.000
#> GSM509779 4 0.0146 0.836401 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM509781 4 0.0146 0.836401 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM509783 4 0.0146 0.836401 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM509785 4 0.0000 0.833031 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM509752 2 0.0000 0.908524 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509754 2 0.0000 0.908524 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509756 2 0.0146 0.907595 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM509758 2 0.0000 0.908524 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509760 2 0.1327 0.876660 0.000 0.936 0.000 0.064 0.000 0.000
#> GSM509762 2 0.0000 0.908524 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509764 2 0.3920 0.607730 0.000 0.736 0.048 0.000 0.000 0.216
#> GSM509766 4 0.3531 0.526826 0.000 0.328 0.000 0.672 0.000 0.000
#> GSM509768 2 0.3866 0.000598 0.000 0.516 0.000 0.484 0.000 0.000
#> GSM509770 2 0.1267 0.884161 0.000 0.940 0.000 0.060 0.000 0.000
#> GSM509772 2 0.0000 0.908524 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509774 4 0.0260 0.836108 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM509776 4 0.3428 0.573791 0.000 0.304 0.000 0.696 0.000 0.000
#> GSM509778 4 0.0146 0.836401 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM509780 4 0.3446 0.559679 0.000 0.308 0.000 0.692 0.000 0.000
#> GSM509782 4 0.0146 0.836401 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM509784 4 0.0458 0.834372 0.000 0.016 0.000 0.984 0.000 0.000
#> GSM509786 4 0.0146 0.836401 0.000 0.004 0.000 0.996 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 disease.state(p) time(p) k
#> CV:pam 74 3.66e-13 6.07e-10 2
#> CV:pam 49 2.29e-11 7.46e-09 3
#> CV:pam 58 6.50e-21 1.04e-06 4
#> CV:pam 63 7.92e-21 1.07e-06 5
#> CV:pam 69 1.30e-23 5.06e-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["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 19175 rows and 81 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 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 0.860 0.978 0.988 0.4938 0.503 0.503
#> 3 3 0.621 0.812 0.879 0.3000 0.832 0.673
#> 4 4 0.782 0.851 0.908 0.0938 0.941 0.837
#> 5 5 0.681 0.701 0.798 0.0763 0.917 0.735
#> 6 6 0.667 0.715 0.765 0.0434 0.958 0.827
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
#> GSM509706 1 0.0000 0.995 1.000 0.000
#> GSM509711 1 0.0000 0.995 1.000 0.000
#> GSM509714 1 0.0376 0.993 0.996 0.004
#> GSM509719 1 0.0376 0.993 0.996 0.004
#> GSM509724 1 0.0000 0.995 1.000 0.000
#> GSM509729 1 0.0376 0.993 0.996 0.004
#> GSM509707 1 0.0000 0.995 1.000 0.000
#> GSM509712 1 0.0000 0.995 1.000 0.000
#> GSM509715 1 0.0376 0.993 0.996 0.004
#> GSM509720 1 0.0376 0.993 0.996 0.004
#> GSM509725 1 0.0000 0.995 1.000 0.000
#> GSM509730 1 0.0376 0.993 0.996 0.004
#> GSM509708 1 0.0000 0.995 1.000 0.000
#> GSM509713 1 0.0000 0.995 1.000 0.000
#> GSM509716 1 0.0376 0.993 0.996 0.004
#> GSM509721 1 0.0376 0.993 0.996 0.004
#> GSM509726 1 0.0000 0.995 1.000 0.000
#> GSM509731 1 0.0376 0.993 0.996 0.004
#> GSM509709 1 0.0000 0.995 1.000 0.000
#> GSM509717 1 0.0376 0.993 0.996 0.004
#> GSM509722 1 0.0376 0.993 0.996 0.004
#> GSM509727 1 0.0000 0.995 1.000 0.000
#> GSM509710 1 0.0000 0.995 1.000 0.000
#> GSM509718 1 0.0376 0.993 0.996 0.004
#> GSM509723 1 0.0376 0.993 0.996 0.004
#> GSM509728 1 0.0000 0.995 1.000 0.000
#> GSM509732 1 0.0000 0.995 1.000 0.000
#> GSM509736 1 0.0000 0.995 1.000 0.000
#> GSM509741 1 0.0000 0.995 1.000 0.000
#> GSM509746 1 0.0000 0.995 1.000 0.000
#> GSM509733 1 0.0000 0.995 1.000 0.000
#> GSM509737 1 0.0000 0.995 1.000 0.000
#> GSM509742 1 0.0000 0.995 1.000 0.000
#> GSM509747 1 0.0000 0.995 1.000 0.000
#> GSM509734 1 0.0000 0.995 1.000 0.000
#> GSM509738 1 0.0000 0.995 1.000 0.000
#> GSM509743 1 0.0000 0.995 1.000 0.000
#> GSM509748 1 0.0000 0.995 1.000 0.000
#> GSM509735 1 0.0000 0.995 1.000 0.000
#> GSM509739 1 0.0000 0.995 1.000 0.000
#> GSM509744 1 0.0000 0.995 1.000 0.000
#> GSM509749 1 0.0000 0.995 1.000 0.000
#> GSM509740 1 0.0000 0.995 1.000 0.000
#> GSM509745 1 0.0000 0.995 1.000 0.000
#> GSM509750 1 0.0000 0.995 1.000 0.000
#> GSM509751 2 0.0000 0.978 0.000 1.000
#> GSM509753 2 0.0000 0.978 0.000 1.000
#> GSM509755 2 0.0000 0.978 0.000 1.000
#> GSM509757 2 0.0000 0.978 0.000 1.000
#> GSM509759 2 0.0000 0.978 0.000 1.000
#> GSM509761 2 0.0000 0.978 0.000 1.000
#> GSM509763 2 0.0000 0.978 0.000 1.000
#> GSM509765 2 0.0000 0.978 0.000 1.000
#> GSM509767 2 0.0000 0.978 0.000 1.000
#> GSM509769 2 0.0000 0.978 0.000 1.000
#> GSM509771 2 0.0000 0.978 0.000 1.000
#> GSM509773 2 0.0000 0.978 0.000 1.000
#> GSM509775 2 0.0000 0.978 0.000 1.000
#> GSM509777 2 0.0000 0.978 0.000 1.000
#> GSM509779 2 0.0000 0.978 0.000 1.000
#> GSM509781 2 0.4690 0.908 0.100 0.900
#> GSM509783 2 0.4690 0.908 0.100 0.900
#> GSM509785 2 0.4690 0.908 0.100 0.900
#> GSM509752 2 0.0000 0.978 0.000 1.000
#> GSM509754 2 0.0000 0.978 0.000 1.000
#> GSM509756 2 0.0000 0.978 0.000 1.000
#> GSM509758 2 0.0000 0.978 0.000 1.000
#> GSM509760 2 0.0000 0.978 0.000 1.000
#> GSM509762 2 0.0000 0.978 0.000 1.000
#> GSM509764 1 0.6801 0.774 0.820 0.180
#> GSM509766 2 0.0000 0.978 0.000 1.000
#> GSM509768 2 0.0000 0.978 0.000 1.000
#> GSM509770 2 0.0000 0.978 0.000 1.000
#> GSM509772 2 0.0000 0.978 0.000 1.000
#> GSM509774 2 0.4690 0.908 0.100 0.900
#> GSM509776 2 0.0000 0.978 0.000 1.000
#> GSM509778 2 0.4690 0.908 0.100 0.900
#> GSM509780 2 0.0000 0.978 0.000 1.000
#> GSM509782 2 0.5178 0.891 0.116 0.884
#> GSM509784 2 0.1414 0.966 0.020 0.980
#> GSM509786 2 0.4690 0.908 0.100 0.900
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM509706 1 0.1964 0.7922 0.944 0.000 0.056
#> GSM509711 1 0.2066 0.7919 0.940 0.000 0.060
#> GSM509714 1 0.3112 0.7564 0.900 0.004 0.096
#> GSM509719 1 0.6228 0.3232 0.624 0.004 0.372
#> GSM509724 1 0.2066 0.7918 0.940 0.000 0.060
#> GSM509729 1 0.3349 0.7476 0.888 0.004 0.108
#> GSM509707 1 0.1964 0.7922 0.944 0.000 0.056
#> GSM509712 1 0.1753 0.7866 0.952 0.000 0.048
#> GSM509715 1 0.3500 0.7517 0.880 0.004 0.116
#> GSM509720 1 0.6228 0.3232 0.624 0.004 0.372
#> GSM509725 1 0.2448 0.7915 0.924 0.000 0.076
#> GSM509730 1 0.6264 0.3244 0.616 0.004 0.380
#> GSM509708 1 0.1964 0.7922 0.944 0.000 0.056
#> GSM509713 1 0.2537 0.7907 0.920 0.000 0.080
#> GSM509716 1 0.3500 0.7517 0.880 0.004 0.116
#> GSM509721 1 0.6228 0.3232 0.624 0.004 0.372
#> GSM509726 1 0.2537 0.7907 0.920 0.000 0.080
#> GSM509731 1 0.3500 0.7517 0.880 0.004 0.116
#> GSM509709 1 0.1964 0.7922 0.944 0.000 0.056
#> GSM509717 1 0.3500 0.7517 0.880 0.004 0.116
#> GSM509722 1 0.6228 0.3232 0.624 0.004 0.372
#> GSM509727 1 0.5397 0.5415 0.720 0.000 0.280
#> GSM509710 1 0.2625 0.7916 0.916 0.000 0.084
#> GSM509718 1 0.2711 0.7647 0.912 0.000 0.088
#> GSM509723 1 0.6228 0.3232 0.624 0.004 0.372
#> GSM509728 1 0.5397 0.5434 0.720 0.000 0.280
#> GSM509732 3 0.3482 0.9571 0.128 0.000 0.872
#> GSM509736 3 0.3482 0.9571 0.128 0.000 0.872
#> GSM509741 3 0.3482 0.9571 0.128 0.000 0.872
#> GSM509746 3 0.3482 0.9571 0.128 0.000 0.872
#> GSM509733 3 0.3482 0.9571 0.128 0.000 0.872
#> GSM509737 3 0.3551 0.9550 0.132 0.000 0.868
#> GSM509742 3 0.3482 0.9571 0.128 0.000 0.872
#> GSM509747 3 0.3482 0.9571 0.128 0.000 0.872
#> GSM509734 3 0.5216 0.7731 0.260 0.000 0.740
#> GSM509738 3 0.3941 0.9307 0.156 0.000 0.844
#> GSM509743 3 0.3482 0.9571 0.128 0.000 0.872
#> GSM509748 3 0.3482 0.9571 0.128 0.000 0.872
#> GSM509735 1 0.2066 0.7918 0.940 0.000 0.060
#> GSM509739 1 0.2537 0.7907 0.920 0.000 0.080
#> GSM509744 3 0.3551 0.9550 0.132 0.000 0.868
#> GSM509749 3 0.3482 0.9571 0.128 0.000 0.872
#> GSM509740 1 0.6309 -0.0843 0.504 0.000 0.496
#> GSM509745 3 0.5859 0.5586 0.344 0.000 0.656
#> GSM509750 3 0.4002 0.9258 0.160 0.000 0.840
#> GSM509751 2 0.0000 0.9458 0.000 1.000 0.000
#> GSM509753 2 0.0000 0.9458 0.000 1.000 0.000
#> GSM509755 2 0.0000 0.9458 0.000 1.000 0.000
#> GSM509757 2 0.0000 0.9458 0.000 1.000 0.000
#> GSM509759 2 0.0237 0.9445 0.000 0.996 0.004
#> GSM509761 2 0.0000 0.9458 0.000 1.000 0.000
#> GSM509763 2 0.0000 0.9458 0.000 1.000 0.000
#> GSM509765 2 0.0237 0.9450 0.000 0.996 0.004
#> GSM509767 2 0.0000 0.9458 0.000 1.000 0.000
#> GSM509769 2 0.0000 0.9458 0.000 1.000 0.000
#> GSM509771 2 0.0000 0.9458 0.000 1.000 0.000
#> GSM509773 2 0.0000 0.9458 0.000 1.000 0.000
#> GSM509775 2 0.0000 0.9458 0.000 1.000 0.000
#> GSM509777 2 0.1753 0.9273 0.000 0.952 0.048
#> GSM509779 2 0.2959 0.9033 0.000 0.900 0.100
#> GSM509781 2 0.6486 0.7961 0.096 0.760 0.144
#> GSM509783 2 0.8408 0.5749 0.244 0.612 0.144
#> GSM509785 2 0.6975 0.7635 0.124 0.732 0.144
#> GSM509752 2 0.0000 0.9458 0.000 1.000 0.000
#> GSM509754 2 0.0000 0.9458 0.000 1.000 0.000
#> GSM509756 2 0.0000 0.9458 0.000 1.000 0.000
#> GSM509758 2 0.0000 0.9458 0.000 1.000 0.000
#> GSM509760 2 0.0424 0.9442 0.000 0.992 0.008
#> GSM509762 2 0.0000 0.9458 0.000 1.000 0.000
#> GSM509764 2 0.3713 0.8639 0.076 0.892 0.032
#> GSM509766 2 0.0237 0.9450 0.000 0.996 0.004
#> GSM509768 2 0.0000 0.9458 0.000 1.000 0.000
#> GSM509770 2 0.0237 0.9445 0.000 0.996 0.004
#> GSM509772 2 0.0237 0.9445 0.000 0.996 0.004
#> GSM509774 2 0.3267 0.8943 0.000 0.884 0.116
#> GSM509776 2 0.0000 0.9458 0.000 1.000 0.000
#> GSM509778 2 0.6634 0.7873 0.104 0.752 0.144
#> GSM509780 2 0.0237 0.9450 0.000 0.996 0.004
#> GSM509782 2 0.7163 0.7481 0.136 0.720 0.144
#> GSM509784 2 0.3528 0.8994 0.016 0.892 0.092
#> GSM509786 2 0.6486 0.7961 0.096 0.760 0.144
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM509706 1 0.4904 0.671 0.744 0.000 0.040 0.216
#> GSM509711 4 0.5420 0.771 0.272 0.000 0.044 0.684
#> GSM509714 4 0.4955 0.798 0.268 0.000 0.024 0.708
#> GSM509719 1 0.0000 0.838 1.000 0.000 0.000 0.000
#> GSM509724 1 0.2036 0.854 0.936 0.000 0.032 0.032
#> GSM509729 1 0.2224 0.849 0.928 0.000 0.032 0.040
#> GSM509707 1 0.3372 0.815 0.868 0.000 0.036 0.096
#> GSM509712 1 0.5807 0.403 0.612 0.000 0.044 0.344
#> GSM509715 4 0.3196 0.885 0.136 0.000 0.008 0.856
#> GSM509720 1 0.0000 0.838 1.000 0.000 0.000 0.000
#> GSM509725 1 0.2214 0.851 0.928 0.000 0.044 0.028
#> GSM509730 1 0.1209 0.851 0.964 0.000 0.032 0.004
#> GSM509708 1 0.3279 0.816 0.872 0.000 0.032 0.096
#> GSM509713 1 0.5830 0.432 0.620 0.000 0.048 0.332
#> GSM509716 4 0.3401 0.885 0.152 0.000 0.008 0.840
#> GSM509721 1 0.0000 0.838 1.000 0.000 0.000 0.000
#> GSM509726 1 0.2483 0.847 0.916 0.000 0.052 0.032
#> GSM509731 4 0.3196 0.885 0.136 0.000 0.008 0.856
#> GSM509709 1 0.3372 0.815 0.868 0.000 0.036 0.096
#> GSM509717 4 0.3196 0.885 0.136 0.000 0.008 0.856
#> GSM509722 1 0.0000 0.838 1.000 0.000 0.000 0.000
#> GSM509727 1 0.6005 0.453 0.616 0.000 0.324 0.060
#> GSM509710 1 0.2214 0.851 0.928 0.000 0.044 0.028
#> GSM509718 4 0.5457 0.811 0.184 0.000 0.088 0.728
#> GSM509723 1 0.0000 0.838 1.000 0.000 0.000 0.000
#> GSM509728 1 0.5172 0.587 0.704 0.000 0.260 0.036
#> GSM509732 3 0.0000 0.936 0.000 0.000 1.000 0.000
#> GSM509736 3 0.0000 0.936 0.000 0.000 1.000 0.000
#> GSM509741 3 0.0000 0.936 0.000 0.000 1.000 0.000
#> GSM509746 3 0.0000 0.936 0.000 0.000 1.000 0.000
#> GSM509733 3 0.0000 0.936 0.000 0.000 1.000 0.000
#> GSM509737 3 0.0188 0.935 0.004 0.000 0.996 0.000
#> GSM509742 3 0.0000 0.936 0.000 0.000 1.000 0.000
#> GSM509747 3 0.0000 0.936 0.000 0.000 1.000 0.000
#> GSM509734 3 0.3300 0.801 0.144 0.000 0.848 0.008
#> GSM509738 3 0.1970 0.892 0.060 0.000 0.932 0.008
#> GSM509743 3 0.0000 0.936 0.000 0.000 1.000 0.000
#> GSM509748 3 0.0000 0.936 0.000 0.000 1.000 0.000
#> GSM509735 1 0.2131 0.852 0.932 0.000 0.036 0.032
#> GSM509739 1 0.2300 0.850 0.924 0.000 0.048 0.028
#> GSM509744 3 0.0376 0.933 0.004 0.000 0.992 0.004
#> GSM509749 3 0.0000 0.936 0.000 0.000 1.000 0.000
#> GSM509740 3 0.3852 0.748 0.180 0.000 0.808 0.012
#> GSM509745 3 0.2676 0.859 0.092 0.000 0.896 0.012
#> GSM509750 3 0.4360 0.642 0.248 0.000 0.744 0.008
#> GSM509751 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM509753 2 0.0336 0.931 0.000 0.992 0.000 0.008
#> GSM509755 2 0.1022 0.923 0.000 0.968 0.000 0.032
#> GSM509757 2 0.0921 0.925 0.000 0.972 0.000 0.028
#> GSM509759 2 0.1305 0.920 0.004 0.960 0.000 0.036
#> GSM509761 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM509763 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM509765 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM509767 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM509769 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM509771 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM509773 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM509775 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM509777 2 0.0817 0.925 0.000 0.976 0.000 0.024
#> GSM509779 2 0.2704 0.871 0.000 0.876 0.000 0.124
#> GSM509781 2 0.4193 0.746 0.000 0.732 0.000 0.268
#> GSM509783 2 0.4830 0.560 0.000 0.608 0.000 0.392
#> GSM509785 2 0.4331 0.723 0.000 0.712 0.000 0.288
#> GSM509752 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM509754 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM509756 2 0.0707 0.928 0.000 0.980 0.000 0.020
#> GSM509758 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM509760 2 0.0921 0.925 0.000 0.972 0.000 0.028
#> GSM509762 2 0.0469 0.930 0.000 0.988 0.000 0.012
#> GSM509764 2 0.3295 0.867 0.008 0.884 0.072 0.036
#> GSM509766 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM509768 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM509770 2 0.0921 0.925 0.000 0.972 0.000 0.028
#> GSM509772 2 0.1118 0.921 0.000 0.964 0.000 0.036
#> GSM509774 2 0.2345 0.887 0.000 0.900 0.000 0.100
#> GSM509776 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM509778 2 0.4193 0.746 0.000 0.732 0.000 0.268
#> GSM509780 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM509782 2 0.4564 0.668 0.000 0.672 0.000 0.328
#> GSM509784 2 0.2408 0.884 0.000 0.896 0.000 0.104
#> GSM509786 2 0.4250 0.737 0.000 0.724 0.000 0.276
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM509706 1 0.3059 0.5481 0.860 0.000 0.028 0.004 0.108
#> GSM509711 1 0.5134 -0.0784 0.664 0.000 0.020 0.036 0.280
#> GSM509714 5 0.5161 0.8555 0.432 0.000 0.004 0.032 0.532
#> GSM509719 1 0.4730 0.1757 0.568 0.000 0.004 0.012 0.416
#> GSM509724 1 0.1808 0.6027 0.936 0.000 0.044 0.008 0.012
#> GSM509729 1 0.4240 0.2191 0.684 0.000 0.004 0.008 0.304
#> GSM509707 1 0.2846 0.5858 0.884 0.000 0.028 0.012 0.076
#> GSM509712 1 0.5269 -0.1976 0.608 0.000 0.028 0.020 0.344
#> GSM509715 5 0.5591 0.9322 0.396 0.000 0.000 0.076 0.528
#> GSM509720 1 0.4730 0.1757 0.568 0.000 0.004 0.012 0.416
#> GSM509725 1 0.1197 0.6021 0.952 0.000 0.048 0.000 0.000
#> GSM509730 1 0.4502 0.2038 0.668 0.000 0.012 0.008 0.312
#> GSM509708 1 0.2727 0.5804 0.888 0.000 0.020 0.012 0.080
#> GSM509713 1 0.4251 0.3636 0.784 0.000 0.028 0.028 0.160
#> GSM509716 5 0.5550 0.9294 0.400 0.000 0.000 0.072 0.528
#> GSM509721 1 0.4722 0.1750 0.572 0.000 0.004 0.012 0.412
#> GSM509726 1 0.1557 0.5978 0.940 0.000 0.052 0.000 0.008
#> GSM509731 5 0.5591 0.9322 0.396 0.000 0.000 0.076 0.528
#> GSM509709 1 0.2727 0.5803 0.888 0.000 0.020 0.012 0.080
#> GSM509717 5 0.5591 0.9322 0.396 0.000 0.000 0.076 0.528
#> GSM509722 1 0.4730 0.1757 0.568 0.000 0.004 0.012 0.416
#> GSM509727 1 0.3934 0.4443 0.796 0.000 0.160 0.008 0.036
#> GSM509710 1 0.1270 0.6011 0.948 0.000 0.052 0.000 0.000
#> GSM509718 5 0.6617 0.7817 0.392 0.000 0.084 0.044 0.480
#> GSM509723 1 0.4730 0.1757 0.568 0.000 0.004 0.012 0.416
#> GSM509728 1 0.3183 0.4796 0.828 0.000 0.156 0.000 0.016
#> GSM509732 3 0.1836 0.8694 0.036 0.000 0.932 0.000 0.032
#> GSM509736 3 0.0290 0.8664 0.008 0.000 0.992 0.000 0.000
#> GSM509741 3 0.0324 0.8651 0.004 0.000 0.992 0.000 0.004
#> GSM509746 3 0.1918 0.8686 0.036 0.000 0.928 0.000 0.036
#> GSM509733 3 0.1836 0.8694 0.036 0.000 0.932 0.000 0.032
#> GSM509737 3 0.0290 0.8664 0.008 0.000 0.992 0.000 0.000
#> GSM509742 3 0.0324 0.8651 0.004 0.000 0.992 0.000 0.004
#> GSM509747 3 0.2078 0.8675 0.036 0.000 0.924 0.004 0.036
#> GSM509734 3 0.2787 0.8151 0.136 0.000 0.856 0.004 0.004
#> GSM509738 3 0.3766 0.6084 0.268 0.000 0.728 0.000 0.004
#> GSM509743 3 0.0324 0.8651 0.004 0.000 0.992 0.000 0.004
#> GSM509748 3 0.1836 0.8688 0.036 0.000 0.932 0.000 0.032
#> GSM509735 1 0.1357 0.6016 0.948 0.000 0.048 0.000 0.004
#> GSM509739 1 0.1430 0.6000 0.944 0.000 0.052 0.000 0.004
#> GSM509744 3 0.0451 0.8659 0.008 0.000 0.988 0.000 0.004
#> GSM509749 3 0.2067 0.8664 0.048 0.000 0.920 0.000 0.032
#> GSM509740 3 0.4366 0.4995 0.320 0.000 0.664 0.000 0.016
#> GSM509745 3 0.3814 0.5966 0.276 0.000 0.720 0.000 0.004
#> GSM509750 3 0.4425 0.3810 0.392 0.000 0.600 0.000 0.008
#> GSM509751 2 0.2249 0.8519 0.000 0.896 0.000 0.008 0.096
#> GSM509753 2 0.2074 0.8524 0.000 0.896 0.000 0.000 0.104
#> GSM509755 2 0.2707 0.8420 0.000 0.876 0.000 0.024 0.100
#> GSM509757 2 0.2505 0.8491 0.000 0.888 0.000 0.020 0.092
#> GSM509759 2 0.3569 0.8008 0.000 0.828 0.000 0.068 0.104
#> GSM509761 2 0.1282 0.8709 0.000 0.952 0.000 0.004 0.044
#> GSM509763 2 0.2674 0.8229 0.000 0.856 0.000 0.004 0.140
#> GSM509765 2 0.3039 0.8120 0.000 0.836 0.000 0.012 0.152
#> GSM509767 2 0.1043 0.8755 0.000 0.960 0.000 0.000 0.040
#> GSM509769 2 0.0324 0.8776 0.000 0.992 0.000 0.004 0.004
#> GSM509771 2 0.1043 0.8755 0.000 0.960 0.000 0.000 0.040
#> GSM509773 2 0.1195 0.8736 0.000 0.960 0.000 0.012 0.028
#> GSM509775 2 0.1282 0.8709 0.000 0.952 0.000 0.004 0.044
#> GSM509777 2 0.4569 0.6942 0.000 0.748 0.000 0.104 0.148
#> GSM509779 4 0.5915 0.6673 0.000 0.324 0.000 0.552 0.124
#> GSM509781 4 0.2813 0.8793 0.000 0.168 0.000 0.832 0.000
#> GSM509783 4 0.4293 0.8416 0.028 0.156 0.000 0.784 0.032
#> GSM509785 4 0.2930 0.8766 0.000 0.164 0.000 0.832 0.004
#> GSM509752 2 0.1357 0.8749 0.000 0.948 0.000 0.004 0.048
#> GSM509754 2 0.1043 0.8755 0.000 0.960 0.000 0.000 0.040
#> GSM509756 2 0.1082 0.8771 0.000 0.964 0.000 0.008 0.028
#> GSM509758 2 0.0451 0.8775 0.000 0.988 0.000 0.008 0.004
#> GSM509760 2 0.2825 0.8345 0.000 0.860 0.000 0.016 0.124
#> GSM509762 2 0.1331 0.8744 0.000 0.952 0.000 0.008 0.040
#> GSM509764 2 0.6070 0.6021 0.048 0.672 0.016 0.200 0.064
#> GSM509766 2 0.2929 0.8113 0.000 0.840 0.000 0.008 0.152
#> GSM509768 2 0.2929 0.8113 0.000 0.840 0.000 0.008 0.152
#> GSM509770 2 0.0798 0.8783 0.000 0.976 0.000 0.016 0.008
#> GSM509772 2 0.3012 0.8306 0.000 0.860 0.000 0.036 0.104
#> GSM509774 4 0.5720 0.7481 0.000 0.276 0.000 0.600 0.124
#> GSM509776 2 0.2886 0.8131 0.000 0.844 0.000 0.008 0.148
#> GSM509778 4 0.2852 0.8782 0.000 0.172 0.000 0.828 0.000
#> GSM509780 2 0.3098 0.8066 0.000 0.836 0.000 0.016 0.148
#> GSM509782 4 0.3863 0.8512 0.000 0.152 0.000 0.796 0.052
#> GSM509784 4 0.5834 0.7317 0.000 0.284 0.000 0.584 0.132
#> GSM509786 4 0.2813 0.8793 0.000 0.168 0.000 0.832 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM509706 1 0.4505 0.843 0.612 0.000 0.008 0.004 0.356 0.020
#> GSM509711 1 0.5674 0.674 0.536 0.000 0.004 0.012 0.340 0.108
#> GSM509714 5 0.4923 0.311 0.200 0.000 0.000 0.008 0.672 0.120
#> GSM509719 5 0.0260 0.624 0.000 0.000 0.000 0.008 0.992 0.000
#> GSM509724 1 0.4410 0.867 0.640 0.000 0.008 0.004 0.328 0.020
#> GSM509729 5 0.3758 0.397 0.284 0.000 0.000 0.000 0.700 0.016
#> GSM509707 1 0.4344 0.802 0.568 0.000 0.008 0.000 0.412 0.012
#> GSM509712 5 0.5071 0.221 0.340 0.000 0.004 0.008 0.588 0.060
#> GSM509715 6 0.6659 1.000 0.336 0.000 0.000 0.028 0.292 0.344
#> GSM509720 5 0.0000 0.629 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM509725 1 0.3634 0.875 0.696 0.000 0.008 0.000 0.296 0.000
#> GSM509730 5 0.3420 0.485 0.240 0.000 0.000 0.000 0.748 0.012
#> GSM509708 1 0.4158 0.799 0.572 0.000 0.004 0.000 0.416 0.008
#> GSM509713 1 0.4736 0.835 0.644 0.000 0.004 0.012 0.300 0.040
#> GSM509716 6 0.6659 1.000 0.336 0.000 0.000 0.028 0.292 0.344
#> GSM509721 5 0.0363 0.621 0.000 0.000 0.000 0.012 0.988 0.000
#> GSM509726 1 0.3690 0.874 0.700 0.000 0.012 0.000 0.288 0.000
#> GSM509731 6 0.6659 1.000 0.336 0.000 0.000 0.028 0.292 0.344
#> GSM509709 1 0.4242 0.801 0.572 0.000 0.004 0.000 0.412 0.012
#> GSM509717 6 0.6659 1.000 0.336 0.000 0.000 0.028 0.292 0.344
#> GSM509722 5 0.0000 0.629 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM509727 1 0.4405 0.842 0.688 0.000 0.036 0.004 0.264 0.008
#> GSM509710 1 0.3972 0.874 0.680 0.000 0.016 0.004 0.300 0.000
#> GSM509718 5 0.7316 -0.694 0.296 0.000 0.048 0.020 0.344 0.292
#> GSM509723 5 0.0000 0.629 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM509728 1 0.4191 0.800 0.704 0.000 0.056 0.000 0.240 0.000
#> GSM509732 3 0.1391 0.757 0.040 0.000 0.944 0.000 0.000 0.016
#> GSM509736 3 0.4639 0.755 0.132 0.000 0.748 0.004 0.040 0.076
#> GSM509741 3 0.3605 0.753 0.108 0.000 0.804 0.004 0.000 0.084
#> GSM509746 3 0.1536 0.755 0.040 0.000 0.940 0.004 0.000 0.016
#> GSM509733 3 0.1367 0.760 0.044 0.000 0.944 0.000 0.000 0.012
#> GSM509737 3 0.4787 0.753 0.128 0.000 0.740 0.004 0.052 0.076
#> GSM509742 3 0.3605 0.753 0.108 0.000 0.804 0.004 0.000 0.084
#> GSM509747 3 0.1268 0.757 0.036 0.000 0.952 0.004 0.000 0.008
#> GSM509734 3 0.4340 0.664 0.200 0.000 0.712 0.000 0.088 0.000
#> GSM509738 3 0.5700 0.449 0.220 0.000 0.564 0.008 0.208 0.000
#> GSM509743 3 0.3649 0.754 0.112 0.000 0.800 0.004 0.000 0.084
#> GSM509748 3 0.1734 0.760 0.048 0.000 0.932 0.004 0.008 0.008
#> GSM509735 1 0.3595 0.874 0.704 0.000 0.008 0.000 0.288 0.000
#> GSM509739 1 0.3690 0.874 0.700 0.000 0.012 0.000 0.288 0.000
#> GSM509744 3 0.4715 0.754 0.140 0.000 0.740 0.004 0.040 0.076
#> GSM509749 3 0.2308 0.760 0.056 0.000 0.904 0.004 0.028 0.008
#> GSM509740 3 0.6013 0.260 0.260 0.000 0.496 0.008 0.236 0.000
#> GSM509745 3 0.5780 0.420 0.236 0.000 0.548 0.008 0.208 0.000
#> GSM509750 3 0.5757 0.401 0.244 0.000 0.536 0.004 0.216 0.000
#> GSM509751 2 0.3531 0.678 0.000 0.672 0.000 0.000 0.000 0.328
#> GSM509753 2 0.3647 0.656 0.000 0.640 0.000 0.000 0.000 0.360
#> GSM509755 2 0.3807 0.649 0.000 0.628 0.000 0.004 0.000 0.368
#> GSM509757 2 0.3795 0.652 0.000 0.632 0.000 0.004 0.000 0.364
#> GSM509759 2 0.4964 0.569 0.000 0.540 0.000 0.072 0.000 0.388
#> GSM509761 2 0.0935 0.789 0.000 0.964 0.000 0.004 0.000 0.032
#> GSM509763 2 0.2520 0.736 0.000 0.844 0.000 0.004 0.000 0.152
#> GSM509765 2 0.3017 0.718 0.000 0.816 0.000 0.020 0.000 0.164
#> GSM509767 2 0.1387 0.792 0.000 0.932 0.000 0.000 0.000 0.068
#> GSM509769 2 0.0260 0.791 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM509771 2 0.1075 0.794 0.000 0.952 0.000 0.000 0.000 0.048
#> GSM509773 2 0.1007 0.786 0.000 0.956 0.000 0.000 0.000 0.044
#> GSM509775 2 0.1327 0.780 0.000 0.936 0.000 0.000 0.000 0.064
#> GSM509777 2 0.5028 0.519 0.004 0.656 0.000 0.176 0.000 0.164
#> GSM509779 4 0.5135 0.739 0.004 0.216 0.000 0.636 0.000 0.144
#> GSM509781 4 0.1957 0.913 0.000 0.112 0.000 0.888 0.000 0.000
#> GSM509783 4 0.2101 0.904 0.004 0.100 0.000 0.892 0.000 0.004
#> GSM509785 4 0.2006 0.909 0.004 0.104 0.000 0.892 0.000 0.000
#> GSM509752 2 0.1910 0.785 0.000 0.892 0.000 0.000 0.000 0.108
#> GSM509754 2 0.1141 0.794 0.000 0.948 0.000 0.000 0.000 0.052
#> GSM509756 2 0.2597 0.762 0.000 0.824 0.000 0.000 0.000 0.176
#> GSM509758 2 0.0603 0.795 0.000 0.980 0.000 0.004 0.000 0.016
#> GSM509760 2 0.2454 0.779 0.000 0.840 0.000 0.000 0.000 0.160
#> GSM509762 2 0.2340 0.773 0.000 0.852 0.000 0.000 0.000 0.148
#> GSM509764 2 0.6942 0.417 0.016 0.436 0.024 0.204 0.008 0.312
#> GSM509766 2 0.2743 0.727 0.000 0.828 0.000 0.008 0.000 0.164
#> GSM509768 2 0.2558 0.733 0.000 0.840 0.000 0.004 0.000 0.156
#> GSM509770 2 0.1663 0.791 0.000 0.912 0.000 0.000 0.000 0.088
#> GSM509772 2 0.4131 0.626 0.000 0.600 0.000 0.016 0.000 0.384
#> GSM509774 4 0.4490 0.844 0.004 0.148 0.000 0.720 0.000 0.128
#> GSM509776 2 0.2491 0.732 0.000 0.836 0.000 0.000 0.000 0.164
#> GSM509778 4 0.1957 0.913 0.000 0.112 0.000 0.888 0.000 0.000
#> GSM509780 2 0.2743 0.725 0.000 0.828 0.000 0.008 0.000 0.164
#> GSM509782 4 0.2070 0.905 0.008 0.100 0.000 0.892 0.000 0.000
#> GSM509784 4 0.4771 0.815 0.004 0.164 0.000 0.688 0.000 0.144
#> GSM509786 4 0.1957 0.913 0.000 0.112 0.000 0.888 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 disease.state(p) time(p) k
#> CV:mclust 81 1.87e-17 1.38e-14 2
#> CV:mclust 74 6.00e-28 2.93e-11 3
#> CV:mclust 78 2.73e-28 7.14e-10 4
#> CV:mclust 67 3.26e-22 1.19e-06 5
#> CV:mclust 71 1.15e-22 4.08e-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", "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 19175 rows and 81 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 1.000 0.998 0.999 0.5061 0.494 0.494
#> 3 3 0.718 0.814 0.903 0.2527 0.819 0.649
#> 4 4 0.741 0.803 0.888 0.1750 0.799 0.498
#> 5 5 0.717 0.642 0.797 0.0566 0.976 0.901
#> 6 6 0.756 0.716 0.841 0.0364 0.932 0.707
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
#> GSM509706 1 0.0000 1.000 1.000 0.000
#> GSM509711 1 0.0000 1.000 1.000 0.000
#> GSM509714 2 0.3431 0.932 0.064 0.936
#> GSM509719 1 0.0000 1.000 1.000 0.000
#> GSM509724 1 0.0000 1.000 1.000 0.000
#> GSM509729 1 0.0000 1.000 1.000 0.000
#> GSM509707 1 0.0000 1.000 1.000 0.000
#> GSM509712 1 0.0000 1.000 1.000 0.000
#> GSM509715 2 0.0000 0.998 0.000 1.000
#> GSM509720 1 0.0000 1.000 1.000 0.000
#> GSM509725 1 0.0000 1.000 1.000 0.000
#> GSM509730 1 0.0000 1.000 1.000 0.000
#> GSM509708 1 0.0000 1.000 1.000 0.000
#> GSM509713 1 0.0000 1.000 1.000 0.000
#> GSM509716 2 0.0000 0.998 0.000 1.000
#> GSM509721 1 0.0000 1.000 1.000 0.000
#> GSM509726 1 0.0000 1.000 1.000 0.000
#> GSM509731 2 0.0000 0.998 0.000 1.000
#> GSM509709 1 0.0000 1.000 1.000 0.000
#> GSM509717 2 0.0000 0.998 0.000 1.000
#> GSM509722 1 0.1184 0.984 0.984 0.016
#> GSM509727 1 0.0000 1.000 1.000 0.000
#> GSM509710 1 0.0000 1.000 1.000 0.000
#> GSM509718 2 0.0672 0.991 0.008 0.992
#> GSM509723 1 0.0000 1.000 1.000 0.000
#> GSM509728 1 0.0000 1.000 1.000 0.000
#> GSM509732 1 0.0000 1.000 1.000 0.000
#> GSM509736 1 0.0000 1.000 1.000 0.000
#> GSM509741 1 0.0000 1.000 1.000 0.000
#> GSM509746 1 0.0000 1.000 1.000 0.000
#> GSM509733 1 0.0000 1.000 1.000 0.000
#> GSM509737 1 0.0000 1.000 1.000 0.000
#> GSM509742 1 0.0000 1.000 1.000 0.000
#> GSM509747 1 0.0000 1.000 1.000 0.000
#> GSM509734 1 0.0000 1.000 1.000 0.000
#> GSM509738 1 0.0000 1.000 1.000 0.000
#> GSM509743 1 0.0000 1.000 1.000 0.000
#> GSM509748 1 0.0000 1.000 1.000 0.000
#> GSM509735 1 0.0000 1.000 1.000 0.000
#> GSM509739 1 0.0000 1.000 1.000 0.000
#> GSM509744 1 0.0000 1.000 1.000 0.000
#> GSM509749 1 0.0000 1.000 1.000 0.000
#> GSM509740 1 0.0000 1.000 1.000 0.000
#> GSM509745 1 0.0000 1.000 1.000 0.000
#> GSM509750 1 0.0000 1.000 1.000 0.000
#> GSM509751 2 0.0000 0.998 0.000 1.000
#> GSM509753 2 0.0000 0.998 0.000 1.000
#> GSM509755 2 0.0000 0.998 0.000 1.000
#> GSM509757 2 0.0000 0.998 0.000 1.000
#> GSM509759 2 0.0376 0.995 0.004 0.996
#> GSM509761 2 0.0000 0.998 0.000 1.000
#> GSM509763 2 0.0000 0.998 0.000 1.000
#> GSM509765 2 0.0000 0.998 0.000 1.000
#> GSM509767 2 0.0000 0.998 0.000 1.000
#> GSM509769 2 0.0000 0.998 0.000 1.000
#> GSM509771 2 0.0000 0.998 0.000 1.000
#> GSM509773 2 0.0000 0.998 0.000 1.000
#> GSM509775 2 0.0000 0.998 0.000 1.000
#> GSM509777 2 0.0000 0.998 0.000 1.000
#> GSM509779 2 0.0000 0.998 0.000 1.000
#> GSM509781 2 0.0000 0.998 0.000 1.000
#> GSM509783 2 0.0000 0.998 0.000 1.000
#> GSM509785 2 0.0000 0.998 0.000 1.000
#> GSM509752 2 0.0000 0.998 0.000 1.000
#> GSM509754 2 0.0000 0.998 0.000 1.000
#> GSM509756 2 0.0000 0.998 0.000 1.000
#> GSM509758 2 0.0000 0.998 0.000 1.000
#> GSM509760 2 0.0000 0.998 0.000 1.000
#> GSM509762 2 0.0000 0.998 0.000 1.000
#> GSM509764 2 0.0000 0.998 0.000 1.000
#> GSM509766 2 0.0000 0.998 0.000 1.000
#> GSM509768 2 0.0000 0.998 0.000 1.000
#> GSM509770 2 0.0000 0.998 0.000 1.000
#> GSM509772 2 0.0000 0.998 0.000 1.000
#> GSM509774 2 0.0000 0.998 0.000 1.000
#> GSM509776 2 0.0000 0.998 0.000 1.000
#> GSM509778 2 0.0000 0.998 0.000 1.000
#> GSM509780 2 0.0000 0.998 0.000 1.000
#> GSM509782 2 0.0000 0.998 0.000 1.000
#> GSM509784 2 0.0000 0.998 0.000 1.000
#> GSM509786 2 0.0000 0.998 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM509706 1 0.0424 0.931 0.992 0.000 0.008
#> GSM509711 1 0.0661 0.927 0.988 0.004 0.008
#> GSM509714 1 0.3965 0.733 0.860 0.132 0.008
#> GSM509719 1 0.0237 0.934 0.996 0.000 0.004
#> GSM509724 1 0.0237 0.934 0.996 0.000 0.004
#> GSM509729 1 0.0424 0.931 0.992 0.000 0.008
#> GSM509707 1 0.0237 0.934 0.996 0.000 0.004
#> GSM509712 1 0.0424 0.931 0.992 0.000 0.008
#> GSM509715 2 0.2774 0.864 0.072 0.920 0.008
#> GSM509720 1 0.0424 0.931 0.992 0.000 0.008
#> GSM509725 1 0.1031 0.923 0.976 0.000 0.024
#> GSM509730 1 0.0237 0.934 0.996 0.000 0.004
#> GSM509708 1 0.0000 0.934 1.000 0.000 0.000
#> GSM509713 1 0.0424 0.931 0.992 0.000 0.008
#> GSM509716 2 0.4353 0.770 0.156 0.836 0.008
#> GSM509721 1 0.0237 0.934 0.996 0.000 0.004
#> GSM509726 1 0.0237 0.934 0.996 0.000 0.004
#> GSM509731 2 0.5420 0.651 0.240 0.752 0.008
#> GSM509709 1 0.0000 0.934 1.000 0.000 0.000
#> GSM509717 2 0.5580 0.625 0.256 0.736 0.008
#> GSM509722 1 0.0848 0.923 0.984 0.008 0.008
#> GSM509727 1 0.0237 0.934 0.996 0.000 0.004
#> GSM509710 1 0.0592 0.931 0.988 0.000 0.012
#> GSM509718 2 0.0000 0.926 0.000 1.000 0.000
#> GSM509723 1 0.0000 0.934 1.000 0.000 0.000
#> GSM509728 1 0.1860 0.897 0.948 0.000 0.052
#> GSM509732 3 0.5138 0.721 0.252 0.000 0.748
#> GSM509736 3 0.3941 0.717 0.156 0.000 0.844
#> GSM509741 3 0.4062 0.733 0.164 0.000 0.836
#> GSM509746 3 0.4702 0.734 0.212 0.000 0.788
#> GSM509733 3 0.4842 0.732 0.224 0.000 0.776
#> GSM509737 3 0.6225 0.450 0.432 0.000 0.568
#> GSM509742 3 0.5138 0.721 0.252 0.000 0.748
#> GSM509747 3 0.5431 0.690 0.284 0.000 0.716
#> GSM509734 1 0.5810 0.346 0.664 0.000 0.336
#> GSM509738 1 0.4002 0.751 0.840 0.000 0.160
#> GSM509743 3 0.1031 0.690 0.024 0.000 0.976
#> GSM509748 3 0.5216 0.715 0.260 0.000 0.740
#> GSM509735 1 0.0892 0.926 0.980 0.000 0.020
#> GSM509739 1 0.0237 0.934 0.996 0.000 0.004
#> GSM509744 3 0.6291 0.352 0.468 0.000 0.532
#> GSM509749 3 0.6126 0.514 0.400 0.000 0.600
#> GSM509740 1 0.0892 0.926 0.980 0.000 0.020
#> GSM509745 1 0.2959 0.839 0.900 0.000 0.100
#> GSM509750 1 0.5968 0.263 0.636 0.000 0.364
#> GSM509751 2 0.6111 0.478 0.000 0.604 0.396
#> GSM509753 3 0.5058 0.467 0.000 0.244 0.756
#> GSM509755 2 0.6267 0.345 0.000 0.548 0.452
#> GSM509757 2 0.4346 0.802 0.000 0.816 0.184
#> GSM509759 3 0.4842 0.506 0.000 0.224 0.776
#> GSM509761 2 0.0892 0.924 0.000 0.980 0.020
#> GSM509763 2 0.0892 0.924 0.000 0.980 0.020
#> GSM509765 2 0.0000 0.926 0.000 1.000 0.000
#> GSM509767 2 0.1753 0.913 0.000 0.952 0.048
#> GSM509769 2 0.1031 0.923 0.000 0.976 0.024
#> GSM509771 2 0.2625 0.891 0.000 0.916 0.084
#> GSM509773 2 0.1031 0.923 0.000 0.976 0.024
#> GSM509775 2 0.1031 0.923 0.000 0.976 0.024
#> GSM509777 2 0.0000 0.926 0.000 1.000 0.000
#> GSM509779 2 0.0000 0.926 0.000 1.000 0.000
#> GSM509781 2 0.0237 0.925 0.000 0.996 0.004
#> GSM509783 2 0.0661 0.921 0.004 0.988 0.008
#> GSM509785 2 0.0237 0.925 0.000 0.996 0.004
#> GSM509752 2 0.4931 0.747 0.000 0.768 0.232
#> GSM509754 2 0.2066 0.907 0.000 0.940 0.060
#> GSM509756 2 0.1643 0.915 0.000 0.956 0.044
#> GSM509758 2 0.1031 0.923 0.000 0.976 0.024
#> GSM509760 2 0.0000 0.926 0.000 1.000 0.000
#> GSM509762 2 0.2625 0.891 0.000 0.916 0.084
#> GSM509764 3 0.1964 0.671 0.000 0.056 0.944
#> GSM509766 2 0.0424 0.926 0.000 0.992 0.008
#> GSM509768 2 0.0424 0.926 0.000 0.992 0.008
#> GSM509770 2 0.1031 0.923 0.000 0.976 0.024
#> GSM509772 3 0.5948 0.199 0.000 0.360 0.640
#> GSM509774 2 0.0000 0.926 0.000 1.000 0.000
#> GSM509776 2 0.0424 0.926 0.000 0.992 0.008
#> GSM509778 2 0.0237 0.925 0.000 0.996 0.004
#> GSM509780 2 0.0000 0.926 0.000 1.000 0.000
#> GSM509782 2 0.0237 0.925 0.000 0.996 0.004
#> GSM509784 2 0.0000 0.926 0.000 1.000 0.000
#> GSM509786 2 0.0237 0.925 0.000 0.996 0.004
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM509706 1 0.1109 0.9161 0.968 0.000 0.028 0.004
#> GSM509711 1 0.0672 0.9168 0.984 0.000 0.008 0.008
#> GSM509714 1 0.1059 0.9143 0.972 0.000 0.012 0.016
#> GSM509719 1 0.2402 0.8778 0.912 0.076 0.012 0.000
#> GSM509724 1 0.2266 0.8997 0.912 0.000 0.084 0.004
#> GSM509729 1 0.1004 0.9172 0.972 0.000 0.024 0.004
#> GSM509707 1 0.0524 0.9164 0.988 0.000 0.008 0.004
#> GSM509712 1 0.2441 0.9084 0.916 0.004 0.068 0.012
#> GSM509715 4 0.1256 0.8161 0.008 0.000 0.028 0.964
#> GSM509720 1 0.1674 0.9060 0.952 0.032 0.012 0.004
#> GSM509725 1 0.2773 0.8811 0.880 0.000 0.116 0.004
#> GSM509730 1 0.1247 0.9136 0.968 0.012 0.016 0.004
#> GSM509708 1 0.0188 0.9148 0.996 0.000 0.000 0.004
#> GSM509713 1 0.2382 0.9025 0.912 0.004 0.080 0.004
#> GSM509716 4 0.1489 0.8114 0.044 0.000 0.004 0.952
#> GSM509721 1 0.2610 0.8669 0.900 0.088 0.012 0.000
#> GSM509726 1 0.3765 0.8111 0.812 0.004 0.180 0.004
#> GSM509731 4 0.0779 0.8340 0.016 0.004 0.000 0.980
#> GSM509709 1 0.0376 0.9157 0.992 0.000 0.004 0.004
#> GSM509717 4 0.1209 0.8210 0.032 0.000 0.004 0.964
#> GSM509722 1 0.1575 0.9075 0.956 0.028 0.012 0.004
#> GSM509727 1 0.5138 0.3946 0.600 0.000 0.392 0.008
#> GSM509710 1 0.2197 0.9025 0.916 0.000 0.080 0.004
#> GSM509718 4 0.3798 0.7268 0.016 0.016 0.120 0.848
#> GSM509723 1 0.1488 0.9062 0.956 0.032 0.012 0.000
#> GSM509728 3 0.4877 0.2754 0.408 0.000 0.592 0.000
#> GSM509732 3 0.2402 0.9080 0.012 0.076 0.912 0.000
#> GSM509736 3 0.0672 0.9115 0.008 0.008 0.984 0.000
#> GSM509741 3 0.1302 0.9142 0.000 0.044 0.956 0.000
#> GSM509746 3 0.3088 0.8713 0.008 0.128 0.864 0.000
#> GSM509733 3 0.2053 0.9098 0.004 0.072 0.924 0.000
#> GSM509737 3 0.0895 0.9096 0.020 0.004 0.976 0.000
#> GSM509742 3 0.1576 0.9150 0.004 0.048 0.948 0.000
#> GSM509747 3 0.2813 0.9042 0.024 0.080 0.896 0.000
#> GSM509734 3 0.2814 0.8408 0.132 0.000 0.868 0.000
#> GSM509738 3 0.1930 0.8977 0.056 0.004 0.936 0.004
#> GSM509743 3 0.1211 0.9135 0.000 0.040 0.960 0.000
#> GSM509748 3 0.2053 0.9098 0.004 0.072 0.924 0.000
#> GSM509735 1 0.2760 0.8774 0.872 0.000 0.128 0.000
#> GSM509739 1 0.3355 0.8441 0.836 0.000 0.160 0.004
#> GSM509744 3 0.0779 0.9122 0.004 0.016 0.980 0.000
#> GSM509749 3 0.2385 0.9125 0.028 0.052 0.920 0.000
#> GSM509740 3 0.4239 0.7972 0.152 0.004 0.812 0.032
#> GSM509745 3 0.1953 0.9000 0.044 0.004 0.940 0.012
#> GSM509750 3 0.2412 0.8849 0.084 0.008 0.908 0.000
#> GSM509751 2 0.1022 0.8312 0.000 0.968 0.000 0.032
#> GSM509753 2 0.0592 0.8231 0.000 0.984 0.000 0.016
#> GSM509755 2 0.1004 0.8277 0.004 0.972 0.000 0.024
#> GSM509757 2 0.1022 0.8312 0.000 0.968 0.000 0.032
#> GSM509759 2 0.0524 0.8101 0.008 0.988 0.004 0.000
#> GSM509761 2 0.4877 0.4018 0.000 0.592 0.000 0.408
#> GSM509763 4 0.4776 0.3902 0.000 0.376 0.000 0.624
#> GSM509765 4 0.4250 0.6227 0.000 0.276 0.000 0.724
#> GSM509767 2 0.2281 0.8417 0.000 0.904 0.000 0.096
#> GSM509769 2 0.3801 0.7588 0.000 0.780 0.000 0.220
#> GSM509771 2 0.2216 0.8423 0.000 0.908 0.000 0.092
#> GSM509773 2 0.4999 0.0883 0.000 0.508 0.000 0.492
#> GSM509775 2 0.4679 0.5475 0.000 0.648 0.000 0.352
#> GSM509777 4 0.2760 0.7885 0.000 0.128 0.000 0.872
#> GSM509779 4 0.1637 0.8340 0.000 0.060 0.000 0.940
#> GSM509781 4 0.0592 0.8450 0.000 0.016 0.000 0.984
#> GSM509783 4 0.0592 0.8450 0.000 0.016 0.000 0.984
#> GSM509785 4 0.0592 0.8450 0.000 0.016 0.000 0.984
#> GSM509752 2 0.1940 0.8413 0.000 0.924 0.000 0.076
#> GSM509754 2 0.3528 0.7883 0.000 0.808 0.000 0.192
#> GSM509756 2 0.2530 0.8372 0.000 0.888 0.000 0.112
#> GSM509758 2 0.3356 0.8013 0.000 0.824 0.000 0.176
#> GSM509760 2 0.4677 0.6136 0.004 0.680 0.000 0.316
#> GSM509762 2 0.2216 0.8427 0.000 0.908 0.000 0.092
#> GSM509764 2 0.2466 0.7382 0.000 0.900 0.096 0.004
#> GSM509766 4 0.4522 0.5395 0.000 0.320 0.000 0.680
#> GSM509768 4 0.4356 0.5956 0.000 0.292 0.000 0.708
#> GSM509770 2 0.2704 0.8327 0.000 0.876 0.000 0.124
#> GSM509772 2 0.0336 0.8172 0.000 0.992 0.000 0.008
#> GSM509774 4 0.1211 0.8417 0.000 0.040 0.000 0.960
#> GSM509776 4 0.4624 0.4923 0.000 0.340 0.000 0.660
#> GSM509778 4 0.0592 0.8450 0.000 0.016 0.000 0.984
#> GSM509780 4 0.4164 0.6410 0.000 0.264 0.000 0.736
#> GSM509782 4 0.0592 0.8450 0.000 0.016 0.000 0.984
#> GSM509784 4 0.1389 0.8393 0.000 0.048 0.000 0.952
#> GSM509786 4 0.0592 0.8450 0.000 0.016 0.000 0.984
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM509706 1 0.4127 0.6197 0.680 0.000 0.008 0.000 0.312
#> GSM509711 1 0.3796 0.6294 0.700 0.000 0.000 0.000 0.300
#> GSM509714 1 0.4565 0.4782 0.752 0.008 0.000 0.064 0.176
#> GSM509719 1 0.4390 0.4984 0.760 0.084 0.000 0.000 0.156
#> GSM509724 1 0.4268 0.5981 0.648 0.000 0.008 0.000 0.344
#> GSM509729 1 0.0932 0.5957 0.972 0.004 0.020 0.000 0.004
#> GSM509707 1 0.4200 0.6159 0.672 0.004 0.004 0.000 0.320
#> GSM509712 1 0.4552 0.6001 0.632 0.000 0.004 0.012 0.352
#> GSM509715 4 0.4026 0.5727 0.020 0.000 0.000 0.736 0.244
#> GSM509720 1 0.4138 0.5091 0.776 0.064 0.000 0.000 0.160
#> GSM509725 1 0.4467 0.5897 0.640 0.000 0.016 0.000 0.344
#> GSM509730 1 0.3756 0.5397 0.836 0.032 0.036 0.000 0.096
#> GSM509708 1 0.3452 0.6354 0.756 0.000 0.000 0.000 0.244
#> GSM509713 1 0.4310 0.5543 0.604 0.000 0.004 0.000 0.392
#> GSM509716 4 0.4527 0.5868 0.064 0.000 0.000 0.732 0.204
#> GSM509721 1 0.4417 0.4986 0.760 0.092 0.000 0.000 0.148
#> GSM509726 1 0.4713 0.4707 0.544 0.000 0.016 0.000 0.440
#> GSM509731 4 0.2236 0.7416 0.024 0.000 0.000 0.908 0.068
#> GSM509709 1 0.3861 0.6298 0.712 0.000 0.004 0.000 0.284
#> GSM509717 4 0.4066 0.6203 0.032 0.004 0.000 0.768 0.196
#> GSM509722 1 0.4010 0.5185 0.784 0.056 0.000 0.000 0.160
#> GSM509727 1 0.6635 0.2172 0.484 0.000 0.284 0.004 0.228
#> GSM509710 1 0.4706 0.3925 0.500 0.008 0.004 0.000 0.488
#> GSM509718 5 0.5286 0.1332 0.004 0.028 0.016 0.332 0.620
#> GSM509723 1 0.3994 0.5208 0.792 0.068 0.000 0.000 0.140
#> GSM509728 3 0.4678 0.5001 0.224 0.000 0.712 0.000 0.064
#> GSM509732 3 0.0740 0.8453 0.008 0.004 0.980 0.000 0.008
#> GSM509736 3 0.4561 0.0532 0.000 0.008 0.504 0.000 0.488
#> GSM509741 3 0.0703 0.8449 0.000 0.000 0.976 0.000 0.024
#> GSM509746 3 0.1153 0.8397 0.008 0.004 0.964 0.000 0.024
#> GSM509733 3 0.0162 0.8466 0.000 0.000 0.996 0.000 0.004
#> GSM509737 5 0.4294 -0.1847 0.000 0.000 0.468 0.000 0.532
#> GSM509742 3 0.0609 0.8454 0.000 0.000 0.980 0.000 0.020
#> GSM509747 3 0.0451 0.8471 0.008 0.000 0.988 0.000 0.004
#> GSM509734 3 0.1892 0.7968 0.080 0.000 0.916 0.000 0.004
#> GSM509738 3 0.3826 0.6920 0.004 0.000 0.752 0.008 0.236
#> GSM509743 3 0.3750 0.6648 0.000 0.012 0.756 0.000 0.232
#> GSM509748 3 0.0324 0.8471 0.000 0.004 0.992 0.000 0.004
#> GSM509735 1 0.4748 0.5801 0.728 0.000 0.100 0.000 0.172
#> GSM509739 5 0.4659 -0.5370 0.488 0.000 0.012 0.000 0.500
#> GSM509744 3 0.2424 0.7954 0.000 0.000 0.868 0.000 0.132
#> GSM509749 3 0.0898 0.8443 0.020 0.000 0.972 0.000 0.008
#> GSM509740 5 0.5389 0.2422 0.040 0.000 0.300 0.024 0.636
#> GSM509745 3 0.3360 0.7593 0.004 0.000 0.816 0.012 0.168
#> GSM509750 3 0.2067 0.8219 0.048 0.000 0.920 0.000 0.032
#> GSM509751 2 0.0613 0.8705 0.000 0.984 0.004 0.004 0.008
#> GSM509753 2 0.1012 0.8659 0.000 0.968 0.012 0.000 0.020
#> GSM509755 2 0.0932 0.8679 0.000 0.972 0.004 0.004 0.020
#> GSM509757 2 0.0898 0.8695 0.000 0.972 0.000 0.008 0.020
#> GSM509759 2 0.2131 0.8452 0.016 0.920 0.008 0.000 0.056
#> GSM509761 2 0.4213 0.5642 0.000 0.680 0.000 0.308 0.012
#> GSM509763 4 0.4610 0.2439 0.000 0.432 0.000 0.556 0.012
#> GSM509765 4 0.3689 0.6413 0.000 0.256 0.000 0.740 0.004
#> GSM509767 2 0.2139 0.8738 0.000 0.916 0.000 0.052 0.032
#> GSM509769 2 0.3278 0.8041 0.000 0.824 0.000 0.156 0.020
#> GSM509771 2 0.1628 0.8724 0.000 0.936 0.000 0.056 0.008
#> GSM509773 2 0.4410 0.1822 0.000 0.556 0.000 0.440 0.004
#> GSM509775 2 0.3967 0.6520 0.000 0.724 0.000 0.264 0.012
#> GSM509777 4 0.2127 0.7780 0.000 0.108 0.000 0.892 0.000
#> GSM509779 4 0.1197 0.7951 0.000 0.048 0.000 0.952 0.000
#> GSM509781 4 0.0451 0.7913 0.000 0.008 0.000 0.988 0.004
#> GSM509783 4 0.0451 0.7873 0.000 0.004 0.000 0.988 0.008
#> GSM509785 4 0.0451 0.7913 0.000 0.008 0.000 0.988 0.004
#> GSM509752 2 0.1579 0.8716 0.000 0.944 0.000 0.032 0.024
#> GSM509754 2 0.2046 0.8644 0.000 0.916 0.000 0.068 0.016
#> GSM509756 2 0.1012 0.8738 0.000 0.968 0.000 0.020 0.012
#> GSM509758 2 0.1956 0.8648 0.000 0.916 0.000 0.076 0.008
#> GSM509760 2 0.5184 0.6816 0.024 0.704 0.000 0.212 0.060
#> GSM509762 2 0.1408 0.8734 0.000 0.948 0.000 0.044 0.008
#> GSM509764 2 0.3077 0.8198 0.000 0.872 0.024 0.020 0.084
#> GSM509766 4 0.4182 0.4769 0.000 0.352 0.000 0.644 0.004
#> GSM509768 4 0.3969 0.5715 0.000 0.304 0.000 0.692 0.004
#> GSM509770 2 0.3133 0.8492 0.004 0.864 0.000 0.080 0.052
#> GSM509772 2 0.1492 0.8635 0.000 0.948 0.004 0.008 0.040
#> GSM509774 4 0.1571 0.7937 0.000 0.060 0.000 0.936 0.004
#> GSM509776 4 0.4341 0.3445 0.000 0.404 0.000 0.592 0.004
#> GSM509778 4 0.0324 0.7890 0.000 0.004 0.000 0.992 0.004
#> GSM509780 4 0.3395 0.6675 0.000 0.236 0.000 0.764 0.000
#> GSM509782 4 0.0162 0.7868 0.000 0.000 0.000 0.996 0.004
#> GSM509784 4 0.1043 0.7951 0.000 0.040 0.000 0.960 0.000
#> GSM509786 4 0.0451 0.7913 0.000 0.008 0.000 0.988 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM509706 1 0.0806 0.895 0.972 0.000 0.000 0.000 0.020 0.008
#> GSM509711 1 0.2604 0.850 0.872 0.000 0.000 0.008 0.100 0.020
#> GSM509714 5 0.3874 0.709 0.064 0.004 0.000 0.060 0.816 0.056
#> GSM509719 5 0.2420 0.759 0.076 0.040 0.000 0.000 0.884 0.000
#> GSM509724 1 0.0363 0.896 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM509729 1 0.5024 0.376 0.588 0.000 0.012 0.008 0.352 0.040
#> GSM509707 1 0.0820 0.897 0.972 0.000 0.000 0.000 0.012 0.016
#> GSM509712 1 0.3103 0.834 0.848 0.000 0.000 0.016 0.100 0.036
#> GSM509715 6 0.5835 0.126 0.000 0.004 0.000 0.204 0.280 0.512
#> GSM509720 5 0.2515 0.765 0.072 0.024 0.000 0.000 0.888 0.016
#> GSM509725 1 0.0260 0.896 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM509730 5 0.6068 0.425 0.272 0.004 0.072 0.008 0.584 0.060
#> GSM509708 1 0.1802 0.879 0.916 0.000 0.000 0.000 0.072 0.012
#> GSM509713 1 0.1418 0.893 0.944 0.000 0.000 0.000 0.024 0.032
#> GSM509716 5 0.5805 0.294 0.000 0.008 0.000 0.176 0.528 0.288
#> GSM509721 5 0.2591 0.752 0.064 0.052 0.004 0.000 0.880 0.000
#> GSM509726 1 0.1152 0.887 0.952 0.000 0.000 0.000 0.004 0.044
#> GSM509731 4 0.3770 0.550 0.000 0.000 0.000 0.776 0.148 0.076
#> GSM509709 1 0.0891 0.894 0.968 0.000 0.000 0.000 0.024 0.008
#> GSM509717 5 0.5832 0.263 0.000 0.004 0.000 0.196 0.508 0.292
#> GSM509722 5 0.2195 0.763 0.068 0.012 0.000 0.000 0.904 0.016
#> GSM509727 1 0.4359 0.638 0.724 0.000 0.212 0.000 0.040 0.024
#> GSM509710 1 0.1010 0.888 0.960 0.000 0.000 0.000 0.004 0.036
#> GSM509718 6 0.3371 0.599 0.020 0.008 0.012 0.084 0.024 0.852
#> GSM509723 5 0.2393 0.760 0.092 0.020 0.000 0.000 0.884 0.004
#> GSM509728 3 0.4429 0.587 0.192 0.000 0.732 0.000 0.036 0.040
#> GSM509732 3 0.0777 0.839 0.000 0.004 0.972 0.000 0.000 0.024
#> GSM509736 6 0.4607 0.618 0.044 0.028 0.208 0.000 0.004 0.716
#> GSM509741 3 0.1663 0.830 0.000 0.000 0.912 0.000 0.000 0.088
#> GSM509746 3 0.0692 0.841 0.000 0.004 0.976 0.000 0.000 0.020
#> GSM509733 3 0.0508 0.848 0.000 0.004 0.984 0.000 0.000 0.012
#> GSM509737 6 0.4848 0.613 0.072 0.020 0.208 0.000 0.004 0.696
#> GSM509742 3 0.1444 0.838 0.000 0.000 0.928 0.000 0.000 0.072
#> GSM509747 3 0.0508 0.848 0.000 0.004 0.984 0.000 0.000 0.012
#> GSM509734 3 0.1074 0.843 0.028 0.000 0.960 0.000 0.000 0.012
#> GSM509738 6 0.5038 0.167 0.008 0.000 0.428 0.004 0.044 0.516
#> GSM509743 3 0.4779 0.290 0.016 0.016 0.576 0.000 0.008 0.384
#> GSM509748 3 0.1075 0.847 0.000 0.000 0.952 0.000 0.000 0.048
#> GSM509735 1 0.2585 0.853 0.880 0.000 0.024 0.000 0.084 0.012
#> GSM509739 1 0.1471 0.876 0.932 0.000 0.000 0.000 0.004 0.064
#> GSM509744 3 0.3702 0.620 0.012 0.000 0.720 0.004 0.000 0.264
#> GSM509749 3 0.0260 0.850 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM509740 6 0.4545 0.633 0.048 0.000 0.072 0.024 0.076 0.780
#> GSM509745 3 0.3673 0.651 0.016 0.000 0.736 0.004 0.000 0.244
#> GSM509750 3 0.1624 0.845 0.000 0.000 0.936 0.004 0.020 0.040
#> GSM509751 2 0.1148 0.839 0.000 0.960 0.000 0.004 0.020 0.016
#> GSM509753 2 0.1173 0.843 0.000 0.960 0.000 0.008 0.016 0.016
#> GSM509755 2 0.1461 0.831 0.000 0.940 0.000 0.000 0.044 0.016
#> GSM509757 2 0.1297 0.836 0.000 0.948 0.000 0.000 0.040 0.012
#> GSM509759 2 0.2821 0.801 0.000 0.860 0.000 0.004 0.096 0.040
#> GSM509761 2 0.3493 0.697 0.000 0.756 0.000 0.228 0.008 0.008
#> GSM509763 4 0.4303 0.184 0.000 0.460 0.000 0.524 0.012 0.004
#> GSM509765 4 0.3559 0.684 0.000 0.240 0.000 0.744 0.012 0.004
#> GSM509767 2 0.2807 0.832 0.000 0.868 0.000 0.088 0.016 0.028
#> GSM509769 2 0.3831 0.700 0.000 0.744 0.000 0.224 0.012 0.020
#> GSM509771 2 0.2617 0.830 0.000 0.872 0.000 0.100 0.012 0.016
#> GSM509773 2 0.4447 0.178 0.000 0.556 0.000 0.420 0.012 0.012
#> GSM509775 2 0.3774 0.488 0.000 0.664 0.000 0.328 0.008 0.000
#> GSM509777 4 0.2362 0.774 0.000 0.136 0.000 0.860 0.004 0.000
#> GSM509779 4 0.1007 0.804 0.000 0.044 0.000 0.956 0.000 0.000
#> GSM509781 4 0.0458 0.796 0.000 0.016 0.000 0.984 0.000 0.000
#> GSM509783 4 0.0622 0.786 0.000 0.008 0.000 0.980 0.012 0.000
#> GSM509785 4 0.0508 0.793 0.000 0.012 0.000 0.984 0.004 0.000
#> GSM509752 2 0.1321 0.844 0.000 0.952 0.000 0.024 0.004 0.020
#> GSM509754 2 0.2306 0.834 0.000 0.888 0.000 0.092 0.004 0.016
#> GSM509756 2 0.1401 0.848 0.000 0.948 0.000 0.028 0.004 0.020
#> GSM509758 2 0.1901 0.842 0.000 0.912 0.000 0.076 0.008 0.004
#> GSM509760 2 0.4930 0.744 0.000 0.712 0.000 0.120 0.132 0.036
#> GSM509762 2 0.1332 0.848 0.000 0.952 0.000 0.028 0.008 0.012
#> GSM509764 2 0.3332 0.729 0.000 0.808 0.004 0.012 0.012 0.164
#> GSM509766 4 0.3955 0.576 0.000 0.316 0.000 0.668 0.012 0.004
#> GSM509768 4 0.4009 0.593 0.000 0.304 0.000 0.676 0.012 0.008
#> GSM509770 2 0.3835 0.811 0.000 0.808 0.004 0.112 0.044 0.032
#> GSM509772 2 0.2100 0.835 0.000 0.916 0.004 0.008 0.048 0.024
#> GSM509774 4 0.1204 0.804 0.000 0.056 0.000 0.944 0.000 0.000
#> GSM509776 4 0.4229 0.269 0.000 0.436 0.000 0.548 0.016 0.000
#> GSM509778 4 0.0862 0.781 0.000 0.008 0.000 0.972 0.016 0.004
#> GSM509780 4 0.3103 0.719 0.000 0.208 0.000 0.784 0.008 0.000
#> GSM509782 4 0.0767 0.784 0.000 0.008 0.000 0.976 0.012 0.004
#> GSM509784 4 0.0937 0.804 0.000 0.040 0.000 0.960 0.000 0.000
#> GSM509786 4 0.0713 0.800 0.000 0.028 0.000 0.972 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 disease.state(p) time(p) k
#> CV:NMF 81 2.66e-14 3.66e-11 2
#> CV:NMF 73 9.31e-17 1.77e-07 3
#> CV:NMF 75 6.77e-23 6.06e-07 4
#> CV:NMF 66 2.10e-19 1.51e-06 5
#> CV:NMF 70 6.40e-19 3.29e-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["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 19175 rows and 81 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 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.497 0.0676 0.621 0.4535 0.568 0.568
#> 3 3 0.549 0.5497 0.760 0.4114 0.514 0.300
#> 4 4 0.768 0.8424 0.850 0.1603 0.868 0.628
#> 5 5 0.815 0.7893 0.851 0.0635 0.972 0.886
#> 6 6 0.887 0.8437 0.905 0.0325 0.943 0.752
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
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
#> GSM509706 2 1.0000 -0.03669 0.500 0.500
#> GSM509711 2 0.9635 0.10274 0.388 0.612
#> GSM509714 2 0.8327 0.18407 0.264 0.736
#> GSM509719 2 1.0000 -0.03669 0.500 0.500
#> GSM509724 1 1.0000 -0.02123 0.500 0.500
#> GSM509729 1 1.0000 -0.02123 0.500 0.500
#> GSM509707 1 1.0000 -0.02123 0.500 0.500
#> GSM509712 2 0.9635 0.10274 0.388 0.612
#> GSM509715 1 0.9044 0.08483 0.680 0.320
#> GSM509720 2 1.0000 -0.03669 0.500 0.500
#> GSM509725 1 1.0000 -0.02123 0.500 0.500
#> GSM509730 2 1.0000 -0.03669 0.500 0.500
#> GSM509708 1 1.0000 -0.02123 0.500 0.500
#> GSM509713 2 0.9635 0.10274 0.388 0.612
#> GSM509716 1 0.9044 0.08483 0.680 0.320
#> GSM509721 2 1.0000 -0.03669 0.500 0.500
#> GSM509726 1 1.0000 -0.02123 0.500 0.500
#> GSM509731 1 0.9044 0.08483 0.680 0.320
#> GSM509709 1 1.0000 -0.02123 0.500 0.500
#> GSM509717 1 0.9044 0.08483 0.680 0.320
#> GSM509722 1 1.0000 -0.02123 0.500 0.500
#> GSM509727 2 0.9998 -0.02230 0.492 0.508
#> GSM509710 2 1.0000 -0.03669 0.500 0.500
#> GSM509718 1 0.9044 0.08483 0.680 0.320
#> GSM509723 1 1.0000 -0.02123 0.500 0.500
#> GSM509728 2 0.9998 -0.02230 0.492 0.508
#> GSM509732 1 1.0000 -0.02123 0.500 0.500
#> GSM509736 2 0.9983 0.00353 0.476 0.524
#> GSM509741 1 1.0000 -0.02123 0.500 0.500
#> GSM509746 1 1.0000 -0.02123 0.500 0.500
#> GSM509733 2 1.0000 -0.03669 0.500 0.500
#> GSM509737 2 0.9983 0.00353 0.476 0.524
#> GSM509742 2 1.0000 -0.03669 0.500 0.500
#> GSM509747 1 1.0000 -0.02123 0.500 0.500
#> GSM509734 2 1.0000 -0.03669 0.500 0.500
#> GSM509738 2 0.9983 0.00353 0.476 0.524
#> GSM509743 2 1.0000 -0.03669 0.500 0.500
#> GSM509748 2 1.0000 -0.03669 0.500 0.500
#> GSM509735 1 1.0000 -0.02123 0.500 0.500
#> GSM509739 2 1.0000 -0.03669 0.500 0.500
#> GSM509744 2 1.0000 -0.03669 0.500 0.500
#> GSM509749 2 1.0000 -0.03669 0.500 0.500
#> GSM509740 2 0.9795 0.07567 0.416 0.584
#> GSM509745 2 0.9833 0.06773 0.424 0.576
#> GSM509750 2 0.9983 0.00350 0.476 0.524
#> GSM509751 2 0.0000 0.33036 0.000 1.000
#> GSM509753 2 0.0000 0.33036 0.000 1.000
#> GSM509755 2 0.0000 0.33036 0.000 1.000
#> GSM509757 2 0.0000 0.33036 0.000 1.000
#> GSM509759 2 0.0000 0.33036 0.000 1.000
#> GSM509761 2 0.0000 0.33036 0.000 1.000
#> GSM509763 2 1.0000 -0.07072 0.496 0.504
#> GSM509765 2 1.0000 -0.07072 0.496 0.504
#> GSM509767 2 0.0000 0.33036 0.000 1.000
#> GSM509769 2 0.0376 0.32691 0.004 0.996
#> GSM509771 2 0.0000 0.33036 0.000 1.000
#> GSM509773 2 0.9996 -0.06698 0.488 0.512
#> GSM509775 2 0.9850 -0.03668 0.428 0.572
#> GSM509777 2 1.0000 -0.07356 0.500 0.500
#> GSM509779 2 1.0000 -0.07356 0.500 0.500
#> GSM509781 2 1.0000 -0.07356 0.500 0.500
#> GSM509783 1 1.0000 0.01741 0.500 0.500
#> GSM509785 1 1.0000 0.01741 0.500 0.500
#> GSM509752 2 0.0000 0.33036 0.000 1.000
#> GSM509754 2 0.0000 0.33036 0.000 1.000
#> GSM509756 2 0.0000 0.33036 0.000 1.000
#> GSM509758 2 0.0000 0.33036 0.000 1.000
#> GSM509760 2 0.0000 0.33036 0.000 1.000
#> GSM509762 2 0.0000 0.33036 0.000 1.000
#> GSM509764 2 0.0000 0.33036 0.000 1.000
#> GSM509766 2 1.0000 -0.07072 0.496 0.504
#> GSM509768 2 1.0000 -0.07072 0.496 0.504
#> GSM509770 2 0.0000 0.33036 0.000 1.000
#> GSM509772 2 0.0000 0.33036 0.000 1.000
#> GSM509774 1 1.0000 0.01741 0.500 0.500
#> GSM509776 2 0.9850 -0.03668 0.428 0.572
#> GSM509778 1 1.0000 0.01741 0.500 0.500
#> GSM509780 1 1.0000 0.01741 0.500 0.500
#> GSM509782 2 1.0000 -0.07356 0.500 0.500
#> GSM509784 2 1.0000 -0.07356 0.500 0.500
#> GSM509786 1 1.0000 0.01741 0.500 0.500
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM509706 1 0.5905 0.901 0.648 0.000 0.352
#> GSM509711 1 0.0237 0.647 0.996 0.000 0.004
#> GSM509714 1 0.3784 0.523 0.864 0.132 0.004
#> GSM509719 1 0.5835 0.897 0.660 0.000 0.340
#> GSM509724 1 0.5905 0.901 0.648 0.000 0.352
#> GSM509729 1 0.5835 0.897 0.660 0.000 0.340
#> GSM509707 1 0.5905 0.901 0.648 0.000 0.352
#> GSM509712 1 0.0237 0.647 0.996 0.000 0.004
#> GSM509715 2 0.5733 0.513 0.324 0.676 0.000
#> GSM509720 1 0.5835 0.897 0.660 0.000 0.340
#> GSM509725 1 0.5905 0.901 0.648 0.000 0.352
#> GSM509730 1 0.5835 0.897 0.660 0.000 0.340
#> GSM509708 1 0.5905 0.901 0.648 0.000 0.352
#> GSM509713 1 0.0237 0.647 0.996 0.000 0.004
#> GSM509716 2 0.5733 0.513 0.324 0.676 0.000
#> GSM509721 1 0.5835 0.897 0.660 0.000 0.340
#> GSM509726 1 0.5882 0.900 0.652 0.000 0.348
#> GSM509731 2 0.5733 0.513 0.324 0.676 0.000
#> GSM509709 1 0.5905 0.901 0.648 0.000 0.352
#> GSM509717 2 0.5733 0.513 0.324 0.676 0.000
#> GSM509722 1 0.5835 0.897 0.660 0.000 0.340
#> GSM509727 3 0.6204 0.343 0.424 0.000 0.576
#> GSM509710 1 0.5905 0.901 0.648 0.000 0.352
#> GSM509718 2 0.5733 0.513 0.324 0.676 0.000
#> GSM509723 1 0.5835 0.897 0.660 0.000 0.340
#> GSM509728 3 0.6204 0.343 0.424 0.000 0.576
#> GSM509732 3 0.0000 0.517 0.000 0.000 1.000
#> GSM509736 3 0.5968 0.399 0.364 0.000 0.636
#> GSM509741 3 0.0000 0.517 0.000 0.000 1.000
#> GSM509746 3 0.0000 0.517 0.000 0.000 1.000
#> GSM509733 3 0.0000 0.517 0.000 0.000 1.000
#> GSM509737 3 0.5968 0.399 0.364 0.000 0.636
#> GSM509742 3 0.0000 0.517 0.000 0.000 1.000
#> GSM509747 3 0.0000 0.517 0.000 0.000 1.000
#> GSM509734 3 0.0000 0.517 0.000 0.000 1.000
#> GSM509738 3 0.5968 0.399 0.364 0.000 0.636
#> GSM509743 3 0.0237 0.519 0.004 0.000 0.996
#> GSM509748 3 0.1031 0.493 0.024 0.000 0.976
#> GSM509735 1 0.5905 0.901 0.648 0.000 0.352
#> GSM509739 1 0.5905 0.901 0.648 0.000 0.352
#> GSM509744 3 0.4062 0.487 0.164 0.000 0.836
#> GSM509749 3 0.1031 0.493 0.024 0.000 0.976
#> GSM509740 3 0.6520 0.368 0.488 0.004 0.508
#> GSM509745 3 0.6468 0.416 0.444 0.004 0.552
#> GSM509750 3 0.5178 0.496 0.256 0.000 0.744
#> GSM509751 3 0.6309 0.249 0.000 0.500 0.500
#> GSM509753 3 0.6309 0.249 0.000 0.500 0.500
#> GSM509755 2 0.6309 -0.298 0.000 0.500 0.500
#> GSM509757 3 0.6309 0.249 0.000 0.500 0.500
#> GSM509759 3 0.6309 0.249 0.000 0.500 0.500
#> GSM509761 3 0.6309 0.249 0.000 0.500 0.500
#> GSM509763 2 0.0237 0.766 0.000 0.996 0.004
#> GSM509765 2 0.0237 0.766 0.000 0.996 0.004
#> GSM509767 3 0.6309 0.249 0.000 0.500 0.500
#> GSM509769 2 0.6309 -0.289 0.000 0.504 0.496
#> GSM509771 3 0.6309 0.249 0.000 0.500 0.500
#> GSM509773 2 0.0592 0.761 0.000 0.988 0.012
#> GSM509775 2 0.2356 0.703 0.000 0.928 0.072
#> GSM509777 2 0.0000 0.768 0.000 1.000 0.000
#> GSM509779 2 0.0000 0.768 0.000 1.000 0.000
#> GSM509781 2 0.0000 0.768 0.000 1.000 0.000
#> GSM509783 2 0.0000 0.768 0.000 1.000 0.000
#> GSM509785 2 0.0000 0.768 0.000 1.000 0.000
#> GSM509752 2 0.6309 -0.298 0.000 0.500 0.500
#> GSM509754 3 0.6309 0.249 0.000 0.500 0.500
#> GSM509756 3 0.6309 0.249 0.000 0.500 0.500
#> GSM509758 3 0.6309 0.249 0.000 0.500 0.500
#> GSM509760 2 0.6309 -0.298 0.000 0.500 0.500
#> GSM509762 3 0.6309 0.249 0.000 0.500 0.500
#> GSM509764 3 0.6309 0.249 0.000 0.500 0.500
#> GSM509766 2 0.0237 0.766 0.000 0.996 0.004
#> GSM509768 2 0.0237 0.766 0.000 0.996 0.004
#> GSM509770 2 0.6309 -0.298 0.000 0.500 0.500
#> GSM509772 3 0.6309 0.249 0.000 0.500 0.500
#> GSM509774 2 0.0000 0.768 0.000 1.000 0.000
#> GSM509776 2 0.2356 0.703 0.000 0.928 0.072
#> GSM509778 2 0.0000 0.768 0.000 1.000 0.000
#> GSM509780 2 0.0000 0.768 0.000 1.000 0.000
#> GSM509782 2 0.0000 0.768 0.000 1.000 0.000
#> GSM509784 2 0.0000 0.768 0.000 1.000 0.000
#> GSM509786 2 0.0000 0.768 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM509706 1 0.0000 0.874 1.000 0.000 0.000 0.000
#> GSM509711 1 0.5857 0.541 0.636 0.000 0.308 0.056
#> GSM509714 1 0.7216 0.429 0.548 0.000 0.244 0.208
#> GSM509719 1 0.1302 0.869 0.956 0.000 0.044 0.000
#> GSM509724 1 0.0000 0.874 1.000 0.000 0.000 0.000
#> GSM509729 1 0.1302 0.869 0.956 0.000 0.044 0.000
#> GSM509707 1 0.0000 0.874 1.000 0.000 0.000 0.000
#> GSM509712 1 0.5857 0.541 0.636 0.000 0.308 0.056
#> GSM509715 4 0.4008 0.689 0.000 0.000 0.244 0.756
#> GSM509720 1 0.1302 0.869 0.956 0.000 0.044 0.000
#> GSM509725 1 0.0000 0.874 1.000 0.000 0.000 0.000
#> GSM509730 1 0.1302 0.869 0.956 0.000 0.044 0.000
#> GSM509708 1 0.0000 0.874 1.000 0.000 0.000 0.000
#> GSM509713 1 0.5857 0.541 0.636 0.000 0.308 0.056
#> GSM509716 4 0.4008 0.689 0.000 0.000 0.244 0.756
#> GSM509721 1 0.1302 0.869 0.956 0.000 0.044 0.000
#> GSM509726 1 0.0188 0.873 0.996 0.000 0.004 0.000
#> GSM509731 4 0.4008 0.689 0.000 0.000 0.244 0.756
#> GSM509709 1 0.0000 0.874 1.000 0.000 0.000 0.000
#> GSM509717 4 0.4008 0.689 0.000 0.000 0.244 0.756
#> GSM509722 1 0.1302 0.869 0.956 0.000 0.044 0.000
#> GSM509727 3 0.5227 0.651 0.256 0.000 0.704 0.040
#> GSM509710 1 0.0000 0.874 1.000 0.000 0.000 0.000
#> GSM509718 4 0.4008 0.689 0.000 0.000 0.244 0.756
#> GSM509723 1 0.1302 0.869 0.956 0.000 0.044 0.000
#> GSM509728 3 0.5227 0.651 0.256 0.000 0.704 0.040
#> GSM509732 3 0.4908 0.793 0.292 0.016 0.692 0.000
#> GSM509736 3 0.5179 0.706 0.220 0.000 0.728 0.052
#> GSM509741 3 0.4908 0.793 0.292 0.016 0.692 0.000
#> GSM509746 3 0.4908 0.793 0.292 0.016 0.692 0.000
#> GSM509733 3 0.4908 0.793 0.292 0.016 0.692 0.000
#> GSM509737 3 0.5179 0.706 0.220 0.000 0.728 0.052
#> GSM509742 3 0.4908 0.793 0.292 0.016 0.692 0.000
#> GSM509747 3 0.4908 0.793 0.292 0.016 0.692 0.000
#> GSM509734 3 0.4908 0.793 0.292 0.016 0.692 0.000
#> GSM509738 3 0.5179 0.706 0.220 0.000 0.728 0.052
#> GSM509743 3 0.4883 0.794 0.288 0.016 0.696 0.000
#> GSM509748 3 0.5047 0.784 0.316 0.016 0.668 0.000
#> GSM509735 1 0.0000 0.874 1.000 0.000 0.000 0.000
#> GSM509739 1 0.0000 0.874 1.000 0.000 0.000 0.000
#> GSM509744 3 0.5533 0.772 0.272 0.016 0.688 0.024
#> GSM509749 3 0.5047 0.784 0.316 0.016 0.668 0.000
#> GSM509740 3 0.4852 0.606 0.152 0.000 0.776 0.072
#> GSM509745 3 0.5050 0.644 0.152 0.016 0.780 0.052
#> GSM509750 3 0.4359 0.749 0.164 0.016 0.804 0.016
#> GSM509751 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM509753 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM509755 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM509757 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM509759 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM509761 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM509763 4 0.2149 0.901 0.000 0.088 0.000 0.912
#> GSM509765 4 0.2149 0.901 0.000 0.088 0.000 0.912
#> GSM509767 2 0.0188 0.996 0.000 0.996 0.000 0.004
#> GSM509769 2 0.0188 0.995 0.000 0.996 0.000 0.004
#> GSM509771 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM509773 4 0.2281 0.896 0.000 0.096 0.000 0.904
#> GSM509775 4 0.3801 0.788 0.000 0.220 0.000 0.780
#> GSM509777 4 0.2081 0.902 0.000 0.084 0.000 0.916
#> GSM509779 4 0.2081 0.902 0.000 0.084 0.000 0.916
#> GSM509781 4 0.2081 0.902 0.000 0.084 0.000 0.916
#> GSM509783 4 0.2081 0.902 0.000 0.084 0.000 0.916
#> GSM509785 4 0.2081 0.902 0.000 0.084 0.000 0.916
#> GSM509752 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM509754 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM509756 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM509758 2 0.0336 0.991 0.000 0.992 0.000 0.008
#> GSM509760 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM509762 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM509764 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM509766 4 0.2149 0.901 0.000 0.088 0.000 0.912
#> GSM509768 4 0.4103 0.749 0.000 0.256 0.000 0.744
#> GSM509770 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM509772 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM509774 4 0.2081 0.902 0.000 0.084 0.000 0.916
#> GSM509776 4 0.3837 0.784 0.000 0.224 0.000 0.776
#> GSM509778 4 0.2081 0.902 0.000 0.084 0.000 0.916
#> GSM509780 4 0.2081 0.902 0.000 0.084 0.000 0.916
#> GSM509782 4 0.2081 0.902 0.000 0.084 0.000 0.916
#> GSM509784 4 0.2081 0.902 0.000 0.084 0.000 0.916
#> GSM509786 4 0.2081 0.902 0.000 0.084 0.000 0.916
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM509706 1 0.0000 0.857 1.000 0.000 0.000 0.000 0.000
#> GSM509711 1 0.4288 0.525 0.612 0.000 0.004 0.000 0.384
#> GSM509714 1 0.6261 0.360 0.464 0.000 0.004 0.128 0.404
#> GSM509719 1 0.2605 0.830 0.852 0.000 0.000 0.000 0.148
#> GSM509724 1 0.0162 0.856 0.996 0.000 0.004 0.000 0.000
#> GSM509729 1 0.2605 0.830 0.852 0.000 0.000 0.000 0.148
#> GSM509707 1 0.0000 0.857 1.000 0.000 0.000 0.000 0.000
#> GSM509712 1 0.4288 0.525 0.612 0.000 0.004 0.000 0.384
#> GSM509715 4 0.4331 0.578 0.000 0.000 0.004 0.596 0.400
#> GSM509720 1 0.2605 0.830 0.852 0.000 0.000 0.000 0.148
#> GSM509725 1 0.0162 0.856 0.996 0.000 0.004 0.000 0.000
#> GSM509730 1 0.2605 0.830 0.852 0.000 0.000 0.000 0.148
#> GSM509708 1 0.0000 0.857 1.000 0.000 0.000 0.000 0.000
#> GSM509713 1 0.4288 0.525 0.612 0.000 0.004 0.000 0.384
#> GSM509716 4 0.4331 0.578 0.000 0.000 0.004 0.596 0.400
#> GSM509721 1 0.2605 0.830 0.852 0.000 0.000 0.000 0.148
#> GSM509726 1 0.0671 0.851 0.980 0.000 0.016 0.000 0.004
#> GSM509731 4 0.4331 0.578 0.000 0.000 0.004 0.596 0.400
#> GSM509709 1 0.0000 0.857 1.000 0.000 0.000 0.000 0.000
#> GSM509717 4 0.4331 0.578 0.000 0.000 0.004 0.596 0.400
#> GSM509722 1 0.2605 0.830 0.852 0.000 0.000 0.000 0.148
#> GSM509727 5 0.4489 0.759 0.068 0.000 0.192 0.000 0.740
#> GSM509710 1 0.0000 0.857 1.000 0.000 0.000 0.000 0.000
#> GSM509718 4 0.4331 0.578 0.000 0.000 0.004 0.596 0.400
#> GSM509723 1 0.2605 0.830 0.852 0.000 0.000 0.000 0.148
#> GSM509728 5 0.4489 0.759 0.068 0.000 0.192 0.000 0.740
#> GSM509732 3 0.0290 0.638 0.008 0.000 0.992 0.000 0.000
#> GSM509736 5 0.3521 0.795 0.004 0.000 0.232 0.000 0.764
#> GSM509741 3 0.4310 0.390 0.004 0.000 0.604 0.000 0.392
#> GSM509746 3 0.0290 0.638 0.008 0.000 0.992 0.000 0.000
#> GSM509733 3 0.0290 0.638 0.008 0.000 0.992 0.000 0.000
#> GSM509737 5 0.3521 0.795 0.004 0.000 0.232 0.000 0.764
#> GSM509742 3 0.4310 0.390 0.004 0.000 0.604 0.000 0.392
#> GSM509747 3 0.0290 0.638 0.008 0.000 0.992 0.000 0.000
#> GSM509734 3 0.0609 0.625 0.020 0.000 0.980 0.000 0.000
#> GSM509738 5 0.3521 0.795 0.004 0.000 0.232 0.000 0.764
#> GSM509743 3 0.4171 0.382 0.000 0.000 0.604 0.000 0.396
#> GSM509748 3 0.4375 0.319 0.004 0.000 0.576 0.000 0.420
#> GSM509735 1 0.0000 0.857 1.000 0.000 0.000 0.000 0.000
#> GSM509739 1 0.0000 0.857 1.000 0.000 0.000 0.000 0.000
#> GSM509744 5 0.4249 0.318 0.000 0.000 0.432 0.000 0.568
#> GSM509749 3 0.4375 0.319 0.004 0.000 0.576 0.000 0.420
#> GSM509740 5 0.2233 0.733 0.004 0.000 0.104 0.000 0.892
#> GSM509745 5 0.2605 0.759 0.000 0.000 0.148 0.000 0.852
#> GSM509750 5 0.3983 0.600 0.000 0.000 0.340 0.000 0.660
#> GSM509751 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM509753 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM509755 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM509757 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM509759 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM509761 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM509763 4 0.0162 0.881 0.000 0.004 0.000 0.996 0.000
#> GSM509765 4 0.0162 0.881 0.000 0.004 0.000 0.996 0.000
#> GSM509767 2 0.0162 0.995 0.000 0.996 0.000 0.004 0.000
#> GSM509769 2 0.0162 0.995 0.000 0.996 0.000 0.004 0.000
#> GSM509771 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM509773 4 0.0404 0.877 0.000 0.012 0.000 0.988 0.000
#> GSM509775 4 0.2690 0.773 0.000 0.156 0.000 0.844 0.000
#> GSM509777 4 0.0000 0.881 0.000 0.000 0.000 1.000 0.000
#> GSM509779 4 0.0000 0.881 0.000 0.000 0.000 1.000 0.000
#> GSM509781 4 0.0000 0.881 0.000 0.000 0.000 1.000 0.000
#> GSM509783 4 0.0000 0.881 0.000 0.000 0.000 1.000 0.000
#> GSM509785 4 0.0000 0.881 0.000 0.000 0.000 1.000 0.000
#> GSM509752 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM509754 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM509756 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM509758 2 0.0404 0.986 0.000 0.988 0.000 0.012 0.000
#> GSM509760 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM509762 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM509764 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM509766 4 0.0162 0.881 0.000 0.004 0.000 0.996 0.000
#> GSM509768 4 0.3109 0.730 0.000 0.200 0.000 0.800 0.000
#> GSM509770 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM509772 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM509774 4 0.0000 0.881 0.000 0.000 0.000 1.000 0.000
#> GSM509776 4 0.2773 0.767 0.000 0.164 0.000 0.836 0.000
#> GSM509778 4 0.0000 0.881 0.000 0.000 0.000 1.000 0.000
#> GSM509780 4 0.0000 0.881 0.000 0.000 0.000 1.000 0.000
#> GSM509782 4 0.0000 0.881 0.000 0.000 0.000 1.000 0.000
#> GSM509784 4 0.0000 0.881 0.000 0.000 0.000 1.000 0.000
#> GSM509786 4 0.0000 0.881 0.000 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM509706 1 0.0000 0.856 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509711 1 0.5238 0.412 0.604 0.000 0.000 0.000 0.236 0.160
#> GSM509714 5 0.5190 -0.230 0.452 0.000 0.000 0.000 0.460 0.088
#> GSM509719 1 0.2669 0.820 0.836 0.000 0.000 0.000 0.008 0.156
#> GSM509724 1 0.0146 0.855 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM509729 1 0.2669 0.820 0.836 0.000 0.000 0.000 0.008 0.156
#> GSM509707 1 0.0000 0.856 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509712 1 0.5238 0.412 0.604 0.000 0.000 0.000 0.236 0.160
#> GSM509715 5 0.0260 0.843 0.000 0.000 0.000 0.008 0.992 0.000
#> GSM509720 1 0.2669 0.820 0.836 0.000 0.000 0.000 0.008 0.156
#> GSM509725 1 0.0146 0.855 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM509730 1 0.2669 0.820 0.836 0.000 0.000 0.000 0.008 0.156
#> GSM509708 1 0.0000 0.856 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509713 1 0.5238 0.412 0.604 0.000 0.000 0.000 0.236 0.160
#> GSM509716 5 0.0260 0.843 0.000 0.000 0.000 0.008 0.992 0.000
#> GSM509721 1 0.2669 0.820 0.836 0.000 0.000 0.000 0.008 0.156
#> GSM509726 1 0.0603 0.849 0.980 0.000 0.004 0.000 0.000 0.016
#> GSM509731 5 0.0260 0.843 0.000 0.000 0.000 0.008 0.992 0.000
#> GSM509709 1 0.0000 0.856 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509717 5 0.0260 0.843 0.000 0.000 0.000 0.008 0.992 0.000
#> GSM509722 1 0.2669 0.820 0.836 0.000 0.000 0.000 0.008 0.156
#> GSM509727 6 0.1563 0.698 0.056 0.000 0.012 0.000 0.000 0.932
#> GSM509710 1 0.0000 0.856 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509718 5 0.0717 0.833 0.000 0.000 0.000 0.008 0.976 0.016
#> GSM509723 1 0.2669 0.820 0.836 0.000 0.000 0.000 0.008 0.156
#> GSM509728 6 0.1563 0.698 0.056 0.000 0.012 0.000 0.000 0.932
#> GSM509732 3 0.0000 0.992 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509736 6 0.2474 0.741 0.000 0.000 0.080 0.000 0.040 0.880
#> GSM509741 6 0.3843 0.525 0.000 0.000 0.452 0.000 0.000 0.548
#> GSM509746 3 0.0000 0.992 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509733 3 0.0000 0.992 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509737 6 0.2474 0.741 0.000 0.000 0.080 0.000 0.040 0.880
#> GSM509742 6 0.3843 0.525 0.000 0.000 0.452 0.000 0.000 0.548
#> GSM509747 3 0.0000 0.992 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509734 3 0.0820 0.966 0.016 0.000 0.972 0.000 0.000 0.012
#> GSM509738 6 0.2474 0.741 0.000 0.000 0.080 0.000 0.040 0.880
#> GSM509743 6 0.3838 0.531 0.000 0.000 0.448 0.000 0.000 0.552
#> GSM509748 6 0.3756 0.594 0.000 0.000 0.400 0.000 0.000 0.600
#> GSM509735 1 0.0000 0.856 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509739 1 0.0000 0.856 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509744 6 0.3151 0.700 0.000 0.000 0.252 0.000 0.000 0.748
#> GSM509749 6 0.3756 0.594 0.000 0.000 0.400 0.000 0.000 0.600
#> GSM509740 6 0.1765 0.680 0.000 0.000 0.000 0.000 0.096 0.904
#> GSM509745 6 0.2221 0.702 0.000 0.000 0.032 0.000 0.072 0.896
#> GSM509750 6 0.3269 0.728 0.000 0.000 0.184 0.000 0.024 0.792
#> GSM509751 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509753 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509755 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509757 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509759 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509761 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509763 4 0.0146 0.959 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM509765 4 0.0146 0.959 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM509767 2 0.0146 0.995 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM509769 2 0.0146 0.995 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM509771 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509773 4 0.0363 0.953 0.000 0.012 0.000 0.988 0.000 0.000
#> GSM509775 4 0.2416 0.810 0.000 0.156 0.000 0.844 0.000 0.000
#> GSM509777 4 0.0000 0.960 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM509779 4 0.0000 0.960 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM509781 4 0.0000 0.960 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM509783 4 0.0000 0.960 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM509785 4 0.0000 0.960 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM509752 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509754 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509756 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509758 2 0.0363 0.986 0.000 0.988 0.000 0.012 0.000 0.000
#> GSM509760 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509762 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509764 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509766 4 0.0146 0.959 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM509768 4 0.2793 0.746 0.000 0.200 0.000 0.800 0.000 0.000
#> GSM509770 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509772 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509774 4 0.0000 0.960 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM509776 4 0.2491 0.801 0.000 0.164 0.000 0.836 0.000 0.000
#> GSM509778 4 0.0000 0.960 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM509780 4 0.0000 0.960 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM509782 4 0.0000 0.960 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM509784 4 0.0000 0.960 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM509786 4 0.0000 0.960 0.000 0.000 0.000 1.000 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 disease.state(p) time(p) k
#> MAD:hclust 0 NA NA 2
#> MAD:hclust 52 1.47e-14 5.95e-05 3
#> MAD:hclust 80 7.11e-22 1.39e-07 4
#> MAD:hclust 74 4.64e-18 1.27e-07 5
#> MAD:hclust 77 1.36e-22 3.65e-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", "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 19175 rows and 81 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 1.000 0.974 0.990 0.5061 0.494 0.494
#> 3 3 0.652 0.457 0.765 0.2470 0.966 0.931
#> 4 4 0.710 0.716 0.783 0.1457 0.767 0.508
#> 5 5 0.680 0.777 0.833 0.0663 0.931 0.743
#> 6 6 0.780 0.714 0.790 0.0470 0.982 0.919
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
#> GSM509706 1 0.00 1.0000 1.000 0.000
#> GSM509711 1 0.00 1.0000 1.000 0.000
#> GSM509714 1 0.00 1.0000 1.000 0.000
#> GSM509719 1 0.00 1.0000 1.000 0.000
#> GSM509724 1 0.00 1.0000 1.000 0.000
#> GSM509729 1 0.00 1.0000 1.000 0.000
#> GSM509707 1 0.00 1.0000 1.000 0.000
#> GSM509712 1 0.00 1.0000 1.000 0.000
#> GSM509715 2 0.43 0.9016 0.088 0.912
#> GSM509720 1 0.00 1.0000 1.000 0.000
#> GSM509725 1 0.00 1.0000 1.000 0.000
#> GSM509730 1 0.00 1.0000 1.000 0.000
#> GSM509708 1 0.00 1.0000 1.000 0.000
#> GSM509713 1 0.00 1.0000 1.000 0.000
#> GSM509716 2 0.43 0.9016 0.088 0.912
#> GSM509721 1 0.00 1.0000 1.000 0.000
#> GSM509726 1 0.00 1.0000 1.000 0.000
#> GSM509731 2 1.00 0.0767 0.488 0.512
#> GSM509709 1 0.00 1.0000 1.000 0.000
#> GSM509717 2 0.43 0.9016 0.088 0.912
#> GSM509722 1 0.00 1.0000 1.000 0.000
#> GSM509727 1 0.00 1.0000 1.000 0.000
#> GSM509710 1 0.00 1.0000 1.000 0.000
#> GSM509718 2 0.43 0.9016 0.088 0.912
#> GSM509723 1 0.00 1.0000 1.000 0.000
#> GSM509728 1 0.00 1.0000 1.000 0.000
#> GSM509732 1 0.00 1.0000 1.000 0.000
#> GSM509736 1 0.00 1.0000 1.000 0.000
#> GSM509741 1 0.00 1.0000 1.000 0.000
#> GSM509746 1 0.00 1.0000 1.000 0.000
#> GSM509733 1 0.00 1.0000 1.000 0.000
#> GSM509737 1 0.00 1.0000 1.000 0.000
#> GSM509742 1 0.00 1.0000 1.000 0.000
#> GSM509747 1 0.00 1.0000 1.000 0.000
#> GSM509734 1 0.00 1.0000 1.000 0.000
#> GSM509738 1 0.00 1.0000 1.000 0.000
#> GSM509743 1 0.00 1.0000 1.000 0.000
#> GSM509748 1 0.00 1.0000 1.000 0.000
#> GSM509735 1 0.00 1.0000 1.000 0.000
#> GSM509739 1 0.00 1.0000 1.000 0.000
#> GSM509744 1 0.00 1.0000 1.000 0.000
#> GSM509749 1 0.00 1.0000 1.000 0.000
#> GSM509740 1 0.00 1.0000 1.000 0.000
#> GSM509745 1 0.00 1.0000 1.000 0.000
#> GSM509750 1 0.00 1.0000 1.000 0.000
#> GSM509751 2 0.00 0.9789 0.000 1.000
#> GSM509753 2 0.00 0.9789 0.000 1.000
#> GSM509755 2 0.00 0.9789 0.000 1.000
#> GSM509757 2 0.00 0.9789 0.000 1.000
#> GSM509759 2 0.00 0.9789 0.000 1.000
#> GSM509761 2 0.00 0.9789 0.000 1.000
#> GSM509763 2 0.00 0.9789 0.000 1.000
#> GSM509765 2 0.00 0.9789 0.000 1.000
#> GSM509767 2 0.00 0.9789 0.000 1.000
#> GSM509769 2 0.00 0.9789 0.000 1.000
#> GSM509771 2 0.00 0.9789 0.000 1.000
#> GSM509773 2 0.00 0.9789 0.000 1.000
#> GSM509775 2 0.00 0.9789 0.000 1.000
#> GSM509777 2 0.00 0.9789 0.000 1.000
#> GSM509779 2 0.00 0.9789 0.000 1.000
#> GSM509781 2 0.00 0.9789 0.000 1.000
#> GSM509783 2 0.00 0.9789 0.000 1.000
#> GSM509785 2 0.00 0.9789 0.000 1.000
#> GSM509752 2 0.00 0.9789 0.000 1.000
#> GSM509754 2 0.00 0.9789 0.000 1.000
#> GSM509756 2 0.00 0.9789 0.000 1.000
#> GSM509758 2 0.00 0.9789 0.000 1.000
#> GSM509760 2 0.00 0.9789 0.000 1.000
#> GSM509762 2 0.00 0.9789 0.000 1.000
#> GSM509764 2 0.00 0.9789 0.000 1.000
#> GSM509766 2 0.00 0.9789 0.000 1.000
#> GSM509768 2 0.00 0.9789 0.000 1.000
#> GSM509770 2 0.00 0.9789 0.000 1.000
#> GSM509772 2 0.00 0.9789 0.000 1.000
#> GSM509774 2 0.00 0.9789 0.000 1.000
#> GSM509776 2 0.00 0.9789 0.000 1.000
#> GSM509778 2 0.00 0.9789 0.000 1.000
#> GSM509780 2 0.00 0.9789 0.000 1.000
#> GSM509782 2 0.00 0.9789 0.000 1.000
#> GSM509784 2 0.00 0.9789 0.000 1.000
#> GSM509786 2 0.00 0.9789 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM509706 1 0.0000 0.506 1.000 0.000 0.000
#> GSM509711 1 0.4235 0.379 0.824 0.000 0.176
#> GSM509714 1 0.7556 0.226 0.676 0.100 0.224
#> GSM509719 1 0.3941 0.434 0.844 0.000 0.156
#> GSM509724 1 0.0000 0.506 1.000 0.000 0.000
#> GSM509729 1 0.0592 0.503 0.988 0.000 0.012
#> GSM509707 1 0.0000 0.506 1.000 0.000 0.000
#> GSM509712 1 0.4654 0.367 0.792 0.000 0.208
#> GSM509715 2 0.6940 0.336 0.068 0.708 0.224
#> GSM509720 1 0.3941 0.434 0.844 0.000 0.156
#> GSM509725 1 0.0000 0.506 1.000 0.000 0.000
#> GSM509730 1 0.2625 0.454 0.916 0.000 0.084
#> GSM509708 1 0.0000 0.506 1.000 0.000 0.000
#> GSM509713 1 0.4235 0.379 0.824 0.000 0.176
#> GSM509716 2 0.6940 0.336 0.068 0.708 0.224
#> GSM509721 1 0.3941 0.434 0.844 0.000 0.156
#> GSM509726 1 0.0000 0.506 1.000 0.000 0.000
#> GSM509731 2 0.9684 -0.240 0.340 0.436 0.224
#> GSM509709 1 0.0000 0.506 1.000 0.000 0.000
#> GSM509717 2 0.6940 0.336 0.068 0.708 0.224
#> GSM509722 1 0.4452 0.403 0.808 0.000 0.192
#> GSM509727 1 0.4750 0.364 0.784 0.000 0.216
#> GSM509710 1 0.0000 0.506 1.000 0.000 0.000
#> GSM509718 2 0.6940 0.336 0.068 0.708 0.224
#> GSM509723 1 0.3941 0.434 0.844 0.000 0.156
#> GSM509728 1 0.2796 0.424 0.908 0.000 0.092
#> GSM509732 1 0.6235 -0.474 0.564 0.000 0.436
#> GSM509736 1 0.6252 -0.500 0.556 0.000 0.444
#> GSM509741 1 0.6235 -0.474 0.564 0.000 0.436
#> GSM509746 1 0.6235 -0.474 0.564 0.000 0.436
#> GSM509733 1 0.6235 -0.474 0.564 0.000 0.436
#> GSM509737 1 0.6252 -0.500 0.556 0.000 0.444
#> GSM509742 1 0.6235 -0.474 0.564 0.000 0.436
#> GSM509747 1 0.6235 -0.474 0.564 0.000 0.436
#> GSM509734 1 0.6235 -0.474 0.564 0.000 0.436
#> GSM509738 3 0.6260 0.921 0.448 0.000 0.552
#> GSM509743 1 0.6235 -0.474 0.564 0.000 0.436
#> GSM509748 1 0.6235 -0.474 0.564 0.000 0.436
#> GSM509735 1 0.0000 0.506 1.000 0.000 0.000
#> GSM509739 1 0.0000 0.506 1.000 0.000 0.000
#> GSM509744 1 0.6309 -0.699 0.500 0.000 0.500
#> GSM509749 1 0.6235 -0.474 0.564 0.000 0.436
#> GSM509740 1 0.5098 0.336 0.752 0.000 0.248
#> GSM509745 3 0.6204 0.900 0.424 0.000 0.576
#> GSM509750 3 0.6215 0.906 0.428 0.000 0.572
#> GSM509751 2 0.6079 0.845 0.000 0.612 0.388
#> GSM509753 2 0.6079 0.845 0.000 0.612 0.388
#> GSM509755 2 0.6079 0.845 0.000 0.612 0.388
#> GSM509757 2 0.6079 0.845 0.000 0.612 0.388
#> GSM509759 2 0.6079 0.845 0.000 0.612 0.388
#> GSM509761 2 0.6079 0.845 0.000 0.612 0.388
#> GSM509763 2 0.6079 0.845 0.000 0.612 0.388
#> GSM509765 2 0.6079 0.845 0.000 0.612 0.388
#> GSM509767 2 0.6079 0.845 0.000 0.612 0.388
#> GSM509769 2 0.6079 0.845 0.000 0.612 0.388
#> GSM509771 2 0.6079 0.845 0.000 0.612 0.388
#> GSM509773 2 0.6079 0.845 0.000 0.612 0.388
#> GSM509775 2 0.6079 0.845 0.000 0.612 0.388
#> GSM509777 2 0.5016 0.792 0.000 0.760 0.240
#> GSM509779 2 0.0000 0.686 0.000 1.000 0.000
#> GSM509781 2 0.0000 0.686 0.000 1.000 0.000
#> GSM509783 2 0.0000 0.686 0.000 1.000 0.000
#> GSM509785 2 0.0000 0.686 0.000 1.000 0.000
#> GSM509752 2 0.6079 0.845 0.000 0.612 0.388
#> GSM509754 2 0.6079 0.845 0.000 0.612 0.388
#> GSM509756 2 0.6079 0.845 0.000 0.612 0.388
#> GSM509758 2 0.6079 0.845 0.000 0.612 0.388
#> GSM509760 2 0.6079 0.845 0.000 0.612 0.388
#> GSM509762 2 0.6079 0.845 0.000 0.612 0.388
#> GSM509764 2 0.6079 0.845 0.000 0.612 0.388
#> GSM509766 2 0.6079 0.845 0.000 0.612 0.388
#> GSM509768 2 0.6079 0.845 0.000 0.612 0.388
#> GSM509770 2 0.6079 0.845 0.000 0.612 0.388
#> GSM509772 2 0.6079 0.845 0.000 0.612 0.388
#> GSM509774 2 0.3340 0.742 0.000 0.880 0.120
#> GSM509776 2 0.6079 0.845 0.000 0.612 0.388
#> GSM509778 2 0.0000 0.686 0.000 1.000 0.000
#> GSM509780 2 0.6079 0.845 0.000 0.612 0.388
#> GSM509782 2 0.0000 0.686 0.000 1.000 0.000
#> GSM509784 2 0.0000 0.686 0.000 1.000 0.000
#> GSM509786 2 0.0000 0.686 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM509706 1 0.4817 0.638 0.612 0.000 0.388 0.000
#> GSM509711 1 0.5056 0.447 0.732 0.000 0.044 0.224
#> GSM509714 1 0.4795 0.349 0.696 0.000 0.012 0.292
#> GSM509719 1 0.7198 0.577 0.520 0.000 0.320 0.160
#> GSM509724 1 0.4817 0.638 0.612 0.000 0.388 0.000
#> GSM509729 1 0.4964 0.638 0.616 0.000 0.380 0.004
#> GSM509707 1 0.4817 0.638 0.612 0.000 0.388 0.000
#> GSM509712 1 0.5123 0.440 0.724 0.000 0.044 0.232
#> GSM509715 4 0.4990 0.384 0.352 0.000 0.008 0.640
#> GSM509720 1 0.7184 0.577 0.524 0.000 0.316 0.160
#> GSM509725 1 0.4817 0.638 0.612 0.000 0.388 0.000
#> GSM509730 1 0.5620 0.596 0.560 0.000 0.416 0.024
#> GSM509708 1 0.4817 0.638 0.612 0.000 0.388 0.000
#> GSM509713 1 0.1820 0.534 0.944 0.000 0.036 0.020
#> GSM509716 4 0.4990 0.384 0.352 0.000 0.008 0.640
#> GSM509721 1 0.7184 0.577 0.524 0.000 0.316 0.160
#> GSM509726 1 0.4817 0.638 0.612 0.000 0.388 0.000
#> GSM509731 4 0.5007 0.382 0.356 0.000 0.008 0.636
#> GSM509709 1 0.4817 0.638 0.612 0.000 0.388 0.000
#> GSM509717 4 0.4990 0.384 0.352 0.000 0.008 0.640
#> GSM509722 1 0.6429 0.542 0.648 0.000 0.192 0.160
#> GSM509727 1 0.5632 0.482 0.712 0.000 0.092 0.196
#> GSM509710 1 0.4817 0.638 0.612 0.000 0.388 0.000
#> GSM509718 4 0.4990 0.384 0.352 0.000 0.008 0.640
#> GSM509723 1 0.7184 0.577 0.524 0.000 0.316 0.160
#> GSM509728 3 0.5827 -0.432 0.436 0.000 0.532 0.032
#> GSM509732 3 0.0469 0.829 0.012 0.000 0.988 0.000
#> GSM509736 3 0.1545 0.812 0.008 0.000 0.952 0.040
#> GSM509741 3 0.0000 0.832 0.000 0.000 1.000 0.000
#> GSM509746 3 0.0469 0.829 0.012 0.000 0.988 0.000
#> GSM509733 3 0.0469 0.829 0.012 0.000 0.988 0.000
#> GSM509737 3 0.1545 0.812 0.008 0.000 0.952 0.040
#> GSM509742 3 0.0000 0.832 0.000 0.000 1.000 0.000
#> GSM509747 3 0.0469 0.829 0.012 0.000 0.988 0.000
#> GSM509734 3 0.0469 0.829 0.012 0.000 0.988 0.000
#> GSM509738 3 0.6001 0.521 0.184 0.000 0.688 0.128
#> GSM509743 3 0.0188 0.831 0.000 0.000 0.996 0.004
#> GSM509748 3 0.0469 0.829 0.012 0.000 0.988 0.000
#> GSM509735 1 0.4817 0.638 0.612 0.000 0.388 0.000
#> GSM509739 1 0.4817 0.638 0.612 0.000 0.388 0.000
#> GSM509744 3 0.3182 0.739 0.096 0.000 0.876 0.028
#> GSM509749 3 0.0188 0.831 0.000 0.000 0.996 0.004
#> GSM509740 1 0.5837 0.404 0.668 0.000 0.072 0.260
#> GSM509745 3 0.7098 0.312 0.312 0.000 0.536 0.152
#> GSM509750 3 0.4679 0.626 0.184 0.000 0.772 0.044
#> GSM509751 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM509753 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM509755 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM509757 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM509759 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM509761 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM509763 2 0.2943 0.887 0.032 0.892 0.000 0.076
#> GSM509765 2 0.2644 0.906 0.032 0.908 0.000 0.060
#> GSM509767 2 0.0921 0.962 0.028 0.972 0.000 0.000
#> GSM509769 2 0.0188 0.971 0.004 0.996 0.000 0.000
#> GSM509771 2 0.0921 0.962 0.028 0.972 0.000 0.000
#> GSM509773 2 0.1022 0.960 0.032 0.968 0.000 0.000
#> GSM509775 2 0.1022 0.960 0.032 0.968 0.000 0.000
#> GSM509777 4 0.5838 0.306 0.032 0.444 0.000 0.524
#> GSM509779 4 0.5085 0.675 0.032 0.260 0.000 0.708
#> GSM509781 4 0.4134 0.692 0.000 0.260 0.000 0.740
#> GSM509783 4 0.4134 0.692 0.000 0.260 0.000 0.740
#> GSM509785 4 0.4134 0.692 0.000 0.260 0.000 0.740
#> GSM509752 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM509754 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM509756 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM509758 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM509760 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM509762 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM509764 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM509766 2 0.2565 0.911 0.032 0.912 0.000 0.056
#> GSM509768 2 0.1022 0.960 0.032 0.968 0.000 0.000
#> GSM509770 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM509772 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM509774 4 0.5432 0.598 0.032 0.316 0.000 0.652
#> GSM509776 2 0.1022 0.960 0.032 0.968 0.000 0.000
#> GSM509778 4 0.4134 0.692 0.000 0.260 0.000 0.740
#> GSM509780 2 0.3523 0.838 0.032 0.856 0.000 0.112
#> GSM509782 4 0.4134 0.692 0.000 0.260 0.000 0.740
#> GSM509784 4 0.5085 0.675 0.032 0.260 0.000 0.708
#> GSM509786 4 0.4134 0.692 0.000 0.260 0.000 0.740
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM509706 1 0.0162 0.7679 0.996 0.000 0.004 0.000 0.000
#> GSM509711 5 0.4180 0.6078 0.220 0.000 0.000 0.036 0.744
#> GSM509714 5 0.2305 0.7319 0.092 0.000 0.000 0.012 0.896
#> GSM509719 1 0.6570 0.4439 0.528 0.000 0.040 0.096 0.336
#> GSM509724 1 0.0671 0.7637 0.980 0.000 0.004 0.016 0.000
#> GSM509729 1 0.3579 0.7116 0.828 0.000 0.000 0.100 0.072
#> GSM509707 1 0.0162 0.7679 0.996 0.000 0.004 0.000 0.000
#> GSM509712 5 0.3954 0.6314 0.192 0.000 0.000 0.036 0.772
#> GSM509715 5 0.2124 0.7812 0.004 0.000 0.000 0.096 0.900
#> GSM509720 1 0.6570 0.4439 0.528 0.000 0.040 0.096 0.336
#> GSM509725 1 0.0671 0.7637 0.980 0.000 0.004 0.016 0.000
#> GSM509730 1 0.5056 0.6723 0.752 0.000 0.040 0.100 0.108
#> GSM509708 1 0.0162 0.7679 0.996 0.000 0.004 0.000 0.000
#> GSM509713 1 0.4479 0.4950 0.700 0.000 0.000 0.036 0.264
#> GSM509716 5 0.2124 0.7812 0.004 0.000 0.000 0.096 0.900
#> GSM509721 1 0.6570 0.4439 0.528 0.000 0.040 0.096 0.336
#> GSM509726 1 0.1041 0.7597 0.964 0.000 0.004 0.032 0.000
#> GSM509731 5 0.1892 0.7814 0.004 0.000 0.000 0.080 0.916
#> GSM509709 1 0.0162 0.7679 0.996 0.000 0.004 0.000 0.000
#> GSM509717 5 0.2124 0.7812 0.004 0.000 0.000 0.096 0.900
#> GSM509722 1 0.6595 0.3585 0.492 0.000 0.036 0.096 0.376
#> GSM509727 5 0.5564 0.4523 0.284 0.000 0.004 0.092 0.620
#> GSM509710 1 0.0162 0.7679 0.996 0.000 0.004 0.000 0.000
#> GSM509718 5 0.2338 0.7774 0.004 0.000 0.000 0.112 0.884
#> GSM509723 1 0.6570 0.4439 0.528 0.000 0.040 0.096 0.336
#> GSM509728 1 0.7225 -0.1915 0.436 0.000 0.384 0.092 0.088
#> GSM509732 3 0.2286 0.9075 0.108 0.000 0.888 0.004 0.000
#> GSM509736 3 0.5531 0.8538 0.108 0.000 0.724 0.080 0.088
#> GSM509741 3 0.2127 0.9074 0.108 0.000 0.892 0.000 0.000
#> GSM509746 3 0.2286 0.9075 0.108 0.000 0.888 0.004 0.000
#> GSM509733 3 0.2286 0.9075 0.108 0.000 0.888 0.004 0.000
#> GSM509737 3 0.5531 0.8538 0.108 0.000 0.724 0.080 0.088
#> GSM509742 3 0.2127 0.9074 0.108 0.000 0.892 0.000 0.000
#> GSM509747 3 0.2286 0.9075 0.108 0.000 0.888 0.004 0.000
#> GSM509734 3 0.2286 0.9075 0.108 0.000 0.888 0.004 0.000
#> GSM509738 3 0.6837 0.4172 0.068 0.000 0.496 0.080 0.356
#> GSM509743 3 0.4461 0.8851 0.108 0.000 0.792 0.068 0.032
#> GSM509748 3 0.2286 0.9075 0.108 0.000 0.888 0.004 0.000
#> GSM509735 1 0.0162 0.7679 0.996 0.000 0.004 0.000 0.000
#> GSM509739 1 0.0324 0.7669 0.992 0.000 0.004 0.004 0.000
#> GSM509744 3 0.5325 0.8471 0.084 0.000 0.740 0.076 0.100
#> GSM509749 3 0.3654 0.8979 0.108 0.000 0.836 0.036 0.020
#> GSM509740 5 0.2983 0.7281 0.056 0.000 0.000 0.076 0.868
#> GSM509745 5 0.6357 -0.0356 0.024 0.000 0.384 0.092 0.500
#> GSM509750 3 0.5466 0.8175 0.068 0.000 0.724 0.076 0.132
#> GSM509751 2 0.0290 0.9128 0.000 0.992 0.008 0.000 0.000
#> GSM509753 2 0.0290 0.9128 0.000 0.992 0.008 0.000 0.000
#> GSM509755 2 0.0290 0.9128 0.000 0.992 0.008 0.000 0.000
#> GSM509757 2 0.0404 0.9118 0.000 0.988 0.012 0.000 0.000
#> GSM509759 2 0.0609 0.9083 0.000 0.980 0.020 0.000 0.000
#> GSM509761 2 0.0404 0.9127 0.000 0.988 0.012 0.000 0.000
#> GSM509763 2 0.4675 0.7001 0.000 0.744 0.088 0.164 0.004
#> GSM509765 2 0.4675 0.7001 0.000 0.744 0.088 0.164 0.004
#> GSM509767 2 0.1757 0.9001 0.000 0.936 0.048 0.012 0.004
#> GSM509769 2 0.0932 0.9077 0.000 0.972 0.020 0.004 0.004
#> GSM509771 2 0.1757 0.9001 0.000 0.936 0.048 0.012 0.004
#> GSM509773 2 0.3178 0.8451 0.000 0.860 0.088 0.048 0.004
#> GSM509775 2 0.3178 0.8451 0.000 0.860 0.088 0.048 0.004
#> GSM509777 4 0.5279 0.7970 0.000 0.268 0.076 0.652 0.004
#> GSM509779 4 0.4021 0.9130 0.000 0.200 0.036 0.764 0.000
#> GSM509781 4 0.4237 0.9361 0.000 0.200 0.000 0.752 0.048
#> GSM509783 4 0.4237 0.9361 0.000 0.200 0.000 0.752 0.048
#> GSM509785 4 0.4237 0.9361 0.000 0.200 0.000 0.752 0.048
#> GSM509752 2 0.0000 0.9140 0.000 1.000 0.000 0.000 0.000
#> GSM509754 2 0.0162 0.9136 0.000 0.996 0.004 0.000 0.000
#> GSM509756 2 0.0000 0.9140 0.000 1.000 0.000 0.000 0.000
#> GSM509758 2 0.0000 0.9140 0.000 1.000 0.000 0.000 0.000
#> GSM509760 2 0.0162 0.9136 0.000 0.996 0.004 0.000 0.000
#> GSM509762 2 0.0000 0.9140 0.000 1.000 0.000 0.000 0.000
#> GSM509764 2 0.0000 0.9140 0.000 1.000 0.000 0.000 0.000
#> GSM509766 2 0.4559 0.7193 0.000 0.756 0.088 0.152 0.004
#> GSM509768 2 0.3178 0.8451 0.000 0.860 0.088 0.048 0.004
#> GSM509770 2 0.0404 0.9139 0.000 0.988 0.012 0.000 0.000
#> GSM509772 2 0.0609 0.9083 0.000 0.980 0.020 0.000 0.000
#> GSM509774 4 0.5004 0.8642 0.000 0.224 0.076 0.696 0.004
#> GSM509776 2 0.3178 0.8451 0.000 0.860 0.088 0.048 0.004
#> GSM509778 4 0.4168 0.9358 0.000 0.200 0.000 0.756 0.044
#> GSM509780 2 0.5067 0.6196 0.000 0.700 0.092 0.204 0.004
#> GSM509782 4 0.4237 0.9361 0.000 0.200 0.000 0.752 0.048
#> GSM509784 4 0.4459 0.9032 0.000 0.200 0.052 0.744 0.004
#> GSM509786 4 0.4237 0.9361 0.000 0.200 0.000 0.752 0.048
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM509706 1 0.0653 0.738 0.980 0.000 0.012 0.004 0.000 NA
#> GSM509711 5 0.5159 0.576 0.188 0.000 0.000 0.032 0.676 NA
#> GSM509714 5 0.1794 0.749 0.036 0.000 0.000 0.000 0.924 NA
#> GSM509719 1 0.6332 0.442 0.424 0.000 0.016 0.000 0.232 NA
#> GSM509724 1 0.0912 0.733 0.972 0.000 0.012 0.004 0.008 NA
#> GSM509729 1 0.5044 0.609 0.616 0.000 0.004 0.016 0.052 NA
#> GSM509707 1 0.0653 0.738 0.980 0.000 0.012 0.004 0.000 NA
#> GSM509712 5 0.5082 0.594 0.172 0.000 0.000 0.032 0.688 NA
#> GSM509715 5 0.1863 0.792 0.000 0.000 0.000 0.104 0.896 NA
#> GSM509720 1 0.6332 0.442 0.424 0.000 0.016 0.000 0.232 NA
#> GSM509725 1 0.0912 0.733 0.972 0.000 0.012 0.004 0.008 NA
#> GSM509730 1 0.5624 0.581 0.568 0.000 0.020 0.016 0.064 NA
#> GSM509708 1 0.0653 0.738 0.980 0.000 0.012 0.004 0.000 NA
#> GSM509713 1 0.5295 0.479 0.656 0.000 0.000 0.032 0.208 NA
#> GSM509716 5 0.1863 0.792 0.000 0.000 0.000 0.104 0.896 NA
#> GSM509721 1 0.6332 0.442 0.424 0.000 0.016 0.000 0.232 NA
#> GSM509726 1 0.2911 0.688 0.880 0.000 0.012 0.028 0.032 NA
#> GSM509731 5 0.2006 0.791 0.000 0.000 0.000 0.104 0.892 NA
#> GSM509709 1 0.0653 0.738 0.980 0.000 0.012 0.004 0.000 NA
#> GSM509717 5 0.1863 0.792 0.000 0.000 0.000 0.104 0.896 NA
#> GSM509722 1 0.6381 0.413 0.408 0.000 0.016 0.000 0.248 NA
#> GSM509727 5 0.6706 0.453 0.184 0.000 0.004 0.060 0.492 NA
#> GSM509710 1 0.0653 0.738 0.980 0.000 0.012 0.004 0.000 NA
#> GSM509718 5 0.2006 0.791 0.000 0.000 0.000 0.104 0.892 NA
#> GSM509723 1 0.6332 0.442 0.424 0.000 0.016 0.000 0.232 NA
#> GSM509728 3 0.8001 0.269 0.300 0.000 0.304 0.064 0.068 NA
#> GSM509732 3 0.1477 0.784 0.048 0.000 0.940 0.004 0.000 NA
#> GSM509736 3 0.5880 0.715 0.048 0.000 0.612 0.036 0.044 NA
#> GSM509741 3 0.1219 0.785 0.048 0.000 0.948 0.000 0.000 NA
#> GSM509746 3 0.1477 0.784 0.048 0.000 0.940 0.004 0.000 NA
#> GSM509733 3 0.1477 0.784 0.048 0.000 0.940 0.004 0.000 NA
#> GSM509737 3 0.5880 0.715 0.048 0.000 0.612 0.036 0.044 NA
#> GSM509742 3 0.1219 0.785 0.048 0.000 0.948 0.000 0.000 NA
#> GSM509747 3 0.1477 0.784 0.048 0.000 0.940 0.004 0.000 NA
#> GSM509734 3 0.1477 0.784 0.048 0.000 0.940 0.004 0.000 NA
#> GSM509738 3 0.7173 0.400 0.020 0.000 0.396 0.044 0.236 NA
#> GSM509743 3 0.4722 0.758 0.048 0.000 0.732 0.028 0.016 NA
#> GSM509748 3 0.1333 0.784 0.048 0.000 0.944 0.000 0.000 NA
#> GSM509735 1 0.0363 0.738 0.988 0.000 0.012 0.000 0.000 NA
#> GSM509739 1 0.0363 0.738 0.988 0.000 0.012 0.000 0.000 NA
#> GSM509744 3 0.5621 0.725 0.036 0.000 0.652 0.036 0.052 NA
#> GSM509749 3 0.3912 0.773 0.048 0.000 0.808 0.024 0.012 NA
#> GSM509740 5 0.4686 0.589 0.008 0.000 0.004 0.044 0.648 NA
#> GSM509745 3 0.7072 0.218 0.008 0.000 0.336 0.044 0.312 NA
#> GSM509750 3 0.6040 0.680 0.020 0.000 0.604 0.044 0.092 NA
#> GSM509751 2 0.0508 0.837 0.000 0.984 0.012 0.000 0.000 NA
#> GSM509753 2 0.0653 0.837 0.000 0.980 0.012 0.000 0.004 NA
#> GSM509755 2 0.0653 0.837 0.000 0.980 0.012 0.000 0.004 NA
#> GSM509757 2 0.0767 0.836 0.000 0.976 0.012 0.000 0.004 NA
#> GSM509759 2 0.1478 0.825 0.000 0.944 0.020 0.000 0.004 NA
#> GSM509761 2 0.1219 0.838 0.000 0.948 0.004 0.000 0.000 NA
#> GSM509763 2 0.5195 0.587 0.000 0.568 0.016 0.064 0.000 NA
#> GSM509765 2 0.4717 0.611 0.000 0.580 0.000 0.056 0.000 NA
#> GSM509767 2 0.2783 0.807 0.000 0.836 0.016 0.000 0.000 NA
#> GSM509769 2 0.2361 0.818 0.000 0.880 0.012 0.000 0.004 NA
#> GSM509771 2 0.2783 0.807 0.000 0.836 0.016 0.000 0.000 NA
#> GSM509773 2 0.3769 0.682 0.000 0.640 0.004 0.000 0.000 NA
#> GSM509775 2 0.3861 0.683 0.000 0.640 0.008 0.000 0.000 NA
#> GSM509777 4 0.5714 0.688 0.000 0.128 0.016 0.544 0.000 NA
#> GSM509779 4 0.4341 0.819 0.000 0.084 0.016 0.748 0.000 NA
#> GSM509781 4 0.1610 0.864 0.000 0.084 0.000 0.916 0.000 NA
#> GSM509783 4 0.1610 0.864 0.000 0.084 0.000 0.916 0.000 NA
#> GSM509785 4 0.1610 0.864 0.000 0.084 0.000 0.916 0.000 NA
#> GSM509752 2 0.0260 0.840 0.000 0.992 0.000 0.000 0.000 NA
#> GSM509754 2 0.0000 0.839 0.000 1.000 0.000 0.000 0.000 NA
#> GSM509756 2 0.0665 0.840 0.000 0.980 0.008 0.000 0.004 NA
#> GSM509758 2 0.0363 0.841 0.000 0.988 0.000 0.000 0.000 NA
#> GSM509760 2 0.0665 0.839 0.000 0.980 0.008 0.000 0.004 NA
#> GSM509762 2 0.0603 0.841 0.000 0.980 0.004 0.000 0.000 NA
#> GSM509764 2 0.0665 0.840 0.000 0.980 0.008 0.000 0.004 NA
#> GSM509766 2 0.4717 0.611 0.000 0.580 0.000 0.056 0.000 NA
#> GSM509768 2 0.3861 0.683 0.000 0.640 0.008 0.000 0.000 NA
#> GSM509770 2 0.1578 0.836 0.000 0.936 0.012 0.000 0.004 NA
#> GSM509772 2 0.1485 0.828 0.000 0.944 0.024 0.000 0.004 NA
#> GSM509774 4 0.5452 0.722 0.000 0.100 0.016 0.576 0.000 NA
#> GSM509776 2 0.3969 0.685 0.000 0.644 0.008 0.000 0.004 NA
#> GSM509778 4 0.1897 0.862 0.004 0.084 0.000 0.908 0.000 NA
#> GSM509780 2 0.5597 0.516 0.000 0.524 0.016 0.100 0.000 NA
#> GSM509782 4 0.1610 0.864 0.000 0.084 0.000 0.916 0.000 NA
#> GSM509784 4 0.4995 0.774 0.000 0.084 0.016 0.656 0.000 NA
#> GSM509786 4 0.1610 0.864 0.000 0.084 0.000 0.916 0.000 NA
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 disease.state(p) time(p) k
#> MAD:kmeans 80 3.52e-15 2.80e-12 2
#> MAD:kmeans 50 2.49e-15 1.53e-10 3
#> MAD:kmeans 68 8.55e-24 5.14e-08 4
#> MAD:kmeans 71 1.83e-22 3.13e-07 5
#> MAD:kmeans 71 1.83e-22 3.13e-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["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 19175 rows and 81 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 1.000 0.987 0.995 0.5067 0.494 0.494
#> 3 3 0.859 0.923 0.932 0.2613 0.800 0.618
#> 4 4 0.883 0.928 0.957 0.1509 0.864 0.635
#> 5 5 0.846 0.818 0.899 0.0704 0.914 0.691
#> 6 6 0.825 0.744 0.850 0.0350 0.974 0.876
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
#> GSM509706 1 0.000 0.990 1.000 0.000
#> GSM509711 1 0.000 0.990 1.000 0.000
#> GSM509714 1 0.000 0.990 1.000 0.000
#> GSM509719 1 0.000 0.990 1.000 0.000
#> GSM509724 1 0.000 0.990 1.000 0.000
#> GSM509729 1 0.000 0.990 1.000 0.000
#> GSM509707 1 0.000 0.990 1.000 0.000
#> GSM509712 1 0.000 0.990 1.000 0.000
#> GSM509715 2 0.000 1.000 0.000 1.000
#> GSM509720 1 0.000 0.990 1.000 0.000
#> GSM509725 1 0.000 0.990 1.000 0.000
#> GSM509730 1 0.000 0.990 1.000 0.000
#> GSM509708 1 0.000 0.990 1.000 0.000
#> GSM509713 1 0.000 0.990 1.000 0.000
#> GSM509716 2 0.000 1.000 0.000 1.000
#> GSM509721 1 0.000 0.990 1.000 0.000
#> GSM509726 1 0.000 0.990 1.000 0.000
#> GSM509731 1 0.969 0.344 0.604 0.396
#> GSM509709 1 0.000 0.990 1.000 0.000
#> GSM509717 2 0.000 1.000 0.000 1.000
#> GSM509722 1 0.000 0.990 1.000 0.000
#> GSM509727 1 0.000 0.990 1.000 0.000
#> GSM509710 1 0.000 0.990 1.000 0.000
#> GSM509718 2 0.000 1.000 0.000 1.000
#> GSM509723 1 0.000 0.990 1.000 0.000
#> GSM509728 1 0.000 0.990 1.000 0.000
#> GSM509732 1 0.000 0.990 1.000 0.000
#> GSM509736 1 0.000 0.990 1.000 0.000
#> GSM509741 1 0.000 0.990 1.000 0.000
#> GSM509746 1 0.000 0.990 1.000 0.000
#> GSM509733 1 0.000 0.990 1.000 0.000
#> GSM509737 1 0.000 0.990 1.000 0.000
#> GSM509742 1 0.000 0.990 1.000 0.000
#> GSM509747 1 0.000 0.990 1.000 0.000
#> GSM509734 1 0.000 0.990 1.000 0.000
#> GSM509738 1 0.000 0.990 1.000 0.000
#> GSM509743 1 0.000 0.990 1.000 0.000
#> GSM509748 1 0.000 0.990 1.000 0.000
#> GSM509735 1 0.000 0.990 1.000 0.000
#> GSM509739 1 0.000 0.990 1.000 0.000
#> GSM509744 1 0.000 0.990 1.000 0.000
#> GSM509749 1 0.000 0.990 1.000 0.000
#> GSM509740 1 0.000 0.990 1.000 0.000
#> GSM509745 1 0.000 0.990 1.000 0.000
#> GSM509750 1 0.000 0.990 1.000 0.000
#> GSM509751 2 0.000 1.000 0.000 1.000
#> GSM509753 2 0.000 1.000 0.000 1.000
#> GSM509755 2 0.000 1.000 0.000 1.000
#> GSM509757 2 0.000 1.000 0.000 1.000
#> GSM509759 2 0.000 1.000 0.000 1.000
#> GSM509761 2 0.000 1.000 0.000 1.000
#> GSM509763 2 0.000 1.000 0.000 1.000
#> GSM509765 2 0.000 1.000 0.000 1.000
#> GSM509767 2 0.000 1.000 0.000 1.000
#> GSM509769 2 0.000 1.000 0.000 1.000
#> GSM509771 2 0.000 1.000 0.000 1.000
#> GSM509773 2 0.000 1.000 0.000 1.000
#> GSM509775 2 0.000 1.000 0.000 1.000
#> GSM509777 2 0.000 1.000 0.000 1.000
#> GSM509779 2 0.000 1.000 0.000 1.000
#> GSM509781 2 0.000 1.000 0.000 1.000
#> GSM509783 2 0.000 1.000 0.000 1.000
#> GSM509785 2 0.000 1.000 0.000 1.000
#> GSM509752 2 0.000 1.000 0.000 1.000
#> GSM509754 2 0.000 1.000 0.000 1.000
#> GSM509756 2 0.000 1.000 0.000 1.000
#> GSM509758 2 0.000 1.000 0.000 1.000
#> GSM509760 2 0.000 1.000 0.000 1.000
#> GSM509762 2 0.000 1.000 0.000 1.000
#> GSM509764 2 0.000 1.000 0.000 1.000
#> GSM509766 2 0.000 1.000 0.000 1.000
#> GSM509768 2 0.000 1.000 0.000 1.000
#> GSM509770 2 0.000 1.000 0.000 1.000
#> GSM509772 2 0.000 1.000 0.000 1.000
#> GSM509774 2 0.000 1.000 0.000 1.000
#> GSM509776 2 0.000 1.000 0.000 1.000
#> GSM509778 2 0.000 1.000 0.000 1.000
#> GSM509780 2 0.000 1.000 0.000 1.000
#> GSM509782 2 0.000 1.000 0.000 1.000
#> GSM509784 2 0.000 1.000 0.000 1.000
#> GSM509786 2 0.000 1.000 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM509706 1 0.5016 0.885 0.760 0.000 0.240
#> GSM509711 1 0.1860 0.821 0.948 0.000 0.052
#> GSM509714 1 0.0000 0.790 1.000 0.000 0.000
#> GSM509719 1 0.4931 0.886 0.768 0.000 0.232
#> GSM509724 1 0.5016 0.885 0.760 0.000 0.240
#> GSM509729 1 0.5016 0.885 0.760 0.000 0.240
#> GSM509707 1 0.5016 0.885 0.760 0.000 0.240
#> GSM509712 1 0.1860 0.821 0.948 0.000 0.052
#> GSM509715 1 0.0424 0.785 0.992 0.008 0.000
#> GSM509720 1 0.4931 0.886 0.768 0.000 0.232
#> GSM509725 1 0.5016 0.885 0.760 0.000 0.240
#> GSM509730 1 0.5016 0.885 0.760 0.000 0.240
#> GSM509708 1 0.5016 0.885 0.760 0.000 0.240
#> GSM509713 1 0.1860 0.821 0.948 0.000 0.052
#> GSM509716 1 0.0000 0.790 1.000 0.000 0.000
#> GSM509721 1 0.4931 0.886 0.768 0.000 0.232
#> GSM509726 1 0.5016 0.885 0.760 0.000 0.240
#> GSM509731 1 0.0000 0.790 1.000 0.000 0.000
#> GSM509709 1 0.5016 0.885 0.760 0.000 0.240
#> GSM509717 1 0.0237 0.788 0.996 0.004 0.000
#> GSM509722 1 0.4931 0.886 0.768 0.000 0.232
#> GSM509727 1 0.4796 0.882 0.780 0.000 0.220
#> GSM509710 1 0.5016 0.885 0.760 0.000 0.240
#> GSM509718 1 0.3686 0.638 0.860 0.140 0.000
#> GSM509723 1 0.4931 0.886 0.768 0.000 0.232
#> GSM509728 3 0.5560 0.378 0.300 0.000 0.700
#> GSM509732 3 0.0000 0.961 0.000 0.000 1.000
#> GSM509736 3 0.0000 0.961 0.000 0.000 1.000
#> GSM509741 3 0.0000 0.961 0.000 0.000 1.000
#> GSM509746 3 0.0000 0.961 0.000 0.000 1.000
#> GSM509733 3 0.0000 0.961 0.000 0.000 1.000
#> GSM509737 3 0.0000 0.961 0.000 0.000 1.000
#> GSM509742 3 0.0000 0.961 0.000 0.000 1.000
#> GSM509747 3 0.0000 0.961 0.000 0.000 1.000
#> GSM509734 3 0.0000 0.961 0.000 0.000 1.000
#> GSM509738 3 0.0000 0.961 0.000 0.000 1.000
#> GSM509743 3 0.0000 0.961 0.000 0.000 1.000
#> GSM509748 3 0.0000 0.961 0.000 0.000 1.000
#> GSM509735 1 0.5016 0.885 0.760 0.000 0.240
#> GSM509739 1 0.5016 0.885 0.760 0.000 0.240
#> GSM509744 3 0.0000 0.961 0.000 0.000 1.000
#> GSM509749 3 0.0000 0.961 0.000 0.000 1.000
#> GSM509740 1 0.1964 0.820 0.944 0.000 0.056
#> GSM509745 3 0.4291 0.747 0.180 0.000 0.820
#> GSM509750 3 0.0000 0.961 0.000 0.000 1.000
#> GSM509751 2 0.0000 0.989 0.000 1.000 0.000
#> GSM509753 2 0.0000 0.989 0.000 1.000 0.000
#> GSM509755 2 0.0000 0.989 0.000 1.000 0.000
#> GSM509757 2 0.0000 0.989 0.000 1.000 0.000
#> GSM509759 2 0.0000 0.989 0.000 1.000 0.000
#> GSM509761 2 0.0000 0.989 0.000 1.000 0.000
#> GSM509763 2 0.0000 0.989 0.000 1.000 0.000
#> GSM509765 2 0.0000 0.989 0.000 1.000 0.000
#> GSM509767 2 0.0000 0.989 0.000 1.000 0.000
#> GSM509769 2 0.0000 0.989 0.000 1.000 0.000
#> GSM509771 2 0.0000 0.989 0.000 1.000 0.000
#> GSM509773 2 0.0000 0.989 0.000 1.000 0.000
#> GSM509775 2 0.0000 0.989 0.000 1.000 0.000
#> GSM509777 2 0.0000 0.989 0.000 1.000 0.000
#> GSM509779 2 0.1860 0.962 0.052 0.948 0.000
#> GSM509781 2 0.1860 0.962 0.052 0.948 0.000
#> GSM509783 2 0.1860 0.962 0.052 0.948 0.000
#> GSM509785 2 0.1860 0.962 0.052 0.948 0.000
#> GSM509752 2 0.0000 0.989 0.000 1.000 0.000
#> GSM509754 2 0.0000 0.989 0.000 1.000 0.000
#> GSM509756 2 0.0000 0.989 0.000 1.000 0.000
#> GSM509758 2 0.0000 0.989 0.000 1.000 0.000
#> GSM509760 2 0.0000 0.989 0.000 1.000 0.000
#> GSM509762 2 0.0000 0.989 0.000 1.000 0.000
#> GSM509764 2 0.0000 0.989 0.000 1.000 0.000
#> GSM509766 2 0.0000 0.989 0.000 1.000 0.000
#> GSM509768 2 0.0000 0.989 0.000 1.000 0.000
#> GSM509770 2 0.0000 0.989 0.000 1.000 0.000
#> GSM509772 2 0.0000 0.989 0.000 1.000 0.000
#> GSM509774 2 0.0237 0.987 0.004 0.996 0.000
#> GSM509776 2 0.0000 0.989 0.000 1.000 0.000
#> GSM509778 2 0.1860 0.962 0.052 0.948 0.000
#> GSM509780 2 0.0000 0.989 0.000 1.000 0.000
#> GSM509782 2 0.1860 0.962 0.052 0.948 0.000
#> GSM509784 2 0.1860 0.962 0.052 0.948 0.000
#> GSM509786 2 0.1860 0.962 0.052 0.948 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM509706 1 0.0000 0.9570 1.000 0.000 0.000 0.000
#> GSM509711 1 0.3219 0.8448 0.836 0.000 0.000 0.164
#> GSM509714 1 0.3486 0.8240 0.812 0.000 0.000 0.188
#> GSM509719 1 0.0000 0.9570 1.000 0.000 0.000 0.000
#> GSM509724 1 0.0000 0.9570 1.000 0.000 0.000 0.000
#> GSM509729 1 0.0000 0.9570 1.000 0.000 0.000 0.000
#> GSM509707 1 0.0000 0.9570 1.000 0.000 0.000 0.000
#> GSM509712 1 0.3219 0.8448 0.836 0.000 0.000 0.164
#> GSM509715 4 0.0000 0.8208 0.000 0.000 0.000 1.000
#> GSM509720 1 0.0000 0.9570 1.000 0.000 0.000 0.000
#> GSM509725 1 0.0000 0.9570 1.000 0.000 0.000 0.000
#> GSM509730 1 0.0000 0.9570 1.000 0.000 0.000 0.000
#> GSM509708 1 0.0000 0.9570 1.000 0.000 0.000 0.000
#> GSM509713 1 0.0336 0.9532 0.992 0.000 0.000 0.008
#> GSM509716 4 0.0000 0.8208 0.000 0.000 0.000 1.000
#> GSM509721 1 0.0000 0.9570 1.000 0.000 0.000 0.000
#> GSM509726 1 0.0000 0.9570 1.000 0.000 0.000 0.000
#> GSM509731 4 0.0336 0.8160 0.008 0.000 0.000 0.992
#> GSM509709 1 0.0000 0.9570 1.000 0.000 0.000 0.000
#> GSM509717 4 0.0000 0.8208 0.000 0.000 0.000 1.000
#> GSM509722 1 0.0000 0.9570 1.000 0.000 0.000 0.000
#> GSM509727 1 0.0336 0.9533 0.992 0.000 0.000 0.008
#> GSM509710 1 0.0000 0.9570 1.000 0.000 0.000 0.000
#> GSM509718 4 0.0000 0.8208 0.000 0.000 0.000 1.000
#> GSM509723 1 0.0000 0.9570 1.000 0.000 0.000 0.000
#> GSM509728 1 0.3649 0.7479 0.796 0.000 0.204 0.000
#> GSM509732 3 0.0000 0.9933 0.000 0.000 1.000 0.000
#> GSM509736 3 0.0000 0.9933 0.000 0.000 1.000 0.000
#> GSM509741 3 0.0000 0.9933 0.000 0.000 1.000 0.000
#> GSM509746 3 0.0000 0.9933 0.000 0.000 1.000 0.000
#> GSM509733 3 0.0000 0.9933 0.000 0.000 1.000 0.000
#> GSM509737 3 0.0000 0.9933 0.000 0.000 1.000 0.000
#> GSM509742 3 0.0000 0.9933 0.000 0.000 1.000 0.000
#> GSM509747 3 0.0000 0.9933 0.000 0.000 1.000 0.000
#> GSM509734 3 0.0000 0.9933 0.000 0.000 1.000 0.000
#> GSM509738 3 0.0188 0.9903 0.000 0.000 0.996 0.004
#> GSM509743 3 0.0000 0.9933 0.000 0.000 1.000 0.000
#> GSM509748 3 0.0000 0.9933 0.000 0.000 1.000 0.000
#> GSM509735 1 0.0000 0.9570 1.000 0.000 0.000 0.000
#> GSM509739 1 0.0000 0.9570 1.000 0.000 0.000 0.000
#> GSM509744 3 0.0000 0.9933 0.000 0.000 1.000 0.000
#> GSM509749 3 0.0000 0.9933 0.000 0.000 1.000 0.000
#> GSM509740 1 0.6260 0.6735 0.664 0.000 0.144 0.192
#> GSM509745 3 0.2408 0.8964 0.000 0.000 0.896 0.104
#> GSM509750 3 0.0000 0.9933 0.000 0.000 1.000 0.000
#> GSM509751 2 0.0000 0.9772 0.000 1.000 0.000 0.000
#> GSM509753 2 0.0000 0.9772 0.000 1.000 0.000 0.000
#> GSM509755 2 0.0000 0.9772 0.000 1.000 0.000 0.000
#> GSM509757 2 0.0000 0.9772 0.000 1.000 0.000 0.000
#> GSM509759 2 0.0000 0.9772 0.000 1.000 0.000 0.000
#> GSM509761 2 0.0000 0.9772 0.000 1.000 0.000 0.000
#> GSM509763 2 0.0188 0.9738 0.000 0.996 0.000 0.004
#> GSM509765 2 0.0336 0.9698 0.000 0.992 0.000 0.008
#> GSM509767 2 0.0000 0.9772 0.000 1.000 0.000 0.000
#> GSM509769 2 0.0000 0.9772 0.000 1.000 0.000 0.000
#> GSM509771 2 0.0000 0.9772 0.000 1.000 0.000 0.000
#> GSM509773 2 0.0000 0.9772 0.000 1.000 0.000 0.000
#> GSM509775 2 0.0000 0.9772 0.000 1.000 0.000 0.000
#> GSM509777 2 0.4955 -0.0793 0.000 0.556 0.000 0.444
#> GSM509779 4 0.3569 0.8888 0.000 0.196 0.000 0.804
#> GSM509781 4 0.3528 0.8918 0.000 0.192 0.000 0.808
#> GSM509783 4 0.3528 0.8918 0.000 0.192 0.000 0.808
#> GSM509785 4 0.3528 0.8918 0.000 0.192 0.000 0.808
#> GSM509752 2 0.0000 0.9772 0.000 1.000 0.000 0.000
#> GSM509754 2 0.0000 0.9772 0.000 1.000 0.000 0.000
#> GSM509756 2 0.0000 0.9772 0.000 1.000 0.000 0.000
#> GSM509758 2 0.0000 0.9772 0.000 1.000 0.000 0.000
#> GSM509760 2 0.0000 0.9772 0.000 1.000 0.000 0.000
#> GSM509762 2 0.0000 0.9772 0.000 1.000 0.000 0.000
#> GSM509764 2 0.0000 0.9772 0.000 1.000 0.000 0.000
#> GSM509766 2 0.0000 0.9772 0.000 1.000 0.000 0.000
#> GSM509768 2 0.0188 0.9738 0.000 0.996 0.000 0.004
#> GSM509770 2 0.0000 0.9772 0.000 1.000 0.000 0.000
#> GSM509772 2 0.0000 0.9772 0.000 1.000 0.000 0.000
#> GSM509774 4 0.4193 0.7964 0.000 0.268 0.000 0.732
#> GSM509776 2 0.0000 0.9772 0.000 1.000 0.000 0.000
#> GSM509778 4 0.3528 0.8918 0.000 0.192 0.000 0.808
#> GSM509780 2 0.1118 0.9386 0.000 0.964 0.000 0.036
#> GSM509782 4 0.3528 0.8918 0.000 0.192 0.000 0.808
#> GSM509784 4 0.3569 0.8888 0.000 0.196 0.000 0.804
#> GSM509786 4 0.3528 0.8918 0.000 0.192 0.000 0.808
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM509706 1 0.0000 0.869 1.000 0.000 0.000 0.000 0.000
#> GSM509711 1 0.4341 0.286 0.592 0.000 0.000 0.004 0.404
#> GSM509714 5 0.2377 0.695 0.128 0.000 0.000 0.000 0.872
#> GSM509719 1 0.3650 0.796 0.796 0.000 0.000 0.028 0.176
#> GSM509724 1 0.0000 0.869 1.000 0.000 0.000 0.000 0.000
#> GSM509729 1 0.2079 0.847 0.916 0.000 0.000 0.020 0.064
#> GSM509707 1 0.0000 0.869 1.000 0.000 0.000 0.000 0.000
#> GSM509712 1 0.4367 0.260 0.580 0.000 0.000 0.004 0.416
#> GSM509715 5 0.3210 0.891 0.000 0.000 0.000 0.212 0.788
#> GSM509720 1 0.3650 0.796 0.796 0.000 0.000 0.028 0.176
#> GSM509725 1 0.0000 0.869 1.000 0.000 0.000 0.000 0.000
#> GSM509730 1 0.2616 0.834 0.880 0.000 0.000 0.020 0.100
#> GSM509708 1 0.0000 0.869 1.000 0.000 0.000 0.000 0.000
#> GSM509713 1 0.0771 0.858 0.976 0.000 0.000 0.004 0.020
#> GSM509716 5 0.3177 0.891 0.000 0.000 0.000 0.208 0.792
#> GSM509721 1 0.3650 0.796 0.796 0.000 0.000 0.028 0.176
#> GSM509726 1 0.0162 0.867 0.996 0.000 0.000 0.004 0.000
#> GSM509731 5 0.3210 0.891 0.000 0.000 0.000 0.212 0.788
#> GSM509709 1 0.0000 0.869 1.000 0.000 0.000 0.000 0.000
#> GSM509717 5 0.3210 0.891 0.000 0.000 0.000 0.212 0.788
#> GSM509722 1 0.3724 0.790 0.788 0.000 0.000 0.028 0.184
#> GSM509727 1 0.2563 0.789 0.872 0.000 0.000 0.008 0.120
#> GSM509710 1 0.0000 0.869 1.000 0.000 0.000 0.000 0.000
#> GSM509718 5 0.3177 0.891 0.000 0.000 0.000 0.208 0.792
#> GSM509723 1 0.3650 0.796 0.796 0.000 0.000 0.028 0.176
#> GSM509728 1 0.5036 0.460 0.648 0.000 0.304 0.008 0.040
#> GSM509732 3 0.0000 0.966 0.000 0.000 1.000 0.000 0.000
#> GSM509736 3 0.1809 0.949 0.000 0.000 0.928 0.012 0.060
#> GSM509741 3 0.0000 0.966 0.000 0.000 1.000 0.000 0.000
#> GSM509746 3 0.0000 0.966 0.000 0.000 1.000 0.000 0.000
#> GSM509733 3 0.0000 0.966 0.000 0.000 1.000 0.000 0.000
#> GSM509737 3 0.1877 0.948 0.000 0.000 0.924 0.012 0.064
#> GSM509742 3 0.0000 0.966 0.000 0.000 1.000 0.000 0.000
#> GSM509747 3 0.0000 0.966 0.000 0.000 1.000 0.000 0.000
#> GSM509734 3 0.0000 0.966 0.000 0.000 1.000 0.000 0.000
#> GSM509738 3 0.1981 0.945 0.000 0.000 0.920 0.016 0.064
#> GSM509743 3 0.1124 0.959 0.000 0.000 0.960 0.004 0.036
#> GSM509748 3 0.0000 0.966 0.000 0.000 1.000 0.000 0.000
#> GSM509735 1 0.0000 0.869 1.000 0.000 0.000 0.000 0.000
#> GSM509739 1 0.0000 0.869 1.000 0.000 0.000 0.000 0.000
#> GSM509744 3 0.1877 0.948 0.000 0.000 0.924 0.012 0.064
#> GSM509749 3 0.0162 0.965 0.000 0.000 0.996 0.000 0.004
#> GSM509740 5 0.4375 0.688 0.136 0.000 0.064 0.016 0.784
#> GSM509745 3 0.3419 0.825 0.000 0.000 0.804 0.016 0.180
#> GSM509750 3 0.1430 0.955 0.000 0.000 0.944 0.004 0.052
#> GSM509751 2 0.0000 0.929 0.000 1.000 0.000 0.000 0.000
#> GSM509753 2 0.0000 0.929 0.000 1.000 0.000 0.000 0.000
#> GSM509755 2 0.0000 0.929 0.000 1.000 0.000 0.000 0.000
#> GSM509757 2 0.0000 0.929 0.000 1.000 0.000 0.000 0.000
#> GSM509759 2 0.0000 0.929 0.000 1.000 0.000 0.000 0.000
#> GSM509761 2 0.1197 0.894 0.000 0.952 0.000 0.048 0.000
#> GSM509763 4 0.3837 0.647 0.000 0.308 0.000 0.692 0.000
#> GSM509765 4 0.3857 0.640 0.000 0.312 0.000 0.688 0.000
#> GSM509767 2 0.0290 0.927 0.000 0.992 0.000 0.008 0.000
#> GSM509769 2 0.0963 0.910 0.000 0.964 0.000 0.036 0.000
#> GSM509771 2 0.0404 0.925 0.000 0.988 0.000 0.012 0.000
#> GSM509773 2 0.2583 0.794 0.000 0.864 0.000 0.132 0.004
#> GSM509775 2 0.4294 -0.133 0.000 0.532 0.000 0.468 0.000
#> GSM509777 4 0.2280 0.798 0.000 0.120 0.000 0.880 0.000
#> GSM509779 4 0.1408 0.808 0.000 0.044 0.000 0.948 0.008
#> GSM509781 4 0.1725 0.806 0.000 0.044 0.000 0.936 0.020
#> GSM509783 4 0.1725 0.806 0.000 0.044 0.000 0.936 0.020
#> GSM509785 4 0.1725 0.806 0.000 0.044 0.000 0.936 0.020
#> GSM509752 2 0.0162 0.928 0.000 0.996 0.000 0.004 0.000
#> GSM509754 2 0.0000 0.929 0.000 1.000 0.000 0.000 0.000
#> GSM509756 2 0.0000 0.929 0.000 1.000 0.000 0.000 0.000
#> GSM509758 2 0.0290 0.927 0.000 0.992 0.000 0.008 0.000
#> GSM509760 2 0.0671 0.923 0.000 0.980 0.000 0.016 0.004
#> GSM509762 2 0.0000 0.929 0.000 1.000 0.000 0.000 0.000
#> GSM509764 2 0.0000 0.929 0.000 1.000 0.000 0.000 0.000
#> GSM509766 4 0.4126 0.515 0.000 0.380 0.000 0.620 0.000
#> GSM509768 2 0.4350 0.121 0.000 0.588 0.000 0.408 0.004
#> GSM509770 2 0.0771 0.920 0.000 0.976 0.000 0.020 0.004
#> GSM509772 2 0.0000 0.929 0.000 1.000 0.000 0.000 0.000
#> GSM509774 4 0.1908 0.806 0.000 0.092 0.000 0.908 0.000
#> GSM509776 4 0.4450 0.199 0.000 0.488 0.000 0.508 0.004
#> GSM509778 4 0.1725 0.806 0.000 0.044 0.000 0.936 0.020
#> GSM509780 4 0.3333 0.754 0.000 0.208 0.000 0.788 0.004
#> GSM509782 4 0.1725 0.806 0.000 0.044 0.000 0.936 0.020
#> GSM509784 4 0.1430 0.810 0.000 0.052 0.000 0.944 0.004
#> GSM509786 4 0.1725 0.806 0.000 0.044 0.000 0.936 0.020
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM509706 1 0.0000 0.7605 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509711 1 0.4530 0.4834 0.692 0.000 0.000 0.000 0.208 0.100
#> GSM509714 5 0.3758 0.6767 0.048 0.000 0.000 0.004 0.772 0.176
#> GSM509719 6 0.4175 0.9898 0.464 0.000 0.000 0.000 0.012 0.524
#> GSM509724 1 0.0291 0.7579 0.992 0.000 0.000 0.000 0.004 0.004
#> GSM509729 1 0.3428 -0.2702 0.696 0.000 0.000 0.000 0.000 0.304
#> GSM509707 1 0.0000 0.7605 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509712 1 0.4791 0.4258 0.652 0.000 0.000 0.000 0.244 0.104
#> GSM509715 5 0.2003 0.8654 0.000 0.000 0.000 0.116 0.884 0.000
#> GSM509720 6 0.4175 0.9898 0.464 0.000 0.000 0.000 0.012 0.524
#> GSM509725 1 0.0146 0.7585 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM509730 1 0.3890 -0.6482 0.596 0.000 0.004 0.000 0.000 0.400
#> GSM509708 1 0.0000 0.7605 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509713 1 0.2647 0.6749 0.868 0.000 0.000 0.000 0.044 0.088
#> GSM509716 5 0.2100 0.8662 0.000 0.000 0.000 0.112 0.884 0.004
#> GSM509721 6 0.4175 0.9898 0.464 0.000 0.000 0.000 0.012 0.524
#> GSM509726 1 0.1049 0.7433 0.960 0.000 0.000 0.000 0.008 0.032
#> GSM509731 5 0.2312 0.8627 0.000 0.000 0.000 0.112 0.876 0.012
#> GSM509709 1 0.0000 0.7605 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509717 5 0.1957 0.8664 0.000 0.000 0.000 0.112 0.888 0.000
#> GSM509722 6 0.4314 0.9597 0.444 0.000 0.000 0.000 0.020 0.536
#> GSM509727 1 0.3481 0.5879 0.776 0.000 0.000 0.000 0.032 0.192
#> GSM509710 1 0.0000 0.7605 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509718 5 0.2070 0.8581 0.000 0.000 0.000 0.100 0.892 0.008
#> GSM509723 6 0.4175 0.9898 0.464 0.000 0.000 0.000 0.012 0.524
#> GSM509728 1 0.4575 0.4869 0.728 0.000 0.088 0.000 0.020 0.164
#> GSM509732 3 0.0000 0.8603 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509736 3 0.4733 0.7441 0.000 0.000 0.648 0.004 0.072 0.276
#> GSM509741 3 0.0260 0.8603 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM509746 3 0.0000 0.8603 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509733 3 0.0000 0.8603 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509737 3 0.4733 0.7441 0.000 0.000 0.648 0.004 0.072 0.276
#> GSM509742 3 0.0405 0.8602 0.000 0.000 0.988 0.000 0.008 0.004
#> GSM509747 3 0.0000 0.8603 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509734 3 0.0000 0.8603 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509738 3 0.4886 0.7223 0.000 0.000 0.620 0.004 0.076 0.300
#> GSM509743 3 0.2908 0.8297 0.000 0.000 0.848 0.000 0.048 0.104
#> GSM509748 3 0.0000 0.8603 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509735 1 0.0000 0.7605 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509739 1 0.0000 0.7605 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509744 3 0.4637 0.7587 0.000 0.000 0.672 0.004 0.076 0.248
#> GSM509749 3 0.0405 0.8606 0.000 0.000 0.988 0.000 0.008 0.004
#> GSM509740 5 0.6128 0.4041 0.092 0.000 0.044 0.004 0.484 0.376
#> GSM509745 3 0.5648 0.6039 0.004 0.000 0.516 0.004 0.124 0.352
#> GSM509750 3 0.3424 0.8118 0.000 0.000 0.800 0.004 0.036 0.160
#> GSM509751 2 0.0405 0.9024 0.000 0.988 0.000 0.000 0.004 0.008
#> GSM509753 2 0.0508 0.9015 0.000 0.984 0.000 0.000 0.004 0.012
#> GSM509755 2 0.0603 0.9011 0.000 0.980 0.000 0.000 0.004 0.016
#> GSM509757 2 0.0837 0.9016 0.000 0.972 0.000 0.004 0.004 0.020
#> GSM509759 2 0.1297 0.8909 0.000 0.948 0.000 0.000 0.012 0.040
#> GSM509761 2 0.1471 0.8754 0.000 0.932 0.000 0.064 0.000 0.004
#> GSM509763 4 0.3807 0.6768 0.000 0.228 0.000 0.740 0.004 0.028
#> GSM509765 4 0.3878 0.6711 0.000 0.228 0.000 0.736 0.004 0.032
#> GSM509767 2 0.2164 0.8859 0.000 0.912 0.000 0.028 0.016 0.044
#> GSM509769 2 0.1565 0.8914 0.000 0.940 0.000 0.028 0.004 0.028
#> GSM509771 2 0.2186 0.8809 0.000 0.908 0.000 0.024 0.012 0.056
#> GSM509773 2 0.3770 0.6640 0.000 0.752 0.000 0.212 0.004 0.032
#> GSM509775 2 0.4723 -0.0736 0.000 0.488 0.000 0.472 0.004 0.036
#> GSM509777 4 0.1267 0.8070 0.000 0.060 0.000 0.940 0.000 0.000
#> GSM509779 4 0.0972 0.8195 0.000 0.008 0.000 0.964 0.028 0.000
#> GSM509781 4 0.1477 0.8147 0.000 0.004 0.000 0.940 0.048 0.008
#> GSM509783 4 0.1477 0.8147 0.000 0.004 0.000 0.940 0.048 0.008
#> GSM509785 4 0.1477 0.8147 0.000 0.004 0.000 0.940 0.048 0.008
#> GSM509752 2 0.0603 0.9029 0.000 0.980 0.000 0.016 0.000 0.004
#> GSM509754 2 0.0146 0.9038 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM509756 2 0.0405 0.9037 0.000 0.988 0.000 0.004 0.000 0.008
#> GSM509758 2 0.0363 0.9037 0.000 0.988 0.000 0.012 0.000 0.000
#> GSM509760 2 0.1138 0.9002 0.000 0.960 0.000 0.012 0.004 0.024
#> GSM509762 2 0.0260 0.9041 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM509764 2 0.0291 0.9036 0.000 0.992 0.000 0.004 0.000 0.004
#> GSM509766 4 0.4065 0.5669 0.000 0.300 0.000 0.672 0.000 0.028
#> GSM509768 2 0.4594 -0.0827 0.000 0.488 0.000 0.476 0.000 0.036
#> GSM509770 2 0.1370 0.8971 0.000 0.948 0.000 0.012 0.004 0.036
#> GSM509772 2 0.1461 0.8895 0.000 0.940 0.000 0.000 0.016 0.044
#> GSM509774 4 0.0858 0.8152 0.000 0.028 0.000 0.968 0.000 0.004
#> GSM509776 4 0.4860 0.1603 0.000 0.436 0.000 0.516 0.008 0.040
#> GSM509778 4 0.1410 0.8159 0.000 0.004 0.000 0.944 0.044 0.008
#> GSM509780 4 0.2466 0.7761 0.000 0.112 0.000 0.872 0.008 0.008
#> GSM509782 4 0.1477 0.8147 0.000 0.004 0.000 0.940 0.048 0.008
#> GSM509784 4 0.0862 0.8195 0.000 0.008 0.000 0.972 0.016 0.004
#> GSM509786 4 0.1477 0.8147 0.000 0.004 0.000 0.940 0.048 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 disease.state(p) time(p) k
#> MAD:skmeans 80 3.52e-15 2.80e-12 2
#> MAD:skmeans 80 2.62e-29 2.47e-12 3
#> MAD:skmeans 80 2.81e-24 4.12e-08 4
#> MAD:skmeans 75 1.82e-24 5.75e-08 5
#> MAD:skmeans 72 2.18e-23 5.08e-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["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 19175 rows and 81 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 0.924 0.960 0.982 0.5054 0.494 0.494
#> 3 3 0.785 0.828 0.886 0.2904 0.794 0.606
#> 4 4 0.669 0.771 0.852 0.1450 0.903 0.717
#> 5 5 0.827 0.832 0.917 0.0667 0.867 0.540
#> 6 6 0.865 0.834 0.920 0.0312 0.973 0.864
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
#> GSM509706 1 0.000 0.996 1.000 0.000
#> GSM509711 1 0.000 0.996 1.000 0.000
#> GSM509714 1 0.615 0.809 0.848 0.152
#> GSM509719 1 0.000 0.996 1.000 0.000
#> GSM509724 1 0.000 0.996 1.000 0.000
#> GSM509729 1 0.000 0.996 1.000 0.000
#> GSM509707 1 0.000 0.996 1.000 0.000
#> GSM509712 1 0.000 0.996 1.000 0.000
#> GSM509715 2 0.689 0.783 0.184 0.816
#> GSM509720 1 0.000 0.996 1.000 0.000
#> GSM509725 1 0.000 0.996 1.000 0.000
#> GSM509730 1 0.000 0.996 1.000 0.000
#> GSM509708 1 0.000 0.996 1.000 0.000
#> GSM509713 1 0.000 0.996 1.000 0.000
#> GSM509716 2 0.706 0.773 0.192 0.808
#> GSM509721 1 0.000 0.996 1.000 0.000
#> GSM509726 1 0.000 0.996 1.000 0.000
#> GSM509731 2 0.921 0.529 0.336 0.664
#> GSM509709 1 0.000 0.996 1.000 0.000
#> GSM509717 2 0.689 0.783 0.184 0.816
#> GSM509722 1 0.000 0.996 1.000 0.000
#> GSM509727 1 0.000 0.996 1.000 0.000
#> GSM509710 1 0.000 0.996 1.000 0.000
#> GSM509718 2 0.958 0.429 0.380 0.620
#> GSM509723 1 0.000 0.996 1.000 0.000
#> GSM509728 1 0.000 0.996 1.000 0.000
#> GSM509732 1 0.000 0.996 1.000 0.000
#> GSM509736 1 0.000 0.996 1.000 0.000
#> GSM509741 1 0.000 0.996 1.000 0.000
#> GSM509746 1 0.000 0.996 1.000 0.000
#> GSM509733 1 0.000 0.996 1.000 0.000
#> GSM509737 1 0.000 0.996 1.000 0.000
#> GSM509742 1 0.000 0.996 1.000 0.000
#> GSM509747 1 0.000 0.996 1.000 0.000
#> GSM509734 1 0.000 0.996 1.000 0.000
#> GSM509738 1 0.000 0.996 1.000 0.000
#> GSM509743 1 0.000 0.996 1.000 0.000
#> GSM509748 1 0.000 0.996 1.000 0.000
#> GSM509735 1 0.000 0.996 1.000 0.000
#> GSM509739 1 0.000 0.996 1.000 0.000
#> GSM509744 1 0.000 0.996 1.000 0.000
#> GSM509749 1 0.000 0.996 1.000 0.000
#> GSM509740 1 0.000 0.996 1.000 0.000
#> GSM509745 1 0.000 0.996 1.000 0.000
#> GSM509750 1 0.000 0.996 1.000 0.000
#> GSM509751 2 0.000 0.968 0.000 1.000
#> GSM509753 2 0.000 0.968 0.000 1.000
#> GSM509755 2 0.000 0.968 0.000 1.000
#> GSM509757 2 0.000 0.968 0.000 1.000
#> GSM509759 2 0.000 0.968 0.000 1.000
#> GSM509761 2 0.000 0.968 0.000 1.000
#> GSM509763 2 0.000 0.968 0.000 1.000
#> GSM509765 2 0.000 0.968 0.000 1.000
#> GSM509767 2 0.000 0.968 0.000 1.000
#> GSM509769 2 0.000 0.968 0.000 1.000
#> GSM509771 2 0.000 0.968 0.000 1.000
#> GSM509773 2 0.000 0.968 0.000 1.000
#> GSM509775 2 0.000 0.968 0.000 1.000
#> GSM509777 2 0.000 0.968 0.000 1.000
#> GSM509779 2 0.000 0.968 0.000 1.000
#> GSM509781 2 0.000 0.968 0.000 1.000
#> GSM509783 2 0.000 0.968 0.000 1.000
#> GSM509785 2 0.000 0.968 0.000 1.000
#> GSM509752 2 0.000 0.968 0.000 1.000
#> GSM509754 2 0.000 0.968 0.000 1.000
#> GSM509756 2 0.000 0.968 0.000 1.000
#> GSM509758 2 0.000 0.968 0.000 1.000
#> GSM509760 2 0.000 0.968 0.000 1.000
#> GSM509762 2 0.000 0.968 0.000 1.000
#> GSM509764 2 0.000 0.968 0.000 1.000
#> GSM509766 2 0.000 0.968 0.000 1.000
#> GSM509768 2 0.000 0.968 0.000 1.000
#> GSM509770 2 0.000 0.968 0.000 1.000
#> GSM509772 2 0.000 0.968 0.000 1.000
#> GSM509774 2 0.000 0.968 0.000 1.000
#> GSM509776 2 0.000 0.968 0.000 1.000
#> GSM509778 2 0.000 0.968 0.000 1.000
#> GSM509780 2 0.000 0.968 0.000 1.000
#> GSM509782 2 0.000 0.968 0.000 1.000
#> GSM509784 2 0.000 0.968 0.000 1.000
#> GSM509786 2 0.000 0.968 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM509706 1 0.0000 0.752 1.000 0.000 0.000
#> GSM509711 3 0.5650 0.715 0.312 0.000 0.688
#> GSM509714 3 0.5845 0.717 0.308 0.004 0.688
#> GSM509719 3 0.5291 0.736 0.268 0.000 0.732
#> GSM509724 1 0.2878 0.786 0.904 0.000 0.096
#> GSM509729 1 0.4178 0.525 0.828 0.000 0.172
#> GSM509707 1 0.0000 0.752 1.000 0.000 0.000
#> GSM509712 3 0.5650 0.715 0.312 0.000 0.688
#> GSM509715 3 0.7147 0.668 0.156 0.124 0.720
#> GSM509720 3 0.5291 0.736 0.268 0.000 0.732
#> GSM509725 1 0.4121 0.794 0.832 0.000 0.168
#> GSM509730 1 0.4346 0.580 0.816 0.000 0.184
#> GSM509708 1 0.0424 0.745 0.992 0.000 0.008
#> GSM509713 1 0.4399 0.497 0.812 0.000 0.188
#> GSM509716 3 0.6578 0.708 0.224 0.052 0.724
#> GSM509721 3 0.5291 0.736 0.268 0.000 0.732
#> GSM509726 1 0.4605 0.790 0.796 0.000 0.204
#> GSM509731 3 0.6565 0.707 0.232 0.048 0.720
#> GSM509709 1 0.0000 0.752 1.000 0.000 0.000
#> GSM509717 3 0.7097 0.679 0.172 0.108 0.720
#> GSM509722 3 0.5327 0.735 0.272 0.000 0.728
#> GSM509727 3 0.3412 0.697 0.124 0.000 0.876
#> GSM509710 1 0.3482 0.792 0.872 0.000 0.128
#> GSM509718 3 0.2947 0.695 0.020 0.060 0.920
#> GSM509723 3 0.5363 0.734 0.276 0.000 0.724
#> GSM509728 1 0.4887 0.783 0.772 0.000 0.228
#> GSM509732 1 0.5363 0.777 0.724 0.000 0.276
#> GSM509736 3 0.4842 0.547 0.224 0.000 0.776
#> GSM509741 1 0.5397 0.775 0.720 0.000 0.280
#> GSM509746 1 0.5397 0.775 0.720 0.000 0.280
#> GSM509733 1 0.5363 0.777 0.724 0.000 0.276
#> GSM509737 3 0.4842 0.547 0.224 0.000 0.776
#> GSM509742 1 0.5397 0.775 0.720 0.000 0.280
#> GSM509747 1 0.5363 0.777 0.724 0.000 0.276
#> GSM509734 1 0.5363 0.777 0.724 0.000 0.276
#> GSM509738 3 0.2625 0.678 0.084 0.000 0.916
#> GSM509743 3 0.4887 0.539 0.228 0.000 0.772
#> GSM509748 1 0.5397 0.775 0.720 0.000 0.280
#> GSM509735 1 0.0000 0.752 1.000 0.000 0.000
#> GSM509739 1 0.0000 0.752 1.000 0.000 0.000
#> GSM509744 3 0.4842 0.547 0.224 0.000 0.776
#> GSM509749 3 0.4842 0.547 0.224 0.000 0.776
#> GSM509740 3 0.1411 0.699 0.036 0.000 0.964
#> GSM509745 3 0.2165 0.689 0.064 0.000 0.936
#> GSM509750 3 0.4842 0.547 0.224 0.000 0.776
#> GSM509751 2 0.0000 0.990 0.000 1.000 0.000
#> GSM509753 2 0.0000 0.990 0.000 1.000 0.000
#> GSM509755 2 0.0000 0.990 0.000 1.000 0.000
#> GSM509757 2 0.0000 0.990 0.000 1.000 0.000
#> GSM509759 2 0.0000 0.990 0.000 1.000 0.000
#> GSM509761 2 0.0000 0.990 0.000 1.000 0.000
#> GSM509763 2 0.0237 0.990 0.000 0.996 0.004
#> GSM509765 2 0.0237 0.990 0.000 0.996 0.004
#> GSM509767 2 0.0000 0.990 0.000 1.000 0.000
#> GSM509769 2 0.0000 0.990 0.000 1.000 0.000
#> GSM509771 2 0.0000 0.990 0.000 1.000 0.000
#> GSM509773 2 0.0000 0.990 0.000 1.000 0.000
#> GSM509775 2 0.0237 0.990 0.000 0.996 0.004
#> GSM509777 2 0.1289 0.979 0.000 0.968 0.032
#> GSM509779 2 0.1411 0.978 0.000 0.964 0.036
#> GSM509781 2 0.1411 0.978 0.000 0.964 0.036
#> GSM509783 2 0.1411 0.978 0.000 0.964 0.036
#> GSM509785 2 0.1411 0.978 0.000 0.964 0.036
#> GSM509752 2 0.0000 0.990 0.000 1.000 0.000
#> GSM509754 2 0.0000 0.990 0.000 1.000 0.000
#> GSM509756 2 0.0000 0.990 0.000 1.000 0.000
#> GSM509758 2 0.0000 0.990 0.000 1.000 0.000
#> GSM509760 2 0.0000 0.990 0.000 1.000 0.000
#> GSM509762 2 0.0000 0.990 0.000 1.000 0.000
#> GSM509764 2 0.0000 0.990 0.000 1.000 0.000
#> GSM509766 2 0.0237 0.990 0.000 0.996 0.004
#> GSM509768 2 0.0424 0.989 0.000 0.992 0.008
#> GSM509770 2 0.0000 0.990 0.000 1.000 0.000
#> GSM509772 2 0.0000 0.990 0.000 1.000 0.000
#> GSM509774 2 0.1411 0.978 0.000 0.964 0.036
#> GSM509776 2 0.0424 0.989 0.000 0.992 0.008
#> GSM509778 2 0.1411 0.978 0.000 0.964 0.036
#> GSM509780 2 0.0424 0.989 0.000 0.992 0.008
#> GSM509782 2 0.1411 0.978 0.000 0.964 0.036
#> GSM509784 2 0.1411 0.978 0.000 0.964 0.036
#> GSM509786 2 0.1411 0.978 0.000 0.964 0.036
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM509706 1 0.0000 0.755 1.000 0.000 0.000 0.000
#> GSM509711 3 0.5136 0.730 0.224 0.000 0.728 0.048
#> GSM509714 3 0.5318 0.738 0.196 0.000 0.732 0.072
#> GSM509719 3 0.4957 0.741 0.204 0.000 0.748 0.048
#> GSM509724 1 0.1867 0.778 0.928 0.000 0.072 0.000
#> GSM509729 1 0.4472 0.480 0.760 0.000 0.220 0.020
#> GSM509707 1 0.0000 0.755 1.000 0.000 0.000 0.000
#> GSM509712 3 0.5102 0.733 0.220 0.000 0.732 0.048
#> GSM509715 3 0.5563 0.705 0.076 0.004 0.724 0.196
#> GSM509720 3 0.4957 0.741 0.204 0.000 0.748 0.048
#> GSM509725 1 0.2704 0.782 0.876 0.000 0.124 0.000
#> GSM509730 1 0.4501 0.528 0.764 0.000 0.212 0.024
#> GSM509708 1 0.0469 0.746 0.988 0.000 0.012 0.000
#> GSM509713 1 0.4610 0.451 0.744 0.000 0.236 0.020
#> GSM509716 3 0.5591 0.736 0.168 0.004 0.732 0.096
#> GSM509721 3 0.4957 0.741 0.204 0.000 0.748 0.048
#> GSM509726 1 0.3625 0.779 0.828 0.000 0.160 0.012
#> GSM509731 3 0.5619 0.725 0.124 0.000 0.724 0.152
#> GSM509709 1 0.0000 0.755 1.000 0.000 0.000 0.000
#> GSM509717 3 0.5569 0.719 0.104 0.000 0.724 0.172
#> GSM509722 3 0.4957 0.741 0.204 0.000 0.748 0.048
#> GSM509727 3 0.2814 0.701 0.132 0.000 0.868 0.000
#> GSM509710 1 0.2281 0.781 0.904 0.000 0.096 0.000
#> GSM509718 3 0.1716 0.710 0.000 0.000 0.936 0.064
#> GSM509723 3 0.5031 0.737 0.212 0.000 0.740 0.048
#> GSM509728 1 0.4920 0.768 0.756 0.000 0.192 0.052
#> GSM509732 1 0.5573 0.748 0.676 0.000 0.272 0.052
#> GSM509736 3 0.4880 0.503 0.188 0.000 0.760 0.052
#> GSM509741 1 0.5599 0.746 0.672 0.000 0.276 0.052
#> GSM509746 1 0.5599 0.746 0.672 0.000 0.276 0.052
#> GSM509733 1 0.5573 0.748 0.676 0.000 0.272 0.052
#> GSM509737 3 0.4880 0.503 0.188 0.000 0.760 0.052
#> GSM509742 1 0.5599 0.746 0.672 0.000 0.276 0.052
#> GSM509747 1 0.5573 0.748 0.676 0.000 0.272 0.052
#> GSM509734 1 0.5573 0.748 0.676 0.000 0.272 0.052
#> GSM509738 3 0.1975 0.671 0.048 0.000 0.936 0.016
#> GSM509743 3 0.4920 0.496 0.192 0.000 0.756 0.052
#> GSM509748 1 0.5599 0.746 0.672 0.000 0.276 0.052
#> GSM509735 1 0.0188 0.757 0.996 0.000 0.004 0.000
#> GSM509739 1 0.0188 0.752 0.996 0.000 0.004 0.000
#> GSM509744 3 0.4880 0.503 0.188 0.000 0.760 0.052
#> GSM509749 3 0.4880 0.503 0.188 0.000 0.760 0.052
#> GSM509740 3 0.0779 0.698 0.004 0.000 0.980 0.016
#> GSM509745 3 0.1406 0.686 0.024 0.000 0.960 0.016
#> GSM509750 3 0.4880 0.503 0.188 0.000 0.760 0.052
#> GSM509751 2 0.0000 0.956 0.000 1.000 0.000 0.000
#> GSM509753 2 0.0000 0.956 0.000 1.000 0.000 0.000
#> GSM509755 2 0.0000 0.956 0.000 1.000 0.000 0.000
#> GSM509757 2 0.0000 0.956 0.000 1.000 0.000 0.000
#> GSM509759 2 0.0000 0.956 0.000 1.000 0.000 0.000
#> GSM509761 2 0.0000 0.956 0.000 1.000 0.000 0.000
#> GSM509763 4 0.4103 0.810 0.000 0.256 0.000 0.744
#> GSM509765 4 0.4431 0.753 0.000 0.304 0.000 0.696
#> GSM509767 2 0.0000 0.956 0.000 1.000 0.000 0.000
#> GSM509769 2 0.0000 0.956 0.000 1.000 0.000 0.000
#> GSM509771 2 0.0000 0.956 0.000 1.000 0.000 0.000
#> GSM509773 2 0.0469 0.944 0.000 0.988 0.000 0.012
#> GSM509775 2 0.3688 0.642 0.000 0.792 0.000 0.208
#> GSM509777 4 0.2589 0.905 0.000 0.116 0.000 0.884
#> GSM509779 4 0.2345 0.911 0.000 0.100 0.000 0.900
#> GSM509781 4 0.2345 0.911 0.000 0.100 0.000 0.900
#> GSM509783 4 0.2345 0.911 0.000 0.100 0.000 0.900
#> GSM509785 4 0.2345 0.911 0.000 0.100 0.000 0.900
#> GSM509752 2 0.0000 0.956 0.000 1.000 0.000 0.000
#> GSM509754 2 0.0000 0.956 0.000 1.000 0.000 0.000
#> GSM509756 2 0.0000 0.956 0.000 1.000 0.000 0.000
#> GSM509758 2 0.0000 0.956 0.000 1.000 0.000 0.000
#> GSM509760 2 0.0000 0.956 0.000 1.000 0.000 0.000
#> GSM509762 2 0.0000 0.956 0.000 1.000 0.000 0.000
#> GSM509764 2 0.0000 0.956 0.000 1.000 0.000 0.000
#> GSM509766 4 0.4382 0.765 0.000 0.296 0.000 0.704
#> GSM509768 2 0.4992 -0.264 0.000 0.524 0.000 0.476
#> GSM509770 2 0.0000 0.956 0.000 1.000 0.000 0.000
#> GSM509772 2 0.0000 0.956 0.000 1.000 0.000 0.000
#> GSM509774 4 0.2345 0.911 0.000 0.100 0.000 0.900
#> GSM509776 4 0.4898 0.534 0.000 0.416 0.000 0.584
#> GSM509778 4 0.2345 0.911 0.000 0.100 0.000 0.900
#> GSM509780 4 0.3975 0.827 0.000 0.240 0.000 0.760
#> GSM509782 4 0.2345 0.911 0.000 0.100 0.000 0.900
#> GSM509784 4 0.2345 0.911 0.000 0.100 0.000 0.900
#> GSM509786 4 0.2345 0.911 0.000 0.100 0.000 0.900
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM509706 1 0.0000 0.982 1.000 0.000 0.000 0.000 0.000
#> GSM509711 5 0.2329 0.775 0.124 0.000 0.000 0.000 0.876
#> GSM509714 5 0.0000 0.847 0.000 0.000 0.000 0.000 1.000
#> GSM509719 5 0.0000 0.847 0.000 0.000 0.000 0.000 1.000
#> GSM509724 1 0.0000 0.982 1.000 0.000 0.000 0.000 0.000
#> GSM509729 5 0.4283 0.481 0.348 0.000 0.008 0.000 0.644
#> GSM509707 1 0.0000 0.982 1.000 0.000 0.000 0.000 0.000
#> GSM509712 5 0.0162 0.846 0.000 0.000 0.000 0.004 0.996
#> GSM509715 5 0.2127 0.804 0.000 0.000 0.000 0.108 0.892
#> GSM509720 5 0.0000 0.847 0.000 0.000 0.000 0.000 1.000
#> GSM509725 1 0.0404 0.976 0.988 0.000 0.012 0.000 0.000
#> GSM509730 5 0.3060 0.768 0.128 0.000 0.024 0.000 0.848
#> GSM509708 1 0.0000 0.982 1.000 0.000 0.000 0.000 0.000
#> GSM509713 5 0.4700 0.200 0.472 0.000 0.008 0.004 0.516
#> GSM509716 5 0.0162 0.846 0.000 0.000 0.000 0.004 0.996
#> GSM509721 5 0.0000 0.847 0.000 0.000 0.000 0.000 1.000
#> GSM509726 1 0.3012 0.852 0.872 0.000 0.052 0.004 0.072
#> GSM509731 5 0.1608 0.825 0.000 0.000 0.000 0.072 0.928
#> GSM509709 1 0.0000 0.982 1.000 0.000 0.000 0.000 0.000
#> GSM509717 5 0.1851 0.816 0.000 0.000 0.000 0.088 0.912
#> GSM509722 5 0.0000 0.847 0.000 0.000 0.000 0.000 1.000
#> GSM509727 5 0.4576 0.275 0.456 0.000 0.004 0.004 0.536
#> GSM509710 1 0.0000 0.982 1.000 0.000 0.000 0.000 0.000
#> GSM509718 5 0.4697 0.145 0.000 0.000 0.388 0.020 0.592
#> GSM509723 5 0.0000 0.847 0.000 0.000 0.000 0.000 1.000
#> GSM509728 3 0.6153 0.457 0.300 0.000 0.552 0.004 0.144
#> GSM509732 3 0.0000 0.850 0.000 0.000 1.000 0.000 0.000
#> GSM509736 3 0.2890 0.819 0.000 0.000 0.836 0.004 0.160
#> GSM509741 3 0.0000 0.850 0.000 0.000 1.000 0.000 0.000
#> GSM509746 3 0.0000 0.850 0.000 0.000 1.000 0.000 0.000
#> GSM509733 3 0.0000 0.850 0.000 0.000 1.000 0.000 0.000
#> GSM509737 3 0.2890 0.819 0.000 0.000 0.836 0.004 0.160
#> GSM509742 3 0.0000 0.850 0.000 0.000 1.000 0.000 0.000
#> GSM509747 3 0.0000 0.850 0.000 0.000 1.000 0.000 0.000
#> GSM509734 3 0.0000 0.850 0.000 0.000 1.000 0.000 0.000
#> GSM509738 3 0.3906 0.674 0.000 0.000 0.704 0.004 0.292
#> GSM509743 3 0.2561 0.827 0.000 0.000 0.856 0.000 0.144
#> GSM509748 3 0.0000 0.850 0.000 0.000 1.000 0.000 0.000
#> GSM509735 1 0.0404 0.976 0.988 0.000 0.012 0.000 0.000
#> GSM509739 1 0.0000 0.982 1.000 0.000 0.000 0.000 0.000
#> GSM509744 3 0.2648 0.824 0.000 0.000 0.848 0.000 0.152
#> GSM509749 3 0.1282 0.847 0.000 0.000 0.952 0.004 0.044
#> GSM509740 3 0.4390 0.399 0.000 0.000 0.568 0.004 0.428
#> GSM509745 3 0.4211 0.557 0.000 0.000 0.636 0.004 0.360
#> GSM509750 3 0.2890 0.819 0.000 0.000 0.836 0.004 0.160
#> GSM509751 2 0.0000 0.984 0.000 1.000 0.000 0.000 0.000
#> GSM509753 2 0.0000 0.984 0.000 1.000 0.000 0.000 0.000
#> GSM509755 2 0.0000 0.984 0.000 1.000 0.000 0.000 0.000
#> GSM509757 2 0.0000 0.984 0.000 1.000 0.000 0.000 0.000
#> GSM509759 2 0.0000 0.984 0.000 1.000 0.000 0.000 0.000
#> GSM509761 2 0.0000 0.984 0.000 1.000 0.000 0.000 0.000
#> GSM509763 4 0.2813 0.812 0.000 0.168 0.000 0.832 0.000
#> GSM509765 4 0.3336 0.758 0.000 0.228 0.000 0.772 0.000
#> GSM509767 2 0.0000 0.984 0.000 1.000 0.000 0.000 0.000
#> GSM509769 2 0.0000 0.984 0.000 1.000 0.000 0.000 0.000
#> GSM509771 2 0.0000 0.984 0.000 1.000 0.000 0.000 0.000
#> GSM509773 2 0.0404 0.972 0.000 0.988 0.000 0.012 0.000
#> GSM509775 2 0.3424 0.613 0.000 0.760 0.000 0.240 0.000
#> GSM509777 4 0.0794 0.870 0.000 0.028 0.000 0.972 0.000
#> GSM509779 4 0.0162 0.875 0.000 0.004 0.000 0.996 0.000
#> GSM509781 4 0.0162 0.875 0.000 0.004 0.000 0.996 0.000
#> GSM509783 4 0.0162 0.875 0.000 0.004 0.000 0.996 0.000
#> GSM509785 4 0.0162 0.875 0.000 0.004 0.000 0.996 0.000
#> GSM509752 2 0.0000 0.984 0.000 1.000 0.000 0.000 0.000
#> GSM509754 2 0.0000 0.984 0.000 1.000 0.000 0.000 0.000
#> GSM509756 2 0.0000 0.984 0.000 1.000 0.000 0.000 0.000
#> GSM509758 2 0.0000 0.984 0.000 1.000 0.000 0.000 0.000
#> GSM509760 2 0.0000 0.984 0.000 1.000 0.000 0.000 0.000
#> GSM509762 2 0.0000 0.984 0.000 1.000 0.000 0.000 0.000
#> GSM509764 2 0.0000 0.984 0.000 1.000 0.000 0.000 0.000
#> GSM509766 4 0.3242 0.771 0.000 0.216 0.000 0.784 0.000
#> GSM509768 4 0.4297 0.269 0.000 0.472 0.000 0.528 0.000
#> GSM509770 2 0.0000 0.984 0.000 1.000 0.000 0.000 0.000
#> GSM509772 2 0.0000 0.984 0.000 1.000 0.000 0.000 0.000
#> GSM509774 4 0.0290 0.874 0.000 0.008 0.000 0.992 0.000
#> GSM509776 4 0.4060 0.555 0.000 0.360 0.000 0.640 0.000
#> GSM509778 4 0.0162 0.875 0.000 0.004 0.000 0.996 0.000
#> GSM509780 4 0.2648 0.825 0.000 0.152 0.000 0.848 0.000
#> GSM509782 4 0.0162 0.875 0.000 0.004 0.000 0.996 0.000
#> GSM509784 4 0.0162 0.875 0.000 0.004 0.000 0.996 0.000
#> GSM509786 4 0.0162 0.875 0.000 0.004 0.000 0.996 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM509706 1 0.0000 0.935 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509711 6 0.4202 0.600 0.064 0.000 0.000 0.000 0.224 0.712
#> GSM509714 6 0.2823 0.639 0.000 0.000 0.000 0.000 0.204 0.796
#> GSM509719 5 0.0000 0.985 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM509724 1 0.0000 0.935 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509729 5 0.1285 0.927 0.052 0.000 0.000 0.000 0.944 0.004
#> GSM509707 1 0.0000 0.935 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509712 6 0.3862 0.184 0.000 0.000 0.000 0.000 0.476 0.524
#> GSM509715 6 0.0000 0.797 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM509720 5 0.0000 0.985 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM509725 1 0.0000 0.935 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509730 5 0.0146 0.985 0.000 0.000 0.000 0.000 0.996 0.004
#> GSM509708 1 0.0000 0.935 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509713 1 0.4668 0.340 0.620 0.000 0.000 0.000 0.064 0.316
#> GSM509716 6 0.0146 0.797 0.000 0.000 0.000 0.000 0.004 0.996
#> GSM509721 5 0.0000 0.985 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM509726 1 0.3549 0.723 0.808 0.000 0.032 0.000 0.020 0.140
#> GSM509731 6 0.0405 0.795 0.000 0.000 0.000 0.004 0.008 0.988
#> GSM509709 1 0.0000 0.935 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509717 6 0.0000 0.797 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM509722 5 0.0146 0.985 0.000 0.000 0.000 0.000 0.996 0.004
#> GSM509727 6 0.4452 0.134 0.428 0.000 0.016 0.000 0.008 0.548
#> GSM509710 1 0.0000 0.935 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509718 6 0.0458 0.788 0.000 0.000 0.016 0.000 0.000 0.984
#> GSM509723 5 0.0146 0.985 0.000 0.000 0.000 0.000 0.996 0.004
#> GSM509728 3 0.5820 0.421 0.288 0.000 0.512 0.000 0.004 0.196
#> GSM509732 3 0.0000 0.839 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509736 3 0.2933 0.790 0.000 0.000 0.796 0.000 0.004 0.200
#> GSM509741 3 0.0000 0.839 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509746 3 0.0000 0.839 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509733 3 0.0000 0.839 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509737 3 0.2933 0.790 0.000 0.000 0.796 0.000 0.004 0.200
#> GSM509742 3 0.0000 0.839 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509747 3 0.0000 0.839 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509734 3 0.0000 0.839 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509738 3 0.4769 0.663 0.000 0.000 0.644 0.000 0.092 0.264
#> GSM509743 3 0.2146 0.823 0.000 0.000 0.880 0.000 0.004 0.116
#> GSM509748 3 0.0000 0.839 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509735 1 0.0000 0.935 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509739 1 0.0000 0.935 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509744 3 0.2362 0.818 0.000 0.000 0.860 0.000 0.004 0.136
#> GSM509749 3 0.1327 0.833 0.000 0.000 0.936 0.000 0.000 0.064
#> GSM509740 3 0.3982 0.410 0.000 0.000 0.536 0.000 0.004 0.460
#> GSM509745 3 0.3890 0.540 0.000 0.000 0.596 0.000 0.004 0.400
#> GSM509750 3 0.2933 0.790 0.000 0.000 0.796 0.000 0.004 0.200
#> GSM509751 2 0.0000 0.985 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509753 2 0.0000 0.985 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509755 2 0.0000 0.985 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509757 2 0.0000 0.985 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509759 2 0.0000 0.985 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509761 2 0.0000 0.985 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509763 4 0.2135 0.827 0.000 0.128 0.000 0.872 0.000 0.000
#> GSM509765 4 0.2823 0.770 0.000 0.204 0.000 0.796 0.000 0.000
#> GSM509767 2 0.0000 0.985 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509769 2 0.0000 0.985 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509771 2 0.0000 0.985 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509773 2 0.0363 0.973 0.000 0.988 0.000 0.012 0.000 0.000
#> GSM509775 2 0.3076 0.621 0.000 0.760 0.000 0.240 0.000 0.000
#> GSM509777 4 0.0632 0.869 0.000 0.024 0.000 0.976 0.000 0.000
#> GSM509779 4 0.0000 0.874 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM509781 4 0.0000 0.874 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM509783 4 0.0000 0.874 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM509785 4 0.0000 0.874 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM509752 2 0.0000 0.985 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509754 2 0.0000 0.985 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509756 2 0.0000 0.985 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509758 2 0.0000 0.985 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509760 2 0.0000 0.985 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509762 2 0.0000 0.985 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509764 2 0.0000 0.985 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509766 4 0.2697 0.785 0.000 0.188 0.000 0.812 0.000 0.000
#> GSM509768 4 0.3847 0.299 0.000 0.456 0.000 0.544 0.000 0.000
#> GSM509770 2 0.0000 0.985 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509772 2 0.0000 0.985 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509774 4 0.0146 0.874 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM509776 4 0.3620 0.558 0.000 0.352 0.000 0.648 0.000 0.000
#> GSM509778 4 0.0000 0.874 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM509780 4 0.2178 0.826 0.000 0.132 0.000 0.868 0.000 0.000
#> GSM509782 4 0.0000 0.874 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM509784 4 0.0000 0.874 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM509786 4 0.0000 0.874 0.000 0.000 0.000 1.000 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 disease.state(p) time(p) k
#> MAD:pam 80 3.52e-15 2.13e-12 2
#> MAD:pam 80 1.31e-16 5.09e-13 3
#> MAD:pam 77 7.44e-15 4.55e-10 4
#> MAD:pam 74 1.78e-25 1.42e-07 5
#> MAD:pam 75 1.15e-24 2.15e-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["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 19175 rows and 81 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.5005 0.500 0.500
#> 3 3 0.901 0.973 0.983 0.2874 0.857 0.714
#> 4 4 0.988 0.958 0.971 0.0864 0.934 0.817
#> 5 5 0.837 0.822 0.893 0.0821 0.905 0.699
#> 6 6 0.781 0.757 0.817 0.0439 0.952 0.808
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 2 3
There is also optional best \(k\) = 2 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM509706 1 0 1 1 0
#> GSM509711 1 0 1 1 0
#> GSM509714 1 0 1 1 0
#> GSM509719 1 0 1 1 0
#> GSM509724 1 0 1 1 0
#> GSM509729 1 0 1 1 0
#> GSM509707 1 0 1 1 0
#> GSM509712 1 0 1 1 0
#> GSM509715 1 0 1 1 0
#> GSM509720 1 0 1 1 0
#> GSM509725 1 0 1 1 0
#> GSM509730 1 0 1 1 0
#> GSM509708 1 0 1 1 0
#> GSM509713 1 0 1 1 0
#> GSM509716 1 0 1 1 0
#> GSM509721 1 0 1 1 0
#> GSM509726 1 0 1 1 0
#> GSM509731 1 0 1 1 0
#> GSM509709 1 0 1 1 0
#> GSM509717 1 0 1 1 0
#> GSM509722 1 0 1 1 0
#> GSM509727 1 0 1 1 0
#> GSM509710 1 0 1 1 0
#> GSM509718 1 0 1 1 0
#> GSM509723 1 0 1 1 0
#> GSM509728 1 0 1 1 0
#> GSM509732 1 0 1 1 0
#> GSM509736 1 0 1 1 0
#> GSM509741 1 0 1 1 0
#> GSM509746 1 0 1 1 0
#> GSM509733 1 0 1 1 0
#> GSM509737 1 0 1 1 0
#> GSM509742 1 0 1 1 0
#> GSM509747 1 0 1 1 0
#> GSM509734 1 0 1 1 0
#> GSM509738 1 0 1 1 0
#> GSM509743 1 0 1 1 0
#> GSM509748 1 0 1 1 0
#> GSM509735 1 0 1 1 0
#> GSM509739 1 0 1 1 0
#> GSM509744 1 0 1 1 0
#> GSM509749 1 0 1 1 0
#> GSM509740 1 0 1 1 0
#> GSM509745 1 0 1 1 0
#> GSM509750 1 0 1 1 0
#> GSM509751 2 0 1 0 1
#> GSM509753 2 0 1 0 1
#> GSM509755 2 0 1 0 1
#> GSM509757 2 0 1 0 1
#> GSM509759 2 0 1 0 1
#> GSM509761 2 0 1 0 1
#> GSM509763 2 0 1 0 1
#> GSM509765 2 0 1 0 1
#> GSM509767 2 0 1 0 1
#> GSM509769 2 0 1 0 1
#> GSM509771 2 0 1 0 1
#> GSM509773 2 0 1 0 1
#> GSM509775 2 0 1 0 1
#> GSM509777 2 0 1 0 1
#> GSM509779 2 0 1 0 1
#> GSM509781 2 0 1 0 1
#> GSM509783 2 0 1 0 1
#> GSM509785 2 0 1 0 1
#> GSM509752 2 0 1 0 1
#> GSM509754 2 0 1 0 1
#> GSM509756 2 0 1 0 1
#> GSM509758 2 0 1 0 1
#> GSM509760 2 0 1 0 1
#> GSM509762 2 0 1 0 1
#> GSM509764 2 0 1 0 1
#> GSM509766 2 0 1 0 1
#> GSM509768 2 0 1 0 1
#> GSM509770 2 0 1 0 1
#> GSM509772 2 0 1 0 1
#> GSM509774 2 0 1 0 1
#> GSM509776 2 0 1 0 1
#> GSM509778 2 0 1 0 1
#> GSM509780 2 0 1 0 1
#> GSM509782 2 0 1 0 1
#> GSM509784 2 0 1 0 1
#> GSM509786 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM509706 1 0.000 0.990 1.000 0 0.000
#> GSM509711 3 0.334 0.903 0.120 0 0.880
#> GSM509714 3 0.334 0.903 0.120 0 0.880
#> GSM509719 1 0.000 0.990 1.000 0 0.000
#> GSM509724 1 0.000 0.990 1.000 0 0.000
#> GSM509729 1 0.000 0.990 1.000 0 0.000
#> GSM509707 1 0.000 0.990 1.000 0 0.000
#> GSM509712 3 0.334 0.903 0.120 0 0.880
#> GSM509715 3 0.319 0.909 0.112 0 0.888
#> GSM509720 1 0.000 0.990 1.000 0 0.000
#> GSM509725 1 0.000 0.990 1.000 0 0.000
#> GSM509730 1 0.000 0.990 1.000 0 0.000
#> GSM509708 1 0.000 0.990 1.000 0 0.000
#> GSM509713 3 0.334 0.903 0.120 0 0.880
#> GSM509716 3 0.319 0.909 0.112 0 0.888
#> GSM509721 1 0.000 0.990 1.000 0 0.000
#> GSM509726 3 0.429 0.838 0.180 0 0.820
#> GSM509731 3 0.319 0.909 0.112 0 0.888
#> GSM509709 1 0.000 0.990 1.000 0 0.000
#> GSM509717 3 0.319 0.909 0.112 0 0.888
#> GSM509722 1 0.355 0.834 0.868 0 0.132
#> GSM509727 3 0.000 0.954 0.000 0 1.000
#> GSM509710 1 0.000 0.990 1.000 0 0.000
#> GSM509718 3 0.319 0.909 0.112 0 0.888
#> GSM509723 1 0.000 0.990 1.000 0 0.000
#> GSM509728 3 0.000 0.954 0.000 0 1.000
#> GSM509732 3 0.000 0.954 0.000 0 1.000
#> GSM509736 3 0.000 0.954 0.000 0 1.000
#> GSM509741 3 0.000 0.954 0.000 0 1.000
#> GSM509746 3 0.000 0.954 0.000 0 1.000
#> GSM509733 3 0.000 0.954 0.000 0 1.000
#> GSM509737 3 0.000 0.954 0.000 0 1.000
#> GSM509742 3 0.000 0.954 0.000 0 1.000
#> GSM509747 3 0.000 0.954 0.000 0 1.000
#> GSM509734 3 0.000 0.954 0.000 0 1.000
#> GSM509738 3 0.000 0.954 0.000 0 1.000
#> GSM509743 3 0.000 0.954 0.000 0 1.000
#> GSM509748 3 0.000 0.954 0.000 0 1.000
#> GSM509735 1 0.000 0.990 1.000 0 0.000
#> GSM509739 1 0.000 0.990 1.000 0 0.000
#> GSM509744 3 0.000 0.954 0.000 0 1.000
#> GSM509749 3 0.000 0.954 0.000 0 1.000
#> GSM509740 3 0.000 0.954 0.000 0 1.000
#> GSM509745 3 0.000 0.954 0.000 0 1.000
#> GSM509750 3 0.000 0.954 0.000 0 1.000
#> GSM509751 2 0.000 1.000 0.000 1 0.000
#> GSM509753 2 0.000 1.000 0.000 1 0.000
#> GSM509755 2 0.000 1.000 0.000 1 0.000
#> GSM509757 2 0.000 1.000 0.000 1 0.000
#> GSM509759 2 0.000 1.000 0.000 1 0.000
#> GSM509761 2 0.000 1.000 0.000 1 0.000
#> GSM509763 2 0.000 1.000 0.000 1 0.000
#> GSM509765 2 0.000 1.000 0.000 1 0.000
#> GSM509767 2 0.000 1.000 0.000 1 0.000
#> GSM509769 2 0.000 1.000 0.000 1 0.000
#> GSM509771 2 0.000 1.000 0.000 1 0.000
#> GSM509773 2 0.000 1.000 0.000 1 0.000
#> GSM509775 2 0.000 1.000 0.000 1 0.000
#> GSM509777 2 0.000 1.000 0.000 1 0.000
#> GSM509779 2 0.000 1.000 0.000 1 0.000
#> GSM509781 2 0.000 1.000 0.000 1 0.000
#> GSM509783 2 0.000 1.000 0.000 1 0.000
#> GSM509785 2 0.000 1.000 0.000 1 0.000
#> GSM509752 2 0.000 1.000 0.000 1 0.000
#> GSM509754 2 0.000 1.000 0.000 1 0.000
#> GSM509756 2 0.000 1.000 0.000 1 0.000
#> GSM509758 2 0.000 1.000 0.000 1 0.000
#> GSM509760 2 0.000 1.000 0.000 1 0.000
#> GSM509762 2 0.000 1.000 0.000 1 0.000
#> GSM509764 2 0.000 1.000 0.000 1 0.000
#> GSM509766 2 0.000 1.000 0.000 1 0.000
#> GSM509768 2 0.000 1.000 0.000 1 0.000
#> GSM509770 2 0.000 1.000 0.000 1 0.000
#> GSM509772 2 0.000 1.000 0.000 1 0.000
#> GSM509774 2 0.000 1.000 0.000 1 0.000
#> GSM509776 2 0.000 1.000 0.000 1 0.000
#> GSM509778 2 0.000 1.000 0.000 1 0.000
#> GSM509780 2 0.000 1.000 0.000 1 0.000
#> GSM509782 2 0.000 1.000 0.000 1 0.000
#> GSM509784 2 0.000 1.000 0.000 1 0.000
#> GSM509786 2 0.000 1.000 0.000 1 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM509706 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM509711 4 0.2589 0.904 0.116 0.000 0.000 0.884
#> GSM509714 4 0.2589 0.904 0.116 0.000 0.000 0.884
#> GSM509719 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM509724 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM509729 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM509707 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM509712 4 0.4193 0.760 0.268 0.000 0.000 0.732
#> GSM509715 4 0.1716 0.918 0.064 0.000 0.000 0.936
#> GSM509720 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM509725 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM509730 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM509708 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM509713 4 0.4697 0.617 0.356 0.000 0.000 0.644
#> GSM509716 4 0.1716 0.918 0.064 0.000 0.000 0.936
#> GSM509721 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM509726 1 0.0188 0.995 0.996 0.000 0.000 0.004
#> GSM509731 4 0.1716 0.918 0.064 0.000 0.000 0.936
#> GSM509709 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM509717 4 0.1716 0.918 0.064 0.000 0.000 0.936
#> GSM509722 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM509727 3 0.5494 0.615 0.208 0.000 0.716 0.076
#> GSM509710 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM509718 4 0.1716 0.918 0.064 0.000 0.000 0.936
#> GSM509723 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM509728 3 0.1743 0.915 0.056 0.000 0.940 0.004
#> GSM509732 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM509736 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM509741 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM509746 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM509733 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM509737 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM509742 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM509747 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM509734 3 0.1211 0.932 0.040 0.000 0.960 0.000
#> GSM509738 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM509743 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM509748 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM509735 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM509739 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM509744 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM509749 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM509740 3 0.3885 0.806 0.064 0.000 0.844 0.092
#> GSM509745 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM509750 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM509751 2 0.0000 0.984 0.000 1.000 0.000 0.000
#> GSM509753 2 0.0000 0.984 0.000 1.000 0.000 0.000
#> GSM509755 2 0.0000 0.984 0.000 1.000 0.000 0.000
#> GSM509757 2 0.0000 0.984 0.000 1.000 0.000 0.000
#> GSM509759 2 0.0000 0.984 0.000 1.000 0.000 0.000
#> GSM509761 2 0.0000 0.984 0.000 1.000 0.000 0.000
#> GSM509763 2 0.0000 0.984 0.000 1.000 0.000 0.000
#> GSM509765 2 0.0000 0.984 0.000 1.000 0.000 0.000
#> GSM509767 2 0.0000 0.984 0.000 1.000 0.000 0.000
#> GSM509769 2 0.0000 0.984 0.000 1.000 0.000 0.000
#> GSM509771 2 0.0000 0.984 0.000 1.000 0.000 0.000
#> GSM509773 2 0.0000 0.984 0.000 1.000 0.000 0.000
#> GSM509775 2 0.0000 0.984 0.000 1.000 0.000 0.000
#> GSM509777 2 0.0000 0.984 0.000 1.000 0.000 0.000
#> GSM509779 2 0.1716 0.949 0.000 0.936 0.000 0.064
#> GSM509781 2 0.2011 0.938 0.000 0.920 0.000 0.080
#> GSM509783 2 0.2081 0.935 0.000 0.916 0.000 0.084
#> GSM509785 2 0.2081 0.935 0.000 0.916 0.000 0.084
#> GSM509752 2 0.0000 0.984 0.000 1.000 0.000 0.000
#> GSM509754 2 0.0000 0.984 0.000 1.000 0.000 0.000
#> GSM509756 2 0.0000 0.984 0.000 1.000 0.000 0.000
#> GSM509758 2 0.0000 0.984 0.000 1.000 0.000 0.000
#> GSM509760 2 0.0000 0.984 0.000 1.000 0.000 0.000
#> GSM509762 2 0.0000 0.984 0.000 1.000 0.000 0.000
#> GSM509764 2 0.0000 0.984 0.000 1.000 0.000 0.000
#> GSM509766 2 0.0000 0.984 0.000 1.000 0.000 0.000
#> GSM509768 2 0.0000 0.984 0.000 1.000 0.000 0.000
#> GSM509770 2 0.0000 0.984 0.000 1.000 0.000 0.000
#> GSM509772 2 0.0000 0.984 0.000 1.000 0.000 0.000
#> GSM509774 2 0.0188 0.982 0.000 0.996 0.000 0.004
#> GSM509776 2 0.0000 0.984 0.000 1.000 0.000 0.000
#> GSM509778 2 0.1867 0.944 0.000 0.928 0.000 0.072
#> GSM509780 2 0.0000 0.984 0.000 1.000 0.000 0.000
#> GSM509782 2 0.2149 0.932 0.000 0.912 0.000 0.088
#> GSM509784 2 0.1716 0.949 0.000 0.936 0.000 0.064
#> GSM509786 2 0.2081 0.935 0.000 0.916 0.000 0.084
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM509706 1 0.0290 0.8823 0.992 0.000 0.000 0.000 0.008
#> GSM509711 5 0.4300 0.2985 0.476 0.000 0.000 0.000 0.524
#> GSM509714 5 0.4446 0.2940 0.476 0.000 0.000 0.004 0.520
#> GSM509719 1 0.0000 0.8828 1.000 0.000 0.000 0.000 0.000
#> GSM509724 1 0.0404 0.8772 0.988 0.000 0.000 0.000 0.012
#> GSM509729 1 0.0290 0.8823 0.992 0.000 0.000 0.000 0.008
#> GSM509707 1 0.0290 0.8823 0.992 0.000 0.000 0.000 0.008
#> GSM509712 1 0.4448 -0.2991 0.516 0.000 0.000 0.004 0.480
#> GSM509715 5 0.1410 0.7757 0.060 0.000 0.000 0.000 0.940
#> GSM509720 1 0.0324 0.8821 0.992 0.000 0.000 0.004 0.004
#> GSM509725 1 0.0000 0.8828 1.000 0.000 0.000 0.000 0.000
#> GSM509730 1 0.0000 0.8828 1.000 0.000 0.000 0.000 0.000
#> GSM509708 1 0.0290 0.8823 0.992 0.000 0.000 0.000 0.008
#> GSM509713 1 0.4425 -0.2055 0.544 0.000 0.000 0.004 0.452
#> GSM509716 5 0.1410 0.7757 0.060 0.000 0.000 0.000 0.940
#> GSM509721 1 0.0000 0.8828 1.000 0.000 0.000 0.000 0.000
#> GSM509726 1 0.0693 0.8739 0.980 0.000 0.000 0.008 0.012
#> GSM509731 5 0.3210 0.7103 0.212 0.000 0.000 0.000 0.788
#> GSM509709 1 0.0290 0.8823 0.992 0.000 0.000 0.000 0.008
#> GSM509717 5 0.1410 0.7757 0.060 0.000 0.000 0.000 0.940
#> GSM509722 1 0.0671 0.8749 0.980 0.000 0.000 0.004 0.016
#> GSM509727 1 0.6639 -0.0841 0.424 0.000 0.412 0.152 0.012
#> GSM509710 1 0.0000 0.8828 1.000 0.000 0.000 0.000 0.000
#> GSM509718 5 0.2703 0.7564 0.060 0.000 0.024 0.020 0.896
#> GSM509723 1 0.0000 0.8828 1.000 0.000 0.000 0.000 0.000
#> GSM509728 3 0.3512 0.8643 0.012 0.000 0.816 0.160 0.012
#> GSM509732 3 0.0290 0.9356 0.000 0.000 0.992 0.008 0.000
#> GSM509736 3 0.0880 0.9326 0.000 0.000 0.968 0.032 0.000
#> GSM509741 3 0.0162 0.9351 0.000 0.000 0.996 0.004 0.000
#> GSM509746 3 0.0290 0.9356 0.000 0.000 0.992 0.008 0.000
#> GSM509733 3 0.0290 0.9356 0.000 0.000 0.992 0.008 0.000
#> GSM509737 3 0.1410 0.9254 0.000 0.000 0.940 0.060 0.000
#> GSM509742 3 0.0162 0.9351 0.000 0.000 0.996 0.004 0.000
#> GSM509747 3 0.0290 0.9356 0.000 0.000 0.992 0.008 0.000
#> GSM509734 3 0.1043 0.9318 0.000 0.000 0.960 0.040 0.000
#> GSM509738 3 0.2605 0.8826 0.000 0.000 0.852 0.148 0.000
#> GSM509743 3 0.0162 0.9351 0.000 0.000 0.996 0.004 0.000
#> GSM509748 3 0.0290 0.9356 0.000 0.000 0.992 0.008 0.000
#> GSM509735 1 0.0404 0.8772 0.988 0.000 0.000 0.000 0.012
#> GSM509739 1 0.0000 0.8828 1.000 0.000 0.000 0.000 0.000
#> GSM509744 3 0.0963 0.9315 0.000 0.000 0.964 0.036 0.000
#> GSM509749 3 0.0290 0.9356 0.000 0.000 0.992 0.008 0.000
#> GSM509740 3 0.6164 0.4725 0.248 0.000 0.592 0.148 0.012
#> GSM509745 3 0.2605 0.8826 0.000 0.000 0.852 0.148 0.000
#> GSM509750 3 0.2471 0.8887 0.000 0.000 0.864 0.136 0.000
#> GSM509751 2 0.0703 0.9187 0.000 0.976 0.000 0.024 0.000
#> GSM509753 2 0.0510 0.9189 0.000 0.984 0.000 0.016 0.000
#> GSM509755 2 0.0609 0.9110 0.000 0.980 0.000 0.020 0.000
#> GSM509757 2 0.0609 0.9110 0.000 0.980 0.000 0.020 0.000
#> GSM509759 2 0.0794 0.9064 0.000 0.972 0.000 0.028 0.000
#> GSM509761 2 0.2012 0.9082 0.000 0.920 0.000 0.020 0.060
#> GSM509763 2 0.2853 0.8770 0.000 0.876 0.000 0.072 0.052
#> GSM509765 2 0.2438 0.8993 0.000 0.900 0.000 0.040 0.060
#> GSM509767 2 0.0000 0.9171 0.000 1.000 0.000 0.000 0.000
#> GSM509769 2 0.1117 0.9206 0.000 0.964 0.000 0.020 0.016
#> GSM509771 2 0.0609 0.9110 0.000 0.980 0.000 0.020 0.000
#> GSM509773 2 0.1197 0.9114 0.000 0.952 0.000 0.048 0.000
#> GSM509775 2 0.2012 0.9082 0.000 0.920 0.000 0.020 0.060
#> GSM509777 2 0.4433 0.6565 0.000 0.740 0.000 0.200 0.060
#> GSM509779 4 0.4780 0.8719 0.000 0.248 0.000 0.692 0.060
#> GSM509781 4 0.3074 0.9544 0.000 0.196 0.000 0.804 0.000
#> GSM509783 4 0.3550 0.9441 0.000 0.184 0.000 0.796 0.020
#> GSM509785 4 0.3074 0.9544 0.000 0.196 0.000 0.804 0.000
#> GSM509752 2 0.0794 0.9183 0.000 0.972 0.000 0.028 0.000
#> GSM509754 2 0.0794 0.9183 0.000 0.972 0.000 0.028 0.000
#> GSM509756 2 0.1725 0.9135 0.000 0.936 0.000 0.020 0.044
#> GSM509758 2 0.1399 0.9186 0.000 0.952 0.000 0.028 0.020
#> GSM509760 2 0.2012 0.9084 0.000 0.920 0.000 0.020 0.060
#> GSM509762 2 0.0510 0.9127 0.000 0.984 0.000 0.016 0.000
#> GSM509764 2 0.1270 0.9002 0.000 0.948 0.000 0.052 0.000
#> GSM509766 2 0.2438 0.8990 0.000 0.900 0.000 0.040 0.060
#> GSM509768 2 0.2278 0.9036 0.000 0.908 0.000 0.032 0.060
#> GSM509770 2 0.0609 0.9110 0.000 0.980 0.000 0.020 0.000
#> GSM509772 2 0.0880 0.9036 0.000 0.968 0.000 0.032 0.000
#> GSM509774 2 0.5401 -0.0622 0.000 0.536 0.000 0.404 0.060
#> GSM509776 2 0.2193 0.9054 0.000 0.912 0.000 0.028 0.060
#> GSM509778 4 0.3074 0.9544 0.000 0.196 0.000 0.804 0.000
#> GSM509780 2 0.2193 0.9110 0.000 0.912 0.000 0.028 0.060
#> GSM509782 4 0.3353 0.9527 0.000 0.196 0.000 0.796 0.008
#> GSM509784 4 0.4806 0.8753 0.000 0.252 0.000 0.688 0.060
#> GSM509786 4 0.3492 0.9480 0.000 0.188 0.000 0.796 0.016
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM509706 1 0.0260 0.8899 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM509711 1 0.4810 0.4222 0.660 0.000 0.000 0.000 0.220 0.120
#> GSM509714 1 0.3578 0.3133 0.660 0.000 0.000 0.000 0.340 0.000
#> GSM509719 1 0.0000 0.8896 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509724 1 0.0972 0.8736 0.964 0.000 0.028 0.000 0.000 0.008
#> GSM509729 1 0.0260 0.8899 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM509707 1 0.0260 0.8899 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM509712 1 0.4653 0.4704 0.684 0.000 0.000 0.000 0.196 0.120
#> GSM509715 5 0.3136 0.9370 0.228 0.000 0.000 0.004 0.768 0.000
#> GSM509720 1 0.0146 0.8899 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM509725 1 0.0972 0.8736 0.964 0.000 0.028 0.000 0.000 0.008
#> GSM509730 1 0.0000 0.8896 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509708 1 0.0260 0.8899 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM509713 1 0.4536 0.5065 0.700 0.000 0.000 0.000 0.180 0.120
#> GSM509716 5 0.3136 0.9370 0.228 0.000 0.000 0.004 0.768 0.000
#> GSM509721 1 0.0000 0.8896 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509726 1 0.2586 0.7826 0.868 0.000 0.032 0.000 0.000 0.100
#> GSM509731 5 0.3819 0.7155 0.372 0.000 0.000 0.004 0.624 0.000
#> GSM509709 1 0.0260 0.8899 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM509717 5 0.3136 0.9370 0.228 0.000 0.000 0.004 0.768 0.000
#> GSM509722 1 0.0260 0.8899 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM509727 6 0.3975 0.0754 0.392 0.000 0.008 0.000 0.000 0.600
#> GSM509710 1 0.0972 0.8736 0.964 0.000 0.028 0.000 0.000 0.008
#> GSM509718 5 0.3599 0.9200 0.220 0.000 0.000 0.004 0.756 0.020
#> GSM509723 1 0.0000 0.8896 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509728 6 0.0547 0.6789 0.000 0.000 0.020 0.000 0.000 0.980
#> GSM509732 3 0.2178 0.8770 0.000 0.000 0.868 0.000 0.000 0.132
#> GSM509736 6 0.2260 0.6231 0.000 0.000 0.140 0.000 0.000 0.860
#> GSM509741 3 0.3428 0.7912 0.000 0.000 0.696 0.000 0.000 0.304
#> GSM509746 3 0.2178 0.8770 0.000 0.000 0.868 0.000 0.000 0.132
#> GSM509733 3 0.2178 0.8770 0.000 0.000 0.868 0.000 0.000 0.132
#> GSM509737 6 0.1610 0.6613 0.000 0.000 0.084 0.000 0.000 0.916
#> GSM509742 3 0.3409 0.7956 0.000 0.000 0.700 0.000 0.000 0.300
#> GSM509747 3 0.2219 0.8748 0.000 0.000 0.864 0.000 0.000 0.136
#> GSM509734 6 0.3244 0.4661 0.000 0.000 0.268 0.000 0.000 0.732
#> GSM509738 6 0.0458 0.6823 0.000 0.000 0.016 0.000 0.000 0.984
#> GSM509743 3 0.3428 0.7912 0.000 0.000 0.696 0.000 0.000 0.304
#> GSM509748 3 0.2416 0.8749 0.000 0.000 0.844 0.000 0.000 0.156
#> GSM509735 1 0.0972 0.8736 0.964 0.000 0.028 0.000 0.000 0.008
#> GSM509739 1 0.0000 0.8896 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509744 6 0.3810 -0.1533 0.000 0.000 0.428 0.000 0.000 0.572
#> GSM509749 3 0.3221 0.8120 0.000 0.000 0.736 0.000 0.000 0.264
#> GSM509740 6 0.3168 0.5293 0.192 0.000 0.016 0.000 0.000 0.792
#> GSM509745 6 0.0458 0.6823 0.000 0.000 0.016 0.000 0.000 0.984
#> GSM509750 6 0.3175 0.4136 0.000 0.000 0.256 0.000 0.000 0.744
#> GSM509751 2 0.4340 0.7976 0.000 0.708 0.064 0.004 0.224 0.000
#> GSM509753 2 0.4454 0.7894 0.000 0.692 0.084 0.000 0.224 0.000
#> GSM509755 2 0.4637 0.7864 0.000 0.684 0.088 0.004 0.224 0.000
#> GSM509757 2 0.4744 0.7867 0.000 0.684 0.080 0.012 0.224 0.000
#> GSM509759 2 0.5637 0.7512 0.000 0.628 0.088 0.060 0.224 0.000
#> GSM509761 2 0.1340 0.7586 0.000 0.948 0.040 0.004 0.008 0.000
#> GSM509763 2 0.2709 0.7529 0.000 0.884 0.040 0.044 0.032 0.000
#> GSM509765 2 0.1737 0.7544 0.000 0.932 0.040 0.020 0.008 0.000
#> GSM509767 2 0.4147 0.7981 0.000 0.716 0.060 0.000 0.224 0.000
#> GSM509769 2 0.2416 0.8118 0.000 0.844 0.000 0.000 0.156 0.000
#> GSM509771 2 0.4340 0.7976 0.000 0.708 0.064 0.004 0.224 0.000
#> GSM509773 2 0.3728 0.8021 0.000 0.772 0.004 0.044 0.180 0.000
#> GSM509775 2 0.1116 0.7649 0.000 0.960 0.028 0.004 0.008 0.000
#> GSM509777 2 0.3706 0.5368 0.000 0.780 0.040 0.172 0.008 0.000
#> GSM509779 4 0.4572 0.7062 0.000 0.316 0.040 0.636 0.008 0.000
#> GSM509781 4 0.1501 0.9037 0.000 0.076 0.000 0.924 0.000 0.000
#> GSM509783 4 0.1501 0.9037 0.000 0.076 0.000 0.924 0.000 0.000
#> GSM509785 4 0.1501 0.9037 0.000 0.076 0.000 0.924 0.000 0.000
#> GSM509752 2 0.3081 0.8109 0.000 0.776 0.000 0.004 0.220 0.000
#> GSM509754 2 0.3426 0.8099 0.000 0.764 0.012 0.004 0.220 0.000
#> GSM509756 2 0.1296 0.7911 0.000 0.952 0.032 0.004 0.012 0.000
#> GSM509758 2 0.2278 0.8093 0.000 0.868 0.004 0.000 0.128 0.000
#> GSM509760 2 0.0551 0.7764 0.000 0.984 0.004 0.004 0.008 0.000
#> GSM509762 2 0.3612 0.8091 0.000 0.764 0.036 0.000 0.200 0.000
#> GSM509764 2 0.5644 0.7498 0.000 0.628 0.064 0.084 0.224 0.000
#> GSM509766 2 0.1340 0.7586 0.000 0.948 0.040 0.004 0.008 0.000
#> GSM509768 2 0.1226 0.7610 0.000 0.952 0.040 0.004 0.004 0.000
#> GSM509770 2 0.4253 0.8034 0.000 0.728 0.072 0.004 0.196 0.000
#> GSM509772 2 0.5787 0.7412 0.000 0.616 0.088 0.072 0.224 0.000
#> GSM509774 2 0.4414 0.2762 0.000 0.672 0.040 0.280 0.008 0.000
#> GSM509776 2 0.1340 0.7586 0.000 0.948 0.040 0.004 0.008 0.000
#> GSM509778 4 0.1501 0.9037 0.000 0.076 0.000 0.924 0.000 0.000
#> GSM509780 2 0.1340 0.7586 0.000 0.948 0.040 0.004 0.008 0.000
#> GSM509782 4 0.1501 0.9037 0.000 0.076 0.000 0.924 0.000 0.000
#> GSM509784 4 0.4572 0.7078 0.000 0.316 0.040 0.636 0.008 0.000
#> GSM509786 4 0.1501 0.9037 0.000 0.076 0.000 0.924 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 disease.state(p) time(p) k
#> MAD:mclust 81 2.58e-18 2.22e-15 2
#> MAD:mclust 81 3.91e-20 4.99e-13 3
#> MAD:mclust 81 7.80e-27 1.38e-10 4
#> MAD:mclust 74 1.01e-23 6.87e-08 5
#> MAD:mclust 73 4.00e-22 1.78e-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 19175 rows and 81 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 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 0.995 0.998 0.5067 0.494 0.494
#> 3 3 0.764 0.822 0.916 0.2860 0.800 0.615
#> 4 4 0.904 0.902 0.945 0.1382 0.760 0.430
#> 5 5 0.866 0.844 0.917 0.0572 0.919 0.707
#> 6 6 0.851 0.785 0.893 0.0330 0.949 0.776
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
#> GSM509706 1 0.000 1.000 1.000 0.000
#> GSM509711 1 0.000 1.000 1.000 0.000
#> GSM509714 1 0.000 1.000 1.000 0.000
#> GSM509719 1 0.000 1.000 1.000 0.000
#> GSM509724 1 0.000 1.000 1.000 0.000
#> GSM509729 1 0.000 1.000 1.000 0.000
#> GSM509707 1 0.000 1.000 1.000 0.000
#> GSM509712 1 0.000 1.000 1.000 0.000
#> GSM509715 2 0.000 0.996 0.000 1.000
#> GSM509720 1 0.000 1.000 1.000 0.000
#> GSM509725 1 0.000 1.000 1.000 0.000
#> GSM509730 1 0.000 1.000 1.000 0.000
#> GSM509708 1 0.000 1.000 1.000 0.000
#> GSM509713 1 0.000 1.000 1.000 0.000
#> GSM509716 2 0.000 0.996 0.000 1.000
#> GSM509721 1 0.000 1.000 1.000 0.000
#> GSM509726 1 0.000 1.000 1.000 0.000
#> GSM509731 2 0.662 0.792 0.172 0.828
#> GSM509709 1 0.000 1.000 1.000 0.000
#> GSM509717 2 0.000 0.996 0.000 1.000
#> GSM509722 1 0.000 1.000 1.000 0.000
#> GSM509727 1 0.000 1.000 1.000 0.000
#> GSM509710 1 0.000 1.000 1.000 0.000
#> GSM509718 2 0.000 0.996 0.000 1.000
#> GSM509723 1 0.000 1.000 1.000 0.000
#> GSM509728 1 0.000 1.000 1.000 0.000
#> GSM509732 1 0.000 1.000 1.000 0.000
#> GSM509736 1 0.000 1.000 1.000 0.000
#> GSM509741 1 0.000 1.000 1.000 0.000
#> GSM509746 1 0.000 1.000 1.000 0.000
#> GSM509733 1 0.000 1.000 1.000 0.000
#> GSM509737 1 0.000 1.000 1.000 0.000
#> GSM509742 1 0.000 1.000 1.000 0.000
#> GSM509747 1 0.000 1.000 1.000 0.000
#> GSM509734 1 0.000 1.000 1.000 0.000
#> GSM509738 1 0.000 1.000 1.000 0.000
#> GSM509743 1 0.000 1.000 1.000 0.000
#> GSM509748 1 0.000 1.000 1.000 0.000
#> GSM509735 1 0.000 1.000 1.000 0.000
#> GSM509739 1 0.000 1.000 1.000 0.000
#> GSM509744 1 0.000 1.000 1.000 0.000
#> GSM509749 1 0.000 1.000 1.000 0.000
#> GSM509740 1 0.000 1.000 1.000 0.000
#> GSM509745 1 0.000 1.000 1.000 0.000
#> GSM509750 1 0.000 1.000 1.000 0.000
#> GSM509751 2 0.000 0.996 0.000 1.000
#> GSM509753 2 0.000 0.996 0.000 1.000
#> GSM509755 2 0.000 0.996 0.000 1.000
#> GSM509757 2 0.000 0.996 0.000 1.000
#> GSM509759 2 0.000 0.996 0.000 1.000
#> GSM509761 2 0.000 0.996 0.000 1.000
#> GSM509763 2 0.000 0.996 0.000 1.000
#> GSM509765 2 0.000 0.996 0.000 1.000
#> GSM509767 2 0.000 0.996 0.000 1.000
#> GSM509769 2 0.000 0.996 0.000 1.000
#> GSM509771 2 0.000 0.996 0.000 1.000
#> GSM509773 2 0.000 0.996 0.000 1.000
#> GSM509775 2 0.000 0.996 0.000 1.000
#> GSM509777 2 0.000 0.996 0.000 1.000
#> GSM509779 2 0.000 0.996 0.000 1.000
#> GSM509781 2 0.000 0.996 0.000 1.000
#> GSM509783 2 0.000 0.996 0.000 1.000
#> GSM509785 2 0.000 0.996 0.000 1.000
#> GSM509752 2 0.000 0.996 0.000 1.000
#> GSM509754 2 0.000 0.996 0.000 1.000
#> GSM509756 2 0.000 0.996 0.000 1.000
#> GSM509758 2 0.000 0.996 0.000 1.000
#> GSM509760 2 0.000 0.996 0.000 1.000
#> GSM509762 2 0.000 0.996 0.000 1.000
#> GSM509764 2 0.000 0.996 0.000 1.000
#> GSM509766 2 0.000 0.996 0.000 1.000
#> GSM509768 2 0.000 0.996 0.000 1.000
#> GSM509770 2 0.000 0.996 0.000 1.000
#> GSM509772 2 0.000 0.996 0.000 1.000
#> GSM509774 2 0.000 0.996 0.000 1.000
#> GSM509776 2 0.000 0.996 0.000 1.000
#> GSM509778 2 0.000 0.996 0.000 1.000
#> GSM509780 2 0.000 0.996 0.000 1.000
#> GSM509782 2 0.000 0.996 0.000 1.000
#> GSM509784 2 0.000 0.996 0.000 1.000
#> GSM509786 2 0.000 0.996 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM509706 1 0.0000 0.978 1.000 0.000 0.000
#> GSM509711 1 0.0000 0.978 1.000 0.000 0.000
#> GSM509714 1 0.1753 0.923 0.952 0.048 0.000
#> GSM509719 1 0.0000 0.978 1.000 0.000 0.000
#> GSM509724 1 0.0000 0.978 1.000 0.000 0.000
#> GSM509729 1 0.0000 0.978 1.000 0.000 0.000
#> GSM509707 1 0.0000 0.978 1.000 0.000 0.000
#> GSM509712 1 0.0000 0.978 1.000 0.000 0.000
#> GSM509715 2 0.0892 0.875 0.020 0.980 0.000
#> GSM509720 1 0.0000 0.978 1.000 0.000 0.000
#> GSM509725 1 0.0000 0.978 1.000 0.000 0.000
#> GSM509730 1 0.0000 0.978 1.000 0.000 0.000
#> GSM509708 1 0.0000 0.978 1.000 0.000 0.000
#> GSM509713 1 0.0000 0.978 1.000 0.000 0.000
#> GSM509716 2 0.1529 0.858 0.040 0.960 0.000
#> GSM509721 1 0.0000 0.978 1.000 0.000 0.000
#> GSM509726 1 0.0000 0.978 1.000 0.000 0.000
#> GSM509731 2 0.5327 0.549 0.272 0.728 0.000
#> GSM509709 1 0.0000 0.978 1.000 0.000 0.000
#> GSM509717 2 0.0892 0.875 0.020 0.980 0.000
#> GSM509722 1 0.0000 0.978 1.000 0.000 0.000
#> GSM509727 1 0.0000 0.978 1.000 0.000 0.000
#> GSM509710 1 0.0000 0.978 1.000 0.000 0.000
#> GSM509718 2 0.0592 0.880 0.012 0.988 0.000
#> GSM509723 1 0.0000 0.978 1.000 0.000 0.000
#> GSM509728 1 0.0000 0.978 1.000 0.000 0.000
#> GSM509732 3 0.1031 0.777 0.024 0.000 0.976
#> GSM509736 1 0.3267 0.859 0.884 0.000 0.116
#> GSM509741 3 0.6260 0.258 0.448 0.000 0.552
#> GSM509746 3 0.1031 0.777 0.024 0.000 0.976
#> GSM509733 3 0.0747 0.777 0.016 0.000 0.984
#> GSM509737 1 0.1163 0.955 0.972 0.000 0.028
#> GSM509742 3 0.5650 0.551 0.312 0.000 0.688
#> GSM509747 3 0.3482 0.747 0.128 0.000 0.872
#> GSM509734 1 0.2356 0.913 0.928 0.000 0.072
#> GSM509738 1 0.0000 0.978 1.000 0.000 0.000
#> GSM509743 3 0.5216 0.626 0.260 0.000 0.740
#> GSM509748 3 0.6008 0.445 0.372 0.000 0.628
#> GSM509735 1 0.0000 0.978 1.000 0.000 0.000
#> GSM509739 1 0.0000 0.978 1.000 0.000 0.000
#> GSM509744 1 0.2711 0.895 0.912 0.000 0.088
#> GSM509749 3 0.6309 0.102 0.496 0.000 0.504
#> GSM509740 1 0.0000 0.978 1.000 0.000 0.000
#> GSM509745 1 0.0000 0.978 1.000 0.000 0.000
#> GSM509750 1 0.4605 0.722 0.796 0.000 0.204
#> GSM509751 3 0.4452 0.616 0.000 0.192 0.808
#> GSM509753 3 0.1411 0.764 0.000 0.036 0.964
#> GSM509755 3 0.1411 0.764 0.000 0.036 0.964
#> GSM509757 3 0.1643 0.760 0.000 0.044 0.956
#> GSM509759 3 0.0000 0.772 0.000 0.000 1.000
#> GSM509761 2 0.1411 0.878 0.000 0.964 0.036
#> GSM509763 2 0.1753 0.874 0.000 0.952 0.048
#> GSM509765 2 0.0000 0.886 0.000 1.000 0.000
#> GSM509767 3 0.5291 0.478 0.000 0.268 0.732
#> GSM509769 2 0.5497 0.669 0.000 0.708 0.292
#> GSM509771 3 0.4931 0.552 0.000 0.232 0.768
#> GSM509773 2 0.4796 0.752 0.000 0.780 0.220
#> GSM509775 2 0.2066 0.869 0.000 0.940 0.060
#> GSM509777 2 0.0000 0.886 0.000 1.000 0.000
#> GSM509779 2 0.0000 0.886 0.000 1.000 0.000
#> GSM509781 2 0.0000 0.886 0.000 1.000 0.000
#> GSM509783 2 0.0000 0.886 0.000 1.000 0.000
#> GSM509785 2 0.0000 0.886 0.000 1.000 0.000
#> GSM509752 2 0.5968 0.554 0.000 0.636 0.364
#> GSM509754 2 0.6204 0.433 0.000 0.576 0.424
#> GSM509756 2 0.5058 0.726 0.000 0.756 0.244
#> GSM509758 2 0.4842 0.748 0.000 0.776 0.224
#> GSM509760 2 0.3038 0.844 0.000 0.896 0.104
#> GSM509762 2 0.5560 0.647 0.000 0.700 0.300
#> GSM509764 3 0.3941 0.669 0.000 0.156 0.844
#> GSM509766 2 0.0747 0.884 0.000 0.984 0.016
#> GSM509768 2 0.1860 0.873 0.000 0.948 0.052
#> GSM509770 2 0.6280 0.342 0.000 0.540 0.460
#> GSM509772 3 0.0000 0.772 0.000 0.000 1.000
#> GSM509774 2 0.0000 0.886 0.000 1.000 0.000
#> GSM509776 2 0.0424 0.885 0.000 0.992 0.008
#> GSM509778 2 0.0000 0.886 0.000 1.000 0.000
#> GSM509780 2 0.0424 0.885 0.000 0.992 0.008
#> GSM509782 2 0.0000 0.886 0.000 1.000 0.000
#> GSM509784 2 0.0000 0.886 0.000 1.000 0.000
#> GSM509786 2 0.0000 0.886 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM509706 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM509711 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM509714 1 0.0707 0.972 0.980 0.000 0.000 0.020
#> GSM509719 1 0.0188 0.984 0.996 0.004 0.000 0.000
#> GSM509724 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM509729 1 0.0188 0.984 0.996 0.000 0.004 0.000
#> GSM509707 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM509712 1 0.0376 0.983 0.992 0.000 0.004 0.004
#> GSM509715 4 0.0524 0.906 0.004 0.000 0.008 0.988
#> GSM509720 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM509725 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM509730 1 0.0188 0.984 0.996 0.000 0.004 0.000
#> GSM509708 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM509713 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM509716 4 0.0376 0.913 0.004 0.004 0.000 0.992
#> GSM509721 1 0.0188 0.984 0.996 0.004 0.000 0.000
#> GSM509726 1 0.0592 0.975 0.984 0.000 0.016 0.000
#> GSM509731 4 0.0672 0.915 0.008 0.008 0.000 0.984
#> GSM509709 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM509717 4 0.0657 0.908 0.000 0.004 0.012 0.984
#> GSM509722 1 0.0188 0.984 0.996 0.004 0.000 0.000
#> GSM509727 1 0.4054 0.743 0.796 0.000 0.188 0.016
#> GSM509710 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM509718 4 0.0921 0.890 0.000 0.000 0.028 0.972
#> GSM509723 1 0.0188 0.984 0.996 0.004 0.000 0.000
#> GSM509728 3 0.3933 0.750 0.200 0.000 0.792 0.008
#> GSM509732 3 0.1118 0.921 0.000 0.036 0.964 0.000
#> GSM509736 3 0.1174 0.929 0.012 0.000 0.968 0.020
#> GSM509741 3 0.0000 0.931 0.000 0.000 1.000 0.000
#> GSM509746 3 0.1022 0.923 0.000 0.032 0.968 0.000
#> GSM509733 3 0.1022 0.923 0.000 0.032 0.968 0.000
#> GSM509737 3 0.1488 0.925 0.012 0.000 0.956 0.032
#> GSM509742 3 0.0000 0.931 0.000 0.000 1.000 0.000
#> GSM509747 3 0.1118 0.921 0.000 0.036 0.964 0.000
#> GSM509734 3 0.1389 0.915 0.048 0.000 0.952 0.000
#> GSM509738 3 0.2089 0.916 0.020 0.000 0.932 0.048
#> GSM509743 3 0.0000 0.931 0.000 0.000 1.000 0.000
#> GSM509748 3 0.0895 0.927 0.004 0.020 0.976 0.000
#> GSM509735 1 0.0336 0.982 0.992 0.000 0.008 0.000
#> GSM509739 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM509744 3 0.1305 0.926 0.004 0.000 0.960 0.036
#> GSM509749 3 0.0188 0.931 0.004 0.000 0.996 0.000
#> GSM509740 3 0.6332 0.206 0.060 0.000 0.488 0.452
#> GSM509745 3 0.2376 0.907 0.016 0.000 0.916 0.068
#> GSM509750 3 0.1209 0.927 0.004 0.000 0.964 0.032
#> GSM509751 2 0.0592 0.915 0.000 0.984 0.016 0.000
#> GSM509753 2 0.0921 0.908 0.000 0.972 0.028 0.000
#> GSM509755 2 0.0469 0.916 0.000 0.988 0.012 0.000
#> GSM509757 2 0.0592 0.915 0.000 0.984 0.016 0.000
#> GSM509759 2 0.1389 0.889 0.000 0.952 0.048 0.000
#> GSM509761 2 0.1716 0.909 0.000 0.936 0.000 0.064
#> GSM509763 2 0.2814 0.865 0.000 0.868 0.000 0.132
#> GSM509765 2 0.3172 0.837 0.000 0.840 0.000 0.160
#> GSM509767 2 0.0469 0.917 0.000 0.988 0.012 0.000
#> GSM509769 2 0.0707 0.922 0.000 0.980 0.000 0.020
#> GSM509771 2 0.0469 0.917 0.000 0.988 0.012 0.000
#> GSM509773 2 0.1022 0.920 0.000 0.968 0.000 0.032
#> GSM509775 2 0.1940 0.904 0.000 0.924 0.000 0.076
#> GSM509777 2 0.4761 0.465 0.000 0.628 0.000 0.372
#> GSM509779 4 0.3400 0.802 0.000 0.180 0.000 0.820
#> GSM509781 4 0.1716 0.928 0.000 0.064 0.000 0.936
#> GSM509783 4 0.1557 0.931 0.000 0.056 0.000 0.944
#> GSM509785 4 0.1557 0.931 0.000 0.056 0.000 0.944
#> GSM509752 2 0.0707 0.922 0.000 0.980 0.000 0.020
#> GSM509754 2 0.0376 0.920 0.000 0.992 0.004 0.004
#> GSM509756 2 0.0817 0.921 0.000 0.976 0.000 0.024
#> GSM509758 2 0.0817 0.921 0.000 0.976 0.000 0.024
#> GSM509760 2 0.0921 0.921 0.000 0.972 0.000 0.028
#> GSM509762 2 0.0707 0.922 0.000 0.980 0.000 0.020
#> GSM509764 2 0.0895 0.916 0.000 0.976 0.020 0.004
#> GSM509766 2 0.2589 0.878 0.000 0.884 0.000 0.116
#> GSM509768 2 0.2149 0.897 0.000 0.912 0.000 0.088
#> GSM509770 2 0.0188 0.920 0.000 0.996 0.000 0.004
#> GSM509772 2 0.1211 0.899 0.000 0.960 0.040 0.000
#> GSM509774 2 0.4877 0.367 0.000 0.592 0.000 0.408
#> GSM509776 2 0.2589 0.879 0.000 0.884 0.000 0.116
#> GSM509778 4 0.1637 0.931 0.000 0.060 0.000 0.940
#> GSM509780 2 0.3123 0.842 0.000 0.844 0.000 0.156
#> GSM509782 4 0.1637 0.931 0.000 0.060 0.000 0.940
#> GSM509784 4 0.4222 0.643 0.000 0.272 0.000 0.728
#> GSM509786 4 0.1637 0.931 0.000 0.060 0.000 0.940
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM509706 1 0.0451 0.9624 0.988 0.000 0.008 0.000 0.004
#> GSM509711 1 0.0671 0.9594 0.980 0.000 0.004 0.000 0.016
#> GSM509714 1 0.3142 0.8774 0.864 0.000 0.004 0.076 0.056
#> GSM509719 1 0.2271 0.9254 0.904 0.004 0.004 0.004 0.084
#> GSM509724 1 0.0579 0.9616 0.984 0.000 0.008 0.000 0.008
#> GSM509729 1 0.1753 0.9436 0.936 0.000 0.032 0.000 0.032
#> GSM509707 1 0.0451 0.9622 0.988 0.000 0.004 0.000 0.008
#> GSM509712 1 0.0290 0.9619 0.992 0.000 0.000 0.000 0.008
#> GSM509715 5 0.3684 0.5777 0.000 0.000 0.000 0.280 0.720
#> GSM509720 1 0.2233 0.9187 0.892 0.000 0.004 0.000 0.104
#> GSM509725 1 0.0451 0.9622 0.988 0.000 0.008 0.000 0.004
#> GSM509730 1 0.2632 0.9060 0.888 0.000 0.072 0.000 0.040
#> GSM509708 1 0.0451 0.9622 0.988 0.000 0.004 0.000 0.008
#> GSM509713 1 0.0290 0.9625 0.992 0.000 0.008 0.000 0.000
#> GSM509716 5 0.4109 0.5397 0.012 0.000 0.000 0.288 0.700
#> GSM509721 1 0.2151 0.9306 0.912 0.004 0.004 0.004 0.076
#> GSM509726 1 0.0693 0.9610 0.980 0.000 0.008 0.000 0.012
#> GSM509731 4 0.0865 0.8479 0.000 0.000 0.004 0.972 0.024
#> GSM509709 1 0.0324 0.9625 0.992 0.000 0.004 0.000 0.004
#> GSM509717 4 0.4227 0.0920 0.000 0.000 0.000 0.580 0.420
#> GSM509722 1 0.1892 0.9344 0.916 0.000 0.004 0.000 0.080
#> GSM509727 5 0.4232 0.5281 0.312 0.000 0.012 0.000 0.676
#> GSM509710 1 0.0451 0.9620 0.988 0.000 0.004 0.000 0.008
#> GSM509718 5 0.3010 0.7019 0.000 0.000 0.004 0.172 0.824
#> GSM509723 1 0.1430 0.9478 0.944 0.000 0.004 0.000 0.052
#> GSM509728 5 0.5104 0.5607 0.068 0.000 0.284 0.000 0.648
#> GSM509732 3 0.0671 0.9318 0.004 0.000 0.980 0.000 0.016
#> GSM509736 5 0.1671 0.7513 0.000 0.000 0.076 0.000 0.924
#> GSM509741 3 0.1121 0.9332 0.000 0.000 0.956 0.000 0.044
#> GSM509746 3 0.0324 0.9391 0.004 0.000 0.992 0.000 0.004
#> GSM509733 3 0.0162 0.9403 0.004 0.000 0.996 0.000 0.000
#> GSM509737 5 0.1908 0.7464 0.000 0.000 0.092 0.000 0.908
#> GSM509742 3 0.0963 0.9375 0.000 0.000 0.964 0.000 0.036
#> GSM509747 3 0.0671 0.9321 0.004 0.000 0.980 0.000 0.016
#> GSM509734 3 0.0671 0.9414 0.004 0.000 0.980 0.000 0.016
#> GSM509738 5 0.1544 0.7523 0.000 0.000 0.068 0.000 0.932
#> GSM509743 3 0.3305 0.6972 0.000 0.000 0.776 0.000 0.224
#> GSM509748 3 0.0451 0.9408 0.004 0.000 0.988 0.000 0.008
#> GSM509735 1 0.0510 0.9608 0.984 0.000 0.016 0.000 0.000
#> GSM509739 1 0.0324 0.9624 0.992 0.000 0.004 0.000 0.004
#> GSM509744 5 0.4300 0.1611 0.000 0.000 0.476 0.000 0.524
#> GSM509749 3 0.0963 0.9376 0.000 0.000 0.964 0.000 0.036
#> GSM509740 5 0.1815 0.7492 0.020 0.000 0.024 0.016 0.940
#> GSM509745 5 0.3969 0.5658 0.000 0.000 0.304 0.004 0.692
#> GSM509750 3 0.2127 0.8709 0.000 0.000 0.892 0.000 0.108
#> GSM509751 2 0.0000 0.9320 0.000 1.000 0.000 0.000 0.000
#> GSM509753 2 0.0162 0.9307 0.000 0.996 0.000 0.004 0.000
#> GSM509755 2 0.0324 0.9290 0.000 0.992 0.000 0.004 0.004
#> GSM509757 2 0.0000 0.9320 0.000 1.000 0.000 0.000 0.000
#> GSM509759 2 0.0324 0.9303 0.000 0.992 0.000 0.004 0.004
#> GSM509761 2 0.1041 0.9261 0.000 0.964 0.000 0.032 0.004
#> GSM509763 2 0.4304 0.0926 0.000 0.516 0.000 0.484 0.000
#> GSM509765 2 0.3424 0.7179 0.000 0.760 0.000 0.240 0.000
#> GSM509767 2 0.1116 0.9263 0.000 0.964 0.004 0.028 0.004
#> GSM509769 2 0.0290 0.9325 0.000 0.992 0.000 0.008 0.000
#> GSM509771 2 0.2037 0.9044 0.000 0.920 0.012 0.064 0.004
#> GSM509773 2 0.1205 0.9221 0.000 0.956 0.000 0.040 0.004
#> GSM509775 2 0.2536 0.8588 0.000 0.868 0.000 0.128 0.004
#> GSM509777 4 0.1965 0.8157 0.000 0.096 0.000 0.904 0.000
#> GSM509779 4 0.0609 0.8722 0.000 0.020 0.000 0.980 0.000
#> GSM509781 4 0.0290 0.8757 0.000 0.008 0.000 0.992 0.000
#> GSM509783 4 0.0162 0.8731 0.000 0.004 0.000 0.996 0.000
#> GSM509785 4 0.0162 0.8731 0.000 0.004 0.000 0.996 0.000
#> GSM509752 2 0.0324 0.9325 0.000 0.992 0.000 0.004 0.004
#> GSM509754 2 0.0451 0.9324 0.000 0.988 0.000 0.008 0.004
#> GSM509756 2 0.0324 0.9304 0.000 0.992 0.000 0.004 0.004
#> GSM509758 2 0.0566 0.9319 0.000 0.984 0.000 0.012 0.004
#> GSM509760 2 0.0290 0.9325 0.000 0.992 0.000 0.008 0.000
#> GSM509762 2 0.0162 0.9318 0.000 0.996 0.000 0.000 0.004
#> GSM509764 2 0.0566 0.9267 0.000 0.984 0.000 0.004 0.012
#> GSM509766 2 0.3074 0.7812 0.000 0.804 0.000 0.196 0.000
#> GSM509768 2 0.2719 0.8424 0.000 0.852 0.000 0.144 0.004
#> GSM509770 2 0.0451 0.9320 0.000 0.988 0.000 0.008 0.004
#> GSM509772 2 0.0162 0.9317 0.000 0.996 0.000 0.000 0.004
#> GSM509774 4 0.3003 0.7191 0.000 0.188 0.000 0.812 0.000
#> GSM509776 2 0.1952 0.8952 0.000 0.912 0.000 0.084 0.004
#> GSM509778 4 0.0290 0.8757 0.000 0.008 0.000 0.992 0.000
#> GSM509780 4 0.4009 0.5124 0.000 0.312 0.000 0.684 0.004
#> GSM509782 4 0.0290 0.8757 0.000 0.008 0.000 0.992 0.000
#> GSM509784 4 0.0963 0.8636 0.000 0.036 0.000 0.964 0.000
#> GSM509786 4 0.0290 0.8757 0.000 0.008 0.000 0.992 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM509706 1 0.0260 0.8907 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM509711 1 0.0858 0.8836 0.968 0.000 0.000 0.004 0.028 0.000
#> GSM509714 5 0.5192 0.6867 0.048 0.000 0.000 0.140 0.692 0.120
#> GSM509719 5 0.2278 0.8668 0.044 0.004 0.000 0.000 0.900 0.052
#> GSM509724 1 0.0146 0.8901 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM509729 1 0.4706 -0.0709 0.500 0.000 0.016 0.004 0.468 0.012
#> GSM509707 1 0.0547 0.8881 0.980 0.000 0.000 0.000 0.020 0.000
#> GSM509712 1 0.1826 0.8614 0.924 0.000 0.000 0.020 0.052 0.004
#> GSM509715 6 0.4769 0.5610 0.000 0.000 0.000 0.240 0.104 0.656
#> GSM509720 5 0.2558 0.8471 0.028 0.000 0.000 0.000 0.868 0.104
#> GSM509725 1 0.0000 0.8907 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509730 5 0.5522 0.6331 0.168 0.000 0.148 0.008 0.652 0.024
#> GSM509708 1 0.0865 0.8806 0.964 0.000 0.000 0.000 0.036 0.000
#> GSM509713 1 0.0458 0.8902 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM509716 6 0.5468 0.3337 0.000 0.000 0.000 0.156 0.296 0.548
#> GSM509721 5 0.2314 0.8647 0.036 0.008 0.000 0.000 0.900 0.056
#> GSM509726 1 0.0291 0.8888 0.992 0.000 0.000 0.000 0.004 0.004
#> GSM509731 4 0.3534 0.5626 0.004 0.000 0.000 0.772 0.200 0.024
#> GSM509709 1 0.0146 0.8907 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM509717 6 0.5561 0.2680 0.000 0.000 0.000 0.428 0.136 0.436
#> GSM509722 5 0.2604 0.8647 0.044 0.004 0.000 0.004 0.884 0.064
#> GSM509727 1 0.3604 0.6581 0.760 0.000 0.012 0.000 0.012 0.216
#> GSM509710 1 0.0291 0.8888 0.992 0.000 0.000 0.000 0.004 0.004
#> GSM509718 6 0.2889 0.6760 0.000 0.000 0.000 0.108 0.044 0.848
#> GSM509723 5 0.1141 0.8518 0.052 0.000 0.000 0.000 0.948 0.000
#> GSM509728 1 0.5793 0.0416 0.472 0.000 0.128 0.000 0.012 0.388
#> GSM509732 3 0.0436 0.9022 0.004 0.000 0.988 0.000 0.004 0.004
#> GSM509736 6 0.1588 0.6969 0.000 0.000 0.072 0.000 0.004 0.924
#> GSM509741 3 0.1327 0.8867 0.000 0.000 0.936 0.000 0.000 0.064
#> GSM509746 3 0.0291 0.9027 0.004 0.000 0.992 0.000 0.000 0.004
#> GSM509733 3 0.0146 0.9037 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM509737 6 0.2445 0.6873 0.000 0.000 0.108 0.000 0.020 0.872
#> GSM509742 3 0.1267 0.8897 0.000 0.000 0.940 0.000 0.000 0.060
#> GSM509747 3 0.1116 0.8859 0.004 0.000 0.960 0.000 0.028 0.008
#> GSM509734 3 0.1418 0.8949 0.024 0.000 0.944 0.000 0.000 0.032
#> GSM509738 6 0.1434 0.6917 0.000 0.000 0.012 0.000 0.048 0.940
#> GSM509743 3 0.4195 0.1759 0.004 0.000 0.548 0.000 0.008 0.440
#> GSM509748 3 0.0260 0.9034 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM509735 1 0.0713 0.8846 0.972 0.000 0.000 0.000 0.028 0.000
#> GSM509739 1 0.0000 0.8907 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509744 6 0.3634 0.3309 0.000 0.000 0.356 0.000 0.000 0.644
#> GSM509749 3 0.0717 0.9041 0.000 0.000 0.976 0.000 0.008 0.016
#> GSM509740 6 0.1584 0.6843 0.000 0.000 0.008 0.000 0.064 0.928
#> GSM509745 6 0.3933 0.4539 0.000 0.000 0.308 0.008 0.008 0.676
#> GSM509750 3 0.2482 0.8061 0.000 0.000 0.848 0.000 0.004 0.148
#> GSM509751 2 0.0260 0.9468 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM509753 2 0.0547 0.9427 0.000 0.980 0.000 0.000 0.020 0.000
#> GSM509755 2 0.0790 0.9364 0.000 0.968 0.000 0.000 0.032 0.000
#> GSM509757 2 0.0547 0.9447 0.000 0.980 0.000 0.000 0.020 0.000
#> GSM509759 2 0.1285 0.9205 0.000 0.944 0.000 0.004 0.052 0.000
#> GSM509761 2 0.0363 0.9468 0.000 0.988 0.000 0.012 0.000 0.000
#> GSM509763 2 0.3265 0.6799 0.000 0.748 0.000 0.248 0.004 0.000
#> GSM509765 2 0.2454 0.8278 0.000 0.840 0.000 0.160 0.000 0.000
#> GSM509767 2 0.0820 0.9439 0.000 0.972 0.000 0.016 0.012 0.000
#> GSM509769 2 0.0146 0.9477 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM509771 2 0.1578 0.9270 0.000 0.936 0.004 0.048 0.012 0.000
#> GSM509773 2 0.1082 0.9357 0.000 0.956 0.000 0.040 0.004 0.000
#> GSM509775 2 0.1714 0.9014 0.000 0.908 0.000 0.092 0.000 0.000
#> GSM509777 4 0.2915 0.6959 0.000 0.184 0.000 0.808 0.008 0.000
#> GSM509779 4 0.0858 0.8160 0.000 0.028 0.000 0.968 0.004 0.000
#> GSM509781 4 0.0363 0.8164 0.000 0.012 0.000 0.988 0.000 0.000
#> GSM509783 4 0.0436 0.8079 0.000 0.004 0.000 0.988 0.004 0.004
#> GSM509785 4 0.0260 0.8143 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM509752 2 0.0146 0.9479 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM509754 2 0.0000 0.9473 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509756 2 0.0508 0.9460 0.000 0.984 0.000 0.000 0.012 0.004
#> GSM509758 2 0.0000 0.9473 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509760 2 0.0508 0.9478 0.000 0.984 0.000 0.000 0.012 0.004
#> GSM509762 2 0.0291 0.9475 0.000 0.992 0.000 0.000 0.004 0.004
#> GSM509764 2 0.0458 0.9458 0.000 0.984 0.000 0.000 0.016 0.000
#> GSM509766 2 0.2048 0.8744 0.000 0.880 0.000 0.120 0.000 0.000
#> GSM509768 2 0.1910 0.8864 0.000 0.892 0.000 0.108 0.000 0.000
#> GSM509770 2 0.0291 0.9482 0.000 0.992 0.000 0.004 0.004 0.000
#> GSM509772 2 0.0692 0.9424 0.000 0.976 0.000 0.004 0.020 0.000
#> GSM509774 4 0.3717 0.4094 0.000 0.384 0.000 0.616 0.000 0.000
#> GSM509776 2 0.1556 0.9112 0.000 0.920 0.000 0.080 0.000 0.000
#> GSM509778 4 0.0622 0.8147 0.000 0.012 0.000 0.980 0.008 0.000
#> GSM509780 4 0.3966 0.2321 0.000 0.444 0.000 0.552 0.004 0.000
#> GSM509782 4 0.0363 0.8166 0.000 0.012 0.000 0.988 0.000 0.000
#> GSM509784 4 0.1267 0.8001 0.000 0.060 0.000 0.940 0.000 0.000
#> GSM509786 4 0.0547 0.8176 0.000 0.020 0.000 0.980 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 disease.state(p) time(p) k
#> MAD:NMF 81 8.31e-15 6.68e-12 2
#> MAD:NMF 75 7.19e-11 5.22e-07 3
#> MAD:NMF 78 2.10e-23 5.21e-08 4
#> MAD:NMF 78 5.39e-22 4.75e-09 5
#> MAD:NMF 72 4.21e-20 1.81e-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", "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 19175 rows and 81 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 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 0.664 0.896 0.932 0.4824 0.494 0.494
#> 3 3 0.908 0.928 0.960 0.2544 0.896 0.790
#> 4 4 0.809 0.843 0.898 0.1441 0.944 0.858
#> 5 5 0.857 0.403 0.681 0.0754 0.821 0.498
#> 6 6 0.801 0.769 0.879 0.0442 0.841 0.448
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
#> GSM509706 1 0.0000 0.857 1.000 0.000
#> GSM509711 1 0.0000 0.857 1.000 0.000
#> GSM509714 1 0.1843 0.860 0.972 0.028
#> GSM509719 1 0.2043 0.860 0.968 0.032
#> GSM509724 1 0.0000 0.857 1.000 0.000
#> GSM509729 1 0.0000 0.857 1.000 0.000
#> GSM509707 1 0.0000 0.857 1.000 0.000
#> GSM509712 1 0.1843 0.860 0.972 0.028
#> GSM509715 2 0.2778 0.943 0.048 0.952
#> GSM509720 1 0.2043 0.860 0.968 0.032
#> GSM509725 1 0.0000 0.857 1.000 0.000
#> GSM509730 1 0.0376 0.857 0.996 0.004
#> GSM509708 1 0.0000 0.857 1.000 0.000
#> GSM509713 1 0.0000 0.857 1.000 0.000
#> GSM509716 2 0.2778 0.943 0.048 0.952
#> GSM509721 1 0.2043 0.860 0.968 0.032
#> GSM509726 1 0.0000 0.857 1.000 0.000
#> GSM509731 2 0.2778 0.943 0.048 0.952
#> GSM509709 1 0.0000 0.857 1.000 0.000
#> GSM509717 2 0.2778 0.943 0.048 0.952
#> GSM509722 1 0.2043 0.860 0.968 0.032
#> GSM509727 1 0.7815 0.755 0.768 0.232
#> GSM509710 1 0.0000 0.857 1.000 0.000
#> GSM509718 2 0.2778 0.943 0.048 0.952
#> GSM509723 1 0.2043 0.860 0.968 0.032
#> GSM509728 1 0.7815 0.755 0.768 0.232
#> GSM509732 1 0.8608 0.742 0.716 0.284
#> GSM509736 1 0.8267 0.738 0.740 0.260
#> GSM509741 1 0.8608 0.742 0.716 0.284
#> GSM509746 1 0.8608 0.742 0.716 0.284
#> GSM509733 1 0.8608 0.742 0.716 0.284
#> GSM509737 1 0.8443 0.727 0.728 0.272
#> GSM509742 1 0.8608 0.742 0.716 0.284
#> GSM509747 1 0.8608 0.742 0.716 0.284
#> GSM509734 1 0.6973 0.804 0.812 0.188
#> GSM509738 1 0.8267 0.738 0.740 0.260
#> GSM509743 1 0.8713 0.734 0.708 0.292
#> GSM509748 1 0.8608 0.742 0.716 0.284
#> GSM509735 1 0.0000 0.857 1.000 0.000
#> GSM509739 1 0.0000 0.857 1.000 0.000
#> GSM509744 1 0.8713 0.734 0.708 0.292
#> GSM509749 1 0.8608 0.742 0.716 0.284
#> GSM509740 1 0.7883 0.753 0.764 0.236
#> GSM509745 1 0.8267 0.738 0.740 0.260
#> GSM509750 1 0.8713 0.734 0.708 0.292
#> GSM509751 2 0.0000 0.992 0.000 1.000
#> GSM509753 2 0.0000 0.992 0.000 1.000
#> GSM509755 2 0.0000 0.992 0.000 1.000
#> GSM509757 2 0.0000 0.992 0.000 1.000
#> GSM509759 2 0.0000 0.992 0.000 1.000
#> GSM509761 2 0.0000 0.992 0.000 1.000
#> GSM509763 2 0.0000 0.992 0.000 1.000
#> GSM509765 2 0.0000 0.992 0.000 1.000
#> GSM509767 2 0.0000 0.992 0.000 1.000
#> GSM509769 2 0.0000 0.992 0.000 1.000
#> GSM509771 2 0.0000 0.992 0.000 1.000
#> GSM509773 2 0.0000 0.992 0.000 1.000
#> GSM509775 2 0.0000 0.992 0.000 1.000
#> GSM509777 2 0.0000 0.992 0.000 1.000
#> GSM509779 2 0.0000 0.992 0.000 1.000
#> GSM509781 2 0.0000 0.992 0.000 1.000
#> GSM509783 2 0.0000 0.992 0.000 1.000
#> GSM509785 2 0.0000 0.992 0.000 1.000
#> GSM509752 2 0.0000 0.992 0.000 1.000
#> GSM509754 2 0.0000 0.992 0.000 1.000
#> GSM509756 2 0.0000 0.992 0.000 1.000
#> GSM509758 2 0.0000 0.992 0.000 1.000
#> GSM509760 2 0.0000 0.992 0.000 1.000
#> GSM509762 2 0.0000 0.992 0.000 1.000
#> GSM509764 2 0.0000 0.992 0.000 1.000
#> GSM509766 2 0.0000 0.992 0.000 1.000
#> GSM509768 2 0.0000 0.992 0.000 1.000
#> GSM509770 2 0.0000 0.992 0.000 1.000
#> GSM509772 2 0.0000 0.992 0.000 1.000
#> GSM509774 2 0.0000 0.992 0.000 1.000
#> GSM509776 2 0.0000 0.992 0.000 1.000
#> GSM509778 2 0.0000 0.992 0.000 1.000
#> GSM509780 2 0.0000 0.992 0.000 1.000
#> GSM509782 2 0.0000 0.992 0.000 1.000
#> GSM509784 2 0.0000 0.992 0.000 1.000
#> GSM509786 2 0.0000 0.992 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM509706 1 0.0000 0.889 1.000 0.000 0.000
#> GSM509711 1 0.0000 0.889 1.000 0.000 0.000
#> GSM509714 1 0.2356 0.874 0.928 0.000 0.072
#> GSM509719 1 0.2448 0.873 0.924 0.000 0.076
#> GSM509724 1 0.0000 0.889 1.000 0.000 0.000
#> GSM509729 1 0.0000 0.889 1.000 0.000 0.000
#> GSM509707 1 0.0000 0.889 1.000 0.000 0.000
#> GSM509712 1 0.2356 0.874 0.928 0.000 0.072
#> GSM509715 2 0.2878 0.895 0.000 0.904 0.096
#> GSM509720 1 0.2448 0.873 0.924 0.000 0.076
#> GSM509725 1 0.0000 0.889 1.000 0.000 0.000
#> GSM509730 1 0.0237 0.888 0.996 0.000 0.004
#> GSM509708 1 0.0000 0.889 1.000 0.000 0.000
#> GSM509713 1 0.0000 0.889 1.000 0.000 0.000
#> GSM509716 2 0.2878 0.895 0.000 0.904 0.096
#> GSM509721 1 0.2448 0.873 0.924 0.000 0.076
#> GSM509726 1 0.0000 0.889 1.000 0.000 0.000
#> GSM509731 2 0.2878 0.895 0.000 0.904 0.096
#> GSM509709 1 0.0000 0.889 1.000 0.000 0.000
#> GSM509717 2 0.2878 0.895 0.000 0.904 0.096
#> GSM509722 1 0.2448 0.873 0.924 0.000 0.076
#> GSM509727 1 0.7108 0.721 0.716 0.184 0.100
#> GSM509710 1 0.0000 0.889 1.000 0.000 0.000
#> GSM509718 2 0.2878 0.895 0.000 0.904 0.096
#> GSM509723 1 0.2448 0.873 0.924 0.000 0.076
#> GSM509728 1 0.7108 0.721 0.716 0.184 0.100
#> GSM509732 3 0.0000 0.986 0.000 0.000 1.000
#> GSM509736 1 0.7572 0.700 0.688 0.184 0.128
#> GSM509741 3 0.0000 0.986 0.000 0.000 1.000
#> GSM509746 3 0.0000 0.986 0.000 0.000 1.000
#> GSM509733 3 0.0000 0.986 0.000 0.000 1.000
#> GSM509737 1 0.7750 0.688 0.676 0.184 0.140
#> GSM509742 3 0.0000 0.986 0.000 0.000 1.000
#> GSM509747 3 0.0000 0.986 0.000 0.000 1.000
#> GSM509734 3 0.3340 0.861 0.120 0.000 0.880
#> GSM509738 1 0.7572 0.700 0.688 0.184 0.128
#> GSM509743 3 0.0424 0.981 0.000 0.008 0.992
#> GSM509748 3 0.0000 0.986 0.000 0.000 1.000
#> GSM509735 1 0.0000 0.889 1.000 0.000 0.000
#> GSM509739 1 0.0000 0.889 1.000 0.000 0.000
#> GSM509744 3 0.0424 0.981 0.000 0.008 0.992
#> GSM509749 3 0.0000 0.986 0.000 0.000 1.000
#> GSM509740 1 0.7179 0.719 0.712 0.184 0.104
#> GSM509745 1 0.7572 0.700 0.688 0.184 0.128
#> GSM509750 3 0.0424 0.981 0.000 0.008 0.992
#> GSM509751 2 0.0000 0.987 0.000 1.000 0.000
#> GSM509753 2 0.0000 0.987 0.000 1.000 0.000
#> GSM509755 2 0.0000 0.987 0.000 1.000 0.000
#> GSM509757 2 0.0000 0.987 0.000 1.000 0.000
#> GSM509759 2 0.0000 0.987 0.000 1.000 0.000
#> GSM509761 2 0.0000 0.987 0.000 1.000 0.000
#> GSM509763 2 0.0000 0.987 0.000 1.000 0.000
#> GSM509765 2 0.0000 0.987 0.000 1.000 0.000
#> GSM509767 2 0.0000 0.987 0.000 1.000 0.000
#> GSM509769 2 0.0000 0.987 0.000 1.000 0.000
#> GSM509771 2 0.0000 0.987 0.000 1.000 0.000
#> GSM509773 2 0.0000 0.987 0.000 1.000 0.000
#> GSM509775 2 0.0000 0.987 0.000 1.000 0.000
#> GSM509777 2 0.0000 0.987 0.000 1.000 0.000
#> GSM509779 2 0.0000 0.987 0.000 1.000 0.000
#> GSM509781 2 0.0000 0.987 0.000 1.000 0.000
#> GSM509783 2 0.0000 0.987 0.000 1.000 0.000
#> GSM509785 2 0.0000 0.987 0.000 1.000 0.000
#> GSM509752 2 0.0000 0.987 0.000 1.000 0.000
#> GSM509754 2 0.0000 0.987 0.000 1.000 0.000
#> GSM509756 2 0.0000 0.987 0.000 1.000 0.000
#> GSM509758 2 0.0000 0.987 0.000 1.000 0.000
#> GSM509760 2 0.0000 0.987 0.000 1.000 0.000
#> GSM509762 2 0.0000 0.987 0.000 1.000 0.000
#> GSM509764 2 0.0000 0.987 0.000 1.000 0.000
#> GSM509766 2 0.0000 0.987 0.000 1.000 0.000
#> GSM509768 2 0.0000 0.987 0.000 1.000 0.000
#> GSM509770 2 0.0000 0.987 0.000 1.000 0.000
#> GSM509772 2 0.0000 0.987 0.000 1.000 0.000
#> GSM509774 2 0.0000 0.987 0.000 1.000 0.000
#> GSM509776 2 0.0000 0.987 0.000 1.000 0.000
#> GSM509778 2 0.0000 0.987 0.000 1.000 0.000
#> GSM509780 2 0.0000 0.987 0.000 1.000 0.000
#> GSM509782 2 0.0000 0.987 0.000 1.000 0.000
#> GSM509784 2 0.0000 0.987 0.000 1.000 0.000
#> GSM509786 2 0.0000 0.987 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM509706 1 0.3074 0.821 0.848 0.000 0.000 0.152
#> GSM509711 1 0.2589 0.826 0.884 0.000 0.000 0.116
#> GSM509714 1 0.1867 0.823 0.928 0.000 0.000 0.072
#> GSM509719 1 0.2053 0.823 0.924 0.000 0.004 0.072
#> GSM509724 1 0.3074 0.821 0.848 0.000 0.000 0.152
#> GSM509729 1 0.0000 0.829 1.000 0.000 0.000 0.000
#> GSM509707 1 0.3074 0.821 0.848 0.000 0.000 0.152
#> GSM509712 1 0.1867 0.823 0.928 0.000 0.000 0.072
#> GSM509715 4 0.3074 1.000 0.000 0.152 0.000 0.848
#> GSM509720 1 0.2053 0.823 0.924 0.000 0.004 0.072
#> GSM509725 1 0.3074 0.821 0.848 0.000 0.000 0.152
#> GSM509730 1 0.0188 0.829 0.996 0.000 0.000 0.004
#> GSM509708 1 0.3074 0.821 0.848 0.000 0.000 0.152
#> GSM509713 1 0.2589 0.826 0.884 0.000 0.000 0.116
#> GSM509716 4 0.3074 1.000 0.000 0.152 0.000 0.848
#> GSM509721 1 0.2053 0.823 0.924 0.000 0.004 0.072
#> GSM509726 1 0.3074 0.821 0.848 0.000 0.000 0.152
#> GSM509731 4 0.3074 1.000 0.000 0.152 0.000 0.848
#> GSM509709 1 0.3074 0.821 0.848 0.000 0.000 0.152
#> GSM509717 4 0.3074 1.000 0.000 0.152 0.000 0.848
#> GSM509722 1 0.2053 0.823 0.924 0.000 0.004 0.072
#> GSM509727 1 0.4828 0.680 0.716 0.008 0.008 0.268
#> GSM509710 1 0.3074 0.821 0.848 0.000 0.000 0.152
#> GSM509718 4 0.3074 1.000 0.000 0.152 0.000 0.848
#> GSM509723 1 0.2053 0.823 0.924 0.000 0.004 0.072
#> GSM509728 1 0.4828 0.680 0.716 0.008 0.008 0.268
#> GSM509732 3 0.0000 0.971 0.000 0.000 1.000 0.000
#> GSM509736 1 0.5652 0.656 0.688 0.008 0.044 0.260
#> GSM509741 3 0.0469 0.972 0.000 0.000 0.988 0.012
#> GSM509746 3 0.0188 0.971 0.000 0.000 0.996 0.004
#> GSM509733 3 0.0000 0.971 0.000 0.000 1.000 0.000
#> GSM509737 1 0.5879 0.647 0.676 0.008 0.056 0.260
#> GSM509742 3 0.0469 0.972 0.000 0.000 0.988 0.012
#> GSM509747 3 0.0188 0.971 0.000 0.000 0.996 0.004
#> GSM509734 3 0.3105 0.834 0.120 0.000 0.868 0.012
#> GSM509738 1 0.5652 0.656 0.688 0.008 0.044 0.260
#> GSM509743 3 0.1256 0.962 0.000 0.008 0.964 0.028
#> GSM509748 3 0.0000 0.971 0.000 0.000 1.000 0.000
#> GSM509735 1 0.3074 0.821 0.848 0.000 0.000 0.152
#> GSM509739 1 0.3074 0.821 0.848 0.000 0.000 0.152
#> GSM509744 3 0.1256 0.962 0.000 0.008 0.964 0.028
#> GSM509749 3 0.0336 0.972 0.000 0.000 0.992 0.008
#> GSM509740 1 0.4952 0.678 0.712 0.008 0.012 0.268
#> GSM509745 1 0.5600 0.661 0.688 0.008 0.040 0.264
#> GSM509750 3 0.1256 0.962 0.000 0.008 0.964 0.028
#> GSM509751 2 0.0000 0.923 0.000 1.000 0.000 0.000
#> GSM509753 2 0.0000 0.923 0.000 1.000 0.000 0.000
#> GSM509755 2 0.0000 0.923 0.000 1.000 0.000 0.000
#> GSM509757 2 0.0000 0.923 0.000 1.000 0.000 0.000
#> GSM509759 2 0.0000 0.923 0.000 1.000 0.000 0.000
#> GSM509761 2 0.0000 0.923 0.000 1.000 0.000 0.000
#> GSM509763 2 0.0000 0.923 0.000 1.000 0.000 0.000
#> GSM509765 2 0.0000 0.923 0.000 1.000 0.000 0.000
#> GSM509767 2 0.0000 0.923 0.000 1.000 0.000 0.000
#> GSM509769 2 0.0000 0.923 0.000 1.000 0.000 0.000
#> GSM509771 2 0.0000 0.923 0.000 1.000 0.000 0.000
#> GSM509773 2 0.0000 0.923 0.000 1.000 0.000 0.000
#> GSM509775 2 0.0000 0.923 0.000 1.000 0.000 0.000
#> GSM509777 2 0.0000 0.923 0.000 1.000 0.000 0.000
#> GSM509779 2 0.0592 0.909 0.000 0.984 0.000 0.016
#> GSM509781 2 0.4804 0.315 0.000 0.616 0.000 0.384
#> GSM509783 2 0.4790 0.326 0.000 0.620 0.000 0.380
#> GSM509785 2 0.4804 0.315 0.000 0.616 0.000 0.384
#> GSM509752 2 0.0000 0.923 0.000 1.000 0.000 0.000
#> GSM509754 2 0.0000 0.923 0.000 1.000 0.000 0.000
#> GSM509756 2 0.0000 0.923 0.000 1.000 0.000 0.000
#> GSM509758 2 0.0000 0.923 0.000 1.000 0.000 0.000
#> GSM509760 2 0.0000 0.923 0.000 1.000 0.000 0.000
#> GSM509762 2 0.0000 0.923 0.000 1.000 0.000 0.000
#> GSM509764 2 0.0000 0.923 0.000 1.000 0.000 0.000
#> GSM509766 2 0.0000 0.923 0.000 1.000 0.000 0.000
#> GSM509768 2 0.0000 0.923 0.000 1.000 0.000 0.000
#> GSM509770 2 0.0000 0.923 0.000 1.000 0.000 0.000
#> GSM509772 2 0.0000 0.923 0.000 1.000 0.000 0.000
#> GSM509774 2 0.0000 0.923 0.000 1.000 0.000 0.000
#> GSM509776 2 0.0000 0.923 0.000 1.000 0.000 0.000
#> GSM509778 2 0.4790 0.326 0.000 0.620 0.000 0.380
#> GSM509780 2 0.0000 0.923 0.000 1.000 0.000 0.000
#> GSM509782 2 0.3907 0.636 0.000 0.768 0.000 0.232
#> GSM509784 2 0.0707 0.906 0.000 0.980 0.000 0.020
#> GSM509786 2 0.4804 0.315 0.000 0.616 0.000 0.384
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM509706 1 0.4305 0.726 0.512 0.488 0.000 0.000 0.000
#> GSM509711 2 0.6695 -0.712 0.368 0.392 0.000 0.000 0.240
#> GSM509714 1 0.0000 0.560 1.000 0.000 0.000 0.000 0.000
#> GSM509719 1 0.0162 0.560 0.996 0.000 0.004 0.000 0.000
#> GSM509724 1 0.4305 0.726 0.512 0.488 0.000 0.000 0.000
#> GSM509729 1 0.2020 0.613 0.900 0.100 0.000 0.000 0.000
#> GSM509707 1 0.4305 0.726 0.512 0.488 0.000 0.000 0.000
#> GSM509712 1 0.4847 0.178 0.692 0.068 0.000 0.000 0.240
#> GSM509715 5 0.4201 0.501 0.000 0.008 0.000 0.328 0.664
#> GSM509720 1 0.0162 0.560 0.996 0.000 0.004 0.000 0.000
#> GSM509725 1 0.4305 0.726 0.512 0.488 0.000 0.000 0.000
#> GSM509730 1 0.1965 0.611 0.904 0.096 0.000 0.000 0.000
#> GSM509708 1 0.4305 0.726 0.512 0.488 0.000 0.000 0.000
#> GSM509713 2 0.6693 -0.712 0.364 0.396 0.000 0.000 0.240
#> GSM509716 5 0.4201 0.501 0.000 0.008 0.000 0.328 0.664
#> GSM509721 1 0.0162 0.560 0.996 0.000 0.004 0.000 0.000
#> GSM509726 1 0.4305 0.726 0.512 0.488 0.000 0.000 0.000
#> GSM509731 5 0.4201 0.501 0.000 0.008 0.000 0.328 0.664
#> GSM509709 1 0.4305 0.726 0.512 0.488 0.000 0.000 0.000
#> GSM509717 5 0.4201 0.501 0.000 0.008 0.000 0.328 0.664
#> GSM509722 1 0.0162 0.560 0.996 0.000 0.004 0.000 0.000
#> GSM509727 5 0.4294 0.550 0.468 0.000 0.000 0.000 0.532
#> GSM509710 1 0.4305 0.726 0.512 0.488 0.000 0.000 0.000
#> GSM509718 5 0.4201 0.501 0.000 0.008 0.000 0.328 0.664
#> GSM509723 1 0.0162 0.560 0.996 0.000 0.004 0.000 0.000
#> GSM509728 5 0.4294 0.550 0.468 0.000 0.000 0.000 0.532
#> GSM509732 3 0.0000 0.970 0.000 0.000 1.000 0.000 0.000
#> GSM509736 5 0.5083 0.561 0.432 0.000 0.036 0.000 0.532
#> GSM509741 3 0.0579 0.971 0.008 0.000 0.984 0.000 0.008
#> GSM509746 3 0.0162 0.971 0.004 0.000 0.996 0.000 0.000
#> GSM509733 3 0.0000 0.970 0.000 0.000 1.000 0.000 0.000
#> GSM509737 5 0.5256 0.558 0.420 0.000 0.048 0.000 0.532
#> GSM509742 3 0.0579 0.971 0.008 0.000 0.984 0.000 0.008
#> GSM509747 3 0.0162 0.971 0.004 0.000 0.996 0.000 0.000
#> GSM509734 3 0.2957 0.845 0.120 0.012 0.860 0.000 0.008
#> GSM509738 5 0.5083 0.561 0.432 0.000 0.036 0.000 0.532
#> GSM509743 3 0.1251 0.960 0.008 0.000 0.956 0.000 0.036
#> GSM509748 3 0.0000 0.970 0.000 0.000 1.000 0.000 0.000
#> GSM509735 1 0.4305 0.726 0.512 0.488 0.000 0.000 0.000
#> GSM509739 1 0.4305 0.726 0.512 0.488 0.000 0.000 0.000
#> GSM509744 3 0.1251 0.960 0.008 0.000 0.956 0.000 0.036
#> GSM509749 3 0.0290 0.971 0.008 0.000 0.992 0.000 0.000
#> GSM509740 5 0.4437 0.551 0.464 0.000 0.004 0.000 0.532
#> GSM509745 5 0.5019 0.561 0.436 0.000 0.032 0.000 0.532
#> GSM509750 3 0.1251 0.960 0.008 0.000 0.956 0.000 0.036
#> GSM509751 2 0.4307 0.390 0.000 0.504 0.000 0.496 0.000
#> GSM509753 2 0.4307 0.390 0.000 0.504 0.000 0.496 0.000
#> GSM509755 2 0.4307 0.390 0.000 0.504 0.000 0.496 0.000
#> GSM509757 2 0.4307 0.390 0.000 0.504 0.000 0.496 0.000
#> GSM509759 2 0.4307 0.390 0.000 0.504 0.000 0.496 0.000
#> GSM509761 2 0.4307 0.390 0.000 0.504 0.000 0.496 0.000
#> GSM509763 4 0.4307 -0.396 0.000 0.496 0.000 0.504 0.000
#> GSM509765 4 0.4307 -0.396 0.000 0.496 0.000 0.504 0.000
#> GSM509767 2 0.4307 0.390 0.000 0.504 0.000 0.496 0.000
#> GSM509769 4 0.4307 -0.396 0.000 0.496 0.000 0.504 0.000
#> GSM509771 2 0.4307 0.390 0.000 0.504 0.000 0.496 0.000
#> GSM509773 4 0.4307 -0.396 0.000 0.496 0.000 0.504 0.000
#> GSM509775 4 0.4307 -0.396 0.000 0.496 0.000 0.504 0.000
#> GSM509777 4 0.4307 -0.396 0.000 0.496 0.000 0.504 0.000
#> GSM509779 4 0.4300 -0.333 0.000 0.476 0.000 0.524 0.000
#> GSM509781 4 0.1341 0.300 0.000 0.000 0.000 0.944 0.056
#> GSM509783 4 0.1502 0.301 0.000 0.004 0.000 0.940 0.056
#> GSM509785 4 0.1341 0.300 0.000 0.000 0.000 0.944 0.056
#> GSM509752 2 0.4307 0.390 0.000 0.504 0.000 0.496 0.000
#> GSM509754 2 0.4307 0.390 0.000 0.504 0.000 0.496 0.000
#> GSM509756 2 0.4307 0.390 0.000 0.504 0.000 0.496 0.000
#> GSM509758 2 0.4307 0.390 0.000 0.504 0.000 0.496 0.000
#> GSM509760 2 0.4307 0.390 0.000 0.504 0.000 0.496 0.000
#> GSM509762 2 0.4307 0.390 0.000 0.504 0.000 0.496 0.000
#> GSM509764 2 0.4307 0.390 0.000 0.504 0.000 0.496 0.000
#> GSM509766 4 0.4307 -0.396 0.000 0.496 0.000 0.504 0.000
#> GSM509768 4 0.4307 -0.396 0.000 0.496 0.000 0.504 0.000
#> GSM509770 2 0.4307 0.390 0.000 0.504 0.000 0.496 0.000
#> GSM509772 2 0.4307 0.390 0.000 0.504 0.000 0.496 0.000
#> GSM509774 4 0.4307 -0.396 0.000 0.496 0.000 0.504 0.000
#> GSM509776 2 0.4307 0.390 0.000 0.504 0.000 0.496 0.000
#> GSM509778 4 0.1502 0.301 0.000 0.004 0.000 0.940 0.056
#> GSM509780 4 0.4307 -0.396 0.000 0.496 0.000 0.504 0.000
#> GSM509782 4 0.3929 0.219 0.000 0.208 0.000 0.764 0.028
#> GSM509784 4 0.4297 -0.319 0.000 0.472 0.000 0.528 0.000
#> GSM509786 4 0.1341 0.300 0.000 0.000 0.000 0.944 0.056
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM509706 1 0.0000 0.824 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509711 1 0.3883 0.414 0.656 0.000 0.000 0.012 0.000 0.332
#> GSM509714 6 0.5300 0.332 0.400 0.000 0.000 0.104 0.000 0.496
#> GSM509719 6 0.5265 0.338 0.400 0.000 0.000 0.100 0.000 0.500
#> GSM509724 1 0.0000 0.824 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509729 1 0.5462 -0.206 0.476 0.000 0.000 0.124 0.000 0.400
#> GSM509707 1 0.0000 0.824 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509712 6 0.5081 0.335 0.308 0.000 0.000 0.104 0.000 0.588
#> GSM509715 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM509720 6 0.5265 0.338 0.400 0.000 0.000 0.100 0.000 0.500
#> GSM509725 1 0.0000 0.824 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509730 1 0.5492 -0.214 0.472 0.000 0.000 0.128 0.000 0.400
#> GSM509708 1 0.0000 0.824 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509713 1 0.3789 0.417 0.660 0.000 0.000 0.008 0.000 0.332
#> GSM509716 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM509721 6 0.5265 0.338 0.400 0.000 0.000 0.100 0.000 0.500
#> GSM509726 1 0.0000 0.824 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509731 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM509709 1 0.0000 0.824 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509717 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM509722 6 0.5265 0.338 0.400 0.000 0.000 0.100 0.000 0.500
#> GSM509727 6 0.2006 0.570 0.000 0.000 0.000 0.004 0.104 0.892
#> GSM509710 1 0.0000 0.824 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509718 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM509723 6 0.5265 0.338 0.400 0.000 0.000 0.100 0.000 0.500
#> GSM509728 6 0.2118 0.570 0.000 0.000 0.000 0.008 0.104 0.888
#> GSM509732 3 0.0790 0.951 0.000 0.000 0.968 0.032 0.000 0.000
#> GSM509736 6 0.2776 0.560 0.000 0.000 0.032 0.004 0.104 0.860
#> GSM509741 3 0.0603 0.964 0.000 0.000 0.980 0.004 0.000 0.016
#> GSM509746 3 0.0260 0.963 0.000 0.000 0.992 0.008 0.000 0.000
#> GSM509733 3 0.0790 0.951 0.000 0.000 0.968 0.032 0.000 0.000
#> GSM509737 6 0.2984 0.549 0.000 0.000 0.044 0.004 0.104 0.848
#> GSM509742 3 0.0603 0.964 0.000 0.000 0.980 0.004 0.000 0.016
#> GSM509747 3 0.0260 0.963 0.000 0.000 0.992 0.008 0.000 0.000
#> GSM509734 3 0.2998 0.850 0.008 0.000 0.856 0.064 0.000 0.072
#> GSM509738 6 0.2776 0.560 0.000 0.000 0.032 0.004 0.104 0.860
#> GSM509743 3 0.1152 0.954 0.000 0.000 0.952 0.004 0.000 0.044
#> GSM509748 3 0.0146 0.962 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM509735 1 0.0000 0.824 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509739 1 0.0000 0.824 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509744 3 0.1152 0.954 0.000 0.000 0.952 0.004 0.000 0.044
#> GSM509749 3 0.0260 0.964 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM509740 6 0.1863 0.571 0.000 0.000 0.000 0.000 0.104 0.896
#> GSM509745 6 0.2633 0.560 0.000 0.000 0.032 0.000 0.104 0.864
#> GSM509750 3 0.1152 0.954 0.000 0.000 0.952 0.004 0.000 0.044
#> GSM509751 2 0.0000 0.902 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509753 2 0.0000 0.902 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509755 2 0.0000 0.902 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509757 2 0.0000 0.902 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509759 2 0.0000 0.902 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509761 2 0.0000 0.902 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509763 2 0.2597 0.815 0.000 0.824 0.000 0.176 0.000 0.000
#> GSM509765 2 0.2491 0.825 0.000 0.836 0.000 0.164 0.000 0.000
#> GSM509767 2 0.0000 0.902 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509769 2 0.0547 0.898 0.000 0.980 0.000 0.020 0.000 0.000
#> GSM509771 2 0.0000 0.902 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509773 2 0.2597 0.815 0.000 0.824 0.000 0.176 0.000 0.000
#> GSM509775 2 0.1910 0.860 0.000 0.892 0.000 0.108 0.000 0.000
#> GSM509777 2 0.2631 0.811 0.000 0.820 0.000 0.180 0.000 0.000
#> GSM509779 2 0.2793 0.785 0.000 0.800 0.000 0.200 0.000 0.000
#> GSM509781 4 0.2668 0.908 0.000 0.168 0.000 0.828 0.004 0.000
#> GSM509783 4 0.2562 0.906 0.000 0.172 0.000 0.828 0.000 0.000
#> GSM509785 4 0.2668 0.908 0.000 0.168 0.000 0.828 0.004 0.000
#> GSM509752 2 0.0000 0.902 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509754 2 0.0000 0.902 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509756 2 0.0000 0.902 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509758 2 0.0000 0.902 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509760 2 0.0260 0.901 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM509762 2 0.0000 0.902 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509764 2 0.0000 0.902 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509766 2 0.2491 0.825 0.000 0.836 0.000 0.164 0.000 0.000
#> GSM509768 2 0.2597 0.815 0.000 0.824 0.000 0.176 0.000 0.000
#> GSM509770 2 0.0260 0.901 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM509772 2 0.0000 0.902 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509774 2 0.2631 0.811 0.000 0.820 0.000 0.180 0.000 0.000
#> GSM509776 2 0.1814 0.864 0.000 0.900 0.000 0.100 0.000 0.000
#> GSM509778 4 0.2562 0.906 0.000 0.172 0.000 0.828 0.000 0.000
#> GSM509780 2 0.2631 0.811 0.000 0.820 0.000 0.180 0.000 0.000
#> GSM509782 4 0.3810 0.420 0.000 0.428 0.000 0.572 0.000 0.000
#> GSM509784 2 0.2912 0.760 0.000 0.784 0.000 0.216 0.000 0.000
#> GSM509786 4 0.2668 0.908 0.000 0.168 0.000 0.828 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 disease.state(p) time(p) k
#> ATC:hclust 81 8.31e-15 6.68e-12 2
#> ATC:hclust 81 1.14e-20 2.30e-09 3
#> ATC:hclust 76 1.33e-22 6.02e-10 4
#> ATC:hclust 42 9.88e-06 7.67e-01 5
#> ATC:hclust 69 1.28e-19 8.02e-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 19175 rows and 81 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 1.000 1.000 0.5067 0.494 0.494
#> 3 3 0.695 0.792 0.828 0.2336 0.880 0.756
#> 4 4 0.808 0.681 0.839 0.1397 0.819 0.558
#> 5 5 0.725 0.668 0.751 0.0779 0.885 0.625
#> 6 6 0.701 0.652 0.778 0.0458 0.940 0.751
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
#> GSM509706 1 0 1 1 0
#> GSM509711 1 0 1 1 0
#> GSM509714 1 0 1 1 0
#> GSM509719 1 0 1 1 0
#> GSM509724 1 0 1 1 0
#> GSM509729 1 0 1 1 0
#> GSM509707 1 0 1 1 0
#> GSM509712 1 0 1 1 0
#> GSM509715 2 0 1 0 1
#> GSM509720 1 0 1 1 0
#> GSM509725 1 0 1 1 0
#> GSM509730 1 0 1 1 0
#> GSM509708 1 0 1 1 0
#> GSM509713 1 0 1 1 0
#> GSM509716 2 0 1 0 1
#> GSM509721 1 0 1 1 0
#> GSM509726 1 0 1 1 0
#> GSM509731 1 0 1 1 0
#> GSM509709 1 0 1 1 0
#> GSM509717 2 0 1 0 1
#> GSM509722 1 0 1 1 0
#> GSM509727 1 0 1 1 0
#> GSM509710 1 0 1 1 0
#> GSM509718 2 0 1 0 1
#> GSM509723 1 0 1 1 0
#> GSM509728 1 0 1 1 0
#> GSM509732 1 0 1 1 0
#> GSM509736 1 0 1 1 0
#> GSM509741 1 0 1 1 0
#> GSM509746 1 0 1 1 0
#> GSM509733 1 0 1 1 0
#> GSM509737 1 0 1 1 0
#> GSM509742 1 0 1 1 0
#> GSM509747 1 0 1 1 0
#> GSM509734 1 0 1 1 0
#> GSM509738 1 0 1 1 0
#> GSM509743 1 0 1 1 0
#> GSM509748 1 0 1 1 0
#> GSM509735 1 0 1 1 0
#> GSM509739 1 0 1 1 0
#> GSM509744 1 0 1 1 0
#> GSM509749 1 0 1 1 0
#> GSM509740 1 0 1 1 0
#> GSM509745 1 0 1 1 0
#> GSM509750 1 0 1 1 0
#> GSM509751 2 0 1 0 1
#> GSM509753 2 0 1 0 1
#> GSM509755 2 0 1 0 1
#> GSM509757 2 0 1 0 1
#> GSM509759 2 0 1 0 1
#> GSM509761 2 0 1 0 1
#> GSM509763 2 0 1 0 1
#> GSM509765 2 0 1 0 1
#> GSM509767 2 0 1 0 1
#> GSM509769 2 0 1 0 1
#> GSM509771 2 0 1 0 1
#> GSM509773 2 0 1 0 1
#> GSM509775 2 0 1 0 1
#> GSM509777 2 0 1 0 1
#> GSM509779 2 0 1 0 1
#> GSM509781 2 0 1 0 1
#> GSM509783 2 0 1 0 1
#> GSM509785 2 0 1 0 1
#> GSM509752 2 0 1 0 1
#> GSM509754 2 0 1 0 1
#> GSM509756 2 0 1 0 1
#> GSM509758 2 0 1 0 1
#> GSM509760 2 0 1 0 1
#> GSM509762 2 0 1 0 1
#> GSM509764 2 0 1 0 1
#> GSM509766 2 0 1 0 1
#> GSM509768 2 0 1 0 1
#> GSM509770 2 0 1 0 1
#> GSM509772 2 0 1 0 1
#> GSM509774 2 0 1 0 1
#> GSM509776 2 0 1 0 1
#> GSM509778 2 0 1 0 1
#> GSM509780 2 0 1 0 1
#> GSM509782 2 0 1 0 1
#> GSM509784 2 0 1 0 1
#> GSM509786 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM509706 1 0.4504 0.920 0.804 0.000 0.196
#> GSM509711 1 0.4504 0.920 0.804 0.000 0.196
#> GSM509714 3 0.6260 0.150 0.448 0.000 0.552
#> GSM509719 3 0.5968 0.441 0.364 0.000 0.636
#> GSM509724 1 0.4504 0.920 0.804 0.000 0.196
#> GSM509729 1 0.4504 0.920 0.804 0.000 0.196
#> GSM509707 1 0.4504 0.920 0.804 0.000 0.196
#> GSM509712 1 0.6215 0.353 0.572 0.000 0.428
#> GSM509715 2 0.8758 0.575 0.192 0.588 0.220
#> GSM509720 3 0.5968 0.441 0.364 0.000 0.636
#> GSM509725 1 0.4504 0.920 0.804 0.000 0.196
#> GSM509730 3 0.6026 0.411 0.376 0.000 0.624
#> GSM509708 1 0.4504 0.920 0.804 0.000 0.196
#> GSM509713 1 0.4504 0.920 0.804 0.000 0.196
#> GSM509716 2 0.8758 0.575 0.192 0.588 0.220
#> GSM509721 3 0.5968 0.441 0.364 0.000 0.636
#> GSM509726 1 0.4504 0.920 0.804 0.000 0.196
#> GSM509731 1 0.6896 -0.103 0.588 0.020 0.392
#> GSM509709 1 0.4504 0.920 0.804 0.000 0.196
#> GSM509717 2 0.8758 0.575 0.192 0.588 0.220
#> GSM509722 3 0.5968 0.441 0.364 0.000 0.636
#> GSM509727 3 0.6154 0.275 0.408 0.000 0.592
#> GSM509710 1 0.4504 0.920 0.804 0.000 0.196
#> GSM509718 2 0.8758 0.575 0.192 0.588 0.220
#> GSM509723 3 0.5968 0.441 0.364 0.000 0.636
#> GSM509728 3 0.5678 0.523 0.316 0.000 0.684
#> GSM509732 3 0.0237 0.775 0.000 0.004 0.996
#> GSM509736 3 0.3116 0.741 0.108 0.000 0.892
#> GSM509741 3 0.0237 0.775 0.000 0.004 0.996
#> GSM509746 3 0.0237 0.775 0.000 0.004 0.996
#> GSM509733 3 0.0237 0.775 0.000 0.004 0.996
#> GSM509737 3 0.3619 0.724 0.136 0.000 0.864
#> GSM509742 3 0.0237 0.775 0.000 0.004 0.996
#> GSM509747 3 0.0237 0.775 0.004 0.000 0.996
#> GSM509734 3 0.2165 0.754 0.064 0.000 0.936
#> GSM509738 3 0.2066 0.763 0.060 0.000 0.940
#> GSM509743 3 0.0237 0.775 0.000 0.004 0.996
#> GSM509748 3 0.0237 0.775 0.004 0.000 0.996
#> GSM509735 1 0.4504 0.920 0.804 0.000 0.196
#> GSM509739 1 0.4504 0.920 0.804 0.000 0.196
#> GSM509744 3 0.0000 0.774 0.000 0.000 1.000
#> GSM509749 3 0.0237 0.775 0.000 0.004 0.996
#> GSM509740 3 0.3116 0.741 0.108 0.000 0.892
#> GSM509745 3 0.0424 0.775 0.008 0.000 0.992
#> GSM509750 3 0.0475 0.771 0.004 0.004 0.992
#> GSM509751 2 0.0237 0.934 0.004 0.996 0.000
#> GSM509753 2 0.0237 0.934 0.004 0.996 0.000
#> GSM509755 2 0.0237 0.934 0.004 0.996 0.000
#> GSM509757 2 0.0237 0.934 0.004 0.996 0.000
#> GSM509759 2 0.0237 0.934 0.004 0.996 0.000
#> GSM509761 2 0.0237 0.934 0.004 0.996 0.000
#> GSM509763 2 0.0237 0.934 0.004 0.996 0.000
#> GSM509765 2 0.0237 0.934 0.004 0.996 0.000
#> GSM509767 2 0.0000 0.934 0.000 1.000 0.000
#> GSM509769 2 0.0237 0.934 0.004 0.996 0.000
#> GSM509771 2 0.0000 0.934 0.000 1.000 0.000
#> GSM509773 2 0.0237 0.934 0.004 0.996 0.000
#> GSM509775 2 0.0237 0.934 0.004 0.996 0.000
#> GSM509777 2 0.0237 0.934 0.004 0.996 0.000
#> GSM509779 2 0.0237 0.934 0.004 0.996 0.000
#> GSM509781 2 0.4682 0.831 0.192 0.804 0.004
#> GSM509783 2 0.4682 0.831 0.192 0.804 0.004
#> GSM509785 2 0.4682 0.831 0.192 0.804 0.004
#> GSM509752 2 0.0237 0.934 0.004 0.996 0.000
#> GSM509754 2 0.0237 0.934 0.004 0.996 0.000
#> GSM509756 2 0.0237 0.934 0.004 0.996 0.000
#> GSM509758 2 0.0237 0.934 0.004 0.996 0.000
#> GSM509760 2 0.0237 0.934 0.004 0.996 0.000
#> GSM509762 2 0.0237 0.934 0.004 0.996 0.000
#> GSM509764 2 0.0237 0.934 0.004 0.996 0.000
#> GSM509766 2 0.0237 0.934 0.004 0.996 0.000
#> GSM509768 2 0.0237 0.934 0.004 0.996 0.000
#> GSM509770 2 0.0237 0.934 0.004 0.996 0.000
#> GSM509772 2 0.0237 0.934 0.004 0.996 0.000
#> GSM509774 2 0.0237 0.934 0.004 0.996 0.000
#> GSM509776 2 0.0237 0.934 0.004 0.996 0.000
#> GSM509778 2 0.4629 0.833 0.188 0.808 0.004
#> GSM509780 2 0.0237 0.934 0.004 0.996 0.000
#> GSM509782 2 0.4521 0.838 0.180 0.816 0.004
#> GSM509784 2 0.0237 0.934 0.004 0.996 0.000
#> GSM509786 2 0.4682 0.831 0.192 0.804 0.004
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM509706 1 0.0336 0.78092 0.992 0.000 0.008 0.000
#> GSM509711 1 0.0469 0.77746 0.988 0.000 0.012 0.000
#> GSM509714 4 0.7661 -0.34909 0.376 0.000 0.212 0.412
#> GSM509719 1 0.7693 0.19845 0.432 0.000 0.340 0.228
#> GSM509724 1 0.0336 0.78092 0.992 0.000 0.008 0.000
#> GSM509729 1 0.0336 0.78092 0.992 0.000 0.008 0.000
#> GSM509707 1 0.0336 0.78092 0.992 0.000 0.008 0.000
#> GSM509712 1 0.6617 0.48551 0.608 0.000 0.128 0.264
#> GSM509715 4 0.2861 0.35150 0.000 0.016 0.096 0.888
#> GSM509720 1 0.7693 0.19845 0.432 0.000 0.340 0.228
#> GSM509725 1 0.0336 0.78092 0.992 0.000 0.008 0.000
#> GSM509730 1 0.6140 0.38480 0.596 0.000 0.340 0.064
#> GSM509708 1 0.0336 0.78092 0.992 0.000 0.008 0.000
#> GSM509713 1 0.0336 0.78092 0.992 0.000 0.008 0.000
#> GSM509716 4 0.2861 0.35150 0.000 0.016 0.096 0.888
#> GSM509721 1 0.7693 0.19845 0.432 0.000 0.340 0.228
#> GSM509726 1 0.0336 0.78092 0.992 0.000 0.008 0.000
#> GSM509731 4 0.2480 0.31711 0.008 0.000 0.088 0.904
#> GSM509709 1 0.0336 0.78092 0.992 0.000 0.008 0.000
#> GSM509717 4 0.2861 0.35150 0.000 0.016 0.096 0.888
#> GSM509722 1 0.7693 0.19845 0.432 0.000 0.340 0.228
#> GSM509727 4 0.7679 -0.30976 0.356 0.000 0.220 0.424
#> GSM509710 1 0.0336 0.78092 0.992 0.000 0.008 0.000
#> GSM509718 4 0.2861 0.35150 0.000 0.016 0.096 0.888
#> GSM509723 1 0.7693 0.19845 0.432 0.000 0.340 0.228
#> GSM509728 3 0.7816 0.00825 0.340 0.000 0.400 0.260
#> GSM509732 3 0.0376 0.81203 0.004 0.000 0.992 0.004
#> GSM509736 3 0.6314 0.57560 0.068 0.000 0.560 0.372
#> GSM509741 3 0.0188 0.81339 0.004 0.000 0.996 0.000
#> GSM509746 3 0.0376 0.81203 0.004 0.000 0.992 0.004
#> GSM509733 3 0.0376 0.81203 0.004 0.000 0.992 0.004
#> GSM509737 3 0.6868 0.52846 0.152 0.000 0.584 0.264
#> GSM509742 3 0.0188 0.81339 0.004 0.000 0.996 0.000
#> GSM509747 3 0.0376 0.81293 0.004 0.000 0.992 0.004
#> GSM509734 3 0.3156 0.75935 0.068 0.000 0.884 0.048
#> GSM509738 3 0.5138 0.59939 0.008 0.000 0.600 0.392
#> GSM509743 3 0.0000 0.81229 0.000 0.000 1.000 0.000
#> GSM509748 3 0.0376 0.81293 0.004 0.000 0.992 0.004
#> GSM509735 1 0.0336 0.78092 0.992 0.000 0.008 0.000
#> GSM509739 1 0.0336 0.78092 0.992 0.000 0.008 0.000
#> GSM509744 3 0.3024 0.76360 0.000 0.000 0.852 0.148
#> GSM509749 3 0.0188 0.81339 0.004 0.000 0.996 0.000
#> GSM509740 3 0.6392 0.54220 0.068 0.000 0.528 0.404
#> GSM509745 3 0.4564 0.65824 0.000 0.000 0.672 0.328
#> GSM509750 3 0.1302 0.80348 0.000 0.000 0.956 0.044
#> GSM509751 2 0.0188 0.95503 0.000 0.996 0.000 0.004
#> GSM509753 2 0.0188 0.95503 0.000 0.996 0.000 0.004
#> GSM509755 2 0.0188 0.95503 0.000 0.996 0.000 0.004
#> GSM509757 2 0.0188 0.95503 0.000 0.996 0.000 0.004
#> GSM509759 2 0.0188 0.95503 0.000 0.996 0.000 0.004
#> GSM509761 2 0.0000 0.95610 0.000 1.000 0.000 0.000
#> GSM509763 2 0.2271 0.92732 0.008 0.916 0.000 0.076
#> GSM509765 2 0.2342 0.92473 0.008 0.912 0.000 0.080
#> GSM509767 2 0.0188 0.95503 0.000 0.996 0.000 0.004
#> GSM509769 2 0.0000 0.95610 0.000 1.000 0.000 0.000
#> GSM509771 2 0.0188 0.95503 0.000 0.996 0.000 0.004
#> GSM509773 2 0.1389 0.94245 0.000 0.952 0.000 0.048
#> GSM509775 2 0.2198 0.92968 0.008 0.920 0.000 0.072
#> GSM509777 2 0.2342 0.92473 0.008 0.912 0.000 0.080
#> GSM509779 2 0.2342 0.92473 0.008 0.912 0.000 0.080
#> GSM509781 4 0.5292 0.19863 0.008 0.480 0.000 0.512
#> GSM509783 4 0.5292 0.19863 0.008 0.480 0.000 0.512
#> GSM509785 4 0.5292 0.19863 0.008 0.480 0.000 0.512
#> GSM509752 2 0.0000 0.95610 0.000 1.000 0.000 0.000
#> GSM509754 2 0.0000 0.95610 0.000 1.000 0.000 0.000
#> GSM509756 2 0.0000 0.95610 0.000 1.000 0.000 0.000
#> GSM509758 2 0.0000 0.95610 0.000 1.000 0.000 0.000
#> GSM509760 2 0.0000 0.95610 0.000 1.000 0.000 0.000
#> GSM509762 2 0.0000 0.95610 0.000 1.000 0.000 0.000
#> GSM509764 2 0.0188 0.95503 0.000 0.996 0.000 0.004
#> GSM509766 2 0.1792 0.93505 0.000 0.932 0.000 0.068
#> GSM509768 2 0.2198 0.92968 0.008 0.920 0.000 0.072
#> GSM509770 2 0.0000 0.95610 0.000 1.000 0.000 0.000
#> GSM509772 2 0.0188 0.95503 0.000 0.996 0.000 0.004
#> GSM509774 2 0.2342 0.92473 0.008 0.912 0.000 0.080
#> GSM509776 2 0.2198 0.92968 0.008 0.920 0.000 0.072
#> GSM509778 4 0.5292 0.19863 0.008 0.480 0.000 0.512
#> GSM509780 2 0.2342 0.92473 0.008 0.912 0.000 0.080
#> GSM509782 4 0.5295 0.17299 0.008 0.488 0.000 0.504
#> GSM509784 2 0.2342 0.92473 0.008 0.912 0.000 0.080
#> GSM509786 4 0.5292 0.19863 0.008 0.480 0.000 0.512
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM509706 1 0.0794 0.978 0.972 0.000 0.000 0.028 0.000
#> GSM509711 1 0.0693 0.977 0.980 0.000 0.000 0.012 0.008
#> GSM509714 5 0.3800 0.561 0.052 0.000 0.084 0.028 0.836
#> GSM509719 5 0.6891 0.533 0.284 0.000 0.204 0.020 0.492
#> GSM509724 1 0.0671 0.982 0.980 0.000 0.000 0.016 0.004
#> GSM509729 1 0.1117 0.953 0.964 0.000 0.000 0.016 0.020
#> GSM509707 1 0.0794 0.978 0.972 0.000 0.000 0.028 0.000
#> GSM509712 5 0.6347 0.418 0.372 0.000 0.080 0.032 0.516
#> GSM509715 5 0.4551 0.348 0.000 0.004 0.004 0.436 0.556
#> GSM509720 5 0.6891 0.533 0.284 0.000 0.204 0.020 0.492
#> GSM509725 1 0.0324 0.981 0.992 0.000 0.000 0.004 0.004
#> GSM509730 5 0.6975 0.446 0.360 0.000 0.204 0.016 0.420
#> GSM509708 1 0.0404 0.982 0.988 0.000 0.000 0.012 0.000
#> GSM509713 1 0.0566 0.979 0.984 0.000 0.000 0.012 0.004
#> GSM509716 5 0.4551 0.348 0.000 0.004 0.004 0.436 0.556
#> GSM509721 5 0.6891 0.533 0.284 0.000 0.204 0.020 0.492
#> GSM509726 1 0.0579 0.979 0.984 0.000 0.000 0.008 0.008
#> GSM509731 5 0.4060 0.408 0.000 0.000 0.000 0.360 0.640
#> GSM509709 1 0.0794 0.978 0.972 0.000 0.000 0.028 0.000
#> GSM509717 5 0.4551 0.348 0.000 0.004 0.004 0.436 0.556
#> GSM509722 5 0.6891 0.533 0.284 0.000 0.204 0.020 0.492
#> GSM509727 5 0.3970 0.537 0.016 0.000 0.084 0.080 0.820
#> GSM509710 1 0.0794 0.978 0.972 0.000 0.000 0.028 0.000
#> GSM509718 5 0.4551 0.348 0.000 0.004 0.004 0.436 0.556
#> GSM509723 5 0.6891 0.533 0.284 0.000 0.204 0.020 0.492
#> GSM509728 5 0.6367 0.520 0.228 0.000 0.204 0.008 0.560
#> GSM509732 3 0.0404 0.897 0.000 0.000 0.988 0.012 0.000
#> GSM509736 5 0.4031 0.515 0.004 0.000 0.160 0.048 0.788
#> GSM509741 3 0.0609 0.896 0.000 0.000 0.980 0.000 0.020
#> GSM509746 3 0.0404 0.897 0.000 0.000 0.988 0.012 0.000
#> GSM509733 3 0.0404 0.897 0.000 0.000 0.988 0.012 0.000
#> GSM509737 5 0.6592 0.489 0.196 0.000 0.244 0.016 0.544
#> GSM509742 3 0.0609 0.896 0.000 0.000 0.980 0.000 0.020
#> GSM509747 3 0.0404 0.897 0.000 0.000 0.988 0.012 0.000
#> GSM509734 3 0.5275 0.329 0.084 0.000 0.640 0.000 0.276
#> GSM509738 5 0.3622 0.520 0.000 0.000 0.136 0.048 0.816
#> GSM509743 3 0.1197 0.883 0.000 0.000 0.952 0.000 0.048
#> GSM509748 3 0.0404 0.897 0.000 0.000 0.988 0.012 0.000
#> GSM509735 1 0.0000 0.982 1.000 0.000 0.000 0.000 0.000
#> GSM509739 1 0.0000 0.982 1.000 0.000 0.000 0.000 0.000
#> GSM509744 3 0.4197 0.625 0.000 0.000 0.728 0.028 0.244
#> GSM509749 3 0.0609 0.896 0.000 0.000 0.980 0.000 0.020
#> GSM509740 5 0.3497 0.530 0.004 0.000 0.112 0.048 0.836
#> GSM509745 5 0.4223 0.448 0.000 0.000 0.248 0.028 0.724
#> GSM509750 3 0.3152 0.787 0.000 0.000 0.840 0.024 0.136
#> GSM509751 2 0.0000 0.779 0.000 1.000 0.000 0.000 0.000
#> GSM509753 2 0.0000 0.779 0.000 1.000 0.000 0.000 0.000
#> GSM509755 2 0.0000 0.779 0.000 1.000 0.000 0.000 0.000
#> GSM509757 2 0.0000 0.779 0.000 1.000 0.000 0.000 0.000
#> GSM509759 2 0.0000 0.779 0.000 1.000 0.000 0.000 0.000
#> GSM509761 2 0.0000 0.779 0.000 1.000 0.000 0.000 0.000
#> GSM509763 2 0.4030 0.337 0.000 0.648 0.000 0.352 0.000
#> GSM509765 2 0.4045 0.327 0.000 0.644 0.000 0.356 0.000
#> GSM509767 2 0.0290 0.777 0.000 0.992 0.000 0.008 0.000
#> GSM509769 2 0.0510 0.773 0.000 0.984 0.000 0.016 0.000
#> GSM509771 2 0.0290 0.777 0.000 0.992 0.000 0.008 0.000
#> GSM509773 2 0.2377 0.680 0.000 0.872 0.000 0.128 0.000
#> GSM509775 2 0.4030 0.337 0.000 0.648 0.000 0.352 0.000
#> GSM509777 2 0.4302 -0.189 0.000 0.520 0.000 0.480 0.000
#> GSM509779 2 0.4307 -0.256 0.000 0.504 0.000 0.496 0.000
#> GSM509781 4 0.3779 0.910 0.000 0.236 0.000 0.752 0.012
#> GSM509783 4 0.3671 0.910 0.000 0.236 0.000 0.756 0.008
#> GSM509785 4 0.3779 0.910 0.000 0.236 0.000 0.752 0.012
#> GSM509752 2 0.0162 0.778 0.000 0.996 0.000 0.004 0.000
#> GSM509754 2 0.0000 0.779 0.000 1.000 0.000 0.000 0.000
#> GSM509756 2 0.0000 0.779 0.000 1.000 0.000 0.000 0.000
#> GSM509758 2 0.0000 0.779 0.000 1.000 0.000 0.000 0.000
#> GSM509760 2 0.0000 0.779 0.000 1.000 0.000 0.000 0.000
#> GSM509762 2 0.0000 0.779 0.000 1.000 0.000 0.000 0.000
#> GSM509764 2 0.0000 0.779 0.000 1.000 0.000 0.000 0.000
#> GSM509766 2 0.3561 0.510 0.000 0.740 0.000 0.260 0.000
#> GSM509768 2 0.4030 0.337 0.000 0.648 0.000 0.352 0.000
#> GSM509770 2 0.0404 0.775 0.000 0.988 0.000 0.012 0.000
#> GSM509772 2 0.0000 0.779 0.000 1.000 0.000 0.000 0.000
#> GSM509774 2 0.4307 -0.256 0.000 0.504 0.000 0.496 0.000
#> GSM509776 2 0.4045 0.327 0.000 0.644 0.000 0.356 0.000
#> GSM509778 4 0.3424 0.905 0.000 0.240 0.000 0.760 0.000
#> GSM509780 2 0.4088 0.290 0.000 0.632 0.000 0.368 0.000
#> GSM509782 4 0.3452 0.901 0.000 0.244 0.000 0.756 0.000
#> GSM509784 4 0.4300 0.250 0.000 0.476 0.000 0.524 0.000
#> GSM509786 4 0.3779 0.910 0.000 0.236 0.000 0.752 0.012
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM509706 1 0.1245 0.9409 0.952 0.000 0.000 0.016 0.032 0.000
#> GSM509711 1 0.2007 0.9288 0.920 0.000 0.000 0.036 0.012 0.032
#> GSM509714 6 0.4551 0.4540 0.012 0.000 0.028 0.008 0.280 0.672
#> GSM509719 6 0.5037 0.7779 0.160 0.000 0.120 0.000 0.028 0.692
#> GSM509724 1 0.0806 0.9454 0.972 0.000 0.000 0.008 0.020 0.000
#> GSM509729 1 0.3245 0.7757 0.796 0.000 0.000 0.016 0.004 0.184
#> GSM509707 1 0.1245 0.9409 0.952 0.000 0.000 0.016 0.032 0.000
#> GSM509712 6 0.5700 0.6360 0.216 0.000 0.028 0.036 0.072 0.648
#> GSM509715 5 0.3134 0.6785 0.000 0.000 0.004 0.208 0.784 0.004
#> GSM509720 6 0.5037 0.7779 0.160 0.000 0.120 0.000 0.028 0.692
#> GSM509725 1 0.0777 0.9445 0.972 0.000 0.000 0.004 0.000 0.024
#> GSM509730 6 0.4741 0.7586 0.180 0.000 0.116 0.000 0.008 0.696
#> GSM509708 1 0.0692 0.9451 0.976 0.000 0.000 0.004 0.020 0.000
#> GSM509713 1 0.1755 0.9341 0.932 0.000 0.000 0.028 0.008 0.032
#> GSM509716 5 0.3134 0.6785 0.000 0.000 0.004 0.208 0.784 0.004
#> GSM509721 6 0.5037 0.7779 0.160 0.000 0.120 0.000 0.028 0.692
#> GSM509726 1 0.1592 0.9372 0.940 0.000 0.000 0.020 0.008 0.032
#> GSM509731 5 0.3578 0.6527 0.000 0.000 0.000 0.164 0.784 0.052
#> GSM509709 1 0.1245 0.9409 0.952 0.000 0.000 0.016 0.032 0.000
#> GSM509717 5 0.3134 0.6785 0.000 0.000 0.004 0.208 0.784 0.004
#> GSM509722 6 0.5037 0.7779 0.160 0.000 0.120 0.000 0.028 0.692
#> GSM509727 5 0.5000 0.0290 0.000 0.000 0.028 0.032 0.576 0.364
#> GSM509710 1 0.1245 0.9409 0.952 0.000 0.000 0.016 0.032 0.000
#> GSM509718 5 0.3134 0.6785 0.000 0.000 0.004 0.208 0.784 0.004
#> GSM509723 6 0.5037 0.7779 0.160 0.000 0.120 0.000 0.028 0.692
#> GSM509728 6 0.7066 0.6535 0.128 0.000 0.132 0.028 0.172 0.540
#> GSM509732 3 0.1268 0.8408 0.000 0.000 0.952 0.036 0.004 0.008
#> GSM509736 6 0.5634 0.1444 0.000 0.000 0.104 0.012 0.424 0.460
#> GSM509741 3 0.1296 0.8409 0.000 0.000 0.952 0.004 0.032 0.012
#> GSM509746 3 0.1268 0.8408 0.000 0.000 0.952 0.036 0.004 0.008
#> GSM509733 3 0.1268 0.8408 0.000 0.000 0.952 0.036 0.004 0.008
#> GSM509737 6 0.6524 0.6707 0.112 0.000 0.152 0.008 0.148 0.580
#> GSM509742 3 0.1296 0.8409 0.000 0.000 0.952 0.004 0.032 0.012
#> GSM509747 3 0.1268 0.8408 0.000 0.000 0.952 0.036 0.004 0.008
#> GSM509734 3 0.5484 -0.0669 0.048 0.000 0.524 0.020 0.012 0.396
#> GSM509738 5 0.5378 -0.2235 0.000 0.000 0.084 0.008 0.460 0.448
#> GSM509743 3 0.3240 0.7693 0.000 0.000 0.820 0.008 0.144 0.028
#> GSM509748 3 0.0909 0.8431 0.000 0.000 0.968 0.020 0.000 0.012
#> GSM509735 1 0.0777 0.9444 0.972 0.000 0.000 0.000 0.004 0.024
#> GSM509739 1 0.1313 0.9398 0.952 0.000 0.000 0.016 0.004 0.028
#> GSM509744 3 0.4499 0.5604 0.000 0.000 0.636 0.012 0.324 0.028
#> GSM509749 3 0.1503 0.8392 0.000 0.000 0.944 0.008 0.032 0.016
#> GSM509740 5 0.4932 -0.2289 0.000 0.000 0.044 0.008 0.480 0.468
#> GSM509745 6 0.5929 0.2882 0.000 0.000 0.168 0.008 0.360 0.464
#> GSM509750 3 0.4039 0.6781 0.000 0.000 0.716 0.008 0.248 0.028
#> GSM509751 2 0.0260 0.7637 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM509753 2 0.0000 0.7660 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509755 2 0.0146 0.7648 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM509757 2 0.1398 0.7423 0.000 0.940 0.000 0.000 0.008 0.052
#> GSM509759 2 0.1398 0.7423 0.000 0.940 0.000 0.000 0.008 0.052
#> GSM509761 2 0.0000 0.7660 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509763 2 0.5624 0.1863 0.000 0.524 0.000 0.296 0.000 0.180
#> GSM509765 2 0.5660 0.1444 0.000 0.512 0.000 0.308 0.000 0.180
#> GSM509767 2 0.2431 0.7262 0.000 0.860 0.000 0.000 0.008 0.132
#> GSM509769 2 0.2932 0.6779 0.000 0.820 0.000 0.016 0.000 0.164
#> GSM509771 2 0.2431 0.7262 0.000 0.860 0.000 0.000 0.008 0.132
#> GSM509773 2 0.4283 0.5780 0.000 0.724 0.000 0.096 0.000 0.180
#> GSM509775 2 0.5624 0.1863 0.000 0.524 0.000 0.296 0.000 0.180
#> GSM509777 4 0.5757 0.3962 0.000 0.352 0.000 0.468 0.000 0.180
#> GSM509779 4 0.5580 0.4942 0.000 0.324 0.000 0.516 0.000 0.160
#> GSM509781 4 0.2581 0.7341 0.000 0.120 0.000 0.860 0.020 0.000
#> GSM509783 4 0.2302 0.7436 0.000 0.120 0.000 0.872 0.000 0.008
#> GSM509785 4 0.2581 0.7341 0.000 0.120 0.000 0.860 0.020 0.000
#> GSM509752 2 0.0000 0.7660 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509754 2 0.0000 0.7660 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509756 2 0.0146 0.7648 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM509758 2 0.0000 0.7660 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509760 2 0.0146 0.7648 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM509762 2 0.0000 0.7660 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509764 2 0.0146 0.7648 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM509766 2 0.5198 0.4024 0.000 0.616 0.000 0.204 0.000 0.180
#> GSM509768 2 0.5624 0.1863 0.000 0.524 0.000 0.296 0.000 0.180
#> GSM509770 2 0.2932 0.6779 0.000 0.820 0.000 0.016 0.000 0.164
#> GSM509772 2 0.1563 0.7396 0.000 0.932 0.000 0.000 0.012 0.056
#> GSM509774 4 0.5702 0.4702 0.000 0.324 0.000 0.496 0.000 0.180
#> GSM509776 2 0.5648 0.1617 0.000 0.516 0.000 0.304 0.000 0.180
#> GSM509778 4 0.2389 0.7479 0.000 0.128 0.000 0.864 0.000 0.008
#> GSM509780 2 0.5896 0.0555 0.000 0.480 0.000 0.324 0.004 0.192
#> GSM509782 4 0.2135 0.7488 0.000 0.128 0.000 0.872 0.000 0.000
#> GSM509784 4 0.5558 0.5085 0.000 0.316 0.000 0.524 0.000 0.160
#> GSM509786 4 0.2581 0.7341 0.000 0.120 0.000 0.860 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 disease.state(p) time(p) k
#> ATC:kmeans 81 2.25e-15 1.79e-12 2
#> ATC:kmeans 71 3.57e-20 1.36e-08 3
#> ATC:kmeans 60 6.88e-22 6.36e-09 4
#> ATC:kmeans 61 4.93e-17 7.00e-06 5
#> ATC:kmeans 64 7.33e-19 6.72e-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", "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 19175 rows and 81 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 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.5067 0.494 0.494
#> 3 3 1.000 0.970 0.986 0.2096 0.898 0.794
#> 4 4 0.920 0.922 0.957 0.1299 0.895 0.735
#> 5 5 0.857 0.876 0.925 0.1137 0.869 0.590
#> 6 6 0.849 0.874 0.914 0.0428 0.965 0.840
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 2 3
There is also optional best \(k\) = 2 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM509706 1 0 1 1 0
#> GSM509711 1 0 1 1 0
#> GSM509714 1 0 1 1 0
#> GSM509719 1 0 1 1 0
#> GSM509724 1 0 1 1 0
#> GSM509729 1 0 1 1 0
#> GSM509707 1 0 1 1 0
#> GSM509712 1 0 1 1 0
#> GSM509715 2 0 1 0 1
#> GSM509720 1 0 1 1 0
#> GSM509725 1 0 1 1 0
#> GSM509730 1 0 1 1 0
#> GSM509708 1 0 1 1 0
#> GSM509713 1 0 1 1 0
#> GSM509716 2 0 1 0 1
#> GSM509721 1 0 1 1 0
#> GSM509726 1 0 1 1 0
#> GSM509731 1 0 1 1 0
#> GSM509709 1 0 1 1 0
#> GSM509717 2 0 1 0 1
#> GSM509722 1 0 1 1 0
#> GSM509727 1 0 1 1 0
#> GSM509710 1 0 1 1 0
#> GSM509718 2 0 1 0 1
#> GSM509723 1 0 1 1 0
#> GSM509728 1 0 1 1 0
#> GSM509732 1 0 1 1 0
#> GSM509736 1 0 1 1 0
#> GSM509741 1 0 1 1 0
#> GSM509746 1 0 1 1 0
#> GSM509733 1 0 1 1 0
#> GSM509737 1 0 1 1 0
#> GSM509742 1 0 1 1 0
#> GSM509747 1 0 1 1 0
#> GSM509734 1 0 1 1 0
#> GSM509738 1 0 1 1 0
#> GSM509743 1 0 1 1 0
#> GSM509748 1 0 1 1 0
#> GSM509735 1 0 1 1 0
#> GSM509739 1 0 1 1 0
#> GSM509744 1 0 1 1 0
#> GSM509749 1 0 1 1 0
#> GSM509740 1 0 1 1 0
#> GSM509745 1 0 1 1 0
#> GSM509750 1 0 1 1 0
#> GSM509751 2 0 1 0 1
#> GSM509753 2 0 1 0 1
#> GSM509755 2 0 1 0 1
#> GSM509757 2 0 1 0 1
#> GSM509759 2 0 1 0 1
#> GSM509761 2 0 1 0 1
#> GSM509763 2 0 1 0 1
#> GSM509765 2 0 1 0 1
#> GSM509767 2 0 1 0 1
#> GSM509769 2 0 1 0 1
#> GSM509771 2 0 1 0 1
#> GSM509773 2 0 1 0 1
#> GSM509775 2 0 1 0 1
#> GSM509777 2 0 1 0 1
#> GSM509779 2 0 1 0 1
#> GSM509781 2 0 1 0 1
#> GSM509783 2 0 1 0 1
#> GSM509785 2 0 1 0 1
#> GSM509752 2 0 1 0 1
#> GSM509754 2 0 1 0 1
#> GSM509756 2 0 1 0 1
#> GSM509758 2 0 1 0 1
#> GSM509760 2 0 1 0 1
#> GSM509762 2 0 1 0 1
#> GSM509764 2 0 1 0 1
#> GSM509766 2 0 1 0 1
#> GSM509768 2 0 1 0 1
#> GSM509770 2 0 1 0 1
#> GSM509772 2 0 1 0 1
#> GSM509774 2 0 1 0 1
#> GSM509776 2 0 1 0 1
#> GSM509778 2 0 1 0 1
#> GSM509780 2 0 1 0 1
#> GSM509782 2 0 1 0 1
#> GSM509784 2 0 1 0 1
#> GSM509786 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM509706 1 0.0000 0.968 1.000 0.000 0.000
#> GSM509711 1 0.0000 0.968 1.000 0.000 0.000
#> GSM509714 1 0.0000 0.968 1.000 0.000 0.000
#> GSM509719 1 0.0000 0.968 1.000 0.000 0.000
#> GSM509724 1 0.0000 0.968 1.000 0.000 0.000
#> GSM509729 1 0.0000 0.968 1.000 0.000 0.000
#> GSM509707 1 0.0000 0.968 1.000 0.000 0.000
#> GSM509712 1 0.0000 0.968 1.000 0.000 0.000
#> GSM509715 2 0.0592 0.991 0.000 0.988 0.012
#> GSM509720 1 0.0000 0.968 1.000 0.000 0.000
#> GSM509725 1 0.0000 0.968 1.000 0.000 0.000
#> GSM509730 1 0.0000 0.968 1.000 0.000 0.000
#> GSM509708 1 0.0000 0.968 1.000 0.000 0.000
#> GSM509713 1 0.0000 0.968 1.000 0.000 0.000
#> GSM509716 2 0.0592 0.991 0.000 0.988 0.012
#> GSM509721 1 0.0000 0.968 1.000 0.000 0.000
#> GSM509726 1 0.0000 0.968 1.000 0.000 0.000
#> GSM509731 1 0.0592 0.958 0.988 0.000 0.012
#> GSM509709 1 0.0000 0.968 1.000 0.000 0.000
#> GSM509717 2 0.0592 0.991 0.000 0.988 0.012
#> GSM509722 1 0.0000 0.968 1.000 0.000 0.000
#> GSM509727 1 0.0237 0.965 0.996 0.000 0.004
#> GSM509710 1 0.0000 0.968 1.000 0.000 0.000
#> GSM509718 2 0.0592 0.991 0.000 0.988 0.012
#> GSM509723 1 0.0000 0.968 1.000 0.000 0.000
#> GSM509728 1 0.0000 0.968 1.000 0.000 0.000
#> GSM509732 3 0.0592 0.997 0.012 0.000 0.988
#> GSM509736 1 0.0237 0.965 0.996 0.000 0.004
#> GSM509741 3 0.0424 0.998 0.008 0.000 0.992
#> GSM509746 3 0.0592 0.997 0.012 0.000 0.988
#> GSM509733 3 0.0592 0.997 0.012 0.000 0.988
#> GSM509737 1 0.0000 0.968 1.000 0.000 0.000
#> GSM509742 3 0.0424 0.998 0.008 0.000 0.992
#> GSM509747 3 0.0592 0.997 0.012 0.000 0.988
#> GSM509734 1 0.6095 0.378 0.608 0.000 0.392
#> GSM509738 1 0.3038 0.868 0.896 0.000 0.104
#> GSM509743 3 0.0424 0.998 0.008 0.000 0.992
#> GSM509748 3 0.0592 0.997 0.012 0.000 0.988
#> GSM509735 1 0.0000 0.968 1.000 0.000 0.000
#> GSM509739 1 0.0000 0.968 1.000 0.000 0.000
#> GSM509744 3 0.0424 0.998 0.008 0.000 0.992
#> GSM509749 3 0.0424 0.998 0.008 0.000 0.992
#> GSM509740 1 0.0237 0.965 0.996 0.000 0.004
#> GSM509745 1 0.6111 0.373 0.604 0.000 0.396
#> GSM509750 3 0.0424 0.998 0.008 0.000 0.992
#> GSM509751 2 0.0000 0.998 0.000 1.000 0.000
#> GSM509753 2 0.0000 0.998 0.000 1.000 0.000
#> GSM509755 2 0.0000 0.998 0.000 1.000 0.000
#> GSM509757 2 0.0000 0.998 0.000 1.000 0.000
#> GSM509759 2 0.0000 0.998 0.000 1.000 0.000
#> GSM509761 2 0.0000 0.998 0.000 1.000 0.000
#> GSM509763 2 0.0000 0.998 0.000 1.000 0.000
#> GSM509765 2 0.0000 0.998 0.000 1.000 0.000
#> GSM509767 2 0.0000 0.998 0.000 1.000 0.000
#> GSM509769 2 0.0000 0.998 0.000 1.000 0.000
#> GSM509771 2 0.0000 0.998 0.000 1.000 0.000
#> GSM509773 2 0.0000 0.998 0.000 1.000 0.000
#> GSM509775 2 0.0000 0.998 0.000 1.000 0.000
#> GSM509777 2 0.0000 0.998 0.000 1.000 0.000
#> GSM509779 2 0.0000 0.998 0.000 1.000 0.000
#> GSM509781 2 0.0237 0.996 0.000 0.996 0.004
#> GSM509783 2 0.0237 0.996 0.000 0.996 0.004
#> GSM509785 2 0.0237 0.996 0.000 0.996 0.004
#> GSM509752 2 0.0000 0.998 0.000 1.000 0.000
#> GSM509754 2 0.0000 0.998 0.000 1.000 0.000
#> GSM509756 2 0.0000 0.998 0.000 1.000 0.000
#> GSM509758 2 0.0000 0.998 0.000 1.000 0.000
#> GSM509760 2 0.0000 0.998 0.000 1.000 0.000
#> GSM509762 2 0.0000 0.998 0.000 1.000 0.000
#> GSM509764 2 0.0000 0.998 0.000 1.000 0.000
#> GSM509766 2 0.0000 0.998 0.000 1.000 0.000
#> GSM509768 2 0.0000 0.998 0.000 1.000 0.000
#> GSM509770 2 0.0000 0.998 0.000 1.000 0.000
#> GSM509772 2 0.0000 0.998 0.000 1.000 0.000
#> GSM509774 2 0.0000 0.998 0.000 1.000 0.000
#> GSM509776 2 0.0000 0.998 0.000 1.000 0.000
#> GSM509778 2 0.0237 0.996 0.000 0.996 0.004
#> GSM509780 2 0.0000 0.998 0.000 1.000 0.000
#> GSM509782 2 0.0237 0.996 0.000 0.996 0.004
#> GSM509784 2 0.0000 0.998 0.000 1.000 0.000
#> GSM509786 2 0.0237 0.996 0.000 0.996 0.004
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM509706 1 0.0000 0.965 1.000 0.000 0.000 0.000
#> GSM509711 1 0.0000 0.965 1.000 0.000 0.000 0.000
#> GSM509714 1 0.0000 0.965 1.000 0.000 0.000 0.000
#> GSM509719 1 0.0000 0.965 1.000 0.000 0.000 0.000
#> GSM509724 1 0.0000 0.965 1.000 0.000 0.000 0.000
#> GSM509729 1 0.0000 0.965 1.000 0.000 0.000 0.000
#> GSM509707 1 0.0000 0.965 1.000 0.000 0.000 0.000
#> GSM509712 1 0.0000 0.965 1.000 0.000 0.000 0.000
#> GSM509715 4 0.0000 0.630 0.000 0.000 0.000 1.000
#> GSM509720 1 0.0000 0.965 1.000 0.000 0.000 0.000
#> GSM509725 1 0.0000 0.965 1.000 0.000 0.000 0.000
#> GSM509730 1 0.0000 0.965 1.000 0.000 0.000 0.000
#> GSM509708 1 0.0000 0.965 1.000 0.000 0.000 0.000
#> GSM509713 1 0.0000 0.965 1.000 0.000 0.000 0.000
#> GSM509716 4 0.0000 0.630 0.000 0.000 0.000 1.000
#> GSM509721 1 0.0000 0.965 1.000 0.000 0.000 0.000
#> GSM509726 1 0.0000 0.965 1.000 0.000 0.000 0.000
#> GSM509731 4 0.0000 0.630 0.000 0.000 0.000 1.000
#> GSM509709 1 0.0000 0.965 1.000 0.000 0.000 0.000
#> GSM509717 4 0.0000 0.630 0.000 0.000 0.000 1.000
#> GSM509722 1 0.0000 0.965 1.000 0.000 0.000 0.000
#> GSM509727 1 0.0592 0.955 0.984 0.000 0.000 0.016
#> GSM509710 1 0.0000 0.965 1.000 0.000 0.000 0.000
#> GSM509718 4 0.0000 0.630 0.000 0.000 0.000 1.000
#> GSM509723 1 0.0000 0.965 1.000 0.000 0.000 0.000
#> GSM509728 1 0.0000 0.965 1.000 0.000 0.000 0.000
#> GSM509732 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM509736 1 0.0592 0.955 0.984 0.000 0.000 0.016
#> GSM509741 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM509746 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM509733 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM509737 1 0.0000 0.965 1.000 0.000 0.000 0.000
#> GSM509742 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM509747 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM509734 1 0.4713 0.472 0.640 0.000 0.360 0.000
#> GSM509738 1 0.3790 0.786 0.820 0.000 0.164 0.016
#> GSM509743 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM509748 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM509735 1 0.0000 0.965 1.000 0.000 0.000 0.000
#> GSM509739 1 0.0000 0.965 1.000 0.000 0.000 0.000
#> GSM509744 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM509749 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM509740 1 0.0592 0.955 0.984 0.000 0.000 0.016
#> GSM509745 1 0.4830 0.400 0.608 0.000 0.392 0.000
#> GSM509750 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM509751 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM509753 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM509755 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM509757 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM509759 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM509761 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM509763 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM509765 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM509767 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM509769 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM509771 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM509773 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM509775 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM509777 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM509779 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM509781 4 0.4888 0.648 0.000 0.412 0.000 0.588
#> GSM509783 4 0.4888 0.648 0.000 0.412 0.000 0.588
#> GSM509785 4 0.4888 0.648 0.000 0.412 0.000 0.588
#> GSM509752 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM509754 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM509756 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM509758 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM509760 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM509762 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM509764 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM509766 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM509768 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM509770 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM509772 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM509774 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM509776 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM509778 4 0.4888 0.648 0.000 0.412 0.000 0.588
#> GSM509780 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM509782 4 0.4898 0.640 0.000 0.416 0.000 0.584
#> GSM509784 2 0.0592 0.978 0.000 0.984 0.000 0.016
#> GSM509786 4 0.4888 0.648 0.000 0.412 0.000 0.588
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM509706 1 0.0000 0.935 1.000 0.000 0.000 0.000 0.000
#> GSM509711 1 0.0000 0.935 1.000 0.000 0.000 0.000 0.000
#> GSM509714 1 0.0000 0.935 1.000 0.000 0.000 0.000 0.000
#> GSM509719 1 0.0898 0.923 0.972 0.000 0.000 0.020 0.008
#> GSM509724 1 0.0000 0.935 1.000 0.000 0.000 0.000 0.000
#> GSM509729 1 0.0162 0.934 0.996 0.000 0.000 0.000 0.004
#> GSM509707 1 0.0000 0.935 1.000 0.000 0.000 0.000 0.000
#> GSM509712 1 0.0000 0.935 1.000 0.000 0.000 0.000 0.000
#> GSM509715 5 0.2074 0.685 0.000 0.000 0.000 0.104 0.896
#> GSM509720 1 0.0898 0.923 0.972 0.000 0.000 0.020 0.008
#> GSM509725 1 0.0000 0.935 1.000 0.000 0.000 0.000 0.000
#> GSM509730 1 0.0162 0.934 0.996 0.000 0.000 0.000 0.004
#> GSM509708 1 0.0000 0.935 1.000 0.000 0.000 0.000 0.000
#> GSM509713 1 0.0000 0.935 1.000 0.000 0.000 0.000 0.000
#> GSM509716 5 0.2074 0.685 0.000 0.000 0.000 0.104 0.896
#> GSM509721 1 0.0898 0.923 0.972 0.000 0.000 0.020 0.008
#> GSM509726 1 0.0000 0.935 1.000 0.000 0.000 0.000 0.000
#> GSM509731 5 0.2074 0.685 0.000 0.000 0.000 0.104 0.896
#> GSM509709 1 0.0000 0.935 1.000 0.000 0.000 0.000 0.000
#> GSM509717 5 0.2074 0.685 0.000 0.000 0.000 0.104 0.896
#> GSM509722 1 0.0898 0.923 0.972 0.000 0.000 0.020 0.008
#> GSM509727 5 0.4640 0.467 0.400 0.000 0.000 0.016 0.584
#> GSM509710 1 0.0000 0.935 1.000 0.000 0.000 0.000 0.000
#> GSM509718 5 0.2074 0.685 0.000 0.000 0.000 0.104 0.896
#> GSM509723 1 0.0898 0.923 0.972 0.000 0.000 0.020 0.008
#> GSM509728 1 0.2464 0.825 0.888 0.000 0.000 0.016 0.096
#> GSM509732 3 0.0000 0.990 0.000 0.000 1.000 0.000 0.000
#> GSM509736 5 0.5052 0.416 0.412 0.000 0.000 0.036 0.552
#> GSM509741 3 0.0000 0.990 0.000 0.000 1.000 0.000 0.000
#> GSM509746 3 0.0000 0.990 0.000 0.000 1.000 0.000 0.000
#> GSM509733 3 0.0000 0.990 0.000 0.000 1.000 0.000 0.000
#> GSM509737 1 0.2959 0.807 0.864 0.000 0.000 0.036 0.100
#> GSM509742 3 0.0000 0.990 0.000 0.000 1.000 0.000 0.000
#> GSM509747 3 0.0000 0.990 0.000 0.000 1.000 0.000 0.000
#> GSM509734 1 0.4126 0.363 0.620 0.000 0.380 0.000 0.000
#> GSM509738 5 0.4969 0.486 0.376 0.000 0.000 0.036 0.588
#> GSM509743 3 0.0000 0.990 0.000 0.000 1.000 0.000 0.000
#> GSM509748 3 0.0000 0.990 0.000 0.000 1.000 0.000 0.000
#> GSM509735 1 0.0000 0.935 1.000 0.000 0.000 0.000 0.000
#> GSM509739 1 0.0000 0.935 1.000 0.000 0.000 0.000 0.000
#> GSM509744 3 0.2136 0.896 0.000 0.000 0.904 0.008 0.088
#> GSM509749 3 0.0000 0.990 0.000 0.000 1.000 0.000 0.000
#> GSM509740 5 0.5077 0.457 0.392 0.000 0.000 0.040 0.568
#> GSM509745 1 0.6408 0.204 0.524 0.000 0.352 0.028 0.096
#> GSM509750 3 0.0000 0.990 0.000 0.000 1.000 0.000 0.000
#> GSM509751 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000
#> GSM509753 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000
#> GSM509755 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000
#> GSM509757 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000
#> GSM509759 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000
#> GSM509761 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000
#> GSM509763 4 0.3210 0.860 0.000 0.212 0.000 0.788 0.000
#> GSM509765 4 0.2732 0.898 0.000 0.160 0.000 0.840 0.000
#> GSM509767 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000
#> GSM509769 2 0.0290 0.985 0.000 0.992 0.000 0.008 0.000
#> GSM509771 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000
#> GSM509773 2 0.0963 0.955 0.000 0.964 0.000 0.036 0.000
#> GSM509775 4 0.2929 0.886 0.000 0.180 0.000 0.820 0.000
#> GSM509777 4 0.2561 0.904 0.000 0.144 0.000 0.856 0.000
#> GSM509779 4 0.2561 0.904 0.000 0.144 0.000 0.856 0.000
#> GSM509781 4 0.1043 0.861 0.000 0.040 0.000 0.960 0.000
#> GSM509783 4 0.1043 0.861 0.000 0.040 0.000 0.960 0.000
#> GSM509785 4 0.1043 0.861 0.000 0.040 0.000 0.960 0.000
#> GSM509752 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000
#> GSM509754 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000
#> GSM509756 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000
#> GSM509758 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000
#> GSM509760 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000
#> GSM509762 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000
#> GSM509764 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000
#> GSM509766 4 0.4287 0.399 0.000 0.460 0.000 0.540 0.000
#> GSM509768 4 0.3534 0.811 0.000 0.256 0.000 0.744 0.000
#> GSM509770 2 0.1608 0.909 0.000 0.928 0.000 0.072 0.000
#> GSM509772 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000
#> GSM509774 4 0.2561 0.904 0.000 0.144 0.000 0.856 0.000
#> GSM509776 4 0.2690 0.900 0.000 0.156 0.000 0.844 0.000
#> GSM509778 4 0.1043 0.861 0.000 0.040 0.000 0.960 0.000
#> GSM509780 4 0.2561 0.904 0.000 0.144 0.000 0.856 0.000
#> GSM509782 4 0.1121 0.864 0.000 0.044 0.000 0.956 0.000
#> GSM509784 4 0.2516 0.903 0.000 0.140 0.000 0.860 0.000
#> GSM509786 4 0.1043 0.861 0.000 0.040 0.000 0.960 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM509706 1 0.0000 0.891 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509711 1 0.0458 0.883 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM509714 1 0.0458 0.883 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM509719 1 0.4193 0.729 0.736 0.000 0.000 0.004 0.072 0.188
#> GSM509724 1 0.0000 0.891 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509729 1 0.0858 0.878 0.968 0.000 0.000 0.000 0.004 0.028
#> GSM509707 1 0.0000 0.891 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509712 1 0.0458 0.883 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM509715 5 0.1444 0.995 0.000 0.000 0.000 0.072 0.928 0.000
#> GSM509720 1 0.4193 0.729 0.736 0.000 0.000 0.004 0.072 0.188
#> GSM509725 1 0.0000 0.891 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509730 1 0.2594 0.831 0.880 0.000 0.000 0.004 0.056 0.060
#> GSM509708 1 0.0000 0.891 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509713 1 0.0146 0.889 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM509716 5 0.1444 0.995 0.000 0.000 0.000 0.072 0.928 0.000
#> GSM509721 1 0.4193 0.729 0.736 0.000 0.000 0.004 0.072 0.188
#> GSM509726 1 0.0000 0.891 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509731 5 0.2066 0.979 0.000 0.000 0.000 0.072 0.904 0.024
#> GSM509709 1 0.0000 0.891 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509717 5 0.1444 0.995 0.000 0.000 0.000 0.072 0.928 0.000
#> GSM509722 1 0.4193 0.729 0.736 0.000 0.000 0.004 0.072 0.188
#> GSM509727 6 0.4107 0.795 0.256 0.000 0.000 0.000 0.044 0.700
#> GSM509710 1 0.0000 0.891 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509718 5 0.1444 0.995 0.000 0.000 0.000 0.072 0.928 0.000
#> GSM509723 1 0.4193 0.729 0.736 0.000 0.000 0.004 0.072 0.188
#> GSM509728 6 0.3620 0.716 0.352 0.000 0.000 0.000 0.000 0.648
#> GSM509732 3 0.0000 0.987 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509736 6 0.3352 0.832 0.176 0.000 0.000 0.000 0.032 0.792
#> GSM509741 3 0.0363 0.986 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM509746 3 0.0000 0.987 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509733 3 0.0000 0.987 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509737 6 0.3076 0.819 0.240 0.000 0.000 0.000 0.000 0.760
#> GSM509742 3 0.0363 0.986 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM509747 3 0.0000 0.987 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509734 1 0.4141 0.277 0.596 0.000 0.388 0.000 0.000 0.016
#> GSM509738 6 0.3041 0.807 0.128 0.000 0.000 0.000 0.040 0.832
#> GSM509743 3 0.0935 0.976 0.000 0.000 0.964 0.004 0.000 0.032
#> GSM509748 3 0.0000 0.987 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509735 1 0.0000 0.891 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509739 1 0.0000 0.891 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509744 6 0.3714 0.377 0.000 0.000 0.340 0.004 0.000 0.656
#> GSM509749 3 0.0777 0.980 0.000 0.000 0.972 0.004 0.000 0.024
#> GSM509740 6 0.3054 0.796 0.136 0.000 0.000 0.000 0.036 0.828
#> GSM509745 6 0.3422 0.830 0.168 0.000 0.040 0.000 0.000 0.792
#> GSM509750 3 0.1349 0.958 0.000 0.000 0.940 0.004 0.000 0.056
#> GSM509751 2 0.0000 0.970 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509753 2 0.0000 0.970 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509755 2 0.0000 0.970 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509757 2 0.0146 0.969 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM509759 2 0.0260 0.967 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM509761 2 0.0000 0.970 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509763 4 0.2631 0.821 0.000 0.180 0.000 0.820 0.000 0.000
#> GSM509765 4 0.2135 0.861 0.000 0.128 0.000 0.872 0.000 0.000
#> GSM509767 2 0.1049 0.951 0.000 0.960 0.000 0.032 0.000 0.008
#> GSM509769 2 0.1556 0.911 0.000 0.920 0.000 0.080 0.000 0.000
#> GSM509771 2 0.1049 0.951 0.000 0.960 0.000 0.032 0.000 0.008
#> GSM509773 2 0.2219 0.844 0.000 0.864 0.000 0.136 0.000 0.000
#> GSM509775 4 0.2416 0.842 0.000 0.156 0.000 0.844 0.000 0.000
#> GSM509777 4 0.1556 0.879 0.000 0.080 0.000 0.920 0.000 0.000
#> GSM509779 4 0.1812 0.879 0.000 0.080 0.000 0.912 0.000 0.008
#> GSM509781 4 0.1390 0.835 0.000 0.004 0.000 0.948 0.016 0.032
#> GSM509783 4 0.1296 0.837 0.000 0.004 0.000 0.952 0.012 0.032
#> GSM509785 4 0.1390 0.835 0.000 0.004 0.000 0.948 0.016 0.032
#> GSM509752 2 0.0000 0.970 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509754 2 0.0000 0.970 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509756 2 0.0000 0.970 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509758 2 0.0000 0.970 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509760 2 0.0000 0.970 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509762 2 0.0000 0.970 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509764 2 0.0000 0.970 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509766 4 0.3782 0.421 0.000 0.412 0.000 0.588 0.000 0.000
#> GSM509768 4 0.3330 0.697 0.000 0.284 0.000 0.716 0.000 0.000
#> GSM509770 2 0.2562 0.791 0.000 0.828 0.000 0.172 0.000 0.000
#> GSM509772 2 0.0260 0.967 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM509774 4 0.1556 0.879 0.000 0.080 0.000 0.920 0.000 0.000
#> GSM509776 4 0.2003 0.867 0.000 0.116 0.000 0.884 0.000 0.000
#> GSM509778 4 0.1049 0.844 0.000 0.008 0.000 0.960 0.000 0.032
#> GSM509780 4 0.1556 0.879 0.000 0.080 0.000 0.920 0.000 0.000
#> GSM509782 4 0.1151 0.847 0.000 0.012 0.000 0.956 0.000 0.032
#> GSM509784 4 0.2255 0.876 0.000 0.080 0.000 0.892 0.000 0.028
#> GSM509786 4 0.1390 0.835 0.000 0.004 0.000 0.948 0.016 0.032
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 disease.state(p) time(p) k
#> ATC:skmeans 81 2.25e-15 1.79e-12 2
#> ATC:skmeans 79 2.34e-21 2.10e-09 3
#> ATC:skmeans 79 5.71e-21 3.22e-08 4
#> ATC:skmeans 74 1.51e-23 7.66e-08 5
#> ATC:skmeans 78 2.39e-23 3.26e-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", "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 19175 rows and 81 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 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.999 0.999 0.5066 0.494 0.494
#> 3 3 0.867 0.852 0.905 0.2354 0.809 0.638
#> 4 4 0.894 0.870 0.939 0.0989 0.862 0.668
#> 5 5 0.862 0.925 0.935 0.1419 0.868 0.596
#> 6 6 0.905 0.811 0.909 0.0543 0.887 0.529
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2
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
#> GSM509706 1 0.00 1.000 1.000 0.000
#> GSM509711 1 0.00 1.000 1.000 0.000
#> GSM509714 1 0.00 1.000 1.000 0.000
#> GSM509719 1 0.00 1.000 1.000 0.000
#> GSM509724 1 0.00 1.000 1.000 0.000
#> GSM509729 1 0.00 1.000 1.000 0.000
#> GSM509707 1 0.00 1.000 1.000 0.000
#> GSM509712 1 0.00 1.000 1.000 0.000
#> GSM509715 2 0.00 0.999 0.000 1.000
#> GSM509720 1 0.00 1.000 1.000 0.000
#> GSM509725 1 0.00 1.000 1.000 0.000
#> GSM509730 1 0.00 1.000 1.000 0.000
#> GSM509708 1 0.00 1.000 1.000 0.000
#> GSM509713 1 0.00 1.000 1.000 0.000
#> GSM509716 2 0.26 0.954 0.044 0.956
#> GSM509721 1 0.00 1.000 1.000 0.000
#> GSM509726 1 0.00 1.000 1.000 0.000
#> GSM509731 1 0.00 1.000 1.000 0.000
#> GSM509709 1 0.00 1.000 1.000 0.000
#> GSM509717 2 0.00 0.999 0.000 1.000
#> GSM509722 1 0.00 1.000 1.000 0.000
#> GSM509727 1 0.00 1.000 1.000 0.000
#> GSM509710 1 0.00 1.000 1.000 0.000
#> GSM509718 2 0.00 0.999 0.000 1.000
#> GSM509723 1 0.00 1.000 1.000 0.000
#> GSM509728 1 0.00 1.000 1.000 0.000
#> GSM509732 1 0.00 1.000 1.000 0.000
#> GSM509736 1 0.00 1.000 1.000 0.000
#> GSM509741 1 0.00 1.000 1.000 0.000
#> GSM509746 1 0.00 1.000 1.000 0.000
#> GSM509733 1 0.00 1.000 1.000 0.000
#> GSM509737 1 0.00 1.000 1.000 0.000
#> GSM509742 1 0.00 1.000 1.000 0.000
#> GSM509747 1 0.00 1.000 1.000 0.000
#> GSM509734 1 0.00 1.000 1.000 0.000
#> GSM509738 1 0.00 1.000 1.000 0.000
#> GSM509743 1 0.00 1.000 1.000 0.000
#> GSM509748 1 0.00 1.000 1.000 0.000
#> GSM509735 1 0.00 1.000 1.000 0.000
#> GSM509739 1 0.00 1.000 1.000 0.000
#> GSM509744 1 0.00 1.000 1.000 0.000
#> GSM509749 1 0.00 1.000 1.000 0.000
#> GSM509740 1 0.00 1.000 1.000 0.000
#> GSM509745 1 0.00 1.000 1.000 0.000
#> GSM509750 1 0.00 1.000 1.000 0.000
#> GSM509751 2 0.00 0.999 0.000 1.000
#> GSM509753 2 0.00 0.999 0.000 1.000
#> GSM509755 2 0.00 0.999 0.000 1.000
#> GSM509757 2 0.00 0.999 0.000 1.000
#> GSM509759 2 0.00 0.999 0.000 1.000
#> GSM509761 2 0.00 0.999 0.000 1.000
#> GSM509763 2 0.00 0.999 0.000 1.000
#> GSM509765 2 0.00 0.999 0.000 1.000
#> GSM509767 2 0.00 0.999 0.000 1.000
#> GSM509769 2 0.00 0.999 0.000 1.000
#> GSM509771 2 0.00 0.999 0.000 1.000
#> GSM509773 2 0.00 0.999 0.000 1.000
#> GSM509775 2 0.00 0.999 0.000 1.000
#> GSM509777 2 0.00 0.999 0.000 1.000
#> GSM509779 2 0.00 0.999 0.000 1.000
#> GSM509781 2 0.00 0.999 0.000 1.000
#> GSM509783 2 0.00 0.999 0.000 1.000
#> GSM509785 2 0.00 0.999 0.000 1.000
#> GSM509752 2 0.00 0.999 0.000 1.000
#> GSM509754 2 0.00 0.999 0.000 1.000
#> GSM509756 2 0.00 0.999 0.000 1.000
#> GSM509758 2 0.00 0.999 0.000 1.000
#> GSM509760 2 0.00 0.999 0.000 1.000
#> GSM509762 2 0.00 0.999 0.000 1.000
#> GSM509764 2 0.00 0.999 0.000 1.000
#> GSM509766 2 0.00 0.999 0.000 1.000
#> GSM509768 2 0.00 0.999 0.000 1.000
#> GSM509770 2 0.00 0.999 0.000 1.000
#> GSM509772 2 0.00 0.999 0.000 1.000
#> GSM509774 2 0.00 0.999 0.000 1.000
#> GSM509776 2 0.00 0.999 0.000 1.000
#> GSM509778 2 0.00 0.999 0.000 1.000
#> GSM509780 2 0.00 0.999 0.000 1.000
#> GSM509782 2 0.00 0.999 0.000 1.000
#> GSM509784 2 0.00 0.999 0.000 1.000
#> GSM509786 2 0.00 0.999 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM509706 1 0.000 1.000 1.000 0.000 0.000
#> GSM509711 1 0.000 1.000 1.000 0.000 0.000
#> GSM509714 3 0.611 0.627 0.396 0.000 0.604
#> GSM509719 3 0.611 0.627 0.396 0.000 0.604
#> GSM509724 1 0.000 1.000 1.000 0.000 0.000
#> GSM509729 1 0.000 1.000 1.000 0.000 0.000
#> GSM509707 1 0.000 1.000 1.000 0.000 0.000
#> GSM509712 3 0.625 0.554 0.444 0.000 0.556
#> GSM509715 3 0.611 0.436 0.000 0.396 0.604
#> GSM509720 3 0.611 0.627 0.396 0.000 0.604
#> GSM509725 1 0.000 1.000 1.000 0.000 0.000
#> GSM509730 3 0.629 0.516 0.464 0.000 0.536
#> GSM509708 1 0.000 1.000 1.000 0.000 0.000
#> GSM509713 1 0.000 1.000 1.000 0.000 0.000
#> GSM509716 3 0.744 0.496 0.048 0.348 0.604
#> GSM509721 3 0.611 0.627 0.396 0.000 0.604
#> GSM509726 1 0.000 1.000 1.000 0.000 0.000
#> GSM509731 3 0.611 0.627 0.396 0.000 0.604
#> GSM509709 1 0.000 1.000 1.000 0.000 0.000
#> GSM509717 3 0.631 0.444 0.004 0.392 0.604
#> GSM509722 3 0.611 0.627 0.396 0.000 0.604
#> GSM509727 3 0.611 0.627 0.396 0.000 0.604
#> GSM509710 1 0.000 1.000 1.000 0.000 0.000
#> GSM509718 3 0.611 0.436 0.000 0.396 0.604
#> GSM509723 3 0.611 0.627 0.396 0.000 0.604
#> GSM509728 3 0.000 0.695 0.000 0.000 1.000
#> GSM509732 3 0.000 0.695 0.000 0.000 1.000
#> GSM509736 3 0.611 0.627 0.396 0.000 0.604
#> GSM509741 3 0.000 0.695 0.000 0.000 1.000
#> GSM509746 3 0.000 0.695 0.000 0.000 1.000
#> GSM509733 3 0.000 0.695 0.000 0.000 1.000
#> GSM509737 3 0.611 0.627 0.396 0.000 0.604
#> GSM509742 3 0.000 0.695 0.000 0.000 1.000
#> GSM509747 3 0.000 0.695 0.000 0.000 1.000
#> GSM509734 3 0.175 0.665 0.048 0.000 0.952
#> GSM509738 3 0.610 0.629 0.392 0.000 0.608
#> GSM509743 3 0.000 0.695 0.000 0.000 1.000
#> GSM509748 3 0.000 0.695 0.000 0.000 1.000
#> GSM509735 1 0.000 1.000 1.000 0.000 0.000
#> GSM509739 1 0.000 1.000 1.000 0.000 0.000
#> GSM509744 3 0.000 0.695 0.000 0.000 1.000
#> GSM509749 3 0.000 0.695 0.000 0.000 1.000
#> GSM509740 3 0.611 0.627 0.396 0.000 0.604
#> GSM509745 3 0.610 0.629 0.392 0.000 0.608
#> GSM509750 3 0.000 0.695 0.000 0.000 1.000
#> GSM509751 2 0.000 1.000 0.000 1.000 0.000
#> GSM509753 2 0.000 1.000 0.000 1.000 0.000
#> GSM509755 2 0.000 1.000 0.000 1.000 0.000
#> GSM509757 2 0.000 1.000 0.000 1.000 0.000
#> GSM509759 2 0.000 1.000 0.000 1.000 0.000
#> GSM509761 2 0.000 1.000 0.000 1.000 0.000
#> GSM509763 2 0.000 1.000 0.000 1.000 0.000
#> GSM509765 2 0.000 1.000 0.000 1.000 0.000
#> GSM509767 2 0.000 1.000 0.000 1.000 0.000
#> GSM509769 2 0.000 1.000 0.000 1.000 0.000
#> GSM509771 2 0.000 1.000 0.000 1.000 0.000
#> GSM509773 2 0.000 1.000 0.000 1.000 0.000
#> GSM509775 2 0.000 1.000 0.000 1.000 0.000
#> GSM509777 2 0.000 1.000 0.000 1.000 0.000
#> GSM509779 2 0.000 1.000 0.000 1.000 0.000
#> GSM509781 2 0.000 1.000 0.000 1.000 0.000
#> GSM509783 2 0.000 1.000 0.000 1.000 0.000
#> GSM509785 2 0.000 1.000 0.000 1.000 0.000
#> GSM509752 2 0.000 1.000 0.000 1.000 0.000
#> GSM509754 2 0.000 1.000 0.000 1.000 0.000
#> GSM509756 2 0.000 1.000 0.000 1.000 0.000
#> GSM509758 2 0.000 1.000 0.000 1.000 0.000
#> GSM509760 2 0.000 1.000 0.000 1.000 0.000
#> GSM509762 2 0.000 1.000 0.000 1.000 0.000
#> GSM509764 2 0.000 1.000 0.000 1.000 0.000
#> GSM509766 2 0.000 1.000 0.000 1.000 0.000
#> GSM509768 2 0.000 1.000 0.000 1.000 0.000
#> GSM509770 2 0.000 1.000 0.000 1.000 0.000
#> GSM509772 2 0.000 1.000 0.000 1.000 0.000
#> GSM509774 2 0.000 1.000 0.000 1.000 0.000
#> GSM509776 2 0.000 1.000 0.000 1.000 0.000
#> GSM509778 2 0.000 1.000 0.000 1.000 0.000
#> GSM509780 2 0.000 1.000 0.000 1.000 0.000
#> GSM509782 2 0.000 1.000 0.000 1.000 0.000
#> GSM509784 2 0.000 1.000 0.000 1.000 0.000
#> GSM509786 2 0.000 1.000 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM509706 1 0.0469 0.975 0.988 0.000 0.000 0.012
#> GSM509711 1 0.0469 0.975 0.988 0.000 0.000 0.012
#> GSM509714 4 0.0188 0.901 0.004 0.000 0.000 0.996
#> GSM509719 4 0.0188 0.902 0.000 0.000 0.004 0.996
#> GSM509724 1 0.0469 0.975 0.988 0.000 0.000 0.012
#> GSM509729 1 0.4250 0.624 0.724 0.000 0.000 0.276
#> GSM509707 1 0.0469 0.975 0.988 0.000 0.000 0.012
#> GSM509712 4 0.0188 0.901 0.004 0.000 0.000 0.996
#> GSM509715 2 0.6060 0.441 0.012 0.612 0.036 0.340
#> GSM509720 4 0.0188 0.902 0.000 0.000 0.004 0.996
#> GSM509725 1 0.0469 0.975 0.988 0.000 0.000 0.012
#> GSM509730 4 0.4934 0.572 0.028 0.000 0.252 0.720
#> GSM509708 1 0.0469 0.975 0.988 0.000 0.000 0.012
#> GSM509713 1 0.0469 0.975 0.988 0.000 0.000 0.012
#> GSM509716 2 0.6296 0.237 0.012 0.532 0.036 0.420
#> GSM509721 4 0.0188 0.902 0.000 0.000 0.004 0.996
#> GSM509726 1 0.0469 0.975 0.988 0.000 0.000 0.012
#> GSM509731 4 0.0336 0.901 0.000 0.000 0.008 0.992
#> GSM509709 1 0.0469 0.975 0.988 0.000 0.000 0.012
#> GSM509717 2 0.6060 0.441 0.012 0.612 0.036 0.340
#> GSM509722 4 0.0188 0.902 0.000 0.000 0.004 0.996
#> GSM509727 4 0.1305 0.887 0.004 0.000 0.036 0.960
#> GSM509710 1 0.0469 0.975 0.988 0.000 0.000 0.012
#> GSM509718 2 0.6060 0.441 0.012 0.612 0.036 0.340
#> GSM509723 4 0.3610 0.689 0.000 0.000 0.200 0.800
#> GSM509728 4 0.2944 0.788 0.004 0.000 0.128 0.868
#> GSM509732 3 0.0592 0.869 0.000 0.000 0.984 0.016
#> GSM509736 4 0.4817 0.276 0.000 0.000 0.388 0.612
#> GSM509741 3 0.0469 0.871 0.000 0.000 0.988 0.012
#> GSM509746 3 0.0336 0.870 0.000 0.000 0.992 0.008
#> GSM509733 3 0.0336 0.870 0.000 0.000 0.992 0.008
#> GSM509737 4 0.0469 0.902 0.000 0.000 0.012 0.988
#> GSM509742 3 0.0469 0.871 0.000 0.000 0.988 0.012
#> GSM509747 3 0.1302 0.859 0.000 0.000 0.956 0.044
#> GSM509734 3 0.2401 0.828 0.004 0.000 0.904 0.092
#> GSM509738 4 0.1940 0.866 0.000 0.000 0.076 0.924
#> GSM509743 3 0.4134 0.646 0.000 0.000 0.740 0.260
#> GSM509748 3 0.1389 0.858 0.000 0.000 0.952 0.048
#> GSM509735 1 0.0469 0.975 0.988 0.000 0.000 0.012
#> GSM509739 1 0.0469 0.975 0.988 0.000 0.000 0.012
#> GSM509744 3 0.4605 0.522 0.000 0.000 0.664 0.336
#> GSM509749 3 0.1792 0.845 0.000 0.000 0.932 0.068
#> GSM509740 4 0.0469 0.902 0.000 0.000 0.012 0.988
#> GSM509745 4 0.1557 0.879 0.000 0.000 0.056 0.944
#> GSM509750 3 0.4605 0.522 0.000 0.000 0.664 0.336
#> GSM509751 2 0.0000 0.948 0.000 1.000 0.000 0.000
#> GSM509753 2 0.0000 0.948 0.000 1.000 0.000 0.000
#> GSM509755 2 0.0000 0.948 0.000 1.000 0.000 0.000
#> GSM509757 2 0.0000 0.948 0.000 1.000 0.000 0.000
#> GSM509759 2 0.0000 0.948 0.000 1.000 0.000 0.000
#> GSM509761 2 0.0000 0.948 0.000 1.000 0.000 0.000
#> GSM509763 2 0.0469 0.947 0.012 0.988 0.000 0.000
#> GSM509765 2 0.0992 0.946 0.012 0.976 0.008 0.004
#> GSM509767 2 0.0000 0.948 0.000 1.000 0.000 0.000
#> GSM509769 2 0.0000 0.948 0.000 1.000 0.000 0.000
#> GSM509771 2 0.0000 0.948 0.000 1.000 0.000 0.000
#> GSM509773 2 0.0000 0.948 0.000 1.000 0.000 0.000
#> GSM509775 2 0.0992 0.946 0.012 0.976 0.008 0.004
#> GSM509777 2 0.0992 0.946 0.012 0.976 0.008 0.004
#> GSM509779 2 0.0992 0.946 0.012 0.976 0.008 0.004
#> GSM509781 2 0.0992 0.946 0.012 0.976 0.008 0.004
#> GSM509783 2 0.0992 0.946 0.012 0.976 0.008 0.004
#> GSM509785 2 0.0992 0.946 0.012 0.976 0.008 0.004
#> GSM509752 2 0.0000 0.948 0.000 1.000 0.000 0.000
#> GSM509754 2 0.0000 0.948 0.000 1.000 0.000 0.000
#> GSM509756 2 0.0000 0.948 0.000 1.000 0.000 0.000
#> GSM509758 2 0.0000 0.948 0.000 1.000 0.000 0.000
#> GSM509760 2 0.0000 0.948 0.000 1.000 0.000 0.000
#> GSM509762 2 0.0000 0.948 0.000 1.000 0.000 0.000
#> GSM509764 2 0.0000 0.948 0.000 1.000 0.000 0.000
#> GSM509766 2 0.0000 0.948 0.000 1.000 0.000 0.000
#> GSM509768 2 0.0992 0.946 0.012 0.976 0.008 0.004
#> GSM509770 2 0.0524 0.947 0.000 0.988 0.008 0.004
#> GSM509772 2 0.0000 0.948 0.000 1.000 0.000 0.000
#> GSM509774 2 0.0992 0.946 0.012 0.976 0.008 0.004
#> GSM509776 2 0.0992 0.946 0.012 0.976 0.008 0.004
#> GSM509778 2 0.0992 0.946 0.012 0.976 0.008 0.004
#> GSM509780 2 0.0992 0.946 0.012 0.976 0.008 0.004
#> GSM509782 2 0.0992 0.946 0.012 0.976 0.008 0.004
#> GSM509784 2 0.0992 0.946 0.012 0.976 0.008 0.004
#> GSM509786 2 0.0992 0.946 0.012 0.976 0.008 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM509706 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM509711 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM509714 5 0.0000 0.919 0.000 0.000 0.000 0.000 1.000
#> GSM509719 5 0.0000 0.919 0.000 0.000 0.000 0.000 1.000
#> GSM509724 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM509729 5 0.4171 0.369 0.396 0.000 0.000 0.000 0.604
#> GSM509707 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM509712 5 0.0000 0.919 0.000 0.000 0.000 0.000 1.000
#> GSM509715 4 0.0000 0.762 0.000 0.000 0.000 1.000 0.000
#> GSM509720 5 0.0000 0.919 0.000 0.000 0.000 0.000 1.000
#> GSM509725 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM509730 5 0.0000 0.919 0.000 0.000 0.000 0.000 1.000
#> GSM509708 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM509713 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM509716 4 0.0000 0.762 0.000 0.000 0.000 1.000 0.000
#> GSM509721 5 0.0000 0.919 0.000 0.000 0.000 0.000 1.000
#> GSM509726 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM509731 5 0.3242 0.780 0.000 0.000 0.000 0.216 0.784
#> GSM509709 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM509717 4 0.0000 0.762 0.000 0.000 0.000 1.000 0.000
#> GSM509722 5 0.0000 0.919 0.000 0.000 0.000 0.000 1.000
#> GSM509727 5 0.0290 0.918 0.000 0.000 0.000 0.008 0.992
#> GSM509710 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM509718 4 0.0000 0.762 0.000 0.000 0.000 1.000 0.000
#> GSM509723 5 0.0000 0.919 0.000 0.000 0.000 0.000 1.000
#> GSM509728 5 0.3551 0.691 0.000 0.000 0.220 0.008 0.772
#> GSM509732 3 0.0000 0.990 0.000 0.000 1.000 0.000 0.000
#> GSM509736 5 0.4392 0.405 0.000 0.000 0.380 0.008 0.612
#> GSM509741 3 0.0000 0.990 0.000 0.000 1.000 0.000 0.000
#> GSM509746 3 0.0000 0.990 0.000 0.000 1.000 0.000 0.000
#> GSM509733 3 0.0000 0.990 0.000 0.000 1.000 0.000 0.000
#> GSM509737 5 0.0290 0.918 0.000 0.000 0.000 0.008 0.992
#> GSM509742 3 0.0000 0.990 0.000 0.000 1.000 0.000 0.000
#> GSM509747 3 0.0000 0.990 0.000 0.000 1.000 0.000 0.000
#> GSM509734 3 0.1608 0.925 0.000 0.000 0.928 0.000 0.072
#> GSM509738 5 0.0898 0.910 0.000 0.000 0.020 0.008 0.972
#> GSM509743 3 0.0000 0.990 0.000 0.000 1.000 0.000 0.000
#> GSM509748 3 0.0510 0.979 0.000 0.000 0.984 0.000 0.016
#> GSM509735 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM509739 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM509744 3 0.0290 0.986 0.000 0.000 0.992 0.008 0.000
#> GSM509749 3 0.0000 0.990 0.000 0.000 1.000 0.000 0.000
#> GSM509740 5 0.0290 0.918 0.000 0.000 0.000 0.008 0.992
#> GSM509745 5 0.0898 0.910 0.000 0.000 0.020 0.008 0.972
#> GSM509750 3 0.0290 0.986 0.000 0.000 0.992 0.008 0.000
#> GSM509751 2 0.0000 0.997 0.000 1.000 0.000 0.000 0.000
#> GSM509753 2 0.0000 0.997 0.000 1.000 0.000 0.000 0.000
#> GSM509755 2 0.0000 0.997 0.000 1.000 0.000 0.000 0.000
#> GSM509757 2 0.0000 0.997 0.000 1.000 0.000 0.000 0.000
#> GSM509759 2 0.0000 0.997 0.000 1.000 0.000 0.000 0.000
#> GSM509761 2 0.0000 0.997 0.000 1.000 0.000 0.000 0.000
#> GSM509763 4 0.3857 0.808 0.000 0.312 0.000 0.688 0.000
#> GSM509765 4 0.4074 0.723 0.000 0.364 0.000 0.636 0.000
#> GSM509767 2 0.0000 0.997 0.000 1.000 0.000 0.000 0.000
#> GSM509769 2 0.0000 0.997 0.000 1.000 0.000 0.000 0.000
#> GSM509771 2 0.0000 0.997 0.000 1.000 0.000 0.000 0.000
#> GSM509773 2 0.0000 0.997 0.000 1.000 0.000 0.000 0.000
#> GSM509775 4 0.3210 0.911 0.000 0.212 0.000 0.788 0.000
#> GSM509777 4 0.3210 0.911 0.000 0.212 0.000 0.788 0.000
#> GSM509779 4 0.3177 0.912 0.000 0.208 0.000 0.792 0.000
#> GSM509781 4 0.3177 0.912 0.000 0.208 0.000 0.792 0.000
#> GSM509783 4 0.3109 0.908 0.000 0.200 0.000 0.800 0.000
#> GSM509785 4 0.3177 0.912 0.000 0.208 0.000 0.792 0.000
#> GSM509752 2 0.0000 0.997 0.000 1.000 0.000 0.000 0.000
#> GSM509754 2 0.0000 0.997 0.000 1.000 0.000 0.000 0.000
#> GSM509756 2 0.0000 0.997 0.000 1.000 0.000 0.000 0.000
#> GSM509758 2 0.0000 0.997 0.000 1.000 0.000 0.000 0.000
#> GSM509760 2 0.0000 0.997 0.000 1.000 0.000 0.000 0.000
#> GSM509762 2 0.0000 0.997 0.000 1.000 0.000 0.000 0.000
#> GSM509764 2 0.0000 0.997 0.000 1.000 0.000 0.000 0.000
#> GSM509766 2 0.0000 0.997 0.000 1.000 0.000 0.000 0.000
#> GSM509768 4 0.4126 0.694 0.000 0.380 0.000 0.620 0.000
#> GSM509770 2 0.1197 0.934 0.000 0.952 0.000 0.048 0.000
#> GSM509772 2 0.0000 0.997 0.000 1.000 0.000 0.000 0.000
#> GSM509774 4 0.3210 0.911 0.000 0.212 0.000 0.788 0.000
#> GSM509776 4 0.3210 0.911 0.000 0.212 0.000 0.788 0.000
#> GSM509778 4 0.3177 0.912 0.000 0.208 0.000 0.792 0.000
#> GSM509780 4 0.3210 0.911 0.000 0.212 0.000 0.788 0.000
#> GSM509782 4 0.3177 0.912 0.000 0.208 0.000 0.792 0.000
#> GSM509784 4 0.3177 0.912 0.000 0.208 0.000 0.792 0.000
#> GSM509786 4 0.3177 0.912 0.000 0.208 0.000 0.792 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM509706 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509711 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509714 5 0.0000 0.920 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM509719 5 0.0000 0.920 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM509724 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509729 5 0.3765 0.238 0.404 0.000 0.000 0.000 0.596 0.000
#> GSM509707 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509712 5 0.0000 0.920 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM509715 6 0.0000 0.645 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM509720 5 0.0000 0.920 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM509725 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509730 5 0.0000 0.920 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM509708 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509713 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509716 6 0.0000 0.645 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM509721 5 0.0000 0.920 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM509726 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509731 6 0.0000 0.645 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM509709 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509717 6 0.0000 0.645 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM509722 5 0.0000 0.920 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM509727 6 0.3659 0.556 0.000 0.000 0.000 0.000 0.364 0.636
#> GSM509710 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509718 6 0.0000 0.645 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM509723 5 0.0000 0.920 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM509728 6 0.3862 0.482 0.000 0.000 0.000 0.000 0.476 0.524
#> GSM509732 3 0.0000 0.940 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509736 6 0.5337 0.398 0.000 0.000 0.360 0.000 0.116 0.524
#> GSM509741 3 0.0000 0.940 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509746 3 0.0000 0.940 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509733 3 0.0000 0.940 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509737 6 0.3862 0.482 0.000 0.000 0.000 0.000 0.476 0.524
#> GSM509742 3 0.0000 0.940 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509747 3 0.0000 0.940 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM509734 3 0.1501 0.872 0.000 0.000 0.924 0.000 0.076 0.000
#> GSM509738 6 0.4393 0.502 0.000 0.000 0.024 0.000 0.452 0.524
#> GSM509743 3 0.2527 0.765 0.000 0.000 0.832 0.000 0.000 0.168
#> GSM509748 3 0.0458 0.930 0.000 0.000 0.984 0.000 0.016 0.000
#> GSM509735 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509739 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509744 6 0.3862 0.195 0.000 0.000 0.476 0.000 0.000 0.524
#> GSM509749 3 0.2378 0.789 0.000 0.000 0.848 0.000 0.000 0.152
#> GSM509740 6 0.3862 0.482 0.000 0.000 0.000 0.000 0.476 0.524
#> GSM509745 6 0.4393 0.502 0.000 0.000 0.024 0.000 0.452 0.524
#> GSM509750 6 0.3862 0.195 0.000 0.000 0.476 0.000 0.000 0.524
#> GSM509751 2 0.0000 0.962 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509753 2 0.0000 0.962 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509755 2 0.0000 0.962 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509757 2 0.0000 0.962 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509759 2 0.0000 0.962 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509761 2 0.0000 0.962 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509763 4 0.1610 0.832 0.000 0.084 0.000 0.916 0.000 0.000
#> GSM509765 4 0.0790 0.864 0.000 0.032 0.000 0.968 0.000 0.000
#> GSM509767 4 0.3817 0.373 0.000 0.432 0.000 0.568 0.000 0.000
#> GSM509769 2 0.0458 0.947 0.000 0.984 0.000 0.016 0.000 0.000
#> GSM509771 4 0.3847 0.311 0.000 0.456 0.000 0.544 0.000 0.000
#> GSM509773 4 0.3782 0.416 0.000 0.412 0.000 0.588 0.000 0.000
#> GSM509775 4 0.0000 0.878 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM509777 4 0.0000 0.878 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM509779 4 0.0000 0.878 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM509781 4 0.0000 0.878 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM509783 4 0.0000 0.878 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM509785 4 0.0000 0.878 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM509752 2 0.0000 0.962 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509754 2 0.0000 0.962 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509756 2 0.0000 0.962 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509758 2 0.0000 0.962 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509760 2 0.0000 0.962 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509762 2 0.0000 0.962 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509764 2 0.0000 0.962 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509766 4 0.3782 0.416 0.000 0.412 0.000 0.588 0.000 0.000
#> GSM509768 4 0.1075 0.856 0.000 0.048 0.000 0.952 0.000 0.000
#> GSM509770 2 0.1327 0.899 0.000 0.936 0.000 0.064 0.000 0.000
#> GSM509772 2 0.0000 0.962 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM509774 4 0.0000 0.878 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM509776 2 0.3847 0.136 0.000 0.544 0.000 0.456 0.000 0.000
#> GSM509778 4 0.0000 0.878 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM509780 4 0.0000 0.878 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM509782 4 0.0000 0.878 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM509784 4 0.0000 0.878 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM509786 4 0.0000 0.878 0.000 0.000 0.000 1.000 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 disease.state(p) time(p) k
#> ATC:pam 81 2.25e-15 1.79e-12 2
#> ATC:pam 77 9.00e-19 3.70e-12 3
#> ATC:pam 76 8.89e-23 1.89e-10 4
#> ATC:pam 79 2.36e-19 7.35e-07 5
#> ATC:pam 69 1.16e-19 3.70e-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", "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 19175 rows and 81 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 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 1.000 1.000 0.5005 0.500 0.500
#> 3 3 0.928 0.962 0.979 0.3014 0.844 0.689
#> 4 4 0.789 0.839 0.889 0.0894 0.911 0.748
#> 5 5 0.776 0.799 0.864 0.0716 0.922 0.724
#> 6 6 0.880 0.861 0.906 0.0396 0.962 0.838
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
#> GSM509706 1 0 1 1 0
#> GSM509711 1 0 1 1 0
#> GSM509714 1 0 1 1 0
#> GSM509719 1 0 1 1 0
#> GSM509724 1 0 1 1 0
#> GSM509729 1 0 1 1 0
#> GSM509707 1 0 1 1 0
#> GSM509712 1 0 1 1 0
#> GSM509715 1 0 1 1 0
#> GSM509720 1 0 1 1 0
#> GSM509725 1 0 1 1 0
#> GSM509730 1 0 1 1 0
#> GSM509708 1 0 1 1 0
#> GSM509713 1 0 1 1 0
#> GSM509716 1 0 1 1 0
#> GSM509721 1 0 1 1 0
#> GSM509726 1 0 1 1 0
#> GSM509731 1 0 1 1 0
#> GSM509709 1 0 1 1 0
#> GSM509717 1 0 1 1 0
#> GSM509722 1 0 1 1 0
#> GSM509727 1 0 1 1 0
#> GSM509710 1 0 1 1 0
#> GSM509718 1 0 1 1 0
#> GSM509723 1 0 1 1 0
#> GSM509728 1 0 1 1 0
#> GSM509732 1 0 1 1 0
#> GSM509736 1 0 1 1 0
#> GSM509741 1 0 1 1 0
#> GSM509746 1 0 1 1 0
#> GSM509733 1 0 1 1 0
#> GSM509737 1 0 1 1 0
#> GSM509742 1 0 1 1 0
#> GSM509747 1 0 1 1 0
#> GSM509734 1 0 1 1 0
#> GSM509738 1 0 1 1 0
#> GSM509743 1 0 1 1 0
#> GSM509748 1 0 1 1 0
#> GSM509735 1 0 1 1 0
#> GSM509739 1 0 1 1 0
#> GSM509744 1 0 1 1 0
#> GSM509749 1 0 1 1 0
#> GSM509740 1 0 1 1 0
#> GSM509745 1 0 1 1 0
#> GSM509750 1 0 1 1 0
#> GSM509751 2 0 1 0 1
#> GSM509753 2 0 1 0 1
#> GSM509755 2 0 1 0 1
#> GSM509757 2 0 1 0 1
#> GSM509759 2 0 1 0 1
#> GSM509761 2 0 1 0 1
#> GSM509763 2 0 1 0 1
#> GSM509765 2 0 1 0 1
#> GSM509767 2 0 1 0 1
#> GSM509769 2 0 1 0 1
#> GSM509771 2 0 1 0 1
#> GSM509773 2 0 1 0 1
#> GSM509775 2 0 1 0 1
#> GSM509777 2 0 1 0 1
#> GSM509779 2 0 1 0 1
#> GSM509781 2 0 1 0 1
#> GSM509783 2 0 1 0 1
#> GSM509785 2 0 1 0 1
#> GSM509752 2 0 1 0 1
#> GSM509754 2 0 1 0 1
#> GSM509756 2 0 1 0 1
#> GSM509758 2 0 1 0 1
#> GSM509760 2 0 1 0 1
#> GSM509762 2 0 1 0 1
#> GSM509764 2 0 1 0 1
#> GSM509766 2 0 1 0 1
#> GSM509768 2 0 1 0 1
#> GSM509770 2 0 1 0 1
#> GSM509772 2 0 1 0 1
#> GSM509774 2 0 1 0 1
#> GSM509776 2 0 1 0 1
#> GSM509778 2 0 1 0 1
#> GSM509780 2 0 1 0 1
#> GSM509782 2 0 1 0 1
#> GSM509784 2 0 1 0 1
#> GSM509786 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM509706 1 0.000 0.912 1.000 0 0.000
#> GSM509711 1 0.533 0.657 0.728 0 0.272
#> GSM509714 1 0.606 0.509 0.616 0 0.384
#> GSM509719 1 0.319 0.878 0.888 0 0.112
#> GSM509724 1 0.000 0.912 1.000 0 0.000
#> GSM509729 1 0.000 0.912 1.000 0 0.000
#> GSM509707 1 0.000 0.912 1.000 0 0.000
#> GSM509712 1 0.606 0.509 0.616 0 0.384
#> GSM509715 3 0.000 1.000 0.000 0 1.000
#> GSM509720 1 0.319 0.878 0.888 0 0.112
#> GSM509725 1 0.000 0.912 1.000 0 0.000
#> GSM509730 1 0.319 0.878 0.888 0 0.112
#> GSM509708 1 0.000 0.912 1.000 0 0.000
#> GSM509713 1 0.000 0.912 1.000 0 0.000
#> GSM509716 3 0.000 1.000 0.000 0 1.000
#> GSM509721 1 0.319 0.878 0.888 0 0.112
#> GSM509726 1 0.000 0.912 1.000 0 0.000
#> GSM509731 3 0.000 1.000 0.000 0 1.000
#> GSM509709 1 0.000 0.912 1.000 0 0.000
#> GSM509717 3 0.000 1.000 0.000 0 1.000
#> GSM509722 1 0.319 0.878 0.888 0 0.112
#> GSM509727 3 0.000 1.000 0.000 0 1.000
#> GSM509710 1 0.000 0.912 1.000 0 0.000
#> GSM509718 3 0.000 1.000 0.000 0 1.000
#> GSM509723 1 0.319 0.878 0.888 0 0.112
#> GSM509728 3 0.000 1.000 0.000 0 1.000
#> GSM509732 3 0.000 1.000 0.000 0 1.000
#> GSM509736 3 0.000 1.000 0.000 0 1.000
#> GSM509741 3 0.000 1.000 0.000 0 1.000
#> GSM509746 3 0.000 1.000 0.000 0 1.000
#> GSM509733 3 0.000 1.000 0.000 0 1.000
#> GSM509737 3 0.000 1.000 0.000 0 1.000
#> GSM509742 3 0.000 1.000 0.000 0 1.000
#> GSM509747 3 0.000 1.000 0.000 0 1.000
#> GSM509734 3 0.000 1.000 0.000 0 1.000
#> GSM509738 3 0.000 1.000 0.000 0 1.000
#> GSM509743 3 0.000 1.000 0.000 0 1.000
#> GSM509748 3 0.000 1.000 0.000 0 1.000
#> GSM509735 1 0.000 0.912 1.000 0 0.000
#> GSM509739 1 0.000 0.912 1.000 0 0.000
#> GSM509744 3 0.000 1.000 0.000 0 1.000
#> GSM509749 3 0.000 1.000 0.000 0 1.000
#> GSM509740 3 0.000 1.000 0.000 0 1.000
#> GSM509745 3 0.000 1.000 0.000 0 1.000
#> GSM509750 3 0.000 1.000 0.000 0 1.000
#> GSM509751 2 0.000 1.000 0.000 1 0.000
#> GSM509753 2 0.000 1.000 0.000 1 0.000
#> GSM509755 2 0.000 1.000 0.000 1 0.000
#> GSM509757 2 0.000 1.000 0.000 1 0.000
#> GSM509759 2 0.000 1.000 0.000 1 0.000
#> GSM509761 2 0.000 1.000 0.000 1 0.000
#> GSM509763 2 0.000 1.000 0.000 1 0.000
#> GSM509765 2 0.000 1.000 0.000 1 0.000
#> GSM509767 2 0.000 1.000 0.000 1 0.000
#> GSM509769 2 0.000 1.000 0.000 1 0.000
#> GSM509771 2 0.000 1.000 0.000 1 0.000
#> GSM509773 2 0.000 1.000 0.000 1 0.000
#> GSM509775 2 0.000 1.000 0.000 1 0.000
#> GSM509777 2 0.000 1.000 0.000 1 0.000
#> GSM509779 2 0.000 1.000 0.000 1 0.000
#> GSM509781 2 0.000 1.000 0.000 1 0.000
#> GSM509783 2 0.000 1.000 0.000 1 0.000
#> GSM509785 2 0.000 1.000 0.000 1 0.000
#> GSM509752 2 0.000 1.000 0.000 1 0.000
#> GSM509754 2 0.000 1.000 0.000 1 0.000
#> GSM509756 2 0.000 1.000 0.000 1 0.000
#> GSM509758 2 0.000 1.000 0.000 1 0.000
#> GSM509760 2 0.000 1.000 0.000 1 0.000
#> GSM509762 2 0.000 1.000 0.000 1 0.000
#> GSM509764 2 0.000 1.000 0.000 1 0.000
#> GSM509766 2 0.000 1.000 0.000 1 0.000
#> GSM509768 2 0.000 1.000 0.000 1 0.000
#> GSM509770 2 0.000 1.000 0.000 1 0.000
#> GSM509772 2 0.000 1.000 0.000 1 0.000
#> GSM509774 2 0.000 1.000 0.000 1 0.000
#> GSM509776 2 0.000 1.000 0.000 1 0.000
#> GSM509778 2 0.000 1.000 0.000 1 0.000
#> GSM509780 2 0.000 1.000 0.000 1 0.000
#> GSM509782 2 0.000 1.000 0.000 1 0.000
#> GSM509784 2 0.000 1.000 0.000 1 0.000
#> GSM509786 2 0.000 1.000 0.000 1 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM509706 1 0.0000 0.908 1.000 0.000 0.000 0.000
#> GSM509711 1 0.0469 0.909 0.988 0.000 0.012 0.000
#> GSM509714 1 0.3311 0.860 0.828 0.000 0.172 0.000
#> GSM509719 1 0.3311 0.860 0.828 0.000 0.172 0.000
#> GSM509724 1 0.0000 0.908 1.000 0.000 0.000 0.000
#> GSM509729 1 0.1118 0.905 0.964 0.000 0.036 0.000
#> GSM509707 1 0.0000 0.908 1.000 0.000 0.000 0.000
#> GSM509712 1 0.3311 0.860 0.828 0.000 0.172 0.000
#> GSM509715 3 0.4941 0.631 0.000 0.000 0.564 0.436
#> GSM509720 1 0.3311 0.860 0.828 0.000 0.172 0.000
#> GSM509725 1 0.0000 0.908 1.000 0.000 0.000 0.000
#> GSM509730 1 0.3311 0.860 0.828 0.000 0.172 0.000
#> GSM509708 1 0.0000 0.908 1.000 0.000 0.000 0.000
#> GSM509713 1 0.0336 0.909 0.992 0.000 0.008 0.000
#> GSM509716 3 0.4941 0.631 0.000 0.000 0.564 0.436
#> GSM509721 1 0.3311 0.860 0.828 0.000 0.172 0.000
#> GSM509726 1 0.0592 0.905 0.984 0.000 0.016 0.000
#> GSM509731 1 0.4356 0.687 0.708 0.000 0.292 0.000
#> GSM509709 1 0.0000 0.908 1.000 0.000 0.000 0.000
#> GSM509717 3 0.4941 0.631 0.000 0.000 0.564 0.436
#> GSM509722 1 0.3311 0.860 0.828 0.000 0.172 0.000
#> GSM509727 3 0.0000 0.930 0.000 0.000 1.000 0.000
#> GSM509710 1 0.0000 0.908 1.000 0.000 0.000 0.000
#> GSM509718 3 0.4941 0.631 0.000 0.000 0.564 0.436
#> GSM509723 1 0.3311 0.860 0.828 0.000 0.172 0.000
#> GSM509728 3 0.0000 0.930 0.000 0.000 1.000 0.000
#> GSM509732 3 0.0000 0.930 0.000 0.000 1.000 0.000
#> GSM509736 3 0.0000 0.930 0.000 0.000 1.000 0.000
#> GSM509741 3 0.0000 0.930 0.000 0.000 1.000 0.000
#> GSM509746 3 0.0000 0.930 0.000 0.000 1.000 0.000
#> GSM509733 3 0.0000 0.930 0.000 0.000 1.000 0.000
#> GSM509737 3 0.0000 0.930 0.000 0.000 1.000 0.000
#> GSM509742 3 0.0000 0.930 0.000 0.000 1.000 0.000
#> GSM509747 3 0.0000 0.930 0.000 0.000 1.000 0.000
#> GSM509734 3 0.0000 0.930 0.000 0.000 1.000 0.000
#> GSM509738 3 0.0000 0.930 0.000 0.000 1.000 0.000
#> GSM509743 3 0.0000 0.930 0.000 0.000 1.000 0.000
#> GSM509748 3 0.0000 0.930 0.000 0.000 1.000 0.000
#> GSM509735 1 0.0000 0.908 1.000 0.000 0.000 0.000
#> GSM509739 1 0.0336 0.909 0.992 0.000 0.008 0.000
#> GSM509744 3 0.0000 0.930 0.000 0.000 1.000 0.000
#> GSM509749 3 0.0000 0.930 0.000 0.000 1.000 0.000
#> GSM509740 3 0.1867 0.864 0.072 0.000 0.928 0.000
#> GSM509745 3 0.0000 0.930 0.000 0.000 1.000 0.000
#> GSM509750 3 0.0000 0.930 0.000 0.000 1.000 0.000
#> GSM509751 2 0.0000 0.900 0.000 1.000 0.000 0.000
#> GSM509753 2 0.0000 0.900 0.000 1.000 0.000 0.000
#> GSM509755 2 0.0336 0.893 0.000 0.992 0.000 0.008
#> GSM509757 2 0.0336 0.893 0.000 0.992 0.000 0.008
#> GSM509759 2 0.0336 0.893 0.000 0.992 0.000 0.008
#> GSM509761 2 0.0000 0.900 0.000 1.000 0.000 0.000
#> GSM509763 2 0.0000 0.900 0.000 1.000 0.000 0.000
#> GSM509765 2 0.0000 0.900 0.000 1.000 0.000 0.000
#> GSM509767 2 0.0000 0.900 0.000 1.000 0.000 0.000
#> GSM509769 2 0.0000 0.900 0.000 1.000 0.000 0.000
#> GSM509771 2 0.0000 0.900 0.000 1.000 0.000 0.000
#> GSM509773 2 0.0000 0.900 0.000 1.000 0.000 0.000
#> GSM509775 2 0.3074 0.593 0.000 0.848 0.000 0.152
#> GSM509777 2 0.0000 0.900 0.000 1.000 0.000 0.000
#> GSM509779 2 0.4977 -0.773 0.000 0.540 0.000 0.460
#> GSM509781 4 0.4955 0.995 0.000 0.444 0.000 0.556
#> GSM509783 4 0.4955 0.995 0.000 0.444 0.000 0.556
#> GSM509785 4 0.4955 0.995 0.000 0.444 0.000 0.556
#> GSM509752 2 0.0000 0.900 0.000 1.000 0.000 0.000
#> GSM509754 2 0.0000 0.900 0.000 1.000 0.000 0.000
#> GSM509756 2 0.0000 0.900 0.000 1.000 0.000 0.000
#> GSM509758 2 0.0000 0.900 0.000 1.000 0.000 0.000
#> GSM509760 4 0.4977 0.968 0.000 0.460 0.000 0.540
#> GSM509762 2 0.0000 0.900 0.000 1.000 0.000 0.000
#> GSM509764 2 0.0336 0.893 0.000 0.992 0.000 0.008
#> GSM509766 2 0.0000 0.900 0.000 1.000 0.000 0.000
#> GSM509768 2 0.4697 -0.409 0.000 0.644 0.000 0.356
#> GSM509770 4 0.4961 0.990 0.000 0.448 0.000 0.552
#> GSM509772 2 0.0336 0.893 0.000 0.992 0.000 0.008
#> GSM509774 2 0.4804 -0.522 0.000 0.616 0.000 0.384
#> GSM509776 4 0.4955 0.995 0.000 0.444 0.000 0.556
#> GSM509778 2 0.0469 0.885 0.000 0.988 0.000 0.012
#> GSM509780 2 0.0000 0.900 0.000 1.000 0.000 0.000
#> GSM509782 4 0.4955 0.995 0.000 0.444 0.000 0.556
#> GSM509784 4 0.4955 0.995 0.000 0.444 0.000 0.556
#> GSM509786 4 0.4955 0.995 0.000 0.444 0.000 0.556
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM509706 1 0.0000 0.920 1.000 0.000 0.000 0.000 0.000
#> GSM509711 1 0.0000 0.920 1.000 0.000 0.000 0.000 0.000
#> GSM509714 1 0.2891 0.870 0.824 0.000 0.176 0.000 0.000
#> GSM509719 1 0.2891 0.870 0.824 0.000 0.176 0.000 0.000
#> GSM509724 1 0.0000 0.920 1.000 0.000 0.000 0.000 0.000
#> GSM509729 1 0.0000 0.920 1.000 0.000 0.000 0.000 0.000
#> GSM509707 1 0.0000 0.920 1.000 0.000 0.000 0.000 0.000
#> GSM509712 1 0.2891 0.870 0.824 0.000 0.176 0.000 0.000
#> GSM509715 5 0.6551 0.275 0.000 0.000 0.384 0.200 0.416
#> GSM509720 1 0.2891 0.870 0.824 0.000 0.176 0.000 0.000
#> GSM509725 1 0.0000 0.920 1.000 0.000 0.000 0.000 0.000
#> GSM509730 1 0.2891 0.870 0.824 0.000 0.176 0.000 0.000
#> GSM509708 1 0.0000 0.920 1.000 0.000 0.000 0.000 0.000
#> GSM509713 1 0.0000 0.920 1.000 0.000 0.000 0.000 0.000
#> GSM509716 5 0.6551 0.275 0.000 0.000 0.384 0.200 0.416
#> GSM509721 1 0.2891 0.870 0.824 0.000 0.176 0.000 0.000
#> GSM509726 1 0.0000 0.920 1.000 0.000 0.000 0.000 0.000
#> GSM509731 1 0.3988 0.787 0.776 0.000 0.024 0.192 0.008
#> GSM509709 1 0.0000 0.920 1.000 0.000 0.000 0.000 0.000
#> GSM509717 5 0.6551 0.275 0.000 0.000 0.384 0.200 0.416
#> GSM509722 1 0.2891 0.870 0.824 0.000 0.176 0.000 0.000
#> GSM509727 3 0.0000 0.787 0.000 0.000 1.000 0.000 0.000
#> GSM509710 1 0.0000 0.920 1.000 0.000 0.000 0.000 0.000
#> GSM509718 5 0.6551 0.275 0.000 0.000 0.384 0.200 0.416
#> GSM509723 1 0.2891 0.870 0.824 0.000 0.176 0.000 0.000
#> GSM509728 3 0.0000 0.787 0.000 0.000 1.000 0.000 0.000
#> GSM509732 5 0.4219 0.258 0.000 0.000 0.416 0.000 0.584
#> GSM509736 3 0.0290 0.780 0.008 0.000 0.992 0.000 0.000
#> GSM509741 3 0.3039 0.717 0.000 0.000 0.808 0.000 0.192
#> GSM509746 5 0.4219 0.258 0.000 0.000 0.416 0.000 0.584
#> GSM509733 5 0.4235 0.247 0.000 0.000 0.424 0.000 0.576
#> GSM509737 3 0.0162 0.785 0.004 0.000 0.996 0.000 0.000
#> GSM509742 3 0.3039 0.717 0.000 0.000 0.808 0.000 0.192
#> GSM509747 5 0.4256 0.249 0.000 0.000 0.436 0.000 0.564
#> GSM509734 3 0.2127 0.598 0.108 0.000 0.892 0.000 0.000
#> GSM509738 3 0.0000 0.787 0.000 0.000 1.000 0.000 0.000
#> GSM509743 3 0.3039 0.717 0.000 0.000 0.808 0.000 0.192
#> GSM509748 5 0.4256 0.249 0.000 0.000 0.436 0.000 0.564
#> GSM509735 1 0.0000 0.920 1.000 0.000 0.000 0.000 0.000
#> GSM509739 1 0.0000 0.920 1.000 0.000 0.000 0.000 0.000
#> GSM509744 3 0.3039 0.717 0.000 0.000 0.808 0.000 0.192
#> GSM509749 3 0.3039 0.717 0.000 0.000 0.808 0.000 0.192
#> GSM509740 3 0.0963 0.742 0.036 0.000 0.964 0.000 0.000
#> GSM509745 3 0.0000 0.787 0.000 0.000 1.000 0.000 0.000
#> GSM509750 3 0.3039 0.717 0.000 0.000 0.808 0.000 0.192
#> GSM509751 2 0.0000 0.935 0.000 1.000 0.000 0.000 0.000
#> GSM509753 2 0.0000 0.935 0.000 1.000 0.000 0.000 0.000
#> GSM509755 2 0.0290 0.931 0.000 0.992 0.000 0.008 0.000
#> GSM509757 2 0.0404 0.929 0.000 0.988 0.000 0.012 0.000
#> GSM509759 2 0.0404 0.929 0.000 0.988 0.000 0.012 0.000
#> GSM509761 2 0.0510 0.939 0.000 0.984 0.000 0.016 0.000
#> GSM509763 2 0.0510 0.939 0.000 0.984 0.000 0.016 0.000
#> GSM509765 2 0.0510 0.939 0.000 0.984 0.000 0.016 0.000
#> GSM509767 2 0.0290 0.931 0.000 0.992 0.000 0.008 0.000
#> GSM509769 2 0.0510 0.939 0.000 0.984 0.000 0.016 0.000
#> GSM509771 2 0.0290 0.931 0.000 0.992 0.000 0.008 0.000
#> GSM509773 2 0.0510 0.939 0.000 0.984 0.000 0.016 0.000
#> GSM509775 2 0.2605 0.766 0.000 0.852 0.000 0.148 0.000
#> GSM509777 2 0.0510 0.939 0.000 0.984 0.000 0.016 0.000
#> GSM509779 4 0.3242 0.989 0.000 0.216 0.000 0.784 0.000
#> GSM509781 4 0.3210 0.992 0.000 0.212 0.000 0.788 0.000
#> GSM509783 4 0.3210 0.992 0.000 0.212 0.000 0.788 0.000
#> GSM509785 4 0.3210 0.992 0.000 0.212 0.000 0.788 0.000
#> GSM509752 2 0.0510 0.939 0.000 0.984 0.000 0.016 0.000
#> GSM509754 2 0.0510 0.939 0.000 0.984 0.000 0.016 0.000
#> GSM509756 2 0.0510 0.939 0.000 0.984 0.000 0.016 0.000
#> GSM509758 2 0.0510 0.939 0.000 0.984 0.000 0.016 0.000
#> GSM509760 2 0.4302 -0.323 0.000 0.520 0.000 0.480 0.000
#> GSM509762 2 0.0510 0.939 0.000 0.984 0.000 0.016 0.000
#> GSM509764 2 0.0404 0.929 0.000 0.988 0.000 0.012 0.000
#> GSM509766 2 0.0510 0.939 0.000 0.984 0.000 0.016 0.000
#> GSM509768 4 0.3534 0.938 0.000 0.256 0.000 0.744 0.000
#> GSM509770 4 0.3210 0.992 0.000 0.212 0.000 0.788 0.000
#> GSM509772 2 0.0404 0.929 0.000 0.988 0.000 0.012 0.000
#> GSM509774 4 0.3274 0.986 0.000 0.220 0.000 0.780 0.000
#> GSM509776 4 0.3210 0.992 0.000 0.212 0.000 0.788 0.000
#> GSM509778 2 0.3837 0.398 0.000 0.692 0.000 0.308 0.000
#> GSM509780 2 0.0510 0.939 0.000 0.984 0.000 0.016 0.000
#> GSM509782 4 0.3210 0.992 0.000 0.212 0.000 0.788 0.000
#> GSM509784 4 0.3210 0.992 0.000 0.212 0.000 0.788 0.000
#> GSM509786 4 0.3210 0.992 0.000 0.212 0.000 0.788 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM509706 1 0.0000 0.932 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509711 1 0.0146 0.931 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM509714 1 0.1501 0.914 0.924 0.000 0.000 0.000 0.000 0.076
#> GSM509719 1 0.1444 0.916 0.928 0.000 0.000 0.000 0.000 0.072
#> GSM509724 1 0.0000 0.932 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509729 1 0.0000 0.932 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509707 1 0.0000 0.932 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509712 1 0.1501 0.914 0.924 0.000 0.000 0.000 0.000 0.076
#> GSM509715 5 0.3240 1.000 0.000 0.000 0.000 0.004 0.752 0.244
#> GSM509720 1 0.1444 0.916 0.928 0.000 0.000 0.000 0.000 0.072
#> GSM509725 1 0.0000 0.932 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509730 1 0.1444 0.916 0.928 0.000 0.000 0.000 0.000 0.072
#> GSM509708 1 0.0000 0.932 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509713 1 0.0000 0.932 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509716 5 0.3240 1.000 0.000 0.000 0.000 0.004 0.752 0.244
#> GSM509721 1 0.1444 0.916 0.928 0.000 0.000 0.000 0.000 0.072
#> GSM509726 1 0.0000 0.932 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509731 1 0.4962 0.420 0.628 0.000 0.000 0.004 0.092 0.276
#> GSM509709 1 0.0000 0.932 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509717 5 0.3240 1.000 0.000 0.000 0.000 0.004 0.752 0.244
#> GSM509722 1 0.1444 0.916 0.928 0.000 0.000 0.000 0.000 0.072
#> GSM509727 6 0.0146 0.862 0.000 0.000 0.000 0.000 0.004 0.996
#> GSM509710 1 0.0000 0.932 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509718 5 0.3240 1.000 0.000 0.000 0.000 0.004 0.752 0.244
#> GSM509723 1 0.1444 0.916 0.928 0.000 0.000 0.000 0.000 0.072
#> GSM509728 6 0.0000 0.864 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM509732 3 0.1327 0.966 0.000 0.000 0.936 0.000 0.000 0.064
#> GSM509736 6 0.0000 0.864 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM509741 6 0.1714 0.864 0.000 0.000 0.092 0.000 0.000 0.908
#> GSM509746 3 0.1327 0.966 0.000 0.000 0.936 0.000 0.000 0.064
#> GSM509733 3 0.1863 0.936 0.000 0.000 0.896 0.000 0.000 0.104
#> GSM509737 6 0.1411 0.790 0.060 0.000 0.004 0.000 0.000 0.936
#> GSM509742 6 0.1714 0.864 0.000 0.000 0.092 0.000 0.000 0.908
#> GSM509747 3 0.1753 0.959 0.004 0.000 0.912 0.000 0.000 0.084
#> GSM509734 6 0.3707 0.367 0.312 0.000 0.008 0.000 0.000 0.680
#> GSM509738 6 0.0000 0.864 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM509743 6 0.1714 0.864 0.000 0.000 0.092 0.000 0.000 0.908
#> GSM509748 3 0.1663 0.961 0.000 0.000 0.912 0.000 0.000 0.088
#> GSM509735 1 0.0000 0.932 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509739 1 0.0000 0.932 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM509744 6 0.1714 0.864 0.000 0.000 0.092 0.000 0.000 0.908
#> GSM509749 6 0.1714 0.864 0.000 0.000 0.092 0.000 0.000 0.908
#> GSM509740 1 0.3804 0.362 0.576 0.000 0.000 0.000 0.000 0.424
#> GSM509745 6 0.0000 0.864 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM509750 6 0.1714 0.864 0.000 0.000 0.092 0.000 0.000 0.908
#> GSM509751 2 0.0603 0.880 0.000 0.980 0.000 0.016 0.004 0.000
#> GSM509753 2 0.0291 0.876 0.000 0.992 0.000 0.004 0.004 0.000
#> GSM509755 2 0.3227 0.783 0.000 0.824 0.060 0.000 0.116 0.000
#> GSM509757 2 0.4294 0.677 0.000 0.692 0.060 0.000 0.248 0.000
#> GSM509759 2 0.4294 0.677 0.000 0.692 0.060 0.000 0.248 0.000
#> GSM509761 2 0.1444 0.895 0.000 0.928 0.000 0.072 0.000 0.000
#> GSM509763 2 0.1444 0.895 0.000 0.928 0.000 0.072 0.000 0.000
#> GSM509765 2 0.1444 0.895 0.000 0.928 0.000 0.072 0.000 0.000
#> GSM509767 2 0.0405 0.878 0.000 0.988 0.000 0.008 0.004 0.000
#> GSM509769 2 0.1444 0.895 0.000 0.928 0.000 0.072 0.000 0.000
#> GSM509771 2 0.0405 0.878 0.000 0.988 0.000 0.008 0.004 0.000
#> GSM509773 2 0.1444 0.895 0.000 0.928 0.000 0.072 0.000 0.000
#> GSM509775 2 0.2883 0.762 0.000 0.788 0.000 0.212 0.000 0.000
#> GSM509777 2 0.1444 0.895 0.000 0.928 0.000 0.072 0.000 0.000
#> GSM509779 4 0.0865 0.904 0.000 0.036 0.000 0.964 0.000 0.000
#> GSM509781 4 0.0632 0.905 0.000 0.024 0.000 0.976 0.000 0.000
#> GSM509783 4 0.0632 0.905 0.000 0.024 0.000 0.976 0.000 0.000
#> GSM509785 4 0.0632 0.905 0.000 0.024 0.000 0.976 0.000 0.000
#> GSM509752 2 0.1444 0.895 0.000 0.928 0.000 0.072 0.000 0.000
#> GSM509754 2 0.1387 0.895 0.000 0.932 0.000 0.068 0.000 0.000
#> GSM509756 2 0.2941 0.868 0.000 0.868 0.024 0.060 0.048 0.000
#> GSM509758 2 0.1444 0.895 0.000 0.928 0.000 0.072 0.000 0.000
#> GSM509760 4 0.3076 0.698 0.000 0.240 0.000 0.760 0.000 0.000
#> GSM509762 2 0.1387 0.895 0.000 0.932 0.000 0.068 0.000 0.000
#> GSM509764 2 0.4537 0.683 0.000 0.684 0.060 0.008 0.248 0.000
#> GSM509766 2 0.1444 0.895 0.000 0.928 0.000 0.072 0.000 0.000
#> GSM509768 4 0.2340 0.806 0.000 0.148 0.000 0.852 0.000 0.000
#> GSM509770 4 0.1007 0.900 0.000 0.044 0.000 0.956 0.000 0.000
#> GSM509772 2 0.4294 0.677 0.000 0.692 0.060 0.000 0.248 0.000
#> GSM509774 4 0.1007 0.901 0.000 0.044 0.000 0.956 0.000 0.000
#> GSM509776 4 0.0713 0.905 0.000 0.028 0.000 0.972 0.000 0.000
#> GSM509778 4 0.3857 0.120 0.000 0.468 0.000 0.532 0.000 0.000
#> GSM509780 2 0.1501 0.893 0.000 0.924 0.000 0.076 0.000 0.000
#> GSM509782 4 0.0632 0.905 0.000 0.024 0.000 0.976 0.000 0.000
#> GSM509784 4 0.0713 0.905 0.000 0.028 0.000 0.972 0.000 0.000
#> GSM509786 4 0.0632 0.905 0.000 0.024 0.000 0.976 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 disease.state(p) time(p) k
#> ATC:mclust 81 2.58e-18 2.22e-15 2
#> ATC:mclust 81 2.64e-23 5.91e-13 3
#> ATC:mclust 78 9.56e-22 1.24e-10 4
#> ATC:mclust 70 1.20e-21 1.07e-09 5
#> ATC:mclust 77 1.48e-22 1.54e-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", "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 19175 rows and 81 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 0.970 0.987 0.5032 0.496 0.496
#> 3 3 0.953 0.942 0.976 0.2792 0.811 0.635
#> 4 4 0.733 0.738 0.854 0.1256 0.822 0.571
#> 5 5 0.864 0.868 0.922 0.0861 0.881 0.625
#> 6 6 0.771 0.768 0.859 0.0194 0.954 0.794
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
#> GSM509706 1 0.000 0.978 1.000 0.000
#> GSM509711 1 0.000 0.978 1.000 0.000
#> GSM509714 1 0.000 0.978 1.000 0.000
#> GSM509719 1 0.000 0.978 1.000 0.000
#> GSM509724 1 0.000 0.978 1.000 0.000
#> GSM509729 1 0.000 0.978 1.000 0.000
#> GSM509707 1 0.000 0.978 1.000 0.000
#> GSM509712 1 0.000 0.978 1.000 0.000
#> GSM509715 2 0.000 0.993 0.000 1.000
#> GSM509720 1 0.000 0.978 1.000 0.000
#> GSM509725 1 0.000 0.978 1.000 0.000
#> GSM509730 1 0.000 0.978 1.000 0.000
#> GSM509708 1 0.000 0.978 1.000 0.000
#> GSM509713 1 0.000 0.978 1.000 0.000
#> GSM509716 2 0.000 0.993 0.000 1.000
#> GSM509721 1 0.000 0.978 1.000 0.000
#> GSM509726 1 0.000 0.978 1.000 0.000
#> GSM509731 1 0.469 0.885 0.900 0.100
#> GSM509709 1 0.000 0.978 1.000 0.000
#> GSM509717 2 0.000 0.993 0.000 1.000
#> GSM509722 1 0.000 0.978 1.000 0.000
#> GSM509727 1 0.000 0.978 1.000 0.000
#> GSM509710 1 0.000 0.978 1.000 0.000
#> GSM509718 2 0.000 0.993 0.000 1.000
#> GSM509723 1 0.000 0.978 1.000 0.000
#> GSM509728 1 0.000 0.978 1.000 0.000
#> GSM509732 1 0.141 0.963 0.980 0.020
#> GSM509736 1 0.000 0.978 1.000 0.000
#> GSM509741 1 0.000 0.978 1.000 0.000
#> GSM509746 1 0.141 0.963 0.980 0.020
#> GSM509733 2 0.788 0.680 0.236 0.764
#> GSM509737 1 0.000 0.978 1.000 0.000
#> GSM509742 1 0.861 0.620 0.716 0.284
#> GSM509747 1 0.000 0.978 1.000 0.000
#> GSM509734 1 0.000 0.978 1.000 0.000
#> GSM509738 1 0.000 0.978 1.000 0.000
#> GSM509743 2 0.295 0.939 0.052 0.948
#> GSM509748 1 0.000 0.978 1.000 0.000
#> GSM509735 1 0.000 0.978 1.000 0.000
#> GSM509739 1 0.000 0.978 1.000 0.000
#> GSM509744 1 0.891 0.573 0.692 0.308
#> GSM509749 1 0.358 0.919 0.932 0.068
#> GSM509740 1 0.000 0.978 1.000 0.000
#> GSM509745 1 0.000 0.978 1.000 0.000
#> GSM509750 2 0.000 0.993 0.000 1.000
#> GSM509751 2 0.000 0.993 0.000 1.000
#> GSM509753 2 0.000 0.993 0.000 1.000
#> GSM509755 2 0.000 0.993 0.000 1.000
#> GSM509757 2 0.000 0.993 0.000 1.000
#> GSM509759 2 0.000 0.993 0.000 1.000
#> GSM509761 2 0.000 0.993 0.000 1.000
#> GSM509763 2 0.000 0.993 0.000 1.000
#> GSM509765 2 0.000 0.993 0.000 1.000
#> GSM509767 2 0.000 0.993 0.000 1.000
#> GSM509769 2 0.000 0.993 0.000 1.000
#> GSM509771 2 0.000 0.993 0.000 1.000
#> GSM509773 2 0.000 0.993 0.000 1.000
#> GSM509775 2 0.000 0.993 0.000 1.000
#> GSM509777 2 0.000 0.993 0.000 1.000
#> GSM509779 2 0.000 0.993 0.000 1.000
#> GSM509781 2 0.000 0.993 0.000 1.000
#> GSM509783 2 0.000 0.993 0.000 1.000
#> GSM509785 2 0.000 0.993 0.000 1.000
#> GSM509752 2 0.000 0.993 0.000 1.000
#> GSM509754 2 0.000 0.993 0.000 1.000
#> GSM509756 2 0.000 0.993 0.000 1.000
#> GSM509758 2 0.000 0.993 0.000 1.000
#> GSM509760 2 0.000 0.993 0.000 1.000
#> GSM509762 2 0.000 0.993 0.000 1.000
#> GSM509764 2 0.000 0.993 0.000 1.000
#> GSM509766 2 0.000 0.993 0.000 1.000
#> GSM509768 2 0.000 0.993 0.000 1.000
#> GSM509770 2 0.000 0.993 0.000 1.000
#> GSM509772 2 0.000 0.993 0.000 1.000
#> GSM509774 2 0.000 0.993 0.000 1.000
#> GSM509776 2 0.000 0.993 0.000 1.000
#> GSM509778 2 0.000 0.993 0.000 1.000
#> GSM509780 2 0.000 0.993 0.000 1.000
#> GSM509782 2 0.000 0.993 0.000 1.000
#> GSM509784 2 0.000 0.993 0.000 1.000
#> GSM509786 2 0.000 0.993 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM509706 1 0.0000 0.992 1.000 0.000 0.000
#> GSM509711 1 0.0000 0.992 1.000 0.000 0.000
#> GSM509714 1 0.0000 0.992 1.000 0.000 0.000
#> GSM509719 1 0.0000 0.992 1.000 0.000 0.000
#> GSM509724 1 0.0000 0.992 1.000 0.000 0.000
#> GSM509729 1 0.0000 0.992 1.000 0.000 0.000
#> GSM509707 1 0.0000 0.992 1.000 0.000 0.000
#> GSM509712 1 0.0000 0.992 1.000 0.000 0.000
#> GSM509715 2 0.0000 0.985 0.000 1.000 0.000
#> GSM509720 1 0.0000 0.992 1.000 0.000 0.000
#> GSM509725 1 0.0000 0.992 1.000 0.000 0.000
#> GSM509730 1 0.0000 0.992 1.000 0.000 0.000
#> GSM509708 1 0.0000 0.992 1.000 0.000 0.000
#> GSM509713 1 0.0000 0.992 1.000 0.000 0.000
#> GSM509716 2 0.0000 0.985 0.000 1.000 0.000
#> GSM509721 1 0.0000 0.992 1.000 0.000 0.000
#> GSM509726 1 0.0000 0.992 1.000 0.000 0.000
#> GSM509731 1 0.4399 0.740 0.812 0.188 0.000
#> GSM509709 1 0.0000 0.992 1.000 0.000 0.000
#> GSM509717 2 0.0000 0.985 0.000 1.000 0.000
#> GSM509722 1 0.0000 0.992 1.000 0.000 0.000
#> GSM509727 1 0.0000 0.992 1.000 0.000 0.000
#> GSM509710 1 0.0000 0.992 1.000 0.000 0.000
#> GSM509718 2 0.0000 0.985 0.000 1.000 0.000
#> GSM509723 1 0.0000 0.992 1.000 0.000 0.000
#> GSM509728 1 0.0000 0.992 1.000 0.000 0.000
#> GSM509732 3 0.0000 0.915 0.000 0.000 1.000
#> GSM509736 1 0.0237 0.988 0.996 0.000 0.004
#> GSM509741 3 0.0000 0.915 0.000 0.000 1.000
#> GSM509746 3 0.0000 0.915 0.000 0.000 1.000
#> GSM509733 3 0.0000 0.915 0.000 0.000 1.000
#> GSM509737 1 0.0000 0.992 1.000 0.000 0.000
#> GSM509742 3 0.0000 0.915 0.000 0.000 1.000
#> GSM509747 3 0.0000 0.915 0.000 0.000 1.000
#> GSM509734 3 0.5216 0.613 0.260 0.000 0.740
#> GSM509738 1 0.0000 0.992 1.000 0.000 0.000
#> GSM509743 3 0.0000 0.915 0.000 0.000 1.000
#> GSM509748 3 0.0000 0.915 0.000 0.000 1.000
#> GSM509735 1 0.0000 0.992 1.000 0.000 0.000
#> GSM509739 1 0.0000 0.992 1.000 0.000 0.000
#> GSM509744 3 0.0000 0.915 0.000 0.000 1.000
#> GSM509749 3 0.0000 0.915 0.000 0.000 1.000
#> GSM509740 1 0.0000 0.992 1.000 0.000 0.000
#> GSM509745 1 0.0000 0.992 1.000 0.000 0.000
#> GSM509750 3 0.0000 0.915 0.000 0.000 1.000
#> GSM509751 2 0.4291 0.776 0.000 0.820 0.180
#> GSM509753 2 0.2711 0.900 0.000 0.912 0.088
#> GSM509755 2 0.2165 0.926 0.000 0.936 0.064
#> GSM509757 3 0.4121 0.767 0.000 0.168 0.832
#> GSM509759 3 0.0000 0.915 0.000 0.000 1.000
#> GSM509761 2 0.0000 0.985 0.000 1.000 0.000
#> GSM509763 2 0.0237 0.983 0.000 0.996 0.004
#> GSM509765 2 0.0000 0.985 0.000 1.000 0.000
#> GSM509767 3 0.6295 0.141 0.000 0.472 0.528
#> GSM509769 2 0.0000 0.985 0.000 1.000 0.000
#> GSM509771 3 0.6026 0.419 0.000 0.376 0.624
#> GSM509773 2 0.0237 0.983 0.000 0.996 0.004
#> GSM509775 2 0.0000 0.985 0.000 1.000 0.000
#> GSM509777 2 0.0000 0.985 0.000 1.000 0.000
#> GSM509779 2 0.0000 0.985 0.000 1.000 0.000
#> GSM509781 2 0.0000 0.985 0.000 1.000 0.000
#> GSM509783 2 0.0000 0.985 0.000 1.000 0.000
#> GSM509785 2 0.0000 0.985 0.000 1.000 0.000
#> GSM509752 2 0.0237 0.983 0.000 0.996 0.004
#> GSM509754 2 0.0237 0.983 0.000 0.996 0.004
#> GSM509756 2 0.0000 0.985 0.000 1.000 0.000
#> GSM509758 2 0.0000 0.985 0.000 1.000 0.000
#> GSM509760 2 0.0000 0.985 0.000 1.000 0.000
#> GSM509762 2 0.0237 0.983 0.000 0.996 0.004
#> GSM509764 2 0.3340 0.861 0.000 0.880 0.120
#> GSM509766 2 0.0000 0.985 0.000 1.000 0.000
#> GSM509768 2 0.0000 0.985 0.000 1.000 0.000
#> GSM509770 2 0.0000 0.985 0.000 1.000 0.000
#> GSM509772 3 0.0000 0.915 0.000 0.000 1.000
#> GSM509774 2 0.0000 0.985 0.000 1.000 0.000
#> GSM509776 2 0.0000 0.985 0.000 1.000 0.000
#> GSM509778 2 0.0000 0.985 0.000 1.000 0.000
#> GSM509780 2 0.0237 0.983 0.000 0.996 0.004
#> GSM509782 2 0.0000 0.985 0.000 1.000 0.000
#> GSM509784 2 0.0000 0.985 0.000 1.000 0.000
#> GSM509786 2 0.0000 0.985 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM509706 1 0.0188 0.9850 0.996 0.000 0.000 0.004
#> GSM509711 1 0.0817 0.9735 0.976 0.000 0.000 0.024
#> GSM509714 1 0.0592 0.9802 0.984 0.000 0.000 0.016
#> GSM509719 1 0.0336 0.9850 0.992 0.000 0.000 0.008
#> GSM509724 1 0.0469 0.9826 0.988 0.000 0.000 0.012
#> GSM509729 1 0.1022 0.9680 0.968 0.000 0.000 0.032
#> GSM509707 1 0.0592 0.9800 0.984 0.000 0.000 0.016
#> GSM509712 1 0.0336 0.9842 0.992 0.000 0.000 0.008
#> GSM509715 4 0.3257 0.6163 0.000 0.152 0.004 0.844
#> GSM509720 1 0.0336 0.9842 0.992 0.000 0.000 0.008
#> GSM509725 1 0.0336 0.9842 0.992 0.000 0.000 0.008
#> GSM509730 1 0.1118 0.9656 0.964 0.000 0.000 0.036
#> GSM509708 1 0.0336 0.9854 0.992 0.000 0.000 0.008
#> GSM509713 1 0.0188 0.9850 0.996 0.000 0.000 0.004
#> GSM509716 4 0.3377 0.6255 0.012 0.140 0.000 0.848
#> GSM509721 1 0.1297 0.9607 0.964 0.020 0.000 0.016
#> GSM509726 1 0.0592 0.9802 0.984 0.000 0.000 0.016
#> GSM509731 4 0.5532 0.5670 0.228 0.068 0.000 0.704
#> GSM509709 1 0.0336 0.9853 0.992 0.000 0.000 0.008
#> GSM509717 4 0.3123 0.6113 0.000 0.156 0.000 0.844
#> GSM509722 1 0.0188 0.9848 0.996 0.000 0.000 0.004
#> GSM509727 4 0.5936 0.4699 0.324 0.000 0.056 0.620
#> GSM509710 1 0.0469 0.9823 0.988 0.000 0.000 0.012
#> GSM509718 4 0.3257 0.6173 0.004 0.152 0.000 0.844
#> GSM509723 1 0.0707 0.9785 0.980 0.000 0.000 0.020
#> GSM509728 3 0.7042 0.2912 0.132 0.000 0.516 0.352
#> GSM509732 3 0.1022 0.8217 0.000 0.000 0.968 0.032
#> GSM509736 4 0.7602 -0.0484 0.200 0.000 0.380 0.420
#> GSM509741 3 0.0817 0.8280 0.000 0.000 0.976 0.024
#> GSM509746 3 0.1022 0.8217 0.000 0.000 0.968 0.032
#> GSM509733 3 0.0921 0.8236 0.000 0.000 0.972 0.028
#> GSM509737 3 0.5056 0.6959 0.076 0.000 0.760 0.164
#> GSM509742 3 0.0469 0.8293 0.000 0.000 0.988 0.012
#> GSM509747 3 0.2076 0.8084 0.008 0.004 0.932 0.056
#> GSM509734 3 0.2214 0.8033 0.044 0.000 0.928 0.028
#> GSM509738 4 0.6011 -0.2841 0.040 0.000 0.480 0.480
#> GSM509743 3 0.2921 0.7791 0.000 0.000 0.860 0.140
#> GSM509748 3 0.0921 0.8236 0.000 0.000 0.972 0.028
#> GSM509735 1 0.0188 0.9850 0.996 0.000 0.000 0.004
#> GSM509739 1 0.0336 0.9836 0.992 0.000 0.000 0.008
#> GSM509744 3 0.4564 0.5673 0.000 0.000 0.672 0.328
#> GSM509749 3 0.0336 0.8292 0.000 0.000 0.992 0.008
#> GSM509740 4 0.6400 0.3309 0.408 0.000 0.068 0.524
#> GSM509745 3 0.5699 0.4407 0.032 0.000 0.588 0.380
#> GSM509750 3 0.2973 0.7763 0.000 0.000 0.856 0.144
#> GSM509751 2 0.3587 0.7205 0.000 0.856 0.040 0.104
#> GSM509753 2 0.3634 0.7205 0.000 0.856 0.048 0.096
#> GSM509755 2 0.3612 0.7204 0.000 0.856 0.044 0.100
#> GSM509757 2 0.4389 0.6861 0.000 0.812 0.072 0.116
#> GSM509759 2 0.6928 0.2053 0.000 0.512 0.372 0.116
#> GSM509761 2 0.0336 0.7891 0.000 0.992 0.000 0.008
#> GSM509763 2 0.2589 0.7855 0.000 0.884 0.000 0.116
#> GSM509765 2 0.2216 0.7907 0.000 0.908 0.000 0.092
#> GSM509767 2 0.3958 0.7383 0.000 0.836 0.052 0.112
#> GSM509769 2 0.0188 0.7897 0.000 0.996 0.000 0.004
#> GSM509771 2 0.4356 0.7254 0.000 0.812 0.064 0.124
#> GSM509773 2 0.1557 0.7943 0.000 0.944 0.000 0.056
#> GSM509775 2 0.2704 0.7830 0.000 0.876 0.000 0.124
#> GSM509777 2 0.2760 0.7818 0.000 0.872 0.000 0.128
#> GSM509779 2 0.4454 0.6481 0.000 0.692 0.000 0.308
#> GSM509781 2 0.4972 0.4329 0.000 0.544 0.000 0.456
#> GSM509783 2 0.4916 0.4931 0.000 0.576 0.000 0.424
#> GSM509785 2 0.4977 0.4242 0.000 0.540 0.000 0.460
#> GSM509752 2 0.0895 0.7829 0.000 0.976 0.004 0.020
#> GSM509754 2 0.0188 0.7881 0.000 0.996 0.000 0.004
#> GSM509756 2 0.0592 0.7849 0.000 0.984 0.000 0.016
#> GSM509758 2 0.0817 0.7922 0.000 0.976 0.000 0.024
#> GSM509760 2 0.1389 0.7940 0.000 0.952 0.000 0.048
#> GSM509762 2 0.0817 0.7824 0.000 0.976 0.000 0.024
#> GSM509764 2 0.2714 0.7388 0.000 0.884 0.004 0.112
#> GSM509766 2 0.1792 0.7937 0.000 0.932 0.000 0.068
#> GSM509768 2 0.2647 0.7848 0.000 0.880 0.000 0.120
#> GSM509770 2 0.2216 0.7918 0.000 0.908 0.000 0.092
#> GSM509772 2 0.6134 0.5138 0.000 0.668 0.216 0.116
#> GSM509774 2 0.3569 0.7449 0.000 0.804 0.000 0.196
#> GSM509776 2 0.3764 0.7304 0.000 0.784 0.000 0.216
#> GSM509778 2 0.4790 0.5603 0.000 0.620 0.000 0.380
#> GSM509780 2 0.2814 0.7810 0.000 0.868 0.000 0.132
#> GSM509782 2 0.4877 0.5191 0.000 0.592 0.000 0.408
#> GSM509784 2 0.4643 0.6069 0.000 0.656 0.000 0.344
#> GSM509786 2 0.4967 0.4410 0.000 0.548 0.000 0.452
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM509706 1 0.0404 0.964 0.988 0.000 0.000 0.000 0.012
#> GSM509711 1 0.1270 0.956 0.948 0.000 0.000 0.000 0.052
#> GSM509714 1 0.1043 0.960 0.960 0.000 0.000 0.000 0.040
#> GSM509719 1 0.1364 0.951 0.952 0.036 0.000 0.000 0.012
#> GSM509724 1 0.1544 0.947 0.932 0.000 0.000 0.000 0.068
#> GSM509729 1 0.1282 0.951 0.952 0.000 0.004 0.000 0.044
#> GSM509707 1 0.0703 0.962 0.976 0.000 0.000 0.000 0.024
#> GSM509712 1 0.0290 0.965 0.992 0.000 0.000 0.000 0.008
#> GSM509715 5 0.2561 0.816 0.000 0.000 0.000 0.144 0.856
#> GSM509720 1 0.0963 0.961 0.964 0.000 0.000 0.000 0.036
#> GSM509725 1 0.1197 0.957 0.952 0.000 0.000 0.000 0.048
#> GSM509730 1 0.2304 0.920 0.908 0.000 0.048 0.000 0.044
#> GSM509708 1 0.0290 0.966 0.992 0.000 0.000 0.000 0.008
#> GSM509713 1 0.0703 0.962 0.976 0.000 0.000 0.000 0.024
#> GSM509716 5 0.2424 0.819 0.000 0.000 0.000 0.132 0.868
#> GSM509721 1 0.2329 0.865 0.876 0.124 0.000 0.000 0.000
#> GSM509726 1 0.1732 0.939 0.920 0.000 0.000 0.000 0.080
#> GSM509731 4 0.1444 0.875 0.040 0.000 0.000 0.948 0.012
#> GSM509709 1 0.0609 0.965 0.980 0.000 0.000 0.000 0.020
#> GSM509717 5 0.2561 0.816 0.000 0.000 0.000 0.144 0.856
#> GSM509722 1 0.0162 0.966 0.996 0.000 0.000 0.000 0.004
#> GSM509727 5 0.1205 0.817 0.040 0.000 0.004 0.000 0.956
#> GSM509710 1 0.0510 0.966 0.984 0.000 0.000 0.000 0.016
#> GSM509718 5 0.2773 0.800 0.000 0.000 0.000 0.164 0.836
#> GSM509723 1 0.0955 0.959 0.968 0.004 0.000 0.000 0.028
#> GSM509728 5 0.1952 0.824 0.004 0.000 0.084 0.000 0.912
#> GSM509732 3 0.0290 0.949 0.000 0.008 0.992 0.000 0.000
#> GSM509736 5 0.1564 0.823 0.024 0.004 0.024 0.000 0.948
#> GSM509741 3 0.1410 0.941 0.000 0.000 0.940 0.000 0.060
#> GSM509746 3 0.0404 0.949 0.000 0.012 0.988 0.000 0.000
#> GSM509733 3 0.0510 0.947 0.000 0.016 0.984 0.000 0.000
#> GSM509737 5 0.4727 0.233 0.016 0.000 0.452 0.000 0.532
#> GSM509742 3 0.1410 0.941 0.000 0.000 0.940 0.000 0.060
#> GSM509747 3 0.0451 0.947 0.000 0.008 0.988 0.000 0.004
#> GSM509734 3 0.0566 0.948 0.004 0.000 0.984 0.000 0.012
#> GSM509738 5 0.1965 0.820 0.000 0.000 0.096 0.000 0.904
#> GSM509743 5 0.3395 0.706 0.000 0.000 0.236 0.000 0.764
#> GSM509748 3 0.0290 0.949 0.000 0.008 0.992 0.000 0.000
#> GSM509735 1 0.0404 0.966 0.988 0.000 0.000 0.000 0.012
#> GSM509739 1 0.0510 0.964 0.984 0.000 0.000 0.000 0.016
#> GSM509744 5 0.2561 0.796 0.000 0.000 0.144 0.000 0.856
#> GSM509749 3 0.1270 0.944 0.000 0.000 0.948 0.000 0.052
#> GSM509740 5 0.3300 0.673 0.204 0.000 0.004 0.000 0.792
#> GSM509745 3 0.1732 0.927 0.000 0.000 0.920 0.000 0.080
#> GSM509750 3 0.2929 0.799 0.000 0.000 0.820 0.000 0.180
#> GSM509751 2 0.0162 0.891 0.000 0.996 0.000 0.004 0.000
#> GSM509753 2 0.0000 0.890 0.000 1.000 0.000 0.000 0.000
#> GSM509755 2 0.0000 0.890 0.000 1.000 0.000 0.000 0.000
#> GSM509757 2 0.0162 0.891 0.000 0.996 0.000 0.004 0.000
#> GSM509759 2 0.0000 0.890 0.000 1.000 0.000 0.000 0.000
#> GSM509761 2 0.1270 0.880 0.000 0.948 0.000 0.052 0.000
#> GSM509763 4 0.3913 0.451 0.000 0.324 0.000 0.676 0.000
#> GSM509765 2 0.3661 0.696 0.000 0.724 0.000 0.276 0.000
#> GSM509767 2 0.3381 0.796 0.000 0.808 0.016 0.176 0.000
#> GSM509769 2 0.0880 0.888 0.000 0.968 0.000 0.032 0.000
#> GSM509771 2 0.6410 0.396 0.000 0.504 0.284 0.212 0.000
#> GSM509773 2 0.2648 0.821 0.000 0.848 0.000 0.152 0.000
#> GSM509775 2 0.3966 0.596 0.000 0.664 0.000 0.336 0.000
#> GSM509777 4 0.1410 0.912 0.000 0.060 0.000 0.940 0.000
#> GSM509779 4 0.0880 0.925 0.000 0.032 0.000 0.968 0.000
#> GSM509781 4 0.0000 0.924 0.000 0.000 0.000 1.000 0.000
#> GSM509783 4 0.0000 0.924 0.000 0.000 0.000 1.000 0.000
#> GSM509785 4 0.0000 0.924 0.000 0.000 0.000 1.000 0.000
#> GSM509752 2 0.0162 0.891 0.000 0.996 0.000 0.004 0.000
#> GSM509754 2 0.0290 0.892 0.000 0.992 0.000 0.008 0.000
#> GSM509756 2 0.0290 0.892 0.000 0.992 0.000 0.008 0.000
#> GSM509758 2 0.0963 0.887 0.000 0.964 0.000 0.036 0.000
#> GSM509760 2 0.0404 0.892 0.000 0.988 0.000 0.012 0.000
#> GSM509762 2 0.0290 0.892 0.000 0.992 0.000 0.008 0.000
#> GSM509764 2 0.0000 0.890 0.000 1.000 0.000 0.000 0.000
#> GSM509766 2 0.3242 0.767 0.000 0.784 0.000 0.216 0.000
#> GSM509768 2 0.3480 0.732 0.000 0.752 0.000 0.248 0.000
#> GSM509770 2 0.0510 0.891 0.000 0.984 0.000 0.016 0.000
#> GSM509772 2 0.0162 0.891 0.000 0.996 0.000 0.004 0.000
#> GSM509774 4 0.1732 0.896 0.000 0.080 0.000 0.920 0.000
#> GSM509776 2 0.3816 0.653 0.000 0.696 0.000 0.304 0.000
#> GSM509778 4 0.0000 0.924 0.000 0.000 0.000 1.000 0.000
#> GSM509780 4 0.1608 0.904 0.000 0.072 0.000 0.928 0.000
#> GSM509782 4 0.0510 0.926 0.000 0.016 0.000 0.984 0.000
#> GSM509784 4 0.1121 0.921 0.000 0.044 0.000 0.956 0.000
#> GSM509786 4 0.0000 0.924 0.000 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM509706 1 0.0458 0.889 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM509711 1 0.1391 0.876 0.944 0.000 0.000 0.000 0.040 0.016
#> GSM509714 1 0.6588 -0.436 0.416 0.000 0.000 0.056 0.376 0.152
#> GSM509719 5 0.4237 0.839 0.244 0.004 0.000 0.000 0.704 0.048
#> GSM509724 1 0.1334 0.877 0.948 0.000 0.000 0.000 0.032 0.020
#> GSM509729 1 0.3074 0.596 0.792 0.000 0.004 0.000 0.200 0.004
#> GSM509707 1 0.0458 0.889 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM509712 1 0.1364 0.864 0.944 0.000 0.000 0.004 0.048 0.004
#> GSM509715 6 0.1921 0.795 0.000 0.000 0.000 0.052 0.032 0.916
#> GSM509720 5 0.5155 0.799 0.188 0.004 0.004 0.000 0.652 0.152
#> GSM509725 1 0.1257 0.879 0.952 0.000 0.000 0.000 0.028 0.020
#> GSM509730 5 0.5140 0.486 0.424 0.000 0.052 0.008 0.512 0.004
#> GSM509708 1 0.0291 0.893 0.992 0.000 0.000 0.000 0.004 0.004
#> GSM509713 1 0.0260 0.892 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM509716 6 0.1719 0.795 0.004 0.000 0.000 0.032 0.032 0.932
#> GSM509721 5 0.4914 0.823 0.176 0.056 0.000 0.000 0.708 0.060
#> GSM509726 1 0.1341 0.877 0.948 0.000 0.000 0.000 0.028 0.024
#> GSM509731 4 0.2401 0.604 0.048 0.000 0.000 0.900 0.028 0.024
#> GSM509709 1 0.0508 0.892 0.984 0.000 0.000 0.000 0.012 0.004
#> GSM509717 6 0.2277 0.787 0.000 0.000 0.000 0.076 0.032 0.892
#> GSM509722 5 0.4177 0.852 0.216 0.000 0.004 0.000 0.724 0.056
#> GSM509727 6 0.1821 0.786 0.040 0.000 0.008 0.000 0.024 0.928
#> GSM509710 1 0.0363 0.891 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM509718 6 0.3387 0.736 0.000 0.000 0.000 0.164 0.040 0.796
#> GSM509723 5 0.3560 0.841 0.204 0.004 0.008 0.000 0.772 0.012
#> GSM509728 6 0.5664 0.534 0.136 0.000 0.232 0.000 0.028 0.604
#> GSM509732 3 0.1500 0.848 0.000 0.012 0.936 0.000 0.052 0.000
#> GSM509736 6 0.2265 0.793 0.012 0.000 0.056 0.000 0.028 0.904
#> GSM509741 3 0.1890 0.858 0.000 0.000 0.916 0.000 0.024 0.060
#> GSM509746 3 0.1426 0.861 0.000 0.016 0.948 0.000 0.028 0.008
#> GSM509733 3 0.0862 0.861 0.000 0.016 0.972 0.000 0.008 0.004
#> GSM509737 6 0.4912 0.379 0.060 0.000 0.368 0.000 0.004 0.568
#> GSM509742 3 0.2094 0.857 0.000 0.004 0.908 0.000 0.024 0.064
#> GSM509747 3 0.1829 0.841 0.000 0.012 0.920 0.000 0.064 0.004
#> GSM509734 3 0.2170 0.848 0.044 0.000 0.916 0.008 0.016 0.016
#> GSM509738 6 0.1349 0.796 0.000 0.000 0.056 0.000 0.004 0.940
#> GSM509743 3 0.4449 0.127 0.000 0.000 0.532 0.000 0.028 0.440
#> GSM509748 3 0.2308 0.817 0.000 0.000 0.880 0.008 0.108 0.004
#> GSM509735 1 0.0820 0.890 0.972 0.000 0.000 0.000 0.012 0.016
#> GSM509739 1 0.0713 0.881 0.972 0.000 0.000 0.000 0.028 0.000
#> GSM509744 6 0.3758 0.484 0.000 0.000 0.324 0.000 0.008 0.668
#> GSM509749 3 0.2066 0.860 0.000 0.000 0.908 0.000 0.040 0.052
#> GSM509740 6 0.3053 0.705 0.020 0.000 0.000 0.000 0.168 0.812
#> GSM509745 3 0.3065 0.800 0.000 0.000 0.820 0.000 0.028 0.152
#> GSM509750 3 0.3587 0.751 0.000 0.000 0.772 0.000 0.040 0.188
#> GSM509751 2 0.0909 0.875 0.000 0.968 0.012 0.000 0.020 0.000
#> GSM509753 2 0.0717 0.878 0.000 0.976 0.008 0.000 0.016 0.000
#> GSM509755 2 0.0972 0.872 0.000 0.964 0.008 0.000 0.028 0.000
#> GSM509757 2 0.1333 0.863 0.000 0.944 0.008 0.000 0.048 0.000
#> GSM509759 2 0.1858 0.828 0.000 0.912 0.012 0.000 0.076 0.000
#> GSM509761 2 0.1049 0.887 0.000 0.960 0.000 0.032 0.008 0.000
#> GSM509763 2 0.3729 0.538 0.000 0.692 0.000 0.296 0.012 0.000
#> GSM509765 2 0.2912 0.787 0.000 0.816 0.000 0.172 0.012 0.000
#> GSM509767 2 0.2349 0.862 0.000 0.892 0.020 0.080 0.008 0.000
#> GSM509769 2 0.1333 0.881 0.000 0.944 0.000 0.048 0.008 0.000
#> GSM509771 2 0.3993 0.779 0.000 0.788 0.060 0.124 0.028 0.000
#> GSM509773 2 0.2118 0.854 0.000 0.888 0.000 0.104 0.008 0.000
#> GSM509775 2 0.2877 0.792 0.000 0.820 0.000 0.168 0.012 0.000
#> GSM509777 4 0.3717 0.552 0.000 0.384 0.000 0.616 0.000 0.000
#> GSM509779 4 0.2969 0.762 0.000 0.224 0.000 0.776 0.000 0.000
#> GSM509781 4 0.2135 0.784 0.000 0.128 0.000 0.872 0.000 0.000
#> GSM509783 4 0.0405 0.702 0.000 0.008 0.000 0.988 0.004 0.000
#> GSM509785 4 0.1663 0.771 0.000 0.088 0.000 0.912 0.000 0.000
#> GSM509752 2 0.0767 0.888 0.000 0.976 0.004 0.012 0.008 0.000
#> GSM509754 2 0.0260 0.888 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM509756 2 0.0891 0.884 0.000 0.968 0.000 0.008 0.024 0.000
#> GSM509758 2 0.0632 0.887 0.000 0.976 0.000 0.024 0.000 0.000
#> GSM509760 2 0.0508 0.887 0.000 0.984 0.000 0.004 0.012 0.000
#> GSM509762 2 0.0508 0.885 0.000 0.984 0.000 0.004 0.012 0.000
#> GSM509764 2 0.3533 0.646 0.000 0.748 0.012 0.000 0.236 0.004
#> GSM509766 2 0.2191 0.844 0.000 0.876 0.000 0.120 0.004 0.000
#> GSM509768 2 0.2680 0.835 0.000 0.856 0.000 0.124 0.016 0.004
#> GSM509770 2 0.1894 0.881 0.000 0.928 0.004 0.040 0.016 0.012
#> GSM509772 2 0.0405 0.886 0.000 0.988 0.008 0.000 0.004 0.000
#> GSM509774 4 0.4157 0.379 0.000 0.444 0.000 0.544 0.012 0.000
#> GSM509776 2 0.3000 0.802 0.000 0.824 0.000 0.156 0.016 0.004
#> GSM509778 4 0.1088 0.697 0.000 0.016 0.000 0.960 0.024 0.000
#> GSM509780 4 0.4066 0.526 0.000 0.392 0.000 0.596 0.012 0.000
#> GSM509782 4 0.2454 0.787 0.000 0.160 0.000 0.840 0.000 0.000
#> GSM509784 4 0.3244 0.725 0.000 0.268 0.000 0.732 0.000 0.000
#> GSM509786 4 0.1663 0.771 0.000 0.088 0.000 0.912 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 disease.state(p) time(p) k
#> ATC:NMF 81 3.67e-13 7.52e-11 2
#> ATC:NMF 79 1.35e-17 1.03e-07 3
#> ATC:NMF 70 7.81e-25 5.24e-09 4
#> ATC:NMF 78 9.09e-22 1.39e-08 5
#> ATC:NMF 75 2.99e-20 1.72e-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.
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