Date: 2019-12-25 20:46:58 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 51941 rows and 82 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] 51941 82
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 | 0.992 | 0.996 | ** | |
| SD:mclust | 2 | 1.000 | 0.965 | 0.987 | ** | |
| SD:NMF | 2 | 1.000 | 0.980 | 0.992 | ** | |
| CV:kmeans | 2 | 1.000 | 0.982 | 0.994 | ** | |
| CV:NMF | 2 | 1.000 | 0.983 | 0.993 | ** | |
| MAD:hclust | 2 | 1.000 | 0.979 | 0.990 | ** | |
| MAD:kmeans | 2 | 1.000 | 0.994 | 0.997 | ** | |
| MAD:skmeans | 3 | 1.000 | 0.969 | 0.987 | ** | 2 |
| MAD:pam | 2 | 1.000 | 0.982 | 0.992 | ** | |
| MAD:mclust | 4 | 1.000 | 0.965 | 0.983 | ** | 2 |
| ATC:kmeans | 2 | 1.000 | 1.000 | 1.000 | ** | |
| ATC:mclust | 2 | 1.000 | 0.983 | 0.990 | ** | |
| CV:skmeans | 4 | 0.999 | 0.969 | 0.978 | ** | 2,3 |
| MAD:NMF | 3 | 0.996 | 0.970 | 0.984 | ** | 2 |
| SD:skmeans | 4 | 0.974 | 0.956 | 0.971 | ** | 2,3 |
| ATC:NMF | 2 | 0.949 | 0.943 | 0.976 | * | |
| CV:mclust | 5 | 0.948 | 0.913 | 0.958 | * | 2,3,4 |
| ATC:skmeans | 4 | 0.946 | 0.919 | 0.948 | * | 2,3 |
| CV:pam | 3 | 0.940 | 0.946 | 0.974 | * | 2 |
| SD:pam | 3 | 0.904 | 0.867 | 0.944 | * | 2 |
| ATC:pam | 5 | 0.901 | 0.853 | 0.910 | * | 2,4 |
| ATC:hclust | 2 | 0.877 | 0.910 | 0.963 | ||
| SD:hclust | 3 | 0.857 | 0.936 | 0.953 | ||
| CV:hclust | 3 | 0.721 | 0.925 | 0.924 |
**: 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 0.980 0.992 0.482 0.518 0.518
#> CV:NMF 2 1.000 0.983 0.993 0.484 0.518 0.518
#> MAD:NMF 2 1.000 1.000 1.000 0.487 0.513 0.513
#> ATC:NMF 2 0.949 0.943 0.976 0.501 0.499 0.499
#> SD:skmeans 2 1.000 0.990 0.996 0.490 0.509 0.509
#> CV:skmeans 2 1.000 0.996 0.998 0.491 0.509 0.509
#> MAD:skmeans 2 1.000 0.985 0.995 0.489 0.513 0.513
#> ATC:skmeans 2 1.000 0.988 0.995 0.493 0.509 0.509
#> SD:mclust 2 1.000 0.965 0.987 0.470 0.537 0.537
#> CV:mclust 2 1.000 0.986 0.994 0.483 0.518 0.518
#> MAD:mclust 2 1.000 0.973 0.988 0.476 0.518 0.518
#> ATC:mclust 2 1.000 0.983 0.990 0.474 0.530 0.530
#> SD:kmeans 2 1.000 0.992 0.996 0.478 0.524 0.524
#> CV:kmeans 2 1.000 0.982 0.994 0.479 0.524 0.524
#> MAD:kmeans 2 1.000 0.994 0.997 0.486 0.513 0.513
#> ATC:kmeans 2 1.000 1.000 1.000 0.492 0.509 0.509
#> SD:pam 2 1.000 0.965 0.987 0.482 0.518 0.518
#> CV:pam 2 0.949 0.960 0.982 0.487 0.513 0.513
#> MAD:pam 2 1.000 0.982 0.992 0.485 0.513 0.513
#> ATC:pam 2 1.000 0.970 0.988 0.498 0.505 0.505
#> SD:hclust 2 0.561 0.837 0.899 0.470 0.518 0.518
#> CV:hclust 2 0.582 0.781 0.880 0.469 0.513 0.513
#> MAD:hclust 2 1.000 0.979 0.990 0.480 0.518 0.518
#> ATC:hclust 2 0.877 0.910 0.963 0.479 0.518 0.518
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 0.893 0.919 0.963 0.389 0.796 0.611
#> CV:NMF 3 0.883 0.907 0.951 0.384 0.780 0.588
#> MAD:NMF 3 0.996 0.970 0.984 0.358 0.825 0.660
#> ATC:NMF 3 0.848 0.862 0.937 0.305 0.755 0.552
#> SD:skmeans 3 0.970 0.930 0.972 0.333 0.826 0.662
#> CV:skmeans 3 0.971 0.930 0.971 0.335 0.822 0.654
#> MAD:skmeans 3 1.000 0.969 0.987 0.338 0.828 0.665
#> ATC:skmeans 3 0.944 0.882 0.954 0.301 0.851 0.707
#> SD:mclust 3 0.737 0.758 0.836 0.376 0.790 0.610
#> CV:mclust 3 1.000 0.961 0.985 0.359 0.808 0.635
#> MAD:mclust 3 0.729 0.841 0.902 0.369 0.801 0.623
#> ATC:mclust 3 0.753 0.801 0.877 0.283 0.874 0.761
#> SD:kmeans 3 0.739 0.863 0.904 0.366 0.808 0.633
#> CV:kmeans 3 0.865 0.880 0.927 0.381 0.804 0.626
#> MAD:kmeans 3 0.691 0.850 0.889 0.334 0.795 0.609
#> ATC:kmeans 3 0.890 0.911 0.961 0.369 0.741 0.526
#> SD:pam 3 0.904 0.867 0.944 0.394 0.795 0.610
#> CV:pam 3 0.940 0.946 0.974 0.378 0.786 0.595
#> MAD:pam 3 0.860 0.926 0.964 0.386 0.787 0.597
#> ATC:pam 3 0.833 0.916 0.960 0.348 0.720 0.496
#> SD:hclust 3 0.857 0.936 0.953 0.401 0.813 0.639
#> CV:hclust 3 0.721 0.925 0.924 0.387 0.805 0.625
#> MAD:hclust 3 0.721 0.768 0.883 0.335 0.819 0.651
#> ATC:hclust 3 0.659 0.738 0.874 0.341 0.822 0.662
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.853 0.861 0.920 0.1022 0.858 0.612
#> CV:NMF 4 0.861 0.865 0.928 0.1008 0.852 0.602
#> MAD:NMF 4 0.842 0.819 0.913 0.1142 0.843 0.585
#> ATC:NMF 4 0.863 0.872 0.925 0.0958 0.845 0.609
#> SD:skmeans 4 0.974 0.956 0.971 0.1221 0.867 0.641
#> CV:skmeans 4 0.999 0.969 0.978 0.1195 0.874 0.655
#> MAD:skmeans 4 0.888 0.882 0.933 0.1043 0.895 0.710
#> ATC:skmeans 4 0.946 0.919 0.948 0.0647 0.933 0.817
#> SD:mclust 4 0.789 0.869 0.852 0.1206 0.896 0.701
#> CV:mclust 4 0.999 0.970 0.982 0.1178 0.922 0.773
#> MAD:mclust 4 1.000 0.965 0.983 0.1258 0.918 0.762
#> ATC:mclust 4 0.898 0.881 0.947 0.1605 0.833 0.612
#> SD:kmeans 4 0.671 0.606 0.773 0.1206 0.969 0.908
#> CV:kmeans 4 0.713 0.626 0.806 0.1097 0.961 0.884
#> MAD:kmeans 4 0.684 0.686 0.769 0.1249 0.896 0.701
#> ATC:kmeans 4 0.786 0.769 0.844 0.0981 0.854 0.594
#> SD:pam 4 0.755 0.651 0.809 0.1067 0.928 0.785
#> CV:pam 4 0.767 0.719 0.823 0.1053 0.914 0.747
#> MAD:pam 4 0.762 0.767 0.840 0.1101 0.873 0.640
#> ATC:pam 4 1.000 0.962 0.983 0.1192 0.850 0.585
#> SD:hclust 4 0.803 0.844 0.900 0.0690 0.982 0.945
#> CV:hclust 4 0.776 0.733 0.875 0.0935 0.978 0.935
#> MAD:hclust 4 0.692 0.725 0.826 0.1024 0.921 0.787
#> ATC:hclust 4 0.710 0.680 0.847 0.0791 0.853 0.633
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.786 0.716 0.863 0.0430 0.942 0.792
#> CV:NMF 5 0.799 0.695 0.853 0.0463 0.948 0.811
#> MAD:NMF 5 0.792 0.779 0.869 0.0379 0.946 0.805
#> ATC:NMF 5 0.831 0.804 0.892 0.0531 0.932 0.773
#> SD:skmeans 5 0.825 0.741 0.858 0.0581 0.986 0.948
#> CV:skmeans 5 0.851 0.630 0.836 0.0530 0.985 0.945
#> MAD:skmeans 5 0.808 0.659 0.824 0.0587 0.944 0.808
#> ATC:skmeans 5 0.867 0.871 0.913 0.0506 0.980 0.935
#> SD:mclust 5 0.680 0.700 0.806 0.0657 0.965 0.872
#> CV:mclust 5 0.948 0.913 0.958 0.0857 0.924 0.721
#> MAD:mclust 5 0.730 0.669 0.848 0.0502 0.945 0.807
#> ATC:mclust 5 0.723 0.726 0.805 0.0855 0.926 0.750
#> SD:kmeans 5 0.681 0.582 0.716 0.0694 0.819 0.467
#> CV:kmeans 5 0.674 0.570 0.733 0.0660 0.787 0.401
#> MAD:kmeans 5 0.673 0.504 0.700 0.0732 0.936 0.761
#> ATC:kmeans 5 0.733 0.728 0.816 0.0568 0.913 0.687
#> SD:pam 5 0.817 0.766 0.891 0.0798 0.871 0.567
#> CV:pam 5 0.763 0.801 0.872 0.0755 0.895 0.630
#> MAD:pam 5 0.861 0.845 0.924 0.0770 0.894 0.617
#> ATC:pam 5 0.901 0.853 0.910 0.0407 0.945 0.788
#> SD:hclust 5 0.784 0.778 0.853 0.0537 0.978 0.930
#> CV:hclust 5 0.791 0.818 0.872 0.0429 0.932 0.784
#> MAD:hclust 5 0.635 0.587 0.773 0.0742 0.890 0.680
#> ATC:hclust 5 0.676 0.574 0.763 0.0575 0.886 0.649
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.778 0.685 0.829 0.0320 0.950 0.801
#> CV:NMF 6 0.802 0.730 0.857 0.0337 0.950 0.798
#> MAD:NMF 6 0.746 0.618 0.771 0.0427 0.933 0.734
#> ATC:NMF 6 0.803 0.778 0.859 0.0551 0.927 0.718
#> SD:skmeans 6 0.832 0.793 0.853 0.0446 0.906 0.657
#> CV:skmeans 6 0.807 0.801 0.860 0.0471 0.900 0.634
#> MAD:skmeans 6 0.769 0.732 0.826 0.0521 0.897 0.620
#> ATC:skmeans 6 0.849 0.751 0.869 0.0455 0.991 0.969
#> SD:mclust 6 0.770 0.614 0.793 0.0484 0.907 0.646
#> CV:mclust 6 0.855 0.834 0.876 0.0315 1.000 1.000
#> MAD:mclust 6 0.755 0.736 0.832 0.0692 0.856 0.482
#> ATC:mclust 6 0.823 0.831 0.908 0.0671 0.896 0.594
#> SD:kmeans 6 0.717 0.666 0.767 0.0475 0.943 0.733
#> CV:kmeans 6 0.710 0.677 0.770 0.0439 0.902 0.574
#> MAD:kmeans 6 0.695 0.625 0.703 0.0452 0.905 0.607
#> ATC:kmeans 6 0.754 0.637 0.791 0.0380 0.979 0.905
#> SD:pam 6 0.867 0.812 0.915 0.0344 0.971 0.854
#> CV:pam 6 0.857 0.802 0.908 0.0365 0.943 0.727
#> MAD:pam 6 0.867 0.759 0.894 0.0339 0.939 0.713
#> ATC:pam 6 0.899 0.811 0.911 0.0365 0.951 0.786
#> SD:hclust 6 0.793 0.686 0.835 0.0357 0.958 0.856
#> CV:hclust 6 0.852 0.824 0.904 0.0293 0.987 0.950
#> MAD:hclust 6 0.679 0.675 0.793 0.0293 0.955 0.820
#> ATC:hclust 6 0.733 0.599 0.803 0.0677 0.918 0.690
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) specimen(p) individual(p) k
#> SD:NMF 81 9.58e-05 1.96e-17 1.000 2
#> CV:NMF 81 9.58e-05 1.96e-17 1.000 2
#> MAD:NMF 82 3.35e-04 8.50e-17 0.999 2
#> ATC:NMF 80 1.97e-04 1.23e-15 0.997 2
#> SD:skmeans 81 2.72e-04 1.85e-17 1.000 2
#> CV:skmeans 82 2.14e-04 1.11e-17 1.000 2
#> MAD:skmeans 81 2.72e-04 1.85e-17 1.000 2
#> ATC:skmeans 81 1.71e-04 1.32e-16 0.998 2
#> SD:mclust 80 1.70e-04 2.43e-16 0.998 2
#> CV:mclust 82 6.57e-05 1.20e-17 1.000 2
#> MAD:mclust 81 8.44e-05 2.00e-17 0.999 2
#> ATC:mclust 82 1.61e-04 5.58e-16 0.998 2
#> SD:kmeans 82 1.04e-04 8.49e-17 0.999 2
#> CV:kmeans 81 8.44e-05 2.00e-17 0.999 2
#> MAD:kmeans 82 3.35e-04 8.50e-17 0.999 2
#> ATC:kmeans 82 2.14e-04 5.97e-16 0.998 2
#> SD:pam 80 1.22e-04 3.27e-17 0.999 2
#> CV:pam 82 3.35e-04 8.50e-17 0.999 2
#> MAD:pam 82 3.35e-04 8.50e-17 0.999 2
#> ATC:pam 80 3.09e-04 2.07e-16 0.999 2
#> SD:hclust 82 5.16e-04 5.99e-16 0.999 2
#> CV:hclust 75 1.05e-04 3.63e-16 0.990 2
#> MAD:hclust 82 5.16e-04 5.99e-16 0.999 2
#> ATC:hclust 78 1.26e-04 8.92e-17 0.998 2
test_to_known_factors(res_list, k = 3)
#> n disease.state(p) specimen(p) individual(p) k
#> SD:NMF 79 1.70e-06 8.58e-19 0.949 3
#> CV:NMF 79 1.70e-06 8.58e-19 0.949 3
#> MAD:NMF 82 6.72e-05 1.37e-16 0.972 3
#> ATC:NMF 77 9.19e-04 1.50e-13 0.876 3
#> SD:skmeans 78 1.16e-05 1.11e-16 0.943 3
#> CV:skmeans 80 1.78e-05 2.20e-17 0.962 3
#> MAD:skmeans 80 1.82e-05 1.33e-16 0.949 3
#> ATC:skmeans 73 2.36e-04 2.01e-14 0.946 3
#> SD:mclust 76 2.22e-12 1.36e-25 0.861 3
#> CV:mclust 80 4.65e-15 1.09e-29 0.814 3
#> MAD:mclust 78 1.07e-14 9.35e-28 0.743 3
#> ATC:mclust 74 2.00e-03 1.61e-14 0.767 3
#> SD:kmeans 79 1.32e-05 4.98e-16 0.894 3
#> CV:kmeans 77 1.29e-06 2.39e-16 0.830 3
#> MAD:kmeans 79 2.72e-05 6.42e-16 0.913 3
#> ATC:kmeans 81 2.50e-04 2.61e-13 0.911 3
#> SD:pam 72 3.33e-06 5.09e-15 0.850 3
#> CV:pam 81 3.32e-04 3.66e-14 0.900 3
#> MAD:pam 82 2.82e-04 2.77e-14 0.900 3
#> ATC:pam 81 4.50e-05 2.60e-13 0.909 3
#> SD:hclust 82 3.40e-04 7.97e-15 0.897 3
#> CV:hclust 82 3.40e-04 7.97e-15 0.897 3
#> MAD:hclust 71 3.87e-05 2.98e-14 0.842 3
#> ATC:hclust 69 1.91e-04 1.74e-13 0.876 3
test_to_known_factors(res_list, k = 4)
#> n disease.state(p) specimen(p) individual(p) k
#> SD:NMF 77 9.48e-14 1.61e-25 0.852 4
#> CV:NMF 78 6.13e-14 1.15e-26 0.845 4
#> MAD:NMF 74 2.92e-13 2.10e-24 0.865 4
#> ATC:NMF 80 6.06e-05 9.14e-16 0.626 4
#> SD:skmeans 81 5.54e-14 7.14e-26 0.701 4
#> CV:skmeans 82 3.61e-14 2.63e-26 0.704 4
#> MAD:skmeans 78 6.21e-12 6.60e-25 0.784 4
#> ATC:skmeans 78 5.67e-04 1.54e-14 0.699 4
#> SD:mclust 78 8.10e-12 3.39e-23 0.928 4
#> CV:mclust 82 8.45e-15 1.99e-27 0.909 4
#> MAD:mclust 81 1.12e-11 1.84e-23 0.943 4
#> ATC:mclust 81 2.15e-04 1.09e-14 0.489 4
#> SD:kmeans 57 2.64e-03 1.86e-13 0.974 4
#> CV:kmeans 64 5.58e-08 1.08e-18 0.916 4
#> MAD:kmeans 72 2.73e-04 1.45e-14 0.891 4
#> ATC:kmeans 72 4.16e-04 1.57e-13 0.842 4
#> SD:pam 62 4.24e-06 2.20e-16 0.472 4
#> CV:pam 71 1.33e-09 2.24e-20 0.511 4
#> MAD:pam 75 1.03e-03 3.20e-14 0.931 4
#> ATC:pam 81 1.96e-04 7.74e-14 0.864 4
#> SD:hclust 81 4.53e-04 6.01e-14 0.712 4
#> CV:hclust 72 1.98e-04 9.06e-14 0.367 4
#> MAD:hclust 72 3.28e-05 1.26e-14 0.854 4
#> ATC:hclust 62 2.57e-04 3.33e-11 0.693 4
test_to_known_factors(res_list, k = 5)
#> n disease.state(p) specimen(p) individual(p) k
#> SD:NMF 68 4.20e-12 9.80e-23 0.707 5
#> CV:NMF 64 4.36e-11 1.05e-21 0.703 5
#> MAD:NMF 77 2.43e-11 1.72e-21 0.289 5
#> ATC:NMF 77 1.10e-08 3.37e-19 0.349 5
#> SD:skmeans 77 3.08e-13 2.12e-26 0.826 5
#> CV:skmeans 59 3.59e-02 5.23e-13 0.987 5
#> MAD:skmeans 63 2.17e-10 4.60e-21 0.686 5
#> ATC:skmeans 78 3.10e-06 1.21e-16 0.417 5
#> SD:mclust 74 8.45e-11 2.18e-22 0.639 5
#> CV:mclust 79 1.44e-13 1.13e-26 0.861 5
#> MAD:mclust 70 2.64e-12 3.15e-24 0.750 5
#> ATC:mclust 72 2.25e-03 1.43e-11 0.617 5
#> SD:kmeans 59 3.52e-08 2.11e-17 0.551 5
#> CV:kmeans 57 6.10e-09 6.12e-18 0.567 5
#> MAD:kmeans 55 1.51e-05 1.01e-12 0.459 5
#> ATC:kmeans 74 8.49e-04 1.26e-12 0.683 5
#> SD:pam 68 1.60e-10 2.74e-21 0.794 5
#> CV:pam 75 1.17e-11 7.57e-23 0.708 5
#> MAD:pam 77 2.51e-10 2.68e-22 0.806 5
#> ATC:pam 77 1.12e-03 1.01e-12 0.908 5
#> SD:hclust 80 4.70e-05 1.58e-14 0.298 5
#> CV:hclust 75 2.64e-07 3.46e-17 0.419 5
#> MAD:hclust 52 6.36e-06 1.81e-10 0.467 5
#> ATC:hclust 57 8.86e-04 1.64e-10 0.395 5
test_to_known_factors(res_list, k = 6)
#> n disease.state(p) specimen(p) individual(p) k
#> SD:NMF 66 1.17e-09 6.05e-19 0.6485 6
#> CV:NMF 70 1.39e-09 4.58e-18 0.1899 6
#> MAD:NMF 59 1.20e-09 8.26e-18 0.3196 6
#> ATC:NMF 75 1.04e-08 9.09e-19 0.4446 6
#> SD:skmeans 79 5.83e-12 2.88e-23 0.6031 6
#> CV:skmeans 78 1.07e-11 1.12e-23 0.6041 6
#> MAD:skmeans 71 2.80e-10 6.74e-21 0.5731 6
#> ATC:skmeans 74 1.18e-06 4.55e-16 0.4798 6
#> SD:mclust 65 1.40e-10 1.71e-20 0.2771 6
#> CV:mclust 79 1.34e-13 1.17e-26 0.8909 6
#> MAD:mclust 71 1.83e-11 2.55e-22 0.5077 6
#> ATC:mclust 77 2.35e-04 1.52e-13 0.5034 6
#> SD:kmeans 65 7.66e-11 8.85e-21 0.4241 6
#> CV:kmeans 72 7.05e-11 6.46e-22 0.4239 6
#> MAD:kmeans 69 4.00e-10 2.31e-20 0.5203 6
#> ATC:kmeans 68 7.37e-04 3.37e-10 0.3406 6
#> SD:pam 71 1.55e-10 3.32e-21 0.5303 6
#> CV:pam 76 3.08e-11 5.95e-23 0.4254 6
#> MAD:pam 71 8.03e-10 1.83e-20 0.4857 6
#> ATC:pam 73 2.11e-03 2.34e-12 0.6580 6
#> SD:hclust 72 4.38e-07 8.74e-16 0.1370 6
#> CV:hclust 76 8.55e-08 2.75e-17 0.0682 6
#> MAD:hclust 72 4.70e-06 4.66e-15 0.3679 6
#> ATC:hclust 67 8.40e-04 3.20e-11 0.9687 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 51941 rows and 82 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.561 0.837 0.899 0.4702 0.518 0.518
#> 3 3 0.857 0.936 0.953 0.4011 0.813 0.639
#> 4 4 0.803 0.844 0.900 0.0690 0.982 0.945
#> 5 5 0.784 0.778 0.853 0.0537 0.978 0.930
#> 6 6 0.793 0.686 0.835 0.0357 0.958 0.856
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
#> GSM372286 2 0.0000 0.817 0.000 1.000
#> GSM372287 2 0.0000 0.817 0.000 1.000
#> GSM372288 2 0.0000 0.817 0.000 1.000
#> GSM372289 2 0.0000 0.817 0.000 1.000
#> GSM372290 2 0.0000 0.817 0.000 1.000
#> GSM372291 1 0.7950 0.577 0.760 0.240
#> GSM372292 2 0.8555 0.731 0.280 0.720
#> GSM372293 2 0.8861 0.720 0.304 0.696
#> GSM372294 2 0.0000 0.817 0.000 1.000
#> GSM372295 2 0.8861 0.719 0.304 0.696
#> GSM372296 2 0.0000 0.817 0.000 1.000
#> GSM372297 2 0.0000 0.817 0.000 1.000
#> GSM372298 2 0.0000 0.817 0.000 1.000
#> GSM372299 2 0.8861 0.719 0.304 0.696
#> GSM372300 2 0.8861 0.720 0.304 0.696
#> GSM372301 2 0.8555 0.731 0.280 0.720
#> GSM372302 2 0.0000 0.817 0.000 1.000
#> GSM372303 2 0.8861 0.720 0.304 0.696
#> GSM372304 2 0.0000 0.817 0.000 1.000
#> GSM372305 2 0.0000 0.817 0.000 1.000
#> GSM372306 2 0.0000 0.817 0.000 1.000
#> GSM372307 2 0.0000 0.817 0.000 1.000
#> GSM372309 2 0.0000 0.817 0.000 1.000
#> GSM372311 2 0.0000 0.817 0.000 1.000
#> GSM372313 2 0.0000 0.817 0.000 1.000
#> GSM372315 2 0.0000 0.817 0.000 1.000
#> GSM372317 2 0.0000 0.817 0.000 1.000
#> GSM372319 2 0.9248 0.692 0.340 0.660
#> GSM372321 2 0.9248 0.692 0.340 0.660
#> GSM372323 2 0.9393 0.677 0.356 0.644
#> GSM372326 2 0.9248 0.692 0.340 0.660
#> GSM372328 2 0.9393 0.677 0.356 0.644
#> GSM372330 2 0.0000 0.817 0.000 1.000
#> GSM372332 2 0.9393 0.677 0.356 0.644
#> GSM372335 2 0.0376 0.816 0.004 0.996
#> GSM372337 2 0.9393 0.677 0.356 0.644
#> GSM372339 2 0.9393 0.677 0.356 0.644
#> GSM372341 2 0.9393 0.677 0.356 0.644
#> GSM372343 2 0.9393 0.677 0.356 0.644
#> GSM372345 2 0.9393 0.677 0.356 0.644
#> GSM372347 2 0.9393 0.677 0.356 0.644
#> GSM372349 2 0.9393 0.677 0.356 0.644
#> GSM372351 2 0.9248 0.692 0.340 0.660
#> GSM372353 2 0.0376 0.816 0.004 0.996
#> GSM372355 2 0.0000 0.817 0.000 1.000
#> GSM372357 2 0.0000 0.817 0.000 1.000
#> GSM372359 2 0.0376 0.816 0.004 0.996
#> GSM372361 2 0.0000 0.817 0.000 1.000
#> GSM372363 2 0.0000 0.817 0.000 1.000
#> GSM372308 1 0.0672 0.974 0.992 0.008
#> GSM372310 1 0.0672 0.974 0.992 0.008
#> GSM372312 1 0.4690 0.857 0.900 0.100
#> GSM372314 1 0.0672 0.974 0.992 0.008
#> GSM372316 1 0.0000 0.980 1.000 0.000
#> GSM372318 1 0.0000 0.980 1.000 0.000
#> GSM372320 1 0.0000 0.980 1.000 0.000
#> GSM372322 1 0.0000 0.980 1.000 0.000
#> GSM372324 1 0.0672 0.974 0.992 0.008
#> GSM372325 1 0.0672 0.974 0.992 0.008
#> GSM372327 1 0.0000 0.980 1.000 0.000
#> GSM372329 1 0.0000 0.980 1.000 0.000
#> GSM372331 1 0.0672 0.974 0.992 0.008
#> GSM372333 2 0.9635 0.623 0.388 0.612
#> GSM372334 1 0.0000 0.980 1.000 0.000
#> GSM372336 1 0.0000 0.980 1.000 0.000
#> GSM372338 1 0.0000 0.980 1.000 0.000
#> GSM372340 1 0.0000 0.980 1.000 0.000
#> GSM372342 1 0.0000 0.980 1.000 0.000
#> GSM372344 1 0.0000 0.980 1.000 0.000
#> GSM372346 1 0.0000 0.980 1.000 0.000
#> GSM372348 1 0.0000 0.980 1.000 0.000
#> GSM372350 1 0.4690 0.857 0.900 0.100
#> GSM372352 2 0.9393 0.677 0.356 0.644
#> GSM372354 1 0.0000 0.980 1.000 0.000
#> GSM372356 1 0.0000 0.980 1.000 0.000
#> GSM372358 1 0.0000 0.980 1.000 0.000
#> GSM372360 1 0.0000 0.980 1.000 0.000
#> GSM372362 1 0.0000 0.980 1.000 0.000
#> GSM372364 1 0.0000 0.980 1.000 0.000
#> GSM372365 1 0.0000 0.980 1.000 0.000
#> GSM372366 1 0.0000 0.980 1.000 0.000
#> GSM372367 1 0.0000 0.980 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM372286 2 0.2165 0.954 0.000 0.936 0.064
#> GSM372287 2 0.0892 0.929 0.000 0.980 0.020
#> GSM372288 2 0.0000 0.926 0.000 1.000 0.000
#> GSM372289 2 0.0000 0.926 0.000 1.000 0.000
#> GSM372290 2 0.1289 0.947 0.000 0.968 0.032
#> GSM372291 1 0.5016 0.695 0.760 0.000 0.240
#> GSM372292 3 0.4842 0.758 0.000 0.224 0.776
#> GSM372293 3 0.3272 0.880 0.004 0.104 0.892
#> GSM372294 2 0.3116 0.916 0.000 0.892 0.108
#> GSM372295 3 0.5178 0.691 0.000 0.256 0.744
#> GSM372296 2 0.1529 0.948 0.000 0.960 0.040
#> GSM372297 2 0.1289 0.926 0.000 0.968 0.032
#> GSM372298 2 0.1031 0.931 0.000 0.976 0.024
#> GSM372299 3 0.5178 0.691 0.000 0.256 0.744
#> GSM372300 3 0.3272 0.880 0.004 0.104 0.892
#> GSM372301 3 0.4842 0.758 0.000 0.224 0.776
#> GSM372302 2 0.1529 0.948 0.000 0.960 0.040
#> GSM372303 3 0.3272 0.880 0.004 0.104 0.892
#> GSM372304 2 0.1289 0.926 0.000 0.968 0.032
#> GSM372305 2 0.2796 0.953 0.000 0.908 0.092
#> GSM372306 2 0.2796 0.953 0.000 0.908 0.092
#> GSM372307 2 0.1643 0.951 0.000 0.956 0.044
#> GSM372309 2 0.2878 0.952 0.000 0.904 0.096
#> GSM372311 2 0.2711 0.955 0.000 0.912 0.088
#> GSM372313 2 0.2711 0.955 0.000 0.912 0.088
#> GSM372315 2 0.2711 0.955 0.000 0.912 0.088
#> GSM372317 2 0.2878 0.951 0.000 0.904 0.096
#> GSM372319 3 0.1411 0.920 0.000 0.036 0.964
#> GSM372321 3 0.1411 0.920 0.000 0.036 0.964
#> GSM372323 3 0.1015 0.926 0.012 0.008 0.980
#> GSM372326 3 0.1163 0.922 0.000 0.028 0.972
#> GSM372328 3 0.0237 0.924 0.004 0.000 0.996
#> GSM372330 2 0.2711 0.955 0.000 0.912 0.088
#> GSM372332 3 0.0237 0.924 0.004 0.000 0.996
#> GSM372335 2 0.3116 0.943 0.000 0.892 0.108
#> GSM372337 3 0.1015 0.926 0.012 0.008 0.980
#> GSM372339 3 0.0237 0.924 0.004 0.000 0.996
#> GSM372341 3 0.0237 0.924 0.004 0.000 0.996
#> GSM372343 3 0.0237 0.924 0.004 0.000 0.996
#> GSM372345 3 0.1015 0.926 0.012 0.008 0.980
#> GSM372347 3 0.1015 0.926 0.012 0.008 0.980
#> GSM372349 3 0.0829 0.925 0.012 0.004 0.984
#> GSM372351 3 0.1163 0.922 0.000 0.028 0.972
#> GSM372353 2 0.3267 0.936 0.000 0.884 0.116
#> GSM372355 2 0.2711 0.955 0.000 0.912 0.088
#> GSM372357 2 0.2711 0.955 0.000 0.912 0.088
#> GSM372359 2 0.3267 0.936 0.000 0.884 0.116
#> GSM372361 2 0.1964 0.953 0.000 0.944 0.056
#> GSM372363 2 0.2066 0.954 0.000 0.940 0.060
#> GSM372308 1 0.0424 0.979 0.992 0.000 0.008
#> GSM372310 1 0.0424 0.979 0.992 0.000 0.008
#> GSM372312 1 0.2959 0.889 0.900 0.000 0.100
#> GSM372314 1 0.0424 0.979 0.992 0.000 0.008
#> GSM372316 1 0.0000 0.984 1.000 0.000 0.000
#> GSM372318 1 0.0000 0.984 1.000 0.000 0.000
#> GSM372320 1 0.0000 0.984 1.000 0.000 0.000
#> GSM372322 1 0.0000 0.984 1.000 0.000 0.000
#> GSM372324 1 0.0424 0.979 0.992 0.000 0.008
#> GSM372325 1 0.0424 0.979 0.992 0.000 0.008
#> GSM372327 1 0.0000 0.984 1.000 0.000 0.000
#> GSM372329 1 0.0000 0.984 1.000 0.000 0.000
#> GSM372331 1 0.0424 0.979 0.992 0.000 0.008
#> GSM372333 3 0.2280 0.899 0.052 0.008 0.940
#> GSM372334 1 0.0000 0.984 1.000 0.000 0.000
#> GSM372336 1 0.0000 0.984 1.000 0.000 0.000
#> GSM372338 1 0.0000 0.984 1.000 0.000 0.000
#> GSM372340 1 0.0000 0.984 1.000 0.000 0.000
#> GSM372342 1 0.0000 0.984 1.000 0.000 0.000
#> GSM372344 1 0.0000 0.984 1.000 0.000 0.000
#> GSM372346 1 0.0000 0.984 1.000 0.000 0.000
#> GSM372348 1 0.0000 0.984 1.000 0.000 0.000
#> GSM372350 1 0.2959 0.889 0.900 0.000 0.100
#> GSM372352 3 0.1015 0.926 0.012 0.008 0.980
#> GSM372354 1 0.0000 0.984 1.000 0.000 0.000
#> GSM372356 1 0.0000 0.984 1.000 0.000 0.000
#> GSM372358 1 0.0000 0.984 1.000 0.000 0.000
#> GSM372360 1 0.0000 0.984 1.000 0.000 0.000
#> GSM372362 1 0.0000 0.984 1.000 0.000 0.000
#> GSM372364 1 0.0000 0.984 1.000 0.000 0.000
#> GSM372365 1 0.0000 0.984 1.000 0.000 0.000
#> GSM372366 1 0.0000 0.984 1.000 0.000 0.000
#> GSM372367 1 0.0000 0.984 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM372286 2 0.3342 0.902 0.000 0.868 0.032 0.100
#> GSM372287 2 0.3444 0.865 0.000 0.816 0.000 0.184
#> GSM372288 2 0.3123 0.874 0.000 0.844 0.000 0.156
#> GSM372289 2 0.3123 0.874 0.000 0.844 0.000 0.156
#> GSM372290 2 0.3495 0.890 0.000 0.844 0.016 0.140
#> GSM372291 4 0.6214 0.756 0.360 0.000 0.064 0.576
#> GSM372292 3 0.5674 0.742 0.000 0.132 0.720 0.148
#> GSM372293 3 0.3547 0.838 0.000 0.016 0.840 0.144
#> GSM372294 2 0.4422 0.834 0.000 0.736 0.008 0.256
#> GSM372295 3 0.6414 0.649 0.000 0.124 0.636 0.240
#> GSM372296 2 0.4175 0.865 0.000 0.784 0.016 0.200
#> GSM372297 2 0.4072 0.822 0.000 0.748 0.000 0.252
#> GSM372298 2 0.4040 0.824 0.000 0.752 0.000 0.248
#> GSM372299 3 0.6414 0.649 0.000 0.124 0.636 0.240
#> GSM372300 3 0.3547 0.838 0.000 0.016 0.840 0.144
#> GSM372301 3 0.5674 0.742 0.000 0.132 0.720 0.148
#> GSM372302 2 0.4175 0.865 0.000 0.784 0.016 0.200
#> GSM372303 3 0.3547 0.838 0.000 0.016 0.840 0.144
#> GSM372304 2 0.4072 0.822 0.000 0.748 0.000 0.252
#> GSM372305 2 0.1389 0.901 0.000 0.952 0.048 0.000
#> GSM372306 2 0.1389 0.901 0.000 0.952 0.048 0.000
#> GSM372307 2 0.3278 0.896 0.000 0.864 0.020 0.116
#> GSM372309 2 0.3088 0.903 0.000 0.888 0.052 0.060
#> GSM372311 2 0.1302 0.903 0.000 0.956 0.044 0.000
#> GSM372313 2 0.1302 0.903 0.000 0.956 0.044 0.000
#> GSM372315 2 0.1302 0.903 0.000 0.956 0.044 0.000
#> GSM372317 2 0.1474 0.900 0.000 0.948 0.052 0.000
#> GSM372319 3 0.1637 0.893 0.000 0.060 0.940 0.000
#> GSM372321 3 0.1637 0.893 0.000 0.060 0.940 0.000
#> GSM372323 3 0.1151 0.902 0.008 0.024 0.968 0.000
#> GSM372326 3 0.1474 0.895 0.000 0.052 0.948 0.000
#> GSM372328 3 0.0000 0.899 0.000 0.000 1.000 0.000
#> GSM372330 2 0.1302 0.903 0.000 0.956 0.044 0.000
#> GSM372332 3 0.0000 0.899 0.000 0.000 1.000 0.000
#> GSM372335 2 0.1716 0.893 0.000 0.936 0.064 0.000
#> GSM372337 3 0.1151 0.902 0.008 0.024 0.968 0.000
#> GSM372339 3 0.0000 0.899 0.000 0.000 1.000 0.000
#> GSM372341 3 0.0000 0.899 0.000 0.000 1.000 0.000
#> GSM372343 3 0.0000 0.899 0.000 0.000 1.000 0.000
#> GSM372345 3 0.1151 0.902 0.008 0.024 0.968 0.000
#> GSM372347 3 0.1151 0.902 0.008 0.024 0.968 0.000
#> GSM372349 3 0.1042 0.902 0.000 0.020 0.972 0.008
#> GSM372351 3 0.1474 0.895 0.000 0.052 0.948 0.000
#> GSM372353 2 0.1867 0.888 0.000 0.928 0.072 0.000
#> GSM372355 2 0.1302 0.903 0.000 0.956 0.044 0.000
#> GSM372357 2 0.1489 0.902 0.000 0.952 0.044 0.004
#> GSM372359 2 0.1867 0.888 0.000 0.928 0.072 0.000
#> GSM372361 2 0.3464 0.898 0.000 0.860 0.032 0.108
#> GSM372363 2 0.3215 0.903 0.000 0.876 0.032 0.092
#> GSM372308 1 0.3142 0.786 0.860 0.008 0.000 0.132
#> GSM372310 1 0.3142 0.786 0.860 0.008 0.000 0.132
#> GSM372312 1 0.5294 -0.810 0.508 0.000 0.008 0.484
#> GSM372314 1 0.3351 0.767 0.844 0.008 0.000 0.148
#> GSM372316 1 0.0000 0.898 1.000 0.000 0.000 0.000
#> GSM372318 1 0.0000 0.898 1.000 0.000 0.000 0.000
#> GSM372320 1 0.0469 0.894 0.988 0.000 0.000 0.012
#> GSM372322 1 0.0188 0.898 0.996 0.000 0.000 0.004
#> GSM372324 1 0.3351 0.767 0.844 0.008 0.000 0.148
#> GSM372325 1 0.3351 0.767 0.844 0.008 0.000 0.148
#> GSM372327 1 0.0188 0.898 0.996 0.000 0.000 0.004
#> GSM372329 1 0.0188 0.898 0.996 0.000 0.000 0.004
#> GSM372331 1 0.3351 0.767 0.844 0.008 0.000 0.148
#> GSM372333 3 0.2418 0.880 0.032 0.024 0.928 0.016
#> GSM372334 1 0.0469 0.894 0.988 0.000 0.000 0.012
#> GSM372336 1 0.2216 0.835 0.908 0.000 0.000 0.092
#> GSM372338 1 0.0469 0.894 0.988 0.000 0.000 0.012
#> GSM372340 1 0.0469 0.894 0.988 0.000 0.000 0.012
#> GSM372342 1 0.0188 0.898 0.996 0.000 0.000 0.004
#> GSM372344 1 0.0469 0.894 0.988 0.000 0.000 0.012
#> GSM372346 1 0.0188 0.898 0.996 0.000 0.000 0.004
#> GSM372348 1 0.2216 0.835 0.908 0.000 0.000 0.092
#> GSM372350 4 0.5296 0.693 0.492 0.000 0.008 0.500
#> GSM372352 3 0.1191 0.902 0.004 0.024 0.968 0.004
#> GSM372354 1 0.0188 0.898 0.996 0.000 0.000 0.004
#> GSM372356 1 0.0188 0.899 0.996 0.000 0.000 0.004
#> GSM372358 1 0.0188 0.899 0.996 0.000 0.000 0.004
#> GSM372360 1 0.0336 0.898 0.992 0.000 0.000 0.008
#> GSM372362 1 0.0336 0.898 0.992 0.000 0.000 0.008
#> GSM372364 1 0.0336 0.898 0.992 0.000 0.000 0.008
#> GSM372365 1 0.0336 0.898 0.992 0.000 0.000 0.008
#> GSM372366 1 0.0000 0.898 1.000 0.000 0.000 0.000
#> GSM372367 1 0.1474 0.870 0.948 0.000 0.000 0.052
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM372286 2 0.3579 0.781 0.000 0.756 0.004 0.240 0.000
#> GSM372287 2 0.4192 0.709 0.000 0.596 0.000 0.404 0.000
#> GSM372288 2 0.4101 0.729 0.000 0.628 0.000 0.372 0.000
#> GSM372289 2 0.4101 0.729 0.000 0.628 0.000 0.372 0.000
#> GSM372290 2 0.3796 0.764 0.000 0.700 0.000 0.300 0.000
#> GSM372291 5 0.4638 0.727 0.104 0.000 0.044 0.068 0.784
#> GSM372292 3 0.5202 0.308 0.000 0.104 0.716 0.164 0.016
#> GSM372293 3 0.3292 0.637 0.000 0.008 0.836 0.140 0.016
#> GSM372294 2 0.5544 0.708 0.000 0.608 0.000 0.292 0.100
#> GSM372295 4 0.7475 1.000 0.000 0.092 0.392 0.400 0.116
#> GSM372296 2 0.4101 0.719 0.000 0.628 0.000 0.372 0.000
#> GSM372297 2 0.4297 0.636 0.000 0.528 0.000 0.472 0.000
#> GSM372298 2 0.4437 0.636 0.000 0.532 0.000 0.464 0.004
#> GSM372299 4 0.7475 1.000 0.000 0.092 0.392 0.400 0.116
#> GSM372300 3 0.3292 0.637 0.000 0.008 0.836 0.140 0.016
#> GSM372301 3 0.5202 0.308 0.000 0.104 0.716 0.164 0.016
#> GSM372302 2 0.4101 0.719 0.000 0.628 0.000 0.372 0.000
#> GSM372303 3 0.3292 0.637 0.000 0.008 0.836 0.140 0.016
#> GSM372304 2 0.4297 0.636 0.000 0.528 0.000 0.472 0.000
#> GSM372305 2 0.0162 0.800 0.000 0.996 0.000 0.004 0.000
#> GSM372306 2 0.0162 0.800 0.000 0.996 0.000 0.004 0.000
#> GSM372307 2 0.3452 0.782 0.000 0.756 0.000 0.244 0.000
#> GSM372309 2 0.2054 0.796 0.000 0.916 0.004 0.072 0.008
#> GSM372311 2 0.0000 0.801 0.000 1.000 0.000 0.000 0.000
#> GSM372313 2 0.0000 0.801 0.000 1.000 0.000 0.000 0.000
#> GSM372315 2 0.0000 0.801 0.000 1.000 0.000 0.000 0.000
#> GSM372317 2 0.0324 0.798 0.000 0.992 0.004 0.004 0.000
#> GSM372319 3 0.1851 0.808 0.000 0.088 0.912 0.000 0.000
#> GSM372321 3 0.1851 0.808 0.000 0.088 0.912 0.000 0.000
#> GSM372323 3 0.1597 0.839 0.000 0.048 0.940 0.012 0.000
#> GSM372326 3 0.1732 0.815 0.000 0.080 0.920 0.000 0.000
#> GSM372328 3 0.0000 0.825 0.000 0.000 1.000 0.000 0.000
#> GSM372330 2 0.0000 0.801 0.000 1.000 0.000 0.000 0.000
#> GSM372332 3 0.0000 0.825 0.000 0.000 1.000 0.000 0.000
#> GSM372335 2 0.0671 0.789 0.000 0.980 0.016 0.004 0.000
#> GSM372337 3 0.1597 0.839 0.000 0.048 0.940 0.012 0.000
#> GSM372339 3 0.0000 0.825 0.000 0.000 1.000 0.000 0.000
#> GSM372341 3 0.0000 0.825 0.000 0.000 1.000 0.000 0.000
#> GSM372343 3 0.0000 0.825 0.000 0.000 1.000 0.000 0.000
#> GSM372345 3 0.1597 0.839 0.000 0.048 0.940 0.012 0.000
#> GSM372347 3 0.1597 0.839 0.000 0.048 0.940 0.012 0.000
#> GSM372349 3 0.1408 0.839 0.000 0.044 0.948 0.000 0.008
#> GSM372351 3 0.1732 0.815 0.000 0.080 0.920 0.000 0.000
#> GSM372353 2 0.0865 0.784 0.000 0.972 0.024 0.004 0.000
#> GSM372355 2 0.0000 0.801 0.000 1.000 0.000 0.000 0.000
#> GSM372357 2 0.0290 0.799 0.000 0.992 0.000 0.008 0.000
#> GSM372359 2 0.0865 0.784 0.000 0.972 0.024 0.004 0.000
#> GSM372361 2 0.3858 0.783 0.000 0.760 0.008 0.224 0.008
#> GSM372363 2 0.2886 0.796 0.000 0.844 0.000 0.148 0.008
#> GSM372308 1 0.4083 0.698 0.728 0.008 0.000 0.256 0.008
#> GSM372310 1 0.4083 0.698 0.728 0.008 0.000 0.256 0.008
#> GSM372312 5 0.3766 0.734 0.268 0.000 0.000 0.004 0.728
#> GSM372314 1 0.4433 0.665 0.696 0.008 0.000 0.280 0.016
#> GSM372316 1 0.0000 0.861 1.000 0.000 0.000 0.000 0.000
#> GSM372318 1 0.0000 0.861 1.000 0.000 0.000 0.000 0.000
#> GSM372320 1 0.2179 0.819 0.888 0.000 0.000 0.000 0.112
#> GSM372322 1 0.1544 0.845 0.932 0.000 0.000 0.000 0.068
#> GSM372324 1 0.4433 0.665 0.696 0.008 0.000 0.280 0.016
#> GSM372325 1 0.4433 0.665 0.696 0.008 0.000 0.280 0.016
#> GSM372327 1 0.1544 0.845 0.932 0.000 0.000 0.000 0.068
#> GSM372329 1 0.1544 0.845 0.932 0.000 0.000 0.000 0.068
#> GSM372331 1 0.4433 0.665 0.696 0.008 0.000 0.280 0.016
#> GSM372333 3 0.2585 0.803 0.024 0.048 0.904 0.024 0.000
#> GSM372334 1 0.2179 0.819 0.888 0.000 0.000 0.000 0.112
#> GSM372336 1 0.3109 0.755 0.800 0.000 0.000 0.200 0.000
#> GSM372338 1 0.2179 0.819 0.888 0.000 0.000 0.000 0.112
#> GSM372340 1 0.2179 0.819 0.888 0.000 0.000 0.000 0.112
#> GSM372342 1 0.1544 0.845 0.932 0.000 0.000 0.000 0.068
#> GSM372344 1 0.2179 0.819 0.888 0.000 0.000 0.000 0.112
#> GSM372346 1 0.1544 0.845 0.932 0.000 0.000 0.000 0.068
#> GSM372348 1 0.3109 0.755 0.800 0.000 0.000 0.200 0.000
#> GSM372350 5 0.2471 0.788 0.136 0.000 0.000 0.000 0.864
#> GSM372352 3 0.1644 0.838 0.000 0.048 0.940 0.008 0.004
#> GSM372354 1 0.0290 0.861 0.992 0.000 0.000 0.000 0.008
#> GSM372356 1 0.0162 0.861 0.996 0.000 0.000 0.004 0.000
#> GSM372358 1 0.0162 0.861 0.996 0.000 0.000 0.004 0.000
#> GSM372360 1 0.0451 0.861 0.988 0.000 0.000 0.004 0.008
#> GSM372362 1 0.0451 0.861 0.988 0.000 0.000 0.004 0.008
#> GSM372364 1 0.0451 0.861 0.988 0.000 0.000 0.004 0.008
#> GSM372365 1 0.0451 0.861 0.988 0.000 0.000 0.004 0.008
#> GSM372366 1 0.0000 0.861 1.000 0.000 0.000 0.000 0.000
#> GSM372367 1 0.1981 0.836 0.920 0.000 0.000 0.064 0.016
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM372286 2 0.3965 -0.318 0.000 0.616 0.004 0.376 0.000 0.004
#> GSM372287 4 0.4039 0.837 0.000 0.424 0.000 0.568 0.000 0.008
#> GSM372288 4 0.3847 0.819 0.000 0.456 0.000 0.544 0.000 0.000
#> GSM372289 4 0.3847 0.819 0.000 0.456 0.000 0.544 0.000 0.000
#> GSM372290 2 0.4428 -0.477 0.000 0.580 0.000 0.388 0.000 0.032
#> GSM372291 5 0.2890 0.689 0.000 0.000 0.012 0.032 0.860 0.096
#> GSM372292 3 0.5125 0.628 0.000 0.084 0.696 0.056 0.000 0.164
#> GSM372293 3 0.3062 0.775 0.000 0.000 0.816 0.024 0.000 0.160
#> GSM372294 4 0.5520 0.749 0.000 0.440 0.000 0.452 0.100 0.008
#> GSM372295 6 0.2457 1.000 0.000 0.000 0.036 0.084 0.000 0.880
#> GSM372296 2 0.5065 -0.652 0.000 0.524 0.000 0.396 0.000 0.080
#> GSM372297 4 0.5265 0.826 0.000 0.400 0.000 0.500 0.000 0.100
#> GSM372298 4 0.5478 0.800 0.000 0.424 0.000 0.452 0.000 0.124
#> GSM372299 6 0.2457 1.000 0.000 0.000 0.036 0.084 0.000 0.880
#> GSM372300 3 0.3062 0.775 0.000 0.000 0.816 0.024 0.000 0.160
#> GSM372301 3 0.5125 0.628 0.000 0.084 0.696 0.056 0.000 0.164
#> GSM372302 2 0.5065 -0.652 0.000 0.524 0.000 0.396 0.000 0.080
#> GSM372303 3 0.3062 0.775 0.000 0.000 0.816 0.024 0.000 0.160
#> GSM372304 4 0.5265 0.826 0.000 0.400 0.000 0.500 0.000 0.100
#> GSM372305 2 0.0260 0.729 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM372306 2 0.0260 0.729 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM372307 2 0.3728 -0.157 0.000 0.652 0.000 0.344 0.000 0.004
#> GSM372309 2 0.1908 0.661 0.000 0.916 0.000 0.056 0.000 0.028
#> GSM372311 2 0.0000 0.730 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM372313 2 0.0000 0.730 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM372315 2 0.0000 0.730 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM372317 2 0.0291 0.728 0.000 0.992 0.004 0.000 0.000 0.004
#> GSM372319 3 0.1663 0.879 0.000 0.088 0.912 0.000 0.000 0.000
#> GSM372321 3 0.1663 0.879 0.000 0.088 0.912 0.000 0.000 0.000
#> GSM372323 3 0.1523 0.897 0.000 0.044 0.940 0.008 0.000 0.008
#> GSM372326 3 0.1556 0.883 0.000 0.080 0.920 0.000 0.000 0.000
#> GSM372328 3 0.0000 0.888 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372330 2 0.0000 0.730 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM372332 3 0.0000 0.888 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372335 2 0.0717 0.716 0.000 0.976 0.016 0.000 0.000 0.008
#> GSM372337 3 0.1523 0.897 0.000 0.044 0.940 0.008 0.000 0.008
#> GSM372339 3 0.0000 0.888 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372341 3 0.0000 0.888 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372343 3 0.0000 0.888 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372345 3 0.1523 0.897 0.000 0.044 0.940 0.008 0.000 0.008
#> GSM372347 3 0.1523 0.897 0.000 0.044 0.940 0.008 0.000 0.008
#> GSM372349 3 0.1265 0.897 0.000 0.044 0.948 0.000 0.008 0.000
#> GSM372351 3 0.1556 0.883 0.000 0.080 0.920 0.000 0.000 0.000
#> GSM372353 2 0.0891 0.708 0.000 0.968 0.024 0.000 0.000 0.008
#> GSM372355 2 0.0000 0.730 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM372357 2 0.0260 0.728 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM372359 2 0.0891 0.708 0.000 0.968 0.024 0.000 0.000 0.008
#> GSM372361 2 0.4040 0.111 0.000 0.688 0.000 0.280 0.000 0.032
#> GSM372363 2 0.2830 0.533 0.000 0.836 0.000 0.144 0.000 0.020
#> GSM372308 1 0.4058 0.569 0.616 0.008 0.000 0.372 0.000 0.004
#> GSM372310 1 0.4058 0.569 0.616 0.008 0.000 0.372 0.000 0.004
#> GSM372312 5 0.3707 0.629 0.144 0.000 0.000 0.016 0.796 0.044
#> GSM372314 1 0.4947 0.466 0.528 0.008 0.000 0.416 0.000 0.048
#> GSM372316 1 0.0000 0.815 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372318 1 0.0000 0.815 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372320 1 0.2300 0.769 0.856 0.000 0.000 0.000 0.144 0.000
#> GSM372322 1 0.1714 0.797 0.908 0.000 0.000 0.000 0.092 0.000
#> GSM372324 1 0.4947 0.466 0.528 0.008 0.000 0.416 0.000 0.048
#> GSM372325 1 0.4947 0.466 0.528 0.008 0.000 0.416 0.000 0.048
#> GSM372327 1 0.1714 0.797 0.908 0.000 0.000 0.000 0.092 0.000
#> GSM372329 1 0.1714 0.797 0.908 0.000 0.000 0.000 0.092 0.000
#> GSM372331 1 0.4947 0.466 0.528 0.008 0.000 0.416 0.000 0.048
#> GSM372333 3 0.2334 0.881 0.004 0.044 0.904 0.040 0.000 0.008
#> GSM372334 1 0.2300 0.769 0.856 0.000 0.000 0.000 0.144 0.000
#> GSM372336 1 0.3508 0.647 0.704 0.000 0.000 0.292 0.000 0.004
#> GSM372338 1 0.2300 0.769 0.856 0.000 0.000 0.000 0.144 0.000
#> GSM372340 1 0.2300 0.769 0.856 0.000 0.000 0.000 0.144 0.000
#> GSM372342 1 0.1714 0.797 0.908 0.000 0.000 0.000 0.092 0.000
#> GSM372344 1 0.2300 0.769 0.856 0.000 0.000 0.000 0.144 0.000
#> GSM372346 1 0.1714 0.797 0.908 0.000 0.000 0.000 0.092 0.000
#> GSM372348 1 0.3508 0.647 0.704 0.000 0.000 0.292 0.000 0.004
#> GSM372350 5 0.0000 0.697 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM372352 3 0.1554 0.897 0.000 0.044 0.940 0.004 0.004 0.008
#> GSM372354 1 0.0260 0.815 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM372356 1 0.0260 0.816 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM372358 1 0.0260 0.816 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM372360 1 0.0363 0.815 0.988 0.000 0.000 0.012 0.000 0.000
#> GSM372362 1 0.0363 0.815 0.988 0.000 0.000 0.012 0.000 0.000
#> GSM372364 1 0.0458 0.814 0.984 0.000 0.000 0.016 0.000 0.000
#> GSM372365 1 0.0363 0.815 0.988 0.000 0.000 0.012 0.000 0.000
#> GSM372366 1 0.0000 0.815 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372367 1 0.2842 0.755 0.852 0.000 0.000 0.104 0.000 0.044
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) specimen(p) individual(p) k
#> SD:hclust 82 5.16e-04 5.99e-16 0.999 2
#> SD:hclust 82 3.40e-04 7.97e-15 0.897 3
#> SD:hclust 81 4.53e-04 6.01e-14 0.712 4
#> SD:hclust 80 4.70e-05 1.58e-14 0.298 5
#> SD:hclust 72 4.38e-07 8.74e-16 0.137 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 51941 rows and 82 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 0.992 0.996 0.4782 0.524 0.524
#> 3 3 0.739 0.863 0.904 0.3664 0.808 0.633
#> 4 4 0.671 0.606 0.773 0.1206 0.969 0.908
#> 5 5 0.681 0.582 0.716 0.0694 0.819 0.467
#> 6 6 0.717 0.666 0.767 0.0475 0.943 0.733
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
#> GSM372286 2 0.000 0.994 0.000 1.000
#> GSM372287 2 0.000 0.994 0.000 1.000
#> GSM372288 2 0.000 0.994 0.000 1.000
#> GSM372289 2 0.000 0.994 0.000 1.000
#> GSM372290 2 0.000 0.994 0.000 1.000
#> GSM372291 2 0.224 0.959 0.036 0.964
#> GSM372292 2 0.000 0.994 0.000 1.000
#> GSM372293 2 0.000 0.994 0.000 1.000
#> GSM372294 2 0.000 0.994 0.000 1.000
#> GSM372295 2 0.000 0.994 0.000 1.000
#> GSM372296 2 0.000 0.994 0.000 1.000
#> GSM372297 2 0.000 0.994 0.000 1.000
#> GSM372298 2 0.000 0.994 0.000 1.000
#> GSM372299 2 0.000 0.994 0.000 1.000
#> GSM372300 2 0.000 0.994 0.000 1.000
#> GSM372301 2 0.000 0.994 0.000 1.000
#> GSM372302 2 0.000 0.994 0.000 1.000
#> GSM372303 2 0.000 0.994 0.000 1.000
#> GSM372304 2 0.000 0.994 0.000 1.000
#> GSM372305 2 0.000 0.994 0.000 1.000
#> GSM372306 2 0.000 0.994 0.000 1.000
#> GSM372307 2 0.000 0.994 0.000 1.000
#> GSM372309 2 0.000 0.994 0.000 1.000
#> GSM372311 2 0.000 0.994 0.000 1.000
#> GSM372313 2 0.000 0.994 0.000 1.000
#> GSM372315 2 0.000 0.994 0.000 1.000
#> GSM372317 2 0.000 0.994 0.000 1.000
#> GSM372319 2 0.000 0.994 0.000 1.000
#> GSM372321 2 0.000 0.994 0.000 1.000
#> GSM372323 2 0.000 0.994 0.000 1.000
#> GSM372326 2 0.000 0.994 0.000 1.000
#> GSM372328 2 0.000 0.994 0.000 1.000
#> GSM372330 2 0.000 0.994 0.000 1.000
#> GSM372332 2 0.000 0.994 0.000 1.000
#> GSM372335 2 0.000 0.994 0.000 1.000
#> GSM372337 2 0.000 0.994 0.000 1.000
#> GSM372339 2 0.000 0.994 0.000 1.000
#> GSM372341 2 0.000 0.994 0.000 1.000
#> GSM372343 2 0.000 0.994 0.000 1.000
#> GSM372345 2 0.000 0.994 0.000 1.000
#> GSM372347 2 0.000 0.994 0.000 1.000
#> GSM372349 2 0.000 0.994 0.000 1.000
#> GSM372351 2 0.000 0.994 0.000 1.000
#> GSM372353 2 0.000 0.994 0.000 1.000
#> GSM372355 2 0.000 0.994 0.000 1.000
#> GSM372357 2 0.000 0.994 0.000 1.000
#> GSM372359 2 0.000 0.994 0.000 1.000
#> GSM372361 2 0.000 0.994 0.000 1.000
#> GSM372363 2 0.000 0.994 0.000 1.000
#> GSM372308 1 0.000 1.000 1.000 0.000
#> GSM372310 1 0.000 1.000 1.000 0.000
#> GSM372312 1 0.000 1.000 1.000 0.000
#> GSM372314 1 0.000 1.000 1.000 0.000
#> GSM372316 1 0.000 1.000 1.000 0.000
#> GSM372318 1 0.000 1.000 1.000 0.000
#> GSM372320 1 0.000 1.000 1.000 0.000
#> GSM372322 1 0.000 1.000 1.000 0.000
#> GSM372324 1 0.000 1.000 1.000 0.000
#> GSM372325 1 0.000 1.000 1.000 0.000
#> GSM372327 1 0.000 1.000 1.000 0.000
#> GSM372329 1 0.000 1.000 1.000 0.000
#> GSM372331 1 0.000 1.000 1.000 0.000
#> GSM372333 2 0.827 0.651 0.260 0.740
#> GSM372334 1 0.000 1.000 1.000 0.000
#> GSM372336 1 0.000 1.000 1.000 0.000
#> GSM372338 1 0.000 1.000 1.000 0.000
#> GSM372340 1 0.000 1.000 1.000 0.000
#> GSM372342 1 0.000 1.000 1.000 0.000
#> GSM372344 1 0.000 1.000 1.000 0.000
#> GSM372346 1 0.000 1.000 1.000 0.000
#> GSM372348 1 0.000 1.000 1.000 0.000
#> GSM372350 1 0.000 1.000 1.000 0.000
#> GSM372352 2 0.000 0.994 0.000 1.000
#> GSM372354 1 0.000 1.000 1.000 0.000
#> GSM372356 1 0.000 1.000 1.000 0.000
#> GSM372358 1 0.000 1.000 1.000 0.000
#> GSM372360 1 0.000 1.000 1.000 0.000
#> GSM372362 1 0.000 1.000 1.000 0.000
#> GSM372364 1 0.000 1.000 1.000 0.000
#> GSM372365 1 0.000 1.000 1.000 0.000
#> GSM372366 1 0.000 1.000 1.000 0.000
#> GSM372367 1 0.000 1.000 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM372286 2 0.0000 0.873 0.000 1.000 0.000
#> GSM372287 2 0.0592 0.865 0.000 0.988 0.012
#> GSM372288 2 0.0000 0.873 0.000 1.000 0.000
#> GSM372289 2 0.0000 0.873 0.000 1.000 0.000
#> GSM372290 2 0.0000 0.873 0.000 1.000 0.000
#> GSM372291 3 0.7180 0.615 0.196 0.096 0.708
#> GSM372292 2 0.5678 0.506 0.000 0.684 0.316
#> GSM372293 3 0.4002 0.902 0.000 0.160 0.840
#> GSM372294 2 0.0592 0.865 0.000 0.988 0.012
#> GSM372295 2 0.0747 0.864 0.000 0.984 0.016
#> GSM372296 2 0.0000 0.873 0.000 1.000 0.000
#> GSM372297 2 0.0000 0.873 0.000 1.000 0.000
#> GSM372298 2 0.0000 0.873 0.000 1.000 0.000
#> GSM372299 2 0.5948 0.399 0.000 0.640 0.360
#> GSM372300 3 0.4796 0.847 0.000 0.220 0.780
#> GSM372301 3 0.6095 0.516 0.000 0.392 0.608
#> GSM372302 2 0.0000 0.873 0.000 1.000 0.000
#> GSM372303 3 0.3941 0.904 0.000 0.156 0.844
#> GSM372304 2 0.0000 0.873 0.000 1.000 0.000
#> GSM372305 2 0.1163 0.865 0.000 0.972 0.028
#> GSM372306 2 0.6026 0.394 0.000 0.624 0.376
#> GSM372307 2 0.0000 0.873 0.000 1.000 0.000
#> GSM372309 2 0.5733 0.521 0.000 0.676 0.324
#> GSM372311 2 0.1163 0.865 0.000 0.972 0.028
#> GSM372313 2 0.1163 0.865 0.000 0.972 0.028
#> GSM372315 2 0.0000 0.873 0.000 1.000 0.000
#> GSM372317 2 0.4178 0.741 0.000 0.828 0.172
#> GSM372319 3 0.5363 0.739 0.000 0.276 0.724
#> GSM372321 3 0.3482 0.921 0.000 0.128 0.872
#> GSM372323 3 0.3482 0.921 0.000 0.128 0.872
#> GSM372326 3 0.3482 0.921 0.000 0.128 0.872
#> GSM372328 3 0.3482 0.921 0.000 0.128 0.872
#> GSM372330 2 0.1163 0.865 0.000 0.972 0.028
#> GSM372332 3 0.3482 0.921 0.000 0.128 0.872
#> GSM372335 2 0.6168 0.281 0.000 0.588 0.412
#> GSM372337 3 0.3482 0.921 0.000 0.128 0.872
#> GSM372339 3 0.3482 0.921 0.000 0.128 0.872
#> GSM372341 3 0.3482 0.921 0.000 0.128 0.872
#> GSM372343 3 0.3482 0.921 0.000 0.128 0.872
#> GSM372345 3 0.3482 0.921 0.000 0.128 0.872
#> GSM372347 3 0.2448 0.880 0.000 0.076 0.924
#> GSM372349 3 0.3267 0.914 0.000 0.116 0.884
#> GSM372351 3 0.3482 0.921 0.000 0.128 0.872
#> GSM372353 3 0.5431 0.726 0.000 0.284 0.716
#> GSM372355 2 0.1163 0.865 0.000 0.972 0.028
#> GSM372357 2 0.5733 0.521 0.000 0.676 0.324
#> GSM372359 2 0.5785 0.504 0.000 0.668 0.332
#> GSM372361 2 0.0000 0.873 0.000 1.000 0.000
#> GSM372363 2 0.1163 0.865 0.000 0.972 0.028
#> GSM372308 1 0.2356 0.955 0.928 0.000 0.072
#> GSM372310 1 0.2356 0.955 0.928 0.000 0.072
#> GSM372312 1 0.2625 0.950 0.916 0.000 0.084
#> GSM372314 1 0.2356 0.955 0.928 0.000 0.072
#> GSM372316 1 0.0237 0.963 0.996 0.000 0.004
#> GSM372318 1 0.1529 0.959 0.960 0.000 0.040
#> GSM372320 1 0.1643 0.958 0.956 0.000 0.044
#> GSM372322 1 0.1643 0.958 0.956 0.000 0.044
#> GSM372324 1 0.2356 0.955 0.928 0.000 0.072
#> GSM372325 1 0.2356 0.955 0.928 0.000 0.072
#> GSM372327 1 0.1643 0.958 0.956 0.000 0.044
#> GSM372329 1 0.1643 0.958 0.956 0.000 0.044
#> GSM372331 1 0.2356 0.955 0.928 0.000 0.072
#> GSM372333 3 0.2173 0.849 0.008 0.048 0.944
#> GSM372334 1 0.1643 0.958 0.956 0.000 0.044
#> GSM372336 1 0.1964 0.959 0.944 0.000 0.056
#> GSM372338 1 0.1643 0.958 0.956 0.000 0.044
#> GSM372340 1 0.1643 0.958 0.956 0.000 0.044
#> GSM372342 1 0.1643 0.958 0.956 0.000 0.044
#> GSM372344 1 0.1643 0.958 0.956 0.000 0.044
#> GSM372346 1 0.1529 0.959 0.960 0.000 0.040
#> GSM372348 1 0.2356 0.955 0.928 0.000 0.072
#> GSM372350 1 0.2959 0.951 0.900 0.000 0.100
#> GSM372352 3 0.2356 0.877 0.000 0.072 0.928
#> GSM372354 1 0.0000 0.964 1.000 0.000 0.000
#> GSM372356 1 0.0892 0.963 0.980 0.000 0.020
#> GSM372358 1 0.0892 0.963 0.980 0.000 0.020
#> GSM372360 1 0.0892 0.963 0.980 0.000 0.020
#> GSM372362 1 0.0424 0.964 0.992 0.000 0.008
#> GSM372364 1 0.0892 0.963 0.980 0.000 0.020
#> GSM372365 1 0.2165 0.957 0.936 0.000 0.064
#> GSM372366 1 0.0000 0.964 1.000 0.000 0.000
#> GSM372367 1 0.2356 0.955 0.928 0.000 0.072
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM372286 2 0.1557 0.6219 0.000 0.944 0.000 0.056
#> GSM372287 2 0.4866 0.1717 0.000 0.596 0.000 0.404
#> GSM372288 2 0.4431 0.3835 0.000 0.696 0.000 0.304
#> GSM372289 2 0.2921 0.5746 0.000 0.860 0.000 0.140
#> GSM372290 2 0.4431 0.3835 0.000 0.696 0.000 0.304
#> GSM372291 4 0.3895 0.2229 0.000 0.012 0.184 0.804
#> GSM372292 4 0.7740 0.4496 0.000 0.328 0.244 0.428
#> GSM372293 3 0.5349 0.4023 0.000 0.024 0.640 0.336
#> GSM372294 2 0.4830 0.2472 0.000 0.608 0.000 0.392
#> GSM372295 4 0.5143 -0.0474 0.000 0.456 0.004 0.540
#> GSM372296 2 0.4431 0.3835 0.000 0.696 0.000 0.304
#> GSM372297 2 0.4916 0.1101 0.000 0.576 0.000 0.424
#> GSM372298 2 0.4916 0.1101 0.000 0.576 0.000 0.424
#> GSM372299 4 0.7756 0.4499 0.000 0.320 0.252 0.428
#> GSM372300 3 0.6074 0.3045 0.000 0.060 0.600 0.340
#> GSM372301 3 0.7421 -0.2281 0.000 0.172 0.456 0.372
#> GSM372302 2 0.4830 0.1921 0.000 0.608 0.000 0.392
#> GSM372303 3 0.5460 0.3850 0.000 0.028 0.632 0.340
#> GSM372304 2 0.4830 0.1921 0.000 0.608 0.000 0.392
#> GSM372305 2 0.0188 0.6322 0.000 0.996 0.004 0.000
#> GSM372306 2 0.4567 0.3176 0.000 0.716 0.276 0.008
#> GSM372307 2 0.2081 0.6100 0.000 0.916 0.000 0.084
#> GSM372309 2 0.4775 0.3697 0.000 0.740 0.232 0.028
#> GSM372311 2 0.0188 0.6322 0.000 0.996 0.004 0.000
#> GSM372313 2 0.0188 0.6322 0.000 0.996 0.004 0.000
#> GSM372315 2 0.0000 0.6319 0.000 1.000 0.000 0.000
#> GSM372317 2 0.2466 0.5576 0.000 0.900 0.096 0.004
#> GSM372319 3 0.2921 0.6772 0.000 0.140 0.860 0.000
#> GSM372321 3 0.0707 0.7795 0.000 0.020 0.980 0.000
#> GSM372323 3 0.0707 0.7795 0.000 0.020 0.980 0.000
#> GSM372326 3 0.0707 0.7795 0.000 0.020 0.980 0.000
#> GSM372328 3 0.1624 0.7806 0.000 0.020 0.952 0.028
#> GSM372330 2 0.0376 0.6308 0.000 0.992 0.004 0.004
#> GSM372332 3 0.1624 0.7806 0.000 0.020 0.952 0.028
#> GSM372335 2 0.4804 0.3016 0.000 0.708 0.276 0.016
#> GSM372337 3 0.0707 0.7795 0.000 0.020 0.980 0.000
#> GSM372339 3 0.1624 0.7806 0.000 0.020 0.952 0.028
#> GSM372341 3 0.1624 0.7806 0.000 0.020 0.952 0.028
#> GSM372343 3 0.1624 0.7806 0.000 0.020 0.952 0.028
#> GSM372345 3 0.0707 0.7795 0.000 0.020 0.980 0.000
#> GSM372347 3 0.4215 0.6589 0.000 0.072 0.824 0.104
#> GSM372349 3 0.2737 0.7236 0.000 0.008 0.888 0.104
#> GSM372351 3 0.1624 0.7806 0.000 0.020 0.952 0.028
#> GSM372353 3 0.5691 0.2023 0.000 0.408 0.564 0.028
#> GSM372355 2 0.0188 0.6322 0.000 0.996 0.004 0.000
#> GSM372357 2 0.4775 0.3697 0.000 0.740 0.232 0.028
#> GSM372359 2 0.4502 0.3704 0.000 0.748 0.236 0.016
#> GSM372361 2 0.2216 0.6113 0.000 0.908 0.000 0.092
#> GSM372363 2 0.0657 0.6274 0.000 0.984 0.004 0.012
#> GSM372308 1 0.4690 0.7662 0.724 0.000 0.016 0.260
#> GSM372310 1 0.4690 0.7662 0.724 0.000 0.016 0.260
#> GSM372312 1 0.4746 0.6856 0.632 0.000 0.000 0.368
#> GSM372314 1 0.4576 0.7661 0.728 0.000 0.012 0.260
#> GSM372316 1 0.0188 0.8353 0.996 0.000 0.000 0.004
#> GSM372318 1 0.2868 0.8193 0.864 0.000 0.000 0.136
#> GSM372320 1 0.3208 0.8154 0.848 0.000 0.004 0.148
#> GSM372322 1 0.3074 0.8156 0.848 0.000 0.000 0.152
#> GSM372324 1 0.4546 0.7684 0.732 0.000 0.012 0.256
#> GSM372325 1 0.5256 0.7454 0.700 0.000 0.040 0.260
#> GSM372327 1 0.3074 0.8156 0.848 0.000 0.000 0.152
#> GSM372329 1 0.3074 0.8156 0.848 0.000 0.000 0.152
#> GSM372331 1 0.4576 0.7661 0.728 0.000 0.012 0.260
#> GSM372333 3 0.6112 0.4700 0.016 0.056 0.668 0.260
#> GSM372334 1 0.3208 0.8154 0.848 0.000 0.004 0.148
#> GSM372336 1 0.4098 0.7911 0.784 0.000 0.012 0.204
#> GSM372338 1 0.3208 0.8154 0.848 0.000 0.004 0.148
#> GSM372340 1 0.3208 0.8154 0.848 0.000 0.004 0.148
#> GSM372342 1 0.3074 0.8156 0.848 0.000 0.000 0.152
#> GSM372344 1 0.3208 0.8154 0.848 0.000 0.004 0.148
#> GSM372346 1 0.2973 0.8175 0.856 0.000 0.000 0.144
#> GSM372348 1 0.4485 0.7747 0.740 0.000 0.012 0.248
#> GSM372350 1 0.5158 0.6883 0.524 0.000 0.004 0.472
#> GSM372352 3 0.6215 0.4089 0.000 0.072 0.600 0.328
#> GSM372354 1 0.0657 0.8349 0.984 0.000 0.004 0.012
#> GSM372356 1 0.0592 0.8343 0.984 0.000 0.000 0.016
#> GSM372358 1 0.0592 0.8350 0.984 0.000 0.000 0.016
#> GSM372360 1 0.0779 0.8343 0.980 0.000 0.004 0.016
#> GSM372362 1 0.0524 0.8348 0.988 0.000 0.004 0.008
#> GSM372364 1 0.0779 0.8343 0.980 0.000 0.004 0.016
#> GSM372365 1 0.4502 0.7779 0.748 0.000 0.016 0.236
#> GSM372366 1 0.0657 0.8349 0.984 0.000 0.004 0.012
#> GSM372367 1 0.4576 0.7661 0.728 0.000 0.012 0.260
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM372286 2 0.3305 0.5257 0.000 0.776 0.000 0.224 0.000
#> GSM372287 4 0.4015 0.5085 0.000 0.348 0.000 0.652 0.000
#> GSM372288 4 0.4249 0.3908 0.000 0.432 0.000 0.568 0.000
#> GSM372289 2 0.4088 0.2141 0.000 0.632 0.000 0.368 0.000
#> GSM372290 4 0.4249 0.3908 0.000 0.432 0.000 0.568 0.000
#> GSM372291 5 0.4824 -0.3007 0.000 0.000 0.020 0.468 0.512
#> GSM372292 4 0.7612 0.5009 0.000 0.124 0.216 0.504 0.156
#> GSM372293 4 0.6659 0.2245 0.000 0.012 0.396 0.436 0.156
#> GSM372294 4 0.5618 0.4375 0.000 0.280 0.000 0.608 0.112
#> GSM372295 4 0.5550 0.4685 0.000 0.148 0.004 0.660 0.188
#> GSM372296 4 0.4235 0.4027 0.000 0.424 0.000 0.576 0.000
#> GSM372297 4 0.4522 0.5279 0.000 0.316 0.000 0.660 0.024
#> GSM372298 4 0.5699 0.5125 0.000 0.308 0.000 0.584 0.108
#> GSM372299 4 0.8089 0.4453 0.000 0.164 0.208 0.436 0.192
#> GSM372300 4 0.6889 0.2543 0.000 0.024 0.384 0.436 0.156
#> GSM372301 4 0.7295 0.3572 0.000 0.056 0.328 0.460 0.156
#> GSM372302 4 0.4015 0.5085 0.000 0.348 0.000 0.652 0.000
#> GSM372303 4 0.6659 0.2245 0.000 0.012 0.396 0.436 0.156
#> GSM372304 4 0.3999 0.5115 0.000 0.344 0.000 0.656 0.000
#> GSM372305 2 0.0324 0.7702 0.000 0.992 0.004 0.004 0.000
#> GSM372306 2 0.4088 0.7161 0.000 0.812 0.116 0.040 0.032
#> GSM372307 2 0.4130 0.3972 0.000 0.696 0.000 0.292 0.012
#> GSM372309 2 0.4616 0.7152 0.000 0.788 0.096 0.060 0.056
#> GSM372311 2 0.0162 0.7715 0.000 0.996 0.004 0.000 0.000
#> GSM372313 2 0.0671 0.7732 0.000 0.980 0.004 0.000 0.016
#> GSM372315 2 0.0404 0.7655 0.000 0.988 0.000 0.012 0.000
#> GSM372317 2 0.2483 0.7611 0.000 0.908 0.048 0.028 0.016
#> GSM372319 3 0.1430 0.8800 0.000 0.052 0.944 0.004 0.000
#> GSM372321 3 0.0324 0.9203 0.000 0.004 0.992 0.000 0.004
#> GSM372323 3 0.0162 0.9213 0.000 0.000 0.996 0.000 0.004
#> GSM372326 3 0.0162 0.9216 0.000 0.000 0.996 0.004 0.000
#> GSM372328 3 0.0510 0.9224 0.000 0.000 0.984 0.016 0.000
#> GSM372330 2 0.0865 0.7717 0.000 0.972 0.004 0.024 0.000
#> GSM372332 3 0.0510 0.9224 0.000 0.000 0.984 0.016 0.000
#> GSM372335 2 0.4253 0.7099 0.000 0.804 0.112 0.052 0.032
#> GSM372337 3 0.0703 0.9130 0.000 0.000 0.976 0.000 0.024
#> GSM372339 3 0.0510 0.9224 0.000 0.000 0.984 0.016 0.000
#> GSM372341 3 0.0510 0.9224 0.000 0.000 0.984 0.016 0.000
#> GSM372343 3 0.0510 0.9224 0.000 0.000 0.984 0.016 0.000
#> GSM372345 3 0.0703 0.9130 0.000 0.000 0.976 0.000 0.024
#> GSM372347 3 0.5733 0.4406 0.000 0.096 0.588 0.004 0.312
#> GSM372349 3 0.4801 0.6677 0.000 0.000 0.728 0.124 0.148
#> GSM372351 3 0.0703 0.9191 0.000 0.000 0.976 0.024 0.000
#> GSM372353 2 0.5743 0.4723 0.000 0.632 0.276 0.060 0.032
#> GSM372355 2 0.0162 0.7715 0.000 0.996 0.004 0.000 0.000
#> GSM372357 2 0.4410 0.7173 0.000 0.800 0.096 0.060 0.044
#> GSM372359 2 0.4101 0.7199 0.000 0.816 0.100 0.052 0.032
#> GSM372361 2 0.4054 0.5340 0.000 0.748 0.000 0.224 0.028
#> GSM372363 2 0.1743 0.7550 0.000 0.940 0.004 0.028 0.028
#> GSM372308 5 0.4874 0.5207 0.368 0.000 0.000 0.032 0.600
#> GSM372310 5 0.4874 0.5207 0.368 0.000 0.000 0.032 0.600
#> GSM372312 5 0.5295 0.4212 0.200 0.000 0.000 0.128 0.672
#> GSM372314 5 0.4201 0.5570 0.328 0.008 0.000 0.000 0.664
#> GSM372316 1 0.3551 0.6842 0.820 0.000 0.000 0.044 0.136
#> GSM372318 1 0.0865 0.7542 0.972 0.000 0.000 0.004 0.024
#> GSM372320 1 0.0727 0.7527 0.980 0.004 0.000 0.012 0.004
#> GSM372322 1 0.0000 0.7550 1.000 0.000 0.000 0.000 0.000
#> GSM372324 5 0.4088 0.5337 0.368 0.000 0.000 0.000 0.632
#> GSM372325 5 0.4183 0.5570 0.324 0.008 0.000 0.000 0.668
#> GSM372327 1 0.0000 0.7550 1.000 0.000 0.000 0.000 0.000
#> GSM372329 1 0.0290 0.7553 0.992 0.000 0.000 0.008 0.000
#> GSM372331 5 0.4235 0.5557 0.336 0.008 0.000 0.000 0.656
#> GSM372333 5 0.5189 -0.1710 0.004 0.032 0.464 0.000 0.500
#> GSM372334 1 0.0727 0.7527 0.980 0.004 0.000 0.012 0.004
#> GSM372336 1 0.5346 -0.1872 0.496 0.000 0.000 0.052 0.452
#> GSM372338 1 0.0727 0.7527 0.980 0.004 0.000 0.012 0.004
#> GSM372340 1 0.0451 0.7518 0.988 0.004 0.000 0.008 0.000
#> GSM372342 1 0.0000 0.7550 1.000 0.000 0.000 0.000 0.000
#> GSM372344 1 0.0727 0.7527 0.980 0.004 0.000 0.012 0.004
#> GSM372346 1 0.0566 0.7559 0.984 0.000 0.000 0.004 0.012
#> GSM372348 5 0.4825 0.4588 0.408 0.000 0.000 0.024 0.568
#> GSM372350 1 0.6121 -0.0749 0.488 0.000 0.000 0.132 0.380
#> GSM372352 5 0.6298 -0.0792 0.000 0.044 0.352 0.064 0.540
#> GSM372354 1 0.4409 0.6638 0.768 0.004 0.000 0.080 0.148
#> GSM372356 1 0.5136 0.5042 0.660 0.000 0.000 0.080 0.260
#> GSM372358 1 0.5013 0.5350 0.680 0.000 0.000 0.080 0.240
#> GSM372360 1 0.5136 0.5042 0.660 0.000 0.000 0.080 0.260
#> GSM372362 1 0.4449 0.6376 0.752 0.000 0.000 0.080 0.168
#> GSM372364 1 0.5136 0.5042 0.660 0.000 0.000 0.080 0.260
#> GSM372365 5 0.5684 0.2840 0.432 0.000 0.000 0.080 0.488
#> GSM372366 1 0.4254 0.6582 0.772 0.000 0.000 0.080 0.148
#> GSM372367 5 0.5480 0.4765 0.368 0.000 0.000 0.072 0.560
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM372286 2 0.4214 -0.0798 0.000 0.528 0.000 0.460 0.004 0.008
#> GSM372287 4 0.2673 0.7435 0.000 0.132 0.000 0.852 0.004 0.012
#> GSM372288 4 0.2805 0.7544 0.000 0.184 0.000 0.812 0.004 0.000
#> GSM372289 4 0.3699 0.5569 0.000 0.336 0.000 0.660 0.004 0.000
#> GSM372290 4 0.2805 0.7544 0.000 0.184 0.000 0.812 0.004 0.000
#> GSM372291 6 0.5992 0.2233 0.000 0.004 0.000 0.284 0.236 0.476
#> GSM372292 6 0.6936 0.6403 0.000 0.084 0.176 0.320 0.000 0.420
#> GSM372293 6 0.6499 0.7639 0.000 0.028 0.316 0.228 0.000 0.428
#> GSM372294 4 0.5248 0.5023 0.000 0.100 0.000 0.684 0.052 0.164
#> GSM372295 4 0.6011 0.1430 0.000 0.052 0.000 0.536 0.096 0.316
#> GSM372296 4 0.2664 0.7546 0.000 0.184 0.000 0.816 0.000 0.000
#> GSM372297 4 0.3748 0.6622 0.000 0.112 0.000 0.792 0.004 0.092
#> GSM372298 4 0.5172 0.2829 0.000 0.124 0.000 0.592 0.000 0.284
#> GSM372299 6 0.7694 0.6066 0.000 0.172 0.148 0.216 0.028 0.436
#> GSM372300 6 0.6679 0.7736 0.000 0.040 0.300 0.240 0.000 0.420
#> GSM372301 6 0.6811 0.7671 0.000 0.052 0.280 0.248 0.000 0.420
#> GSM372302 4 0.2573 0.7435 0.000 0.132 0.000 0.856 0.004 0.008
#> GSM372303 6 0.6506 0.7683 0.000 0.028 0.312 0.232 0.000 0.428
#> GSM372304 4 0.2573 0.7435 0.000 0.132 0.000 0.856 0.004 0.008
#> GSM372305 2 0.1757 0.8351 0.000 0.916 0.000 0.076 0.008 0.000
#> GSM372306 2 0.1442 0.8244 0.000 0.944 0.040 0.000 0.004 0.012
#> GSM372307 4 0.3975 0.4255 0.000 0.392 0.000 0.600 0.008 0.000
#> GSM372309 2 0.1962 0.8213 0.000 0.924 0.028 0.000 0.028 0.020
#> GSM372311 2 0.1643 0.8400 0.000 0.924 0.000 0.068 0.008 0.000
#> GSM372313 2 0.1267 0.8451 0.000 0.940 0.000 0.060 0.000 0.000
#> GSM372315 2 0.1701 0.8378 0.000 0.920 0.000 0.072 0.008 0.000
#> GSM372317 2 0.0717 0.8430 0.000 0.976 0.000 0.016 0.000 0.008
#> GSM372319 3 0.1285 0.9083 0.000 0.052 0.944 0.000 0.004 0.000
#> GSM372321 3 0.0935 0.9251 0.000 0.032 0.964 0.000 0.004 0.000
#> GSM372323 3 0.0865 0.9244 0.000 0.036 0.964 0.000 0.000 0.000
#> GSM372326 3 0.0790 0.9257 0.000 0.032 0.968 0.000 0.000 0.000
#> GSM372328 3 0.0508 0.9233 0.000 0.000 0.984 0.000 0.004 0.012
#> GSM372330 2 0.1267 0.8451 0.000 0.940 0.000 0.060 0.000 0.000
#> GSM372332 3 0.0508 0.9233 0.000 0.000 0.984 0.000 0.004 0.012
#> GSM372335 2 0.1511 0.8209 0.000 0.940 0.044 0.000 0.004 0.012
#> GSM372337 3 0.1010 0.9232 0.000 0.036 0.960 0.000 0.000 0.004
#> GSM372339 3 0.0508 0.9233 0.000 0.000 0.984 0.000 0.004 0.012
#> GSM372341 3 0.0508 0.9233 0.000 0.000 0.984 0.000 0.004 0.012
#> GSM372343 3 0.0508 0.9233 0.000 0.000 0.984 0.000 0.004 0.012
#> GSM372345 3 0.1010 0.9232 0.000 0.036 0.960 0.000 0.000 0.004
#> GSM372347 5 0.5858 0.2818 0.000 0.140 0.312 0.004 0.532 0.012
#> GSM372349 3 0.5912 0.4496 0.000 0.008 0.624 0.084 0.072 0.212
#> GSM372351 3 0.0146 0.9250 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM372353 2 0.2699 0.7334 0.000 0.864 0.108 0.000 0.008 0.020
#> GSM372355 2 0.1267 0.8451 0.000 0.940 0.000 0.060 0.000 0.000
#> GSM372357 2 0.1313 0.8303 0.000 0.952 0.028 0.000 0.004 0.016
#> GSM372359 2 0.1080 0.8305 0.000 0.960 0.032 0.000 0.004 0.004
#> GSM372361 2 0.5029 0.1667 0.000 0.564 0.000 0.376 0.032 0.028
#> GSM372363 2 0.2502 0.8222 0.000 0.884 0.000 0.084 0.020 0.012
#> GSM372308 5 0.3637 0.7038 0.124 0.000 0.000 0.000 0.792 0.084
#> GSM372310 5 0.3678 0.7016 0.128 0.000 0.000 0.000 0.788 0.084
#> GSM372312 5 0.5587 0.4307 0.036 0.000 0.000 0.108 0.616 0.240
#> GSM372314 5 0.2257 0.7191 0.116 0.008 0.000 0.000 0.876 0.000
#> GSM372316 1 0.4256 0.6297 0.744 0.000 0.000 0.004 0.140 0.112
#> GSM372318 1 0.1257 0.7310 0.952 0.000 0.000 0.000 0.028 0.020
#> GSM372320 1 0.1461 0.7259 0.940 0.000 0.000 0.016 0.000 0.044
#> GSM372322 1 0.0000 0.7334 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372324 5 0.2278 0.7159 0.128 0.000 0.000 0.004 0.868 0.000
#> GSM372325 5 0.2551 0.7180 0.108 0.012 0.004 0.004 0.872 0.000
#> GSM372327 1 0.0000 0.7334 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372329 1 0.0363 0.7336 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM372331 5 0.2400 0.7191 0.116 0.008 0.000 0.004 0.872 0.000
#> GSM372333 5 0.4702 0.4747 0.000 0.052 0.256 0.004 0.676 0.012
#> GSM372334 1 0.1461 0.7259 0.940 0.000 0.000 0.016 0.000 0.044
#> GSM372336 5 0.5415 0.3788 0.304 0.000 0.000 0.004 0.564 0.128
#> GSM372338 1 0.1461 0.7259 0.940 0.000 0.000 0.016 0.000 0.044
#> GSM372340 1 0.1151 0.7267 0.956 0.000 0.000 0.012 0.000 0.032
#> GSM372342 1 0.0000 0.7334 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372344 1 0.1461 0.7259 0.940 0.000 0.000 0.016 0.000 0.044
#> GSM372346 1 0.0862 0.7322 0.972 0.000 0.000 0.004 0.016 0.008
#> GSM372348 5 0.4415 0.5906 0.236 0.000 0.000 0.004 0.696 0.064
#> GSM372350 1 0.7364 -0.1092 0.352 0.000 0.000 0.116 0.292 0.240
#> GSM372352 5 0.5533 0.4327 0.000 0.052 0.208 0.008 0.656 0.076
#> GSM372354 1 0.5196 0.5876 0.616 0.000 0.000 0.004 0.128 0.252
#> GSM372356 1 0.5783 0.3692 0.496 0.000 0.000 0.000 0.292 0.212
#> GSM372358 1 0.5807 0.4070 0.520 0.000 0.000 0.004 0.272 0.204
#> GSM372360 1 0.5805 0.3770 0.496 0.000 0.000 0.000 0.276 0.228
#> GSM372362 1 0.5282 0.5355 0.600 0.000 0.000 0.000 0.172 0.228
#> GSM372364 1 0.5818 0.3688 0.492 0.000 0.000 0.000 0.280 0.228
#> GSM372365 5 0.5388 0.5121 0.188 0.000 0.000 0.000 0.584 0.228
#> GSM372366 1 0.4977 0.5795 0.636 0.000 0.000 0.000 0.128 0.236
#> GSM372367 5 0.4613 0.6351 0.128 0.000 0.000 0.000 0.692 0.180
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) specimen(p) individual(p) k
#> SD:kmeans 82 1.04e-04 8.49e-17 0.999 2
#> SD:kmeans 79 1.32e-05 4.98e-16 0.894 3
#> SD:kmeans 57 2.64e-03 1.86e-13 0.974 4
#> SD:kmeans 59 3.52e-08 2.11e-17 0.551 5
#> SD:kmeans 65 7.66e-11 8.85e-21 0.424 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 51941 rows and 82 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 0.990 0.996 0.4904 0.509 0.509
#> 3 3 0.970 0.930 0.972 0.3334 0.826 0.662
#> 4 4 0.974 0.956 0.971 0.1221 0.867 0.641
#> 5 5 0.825 0.741 0.858 0.0581 0.986 0.948
#> 6 6 0.832 0.793 0.853 0.0446 0.906 0.657
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 2 3
There is also optional best \(k\) = 2 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM372286 2 0.0000 1.000 0.000 1.000
#> GSM372287 2 0.0000 1.000 0.000 1.000
#> GSM372288 2 0.0000 1.000 0.000 1.000
#> GSM372289 2 0.0000 1.000 0.000 1.000
#> GSM372290 2 0.0000 1.000 0.000 1.000
#> GSM372291 1 0.0000 0.990 1.000 0.000
#> GSM372292 2 0.0000 1.000 0.000 1.000
#> GSM372293 2 0.0000 1.000 0.000 1.000
#> GSM372294 2 0.0000 1.000 0.000 1.000
#> GSM372295 2 0.0000 1.000 0.000 1.000
#> GSM372296 2 0.0000 1.000 0.000 1.000
#> GSM372297 2 0.0000 1.000 0.000 1.000
#> GSM372298 2 0.0000 1.000 0.000 1.000
#> GSM372299 2 0.0000 1.000 0.000 1.000
#> GSM372300 2 0.0000 1.000 0.000 1.000
#> GSM372301 2 0.0000 1.000 0.000 1.000
#> GSM372302 2 0.0000 1.000 0.000 1.000
#> GSM372303 2 0.0000 1.000 0.000 1.000
#> GSM372304 2 0.0000 1.000 0.000 1.000
#> GSM372305 2 0.0000 1.000 0.000 1.000
#> GSM372306 2 0.0000 1.000 0.000 1.000
#> GSM372307 2 0.0000 1.000 0.000 1.000
#> GSM372309 2 0.0000 1.000 0.000 1.000
#> GSM372311 2 0.0000 1.000 0.000 1.000
#> GSM372313 2 0.0000 1.000 0.000 1.000
#> GSM372315 2 0.0000 1.000 0.000 1.000
#> GSM372317 2 0.0000 1.000 0.000 1.000
#> GSM372319 2 0.0000 1.000 0.000 1.000
#> GSM372321 2 0.0000 1.000 0.000 1.000
#> GSM372323 2 0.0000 1.000 0.000 1.000
#> GSM372326 2 0.0000 1.000 0.000 1.000
#> GSM372328 2 0.0000 1.000 0.000 1.000
#> GSM372330 2 0.0000 1.000 0.000 1.000
#> GSM372332 2 0.0000 1.000 0.000 1.000
#> GSM372335 2 0.0000 1.000 0.000 1.000
#> GSM372337 2 0.0000 1.000 0.000 1.000
#> GSM372339 2 0.0000 1.000 0.000 1.000
#> GSM372341 2 0.0000 1.000 0.000 1.000
#> GSM372343 2 0.0000 1.000 0.000 1.000
#> GSM372345 2 0.0000 1.000 0.000 1.000
#> GSM372347 2 0.0000 1.000 0.000 1.000
#> GSM372349 2 0.0000 1.000 0.000 1.000
#> GSM372351 2 0.0000 1.000 0.000 1.000
#> GSM372353 2 0.0000 1.000 0.000 1.000
#> GSM372355 2 0.0000 1.000 0.000 1.000
#> GSM372357 2 0.0000 1.000 0.000 1.000
#> GSM372359 2 0.0000 1.000 0.000 1.000
#> GSM372361 2 0.0000 1.000 0.000 1.000
#> GSM372363 2 0.0000 1.000 0.000 1.000
#> GSM372308 1 0.0000 0.990 1.000 0.000
#> GSM372310 1 0.0000 0.990 1.000 0.000
#> GSM372312 1 0.0000 0.990 1.000 0.000
#> GSM372314 1 0.0000 0.990 1.000 0.000
#> GSM372316 1 0.0000 0.990 1.000 0.000
#> GSM372318 1 0.0000 0.990 1.000 0.000
#> GSM372320 1 0.0000 0.990 1.000 0.000
#> GSM372322 1 0.0000 0.990 1.000 0.000
#> GSM372324 1 0.0000 0.990 1.000 0.000
#> GSM372325 1 0.0000 0.990 1.000 0.000
#> GSM372327 1 0.0000 0.990 1.000 0.000
#> GSM372329 1 0.0000 0.990 1.000 0.000
#> GSM372331 1 0.0000 0.990 1.000 0.000
#> GSM372333 1 0.0672 0.982 0.992 0.008
#> GSM372334 1 0.0000 0.990 1.000 0.000
#> GSM372336 1 0.0000 0.990 1.000 0.000
#> GSM372338 1 0.0000 0.990 1.000 0.000
#> GSM372340 1 0.0000 0.990 1.000 0.000
#> GSM372342 1 0.0000 0.990 1.000 0.000
#> GSM372344 1 0.0000 0.990 1.000 0.000
#> GSM372346 1 0.0000 0.990 1.000 0.000
#> GSM372348 1 0.0000 0.990 1.000 0.000
#> GSM372350 1 0.0000 0.990 1.000 0.000
#> GSM372352 1 0.9209 0.495 0.664 0.336
#> GSM372354 1 0.0000 0.990 1.000 0.000
#> GSM372356 1 0.0000 0.990 1.000 0.000
#> GSM372358 1 0.0000 0.990 1.000 0.000
#> GSM372360 1 0.0000 0.990 1.000 0.000
#> GSM372362 1 0.0000 0.990 1.000 0.000
#> GSM372364 1 0.0000 0.990 1.000 0.000
#> GSM372365 1 0.0000 0.990 1.000 0.000
#> GSM372366 1 0.0000 0.990 1.000 0.000
#> GSM372367 1 0.0000 0.990 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM372286 2 0.0000 0.977 0.000 1.000 0.000
#> GSM372287 2 0.0000 0.977 0.000 1.000 0.000
#> GSM372288 2 0.0000 0.977 0.000 1.000 0.000
#> GSM372289 2 0.0000 0.977 0.000 1.000 0.000
#> GSM372290 2 0.0000 0.977 0.000 1.000 0.000
#> GSM372291 1 0.0237 0.984 0.996 0.000 0.004
#> GSM372292 2 0.0000 0.977 0.000 1.000 0.000
#> GSM372293 3 0.4887 0.708 0.000 0.228 0.772
#> GSM372294 2 0.0000 0.977 0.000 1.000 0.000
#> GSM372295 2 0.0000 0.977 0.000 1.000 0.000
#> GSM372296 2 0.0000 0.977 0.000 1.000 0.000
#> GSM372297 2 0.0000 0.977 0.000 1.000 0.000
#> GSM372298 2 0.0000 0.977 0.000 1.000 0.000
#> GSM372299 2 0.0000 0.977 0.000 1.000 0.000
#> GSM372300 3 0.6095 0.408 0.000 0.392 0.608
#> GSM372301 2 0.6225 0.130 0.000 0.568 0.432
#> GSM372302 2 0.0000 0.977 0.000 1.000 0.000
#> GSM372303 3 0.3340 0.832 0.000 0.120 0.880
#> GSM372304 2 0.0000 0.977 0.000 1.000 0.000
#> GSM372305 2 0.0000 0.977 0.000 1.000 0.000
#> GSM372306 2 0.0000 0.977 0.000 1.000 0.000
#> GSM372307 2 0.0000 0.977 0.000 1.000 0.000
#> GSM372309 2 0.0000 0.977 0.000 1.000 0.000
#> GSM372311 2 0.0000 0.977 0.000 1.000 0.000
#> GSM372313 2 0.0000 0.977 0.000 1.000 0.000
#> GSM372315 2 0.0000 0.977 0.000 1.000 0.000
#> GSM372317 2 0.0000 0.977 0.000 1.000 0.000
#> GSM372319 2 0.4605 0.722 0.000 0.796 0.204
#> GSM372321 3 0.0000 0.923 0.000 0.000 1.000
#> GSM372323 3 0.0000 0.923 0.000 0.000 1.000
#> GSM372326 3 0.0000 0.923 0.000 0.000 1.000
#> GSM372328 3 0.0000 0.923 0.000 0.000 1.000
#> GSM372330 2 0.0000 0.977 0.000 1.000 0.000
#> GSM372332 3 0.0000 0.923 0.000 0.000 1.000
#> GSM372335 2 0.0000 0.977 0.000 1.000 0.000
#> GSM372337 3 0.0000 0.923 0.000 0.000 1.000
#> GSM372339 3 0.0000 0.923 0.000 0.000 1.000
#> GSM372341 3 0.0000 0.923 0.000 0.000 1.000
#> GSM372343 3 0.0000 0.923 0.000 0.000 1.000
#> GSM372345 3 0.0000 0.923 0.000 0.000 1.000
#> GSM372347 3 0.0000 0.923 0.000 0.000 1.000
#> GSM372349 3 0.0000 0.923 0.000 0.000 1.000
#> GSM372351 3 0.0000 0.923 0.000 0.000 1.000
#> GSM372353 3 0.6140 0.378 0.000 0.404 0.596
#> GSM372355 2 0.0000 0.977 0.000 1.000 0.000
#> GSM372357 2 0.0000 0.977 0.000 1.000 0.000
#> GSM372359 2 0.0000 0.977 0.000 1.000 0.000
#> GSM372361 2 0.0000 0.977 0.000 1.000 0.000
#> GSM372363 2 0.0000 0.977 0.000 1.000 0.000
#> GSM372308 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372310 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372312 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372314 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372316 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372318 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372320 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372322 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372324 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372325 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372327 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372329 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372331 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372333 1 0.6126 0.354 0.600 0.000 0.400
#> GSM372334 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372336 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372338 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372340 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372342 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372344 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372346 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372348 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372350 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372352 3 0.2796 0.842 0.092 0.000 0.908
#> GSM372354 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372356 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372358 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372360 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372362 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372364 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372365 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372366 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372367 1 0.0000 0.987 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM372286 2 0.0817 0.949 0.000 0.976 0.000 0.024
#> GSM372287 4 0.1557 0.957 0.000 0.056 0.000 0.944
#> GSM372288 4 0.2921 0.900 0.000 0.140 0.000 0.860
#> GSM372289 2 0.1211 0.935 0.000 0.960 0.000 0.040
#> GSM372290 4 0.2921 0.900 0.000 0.140 0.000 0.860
#> GSM372291 4 0.0817 0.930 0.024 0.000 0.000 0.976
#> GSM372292 4 0.1474 0.958 0.000 0.052 0.000 0.948
#> GSM372293 4 0.1716 0.924 0.000 0.000 0.064 0.936
#> GSM372294 4 0.2216 0.926 0.000 0.092 0.000 0.908
#> GSM372295 4 0.0817 0.948 0.000 0.024 0.000 0.976
#> GSM372296 4 0.2704 0.915 0.000 0.124 0.000 0.876
#> GSM372297 4 0.1474 0.958 0.000 0.052 0.000 0.948
#> GSM372298 4 0.1474 0.958 0.000 0.052 0.000 0.948
#> GSM372299 4 0.1474 0.958 0.000 0.052 0.000 0.948
#> GSM372300 4 0.1576 0.935 0.000 0.004 0.048 0.948
#> GSM372301 4 0.1635 0.938 0.000 0.008 0.044 0.948
#> GSM372302 4 0.1557 0.957 0.000 0.056 0.000 0.944
#> GSM372303 4 0.1474 0.932 0.000 0.000 0.052 0.948
#> GSM372304 4 0.1474 0.958 0.000 0.052 0.000 0.948
#> GSM372305 2 0.0000 0.965 0.000 1.000 0.000 0.000
#> GSM372306 2 0.0000 0.965 0.000 1.000 0.000 0.000
#> GSM372307 2 0.0336 0.960 0.000 0.992 0.000 0.008
#> GSM372309 2 0.0000 0.965 0.000 1.000 0.000 0.000
#> GSM372311 2 0.0000 0.965 0.000 1.000 0.000 0.000
#> GSM372313 2 0.0000 0.965 0.000 1.000 0.000 0.000
#> GSM372315 2 0.0000 0.965 0.000 1.000 0.000 0.000
#> GSM372317 2 0.0000 0.965 0.000 1.000 0.000 0.000
#> GSM372319 2 0.4877 0.329 0.000 0.592 0.408 0.000
#> GSM372321 3 0.0000 0.970 0.000 0.000 1.000 0.000
#> GSM372323 3 0.0000 0.970 0.000 0.000 1.000 0.000
#> GSM372326 3 0.0000 0.970 0.000 0.000 1.000 0.000
#> GSM372328 3 0.0000 0.970 0.000 0.000 1.000 0.000
#> GSM372330 2 0.0000 0.965 0.000 1.000 0.000 0.000
#> GSM372332 3 0.0000 0.970 0.000 0.000 1.000 0.000
#> GSM372335 2 0.0000 0.965 0.000 1.000 0.000 0.000
#> GSM372337 3 0.0000 0.970 0.000 0.000 1.000 0.000
#> GSM372339 3 0.0000 0.970 0.000 0.000 1.000 0.000
#> GSM372341 3 0.0000 0.970 0.000 0.000 1.000 0.000
#> GSM372343 3 0.0000 0.970 0.000 0.000 1.000 0.000
#> GSM372345 3 0.0000 0.970 0.000 0.000 1.000 0.000
#> GSM372347 3 0.1520 0.945 0.000 0.020 0.956 0.024
#> GSM372349 3 0.0921 0.953 0.000 0.000 0.972 0.028
#> GSM372351 3 0.0000 0.970 0.000 0.000 1.000 0.000
#> GSM372353 2 0.2281 0.872 0.000 0.904 0.096 0.000
#> GSM372355 2 0.0000 0.965 0.000 1.000 0.000 0.000
#> GSM372357 2 0.0000 0.965 0.000 1.000 0.000 0.000
#> GSM372359 2 0.0000 0.965 0.000 1.000 0.000 0.000
#> GSM372361 2 0.0817 0.949 0.000 0.976 0.000 0.024
#> GSM372363 2 0.0000 0.965 0.000 1.000 0.000 0.000
#> GSM372308 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM372310 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM372312 1 0.1389 0.963 0.952 0.000 0.000 0.048
#> GSM372314 1 0.0817 0.980 0.976 0.000 0.000 0.024
#> GSM372316 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM372318 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM372320 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM372322 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM372324 1 0.0817 0.980 0.976 0.000 0.000 0.024
#> GSM372325 1 0.0817 0.980 0.976 0.000 0.000 0.024
#> GSM372327 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM372329 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM372331 1 0.0817 0.980 0.976 0.000 0.000 0.024
#> GSM372333 3 0.4050 0.775 0.168 0.000 0.808 0.024
#> GSM372334 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM372336 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM372338 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM372340 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM372342 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM372344 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM372346 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM372348 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM372350 1 0.0921 0.974 0.972 0.000 0.000 0.028
#> GSM372352 3 0.4595 0.853 0.060 0.056 0.832 0.052
#> GSM372354 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM372356 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM372358 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM372360 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM372362 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM372364 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM372365 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM372366 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM372367 1 0.0000 0.995 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM372286 2 0.4030 0.561 0.000 0.648 0.000 0.352 0.000
#> GSM372287 4 0.1043 0.756 0.000 0.040 0.000 0.960 0.000
#> GSM372288 4 0.1908 0.724 0.000 0.092 0.000 0.908 0.000
#> GSM372289 2 0.4101 0.541 0.000 0.628 0.000 0.372 0.000
#> GSM372290 4 0.1908 0.724 0.000 0.092 0.000 0.908 0.000
#> GSM372291 4 0.4273 0.662 0.000 0.000 0.000 0.552 0.448
#> GSM372292 4 0.4135 0.736 0.000 0.004 0.000 0.656 0.340
#> GSM372293 4 0.4252 0.733 0.000 0.000 0.008 0.652 0.340
#> GSM372294 4 0.3551 0.667 0.000 0.044 0.000 0.820 0.136
#> GSM372295 4 0.2377 0.704 0.000 0.000 0.000 0.872 0.128
#> GSM372296 4 0.1792 0.730 0.000 0.084 0.000 0.916 0.000
#> GSM372297 4 0.1571 0.767 0.000 0.004 0.000 0.936 0.060
#> GSM372298 4 0.3790 0.752 0.000 0.004 0.000 0.724 0.272
#> GSM372299 4 0.4151 0.735 0.000 0.004 0.000 0.652 0.344
#> GSM372300 4 0.4252 0.733 0.000 0.000 0.008 0.652 0.340
#> GSM372301 4 0.4252 0.733 0.000 0.000 0.008 0.652 0.340
#> GSM372302 4 0.0963 0.757 0.000 0.036 0.000 0.964 0.000
#> GSM372303 4 0.4252 0.733 0.000 0.000 0.008 0.652 0.340
#> GSM372304 4 0.0963 0.757 0.000 0.036 0.000 0.964 0.000
#> GSM372305 2 0.0000 0.866 0.000 1.000 0.000 0.000 0.000
#> GSM372306 2 0.0000 0.866 0.000 1.000 0.000 0.000 0.000
#> GSM372307 2 0.3966 0.584 0.000 0.664 0.000 0.336 0.000
#> GSM372309 2 0.0807 0.858 0.000 0.976 0.000 0.012 0.012
#> GSM372311 2 0.0000 0.866 0.000 1.000 0.000 0.000 0.000
#> GSM372313 2 0.0000 0.866 0.000 1.000 0.000 0.000 0.000
#> GSM372315 2 0.0703 0.857 0.000 0.976 0.000 0.024 0.000
#> GSM372317 2 0.0000 0.866 0.000 1.000 0.000 0.000 0.000
#> GSM372319 3 0.3048 0.506 0.000 0.176 0.820 0.004 0.000
#> GSM372321 3 0.0000 0.841 0.000 0.000 1.000 0.000 0.000
#> GSM372323 3 0.0000 0.841 0.000 0.000 1.000 0.000 0.000
#> GSM372326 3 0.0290 0.834 0.000 0.000 0.992 0.000 0.008
#> GSM372328 3 0.0000 0.841 0.000 0.000 1.000 0.000 0.000
#> GSM372330 2 0.0000 0.866 0.000 1.000 0.000 0.000 0.000
#> GSM372332 3 0.0000 0.841 0.000 0.000 1.000 0.000 0.000
#> GSM372335 2 0.0000 0.866 0.000 1.000 0.000 0.000 0.000
#> GSM372337 3 0.0162 0.838 0.000 0.000 0.996 0.000 0.004
#> GSM372339 3 0.0000 0.841 0.000 0.000 1.000 0.000 0.000
#> GSM372341 3 0.0000 0.841 0.000 0.000 1.000 0.000 0.000
#> GSM372343 3 0.0000 0.841 0.000 0.000 1.000 0.000 0.000
#> GSM372345 3 0.0162 0.838 0.000 0.000 0.996 0.000 0.004
#> GSM372347 3 0.6273 -0.561 0.000 0.172 0.512 0.000 0.316
#> GSM372349 3 0.2806 0.619 0.000 0.000 0.844 0.004 0.152
#> GSM372351 3 0.0162 0.838 0.000 0.000 0.996 0.000 0.004
#> GSM372353 2 0.1430 0.800 0.000 0.944 0.052 0.000 0.004
#> GSM372355 2 0.0000 0.866 0.000 1.000 0.000 0.000 0.000
#> GSM372357 2 0.0404 0.861 0.000 0.988 0.000 0.000 0.012
#> GSM372359 2 0.0000 0.866 0.000 1.000 0.000 0.000 0.000
#> GSM372361 2 0.4371 0.570 0.000 0.644 0.000 0.344 0.012
#> GSM372363 2 0.2189 0.811 0.000 0.904 0.000 0.084 0.012
#> GSM372308 1 0.0510 0.831 0.984 0.000 0.000 0.000 0.016
#> GSM372310 1 0.0404 0.833 0.988 0.000 0.000 0.000 0.012
#> GSM372312 1 0.4448 0.572 0.516 0.000 0.000 0.004 0.480
#> GSM372314 1 0.3876 0.496 0.684 0.000 0.000 0.000 0.316
#> GSM372316 1 0.2929 0.860 0.820 0.000 0.000 0.000 0.180
#> GSM372318 1 0.2929 0.860 0.820 0.000 0.000 0.000 0.180
#> GSM372320 1 0.2929 0.860 0.820 0.000 0.000 0.000 0.180
#> GSM372322 1 0.2929 0.860 0.820 0.000 0.000 0.000 0.180
#> GSM372324 1 0.4304 0.548 0.516 0.000 0.000 0.000 0.484
#> GSM372325 1 0.4304 0.541 0.516 0.000 0.000 0.000 0.484
#> GSM372327 1 0.2929 0.860 0.820 0.000 0.000 0.000 0.180
#> GSM372329 1 0.2929 0.860 0.820 0.000 0.000 0.000 0.180
#> GSM372331 1 0.3876 0.496 0.684 0.000 0.000 0.000 0.316
#> GSM372333 3 0.6182 -0.278 0.156 0.000 0.520 0.000 0.324
#> GSM372334 1 0.2929 0.860 0.820 0.000 0.000 0.000 0.180
#> GSM372336 1 0.2690 0.859 0.844 0.000 0.000 0.000 0.156
#> GSM372338 1 0.2929 0.860 0.820 0.000 0.000 0.000 0.180
#> GSM372340 1 0.2929 0.860 0.820 0.000 0.000 0.000 0.180
#> GSM372342 1 0.2929 0.860 0.820 0.000 0.000 0.000 0.180
#> GSM372344 1 0.2929 0.860 0.820 0.000 0.000 0.000 0.180
#> GSM372346 1 0.2929 0.860 0.820 0.000 0.000 0.000 0.180
#> GSM372348 1 0.2852 0.860 0.828 0.000 0.000 0.000 0.172
#> GSM372350 1 0.4084 0.737 0.668 0.000 0.000 0.004 0.328
#> GSM372352 5 0.6724 0.000 0.000 0.228 0.316 0.004 0.452
#> GSM372354 1 0.0162 0.838 0.996 0.000 0.000 0.000 0.004
#> GSM372356 1 0.0000 0.837 1.000 0.000 0.000 0.000 0.000
#> GSM372358 1 0.0000 0.837 1.000 0.000 0.000 0.000 0.000
#> GSM372360 1 0.0000 0.837 1.000 0.000 0.000 0.000 0.000
#> GSM372362 1 0.0000 0.837 1.000 0.000 0.000 0.000 0.000
#> GSM372364 1 0.0000 0.837 1.000 0.000 0.000 0.000 0.000
#> GSM372365 1 0.0000 0.837 1.000 0.000 0.000 0.000 0.000
#> GSM372366 1 0.0162 0.838 0.996 0.000 0.000 0.000 0.004
#> GSM372367 1 0.0162 0.836 0.996 0.000 0.000 0.000 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM372286 4 0.3288 0.651 0.000 0.276 0.000 0.724 0.000 0.000
#> GSM372287 4 0.0405 0.750 0.000 0.008 0.000 0.988 0.000 0.004
#> GSM372288 4 0.0632 0.761 0.000 0.024 0.000 0.976 0.000 0.000
#> GSM372289 4 0.3198 0.660 0.000 0.260 0.000 0.740 0.000 0.000
#> GSM372290 4 0.0632 0.761 0.000 0.024 0.000 0.976 0.000 0.000
#> GSM372291 6 0.5762 0.528 0.012 0.000 0.000 0.280 0.160 0.548
#> GSM372292 6 0.3409 0.885 0.000 0.000 0.000 0.300 0.000 0.700
#> GSM372293 6 0.3690 0.881 0.000 0.000 0.012 0.288 0.000 0.700
#> GSM372294 4 0.3608 0.649 0.000 0.016 0.000 0.816 0.096 0.072
#> GSM372295 4 0.3321 0.647 0.000 0.000 0.000 0.820 0.080 0.100
#> GSM372296 4 0.0632 0.761 0.000 0.024 0.000 0.976 0.000 0.000
#> GSM372297 4 0.2053 0.609 0.000 0.004 0.000 0.888 0.000 0.108
#> GSM372298 6 0.3869 0.601 0.000 0.000 0.000 0.500 0.000 0.500
#> GSM372299 6 0.3428 0.851 0.000 0.000 0.000 0.304 0.000 0.696
#> GSM372300 6 0.3528 0.888 0.000 0.000 0.004 0.296 0.000 0.700
#> GSM372301 6 0.3528 0.888 0.000 0.000 0.004 0.296 0.000 0.700
#> GSM372302 4 0.0520 0.748 0.000 0.008 0.000 0.984 0.000 0.008
#> GSM372303 6 0.3528 0.888 0.000 0.000 0.004 0.296 0.000 0.700
#> GSM372304 4 0.0520 0.748 0.000 0.008 0.000 0.984 0.000 0.008
#> GSM372305 2 0.0458 0.977 0.000 0.984 0.000 0.016 0.000 0.000
#> GSM372306 2 0.0260 0.972 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM372307 4 0.3672 0.618 0.000 0.304 0.000 0.688 0.000 0.008
#> GSM372309 2 0.1391 0.956 0.000 0.944 0.000 0.016 0.000 0.040
#> GSM372311 2 0.0458 0.977 0.000 0.984 0.000 0.016 0.000 0.000
#> GSM372313 2 0.0458 0.977 0.000 0.984 0.000 0.016 0.000 0.000
#> GSM372315 2 0.1007 0.959 0.000 0.956 0.000 0.044 0.000 0.000
#> GSM372317 2 0.0458 0.977 0.000 0.984 0.000 0.016 0.000 0.000
#> GSM372319 3 0.1826 0.890 0.000 0.052 0.924 0.020 0.000 0.004
#> GSM372321 3 0.0000 0.959 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372323 3 0.0458 0.954 0.000 0.000 0.984 0.000 0.016 0.000
#> GSM372326 3 0.0363 0.954 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM372328 3 0.0000 0.959 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372330 2 0.0458 0.977 0.000 0.984 0.000 0.016 0.000 0.000
#> GSM372332 3 0.0000 0.959 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372335 2 0.0146 0.973 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM372337 3 0.0547 0.951 0.000 0.000 0.980 0.000 0.020 0.000
#> GSM372339 3 0.0000 0.959 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372341 3 0.0000 0.959 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372343 3 0.0000 0.959 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372345 3 0.0790 0.945 0.000 0.000 0.968 0.000 0.032 0.000
#> GSM372347 5 0.4865 0.516 0.000 0.096 0.248 0.000 0.652 0.004
#> GSM372349 3 0.4388 0.656 0.000 0.000 0.732 0.008 0.168 0.092
#> GSM372351 3 0.0632 0.947 0.000 0.000 0.976 0.000 0.000 0.024
#> GSM372353 2 0.0806 0.963 0.000 0.972 0.008 0.000 0.000 0.020
#> GSM372355 2 0.0458 0.977 0.000 0.984 0.000 0.016 0.000 0.000
#> GSM372357 2 0.0713 0.964 0.000 0.972 0.000 0.000 0.000 0.028
#> GSM372359 2 0.0260 0.971 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM372361 4 0.4229 0.602 0.000 0.292 0.000 0.668 0.000 0.040
#> GSM372363 2 0.2164 0.918 0.000 0.900 0.000 0.068 0.000 0.032
#> GSM372308 1 0.4871 0.698 0.660 0.000 0.000 0.000 0.196 0.144
#> GSM372310 1 0.4757 0.716 0.676 0.000 0.000 0.000 0.180 0.144
#> GSM372312 1 0.5616 -0.263 0.440 0.000 0.000 0.008 0.440 0.112
#> GSM372314 5 0.3377 0.684 0.188 0.000 0.000 0.000 0.784 0.028
#> GSM372316 1 0.0891 0.809 0.968 0.000 0.000 0.000 0.024 0.008
#> GSM372318 1 0.0000 0.811 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372320 1 0.0000 0.811 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372322 1 0.0000 0.811 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372324 5 0.3446 0.653 0.308 0.000 0.000 0.000 0.692 0.000
#> GSM372325 5 0.3151 0.705 0.252 0.000 0.000 0.000 0.748 0.000
#> GSM372327 1 0.0000 0.811 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372329 1 0.0146 0.811 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM372331 5 0.3301 0.687 0.188 0.000 0.000 0.000 0.788 0.024
#> GSM372333 5 0.3924 0.632 0.052 0.000 0.208 0.000 0.740 0.000
#> GSM372334 1 0.0000 0.811 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372336 1 0.2164 0.797 0.900 0.000 0.000 0.000 0.068 0.032
#> GSM372338 1 0.0000 0.811 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372340 1 0.0000 0.811 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372342 1 0.0000 0.811 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372344 1 0.0000 0.811 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372346 1 0.0363 0.811 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM372348 1 0.1584 0.794 0.928 0.000 0.000 0.000 0.064 0.008
#> GSM372350 1 0.4670 0.425 0.704 0.000 0.000 0.008 0.176 0.112
#> GSM372352 5 0.5900 0.465 0.004 0.040 0.180 0.012 0.640 0.124
#> GSM372354 1 0.4030 0.765 0.756 0.000 0.000 0.000 0.104 0.140
#> GSM372356 1 0.4196 0.763 0.740 0.000 0.000 0.000 0.116 0.144
#> GSM372358 1 0.4196 0.763 0.740 0.000 0.000 0.000 0.116 0.144
#> GSM372360 1 0.4354 0.754 0.724 0.000 0.000 0.000 0.132 0.144
#> GSM372362 1 0.4111 0.763 0.748 0.000 0.000 0.000 0.108 0.144
#> GSM372364 1 0.4354 0.754 0.724 0.000 0.000 0.000 0.132 0.144
#> GSM372365 1 0.4354 0.754 0.724 0.000 0.000 0.000 0.132 0.144
#> GSM372366 1 0.3893 0.770 0.768 0.000 0.000 0.000 0.092 0.140
#> GSM372367 1 0.4602 0.734 0.696 0.000 0.000 0.000 0.160 0.144
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) specimen(p) individual(p) k
#> SD:skmeans 81 2.72e-04 1.85e-17 1.000 2
#> SD:skmeans 78 1.16e-05 1.11e-16 0.943 3
#> SD:skmeans 81 5.54e-14 7.14e-26 0.701 4
#> SD:skmeans 77 3.08e-13 2.12e-26 0.826 5
#> SD:skmeans 79 5.83e-12 2.88e-23 0.603 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 51941 rows and 82 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 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 0.965 0.987 0.4824 0.518 0.518
#> 3 3 0.904 0.867 0.944 0.3943 0.795 0.610
#> 4 4 0.755 0.651 0.809 0.1067 0.928 0.785
#> 5 5 0.817 0.766 0.891 0.0798 0.871 0.567
#> 6 6 0.867 0.812 0.915 0.0344 0.971 0.854
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
#> GSM372286 2 0.0000 0.988 0.000 1.000
#> GSM372287 2 0.0000 0.988 0.000 1.000
#> GSM372288 2 0.0000 0.988 0.000 1.000
#> GSM372289 2 0.0000 0.988 0.000 1.000
#> GSM372290 2 0.0000 0.988 0.000 1.000
#> GSM372291 1 0.9954 0.123 0.540 0.460
#> GSM372292 2 0.0000 0.988 0.000 1.000
#> GSM372293 2 0.0000 0.988 0.000 1.000
#> GSM372294 2 0.0000 0.988 0.000 1.000
#> GSM372295 2 0.0000 0.988 0.000 1.000
#> GSM372296 2 0.0000 0.988 0.000 1.000
#> GSM372297 2 0.0000 0.988 0.000 1.000
#> GSM372298 2 0.0000 0.988 0.000 1.000
#> GSM372299 2 0.0000 0.988 0.000 1.000
#> GSM372300 2 0.0376 0.986 0.004 0.996
#> GSM372301 2 0.0000 0.988 0.000 1.000
#> GSM372302 2 0.0000 0.988 0.000 1.000
#> GSM372303 2 0.0000 0.988 0.000 1.000
#> GSM372304 2 0.0000 0.988 0.000 1.000
#> GSM372305 2 0.0000 0.988 0.000 1.000
#> GSM372306 2 0.0000 0.988 0.000 1.000
#> GSM372307 2 0.0000 0.988 0.000 1.000
#> GSM372309 2 0.0000 0.988 0.000 1.000
#> GSM372311 2 0.0000 0.988 0.000 1.000
#> GSM372313 2 0.0000 0.988 0.000 1.000
#> GSM372315 2 0.0000 0.988 0.000 1.000
#> GSM372317 2 0.0000 0.988 0.000 1.000
#> GSM372319 2 0.0000 0.988 0.000 1.000
#> GSM372321 2 0.0000 0.988 0.000 1.000
#> GSM372323 2 0.0672 0.983 0.008 0.992
#> GSM372326 2 0.0376 0.986 0.004 0.996
#> GSM372328 2 0.0000 0.988 0.000 1.000
#> GSM372330 2 0.0000 0.988 0.000 1.000
#> GSM372332 2 0.0672 0.983 0.008 0.992
#> GSM372335 2 0.0000 0.988 0.000 1.000
#> GSM372337 2 0.0672 0.983 0.008 0.992
#> GSM372339 2 0.0672 0.983 0.008 0.992
#> GSM372341 2 0.1184 0.976 0.016 0.984
#> GSM372343 2 0.2603 0.948 0.044 0.956
#> GSM372345 2 0.0672 0.983 0.008 0.992
#> GSM372347 2 0.0672 0.983 0.008 0.992
#> GSM372349 2 0.0672 0.983 0.008 0.992
#> GSM372351 2 0.0000 0.988 0.000 1.000
#> GSM372353 2 0.0000 0.988 0.000 1.000
#> GSM372355 2 0.0000 0.988 0.000 1.000
#> GSM372357 2 0.0000 0.988 0.000 1.000
#> GSM372359 2 0.0000 0.988 0.000 1.000
#> GSM372361 2 0.0000 0.988 0.000 1.000
#> GSM372363 2 0.0000 0.988 0.000 1.000
#> GSM372308 1 0.0000 0.985 1.000 0.000
#> GSM372310 1 0.0000 0.985 1.000 0.000
#> GSM372312 1 0.0000 0.985 1.000 0.000
#> GSM372314 1 0.0000 0.985 1.000 0.000
#> GSM372316 1 0.0000 0.985 1.000 0.000
#> GSM372318 1 0.0000 0.985 1.000 0.000
#> GSM372320 1 0.0000 0.985 1.000 0.000
#> GSM372322 1 0.0000 0.985 1.000 0.000
#> GSM372324 1 0.0000 0.985 1.000 0.000
#> GSM372325 1 0.0000 0.985 1.000 0.000
#> GSM372327 1 0.0000 0.985 1.000 0.000
#> GSM372329 1 0.0000 0.985 1.000 0.000
#> GSM372331 1 0.0000 0.985 1.000 0.000
#> GSM372333 2 0.9954 0.134 0.460 0.540
#> GSM372334 1 0.0000 0.985 1.000 0.000
#> GSM372336 1 0.0000 0.985 1.000 0.000
#> GSM372338 1 0.0000 0.985 1.000 0.000
#> GSM372340 1 0.0000 0.985 1.000 0.000
#> GSM372342 1 0.0000 0.985 1.000 0.000
#> GSM372344 1 0.0000 0.985 1.000 0.000
#> GSM372346 1 0.0000 0.985 1.000 0.000
#> GSM372348 1 0.0000 0.985 1.000 0.000
#> GSM372350 1 0.0000 0.985 1.000 0.000
#> GSM372352 2 0.0672 0.983 0.008 0.992
#> GSM372354 1 0.0000 0.985 1.000 0.000
#> GSM372356 1 0.0000 0.985 1.000 0.000
#> GSM372358 1 0.0000 0.985 1.000 0.000
#> GSM372360 1 0.0000 0.985 1.000 0.000
#> GSM372362 1 0.0000 0.985 1.000 0.000
#> GSM372364 1 0.0000 0.985 1.000 0.000
#> GSM372365 1 0.0000 0.985 1.000 0.000
#> GSM372366 1 0.0000 0.985 1.000 0.000
#> GSM372367 1 0.0000 0.985 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM372286 2 0.0000 0.908 0.000 1.000 0.000
#> GSM372287 2 0.0000 0.908 0.000 1.000 0.000
#> GSM372288 2 0.0000 0.908 0.000 1.000 0.000
#> GSM372289 2 0.0000 0.908 0.000 1.000 0.000
#> GSM372290 2 0.0000 0.908 0.000 1.000 0.000
#> GSM372291 1 0.8536 0.369 0.576 0.124 0.300
#> GSM372292 3 0.6045 0.469 0.000 0.380 0.620
#> GSM372293 3 0.2261 0.845 0.000 0.068 0.932
#> GSM372294 2 0.0000 0.908 0.000 1.000 0.000
#> GSM372295 3 0.6062 0.462 0.000 0.384 0.616
#> GSM372296 2 0.0000 0.908 0.000 1.000 0.000
#> GSM372297 2 0.0000 0.908 0.000 1.000 0.000
#> GSM372298 2 0.0000 0.908 0.000 1.000 0.000
#> GSM372299 3 0.6079 0.455 0.000 0.388 0.612
#> GSM372300 3 0.5560 0.591 0.000 0.300 0.700
#> GSM372301 3 0.6045 0.469 0.000 0.380 0.620
#> GSM372302 2 0.0000 0.908 0.000 1.000 0.000
#> GSM372303 3 0.0000 0.892 0.000 0.000 1.000
#> GSM372304 2 0.0000 0.908 0.000 1.000 0.000
#> GSM372305 2 0.0000 0.908 0.000 1.000 0.000
#> GSM372306 2 0.6045 0.453 0.000 0.620 0.380
#> GSM372307 2 0.0000 0.908 0.000 1.000 0.000
#> GSM372309 2 0.0424 0.902 0.000 0.992 0.008
#> GSM372311 2 0.0000 0.908 0.000 1.000 0.000
#> GSM372313 2 0.0000 0.908 0.000 1.000 0.000
#> GSM372315 2 0.0000 0.908 0.000 1.000 0.000
#> GSM372317 2 0.6045 0.453 0.000 0.620 0.380
#> GSM372319 3 0.0000 0.892 0.000 0.000 1.000
#> GSM372321 3 0.0000 0.892 0.000 0.000 1.000
#> GSM372323 3 0.0000 0.892 0.000 0.000 1.000
#> GSM372326 3 0.0000 0.892 0.000 0.000 1.000
#> GSM372328 3 0.0000 0.892 0.000 0.000 1.000
#> GSM372330 2 0.5968 0.481 0.000 0.636 0.364
#> GSM372332 3 0.0000 0.892 0.000 0.000 1.000
#> GSM372335 3 0.5650 0.444 0.000 0.312 0.688
#> GSM372337 3 0.0000 0.892 0.000 0.000 1.000
#> GSM372339 3 0.0000 0.892 0.000 0.000 1.000
#> GSM372341 3 0.0000 0.892 0.000 0.000 1.000
#> GSM372343 3 0.0000 0.892 0.000 0.000 1.000
#> GSM372345 3 0.0000 0.892 0.000 0.000 1.000
#> GSM372347 3 0.0000 0.892 0.000 0.000 1.000
#> GSM372349 3 0.0000 0.892 0.000 0.000 1.000
#> GSM372351 3 0.0000 0.892 0.000 0.000 1.000
#> GSM372353 3 0.1163 0.873 0.000 0.028 0.972
#> GSM372355 2 0.0000 0.908 0.000 1.000 0.000
#> GSM372357 2 0.5835 0.520 0.000 0.660 0.340
#> GSM372359 2 0.6045 0.453 0.000 0.620 0.380
#> GSM372361 2 0.0000 0.908 0.000 1.000 0.000
#> GSM372363 2 0.0000 0.908 0.000 1.000 0.000
#> GSM372308 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372310 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372312 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372314 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372316 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372318 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372320 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372322 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372324 1 0.0237 0.983 0.996 0.000 0.004
#> GSM372325 3 0.1643 0.856 0.044 0.000 0.956
#> GSM372327 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372329 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372331 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372333 3 0.0000 0.892 0.000 0.000 1.000
#> GSM372334 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372336 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372338 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372340 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372342 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372344 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372346 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372348 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372350 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372352 3 0.0000 0.892 0.000 0.000 1.000
#> GSM372354 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372356 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372358 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372360 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372362 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372364 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372365 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372366 1 0.0000 0.987 1.000 0.000 0.000
#> GSM372367 1 0.0000 0.987 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM372286 2 0.0000 0.8776 0.000 1.000 0.000 0.000
#> GSM372287 4 0.5366 0.4880 0.000 0.440 0.012 0.548
#> GSM372288 2 0.4382 0.3808 0.000 0.704 0.000 0.296
#> GSM372289 2 0.1302 0.8481 0.000 0.956 0.000 0.044
#> GSM372290 4 0.4948 0.4916 0.000 0.440 0.000 0.560
#> GSM372291 4 0.1598 0.3462 0.020 0.004 0.020 0.956
#> GSM372292 4 0.5112 0.0462 0.000 0.004 0.436 0.560
#> GSM372293 3 0.4961 0.1585 0.000 0.000 0.552 0.448
#> GSM372294 2 0.4972 -0.2767 0.000 0.544 0.000 0.456
#> GSM372295 4 0.3105 0.3802 0.000 0.004 0.140 0.856
#> GSM372296 4 0.5000 0.3452 0.000 0.496 0.000 0.504
#> GSM372297 4 0.5345 0.5056 0.000 0.428 0.012 0.560
#> GSM372298 2 0.4981 -0.3616 0.000 0.536 0.000 0.464
#> GSM372299 4 0.4655 0.2306 0.000 0.004 0.312 0.684
#> GSM372300 3 0.4981 0.1181 0.000 0.000 0.536 0.464
#> GSM372301 3 0.5167 0.0359 0.000 0.004 0.508 0.488
#> GSM372302 4 0.5345 0.5056 0.000 0.428 0.012 0.560
#> GSM372303 3 0.4955 0.1677 0.000 0.000 0.556 0.444
#> GSM372304 4 0.4948 0.4916 0.000 0.440 0.000 0.560
#> GSM372305 2 0.0000 0.8776 0.000 1.000 0.000 0.000
#> GSM372306 2 0.0188 0.8760 0.000 0.996 0.004 0.000
#> GSM372307 2 0.1302 0.8481 0.000 0.956 0.000 0.044
#> GSM372309 2 0.0469 0.8688 0.000 0.988 0.012 0.000
#> GSM372311 2 0.0000 0.8776 0.000 1.000 0.000 0.000
#> GSM372313 2 0.0000 0.8776 0.000 1.000 0.000 0.000
#> GSM372315 2 0.0000 0.8776 0.000 1.000 0.000 0.000
#> GSM372317 2 0.1022 0.8509 0.000 0.968 0.032 0.000
#> GSM372319 3 0.0000 0.7730 0.000 0.000 1.000 0.000
#> GSM372321 3 0.0000 0.7730 0.000 0.000 1.000 0.000
#> GSM372323 3 0.0469 0.7694 0.000 0.000 0.988 0.012
#> GSM372326 3 0.0000 0.7730 0.000 0.000 1.000 0.000
#> GSM372328 3 0.0000 0.7730 0.000 0.000 1.000 0.000
#> GSM372330 2 0.0188 0.8760 0.000 0.996 0.004 0.000
#> GSM372332 3 0.0000 0.7730 0.000 0.000 1.000 0.000
#> GSM372335 3 0.4817 0.2812 0.000 0.388 0.612 0.000
#> GSM372337 3 0.0469 0.7694 0.000 0.000 0.988 0.012
#> GSM372339 3 0.0000 0.7730 0.000 0.000 1.000 0.000
#> GSM372341 3 0.0000 0.7730 0.000 0.000 1.000 0.000
#> GSM372343 3 0.0000 0.7730 0.000 0.000 1.000 0.000
#> GSM372345 3 0.0469 0.7694 0.000 0.000 0.988 0.012
#> GSM372347 3 0.0469 0.7694 0.000 0.000 0.988 0.012
#> GSM372349 3 0.0000 0.7730 0.000 0.000 1.000 0.000
#> GSM372351 3 0.0000 0.7730 0.000 0.000 1.000 0.000
#> GSM372353 3 0.4790 0.3536 0.000 0.380 0.620 0.000
#> GSM372355 2 0.0000 0.8776 0.000 1.000 0.000 0.000
#> GSM372357 2 0.0188 0.8760 0.000 0.996 0.004 0.000
#> GSM372359 2 0.0188 0.8760 0.000 0.996 0.004 0.000
#> GSM372361 2 0.3047 0.7542 0.000 0.872 0.012 0.116
#> GSM372363 2 0.0000 0.8776 0.000 1.000 0.000 0.000
#> GSM372308 1 0.4948 0.7525 0.560 0.000 0.000 0.440
#> GSM372310 1 0.4948 0.7525 0.560 0.000 0.000 0.440
#> GSM372312 1 0.4948 0.7525 0.560 0.000 0.000 0.440
#> GSM372314 1 0.4948 0.7525 0.560 0.000 0.000 0.440
#> GSM372316 1 0.0000 0.7684 1.000 0.000 0.000 0.000
#> GSM372318 1 0.0000 0.7684 1.000 0.000 0.000 0.000
#> GSM372320 1 0.0000 0.7684 1.000 0.000 0.000 0.000
#> GSM372322 1 0.0000 0.7684 1.000 0.000 0.000 0.000
#> GSM372324 1 0.5119 0.7496 0.556 0.000 0.004 0.440
#> GSM372325 3 0.5112 0.3661 0.004 0.000 0.560 0.436
#> GSM372327 1 0.0000 0.7684 1.000 0.000 0.000 0.000
#> GSM372329 1 0.0000 0.7684 1.000 0.000 0.000 0.000
#> GSM372331 1 0.4948 0.7525 0.560 0.000 0.000 0.440
#> GSM372333 3 0.4776 0.4344 0.000 0.000 0.624 0.376
#> GSM372334 1 0.0000 0.7684 1.000 0.000 0.000 0.000
#> GSM372336 1 0.4933 0.7557 0.568 0.000 0.000 0.432
#> GSM372338 1 0.0000 0.7684 1.000 0.000 0.000 0.000
#> GSM372340 1 0.0000 0.7684 1.000 0.000 0.000 0.000
#> GSM372342 1 0.0000 0.7684 1.000 0.000 0.000 0.000
#> GSM372344 1 0.0000 0.7684 1.000 0.000 0.000 0.000
#> GSM372346 1 0.0000 0.7684 1.000 0.000 0.000 0.000
#> GSM372348 1 0.4948 0.7525 0.560 0.000 0.000 0.440
#> GSM372350 1 0.4817 0.7603 0.612 0.000 0.000 0.388
#> GSM372352 3 0.4916 0.3768 0.000 0.000 0.576 0.424
#> GSM372354 1 0.0188 0.7685 0.996 0.000 0.000 0.004
#> GSM372356 1 0.4925 0.7571 0.572 0.000 0.000 0.428
#> GSM372358 1 0.3688 0.7711 0.792 0.000 0.000 0.208
#> GSM372360 1 0.4925 0.7571 0.572 0.000 0.000 0.428
#> GSM372362 1 0.3975 0.7706 0.760 0.000 0.000 0.240
#> GSM372364 1 0.4925 0.7571 0.572 0.000 0.000 0.428
#> GSM372365 1 0.4925 0.7571 0.572 0.000 0.000 0.428
#> GSM372366 1 0.0188 0.7685 0.996 0.000 0.000 0.004
#> GSM372367 1 0.4925 0.7571 0.572 0.000 0.000 0.428
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM372286 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000
#> GSM372287 4 0.1478 0.749 0.000 0.064 0.000 0.936 0.000
#> GSM372288 4 0.4219 0.171 0.000 0.416 0.000 0.584 0.000
#> GSM372289 2 0.1270 0.920 0.000 0.948 0.000 0.052 0.000
#> GSM372290 4 0.0000 0.774 0.000 0.000 0.000 1.000 0.000
#> GSM372291 4 0.3277 0.679 0.148 0.000 0.012 0.832 0.008
#> GSM372292 4 0.0290 0.774 0.008 0.000 0.000 0.992 0.000
#> GSM372293 4 0.4436 0.446 0.008 0.000 0.396 0.596 0.000
#> GSM372294 4 0.3452 0.559 0.000 0.244 0.000 0.756 0.000
#> GSM372295 4 0.0290 0.774 0.008 0.000 0.000 0.992 0.000
#> GSM372296 4 0.1965 0.727 0.000 0.096 0.000 0.904 0.000
#> GSM372297 4 0.0162 0.774 0.004 0.000 0.000 0.996 0.000
#> GSM372298 4 0.4126 0.391 0.000 0.380 0.000 0.620 0.000
#> GSM372299 4 0.4820 0.611 0.068 0.000 0.236 0.696 0.000
#> GSM372300 4 0.4392 0.473 0.008 0.000 0.380 0.612 0.000
#> GSM372301 4 0.4327 0.503 0.008 0.000 0.360 0.632 0.000
#> GSM372302 4 0.0000 0.774 0.000 0.000 0.000 1.000 0.000
#> GSM372303 4 0.4455 0.430 0.008 0.000 0.404 0.588 0.000
#> GSM372304 4 0.0000 0.774 0.000 0.000 0.000 1.000 0.000
#> GSM372305 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000
#> GSM372306 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000
#> GSM372307 2 0.1270 0.920 0.000 0.948 0.000 0.052 0.000
#> GSM372309 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000
#> GSM372311 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000
#> GSM372313 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000
#> GSM372315 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000
#> GSM372317 2 0.0794 0.934 0.000 0.972 0.028 0.000 0.000
#> GSM372319 3 0.0000 0.850 0.000 0.000 1.000 0.000 0.000
#> GSM372321 3 0.0000 0.850 0.000 0.000 1.000 0.000 0.000
#> GSM372323 3 0.0000 0.850 0.000 0.000 1.000 0.000 0.000
#> GSM372326 3 0.0000 0.850 0.000 0.000 1.000 0.000 0.000
#> GSM372328 3 0.0000 0.850 0.000 0.000 1.000 0.000 0.000
#> GSM372330 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000
#> GSM372332 3 0.0000 0.850 0.000 0.000 1.000 0.000 0.000
#> GSM372335 3 0.4126 0.371 0.000 0.380 0.620 0.000 0.000
#> GSM372337 3 0.0000 0.850 0.000 0.000 1.000 0.000 0.000
#> GSM372339 3 0.0000 0.850 0.000 0.000 1.000 0.000 0.000
#> GSM372341 3 0.0000 0.850 0.000 0.000 1.000 0.000 0.000
#> GSM372343 3 0.0000 0.850 0.000 0.000 1.000 0.000 0.000
#> GSM372345 3 0.0000 0.850 0.000 0.000 1.000 0.000 0.000
#> GSM372347 3 0.0703 0.835 0.024 0.000 0.976 0.000 0.000
#> GSM372349 3 0.0000 0.850 0.000 0.000 1.000 0.000 0.000
#> GSM372351 3 0.0000 0.850 0.000 0.000 1.000 0.000 0.000
#> GSM372353 3 0.4171 0.341 0.000 0.396 0.604 0.000 0.000
#> GSM372355 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000
#> GSM372357 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000
#> GSM372359 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000
#> GSM372361 2 0.4192 0.324 0.000 0.596 0.000 0.404 0.000
#> GSM372363 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000
#> GSM372308 1 0.0290 0.821 0.992 0.000 0.000 0.000 0.008
#> GSM372310 1 0.0404 0.822 0.988 0.000 0.000 0.000 0.012
#> GSM372312 1 0.0290 0.821 0.992 0.000 0.000 0.000 0.008
#> GSM372314 1 0.0290 0.821 0.992 0.000 0.000 0.000 0.008
#> GSM372316 5 0.0000 0.962 0.000 0.000 0.000 0.000 1.000
#> GSM372318 5 0.0000 0.962 0.000 0.000 0.000 0.000 1.000
#> GSM372320 5 0.0000 0.962 0.000 0.000 0.000 0.000 1.000
#> GSM372322 5 0.0000 0.962 0.000 0.000 0.000 0.000 1.000
#> GSM372324 1 0.2228 0.784 0.912 0.000 0.048 0.000 0.040
#> GSM372325 3 0.4300 0.279 0.476 0.000 0.524 0.000 0.000
#> GSM372327 5 0.0000 0.962 0.000 0.000 0.000 0.000 1.000
#> GSM372329 5 0.0000 0.962 0.000 0.000 0.000 0.000 1.000
#> GSM372331 1 0.0290 0.821 0.992 0.000 0.000 0.000 0.008
#> GSM372333 3 0.4278 0.333 0.452 0.000 0.548 0.000 0.000
#> GSM372334 5 0.0000 0.962 0.000 0.000 0.000 0.000 1.000
#> GSM372336 1 0.1851 0.832 0.912 0.000 0.000 0.000 0.088
#> GSM372338 5 0.0000 0.962 0.000 0.000 0.000 0.000 1.000
#> GSM372340 5 0.0000 0.962 0.000 0.000 0.000 0.000 1.000
#> GSM372342 5 0.0000 0.962 0.000 0.000 0.000 0.000 1.000
#> GSM372344 5 0.0000 0.962 0.000 0.000 0.000 0.000 1.000
#> GSM372346 5 0.0000 0.962 0.000 0.000 0.000 0.000 1.000
#> GSM372348 1 0.2329 0.764 0.876 0.000 0.000 0.000 0.124
#> GSM372350 5 0.3983 0.310 0.340 0.000 0.000 0.000 0.660
#> GSM372352 3 0.4300 0.279 0.476 0.000 0.524 0.000 0.000
#> GSM372354 1 0.4304 0.305 0.516 0.000 0.000 0.000 0.484
#> GSM372356 1 0.2424 0.829 0.868 0.000 0.000 0.000 0.132
#> GSM372358 1 0.4015 0.599 0.652 0.000 0.000 0.000 0.348
#> GSM372360 1 0.2424 0.829 0.868 0.000 0.000 0.000 0.132
#> GSM372362 1 0.3913 0.636 0.676 0.000 0.000 0.000 0.324
#> GSM372364 1 0.2424 0.829 0.868 0.000 0.000 0.000 0.132
#> GSM372365 1 0.2424 0.829 0.868 0.000 0.000 0.000 0.132
#> GSM372366 1 0.4304 0.305 0.516 0.000 0.000 0.000 0.484
#> GSM372367 1 0.2424 0.829 0.868 0.000 0.000 0.000 0.132
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM372286 2 0.0000 0.934 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM372287 4 0.0000 0.877 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM372288 4 0.0000 0.877 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM372289 2 0.3789 0.367 0.000 0.584 0.000 0.416 0.000 0.000
#> GSM372290 4 0.0000 0.877 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM372291 4 0.4199 0.359 0.000 0.000 0.000 0.568 0.016 0.416
#> GSM372292 6 0.0000 0.960 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM372293 6 0.0000 0.960 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM372294 4 0.0000 0.877 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM372295 4 0.2730 0.738 0.000 0.000 0.000 0.808 0.000 0.192
#> GSM372296 4 0.0000 0.877 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM372297 4 0.3175 0.635 0.000 0.000 0.000 0.744 0.000 0.256
#> GSM372298 6 0.2730 0.731 0.000 0.000 0.000 0.192 0.000 0.808
#> GSM372299 6 0.0260 0.954 0.000 0.000 0.000 0.008 0.000 0.992
#> GSM372300 6 0.0000 0.960 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM372301 6 0.0000 0.960 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM372302 4 0.0260 0.875 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM372303 6 0.0000 0.960 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM372304 4 0.0000 0.877 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM372305 2 0.0000 0.934 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM372306 2 0.0000 0.934 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM372307 2 0.3789 0.367 0.000 0.584 0.000 0.416 0.000 0.000
#> GSM372309 2 0.0000 0.934 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM372311 2 0.0000 0.934 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM372313 2 0.0000 0.934 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM372315 2 0.0000 0.934 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM372317 2 0.0713 0.907 0.000 0.972 0.028 0.000 0.000 0.000
#> GSM372319 3 0.0000 0.865 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372321 3 0.0000 0.865 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372323 3 0.0000 0.865 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372326 3 0.0000 0.865 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372328 3 0.0000 0.865 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372330 2 0.0000 0.934 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM372332 3 0.0000 0.865 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372335 3 0.3706 0.370 0.000 0.380 0.620 0.000 0.000 0.000
#> GSM372337 3 0.0000 0.865 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372339 3 0.0000 0.865 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372341 3 0.0000 0.865 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372343 3 0.0000 0.865 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372345 3 0.0000 0.865 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372347 3 0.0547 0.853 0.000 0.000 0.980 0.000 0.020 0.000
#> GSM372349 3 0.0000 0.865 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372351 3 0.0000 0.865 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372353 3 0.3747 0.345 0.000 0.396 0.604 0.000 0.000 0.000
#> GSM372355 2 0.0000 0.934 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM372357 2 0.0000 0.934 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM372359 2 0.0000 0.934 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM372361 4 0.2730 0.706 0.000 0.192 0.000 0.808 0.000 0.000
#> GSM372363 2 0.0000 0.934 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM372308 5 0.0000 0.827 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM372310 5 0.0000 0.827 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM372312 5 0.0000 0.827 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM372314 5 0.0000 0.827 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM372316 1 0.0000 0.964 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372318 1 0.0000 0.964 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372320 1 0.0000 0.964 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372322 1 0.0000 0.964 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372324 5 0.1930 0.789 0.036 0.000 0.048 0.000 0.916 0.000
#> GSM372325 3 0.3833 0.365 0.000 0.000 0.556 0.000 0.444 0.000
#> GSM372327 1 0.0000 0.964 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372329 1 0.0000 0.964 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372331 5 0.0000 0.827 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM372333 3 0.3823 0.381 0.000 0.000 0.564 0.000 0.436 0.000
#> GSM372334 1 0.0000 0.964 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372336 5 0.1501 0.845 0.076 0.000 0.000 0.000 0.924 0.000
#> GSM372338 1 0.0000 0.964 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372340 1 0.0000 0.964 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372342 1 0.0000 0.964 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372344 1 0.0000 0.964 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372346 1 0.0000 0.964 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372348 5 0.2092 0.769 0.124 0.000 0.000 0.000 0.876 0.000
#> GSM372350 1 0.3547 0.359 0.668 0.000 0.000 0.000 0.332 0.000
#> GSM372352 3 0.3833 0.365 0.000 0.000 0.556 0.000 0.444 0.000
#> GSM372354 5 0.3833 0.397 0.444 0.000 0.000 0.000 0.556 0.000
#> GSM372356 5 0.1957 0.843 0.112 0.000 0.000 0.000 0.888 0.000
#> GSM372358 5 0.3515 0.632 0.324 0.000 0.000 0.000 0.676 0.000
#> GSM372360 5 0.1957 0.843 0.112 0.000 0.000 0.000 0.888 0.000
#> GSM372362 5 0.3428 0.661 0.304 0.000 0.000 0.000 0.696 0.000
#> GSM372364 5 0.1957 0.843 0.112 0.000 0.000 0.000 0.888 0.000
#> GSM372365 5 0.1957 0.843 0.112 0.000 0.000 0.000 0.888 0.000
#> GSM372366 5 0.3833 0.397 0.444 0.000 0.000 0.000 0.556 0.000
#> GSM372367 5 0.1957 0.843 0.112 0.000 0.000 0.000 0.888 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) specimen(p) individual(p) k
#> SD:pam 80 1.22e-04 3.27e-17 0.999 2
#> SD:pam 72 3.33e-06 5.09e-15 0.850 3
#> SD:pam 62 4.24e-06 2.20e-16 0.472 4
#> SD:pam 68 1.60e-10 2.74e-21 0.794 5
#> SD:pam 71 1.55e-10 3.32e-21 0.530 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 51941 rows and 82 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 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 0.965 0.987 0.4696 0.537 0.537
#> 3 3 0.737 0.758 0.836 0.3757 0.790 0.610
#> 4 4 0.789 0.869 0.852 0.1206 0.896 0.701
#> 5 5 0.680 0.700 0.806 0.0657 0.965 0.872
#> 6 6 0.770 0.614 0.793 0.0484 0.907 0.646
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
#> GSM372286 2 0.0000 0.980 0.000 1.000
#> GSM372287 2 0.0000 0.980 0.000 1.000
#> GSM372288 2 0.0000 0.980 0.000 1.000
#> GSM372289 2 0.0000 0.980 0.000 1.000
#> GSM372290 2 0.0000 0.980 0.000 1.000
#> GSM372291 2 0.1184 0.966 0.016 0.984
#> GSM372292 2 0.0000 0.980 0.000 1.000
#> GSM372293 2 0.0000 0.980 0.000 1.000
#> GSM372294 2 0.0000 0.980 0.000 1.000
#> GSM372295 2 0.0000 0.980 0.000 1.000
#> GSM372296 2 0.0000 0.980 0.000 1.000
#> GSM372297 2 0.0000 0.980 0.000 1.000
#> GSM372298 2 0.0000 0.980 0.000 1.000
#> GSM372299 2 0.0000 0.980 0.000 1.000
#> GSM372300 2 0.0000 0.980 0.000 1.000
#> GSM372301 2 0.0000 0.980 0.000 1.000
#> GSM372302 2 0.0000 0.980 0.000 1.000
#> GSM372303 2 0.0000 0.980 0.000 1.000
#> GSM372304 2 0.0000 0.980 0.000 1.000
#> GSM372305 2 0.0000 0.980 0.000 1.000
#> GSM372306 2 0.0000 0.980 0.000 1.000
#> GSM372307 2 0.0000 0.980 0.000 1.000
#> GSM372309 2 0.0000 0.980 0.000 1.000
#> GSM372311 2 0.0000 0.980 0.000 1.000
#> GSM372313 2 0.0000 0.980 0.000 1.000
#> GSM372315 2 0.0000 0.980 0.000 1.000
#> GSM372317 2 0.0000 0.980 0.000 1.000
#> GSM372319 2 0.0000 0.980 0.000 1.000
#> GSM372321 2 0.0000 0.980 0.000 1.000
#> GSM372323 2 0.0000 0.980 0.000 1.000
#> GSM372326 2 0.0000 0.980 0.000 1.000
#> GSM372328 2 0.0000 0.980 0.000 1.000
#> GSM372330 2 0.0000 0.980 0.000 1.000
#> GSM372332 2 0.0000 0.980 0.000 1.000
#> GSM372335 2 0.0000 0.980 0.000 1.000
#> GSM372337 2 0.0000 0.980 0.000 1.000
#> GSM372339 2 0.0000 0.980 0.000 1.000
#> GSM372341 2 0.0000 0.980 0.000 1.000
#> GSM372343 2 0.0000 0.980 0.000 1.000
#> GSM372345 2 0.0000 0.980 0.000 1.000
#> GSM372347 2 0.0000 0.980 0.000 1.000
#> GSM372349 2 0.0000 0.980 0.000 1.000
#> GSM372351 2 0.0000 0.980 0.000 1.000
#> GSM372353 2 0.0000 0.980 0.000 1.000
#> GSM372355 2 0.0000 0.980 0.000 1.000
#> GSM372357 2 0.0000 0.980 0.000 1.000
#> GSM372359 2 0.0000 0.980 0.000 1.000
#> GSM372361 2 0.0000 0.980 0.000 1.000
#> GSM372363 2 0.0000 0.980 0.000 1.000
#> GSM372308 1 0.0000 0.998 1.000 0.000
#> GSM372310 1 0.0000 0.998 1.000 0.000
#> GSM372312 2 0.9881 0.249 0.436 0.564
#> GSM372314 1 0.0000 0.998 1.000 0.000
#> GSM372316 1 0.0000 0.998 1.000 0.000
#> GSM372318 1 0.0000 0.998 1.000 0.000
#> GSM372320 1 0.0000 0.998 1.000 0.000
#> GSM372322 1 0.0000 0.998 1.000 0.000
#> GSM372324 1 0.0938 0.987 0.988 0.012
#> GSM372325 1 0.2603 0.953 0.956 0.044
#> GSM372327 1 0.0000 0.998 1.000 0.000
#> GSM372329 1 0.0000 0.998 1.000 0.000
#> GSM372331 1 0.0000 0.998 1.000 0.000
#> GSM372333 2 0.5629 0.840 0.132 0.868
#> GSM372334 1 0.0000 0.998 1.000 0.000
#> GSM372336 1 0.0000 0.998 1.000 0.000
#> GSM372338 1 0.0000 0.998 1.000 0.000
#> GSM372340 1 0.0000 0.998 1.000 0.000
#> GSM372342 1 0.0000 0.998 1.000 0.000
#> GSM372344 1 0.0000 0.998 1.000 0.000
#> GSM372346 1 0.0000 0.998 1.000 0.000
#> GSM372348 1 0.0000 0.998 1.000 0.000
#> GSM372350 2 0.9881 0.249 0.436 0.564
#> GSM372352 2 0.1633 0.958 0.024 0.976
#> GSM372354 1 0.0000 0.998 1.000 0.000
#> GSM372356 1 0.0000 0.998 1.000 0.000
#> GSM372358 1 0.0000 0.998 1.000 0.000
#> GSM372360 1 0.0000 0.998 1.000 0.000
#> GSM372362 1 0.0000 0.998 1.000 0.000
#> GSM372364 1 0.0000 0.998 1.000 0.000
#> GSM372365 1 0.0000 0.998 1.000 0.000
#> GSM372366 1 0.0000 0.998 1.000 0.000
#> GSM372367 1 0.0000 0.998 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM372286 3 0.6111 0.5012 0.000 0.396 0.604
#> GSM372287 2 0.0000 0.7442 0.000 1.000 0.000
#> GSM372288 2 0.3038 0.7637 0.000 0.896 0.104
#> GSM372289 2 0.4121 0.7500 0.000 0.832 0.168
#> GSM372290 2 0.4121 0.7500 0.000 0.832 0.168
#> GSM372291 2 0.1031 0.7339 0.000 0.976 0.024
#> GSM372292 2 0.4062 0.7517 0.000 0.836 0.164
#> GSM372293 2 0.4887 0.6841 0.000 0.772 0.228
#> GSM372294 2 0.0000 0.7442 0.000 1.000 0.000
#> GSM372295 2 0.0000 0.7442 0.000 1.000 0.000
#> GSM372296 2 0.4178 0.7471 0.000 0.828 0.172
#> GSM372297 2 0.0000 0.7442 0.000 1.000 0.000
#> GSM372298 2 0.2878 0.7641 0.000 0.904 0.096
#> GSM372299 2 0.1031 0.7339 0.000 0.976 0.024
#> GSM372300 2 0.4555 0.7204 0.000 0.800 0.200
#> GSM372301 2 0.4235 0.7446 0.000 0.824 0.176
#> GSM372302 2 0.2448 0.7623 0.000 0.924 0.076
#> GSM372303 2 0.4235 0.7475 0.000 0.824 0.176
#> GSM372304 2 0.0000 0.7442 0.000 1.000 0.000
#> GSM372305 3 0.0592 0.7248 0.000 0.012 0.988
#> GSM372306 3 0.0424 0.7230 0.000 0.008 0.992
#> GSM372307 2 0.4504 0.7260 0.000 0.804 0.196
#> GSM372309 3 0.0592 0.7248 0.000 0.012 0.988
#> GSM372311 3 0.0592 0.7248 0.000 0.012 0.988
#> GSM372313 3 0.0592 0.7248 0.000 0.012 0.988
#> GSM372315 2 0.6286 0.0164 0.000 0.536 0.464
#> GSM372317 3 0.0592 0.7248 0.000 0.012 0.988
#> GSM372319 3 0.5810 0.6182 0.000 0.336 0.664
#> GSM372321 3 0.5810 0.6182 0.000 0.336 0.664
#> GSM372323 3 0.5810 0.6182 0.000 0.336 0.664
#> GSM372326 3 0.5810 0.6182 0.000 0.336 0.664
#> GSM372328 3 0.5882 0.5984 0.000 0.348 0.652
#> GSM372330 3 0.0592 0.7248 0.000 0.012 0.988
#> GSM372332 3 0.5926 0.5835 0.000 0.356 0.644
#> GSM372335 3 0.0424 0.7230 0.000 0.008 0.992
#> GSM372337 3 0.5810 0.6182 0.000 0.336 0.664
#> GSM372339 3 0.5810 0.6182 0.000 0.336 0.664
#> GSM372341 3 0.5810 0.6182 0.000 0.336 0.664
#> GSM372343 3 0.5810 0.6182 0.000 0.336 0.664
#> GSM372345 3 0.5810 0.6182 0.000 0.336 0.664
#> GSM372347 3 0.0000 0.7211 0.000 0.000 1.000
#> GSM372349 3 0.6154 0.4674 0.000 0.408 0.592
#> GSM372351 3 0.5835 0.6154 0.000 0.340 0.660
#> GSM372353 3 0.1163 0.7046 0.000 0.028 0.972
#> GSM372355 3 0.0592 0.7248 0.000 0.012 0.988
#> GSM372357 3 0.0237 0.7221 0.000 0.004 0.996
#> GSM372359 3 0.0424 0.7230 0.000 0.008 0.992
#> GSM372361 2 0.4504 0.7256 0.000 0.804 0.196
#> GSM372363 3 0.0592 0.7248 0.000 0.012 0.988
#> GSM372308 1 0.0000 0.9923 1.000 0.000 0.000
#> GSM372310 1 0.0000 0.9923 1.000 0.000 0.000
#> GSM372312 2 0.7164 0.1179 0.452 0.524 0.024
#> GSM372314 1 0.0237 0.9891 0.996 0.000 0.004
#> GSM372316 1 0.0000 0.9923 1.000 0.000 0.000
#> GSM372318 1 0.0237 0.9895 0.996 0.004 0.000
#> GSM372320 1 0.0000 0.9923 1.000 0.000 0.000
#> GSM372322 1 0.0000 0.9923 1.000 0.000 0.000
#> GSM372324 1 0.3755 0.8737 0.872 0.120 0.008
#> GSM372325 1 0.2680 0.9264 0.924 0.068 0.008
#> GSM372327 1 0.0000 0.9923 1.000 0.000 0.000
#> GSM372329 1 0.0000 0.9923 1.000 0.000 0.000
#> GSM372331 1 0.0000 0.9923 1.000 0.000 0.000
#> GSM372333 3 0.9626 0.2537 0.264 0.264 0.472
#> GSM372334 1 0.0000 0.9923 1.000 0.000 0.000
#> GSM372336 1 0.0000 0.9923 1.000 0.000 0.000
#> GSM372338 1 0.0000 0.9923 1.000 0.000 0.000
#> GSM372340 1 0.0000 0.9923 1.000 0.000 0.000
#> GSM372342 1 0.0000 0.9923 1.000 0.000 0.000
#> GSM372344 1 0.0892 0.9771 0.980 0.020 0.000
#> GSM372346 1 0.0000 0.9923 1.000 0.000 0.000
#> GSM372348 1 0.0000 0.9923 1.000 0.000 0.000
#> GSM372350 2 0.7164 0.1179 0.452 0.524 0.024
#> GSM372352 2 0.7722 -0.2136 0.048 0.520 0.432
#> GSM372354 1 0.0000 0.9923 1.000 0.000 0.000
#> GSM372356 1 0.0000 0.9923 1.000 0.000 0.000
#> GSM372358 1 0.0000 0.9923 1.000 0.000 0.000
#> GSM372360 1 0.0000 0.9923 1.000 0.000 0.000
#> GSM372362 1 0.0000 0.9923 1.000 0.000 0.000
#> GSM372364 1 0.0000 0.9923 1.000 0.000 0.000
#> GSM372365 1 0.0000 0.9923 1.000 0.000 0.000
#> GSM372366 1 0.0000 0.9923 1.000 0.000 0.000
#> GSM372367 1 0.0000 0.9923 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM372286 2 0.6136 0.404 0.000 0.584 0.060 0.356
#> GSM372287 4 0.2412 0.861 0.000 0.008 0.084 0.908
#> GSM372288 4 0.1151 0.877 0.000 0.008 0.024 0.968
#> GSM372289 4 0.0000 0.878 0.000 0.000 0.000 1.000
#> GSM372290 4 0.1302 0.863 0.000 0.044 0.000 0.956
#> GSM372291 4 0.4697 0.614 0.000 0.000 0.356 0.644
#> GSM372292 4 0.0336 0.876 0.000 0.000 0.008 0.992
#> GSM372293 4 0.4697 0.156 0.000 0.000 0.356 0.644
#> GSM372294 4 0.3024 0.819 0.000 0.000 0.148 0.852
#> GSM372295 4 0.2675 0.853 0.000 0.008 0.100 0.892
#> GSM372296 4 0.0469 0.877 0.000 0.012 0.000 0.988
#> GSM372297 4 0.2342 0.862 0.000 0.008 0.080 0.912
#> GSM372298 4 0.0336 0.878 0.000 0.008 0.000 0.992
#> GSM372299 4 0.5010 0.650 0.000 0.024 0.276 0.700
#> GSM372300 4 0.0921 0.871 0.000 0.000 0.028 0.972
#> GSM372301 4 0.0592 0.875 0.000 0.000 0.016 0.984
#> GSM372302 4 0.0336 0.878 0.000 0.008 0.000 0.992
#> GSM372303 4 0.1211 0.864 0.000 0.000 0.040 0.960
#> GSM372304 4 0.2011 0.859 0.000 0.000 0.080 0.920
#> GSM372305 2 0.0592 0.903 0.000 0.984 0.000 0.016
#> GSM372306 2 0.0000 0.907 0.000 1.000 0.000 0.000
#> GSM372307 4 0.1637 0.854 0.000 0.060 0.000 0.940
#> GSM372309 2 0.0817 0.887 0.000 0.976 0.000 0.024
#> GSM372311 2 0.0592 0.903 0.000 0.984 0.000 0.016
#> GSM372313 2 0.2483 0.853 0.000 0.916 0.032 0.052
#> GSM372315 4 0.3982 0.653 0.000 0.220 0.004 0.776
#> GSM372317 2 0.0000 0.907 0.000 1.000 0.000 0.000
#> GSM372319 3 0.6457 0.939 0.000 0.156 0.644 0.200
#> GSM372321 3 0.6457 0.939 0.000 0.156 0.644 0.200
#> GSM372323 3 0.6457 0.939 0.000 0.156 0.644 0.200
#> GSM372326 3 0.7227 0.845 0.000 0.256 0.544 0.200
#> GSM372328 3 0.6449 0.939 0.000 0.152 0.644 0.204
#> GSM372330 2 0.0336 0.906 0.000 0.992 0.000 0.008
#> GSM372332 3 0.6028 0.846 0.000 0.076 0.644 0.280
#> GSM372335 2 0.0000 0.907 0.000 1.000 0.000 0.000
#> GSM372337 3 0.6457 0.939 0.000 0.156 0.644 0.200
#> GSM372339 3 0.6449 0.939 0.000 0.152 0.644 0.204
#> GSM372341 3 0.6449 0.939 0.000 0.152 0.644 0.204
#> GSM372343 3 0.6449 0.939 0.000 0.152 0.644 0.204
#> GSM372345 3 0.6457 0.939 0.000 0.156 0.644 0.200
#> GSM372347 2 0.0000 0.907 0.000 1.000 0.000 0.000
#> GSM372349 3 0.4888 0.594 0.000 0.000 0.588 0.412
#> GSM372351 3 0.7277 0.838 0.000 0.260 0.536 0.204
#> GSM372353 2 0.0000 0.907 0.000 1.000 0.000 0.000
#> GSM372355 2 0.0469 0.905 0.000 0.988 0.000 0.012
#> GSM372357 2 0.0000 0.907 0.000 1.000 0.000 0.000
#> GSM372359 2 0.0000 0.907 0.000 1.000 0.000 0.000
#> GSM372361 4 0.1474 0.859 0.000 0.052 0.000 0.948
#> GSM372363 2 0.0592 0.903 0.000 0.984 0.000 0.016
#> GSM372308 1 0.0000 0.965 1.000 0.000 0.000 0.000
#> GSM372310 1 0.0000 0.965 1.000 0.000 0.000 0.000
#> GSM372312 1 0.6549 0.498 0.556 0.000 0.356 0.088
#> GSM372314 1 0.0000 0.965 1.000 0.000 0.000 0.000
#> GSM372316 1 0.0000 0.965 1.000 0.000 0.000 0.000
#> GSM372318 1 0.0336 0.960 0.992 0.000 0.008 0.000
#> GSM372320 1 0.0000 0.965 1.000 0.000 0.000 0.000
#> GSM372322 1 0.0000 0.965 1.000 0.000 0.000 0.000
#> GSM372324 1 0.2345 0.889 0.900 0.000 0.100 0.000
#> GSM372325 1 0.4364 0.802 0.808 0.056 0.136 0.000
#> GSM372327 1 0.0000 0.965 1.000 0.000 0.000 0.000
#> GSM372329 1 0.0000 0.965 1.000 0.000 0.000 0.000
#> GSM372331 1 0.0000 0.965 1.000 0.000 0.000 0.000
#> GSM372333 2 0.7368 0.587 0.144 0.616 0.204 0.036
#> GSM372334 1 0.0000 0.965 1.000 0.000 0.000 0.000
#> GSM372336 1 0.0000 0.965 1.000 0.000 0.000 0.000
#> GSM372338 1 0.0000 0.965 1.000 0.000 0.000 0.000
#> GSM372340 1 0.0000 0.965 1.000 0.000 0.000 0.000
#> GSM372342 1 0.0000 0.965 1.000 0.000 0.000 0.000
#> GSM372344 1 0.0336 0.960 0.992 0.000 0.008 0.000
#> GSM372346 1 0.0000 0.965 1.000 0.000 0.000 0.000
#> GSM372348 1 0.0000 0.965 1.000 0.000 0.000 0.000
#> GSM372350 1 0.6549 0.498 0.556 0.000 0.356 0.088
#> GSM372352 2 0.6285 0.611 0.000 0.624 0.284 0.092
#> GSM372354 1 0.0000 0.965 1.000 0.000 0.000 0.000
#> GSM372356 1 0.0000 0.965 1.000 0.000 0.000 0.000
#> GSM372358 1 0.0000 0.965 1.000 0.000 0.000 0.000
#> GSM372360 1 0.0000 0.965 1.000 0.000 0.000 0.000
#> GSM372362 1 0.0000 0.965 1.000 0.000 0.000 0.000
#> GSM372364 1 0.0000 0.965 1.000 0.000 0.000 0.000
#> GSM372365 1 0.0188 0.962 0.996 0.000 0.004 0.000
#> GSM372366 1 0.0000 0.965 1.000 0.000 0.000 0.000
#> GSM372367 1 0.0000 0.965 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM372286 2 0.3916 0.573 0.000 0.732 0.000 0.256 0.012
#> GSM372287 4 0.2074 0.657 0.000 0.000 0.000 0.896 0.104
#> GSM372288 4 0.0566 0.702 0.000 0.004 0.000 0.984 0.012
#> GSM372289 4 0.1478 0.698 0.000 0.064 0.000 0.936 0.000
#> GSM372290 4 0.3210 0.691 0.000 0.212 0.000 0.788 0.000
#> GSM372291 5 0.4640 0.537 0.000 0.000 0.048 0.256 0.696
#> GSM372292 4 0.4099 0.695 0.000 0.200 0.032 0.764 0.004
#> GSM372293 4 0.3966 0.475 0.000 0.000 0.336 0.664 0.000
#> GSM372294 4 0.3670 0.626 0.000 0.060 0.008 0.832 0.100
#> GSM372295 4 0.3115 0.641 0.000 0.000 0.036 0.852 0.112
#> GSM372296 4 0.3003 0.703 0.000 0.188 0.000 0.812 0.000
#> GSM372297 4 0.2074 0.657 0.000 0.000 0.000 0.896 0.104
#> GSM372298 4 0.0162 0.703 0.000 0.004 0.000 0.996 0.000
#> GSM372299 4 0.6852 0.239 0.000 0.336 0.048 0.504 0.112
#> GSM372300 4 0.5164 0.675 0.000 0.172 0.112 0.708 0.008
#> GSM372301 4 0.4868 0.685 0.000 0.128 0.124 0.740 0.008
#> GSM372302 4 0.1270 0.721 0.000 0.052 0.000 0.948 0.000
#> GSM372303 4 0.5166 0.619 0.000 0.108 0.212 0.680 0.000
#> GSM372304 4 0.2020 0.661 0.000 0.000 0.000 0.900 0.100
#> GSM372305 2 0.1195 0.846 0.000 0.960 0.012 0.028 0.000
#> GSM372306 2 0.0703 0.846 0.000 0.976 0.024 0.000 0.000
#> GSM372307 4 0.4138 0.461 0.000 0.384 0.000 0.616 0.000
#> GSM372309 2 0.0000 0.852 0.000 1.000 0.000 0.000 0.000
#> GSM372311 2 0.1197 0.833 0.000 0.952 0.000 0.048 0.000
#> GSM372313 2 0.0955 0.846 0.000 0.968 0.004 0.000 0.028
#> GSM372315 2 0.4302 -0.148 0.000 0.520 0.000 0.480 0.000
#> GSM372317 2 0.0510 0.849 0.000 0.984 0.016 0.000 0.000
#> GSM372319 3 0.4276 0.874 0.000 0.168 0.764 0.068 0.000
#> GSM372321 3 0.4049 0.876 0.000 0.164 0.780 0.056 0.000
#> GSM372323 3 0.3616 0.869 0.000 0.164 0.804 0.032 0.000
#> GSM372326 3 0.3876 0.851 0.000 0.192 0.776 0.032 0.000
#> GSM372328 3 0.3526 0.862 0.000 0.096 0.832 0.072 0.000
#> GSM372330 2 0.0609 0.847 0.000 0.980 0.000 0.020 0.000
#> GSM372332 3 0.3283 0.772 0.000 0.028 0.832 0.140 0.000
#> GSM372335 2 0.0404 0.851 0.000 0.988 0.012 0.000 0.000
#> GSM372337 3 0.3656 0.868 0.000 0.168 0.800 0.032 0.000
#> GSM372339 3 0.3527 0.874 0.000 0.116 0.828 0.056 0.000
#> GSM372341 3 0.3442 0.869 0.000 0.104 0.836 0.060 0.000
#> GSM372343 3 0.3622 0.877 0.000 0.124 0.820 0.056 0.000
#> GSM372345 3 0.3694 0.866 0.000 0.172 0.796 0.032 0.000
#> GSM372347 2 0.4130 0.624 0.000 0.696 0.292 0.000 0.012
#> GSM372349 3 0.4562 -0.102 0.000 0.008 0.496 0.496 0.000
#> GSM372351 3 0.5109 0.822 0.000 0.172 0.696 0.132 0.000
#> GSM372353 2 0.1608 0.824 0.000 0.928 0.072 0.000 0.000
#> GSM372355 2 0.0000 0.852 0.000 1.000 0.000 0.000 0.000
#> GSM372357 2 0.0162 0.852 0.000 0.996 0.004 0.000 0.000
#> GSM372359 2 0.0162 0.852 0.000 0.996 0.004 0.000 0.000
#> GSM372361 4 0.3857 0.600 0.000 0.312 0.000 0.688 0.000
#> GSM372363 2 0.1197 0.833 0.000 0.952 0.000 0.048 0.000
#> GSM372308 1 0.5510 0.590 0.648 0.000 0.144 0.000 0.208
#> GSM372310 1 0.5296 0.623 0.676 0.000 0.144 0.000 0.180
#> GSM372312 5 0.4190 0.677 0.140 0.000 0.012 0.056 0.792
#> GSM372314 1 0.5329 0.619 0.672 0.000 0.144 0.000 0.184
#> GSM372316 1 0.0162 0.796 0.996 0.000 0.000 0.000 0.004
#> GSM372318 1 0.3838 0.567 0.716 0.000 0.004 0.000 0.280
#> GSM372320 1 0.2583 0.766 0.864 0.000 0.004 0.000 0.132
#> GSM372322 1 0.2424 0.768 0.868 0.000 0.000 0.000 0.132
#> GSM372324 1 0.5486 0.633 0.684 0.012 0.132 0.000 0.172
#> GSM372325 1 0.6075 0.549 0.612 0.012 0.160 0.000 0.216
#> GSM372327 1 0.2424 0.768 0.868 0.000 0.000 0.000 0.132
#> GSM372329 1 0.2424 0.768 0.868 0.000 0.000 0.000 0.132
#> GSM372331 1 0.2966 0.724 0.816 0.000 0.000 0.000 0.184
#> GSM372333 2 0.6564 0.424 0.028 0.548 0.292 0.000 0.132
#> GSM372334 1 0.2583 0.766 0.864 0.000 0.004 0.000 0.132
#> GSM372336 1 0.0290 0.796 0.992 0.000 0.008 0.000 0.000
#> GSM372338 1 0.2583 0.766 0.864 0.000 0.004 0.000 0.132
#> GSM372340 1 0.2424 0.768 0.868 0.000 0.000 0.000 0.132
#> GSM372342 1 0.2424 0.768 0.868 0.000 0.000 0.000 0.132
#> GSM372344 1 0.4410 0.289 0.556 0.000 0.004 0.000 0.440
#> GSM372346 1 0.3395 0.658 0.764 0.000 0.000 0.000 0.236
#> GSM372348 1 0.0794 0.794 0.972 0.000 0.028 0.000 0.000
#> GSM372350 5 0.3634 0.690 0.080 0.000 0.020 0.056 0.844
#> GSM372352 2 0.6762 0.457 0.000 0.556 0.276 0.056 0.112
#> GSM372354 1 0.0000 0.797 1.000 0.000 0.000 0.000 0.000
#> GSM372356 1 0.4194 0.701 0.780 0.000 0.132 0.000 0.088
#> GSM372358 1 0.0162 0.797 0.996 0.000 0.004 0.000 0.000
#> GSM372360 1 0.0609 0.795 0.980 0.000 0.020 0.000 0.000
#> GSM372362 1 0.0000 0.797 1.000 0.000 0.000 0.000 0.000
#> GSM372364 1 0.0794 0.794 0.972 0.000 0.028 0.000 0.000
#> GSM372365 1 0.5159 0.633 0.692 0.000 0.144 0.000 0.164
#> GSM372366 1 0.0000 0.797 1.000 0.000 0.000 0.000 0.000
#> GSM372367 1 0.5329 0.619 0.672 0.000 0.144 0.000 0.184
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM372286 2 0.3866 -0.1202 0.000 0.516 0.000 0.000 0.000 0.484
#> GSM372287 4 0.3843 0.8729 0.000 0.000 0.000 0.548 0.000 0.452
#> GSM372288 6 0.3823 -0.6774 0.000 0.000 0.000 0.436 0.000 0.564
#> GSM372289 6 0.4367 -0.4875 0.000 0.032 0.000 0.364 0.000 0.604
#> GSM372290 6 0.1866 0.5748 0.000 0.084 0.000 0.008 0.000 0.908
#> GSM372291 4 0.3284 0.5989 0.000 0.000 0.000 0.784 0.020 0.196
#> GSM372292 6 0.2002 0.5798 0.000 0.076 0.012 0.004 0.000 0.908
#> GSM372293 6 0.4355 0.4942 0.000 0.024 0.156 0.052 0.008 0.760
#> GSM372294 6 0.4083 -0.7215 0.000 0.000 0.008 0.460 0.000 0.532
#> GSM372295 4 0.4136 0.8491 0.000 0.000 0.000 0.560 0.012 0.428
#> GSM372296 6 0.1802 0.5697 0.000 0.072 0.000 0.012 0.000 0.916
#> GSM372297 4 0.3843 0.8729 0.000 0.000 0.000 0.548 0.000 0.452
#> GSM372298 6 0.3101 -0.0759 0.000 0.000 0.000 0.244 0.000 0.756
#> GSM372299 6 0.2825 0.5179 0.000 0.008 0.016 0.024 0.076 0.876
#> GSM372300 6 0.3379 0.5816 0.000 0.072 0.028 0.044 0.008 0.848
#> GSM372301 6 0.2965 0.5837 0.000 0.076 0.024 0.036 0.000 0.864
#> GSM372302 6 0.1863 0.3458 0.000 0.000 0.000 0.104 0.000 0.896
#> GSM372303 6 0.3714 0.5768 0.000 0.072 0.036 0.056 0.008 0.828
#> GSM372304 4 0.3843 0.8729 0.000 0.000 0.000 0.548 0.000 0.452
#> GSM372305 2 0.0363 0.8646 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM372306 2 0.0291 0.8686 0.000 0.992 0.004 0.004 0.000 0.000
#> GSM372307 6 0.3774 0.4651 0.000 0.328 0.000 0.008 0.000 0.664
#> GSM372309 2 0.0291 0.8689 0.000 0.992 0.000 0.004 0.000 0.004
#> GSM372311 2 0.0363 0.8646 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM372313 2 0.0000 0.8695 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM372315 6 0.3789 0.3200 0.000 0.416 0.000 0.000 0.000 0.584
#> GSM372317 2 0.0146 0.8695 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM372319 3 0.0858 0.9202 0.000 0.028 0.968 0.000 0.004 0.000
#> GSM372321 3 0.0458 0.9198 0.000 0.016 0.984 0.000 0.000 0.000
#> GSM372323 3 0.1265 0.9157 0.000 0.044 0.948 0.008 0.000 0.000
#> GSM372326 3 0.1333 0.9134 0.000 0.048 0.944 0.008 0.000 0.000
#> GSM372328 3 0.2260 0.8963 0.000 0.000 0.860 0.140 0.000 0.000
#> GSM372330 2 0.0146 0.8686 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM372332 3 0.2219 0.8980 0.000 0.000 0.864 0.136 0.000 0.000
#> GSM372335 2 0.0692 0.8609 0.000 0.976 0.020 0.004 0.000 0.000
#> GSM372337 3 0.1265 0.9157 0.000 0.044 0.948 0.008 0.000 0.000
#> GSM372339 3 0.2704 0.9015 0.000 0.016 0.844 0.140 0.000 0.000
#> GSM372341 3 0.2260 0.8963 0.000 0.000 0.860 0.140 0.000 0.000
#> GSM372343 3 0.2613 0.9008 0.000 0.012 0.848 0.140 0.000 0.000
#> GSM372345 3 0.1462 0.9085 0.000 0.056 0.936 0.008 0.000 0.000
#> GSM372347 2 0.4655 0.6519 0.000 0.720 0.184 0.032 0.064 0.000
#> GSM372349 6 0.6529 0.2162 0.000 0.072 0.352 0.104 0.004 0.468
#> GSM372351 3 0.0777 0.9206 0.000 0.024 0.972 0.000 0.004 0.000
#> GSM372353 2 0.0692 0.8597 0.000 0.976 0.020 0.004 0.000 0.000
#> GSM372355 2 0.0000 0.8695 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM372357 2 0.0146 0.8695 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM372359 2 0.0146 0.8695 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM372361 6 0.3482 0.4754 0.000 0.316 0.000 0.000 0.000 0.684
#> GSM372363 2 0.0363 0.8646 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM372308 5 0.3288 0.8397 0.276 0.000 0.000 0.000 0.724 0.000
#> GSM372310 5 0.3371 0.8435 0.292 0.000 0.000 0.000 0.708 0.000
#> GSM372312 5 0.4289 0.3369 0.216 0.000 0.000 0.044 0.724 0.016
#> GSM372314 5 0.3464 0.8235 0.312 0.000 0.000 0.000 0.688 0.000
#> GSM372316 1 0.2664 0.6487 0.816 0.000 0.000 0.000 0.184 0.000
#> GSM372318 1 0.3417 0.5811 0.796 0.000 0.000 0.160 0.044 0.000
#> GSM372320 1 0.1049 0.6915 0.960 0.000 0.000 0.032 0.008 0.000
#> GSM372322 1 0.0146 0.6986 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM372324 5 0.3993 0.6298 0.400 0.000 0.008 0.000 0.592 0.000
#> GSM372325 5 0.3979 0.8148 0.264 0.000 0.008 0.020 0.708 0.000
#> GSM372327 1 0.0790 0.6947 0.968 0.000 0.000 0.032 0.000 0.000
#> GSM372329 1 0.0405 0.6986 0.988 0.000 0.000 0.004 0.008 0.000
#> GSM372331 1 0.3862 -0.2935 0.524 0.000 0.000 0.000 0.476 0.000
#> GSM372333 2 0.6329 0.4398 0.000 0.520 0.184 0.032 0.260 0.004
#> GSM372334 1 0.1856 0.6680 0.920 0.000 0.000 0.032 0.048 0.000
#> GSM372336 1 0.3103 0.6282 0.784 0.000 0.000 0.008 0.208 0.000
#> GSM372338 1 0.1049 0.6915 0.960 0.000 0.000 0.032 0.008 0.000
#> GSM372340 1 0.0972 0.6931 0.964 0.000 0.000 0.028 0.008 0.000
#> GSM372342 1 0.0547 0.6970 0.980 0.000 0.000 0.020 0.000 0.000
#> GSM372344 1 0.2790 0.5979 0.844 0.000 0.000 0.132 0.024 0.000
#> GSM372346 1 0.3138 0.6226 0.832 0.000 0.000 0.108 0.060 0.000
#> GSM372348 1 0.3103 0.6282 0.784 0.000 0.000 0.008 0.208 0.000
#> GSM372350 1 0.6378 0.1049 0.476 0.000 0.000 0.224 0.272 0.028
#> GSM372352 2 0.6911 0.2661 0.000 0.408 0.192 0.032 0.348 0.020
#> GSM372354 1 0.3694 0.6089 0.740 0.000 0.000 0.028 0.232 0.000
#> GSM372356 1 0.3854 -0.2386 0.536 0.000 0.000 0.000 0.464 0.000
#> GSM372358 1 0.3103 0.6282 0.784 0.000 0.000 0.008 0.208 0.000
#> GSM372360 1 0.3103 0.6282 0.784 0.000 0.000 0.008 0.208 0.000
#> GSM372362 1 0.3073 0.6320 0.788 0.000 0.000 0.008 0.204 0.000
#> GSM372364 1 0.3103 0.6282 0.784 0.000 0.000 0.008 0.208 0.000
#> GSM372365 5 0.3409 0.8374 0.300 0.000 0.000 0.000 0.700 0.000
#> GSM372366 1 0.2762 0.6416 0.804 0.000 0.000 0.000 0.196 0.000
#> GSM372367 5 0.3351 0.8439 0.288 0.000 0.000 0.000 0.712 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) specimen(p) individual(p) k
#> SD:mclust 80 1.70e-04 2.43e-16 0.998 2
#> SD:mclust 76 2.22e-12 1.36e-25 0.861 3
#> SD:mclust 78 8.10e-12 3.39e-23 0.928 4
#> SD:mclust 74 8.45e-11 2.18e-22 0.639 5
#> SD:mclust 65 1.40e-10 1.71e-20 0.277 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 51941 rows and 82 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.980 0.992 0.482 0.518 0.518
#> 3 3 0.893 0.919 0.963 0.389 0.796 0.611
#> 4 4 0.853 0.861 0.920 0.102 0.858 0.612
#> 5 5 0.786 0.716 0.863 0.043 0.942 0.792
#> 6 6 0.778 0.685 0.829 0.032 0.950 0.801
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
#> GSM372286 2 0.0000 0.993 0.000 1.000
#> GSM372287 2 0.0000 0.993 0.000 1.000
#> GSM372288 2 0.0000 0.993 0.000 1.000
#> GSM372289 2 0.0000 0.993 0.000 1.000
#> GSM372290 2 0.0000 0.993 0.000 1.000
#> GSM372291 2 0.9393 0.440 0.356 0.644
#> GSM372292 2 0.0000 0.993 0.000 1.000
#> GSM372293 2 0.0000 0.993 0.000 1.000
#> GSM372294 2 0.0000 0.993 0.000 1.000
#> GSM372295 2 0.0000 0.993 0.000 1.000
#> GSM372296 2 0.0000 0.993 0.000 1.000
#> GSM372297 2 0.0000 0.993 0.000 1.000
#> GSM372298 2 0.0000 0.993 0.000 1.000
#> GSM372299 2 0.0000 0.993 0.000 1.000
#> GSM372300 2 0.0000 0.993 0.000 1.000
#> GSM372301 2 0.0000 0.993 0.000 1.000
#> GSM372302 2 0.0000 0.993 0.000 1.000
#> GSM372303 2 0.0000 0.993 0.000 1.000
#> GSM372304 2 0.0000 0.993 0.000 1.000
#> GSM372305 2 0.0000 0.993 0.000 1.000
#> GSM372306 2 0.0000 0.993 0.000 1.000
#> GSM372307 2 0.0000 0.993 0.000 1.000
#> GSM372309 2 0.0000 0.993 0.000 1.000
#> GSM372311 2 0.0000 0.993 0.000 1.000
#> GSM372313 2 0.0000 0.993 0.000 1.000
#> GSM372315 2 0.0000 0.993 0.000 1.000
#> GSM372317 2 0.0000 0.993 0.000 1.000
#> GSM372319 2 0.0000 0.993 0.000 1.000
#> GSM372321 2 0.0000 0.993 0.000 1.000
#> GSM372323 2 0.0000 0.993 0.000 1.000
#> GSM372326 2 0.0000 0.993 0.000 1.000
#> GSM372328 2 0.0000 0.993 0.000 1.000
#> GSM372330 2 0.0000 0.993 0.000 1.000
#> GSM372332 2 0.0000 0.993 0.000 1.000
#> GSM372335 2 0.0000 0.993 0.000 1.000
#> GSM372337 2 0.0000 0.993 0.000 1.000
#> GSM372339 2 0.0000 0.993 0.000 1.000
#> GSM372341 2 0.0000 0.993 0.000 1.000
#> GSM372343 2 0.0000 0.993 0.000 1.000
#> GSM372345 2 0.0000 0.993 0.000 1.000
#> GSM372347 2 0.0000 0.993 0.000 1.000
#> GSM372349 2 0.0000 0.993 0.000 1.000
#> GSM372351 2 0.0000 0.993 0.000 1.000
#> GSM372353 2 0.0000 0.993 0.000 1.000
#> GSM372355 2 0.0000 0.993 0.000 1.000
#> GSM372357 2 0.0000 0.993 0.000 1.000
#> GSM372359 2 0.0000 0.993 0.000 1.000
#> GSM372361 2 0.0000 0.993 0.000 1.000
#> GSM372363 2 0.0000 0.993 0.000 1.000
#> GSM372308 1 0.0000 0.990 1.000 0.000
#> GSM372310 1 0.0000 0.990 1.000 0.000
#> GSM372312 1 0.0000 0.990 1.000 0.000
#> GSM372314 1 0.0376 0.986 0.996 0.004
#> GSM372316 1 0.0000 0.990 1.000 0.000
#> GSM372318 1 0.0000 0.990 1.000 0.000
#> GSM372320 1 0.0000 0.990 1.000 0.000
#> GSM372322 1 0.0000 0.990 1.000 0.000
#> GSM372324 1 0.0000 0.990 1.000 0.000
#> GSM372325 1 0.0000 0.990 1.000 0.000
#> GSM372327 1 0.0000 0.990 1.000 0.000
#> GSM372329 1 0.0000 0.990 1.000 0.000
#> GSM372331 1 0.0000 0.990 1.000 0.000
#> GSM372333 1 0.8861 0.560 0.696 0.304
#> GSM372334 1 0.0000 0.990 1.000 0.000
#> GSM372336 1 0.0000 0.990 1.000 0.000
#> GSM372338 1 0.0000 0.990 1.000 0.000
#> GSM372340 1 0.0000 0.990 1.000 0.000
#> GSM372342 1 0.0000 0.990 1.000 0.000
#> GSM372344 1 0.0000 0.990 1.000 0.000
#> GSM372346 1 0.0000 0.990 1.000 0.000
#> GSM372348 1 0.0000 0.990 1.000 0.000
#> GSM372350 1 0.0000 0.990 1.000 0.000
#> GSM372352 2 0.0000 0.993 0.000 1.000
#> GSM372354 1 0.0000 0.990 1.000 0.000
#> GSM372356 1 0.0000 0.990 1.000 0.000
#> GSM372358 1 0.0000 0.990 1.000 0.000
#> GSM372360 1 0.0000 0.990 1.000 0.000
#> GSM372362 1 0.0000 0.990 1.000 0.000
#> GSM372364 1 0.0000 0.990 1.000 0.000
#> GSM372365 1 0.0000 0.990 1.000 0.000
#> GSM372366 1 0.0000 0.990 1.000 0.000
#> GSM372367 1 0.0000 0.990 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM372286 2 0.3192 0.858 0.000 0.888 0.112
#> GSM372287 2 0.0000 0.951 0.000 1.000 0.000
#> GSM372288 2 0.0000 0.951 0.000 1.000 0.000
#> GSM372289 2 0.0000 0.951 0.000 1.000 0.000
#> GSM372290 2 0.0237 0.950 0.000 0.996 0.004
#> GSM372291 2 0.4551 0.805 0.140 0.840 0.020
#> GSM372292 3 0.5968 0.449 0.000 0.364 0.636
#> GSM372293 3 0.1643 0.902 0.000 0.044 0.956
#> GSM372294 2 0.0237 0.950 0.000 0.996 0.004
#> GSM372295 2 0.0000 0.951 0.000 1.000 0.000
#> GSM372296 2 0.0000 0.951 0.000 1.000 0.000
#> GSM372297 2 0.0892 0.942 0.000 0.980 0.020
#> GSM372298 2 0.0592 0.947 0.000 0.988 0.012
#> GSM372299 2 0.0237 0.950 0.000 0.996 0.004
#> GSM372300 3 0.3551 0.825 0.000 0.132 0.868
#> GSM372301 3 0.2165 0.889 0.000 0.064 0.936
#> GSM372302 2 0.0747 0.944 0.000 0.984 0.016
#> GSM372303 3 0.0000 0.925 0.000 0.000 1.000
#> GSM372304 2 0.0592 0.947 0.000 0.988 0.012
#> GSM372305 2 0.3816 0.816 0.000 0.852 0.148
#> GSM372306 3 0.4796 0.725 0.000 0.220 0.780
#> GSM372307 2 0.0000 0.951 0.000 1.000 0.000
#> GSM372309 2 0.0000 0.951 0.000 1.000 0.000
#> GSM372311 2 0.0000 0.951 0.000 1.000 0.000
#> GSM372313 2 0.0237 0.950 0.000 0.996 0.004
#> GSM372315 2 0.0000 0.951 0.000 1.000 0.000
#> GSM372317 3 0.4346 0.773 0.000 0.184 0.816
#> GSM372319 3 0.0424 0.922 0.000 0.008 0.992
#> GSM372321 3 0.0000 0.925 0.000 0.000 1.000
#> GSM372323 3 0.0000 0.925 0.000 0.000 1.000
#> GSM372326 3 0.0000 0.925 0.000 0.000 1.000
#> GSM372328 3 0.0000 0.925 0.000 0.000 1.000
#> GSM372330 2 0.4178 0.785 0.000 0.828 0.172
#> GSM372332 3 0.0000 0.925 0.000 0.000 1.000
#> GSM372335 3 0.3551 0.835 0.000 0.132 0.868
#> GSM372337 3 0.0000 0.925 0.000 0.000 1.000
#> GSM372339 3 0.0000 0.925 0.000 0.000 1.000
#> GSM372341 3 0.0000 0.925 0.000 0.000 1.000
#> GSM372343 3 0.0000 0.925 0.000 0.000 1.000
#> GSM372345 3 0.0000 0.925 0.000 0.000 1.000
#> GSM372347 3 0.0892 0.918 0.000 0.020 0.980
#> GSM372349 3 0.0000 0.925 0.000 0.000 1.000
#> GSM372351 3 0.0000 0.925 0.000 0.000 1.000
#> GSM372353 3 0.0892 0.918 0.000 0.020 0.980
#> GSM372355 2 0.0000 0.951 0.000 1.000 0.000
#> GSM372357 2 0.0892 0.940 0.000 0.980 0.020
#> GSM372359 3 0.1529 0.909 0.000 0.040 0.960
#> GSM372361 2 0.0000 0.951 0.000 1.000 0.000
#> GSM372363 2 0.0000 0.951 0.000 1.000 0.000
#> GSM372308 1 0.0000 0.994 1.000 0.000 0.000
#> GSM372310 1 0.0000 0.994 1.000 0.000 0.000
#> GSM372312 1 0.0237 0.990 0.996 0.004 0.000
#> GSM372314 1 0.0000 0.994 1.000 0.000 0.000
#> GSM372316 1 0.0000 0.994 1.000 0.000 0.000
#> GSM372318 1 0.0000 0.994 1.000 0.000 0.000
#> GSM372320 1 0.0000 0.994 1.000 0.000 0.000
#> GSM372322 1 0.0000 0.994 1.000 0.000 0.000
#> GSM372324 1 0.0000 0.994 1.000 0.000 0.000
#> GSM372325 1 0.4178 0.779 0.828 0.000 0.172
#> GSM372327 1 0.0000 0.994 1.000 0.000 0.000
#> GSM372329 1 0.0000 0.994 1.000 0.000 0.000
#> GSM372331 1 0.0000 0.994 1.000 0.000 0.000
#> GSM372333 3 0.6625 0.206 0.440 0.008 0.552
#> GSM372334 1 0.0000 0.994 1.000 0.000 0.000
#> GSM372336 1 0.0000 0.994 1.000 0.000 0.000
#> GSM372338 1 0.0000 0.994 1.000 0.000 0.000
#> GSM372340 1 0.0000 0.994 1.000 0.000 0.000
#> GSM372342 1 0.0000 0.994 1.000 0.000 0.000
#> GSM372344 1 0.0000 0.994 1.000 0.000 0.000
#> GSM372346 1 0.0000 0.994 1.000 0.000 0.000
#> GSM372348 1 0.0000 0.994 1.000 0.000 0.000
#> GSM372350 1 0.0000 0.994 1.000 0.000 0.000
#> GSM372352 2 0.9062 0.280 0.152 0.512 0.336
#> GSM372354 1 0.0000 0.994 1.000 0.000 0.000
#> GSM372356 1 0.0000 0.994 1.000 0.000 0.000
#> GSM372358 1 0.0000 0.994 1.000 0.000 0.000
#> GSM372360 1 0.0000 0.994 1.000 0.000 0.000
#> GSM372362 1 0.0000 0.994 1.000 0.000 0.000
#> GSM372364 1 0.0000 0.994 1.000 0.000 0.000
#> GSM372365 1 0.0000 0.994 1.000 0.000 0.000
#> GSM372366 1 0.0000 0.994 1.000 0.000 0.000
#> GSM372367 1 0.0000 0.994 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM372286 2 0.2943 0.820 0.000 0.892 0.076 0.032
#> GSM372287 4 0.2216 0.896 0.000 0.092 0.000 0.908
#> GSM372288 4 0.2530 0.883 0.000 0.112 0.000 0.888
#> GSM372289 2 0.4564 0.481 0.000 0.672 0.000 0.328
#> GSM372290 4 0.2149 0.898 0.000 0.088 0.000 0.912
#> GSM372291 4 0.0336 0.905 0.000 0.000 0.008 0.992
#> GSM372292 4 0.0817 0.901 0.000 0.000 0.024 0.976
#> GSM372293 4 0.4961 0.193 0.000 0.000 0.448 0.552
#> GSM372294 4 0.1792 0.904 0.000 0.068 0.000 0.932
#> GSM372295 4 0.2149 0.897 0.000 0.088 0.000 0.912
#> GSM372296 4 0.2589 0.882 0.000 0.116 0.000 0.884
#> GSM372297 4 0.0188 0.906 0.000 0.000 0.004 0.996
#> GSM372298 4 0.0336 0.908 0.000 0.008 0.000 0.992
#> GSM372299 4 0.2944 0.872 0.000 0.128 0.004 0.868
#> GSM372300 4 0.1474 0.887 0.000 0.000 0.052 0.948
#> GSM372301 4 0.1557 0.885 0.000 0.000 0.056 0.944
#> GSM372302 4 0.1118 0.909 0.000 0.036 0.000 0.964
#> GSM372303 4 0.2081 0.865 0.000 0.000 0.084 0.916
#> GSM372304 4 0.0469 0.909 0.000 0.012 0.000 0.988
#> GSM372305 2 0.0188 0.836 0.000 0.996 0.004 0.000
#> GSM372306 2 0.2814 0.788 0.000 0.868 0.132 0.000
#> GSM372307 2 0.3074 0.745 0.000 0.848 0.000 0.152
#> GSM372309 2 0.2281 0.795 0.000 0.904 0.000 0.096
#> GSM372311 2 0.0336 0.835 0.000 0.992 0.000 0.008
#> GSM372313 2 0.0188 0.836 0.000 0.996 0.004 0.000
#> GSM372315 2 0.1940 0.809 0.000 0.924 0.000 0.076
#> GSM372317 2 0.3266 0.766 0.000 0.832 0.168 0.000
#> GSM372319 3 0.1637 0.923 0.000 0.060 0.940 0.000
#> GSM372321 3 0.1389 0.932 0.000 0.048 0.952 0.000
#> GSM372323 3 0.1022 0.940 0.000 0.032 0.968 0.000
#> GSM372326 3 0.0188 0.947 0.000 0.004 0.996 0.000
#> GSM372328 3 0.2216 0.862 0.000 0.000 0.908 0.092
#> GSM372330 2 0.2216 0.811 0.000 0.908 0.092 0.000
#> GSM372332 3 0.0188 0.947 0.000 0.004 0.996 0.000
#> GSM372335 2 0.4072 0.683 0.000 0.748 0.252 0.000
#> GSM372337 3 0.0469 0.946 0.000 0.012 0.988 0.000
#> GSM372339 3 0.0188 0.947 0.000 0.004 0.996 0.000
#> GSM372341 3 0.0469 0.939 0.000 0.000 0.988 0.012
#> GSM372343 3 0.0188 0.944 0.000 0.000 0.996 0.004
#> GSM372345 3 0.1211 0.937 0.000 0.040 0.960 0.000
#> GSM372347 3 0.3610 0.751 0.000 0.200 0.800 0.000
#> GSM372349 3 0.0524 0.947 0.000 0.008 0.988 0.004
#> GSM372351 3 0.0188 0.944 0.000 0.000 0.996 0.004
#> GSM372353 3 0.3311 0.820 0.000 0.172 0.828 0.000
#> GSM372355 2 0.0000 0.836 0.000 1.000 0.000 0.000
#> GSM372357 2 0.0000 0.836 0.000 1.000 0.000 0.000
#> GSM372359 2 0.4830 0.404 0.000 0.608 0.392 0.000
#> GSM372361 2 0.4250 0.571 0.000 0.724 0.000 0.276
#> GSM372363 2 0.1211 0.825 0.000 0.960 0.000 0.040
#> GSM372308 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM372310 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM372312 1 0.0188 0.959 0.996 0.004 0.000 0.000
#> GSM372314 1 0.4679 0.469 0.648 0.352 0.000 0.000
#> GSM372316 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM372318 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM372320 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM372322 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM372324 1 0.1867 0.892 0.928 0.000 0.072 0.000
#> GSM372325 1 0.5913 0.599 0.696 0.180 0.124 0.000
#> GSM372327 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM372329 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM372331 1 0.4713 0.449 0.640 0.360 0.000 0.000
#> GSM372333 2 0.3764 0.725 0.000 0.784 0.216 0.000
#> GSM372334 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM372336 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM372338 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM372340 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM372342 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM372344 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM372346 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM372348 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM372350 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM372352 2 0.6567 0.567 0.128 0.616 0.256 0.000
#> GSM372354 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM372356 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM372358 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM372360 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM372362 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM372364 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM372365 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM372366 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM372367 1 0.0000 0.962 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM372286 2 0.1670 0.7203 0.000 0.936 0.000 0.052 0.012
#> GSM372287 4 0.0865 0.7895 0.000 0.004 0.000 0.972 0.024
#> GSM372288 4 0.1300 0.7840 0.000 0.028 0.000 0.956 0.016
#> GSM372289 4 0.5173 -0.0137 0.000 0.460 0.000 0.500 0.040
#> GSM372290 4 0.1331 0.7832 0.000 0.008 0.000 0.952 0.040
#> GSM372291 4 0.1121 0.7835 0.000 0.000 0.000 0.956 0.044
#> GSM372292 4 0.1410 0.7803 0.000 0.000 0.000 0.940 0.060
#> GSM372293 4 0.6801 0.0750 0.000 0.000 0.312 0.376 0.312
#> GSM372294 4 0.2124 0.7574 0.000 0.004 0.000 0.900 0.096
#> GSM372295 5 0.4297 0.1461 0.000 0.000 0.000 0.472 0.528
#> GSM372296 4 0.2110 0.7484 0.000 0.072 0.000 0.912 0.016
#> GSM372297 4 0.0000 0.7933 0.000 0.000 0.000 1.000 0.000
#> GSM372298 4 0.1638 0.7790 0.000 0.004 0.000 0.932 0.064
#> GSM372299 5 0.4367 0.2583 0.000 0.008 0.000 0.372 0.620
#> GSM372300 4 0.4339 0.5938 0.000 0.000 0.020 0.684 0.296
#> GSM372301 4 0.3550 0.6625 0.000 0.000 0.004 0.760 0.236
#> GSM372302 4 0.0451 0.7927 0.000 0.004 0.000 0.988 0.008
#> GSM372303 4 0.4223 0.6294 0.000 0.000 0.028 0.724 0.248
#> GSM372304 4 0.0000 0.7933 0.000 0.000 0.000 1.000 0.000
#> GSM372305 2 0.0703 0.7440 0.000 0.976 0.000 0.000 0.024
#> GSM372306 2 0.1444 0.7423 0.000 0.948 0.040 0.000 0.012
#> GSM372307 2 0.6621 -0.2989 0.000 0.428 0.000 0.224 0.348
#> GSM372309 5 0.4760 0.3443 0.000 0.416 0.000 0.020 0.564
#> GSM372311 2 0.0510 0.7454 0.000 0.984 0.000 0.000 0.016
#> GSM372313 2 0.0000 0.7455 0.000 1.000 0.000 0.000 0.000
#> GSM372315 2 0.2983 0.6358 0.000 0.864 0.000 0.096 0.040
#> GSM372317 2 0.2280 0.6992 0.000 0.880 0.120 0.000 0.000
#> GSM372319 3 0.2416 0.7955 0.000 0.100 0.888 0.000 0.012
#> GSM372321 3 0.0703 0.8528 0.000 0.024 0.976 0.000 0.000
#> GSM372323 3 0.1549 0.8594 0.000 0.016 0.944 0.000 0.040
#> GSM372326 3 0.3816 0.7029 0.000 0.000 0.696 0.000 0.304
#> GSM372328 3 0.2462 0.8373 0.000 0.000 0.880 0.008 0.112
#> GSM372330 2 0.0404 0.7455 0.000 0.988 0.000 0.000 0.012
#> GSM372332 3 0.0404 0.8589 0.000 0.000 0.988 0.000 0.012
#> GSM372335 2 0.2305 0.7143 0.000 0.896 0.092 0.000 0.012
#> GSM372337 3 0.0290 0.8561 0.000 0.008 0.992 0.000 0.000
#> GSM372339 3 0.0290 0.8579 0.000 0.000 0.992 0.000 0.008
#> GSM372341 3 0.2329 0.8350 0.000 0.000 0.876 0.000 0.124
#> GSM372343 3 0.3177 0.7853 0.000 0.000 0.792 0.000 0.208
#> GSM372345 3 0.0771 0.8533 0.000 0.020 0.976 0.000 0.004
#> GSM372347 3 0.4494 0.2895 0.000 0.380 0.608 0.000 0.012
#> GSM372349 3 0.2249 0.7972 0.000 0.000 0.896 0.008 0.096
#> GSM372351 3 0.3366 0.7677 0.000 0.000 0.768 0.000 0.232
#> GSM372353 5 0.6415 -0.3272 0.000 0.172 0.400 0.000 0.428
#> GSM372355 2 0.0510 0.7454 0.000 0.984 0.000 0.000 0.016
#> GSM372357 5 0.4291 0.2685 0.000 0.464 0.000 0.000 0.536
#> GSM372359 2 0.4701 0.5108 0.000 0.720 0.204 0.000 0.076
#> GSM372361 5 0.6043 0.4422 0.000 0.128 0.004 0.308 0.560
#> GSM372363 5 0.4542 0.2894 0.000 0.456 0.000 0.008 0.536
#> GSM372308 1 0.3003 0.7755 0.812 0.000 0.000 0.000 0.188
#> GSM372310 1 0.0000 0.9541 1.000 0.000 0.000 0.000 0.000
#> GSM372312 1 0.4242 0.7952 0.816 0.016 0.028 0.032 0.108
#> GSM372314 1 0.3508 0.6534 0.748 0.252 0.000 0.000 0.000
#> GSM372316 1 0.0000 0.9541 1.000 0.000 0.000 0.000 0.000
#> GSM372318 1 0.0000 0.9541 1.000 0.000 0.000 0.000 0.000
#> GSM372320 1 0.0000 0.9541 1.000 0.000 0.000 0.000 0.000
#> GSM372322 1 0.0000 0.9541 1.000 0.000 0.000 0.000 0.000
#> GSM372324 1 0.0324 0.9495 0.992 0.004 0.000 0.000 0.004
#> GSM372325 1 0.5100 0.3452 0.592 0.372 0.024 0.000 0.012
#> GSM372327 1 0.0000 0.9541 1.000 0.000 0.000 0.000 0.000
#> GSM372329 1 0.0000 0.9541 1.000 0.000 0.000 0.000 0.000
#> GSM372331 2 0.2848 0.5838 0.156 0.840 0.000 0.000 0.004
#> GSM372333 2 0.5294 0.1664 0.004 0.524 0.432 0.000 0.040
#> GSM372334 1 0.0000 0.9541 1.000 0.000 0.000 0.000 0.000
#> GSM372336 1 0.0000 0.9541 1.000 0.000 0.000 0.000 0.000
#> GSM372338 1 0.0000 0.9541 1.000 0.000 0.000 0.000 0.000
#> GSM372340 1 0.0000 0.9541 1.000 0.000 0.000 0.000 0.000
#> GSM372342 1 0.0000 0.9541 1.000 0.000 0.000 0.000 0.000
#> GSM372344 1 0.0000 0.9541 1.000 0.000 0.000 0.000 0.000
#> GSM372346 1 0.0000 0.9541 1.000 0.000 0.000 0.000 0.000
#> GSM372348 1 0.0000 0.9541 1.000 0.000 0.000 0.000 0.000
#> GSM372350 1 0.2897 0.8641 0.884 0.000 0.020 0.024 0.072
#> GSM372352 2 0.6833 0.3825 0.132 0.588 0.204 0.000 0.076
#> GSM372354 1 0.0290 0.9499 0.992 0.000 0.000 0.000 0.008
#> GSM372356 1 0.0000 0.9541 1.000 0.000 0.000 0.000 0.000
#> GSM372358 1 0.0000 0.9541 1.000 0.000 0.000 0.000 0.000
#> GSM372360 1 0.0162 0.9521 0.996 0.000 0.000 0.000 0.004
#> GSM372362 1 0.0162 0.9520 0.996 0.000 0.000 0.000 0.004
#> GSM372364 1 0.0000 0.9541 1.000 0.000 0.000 0.000 0.000
#> GSM372365 1 0.2074 0.8698 0.896 0.000 0.000 0.000 0.104
#> GSM372366 1 0.0000 0.9541 1.000 0.000 0.000 0.000 0.000
#> GSM372367 1 0.0000 0.9541 1.000 0.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM372286 2 0.1799 0.6939 0.000 0.936 0.008 0.016 0.016 0.024
#> GSM372287 4 0.2917 0.7347 0.000 0.016 0.000 0.840 0.136 0.008
#> GSM372288 4 0.3765 0.7010 0.000 0.060 0.000 0.780 0.156 0.004
#> GSM372289 2 0.6327 0.1073 0.000 0.460 0.000 0.284 0.236 0.020
#> GSM372290 4 0.3960 0.6541 0.000 0.032 0.000 0.736 0.224 0.008
#> GSM372291 4 0.3224 0.6838 0.000 0.000 0.004 0.824 0.040 0.132
#> GSM372292 4 0.1285 0.7252 0.000 0.000 0.004 0.944 0.000 0.052
#> GSM372293 6 0.6032 -0.0250 0.000 0.000 0.104 0.424 0.036 0.436
#> GSM372294 4 0.4910 0.5764 0.000 0.048 0.000 0.688 0.048 0.216
#> GSM372295 5 0.3619 0.6058 0.000 0.000 0.000 0.232 0.744 0.024
#> GSM372296 4 0.3634 0.7287 0.000 0.060 0.000 0.820 0.092 0.028
#> GSM372297 4 0.0260 0.7514 0.000 0.000 0.000 0.992 0.008 0.000
#> GSM372298 4 0.1275 0.7509 0.000 0.016 0.000 0.956 0.012 0.016
#> GSM372299 5 0.3582 0.6271 0.000 0.000 0.000 0.196 0.768 0.036
#> GSM372300 4 0.5316 -0.1880 0.000 0.000 0.040 0.528 0.036 0.396
#> GSM372301 4 0.3509 0.5635 0.000 0.000 0.016 0.788 0.016 0.180
#> GSM372302 4 0.2252 0.7561 0.000 0.016 0.000 0.900 0.072 0.012
#> GSM372303 4 0.4173 0.4505 0.000 0.000 0.044 0.732 0.012 0.212
#> GSM372304 4 0.1082 0.7591 0.000 0.000 0.000 0.956 0.040 0.004
#> GSM372305 2 0.2151 0.6884 0.000 0.904 0.008 0.000 0.072 0.016
#> GSM372306 2 0.3596 0.6236 0.000 0.792 0.164 0.000 0.012 0.032
#> GSM372307 5 0.5268 0.5891 0.000 0.224 0.020 0.068 0.668 0.020
#> GSM372309 5 0.2070 0.7798 0.000 0.100 0.008 0.000 0.892 0.000
#> GSM372311 2 0.2316 0.6861 0.000 0.900 0.004 0.004 0.064 0.028
#> GSM372313 2 0.1148 0.6932 0.000 0.960 0.000 0.004 0.016 0.020
#> GSM372315 2 0.5006 0.4827 0.000 0.680 0.000 0.084 0.208 0.028
#> GSM372317 2 0.4502 0.5123 0.000 0.664 0.288 0.000 0.032 0.016
#> GSM372319 3 0.2669 0.7077 0.000 0.072 0.880 0.000 0.016 0.032
#> GSM372321 3 0.1857 0.7302 0.000 0.028 0.928 0.000 0.012 0.032
#> GSM372323 3 0.2712 0.7155 0.000 0.012 0.864 0.000 0.016 0.108
#> GSM372326 3 0.5527 0.3087 0.000 0.000 0.564 0.004 0.156 0.276
#> GSM372328 3 0.3023 0.6481 0.000 0.000 0.808 0.008 0.004 0.180
#> GSM372330 2 0.2046 0.6872 0.000 0.916 0.000 0.008 0.044 0.032
#> GSM372332 3 0.1349 0.7337 0.000 0.000 0.940 0.000 0.004 0.056
#> GSM372335 2 0.4404 0.6232 0.000 0.760 0.080 0.000 0.036 0.124
#> GSM372337 3 0.1606 0.7327 0.000 0.008 0.932 0.000 0.004 0.056
#> GSM372339 3 0.0692 0.7341 0.000 0.000 0.976 0.000 0.004 0.020
#> GSM372341 3 0.1806 0.7191 0.000 0.000 0.908 0.000 0.004 0.088
#> GSM372343 3 0.3925 0.4885 0.000 0.000 0.656 0.004 0.008 0.332
#> GSM372345 3 0.2609 0.7088 0.000 0.036 0.868 0.000 0.000 0.096
#> GSM372347 2 0.5691 0.1657 0.000 0.492 0.380 0.000 0.012 0.116
#> GSM372349 3 0.4648 0.4433 0.000 0.004 0.636 0.004 0.044 0.312
#> GSM372351 3 0.4235 0.5073 0.000 0.000 0.672 0.004 0.032 0.292
#> GSM372353 6 0.7550 0.0632 0.000 0.120 0.264 0.004 0.300 0.312
#> GSM372355 2 0.1838 0.6857 0.000 0.916 0.000 0.000 0.068 0.016
#> GSM372357 5 0.3139 0.7191 0.000 0.152 0.032 0.000 0.816 0.000
#> GSM372359 2 0.5844 0.4008 0.000 0.592 0.084 0.004 0.052 0.268
#> GSM372361 5 0.2240 0.7697 0.000 0.032 0.016 0.044 0.908 0.000
#> GSM372363 5 0.2053 0.7797 0.000 0.108 0.004 0.000 0.888 0.000
#> GSM372308 1 0.2048 0.8484 0.880 0.000 0.000 0.000 0.120 0.000
#> GSM372310 1 0.0146 0.9450 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM372312 1 0.6784 0.3902 0.540 0.044 0.032 0.044 0.044 0.296
#> GSM372314 1 0.3817 0.7321 0.780 0.172 0.008 0.000 0.008 0.032
#> GSM372316 1 0.0146 0.9442 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM372318 1 0.0000 0.9451 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372320 1 0.0146 0.9450 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM372322 1 0.0000 0.9451 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372324 1 0.2755 0.8615 0.880 0.032 0.016 0.000 0.004 0.068
#> GSM372325 2 0.6440 0.3333 0.268 0.544 0.076 0.000 0.008 0.104
#> GSM372327 1 0.0146 0.9450 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM372329 1 0.0260 0.9441 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM372331 2 0.3447 0.5841 0.148 0.804 0.000 0.000 0.004 0.044
#> GSM372333 3 0.5548 0.1622 0.000 0.368 0.504 0.000 0.004 0.124
#> GSM372334 1 0.0146 0.9450 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM372336 1 0.0363 0.9424 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM372338 1 0.0146 0.9450 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM372340 1 0.0146 0.9450 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM372342 1 0.0146 0.9450 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM372344 1 0.0146 0.9450 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM372346 1 0.0260 0.9425 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM372348 1 0.2220 0.8857 0.908 0.020 0.000 0.000 0.020 0.052
#> GSM372350 1 0.5927 0.4712 0.588 0.000 0.028 0.052 0.044 0.288
#> GSM372352 2 0.6073 0.4048 0.004 0.540 0.068 0.008 0.048 0.332
#> GSM372354 1 0.0405 0.9404 0.988 0.000 0.000 0.000 0.004 0.008
#> GSM372356 1 0.0000 0.9451 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372358 1 0.0000 0.9451 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372360 1 0.0000 0.9451 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372362 1 0.0000 0.9451 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372364 1 0.0000 0.9451 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372365 1 0.1444 0.8947 0.928 0.000 0.000 0.000 0.072 0.000
#> GSM372366 1 0.0000 0.9451 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372367 1 0.0000 0.9451 1.000 0.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) specimen(p) individual(p) k
#> SD:NMF 81 9.58e-05 1.96e-17 1.000 2
#> SD:NMF 79 1.70e-06 8.58e-19 0.949 3
#> SD:NMF 77 9.48e-14 1.61e-25 0.852 4
#> SD:NMF 68 4.20e-12 9.80e-23 0.707 5
#> SD:NMF 66 1.17e-09 6.05e-19 0.649 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 51941 rows and 82 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.582 0.781 0.880 0.4692 0.513 0.513
#> 3 3 0.721 0.925 0.924 0.3869 0.805 0.625
#> 4 4 0.776 0.733 0.875 0.0935 0.978 0.935
#> 5 5 0.791 0.818 0.872 0.0429 0.932 0.784
#> 6 6 0.852 0.824 0.904 0.0293 0.987 0.950
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
#> GSM372286 2 0.0000 0.777 0.000 1.000
#> GSM372287 2 0.0000 0.777 0.000 1.000
#> GSM372288 2 0.0000 0.777 0.000 1.000
#> GSM372289 2 0.0000 0.777 0.000 1.000
#> GSM372290 2 0.0000 0.777 0.000 1.000
#> GSM372291 1 0.1633 0.949 0.976 0.024
#> GSM372292 2 0.9393 0.633 0.356 0.644
#> GSM372293 2 0.9393 0.633 0.356 0.644
#> GSM372294 2 0.6343 0.723 0.160 0.840
#> GSM372295 2 0.9686 0.599 0.396 0.604
#> GSM372296 2 0.0000 0.777 0.000 1.000
#> GSM372297 2 0.0000 0.777 0.000 1.000
#> GSM372298 2 0.0000 0.777 0.000 1.000
#> GSM372299 2 0.9686 0.599 0.396 0.604
#> GSM372300 2 0.9393 0.633 0.356 0.644
#> GSM372301 2 0.9393 0.633 0.356 0.644
#> GSM372302 2 0.0000 0.777 0.000 1.000
#> GSM372303 2 0.9393 0.633 0.356 0.644
#> GSM372304 2 0.0000 0.777 0.000 1.000
#> GSM372305 2 0.0000 0.777 0.000 1.000
#> GSM372306 2 0.0000 0.777 0.000 1.000
#> GSM372307 2 0.0000 0.777 0.000 1.000
#> GSM372309 2 0.1184 0.775 0.016 0.984
#> GSM372311 2 0.0000 0.777 0.000 1.000
#> GSM372313 2 0.0000 0.777 0.000 1.000
#> GSM372315 2 0.0000 0.777 0.000 1.000
#> GSM372317 2 0.0000 0.777 0.000 1.000
#> GSM372319 2 0.9686 0.599 0.396 0.604
#> GSM372321 2 0.9686 0.599 0.396 0.604
#> GSM372323 2 0.9963 0.476 0.464 0.536
#> GSM372326 2 0.9686 0.599 0.396 0.604
#> GSM372328 2 0.9686 0.599 0.396 0.604
#> GSM372330 2 0.0000 0.777 0.000 1.000
#> GSM372332 2 0.9686 0.599 0.396 0.604
#> GSM372335 2 0.0376 0.777 0.004 0.996
#> GSM372337 2 0.9963 0.476 0.464 0.536
#> GSM372339 2 0.9686 0.599 0.396 0.604
#> GSM372341 2 0.9686 0.599 0.396 0.604
#> GSM372343 2 0.9686 0.599 0.396 0.604
#> GSM372345 2 0.9963 0.476 0.464 0.536
#> GSM372347 2 0.9963 0.476 0.464 0.536
#> GSM372349 2 0.9963 0.476 0.464 0.536
#> GSM372351 2 0.9686 0.599 0.396 0.604
#> GSM372353 2 0.0376 0.777 0.004 0.996
#> GSM372355 2 0.0000 0.777 0.000 1.000
#> GSM372357 2 0.0376 0.777 0.004 0.996
#> GSM372359 2 0.0000 0.777 0.000 1.000
#> GSM372361 2 0.1184 0.775 0.016 0.984
#> GSM372363 2 0.1184 0.775 0.016 0.984
#> GSM372308 1 0.0376 0.969 0.996 0.004
#> GSM372310 1 0.0376 0.969 0.996 0.004
#> GSM372312 1 0.1633 0.952 0.976 0.024
#> GSM372314 1 0.2236 0.938 0.964 0.036
#> GSM372316 1 0.0000 0.971 1.000 0.000
#> GSM372318 1 0.0000 0.971 1.000 0.000
#> GSM372320 1 0.0000 0.971 1.000 0.000
#> GSM372322 1 0.0000 0.971 1.000 0.000
#> GSM372324 1 0.2236 0.938 0.964 0.036
#> GSM372325 1 0.2236 0.938 0.964 0.036
#> GSM372327 1 0.0000 0.971 1.000 0.000
#> GSM372329 1 0.0000 0.971 1.000 0.000
#> GSM372331 1 0.1414 0.956 0.980 0.020
#> GSM372333 1 0.9970 -0.318 0.532 0.468
#> GSM372334 1 0.0000 0.971 1.000 0.000
#> GSM372336 1 0.0000 0.971 1.000 0.000
#> GSM372338 1 0.0000 0.971 1.000 0.000
#> GSM372340 1 0.0000 0.971 1.000 0.000
#> GSM372342 1 0.0000 0.971 1.000 0.000
#> GSM372344 1 0.0000 0.971 1.000 0.000
#> GSM372346 1 0.0000 0.971 1.000 0.000
#> GSM372348 1 0.0000 0.971 1.000 0.000
#> GSM372350 1 0.0000 0.971 1.000 0.000
#> GSM372352 2 1.0000 0.395 0.496 0.504
#> GSM372354 1 0.0000 0.971 1.000 0.000
#> GSM372356 1 0.0000 0.971 1.000 0.000
#> GSM372358 1 0.0000 0.971 1.000 0.000
#> GSM372360 1 0.0000 0.971 1.000 0.000
#> GSM372362 1 0.0000 0.971 1.000 0.000
#> GSM372364 1 0.0000 0.971 1.000 0.000
#> GSM372365 1 0.0000 0.971 1.000 0.000
#> GSM372366 1 0.0000 0.971 1.000 0.000
#> GSM372367 1 0.1184 0.959 0.984 0.016
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM372286 2 0.2448 0.924 0.000 0.924 0.076
#> GSM372287 2 0.0424 0.930 0.000 0.992 0.008
#> GSM372288 2 0.0237 0.931 0.000 0.996 0.004
#> GSM372289 2 0.0237 0.931 0.000 0.996 0.004
#> GSM372290 2 0.1031 0.935 0.000 0.976 0.024
#> GSM372291 1 0.4645 0.826 0.816 0.008 0.176
#> GSM372292 3 0.5407 0.875 0.040 0.156 0.804
#> GSM372293 3 0.5407 0.875 0.040 0.156 0.804
#> GSM372294 2 0.4062 0.824 0.000 0.836 0.164
#> GSM372295 3 0.6000 0.833 0.040 0.200 0.760
#> GSM372296 2 0.0237 0.931 0.000 0.996 0.004
#> GSM372297 2 0.0592 0.931 0.000 0.988 0.012
#> GSM372298 2 0.0747 0.931 0.000 0.984 0.016
#> GSM372299 3 0.6000 0.833 0.040 0.200 0.760
#> GSM372300 3 0.5407 0.875 0.040 0.156 0.804
#> GSM372301 3 0.5407 0.875 0.040 0.156 0.804
#> GSM372302 2 0.0237 0.931 0.000 0.996 0.004
#> GSM372303 3 0.5407 0.875 0.040 0.156 0.804
#> GSM372304 2 0.0592 0.931 0.000 0.988 0.012
#> GSM372305 2 0.3192 0.913 0.000 0.888 0.112
#> GSM372306 2 0.3192 0.913 0.000 0.888 0.112
#> GSM372307 2 0.1031 0.935 0.000 0.976 0.024
#> GSM372309 2 0.3941 0.855 0.000 0.844 0.156
#> GSM372311 2 0.1411 0.937 0.000 0.964 0.036
#> GSM372313 2 0.1411 0.937 0.000 0.964 0.036
#> GSM372315 2 0.1411 0.937 0.000 0.964 0.036
#> GSM372317 2 0.3192 0.913 0.000 0.888 0.112
#> GSM372319 3 0.3572 0.914 0.040 0.060 0.900
#> GSM372321 3 0.3472 0.914 0.040 0.056 0.904
#> GSM372323 3 0.4964 0.892 0.116 0.048 0.836
#> GSM372326 3 0.3472 0.915 0.040 0.056 0.904
#> GSM372328 3 0.3369 0.915 0.040 0.052 0.908
#> GSM372330 2 0.1411 0.937 0.000 0.964 0.036
#> GSM372332 3 0.3369 0.915 0.040 0.052 0.908
#> GSM372335 2 0.3267 0.910 0.000 0.884 0.116
#> GSM372337 3 0.4964 0.894 0.116 0.048 0.836
#> GSM372339 3 0.3369 0.915 0.040 0.052 0.908
#> GSM372341 3 0.3369 0.915 0.040 0.052 0.908
#> GSM372343 3 0.3369 0.915 0.040 0.052 0.908
#> GSM372345 3 0.4964 0.892 0.116 0.048 0.836
#> GSM372347 3 0.4964 0.892 0.116 0.048 0.836
#> GSM372349 3 0.5067 0.894 0.116 0.052 0.832
#> GSM372351 3 0.3856 0.912 0.040 0.072 0.888
#> GSM372353 2 0.3879 0.881 0.000 0.848 0.152
#> GSM372355 2 0.1411 0.937 0.000 0.964 0.036
#> GSM372357 2 0.3116 0.917 0.000 0.892 0.108
#> GSM372359 2 0.3816 0.885 0.000 0.852 0.148
#> GSM372361 2 0.3879 0.858 0.000 0.848 0.152
#> GSM372363 2 0.3941 0.855 0.000 0.844 0.156
#> GSM372308 1 0.0237 0.977 0.996 0.000 0.004
#> GSM372310 1 0.0237 0.977 0.996 0.000 0.004
#> GSM372312 1 0.4521 0.833 0.816 0.004 0.180
#> GSM372314 1 0.1878 0.945 0.952 0.004 0.044
#> GSM372316 1 0.0000 0.979 1.000 0.000 0.000
#> GSM372318 1 0.0000 0.979 1.000 0.000 0.000
#> GSM372320 1 0.0000 0.979 1.000 0.000 0.000
#> GSM372322 1 0.0000 0.979 1.000 0.000 0.000
#> GSM372324 1 0.1878 0.945 0.952 0.004 0.044
#> GSM372325 1 0.1878 0.945 0.952 0.004 0.044
#> GSM372327 1 0.0000 0.979 1.000 0.000 0.000
#> GSM372329 1 0.0000 0.979 1.000 0.000 0.000
#> GSM372331 1 0.0983 0.967 0.980 0.004 0.016
#> GSM372333 3 0.6446 0.800 0.212 0.052 0.736
#> GSM372334 1 0.0000 0.979 1.000 0.000 0.000
#> GSM372336 1 0.0000 0.979 1.000 0.000 0.000
#> GSM372338 1 0.0000 0.979 1.000 0.000 0.000
#> GSM372340 1 0.0000 0.979 1.000 0.000 0.000
#> GSM372342 1 0.0000 0.979 1.000 0.000 0.000
#> GSM372344 1 0.0000 0.979 1.000 0.000 0.000
#> GSM372346 1 0.0000 0.979 1.000 0.000 0.000
#> GSM372348 1 0.0000 0.979 1.000 0.000 0.000
#> GSM372350 1 0.4002 0.851 0.840 0.000 0.160
#> GSM372352 3 0.6034 0.856 0.152 0.068 0.780
#> GSM372354 1 0.0000 0.979 1.000 0.000 0.000
#> GSM372356 1 0.0000 0.979 1.000 0.000 0.000
#> GSM372358 1 0.0000 0.979 1.000 0.000 0.000
#> GSM372360 1 0.0000 0.979 1.000 0.000 0.000
#> GSM372362 1 0.0000 0.979 1.000 0.000 0.000
#> GSM372364 1 0.0000 0.979 1.000 0.000 0.000
#> GSM372365 1 0.0000 0.979 1.000 0.000 0.000
#> GSM372366 1 0.0000 0.979 1.000 0.000 0.000
#> GSM372367 1 0.0829 0.970 0.984 0.004 0.012
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM372286 2 0.6089 -0.0756 0.000 0.608 0.064 0.328
#> GSM372287 2 0.4981 -0.7417 0.000 0.536 0.000 0.464
#> GSM372288 2 0.4925 -0.6528 0.000 0.572 0.000 0.428
#> GSM372289 2 0.4925 -0.6528 0.000 0.572 0.000 0.428
#> GSM372290 2 0.3105 0.5305 0.000 0.868 0.012 0.120
#> GSM372291 1 0.5228 0.7073 0.696 0.000 0.036 0.268
#> GSM372292 3 0.3372 0.8631 0.000 0.036 0.868 0.096
#> GSM372293 3 0.3372 0.8631 0.000 0.036 0.868 0.096
#> GSM372294 2 0.5685 -0.4880 0.000 0.516 0.024 0.460
#> GSM372295 3 0.4995 0.7286 0.000 0.032 0.720 0.248
#> GSM372296 2 0.4193 0.0673 0.000 0.732 0.000 0.268
#> GSM372297 4 0.5388 0.9673 0.000 0.456 0.012 0.532
#> GSM372298 4 0.5771 0.9345 0.000 0.460 0.028 0.512
#> GSM372299 3 0.4995 0.7286 0.000 0.032 0.720 0.248
#> GSM372300 3 0.3372 0.8631 0.000 0.036 0.868 0.096
#> GSM372301 3 0.3372 0.8631 0.000 0.036 0.868 0.096
#> GSM372302 2 0.4193 0.0673 0.000 0.732 0.000 0.268
#> GSM372303 3 0.3372 0.8631 0.000 0.036 0.868 0.096
#> GSM372304 4 0.5388 0.9673 0.000 0.456 0.012 0.532
#> GSM372305 2 0.2996 0.6253 0.000 0.892 0.064 0.044
#> GSM372306 2 0.2996 0.6253 0.000 0.892 0.064 0.044
#> GSM372307 2 0.3217 0.5224 0.000 0.860 0.012 0.128
#> GSM372309 2 0.5361 0.4910 0.000 0.724 0.068 0.208
#> GSM372311 2 0.0524 0.6116 0.000 0.988 0.004 0.008
#> GSM372313 2 0.0524 0.6116 0.000 0.988 0.004 0.008
#> GSM372315 2 0.0524 0.6116 0.000 0.988 0.004 0.008
#> GSM372317 2 0.2996 0.6253 0.000 0.892 0.064 0.044
#> GSM372319 3 0.1174 0.9039 0.000 0.020 0.968 0.012
#> GSM372321 3 0.1059 0.9045 0.000 0.016 0.972 0.012
#> GSM372323 3 0.3215 0.8845 0.020 0.024 0.892 0.064
#> GSM372326 3 0.0376 0.9062 0.000 0.004 0.992 0.004
#> GSM372328 3 0.0000 0.9063 0.000 0.000 1.000 0.000
#> GSM372330 2 0.0524 0.6116 0.000 0.988 0.004 0.008
#> GSM372332 3 0.0000 0.9063 0.000 0.000 1.000 0.000
#> GSM372335 2 0.3144 0.6217 0.000 0.884 0.072 0.044
#> GSM372337 3 0.2667 0.8884 0.020 0.008 0.912 0.060
#> GSM372339 3 0.0000 0.9063 0.000 0.000 1.000 0.000
#> GSM372341 3 0.0000 0.9063 0.000 0.000 1.000 0.000
#> GSM372343 3 0.0000 0.9063 0.000 0.000 1.000 0.000
#> GSM372345 3 0.3215 0.8845 0.020 0.024 0.892 0.064
#> GSM372347 3 0.3215 0.8845 0.020 0.024 0.892 0.064
#> GSM372349 3 0.2587 0.8894 0.020 0.008 0.916 0.056
#> GSM372351 3 0.1624 0.9001 0.000 0.028 0.952 0.020
#> GSM372353 2 0.3523 0.5927 0.000 0.856 0.112 0.032
#> GSM372355 2 0.0524 0.6116 0.000 0.988 0.004 0.008
#> GSM372357 2 0.3245 0.6216 0.000 0.880 0.056 0.064
#> GSM372359 2 0.3464 0.5974 0.000 0.860 0.108 0.032
#> GSM372361 2 0.5528 0.4716 0.000 0.700 0.064 0.236
#> GSM372363 2 0.5328 0.4942 0.000 0.724 0.064 0.212
#> GSM372308 1 0.0336 0.9602 0.992 0.000 0.000 0.008
#> GSM372310 1 0.0336 0.9602 0.992 0.000 0.000 0.008
#> GSM372312 1 0.5298 0.7154 0.696 0.008 0.024 0.272
#> GSM372314 1 0.3072 0.8960 0.892 0.008 0.024 0.076
#> GSM372316 1 0.0000 0.9628 1.000 0.000 0.000 0.000
#> GSM372318 1 0.0000 0.9628 1.000 0.000 0.000 0.000
#> GSM372320 1 0.0000 0.9628 1.000 0.000 0.000 0.000
#> GSM372322 1 0.0000 0.9628 1.000 0.000 0.000 0.000
#> GSM372324 1 0.3072 0.8960 0.892 0.008 0.024 0.076
#> GSM372325 1 0.3072 0.8960 0.892 0.008 0.024 0.076
#> GSM372327 1 0.0000 0.9628 1.000 0.000 0.000 0.000
#> GSM372329 1 0.0000 0.9628 1.000 0.000 0.000 0.000
#> GSM372331 1 0.1209 0.9460 0.964 0.004 0.000 0.032
#> GSM372333 3 0.4419 0.7988 0.116 0.008 0.820 0.056
#> GSM372334 1 0.0000 0.9628 1.000 0.000 0.000 0.000
#> GSM372336 1 0.0592 0.9565 0.984 0.000 0.000 0.016
#> GSM372338 1 0.0000 0.9628 1.000 0.000 0.000 0.000
#> GSM372340 1 0.0000 0.9628 1.000 0.000 0.000 0.000
#> GSM372342 1 0.0000 0.9628 1.000 0.000 0.000 0.000
#> GSM372344 1 0.0000 0.9628 1.000 0.000 0.000 0.000
#> GSM372346 1 0.0000 0.9628 1.000 0.000 0.000 0.000
#> GSM372348 1 0.0592 0.9565 0.984 0.000 0.000 0.016
#> GSM372350 1 0.4868 0.7347 0.720 0.000 0.024 0.256
#> GSM372352 3 0.4612 0.8485 0.056 0.036 0.828 0.080
#> GSM372354 1 0.0000 0.9628 1.000 0.000 0.000 0.000
#> GSM372356 1 0.0000 0.9628 1.000 0.000 0.000 0.000
#> GSM372358 1 0.0000 0.9628 1.000 0.000 0.000 0.000
#> GSM372360 1 0.0000 0.9628 1.000 0.000 0.000 0.000
#> GSM372362 1 0.0000 0.9628 1.000 0.000 0.000 0.000
#> GSM372364 1 0.0000 0.9628 1.000 0.000 0.000 0.000
#> GSM372365 1 0.0000 0.9628 1.000 0.000 0.000 0.000
#> GSM372366 1 0.0000 0.9628 1.000 0.000 0.000 0.000
#> GSM372367 1 0.0592 0.9549 0.984 0.000 0.000 0.016
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM372286 4 0.5385 0.418 0.000 0.432 0.056 0.512 0.000
#> GSM372287 4 0.2773 0.759 0.000 0.164 0.000 0.836 0.000
#> GSM372288 4 0.3143 0.756 0.000 0.204 0.000 0.796 0.000
#> GSM372289 4 0.3143 0.756 0.000 0.204 0.000 0.796 0.000
#> GSM372290 2 0.4556 0.440 0.000 0.680 0.004 0.292 0.024
#> GSM372291 5 0.4216 0.853 0.260 0.000 0.012 0.008 0.720
#> GSM372292 3 0.3304 0.822 0.000 0.004 0.840 0.128 0.028
#> GSM372293 3 0.3304 0.822 0.000 0.004 0.840 0.128 0.028
#> GSM372294 4 0.6000 0.599 0.000 0.268 0.000 0.572 0.160
#> GSM372295 3 0.7080 0.481 0.000 0.080 0.544 0.124 0.252
#> GSM372296 4 0.4300 0.346 0.000 0.476 0.000 0.524 0.000
#> GSM372297 4 0.2669 0.741 0.000 0.104 0.000 0.876 0.020
#> GSM372298 4 0.2915 0.734 0.000 0.116 0.000 0.860 0.024
#> GSM372299 3 0.7080 0.481 0.000 0.080 0.544 0.124 0.252
#> GSM372300 3 0.3304 0.822 0.000 0.004 0.840 0.128 0.028
#> GSM372301 3 0.3304 0.822 0.000 0.004 0.840 0.128 0.028
#> GSM372302 4 0.4300 0.346 0.000 0.476 0.000 0.524 0.000
#> GSM372303 3 0.3304 0.822 0.000 0.004 0.840 0.128 0.028
#> GSM372304 4 0.2669 0.741 0.000 0.104 0.000 0.876 0.020
#> GSM372305 2 0.1341 0.799 0.000 0.944 0.056 0.000 0.000
#> GSM372306 2 0.1341 0.799 0.000 0.944 0.056 0.000 0.000
#> GSM372307 2 0.4636 0.410 0.000 0.664 0.004 0.308 0.024
#> GSM372309 2 0.4411 0.638 0.000 0.772 0.004 0.096 0.128
#> GSM372311 2 0.2286 0.775 0.000 0.888 0.004 0.108 0.000
#> GSM372313 2 0.2286 0.775 0.000 0.888 0.004 0.108 0.000
#> GSM372315 2 0.2286 0.775 0.000 0.888 0.004 0.108 0.000
#> GSM372317 2 0.1341 0.799 0.000 0.944 0.056 0.000 0.000
#> GSM372319 3 0.0963 0.876 0.000 0.036 0.964 0.000 0.000
#> GSM372321 3 0.0880 0.877 0.000 0.032 0.968 0.000 0.000
#> GSM372323 3 0.2616 0.854 0.000 0.036 0.888 0.000 0.076
#> GSM372326 3 0.0451 0.878 0.000 0.004 0.988 0.000 0.008
#> GSM372328 3 0.0000 0.879 0.000 0.000 1.000 0.000 0.000
#> GSM372330 2 0.2286 0.775 0.000 0.888 0.004 0.108 0.000
#> GSM372332 3 0.0000 0.879 0.000 0.000 1.000 0.000 0.000
#> GSM372335 2 0.1478 0.796 0.000 0.936 0.064 0.000 0.000
#> GSM372337 3 0.2069 0.859 0.000 0.012 0.912 0.000 0.076
#> GSM372339 3 0.0000 0.879 0.000 0.000 1.000 0.000 0.000
#> GSM372341 3 0.0000 0.879 0.000 0.000 1.000 0.000 0.000
#> GSM372343 3 0.0000 0.879 0.000 0.000 1.000 0.000 0.000
#> GSM372345 3 0.2616 0.854 0.000 0.036 0.888 0.000 0.076
#> GSM372347 3 0.2616 0.854 0.000 0.036 0.888 0.000 0.076
#> GSM372349 3 0.1956 0.860 0.000 0.008 0.916 0.000 0.076
#> GSM372351 3 0.1357 0.873 0.000 0.048 0.948 0.000 0.004
#> GSM372353 2 0.2074 0.766 0.000 0.896 0.104 0.000 0.000
#> GSM372355 2 0.2286 0.775 0.000 0.888 0.004 0.108 0.000
#> GSM372357 2 0.1844 0.794 0.000 0.936 0.040 0.012 0.012
#> GSM372359 2 0.2020 0.770 0.000 0.900 0.100 0.000 0.000
#> GSM372361 2 0.5102 0.555 0.000 0.696 0.000 0.176 0.128
#> GSM372363 2 0.4747 0.619 0.000 0.744 0.004 0.124 0.128
#> GSM372308 1 0.0324 0.967 0.992 0.004 0.000 0.000 0.004
#> GSM372310 1 0.0324 0.967 0.992 0.004 0.000 0.000 0.004
#> GSM372312 5 0.4817 0.738 0.404 0.024 0.000 0.000 0.572
#> GSM372314 1 0.3110 0.793 0.872 0.024 0.024 0.000 0.080
#> GSM372316 1 0.0000 0.973 1.000 0.000 0.000 0.000 0.000
#> GSM372318 1 0.0000 0.973 1.000 0.000 0.000 0.000 0.000
#> GSM372320 1 0.0000 0.973 1.000 0.000 0.000 0.000 0.000
#> GSM372322 1 0.0000 0.973 1.000 0.000 0.000 0.000 0.000
#> GSM372324 1 0.3110 0.793 0.872 0.024 0.024 0.000 0.080
#> GSM372325 1 0.3110 0.793 0.872 0.024 0.024 0.000 0.080
#> GSM372327 1 0.0000 0.973 1.000 0.000 0.000 0.000 0.000
#> GSM372329 1 0.0000 0.973 1.000 0.000 0.000 0.000 0.000
#> GSM372331 1 0.1216 0.933 0.960 0.020 0.000 0.000 0.020
#> GSM372333 3 0.3866 0.758 0.096 0.008 0.820 0.000 0.076
#> GSM372334 1 0.0000 0.973 1.000 0.000 0.000 0.000 0.000
#> GSM372336 1 0.0609 0.955 0.980 0.000 0.000 0.000 0.020
#> GSM372338 1 0.0000 0.973 1.000 0.000 0.000 0.000 0.000
#> GSM372340 1 0.0000 0.973 1.000 0.000 0.000 0.000 0.000
#> GSM372342 1 0.0000 0.973 1.000 0.000 0.000 0.000 0.000
#> GSM372344 1 0.0000 0.973 1.000 0.000 0.000 0.000 0.000
#> GSM372346 1 0.0000 0.973 1.000 0.000 0.000 0.000 0.000
#> GSM372348 1 0.0609 0.955 0.980 0.000 0.000 0.000 0.020
#> GSM372350 5 0.3707 0.873 0.284 0.000 0.000 0.000 0.716
#> GSM372352 3 0.4045 0.815 0.036 0.064 0.824 0.000 0.076
#> GSM372354 1 0.0000 0.973 1.000 0.000 0.000 0.000 0.000
#> GSM372356 1 0.0000 0.973 1.000 0.000 0.000 0.000 0.000
#> GSM372358 1 0.0000 0.973 1.000 0.000 0.000 0.000 0.000
#> GSM372360 1 0.0000 0.973 1.000 0.000 0.000 0.000 0.000
#> GSM372362 1 0.0000 0.973 1.000 0.000 0.000 0.000 0.000
#> GSM372364 1 0.0000 0.973 1.000 0.000 0.000 0.000 0.000
#> GSM372365 1 0.0000 0.973 1.000 0.000 0.000 0.000 0.000
#> GSM372366 1 0.0000 0.973 1.000 0.000 0.000 0.000 0.000
#> GSM372367 1 0.0510 0.957 0.984 0.016 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM372286 4 0.4184 0.403 0.000 0.408 0.016 0.576 0.000 0.000
#> GSM372287 4 0.0717 0.731 0.000 0.016 0.000 0.976 0.008 0.000
#> GSM372288 4 0.1327 0.740 0.000 0.064 0.000 0.936 0.000 0.000
#> GSM372289 4 0.1327 0.740 0.000 0.064 0.000 0.936 0.000 0.000
#> GSM372290 2 0.4676 0.255 0.000 0.544 0.004 0.416 0.000 0.036
#> GSM372291 5 0.0653 0.667 0.004 0.000 0.012 0.000 0.980 0.004
#> GSM372292 3 0.3350 0.819 0.000 0.004 0.836 0.064 0.008 0.088
#> GSM372293 3 0.3350 0.819 0.000 0.004 0.836 0.064 0.008 0.088
#> GSM372294 4 0.5027 0.617 0.000 0.200 0.000 0.640 0.160 0.000
#> GSM372295 6 0.1753 1.000 0.000 0.004 0.084 0.000 0.000 0.912
#> GSM372296 4 0.3578 0.455 0.000 0.340 0.000 0.660 0.000 0.000
#> GSM372297 4 0.1584 0.706 0.000 0.000 0.000 0.928 0.008 0.064
#> GSM372298 4 0.2670 0.709 0.000 0.040 0.000 0.872 0.004 0.084
#> GSM372299 6 0.1753 1.000 0.000 0.004 0.084 0.000 0.000 0.912
#> GSM372300 3 0.3350 0.819 0.000 0.004 0.836 0.064 0.008 0.088
#> GSM372301 3 0.3350 0.819 0.000 0.004 0.836 0.064 0.008 0.088
#> GSM372302 4 0.3578 0.455 0.000 0.340 0.000 0.660 0.000 0.000
#> GSM372303 3 0.3350 0.819 0.000 0.004 0.836 0.064 0.008 0.088
#> GSM372304 4 0.1584 0.706 0.000 0.000 0.000 0.928 0.008 0.064
#> GSM372305 2 0.0458 0.803 0.000 0.984 0.016 0.000 0.000 0.000
#> GSM372306 2 0.0458 0.803 0.000 0.984 0.016 0.000 0.000 0.000
#> GSM372307 2 0.4701 0.207 0.000 0.524 0.004 0.436 0.000 0.036
#> GSM372309 2 0.3390 0.643 0.000 0.704 0.000 0.000 0.000 0.296
#> GSM372311 2 0.1863 0.791 0.000 0.896 0.000 0.104 0.000 0.000
#> GSM372313 2 0.1863 0.791 0.000 0.896 0.000 0.104 0.000 0.000
#> GSM372315 2 0.1863 0.791 0.000 0.896 0.000 0.104 0.000 0.000
#> GSM372317 2 0.0458 0.803 0.000 0.984 0.016 0.000 0.000 0.000
#> GSM372319 3 0.1267 0.878 0.000 0.060 0.940 0.000 0.000 0.000
#> GSM372321 3 0.1204 0.879 0.000 0.056 0.944 0.000 0.000 0.000
#> GSM372323 3 0.2554 0.859 0.000 0.048 0.876 0.000 0.076 0.000
#> GSM372326 3 0.0363 0.888 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM372328 3 0.0000 0.890 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372330 2 0.1863 0.791 0.000 0.896 0.000 0.104 0.000 0.000
#> GSM372332 3 0.0000 0.890 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372335 2 0.0632 0.801 0.000 0.976 0.024 0.000 0.000 0.000
#> GSM372337 3 0.1951 0.869 0.000 0.016 0.908 0.000 0.076 0.000
#> GSM372339 3 0.0000 0.890 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372341 3 0.0000 0.890 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372343 3 0.0000 0.890 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372345 3 0.2554 0.859 0.000 0.048 0.876 0.000 0.076 0.000
#> GSM372347 3 0.2554 0.859 0.000 0.048 0.876 0.000 0.076 0.000
#> GSM372349 3 0.1757 0.870 0.000 0.008 0.916 0.000 0.076 0.000
#> GSM372351 3 0.1531 0.876 0.000 0.068 0.928 0.000 0.000 0.004
#> GSM372353 2 0.1327 0.780 0.000 0.936 0.064 0.000 0.000 0.000
#> GSM372355 2 0.1863 0.791 0.000 0.896 0.000 0.104 0.000 0.000
#> GSM372357 2 0.1196 0.800 0.000 0.952 0.008 0.000 0.000 0.040
#> GSM372359 2 0.1267 0.784 0.000 0.940 0.060 0.000 0.000 0.000
#> GSM372361 2 0.5286 0.514 0.000 0.572 0.000 0.132 0.000 0.296
#> GSM372363 2 0.4463 0.609 0.000 0.652 0.000 0.056 0.000 0.292
#> GSM372308 1 0.0291 0.972 0.992 0.004 0.000 0.000 0.000 0.004
#> GSM372310 1 0.0291 0.972 0.992 0.004 0.000 0.000 0.000 0.004
#> GSM372312 5 0.3670 0.469 0.240 0.024 0.000 0.000 0.736 0.000
#> GSM372314 1 0.2882 0.849 0.872 0.024 0.024 0.000 0.076 0.004
#> GSM372316 1 0.0000 0.975 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372318 1 0.0000 0.975 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372320 1 0.0458 0.971 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM372322 1 0.0260 0.974 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM372324 1 0.2882 0.849 0.872 0.024 0.024 0.000 0.076 0.004
#> GSM372325 1 0.2882 0.849 0.872 0.024 0.024 0.000 0.076 0.004
#> GSM372327 1 0.0363 0.972 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM372329 1 0.0363 0.972 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM372331 1 0.1148 0.950 0.960 0.020 0.000 0.000 0.016 0.004
#> GSM372333 3 0.3472 0.763 0.096 0.008 0.820 0.000 0.076 0.000
#> GSM372334 1 0.0458 0.971 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM372336 1 0.0603 0.965 0.980 0.000 0.000 0.000 0.016 0.004
#> GSM372338 1 0.0458 0.971 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM372340 1 0.0458 0.971 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM372342 1 0.0260 0.974 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM372344 1 0.0458 0.971 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM372346 1 0.0260 0.974 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM372348 1 0.0603 0.965 0.980 0.000 0.000 0.000 0.016 0.004
#> GSM372350 5 0.0363 0.682 0.012 0.000 0.000 0.000 0.988 0.000
#> GSM372352 3 0.3901 0.809 0.036 0.084 0.804 0.000 0.076 0.000
#> GSM372354 1 0.0000 0.975 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372356 1 0.0000 0.975 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372358 1 0.0000 0.975 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372360 1 0.0000 0.975 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372362 1 0.0000 0.975 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372364 1 0.0000 0.975 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372365 1 0.0000 0.975 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372366 1 0.0000 0.975 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372367 1 0.0458 0.966 0.984 0.016 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) specimen(p) individual(p) k
#> CV:hclust 75 1.05e-04 3.63e-16 0.9898 2
#> CV:hclust 82 3.40e-04 7.97e-15 0.8970 3
#> CV:hclust 72 1.98e-04 9.06e-14 0.3666 4
#> CV:hclust 75 2.64e-07 3.46e-17 0.4188 5
#> CV:hclust 76 8.55e-08 2.75e-17 0.0682 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 51941 rows and 82 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 0.982 0.994 0.4794 0.524 0.524
#> 3 3 0.865 0.880 0.927 0.3813 0.804 0.626
#> 4 4 0.713 0.626 0.806 0.1097 0.961 0.884
#> 5 5 0.674 0.570 0.733 0.0660 0.787 0.401
#> 6 6 0.710 0.677 0.770 0.0439 0.902 0.574
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
#> GSM372286 2 0 0.9902 0.000 1.000
#> GSM372287 2 0 0.9902 0.000 1.000
#> GSM372288 2 0 0.9902 0.000 1.000
#> GSM372289 2 0 0.9902 0.000 1.000
#> GSM372290 2 0 0.9902 0.000 1.000
#> GSM372291 2 0 0.9902 0.000 1.000
#> GSM372292 2 0 0.9902 0.000 1.000
#> GSM372293 2 0 0.9902 0.000 1.000
#> GSM372294 2 0 0.9902 0.000 1.000
#> GSM372295 2 0 0.9902 0.000 1.000
#> GSM372296 2 0 0.9902 0.000 1.000
#> GSM372297 2 0 0.9902 0.000 1.000
#> GSM372298 2 0 0.9902 0.000 1.000
#> GSM372299 2 0 0.9902 0.000 1.000
#> GSM372300 2 0 0.9902 0.000 1.000
#> GSM372301 2 0 0.9902 0.000 1.000
#> GSM372302 2 0 0.9902 0.000 1.000
#> GSM372303 2 0 0.9902 0.000 1.000
#> GSM372304 2 0 0.9902 0.000 1.000
#> GSM372305 2 0 0.9902 0.000 1.000
#> GSM372306 2 0 0.9902 0.000 1.000
#> GSM372307 2 0 0.9902 0.000 1.000
#> GSM372309 2 0 0.9902 0.000 1.000
#> GSM372311 2 0 0.9902 0.000 1.000
#> GSM372313 2 0 0.9902 0.000 1.000
#> GSM372315 2 0 0.9902 0.000 1.000
#> GSM372317 2 0 0.9902 0.000 1.000
#> GSM372319 2 0 0.9902 0.000 1.000
#> GSM372321 2 0 0.9902 0.000 1.000
#> GSM372323 2 0 0.9902 0.000 1.000
#> GSM372326 2 0 0.9902 0.000 1.000
#> GSM372328 2 0 0.9902 0.000 1.000
#> GSM372330 2 0 0.9902 0.000 1.000
#> GSM372332 2 0 0.9902 0.000 1.000
#> GSM372335 2 0 0.9902 0.000 1.000
#> GSM372337 2 0 0.9902 0.000 1.000
#> GSM372339 2 0 0.9902 0.000 1.000
#> GSM372341 2 0 0.9902 0.000 1.000
#> GSM372343 2 0 0.9902 0.000 1.000
#> GSM372345 2 0 0.9902 0.000 1.000
#> GSM372347 2 0 0.9902 0.000 1.000
#> GSM372349 2 0 0.9902 0.000 1.000
#> GSM372351 2 0 0.9902 0.000 1.000
#> GSM372353 2 0 0.9902 0.000 1.000
#> GSM372355 2 0 0.9902 0.000 1.000
#> GSM372357 2 0 0.9902 0.000 1.000
#> GSM372359 2 0 0.9902 0.000 1.000
#> GSM372361 2 0 0.9902 0.000 1.000
#> GSM372363 2 0 0.9902 0.000 1.000
#> GSM372308 1 0 1.0000 1.000 0.000
#> GSM372310 1 0 1.0000 1.000 0.000
#> GSM372312 1 0 1.0000 1.000 0.000
#> GSM372314 1 0 1.0000 1.000 0.000
#> GSM372316 1 0 1.0000 1.000 0.000
#> GSM372318 1 0 1.0000 1.000 0.000
#> GSM372320 1 0 1.0000 1.000 0.000
#> GSM372322 1 0 1.0000 1.000 0.000
#> GSM372324 1 0 1.0000 1.000 0.000
#> GSM372325 1 0 1.0000 1.000 0.000
#> GSM372327 1 0 1.0000 1.000 0.000
#> GSM372329 1 0 1.0000 1.000 0.000
#> GSM372331 1 0 1.0000 1.000 0.000
#> GSM372333 2 1 0.0469 0.488 0.512
#> GSM372334 1 0 1.0000 1.000 0.000
#> GSM372336 1 0 1.0000 1.000 0.000
#> GSM372338 1 0 1.0000 1.000 0.000
#> GSM372340 1 0 1.0000 1.000 0.000
#> GSM372342 1 0 1.0000 1.000 0.000
#> GSM372344 1 0 1.0000 1.000 0.000
#> GSM372346 1 0 1.0000 1.000 0.000
#> GSM372348 1 0 1.0000 1.000 0.000
#> GSM372350 1 0 1.0000 1.000 0.000
#> GSM372352 2 0 0.9902 0.000 1.000
#> GSM372354 1 0 1.0000 1.000 0.000
#> GSM372356 1 0 1.0000 1.000 0.000
#> GSM372358 1 0 1.0000 1.000 0.000
#> GSM372360 1 0 1.0000 1.000 0.000
#> GSM372362 1 0 1.0000 1.000 0.000
#> GSM372364 1 0 1.0000 1.000 0.000
#> GSM372365 1 0 1.0000 1.000 0.000
#> GSM372366 1 0 1.0000 1.000 0.000
#> GSM372367 1 0 1.0000 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM372286 2 0.0237 0.8941 0.000 0.996 0.004
#> GSM372287 2 0.0237 0.8941 0.000 0.996 0.004
#> GSM372288 2 0.0237 0.8941 0.000 0.996 0.004
#> GSM372289 2 0.0237 0.8941 0.000 0.996 0.004
#> GSM372290 2 0.0237 0.8941 0.000 0.996 0.004
#> GSM372291 3 0.7712 0.6022 0.196 0.128 0.676
#> GSM372292 2 0.1529 0.8760 0.000 0.960 0.040
#> GSM372293 3 0.5254 0.7366 0.000 0.264 0.736
#> GSM372294 2 0.1163 0.8777 0.000 0.972 0.028
#> GSM372295 2 0.1031 0.8757 0.000 0.976 0.024
#> GSM372296 2 0.0237 0.8941 0.000 0.996 0.004
#> GSM372297 2 0.0237 0.8941 0.000 0.996 0.004
#> GSM372298 2 0.0237 0.8941 0.000 0.996 0.004
#> GSM372299 2 0.5882 0.3875 0.000 0.652 0.348
#> GSM372300 3 0.5363 0.7193 0.000 0.276 0.724
#> GSM372301 3 0.5431 0.7066 0.000 0.284 0.716
#> GSM372302 2 0.0237 0.8941 0.000 0.996 0.004
#> GSM372303 3 0.4062 0.8408 0.000 0.164 0.836
#> GSM372304 2 0.0237 0.8941 0.000 0.996 0.004
#> GSM372305 2 0.2796 0.8559 0.000 0.908 0.092
#> GSM372306 3 0.2261 0.9192 0.000 0.068 0.932
#> GSM372307 2 0.0237 0.8941 0.000 0.996 0.004
#> GSM372309 2 0.6154 0.3277 0.000 0.592 0.408
#> GSM372311 2 0.2796 0.8559 0.000 0.908 0.092
#> GSM372313 2 0.2796 0.8559 0.000 0.908 0.092
#> GSM372315 2 0.0424 0.8933 0.000 0.992 0.008
#> GSM372317 3 0.6274 0.0994 0.000 0.456 0.544
#> GSM372319 3 0.2165 0.9209 0.000 0.064 0.936
#> GSM372321 3 0.2165 0.9209 0.000 0.064 0.936
#> GSM372323 3 0.2165 0.9209 0.000 0.064 0.936
#> GSM372326 3 0.2261 0.9191 0.000 0.068 0.932
#> GSM372328 3 0.2165 0.9209 0.000 0.064 0.936
#> GSM372330 2 0.2796 0.8559 0.000 0.908 0.092
#> GSM372332 3 0.2165 0.9209 0.000 0.064 0.936
#> GSM372335 3 0.2261 0.9192 0.000 0.068 0.932
#> GSM372337 3 0.2165 0.9209 0.000 0.064 0.936
#> GSM372339 3 0.2165 0.9209 0.000 0.064 0.936
#> GSM372341 3 0.2165 0.9209 0.000 0.064 0.936
#> GSM372343 3 0.2165 0.9209 0.000 0.064 0.936
#> GSM372345 3 0.2165 0.9209 0.000 0.064 0.936
#> GSM372347 3 0.1964 0.9161 0.000 0.056 0.944
#> GSM372349 3 0.1529 0.9053 0.000 0.040 0.960
#> GSM372351 3 0.2165 0.9209 0.000 0.064 0.936
#> GSM372353 3 0.2625 0.9079 0.000 0.084 0.916
#> GSM372355 2 0.2796 0.8559 0.000 0.908 0.092
#> GSM372357 2 0.6168 0.3161 0.000 0.588 0.412
#> GSM372359 2 0.6235 0.2516 0.000 0.564 0.436
#> GSM372361 2 0.0000 0.8920 0.000 1.000 0.000
#> GSM372363 2 0.2711 0.8554 0.000 0.912 0.088
#> GSM372308 1 0.0892 0.9820 0.980 0.000 0.020
#> GSM372310 1 0.0892 0.9820 0.980 0.000 0.020
#> GSM372312 1 0.1643 0.9706 0.956 0.000 0.044
#> GSM372314 1 0.0892 0.9820 0.980 0.000 0.020
#> GSM372316 1 0.0592 0.9839 0.988 0.000 0.012
#> GSM372318 1 0.0747 0.9835 0.984 0.000 0.016
#> GSM372320 1 0.0892 0.9829 0.980 0.000 0.020
#> GSM372322 1 0.0892 0.9829 0.980 0.000 0.020
#> GSM372324 1 0.0892 0.9820 0.980 0.000 0.020
#> GSM372325 1 0.2878 0.9126 0.904 0.000 0.096
#> GSM372327 1 0.0892 0.9829 0.980 0.000 0.020
#> GSM372329 1 0.0892 0.9829 0.980 0.000 0.020
#> GSM372331 1 0.0892 0.9820 0.980 0.000 0.020
#> GSM372333 3 0.1774 0.8801 0.024 0.016 0.960
#> GSM372334 1 0.0892 0.9829 0.980 0.000 0.020
#> GSM372336 1 0.0424 0.9839 0.992 0.000 0.008
#> GSM372338 1 0.0892 0.9829 0.980 0.000 0.020
#> GSM372340 1 0.0892 0.9829 0.980 0.000 0.020
#> GSM372342 1 0.0892 0.9829 0.980 0.000 0.020
#> GSM372344 1 0.0892 0.9829 0.980 0.000 0.020
#> GSM372346 1 0.0892 0.9829 0.980 0.000 0.020
#> GSM372348 1 0.0424 0.9839 0.992 0.000 0.008
#> GSM372350 1 0.1860 0.9702 0.948 0.000 0.052
#> GSM372352 3 0.1289 0.8991 0.000 0.032 0.968
#> GSM372354 1 0.0592 0.9836 0.988 0.000 0.012
#> GSM372356 1 0.0592 0.9836 0.988 0.000 0.012
#> GSM372358 1 0.0000 0.9842 1.000 0.000 0.000
#> GSM372360 1 0.0592 0.9836 0.988 0.000 0.012
#> GSM372362 1 0.0592 0.9836 0.988 0.000 0.012
#> GSM372364 1 0.0592 0.9836 0.988 0.000 0.012
#> GSM372365 1 0.0592 0.9836 0.988 0.000 0.012
#> GSM372366 1 0.0592 0.9839 0.988 0.000 0.012
#> GSM372367 1 0.0892 0.9820 0.980 0.000 0.020
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM372286 2 0.2589 0.7169 0.000 0.884 0.000 0.116
#> GSM372287 2 0.4454 0.6464 0.000 0.692 0.000 0.308
#> GSM372288 2 0.4072 0.6795 0.000 0.748 0.000 0.252
#> GSM372289 2 0.2345 0.7165 0.000 0.900 0.000 0.100
#> GSM372290 2 0.4103 0.6776 0.000 0.744 0.000 0.256
#> GSM372291 4 0.4444 0.0805 0.008 0.020 0.184 0.788
#> GSM372292 2 0.7113 0.3633 0.000 0.456 0.128 0.416
#> GSM372293 3 0.6568 0.3600 0.000 0.096 0.572 0.332
#> GSM372294 2 0.4781 0.6367 0.000 0.660 0.004 0.336
#> GSM372295 2 0.5137 0.5440 0.000 0.544 0.004 0.452
#> GSM372296 2 0.4072 0.6795 0.000 0.748 0.000 0.252
#> GSM372297 2 0.4843 0.5728 0.000 0.604 0.000 0.396
#> GSM372298 2 0.4888 0.5685 0.000 0.588 0.000 0.412
#> GSM372299 4 0.7785 -0.3721 0.000 0.348 0.248 0.404
#> GSM372300 3 0.6717 0.3378 0.000 0.108 0.560 0.332
#> GSM372301 3 0.6925 0.3000 0.000 0.128 0.544 0.328
#> GSM372302 2 0.4454 0.6464 0.000 0.692 0.000 0.308
#> GSM372303 3 0.6005 0.4207 0.000 0.060 0.616 0.324
#> GSM372304 2 0.4643 0.6171 0.000 0.656 0.000 0.344
#> GSM372305 2 0.1118 0.7014 0.000 0.964 0.036 0.000
#> GSM372306 3 0.5565 0.4860 0.000 0.344 0.624 0.032
#> GSM372307 2 0.1867 0.7172 0.000 0.928 0.000 0.072
#> GSM372309 2 0.5627 0.4685 0.000 0.692 0.240 0.068
#> GSM372311 2 0.1584 0.7002 0.000 0.952 0.036 0.012
#> GSM372313 2 0.1584 0.7002 0.000 0.952 0.036 0.012
#> GSM372315 2 0.0469 0.7085 0.000 0.988 0.000 0.012
#> GSM372317 2 0.5666 0.2738 0.000 0.616 0.348 0.036
#> GSM372319 3 0.0376 0.7782 0.000 0.004 0.992 0.004
#> GSM372321 3 0.0188 0.7782 0.000 0.004 0.996 0.000
#> GSM372323 3 0.0188 0.7782 0.000 0.004 0.996 0.000
#> GSM372326 3 0.0524 0.7777 0.000 0.004 0.988 0.008
#> GSM372328 3 0.0524 0.7786 0.000 0.004 0.988 0.008
#> GSM372330 2 0.1706 0.6990 0.000 0.948 0.036 0.016
#> GSM372332 3 0.0524 0.7786 0.000 0.004 0.988 0.008
#> GSM372335 3 0.5754 0.5077 0.000 0.316 0.636 0.048
#> GSM372337 3 0.1209 0.7684 0.000 0.004 0.964 0.032
#> GSM372339 3 0.0524 0.7786 0.000 0.004 0.988 0.008
#> GSM372341 3 0.0524 0.7786 0.000 0.004 0.988 0.008
#> GSM372343 3 0.0524 0.7786 0.000 0.004 0.988 0.008
#> GSM372345 3 0.1209 0.7684 0.000 0.004 0.964 0.032
#> GSM372347 3 0.3533 0.7170 0.000 0.056 0.864 0.080
#> GSM372349 3 0.2704 0.7078 0.000 0.000 0.876 0.124
#> GSM372351 3 0.0657 0.7781 0.000 0.004 0.984 0.012
#> GSM372353 3 0.5519 0.5639 0.000 0.264 0.684 0.052
#> GSM372355 2 0.1584 0.7002 0.000 0.952 0.036 0.012
#> GSM372357 2 0.5657 0.4629 0.000 0.688 0.244 0.068
#> GSM372359 2 0.5055 0.4715 0.000 0.712 0.256 0.032
#> GSM372361 2 0.2469 0.7132 0.000 0.892 0.000 0.108
#> GSM372363 2 0.2227 0.6884 0.000 0.928 0.036 0.036
#> GSM372308 1 0.4888 0.5384 0.588 0.000 0.000 0.412
#> GSM372310 1 0.4888 0.5384 0.588 0.000 0.000 0.412
#> GSM372312 4 0.5158 -0.5392 0.472 0.000 0.004 0.524
#> GSM372314 1 0.4941 0.4997 0.564 0.000 0.000 0.436
#> GSM372316 1 0.0000 0.8216 1.000 0.000 0.000 0.000
#> GSM372318 1 0.0000 0.8216 1.000 0.000 0.000 0.000
#> GSM372320 1 0.0336 0.8210 0.992 0.000 0.000 0.008
#> GSM372322 1 0.0336 0.8210 0.992 0.000 0.000 0.008
#> GSM372324 1 0.4877 0.5412 0.592 0.000 0.000 0.408
#> GSM372325 1 0.6130 0.3958 0.512 0.000 0.048 0.440
#> GSM372327 1 0.0336 0.8210 0.992 0.000 0.000 0.008
#> GSM372329 1 0.0336 0.8210 0.992 0.000 0.000 0.008
#> GSM372331 1 0.4925 0.5133 0.572 0.000 0.000 0.428
#> GSM372333 3 0.6181 0.2567 0.048 0.004 0.568 0.380
#> GSM372334 1 0.0336 0.8210 0.992 0.000 0.000 0.008
#> GSM372336 1 0.2589 0.7937 0.884 0.000 0.000 0.116
#> GSM372338 1 0.0336 0.8210 0.992 0.000 0.000 0.008
#> GSM372340 1 0.0336 0.8210 0.992 0.000 0.000 0.008
#> GSM372342 1 0.0336 0.8210 0.992 0.000 0.000 0.008
#> GSM372344 1 0.0336 0.8210 0.992 0.000 0.000 0.008
#> GSM372346 1 0.0336 0.8210 0.992 0.000 0.000 0.008
#> GSM372348 1 0.2589 0.7937 0.884 0.000 0.000 0.116
#> GSM372350 1 0.4978 0.4821 0.612 0.000 0.004 0.384
#> GSM372352 3 0.6079 0.3307 0.000 0.052 0.568 0.380
#> GSM372354 1 0.1716 0.8138 0.936 0.000 0.000 0.064
#> GSM372356 1 0.2149 0.8075 0.912 0.000 0.000 0.088
#> GSM372358 1 0.1022 0.8195 0.968 0.000 0.000 0.032
#> GSM372360 1 0.2216 0.8061 0.908 0.000 0.000 0.092
#> GSM372362 1 0.1716 0.8138 0.936 0.000 0.000 0.064
#> GSM372364 1 0.2216 0.8061 0.908 0.000 0.000 0.092
#> GSM372365 1 0.4679 0.6045 0.648 0.000 0.000 0.352
#> GSM372366 1 0.0188 0.8216 0.996 0.000 0.000 0.004
#> GSM372367 1 0.4888 0.5384 0.588 0.000 0.000 0.412
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM372286 2 0.5816 0.2375 0.164 0.608 0.000 0.228 0.000
#> GSM372287 4 0.6268 0.5323 0.204 0.260 0.000 0.536 0.000
#> GSM372288 4 0.6476 0.4712 0.208 0.312 0.000 0.480 0.000
#> GSM372289 2 0.6255 0.0948 0.208 0.540 0.000 0.252 0.000
#> GSM372290 4 0.6444 0.4804 0.204 0.308 0.000 0.488 0.000
#> GSM372291 4 0.6279 0.3921 0.116 0.004 0.036 0.632 0.212
#> GSM372292 4 0.4170 0.5515 0.000 0.140 0.080 0.780 0.000
#> GSM372293 4 0.5016 0.3377 0.000 0.044 0.348 0.608 0.000
#> GSM372294 4 0.6694 0.4905 0.304 0.228 0.004 0.464 0.000
#> GSM372295 4 0.6223 0.5241 0.320 0.144 0.004 0.532 0.000
#> GSM372296 4 0.6552 0.4150 0.208 0.348 0.000 0.444 0.000
#> GSM372297 4 0.4647 0.5797 0.084 0.184 0.000 0.732 0.000
#> GSM372298 4 0.3909 0.5615 0.024 0.216 0.000 0.760 0.000
#> GSM372299 4 0.6260 0.4376 0.048 0.208 0.112 0.632 0.000
#> GSM372300 4 0.5066 0.3459 0.000 0.048 0.344 0.608 0.000
#> GSM372301 4 0.5084 0.3655 0.000 0.052 0.332 0.616 0.000
#> GSM372302 4 0.6286 0.5306 0.204 0.264 0.000 0.532 0.000
#> GSM372303 4 0.4849 0.3085 0.000 0.032 0.360 0.608 0.000
#> GSM372304 4 0.6030 0.5574 0.196 0.224 0.000 0.580 0.000
#> GSM372305 2 0.1310 0.7368 0.000 0.956 0.020 0.024 0.000
#> GSM372306 2 0.3797 0.6290 0.000 0.756 0.232 0.004 0.008
#> GSM372307 2 0.5979 0.2108 0.192 0.588 0.000 0.220 0.000
#> GSM372309 2 0.4123 0.7081 0.048 0.816 0.108 0.024 0.004
#> GSM372311 2 0.0854 0.7402 0.008 0.976 0.012 0.004 0.000
#> GSM372313 2 0.0693 0.7413 0.008 0.980 0.012 0.000 0.000
#> GSM372315 2 0.0798 0.7318 0.008 0.976 0.000 0.016 0.000
#> GSM372317 2 0.2911 0.7098 0.000 0.852 0.136 0.004 0.008
#> GSM372319 3 0.0162 0.9392 0.000 0.004 0.996 0.000 0.000
#> GSM372321 3 0.0162 0.9392 0.000 0.004 0.996 0.000 0.000
#> GSM372323 3 0.0162 0.9392 0.000 0.004 0.996 0.000 0.000
#> GSM372326 3 0.0833 0.9326 0.004 0.004 0.976 0.016 0.000
#> GSM372328 3 0.0451 0.9401 0.000 0.004 0.988 0.008 0.000
#> GSM372330 2 0.0854 0.7413 0.008 0.976 0.012 0.004 0.000
#> GSM372332 3 0.0451 0.9401 0.000 0.004 0.988 0.008 0.000
#> GSM372335 2 0.3947 0.6189 0.000 0.748 0.236 0.008 0.008
#> GSM372337 3 0.0451 0.9355 0.000 0.008 0.988 0.000 0.004
#> GSM372339 3 0.0451 0.9401 0.000 0.004 0.988 0.008 0.000
#> GSM372341 3 0.0451 0.9401 0.000 0.004 0.988 0.008 0.000
#> GSM372343 3 0.0451 0.9401 0.000 0.004 0.988 0.008 0.000
#> GSM372345 3 0.0451 0.9355 0.000 0.008 0.988 0.000 0.004
#> GSM372347 3 0.6054 0.4384 0.000 0.092 0.564 0.016 0.328
#> GSM372349 3 0.4068 0.7618 0.100 0.004 0.820 0.056 0.020
#> GSM372351 3 0.0671 0.9349 0.000 0.004 0.980 0.016 0.000
#> GSM372353 2 0.4181 0.6069 0.000 0.736 0.240 0.016 0.008
#> GSM372355 2 0.0727 0.7409 0.004 0.980 0.012 0.004 0.000
#> GSM372357 2 0.3978 0.7088 0.040 0.824 0.108 0.024 0.004
#> GSM372359 2 0.2729 0.7218 0.004 0.876 0.108 0.008 0.004
#> GSM372361 2 0.6083 0.2692 0.224 0.572 0.000 0.204 0.000
#> GSM372363 2 0.2846 0.7140 0.048 0.888 0.012 0.052 0.000
#> GSM372308 5 0.0693 0.5381 0.008 0.000 0.000 0.012 0.980
#> GSM372310 5 0.0693 0.5365 0.012 0.000 0.000 0.008 0.980
#> GSM372312 5 0.4423 0.4715 0.120 0.004 0.004 0.092 0.780
#> GSM372314 5 0.0671 0.5433 0.000 0.004 0.000 0.016 0.980
#> GSM372316 1 0.4610 0.9054 0.596 0.000 0.000 0.016 0.388
#> GSM372318 1 0.4438 0.9205 0.608 0.004 0.000 0.004 0.384
#> GSM372320 1 0.4402 0.9234 0.620 0.004 0.000 0.004 0.372
#> GSM372322 1 0.4088 0.9241 0.632 0.000 0.000 0.000 0.368
#> GSM372324 5 0.1012 0.5393 0.012 0.000 0.000 0.020 0.968
#> GSM372325 5 0.1646 0.5363 0.000 0.004 0.032 0.020 0.944
#> GSM372327 1 0.4088 0.9241 0.632 0.000 0.000 0.000 0.368
#> GSM372329 1 0.4354 0.9229 0.624 0.000 0.000 0.008 0.368
#> GSM372331 5 0.1059 0.5422 0.008 0.004 0.000 0.020 0.968
#> GSM372333 5 0.5152 -0.1583 0.000 0.016 0.432 0.016 0.536
#> GSM372334 1 0.4402 0.9234 0.620 0.004 0.000 0.004 0.372
#> GSM372336 5 0.4689 -0.5701 0.424 0.000 0.000 0.016 0.560
#> GSM372338 1 0.4402 0.9234 0.620 0.004 0.000 0.004 0.372
#> GSM372340 1 0.4389 0.9222 0.624 0.004 0.000 0.004 0.368
#> GSM372342 1 0.4354 0.9229 0.624 0.000 0.000 0.008 0.368
#> GSM372344 1 0.4402 0.9234 0.620 0.004 0.000 0.004 0.372
#> GSM372346 1 0.4251 0.9230 0.624 0.000 0.000 0.004 0.372
#> GSM372348 5 0.4666 -0.5356 0.412 0.000 0.000 0.016 0.572
#> GSM372350 5 0.5794 0.3005 0.336 0.008 0.004 0.072 0.580
#> GSM372352 5 0.7896 -0.1069 0.096 0.060 0.332 0.052 0.460
#> GSM372354 1 0.5547 0.7595 0.484 0.008 0.000 0.048 0.460
#> GSM372356 5 0.5407 -0.6364 0.424 0.004 0.000 0.048 0.524
#> GSM372358 1 0.5440 0.7186 0.476 0.004 0.000 0.048 0.472
#> GSM372360 5 0.5460 -0.6274 0.420 0.004 0.000 0.052 0.524
#> GSM372362 1 0.5494 0.7517 0.484 0.004 0.000 0.052 0.460
#> GSM372364 5 0.5460 -0.6274 0.420 0.004 0.000 0.052 0.524
#> GSM372365 5 0.3664 0.3446 0.120 0.004 0.000 0.052 0.824
#> GSM372366 1 0.5488 0.8544 0.540 0.008 0.000 0.048 0.404
#> GSM372367 5 0.1442 0.5214 0.012 0.004 0.000 0.032 0.952
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM372286 2 0.4717 -0.496 0.000 0.504 0.000 0.456 0.004 0.036
#> GSM372287 4 0.6031 0.682 0.000 0.216 0.000 0.536 0.020 0.228
#> GSM372288 4 0.5689 0.722 0.000 0.264 0.000 0.556 0.008 0.172
#> GSM372289 4 0.4057 0.587 0.000 0.436 0.000 0.556 0.008 0.000
#> GSM372290 4 0.5490 0.721 0.000 0.260 0.000 0.560 0.000 0.180
#> GSM372291 6 0.5666 0.271 0.000 0.000 0.016 0.136 0.280 0.568
#> GSM372292 6 0.4782 0.577 0.000 0.084 0.060 0.120 0.000 0.736
#> GSM372293 6 0.3668 0.688 0.000 0.028 0.228 0.000 0.000 0.744
#> GSM372294 4 0.6406 0.468 0.000 0.132 0.000 0.540 0.080 0.248
#> GSM372295 4 0.6206 0.271 0.000 0.056 0.000 0.524 0.116 0.304
#> GSM372296 4 0.5410 0.721 0.000 0.280 0.000 0.564 0.000 0.156
#> GSM372297 6 0.6154 -0.272 0.000 0.152 0.000 0.372 0.024 0.452
#> GSM372298 6 0.5232 0.333 0.000 0.144 0.000 0.200 0.012 0.644
#> GSM372299 6 0.6013 0.565 0.000 0.124 0.080 0.096 0.036 0.664
#> GSM372300 6 0.3713 0.689 0.000 0.032 0.224 0.000 0.000 0.744
#> GSM372301 6 0.4002 0.688 0.000 0.036 0.220 0.008 0.000 0.736
#> GSM372302 4 0.5874 0.688 0.000 0.220 0.000 0.544 0.012 0.224
#> GSM372303 6 0.3673 0.675 0.000 0.016 0.244 0.004 0.000 0.736
#> GSM372304 4 0.6112 0.657 0.000 0.204 0.000 0.528 0.024 0.244
#> GSM372305 2 0.0837 0.783 0.000 0.972 0.000 0.020 0.004 0.004
#> GSM372306 2 0.3661 0.743 0.000 0.796 0.160 0.024 0.012 0.008
#> GSM372307 4 0.4224 0.517 0.000 0.476 0.000 0.512 0.004 0.008
#> GSM372309 2 0.4265 0.760 0.000 0.800 0.080 0.052 0.032 0.036
#> GSM372311 2 0.0603 0.784 0.000 0.980 0.000 0.016 0.004 0.000
#> GSM372313 2 0.0603 0.784 0.000 0.980 0.000 0.016 0.004 0.000
#> GSM372315 2 0.0692 0.780 0.000 0.976 0.000 0.020 0.004 0.000
#> GSM372317 2 0.3243 0.778 0.000 0.844 0.108 0.016 0.012 0.020
#> GSM372319 3 0.0912 0.948 0.000 0.004 0.972 0.012 0.008 0.004
#> GSM372321 3 0.0146 0.961 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM372323 3 0.0146 0.961 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM372326 3 0.0696 0.953 0.000 0.004 0.980 0.008 0.004 0.004
#> GSM372328 3 0.0146 0.962 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM372330 2 0.1059 0.786 0.000 0.964 0.000 0.016 0.004 0.016
#> GSM372332 3 0.0146 0.962 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM372335 2 0.4037 0.724 0.000 0.772 0.172 0.024 0.012 0.020
#> GSM372337 3 0.0291 0.960 0.000 0.004 0.992 0.000 0.004 0.000
#> GSM372339 3 0.0146 0.962 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM372341 3 0.0146 0.962 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM372343 3 0.0146 0.962 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM372345 3 0.0291 0.960 0.000 0.004 0.992 0.000 0.004 0.000
#> GSM372347 5 0.4845 0.266 0.000 0.028 0.400 0.012 0.556 0.004
#> GSM372349 3 0.5147 0.604 0.000 0.000 0.704 0.096 0.068 0.132
#> GSM372351 3 0.0551 0.958 0.000 0.000 0.984 0.004 0.004 0.008
#> GSM372353 2 0.4197 0.699 0.000 0.752 0.192 0.020 0.012 0.024
#> GSM372355 2 0.0603 0.784 0.000 0.980 0.000 0.016 0.004 0.000
#> GSM372357 2 0.3561 0.780 0.000 0.836 0.080 0.044 0.008 0.032
#> GSM372359 2 0.2604 0.792 0.000 0.884 0.080 0.008 0.008 0.020
#> GSM372361 4 0.5071 0.408 0.000 0.460 0.000 0.484 0.028 0.028
#> GSM372363 2 0.2793 0.729 0.000 0.872 0.000 0.080 0.024 0.024
#> GSM372308 5 0.4440 0.718 0.156 0.000 0.000 0.116 0.724 0.004
#> GSM372310 5 0.4433 0.716 0.160 0.000 0.000 0.112 0.724 0.004
#> GSM372312 5 0.5697 0.536 0.072 0.000 0.000 0.112 0.644 0.172
#> GSM372314 5 0.2963 0.749 0.152 0.004 0.000 0.016 0.828 0.000
#> GSM372316 1 0.2322 0.782 0.904 0.000 0.000 0.048 0.024 0.024
#> GSM372318 1 0.1699 0.793 0.936 0.000 0.000 0.032 0.016 0.016
#> GSM372320 1 0.1616 0.782 0.932 0.000 0.000 0.048 0.000 0.020
#> GSM372322 1 0.0363 0.789 0.988 0.000 0.000 0.012 0.000 0.000
#> GSM372324 5 0.2595 0.744 0.160 0.000 0.000 0.004 0.836 0.000
#> GSM372325 5 0.2907 0.749 0.148 0.004 0.004 0.004 0.836 0.004
#> GSM372327 1 0.0363 0.789 0.988 0.000 0.000 0.012 0.000 0.000
#> GSM372329 1 0.0508 0.791 0.984 0.000 0.000 0.012 0.000 0.004
#> GSM372331 5 0.2662 0.748 0.152 0.004 0.000 0.004 0.840 0.000
#> GSM372333 5 0.3829 0.563 0.000 0.008 0.260 0.008 0.720 0.004
#> GSM372334 1 0.1616 0.782 0.932 0.000 0.000 0.048 0.000 0.020
#> GSM372336 1 0.4951 0.592 0.660 0.000 0.000 0.064 0.252 0.024
#> GSM372338 1 0.1616 0.782 0.932 0.000 0.000 0.048 0.000 0.020
#> GSM372340 1 0.1549 0.782 0.936 0.000 0.000 0.044 0.000 0.020
#> GSM372342 1 0.0508 0.791 0.984 0.000 0.000 0.012 0.000 0.004
#> GSM372344 1 0.1616 0.782 0.932 0.000 0.000 0.048 0.000 0.020
#> GSM372346 1 0.1262 0.790 0.956 0.000 0.000 0.016 0.020 0.008
#> GSM372348 1 0.4906 0.580 0.656 0.000 0.000 0.056 0.264 0.024
#> GSM372350 1 0.7296 -0.236 0.348 0.000 0.000 0.124 0.340 0.188
#> GSM372352 5 0.5031 0.530 0.000 0.020 0.196 0.064 0.700 0.020
#> GSM372354 1 0.5250 0.690 0.660 0.000 0.000 0.220 0.076 0.044
#> GSM372356 1 0.5570 0.635 0.636 0.000 0.000 0.144 0.184 0.036
#> GSM372358 1 0.5080 0.687 0.696 0.000 0.000 0.140 0.128 0.036
#> GSM372360 1 0.5628 0.617 0.624 0.000 0.000 0.188 0.156 0.032
#> GSM372362 1 0.4995 0.684 0.688 0.000 0.000 0.196 0.084 0.032
#> GSM372364 1 0.5662 0.609 0.620 0.000 0.000 0.184 0.164 0.032
#> GSM372365 5 0.6095 0.486 0.236 0.000 0.000 0.184 0.548 0.032
#> GSM372366 1 0.4046 0.739 0.748 0.000 0.000 0.200 0.016 0.036
#> GSM372367 5 0.4882 0.689 0.160 0.000 0.000 0.128 0.696 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) specimen(p) individual(p) k
#> CV:kmeans 81 8.44e-05 2.00e-17 0.999 2
#> CV:kmeans 77 1.29e-06 2.39e-16 0.830 3
#> CV:kmeans 64 5.58e-08 1.08e-18 0.916 4
#> CV:kmeans 57 6.10e-09 6.12e-18 0.567 5
#> CV:kmeans 72 7.05e-11 6.46e-22 0.424 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 51941 rows and 82 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.996 0.998 0.4913 0.509 0.509
#> 3 3 0.971 0.930 0.971 0.3354 0.822 0.654
#> 4 4 0.999 0.969 0.978 0.1195 0.874 0.655
#> 5 5 0.851 0.630 0.836 0.0530 0.985 0.945
#> 6 6 0.807 0.801 0.860 0.0471 0.900 0.634
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
#> GSM372286 2 0.000 1.000 0.000 1.000
#> GSM372287 2 0.000 1.000 0.000 1.000
#> GSM372288 2 0.000 1.000 0.000 1.000
#> GSM372289 2 0.000 1.000 0.000 1.000
#> GSM372290 2 0.000 1.000 0.000 1.000
#> GSM372291 1 0.000 0.996 1.000 0.000
#> GSM372292 2 0.000 1.000 0.000 1.000
#> GSM372293 2 0.000 1.000 0.000 1.000
#> GSM372294 2 0.000 1.000 0.000 1.000
#> GSM372295 2 0.000 1.000 0.000 1.000
#> GSM372296 2 0.000 1.000 0.000 1.000
#> GSM372297 2 0.000 1.000 0.000 1.000
#> GSM372298 2 0.000 1.000 0.000 1.000
#> GSM372299 2 0.000 1.000 0.000 1.000
#> GSM372300 2 0.000 1.000 0.000 1.000
#> GSM372301 2 0.000 1.000 0.000 1.000
#> GSM372302 2 0.000 1.000 0.000 1.000
#> GSM372303 2 0.000 1.000 0.000 1.000
#> GSM372304 2 0.000 1.000 0.000 1.000
#> GSM372305 2 0.000 1.000 0.000 1.000
#> GSM372306 2 0.000 1.000 0.000 1.000
#> GSM372307 2 0.000 1.000 0.000 1.000
#> GSM372309 2 0.000 1.000 0.000 1.000
#> GSM372311 2 0.000 1.000 0.000 1.000
#> GSM372313 2 0.000 1.000 0.000 1.000
#> GSM372315 2 0.000 1.000 0.000 1.000
#> GSM372317 2 0.000 1.000 0.000 1.000
#> GSM372319 2 0.000 1.000 0.000 1.000
#> GSM372321 2 0.000 1.000 0.000 1.000
#> GSM372323 2 0.000 1.000 0.000 1.000
#> GSM372326 2 0.000 1.000 0.000 1.000
#> GSM372328 2 0.000 1.000 0.000 1.000
#> GSM372330 2 0.000 1.000 0.000 1.000
#> GSM372332 2 0.000 1.000 0.000 1.000
#> GSM372335 2 0.000 1.000 0.000 1.000
#> GSM372337 2 0.000 1.000 0.000 1.000
#> GSM372339 2 0.000 1.000 0.000 1.000
#> GSM372341 2 0.000 1.000 0.000 1.000
#> GSM372343 2 0.000 1.000 0.000 1.000
#> GSM372345 2 0.000 1.000 0.000 1.000
#> GSM372347 2 0.000 1.000 0.000 1.000
#> GSM372349 2 0.000 1.000 0.000 1.000
#> GSM372351 2 0.000 1.000 0.000 1.000
#> GSM372353 2 0.000 1.000 0.000 1.000
#> GSM372355 2 0.000 1.000 0.000 1.000
#> GSM372357 2 0.000 1.000 0.000 1.000
#> GSM372359 2 0.000 1.000 0.000 1.000
#> GSM372361 2 0.000 1.000 0.000 1.000
#> GSM372363 2 0.000 1.000 0.000 1.000
#> GSM372308 1 0.000 0.996 1.000 0.000
#> GSM372310 1 0.000 0.996 1.000 0.000
#> GSM372312 1 0.000 0.996 1.000 0.000
#> GSM372314 1 0.000 0.996 1.000 0.000
#> GSM372316 1 0.000 0.996 1.000 0.000
#> GSM372318 1 0.000 0.996 1.000 0.000
#> GSM372320 1 0.000 0.996 1.000 0.000
#> GSM372322 1 0.000 0.996 1.000 0.000
#> GSM372324 1 0.000 0.996 1.000 0.000
#> GSM372325 1 0.000 0.996 1.000 0.000
#> GSM372327 1 0.000 0.996 1.000 0.000
#> GSM372329 1 0.000 0.996 1.000 0.000
#> GSM372331 1 0.000 0.996 1.000 0.000
#> GSM372333 1 0.000 0.996 1.000 0.000
#> GSM372334 1 0.000 0.996 1.000 0.000
#> GSM372336 1 0.000 0.996 1.000 0.000
#> GSM372338 1 0.000 0.996 1.000 0.000
#> GSM372340 1 0.000 0.996 1.000 0.000
#> GSM372342 1 0.000 0.996 1.000 0.000
#> GSM372344 1 0.000 0.996 1.000 0.000
#> GSM372346 1 0.000 0.996 1.000 0.000
#> GSM372348 1 0.000 0.996 1.000 0.000
#> GSM372350 1 0.000 0.996 1.000 0.000
#> GSM372352 1 0.605 0.826 0.852 0.148
#> GSM372354 1 0.000 0.996 1.000 0.000
#> GSM372356 1 0.000 0.996 1.000 0.000
#> GSM372358 1 0.000 0.996 1.000 0.000
#> GSM372360 1 0.000 0.996 1.000 0.000
#> GSM372362 1 0.000 0.996 1.000 0.000
#> GSM372364 1 0.000 0.996 1.000 0.000
#> GSM372365 1 0.000 0.996 1.000 0.000
#> GSM372366 1 0.000 0.996 1.000 0.000
#> GSM372367 1 0.000 0.996 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM372286 2 0.000 0.97687 0.000 1.000 0.000
#> GSM372287 2 0.000 0.97687 0.000 1.000 0.000
#> GSM372288 2 0.000 0.97687 0.000 1.000 0.000
#> GSM372289 2 0.000 0.97687 0.000 1.000 0.000
#> GSM372290 2 0.000 0.97687 0.000 1.000 0.000
#> GSM372291 1 0.153 0.95126 0.964 0.032 0.004
#> GSM372292 2 0.000 0.97687 0.000 1.000 0.000
#> GSM372293 3 0.525 0.66961 0.000 0.264 0.736
#> GSM372294 2 0.000 0.97687 0.000 1.000 0.000
#> GSM372295 2 0.000 0.97687 0.000 1.000 0.000
#> GSM372296 2 0.000 0.97687 0.000 1.000 0.000
#> GSM372297 2 0.000 0.97687 0.000 1.000 0.000
#> GSM372298 2 0.000 0.97687 0.000 1.000 0.000
#> GSM372299 2 0.000 0.97687 0.000 1.000 0.000
#> GSM372300 3 0.546 0.63270 0.000 0.288 0.712
#> GSM372301 3 0.556 0.61190 0.000 0.300 0.700
#> GSM372302 2 0.000 0.97687 0.000 1.000 0.000
#> GSM372303 3 0.489 0.71586 0.000 0.228 0.772
#> GSM372304 2 0.000 0.97687 0.000 1.000 0.000
#> GSM372305 2 0.000 0.97687 0.000 1.000 0.000
#> GSM372306 2 0.226 0.90708 0.000 0.932 0.068
#> GSM372307 2 0.000 0.97687 0.000 1.000 0.000
#> GSM372309 2 0.000 0.97687 0.000 1.000 0.000
#> GSM372311 2 0.000 0.97687 0.000 1.000 0.000
#> GSM372313 2 0.000 0.97687 0.000 1.000 0.000
#> GSM372315 2 0.000 0.97687 0.000 1.000 0.000
#> GSM372317 2 0.000 0.97687 0.000 1.000 0.000
#> GSM372319 3 0.000 0.91372 0.000 0.000 1.000
#> GSM372321 3 0.000 0.91372 0.000 0.000 1.000
#> GSM372323 3 0.000 0.91372 0.000 0.000 1.000
#> GSM372326 3 0.000 0.91372 0.000 0.000 1.000
#> GSM372328 3 0.000 0.91372 0.000 0.000 1.000
#> GSM372330 2 0.000 0.97687 0.000 1.000 0.000
#> GSM372332 3 0.000 0.91372 0.000 0.000 1.000
#> GSM372335 2 0.226 0.90708 0.000 0.932 0.068
#> GSM372337 3 0.000 0.91372 0.000 0.000 1.000
#> GSM372339 3 0.000 0.91372 0.000 0.000 1.000
#> GSM372341 3 0.000 0.91372 0.000 0.000 1.000
#> GSM372343 3 0.000 0.91372 0.000 0.000 1.000
#> GSM372345 3 0.000 0.91372 0.000 0.000 1.000
#> GSM372347 3 0.000 0.91372 0.000 0.000 1.000
#> GSM372349 3 0.000 0.91372 0.000 0.000 1.000
#> GSM372351 3 0.000 0.91372 0.000 0.000 1.000
#> GSM372353 2 0.629 -0.00729 0.000 0.532 0.468
#> GSM372355 2 0.000 0.97687 0.000 1.000 0.000
#> GSM372357 2 0.000 0.97687 0.000 1.000 0.000
#> GSM372359 2 0.000 0.97687 0.000 1.000 0.000
#> GSM372361 2 0.000 0.97687 0.000 1.000 0.000
#> GSM372363 2 0.000 0.97687 0.000 1.000 0.000
#> GSM372308 1 0.000 0.98971 1.000 0.000 0.000
#> GSM372310 1 0.000 0.98971 1.000 0.000 0.000
#> GSM372312 1 0.000 0.98971 1.000 0.000 0.000
#> GSM372314 1 0.000 0.98971 1.000 0.000 0.000
#> GSM372316 1 0.000 0.98971 1.000 0.000 0.000
#> GSM372318 1 0.000 0.98971 1.000 0.000 0.000
#> GSM372320 1 0.000 0.98971 1.000 0.000 0.000
#> GSM372322 1 0.000 0.98971 1.000 0.000 0.000
#> GSM372324 1 0.000 0.98971 1.000 0.000 0.000
#> GSM372325 1 0.000 0.98971 1.000 0.000 0.000
#> GSM372327 1 0.000 0.98971 1.000 0.000 0.000
#> GSM372329 1 0.000 0.98971 1.000 0.000 0.000
#> GSM372331 1 0.000 0.98971 1.000 0.000 0.000
#> GSM372333 1 0.543 0.60772 0.716 0.000 0.284
#> GSM372334 1 0.000 0.98971 1.000 0.000 0.000
#> GSM372336 1 0.000 0.98971 1.000 0.000 0.000
#> GSM372338 1 0.000 0.98971 1.000 0.000 0.000
#> GSM372340 1 0.000 0.98971 1.000 0.000 0.000
#> GSM372342 1 0.000 0.98971 1.000 0.000 0.000
#> GSM372344 1 0.000 0.98971 1.000 0.000 0.000
#> GSM372346 1 0.000 0.98971 1.000 0.000 0.000
#> GSM372348 1 0.000 0.98971 1.000 0.000 0.000
#> GSM372350 1 0.000 0.98971 1.000 0.000 0.000
#> GSM372352 3 0.595 0.38422 0.360 0.000 0.640
#> GSM372354 1 0.000 0.98971 1.000 0.000 0.000
#> GSM372356 1 0.000 0.98971 1.000 0.000 0.000
#> GSM372358 1 0.000 0.98971 1.000 0.000 0.000
#> GSM372360 1 0.000 0.98971 1.000 0.000 0.000
#> GSM372362 1 0.000 0.98971 1.000 0.000 0.000
#> GSM372364 1 0.000 0.98971 1.000 0.000 0.000
#> GSM372365 1 0.000 0.98971 1.000 0.000 0.000
#> GSM372366 1 0.000 0.98971 1.000 0.000 0.000
#> GSM372367 1 0.000 0.98971 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM372286 2 0.3907 0.703 0.000 0.768 0.000 0.232
#> GSM372287 4 0.1557 0.965 0.000 0.056 0.000 0.944
#> GSM372288 4 0.1940 0.953 0.000 0.076 0.000 0.924
#> GSM372289 2 0.1637 0.937 0.000 0.940 0.000 0.060
#> GSM372290 4 0.1867 0.956 0.000 0.072 0.000 0.928
#> GSM372291 4 0.0672 0.958 0.008 0.000 0.008 0.984
#> GSM372292 4 0.1022 0.967 0.000 0.032 0.000 0.968
#> GSM372293 4 0.1174 0.959 0.000 0.012 0.020 0.968
#> GSM372294 4 0.1637 0.959 0.000 0.060 0.000 0.940
#> GSM372295 4 0.1211 0.967 0.000 0.040 0.000 0.960
#> GSM372296 4 0.1867 0.956 0.000 0.072 0.000 0.928
#> GSM372297 4 0.0921 0.969 0.000 0.028 0.000 0.972
#> GSM372298 4 0.1211 0.968 0.000 0.040 0.000 0.960
#> GSM372299 4 0.1118 0.967 0.000 0.036 0.000 0.964
#> GSM372300 4 0.1174 0.959 0.000 0.012 0.020 0.968
#> GSM372301 4 0.1174 0.959 0.000 0.012 0.020 0.968
#> GSM372302 4 0.1474 0.966 0.000 0.052 0.000 0.948
#> GSM372303 4 0.1174 0.959 0.000 0.012 0.020 0.968
#> GSM372304 4 0.1302 0.968 0.000 0.044 0.000 0.956
#> GSM372305 2 0.0469 0.970 0.000 0.988 0.000 0.012
#> GSM372306 2 0.0469 0.968 0.000 0.988 0.012 0.000
#> GSM372307 2 0.0592 0.969 0.000 0.984 0.000 0.016
#> GSM372309 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM372311 2 0.0188 0.974 0.000 0.996 0.000 0.004
#> GSM372313 2 0.0188 0.974 0.000 0.996 0.000 0.004
#> GSM372315 2 0.0188 0.974 0.000 0.996 0.000 0.004
#> GSM372317 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM372319 3 0.0672 0.964 0.000 0.008 0.984 0.008
#> GSM372321 3 0.0336 0.967 0.000 0.000 0.992 0.008
#> GSM372323 3 0.0336 0.967 0.000 0.000 0.992 0.008
#> GSM372326 3 0.0524 0.966 0.000 0.004 0.988 0.008
#> GSM372328 3 0.0336 0.967 0.000 0.000 0.992 0.008
#> GSM372330 2 0.0188 0.974 0.000 0.996 0.000 0.004
#> GSM372332 3 0.0336 0.967 0.000 0.000 0.992 0.008
#> GSM372335 2 0.0188 0.972 0.000 0.996 0.000 0.004
#> GSM372337 3 0.0000 0.965 0.000 0.000 1.000 0.000
#> GSM372339 3 0.0336 0.967 0.000 0.000 0.992 0.008
#> GSM372341 3 0.0336 0.967 0.000 0.000 0.992 0.008
#> GSM372343 3 0.0336 0.967 0.000 0.000 0.992 0.008
#> GSM372345 3 0.0000 0.965 0.000 0.000 1.000 0.000
#> GSM372347 3 0.1042 0.950 0.000 0.020 0.972 0.008
#> GSM372349 3 0.0469 0.959 0.000 0.000 0.988 0.012
#> GSM372351 3 0.0672 0.964 0.000 0.008 0.984 0.008
#> GSM372353 2 0.1510 0.939 0.000 0.956 0.028 0.016
#> GSM372355 2 0.0188 0.974 0.000 0.996 0.000 0.004
#> GSM372357 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM372359 2 0.0336 0.972 0.000 0.992 0.000 0.008
#> GSM372361 2 0.1118 0.956 0.000 0.964 0.000 0.036
#> GSM372363 2 0.0469 0.970 0.000 0.988 0.000 0.012
#> GSM372308 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM372310 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM372312 1 0.1042 0.978 0.972 0.000 0.008 0.020
#> GSM372314 1 0.0336 0.993 0.992 0.000 0.000 0.008
#> GSM372316 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM372318 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM372320 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM372322 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM372324 1 0.0336 0.993 0.992 0.000 0.000 0.008
#> GSM372325 1 0.0672 0.987 0.984 0.000 0.008 0.008
#> GSM372327 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM372329 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM372331 1 0.0336 0.993 0.992 0.000 0.000 0.008
#> GSM372333 3 0.3088 0.835 0.128 0.000 0.864 0.008
#> GSM372334 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM372336 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM372338 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM372340 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM372342 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM372344 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM372346 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM372348 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM372350 1 0.0804 0.983 0.980 0.000 0.008 0.012
#> GSM372352 3 0.5308 0.735 0.180 0.044 0.756 0.020
#> GSM372354 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM372356 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM372358 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM372360 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM372362 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM372364 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM372365 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM372366 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM372367 1 0.0000 0.997 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM372286 4 0.4235 -0.126 0.000 0.424 0.000 0.576 0.000
#> GSM372287 4 0.0162 0.424 0.000 0.004 0.000 0.996 0.000
#> GSM372288 4 0.0609 0.429 0.000 0.020 0.000 0.980 0.000
#> GSM372289 2 0.4287 0.373 0.000 0.540 0.000 0.460 0.000
#> GSM372290 4 0.0609 0.429 0.000 0.020 0.000 0.980 0.000
#> GSM372291 5 0.4305 0.000 0.000 0.000 0.000 0.488 0.512
#> GSM372292 4 0.4420 -0.728 0.000 0.004 0.000 0.548 0.448
#> GSM372293 4 0.4567 -0.728 0.000 0.004 0.004 0.544 0.448
#> GSM372294 4 0.2079 0.384 0.000 0.020 0.000 0.916 0.064
#> GSM372295 4 0.2124 0.369 0.000 0.004 0.000 0.900 0.096
#> GSM372296 4 0.0703 0.428 0.000 0.024 0.000 0.976 0.000
#> GSM372297 4 0.2763 0.166 0.000 0.004 0.000 0.848 0.148
#> GSM372298 4 0.4331 -0.684 0.000 0.004 0.000 0.596 0.400
#> GSM372299 4 0.4450 -0.754 0.000 0.004 0.000 0.508 0.488
#> GSM372300 4 0.4567 -0.728 0.000 0.004 0.004 0.544 0.448
#> GSM372301 4 0.4567 -0.728 0.000 0.004 0.004 0.544 0.448
#> GSM372302 4 0.0290 0.426 0.000 0.008 0.000 0.992 0.000
#> GSM372303 4 0.4567 -0.728 0.000 0.004 0.004 0.544 0.448
#> GSM372304 4 0.0162 0.424 0.000 0.004 0.000 0.996 0.000
#> GSM372305 2 0.0162 0.889 0.000 0.996 0.000 0.004 0.000
#> GSM372306 2 0.0162 0.889 0.000 0.996 0.004 0.000 0.000
#> GSM372307 2 0.4283 0.380 0.000 0.544 0.000 0.456 0.000
#> GSM372309 2 0.1357 0.866 0.000 0.948 0.000 0.004 0.048
#> GSM372311 2 0.0000 0.890 0.000 1.000 0.000 0.000 0.000
#> GSM372313 2 0.0000 0.890 0.000 1.000 0.000 0.000 0.000
#> GSM372315 2 0.0000 0.890 0.000 1.000 0.000 0.000 0.000
#> GSM372317 2 0.0000 0.890 0.000 1.000 0.000 0.000 0.000
#> GSM372319 3 0.0510 0.889 0.000 0.016 0.984 0.000 0.000
#> GSM372321 3 0.0000 0.896 0.000 0.000 1.000 0.000 0.000
#> GSM372323 3 0.0162 0.895 0.000 0.000 0.996 0.000 0.004
#> GSM372326 3 0.1197 0.873 0.000 0.000 0.952 0.000 0.048
#> GSM372328 3 0.0000 0.896 0.000 0.000 1.000 0.000 0.000
#> GSM372330 2 0.0000 0.890 0.000 1.000 0.000 0.000 0.000
#> GSM372332 3 0.0162 0.895 0.000 0.000 0.996 0.000 0.004
#> GSM372335 2 0.0000 0.890 0.000 1.000 0.000 0.000 0.000
#> GSM372337 3 0.0290 0.894 0.000 0.000 0.992 0.000 0.008
#> GSM372339 3 0.0000 0.896 0.000 0.000 1.000 0.000 0.000
#> GSM372341 3 0.0000 0.896 0.000 0.000 1.000 0.000 0.000
#> GSM372343 3 0.0000 0.896 0.000 0.000 1.000 0.000 0.000
#> GSM372345 3 0.0404 0.894 0.000 0.000 0.988 0.000 0.012
#> GSM372347 3 0.5575 0.614 0.000 0.108 0.612 0.000 0.280
#> GSM372349 3 0.1851 0.851 0.000 0.000 0.912 0.000 0.088
#> GSM372351 3 0.1197 0.875 0.000 0.000 0.952 0.000 0.048
#> GSM372353 2 0.0451 0.886 0.000 0.988 0.000 0.004 0.008
#> GSM372355 2 0.0000 0.890 0.000 1.000 0.000 0.000 0.000
#> GSM372357 2 0.1121 0.870 0.000 0.956 0.000 0.000 0.044
#> GSM372359 2 0.0162 0.888 0.000 0.996 0.000 0.004 0.000
#> GSM372361 2 0.5291 0.341 0.000 0.496 0.000 0.456 0.048
#> GSM372363 2 0.3339 0.794 0.000 0.840 0.000 0.112 0.048
#> GSM372308 1 0.1671 0.907 0.924 0.000 0.000 0.000 0.076
#> GSM372310 1 0.1671 0.907 0.924 0.000 0.000 0.000 0.076
#> GSM372312 1 0.4182 0.597 0.600 0.000 0.000 0.000 0.400
#> GSM372314 1 0.4192 0.641 0.596 0.000 0.000 0.000 0.404
#> GSM372316 1 0.0000 0.920 1.000 0.000 0.000 0.000 0.000
#> GSM372318 1 0.0162 0.920 0.996 0.000 0.000 0.000 0.004
#> GSM372320 1 0.0162 0.920 0.996 0.000 0.000 0.000 0.004
#> GSM372322 1 0.0162 0.920 0.996 0.000 0.000 0.000 0.004
#> GSM372324 1 0.3932 0.672 0.672 0.000 0.000 0.000 0.328
#> GSM372325 1 0.4060 0.639 0.640 0.000 0.000 0.000 0.360
#> GSM372327 1 0.0162 0.920 0.996 0.000 0.000 0.000 0.004
#> GSM372329 1 0.0000 0.920 1.000 0.000 0.000 0.000 0.000
#> GSM372331 1 0.4182 0.642 0.600 0.000 0.000 0.000 0.400
#> GSM372333 3 0.6146 0.458 0.136 0.000 0.488 0.000 0.376
#> GSM372334 1 0.0162 0.920 0.996 0.000 0.000 0.000 0.004
#> GSM372336 1 0.0290 0.920 0.992 0.000 0.000 0.000 0.008
#> GSM372338 1 0.0162 0.920 0.996 0.000 0.000 0.000 0.004
#> GSM372340 1 0.0162 0.920 0.996 0.000 0.000 0.000 0.004
#> GSM372342 1 0.0162 0.920 0.996 0.000 0.000 0.000 0.004
#> GSM372344 1 0.0162 0.920 0.996 0.000 0.000 0.000 0.004
#> GSM372346 1 0.0000 0.920 1.000 0.000 0.000 0.000 0.000
#> GSM372348 1 0.0162 0.919 0.996 0.000 0.000 0.000 0.004
#> GSM372350 1 0.2020 0.863 0.900 0.000 0.000 0.000 0.100
#> GSM372352 3 0.7296 0.394 0.040 0.184 0.404 0.000 0.372
#> GSM372354 1 0.1544 0.909 0.932 0.000 0.000 0.000 0.068
#> GSM372356 1 0.0963 0.916 0.964 0.000 0.000 0.000 0.036
#> GSM372358 1 0.0963 0.916 0.964 0.000 0.000 0.000 0.036
#> GSM372360 1 0.1478 0.909 0.936 0.000 0.000 0.000 0.064
#> GSM372362 1 0.1478 0.909 0.936 0.000 0.000 0.000 0.064
#> GSM372364 1 0.1478 0.909 0.936 0.000 0.000 0.000 0.064
#> GSM372365 1 0.1478 0.909 0.936 0.000 0.000 0.000 0.064
#> GSM372366 1 0.0963 0.916 0.964 0.000 0.000 0.000 0.036
#> GSM372367 1 0.2179 0.890 0.888 0.000 0.000 0.000 0.112
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM372286 4 0.3301 0.679 0.000 0.216 0.000 0.772 0.004 0.008
#> GSM372287 4 0.0622 0.744 0.000 0.008 0.000 0.980 0.000 0.012
#> GSM372288 4 0.0547 0.753 0.000 0.020 0.000 0.980 0.000 0.000
#> GSM372289 4 0.3288 0.639 0.000 0.276 0.000 0.724 0.000 0.000
#> GSM372290 4 0.0653 0.750 0.000 0.012 0.000 0.980 0.004 0.004
#> GSM372291 6 0.5237 0.629 0.004 0.000 0.000 0.268 0.124 0.604
#> GSM372292 6 0.3390 0.889 0.000 0.000 0.000 0.296 0.000 0.704
#> GSM372293 6 0.3738 0.894 0.000 0.000 0.016 0.280 0.000 0.704
#> GSM372294 4 0.2537 0.685 0.000 0.000 0.000 0.872 0.032 0.096
#> GSM372295 4 0.2925 0.695 0.000 0.004 0.000 0.832 0.016 0.148
#> GSM372296 4 0.0713 0.754 0.000 0.028 0.000 0.972 0.000 0.000
#> GSM372297 4 0.3244 0.190 0.000 0.000 0.000 0.732 0.000 0.268
#> GSM372298 6 0.3823 0.721 0.000 0.000 0.000 0.436 0.000 0.564
#> GSM372299 6 0.3329 0.800 0.000 0.004 0.000 0.236 0.004 0.756
#> GSM372300 6 0.3670 0.896 0.000 0.000 0.012 0.284 0.000 0.704
#> GSM372301 6 0.3670 0.896 0.000 0.000 0.012 0.284 0.000 0.704
#> GSM372302 4 0.0717 0.741 0.000 0.008 0.000 0.976 0.000 0.016
#> GSM372303 6 0.3670 0.896 0.000 0.000 0.012 0.284 0.000 0.704
#> GSM372304 4 0.0935 0.727 0.000 0.004 0.000 0.964 0.000 0.032
#> GSM372305 2 0.0622 0.960 0.000 0.980 0.000 0.012 0.008 0.000
#> GSM372306 2 0.0725 0.957 0.000 0.976 0.000 0.000 0.012 0.012
#> GSM372307 4 0.4077 0.572 0.000 0.320 0.000 0.660 0.012 0.008
#> GSM372309 2 0.2449 0.897 0.000 0.888 0.000 0.020 0.012 0.080
#> GSM372311 2 0.0363 0.960 0.000 0.988 0.000 0.012 0.000 0.000
#> GSM372313 2 0.0363 0.960 0.000 0.988 0.000 0.012 0.000 0.000
#> GSM372315 2 0.0632 0.955 0.000 0.976 0.000 0.024 0.000 0.000
#> GSM372317 2 0.0291 0.961 0.000 0.992 0.000 0.004 0.004 0.000
#> GSM372319 3 0.0972 0.921 0.000 0.028 0.964 0.000 0.008 0.000
#> GSM372321 3 0.0000 0.940 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372323 3 0.0291 0.939 0.000 0.000 0.992 0.000 0.004 0.004
#> GSM372326 3 0.1806 0.881 0.000 0.004 0.908 0.000 0.000 0.088
#> GSM372328 3 0.0000 0.940 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372330 2 0.0363 0.960 0.000 0.988 0.000 0.012 0.000 0.000
#> GSM372332 3 0.0146 0.940 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM372335 2 0.0622 0.957 0.000 0.980 0.000 0.000 0.008 0.012
#> GSM372337 3 0.1700 0.895 0.000 0.000 0.916 0.000 0.080 0.004
#> GSM372339 3 0.0000 0.940 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372341 3 0.0000 0.940 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372343 3 0.0000 0.940 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372345 3 0.1812 0.893 0.000 0.000 0.912 0.000 0.080 0.008
#> GSM372347 5 0.4930 0.269 0.000 0.044 0.352 0.000 0.588 0.016
#> GSM372349 3 0.4574 0.662 0.000 0.000 0.720 0.012 0.168 0.100
#> GSM372351 3 0.1644 0.896 0.000 0.004 0.920 0.000 0.000 0.076
#> GSM372353 2 0.1036 0.949 0.000 0.964 0.004 0.000 0.008 0.024
#> GSM372355 2 0.0260 0.961 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM372357 2 0.1701 0.919 0.000 0.920 0.000 0.000 0.008 0.072
#> GSM372359 2 0.0146 0.960 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM372361 4 0.5007 0.573 0.000 0.272 0.000 0.636 0.012 0.080
#> GSM372363 2 0.3849 0.795 0.000 0.792 0.000 0.116 0.012 0.080
#> GSM372308 1 0.4144 0.734 0.728 0.000 0.000 0.000 0.200 0.072
#> GSM372310 1 0.4075 0.751 0.740 0.000 0.000 0.000 0.184 0.076
#> GSM372312 5 0.5520 0.530 0.332 0.000 0.000 0.012 0.548 0.108
#> GSM372314 5 0.3290 0.621 0.252 0.000 0.000 0.000 0.744 0.004
#> GSM372316 1 0.0458 0.872 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM372318 1 0.0000 0.874 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372320 1 0.0000 0.874 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372322 1 0.0000 0.874 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372324 5 0.3727 0.549 0.388 0.000 0.000 0.000 0.612 0.000
#> GSM372325 5 0.3314 0.681 0.256 0.000 0.000 0.000 0.740 0.004
#> GSM372327 1 0.0000 0.874 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372329 1 0.0000 0.874 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372331 5 0.3337 0.622 0.260 0.000 0.000 0.000 0.736 0.004
#> GSM372333 5 0.3852 0.561 0.052 0.000 0.180 0.000 0.764 0.004
#> GSM372334 1 0.0000 0.874 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372336 1 0.1082 0.867 0.956 0.000 0.000 0.000 0.040 0.004
#> GSM372338 1 0.0000 0.874 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372340 1 0.0000 0.874 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372342 1 0.0000 0.874 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372344 1 0.0000 0.874 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372346 1 0.0146 0.873 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM372348 1 0.1010 0.865 0.960 0.000 0.000 0.000 0.036 0.004
#> GSM372350 1 0.4526 0.484 0.728 0.000 0.000 0.012 0.152 0.108
#> GSM372352 5 0.6162 0.424 0.032 0.004 0.220 0.012 0.592 0.140
#> GSM372354 1 0.3627 0.802 0.792 0.000 0.000 0.000 0.128 0.080
#> GSM372356 1 0.2457 0.850 0.880 0.000 0.000 0.000 0.084 0.036
#> GSM372358 1 0.2436 0.850 0.880 0.000 0.000 0.000 0.088 0.032
#> GSM372360 1 0.3784 0.795 0.776 0.000 0.000 0.000 0.144 0.080
#> GSM372362 1 0.3707 0.799 0.784 0.000 0.000 0.000 0.136 0.080
#> GSM372364 1 0.3796 0.795 0.776 0.000 0.000 0.000 0.140 0.084
#> GSM372365 1 0.3834 0.792 0.772 0.000 0.000 0.000 0.144 0.084
#> GSM372366 1 0.2794 0.841 0.860 0.000 0.000 0.000 0.080 0.060
#> GSM372367 1 0.4550 0.686 0.676 0.000 0.000 0.000 0.240 0.084
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) specimen(p) individual(p) k
#> CV:skmeans 82 2.14e-04 1.11e-17 1.000 2
#> CV:skmeans 80 1.78e-05 2.20e-17 0.962 3
#> CV:skmeans 82 3.61e-14 2.63e-26 0.704 4
#> CV:skmeans 59 3.59e-02 5.23e-13 0.987 5
#> CV:skmeans 78 1.07e-11 1.12e-23 0.604 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 51941 rows and 82 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 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 0.949 0.960 0.982 0.4875 0.513 0.513
#> 3 3 0.940 0.946 0.974 0.3785 0.786 0.595
#> 4 4 0.767 0.719 0.823 0.1053 0.914 0.747
#> 5 5 0.763 0.801 0.872 0.0755 0.895 0.630
#> 6 6 0.857 0.802 0.908 0.0365 0.943 0.727
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
#> GSM372286 2 0.0000 0.980 0.000 1.000
#> GSM372287 2 0.0000 0.980 0.000 1.000
#> GSM372288 2 0.0000 0.980 0.000 1.000
#> GSM372289 2 0.0000 0.980 0.000 1.000
#> GSM372290 2 0.0000 0.980 0.000 1.000
#> GSM372291 1 0.8955 0.537 0.688 0.312
#> GSM372292 2 0.0000 0.980 0.000 1.000
#> GSM372293 2 0.0000 0.980 0.000 1.000
#> GSM372294 2 0.7299 0.755 0.204 0.796
#> GSM372295 2 0.0000 0.980 0.000 1.000
#> GSM372296 2 0.0000 0.980 0.000 1.000
#> GSM372297 2 0.0000 0.980 0.000 1.000
#> GSM372298 2 0.0000 0.980 0.000 1.000
#> GSM372299 2 0.0000 0.980 0.000 1.000
#> GSM372300 2 0.0376 0.978 0.004 0.996
#> GSM372301 2 0.0000 0.980 0.000 1.000
#> GSM372302 2 0.0000 0.980 0.000 1.000
#> GSM372303 2 0.0376 0.978 0.004 0.996
#> GSM372304 2 0.0000 0.980 0.000 1.000
#> GSM372305 2 0.0000 0.980 0.000 1.000
#> GSM372306 2 0.0000 0.980 0.000 1.000
#> GSM372307 2 0.0000 0.980 0.000 1.000
#> GSM372309 2 0.2948 0.934 0.052 0.948
#> GSM372311 2 0.0000 0.980 0.000 1.000
#> GSM372313 2 0.7299 0.755 0.204 0.796
#> GSM372315 2 0.0000 0.980 0.000 1.000
#> GSM372317 2 0.0000 0.980 0.000 1.000
#> GSM372319 2 0.0000 0.980 0.000 1.000
#> GSM372321 2 0.0000 0.980 0.000 1.000
#> GSM372323 2 0.0376 0.978 0.004 0.996
#> GSM372326 2 0.0376 0.978 0.004 0.996
#> GSM372328 2 0.0000 0.980 0.000 1.000
#> GSM372330 2 0.0000 0.980 0.000 1.000
#> GSM372332 2 0.0376 0.978 0.004 0.996
#> GSM372335 2 0.0000 0.980 0.000 1.000
#> GSM372337 2 0.0376 0.978 0.004 0.996
#> GSM372339 2 0.0376 0.978 0.004 0.996
#> GSM372341 2 0.0376 0.978 0.004 0.996
#> GSM372343 2 0.0376 0.978 0.004 0.996
#> GSM372345 2 0.0376 0.978 0.004 0.996
#> GSM372347 2 0.7376 0.750 0.208 0.792
#> GSM372349 2 0.0376 0.978 0.004 0.996
#> GSM372351 2 0.0000 0.980 0.000 1.000
#> GSM372353 2 0.0000 0.980 0.000 1.000
#> GSM372355 2 0.0000 0.980 0.000 1.000
#> GSM372357 2 0.0000 0.980 0.000 1.000
#> GSM372359 2 0.0000 0.980 0.000 1.000
#> GSM372361 2 0.0000 0.980 0.000 1.000
#> GSM372363 2 0.0000 0.980 0.000 1.000
#> GSM372308 1 0.0000 0.982 1.000 0.000
#> GSM372310 1 0.0000 0.982 1.000 0.000
#> GSM372312 1 0.0000 0.982 1.000 0.000
#> GSM372314 1 0.0000 0.982 1.000 0.000
#> GSM372316 1 0.0000 0.982 1.000 0.000
#> GSM372318 1 0.0000 0.982 1.000 0.000
#> GSM372320 1 0.0000 0.982 1.000 0.000
#> GSM372322 1 0.0000 0.982 1.000 0.000
#> GSM372324 1 0.0000 0.982 1.000 0.000
#> GSM372325 1 0.0000 0.982 1.000 0.000
#> GSM372327 1 0.0000 0.982 1.000 0.000
#> GSM372329 1 0.0000 0.982 1.000 0.000
#> GSM372331 1 0.0000 0.982 1.000 0.000
#> GSM372333 1 0.8081 0.662 0.752 0.248
#> GSM372334 1 0.0000 0.982 1.000 0.000
#> GSM372336 1 0.0000 0.982 1.000 0.000
#> GSM372338 1 0.0000 0.982 1.000 0.000
#> GSM372340 1 0.0000 0.982 1.000 0.000
#> GSM372342 1 0.0000 0.982 1.000 0.000
#> GSM372344 1 0.0000 0.982 1.000 0.000
#> GSM372346 1 0.0000 0.982 1.000 0.000
#> GSM372348 1 0.0000 0.982 1.000 0.000
#> GSM372350 1 0.0000 0.982 1.000 0.000
#> GSM372352 2 0.7376 0.750 0.208 0.792
#> GSM372354 1 0.0000 0.982 1.000 0.000
#> GSM372356 1 0.0000 0.982 1.000 0.000
#> GSM372358 1 0.0000 0.982 1.000 0.000
#> GSM372360 1 0.0000 0.982 1.000 0.000
#> GSM372362 1 0.0000 0.982 1.000 0.000
#> GSM372364 1 0.0000 0.982 1.000 0.000
#> GSM372365 1 0.0000 0.982 1.000 0.000
#> GSM372366 1 0.0000 0.982 1.000 0.000
#> GSM372367 1 0.0000 0.982 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM372286 2 0.0000 0.966 0.000 1.000 0.000
#> GSM372287 2 0.0000 0.966 0.000 1.000 0.000
#> GSM372288 2 0.0000 0.966 0.000 1.000 0.000
#> GSM372289 2 0.0000 0.966 0.000 1.000 0.000
#> GSM372290 2 0.0000 0.966 0.000 1.000 0.000
#> GSM372291 1 0.7072 0.680 0.724 0.116 0.160
#> GSM372292 3 0.3340 0.873 0.000 0.120 0.880
#> GSM372293 3 0.0237 0.962 0.000 0.004 0.996
#> GSM372294 2 0.0000 0.966 0.000 1.000 0.000
#> GSM372295 3 0.5222 0.826 0.040 0.144 0.816
#> GSM372296 2 0.0000 0.966 0.000 1.000 0.000
#> GSM372297 2 0.0000 0.966 0.000 1.000 0.000
#> GSM372298 2 0.0000 0.966 0.000 1.000 0.000
#> GSM372299 3 0.3752 0.849 0.000 0.144 0.856
#> GSM372300 3 0.1163 0.949 0.000 0.028 0.972
#> GSM372301 3 0.3340 0.873 0.000 0.120 0.880
#> GSM372302 2 0.0000 0.966 0.000 1.000 0.000
#> GSM372303 3 0.0237 0.962 0.000 0.004 0.996
#> GSM372304 2 0.0000 0.966 0.000 1.000 0.000
#> GSM372305 2 0.0000 0.966 0.000 1.000 0.000
#> GSM372306 2 0.6192 0.318 0.000 0.580 0.420
#> GSM372307 2 0.0000 0.966 0.000 1.000 0.000
#> GSM372309 2 0.1753 0.926 0.000 0.952 0.048
#> GSM372311 2 0.0000 0.966 0.000 1.000 0.000
#> GSM372313 2 0.0000 0.966 0.000 1.000 0.000
#> GSM372315 2 0.0000 0.966 0.000 1.000 0.000
#> GSM372317 2 0.4750 0.740 0.000 0.784 0.216
#> GSM372319 3 0.0000 0.963 0.000 0.000 1.000
#> GSM372321 3 0.0000 0.963 0.000 0.000 1.000
#> GSM372323 3 0.0000 0.963 0.000 0.000 1.000
#> GSM372326 3 0.0000 0.963 0.000 0.000 1.000
#> GSM372328 3 0.0000 0.963 0.000 0.000 1.000
#> GSM372330 2 0.0000 0.966 0.000 1.000 0.000
#> GSM372332 3 0.0000 0.963 0.000 0.000 1.000
#> GSM372335 3 0.0000 0.963 0.000 0.000 1.000
#> GSM372337 3 0.0000 0.963 0.000 0.000 1.000
#> GSM372339 3 0.0000 0.963 0.000 0.000 1.000
#> GSM372341 3 0.0000 0.963 0.000 0.000 1.000
#> GSM372343 3 0.0000 0.963 0.000 0.000 1.000
#> GSM372345 3 0.0000 0.963 0.000 0.000 1.000
#> GSM372347 3 0.0000 0.963 0.000 0.000 1.000
#> GSM372349 3 0.0000 0.963 0.000 0.000 1.000
#> GSM372351 3 0.0000 0.963 0.000 0.000 1.000
#> GSM372353 3 0.3752 0.834 0.000 0.144 0.856
#> GSM372355 2 0.0000 0.966 0.000 1.000 0.000
#> GSM372357 2 0.3340 0.853 0.000 0.880 0.120
#> GSM372359 2 0.0000 0.966 0.000 1.000 0.000
#> GSM372361 2 0.0000 0.966 0.000 1.000 0.000
#> GSM372363 2 0.0000 0.966 0.000 1.000 0.000
#> GSM372308 1 0.0000 0.986 1.000 0.000 0.000
#> GSM372310 1 0.0000 0.986 1.000 0.000 0.000
#> GSM372312 1 0.0000 0.986 1.000 0.000 0.000
#> GSM372314 1 0.2878 0.894 0.904 0.000 0.096
#> GSM372316 1 0.0000 0.986 1.000 0.000 0.000
#> GSM372318 1 0.0000 0.986 1.000 0.000 0.000
#> GSM372320 1 0.0000 0.986 1.000 0.000 0.000
#> GSM372322 1 0.0000 0.986 1.000 0.000 0.000
#> GSM372324 1 0.2537 0.911 0.920 0.000 0.080
#> GSM372325 3 0.1753 0.932 0.048 0.000 0.952
#> GSM372327 1 0.0000 0.986 1.000 0.000 0.000
#> GSM372329 1 0.0000 0.986 1.000 0.000 0.000
#> GSM372331 1 0.0000 0.986 1.000 0.000 0.000
#> GSM372333 3 0.1529 0.938 0.040 0.000 0.960
#> GSM372334 1 0.0000 0.986 1.000 0.000 0.000
#> GSM372336 1 0.0000 0.986 1.000 0.000 0.000
#> GSM372338 1 0.0000 0.986 1.000 0.000 0.000
#> GSM372340 1 0.0000 0.986 1.000 0.000 0.000
#> GSM372342 1 0.0000 0.986 1.000 0.000 0.000
#> GSM372344 1 0.0000 0.986 1.000 0.000 0.000
#> GSM372346 1 0.0000 0.986 1.000 0.000 0.000
#> GSM372348 1 0.0000 0.986 1.000 0.000 0.000
#> GSM372350 1 0.0000 0.986 1.000 0.000 0.000
#> GSM372352 3 0.1643 0.935 0.044 0.000 0.956
#> GSM372354 1 0.0000 0.986 1.000 0.000 0.000
#> GSM372356 1 0.0000 0.986 1.000 0.000 0.000
#> GSM372358 1 0.0000 0.986 1.000 0.000 0.000
#> GSM372360 1 0.0000 0.986 1.000 0.000 0.000
#> GSM372362 1 0.0000 0.986 1.000 0.000 0.000
#> GSM372364 1 0.0000 0.986 1.000 0.000 0.000
#> GSM372365 1 0.0000 0.986 1.000 0.000 0.000
#> GSM372366 1 0.0000 0.986 1.000 0.000 0.000
#> GSM372367 1 0.0000 0.986 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM372286 2 0.0000 0.869 0.000 1.000 0.000 0.000
#> GSM372287 2 0.4713 0.406 0.000 0.640 0.000 0.360
#> GSM372288 2 0.3444 0.719 0.000 0.816 0.000 0.184
#> GSM372289 2 0.0000 0.869 0.000 1.000 0.000 0.000
#> GSM372290 4 0.4877 0.225 0.000 0.408 0.000 0.592
#> GSM372291 4 0.5268 0.320 0.452 0.008 0.000 0.540
#> GSM372292 4 0.5150 0.544 0.000 0.008 0.396 0.596
#> GSM372293 4 0.4967 0.501 0.000 0.000 0.452 0.548
#> GSM372294 2 0.4103 0.619 0.000 0.744 0.000 0.256
#> GSM372295 4 0.6970 0.506 0.240 0.004 0.160 0.596
#> GSM372296 2 0.2149 0.818 0.000 0.912 0.000 0.088
#> GSM372297 4 0.4866 0.233 0.000 0.404 0.000 0.596
#> GSM372298 4 0.4955 0.170 0.000 0.444 0.000 0.556
#> GSM372299 4 0.4925 0.525 0.000 0.000 0.428 0.572
#> GSM372300 4 0.4967 0.501 0.000 0.000 0.452 0.548
#> GSM372301 4 0.5250 0.517 0.000 0.008 0.440 0.552
#> GSM372302 2 0.5000 -0.026 0.000 0.504 0.000 0.496
#> GSM372303 4 0.4967 0.501 0.000 0.000 0.452 0.548
#> GSM372304 4 0.4877 0.225 0.000 0.408 0.000 0.592
#> GSM372305 2 0.0000 0.869 0.000 1.000 0.000 0.000
#> GSM372306 2 0.4907 0.299 0.000 0.580 0.420 0.000
#> GSM372307 2 0.0188 0.868 0.000 0.996 0.000 0.004
#> GSM372309 2 0.0672 0.861 0.008 0.984 0.000 0.008
#> GSM372311 2 0.0000 0.869 0.000 1.000 0.000 0.000
#> GSM372313 2 0.0000 0.869 0.000 1.000 0.000 0.000
#> GSM372315 2 0.0000 0.869 0.000 1.000 0.000 0.000
#> GSM372317 2 0.3764 0.638 0.000 0.784 0.216 0.000
#> GSM372319 3 0.0000 0.894 0.000 0.000 1.000 0.000
#> GSM372321 3 0.0000 0.894 0.000 0.000 1.000 0.000
#> GSM372323 3 0.0000 0.894 0.000 0.000 1.000 0.000
#> GSM372326 3 0.0000 0.894 0.000 0.000 1.000 0.000
#> GSM372328 3 0.0000 0.894 0.000 0.000 1.000 0.000
#> GSM372330 2 0.0000 0.869 0.000 1.000 0.000 0.000
#> GSM372332 3 0.0000 0.894 0.000 0.000 1.000 0.000
#> GSM372335 3 0.0000 0.894 0.000 0.000 1.000 0.000
#> GSM372337 3 0.0000 0.894 0.000 0.000 1.000 0.000
#> GSM372339 3 0.0000 0.894 0.000 0.000 1.000 0.000
#> GSM372341 3 0.0000 0.894 0.000 0.000 1.000 0.000
#> GSM372343 3 0.0000 0.894 0.000 0.000 1.000 0.000
#> GSM372345 3 0.0000 0.894 0.000 0.000 1.000 0.000
#> GSM372347 3 0.0000 0.894 0.000 0.000 1.000 0.000
#> GSM372349 3 0.0000 0.894 0.000 0.000 1.000 0.000
#> GSM372351 3 0.0000 0.894 0.000 0.000 1.000 0.000
#> GSM372353 3 0.4103 0.499 0.000 0.256 0.744 0.000
#> GSM372355 2 0.0000 0.869 0.000 1.000 0.000 0.000
#> GSM372357 2 0.0336 0.866 0.000 0.992 0.000 0.008
#> GSM372359 2 0.0000 0.869 0.000 1.000 0.000 0.000
#> GSM372361 2 0.1557 0.844 0.000 0.944 0.000 0.056
#> GSM372363 2 0.0336 0.866 0.000 0.992 0.000 0.008
#> GSM372308 1 0.0000 0.768 1.000 0.000 0.000 0.000
#> GSM372310 1 0.0000 0.768 1.000 0.000 0.000 0.000
#> GSM372312 1 0.0000 0.768 1.000 0.000 0.000 0.000
#> GSM372314 1 0.2281 0.678 0.904 0.000 0.096 0.000
#> GSM372316 1 0.4843 0.790 0.604 0.000 0.000 0.396
#> GSM372318 1 0.4843 0.790 0.604 0.000 0.000 0.396
#> GSM372320 1 0.4843 0.790 0.604 0.000 0.000 0.396
#> GSM372322 1 0.4843 0.790 0.604 0.000 0.000 0.396
#> GSM372324 1 0.2011 0.697 0.920 0.000 0.080 0.000
#> GSM372325 3 0.4843 0.402 0.396 0.000 0.604 0.000
#> GSM372327 1 0.4843 0.790 0.604 0.000 0.000 0.396
#> GSM372329 1 0.4843 0.790 0.604 0.000 0.000 0.396
#> GSM372331 1 0.0000 0.768 1.000 0.000 0.000 0.000
#> GSM372333 3 0.3400 0.679 0.180 0.000 0.820 0.000
#> GSM372334 1 0.4843 0.790 0.604 0.000 0.000 0.396
#> GSM372336 1 0.0000 0.768 1.000 0.000 0.000 0.000
#> GSM372338 1 0.4843 0.790 0.604 0.000 0.000 0.396
#> GSM372340 1 0.4843 0.790 0.604 0.000 0.000 0.396
#> GSM372342 1 0.4843 0.790 0.604 0.000 0.000 0.396
#> GSM372344 1 0.4843 0.790 0.604 0.000 0.000 0.396
#> GSM372346 1 0.4843 0.790 0.604 0.000 0.000 0.396
#> GSM372348 1 0.0188 0.769 0.996 0.000 0.000 0.004
#> GSM372350 1 0.1022 0.772 0.968 0.000 0.000 0.032
#> GSM372352 3 0.4843 0.402 0.396 0.000 0.604 0.000
#> GSM372354 1 0.4830 0.791 0.608 0.000 0.000 0.392
#> GSM372356 1 0.0000 0.768 1.000 0.000 0.000 0.000
#> GSM372358 1 0.4746 0.791 0.632 0.000 0.000 0.368
#> GSM372360 1 0.0000 0.768 1.000 0.000 0.000 0.000
#> GSM372362 1 0.2868 0.781 0.864 0.000 0.000 0.136
#> GSM372364 1 0.0000 0.768 1.000 0.000 0.000 0.000
#> GSM372365 1 0.0000 0.768 1.000 0.000 0.000 0.000
#> GSM372366 1 0.4843 0.790 0.604 0.000 0.000 0.396
#> GSM372367 1 0.0000 0.768 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM372286 2 0.0000 0.846 0.000 1.000 0.000 0.000 0.000
#> GSM372287 2 0.6097 0.209 0.000 0.456 0.000 0.420 0.124
#> GSM372288 2 0.5720 0.531 0.000 0.600 0.000 0.276 0.124
#> GSM372289 2 0.0162 0.844 0.000 0.996 0.000 0.000 0.004
#> GSM372290 4 0.2329 0.833 0.000 0.000 0.000 0.876 0.124
#> GSM372291 5 0.3913 0.473 0.000 0.000 0.000 0.324 0.676
#> GSM372292 4 0.0000 0.857 0.000 0.000 0.000 1.000 0.000
#> GSM372293 4 0.2516 0.852 0.000 0.000 0.140 0.860 0.000
#> GSM372294 2 0.5953 0.428 0.000 0.540 0.000 0.336 0.124
#> GSM372295 4 0.2488 0.832 0.000 0.000 0.004 0.872 0.124
#> GSM372296 2 0.5941 0.406 0.000 0.544 0.000 0.332 0.124
#> GSM372297 4 0.0880 0.856 0.000 0.000 0.000 0.968 0.032
#> GSM372298 4 0.2516 0.776 0.000 0.140 0.000 0.860 0.000
#> GSM372299 4 0.2424 0.857 0.000 0.000 0.132 0.868 0.000
#> GSM372300 4 0.2516 0.852 0.000 0.000 0.140 0.860 0.000
#> GSM372301 4 0.2424 0.857 0.000 0.000 0.132 0.868 0.000
#> GSM372302 4 0.3262 0.805 0.000 0.036 0.000 0.840 0.124
#> GSM372303 4 0.2516 0.852 0.000 0.000 0.140 0.860 0.000
#> GSM372304 4 0.2329 0.833 0.000 0.000 0.000 0.876 0.124
#> GSM372305 2 0.0000 0.846 0.000 1.000 0.000 0.000 0.000
#> GSM372306 2 0.4227 0.298 0.000 0.580 0.420 0.000 0.000
#> GSM372307 2 0.2249 0.800 0.000 0.896 0.000 0.008 0.096
#> GSM372309 2 0.0290 0.841 0.000 0.992 0.000 0.000 0.008
#> GSM372311 2 0.0000 0.846 0.000 1.000 0.000 0.000 0.000
#> GSM372313 2 0.0000 0.846 0.000 1.000 0.000 0.000 0.000
#> GSM372315 2 0.0000 0.846 0.000 1.000 0.000 0.000 0.000
#> GSM372317 2 0.3242 0.672 0.000 0.784 0.216 0.000 0.000
#> GSM372319 3 0.0000 0.959 0.000 0.000 1.000 0.000 0.000
#> GSM372321 3 0.0000 0.959 0.000 0.000 1.000 0.000 0.000
#> GSM372323 3 0.0000 0.959 0.000 0.000 1.000 0.000 0.000
#> GSM372326 3 0.0000 0.959 0.000 0.000 1.000 0.000 0.000
#> GSM372328 3 0.0000 0.959 0.000 0.000 1.000 0.000 0.000
#> GSM372330 2 0.0000 0.846 0.000 1.000 0.000 0.000 0.000
#> GSM372332 3 0.0000 0.959 0.000 0.000 1.000 0.000 0.000
#> GSM372335 3 0.0000 0.959 0.000 0.000 1.000 0.000 0.000
#> GSM372337 3 0.0000 0.959 0.000 0.000 1.000 0.000 0.000
#> GSM372339 3 0.0000 0.959 0.000 0.000 1.000 0.000 0.000
#> GSM372341 3 0.0000 0.959 0.000 0.000 1.000 0.000 0.000
#> GSM372343 3 0.0000 0.959 0.000 0.000 1.000 0.000 0.000
#> GSM372345 3 0.0000 0.959 0.000 0.000 1.000 0.000 0.000
#> GSM372347 3 0.0290 0.953 0.000 0.000 0.992 0.000 0.008
#> GSM372349 3 0.0000 0.959 0.000 0.000 1.000 0.000 0.000
#> GSM372351 3 0.0000 0.959 0.000 0.000 1.000 0.000 0.000
#> GSM372353 3 0.3586 0.611 0.000 0.264 0.736 0.000 0.000
#> GSM372355 2 0.0000 0.846 0.000 1.000 0.000 0.000 0.000
#> GSM372357 2 0.0000 0.846 0.000 1.000 0.000 0.000 0.000
#> GSM372359 2 0.0000 0.846 0.000 1.000 0.000 0.000 0.000
#> GSM372361 2 0.4720 0.684 0.000 0.736 0.000 0.140 0.124
#> GSM372363 2 0.0000 0.846 0.000 1.000 0.000 0.000 0.000
#> GSM372308 5 0.2424 0.771 0.132 0.000 0.000 0.000 0.868
#> GSM372310 5 0.2605 0.774 0.148 0.000 0.000 0.000 0.852
#> GSM372312 5 0.3730 0.738 0.288 0.000 0.000 0.000 0.712
#> GSM372314 5 0.2669 0.763 0.104 0.000 0.020 0.000 0.876
#> GSM372316 1 0.0000 0.948 1.000 0.000 0.000 0.000 0.000
#> GSM372318 1 0.0000 0.948 1.000 0.000 0.000 0.000 0.000
#> GSM372320 1 0.0000 0.948 1.000 0.000 0.000 0.000 0.000
#> GSM372322 1 0.0000 0.948 1.000 0.000 0.000 0.000 0.000
#> GSM372324 5 0.4563 0.730 0.244 0.000 0.048 0.000 0.708
#> GSM372325 5 0.3816 0.509 0.000 0.000 0.304 0.000 0.696
#> GSM372327 1 0.0000 0.948 1.000 0.000 0.000 0.000 0.000
#> GSM372329 1 0.0000 0.948 1.000 0.000 0.000 0.000 0.000
#> GSM372331 5 0.3612 0.751 0.268 0.000 0.000 0.000 0.732
#> GSM372333 3 0.3707 0.585 0.000 0.000 0.716 0.000 0.284
#> GSM372334 1 0.0000 0.948 1.000 0.000 0.000 0.000 0.000
#> GSM372336 5 0.4114 0.692 0.376 0.000 0.000 0.000 0.624
#> GSM372338 1 0.0000 0.948 1.000 0.000 0.000 0.000 0.000
#> GSM372340 1 0.0000 0.948 1.000 0.000 0.000 0.000 0.000
#> GSM372342 1 0.0000 0.948 1.000 0.000 0.000 0.000 0.000
#> GSM372344 1 0.0000 0.948 1.000 0.000 0.000 0.000 0.000
#> GSM372346 1 0.0000 0.948 1.000 0.000 0.000 0.000 0.000
#> GSM372348 5 0.3913 0.714 0.324 0.000 0.000 0.000 0.676
#> GSM372350 5 0.4307 0.493 0.496 0.000 0.000 0.000 0.504
#> GSM372352 5 0.3816 0.509 0.000 0.000 0.304 0.000 0.696
#> GSM372354 1 0.3177 0.725 0.792 0.000 0.000 0.000 0.208
#> GSM372356 5 0.3661 0.752 0.276 0.000 0.000 0.000 0.724
#> GSM372358 1 0.2852 0.774 0.828 0.000 0.000 0.000 0.172
#> GSM372360 5 0.3336 0.759 0.228 0.000 0.000 0.000 0.772
#> GSM372362 5 0.4182 0.499 0.400 0.000 0.000 0.000 0.600
#> GSM372364 5 0.3336 0.759 0.228 0.000 0.000 0.000 0.772
#> GSM372365 5 0.3336 0.759 0.228 0.000 0.000 0.000 0.772
#> GSM372366 1 0.2929 0.758 0.820 0.000 0.000 0.000 0.180
#> GSM372367 5 0.3143 0.769 0.204 0.000 0.000 0.000 0.796
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM372286 2 0.0000 0.9117 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM372287 4 0.1563 0.9206 0.000 0.012 0.000 0.932 0.000 0.056
#> GSM372288 4 0.1563 0.9205 0.000 0.012 0.000 0.932 0.000 0.056
#> GSM372289 2 0.0146 0.9098 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM372290 4 0.1387 0.9212 0.000 0.000 0.000 0.932 0.000 0.068
#> GSM372291 6 0.4407 -0.0779 0.000 0.000 0.000 0.024 0.484 0.492
#> GSM372292 6 0.0000 0.8941 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM372293 6 0.0000 0.8941 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM372294 4 0.1387 0.9212 0.000 0.000 0.000 0.932 0.000 0.068
#> GSM372295 4 0.0000 0.8928 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM372296 4 0.2260 0.8143 0.000 0.140 0.000 0.860 0.000 0.000
#> GSM372297 4 0.3684 0.4935 0.000 0.000 0.000 0.628 0.000 0.372
#> GSM372298 6 0.0000 0.8941 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM372299 6 0.1556 0.8324 0.000 0.000 0.000 0.080 0.000 0.920
#> GSM372300 6 0.0000 0.8941 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM372301 6 0.0000 0.8941 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM372302 4 0.1531 0.9212 0.000 0.004 0.000 0.928 0.000 0.068
#> GSM372303 6 0.0000 0.8941 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM372304 4 0.1387 0.9212 0.000 0.000 0.000 0.932 0.000 0.068
#> GSM372305 2 0.0000 0.9117 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM372306 2 0.3797 0.3254 0.000 0.580 0.420 0.000 0.000 0.000
#> GSM372307 2 0.3592 0.5160 0.000 0.656 0.000 0.344 0.000 0.000
#> GSM372309 2 0.1643 0.8738 0.000 0.924 0.000 0.068 0.008 0.000
#> GSM372311 2 0.0000 0.9117 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM372313 2 0.0000 0.9117 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM372315 2 0.0000 0.9117 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM372317 2 0.2912 0.7114 0.000 0.784 0.216 0.000 0.000 0.000
#> GSM372319 3 0.0000 0.9512 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372321 3 0.0000 0.9512 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372323 3 0.0000 0.9512 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372326 3 0.0146 0.9483 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM372328 3 0.0000 0.9512 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372330 2 0.0000 0.9117 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM372332 3 0.0000 0.9512 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372335 3 0.0000 0.9512 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372337 3 0.0000 0.9512 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372339 3 0.0000 0.9512 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372341 3 0.0000 0.9512 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372343 3 0.0000 0.9512 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372345 3 0.0000 0.9512 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372347 3 0.0937 0.9184 0.000 0.000 0.960 0.000 0.040 0.000
#> GSM372349 3 0.0000 0.9512 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372351 3 0.0000 0.9512 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372353 3 0.3221 0.6155 0.000 0.264 0.736 0.000 0.000 0.000
#> GSM372355 2 0.0000 0.9117 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM372357 2 0.0000 0.9117 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM372359 2 0.0000 0.9117 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM372361 4 0.0000 0.8928 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM372363 2 0.1387 0.8775 0.000 0.932 0.000 0.068 0.000 0.000
#> GSM372308 5 0.0260 0.7412 0.008 0.000 0.000 0.000 0.992 0.000
#> GSM372310 5 0.0713 0.7499 0.028 0.000 0.000 0.000 0.972 0.000
#> GSM372312 5 0.2527 0.7374 0.168 0.000 0.000 0.000 0.832 0.000
#> GSM372314 5 0.0000 0.7363 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM372316 1 0.0000 0.8997 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372318 1 0.0000 0.8997 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372320 1 0.0000 0.8997 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372322 1 0.0000 0.8997 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372324 5 0.2668 0.7363 0.168 0.000 0.004 0.000 0.828 0.000
#> GSM372325 5 0.2941 0.6033 0.000 0.000 0.220 0.000 0.780 0.000
#> GSM372327 1 0.0000 0.8997 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372329 1 0.0000 0.8997 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372331 5 0.2300 0.7486 0.144 0.000 0.000 0.000 0.856 0.000
#> GSM372333 3 0.3756 0.3611 0.000 0.000 0.600 0.000 0.400 0.000
#> GSM372334 1 0.0000 0.8997 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372336 5 0.3620 0.6304 0.352 0.000 0.000 0.000 0.648 0.000
#> GSM372338 1 0.0000 0.8997 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372340 1 0.0000 0.8997 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372342 1 0.0000 0.8997 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372344 1 0.0000 0.8997 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372346 1 0.0000 0.8997 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372348 5 0.2823 0.7160 0.204 0.000 0.000 0.000 0.796 0.000
#> GSM372350 1 0.3868 -0.3902 0.508 0.000 0.000 0.000 0.492 0.000
#> GSM372352 5 0.2941 0.6033 0.000 0.000 0.220 0.000 0.780 0.000
#> GSM372354 1 0.3126 0.6585 0.752 0.000 0.000 0.000 0.248 0.000
#> GSM372356 5 0.3266 0.6913 0.272 0.000 0.000 0.000 0.728 0.000
#> GSM372358 1 0.2883 0.7027 0.788 0.000 0.000 0.000 0.212 0.000
#> GSM372360 5 0.2941 0.7106 0.220 0.000 0.000 0.000 0.780 0.000
#> GSM372362 5 0.3737 0.3933 0.392 0.000 0.000 0.000 0.608 0.000
#> GSM372364 5 0.2941 0.7106 0.220 0.000 0.000 0.000 0.780 0.000
#> GSM372365 5 0.2941 0.7106 0.220 0.000 0.000 0.000 0.780 0.000
#> GSM372366 1 0.2941 0.6912 0.780 0.000 0.000 0.000 0.220 0.000
#> GSM372367 5 0.2730 0.7276 0.192 0.000 0.000 0.000 0.808 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) specimen(p) individual(p) k
#> CV:pam 82 3.35e-04 8.50e-17 0.999 2
#> CV:pam 81 3.32e-04 3.66e-14 0.900 3
#> CV:pam 71 1.33e-09 2.24e-20 0.511 4
#> CV:pam 75 1.17e-11 7.57e-23 0.708 5
#> CV:pam 76 3.08e-11 5.95e-23 0.425 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 51941 rows and 82 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 5.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.986 0.994 0.4825 0.518 0.518
#> 3 3 1.000 0.961 0.985 0.3595 0.808 0.635
#> 4 4 0.999 0.970 0.982 0.1178 0.922 0.773
#> 5 5 0.948 0.913 0.958 0.0857 0.924 0.721
#> 6 6 0.855 0.834 0.876 0.0315 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] 5
#> attr(,"optional")
#> [1] 2 3 4
There is also optional best \(k\) = 2 3 4 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM372286 2 0.000 0.994 0.000 1.000
#> GSM372287 2 0.000 0.994 0.000 1.000
#> GSM372288 2 0.000 0.994 0.000 1.000
#> GSM372289 2 0.000 0.994 0.000 1.000
#> GSM372290 2 0.000 0.994 0.000 1.000
#> GSM372291 2 0.000 0.994 0.000 1.000
#> GSM372292 2 0.000 0.994 0.000 1.000
#> GSM372293 2 0.000 0.994 0.000 1.000
#> GSM372294 2 0.000 0.994 0.000 1.000
#> GSM372295 2 0.000 0.994 0.000 1.000
#> GSM372296 2 0.000 0.994 0.000 1.000
#> GSM372297 2 0.000 0.994 0.000 1.000
#> GSM372298 2 0.000 0.994 0.000 1.000
#> GSM372299 2 0.000 0.994 0.000 1.000
#> GSM372300 2 0.000 0.994 0.000 1.000
#> GSM372301 2 0.000 0.994 0.000 1.000
#> GSM372302 2 0.000 0.994 0.000 1.000
#> GSM372303 2 0.000 0.994 0.000 1.000
#> GSM372304 2 0.000 0.994 0.000 1.000
#> GSM372305 2 0.000 0.994 0.000 1.000
#> GSM372306 2 0.000 0.994 0.000 1.000
#> GSM372307 2 0.000 0.994 0.000 1.000
#> GSM372309 2 0.000 0.994 0.000 1.000
#> GSM372311 2 0.000 0.994 0.000 1.000
#> GSM372313 2 0.000 0.994 0.000 1.000
#> GSM372315 2 0.000 0.994 0.000 1.000
#> GSM372317 2 0.000 0.994 0.000 1.000
#> GSM372319 2 0.000 0.994 0.000 1.000
#> GSM372321 2 0.000 0.994 0.000 1.000
#> GSM372323 2 0.000 0.994 0.000 1.000
#> GSM372326 2 0.000 0.994 0.000 1.000
#> GSM372328 2 0.000 0.994 0.000 1.000
#> GSM372330 2 0.000 0.994 0.000 1.000
#> GSM372332 2 0.000 0.994 0.000 1.000
#> GSM372335 2 0.000 0.994 0.000 1.000
#> GSM372337 2 0.000 0.994 0.000 1.000
#> GSM372339 2 0.000 0.994 0.000 1.000
#> GSM372341 2 0.000 0.994 0.000 1.000
#> GSM372343 2 0.000 0.994 0.000 1.000
#> GSM372345 2 0.000 0.994 0.000 1.000
#> GSM372347 2 0.000 0.994 0.000 1.000
#> GSM372349 2 0.000 0.994 0.000 1.000
#> GSM372351 2 0.000 0.994 0.000 1.000
#> GSM372353 2 0.000 0.994 0.000 1.000
#> GSM372355 2 0.000 0.994 0.000 1.000
#> GSM372357 2 0.000 0.994 0.000 1.000
#> GSM372359 2 0.000 0.994 0.000 1.000
#> GSM372361 2 0.000 0.994 0.000 1.000
#> GSM372363 2 0.000 0.994 0.000 1.000
#> GSM372308 1 0.000 0.993 1.000 0.000
#> GSM372310 1 0.000 0.993 1.000 0.000
#> GSM372312 1 0.000 0.993 1.000 0.000
#> GSM372314 1 0.000 0.993 1.000 0.000
#> GSM372316 1 0.000 0.993 1.000 0.000
#> GSM372318 1 0.000 0.993 1.000 0.000
#> GSM372320 1 0.000 0.993 1.000 0.000
#> GSM372322 1 0.000 0.993 1.000 0.000
#> GSM372324 1 0.000 0.993 1.000 0.000
#> GSM372325 1 0.000 0.993 1.000 0.000
#> GSM372327 1 0.000 0.993 1.000 0.000
#> GSM372329 1 0.000 0.993 1.000 0.000
#> GSM372331 1 0.000 0.993 1.000 0.000
#> GSM372333 1 0.722 0.747 0.800 0.200
#> GSM372334 1 0.000 0.993 1.000 0.000
#> GSM372336 1 0.000 0.993 1.000 0.000
#> GSM372338 1 0.000 0.993 1.000 0.000
#> GSM372340 1 0.000 0.993 1.000 0.000
#> GSM372342 1 0.000 0.993 1.000 0.000
#> GSM372344 1 0.000 0.993 1.000 0.000
#> GSM372346 1 0.000 0.993 1.000 0.000
#> GSM372348 1 0.000 0.993 1.000 0.000
#> GSM372350 1 0.000 0.993 1.000 0.000
#> GSM372352 2 0.844 0.621 0.272 0.728
#> GSM372354 1 0.000 0.993 1.000 0.000
#> GSM372356 1 0.000 0.993 1.000 0.000
#> GSM372358 1 0.000 0.993 1.000 0.000
#> GSM372360 1 0.000 0.993 1.000 0.000
#> GSM372362 1 0.000 0.993 1.000 0.000
#> GSM372364 1 0.000 0.993 1.000 0.000
#> GSM372365 1 0.000 0.993 1.000 0.000
#> GSM372366 1 0.000 0.993 1.000 0.000
#> GSM372367 1 0.000 0.993 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM372286 3 0.0592 0.950 0.000 0.012 0.988
#> GSM372287 2 0.0000 0.995 0.000 1.000 0.000
#> GSM372288 2 0.0000 0.995 0.000 1.000 0.000
#> GSM372289 2 0.0892 0.978 0.000 0.980 0.020
#> GSM372290 2 0.0000 0.995 0.000 1.000 0.000
#> GSM372291 2 0.0000 0.995 0.000 1.000 0.000
#> GSM372292 2 0.0000 0.995 0.000 1.000 0.000
#> GSM372293 2 0.0000 0.995 0.000 1.000 0.000
#> GSM372294 2 0.0000 0.995 0.000 1.000 0.000
#> GSM372295 2 0.0000 0.995 0.000 1.000 0.000
#> GSM372296 2 0.2165 0.932 0.000 0.936 0.064
#> GSM372297 2 0.0000 0.995 0.000 1.000 0.000
#> GSM372298 2 0.0000 0.995 0.000 1.000 0.000
#> GSM372299 2 0.0000 0.995 0.000 1.000 0.000
#> GSM372300 2 0.0000 0.995 0.000 1.000 0.000
#> GSM372301 2 0.0000 0.995 0.000 1.000 0.000
#> GSM372302 2 0.0000 0.995 0.000 1.000 0.000
#> GSM372303 2 0.0000 0.995 0.000 1.000 0.000
#> GSM372304 2 0.0000 0.995 0.000 1.000 0.000
#> GSM372305 3 0.0000 0.960 0.000 0.000 1.000
#> GSM372306 3 0.0000 0.960 0.000 0.000 1.000
#> GSM372307 3 0.1643 0.920 0.000 0.044 0.956
#> GSM372309 3 0.0000 0.960 0.000 0.000 1.000
#> GSM372311 3 0.0000 0.960 0.000 0.000 1.000
#> GSM372313 3 0.0000 0.960 0.000 0.000 1.000
#> GSM372315 3 0.0000 0.960 0.000 0.000 1.000
#> GSM372317 3 0.0000 0.960 0.000 0.000 1.000
#> GSM372319 3 0.0000 0.960 0.000 0.000 1.000
#> GSM372321 3 0.0000 0.960 0.000 0.000 1.000
#> GSM372323 3 0.0000 0.960 0.000 0.000 1.000
#> GSM372326 3 0.0000 0.960 0.000 0.000 1.000
#> GSM372328 3 0.0000 0.960 0.000 0.000 1.000
#> GSM372330 3 0.0000 0.960 0.000 0.000 1.000
#> GSM372332 3 0.0000 0.960 0.000 0.000 1.000
#> GSM372335 3 0.0000 0.960 0.000 0.000 1.000
#> GSM372337 3 0.0000 0.960 0.000 0.000 1.000
#> GSM372339 3 0.0000 0.960 0.000 0.000 1.000
#> GSM372341 3 0.0000 0.960 0.000 0.000 1.000
#> GSM372343 3 0.0000 0.960 0.000 0.000 1.000
#> GSM372345 3 0.0000 0.960 0.000 0.000 1.000
#> GSM372347 3 0.0000 0.960 0.000 0.000 1.000
#> GSM372349 3 0.0000 0.960 0.000 0.000 1.000
#> GSM372351 3 0.0000 0.960 0.000 0.000 1.000
#> GSM372353 3 0.0000 0.960 0.000 0.000 1.000
#> GSM372355 3 0.0000 0.960 0.000 0.000 1.000
#> GSM372357 3 0.0000 0.960 0.000 0.000 1.000
#> GSM372359 3 0.0000 0.960 0.000 0.000 1.000
#> GSM372361 3 0.4842 0.698 0.000 0.224 0.776
#> GSM372363 3 0.0000 0.960 0.000 0.000 1.000
#> GSM372308 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372310 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372312 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372314 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372316 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372318 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372320 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372322 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372324 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372325 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372327 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372329 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372331 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372333 3 0.6252 0.230 0.444 0.000 0.556
#> GSM372334 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372336 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372338 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372340 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372342 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372344 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372346 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372348 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372350 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372352 3 0.6598 0.266 0.428 0.008 0.564
#> GSM372354 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372356 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372358 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372360 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372362 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372364 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372365 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372366 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372367 1 0.0000 1.000 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM372286 2 0.0000 0.949 0.000 1.000 0.000 0.000
#> GSM372287 4 0.0707 0.990 0.000 0.020 0.000 0.980
#> GSM372288 4 0.0592 0.989 0.000 0.016 0.000 0.984
#> GSM372289 4 0.0707 0.990 0.000 0.020 0.000 0.980
#> GSM372290 4 0.0707 0.990 0.000 0.020 0.000 0.980
#> GSM372291 4 0.0000 0.986 0.000 0.000 0.000 1.000
#> GSM372292 4 0.0188 0.988 0.000 0.004 0.000 0.996
#> GSM372293 4 0.0188 0.988 0.000 0.004 0.000 0.996
#> GSM372294 4 0.0592 0.989 0.000 0.016 0.000 0.984
#> GSM372295 4 0.0336 0.989 0.000 0.008 0.000 0.992
#> GSM372296 4 0.1716 0.949 0.000 0.064 0.000 0.936
#> GSM372297 4 0.0707 0.990 0.000 0.020 0.000 0.980
#> GSM372298 4 0.0592 0.989 0.000 0.016 0.000 0.984
#> GSM372299 4 0.0188 0.988 0.000 0.004 0.000 0.996
#> GSM372300 4 0.0188 0.988 0.000 0.004 0.000 0.996
#> GSM372301 4 0.0188 0.988 0.000 0.004 0.000 0.996
#> GSM372302 4 0.0707 0.990 0.000 0.020 0.000 0.980
#> GSM372303 4 0.0188 0.988 0.000 0.004 0.000 0.996
#> GSM372304 4 0.0707 0.990 0.000 0.020 0.000 0.980
#> GSM372305 2 0.0000 0.949 0.000 1.000 0.000 0.000
#> GSM372306 2 0.2081 0.910 0.000 0.916 0.084 0.000
#> GSM372307 2 0.2345 0.871 0.000 0.900 0.000 0.100
#> GSM372309 2 0.0336 0.949 0.000 0.992 0.008 0.000
#> GSM372311 2 0.0000 0.949 0.000 1.000 0.000 0.000
#> GSM372313 2 0.0188 0.949 0.000 0.996 0.004 0.000
#> GSM372315 2 0.0000 0.949 0.000 1.000 0.000 0.000
#> GSM372317 2 0.0707 0.946 0.000 0.980 0.020 0.000
#> GSM372319 3 0.0000 0.980 0.000 0.000 1.000 0.000
#> GSM372321 3 0.0000 0.980 0.000 0.000 1.000 0.000
#> GSM372323 3 0.0000 0.980 0.000 0.000 1.000 0.000
#> GSM372326 3 0.0707 0.966 0.000 0.020 0.980 0.000
#> GSM372328 3 0.0000 0.980 0.000 0.000 1.000 0.000
#> GSM372330 2 0.0000 0.949 0.000 1.000 0.000 0.000
#> GSM372332 3 0.0000 0.980 0.000 0.000 1.000 0.000
#> GSM372335 2 0.1716 0.924 0.000 0.936 0.064 0.000
#> GSM372337 3 0.0000 0.980 0.000 0.000 1.000 0.000
#> GSM372339 3 0.0000 0.980 0.000 0.000 1.000 0.000
#> GSM372341 3 0.0000 0.980 0.000 0.000 1.000 0.000
#> GSM372343 3 0.0000 0.980 0.000 0.000 1.000 0.000
#> GSM372345 3 0.0000 0.980 0.000 0.000 1.000 0.000
#> GSM372347 2 0.3123 0.843 0.000 0.844 0.156 0.000
#> GSM372349 3 0.1940 0.911 0.000 0.076 0.924 0.000
#> GSM372351 3 0.2973 0.845 0.000 0.144 0.856 0.000
#> GSM372353 2 0.0707 0.944 0.000 0.980 0.020 0.000
#> GSM372355 2 0.0000 0.949 0.000 1.000 0.000 0.000
#> GSM372357 2 0.0336 0.949 0.000 0.992 0.008 0.000
#> GSM372359 2 0.0336 0.949 0.000 0.992 0.008 0.000
#> GSM372361 2 0.4103 0.662 0.000 0.744 0.000 0.256
#> GSM372363 2 0.0000 0.949 0.000 1.000 0.000 0.000
#> GSM372308 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM372310 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM372312 1 0.0188 0.995 0.996 0.000 0.000 0.004
#> GSM372314 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM372316 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM372318 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM372320 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM372322 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM372324 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM372325 1 0.1510 0.955 0.956 0.016 0.028 0.000
#> GSM372327 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM372329 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM372331 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM372333 2 0.3088 0.867 0.008 0.864 0.128 0.000
#> GSM372334 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM372336 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM372338 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM372340 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM372342 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM372344 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM372346 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM372348 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM372350 1 0.0188 0.995 0.996 0.000 0.000 0.004
#> GSM372352 2 0.1970 0.922 0.008 0.932 0.060 0.000
#> GSM372354 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM372356 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM372358 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM372360 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM372362 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM372364 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM372365 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM372366 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM372367 1 0.0000 0.998 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM372286 2 0.1478 0.89328 0.000 0.936 0.000 0.064 0.000
#> GSM372287 4 0.0000 0.99012 0.000 0.000 0.000 1.000 0.000
#> GSM372288 4 0.0000 0.99012 0.000 0.000 0.000 1.000 0.000
#> GSM372289 4 0.0609 0.97128 0.000 0.020 0.000 0.980 0.000
#> GSM372290 4 0.0000 0.99012 0.000 0.000 0.000 1.000 0.000
#> GSM372291 4 0.0000 0.99012 0.000 0.000 0.000 1.000 0.000
#> GSM372292 4 0.0000 0.99012 0.000 0.000 0.000 1.000 0.000
#> GSM372293 4 0.0000 0.99012 0.000 0.000 0.000 1.000 0.000
#> GSM372294 4 0.0000 0.99012 0.000 0.000 0.000 1.000 0.000
#> GSM372295 4 0.0000 0.99012 0.000 0.000 0.000 1.000 0.000
#> GSM372296 4 0.2424 0.84426 0.000 0.132 0.000 0.868 0.000
#> GSM372297 4 0.0000 0.99012 0.000 0.000 0.000 1.000 0.000
#> GSM372298 4 0.0000 0.99012 0.000 0.000 0.000 1.000 0.000
#> GSM372299 4 0.0000 0.99012 0.000 0.000 0.000 1.000 0.000
#> GSM372300 4 0.0000 0.99012 0.000 0.000 0.000 1.000 0.000
#> GSM372301 4 0.0000 0.99012 0.000 0.000 0.000 1.000 0.000
#> GSM372302 4 0.0000 0.99012 0.000 0.000 0.000 1.000 0.000
#> GSM372303 4 0.0000 0.99012 0.000 0.000 0.000 1.000 0.000
#> GSM372304 4 0.0000 0.99012 0.000 0.000 0.000 1.000 0.000
#> GSM372305 2 0.0000 0.92860 0.000 1.000 0.000 0.000 0.000
#> GSM372306 2 0.2020 0.86316 0.000 0.900 0.100 0.000 0.000
#> GSM372307 2 0.2329 0.83535 0.000 0.876 0.000 0.124 0.000
#> GSM372309 2 0.0000 0.92860 0.000 1.000 0.000 0.000 0.000
#> GSM372311 2 0.0000 0.92860 0.000 1.000 0.000 0.000 0.000
#> GSM372313 2 0.0000 0.92860 0.000 1.000 0.000 0.000 0.000
#> GSM372315 2 0.1410 0.89603 0.000 0.940 0.000 0.060 0.000
#> GSM372317 2 0.0000 0.92860 0.000 1.000 0.000 0.000 0.000
#> GSM372319 3 0.0290 0.98115 0.000 0.008 0.992 0.000 0.000
#> GSM372321 3 0.0290 0.98115 0.000 0.008 0.992 0.000 0.000
#> GSM372323 3 0.0290 0.98115 0.000 0.008 0.992 0.000 0.000
#> GSM372326 3 0.0510 0.97684 0.000 0.016 0.984 0.000 0.000
#> GSM372328 3 0.0000 0.97821 0.000 0.000 1.000 0.000 0.000
#> GSM372330 2 0.0000 0.92860 0.000 1.000 0.000 0.000 0.000
#> GSM372332 3 0.0290 0.98115 0.000 0.008 0.992 0.000 0.000
#> GSM372335 2 0.1544 0.88836 0.000 0.932 0.068 0.000 0.000
#> GSM372337 3 0.0404 0.97992 0.000 0.012 0.988 0.000 0.000
#> GSM372339 3 0.0000 0.97821 0.000 0.000 1.000 0.000 0.000
#> GSM372341 3 0.0000 0.97821 0.000 0.000 1.000 0.000 0.000
#> GSM372343 3 0.0000 0.97821 0.000 0.000 1.000 0.000 0.000
#> GSM372345 3 0.0404 0.97992 0.000 0.012 0.988 0.000 0.000
#> GSM372347 2 0.3861 0.65113 0.000 0.728 0.264 0.000 0.008
#> GSM372349 3 0.1410 0.93316 0.000 0.060 0.940 0.000 0.000
#> GSM372351 3 0.1908 0.89710 0.000 0.092 0.908 0.000 0.000
#> GSM372353 2 0.1410 0.89794 0.000 0.940 0.060 0.000 0.000
#> GSM372355 2 0.0000 0.92860 0.000 1.000 0.000 0.000 0.000
#> GSM372357 2 0.0000 0.92860 0.000 1.000 0.000 0.000 0.000
#> GSM372359 2 0.0000 0.92860 0.000 1.000 0.000 0.000 0.000
#> GSM372361 2 0.3730 0.62385 0.000 0.712 0.000 0.288 0.000
#> GSM372363 2 0.0000 0.92860 0.000 1.000 0.000 0.000 0.000
#> GSM372308 5 0.0963 0.89257 0.036 0.000 0.000 0.000 0.964
#> GSM372310 5 0.1121 0.88803 0.044 0.000 0.000 0.000 0.956
#> GSM372312 5 0.0703 0.89701 0.024 0.000 0.000 0.000 0.976
#> GSM372314 5 0.0703 0.89701 0.024 0.000 0.000 0.000 0.976
#> GSM372316 1 0.0000 0.96072 1.000 0.000 0.000 0.000 0.000
#> GSM372318 1 0.0000 0.96072 1.000 0.000 0.000 0.000 0.000
#> GSM372320 1 0.0290 0.95533 0.992 0.000 0.000 0.000 0.008
#> GSM372322 1 0.0000 0.96072 1.000 0.000 0.000 0.000 0.000
#> GSM372324 5 0.0703 0.89701 0.024 0.000 0.000 0.000 0.976
#> GSM372325 5 0.0703 0.89701 0.024 0.000 0.000 0.000 0.976
#> GSM372327 1 0.0000 0.96072 1.000 0.000 0.000 0.000 0.000
#> GSM372329 1 0.0000 0.96072 1.000 0.000 0.000 0.000 0.000
#> GSM372331 5 0.0703 0.89701 0.024 0.000 0.000 0.000 0.976
#> GSM372333 5 0.6243 0.43223 0.000 0.284 0.184 0.000 0.532
#> GSM372334 1 0.0609 0.94599 0.980 0.000 0.000 0.000 0.020
#> GSM372336 1 0.0000 0.96072 1.000 0.000 0.000 0.000 0.000
#> GSM372338 1 0.0000 0.96072 1.000 0.000 0.000 0.000 0.000
#> GSM372340 1 0.0000 0.96072 1.000 0.000 0.000 0.000 0.000
#> GSM372342 1 0.0000 0.96072 1.000 0.000 0.000 0.000 0.000
#> GSM372344 1 0.0000 0.96072 1.000 0.000 0.000 0.000 0.000
#> GSM372346 1 0.0000 0.96072 1.000 0.000 0.000 0.000 0.000
#> GSM372348 1 0.0000 0.96072 1.000 0.000 0.000 0.000 0.000
#> GSM372350 1 0.3550 0.66987 0.760 0.000 0.000 0.004 0.236
#> GSM372352 5 0.6000 0.49040 0.000 0.268 0.160 0.000 0.572
#> GSM372354 1 0.0510 0.94930 0.984 0.000 0.000 0.000 0.016
#> GSM372356 1 0.4305 -0.00493 0.512 0.000 0.000 0.000 0.488
#> GSM372358 1 0.0000 0.96072 1.000 0.000 0.000 0.000 0.000
#> GSM372360 1 0.0000 0.96072 1.000 0.000 0.000 0.000 0.000
#> GSM372362 1 0.0000 0.96072 1.000 0.000 0.000 0.000 0.000
#> GSM372364 1 0.0000 0.96072 1.000 0.000 0.000 0.000 0.000
#> GSM372365 5 0.2516 0.80332 0.140 0.000 0.000 0.000 0.860
#> GSM372366 1 0.0000 0.96072 1.000 0.000 0.000 0.000 0.000
#> GSM372367 5 0.0703 0.89701 0.024 0.000 0.000 0.000 0.976
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM372286 2 0.2868 0.8180 0.000 0.852 0.004 0.112 0.000 NA
#> GSM372287 4 0.2730 0.8912 0.000 0.000 0.000 0.808 0.000 NA
#> GSM372288 4 0.3141 0.8869 0.000 0.012 0.000 0.788 0.000 NA
#> GSM372289 4 0.4475 0.8235 0.000 0.088 0.000 0.692 0.000 NA
#> GSM372290 4 0.3364 0.8819 0.000 0.024 0.000 0.780 0.000 NA
#> GSM372291 4 0.2527 0.7806 0.000 0.000 0.000 0.832 0.000 NA
#> GSM372292 4 0.0260 0.8782 0.000 0.000 0.000 0.992 0.000 NA
#> GSM372293 4 0.0260 0.8771 0.000 0.000 0.000 0.992 0.000 NA
#> GSM372294 4 0.2762 0.8897 0.000 0.000 0.000 0.804 0.000 NA
#> GSM372295 4 0.0146 0.8783 0.000 0.000 0.000 0.996 0.000 NA
#> GSM372296 4 0.4999 0.7522 0.000 0.144 0.000 0.640 0.000 NA
#> GSM372297 4 0.2762 0.8910 0.000 0.000 0.000 0.804 0.000 NA
#> GSM372298 4 0.2730 0.8912 0.000 0.000 0.000 0.808 0.000 NA
#> GSM372299 4 0.0520 0.8749 0.000 0.000 0.000 0.984 0.008 NA
#> GSM372300 4 0.0260 0.8771 0.000 0.000 0.000 0.992 0.000 NA
#> GSM372301 4 0.0260 0.8771 0.000 0.000 0.000 0.992 0.000 NA
#> GSM372302 4 0.2664 0.8914 0.000 0.000 0.000 0.816 0.000 NA
#> GSM372303 4 0.0632 0.8720 0.000 0.000 0.000 0.976 0.000 NA
#> GSM372304 4 0.2762 0.8910 0.000 0.000 0.000 0.804 0.000 NA
#> GSM372305 2 0.0000 0.8892 0.000 1.000 0.000 0.000 0.000 NA
#> GSM372306 2 0.1921 0.8584 0.000 0.916 0.032 0.000 0.000 NA
#> GSM372307 2 0.3422 0.7378 0.000 0.788 0.000 0.176 0.000 NA
#> GSM372309 2 0.0000 0.8892 0.000 1.000 0.000 0.000 0.000 NA
#> GSM372311 2 0.0000 0.8892 0.000 1.000 0.000 0.000 0.000 NA
#> GSM372313 2 0.0000 0.8892 0.000 1.000 0.000 0.000 0.000 NA
#> GSM372315 2 0.2658 0.8210 0.000 0.864 0.000 0.100 0.000 NA
#> GSM372317 2 0.0405 0.8867 0.000 0.988 0.008 0.000 0.000 NA
#> GSM372319 3 0.1643 0.9156 0.000 0.068 0.924 0.000 0.000 NA
#> GSM372321 3 0.0260 0.9727 0.000 0.008 0.992 0.000 0.000 NA
#> GSM372323 3 0.0622 0.9699 0.000 0.008 0.980 0.000 0.000 NA
#> GSM372326 3 0.0291 0.9718 0.000 0.000 0.992 0.004 0.000 NA
#> GSM372328 3 0.0000 0.9735 0.000 0.000 1.000 0.000 0.000 NA
#> GSM372330 2 0.0000 0.8892 0.000 1.000 0.000 0.000 0.000 NA
#> GSM372332 3 0.0000 0.9735 0.000 0.000 1.000 0.000 0.000 NA
#> GSM372335 2 0.1440 0.8742 0.000 0.948 0.012 0.004 0.004 NA
#> GSM372337 3 0.0622 0.9699 0.000 0.008 0.980 0.000 0.000 NA
#> GSM372339 3 0.0000 0.9735 0.000 0.000 1.000 0.000 0.000 NA
#> GSM372341 3 0.0000 0.9735 0.000 0.000 1.000 0.000 0.000 NA
#> GSM372343 3 0.0000 0.9735 0.000 0.000 1.000 0.000 0.000 NA
#> GSM372345 3 0.1049 0.9590 0.000 0.008 0.960 0.000 0.000 NA
#> GSM372347 2 0.7539 0.0573 0.000 0.340 0.192 0.000 0.180 NA
#> GSM372349 3 0.0717 0.9653 0.000 0.016 0.976 0.008 0.000 NA
#> GSM372351 3 0.2163 0.8827 0.000 0.096 0.892 0.008 0.000 NA
#> GSM372353 2 0.5374 0.6521 0.000 0.688 0.104 0.000 0.112 NA
#> GSM372355 2 0.0000 0.8892 0.000 1.000 0.000 0.000 0.000 NA
#> GSM372357 2 0.0458 0.8856 0.000 0.984 0.000 0.000 0.000 NA
#> GSM372359 2 0.0260 0.8874 0.000 0.992 0.000 0.000 0.008 NA
#> GSM372361 2 0.4024 0.5996 0.000 0.700 0.000 0.264 0.000 NA
#> GSM372363 2 0.0000 0.8892 0.000 1.000 0.000 0.000 0.000 NA
#> GSM372308 5 0.0260 0.8957 0.008 0.000 0.000 0.000 0.992 NA
#> GSM372310 5 0.0260 0.8957 0.008 0.000 0.000 0.000 0.992 NA
#> GSM372312 5 0.0632 0.8873 0.000 0.000 0.000 0.000 0.976 NA
#> GSM372314 5 0.0260 0.8957 0.008 0.000 0.000 0.000 0.992 NA
#> GSM372316 1 0.0717 0.8281 0.976 0.000 0.000 0.000 0.008 NA
#> GSM372318 1 0.2442 0.7999 0.852 0.000 0.000 0.000 0.004 NA
#> GSM372320 1 0.3482 0.7695 0.684 0.000 0.000 0.000 0.000 NA
#> GSM372322 1 0.1327 0.8299 0.936 0.000 0.000 0.000 0.000 NA
#> GSM372324 5 0.2003 0.8165 0.116 0.000 0.000 0.000 0.884 NA
#> GSM372325 5 0.2416 0.8535 0.000 0.000 0.000 0.000 0.844 NA
#> GSM372327 1 0.3351 0.7803 0.712 0.000 0.000 0.000 0.000 NA
#> GSM372329 1 0.0458 0.8286 0.984 0.000 0.000 0.000 0.000 NA
#> GSM372331 5 0.2092 0.8095 0.124 0.000 0.000 0.000 0.876 NA
#> GSM372333 5 0.4792 0.7252 0.000 0.060 0.008 0.000 0.632 NA
#> GSM372334 1 0.3619 0.7676 0.680 0.000 0.000 0.000 0.004 NA
#> GSM372336 1 0.1320 0.8213 0.948 0.000 0.000 0.000 0.036 NA
#> GSM372338 1 0.3482 0.7695 0.684 0.000 0.000 0.000 0.000 NA
#> GSM372340 1 0.3482 0.7695 0.684 0.000 0.000 0.000 0.000 NA
#> GSM372342 1 0.1267 0.8303 0.940 0.000 0.000 0.000 0.000 NA
#> GSM372344 1 0.3607 0.7550 0.652 0.000 0.000 0.000 0.000 NA
#> GSM372346 1 0.2597 0.7917 0.824 0.000 0.000 0.000 0.000 NA
#> GSM372348 1 0.1245 0.8229 0.952 0.000 0.000 0.000 0.032 NA
#> GSM372350 1 0.6704 0.3231 0.464 0.000 0.000 0.076 0.308 NA
#> GSM372352 5 0.4247 0.7553 0.000 0.040 0.000 0.000 0.664 NA
#> GSM372354 1 0.4134 0.7683 0.656 0.000 0.000 0.000 0.028 NA
#> GSM372356 1 0.3843 0.2841 0.548 0.000 0.000 0.000 0.452 NA
#> GSM372358 1 0.1168 0.8242 0.956 0.000 0.000 0.000 0.028 NA
#> GSM372360 1 0.1245 0.8229 0.952 0.000 0.000 0.000 0.032 NA
#> GSM372362 1 0.0713 0.8279 0.972 0.000 0.000 0.000 0.028 NA
#> GSM372364 1 0.1204 0.8223 0.944 0.000 0.000 0.000 0.056 NA
#> GSM372365 5 0.1327 0.8705 0.064 0.000 0.000 0.000 0.936 NA
#> GSM372366 1 0.1092 0.8316 0.960 0.000 0.000 0.000 0.020 NA
#> GSM372367 5 0.0260 0.8957 0.008 0.000 0.000 0.000 0.992 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) specimen(p) individual(p) k
#> CV:mclust 82 6.57e-05 1.20e-17 1.000 2
#> CV:mclust 80 4.65e-15 1.09e-29 0.814 3
#> CV:mclust 82 8.45e-15 1.99e-27 0.909 4
#> CV:mclust 79 1.44e-13 1.13e-26 0.861 5
#> CV:mclust 79 1.34e-13 1.17e-26 0.891 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 51941 rows and 82 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 0.983 0.993 0.4838 0.518 0.518
#> 3 3 0.883 0.907 0.951 0.3838 0.780 0.588
#> 4 4 0.861 0.865 0.928 0.1008 0.852 0.602
#> 5 5 0.799 0.695 0.853 0.0463 0.948 0.811
#> 6 6 0.802 0.730 0.857 0.0337 0.950 0.798
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
#> GSM372286 2 0.000 0.991 0.000 1.000
#> GSM372287 2 0.000 0.991 0.000 1.000
#> GSM372288 2 0.000 0.991 0.000 1.000
#> GSM372289 2 0.000 0.991 0.000 1.000
#> GSM372290 2 0.000 0.991 0.000 1.000
#> GSM372291 2 0.949 0.417 0.368 0.632
#> GSM372292 2 0.000 0.991 0.000 1.000
#> GSM372293 2 0.000 0.991 0.000 1.000
#> GSM372294 2 0.000 0.991 0.000 1.000
#> GSM372295 2 0.000 0.991 0.000 1.000
#> GSM372296 2 0.000 0.991 0.000 1.000
#> GSM372297 2 0.000 0.991 0.000 1.000
#> GSM372298 2 0.000 0.991 0.000 1.000
#> GSM372299 2 0.000 0.991 0.000 1.000
#> GSM372300 2 0.000 0.991 0.000 1.000
#> GSM372301 2 0.000 0.991 0.000 1.000
#> GSM372302 2 0.000 0.991 0.000 1.000
#> GSM372303 2 0.000 0.991 0.000 1.000
#> GSM372304 2 0.000 0.991 0.000 1.000
#> GSM372305 2 0.000 0.991 0.000 1.000
#> GSM372306 2 0.000 0.991 0.000 1.000
#> GSM372307 2 0.000 0.991 0.000 1.000
#> GSM372309 2 0.000 0.991 0.000 1.000
#> GSM372311 2 0.000 0.991 0.000 1.000
#> GSM372313 2 0.000 0.991 0.000 1.000
#> GSM372315 2 0.000 0.991 0.000 1.000
#> GSM372317 2 0.000 0.991 0.000 1.000
#> GSM372319 2 0.000 0.991 0.000 1.000
#> GSM372321 2 0.000 0.991 0.000 1.000
#> GSM372323 2 0.000 0.991 0.000 1.000
#> GSM372326 2 0.000 0.991 0.000 1.000
#> GSM372328 2 0.000 0.991 0.000 1.000
#> GSM372330 2 0.000 0.991 0.000 1.000
#> GSM372332 2 0.000 0.991 0.000 1.000
#> GSM372335 2 0.000 0.991 0.000 1.000
#> GSM372337 2 0.000 0.991 0.000 1.000
#> GSM372339 2 0.000 0.991 0.000 1.000
#> GSM372341 2 0.000 0.991 0.000 1.000
#> GSM372343 2 0.000 0.991 0.000 1.000
#> GSM372345 2 0.000 0.991 0.000 1.000
#> GSM372347 2 0.000 0.991 0.000 1.000
#> GSM372349 2 0.000 0.991 0.000 1.000
#> GSM372351 2 0.000 0.991 0.000 1.000
#> GSM372353 2 0.000 0.991 0.000 1.000
#> GSM372355 2 0.000 0.991 0.000 1.000
#> GSM372357 2 0.000 0.991 0.000 1.000
#> GSM372359 2 0.000 0.991 0.000 1.000
#> GSM372361 2 0.000 0.991 0.000 1.000
#> GSM372363 2 0.000 0.991 0.000 1.000
#> GSM372308 1 0.000 0.996 1.000 0.000
#> GSM372310 1 0.000 0.996 1.000 0.000
#> GSM372312 1 0.000 0.996 1.000 0.000
#> GSM372314 1 0.000 0.996 1.000 0.000
#> GSM372316 1 0.000 0.996 1.000 0.000
#> GSM372318 1 0.000 0.996 1.000 0.000
#> GSM372320 1 0.000 0.996 1.000 0.000
#> GSM372322 1 0.000 0.996 1.000 0.000
#> GSM372324 1 0.000 0.996 1.000 0.000
#> GSM372325 1 0.000 0.996 1.000 0.000
#> GSM372327 1 0.000 0.996 1.000 0.000
#> GSM372329 1 0.000 0.996 1.000 0.000
#> GSM372331 1 0.000 0.996 1.000 0.000
#> GSM372333 1 0.529 0.861 0.880 0.120
#> GSM372334 1 0.000 0.996 1.000 0.000
#> GSM372336 1 0.000 0.996 1.000 0.000
#> GSM372338 1 0.000 0.996 1.000 0.000
#> GSM372340 1 0.000 0.996 1.000 0.000
#> GSM372342 1 0.000 0.996 1.000 0.000
#> GSM372344 1 0.000 0.996 1.000 0.000
#> GSM372346 1 0.000 0.996 1.000 0.000
#> GSM372348 1 0.000 0.996 1.000 0.000
#> GSM372350 1 0.000 0.996 1.000 0.000
#> GSM372352 2 0.373 0.917 0.072 0.928
#> GSM372354 1 0.000 0.996 1.000 0.000
#> GSM372356 1 0.000 0.996 1.000 0.000
#> GSM372358 1 0.000 0.996 1.000 0.000
#> GSM372360 1 0.000 0.996 1.000 0.000
#> GSM372362 1 0.000 0.996 1.000 0.000
#> GSM372364 1 0.000 0.996 1.000 0.000
#> GSM372365 1 0.000 0.996 1.000 0.000
#> GSM372366 1 0.000 0.996 1.000 0.000
#> GSM372367 1 0.000 0.996 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM372286 2 0.4399 0.820 0.000 0.812 0.188
#> GSM372287 2 0.0747 0.926 0.000 0.984 0.016
#> GSM372288 2 0.0747 0.926 0.000 0.984 0.016
#> GSM372289 2 0.0237 0.927 0.000 0.996 0.004
#> GSM372290 2 0.0747 0.926 0.000 0.984 0.016
#> GSM372291 2 0.3234 0.872 0.072 0.908 0.020
#> GSM372292 2 0.6204 0.225 0.000 0.576 0.424
#> GSM372293 3 0.4002 0.824 0.000 0.160 0.840
#> GSM372294 2 0.0747 0.926 0.000 0.984 0.016
#> GSM372295 2 0.0237 0.926 0.000 0.996 0.004
#> GSM372296 2 0.1411 0.923 0.000 0.964 0.036
#> GSM372297 2 0.0892 0.925 0.000 0.980 0.020
#> GSM372298 2 0.0892 0.925 0.000 0.980 0.020
#> GSM372299 2 0.0424 0.927 0.000 0.992 0.008
#> GSM372300 3 0.4291 0.802 0.000 0.180 0.820
#> GSM372301 3 0.4291 0.802 0.000 0.180 0.820
#> GSM372302 2 0.0892 0.925 0.000 0.980 0.020
#> GSM372303 3 0.2261 0.906 0.000 0.068 0.932
#> GSM372304 2 0.0892 0.925 0.000 0.980 0.020
#> GSM372305 2 0.4291 0.815 0.000 0.820 0.180
#> GSM372306 3 0.2537 0.889 0.000 0.080 0.920
#> GSM372307 2 0.0747 0.926 0.000 0.984 0.016
#> GSM372309 2 0.0892 0.925 0.000 0.980 0.020
#> GSM372311 2 0.2625 0.900 0.000 0.916 0.084
#> GSM372313 2 0.2711 0.897 0.000 0.912 0.088
#> GSM372315 2 0.1860 0.916 0.000 0.948 0.052
#> GSM372317 3 0.0892 0.930 0.000 0.020 0.980
#> GSM372319 3 0.0592 0.932 0.000 0.012 0.988
#> GSM372321 3 0.0592 0.932 0.000 0.012 0.988
#> GSM372323 3 0.0592 0.932 0.000 0.012 0.988
#> GSM372326 3 0.2448 0.908 0.000 0.076 0.924
#> GSM372328 3 0.0747 0.931 0.000 0.016 0.984
#> GSM372330 2 0.4750 0.777 0.000 0.784 0.216
#> GSM372332 3 0.0424 0.933 0.000 0.008 0.992
#> GSM372335 3 0.0747 0.932 0.000 0.016 0.984
#> GSM372337 3 0.0237 0.933 0.000 0.004 0.996
#> GSM372339 3 0.0424 0.932 0.000 0.008 0.992
#> GSM372341 3 0.0747 0.931 0.000 0.016 0.984
#> GSM372343 3 0.0747 0.931 0.000 0.016 0.984
#> GSM372345 3 0.0592 0.932 0.000 0.012 0.988
#> GSM372347 3 0.0747 0.931 0.000 0.016 0.984
#> GSM372349 3 0.0747 0.931 0.000 0.016 0.984
#> GSM372351 3 0.1860 0.914 0.000 0.052 0.948
#> GSM372353 3 0.0747 0.931 0.000 0.016 0.984
#> GSM372355 2 0.2625 0.900 0.000 0.916 0.084
#> GSM372357 2 0.4178 0.828 0.000 0.828 0.172
#> GSM372359 3 0.2625 0.896 0.000 0.084 0.916
#> GSM372361 2 0.0747 0.925 0.000 0.984 0.016
#> GSM372363 2 0.0892 0.925 0.000 0.980 0.020
#> GSM372308 1 0.0237 0.974 0.996 0.004 0.000
#> GSM372310 1 0.0000 0.977 1.000 0.000 0.000
#> GSM372312 1 0.0000 0.977 1.000 0.000 0.000
#> GSM372314 1 0.2651 0.913 0.928 0.012 0.060
#> GSM372316 1 0.0000 0.977 1.000 0.000 0.000
#> GSM372318 1 0.0000 0.977 1.000 0.000 0.000
#> GSM372320 1 0.0000 0.977 1.000 0.000 0.000
#> GSM372322 1 0.0000 0.977 1.000 0.000 0.000
#> GSM372324 1 0.0000 0.977 1.000 0.000 0.000
#> GSM372325 1 0.3941 0.812 0.844 0.000 0.156
#> GSM372327 1 0.0000 0.977 1.000 0.000 0.000
#> GSM372329 1 0.0000 0.977 1.000 0.000 0.000
#> GSM372331 1 0.1964 0.926 0.944 0.000 0.056
#> GSM372333 3 0.6470 0.407 0.356 0.012 0.632
#> GSM372334 1 0.0000 0.977 1.000 0.000 0.000
#> GSM372336 1 0.0000 0.977 1.000 0.000 0.000
#> GSM372338 1 0.0000 0.977 1.000 0.000 0.000
#> GSM372340 1 0.0000 0.977 1.000 0.000 0.000
#> GSM372342 1 0.0000 0.977 1.000 0.000 0.000
#> GSM372344 1 0.0000 0.977 1.000 0.000 0.000
#> GSM372346 1 0.0000 0.977 1.000 0.000 0.000
#> GSM372348 1 0.0000 0.977 1.000 0.000 0.000
#> GSM372350 1 0.0000 0.977 1.000 0.000 0.000
#> GSM372352 1 0.7920 0.334 0.572 0.068 0.360
#> GSM372354 1 0.0000 0.977 1.000 0.000 0.000
#> GSM372356 1 0.0000 0.977 1.000 0.000 0.000
#> GSM372358 1 0.0000 0.977 1.000 0.000 0.000
#> GSM372360 1 0.0000 0.977 1.000 0.000 0.000
#> GSM372362 1 0.0000 0.977 1.000 0.000 0.000
#> GSM372364 1 0.0000 0.977 1.000 0.000 0.000
#> GSM372365 1 0.0237 0.974 0.996 0.004 0.000
#> GSM372366 1 0.0000 0.977 1.000 0.000 0.000
#> GSM372367 1 0.0000 0.977 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM372286 2 0.4610 0.799 0.000 0.800 0.100 0.100
#> GSM372287 4 0.1557 0.911 0.000 0.056 0.000 0.944
#> GSM372288 4 0.1637 0.909 0.000 0.060 0.000 0.940
#> GSM372289 2 0.4992 0.052 0.000 0.524 0.000 0.476
#> GSM372290 4 0.0817 0.919 0.000 0.024 0.000 0.976
#> GSM372291 4 0.0000 0.916 0.000 0.000 0.000 1.000
#> GSM372292 4 0.0336 0.915 0.000 0.000 0.008 0.992
#> GSM372293 4 0.5744 0.188 0.000 0.028 0.436 0.536
#> GSM372294 4 0.1792 0.904 0.000 0.068 0.000 0.932
#> GSM372295 4 0.2408 0.889 0.000 0.104 0.000 0.896
#> GSM372296 4 0.2921 0.846 0.000 0.140 0.000 0.860
#> GSM372297 4 0.0336 0.918 0.000 0.008 0.000 0.992
#> GSM372298 4 0.0592 0.919 0.000 0.016 0.000 0.984
#> GSM372299 4 0.2124 0.901 0.000 0.068 0.008 0.924
#> GSM372300 4 0.2282 0.886 0.000 0.024 0.052 0.924
#> GSM372301 4 0.1209 0.905 0.000 0.004 0.032 0.964
#> GSM372302 4 0.1211 0.916 0.000 0.040 0.000 0.960
#> GSM372303 4 0.2973 0.818 0.000 0.000 0.144 0.856
#> GSM372304 4 0.0707 0.919 0.000 0.020 0.000 0.980
#> GSM372305 2 0.1305 0.836 0.000 0.960 0.036 0.004
#> GSM372306 2 0.3024 0.787 0.000 0.852 0.148 0.000
#> GSM372307 2 0.2281 0.808 0.000 0.904 0.000 0.096
#> GSM372309 2 0.1635 0.824 0.000 0.948 0.008 0.044
#> GSM372311 2 0.1209 0.838 0.000 0.964 0.004 0.032
#> GSM372313 2 0.1209 0.838 0.000 0.964 0.004 0.032
#> GSM372315 2 0.1211 0.836 0.000 0.960 0.000 0.040
#> GSM372317 2 0.3873 0.723 0.000 0.772 0.228 0.000
#> GSM372319 3 0.1211 0.922 0.000 0.040 0.960 0.000
#> GSM372321 3 0.0469 0.941 0.000 0.012 0.988 0.000
#> GSM372323 3 0.0336 0.942 0.000 0.008 0.992 0.000
#> GSM372326 3 0.1833 0.917 0.000 0.032 0.944 0.024
#> GSM372328 3 0.2266 0.878 0.000 0.004 0.912 0.084
#> GSM372330 2 0.2542 0.822 0.000 0.904 0.084 0.012
#> GSM372332 3 0.0188 0.943 0.000 0.004 0.996 0.000
#> GSM372335 2 0.4746 0.502 0.000 0.632 0.368 0.000
#> GSM372337 3 0.0188 0.943 0.000 0.004 0.996 0.000
#> GSM372339 3 0.0000 0.943 0.000 0.000 1.000 0.000
#> GSM372341 3 0.0376 0.941 0.000 0.004 0.992 0.004
#> GSM372343 3 0.0672 0.939 0.000 0.008 0.984 0.008
#> GSM372345 3 0.0592 0.939 0.000 0.016 0.984 0.000
#> GSM372347 3 0.3688 0.705 0.000 0.208 0.792 0.000
#> GSM372349 3 0.0000 0.943 0.000 0.000 1.000 0.000
#> GSM372351 3 0.1520 0.925 0.000 0.024 0.956 0.020
#> GSM372353 3 0.3837 0.750 0.000 0.224 0.776 0.000
#> GSM372355 2 0.1256 0.838 0.000 0.964 0.008 0.028
#> GSM372357 2 0.0817 0.835 0.000 0.976 0.024 0.000
#> GSM372359 2 0.4335 0.757 0.000 0.796 0.168 0.036
#> GSM372361 2 0.2999 0.757 0.000 0.864 0.004 0.132
#> GSM372363 2 0.1635 0.827 0.000 0.948 0.008 0.044
#> GSM372308 1 0.0707 0.957 0.980 0.020 0.000 0.000
#> GSM372310 1 0.0000 0.973 1.000 0.000 0.000 0.000
#> GSM372312 1 0.0000 0.973 1.000 0.000 0.000 0.000
#> GSM372314 1 0.5112 0.347 0.608 0.384 0.008 0.000
#> GSM372316 1 0.0000 0.973 1.000 0.000 0.000 0.000
#> GSM372318 1 0.0000 0.973 1.000 0.000 0.000 0.000
#> GSM372320 1 0.0000 0.973 1.000 0.000 0.000 0.000
#> GSM372322 1 0.0000 0.973 1.000 0.000 0.000 0.000
#> GSM372324 1 0.0000 0.973 1.000 0.000 0.000 0.000
#> GSM372325 1 0.4706 0.738 0.788 0.072 0.140 0.000
#> GSM372327 1 0.0000 0.973 1.000 0.000 0.000 0.000
#> GSM372329 1 0.0000 0.973 1.000 0.000 0.000 0.000
#> GSM372331 1 0.3257 0.804 0.844 0.152 0.004 0.000
#> GSM372333 2 0.4290 0.732 0.016 0.772 0.212 0.000
#> GSM372334 1 0.0000 0.973 1.000 0.000 0.000 0.000
#> GSM372336 1 0.0000 0.973 1.000 0.000 0.000 0.000
#> GSM372338 1 0.0000 0.973 1.000 0.000 0.000 0.000
#> GSM372340 1 0.0000 0.973 1.000 0.000 0.000 0.000
#> GSM372342 1 0.0000 0.973 1.000 0.000 0.000 0.000
#> GSM372344 1 0.0000 0.973 1.000 0.000 0.000 0.000
#> GSM372346 1 0.0000 0.973 1.000 0.000 0.000 0.000
#> GSM372348 1 0.0000 0.973 1.000 0.000 0.000 0.000
#> GSM372350 1 0.0000 0.973 1.000 0.000 0.000 0.000
#> GSM372352 2 0.7741 0.289 0.264 0.440 0.296 0.000
#> GSM372354 1 0.0000 0.973 1.000 0.000 0.000 0.000
#> GSM372356 1 0.0000 0.973 1.000 0.000 0.000 0.000
#> GSM372358 1 0.0000 0.973 1.000 0.000 0.000 0.000
#> GSM372360 1 0.0000 0.973 1.000 0.000 0.000 0.000
#> GSM372362 1 0.0000 0.973 1.000 0.000 0.000 0.000
#> GSM372364 1 0.0000 0.973 1.000 0.000 0.000 0.000
#> GSM372365 1 0.0000 0.973 1.000 0.000 0.000 0.000
#> GSM372366 1 0.0000 0.973 1.000 0.000 0.000 0.000
#> GSM372367 1 0.0000 0.973 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM372286 2 0.3427 0.5644 0.000 0.796 0.000 0.192 0.012
#> GSM372287 4 0.1195 0.7927 0.000 0.012 0.000 0.960 0.028
#> GSM372288 4 0.1485 0.7872 0.000 0.032 0.000 0.948 0.020
#> GSM372289 4 0.4972 0.2378 0.000 0.336 0.000 0.620 0.044
#> GSM372290 4 0.0955 0.7955 0.000 0.004 0.000 0.968 0.028
#> GSM372291 4 0.0771 0.7983 0.000 0.000 0.004 0.976 0.020
#> GSM372292 4 0.1697 0.7738 0.000 0.000 0.008 0.932 0.060
#> GSM372293 5 0.6809 -0.1342 0.000 0.000 0.320 0.312 0.368
#> GSM372294 4 0.1764 0.7777 0.000 0.008 0.000 0.928 0.064
#> GSM372295 5 0.4287 0.2399 0.000 0.000 0.000 0.460 0.540
#> GSM372296 4 0.2448 0.7269 0.000 0.088 0.000 0.892 0.020
#> GSM372297 4 0.0290 0.7998 0.000 0.000 0.000 0.992 0.008
#> GSM372298 4 0.1043 0.7887 0.000 0.000 0.000 0.960 0.040
#> GSM372299 5 0.4620 0.3642 0.000 0.028 0.000 0.320 0.652
#> GSM372300 4 0.5309 0.4023 0.000 0.000 0.060 0.576 0.364
#> GSM372301 4 0.4575 0.4962 0.000 0.000 0.024 0.648 0.328
#> GSM372302 4 0.0912 0.7974 0.000 0.016 0.000 0.972 0.012
#> GSM372303 4 0.4866 0.4617 0.000 0.000 0.036 0.620 0.344
#> GSM372304 4 0.0000 0.8002 0.000 0.000 0.000 1.000 0.000
#> GSM372305 2 0.0880 0.7111 0.000 0.968 0.000 0.000 0.032
#> GSM372306 2 0.1648 0.7102 0.000 0.940 0.040 0.000 0.020
#> GSM372307 2 0.6496 -0.0843 0.000 0.488 0.000 0.232 0.280
#> GSM372309 5 0.4610 0.1158 0.000 0.432 0.000 0.012 0.556
#> GSM372311 2 0.0451 0.7177 0.000 0.988 0.000 0.008 0.004
#> GSM372313 2 0.1041 0.7097 0.000 0.964 0.000 0.032 0.004
#> GSM372315 2 0.1597 0.6961 0.000 0.940 0.000 0.048 0.012
#> GSM372317 2 0.2605 0.6545 0.000 0.852 0.148 0.000 0.000
#> GSM372319 3 0.1956 0.8049 0.000 0.076 0.916 0.000 0.008
#> GSM372321 3 0.1628 0.8132 0.000 0.056 0.936 0.000 0.008
#> GSM372323 3 0.2221 0.8167 0.000 0.052 0.912 0.000 0.036
#> GSM372326 3 0.4150 0.5534 0.000 0.000 0.612 0.000 0.388
#> GSM372328 3 0.2573 0.7753 0.000 0.000 0.880 0.016 0.104
#> GSM372330 2 0.0162 0.7174 0.000 0.996 0.004 0.000 0.000
#> GSM372332 3 0.1408 0.8168 0.000 0.044 0.948 0.000 0.008
#> GSM372335 2 0.3282 0.6126 0.000 0.804 0.188 0.000 0.008
#> GSM372337 3 0.1818 0.8114 0.000 0.044 0.932 0.000 0.024
#> GSM372339 3 0.1251 0.8170 0.000 0.036 0.956 0.000 0.008
#> GSM372341 3 0.1410 0.7980 0.000 0.000 0.940 0.000 0.060
#> GSM372343 3 0.3452 0.6959 0.000 0.000 0.756 0.000 0.244
#> GSM372345 3 0.2036 0.8083 0.000 0.056 0.920 0.000 0.024
#> GSM372347 3 0.4722 0.3371 0.000 0.368 0.608 0.000 0.024
#> GSM372349 3 0.2284 0.7743 0.000 0.004 0.896 0.004 0.096
#> GSM372351 3 0.3586 0.6800 0.000 0.000 0.736 0.000 0.264
#> GSM372353 3 0.6650 0.2936 0.000 0.228 0.412 0.000 0.360
#> GSM372355 2 0.0451 0.7175 0.000 0.988 0.000 0.008 0.004
#> GSM372357 2 0.4306 -0.1323 0.000 0.508 0.000 0.000 0.492
#> GSM372359 2 0.3319 0.6793 0.000 0.868 0.040 0.040 0.052
#> GSM372361 5 0.5851 0.4207 0.000 0.112 0.000 0.340 0.548
#> GSM372363 5 0.4815 0.0792 0.000 0.456 0.000 0.020 0.524
#> GSM372308 1 0.3003 0.7679 0.812 0.000 0.000 0.000 0.188
#> GSM372310 1 0.0000 0.9524 1.000 0.000 0.000 0.000 0.000
#> GSM372312 1 0.4288 0.7760 0.800 0.000 0.044 0.036 0.120
#> GSM372314 1 0.4425 0.1392 0.544 0.452 0.000 0.000 0.004
#> GSM372316 1 0.0162 0.9512 0.996 0.000 0.000 0.000 0.004
#> GSM372318 1 0.0162 0.9512 0.996 0.000 0.000 0.000 0.004
#> GSM372320 1 0.0000 0.9524 1.000 0.000 0.000 0.000 0.000
#> GSM372322 1 0.0000 0.9524 1.000 0.000 0.000 0.000 0.000
#> GSM372324 1 0.0162 0.9512 0.996 0.000 0.000 0.000 0.004
#> GSM372325 1 0.5521 0.5862 0.688 0.208 0.064 0.000 0.040
#> GSM372327 1 0.0000 0.9524 1.000 0.000 0.000 0.000 0.000
#> GSM372329 1 0.0000 0.9524 1.000 0.000 0.000 0.000 0.000
#> GSM372331 2 0.4206 0.4176 0.288 0.696 0.000 0.000 0.016
#> GSM372333 2 0.5793 -0.0352 0.004 0.464 0.456 0.000 0.076
#> GSM372334 1 0.0000 0.9524 1.000 0.000 0.000 0.000 0.000
#> GSM372336 1 0.0162 0.9512 0.996 0.000 0.000 0.000 0.004
#> GSM372338 1 0.0000 0.9524 1.000 0.000 0.000 0.000 0.000
#> GSM372340 1 0.0000 0.9524 1.000 0.000 0.000 0.000 0.000
#> GSM372342 1 0.0000 0.9524 1.000 0.000 0.000 0.000 0.000
#> GSM372344 1 0.0000 0.9524 1.000 0.000 0.000 0.000 0.000
#> GSM372346 1 0.0000 0.9524 1.000 0.000 0.000 0.000 0.000
#> GSM372348 1 0.0162 0.9512 0.996 0.000 0.000 0.000 0.004
#> GSM372350 1 0.2228 0.8830 0.908 0.000 0.012 0.004 0.076
#> GSM372352 2 0.6346 0.4972 0.136 0.652 0.128 0.000 0.084
#> GSM372354 1 0.0000 0.9524 1.000 0.000 0.000 0.000 0.000
#> GSM372356 1 0.0000 0.9524 1.000 0.000 0.000 0.000 0.000
#> GSM372358 1 0.0162 0.9512 0.996 0.000 0.000 0.000 0.004
#> GSM372360 1 0.0000 0.9524 1.000 0.000 0.000 0.000 0.000
#> GSM372362 1 0.0000 0.9524 1.000 0.000 0.000 0.000 0.000
#> GSM372364 1 0.0000 0.9524 1.000 0.000 0.000 0.000 0.000
#> GSM372365 1 0.1410 0.9074 0.940 0.000 0.000 0.000 0.060
#> GSM372366 1 0.0000 0.9524 1.000 0.000 0.000 0.000 0.000
#> GSM372367 1 0.0162 0.9512 0.996 0.000 0.000 0.000 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM372286 2 0.3804 0.643 0.000 0.756 0.016 0.212 0.004 0.012
#> GSM372287 4 0.0146 0.848 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM372288 4 0.0777 0.844 0.000 0.004 0.000 0.972 0.024 0.000
#> GSM372289 4 0.4738 0.307 0.000 0.336 0.000 0.600 0.064 0.000
#> GSM372290 4 0.1075 0.833 0.000 0.000 0.000 0.952 0.048 0.000
#> GSM372291 4 0.2968 0.742 0.000 0.000 0.000 0.816 0.168 0.016
#> GSM372292 4 0.2883 0.695 0.000 0.000 0.000 0.788 0.000 0.212
#> GSM372293 6 0.2147 0.555 0.000 0.000 0.020 0.084 0.000 0.896
#> GSM372294 4 0.3460 0.726 0.000 0.004 0.000 0.796 0.164 0.036
#> GSM372295 5 0.3151 0.715 0.000 0.000 0.000 0.252 0.748 0.000
#> GSM372296 4 0.0713 0.843 0.000 0.028 0.000 0.972 0.000 0.000
#> GSM372297 4 0.1327 0.830 0.000 0.000 0.000 0.936 0.000 0.064
#> GSM372298 4 0.2431 0.785 0.000 0.008 0.000 0.860 0.000 0.132
#> GSM372299 5 0.3860 0.702 0.000 0.000 0.000 0.072 0.764 0.164
#> GSM372300 6 0.3266 0.455 0.000 0.000 0.000 0.272 0.000 0.728
#> GSM372301 6 0.3789 0.213 0.000 0.000 0.000 0.416 0.000 0.584
#> GSM372302 4 0.0000 0.848 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM372303 6 0.3699 0.387 0.000 0.000 0.004 0.336 0.000 0.660
#> GSM372304 4 0.0632 0.847 0.000 0.000 0.000 0.976 0.000 0.024
#> GSM372305 2 0.2414 0.784 0.000 0.896 0.012 0.012 0.072 0.008
#> GSM372306 2 0.2784 0.744 0.000 0.848 0.132 0.000 0.008 0.012
#> GSM372307 5 0.5865 0.559 0.000 0.248 0.004 0.208 0.536 0.004
#> GSM372309 5 0.3186 0.808 0.000 0.100 0.004 0.060 0.836 0.000
#> GSM372311 2 0.1075 0.795 0.000 0.952 0.000 0.000 0.048 0.000
#> GSM372313 2 0.0363 0.795 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM372315 2 0.2277 0.767 0.000 0.892 0.000 0.032 0.076 0.000
#> GSM372317 2 0.4138 0.512 0.000 0.664 0.312 0.000 0.012 0.012
#> GSM372319 3 0.1434 0.801 0.000 0.008 0.948 0.000 0.024 0.020
#> GSM372321 3 0.0622 0.807 0.000 0.000 0.980 0.000 0.008 0.012
#> GSM372323 3 0.1285 0.796 0.000 0.004 0.944 0.000 0.000 0.052
#> GSM372326 6 0.5341 0.370 0.000 0.000 0.312 0.000 0.132 0.556
#> GSM372328 3 0.3351 0.509 0.000 0.000 0.712 0.000 0.000 0.288
#> GSM372330 2 0.1176 0.797 0.000 0.956 0.000 0.000 0.020 0.024
#> GSM372332 3 0.0632 0.807 0.000 0.000 0.976 0.000 0.000 0.024
#> GSM372335 2 0.3800 0.726 0.000 0.776 0.048 0.000 0.008 0.168
#> GSM372337 3 0.1010 0.806 0.000 0.000 0.960 0.000 0.004 0.036
#> GSM372339 3 0.1075 0.802 0.000 0.000 0.952 0.000 0.000 0.048
#> GSM372341 3 0.2491 0.703 0.000 0.000 0.836 0.000 0.000 0.164
#> GSM372343 6 0.3804 0.170 0.000 0.000 0.424 0.000 0.000 0.576
#> GSM372345 3 0.0870 0.801 0.000 0.012 0.972 0.000 0.004 0.012
#> GSM372347 3 0.4433 0.191 0.000 0.416 0.560 0.000 0.008 0.016
#> GSM372349 3 0.4479 0.592 0.000 0.004 0.736 0.012 0.168 0.080
#> GSM372351 6 0.3854 0.091 0.000 0.000 0.464 0.000 0.000 0.536
#> GSM372353 6 0.6102 0.411 0.000 0.184 0.132 0.000 0.084 0.600
#> GSM372355 2 0.1075 0.795 0.000 0.952 0.000 0.000 0.048 0.000
#> GSM372357 5 0.3053 0.749 0.000 0.172 0.012 0.004 0.812 0.000
#> GSM372359 2 0.2980 0.724 0.000 0.808 0.000 0.000 0.012 0.180
#> GSM372361 5 0.2859 0.790 0.000 0.016 0.000 0.156 0.828 0.000
#> GSM372363 5 0.3448 0.809 0.000 0.108 0.004 0.072 0.816 0.000
#> GSM372308 1 0.2191 0.830 0.876 0.004 0.000 0.000 0.120 0.000
#> GSM372310 1 0.0000 0.929 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372312 1 0.6808 0.521 0.604 0.048 0.088 0.020 0.180 0.060
#> GSM372314 1 0.4486 0.334 0.584 0.388 0.020 0.000 0.004 0.004
#> GSM372316 1 0.0000 0.929 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372318 1 0.0000 0.929 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372320 1 0.0000 0.929 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372322 1 0.0000 0.929 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372324 1 0.2165 0.871 0.912 0.024 0.052 0.000 0.008 0.004
#> GSM372325 1 0.6684 0.168 0.472 0.264 0.224 0.000 0.020 0.020
#> GSM372327 1 0.0000 0.929 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372329 1 0.0000 0.929 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372331 2 0.3213 0.576 0.204 0.784 0.004 0.000 0.008 0.000
#> GSM372333 3 0.3705 0.644 0.000 0.180 0.776 0.000 0.008 0.036
#> GSM372334 1 0.0000 0.929 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372336 1 0.0146 0.927 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM372338 1 0.0000 0.929 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372340 1 0.0000 0.929 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372342 1 0.0000 0.929 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372344 1 0.0000 0.929 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372346 1 0.0000 0.929 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372348 1 0.1760 0.885 0.928 0.020 0.004 0.000 0.048 0.000
#> GSM372350 1 0.5208 0.656 0.708 0.004 0.040 0.020 0.176 0.052
#> GSM372352 2 0.6205 0.486 0.008 0.572 0.020 0.008 0.176 0.216
#> GSM372354 1 0.0000 0.929 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372356 1 0.0000 0.929 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372358 1 0.0000 0.929 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372360 1 0.0000 0.929 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372362 1 0.0000 0.929 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372364 1 0.0000 0.929 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372365 1 0.2219 0.817 0.864 0.000 0.000 0.000 0.136 0.000
#> GSM372366 1 0.0000 0.929 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372367 1 0.0146 0.927 0.996 0.000 0.004 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) specimen(p) individual(p) k
#> CV:NMF 81 9.58e-05 1.96e-17 1.000 2
#> CV:NMF 79 1.70e-06 8.58e-19 0.949 3
#> CV:NMF 78 6.13e-14 1.15e-26 0.845 4
#> CV:NMF 64 4.36e-11 1.05e-21 0.703 5
#> CV:NMF 70 1.39e-09 4.58e-18 0.190 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 51941 rows and 82 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.979 0.990 0.4802 0.518 0.518
#> 3 3 0.721 0.768 0.883 0.3347 0.819 0.651
#> 4 4 0.692 0.725 0.826 0.1024 0.921 0.787
#> 5 5 0.635 0.587 0.773 0.0742 0.890 0.680
#> 6 6 0.679 0.675 0.793 0.0293 0.955 0.820
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
#> GSM372286 2 0.0000 0.994 0.000 1.000
#> GSM372287 2 0.0000 0.994 0.000 1.000
#> GSM372288 2 0.0000 0.994 0.000 1.000
#> GSM372289 2 0.0000 0.994 0.000 1.000
#> GSM372290 2 0.0000 0.994 0.000 1.000
#> GSM372291 1 0.7376 0.753 0.792 0.208
#> GSM372292 2 0.0000 0.994 0.000 1.000
#> GSM372293 2 0.0000 0.994 0.000 1.000
#> GSM372294 2 0.0000 0.994 0.000 1.000
#> GSM372295 2 0.0000 0.994 0.000 1.000
#> GSM372296 2 0.0000 0.994 0.000 1.000
#> GSM372297 2 0.0000 0.994 0.000 1.000
#> GSM372298 2 0.0000 0.994 0.000 1.000
#> GSM372299 2 0.0000 0.994 0.000 1.000
#> GSM372300 2 0.0000 0.994 0.000 1.000
#> GSM372301 2 0.0000 0.994 0.000 1.000
#> GSM372302 2 0.0000 0.994 0.000 1.000
#> GSM372303 2 0.0000 0.994 0.000 1.000
#> GSM372304 2 0.0000 0.994 0.000 1.000
#> GSM372305 2 0.0000 0.994 0.000 1.000
#> GSM372306 2 0.0000 0.994 0.000 1.000
#> GSM372307 2 0.0000 0.994 0.000 1.000
#> GSM372309 2 0.0000 0.994 0.000 1.000
#> GSM372311 2 0.0000 0.994 0.000 1.000
#> GSM372313 2 0.0000 0.994 0.000 1.000
#> GSM372315 2 0.0000 0.994 0.000 1.000
#> GSM372317 2 0.0000 0.994 0.000 1.000
#> GSM372319 2 0.0000 0.994 0.000 1.000
#> GSM372321 2 0.0000 0.994 0.000 1.000
#> GSM372323 2 0.0672 0.988 0.008 0.992
#> GSM372326 2 0.0000 0.994 0.000 1.000
#> GSM372328 2 0.0000 0.994 0.000 1.000
#> GSM372330 2 0.0000 0.994 0.000 1.000
#> GSM372332 2 0.0000 0.994 0.000 1.000
#> GSM372335 2 0.0000 0.994 0.000 1.000
#> GSM372337 2 0.0000 0.994 0.000 1.000
#> GSM372339 2 0.0000 0.994 0.000 1.000
#> GSM372341 2 0.0000 0.994 0.000 1.000
#> GSM372343 2 0.0000 0.994 0.000 1.000
#> GSM372345 2 0.0672 0.988 0.008 0.992
#> GSM372347 2 0.0672 0.988 0.008 0.992
#> GSM372349 2 0.0376 0.991 0.004 0.996
#> GSM372351 2 0.0000 0.994 0.000 1.000
#> GSM372353 2 0.0000 0.994 0.000 1.000
#> GSM372355 2 0.0000 0.994 0.000 1.000
#> GSM372357 2 0.0000 0.994 0.000 1.000
#> GSM372359 2 0.0000 0.994 0.000 1.000
#> GSM372361 2 0.0000 0.994 0.000 1.000
#> GSM372363 2 0.0000 0.994 0.000 1.000
#> GSM372308 1 0.0938 0.976 0.988 0.012
#> GSM372310 1 0.0938 0.976 0.988 0.012
#> GSM372312 1 0.5842 0.847 0.860 0.140
#> GSM372314 1 0.0938 0.976 0.988 0.012
#> GSM372316 1 0.0000 0.982 1.000 0.000
#> GSM372318 1 0.0000 0.982 1.000 0.000
#> GSM372320 1 0.0000 0.982 1.000 0.000
#> GSM372322 1 0.0000 0.982 1.000 0.000
#> GSM372324 1 0.0938 0.976 0.988 0.012
#> GSM372325 1 0.0938 0.976 0.988 0.012
#> GSM372327 1 0.0000 0.982 1.000 0.000
#> GSM372329 1 0.0000 0.982 1.000 0.000
#> GSM372331 1 0.0000 0.982 1.000 0.000
#> GSM372333 2 0.7883 0.683 0.236 0.764
#> GSM372334 1 0.0000 0.982 1.000 0.000
#> GSM372336 1 0.0000 0.982 1.000 0.000
#> GSM372338 1 0.0000 0.982 1.000 0.000
#> GSM372340 1 0.0000 0.982 1.000 0.000
#> GSM372342 1 0.0000 0.982 1.000 0.000
#> GSM372344 1 0.0000 0.982 1.000 0.000
#> GSM372346 1 0.0000 0.982 1.000 0.000
#> GSM372348 1 0.0000 0.982 1.000 0.000
#> GSM372350 1 0.5737 0.852 0.864 0.136
#> GSM372352 2 0.0376 0.991 0.004 0.996
#> GSM372354 1 0.0000 0.982 1.000 0.000
#> GSM372356 1 0.0000 0.982 1.000 0.000
#> GSM372358 1 0.0000 0.982 1.000 0.000
#> GSM372360 1 0.0000 0.982 1.000 0.000
#> GSM372362 1 0.0000 0.982 1.000 0.000
#> GSM372364 1 0.0000 0.982 1.000 0.000
#> GSM372365 1 0.0000 0.982 1.000 0.000
#> GSM372366 1 0.0000 0.982 1.000 0.000
#> GSM372367 1 0.0000 0.982 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM372286 2 0.1964 0.78142 0.000 0.944 0.056
#> GSM372287 2 0.1163 0.78828 0.000 0.972 0.028
#> GSM372288 2 0.0000 0.79224 0.000 1.000 0.000
#> GSM372289 2 0.0000 0.79224 0.000 1.000 0.000
#> GSM372290 2 0.0592 0.79899 0.000 0.988 0.012
#> GSM372291 1 0.5402 0.79565 0.792 0.028 0.180
#> GSM372292 2 0.5497 0.47965 0.000 0.708 0.292
#> GSM372293 3 0.5678 0.58792 0.000 0.316 0.684
#> GSM372294 2 0.3752 0.68079 0.000 0.856 0.144
#> GSM372295 2 0.5968 0.29912 0.000 0.636 0.364
#> GSM372296 2 0.0892 0.79986 0.000 0.980 0.020
#> GSM372297 2 0.1163 0.78828 0.000 0.972 0.028
#> GSM372298 2 0.0892 0.80100 0.000 0.980 0.020
#> GSM372299 2 0.5968 0.29912 0.000 0.636 0.364
#> GSM372300 3 0.5678 0.58792 0.000 0.316 0.684
#> GSM372301 2 0.5497 0.47965 0.000 0.708 0.292
#> GSM372302 2 0.0892 0.79986 0.000 0.980 0.020
#> GSM372303 3 0.5678 0.58792 0.000 0.316 0.684
#> GSM372304 2 0.1163 0.78828 0.000 0.972 0.028
#> GSM372305 2 0.5650 0.40104 0.000 0.688 0.312
#> GSM372306 2 0.5948 0.27246 0.000 0.640 0.360
#> GSM372307 2 0.0592 0.79899 0.000 0.988 0.012
#> GSM372309 2 0.6008 0.22834 0.000 0.628 0.372
#> GSM372311 2 0.0892 0.80091 0.000 0.980 0.020
#> GSM372313 2 0.0892 0.80091 0.000 0.980 0.020
#> GSM372315 2 0.0892 0.80091 0.000 0.980 0.020
#> GSM372317 2 0.1289 0.79780 0.000 0.968 0.032
#> GSM372319 3 0.5650 0.70871 0.000 0.312 0.688
#> GSM372321 3 0.5650 0.70871 0.000 0.312 0.688
#> GSM372323 3 0.5896 0.72965 0.008 0.292 0.700
#> GSM372326 3 0.5650 0.71005 0.000 0.312 0.688
#> GSM372328 3 0.1860 0.72987 0.000 0.052 0.948
#> GSM372330 2 0.0892 0.80091 0.000 0.980 0.020
#> GSM372332 3 0.1964 0.73141 0.000 0.056 0.944
#> GSM372335 3 0.6309 0.23324 0.000 0.496 0.504
#> GSM372337 3 0.4842 0.76923 0.000 0.224 0.776
#> GSM372339 3 0.1860 0.72987 0.000 0.052 0.948
#> GSM372341 3 0.1860 0.72987 0.000 0.052 0.948
#> GSM372343 3 0.1860 0.72987 0.000 0.052 0.948
#> GSM372345 3 0.5247 0.76876 0.008 0.224 0.768
#> GSM372347 3 0.5247 0.76876 0.008 0.224 0.768
#> GSM372349 3 0.5070 0.77020 0.004 0.224 0.772
#> GSM372351 3 0.5650 0.71005 0.000 0.312 0.688
#> GSM372353 2 0.6225 0.00757 0.000 0.568 0.432
#> GSM372355 2 0.1031 0.80017 0.000 0.976 0.024
#> GSM372357 2 0.6225 0.00757 0.000 0.568 0.432
#> GSM372359 2 0.6225 0.00757 0.000 0.568 0.432
#> GSM372361 2 0.0747 0.80031 0.000 0.984 0.016
#> GSM372363 2 0.0892 0.80091 0.000 0.980 0.020
#> GSM372308 1 0.0592 0.97831 0.988 0.000 0.012
#> GSM372310 1 0.0592 0.97831 0.988 0.000 0.012
#> GSM372312 1 0.3686 0.87268 0.860 0.000 0.140
#> GSM372314 1 0.0592 0.97831 0.988 0.000 0.012
#> GSM372316 1 0.0000 0.98459 1.000 0.000 0.000
#> GSM372318 1 0.0000 0.98459 1.000 0.000 0.000
#> GSM372320 1 0.0000 0.98459 1.000 0.000 0.000
#> GSM372322 1 0.0000 0.98459 1.000 0.000 0.000
#> GSM372324 1 0.0592 0.97831 0.988 0.000 0.012
#> GSM372325 1 0.0592 0.97831 0.988 0.000 0.012
#> GSM372327 1 0.0000 0.98459 1.000 0.000 0.000
#> GSM372329 1 0.0000 0.98459 1.000 0.000 0.000
#> GSM372331 1 0.0000 0.98459 1.000 0.000 0.000
#> GSM372333 3 0.7673 0.56017 0.236 0.100 0.664
#> GSM372334 1 0.0000 0.98459 1.000 0.000 0.000
#> GSM372336 1 0.0000 0.98459 1.000 0.000 0.000
#> GSM372338 1 0.0000 0.98459 1.000 0.000 0.000
#> GSM372340 1 0.0000 0.98459 1.000 0.000 0.000
#> GSM372342 1 0.0000 0.98459 1.000 0.000 0.000
#> GSM372344 1 0.0000 0.98459 1.000 0.000 0.000
#> GSM372346 1 0.0000 0.98459 1.000 0.000 0.000
#> GSM372348 1 0.0000 0.98459 1.000 0.000 0.000
#> GSM372350 1 0.3619 0.87669 0.864 0.000 0.136
#> GSM372352 3 0.5070 0.77020 0.004 0.224 0.772
#> GSM372354 1 0.0000 0.98459 1.000 0.000 0.000
#> GSM372356 1 0.0000 0.98459 1.000 0.000 0.000
#> GSM372358 1 0.0000 0.98459 1.000 0.000 0.000
#> GSM372360 1 0.0000 0.98459 1.000 0.000 0.000
#> GSM372362 1 0.0000 0.98459 1.000 0.000 0.000
#> GSM372364 1 0.0000 0.98459 1.000 0.000 0.000
#> GSM372365 1 0.0000 0.98459 1.000 0.000 0.000
#> GSM372366 1 0.0000 0.98459 1.000 0.000 0.000
#> GSM372367 1 0.0000 0.98459 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM372286 2 0.2805 0.794 0.000 0.888 0.100 0.012
#> GSM372287 2 0.2647 0.784 0.000 0.880 0.000 0.120
#> GSM372288 2 0.1474 0.807 0.000 0.948 0.000 0.052
#> GSM372289 2 0.1474 0.807 0.000 0.948 0.000 0.052
#> GSM372290 2 0.1635 0.831 0.000 0.948 0.044 0.008
#> GSM372291 1 0.4468 0.754 0.752 0.000 0.016 0.232
#> GSM372292 2 0.7486 0.215 0.000 0.500 0.272 0.228
#> GSM372293 3 0.7149 0.517 0.000 0.132 0.452 0.416
#> GSM372294 2 0.4012 0.721 0.000 0.800 0.016 0.184
#> GSM372295 3 0.7456 0.346 0.000 0.308 0.492 0.200
#> GSM372296 2 0.2179 0.820 0.000 0.924 0.012 0.064
#> GSM372297 2 0.2868 0.782 0.000 0.864 0.000 0.136
#> GSM372298 2 0.4491 0.716 0.000 0.800 0.060 0.140
#> GSM372299 3 0.7456 0.346 0.000 0.308 0.492 0.200
#> GSM372300 3 0.7149 0.517 0.000 0.132 0.452 0.416
#> GSM372301 2 0.7486 0.215 0.000 0.500 0.272 0.228
#> GSM372302 2 0.2179 0.820 0.000 0.924 0.012 0.064
#> GSM372303 3 0.7149 0.517 0.000 0.132 0.452 0.416
#> GSM372304 2 0.2868 0.782 0.000 0.864 0.000 0.136
#> GSM372305 2 0.4994 -0.100 0.000 0.520 0.480 0.000
#> GSM372306 3 0.4989 0.198 0.000 0.472 0.528 0.000
#> GSM372307 2 0.1635 0.831 0.000 0.948 0.044 0.008
#> GSM372309 2 0.4998 -0.157 0.000 0.512 0.488 0.000
#> GSM372311 2 0.1118 0.832 0.000 0.964 0.036 0.000
#> GSM372313 2 0.1118 0.832 0.000 0.964 0.036 0.000
#> GSM372315 2 0.1118 0.832 0.000 0.964 0.036 0.000
#> GSM372317 2 0.1389 0.828 0.000 0.952 0.048 0.000
#> GSM372319 3 0.3377 0.687 0.000 0.140 0.848 0.012
#> GSM372321 3 0.3377 0.687 0.000 0.140 0.848 0.012
#> GSM372323 3 0.2918 0.692 0.000 0.116 0.876 0.008
#> GSM372326 3 0.3479 0.684 0.000 0.148 0.840 0.012
#> GSM372328 3 0.4699 0.607 0.000 0.004 0.676 0.320
#> GSM372330 2 0.1118 0.832 0.000 0.964 0.036 0.000
#> GSM372332 3 0.4608 0.615 0.000 0.004 0.692 0.304
#> GSM372335 3 0.4522 0.513 0.000 0.320 0.680 0.000
#> GSM372337 3 0.1022 0.698 0.000 0.032 0.968 0.000
#> GSM372339 3 0.4699 0.607 0.000 0.004 0.676 0.320
#> GSM372341 3 0.4699 0.607 0.000 0.004 0.676 0.320
#> GSM372343 3 0.4699 0.607 0.000 0.004 0.676 0.320
#> GSM372345 3 0.1356 0.698 0.000 0.032 0.960 0.008
#> GSM372347 3 0.1356 0.698 0.000 0.032 0.960 0.008
#> GSM372349 3 0.1356 0.699 0.000 0.032 0.960 0.008
#> GSM372351 3 0.3479 0.684 0.000 0.148 0.840 0.012
#> GSM372353 3 0.4830 0.400 0.000 0.392 0.608 0.000
#> GSM372355 2 0.1211 0.831 0.000 0.960 0.040 0.000
#> GSM372357 3 0.4830 0.400 0.000 0.392 0.608 0.000
#> GSM372359 3 0.4830 0.400 0.000 0.392 0.608 0.000
#> GSM372361 2 0.1890 0.828 0.000 0.936 0.056 0.008
#> GSM372363 2 0.1389 0.828 0.000 0.952 0.048 0.000
#> GSM372308 1 0.4284 0.852 0.764 0.000 0.012 0.224
#> GSM372310 1 0.4284 0.852 0.764 0.000 0.012 0.224
#> GSM372312 1 0.4883 0.800 0.696 0.000 0.016 0.288
#> GSM372314 1 0.4576 0.830 0.728 0.000 0.012 0.260
#> GSM372316 1 0.0188 0.920 0.996 0.000 0.000 0.004
#> GSM372318 1 0.0000 0.920 1.000 0.000 0.000 0.000
#> GSM372320 1 0.0000 0.920 1.000 0.000 0.000 0.000
#> GSM372322 1 0.0000 0.920 1.000 0.000 0.000 0.000
#> GSM372324 1 0.4576 0.830 0.728 0.000 0.012 0.260
#> GSM372325 1 0.4576 0.830 0.728 0.000 0.012 0.260
#> GSM372327 1 0.0000 0.920 1.000 0.000 0.000 0.000
#> GSM372329 1 0.0000 0.920 1.000 0.000 0.000 0.000
#> GSM372331 1 0.4134 0.836 0.740 0.000 0.000 0.260
#> GSM372333 3 0.5731 0.581 0.128 0.016 0.744 0.112
#> GSM372334 1 0.0000 0.920 1.000 0.000 0.000 0.000
#> GSM372336 1 0.3569 0.870 0.804 0.000 0.000 0.196
#> GSM372338 1 0.0000 0.920 1.000 0.000 0.000 0.000
#> GSM372340 1 0.0000 0.920 1.000 0.000 0.000 0.000
#> GSM372342 1 0.0000 0.920 1.000 0.000 0.000 0.000
#> GSM372344 1 0.0000 0.920 1.000 0.000 0.000 0.000
#> GSM372346 1 0.0000 0.920 1.000 0.000 0.000 0.000
#> GSM372348 1 0.3569 0.870 0.804 0.000 0.000 0.196
#> GSM372350 1 0.3625 0.820 0.828 0.000 0.012 0.160
#> GSM372352 3 0.1356 0.699 0.000 0.032 0.960 0.008
#> GSM372354 1 0.0000 0.920 1.000 0.000 0.000 0.000
#> GSM372356 1 0.1474 0.916 0.948 0.000 0.000 0.052
#> GSM372358 1 0.1302 0.917 0.956 0.000 0.000 0.044
#> GSM372360 1 0.1302 0.917 0.956 0.000 0.000 0.044
#> GSM372362 1 0.1302 0.917 0.956 0.000 0.000 0.044
#> GSM372364 1 0.1474 0.916 0.948 0.000 0.000 0.052
#> GSM372365 1 0.2149 0.908 0.912 0.000 0.000 0.088
#> GSM372366 1 0.0000 0.920 1.000 0.000 0.000 0.000
#> GSM372367 1 0.2921 0.893 0.860 0.000 0.000 0.140
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM372286 2 0.2522 0.7840 0.000 0.880 0.108 0.012 0.000
#> GSM372287 2 0.3909 0.7210 0.000 0.760 0.000 0.216 0.024
#> GSM372288 2 0.2208 0.7986 0.000 0.908 0.000 0.072 0.020
#> GSM372289 2 0.2208 0.7986 0.000 0.908 0.000 0.072 0.020
#> GSM372290 2 0.1701 0.8289 0.000 0.936 0.048 0.016 0.000
#> GSM372291 1 0.4930 0.4212 0.684 0.000 0.000 0.072 0.244
#> GSM372292 2 0.6557 -0.1118 0.000 0.440 0.208 0.352 0.000
#> GSM372293 4 0.5359 1.0000 0.000 0.076 0.316 0.608 0.000
#> GSM372294 2 0.4496 0.7437 0.000 0.764 0.008 0.072 0.156
#> GSM372295 3 0.6290 0.1124 0.000 0.088 0.448 0.444 0.020
#> GSM372296 2 0.2984 0.8069 0.000 0.856 0.016 0.124 0.004
#> GSM372297 2 0.3970 0.7131 0.000 0.744 0.000 0.236 0.020
#> GSM372298 2 0.4073 0.6640 0.000 0.752 0.032 0.216 0.000
#> GSM372299 3 0.6290 0.1124 0.000 0.088 0.448 0.444 0.020
#> GSM372300 4 0.5359 1.0000 0.000 0.076 0.316 0.608 0.000
#> GSM372301 2 0.6557 -0.1118 0.000 0.440 0.208 0.352 0.000
#> GSM372302 2 0.2984 0.8069 0.000 0.856 0.016 0.124 0.004
#> GSM372303 4 0.5359 1.0000 0.000 0.076 0.316 0.608 0.000
#> GSM372304 2 0.3970 0.7131 0.000 0.744 0.000 0.236 0.020
#> GSM372305 3 0.4702 0.2258 0.000 0.476 0.512 0.004 0.008
#> GSM372306 3 0.4651 0.3482 0.000 0.428 0.560 0.004 0.008
#> GSM372307 2 0.1597 0.8284 0.000 0.940 0.048 0.012 0.000
#> GSM372309 3 0.4909 0.2369 0.000 0.472 0.508 0.012 0.008
#> GSM372311 2 0.1569 0.8265 0.000 0.944 0.044 0.004 0.008
#> GSM372313 2 0.1644 0.8261 0.000 0.940 0.048 0.004 0.008
#> GSM372315 2 0.1408 0.8275 0.000 0.948 0.044 0.000 0.008
#> GSM372317 2 0.1788 0.8238 0.000 0.932 0.056 0.004 0.008
#> GSM372319 3 0.2773 0.4717 0.000 0.112 0.868 0.020 0.000
#> GSM372321 3 0.2773 0.4717 0.000 0.112 0.868 0.020 0.000
#> GSM372323 3 0.2689 0.4676 0.000 0.084 0.888 0.012 0.016
#> GSM372326 3 0.3096 0.4705 0.000 0.108 0.860 0.024 0.008
#> GSM372328 3 0.4528 -0.3994 0.000 0.000 0.548 0.444 0.008
#> GSM372330 2 0.1408 0.8275 0.000 0.948 0.044 0.000 0.008
#> GSM372332 3 0.4219 -0.3835 0.000 0.000 0.584 0.416 0.000
#> GSM372335 3 0.4088 0.4545 0.000 0.276 0.712 0.004 0.008
#> GSM372337 3 0.0968 0.4333 0.000 0.004 0.972 0.012 0.012
#> GSM372339 3 0.4528 -0.3994 0.000 0.000 0.548 0.444 0.008
#> GSM372341 3 0.4528 -0.3994 0.000 0.000 0.548 0.444 0.008
#> GSM372343 3 0.4528 -0.3994 0.000 0.000 0.548 0.444 0.008
#> GSM372345 3 0.1173 0.4360 0.000 0.004 0.964 0.012 0.020
#> GSM372347 3 0.1173 0.4360 0.000 0.004 0.964 0.012 0.020
#> GSM372349 3 0.1267 0.4349 0.000 0.004 0.960 0.024 0.012
#> GSM372351 3 0.3096 0.4705 0.000 0.108 0.860 0.024 0.008
#> GSM372353 3 0.4434 0.4356 0.000 0.348 0.640 0.004 0.008
#> GSM372355 2 0.1717 0.8243 0.000 0.936 0.052 0.004 0.008
#> GSM372357 3 0.4434 0.4356 0.000 0.348 0.640 0.004 0.008
#> GSM372359 3 0.4434 0.4356 0.000 0.348 0.640 0.004 0.008
#> GSM372361 2 0.1914 0.8239 0.000 0.924 0.060 0.016 0.000
#> GSM372363 2 0.2199 0.8225 0.000 0.916 0.060 0.016 0.008
#> GSM372308 5 0.3966 0.8190 0.336 0.000 0.000 0.000 0.664
#> GSM372310 5 0.3966 0.8190 0.336 0.000 0.000 0.000 0.664
#> GSM372312 5 0.4641 0.0489 0.456 0.000 0.000 0.012 0.532
#> GSM372314 5 0.3612 0.8330 0.268 0.000 0.000 0.000 0.732
#> GSM372316 1 0.0609 0.8508 0.980 0.000 0.000 0.000 0.020
#> GSM372318 1 0.0404 0.8547 0.988 0.000 0.000 0.000 0.012
#> GSM372320 1 0.0000 0.8566 1.000 0.000 0.000 0.000 0.000
#> GSM372322 1 0.0162 0.8567 0.996 0.000 0.000 0.000 0.004
#> GSM372324 5 0.3612 0.8330 0.268 0.000 0.000 0.000 0.732
#> GSM372325 5 0.3612 0.8330 0.268 0.000 0.000 0.000 0.732
#> GSM372327 1 0.0000 0.8566 1.000 0.000 0.000 0.000 0.000
#> GSM372329 1 0.0000 0.8566 1.000 0.000 0.000 0.000 0.000
#> GSM372331 5 0.3684 0.8327 0.280 0.000 0.000 0.000 0.720
#> GSM372333 3 0.4082 0.2433 0.008 0.000 0.740 0.012 0.240
#> GSM372334 1 0.0000 0.8566 1.000 0.000 0.000 0.000 0.000
#> GSM372336 5 0.4219 0.7298 0.416 0.000 0.000 0.000 0.584
#> GSM372338 1 0.0000 0.8566 1.000 0.000 0.000 0.000 0.000
#> GSM372340 1 0.0000 0.8566 1.000 0.000 0.000 0.000 0.000
#> GSM372342 1 0.0000 0.8566 1.000 0.000 0.000 0.000 0.000
#> GSM372344 1 0.0000 0.8566 1.000 0.000 0.000 0.000 0.000
#> GSM372346 1 0.0162 0.8567 0.996 0.000 0.000 0.000 0.004
#> GSM372348 5 0.4219 0.7298 0.416 0.000 0.000 0.000 0.584
#> GSM372350 1 0.3642 0.5285 0.760 0.000 0.000 0.008 0.232
#> GSM372352 3 0.1267 0.4349 0.000 0.004 0.960 0.024 0.012
#> GSM372354 1 0.0290 0.8557 0.992 0.000 0.000 0.000 0.008
#> GSM372356 1 0.2690 0.7190 0.844 0.000 0.000 0.000 0.156
#> GSM372358 1 0.2561 0.7347 0.856 0.000 0.000 0.000 0.144
#> GSM372360 1 0.2561 0.7347 0.856 0.000 0.000 0.000 0.144
#> GSM372362 1 0.2561 0.7347 0.856 0.000 0.000 0.000 0.144
#> GSM372364 1 0.2690 0.7190 0.844 0.000 0.000 0.000 0.156
#> GSM372365 1 0.3242 0.5954 0.784 0.000 0.000 0.000 0.216
#> GSM372366 1 0.0510 0.8529 0.984 0.000 0.000 0.000 0.016
#> GSM372367 1 0.3837 0.3160 0.692 0.000 0.000 0.000 0.308
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM372286 4 0.2218 0.7461 0.000 0.104 0.000 0.884 0.000 0.012
#> GSM372287 4 0.3670 0.6394 0.000 0.000 0.024 0.736 0.000 0.240
#> GSM372288 4 0.1858 0.7642 0.000 0.000 0.004 0.904 0.000 0.092
#> GSM372289 4 0.1858 0.7642 0.000 0.000 0.004 0.904 0.000 0.092
#> GSM372290 4 0.1391 0.7945 0.000 0.040 0.000 0.944 0.000 0.016
#> GSM372291 1 0.7335 0.0156 0.412 0.000 0.224 0.000 0.216 0.148
#> GSM372292 4 0.7527 -0.1297 0.000 0.168 0.260 0.356 0.000 0.216
#> GSM372293 3 0.5579 0.6036 0.000 0.256 0.564 0.004 0.000 0.176
#> GSM372294 4 0.4365 0.6930 0.000 0.008 0.020 0.768 0.120 0.084
#> GSM372295 6 0.3720 1.0000 0.000 0.108 0.036 0.044 0.000 0.812
#> GSM372296 4 0.2883 0.7607 0.000 0.012 0.012 0.844 0.000 0.132
#> GSM372297 4 0.3778 0.6204 0.000 0.000 0.020 0.708 0.000 0.272
#> GSM372298 4 0.4792 0.5217 0.000 0.000 0.148 0.672 0.000 0.180
#> GSM372299 6 0.3720 1.0000 0.000 0.108 0.036 0.044 0.000 0.812
#> GSM372300 3 0.5579 0.6036 0.000 0.256 0.564 0.004 0.000 0.176
#> GSM372301 4 0.7527 -0.1297 0.000 0.168 0.260 0.356 0.000 0.216
#> GSM372302 4 0.2883 0.7607 0.000 0.012 0.012 0.844 0.000 0.132
#> GSM372303 3 0.5579 0.6036 0.000 0.256 0.564 0.004 0.000 0.176
#> GSM372304 4 0.3778 0.6204 0.000 0.000 0.020 0.708 0.000 0.272
#> GSM372305 2 0.4184 0.3709 0.000 0.504 0.000 0.484 0.000 0.012
#> GSM372306 2 0.4147 0.4881 0.000 0.552 0.000 0.436 0.000 0.012
#> GSM372307 4 0.1297 0.7941 0.000 0.040 0.000 0.948 0.000 0.012
#> GSM372309 2 0.4535 0.3643 0.000 0.488 0.000 0.480 0.000 0.032
#> GSM372311 4 0.1225 0.7929 0.000 0.036 0.000 0.952 0.000 0.012
#> GSM372313 4 0.1297 0.7923 0.000 0.040 0.000 0.948 0.000 0.012
#> GSM372315 4 0.1124 0.7941 0.000 0.036 0.000 0.956 0.000 0.008
#> GSM372317 4 0.1434 0.7902 0.000 0.048 0.000 0.940 0.000 0.012
#> GSM372319 2 0.2843 0.6485 0.000 0.848 0.036 0.116 0.000 0.000
#> GSM372321 2 0.2843 0.6485 0.000 0.848 0.036 0.116 0.000 0.000
#> GSM372323 2 0.2529 0.6500 0.000 0.884 0.012 0.088 0.008 0.008
#> GSM372326 2 0.2844 0.6560 0.000 0.856 0.020 0.112 0.000 0.012
#> GSM372328 3 0.3737 0.7767 0.000 0.392 0.608 0.000 0.000 0.000
#> GSM372330 4 0.1124 0.7941 0.000 0.036 0.000 0.956 0.000 0.008
#> GSM372332 3 0.4264 0.7142 0.000 0.488 0.496 0.000 0.000 0.016
#> GSM372335 2 0.3650 0.6353 0.000 0.708 0.000 0.280 0.000 0.012
#> GSM372337 2 0.0622 0.5630 0.000 0.980 0.012 0.000 0.008 0.000
#> GSM372339 3 0.3737 0.7767 0.000 0.392 0.608 0.000 0.000 0.000
#> GSM372341 3 0.3737 0.7767 0.000 0.392 0.608 0.000 0.000 0.000
#> GSM372343 3 0.3737 0.7767 0.000 0.392 0.608 0.000 0.000 0.000
#> GSM372345 2 0.0820 0.5664 0.000 0.972 0.012 0.000 0.016 0.000
#> GSM372347 2 0.0820 0.5664 0.000 0.972 0.012 0.000 0.016 0.000
#> GSM372349 2 0.0976 0.5656 0.000 0.968 0.016 0.000 0.008 0.008
#> GSM372351 2 0.2844 0.6560 0.000 0.856 0.020 0.112 0.000 0.012
#> GSM372353 2 0.3967 0.5976 0.000 0.632 0.000 0.356 0.000 0.012
#> GSM372355 4 0.1367 0.7904 0.000 0.044 0.000 0.944 0.000 0.012
#> GSM372357 2 0.3967 0.5976 0.000 0.632 0.000 0.356 0.000 0.012
#> GSM372359 2 0.3967 0.5976 0.000 0.632 0.000 0.356 0.000 0.012
#> GSM372361 4 0.1644 0.7910 0.000 0.040 0.000 0.932 0.000 0.028
#> GSM372363 4 0.1765 0.7884 0.000 0.052 0.000 0.924 0.000 0.024
#> GSM372308 5 0.3405 0.8217 0.272 0.004 0.000 0.000 0.724 0.000
#> GSM372310 5 0.3405 0.8217 0.272 0.004 0.000 0.000 0.724 0.000
#> GSM372312 5 0.6436 0.2753 0.252 0.004 0.128 0.000 0.544 0.072
#> GSM372314 5 0.2964 0.8328 0.204 0.004 0.000 0.000 0.792 0.000
#> GSM372316 1 0.0547 0.8333 0.980 0.000 0.000 0.000 0.020 0.000
#> GSM372318 1 0.0363 0.8365 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM372320 1 0.0000 0.8381 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372322 1 0.0146 0.8382 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM372324 5 0.2964 0.8328 0.204 0.004 0.000 0.000 0.792 0.000
#> GSM372325 5 0.2964 0.8328 0.204 0.004 0.000 0.000 0.792 0.000
#> GSM372327 1 0.0000 0.8381 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372329 1 0.0000 0.8381 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372331 5 0.2912 0.8355 0.216 0.000 0.000 0.000 0.784 0.000
#> GSM372333 2 0.4073 0.3134 0.008 0.728 0.012 0.000 0.236 0.016
#> GSM372334 1 0.0000 0.8381 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372336 5 0.3684 0.7089 0.372 0.000 0.000 0.000 0.628 0.000
#> GSM372338 1 0.0000 0.8381 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372340 1 0.0000 0.8381 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372342 1 0.0000 0.8381 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372344 1 0.0000 0.8381 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372346 1 0.0146 0.8382 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM372348 5 0.3684 0.7089 0.372 0.000 0.000 0.000 0.628 0.000
#> GSM372350 1 0.6754 0.1430 0.488 0.000 0.220 0.000 0.216 0.076
#> GSM372352 2 0.0976 0.5656 0.000 0.968 0.016 0.000 0.008 0.008
#> GSM372354 1 0.0260 0.8373 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM372356 1 0.2416 0.7214 0.844 0.000 0.000 0.000 0.156 0.000
#> GSM372358 1 0.2300 0.7341 0.856 0.000 0.000 0.000 0.144 0.000
#> GSM372360 1 0.2300 0.7341 0.856 0.000 0.000 0.000 0.144 0.000
#> GSM372362 1 0.2300 0.7341 0.856 0.000 0.000 0.000 0.144 0.000
#> GSM372364 1 0.2416 0.7214 0.844 0.000 0.000 0.000 0.156 0.000
#> GSM372365 1 0.2912 0.6203 0.784 0.000 0.000 0.000 0.216 0.000
#> GSM372366 1 0.0458 0.8349 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM372367 1 0.3563 0.3063 0.664 0.000 0.000 0.000 0.336 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) specimen(p) individual(p) k
#> MAD:hclust 82 5.16e-04 5.99e-16 0.999 2
#> MAD:hclust 71 3.87e-05 2.98e-14 0.842 3
#> MAD:hclust 72 3.28e-05 1.26e-14 0.854 4
#> MAD:hclust 52 6.36e-06 1.81e-10 0.467 5
#> MAD:hclust 72 4.70e-06 4.66e-15 0.368 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 51941 rows and 82 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 0.994 0.997 0.4861 0.513 0.513
#> 3 3 0.691 0.850 0.889 0.3340 0.795 0.609
#> 4 4 0.684 0.686 0.769 0.1249 0.896 0.701
#> 5 5 0.673 0.504 0.700 0.0732 0.936 0.761
#> 6 6 0.695 0.625 0.703 0.0452 0.905 0.607
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
#> GSM372286 2 0.000 1.000 0.000 1.000
#> GSM372287 2 0.000 1.000 0.000 1.000
#> GSM372288 2 0.000 1.000 0.000 1.000
#> GSM372289 2 0.000 1.000 0.000 1.000
#> GSM372290 2 0.000 1.000 0.000 1.000
#> GSM372291 1 0.595 0.836 0.856 0.144
#> GSM372292 2 0.000 1.000 0.000 1.000
#> GSM372293 2 0.000 1.000 0.000 1.000
#> GSM372294 2 0.000 1.000 0.000 1.000
#> GSM372295 2 0.000 1.000 0.000 1.000
#> GSM372296 2 0.000 1.000 0.000 1.000
#> GSM372297 2 0.000 1.000 0.000 1.000
#> GSM372298 2 0.000 1.000 0.000 1.000
#> GSM372299 2 0.000 1.000 0.000 1.000
#> GSM372300 2 0.000 1.000 0.000 1.000
#> GSM372301 2 0.000 1.000 0.000 1.000
#> GSM372302 2 0.000 1.000 0.000 1.000
#> GSM372303 2 0.000 1.000 0.000 1.000
#> GSM372304 2 0.000 1.000 0.000 1.000
#> GSM372305 2 0.000 1.000 0.000 1.000
#> GSM372306 2 0.000 1.000 0.000 1.000
#> GSM372307 2 0.000 1.000 0.000 1.000
#> GSM372309 2 0.000 1.000 0.000 1.000
#> GSM372311 2 0.000 1.000 0.000 1.000
#> GSM372313 2 0.000 1.000 0.000 1.000
#> GSM372315 2 0.000 1.000 0.000 1.000
#> GSM372317 2 0.000 1.000 0.000 1.000
#> GSM372319 2 0.000 1.000 0.000 1.000
#> GSM372321 2 0.000 1.000 0.000 1.000
#> GSM372323 2 0.000 1.000 0.000 1.000
#> GSM372326 2 0.000 1.000 0.000 1.000
#> GSM372328 2 0.000 1.000 0.000 1.000
#> GSM372330 2 0.000 1.000 0.000 1.000
#> GSM372332 2 0.000 1.000 0.000 1.000
#> GSM372335 2 0.000 1.000 0.000 1.000
#> GSM372337 2 0.000 1.000 0.000 1.000
#> GSM372339 2 0.000 1.000 0.000 1.000
#> GSM372341 2 0.000 1.000 0.000 1.000
#> GSM372343 2 0.000 1.000 0.000 1.000
#> GSM372345 2 0.000 1.000 0.000 1.000
#> GSM372347 2 0.000 1.000 0.000 1.000
#> GSM372349 2 0.000 1.000 0.000 1.000
#> GSM372351 2 0.000 1.000 0.000 1.000
#> GSM372353 2 0.000 1.000 0.000 1.000
#> GSM372355 2 0.000 1.000 0.000 1.000
#> GSM372357 2 0.000 1.000 0.000 1.000
#> GSM372359 2 0.000 1.000 0.000 1.000
#> GSM372361 2 0.000 1.000 0.000 1.000
#> GSM372363 2 0.000 1.000 0.000 1.000
#> GSM372308 1 0.000 0.992 1.000 0.000
#> GSM372310 1 0.000 0.992 1.000 0.000
#> GSM372312 1 0.000 0.992 1.000 0.000
#> GSM372314 1 0.000 0.992 1.000 0.000
#> GSM372316 1 0.000 0.992 1.000 0.000
#> GSM372318 1 0.000 0.992 1.000 0.000
#> GSM372320 1 0.000 0.992 1.000 0.000
#> GSM372322 1 0.000 0.992 1.000 0.000
#> GSM372324 1 0.000 0.992 1.000 0.000
#> GSM372325 1 0.000 0.992 1.000 0.000
#> GSM372327 1 0.000 0.992 1.000 0.000
#> GSM372329 1 0.000 0.992 1.000 0.000
#> GSM372331 1 0.000 0.992 1.000 0.000
#> GSM372333 1 0.482 0.886 0.896 0.104
#> GSM372334 1 0.000 0.992 1.000 0.000
#> GSM372336 1 0.000 0.992 1.000 0.000
#> GSM372338 1 0.000 0.992 1.000 0.000
#> GSM372340 1 0.000 0.992 1.000 0.000
#> GSM372342 1 0.000 0.992 1.000 0.000
#> GSM372344 1 0.000 0.992 1.000 0.000
#> GSM372346 1 0.000 0.992 1.000 0.000
#> GSM372348 1 0.000 0.992 1.000 0.000
#> GSM372350 1 0.000 0.992 1.000 0.000
#> GSM372352 2 0.000 1.000 0.000 1.000
#> GSM372354 1 0.000 0.992 1.000 0.000
#> GSM372356 1 0.000 0.992 1.000 0.000
#> GSM372358 1 0.000 0.992 1.000 0.000
#> GSM372360 1 0.000 0.992 1.000 0.000
#> GSM372362 1 0.000 0.992 1.000 0.000
#> GSM372364 1 0.000 0.992 1.000 0.000
#> GSM372365 1 0.000 0.992 1.000 0.000
#> GSM372366 1 0.000 0.992 1.000 0.000
#> GSM372367 1 0.000 0.992 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM372286 2 0.0000 0.921 0.000 1.000 0.000
#> GSM372287 2 0.0000 0.921 0.000 1.000 0.000
#> GSM372288 2 0.0000 0.921 0.000 1.000 0.000
#> GSM372289 2 0.0000 0.921 0.000 1.000 0.000
#> GSM372290 2 0.0000 0.921 0.000 1.000 0.000
#> GSM372291 3 0.7130 -0.245 0.432 0.024 0.544
#> GSM372292 2 0.6095 0.150 0.000 0.608 0.392
#> GSM372293 3 0.4654 0.871 0.000 0.208 0.792
#> GSM372294 2 0.0747 0.906 0.000 0.984 0.016
#> GSM372295 2 0.4346 0.708 0.000 0.816 0.184
#> GSM372296 2 0.0000 0.921 0.000 1.000 0.000
#> GSM372297 2 0.0000 0.921 0.000 1.000 0.000
#> GSM372298 2 0.0000 0.921 0.000 1.000 0.000
#> GSM372299 3 0.6267 0.436 0.000 0.452 0.548
#> GSM372300 3 0.4654 0.871 0.000 0.208 0.792
#> GSM372301 3 0.6154 0.554 0.000 0.408 0.592
#> GSM372302 2 0.0000 0.921 0.000 1.000 0.000
#> GSM372303 3 0.4654 0.871 0.000 0.208 0.792
#> GSM372304 2 0.0000 0.921 0.000 1.000 0.000
#> GSM372305 2 0.0237 0.920 0.000 0.996 0.004
#> GSM372306 2 0.3816 0.784 0.000 0.852 0.148
#> GSM372307 2 0.0000 0.921 0.000 1.000 0.000
#> GSM372309 2 0.3816 0.784 0.000 0.852 0.148
#> GSM372311 2 0.0237 0.920 0.000 0.996 0.004
#> GSM372313 2 0.0237 0.920 0.000 0.996 0.004
#> GSM372315 2 0.0000 0.921 0.000 1.000 0.000
#> GSM372317 2 0.0237 0.920 0.000 0.996 0.004
#> GSM372319 2 0.2796 0.850 0.000 0.908 0.092
#> GSM372321 3 0.4605 0.873 0.000 0.204 0.796
#> GSM372323 3 0.4605 0.873 0.000 0.204 0.796
#> GSM372326 3 0.4605 0.873 0.000 0.204 0.796
#> GSM372328 3 0.4605 0.873 0.000 0.204 0.796
#> GSM372330 2 0.0237 0.920 0.000 0.996 0.004
#> GSM372332 3 0.4605 0.873 0.000 0.204 0.796
#> GSM372335 2 0.5216 0.581 0.000 0.740 0.260
#> GSM372337 3 0.4555 0.871 0.000 0.200 0.800
#> GSM372339 3 0.4605 0.873 0.000 0.204 0.796
#> GSM372341 3 0.4605 0.873 0.000 0.204 0.796
#> GSM372343 3 0.4605 0.873 0.000 0.204 0.796
#> GSM372345 3 0.4555 0.871 0.000 0.200 0.800
#> GSM372347 3 0.2165 0.752 0.000 0.064 0.936
#> GSM372349 3 0.4399 0.863 0.000 0.188 0.812
#> GSM372351 3 0.4605 0.873 0.000 0.204 0.796
#> GSM372353 3 0.5968 0.643 0.000 0.364 0.636
#> GSM372355 2 0.0237 0.920 0.000 0.996 0.004
#> GSM372357 2 0.3816 0.784 0.000 0.852 0.148
#> GSM372359 2 0.5216 0.581 0.000 0.740 0.260
#> GSM372361 2 0.0000 0.921 0.000 1.000 0.000
#> GSM372363 2 0.0237 0.920 0.000 0.996 0.004
#> GSM372308 1 0.4346 0.898 0.816 0.000 0.184
#> GSM372310 1 0.4346 0.898 0.816 0.000 0.184
#> GSM372312 1 0.4504 0.892 0.804 0.000 0.196
#> GSM372314 1 0.4346 0.898 0.816 0.000 0.184
#> GSM372316 1 0.0000 0.937 1.000 0.000 0.000
#> GSM372318 1 0.0237 0.937 0.996 0.000 0.004
#> GSM372320 1 0.0424 0.936 0.992 0.000 0.008
#> GSM372322 1 0.0424 0.936 0.992 0.000 0.008
#> GSM372324 1 0.4291 0.900 0.820 0.000 0.180
#> GSM372325 1 0.4346 0.898 0.816 0.000 0.184
#> GSM372327 1 0.0424 0.936 0.992 0.000 0.008
#> GSM372329 1 0.0424 0.936 0.992 0.000 0.008
#> GSM372331 1 0.4346 0.898 0.816 0.000 0.184
#> GSM372333 3 0.2796 0.629 0.092 0.000 0.908
#> GSM372334 1 0.0424 0.936 0.992 0.000 0.008
#> GSM372336 1 0.2711 0.927 0.912 0.000 0.088
#> GSM372338 1 0.0424 0.936 0.992 0.000 0.008
#> GSM372340 1 0.0424 0.936 0.992 0.000 0.008
#> GSM372342 1 0.0424 0.936 0.992 0.000 0.008
#> GSM372344 1 0.0424 0.936 0.992 0.000 0.008
#> GSM372346 1 0.0424 0.936 0.992 0.000 0.008
#> GSM372348 1 0.4291 0.900 0.820 0.000 0.180
#> GSM372350 1 0.3752 0.907 0.856 0.000 0.144
#> GSM372352 3 0.1860 0.744 0.000 0.052 0.948
#> GSM372354 1 0.0000 0.937 1.000 0.000 0.000
#> GSM372356 1 0.1529 0.935 0.960 0.000 0.040
#> GSM372358 1 0.1529 0.935 0.960 0.000 0.040
#> GSM372360 1 0.1529 0.935 0.960 0.000 0.040
#> GSM372362 1 0.0592 0.937 0.988 0.000 0.012
#> GSM372364 1 0.1529 0.935 0.960 0.000 0.040
#> GSM372365 1 0.4291 0.900 0.820 0.000 0.180
#> GSM372366 1 0.0000 0.937 1.000 0.000 0.000
#> GSM372367 1 0.4291 0.900 0.820 0.000 0.180
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM372286 2 0.1022 0.8246 0.000 0.968 0.000 0.032
#> GSM372287 2 0.3444 0.7717 0.000 0.816 0.000 0.184
#> GSM372288 2 0.1940 0.8185 0.000 0.924 0.000 0.076
#> GSM372289 2 0.1302 0.8238 0.000 0.956 0.000 0.044
#> GSM372290 2 0.2081 0.8164 0.000 0.916 0.000 0.084
#> GSM372291 4 0.5454 0.2696 0.096 0.000 0.172 0.732
#> GSM372292 3 0.7773 0.2792 0.000 0.308 0.428 0.264
#> GSM372293 3 0.5235 0.7480 0.000 0.048 0.716 0.236
#> GSM372294 2 0.4245 0.7599 0.000 0.784 0.020 0.196
#> GSM372295 2 0.6698 0.4874 0.000 0.532 0.096 0.372
#> GSM372296 2 0.2149 0.8154 0.000 0.912 0.000 0.088
#> GSM372297 2 0.3610 0.7625 0.000 0.800 0.000 0.200
#> GSM372298 2 0.3688 0.7670 0.000 0.792 0.000 0.208
#> GSM372299 3 0.7777 0.3469 0.000 0.268 0.428 0.304
#> GSM372300 3 0.5298 0.7443 0.000 0.048 0.708 0.244
#> GSM372301 3 0.7062 0.5777 0.000 0.176 0.564 0.260
#> GSM372302 2 0.3486 0.7693 0.000 0.812 0.000 0.188
#> GSM372303 3 0.5235 0.7480 0.000 0.048 0.716 0.236
#> GSM372304 2 0.3444 0.7717 0.000 0.816 0.000 0.184
#> GSM372305 2 0.1474 0.8213 0.000 0.948 0.000 0.052
#> GSM372306 2 0.6149 0.5900 0.000 0.676 0.180 0.144
#> GSM372307 2 0.1022 0.8253 0.000 0.968 0.000 0.032
#> GSM372309 2 0.6058 0.5989 0.000 0.684 0.180 0.136
#> GSM372311 2 0.1118 0.8243 0.000 0.964 0.000 0.036
#> GSM372313 2 0.1867 0.8167 0.000 0.928 0.000 0.072
#> GSM372315 2 0.0336 0.8271 0.000 0.992 0.000 0.008
#> GSM372317 2 0.2011 0.8137 0.000 0.920 0.000 0.080
#> GSM372319 2 0.5582 0.2575 0.000 0.576 0.400 0.024
#> GSM372321 3 0.2623 0.8267 0.000 0.064 0.908 0.028
#> GSM372323 3 0.2197 0.8325 0.000 0.048 0.928 0.024
#> GSM372326 3 0.1854 0.8346 0.000 0.048 0.940 0.012
#> GSM372328 3 0.1389 0.8359 0.000 0.048 0.952 0.000
#> GSM372330 2 0.1716 0.8192 0.000 0.936 0.000 0.064
#> GSM372332 3 0.1389 0.8359 0.000 0.048 0.952 0.000
#> GSM372335 2 0.6352 0.5626 0.000 0.656 0.188 0.156
#> GSM372337 3 0.2840 0.8245 0.000 0.044 0.900 0.056
#> GSM372339 3 0.1389 0.8359 0.000 0.048 0.952 0.000
#> GSM372341 3 0.1389 0.8359 0.000 0.048 0.952 0.000
#> GSM372343 3 0.1389 0.8359 0.000 0.048 0.952 0.000
#> GSM372345 3 0.2840 0.8245 0.000 0.044 0.900 0.056
#> GSM372347 3 0.5231 0.4994 0.000 0.012 0.604 0.384
#> GSM372349 3 0.3598 0.7691 0.000 0.028 0.848 0.124
#> GSM372351 3 0.1854 0.8360 0.000 0.048 0.940 0.012
#> GSM372353 3 0.7079 0.5070 0.000 0.276 0.556 0.168
#> GSM372355 2 0.1716 0.8192 0.000 0.936 0.000 0.064
#> GSM372357 2 0.6149 0.5900 0.000 0.676 0.180 0.144
#> GSM372359 2 0.6352 0.5626 0.000 0.656 0.188 0.156
#> GSM372361 2 0.0921 0.8257 0.000 0.972 0.000 0.028
#> GSM372363 2 0.0921 0.8248 0.000 0.972 0.000 0.028
#> GSM372308 4 0.4994 0.6254 0.480 0.000 0.000 0.520
#> GSM372310 4 0.4994 0.6254 0.480 0.000 0.000 0.520
#> GSM372312 4 0.5414 0.5572 0.376 0.000 0.020 0.604
#> GSM372314 4 0.4989 0.6287 0.472 0.000 0.000 0.528
#> GSM372316 1 0.2662 0.8026 0.900 0.000 0.016 0.084
#> GSM372318 1 0.1302 0.8262 0.956 0.000 0.000 0.044
#> GSM372320 1 0.0000 0.8352 1.000 0.000 0.000 0.000
#> GSM372322 1 0.0000 0.8352 1.000 0.000 0.000 0.000
#> GSM372324 4 0.4994 0.6254 0.480 0.000 0.000 0.520
#> GSM372325 4 0.4955 0.6174 0.444 0.000 0.000 0.556
#> GSM372327 1 0.0188 0.8333 0.996 0.000 0.004 0.000
#> GSM372329 1 0.0188 0.8333 0.996 0.000 0.004 0.000
#> GSM372331 4 0.4992 0.6275 0.476 0.000 0.000 0.524
#> GSM372333 4 0.6153 0.2490 0.068 0.000 0.328 0.604
#> GSM372334 1 0.0000 0.8352 1.000 0.000 0.000 0.000
#> GSM372336 1 0.5510 -0.1781 0.600 0.000 0.024 0.376
#> GSM372338 1 0.0000 0.8352 1.000 0.000 0.000 0.000
#> GSM372340 1 0.0000 0.8352 1.000 0.000 0.000 0.000
#> GSM372342 1 0.0000 0.8352 1.000 0.000 0.000 0.000
#> GSM372344 1 0.0188 0.8333 0.996 0.000 0.004 0.000
#> GSM372346 1 0.0000 0.8352 1.000 0.000 0.000 0.000
#> GSM372348 4 0.4998 0.6100 0.488 0.000 0.000 0.512
#> GSM372350 1 0.5636 -0.3317 0.552 0.000 0.024 0.424
#> GSM372352 4 0.5070 -0.0962 0.000 0.008 0.372 0.620
#> GSM372354 1 0.2596 0.8097 0.908 0.000 0.024 0.068
#> GSM372356 1 0.3910 0.7086 0.820 0.000 0.024 0.156
#> GSM372358 1 0.3763 0.7277 0.832 0.000 0.024 0.144
#> GSM372360 1 0.3763 0.7277 0.832 0.000 0.024 0.144
#> GSM372362 1 0.2949 0.7940 0.888 0.000 0.024 0.088
#> GSM372364 1 0.3862 0.7155 0.824 0.000 0.024 0.152
#> GSM372365 4 0.5696 0.5957 0.480 0.000 0.024 0.496
#> GSM372366 1 0.2596 0.8097 0.908 0.000 0.024 0.068
#> GSM372367 4 0.5696 0.5957 0.480 0.000 0.024 0.496
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM372286 4 0.4182 -0.0914 0.000 0.400 0.000 0.600 0.000
#> GSM372287 4 0.2189 0.5125 0.000 0.084 0.000 0.904 0.012
#> GSM372288 4 0.0510 0.5259 0.000 0.016 0.000 0.984 0.000
#> GSM372289 4 0.1544 0.5038 0.000 0.068 0.000 0.932 0.000
#> GSM372290 4 0.0000 0.5283 0.000 0.000 0.000 1.000 0.000
#> GSM372291 5 0.6093 0.1212 0.004 0.288 0.040 0.060 0.608
#> GSM372292 3 0.8163 0.4116 0.000 0.208 0.404 0.248 0.140
#> GSM372293 3 0.6880 0.5997 0.000 0.208 0.580 0.072 0.140
#> GSM372294 4 0.4959 0.3527 0.000 0.160 0.000 0.712 0.128
#> GSM372295 4 0.7254 0.1864 0.000 0.284 0.036 0.460 0.220
#> GSM372296 4 0.0162 0.5282 0.000 0.004 0.000 0.996 0.000
#> GSM372297 4 0.2669 0.4971 0.000 0.104 0.000 0.876 0.020
#> GSM372298 4 0.3888 0.4377 0.000 0.148 0.000 0.796 0.056
#> GSM372299 3 0.8357 0.3798 0.000 0.284 0.352 0.188 0.176
#> GSM372300 3 0.7075 0.5889 0.000 0.208 0.564 0.088 0.140
#> GSM372301 3 0.7784 0.5131 0.000 0.208 0.484 0.168 0.140
#> GSM372302 4 0.2448 0.5078 0.000 0.088 0.000 0.892 0.020
#> GSM372303 3 0.6880 0.5997 0.000 0.208 0.580 0.072 0.140
#> GSM372304 4 0.2189 0.5125 0.000 0.084 0.000 0.904 0.012
#> GSM372305 4 0.4268 -0.1935 0.000 0.444 0.000 0.556 0.000
#> GSM372306 2 0.6130 0.7945 0.000 0.520 0.072 0.384 0.024
#> GSM372307 4 0.1544 0.5038 0.000 0.068 0.000 0.932 0.000
#> GSM372309 2 0.6154 0.7985 0.000 0.520 0.068 0.384 0.028
#> GSM372311 4 0.4262 -0.1830 0.000 0.440 0.000 0.560 0.000
#> GSM372313 4 0.4557 -0.3527 0.000 0.476 0.000 0.516 0.008
#> GSM372315 4 0.3796 0.1822 0.000 0.300 0.000 0.700 0.000
#> GSM372317 4 0.4294 -0.2940 0.000 0.468 0.000 0.532 0.000
#> GSM372319 3 0.5187 0.2877 0.000 0.084 0.656 0.260 0.000
#> GSM372321 3 0.0609 0.7587 0.000 0.020 0.980 0.000 0.000
#> GSM372323 3 0.0671 0.7590 0.000 0.016 0.980 0.000 0.004
#> GSM372326 3 0.0510 0.7596 0.000 0.016 0.984 0.000 0.000
#> GSM372328 3 0.0162 0.7629 0.000 0.000 0.996 0.000 0.004
#> GSM372330 4 0.4268 -0.1935 0.000 0.444 0.000 0.556 0.000
#> GSM372332 3 0.0162 0.7629 0.000 0.000 0.996 0.000 0.004
#> GSM372335 2 0.6054 0.8088 0.000 0.536 0.068 0.372 0.024
#> GSM372337 3 0.1168 0.7525 0.000 0.032 0.960 0.000 0.008
#> GSM372339 3 0.0162 0.7629 0.000 0.000 0.996 0.000 0.004
#> GSM372341 3 0.0162 0.7629 0.000 0.000 0.996 0.000 0.004
#> GSM372343 3 0.0162 0.7629 0.000 0.000 0.996 0.000 0.004
#> GSM372345 3 0.1168 0.7525 0.000 0.032 0.960 0.000 0.008
#> GSM372347 3 0.6797 -0.0359 0.000 0.356 0.356 0.000 0.288
#> GSM372349 3 0.4968 0.5986 0.000 0.152 0.712 0.000 0.136
#> GSM372351 3 0.0898 0.7589 0.000 0.020 0.972 0.000 0.008
#> GSM372353 2 0.6608 0.3657 0.000 0.516 0.340 0.112 0.032
#> GSM372355 4 0.4268 -0.1935 0.000 0.444 0.000 0.556 0.000
#> GSM372357 2 0.6063 0.8082 0.000 0.532 0.068 0.376 0.024
#> GSM372359 2 0.6054 0.8088 0.000 0.536 0.068 0.372 0.024
#> GSM372361 4 0.2629 0.4521 0.000 0.136 0.000 0.860 0.004
#> GSM372363 4 0.4262 -0.1830 0.000 0.440 0.000 0.560 0.000
#> GSM372308 5 0.4526 0.6760 0.300 0.028 0.000 0.000 0.672
#> GSM372310 5 0.4366 0.6608 0.320 0.016 0.000 0.000 0.664
#> GSM372312 5 0.5224 0.5356 0.176 0.140 0.000 0.000 0.684
#> GSM372314 5 0.4420 0.6825 0.280 0.028 0.000 0.000 0.692
#> GSM372316 1 0.3812 0.6978 0.812 0.096 0.000 0.000 0.092
#> GSM372318 1 0.1469 0.7678 0.948 0.016 0.000 0.000 0.036
#> GSM372320 1 0.0404 0.7782 0.988 0.012 0.000 0.000 0.000
#> GSM372322 1 0.0000 0.7800 1.000 0.000 0.000 0.000 0.000
#> GSM372324 5 0.3895 0.6664 0.320 0.000 0.000 0.000 0.680
#> GSM372325 5 0.4428 0.6797 0.268 0.032 0.000 0.000 0.700
#> GSM372327 1 0.0000 0.7800 1.000 0.000 0.000 0.000 0.000
#> GSM372329 1 0.0880 0.7739 0.968 0.032 0.000 0.000 0.000
#> GSM372331 5 0.4420 0.6825 0.280 0.028 0.000 0.000 0.692
#> GSM372333 5 0.5321 0.5648 0.092 0.056 0.116 0.000 0.736
#> GSM372334 1 0.0404 0.7782 0.988 0.012 0.000 0.000 0.000
#> GSM372336 5 0.6037 0.2616 0.436 0.116 0.000 0.000 0.448
#> GSM372338 1 0.0404 0.7782 0.988 0.012 0.000 0.000 0.000
#> GSM372340 1 0.0290 0.7781 0.992 0.008 0.000 0.000 0.000
#> GSM372342 1 0.0000 0.7800 1.000 0.000 0.000 0.000 0.000
#> GSM372344 1 0.0404 0.7782 0.988 0.012 0.000 0.000 0.000
#> GSM372346 1 0.0000 0.7800 1.000 0.000 0.000 0.000 0.000
#> GSM372348 5 0.5002 0.6155 0.344 0.044 0.000 0.000 0.612
#> GSM372350 1 0.6245 -0.2198 0.440 0.144 0.000 0.000 0.416
#> GSM372352 5 0.6118 0.2104 0.000 0.288 0.164 0.000 0.548
#> GSM372354 1 0.3359 0.7265 0.844 0.084 0.000 0.000 0.072
#> GSM372356 1 0.5810 0.3086 0.580 0.124 0.000 0.000 0.296
#> GSM372358 1 0.5549 0.4443 0.632 0.124 0.000 0.000 0.244
#> GSM372360 1 0.5549 0.4443 0.632 0.124 0.000 0.000 0.244
#> GSM372362 1 0.4720 0.6211 0.736 0.124 0.000 0.000 0.140
#> GSM372364 1 0.5739 0.3549 0.596 0.124 0.000 0.000 0.280
#> GSM372365 5 0.5915 0.5569 0.324 0.124 0.000 0.000 0.552
#> GSM372366 1 0.3875 0.6981 0.804 0.124 0.000 0.000 0.072
#> GSM372367 5 0.5888 0.5690 0.316 0.124 0.000 0.000 0.560
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM372286 2 0.1910 0.6258 0.000 0.892 0.000 0.108 0.000 0.000
#> GSM372287 4 0.4163 0.6983 0.000 0.320 0.000 0.656 0.008 0.016
#> GSM372288 4 0.4045 0.6394 0.000 0.428 0.000 0.564 0.000 0.008
#> GSM372289 4 0.4083 0.5934 0.000 0.460 0.000 0.532 0.000 0.008
#> GSM372290 4 0.3765 0.6629 0.000 0.404 0.000 0.596 0.000 0.000
#> GSM372291 4 0.6338 -0.2257 0.004 0.000 0.004 0.368 0.344 0.280
#> GSM372292 6 0.6234 0.8182 0.000 0.044 0.256 0.164 0.000 0.536
#> GSM372293 6 0.5054 0.8483 0.000 0.000 0.368 0.084 0.000 0.548
#> GSM372294 4 0.4177 0.5083 0.000 0.140 0.000 0.772 0.036 0.052
#> GSM372295 4 0.5268 0.1464 0.000 0.048 0.008 0.672 0.056 0.216
#> GSM372296 4 0.3747 0.6671 0.000 0.396 0.000 0.604 0.000 0.000
#> GSM372297 4 0.4582 0.6912 0.000 0.296 0.000 0.652 0.012 0.040
#> GSM372298 4 0.5999 0.5417 0.000 0.292 0.000 0.472 0.004 0.232
#> GSM372299 6 0.6396 0.7664 0.000 0.048 0.184 0.164 0.020 0.584
#> GSM372300 6 0.5399 0.8701 0.000 0.008 0.348 0.100 0.000 0.544
#> GSM372301 6 0.5751 0.8710 0.000 0.024 0.320 0.112 0.000 0.544
#> GSM372302 4 0.4061 0.6984 0.000 0.316 0.000 0.664 0.008 0.012
#> GSM372303 6 0.5054 0.8483 0.000 0.000 0.368 0.084 0.000 0.548
#> GSM372304 4 0.4321 0.6978 0.000 0.316 0.000 0.652 0.012 0.020
#> GSM372305 2 0.0363 0.7387 0.000 0.988 0.000 0.012 0.000 0.000
#> GSM372306 2 0.4384 0.7109 0.000 0.776 0.076 0.004 0.048 0.096
#> GSM372307 4 0.3857 0.5798 0.000 0.468 0.000 0.532 0.000 0.000
#> GSM372309 2 0.4440 0.7114 0.000 0.776 0.072 0.008 0.048 0.096
#> GSM372311 2 0.0508 0.7370 0.000 0.984 0.000 0.012 0.004 0.000
#> GSM372313 2 0.1167 0.7444 0.000 0.960 0.000 0.012 0.008 0.020
#> GSM372315 2 0.2558 0.5068 0.000 0.840 0.000 0.156 0.004 0.000
#> GSM372317 2 0.1515 0.7441 0.000 0.944 0.028 0.000 0.008 0.020
#> GSM372319 3 0.3437 0.5989 0.000 0.188 0.788 0.008 0.004 0.012
#> GSM372321 3 0.1371 0.8418 0.000 0.040 0.948 0.004 0.004 0.004
#> GSM372323 3 0.1275 0.8491 0.000 0.012 0.956 0.000 0.016 0.016
#> GSM372326 3 0.0363 0.8565 0.000 0.012 0.988 0.000 0.000 0.000
#> GSM372328 3 0.0858 0.8570 0.000 0.000 0.968 0.000 0.004 0.028
#> GSM372330 2 0.0622 0.7391 0.000 0.980 0.000 0.012 0.008 0.000
#> GSM372332 3 0.0858 0.8570 0.000 0.000 0.968 0.000 0.004 0.028
#> GSM372335 2 0.4605 0.6995 0.000 0.756 0.076 0.004 0.048 0.116
#> GSM372337 3 0.2201 0.8208 0.000 0.012 0.912 0.004 0.024 0.048
#> GSM372339 3 0.0858 0.8570 0.000 0.000 0.968 0.000 0.004 0.028
#> GSM372341 3 0.0858 0.8570 0.000 0.000 0.968 0.000 0.004 0.028
#> GSM372343 3 0.0858 0.8570 0.000 0.000 0.968 0.000 0.004 0.028
#> GSM372345 3 0.2201 0.8208 0.000 0.012 0.912 0.004 0.024 0.048
#> GSM372347 5 0.7140 -0.1009 0.000 0.332 0.168 0.004 0.400 0.096
#> GSM372349 3 0.6139 0.4023 0.000 0.012 0.600 0.228 0.072 0.088
#> GSM372351 3 0.1588 0.8106 0.000 0.000 0.924 0.000 0.004 0.072
#> GSM372353 2 0.6260 0.4314 0.000 0.580 0.224 0.008 0.060 0.128
#> GSM372355 2 0.0508 0.7400 0.000 0.984 0.000 0.012 0.004 0.000
#> GSM372357 2 0.4475 0.7074 0.000 0.768 0.076 0.004 0.048 0.104
#> GSM372359 2 0.4605 0.6995 0.000 0.756 0.076 0.004 0.048 0.116
#> GSM372361 2 0.4397 -0.4372 0.000 0.528 0.000 0.452 0.012 0.008
#> GSM372363 2 0.0632 0.7313 0.000 0.976 0.000 0.024 0.000 0.000
#> GSM372308 5 0.3876 0.6921 0.156 0.000 0.000 0.004 0.772 0.068
#> GSM372310 5 0.3876 0.6921 0.156 0.000 0.000 0.004 0.772 0.068
#> GSM372312 5 0.5830 0.5009 0.072 0.000 0.000 0.240 0.604 0.084
#> GSM372314 5 0.2300 0.7103 0.144 0.000 0.000 0.000 0.856 0.000
#> GSM372316 1 0.4089 0.6636 0.752 0.000 0.000 0.012 0.052 0.184
#> GSM372318 1 0.2147 0.7257 0.896 0.000 0.000 0.000 0.020 0.084
#> GSM372320 1 0.1644 0.7340 0.932 0.000 0.000 0.040 0.000 0.028
#> GSM372322 1 0.0146 0.7409 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM372324 5 0.2416 0.7072 0.156 0.000 0.000 0.000 0.844 0.000
#> GSM372325 5 0.1910 0.7040 0.108 0.000 0.000 0.000 0.892 0.000
#> GSM372327 1 0.0291 0.7405 0.992 0.000 0.000 0.004 0.000 0.004
#> GSM372329 1 0.1225 0.7364 0.952 0.000 0.000 0.012 0.000 0.036
#> GSM372331 5 0.2553 0.7105 0.144 0.000 0.000 0.000 0.848 0.008
#> GSM372333 5 0.2364 0.6306 0.012 0.004 0.036 0.000 0.904 0.044
#> GSM372334 1 0.1644 0.7340 0.932 0.000 0.000 0.040 0.000 0.028
#> GSM372336 5 0.5876 0.4291 0.276 0.000 0.000 0.012 0.532 0.180
#> GSM372338 1 0.1644 0.7340 0.932 0.000 0.000 0.040 0.000 0.028
#> GSM372340 1 0.1257 0.7345 0.952 0.000 0.000 0.028 0.000 0.020
#> GSM372342 1 0.0291 0.7405 0.992 0.000 0.000 0.004 0.000 0.004
#> GSM372344 1 0.1644 0.7340 0.932 0.000 0.000 0.040 0.000 0.028
#> GSM372346 1 0.0146 0.7409 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM372348 5 0.4450 0.6327 0.236 0.000 0.000 0.012 0.700 0.052
#> GSM372350 1 0.7285 -0.1589 0.340 0.000 0.000 0.272 0.292 0.096
#> GSM372352 5 0.6747 0.2921 0.000 0.048 0.056 0.140 0.576 0.180
#> GSM372354 1 0.4132 0.6788 0.736 0.000 0.000 0.016 0.036 0.212
#> GSM372356 1 0.6300 0.0316 0.392 0.000 0.000 0.012 0.360 0.236
#> GSM372358 1 0.5898 0.3900 0.524 0.000 0.000 0.008 0.228 0.240
#> GSM372360 1 0.5898 0.3900 0.524 0.000 0.000 0.008 0.228 0.240
#> GSM372362 1 0.4861 0.5958 0.660 0.000 0.000 0.008 0.088 0.244
#> GSM372364 1 0.6275 0.1252 0.420 0.000 0.000 0.012 0.332 0.236
#> GSM372365 5 0.5624 0.5457 0.168 0.000 0.000 0.012 0.584 0.236
#> GSM372366 1 0.4130 0.6491 0.716 0.000 0.000 0.008 0.036 0.240
#> GSM372367 5 0.5473 0.5721 0.156 0.000 0.000 0.012 0.608 0.224
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) specimen(p) individual(p) k
#> MAD:kmeans 82 3.35e-04 8.50e-17 0.999 2
#> MAD:kmeans 79 2.72e-05 6.42e-16 0.913 3
#> MAD:kmeans 72 2.73e-04 1.45e-14 0.891 4
#> MAD:kmeans 55 1.51e-05 1.01e-12 0.459 5
#> MAD:kmeans 69 4.00e-10 2.31e-20 0.520 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 51941 rows and 82 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.985 0.995 0.4894 0.513 0.513
#> 3 3 1.000 0.969 0.987 0.3377 0.828 0.665
#> 4 4 0.888 0.882 0.933 0.1043 0.895 0.710
#> 5 5 0.808 0.659 0.824 0.0587 0.944 0.808
#> 6 6 0.769 0.732 0.826 0.0521 0.897 0.620
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
#> GSM372286 2 0.000 0.991 0.000 1.000
#> GSM372287 2 0.000 0.991 0.000 1.000
#> GSM372288 2 0.000 0.991 0.000 1.000
#> GSM372289 2 0.000 0.991 0.000 1.000
#> GSM372290 2 0.000 0.991 0.000 1.000
#> GSM372291 1 0.000 1.000 1.000 0.000
#> GSM372292 2 0.000 0.991 0.000 1.000
#> GSM372293 2 0.000 0.991 0.000 1.000
#> GSM372294 2 0.000 0.991 0.000 1.000
#> GSM372295 2 0.000 0.991 0.000 1.000
#> GSM372296 2 0.000 0.991 0.000 1.000
#> GSM372297 2 0.000 0.991 0.000 1.000
#> GSM372298 2 0.000 0.991 0.000 1.000
#> GSM372299 2 0.000 0.991 0.000 1.000
#> GSM372300 2 0.000 0.991 0.000 1.000
#> GSM372301 2 0.000 0.991 0.000 1.000
#> GSM372302 2 0.000 0.991 0.000 1.000
#> GSM372303 2 0.000 0.991 0.000 1.000
#> GSM372304 2 0.000 0.991 0.000 1.000
#> GSM372305 2 0.000 0.991 0.000 1.000
#> GSM372306 2 0.000 0.991 0.000 1.000
#> GSM372307 2 0.000 0.991 0.000 1.000
#> GSM372309 2 0.000 0.991 0.000 1.000
#> GSM372311 2 0.000 0.991 0.000 1.000
#> GSM372313 2 0.000 0.991 0.000 1.000
#> GSM372315 2 0.000 0.991 0.000 1.000
#> GSM372317 2 0.000 0.991 0.000 1.000
#> GSM372319 2 0.000 0.991 0.000 1.000
#> GSM372321 2 0.000 0.991 0.000 1.000
#> GSM372323 2 0.000 0.991 0.000 1.000
#> GSM372326 2 0.000 0.991 0.000 1.000
#> GSM372328 2 0.000 0.991 0.000 1.000
#> GSM372330 2 0.000 0.991 0.000 1.000
#> GSM372332 2 0.000 0.991 0.000 1.000
#> GSM372335 2 0.000 0.991 0.000 1.000
#> GSM372337 2 0.000 0.991 0.000 1.000
#> GSM372339 2 0.000 0.991 0.000 1.000
#> GSM372341 2 0.000 0.991 0.000 1.000
#> GSM372343 2 0.000 0.991 0.000 1.000
#> GSM372345 2 0.000 0.991 0.000 1.000
#> GSM372347 2 0.000 0.991 0.000 1.000
#> GSM372349 2 0.000 0.991 0.000 1.000
#> GSM372351 2 0.000 0.991 0.000 1.000
#> GSM372353 2 0.000 0.991 0.000 1.000
#> GSM372355 2 0.000 0.991 0.000 1.000
#> GSM372357 2 0.000 0.991 0.000 1.000
#> GSM372359 2 0.000 0.991 0.000 1.000
#> GSM372361 2 0.000 0.991 0.000 1.000
#> GSM372363 2 0.000 0.991 0.000 1.000
#> GSM372308 1 0.000 1.000 1.000 0.000
#> GSM372310 1 0.000 1.000 1.000 0.000
#> GSM372312 1 0.000 1.000 1.000 0.000
#> GSM372314 1 0.000 1.000 1.000 0.000
#> GSM372316 1 0.000 1.000 1.000 0.000
#> GSM372318 1 0.000 1.000 1.000 0.000
#> GSM372320 1 0.000 1.000 1.000 0.000
#> GSM372322 1 0.000 1.000 1.000 0.000
#> GSM372324 1 0.000 1.000 1.000 0.000
#> GSM372325 1 0.000 1.000 1.000 0.000
#> GSM372327 1 0.000 1.000 1.000 0.000
#> GSM372329 1 0.000 1.000 1.000 0.000
#> GSM372331 1 0.000 1.000 1.000 0.000
#> GSM372333 1 0.000 1.000 1.000 0.000
#> GSM372334 1 0.000 1.000 1.000 0.000
#> GSM372336 1 0.000 1.000 1.000 0.000
#> GSM372338 1 0.000 1.000 1.000 0.000
#> GSM372340 1 0.000 1.000 1.000 0.000
#> GSM372342 1 0.000 1.000 1.000 0.000
#> GSM372344 1 0.000 1.000 1.000 0.000
#> GSM372346 1 0.000 1.000 1.000 0.000
#> GSM372348 1 0.000 1.000 1.000 0.000
#> GSM372350 1 0.000 1.000 1.000 0.000
#> GSM372352 2 0.988 0.227 0.436 0.564
#> GSM372354 1 0.000 1.000 1.000 0.000
#> GSM372356 1 0.000 1.000 1.000 0.000
#> GSM372358 1 0.000 1.000 1.000 0.000
#> GSM372360 1 0.000 1.000 1.000 0.000
#> GSM372362 1 0.000 1.000 1.000 0.000
#> GSM372364 1 0.000 1.000 1.000 0.000
#> GSM372365 1 0.000 1.000 1.000 0.000
#> GSM372366 1 0.000 1.000 1.000 0.000
#> GSM372367 1 0.000 1.000 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM372286 2 0.0000 1.000 0.000 1.000 0.000
#> GSM372287 2 0.0000 1.000 0.000 1.000 0.000
#> GSM372288 2 0.0000 1.000 0.000 1.000 0.000
#> GSM372289 2 0.0000 1.000 0.000 1.000 0.000
#> GSM372290 2 0.0000 1.000 0.000 1.000 0.000
#> GSM372291 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372292 2 0.0000 1.000 0.000 1.000 0.000
#> GSM372293 3 0.0237 0.938 0.000 0.004 0.996
#> GSM372294 2 0.0000 1.000 0.000 1.000 0.000
#> GSM372295 2 0.0000 1.000 0.000 1.000 0.000
#> GSM372296 2 0.0000 1.000 0.000 1.000 0.000
#> GSM372297 2 0.0000 1.000 0.000 1.000 0.000
#> GSM372298 2 0.0000 1.000 0.000 1.000 0.000
#> GSM372299 2 0.0000 1.000 0.000 1.000 0.000
#> GSM372300 3 0.3816 0.806 0.000 0.148 0.852
#> GSM372301 3 0.6274 0.229 0.000 0.456 0.544
#> GSM372302 2 0.0000 1.000 0.000 1.000 0.000
#> GSM372303 3 0.0000 0.941 0.000 0.000 1.000
#> GSM372304 2 0.0000 1.000 0.000 1.000 0.000
#> GSM372305 2 0.0000 1.000 0.000 1.000 0.000
#> GSM372306 2 0.0000 1.000 0.000 1.000 0.000
#> GSM372307 2 0.0000 1.000 0.000 1.000 0.000
#> GSM372309 2 0.0000 1.000 0.000 1.000 0.000
#> GSM372311 2 0.0000 1.000 0.000 1.000 0.000
#> GSM372313 2 0.0000 1.000 0.000 1.000 0.000
#> GSM372315 2 0.0000 1.000 0.000 1.000 0.000
#> GSM372317 2 0.0000 1.000 0.000 1.000 0.000
#> GSM372319 2 0.0000 1.000 0.000 1.000 0.000
#> GSM372321 3 0.0000 0.941 0.000 0.000 1.000
#> GSM372323 3 0.0000 0.941 0.000 0.000 1.000
#> GSM372326 3 0.0000 0.941 0.000 0.000 1.000
#> GSM372328 3 0.0000 0.941 0.000 0.000 1.000
#> GSM372330 2 0.0000 1.000 0.000 1.000 0.000
#> GSM372332 3 0.0000 0.941 0.000 0.000 1.000
#> GSM372335 2 0.0000 1.000 0.000 1.000 0.000
#> GSM372337 3 0.0000 0.941 0.000 0.000 1.000
#> GSM372339 3 0.0000 0.941 0.000 0.000 1.000
#> GSM372341 3 0.0000 0.941 0.000 0.000 1.000
#> GSM372343 3 0.0000 0.941 0.000 0.000 1.000
#> GSM372345 3 0.0000 0.941 0.000 0.000 1.000
#> GSM372347 3 0.0000 0.941 0.000 0.000 1.000
#> GSM372349 3 0.0000 0.941 0.000 0.000 1.000
#> GSM372351 3 0.0000 0.941 0.000 0.000 1.000
#> GSM372353 3 0.6140 0.373 0.000 0.404 0.596
#> GSM372355 2 0.0000 1.000 0.000 1.000 0.000
#> GSM372357 2 0.0000 1.000 0.000 1.000 0.000
#> GSM372359 2 0.0000 1.000 0.000 1.000 0.000
#> GSM372361 2 0.0000 1.000 0.000 1.000 0.000
#> GSM372363 2 0.0000 1.000 0.000 1.000 0.000
#> GSM372308 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372310 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372312 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372314 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372316 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372318 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372320 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372322 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372324 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372325 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372327 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372329 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372331 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372333 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372334 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372336 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372338 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372340 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372342 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372344 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372346 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372348 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372350 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372352 3 0.1525 0.914 0.032 0.004 0.964
#> GSM372354 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372356 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372358 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372360 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372362 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372364 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372365 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372366 1 0.0000 1.000 1.000 0.000 0.000
#> GSM372367 1 0.0000 1.000 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM372286 2 0.1302 0.858 0.000 0.956 0.000 0.044
#> GSM372287 4 0.3764 0.801 0.000 0.216 0.000 0.784
#> GSM372288 2 0.4356 0.584 0.000 0.708 0.000 0.292
#> GSM372289 2 0.2011 0.839 0.000 0.920 0.000 0.080
#> GSM372290 2 0.4477 0.547 0.000 0.688 0.000 0.312
#> GSM372291 4 0.3074 0.730 0.152 0.000 0.000 0.848
#> GSM372292 4 0.2610 0.865 0.000 0.088 0.012 0.900
#> GSM372293 4 0.3311 0.764 0.000 0.000 0.172 0.828
#> GSM372294 2 0.4776 0.457 0.000 0.624 0.000 0.376
#> GSM372295 4 0.2868 0.849 0.000 0.136 0.000 0.864
#> GSM372296 2 0.4713 0.441 0.000 0.640 0.000 0.360
#> GSM372297 4 0.3356 0.838 0.000 0.176 0.000 0.824
#> GSM372298 4 0.2704 0.859 0.000 0.124 0.000 0.876
#> GSM372299 4 0.2610 0.865 0.000 0.088 0.012 0.900
#> GSM372300 4 0.2944 0.811 0.000 0.004 0.128 0.868
#> GSM372301 4 0.3037 0.849 0.000 0.036 0.076 0.888
#> GSM372302 4 0.3688 0.812 0.000 0.208 0.000 0.792
#> GSM372303 4 0.2814 0.806 0.000 0.000 0.132 0.868
#> GSM372304 4 0.3688 0.812 0.000 0.208 0.000 0.792
#> GSM372305 2 0.0000 0.871 0.000 1.000 0.000 0.000
#> GSM372306 2 0.0000 0.871 0.000 1.000 0.000 0.000
#> GSM372307 2 0.1940 0.842 0.000 0.924 0.000 0.076
#> GSM372309 2 0.0000 0.871 0.000 1.000 0.000 0.000
#> GSM372311 2 0.0000 0.871 0.000 1.000 0.000 0.000
#> GSM372313 2 0.0000 0.871 0.000 1.000 0.000 0.000
#> GSM372315 2 0.0707 0.867 0.000 0.980 0.000 0.020
#> GSM372317 2 0.0000 0.871 0.000 1.000 0.000 0.000
#> GSM372319 2 0.5386 0.432 0.000 0.612 0.368 0.020
#> GSM372321 3 0.0000 0.951 0.000 0.000 1.000 0.000
#> GSM372323 3 0.0000 0.951 0.000 0.000 1.000 0.000
#> GSM372326 3 0.0000 0.951 0.000 0.000 1.000 0.000
#> GSM372328 3 0.0000 0.951 0.000 0.000 1.000 0.000
#> GSM372330 2 0.0000 0.871 0.000 1.000 0.000 0.000
#> GSM372332 3 0.0000 0.951 0.000 0.000 1.000 0.000
#> GSM372335 2 0.0469 0.865 0.000 0.988 0.000 0.012
#> GSM372337 3 0.0188 0.949 0.000 0.000 0.996 0.004
#> GSM372339 3 0.0000 0.951 0.000 0.000 1.000 0.000
#> GSM372341 3 0.0000 0.951 0.000 0.000 1.000 0.000
#> GSM372343 3 0.0000 0.951 0.000 0.000 1.000 0.000
#> GSM372345 3 0.0188 0.949 0.000 0.000 0.996 0.004
#> GSM372347 3 0.3958 0.819 0.000 0.112 0.836 0.052
#> GSM372349 3 0.1302 0.920 0.000 0.000 0.956 0.044
#> GSM372351 3 0.0000 0.951 0.000 0.000 1.000 0.000
#> GSM372353 2 0.5478 0.541 0.000 0.696 0.248 0.056
#> GSM372355 2 0.0000 0.871 0.000 1.000 0.000 0.000
#> GSM372357 2 0.0000 0.871 0.000 1.000 0.000 0.000
#> GSM372359 2 0.1557 0.834 0.000 0.944 0.000 0.056
#> GSM372361 2 0.2216 0.830 0.000 0.908 0.000 0.092
#> GSM372363 2 0.0592 0.868 0.000 0.984 0.000 0.016
#> GSM372308 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> GSM372310 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> GSM372312 1 0.1389 0.959 0.952 0.000 0.000 0.048
#> GSM372314 1 0.1389 0.959 0.952 0.000 0.000 0.048
#> GSM372316 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> GSM372318 1 0.0336 0.986 0.992 0.000 0.000 0.008
#> GSM372320 1 0.0336 0.986 0.992 0.000 0.000 0.008
#> GSM372322 1 0.0336 0.986 0.992 0.000 0.000 0.008
#> GSM372324 1 0.1389 0.959 0.952 0.000 0.000 0.048
#> GSM372325 1 0.1474 0.957 0.948 0.000 0.000 0.052
#> GSM372327 1 0.0336 0.986 0.992 0.000 0.000 0.008
#> GSM372329 1 0.0336 0.986 0.992 0.000 0.000 0.008
#> GSM372331 1 0.1389 0.959 0.952 0.000 0.000 0.048
#> GSM372333 1 0.2060 0.944 0.932 0.000 0.016 0.052
#> GSM372334 1 0.0336 0.986 0.992 0.000 0.000 0.008
#> GSM372336 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> GSM372338 1 0.0336 0.986 0.992 0.000 0.000 0.008
#> GSM372340 1 0.0336 0.986 0.992 0.000 0.000 0.008
#> GSM372342 1 0.0336 0.986 0.992 0.000 0.000 0.008
#> GSM372344 1 0.0336 0.986 0.992 0.000 0.000 0.008
#> GSM372346 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> GSM372348 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> GSM372350 1 0.1389 0.959 0.952 0.000 0.000 0.048
#> GSM372352 3 0.6951 0.462 0.008 0.304 0.576 0.112
#> GSM372354 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> GSM372356 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> GSM372358 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> GSM372360 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> GSM372362 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> GSM372364 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> GSM372365 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> GSM372366 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> GSM372367 1 0.0000 0.987 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM372286 2 0.4651 0.1756 0.000 0.608 0.000 0.020 0.372
#> GSM372287 5 0.6102 0.1269 0.000 0.124 0.000 0.436 0.440
#> GSM372288 5 0.6363 0.3949 0.000 0.392 0.000 0.164 0.444
#> GSM372289 2 0.5396 -0.1573 0.000 0.500 0.000 0.056 0.444
#> GSM372290 5 0.6510 0.4680 0.000 0.360 0.000 0.196 0.444
#> GSM372291 4 0.5037 0.4221 0.088 0.000 0.000 0.684 0.228
#> GSM372292 4 0.0451 0.6359 0.000 0.008 0.000 0.988 0.004
#> GSM372293 4 0.1341 0.6247 0.000 0.000 0.056 0.944 0.000
#> GSM372294 5 0.5784 0.4198 0.000 0.176 0.000 0.208 0.616
#> GSM372295 5 0.4588 0.0549 0.000 0.016 0.000 0.380 0.604
#> GSM372296 5 0.6655 0.4948 0.000 0.296 0.000 0.260 0.444
#> GSM372297 4 0.5733 -0.2108 0.000 0.084 0.000 0.476 0.440
#> GSM372298 4 0.4622 0.3090 0.000 0.044 0.000 0.692 0.264
#> GSM372299 4 0.1408 0.6218 0.000 0.008 0.000 0.948 0.044
#> GSM372300 4 0.0963 0.6377 0.000 0.000 0.036 0.964 0.000
#> GSM372301 4 0.0510 0.6401 0.000 0.000 0.016 0.984 0.000
#> GSM372302 4 0.6037 -0.2930 0.000 0.116 0.000 0.444 0.440
#> GSM372303 4 0.1121 0.6341 0.000 0.000 0.044 0.956 0.000
#> GSM372304 4 0.6037 -0.2930 0.000 0.116 0.000 0.444 0.440
#> GSM372305 2 0.0000 0.7264 0.000 1.000 0.000 0.000 0.000
#> GSM372306 2 0.0000 0.7264 0.000 1.000 0.000 0.000 0.000
#> GSM372307 2 0.5381 -0.1066 0.000 0.516 0.000 0.056 0.428
#> GSM372309 2 0.0290 0.7230 0.000 0.992 0.000 0.000 0.008
#> GSM372311 2 0.0162 0.7262 0.000 0.996 0.000 0.000 0.004
#> GSM372313 2 0.0000 0.7264 0.000 1.000 0.000 0.000 0.000
#> GSM372315 2 0.4252 0.3722 0.000 0.700 0.000 0.020 0.280
#> GSM372317 2 0.0162 0.7262 0.000 0.996 0.000 0.000 0.004
#> GSM372319 3 0.5025 0.5331 0.000 0.236 0.700 0.024 0.040
#> GSM372321 3 0.0000 0.9493 0.000 0.000 1.000 0.000 0.000
#> GSM372323 3 0.0000 0.9493 0.000 0.000 1.000 0.000 0.000
#> GSM372326 3 0.0000 0.9493 0.000 0.000 1.000 0.000 0.000
#> GSM372328 3 0.0000 0.9493 0.000 0.000 1.000 0.000 0.000
#> GSM372330 2 0.0162 0.7262 0.000 0.996 0.000 0.000 0.004
#> GSM372332 3 0.0000 0.9493 0.000 0.000 1.000 0.000 0.000
#> GSM372335 2 0.0162 0.7262 0.000 0.996 0.000 0.000 0.004
#> GSM372337 3 0.0404 0.9444 0.000 0.000 0.988 0.000 0.012
#> GSM372339 3 0.0000 0.9493 0.000 0.000 1.000 0.000 0.000
#> GSM372341 3 0.0000 0.9493 0.000 0.000 1.000 0.000 0.000
#> GSM372343 3 0.0000 0.9493 0.000 0.000 1.000 0.000 0.000
#> GSM372345 3 0.0404 0.9444 0.000 0.000 0.988 0.000 0.012
#> GSM372347 2 0.6701 0.0275 0.000 0.428 0.300 0.000 0.272
#> GSM372349 3 0.3246 0.7878 0.000 0.000 0.808 0.008 0.184
#> GSM372351 3 0.1121 0.9184 0.000 0.000 0.956 0.044 0.000
#> GSM372353 2 0.3184 0.5750 0.000 0.852 0.100 0.048 0.000
#> GSM372355 2 0.0000 0.7264 0.000 1.000 0.000 0.000 0.000
#> GSM372357 2 0.0000 0.7264 0.000 1.000 0.000 0.000 0.000
#> GSM372359 2 0.0510 0.7131 0.000 0.984 0.000 0.016 0.000
#> GSM372361 2 0.5529 -0.1347 0.000 0.512 0.000 0.068 0.420
#> GSM372363 2 0.4151 0.2820 0.000 0.652 0.000 0.004 0.344
#> GSM372308 1 0.1908 0.8978 0.908 0.000 0.000 0.000 0.092
#> GSM372310 1 0.1792 0.9010 0.916 0.000 0.000 0.000 0.084
#> GSM372312 1 0.4165 0.6918 0.672 0.000 0.000 0.008 0.320
#> GSM372314 1 0.3966 0.7141 0.664 0.000 0.000 0.000 0.336
#> GSM372316 1 0.0162 0.9138 0.996 0.000 0.000 0.000 0.004
#> GSM372318 1 0.0794 0.9110 0.972 0.000 0.000 0.000 0.028
#> GSM372320 1 0.0794 0.9110 0.972 0.000 0.000 0.000 0.028
#> GSM372322 1 0.0794 0.9110 0.972 0.000 0.000 0.000 0.028
#> GSM372324 1 0.3636 0.7487 0.728 0.000 0.000 0.000 0.272
#> GSM372325 1 0.3857 0.7105 0.688 0.000 0.000 0.000 0.312
#> GSM372327 1 0.0794 0.9110 0.972 0.000 0.000 0.000 0.028
#> GSM372329 1 0.0794 0.9110 0.972 0.000 0.000 0.000 0.028
#> GSM372331 1 0.3966 0.7141 0.664 0.000 0.000 0.000 0.336
#> GSM372333 1 0.4437 0.6876 0.664 0.000 0.020 0.000 0.316
#> GSM372334 1 0.0794 0.9110 0.972 0.000 0.000 0.000 0.028
#> GSM372336 1 0.1197 0.9122 0.952 0.000 0.000 0.000 0.048
#> GSM372338 1 0.0794 0.9110 0.972 0.000 0.000 0.000 0.028
#> GSM372340 1 0.0794 0.9110 0.972 0.000 0.000 0.000 0.028
#> GSM372342 1 0.0794 0.9110 0.972 0.000 0.000 0.000 0.028
#> GSM372344 1 0.0794 0.9110 0.972 0.000 0.000 0.000 0.028
#> GSM372346 1 0.0000 0.9136 1.000 0.000 0.000 0.000 0.000
#> GSM372348 1 0.0963 0.9110 0.964 0.000 0.000 0.000 0.036
#> GSM372350 1 0.3421 0.7631 0.788 0.000 0.000 0.008 0.204
#> GSM372352 5 0.7288 -0.1374 0.000 0.368 0.132 0.064 0.436
#> GSM372354 1 0.0963 0.9129 0.964 0.000 0.000 0.000 0.036
#> GSM372356 1 0.1197 0.9116 0.952 0.000 0.000 0.000 0.048
#> GSM372358 1 0.1197 0.9116 0.952 0.000 0.000 0.000 0.048
#> GSM372360 1 0.1197 0.9116 0.952 0.000 0.000 0.000 0.048
#> GSM372362 1 0.0880 0.9127 0.968 0.000 0.000 0.000 0.032
#> GSM372364 1 0.1197 0.9116 0.952 0.000 0.000 0.000 0.048
#> GSM372365 1 0.1197 0.9116 0.952 0.000 0.000 0.000 0.048
#> GSM372366 1 0.0963 0.9129 0.964 0.000 0.000 0.000 0.036
#> GSM372367 1 0.1270 0.9110 0.948 0.000 0.000 0.000 0.052
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM372286 4 0.3823 0.4357 0.000 0.436 0.000 0.564 0.000 0.000
#> GSM372287 4 0.3520 0.7637 0.000 0.100 0.000 0.804 0.000 0.096
#> GSM372288 4 0.3110 0.7762 0.000 0.196 0.000 0.792 0.000 0.012
#> GSM372289 4 0.3428 0.6770 0.000 0.304 0.000 0.696 0.000 0.000
#> GSM372290 4 0.3236 0.7814 0.000 0.180 0.000 0.796 0.000 0.024
#> GSM372291 6 0.7542 0.1481 0.220 0.000 0.000 0.196 0.216 0.368
#> GSM372292 6 0.2048 0.8760 0.000 0.000 0.000 0.120 0.000 0.880
#> GSM372293 6 0.2212 0.8758 0.000 0.000 0.008 0.112 0.000 0.880
#> GSM372294 4 0.2859 0.5642 0.000 0.028 0.000 0.856 0.108 0.008
#> GSM372295 4 0.2680 0.5312 0.000 0.000 0.000 0.860 0.108 0.032
#> GSM372296 4 0.3532 0.7786 0.000 0.140 0.000 0.796 0.000 0.064
#> GSM372297 4 0.3453 0.7263 0.000 0.064 0.000 0.804 0.000 0.132
#> GSM372298 4 0.4400 0.3173 0.000 0.032 0.000 0.592 0.000 0.376
#> GSM372299 6 0.2743 0.8289 0.000 0.000 0.000 0.164 0.008 0.828
#> GSM372300 6 0.2146 0.8768 0.000 0.000 0.004 0.116 0.000 0.880
#> GSM372301 6 0.2048 0.8760 0.000 0.000 0.000 0.120 0.000 0.880
#> GSM372302 4 0.3520 0.7637 0.000 0.100 0.000 0.804 0.000 0.096
#> GSM372303 6 0.2212 0.8758 0.000 0.000 0.008 0.112 0.000 0.880
#> GSM372304 4 0.3520 0.7605 0.000 0.096 0.000 0.804 0.000 0.100
#> GSM372305 2 0.0363 0.9054 0.000 0.988 0.000 0.012 0.000 0.000
#> GSM372306 2 0.0146 0.9056 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM372307 4 0.3446 0.6738 0.000 0.308 0.000 0.692 0.000 0.000
#> GSM372309 2 0.0363 0.9027 0.000 0.988 0.000 0.012 0.000 0.000
#> GSM372311 2 0.0713 0.8933 0.000 0.972 0.000 0.028 0.000 0.000
#> GSM372313 2 0.0146 0.9069 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM372315 2 0.3804 -0.0343 0.000 0.576 0.000 0.424 0.000 0.000
#> GSM372317 2 0.0260 0.9071 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM372319 3 0.3767 0.7025 0.000 0.132 0.780 0.088 0.000 0.000
#> GSM372321 3 0.0000 0.9389 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372323 3 0.0291 0.9371 0.000 0.000 0.992 0.000 0.004 0.004
#> GSM372326 3 0.0000 0.9389 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372328 3 0.0000 0.9389 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372330 2 0.0260 0.9071 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM372332 3 0.0260 0.9372 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM372335 2 0.0291 0.9037 0.000 0.992 0.000 0.000 0.004 0.004
#> GSM372337 3 0.0777 0.9284 0.000 0.000 0.972 0.004 0.024 0.000
#> GSM372339 3 0.0000 0.9389 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372341 3 0.0000 0.9389 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372343 3 0.0000 0.9389 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372345 3 0.1003 0.9251 0.000 0.000 0.964 0.004 0.028 0.004
#> GSM372347 5 0.5870 0.0996 0.000 0.384 0.092 0.008 0.496 0.020
#> GSM372349 3 0.5193 0.5675 0.000 0.000 0.644 0.176 0.172 0.008
#> GSM372351 3 0.1082 0.9111 0.000 0.000 0.956 0.004 0.000 0.040
#> GSM372353 2 0.2414 0.8070 0.000 0.896 0.036 0.000 0.012 0.056
#> GSM372355 2 0.0260 0.9071 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM372357 2 0.0146 0.9056 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM372359 2 0.0717 0.8923 0.000 0.976 0.000 0.000 0.008 0.016
#> GSM372361 4 0.3592 0.6259 0.000 0.344 0.000 0.656 0.000 0.000
#> GSM372363 2 0.3371 0.4497 0.000 0.708 0.000 0.292 0.000 0.000
#> GSM372308 1 0.4983 0.4333 0.564 0.000 0.000 0.000 0.356 0.080
#> GSM372310 1 0.4950 0.4642 0.576 0.000 0.000 0.000 0.344 0.080
#> GSM372312 5 0.6161 0.2632 0.392 0.000 0.000 0.176 0.416 0.016
#> GSM372314 5 0.3541 0.5930 0.260 0.000 0.000 0.000 0.728 0.012
#> GSM372316 1 0.2331 0.8131 0.888 0.000 0.000 0.000 0.080 0.032
#> GSM372318 1 0.0146 0.8099 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM372320 1 0.0000 0.8092 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372322 1 0.0000 0.8092 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372324 5 0.3636 0.5749 0.320 0.000 0.000 0.000 0.676 0.004
#> GSM372325 5 0.3679 0.6313 0.260 0.000 0.000 0.004 0.724 0.012
#> GSM372327 1 0.0000 0.8092 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372329 1 0.0000 0.8092 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372331 5 0.3518 0.5978 0.256 0.000 0.000 0.000 0.732 0.012
#> GSM372333 5 0.4025 0.6353 0.248 0.000 0.004 0.008 0.720 0.020
#> GSM372334 1 0.0000 0.8092 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372336 1 0.3700 0.7816 0.780 0.000 0.000 0.000 0.152 0.068
#> GSM372338 1 0.0000 0.8092 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372340 1 0.0000 0.8092 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372342 1 0.0000 0.8092 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372344 1 0.0000 0.8092 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372346 1 0.1075 0.8132 0.952 0.000 0.000 0.000 0.048 0.000
#> GSM372348 1 0.2442 0.7856 0.852 0.000 0.000 0.000 0.144 0.004
#> GSM372350 1 0.5609 0.0895 0.600 0.000 0.000 0.176 0.208 0.016
#> GSM372352 5 0.7502 0.1264 0.000 0.124 0.088 0.196 0.508 0.084
#> GSM372354 1 0.2910 0.8068 0.852 0.000 0.000 0.000 0.068 0.080
#> GSM372356 1 0.3808 0.7870 0.784 0.000 0.000 0.004 0.132 0.080
#> GSM372358 1 0.3627 0.7905 0.792 0.000 0.000 0.000 0.128 0.080
#> GSM372360 1 0.3627 0.7905 0.792 0.000 0.000 0.000 0.128 0.080
#> GSM372362 1 0.3586 0.7925 0.796 0.000 0.000 0.000 0.124 0.080
#> GSM372364 1 0.3808 0.7870 0.784 0.000 0.000 0.004 0.132 0.080
#> GSM372365 1 0.3808 0.7870 0.784 0.000 0.000 0.004 0.132 0.080
#> GSM372366 1 0.3366 0.8017 0.824 0.000 0.000 0.004 0.092 0.080
#> GSM372367 1 0.4543 0.6868 0.692 0.000 0.000 0.004 0.224 0.080
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) specimen(p) individual(p) k
#> MAD:skmeans 81 2.72e-04 1.85e-17 1.000 2
#> MAD:skmeans 80 1.82e-05 1.33e-16 0.949 3
#> MAD:skmeans 78 6.21e-12 6.60e-25 0.784 4
#> MAD:skmeans 63 2.17e-10 4.60e-21 0.686 5
#> MAD:skmeans 71 2.80e-10 6.74e-21 0.573 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 51941 rows and 82 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 1.000 0.982 0.992 0.4845 0.513 0.513
#> 3 3 0.860 0.926 0.964 0.3857 0.787 0.597
#> 4 4 0.762 0.767 0.840 0.1101 0.873 0.640
#> 5 5 0.861 0.845 0.924 0.0770 0.894 0.617
#> 6 6 0.867 0.759 0.894 0.0339 0.939 0.713
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
#> GSM372286 2 0.000 0.999 0.000 1.000
#> GSM372287 2 0.000 0.999 0.000 1.000
#> GSM372288 2 0.000 0.999 0.000 1.000
#> GSM372289 2 0.000 0.999 0.000 1.000
#> GSM372290 2 0.000 0.999 0.000 1.000
#> GSM372291 1 0.900 0.550 0.684 0.316
#> GSM372292 2 0.000 0.999 0.000 1.000
#> GSM372293 2 0.000 0.999 0.000 1.000
#> GSM372294 2 0.000 0.999 0.000 1.000
#> GSM372295 2 0.000 0.999 0.000 1.000
#> GSM372296 2 0.000 0.999 0.000 1.000
#> GSM372297 2 0.000 0.999 0.000 1.000
#> GSM372298 2 0.000 0.999 0.000 1.000
#> GSM372299 2 0.000 0.999 0.000 1.000
#> GSM372300 2 0.000 0.999 0.000 1.000
#> GSM372301 2 0.000 0.999 0.000 1.000
#> GSM372302 2 0.000 0.999 0.000 1.000
#> GSM372303 2 0.000 0.999 0.000 1.000
#> GSM372304 2 0.000 0.999 0.000 1.000
#> GSM372305 2 0.000 0.999 0.000 1.000
#> GSM372306 2 0.000 0.999 0.000 1.000
#> GSM372307 2 0.000 0.999 0.000 1.000
#> GSM372309 2 0.000 0.999 0.000 1.000
#> GSM372311 2 0.000 0.999 0.000 1.000
#> GSM372313 2 0.000 0.999 0.000 1.000
#> GSM372315 2 0.000 0.999 0.000 1.000
#> GSM372317 2 0.000 0.999 0.000 1.000
#> GSM372319 2 0.000 0.999 0.000 1.000
#> GSM372321 2 0.000 0.999 0.000 1.000
#> GSM372323 2 0.000 0.999 0.000 1.000
#> GSM372326 2 0.000 0.999 0.000 1.000
#> GSM372328 2 0.000 0.999 0.000 1.000
#> GSM372330 2 0.000 0.999 0.000 1.000
#> GSM372332 2 0.224 0.962 0.036 0.964
#> GSM372335 2 0.000 0.999 0.000 1.000
#> GSM372337 2 0.000 0.999 0.000 1.000
#> GSM372339 2 0.000 0.999 0.000 1.000
#> GSM372341 2 0.000 0.999 0.000 1.000
#> GSM372343 2 0.118 0.983 0.016 0.984
#> GSM372345 2 0.000 0.999 0.000 1.000
#> GSM372347 2 0.000 0.999 0.000 1.000
#> GSM372349 2 0.000 0.999 0.000 1.000
#> GSM372351 2 0.000 0.999 0.000 1.000
#> GSM372353 2 0.000 0.999 0.000 1.000
#> GSM372355 2 0.000 0.999 0.000 1.000
#> GSM372357 2 0.000 0.999 0.000 1.000
#> GSM372359 2 0.000 0.999 0.000 1.000
#> GSM372361 2 0.000 0.999 0.000 1.000
#> GSM372363 2 0.000 0.999 0.000 1.000
#> GSM372308 1 0.000 0.982 1.000 0.000
#> GSM372310 1 0.000 0.982 1.000 0.000
#> GSM372312 1 0.000 0.982 1.000 0.000
#> GSM372314 1 0.000 0.982 1.000 0.000
#> GSM372316 1 0.000 0.982 1.000 0.000
#> GSM372318 1 0.000 0.982 1.000 0.000
#> GSM372320 1 0.000 0.982 1.000 0.000
#> GSM372322 1 0.000 0.982 1.000 0.000
#> GSM372324 1 0.000 0.982 1.000 0.000
#> GSM372325 1 0.000 0.982 1.000 0.000
#> GSM372327 1 0.000 0.982 1.000 0.000
#> GSM372329 1 0.000 0.982 1.000 0.000
#> GSM372331 1 0.000 0.982 1.000 0.000
#> GSM372333 1 0.839 0.642 0.732 0.268
#> GSM372334 1 0.000 0.982 1.000 0.000
#> GSM372336 1 0.000 0.982 1.000 0.000
#> GSM372338 1 0.000 0.982 1.000 0.000
#> GSM372340 1 0.000 0.982 1.000 0.000
#> GSM372342 1 0.000 0.982 1.000 0.000
#> GSM372344 1 0.000 0.982 1.000 0.000
#> GSM372346 1 0.000 0.982 1.000 0.000
#> GSM372348 1 0.000 0.982 1.000 0.000
#> GSM372350 1 0.000 0.982 1.000 0.000
#> GSM372352 2 0.000 0.999 0.000 1.000
#> GSM372354 1 0.000 0.982 1.000 0.000
#> GSM372356 1 0.000 0.982 1.000 0.000
#> GSM372358 1 0.000 0.982 1.000 0.000
#> GSM372360 1 0.000 0.982 1.000 0.000
#> GSM372362 1 0.000 0.982 1.000 0.000
#> GSM372364 1 0.000 0.982 1.000 0.000
#> GSM372365 1 0.000 0.982 1.000 0.000
#> GSM372366 1 0.000 0.982 1.000 0.000
#> GSM372367 1 0.000 0.982 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM372286 2 0.000 0.954 0.000 1.000 0.000
#> GSM372287 2 0.000 0.954 0.000 1.000 0.000
#> GSM372288 2 0.000 0.954 0.000 1.000 0.000
#> GSM372289 2 0.000 0.954 0.000 1.000 0.000
#> GSM372290 2 0.000 0.954 0.000 1.000 0.000
#> GSM372291 1 0.375 0.825 0.856 0.000 0.144
#> GSM372292 3 0.455 0.776 0.000 0.200 0.800
#> GSM372293 3 0.000 0.917 0.000 0.000 1.000
#> GSM372294 2 0.000 0.954 0.000 1.000 0.000
#> GSM372295 3 0.601 0.509 0.000 0.372 0.628
#> GSM372296 2 0.000 0.954 0.000 1.000 0.000
#> GSM372297 2 0.000 0.954 0.000 1.000 0.000
#> GSM372298 2 0.000 0.954 0.000 1.000 0.000
#> GSM372299 3 0.455 0.776 0.000 0.200 0.800
#> GSM372300 3 0.455 0.776 0.000 0.200 0.800
#> GSM372301 3 0.455 0.776 0.000 0.200 0.800
#> GSM372302 2 0.000 0.954 0.000 1.000 0.000
#> GSM372303 3 0.000 0.917 0.000 0.000 1.000
#> GSM372304 2 0.000 0.954 0.000 1.000 0.000
#> GSM372305 2 0.000 0.954 0.000 1.000 0.000
#> GSM372306 2 0.455 0.774 0.000 0.800 0.200
#> GSM372307 2 0.000 0.954 0.000 1.000 0.000
#> GSM372309 2 0.000 0.954 0.000 1.000 0.000
#> GSM372311 2 0.000 0.954 0.000 1.000 0.000
#> GSM372313 2 0.000 0.954 0.000 1.000 0.000
#> GSM372315 2 0.000 0.954 0.000 1.000 0.000
#> GSM372317 2 0.455 0.774 0.000 0.800 0.200
#> GSM372319 3 0.319 0.851 0.000 0.112 0.888
#> GSM372321 3 0.000 0.917 0.000 0.000 1.000
#> GSM372323 3 0.000 0.917 0.000 0.000 1.000
#> GSM372326 3 0.000 0.917 0.000 0.000 1.000
#> GSM372328 3 0.000 0.917 0.000 0.000 1.000
#> GSM372330 2 0.000 0.954 0.000 1.000 0.000
#> GSM372332 3 0.000 0.917 0.000 0.000 1.000
#> GSM372335 2 0.455 0.774 0.000 0.800 0.200
#> GSM372337 3 0.000 0.917 0.000 0.000 1.000
#> GSM372339 3 0.000 0.917 0.000 0.000 1.000
#> GSM372341 3 0.000 0.917 0.000 0.000 1.000
#> GSM372343 3 0.000 0.917 0.000 0.000 1.000
#> GSM372345 3 0.000 0.917 0.000 0.000 1.000
#> GSM372347 3 0.000 0.917 0.000 0.000 1.000
#> GSM372349 3 0.000 0.917 0.000 0.000 1.000
#> GSM372351 3 0.000 0.917 0.000 0.000 1.000
#> GSM372353 3 0.470 0.702 0.000 0.212 0.788
#> GSM372355 2 0.000 0.954 0.000 1.000 0.000
#> GSM372357 2 0.455 0.774 0.000 0.800 0.200
#> GSM372359 2 0.455 0.774 0.000 0.800 0.200
#> GSM372361 2 0.000 0.954 0.000 1.000 0.000
#> GSM372363 2 0.000 0.954 0.000 1.000 0.000
#> GSM372308 1 0.000 0.995 1.000 0.000 0.000
#> GSM372310 1 0.000 0.995 1.000 0.000 0.000
#> GSM372312 1 0.000 0.995 1.000 0.000 0.000
#> GSM372314 1 0.000 0.995 1.000 0.000 0.000
#> GSM372316 1 0.000 0.995 1.000 0.000 0.000
#> GSM372318 1 0.000 0.995 1.000 0.000 0.000
#> GSM372320 1 0.000 0.995 1.000 0.000 0.000
#> GSM372322 1 0.000 0.995 1.000 0.000 0.000
#> GSM372324 1 0.000 0.995 1.000 0.000 0.000
#> GSM372325 3 0.506 0.658 0.244 0.000 0.756
#> GSM372327 1 0.000 0.995 1.000 0.000 0.000
#> GSM372329 1 0.000 0.995 1.000 0.000 0.000
#> GSM372331 1 0.000 0.995 1.000 0.000 0.000
#> GSM372333 3 0.000 0.917 0.000 0.000 1.000
#> GSM372334 1 0.000 0.995 1.000 0.000 0.000
#> GSM372336 1 0.000 0.995 1.000 0.000 0.000
#> GSM372338 1 0.000 0.995 1.000 0.000 0.000
#> GSM372340 1 0.000 0.995 1.000 0.000 0.000
#> GSM372342 1 0.000 0.995 1.000 0.000 0.000
#> GSM372344 1 0.000 0.995 1.000 0.000 0.000
#> GSM372346 1 0.000 0.995 1.000 0.000 0.000
#> GSM372348 1 0.000 0.995 1.000 0.000 0.000
#> GSM372350 1 0.000 0.995 1.000 0.000 0.000
#> GSM372352 3 0.240 0.875 0.004 0.064 0.932
#> GSM372354 1 0.000 0.995 1.000 0.000 0.000
#> GSM372356 1 0.000 0.995 1.000 0.000 0.000
#> GSM372358 1 0.000 0.995 1.000 0.000 0.000
#> GSM372360 1 0.000 0.995 1.000 0.000 0.000
#> GSM372362 1 0.000 0.995 1.000 0.000 0.000
#> GSM372364 1 0.000 0.995 1.000 0.000 0.000
#> GSM372365 1 0.000 0.995 1.000 0.000 0.000
#> GSM372366 1 0.000 0.995 1.000 0.000 0.000
#> GSM372367 1 0.000 0.995 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM372286 2 0.0000 0.8979 0.000 1.000 0.000 0.000
#> GSM372287 2 0.4446 0.8236 0.000 0.776 0.028 0.196
#> GSM372288 2 0.2345 0.8779 0.000 0.900 0.000 0.100
#> GSM372289 2 0.0921 0.8960 0.000 0.972 0.000 0.028
#> GSM372290 2 0.4980 0.7600 0.000 0.680 0.016 0.304
#> GSM372291 1 0.4868 0.5470 0.720 0.000 0.024 0.256
#> GSM372292 3 0.4608 0.7174 0.000 0.004 0.692 0.304
#> GSM372293 3 0.4250 0.7399 0.000 0.000 0.724 0.276
#> GSM372294 2 0.3356 0.8462 0.000 0.824 0.000 0.176
#> GSM372295 1 0.8183 -0.0816 0.356 0.008 0.332 0.304
#> GSM372296 2 0.4608 0.7687 0.000 0.692 0.004 0.304
#> GSM372297 2 0.5277 0.7495 0.000 0.668 0.028 0.304
#> GSM372298 2 0.4406 0.7728 0.000 0.700 0.000 0.300
#> GSM372299 1 0.7772 0.2194 0.464 0.004 0.228 0.304
#> GSM372300 3 0.4584 0.7203 0.000 0.004 0.696 0.300
#> GSM372301 3 0.4608 0.7174 0.000 0.004 0.692 0.304
#> GSM372302 2 0.5277 0.7495 0.000 0.668 0.028 0.304
#> GSM372303 3 0.4250 0.7399 0.000 0.000 0.724 0.276
#> GSM372304 2 0.4431 0.7710 0.000 0.696 0.000 0.304
#> GSM372305 2 0.0000 0.8979 0.000 1.000 0.000 0.000
#> GSM372306 2 0.0188 0.8967 0.000 0.996 0.004 0.000
#> GSM372307 2 0.1256 0.8953 0.000 0.964 0.008 0.028
#> GSM372309 2 0.0469 0.8964 0.000 0.988 0.012 0.000
#> GSM372311 2 0.0000 0.8979 0.000 1.000 0.000 0.000
#> GSM372313 2 0.0000 0.8979 0.000 1.000 0.000 0.000
#> GSM372315 2 0.0000 0.8979 0.000 1.000 0.000 0.000
#> GSM372317 2 0.1302 0.8833 0.000 0.956 0.044 0.000
#> GSM372319 3 0.0592 0.8834 0.000 0.000 0.984 0.016
#> GSM372321 3 0.0000 0.8901 0.000 0.000 1.000 0.000
#> GSM372323 3 0.0000 0.8901 0.000 0.000 1.000 0.000
#> GSM372326 3 0.0000 0.8901 0.000 0.000 1.000 0.000
#> GSM372328 3 0.0000 0.8901 0.000 0.000 1.000 0.000
#> GSM372330 2 0.0000 0.8979 0.000 1.000 0.000 0.000
#> GSM372332 3 0.0000 0.8901 0.000 0.000 1.000 0.000
#> GSM372335 2 0.3569 0.7690 0.000 0.804 0.196 0.000
#> GSM372337 3 0.0000 0.8901 0.000 0.000 1.000 0.000
#> GSM372339 3 0.0000 0.8901 0.000 0.000 1.000 0.000
#> GSM372341 3 0.0000 0.8901 0.000 0.000 1.000 0.000
#> GSM372343 3 0.0000 0.8901 0.000 0.000 1.000 0.000
#> GSM372345 3 0.0921 0.8714 0.028 0.000 0.972 0.000
#> GSM372347 3 0.0921 0.8714 0.028 0.000 0.972 0.000
#> GSM372349 3 0.0000 0.8901 0.000 0.000 1.000 0.000
#> GSM372351 3 0.0000 0.8901 0.000 0.000 1.000 0.000
#> GSM372353 3 0.4855 0.4226 0.000 0.400 0.600 0.000
#> GSM372355 2 0.0000 0.8979 0.000 1.000 0.000 0.000
#> GSM372357 2 0.0188 0.8967 0.000 0.996 0.004 0.000
#> GSM372359 2 0.0188 0.8967 0.000 0.996 0.004 0.000
#> GSM372361 2 0.1936 0.8886 0.000 0.940 0.028 0.032
#> GSM372363 2 0.0188 0.8981 0.000 0.996 0.000 0.004
#> GSM372308 1 0.0000 0.7182 1.000 0.000 0.000 0.000
#> GSM372310 1 0.0592 0.7144 0.984 0.000 0.000 0.016
#> GSM372312 1 0.0000 0.7182 1.000 0.000 0.000 0.000
#> GSM372314 1 0.0000 0.7182 1.000 0.000 0.000 0.000
#> GSM372316 4 0.4454 0.9728 0.308 0.000 0.000 0.692
#> GSM372318 4 0.4431 0.9767 0.304 0.000 0.000 0.696
#> GSM372320 4 0.4431 0.9767 0.304 0.000 0.000 0.696
#> GSM372322 4 0.4431 0.9767 0.304 0.000 0.000 0.696
#> GSM372324 1 0.0000 0.7182 1.000 0.000 0.000 0.000
#> GSM372325 1 0.4356 0.5363 0.708 0.000 0.292 0.000
#> GSM372327 4 0.4431 0.9767 0.304 0.000 0.000 0.696
#> GSM372329 4 0.4431 0.9767 0.304 0.000 0.000 0.696
#> GSM372331 1 0.0000 0.7182 1.000 0.000 0.000 0.000
#> GSM372333 1 0.4888 0.3150 0.588 0.000 0.412 0.000
#> GSM372334 4 0.4431 0.9767 0.304 0.000 0.000 0.696
#> GSM372336 1 0.0817 0.7114 0.976 0.000 0.000 0.024
#> GSM372338 4 0.4431 0.9767 0.304 0.000 0.000 0.696
#> GSM372340 4 0.4431 0.9767 0.304 0.000 0.000 0.696
#> GSM372342 4 0.4431 0.9767 0.304 0.000 0.000 0.696
#> GSM372344 4 0.4431 0.9767 0.304 0.000 0.000 0.696
#> GSM372346 4 0.4431 0.9767 0.304 0.000 0.000 0.696
#> GSM372348 1 0.0000 0.7182 1.000 0.000 0.000 0.000
#> GSM372350 1 0.2921 0.5827 0.860 0.000 0.000 0.140
#> GSM372352 1 0.4933 0.2949 0.568 0.000 0.432 0.000
#> GSM372354 4 0.4866 0.8485 0.404 0.000 0.000 0.596
#> GSM372356 1 0.0921 0.7094 0.972 0.000 0.000 0.028
#> GSM372358 1 0.4877 -0.4157 0.592 0.000 0.000 0.408
#> GSM372360 1 0.0921 0.7094 0.972 0.000 0.000 0.028
#> GSM372362 1 0.4925 -0.4779 0.572 0.000 0.000 0.428
#> GSM372364 1 0.0921 0.7094 0.972 0.000 0.000 0.028
#> GSM372365 1 0.0921 0.7094 0.972 0.000 0.000 0.028
#> GSM372366 4 0.4866 0.8485 0.404 0.000 0.000 0.596
#> GSM372367 1 0.0921 0.7094 0.972 0.000 0.000 0.028
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM372286 2 0.0290 0.932 0.000 0.992 0.000 0.008 0.000
#> GSM372287 2 0.4251 0.487 0.000 0.624 0.000 0.372 0.004
#> GSM372288 2 0.2763 0.844 0.000 0.848 0.000 0.148 0.004
#> GSM372289 2 0.1831 0.903 0.000 0.920 0.000 0.076 0.004
#> GSM372290 4 0.0162 0.963 0.000 0.000 0.000 0.996 0.004
#> GSM372291 5 0.3513 0.667 0.020 0.000 0.000 0.180 0.800
#> GSM372292 4 0.0000 0.963 0.000 0.000 0.000 1.000 0.000
#> GSM372293 4 0.1732 0.907 0.000 0.000 0.080 0.920 0.000
#> GSM372294 2 0.3461 0.755 0.000 0.772 0.000 0.224 0.004
#> GSM372295 4 0.0000 0.963 0.000 0.000 0.000 1.000 0.000
#> GSM372296 4 0.0162 0.963 0.000 0.000 0.000 0.996 0.004
#> GSM372297 4 0.0162 0.963 0.000 0.000 0.000 0.996 0.004
#> GSM372298 4 0.0671 0.958 0.000 0.016 0.000 0.980 0.004
#> GSM372299 4 0.0451 0.960 0.000 0.008 0.004 0.988 0.000
#> GSM372300 4 0.0703 0.953 0.000 0.000 0.024 0.976 0.000
#> GSM372301 4 0.0162 0.963 0.000 0.000 0.004 0.996 0.000
#> GSM372302 4 0.0000 0.963 0.000 0.000 0.000 1.000 0.000
#> GSM372303 4 0.1732 0.907 0.000 0.000 0.080 0.920 0.000
#> GSM372304 4 0.2930 0.773 0.000 0.164 0.000 0.832 0.004
#> GSM372305 2 0.0000 0.933 0.000 1.000 0.000 0.000 0.000
#> GSM372306 2 0.0000 0.933 0.000 1.000 0.000 0.000 0.000
#> GSM372307 2 0.1831 0.903 0.000 0.920 0.000 0.076 0.004
#> GSM372309 2 0.0000 0.933 0.000 1.000 0.000 0.000 0.000
#> GSM372311 2 0.0000 0.933 0.000 1.000 0.000 0.000 0.000
#> GSM372313 2 0.0000 0.933 0.000 1.000 0.000 0.000 0.000
#> GSM372315 2 0.0000 0.933 0.000 1.000 0.000 0.000 0.000
#> GSM372317 2 0.1270 0.907 0.000 0.948 0.052 0.000 0.000
#> GSM372319 3 0.1270 0.912 0.000 0.000 0.948 0.052 0.000
#> GSM372321 3 0.0000 0.961 0.000 0.000 1.000 0.000 0.000
#> GSM372323 3 0.0000 0.961 0.000 0.000 1.000 0.000 0.000
#> GSM372326 3 0.0000 0.961 0.000 0.000 1.000 0.000 0.000
#> GSM372328 3 0.0000 0.961 0.000 0.000 1.000 0.000 0.000
#> GSM372330 2 0.0000 0.933 0.000 1.000 0.000 0.000 0.000
#> GSM372332 3 0.0000 0.961 0.000 0.000 1.000 0.000 0.000
#> GSM372335 2 0.3074 0.763 0.000 0.804 0.196 0.000 0.000
#> GSM372337 3 0.0000 0.961 0.000 0.000 1.000 0.000 0.000
#> GSM372339 3 0.0000 0.961 0.000 0.000 1.000 0.000 0.000
#> GSM372341 3 0.0000 0.961 0.000 0.000 1.000 0.000 0.000
#> GSM372343 3 0.0000 0.961 0.000 0.000 1.000 0.000 0.000
#> GSM372345 3 0.0000 0.961 0.000 0.000 1.000 0.000 0.000
#> GSM372347 3 0.0794 0.938 0.000 0.000 0.972 0.000 0.028
#> GSM372349 3 0.0000 0.961 0.000 0.000 1.000 0.000 0.000
#> GSM372351 3 0.0000 0.961 0.000 0.000 1.000 0.000 0.000
#> GSM372353 3 0.4219 0.316 0.000 0.416 0.584 0.000 0.000
#> GSM372355 2 0.0000 0.933 0.000 1.000 0.000 0.000 0.000
#> GSM372357 2 0.0000 0.933 0.000 1.000 0.000 0.000 0.000
#> GSM372359 2 0.0000 0.933 0.000 1.000 0.000 0.000 0.000
#> GSM372361 2 0.1792 0.900 0.000 0.916 0.000 0.084 0.000
#> GSM372363 2 0.0510 0.930 0.000 0.984 0.000 0.016 0.000
#> GSM372308 5 0.0162 0.803 0.004 0.000 0.000 0.000 0.996
#> GSM372310 5 0.2074 0.785 0.104 0.000 0.000 0.000 0.896
#> GSM372312 5 0.0162 0.803 0.004 0.000 0.000 0.000 0.996
#> GSM372314 5 0.0162 0.803 0.004 0.000 0.000 0.000 0.996
#> GSM372316 1 0.0162 0.896 0.996 0.000 0.000 0.000 0.004
#> GSM372318 1 0.0162 0.896 0.996 0.000 0.000 0.000 0.004
#> GSM372320 1 0.0000 0.898 1.000 0.000 0.000 0.000 0.000
#> GSM372322 1 0.0000 0.898 1.000 0.000 0.000 0.000 0.000
#> GSM372324 5 0.0162 0.803 0.004 0.000 0.000 0.000 0.996
#> GSM372325 5 0.3395 0.633 0.000 0.000 0.236 0.000 0.764
#> GSM372327 1 0.0000 0.898 1.000 0.000 0.000 0.000 0.000
#> GSM372329 1 0.0000 0.898 1.000 0.000 0.000 0.000 0.000
#> GSM372331 5 0.0162 0.803 0.004 0.000 0.000 0.000 0.996
#> GSM372333 5 0.3452 0.621 0.000 0.000 0.244 0.000 0.756
#> GSM372334 1 0.0000 0.898 1.000 0.000 0.000 0.000 0.000
#> GSM372336 5 0.3109 0.742 0.200 0.000 0.000 0.000 0.800
#> GSM372338 1 0.0000 0.898 1.000 0.000 0.000 0.000 0.000
#> GSM372340 1 0.0000 0.898 1.000 0.000 0.000 0.000 0.000
#> GSM372342 1 0.0000 0.898 1.000 0.000 0.000 0.000 0.000
#> GSM372344 1 0.0000 0.898 1.000 0.000 0.000 0.000 0.000
#> GSM372346 1 0.0000 0.898 1.000 0.000 0.000 0.000 0.000
#> GSM372348 5 0.0162 0.803 0.004 0.000 0.000 0.000 0.996
#> GSM372350 5 0.4283 0.371 0.456 0.000 0.000 0.000 0.544
#> GSM372352 5 0.3424 0.627 0.000 0.000 0.240 0.000 0.760
#> GSM372354 1 0.3395 0.676 0.764 0.000 0.000 0.000 0.236
#> GSM372356 5 0.3242 0.731 0.216 0.000 0.000 0.000 0.784
#> GSM372358 1 0.4201 0.318 0.592 0.000 0.000 0.000 0.408
#> GSM372360 5 0.3242 0.731 0.216 0.000 0.000 0.000 0.784
#> GSM372362 1 0.4138 0.387 0.616 0.000 0.000 0.000 0.384
#> GSM372364 5 0.3242 0.731 0.216 0.000 0.000 0.000 0.784
#> GSM372365 5 0.3242 0.731 0.216 0.000 0.000 0.000 0.784
#> GSM372366 1 0.3395 0.676 0.764 0.000 0.000 0.000 0.236
#> GSM372367 5 0.3242 0.731 0.216 0.000 0.000 0.000 0.784
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM372286 2 0.0260 0.8994 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM372287 4 0.0632 0.8788 0.000 0.024 0.000 0.976 0.000 0.000
#> GSM372288 2 0.3857 0.2502 0.000 0.532 0.000 0.468 0.000 0.000
#> GSM372289 2 0.3592 0.5379 0.000 0.656 0.000 0.344 0.000 0.000
#> GSM372290 4 0.0000 0.8859 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM372291 5 0.5994 0.1659 0.000 0.000 0.000 0.252 0.432 0.316
#> GSM372292 6 0.1327 0.9605 0.000 0.000 0.000 0.064 0.000 0.936
#> GSM372293 6 0.1411 0.9586 0.000 0.000 0.004 0.060 0.000 0.936
#> GSM372294 4 0.0865 0.8701 0.000 0.036 0.000 0.964 0.000 0.000
#> GSM372295 4 0.2562 0.7660 0.000 0.000 0.000 0.828 0.000 0.172
#> GSM372296 4 0.0000 0.8859 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM372297 4 0.1444 0.8423 0.000 0.000 0.000 0.928 0.000 0.072
#> GSM372298 6 0.3050 0.7496 0.000 0.000 0.000 0.236 0.000 0.764
#> GSM372299 6 0.1471 0.9583 0.000 0.004 0.000 0.064 0.000 0.932
#> GSM372300 6 0.1327 0.9605 0.000 0.000 0.000 0.064 0.000 0.936
#> GSM372301 6 0.1327 0.9605 0.000 0.000 0.000 0.064 0.000 0.936
#> GSM372302 4 0.2416 0.7850 0.000 0.000 0.000 0.844 0.000 0.156
#> GSM372303 6 0.1411 0.9586 0.000 0.000 0.004 0.060 0.000 0.936
#> GSM372304 4 0.0000 0.8859 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM372305 2 0.0000 0.9027 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM372306 2 0.0000 0.9027 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM372307 2 0.3647 0.5092 0.000 0.640 0.000 0.360 0.000 0.000
#> GSM372309 2 0.0000 0.9027 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM372311 2 0.0000 0.9027 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM372313 2 0.0000 0.9027 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM372315 2 0.0146 0.9012 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM372317 2 0.1141 0.8651 0.000 0.948 0.052 0.000 0.000 0.000
#> GSM372319 3 0.2664 0.7390 0.000 0.000 0.816 0.184 0.000 0.000
#> GSM372321 3 0.0000 0.9465 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372323 3 0.0000 0.9465 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372326 3 0.0000 0.9465 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372328 3 0.0000 0.9465 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372330 2 0.0000 0.9027 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM372332 3 0.0000 0.9465 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372335 2 0.2730 0.7229 0.000 0.808 0.192 0.000 0.000 0.000
#> GSM372337 3 0.0000 0.9465 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372339 3 0.0000 0.9465 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372341 3 0.0000 0.9465 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372343 3 0.0000 0.9465 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372345 3 0.0000 0.9465 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372347 3 0.1391 0.8995 0.000 0.000 0.944 0.000 0.016 0.040
#> GSM372349 3 0.0000 0.9465 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372351 3 0.0000 0.9465 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372353 3 0.3789 0.2997 0.000 0.416 0.584 0.000 0.000 0.000
#> GSM372355 2 0.0000 0.9027 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM372357 2 0.0000 0.9027 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM372359 2 0.0000 0.9027 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM372361 4 0.2996 0.6936 0.000 0.228 0.000 0.772 0.000 0.000
#> GSM372363 2 0.0146 0.9011 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM372308 5 0.1007 0.7521 0.000 0.000 0.000 0.000 0.956 0.044
#> GSM372310 5 0.0865 0.7467 0.036 0.000 0.000 0.000 0.964 0.000
#> GSM372312 5 0.1327 0.7515 0.000 0.000 0.000 0.000 0.936 0.064
#> GSM372314 5 0.1327 0.7515 0.000 0.000 0.000 0.000 0.936 0.064
#> GSM372316 1 0.0146 0.8746 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM372318 1 0.0632 0.8590 0.976 0.000 0.000 0.000 0.024 0.000
#> GSM372320 1 0.0000 0.8771 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372322 1 0.0000 0.8771 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372324 5 0.1327 0.7515 0.000 0.000 0.000 0.000 0.936 0.064
#> GSM372325 5 0.4899 0.2540 0.000 0.000 0.404 0.000 0.532 0.064
#> GSM372327 1 0.0000 0.8771 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372329 1 0.0000 0.8771 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372331 5 0.1327 0.7515 0.000 0.000 0.000 0.000 0.936 0.064
#> GSM372333 5 0.4899 0.2540 0.000 0.000 0.404 0.000 0.532 0.064
#> GSM372334 1 0.0000 0.8771 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372336 5 0.1714 0.7338 0.092 0.000 0.000 0.000 0.908 0.000
#> GSM372338 1 0.0000 0.8771 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372340 1 0.0000 0.8771 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372342 1 0.0000 0.8771 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372344 1 0.0000 0.8771 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372346 1 0.0000 0.8771 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372348 5 0.1327 0.7515 0.000 0.000 0.000 0.000 0.936 0.064
#> GSM372350 1 0.3823 0.0391 0.564 0.000 0.000 0.000 0.436 0.000
#> GSM372352 5 0.5152 0.2865 0.000 0.000 0.376 0.000 0.532 0.092
#> GSM372354 1 0.3857 0.1357 0.532 0.000 0.000 0.000 0.468 0.000
#> GSM372356 5 0.1765 0.7322 0.096 0.000 0.000 0.000 0.904 0.000
#> GSM372358 5 0.3857 -0.0330 0.468 0.000 0.000 0.000 0.532 0.000
#> GSM372360 5 0.1765 0.7322 0.096 0.000 0.000 0.000 0.904 0.000
#> GSM372362 5 0.3868 -0.1246 0.496 0.000 0.000 0.000 0.504 0.000
#> GSM372364 5 0.1765 0.7322 0.096 0.000 0.000 0.000 0.904 0.000
#> GSM372365 5 0.1765 0.7322 0.096 0.000 0.000 0.000 0.904 0.000
#> GSM372366 1 0.3857 0.1357 0.532 0.000 0.000 0.000 0.468 0.000
#> GSM372367 5 0.1765 0.7322 0.096 0.000 0.000 0.000 0.904 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) specimen(p) individual(p) k
#> MAD:pam 82 3.35e-04 8.50e-17 0.999 2
#> MAD:pam 82 2.82e-04 2.77e-14 0.900 3
#> MAD:pam 75 1.03e-03 3.20e-14 0.931 4
#> MAD:pam 77 2.51e-10 2.68e-22 0.806 5
#> MAD:pam 71 8.03e-10 1.83e-20 0.486 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 51941 rows and 82 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.973 0.988 0.4759 0.518 0.518
#> 3 3 0.729 0.841 0.902 0.3690 0.801 0.623
#> 4 4 1.000 0.965 0.983 0.1258 0.918 0.762
#> 5 5 0.730 0.669 0.848 0.0502 0.945 0.807
#> 6 6 0.755 0.736 0.832 0.0692 0.856 0.482
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
#> GSM372286 2 0.0000 1.000 0.000 1.000
#> GSM372287 2 0.0000 1.000 0.000 1.000
#> GSM372288 2 0.0000 1.000 0.000 1.000
#> GSM372289 2 0.0000 1.000 0.000 1.000
#> GSM372290 2 0.0000 1.000 0.000 1.000
#> GSM372291 2 0.0672 0.992 0.008 0.992
#> GSM372292 2 0.0000 1.000 0.000 1.000
#> GSM372293 2 0.0000 1.000 0.000 1.000
#> GSM372294 2 0.0000 1.000 0.000 1.000
#> GSM372295 2 0.0000 1.000 0.000 1.000
#> GSM372296 2 0.0000 1.000 0.000 1.000
#> GSM372297 2 0.0000 1.000 0.000 1.000
#> GSM372298 2 0.0000 1.000 0.000 1.000
#> GSM372299 2 0.0000 1.000 0.000 1.000
#> GSM372300 2 0.0000 1.000 0.000 1.000
#> GSM372301 2 0.0000 1.000 0.000 1.000
#> GSM372302 2 0.0000 1.000 0.000 1.000
#> GSM372303 2 0.0000 1.000 0.000 1.000
#> GSM372304 2 0.0000 1.000 0.000 1.000
#> GSM372305 2 0.0000 1.000 0.000 1.000
#> GSM372306 2 0.0000 1.000 0.000 1.000
#> GSM372307 2 0.0000 1.000 0.000 1.000
#> GSM372309 2 0.0000 1.000 0.000 1.000
#> GSM372311 2 0.0000 1.000 0.000 1.000
#> GSM372313 2 0.0000 1.000 0.000 1.000
#> GSM372315 2 0.0000 1.000 0.000 1.000
#> GSM372317 2 0.0000 1.000 0.000 1.000
#> GSM372319 2 0.0000 1.000 0.000 1.000
#> GSM372321 2 0.0000 1.000 0.000 1.000
#> GSM372323 2 0.0000 1.000 0.000 1.000
#> GSM372326 2 0.0000 1.000 0.000 1.000
#> GSM372328 2 0.0000 1.000 0.000 1.000
#> GSM372330 2 0.0000 1.000 0.000 1.000
#> GSM372332 2 0.0000 1.000 0.000 1.000
#> GSM372335 2 0.0000 1.000 0.000 1.000
#> GSM372337 2 0.0000 1.000 0.000 1.000
#> GSM372339 2 0.0000 1.000 0.000 1.000
#> GSM372341 2 0.0000 1.000 0.000 1.000
#> GSM372343 2 0.0000 1.000 0.000 1.000
#> GSM372345 2 0.0000 1.000 0.000 1.000
#> GSM372347 2 0.0000 1.000 0.000 1.000
#> GSM372349 2 0.0000 1.000 0.000 1.000
#> GSM372351 2 0.0000 1.000 0.000 1.000
#> GSM372353 2 0.0000 1.000 0.000 1.000
#> GSM372355 2 0.0000 1.000 0.000 1.000
#> GSM372357 2 0.0000 1.000 0.000 1.000
#> GSM372359 2 0.0000 1.000 0.000 1.000
#> GSM372361 2 0.0000 1.000 0.000 1.000
#> GSM372363 2 0.0000 1.000 0.000 1.000
#> GSM372308 1 0.0000 0.968 1.000 0.000
#> GSM372310 1 0.0000 0.968 1.000 0.000
#> GSM372312 1 0.7528 0.744 0.784 0.216
#> GSM372314 1 0.0000 0.968 1.000 0.000
#> GSM372316 1 0.0000 0.968 1.000 0.000
#> GSM372318 1 0.0000 0.968 1.000 0.000
#> GSM372320 1 0.0000 0.968 1.000 0.000
#> GSM372322 1 0.0000 0.968 1.000 0.000
#> GSM372324 1 0.2043 0.943 0.968 0.032
#> GSM372325 1 0.6148 0.825 0.848 0.152
#> GSM372327 1 0.0000 0.968 1.000 0.000
#> GSM372329 1 0.0000 0.968 1.000 0.000
#> GSM372331 1 0.0000 0.968 1.000 0.000
#> GSM372333 1 0.9608 0.419 0.616 0.384
#> GSM372334 1 0.0000 0.968 1.000 0.000
#> GSM372336 1 0.0000 0.968 1.000 0.000
#> GSM372338 1 0.0000 0.968 1.000 0.000
#> GSM372340 1 0.0000 0.968 1.000 0.000
#> GSM372342 1 0.0000 0.968 1.000 0.000
#> GSM372344 1 0.0000 0.968 1.000 0.000
#> GSM372346 1 0.0000 0.968 1.000 0.000
#> GSM372348 1 0.0000 0.968 1.000 0.000
#> GSM372350 1 0.7528 0.744 0.784 0.216
#> GSM372352 2 0.0672 0.992 0.008 0.992
#> GSM372354 1 0.0000 0.968 1.000 0.000
#> GSM372356 1 0.0000 0.968 1.000 0.000
#> GSM372358 1 0.0000 0.968 1.000 0.000
#> GSM372360 1 0.0000 0.968 1.000 0.000
#> GSM372362 1 0.0000 0.968 1.000 0.000
#> GSM372364 1 0.0000 0.968 1.000 0.000
#> GSM372365 1 0.0000 0.968 1.000 0.000
#> GSM372366 1 0.0000 0.968 1.000 0.000
#> GSM372367 1 0.0000 0.968 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM372286 3 0.0747 0.841 0.000 0.016 0.984
#> GSM372287 2 0.1860 0.872 0.000 0.948 0.052
#> GSM372288 2 0.4062 0.876 0.000 0.836 0.164
#> GSM372289 2 0.4235 0.869 0.000 0.824 0.176
#> GSM372290 2 0.4121 0.872 0.000 0.832 0.168
#> GSM372291 2 0.2229 0.857 0.012 0.944 0.044
#> GSM372292 2 0.3752 0.881 0.000 0.856 0.144
#> GSM372293 2 0.4974 0.777 0.000 0.764 0.236
#> GSM372294 2 0.2261 0.873 0.000 0.932 0.068
#> GSM372295 2 0.1753 0.870 0.000 0.952 0.048
#> GSM372296 2 0.4002 0.877 0.000 0.840 0.160
#> GSM372297 2 0.1860 0.872 0.000 0.948 0.052
#> GSM372298 2 0.3038 0.886 0.000 0.896 0.104
#> GSM372299 2 0.2356 0.863 0.000 0.928 0.072
#> GSM372300 2 0.3619 0.882 0.000 0.864 0.136
#> GSM372301 2 0.3816 0.880 0.000 0.852 0.148
#> GSM372302 2 0.2537 0.882 0.000 0.920 0.080
#> GSM372303 2 0.3816 0.876 0.000 0.852 0.148
#> GSM372304 2 0.1860 0.872 0.000 0.948 0.052
#> GSM372305 3 0.0424 0.841 0.000 0.008 0.992
#> GSM372306 3 0.0424 0.841 0.000 0.008 0.992
#> GSM372307 2 0.6062 0.499 0.000 0.616 0.384
#> GSM372309 3 0.0747 0.841 0.000 0.016 0.984
#> GSM372311 3 0.1031 0.835 0.000 0.024 0.976
#> GSM372313 3 0.0424 0.841 0.000 0.008 0.992
#> GSM372315 3 0.6309 -0.216 0.000 0.500 0.500
#> GSM372317 3 0.0424 0.841 0.000 0.008 0.992
#> GSM372319 3 0.4399 0.781 0.000 0.188 0.812
#> GSM372321 3 0.4452 0.782 0.000 0.192 0.808
#> GSM372323 3 0.3752 0.812 0.000 0.144 0.856
#> GSM372326 3 0.3816 0.810 0.000 0.148 0.852
#> GSM372328 3 0.4702 0.772 0.000 0.212 0.788
#> GSM372330 3 0.0424 0.841 0.000 0.008 0.992
#> GSM372332 3 0.4702 0.772 0.000 0.212 0.788
#> GSM372335 3 0.0424 0.841 0.000 0.008 0.992
#> GSM372337 3 0.3752 0.812 0.000 0.144 0.856
#> GSM372339 3 0.4702 0.772 0.000 0.212 0.788
#> GSM372341 3 0.4702 0.772 0.000 0.212 0.788
#> GSM372343 3 0.4702 0.772 0.000 0.212 0.788
#> GSM372345 3 0.3752 0.812 0.000 0.144 0.856
#> GSM372347 3 0.0237 0.840 0.000 0.004 0.996
#> GSM372349 3 0.4702 0.772 0.000 0.212 0.788
#> GSM372351 3 0.4555 0.778 0.000 0.200 0.800
#> GSM372353 3 0.0892 0.834 0.000 0.020 0.980
#> GSM372355 3 0.0424 0.841 0.000 0.008 0.992
#> GSM372357 3 0.0424 0.841 0.000 0.008 0.992
#> GSM372359 3 0.0424 0.841 0.000 0.008 0.992
#> GSM372361 2 0.6286 0.214 0.000 0.536 0.464
#> GSM372363 3 0.0592 0.840 0.000 0.012 0.988
#> GSM372308 1 0.1643 0.956 0.956 0.044 0.000
#> GSM372310 1 0.1643 0.956 0.956 0.044 0.000
#> GSM372312 1 0.5551 0.788 0.768 0.212 0.020
#> GSM372314 1 0.1643 0.956 0.956 0.044 0.000
#> GSM372316 1 0.0000 0.966 1.000 0.000 0.000
#> GSM372318 1 0.0000 0.966 1.000 0.000 0.000
#> GSM372320 1 0.0000 0.966 1.000 0.000 0.000
#> GSM372322 1 0.0000 0.966 1.000 0.000 0.000
#> GSM372324 1 0.5276 0.861 0.820 0.128 0.052
#> GSM372325 1 0.5067 0.871 0.832 0.116 0.052
#> GSM372327 1 0.0000 0.966 1.000 0.000 0.000
#> GSM372329 1 0.0000 0.966 1.000 0.000 0.000
#> GSM372331 1 0.1643 0.956 0.956 0.044 0.000
#> GSM372333 3 0.8822 0.268 0.324 0.136 0.540
#> GSM372334 1 0.0000 0.966 1.000 0.000 0.000
#> GSM372336 1 0.0237 0.965 0.996 0.004 0.000
#> GSM372338 1 0.0000 0.966 1.000 0.000 0.000
#> GSM372340 1 0.0000 0.966 1.000 0.000 0.000
#> GSM372342 1 0.0000 0.966 1.000 0.000 0.000
#> GSM372344 1 0.1411 0.949 0.964 0.036 0.000
#> GSM372346 1 0.0000 0.966 1.000 0.000 0.000
#> GSM372348 1 0.0237 0.965 0.996 0.004 0.000
#> GSM372350 1 0.6016 0.722 0.724 0.256 0.020
#> GSM372352 3 0.8081 0.559 0.136 0.220 0.644
#> GSM372354 1 0.0000 0.966 1.000 0.000 0.000
#> GSM372356 1 0.1643 0.956 0.956 0.044 0.000
#> GSM372358 1 0.0000 0.966 1.000 0.000 0.000
#> GSM372360 1 0.0000 0.966 1.000 0.000 0.000
#> GSM372362 1 0.0000 0.966 1.000 0.000 0.000
#> GSM372364 1 0.1529 0.957 0.960 0.040 0.000
#> GSM372365 1 0.1643 0.956 0.956 0.044 0.000
#> GSM372366 1 0.0000 0.966 1.000 0.000 0.000
#> GSM372367 1 0.1643 0.956 0.956 0.044 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM372286 2 0.0000 0.992 0.000 1.000 0.000 0.000
#> GSM372287 4 0.0188 0.936 0.000 0.000 0.004 0.996
#> GSM372288 4 0.0000 0.937 0.000 0.000 0.000 1.000
#> GSM372289 4 0.0000 0.937 0.000 0.000 0.000 1.000
#> GSM372290 4 0.0000 0.937 0.000 0.000 0.000 1.000
#> GSM372291 4 0.0524 0.933 0.000 0.008 0.004 0.988
#> GSM372292 4 0.0000 0.937 0.000 0.000 0.000 1.000
#> GSM372293 4 0.4746 0.402 0.000 0.000 0.368 0.632
#> GSM372294 4 0.0469 0.933 0.000 0.012 0.000 0.988
#> GSM372295 4 0.0188 0.936 0.000 0.000 0.004 0.996
#> GSM372296 4 0.0000 0.937 0.000 0.000 0.000 1.000
#> GSM372297 4 0.0188 0.936 0.000 0.000 0.004 0.996
#> GSM372298 4 0.0000 0.937 0.000 0.000 0.000 1.000
#> GSM372299 4 0.0524 0.933 0.000 0.008 0.004 0.988
#> GSM372300 4 0.0336 0.934 0.000 0.000 0.008 0.992
#> GSM372301 4 0.0336 0.934 0.000 0.000 0.008 0.992
#> GSM372302 4 0.0000 0.937 0.000 0.000 0.000 1.000
#> GSM372303 4 0.0592 0.928 0.000 0.000 0.016 0.984
#> GSM372304 4 0.0000 0.937 0.000 0.000 0.000 1.000
#> GSM372305 2 0.0000 0.992 0.000 1.000 0.000 0.000
#> GSM372306 2 0.0336 0.995 0.000 0.992 0.008 0.000
#> GSM372307 4 0.3873 0.720 0.000 0.228 0.000 0.772
#> GSM372309 2 0.0336 0.995 0.000 0.992 0.008 0.000
#> GSM372311 2 0.0000 0.992 0.000 1.000 0.000 0.000
#> GSM372313 2 0.0336 0.995 0.000 0.992 0.008 0.000
#> GSM372315 4 0.4103 0.681 0.000 0.256 0.000 0.744
#> GSM372317 2 0.0336 0.995 0.000 0.992 0.008 0.000
#> GSM372319 3 0.0188 0.996 0.000 0.000 0.996 0.004
#> GSM372321 3 0.0188 0.995 0.000 0.004 0.996 0.000
#> GSM372323 3 0.0188 0.995 0.000 0.004 0.996 0.000
#> GSM372326 3 0.0188 0.995 0.000 0.004 0.996 0.000
#> GSM372328 3 0.0188 0.996 0.000 0.000 0.996 0.004
#> GSM372330 2 0.0336 0.995 0.000 0.992 0.008 0.000
#> GSM372332 3 0.0469 0.990 0.000 0.000 0.988 0.012
#> GSM372335 2 0.0336 0.995 0.000 0.992 0.008 0.000
#> GSM372337 3 0.0188 0.995 0.000 0.004 0.996 0.000
#> GSM372339 3 0.0188 0.996 0.000 0.000 0.996 0.004
#> GSM372341 3 0.0188 0.996 0.000 0.000 0.996 0.004
#> GSM372343 3 0.0188 0.996 0.000 0.000 0.996 0.004
#> GSM372345 3 0.0188 0.995 0.000 0.004 0.996 0.000
#> GSM372347 2 0.0336 0.995 0.000 0.992 0.008 0.000
#> GSM372349 3 0.0469 0.990 0.000 0.000 0.988 0.012
#> GSM372351 3 0.0188 0.996 0.000 0.000 0.996 0.004
#> GSM372353 2 0.0336 0.995 0.000 0.992 0.008 0.000
#> GSM372355 2 0.0336 0.995 0.000 0.992 0.008 0.000
#> GSM372357 2 0.0336 0.995 0.000 0.992 0.008 0.000
#> GSM372359 2 0.0336 0.995 0.000 0.992 0.008 0.000
#> GSM372361 4 0.4072 0.687 0.000 0.252 0.000 0.748
#> GSM372363 2 0.0000 0.992 0.000 1.000 0.000 0.000
#> GSM372308 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM372310 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM372312 1 0.0524 0.989 0.988 0.008 0.004 0.000
#> GSM372314 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM372316 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM372318 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM372320 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM372322 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM372324 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM372325 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM372327 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM372329 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM372331 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM372333 2 0.1022 0.960 0.032 0.968 0.000 0.000
#> GSM372334 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM372336 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM372338 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM372340 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM372342 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM372344 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM372346 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM372348 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM372350 1 0.0524 0.989 0.988 0.008 0.004 0.000
#> GSM372352 2 0.0188 0.989 0.000 0.996 0.004 0.000
#> GSM372354 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM372356 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM372358 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM372360 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM372362 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM372364 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM372365 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM372366 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM372367 1 0.0000 0.999 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM372286 2 0.1485 0.7891 0.000 0.948 0.000 0.020 0.032
#> GSM372287 4 0.0162 0.6346 0.000 0.004 0.000 0.996 0.000
#> GSM372288 4 0.2036 0.6283 0.000 0.056 0.000 0.920 0.024
#> GSM372289 4 0.4021 0.5291 0.000 0.200 0.000 0.764 0.036
#> GSM372290 4 0.4976 0.2986 0.000 0.468 0.000 0.504 0.028
#> GSM372291 5 0.4734 0.1151 0.000 0.000 0.024 0.372 0.604
#> GSM372292 4 0.4384 0.5935 0.000 0.324 0.016 0.660 0.000
#> GSM372293 4 0.4150 0.2522 0.000 0.000 0.388 0.612 0.000
#> GSM372294 4 0.4129 0.5134 0.000 0.204 0.000 0.756 0.040
#> GSM372295 4 0.0510 0.6275 0.000 0.000 0.016 0.984 0.000
#> GSM372296 4 0.4238 0.5432 0.000 0.368 0.000 0.628 0.004
#> GSM372297 4 0.0162 0.6346 0.000 0.004 0.000 0.996 0.000
#> GSM372298 4 0.0162 0.6346 0.000 0.004 0.000 0.996 0.000
#> GSM372299 4 0.5367 0.3700 0.000 0.196 0.020 0.696 0.088
#> GSM372300 4 0.4558 0.5902 0.000 0.324 0.024 0.652 0.000
#> GSM372301 4 0.4384 0.5935 0.000 0.324 0.016 0.660 0.000
#> GSM372302 4 0.3452 0.6522 0.000 0.244 0.000 0.756 0.000
#> GSM372303 4 0.4786 0.5997 0.000 0.308 0.040 0.652 0.000
#> GSM372304 4 0.0162 0.6346 0.000 0.004 0.000 0.996 0.000
#> GSM372305 2 0.0000 0.8119 0.000 1.000 0.000 0.000 0.000
#> GSM372306 2 0.0162 0.8111 0.000 0.996 0.004 0.000 0.000
#> GSM372307 2 0.4733 0.1934 0.000 0.624 0.000 0.348 0.028
#> GSM372309 2 0.0000 0.8119 0.000 1.000 0.000 0.000 0.000
#> GSM372311 2 0.0000 0.8119 0.000 1.000 0.000 0.000 0.000
#> GSM372313 2 0.2843 0.6660 0.000 0.848 0.000 0.144 0.008
#> GSM372315 2 0.4718 0.2021 0.000 0.628 0.000 0.344 0.028
#> GSM372317 2 0.0000 0.8119 0.000 1.000 0.000 0.000 0.000
#> GSM372319 3 0.4028 0.7450 0.000 0.048 0.776 0.176 0.000
#> GSM372321 3 0.0703 0.8857 0.000 0.000 0.976 0.024 0.000
#> GSM372323 3 0.0510 0.8881 0.000 0.016 0.984 0.000 0.000
#> GSM372326 3 0.0000 0.8928 0.000 0.000 1.000 0.000 0.000
#> GSM372328 3 0.0000 0.8928 0.000 0.000 1.000 0.000 0.000
#> GSM372330 2 0.0703 0.8006 0.000 0.976 0.000 0.000 0.024
#> GSM372332 3 0.3655 0.7785 0.000 0.036 0.804 0.160 0.000
#> GSM372335 2 0.0290 0.8092 0.000 0.992 0.008 0.000 0.000
#> GSM372337 3 0.0510 0.8881 0.000 0.016 0.984 0.000 0.000
#> GSM372339 3 0.0000 0.8928 0.000 0.000 1.000 0.000 0.000
#> GSM372341 3 0.0000 0.8928 0.000 0.000 1.000 0.000 0.000
#> GSM372343 3 0.0000 0.8928 0.000 0.000 1.000 0.000 0.000
#> GSM372345 3 0.0510 0.8881 0.000 0.016 0.984 0.000 0.000
#> GSM372347 2 0.2909 0.7022 0.000 0.848 0.140 0.000 0.012
#> GSM372349 3 0.4481 0.6906 0.000 0.048 0.720 0.232 0.000
#> GSM372351 3 0.4150 0.7225 0.000 0.036 0.748 0.216 0.000
#> GSM372353 2 0.1831 0.7592 0.000 0.920 0.076 0.000 0.004
#> GSM372355 2 0.0000 0.8119 0.000 1.000 0.000 0.000 0.000
#> GSM372357 2 0.0000 0.8119 0.000 1.000 0.000 0.000 0.000
#> GSM372359 2 0.0290 0.8092 0.000 0.992 0.008 0.000 0.000
#> GSM372361 2 0.4485 0.3441 0.000 0.680 0.000 0.292 0.028
#> GSM372363 2 0.0000 0.8119 0.000 1.000 0.000 0.000 0.000
#> GSM372308 1 0.3895 0.6225 0.680 0.000 0.000 0.000 0.320
#> GSM372310 1 0.3730 0.6600 0.712 0.000 0.000 0.000 0.288
#> GSM372312 5 0.2813 0.4668 0.168 0.000 0.000 0.000 0.832
#> GSM372314 1 0.3661 0.6707 0.724 0.000 0.000 0.000 0.276
#> GSM372316 1 0.0162 0.8082 0.996 0.000 0.000 0.000 0.004
#> GSM372318 1 0.2424 0.7278 0.868 0.000 0.000 0.000 0.132
#> GSM372320 1 0.2516 0.7396 0.860 0.000 0.000 0.000 0.140
#> GSM372322 1 0.0609 0.8042 0.980 0.000 0.000 0.000 0.020
#> GSM372324 1 0.3661 0.6727 0.724 0.000 0.000 0.000 0.276
#> GSM372325 1 0.3796 0.6469 0.700 0.000 0.000 0.000 0.300
#> GSM372327 1 0.2516 0.7396 0.860 0.000 0.000 0.000 0.140
#> GSM372329 1 0.0404 0.8080 0.988 0.000 0.000 0.000 0.012
#> GSM372331 1 0.3274 0.7113 0.780 0.000 0.000 0.000 0.220
#> GSM372333 2 0.7109 -0.0658 0.228 0.456 0.024 0.000 0.292
#> GSM372334 1 0.2516 0.7396 0.860 0.000 0.000 0.000 0.140
#> GSM372336 1 0.1043 0.8044 0.960 0.000 0.000 0.000 0.040
#> GSM372338 1 0.2516 0.7396 0.860 0.000 0.000 0.000 0.140
#> GSM372340 1 0.2516 0.7396 0.860 0.000 0.000 0.000 0.140
#> GSM372342 1 0.1270 0.7931 0.948 0.000 0.000 0.000 0.052
#> GSM372344 1 0.4074 0.3871 0.636 0.000 0.000 0.000 0.364
#> GSM372346 1 0.2852 0.6762 0.828 0.000 0.000 0.000 0.172
#> GSM372348 1 0.1043 0.8044 0.960 0.000 0.000 0.000 0.040
#> GSM372350 5 0.3817 0.4647 0.252 0.000 0.004 0.004 0.740
#> GSM372352 2 0.7276 -0.0303 0.000 0.404 0.024 0.272 0.300
#> GSM372354 1 0.0510 0.8050 0.984 0.000 0.000 0.000 0.016
#> GSM372356 1 0.3612 0.6774 0.732 0.000 0.000 0.000 0.268
#> GSM372358 1 0.0162 0.8082 0.996 0.000 0.000 0.000 0.004
#> GSM372360 1 0.0162 0.8082 0.996 0.000 0.000 0.000 0.004
#> GSM372362 1 0.0000 0.8080 1.000 0.000 0.000 0.000 0.000
#> GSM372364 1 0.1043 0.8044 0.960 0.000 0.000 0.000 0.040
#> GSM372365 1 0.3949 0.6062 0.668 0.000 0.000 0.000 0.332
#> GSM372366 1 0.0404 0.8061 0.988 0.000 0.000 0.000 0.012
#> GSM372367 1 0.3661 0.6707 0.724 0.000 0.000 0.000 0.276
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM372286 2 0.2491 0.785 0.000 0.836 0.000 0.164 0.000 0.000
#> GSM372287 4 0.2883 0.561 0.000 0.000 0.000 0.788 0.000 0.212
#> GSM372288 4 0.0260 0.667 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM372289 4 0.0458 0.667 0.000 0.016 0.000 0.984 0.000 0.000
#> GSM372290 4 0.2350 0.625 0.000 0.100 0.000 0.880 0.000 0.020
#> GSM372291 6 0.4052 0.698 0.008 0.000 0.048 0.116 0.032 0.796
#> GSM372292 6 0.5137 0.498 0.000 0.064 0.008 0.408 0.000 0.520
#> GSM372293 6 0.5961 0.657 0.000 0.016 0.248 0.200 0.000 0.536
#> GSM372294 4 0.1367 0.663 0.000 0.012 0.000 0.944 0.000 0.044
#> GSM372295 6 0.4201 0.721 0.000 0.000 0.036 0.300 0.000 0.664
#> GSM372296 4 0.2365 0.644 0.000 0.072 0.000 0.888 0.000 0.040
#> GSM372297 4 0.2883 0.561 0.000 0.000 0.000 0.788 0.000 0.212
#> GSM372298 4 0.2340 0.595 0.000 0.000 0.000 0.852 0.000 0.148
#> GSM372299 6 0.5394 0.758 0.000 0.004 0.040 0.216 0.084 0.656
#> GSM372300 6 0.5655 0.793 0.000 0.060 0.072 0.236 0.004 0.628
#> GSM372301 6 0.5456 0.775 0.000 0.064 0.052 0.264 0.000 0.620
#> GSM372302 4 0.2562 0.572 0.000 0.000 0.000 0.828 0.000 0.172
#> GSM372303 6 0.5763 0.787 0.000 0.060 0.100 0.224 0.000 0.616
#> GSM372304 4 0.2823 0.569 0.000 0.000 0.000 0.796 0.000 0.204
#> GSM372305 2 0.1152 0.896 0.000 0.952 0.004 0.044 0.000 0.000
#> GSM372306 2 0.0405 0.892 0.000 0.988 0.004 0.000 0.000 0.008
#> GSM372307 4 0.3819 0.478 0.000 0.280 0.000 0.700 0.000 0.020
#> GSM372309 2 0.0405 0.893 0.000 0.988 0.004 0.000 0.000 0.008
#> GSM372311 2 0.1007 0.896 0.000 0.956 0.000 0.044 0.000 0.000
#> GSM372313 2 0.1152 0.895 0.000 0.952 0.000 0.044 0.000 0.004
#> GSM372315 4 0.4131 0.401 0.000 0.356 0.000 0.624 0.000 0.020
#> GSM372317 2 0.0937 0.896 0.000 0.960 0.000 0.040 0.000 0.000
#> GSM372319 2 0.4620 0.206 0.000 0.532 0.428 0.040 0.000 0.000
#> GSM372321 3 0.2442 0.866 0.000 0.144 0.852 0.004 0.000 0.000
#> GSM372323 3 0.2695 0.862 0.000 0.144 0.844 0.000 0.008 0.004
#> GSM372326 3 0.0972 0.913 0.000 0.028 0.964 0.000 0.008 0.000
#> GSM372328 3 0.0146 0.913 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM372330 2 0.2146 0.838 0.000 0.880 0.000 0.116 0.000 0.004
#> GSM372332 3 0.1149 0.909 0.000 0.024 0.960 0.008 0.000 0.008
#> GSM372335 2 0.0260 0.893 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM372337 3 0.2695 0.862 0.000 0.144 0.844 0.000 0.008 0.004
#> GSM372339 3 0.0146 0.913 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM372341 3 0.0291 0.913 0.000 0.000 0.992 0.004 0.000 0.004
#> GSM372343 3 0.0291 0.913 0.000 0.000 0.992 0.004 0.000 0.004
#> GSM372345 3 0.2695 0.862 0.000 0.144 0.844 0.000 0.008 0.004
#> GSM372347 2 0.4048 0.740 0.000 0.788 0.120 0.000 0.044 0.048
#> GSM372349 3 0.1875 0.883 0.000 0.032 0.928 0.020 0.000 0.020
#> GSM372351 3 0.1251 0.905 0.000 0.012 0.956 0.008 0.000 0.024
#> GSM372353 2 0.2915 0.716 0.000 0.808 0.184 0.000 0.008 0.000
#> GSM372355 2 0.1152 0.895 0.000 0.952 0.000 0.044 0.000 0.004
#> GSM372357 2 0.0260 0.893 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM372359 2 0.0260 0.893 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM372361 4 0.4282 0.254 0.000 0.420 0.000 0.560 0.000 0.020
#> GSM372363 2 0.1007 0.896 0.000 0.956 0.000 0.044 0.000 0.000
#> GSM372308 5 0.1168 0.809 0.028 0.000 0.000 0.000 0.956 0.016
#> GSM372310 5 0.0790 0.812 0.032 0.000 0.000 0.000 0.968 0.000
#> GSM372312 5 0.1644 0.797 0.040 0.000 0.000 0.000 0.932 0.028
#> GSM372314 5 0.1863 0.812 0.060 0.004 0.000 0.000 0.920 0.016
#> GSM372316 1 0.3417 0.760 0.796 0.000 0.000 0.000 0.160 0.044
#> GSM372318 1 0.3563 0.801 0.800 0.000 0.000 0.000 0.092 0.108
#> GSM372320 1 0.1049 0.826 0.960 0.000 0.000 0.000 0.008 0.032
#> GSM372322 1 0.1556 0.831 0.920 0.000 0.000 0.000 0.080 0.000
#> GSM372324 5 0.3516 0.789 0.096 0.004 0.000 0.000 0.812 0.088
#> GSM372325 5 0.2504 0.779 0.028 0.004 0.000 0.000 0.880 0.088
#> GSM372327 1 0.0622 0.829 0.980 0.000 0.000 0.000 0.008 0.012
#> GSM372329 1 0.2199 0.824 0.892 0.000 0.000 0.000 0.088 0.020
#> GSM372331 5 0.2744 0.771 0.144 0.000 0.000 0.000 0.840 0.016
#> GSM372333 5 0.4377 0.679 0.000 0.100 0.044 0.000 0.768 0.088
#> GSM372334 1 0.1049 0.826 0.960 0.000 0.000 0.000 0.008 0.032
#> GSM372336 5 0.4616 0.477 0.316 0.000 0.000 0.000 0.624 0.060
#> GSM372338 1 0.1049 0.826 0.960 0.000 0.000 0.000 0.008 0.032
#> GSM372340 1 0.1049 0.826 0.960 0.000 0.000 0.000 0.008 0.032
#> GSM372342 1 0.1075 0.834 0.952 0.000 0.000 0.000 0.048 0.000
#> GSM372344 1 0.2092 0.772 0.876 0.000 0.000 0.000 0.000 0.124
#> GSM372346 1 0.3514 0.801 0.804 0.000 0.000 0.000 0.088 0.108
#> GSM372348 5 0.4619 0.412 0.348 0.000 0.000 0.000 0.600 0.052
#> GSM372350 1 0.3909 0.703 0.772 0.000 0.000 0.004 0.076 0.148
#> GSM372352 5 0.6071 0.407 0.000 0.176 0.052 0.004 0.600 0.168
#> GSM372354 1 0.2795 0.828 0.856 0.000 0.000 0.000 0.100 0.044
#> GSM372356 5 0.2704 0.759 0.140 0.000 0.000 0.000 0.844 0.016
#> GSM372358 1 0.4845 0.251 0.540 0.000 0.000 0.000 0.400 0.060
#> GSM372360 1 0.4845 0.251 0.540 0.000 0.000 0.000 0.400 0.060
#> GSM372362 1 0.4215 0.634 0.700 0.000 0.000 0.000 0.244 0.056
#> GSM372364 5 0.4724 0.389 0.348 0.000 0.000 0.000 0.592 0.060
#> GSM372365 5 0.0972 0.811 0.028 0.000 0.000 0.000 0.964 0.008
#> GSM372366 1 0.2605 0.813 0.864 0.000 0.000 0.000 0.108 0.028
#> GSM372367 5 0.1152 0.811 0.044 0.000 0.000 0.000 0.952 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) specimen(p) individual(p) k
#> MAD:mclust 81 8.44e-05 2.00e-17 0.999 2
#> MAD:mclust 78 1.07e-14 9.35e-28 0.743 3
#> MAD:mclust 81 1.12e-11 1.84e-23 0.943 4
#> MAD:mclust 70 2.64e-12 3.15e-24 0.750 5
#> MAD:mclust 71 1.83e-11 2.55e-22 0.508 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 51941 rows and 82 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4874 0.513 0.513
#> 3 3 0.996 0.970 0.984 0.3576 0.825 0.660
#> 4 4 0.842 0.819 0.913 0.1142 0.843 0.585
#> 5 5 0.792 0.779 0.869 0.0379 0.946 0.805
#> 6 6 0.746 0.618 0.771 0.0427 0.933 0.734
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
#> GSM372286 2 0.0000 1.000 0.000 1.000
#> GSM372287 2 0.0000 1.000 0.000 1.000
#> GSM372288 2 0.0000 1.000 0.000 1.000
#> GSM372289 2 0.0000 1.000 0.000 1.000
#> GSM372290 2 0.0000 1.000 0.000 1.000
#> GSM372291 1 0.0000 1.000 1.000 0.000
#> GSM372292 2 0.0000 1.000 0.000 1.000
#> GSM372293 2 0.0000 1.000 0.000 1.000
#> GSM372294 2 0.0000 1.000 0.000 1.000
#> GSM372295 2 0.0000 1.000 0.000 1.000
#> GSM372296 2 0.0000 1.000 0.000 1.000
#> GSM372297 2 0.0000 1.000 0.000 1.000
#> GSM372298 2 0.0000 1.000 0.000 1.000
#> GSM372299 2 0.0000 1.000 0.000 1.000
#> GSM372300 2 0.0000 1.000 0.000 1.000
#> GSM372301 2 0.0000 1.000 0.000 1.000
#> GSM372302 2 0.0000 1.000 0.000 1.000
#> GSM372303 2 0.0000 1.000 0.000 1.000
#> GSM372304 2 0.0000 1.000 0.000 1.000
#> GSM372305 2 0.0000 1.000 0.000 1.000
#> GSM372306 2 0.0000 1.000 0.000 1.000
#> GSM372307 2 0.0000 1.000 0.000 1.000
#> GSM372309 2 0.0000 1.000 0.000 1.000
#> GSM372311 2 0.0000 1.000 0.000 1.000
#> GSM372313 2 0.0000 1.000 0.000 1.000
#> GSM372315 2 0.0000 1.000 0.000 1.000
#> GSM372317 2 0.0000 1.000 0.000 1.000
#> GSM372319 2 0.0000 1.000 0.000 1.000
#> GSM372321 2 0.0000 1.000 0.000 1.000
#> GSM372323 2 0.0000 1.000 0.000 1.000
#> GSM372326 2 0.0000 1.000 0.000 1.000
#> GSM372328 2 0.0000 1.000 0.000 1.000
#> GSM372330 2 0.0000 1.000 0.000 1.000
#> GSM372332 2 0.0000 1.000 0.000 1.000
#> GSM372335 2 0.0000 1.000 0.000 1.000
#> GSM372337 2 0.0000 1.000 0.000 1.000
#> GSM372339 2 0.0000 1.000 0.000 1.000
#> GSM372341 2 0.0000 1.000 0.000 1.000
#> GSM372343 2 0.0000 1.000 0.000 1.000
#> GSM372345 2 0.0000 1.000 0.000 1.000
#> GSM372347 2 0.0000 1.000 0.000 1.000
#> GSM372349 2 0.0000 1.000 0.000 1.000
#> GSM372351 2 0.0000 1.000 0.000 1.000
#> GSM372353 2 0.0000 1.000 0.000 1.000
#> GSM372355 2 0.0000 1.000 0.000 1.000
#> GSM372357 2 0.0000 1.000 0.000 1.000
#> GSM372359 2 0.0000 1.000 0.000 1.000
#> GSM372361 2 0.0000 1.000 0.000 1.000
#> GSM372363 2 0.0000 1.000 0.000 1.000
#> GSM372308 1 0.0000 1.000 1.000 0.000
#> GSM372310 1 0.0000 1.000 1.000 0.000
#> GSM372312 1 0.0000 1.000 1.000 0.000
#> GSM372314 1 0.0000 1.000 1.000 0.000
#> GSM372316 1 0.0000 1.000 1.000 0.000
#> GSM372318 1 0.0000 1.000 1.000 0.000
#> GSM372320 1 0.0000 1.000 1.000 0.000
#> GSM372322 1 0.0000 1.000 1.000 0.000
#> GSM372324 1 0.0000 1.000 1.000 0.000
#> GSM372325 1 0.0000 1.000 1.000 0.000
#> GSM372327 1 0.0000 1.000 1.000 0.000
#> GSM372329 1 0.0000 1.000 1.000 0.000
#> GSM372331 1 0.0000 1.000 1.000 0.000
#> GSM372333 1 0.0376 0.996 0.996 0.004
#> GSM372334 1 0.0000 1.000 1.000 0.000
#> GSM372336 1 0.0000 1.000 1.000 0.000
#> GSM372338 1 0.0000 1.000 1.000 0.000
#> GSM372340 1 0.0000 1.000 1.000 0.000
#> GSM372342 1 0.0000 1.000 1.000 0.000
#> GSM372344 1 0.0000 1.000 1.000 0.000
#> GSM372346 1 0.0000 1.000 1.000 0.000
#> GSM372348 1 0.0000 1.000 1.000 0.000
#> GSM372350 1 0.0000 1.000 1.000 0.000
#> GSM372352 2 0.0000 1.000 0.000 1.000
#> GSM372354 1 0.0000 1.000 1.000 0.000
#> GSM372356 1 0.0000 1.000 1.000 0.000
#> GSM372358 1 0.0000 1.000 1.000 0.000
#> GSM372360 1 0.0000 1.000 1.000 0.000
#> GSM372362 1 0.0000 1.000 1.000 0.000
#> GSM372364 1 0.0000 1.000 1.000 0.000
#> GSM372365 1 0.0000 1.000 1.000 0.000
#> GSM372366 1 0.0000 1.000 1.000 0.000
#> GSM372367 1 0.0000 1.000 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM372286 2 0.0000 0.978 0.000 1.000 0.000
#> GSM372287 2 0.0000 0.978 0.000 1.000 0.000
#> GSM372288 2 0.0000 0.978 0.000 1.000 0.000
#> GSM372289 2 0.0000 0.978 0.000 1.000 0.000
#> GSM372290 2 0.0000 0.978 0.000 1.000 0.000
#> GSM372291 1 0.2796 0.895 0.908 0.092 0.000
#> GSM372292 3 0.4178 0.816 0.000 0.172 0.828
#> GSM372293 3 0.0000 0.972 0.000 0.000 1.000
#> GSM372294 2 0.0000 0.978 0.000 1.000 0.000
#> GSM372295 2 0.0000 0.978 0.000 1.000 0.000
#> GSM372296 2 0.0000 0.978 0.000 1.000 0.000
#> GSM372297 2 0.0000 0.978 0.000 1.000 0.000
#> GSM372298 2 0.0000 0.978 0.000 1.000 0.000
#> GSM372299 2 0.0000 0.978 0.000 1.000 0.000
#> GSM372300 3 0.2165 0.927 0.000 0.064 0.936
#> GSM372301 3 0.2878 0.899 0.000 0.096 0.904
#> GSM372302 2 0.0000 0.978 0.000 1.000 0.000
#> GSM372303 3 0.0000 0.972 0.000 0.000 1.000
#> GSM372304 2 0.0000 0.978 0.000 1.000 0.000
#> GSM372305 2 0.0237 0.976 0.000 0.996 0.004
#> GSM372306 2 0.2878 0.901 0.000 0.904 0.096
#> GSM372307 2 0.0000 0.978 0.000 1.000 0.000
#> GSM372309 2 0.0000 0.978 0.000 1.000 0.000
#> GSM372311 2 0.0000 0.978 0.000 1.000 0.000
#> GSM372313 2 0.0000 0.978 0.000 1.000 0.000
#> GSM372315 2 0.0000 0.978 0.000 1.000 0.000
#> GSM372317 2 0.4887 0.732 0.000 0.772 0.228
#> GSM372319 3 0.0237 0.970 0.000 0.004 0.996
#> GSM372321 3 0.0000 0.972 0.000 0.000 1.000
#> GSM372323 3 0.0000 0.972 0.000 0.000 1.000
#> GSM372326 3 0.0000 0.972 0.000 0.000 1.000
#> GSM372328 3 0.0000 0.972 0.000 0.000 1.000
#> GSM372330 2 0.0237 0.976 0.000 0.996 0.004
#> GSM372332 3 0.0000 0.972 0.000 0.000 1.000
#> GSM372335 2 0.2165 0.930 0.000 0.936 0.064
#> GSM372337 3 0.0000 0.972 0.000 0.000 1.000
#> GSM372339 3 0.0000 0.972 0.000 0.000 1.000
#> GSM372341 3 0.0000 0.972 0.000 0.000 1.000
#> GSM372343 3 0.0000 0.972 0.000 0.000 1.000
#> GSM372345 3 0.0000 0.972 0.000 0.000 1.000
#> GSM372347 3 0.0424 0.968 0.000 0.008 0.992
#> GSM372349 3 0.0000 0.972 0.000 0.000 1.000
#> GSM372351 3 0.0000 0.972 0.000 0.000 1.000
#> GSM372353 3 0.4235 0.808 0.000 0.176 0.824
#> GSM372355 2 0.0000 0.978 0.000 1.000 0.000
#> GSM372357 2 0.0237 0.976 0.000 0.996 0.004
#> GSM372359 2 0.3116 0.882 0.000 0.892 0.108
#> GSM372361 2 0.0000 0.978 0.000 1.000 0.000
#> GSM372363 2 0.0000 0.978 0.000 1.000 0.000
#> GSM372308 1 0.0000 0.996 1.000 0.000 0.000
#> GSM372310 1 0.0000 0.996 1.000 0.000 0.000
#> GSM372312 1 0.1031 0.972 0.976 0.024 0.000
#> GSM372314 1 0.0000 0.996 1.000 0.000 0.000
#> GSM372316 1 0.0000 0.996 1.000 0.000 0.000
#> GSM372318 1 0.0000 0.996 1.000 0.000 0.000
#> GSM372320 1 0.0000 0.996 1.000 0.000 0.000
#> GSM372322 1 0.0000 0.996 1.000 0.000 0.000
#> GSM372324 1 0.0000 0.996 1.000 0.000 0.000
#> GSM372325 1 0.0000 0.996 1.000 0.000 0.000
#> GSM372327 1 0.0000 0.996 1.000 0.000 0.000
#> GSM372329 1 0.0000 0.996 1.000 0.000 0.000
#> GSM372331 1 0.0000 0.996 1.000 0.000 0.000
#> GSM372333 1 0.0592 0.985 0.988 0.000 0.012
#> GSM372334 1 0.0000 0.996 1.000 0.000 0.000
#> GSM372336 1 0.0000 0.996 1.000 0.000 0.000
#> GSM372338 1 0.0000 0.996 1.000 0.000 0.000
#> GSM372340 1 0.0000 0.996 1.000 0.000 0.000
#> GSM372342 1 0.0000 0.996 1.000 0.000 0.000
#> GSM372344 1 0.0000 0.996 1.000 0.000 0.000
#> GSM372346 1 0.0000 0.996 1.000 0.000 0.000
#> GSM372348 1 0.0000 0.996 1.000 0.000 0.000
#> GSM372350 1 0.0000 0.996 1.000 0.000 0.000
#> GSM372352 2 0.3805 0.885 0.024 0.884 0.092
#> GSM372354 1 0.0000 0.996 1.000 0.000 0.000
#> GSM372356 1 0.0000 0.996 1.000 0.000 0.000
#> GSM372358 1 0.0000 0.996 1.000 0.000 0.000
#> GSM372360 1 0.0000 0.996 1.000 0.000 0.000
#> GSM372362 1 0.0000 0.996 1.000 0.000 0.000
#> GSM372364 1 0.0000 0.996 1.000 0.000 0.000
#> GSM372365 1 0.0000 0.996 1.000 0.000 0.000
#> GSM372366 1 0.0000 0.996 1.000 0.000 0.000
#> GSM372367 1 0.0000 0.996 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM372286 2 0.0921 0.7894 0.000 0.972 0.000 0.028
#> GSM372287 4 0.2589 0.8295 0.000 0.116 0.000 0.884
#> GSM372288 4 0.3726 0.7635 0.000 0.212 0.000 0.788
#> GSM372289 2 0.4994 -0.2190 0.000 0.520 0.000 0.480
#> GSM372290 4 0.2973 0.8161 0.000 0.144 0.000 0.856
#> GSM372291 4 0.1576 0.8156 0.048 0.004 0.000 0.948
#> GSM372292 4 0.0921 0.8239 0.000 0.000 0.028 0.972
#> GSM372293 4 0.4985 -0.0128 0.000 0.000 0.468 0.532
#> GSM372294 4 0.4103 0.7127 0.000 0.256 0.000 0.744
#> GSM372295 4 0.1716 0.8401 0.000 0.064 0.000 0.936
#> GSM372296 4 0.3172 0.8059 0.000 0.160 0.000 0.840
#> GSM372297 4 0.1302 0.8401 0.000 0.044 0.000 0.956
#> GSM372298 4 0.1004 0.8380 0.000 0.024 0.004 0.972
#> GSM372299 4 0.0672 0.8332 0.000 0.008 0.008 0.984
#> GSM372300 4 0.1211 0.8191 0.000 0.000 0.040 0.960
#> GSM372301 4 0.1022 0.8226 0.000 0.000 0.032 0.968
#> GSM372302 4 0.2149 0.8381 0.000 0.088 0.000 0.912
#> GSM372303 4 0.2081 0.7902 0.000 0.000 0.084 0.916
#> GSM372304 4 0.2081 0.8381 0.000 0.084 0.000 0.916
#> GSM372305 2 0.1389 0.7961 0.000 0.952 0.048 0.000
#> GSM372306 2 0.2647 0.7629 0.000 0.880 0.120 0.000
#> GSM372307 4 0.4998 0.2455 0.000 0.488 0.000 0.512
#> GSM372309 2 0.2662 0.7879 0.000 0.900 0.084 0.016
#> GSM372311 2 0.0707 0.7929 0.000 0.980 0.000 0.020
#> GSM372313 2 0.0592 0.7945 0.000 0.984 0.000 0.016
#> GSM372315 2 0.4040 0.4973 0.000 0.752 0.000 0.248
#> GSM372317 2 0.4040 0.6407 0.000 0.752 0.248 0.000
#> GSM372319 3 0.0817 0.9481 0.000 0.024 0.976 0.000
#> GSM372321 3 0.0921 0.9459 0.000 0.028 0.972 0.000
#> GSM372323 3 0.0707 0.9491 0.000 0.020 0.980 0.000
#> GSM372326 3 0.0804 0.9505 0.000 0.012 0.980 0.008
#> GSM372328 3 0.1792 0.9179 0.000 0.000 0.932 0.068
#> GSM372330 2 0.1042 0.7941 0.000 0.972 0.008 0.020
#> GSM372332 3 0.1474 0.9292 0.000 0.000 0.948 0.052
#> GSM372335 2 0.1706 0.7975 0.000 0.948 0.036 0.016
#> GSM372337 3 0.0817 0.9481 0.000 0.024 0.976 0.000
#> GSM372339 3 0.0000 0.9501 0.000 0.000 1.000 0.000
#> GSM372341 3 0.0817 0.9441 0.000 0.000 0.976 0.024
#> GSM372343 3 0.0817 0.9447 0.000 0.000 0.976 0.024
#> GSM372345 3 0.0921 0.9459 0.000 0.028 0.972 0.000
#> GSM372347 2 0.5000 0.0485 0.000 0.500 0.500 0.000
#> GSM372349 3 0.0779 0.9500 0.000 0.016 0.980 0.004
#> GSM372351 3 0.1557 0.9266 0.000 0.000 0.944 0.056
#> GSM372353 3 0.4188 0.6565 0.000 0.244 0.752 0.004
#> GSM372355 2 0.0592 0.7945 0.000 0.984 0.000 0.016
#> GSM372357 2 0.1557 0.7954 0.000 0.944 0.056 0.000
#> GSM372359 2 0.2675 0.7762 0.000 0.892 0.100 0.008
#> GSM372361 4 0.4877 0.4587 0.000 0.408 0.000 0.592
#> GSM372363 2 0.0779 0.7960 0.000 0.980 0.004 0.016
#> GSM372308 1 0.0000 0.9779 1.000 0.000 0.000 0.000
#> GSM372310 1 0.0000 0.9779 1.000 0.000 0.000 0.000
#> GSM372312 1 0.0592 0.9622 0.984 0.016 0.000 0.000
#> GSM372314 1 0.3528 0.7385 0.808 0.192 0.000 0.000
#> GSM372316 1 0.0000 0.9779 1.000 0.000 0.000 0.000
#> GSM372318 1 0.0000 0.9779 1.000 0.000 0.000 0.000
#> GSM372320 1 0.0000 0.9779 1.000 0.000 0.000 0.000
#> GSM372322 1 0.0000 0.9779 1.000 0.000 0.000 0.000
#> GSM372324 1 0.0000 0.9779 1.000 0.000 0.000 0.000
#> GSM372325 1 0.5174 0.3617 0.620 0.368 0.012 0.000
#> GSM372327 1 0.0000 0.9779 1.000 0.000 0.000 0.000
#> GSM372329 1 0.0000 0.9779 1.000 0.000 0.000 0.000
#> GSM372331 2 0.4697 0.4352 0.356 0.644 0.000 0.000
#> GSM372333 2 0.5111 0.6554 0.056 0.740 0.204 0.000
#> GSM372334 1 0.0000 0.9779 1.000 0.000 0.000 0.000
#> GSM372336 1 0.0000 0.9779 1.000 0.000 0.000 0.000
#> GSM372338 1 0.0000 0.9779 1.000 0.000 0.000 0.000
#> GSM372340 1 0.0000 0.9779 1.000 0.000 0.000 0.000
#> GSM372342 1 0.0000 0.9779 1.000 0.000 0.000 0.000
#> GSM372344 1 0.0000 0.9779 1.000 0.000 0.000 0.000
#> GSM372346 1 0.0000 0.9779 1.000 0.000 0.000 0.000
#> GSM372348 1 0.0000 0.9779 1.000 0.000 0.000 0.000
#> GSM372350 1 0.0188 0.9742 0.996 0.000 0.000 0.004
#> GSM372352 2 0.6569 0.5134 0.284 0.628 0.020 0.068
#> GSM372354 1 0.0000 0.9779 1.000 0.000 0.000 0.000
#> GSM372356 1 0.0000 0.9779 1.000 0.000 0.000 0.000
#> GSM372358 1 0.0000 0.9779 1.000 0.000 0.000 0.000
#> GSM372360 1 0.0000 0.9779 1.000 0.000 0.000 0.000
#> GSM372362 1 0.0000 0.9779 1.000 0.000 0.000 0.000
#> GSM372364 1 0.0000 0.9779 1.000 0.000 0.000 0.000
#> GSM372365 1 0.0000 0.9779 1.000 0.000 0.000 0.000
#> GSM372366 1 0.0000 0.9779 1.000 0.000 0.000 0.000
#> GSM372367 1 0.0000 0.9779 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM372286 2 0.2339 0.805 0.000 0.912 0.008 0.052 0.028
#> GSM372287 4 0.0290 0.810 0.000 0.008 0.000 0.992 0.000
#> GSM372288 4 0.1484 0.802 0.000 0.048 0.000 0.944 0.008
#> GSM372289 4 0.4114 0.575 0.000 0.272 0.000 0.712 0.016
#> GSM372290 4 0.1579 0.807 0.000 0.032 0.000 0.944 0.024
#> GSM372291 4 0.2624 0.741 0.012 0.000 0.000 0.872 0.116
#> GSM372292 5 0.4627 0.522 0.000 0.000 0.012 0.444 0.544
#> GSM372293 5 0.4767 0.715 0.000 0.000 0.088 0.192 0.720
#> GSM372294 4 0.2110 0.785 0.000 0.016 0.000 0.912 0.072
#> GSM372295 4 0.2248 0.780 0.000 0.012 0.000 0.900 0.088
#> GSM372296 4 0.0451 0.810 0.000 0.008 0.000 0.988 0.004
#> GSM372297 4 0.1478 0.775 0.000 0.000 0.000 0.936 0.064
#> GSM372298 4 0.4024 0.560 0.000 0.028 0.000 0.752 0.220
#> GSM372299 4 0.5167 0.032 0.000 0.044 0.000 0.552 0.404
#> GSM372300 5 0.4086 0.730 0.000 0.000 0.024 0.240 0.736
#> GSM372301 5 0.4467 0.690 0.000 0.000 0.016 0.344 0.640
#> GSM372302 4 0.0451 0.808 0.000 0.004 0.000 0.988 0.008
#> GSM372303 5 0.4735 0.733 0.000 0.000 0.044 0.284 0.672
#> GSM372304 4 0.1484 0.789 0.000 0.008 0.000 0.944 0.048
#> GSM372305 2 0.1731 0.823 0.000 0.940 0.012 0.040 0.008
#> GSM372306 2 0.4169 0.615 0.000 0.732 0.240 0.000 0.028
#> GSM372307 4 0.4024 0.638 0.000 0.220 0.000 0.752 0.028
#> GSM372309 2 0.4871 0.744 0.000 0.760 0.128 0.080 0.032
#> GSM372311 2 0.0865 0.822 0.000 0.972 0.000 0.024 0.004
#> GSM372313 2 0.1267 0.814 0.000 0.960 0.004 0.012 0.024
#> GSM372315 2 0.4197 0.619 0.000 0.728 0.000 0.244 0.028
#> GSM372317 2 0.3455 0.680 0.000 0.784 0.208 0.000 0.008
#> GSM372319 3 0.1808 0.790 0.000 0.020 0.936 0.004 0.040
#> GSM372321 3 0.1300 0.789 0.000 0.016 0.956 0.000 0.028
#> GSM372323 3 0.1626 0.790 0.000 0.016 0.940 0.000 0.044
#> GSM372326 3 0.4288 0.530 0.000 0.004 0.612 0.000 0.384
#> GSM372328 3 0.3910 0.659 0.000 0.000 0.720 0.008 0.272
#> GSM372330 2 0.2569 0.811 0.000 0.896 0.004 0.032 0.068
#> GSM372332 3 0.2424 0.758 0.000 0.000 0.868 0.000 0.132
#> GSM372335 2 0.1282 0.811 0.000 0.952 0.004 0.000 0.044
#> GSM372337 3 0.0955 0.789 0.000 0.004 0.968 0.000 0.028
#> GSM372339 3 0.1544 0.788 0.000 0.000 0.932 0.000 0.068
#> GSM372341 3 0.1732 0.785 0.000 0.000 0.920 0.000 0.080
#> GSM372343 3 0.4126 0.538 0.000 0.000 0.620 0.000 0.380
#> GSM372345 3 0.0693 0.778 0.000 0.008 0.980 0.000 0.012
#> GSM372347 3 0.4603 0.490 0.000 0.300 0.668 0.000 0.032
#> GSM372349 3 0.3102 0.698 0.000 0.000 0.860 0.056 0.084
#> GSM372351 3 0.4397 0.436 0.000 0.004 0.564 0.000 0.432
#> GSM372353 5 0.7093 0.194 0.000 0.300 0.192 0.032 0.476
#> GSM372355 2 0.1661 0.821 0.000 0.940 0.000 0.036 0.024
#> GSM372357 2 0.1914 0.819 0.000 0.932 0.004 0.032 0.032
#> GSM372359 2 0.3966 0.727 0.000 0.784 0.004 0.036 0.176
#> GSM372361 4 0.4595 0.689 0.000 0.116 0.056 0.784 0.044
#> GSM372363 2 0.2906 0.802 0.000 0.880 0.012 0.080 0.028
#> GSM372308 1 0.0162 0.967 0.996 0.000 0.000 0.000 0.004
#> GSM372310 1 0.0000 0.967 1.000 0.000 0.000 0.000 0.000
#> GSM372312 1 0.5052 0.714 0.748 0.000 0.040 0.136 0.076
#> GSM372314 1 0.2930 0.784 0.832 0.164 0.000 0.000 0.004
#> GSM372316 1 0.0000 0.967 1.000 0.000 0.000 0.000 0.000
#> GSM372318 1 0.0000 0.967 1.000 0.000 0.000 0.000 0.000
#> GSM372320 1 0.0000 0.967 1.000 0.000 0.000 0.000 0.000
#> GSM372322 1 0.0000 0.967 1.000 0.000 0.000 0.000 0.000
#> GSM372324 1 0.0290 0.962 0.992 0.000 0.000 0.000 0.008
#> GSM372325 1 0.4816 0.642 0.724 0.216 0.028 0.000 0.032
#> GSM372327 1 0.0162 0.967 0.996 0.000 0.000 0.000 0.004
#> GSM372329 1 0.0162 0.967 0.996 0.000 0.000 0.000 0.004
#> GSM372331 2 0.3454 0.679 0.156 0.816 0.000 0.000 0.028
#> GSM372333 3 0.5504 0.531 0.072 0.200 0.692 0.000 0.036
#> GSM372334 1 0.0000 0.967 1.000 0.000 0.000 0.000 0.000
#> GSM372336 1 0.0162 0.967 0.996 0.000 0.000 0.000 0.004
#> GSM372338 1 0.0000 0.967 1.000 0.000 0.000 0.000 0.000
#> GSM372340 1 0.0000 0.967 1.000 0.000 0.000 0.000 0.000
#> GSM372342 1 0.0162 0.967 0.996 0.000 0.000 0.000 0.004
#> GSM372344 1 0.0000 0.967 1.000 0.000 0.000 0.000 0.000
#> GSM372346 1 0.0000 0.967 1.000 0.000 0.000 0.000 0.000
#> GSM372348 1 0.0510 0.957 0.984 0.000 0.000 0.000 0.016
#> GSM372350 1 0.4023 0.797 0.816 0.000 0.016 0.092 0.076
#> GSM372352 2 0.7262 0.260 0.356 0.480 0.016 0.060 0.088
#> GSM372354 1 0.0290 0.965 0.992 0.000 0.000 0.000 0.008
#> GSM372356 1 0.0162 0.967 0.996 0.000 0.000 0.000 0.004
#> GSM372358 1 0.0162 0.967 0.996 0.000 0.000 0.000 0.004
#> GSM372360 1 0.0162 0.967 0.996 0.000 0.000 0.000 0.004
#> GSM372362 1 0.0290 0.965 0.992 0.000 0.000 0.000 0.008
#> GSM372364 1 0.0162 0.967 0.996 0.000 0.000 0.000 0.004
#> GSM372365 1 0.0162 0.967 0.996 0.000 0.000 0.000 0.004
#> GSM372366 1 0.0162 0.967 0.996 0.000 0.000 0.000 0.004
#> GSM372367 1 0.0000 0.967 1.000 0.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM372286 2 0.2364 0.6429 0.000 0.892 0.000 0.072 0.032 0.004
#> GSM372287 4 0.1418 0.6474 0.000 0.000 0.000 0.944 0.032 0.024
#> GSM372288 4 0.1726 0.6424 0.000 0.044 0.000 0.932 0.012 0.012
#> GSM372289 4 0.5430 0.4736 0.000 0.200 0.004 0.652 0.028 0.116
#> GSM372290 4 0.2383 0.6406 0.000 0.040 0.016 0.908 0.020 0.016
#> GSM372291 4 0.4939 -0.0955 0.020 0.000 0.000 0.484 0.468 0.028
#> GSM372292 6 0.4530 0.3777 0.000 0.000 0.012 0.420 0.016 0.552
#> GSM372293 6 0.4907 0.5838 0.000 0.000 0.108 0.096 0.068 0.728
#> GSM372294 5 0.4185 -0.1634 0.000 0.012 0.000 0.492 0.496 0.000
#> GSM372295 4 0.4322 0.5804 0.000 0.008 0.000 0.732 0.184 0.076
#> GSM372296 4 0.2001 0.6206 0.000 0.004 0.000 0.900 0.092 0.004
#> GSM372297 4 0.3125 0.5698 0.000 0.000 0.000 0.836 0.080 0.084
#> GSM372298 4 0.3608 0.3869 0.000 0.012 0.000 0.736 0.004 0.248
#> GSM372299 4 0.5116 0.2458 0.000 0.020 0.000 0.472 0.040 0.468
#> GSM372300 6 0.4481 0.6453 0.000 0.000 0.032 0.176 0.056 0.736
#> GSM372301 6 0.4224 0.6176 0.000 0.000 0.036 0.256 0.008 0.700
#> GSM372302 4 0.1594 0.6376 0.000 0.000 0.000 0.932 0.052 0.016
#> GSM372303 6 0.4627 0.6417 0.000 0.000 0.056 0.216 0.024 0.704
#> GSM372304 4 0.2052 0.6262 0.000 0.004 0.000 0.912 0.056 0.028
#> GSM372305 2 0.5736 0.5860 0.000 0.672 0.032 0.104 0.040 0.152
#> GSM372306 2 0.4428 0.5084 0.000 0.688 0.260 0.000 0.036 0.016
#> GSM372307 4 0.7137 0.4094 0.000 0.120 0.116 0.544 0.044 0.176
#> GSM372309 2 0.8142 0.3273 0.000 0.400 0.140 0.204 0.064 0.192
#> GSM372311 2 0.2024 0.6575 0.000 0.920 0.000 0.036 0.016 0.028
#> GSM372313 2 0.0922 0.6484 0.000 0.968 0.000 0.004 0.024 0.004
#> GSM372315 4 0.6233 -0.0254 0.000 0.392 0.000 0.428 0.028 0.152
#> GSM372317 2 0.3463 0.5525 0.000 0.748 0.240 0.000 0.008 0.004
#> GSM372319 3 0.2788 0.7182 0.000 0.028 0.888 0.020 0.044 0.020
#> GSM372321 3 0.1965 0.7342 0.000 0.024 0.924 0.004 0.040 0.008
#> GSM372323 3 0.4002 0.7241 0.000 0.012 0.780 0.000 0.112 0.096
#> GSM372326 3 0.4002 0.4455 0.000 0.008 0.588 0.000 0.000 0.404
#> GSM372328 3 0.3520 0.6606 0.000 0.000 0.776 0.000 0.036 0.188
#> GSM372330 2 0.3487 0.6309 0.000 0.824 0.000 0.060 0.016 0.100
#> GSM372332 3 0.3083 0.7407 0.000 0.000 0.828 0.000 0.132 0.040
#> GSM372335 2 0.2998 0.6042 0.000 0.856 0.024 0.000 0.024 0.096
#> GSM372337 3 0.2865 0.7222 0.000 0.008 0.840 0.000 0.140 0.012
#> GSM372339 3 0.1257 0.7399 0.000 0.000 0.952 0.000 0.020 0.028
#> GSM372341 3 0.1930 0.7486 0.000 0.000 0.916 0.000 0.036 0.048
#> GSM372343 3 0.3769 0.5175 0.000 0.000 0.640 0.000 0.004 0.356
#> GSM372345 3 0.3449 0.6866 0.000 0.008 0.780 0.000 0.196 0.016
#> GSM372347 2 0.6190 0.2599 0.000 0.512 0.248 0.000 0.216 0.024
#> GSM372349 5 0.4150 -0.1154 0.000 0.004 0.372 0.012 0.612 0.000
#> GSM372351 3 0.3756 0.4258 0.000 0.000 0.600 0.000 0.000 0.400
#> GSM372353 6 0.6124 0.2976 0.008 0.088 0.168 0.040 0.044 0.652
#> GSM372355 2 0.3271 0.6455 0.000 0.844 0.000 0.060 0.020 0.076
#> GSM372357 2 0.6136 0.5450 0.000 0.628 0.036 0.096 0.048 0.192
#> GSM372359 6 0.6240 -0.2294 0.000 0.392 0.060 0.032 0.036 0.480
#> GSM372361 4 0.6974 0.4346 0.000 0.088 0.108 0.560 0.052 0.192
#> GSM372363 2 0.8020 0.1411 0.000 0.352 0.108 0.300 0.052 0.188
#> GSM372308 1 0.0363 0.9545 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM372310 1 0.0000 0.9563 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372312 5 0.4812 0.4490 0.352 0.008 0.000 0.048 0.592 0.000
#> GSM372314 1 0.3663 0.6857 0.784 0.148 0.000 0.000 0.068 0.000
#> GSM372316 1 0.0260 0.9555 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM372318 1 0.0146 0.9564 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM372320 1 0.0146 0.9558 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM372322 1 0.0260 0.9555 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM372324 1 0.2146 0.8337 0.880 0.004 0.000 0.000 0.116 0.000
#> GSM372325 2 0.6503 -0.0730 0.352 0.388 0.024 0.000 0.236 0.000
#> GSM372327 1 0.0260 0.9555 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM372329 1 0.0547 0.9502 0.980 0.000 0.000 0.000 0.020 0.000
#> GSM372331 2 0.3206 0.5646 0.108 0.836 0.000 0.000 0.048 0.008
#> GSM372333 3 0.7032 0.2549 0.108 0.136 0.472 0.000 0.276 0.008
#> GSM372334 1 0.0146 0.9558 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM372336 1 0.0692 0.9483 0.976 0.000 0.000 0.000 0.020 0.004
#> GSM372338 1 0.0146 0.9558 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM372340 1 0.0146 0.9564 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM372342 1 0.0458 0.9519 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM372344 1 0.0865 0.9366 0.964 0.000 0.000 0.000 0.036 0.000
#> GSM372346 1 0.0146 0.9564 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM372348 1 0.3795 0.2916 0.632 0.004 0.000 0.000 0.364 0.000
#> GSM372350 5 0.4763 0.4686 0.344 0.000 0.000 0.064 0.592 0.000
#> GSM372352 5 0.5814 0.2405 0.016 0.292 0.004 0.096 0.580 0.012
#> GSM372354 1 0.0891 0.9407 0.968 0.000 0.000 0.000 0.024 0.008
#> GSM372356 1 0.0146 0.9558 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM372358 1 0.0146 0.9564 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM372360 1 0.0260 0.9550 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM372362 1 0.0260 0.9550 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM372364 1 0.0260 0.9550 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM372365 1 0.0922 0.9390 0.968 0.004 0.000 0.000 0.024 0.004
#> GSM372366 1 0.0146 0.9561 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM372367 1 0.0508 0.9517 0.984 0.000 0.000 0.000 0.012 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) specimen(p) individual(p) k
#> MAD:NMF 82 3.35e-04 8.50e-17 0.999 2
#> MAD:NMF 82 6.72e-05 1.37e-16 0.972 3
#> MAD:NMF 74 2.92e-13 2.10e-24 0.865 4
#> MAD:NMF 77 2.43e-11 1.72e-21 0.289 5
#> MAD:NMF 59 1.20e-09 8.26e-18 0.320 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 51941 rows and 82 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.877 0.910 0.963 0.4792 0.518 0.518
#> 3 3 0.659 0.738 0.874 0.3412 0.822 0.662
#> 4 4 0.710 0.680 0.847 0.0791 0.853 0.633
#> 5 5 0.676 0.574 0.763 0.0575 0.886 0.649
#> 6 6 0.733 0.599 0.803 0.0677 0.918 0.690
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM372286 2 0.0000 0.9638 0.000 1.000
#> GSM372287 2 0.0000 0.9638 0.000 1.000
#> GSM372288 2 0.0000 0.9638 0.000 1.000
#> GSM372289 2 0.0000 0.9638 0.000 1.000
#> GSM372290 2 0.0000 0.9638 0.000 1.000
#> GSM372291 2 0.9933 0.1712 0.452 0.548
#> GSM372292 2 0.0000 0.9638 0.000 1.000
#> GSM372293 2 0.0938 0.9597 0.012 0.988
#> GSM372294 2 0.0000 0.9638 0.000 1.000
#> GSM372295 2 0.0000 0.9638 0.000 1.000
#> GSM372296 2 0.0000 0.9638 0.000 1.000
#> GSM372297 2 0.0000 0.9638 0.000 1.000
#> GSM372298 2 0.0000 0.9638 0.000 1.000
#> GSM372299 2 0.0938 0.9597 0.012 0.988
#> GSM372300 2 0.0938 0.9597 0.012 0.988
#> GSM372301 2 0.0000 0.9638 0.000 1.000
#> GSM372302 2 0.0000 0.9638 0.000 1.000
#> GSM372303 2 0.1633 0.9510 0.024 0.976
#> GSM372304 2 0.0000 0.9638 0.000 1.000
#> GSM372305 2 0.0000 0.9638 0.000 1.000
#> GSM372306 2 0.0000 0.9638 0.000 1.000
#> GSM372307 2 0.0000 0.9638 0.000 1.000
#> GSM372309 2 0.0000 0.9638 0.000 1.000
#> GSM372311 2 0.0000 0.9638 0.000 1.000
#> GSM372313 2 0.0000 0.9638 0.000 1.000
#> GSM372315 2 0.0000 0.9638 0.000 1.000
#> GSM372317 2 0.0000 0.9638 0.000 1.000
#> GSM372319 2 0.0000 0.9638 0.000 1.000
#> GSM372321 2 0.0000 0.9638 0.000 1.000
#> GSM372323 2 0.0938 0.9597 0.012 0.988
#> GSM372326 2 0.0938 0.9597 0.012 0.988
#> GSM372328 2 0.0000 0.9638 0.000 1.000
#> GSM372330 2 0.0000 0.9638 0.000 1.000
#> GSM372332 2 0.9286 0.4854 0.344 0.656
#> GSM372335 2 0.0938 0.9597 0.012 0.988
#> GSM372337 2 0.5842 0.8385 0.140 0.860
#> GSM372339 2 0.0938 0.9597 0.012 0.988
#> GSM372341 2 0.0938 0.9597 0.012 0.988
#> GSM372343 2 0.0938 0.9597 0.012 0.988
#> GSM372345 2 0.5842 0.8385 0.140 0.860
#> GSM372347 2 0.5842 0.8385 0.140 0.860
#> GSM372349 2 0.6247 0.8185 0.156 0.844
#> GSM372351 2 0.0000 0.9638 0.000 1.000
#> GSM372353 2 0.0938 0.9597 0.012 0.988
#> GSM372355 2 0.0000 0.9638 0.000 1.000
#> GSM372357 2 0.0000 0.9638 0.000 1.000
#> GSM372359 2 0.0938 0.9597 0.012 0.988
#> GSM372361 2 0.0000 0.9638 0.000 1.000
#> GSM372363 2 0.0000 0.9638 0.000 1.000
#> GSM372308 1 0.0938 0.9486 0.988 0.012
#> GSM372310 1 0.0938 0.9486 0.988 0.012
#> GSM372312 1 0.9970 0.0937 0.532 0.468
#> GSM372314 1 0.0938 0.9486 0.988 0.012
#> GSM372316 1 0.0000 0.9536 1.000 0.000
#> GSM372318 1 0.0000 0.9536 1.000 0.000
#> GSM372320 1 0.0000 0.9536 1.000 0.000
#> GSM372322 1 0.0000 0.9536 1.000 0.000
#> GSM372324 1 0.0000 0.9536 1.000 0.000
#> GSM372325 1 0.0938 0.9486 0.988 0.012
#> GSM372327 1 0.0000 0.9536 1.000 0.000
#> GSM372329 1 0.0000 0.9536 1.000 0.000
#> GSM372331 1 0.0938 0.9486 0.988 0.012
#> GSM372333 1 0.9044 0.5096 0.680 0.320
#> GSM372334 1 0.0000 0.9536 1.000 0.000
#> GSM372336 1 0.0000 0.9536 1.000 0.000
#> GSM372338 1 0.0000 0.9536 1.000 0.000
#> GSM372340 1 0.0000 0.9536 1.000 0.000
#> GSM372342 1 0.0000 0.9536 1.000 0.000
#> GSM372344 1 0.0000 0.9536 1.000 0.000
#> GSM372346 1 0.0000 0.9536 1.000 0.000
#> GSM372348 1 0.0000 0.9536 1.000 0.000
#> GSM372350 1 0.9933 0.1513 0.548 0.452
#> GSM372352 2 0.5842 0.8385 0.140 0.860
#> GSM372354 1 0.0000 0.9536 1.000 0.000
#> GSM372356 1 0.0938 0.9486 0.988 0.012
#> GSM372358 1 0.0000 0.9536 1.000 0.000
#> GSM372360 1 0.0000 0.9536 1.000 0.000
#> GSM372362 1 0.0000 0.9536 1.000 0.000
#> GSM372364 1 0.0000 0.9536 1.000 0.000
#> GSM372365 1 0.0938 0.9486 0.988 0.012
#> GSM372366 1 0.0000 0.9536 1.000 0.000
#> GSM372367 1 0.0938 0.9486 0.988 0.012
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM372286 2 0.0592 0.779 0.000 0.988 0.012
#> GSM372287 2 0.0000 0.781 0.000 1.000 0.000
#> GSM372288 2 0.0000 0.781 0.000 1.000 0.000
#> GSM372289 2 0.0000 0.781 0.000 1.000 0.000
#> GSM372290 2 0.0000 0.781 0.000 1.000 0.000
#> GSM372291 3 0.5529 0.421 0.296 0.000 0.704
#> GSM372292 2 0.6062 0.512 0.000 0.616 0.384
#> GSM372293 3 0.5058 0.576 0.000 0.244 0.756
#> GSM372294 3 0.5948 0.432 0.000 0.360 0.640
#> GSM372295 3 0.5058 0.608 0.000 0.244 0.756
#> GSM372296 2 0.0000 0.781 0.000 1.000 0.000
#> GSM372297 2 0.0000 0.781 0.000 1.000 0.000
#> GSM372298 2 0.0000 0.781 0.000 1.000 0.000
#> GSM372299 2 0.6286 0.372 0.000 0.536 0.464
#> GSM372300 3 0.5058 0.576 0.000 0.244 0.756
#> GSM372301 2 0.6126 0.490 0.000 0.600 0.400
#> GSM372302 2 0.0000 0.781 0.000 1.000 0.000
#> GSM372303 3 0.3619 0.695 0.000 0.136 0.864
#> GSM372304 2 0.0000 0.781 0.000 1.000 0.000
#> GSM372305 2 0.0000 0.781 0.000 1.000 0.000
#> GSM372306 2 0.5678 0.591 0.000 0.684 0.316
#> GSM372307 2 0.0000 0.781 0.000 1.000 0.000
#> GSM372309 2 0.5678 0.591 0.000 0.684 0.316
#> GSM372311 2 0.0000 0.781 0.000 1.000 0.000
#> GSM372313 2 0.2356 0.757 0.000 0.928 0.072
#> GSM372315 2 0.0000 0.781 0.000 1.000 0.000
#> GSM372317 2 0.4842 0.659 0.000 0.776 0.224
#> GSM372319 2 0.0000 0.781 0.000 1.000 0.000
#> GSM372321 2 0.0000 0.781 0.000 1.000 0.000
#> GSM372323 2 0.6291 0.362 0.000 0.532 0.468
#> GSM372326 2 0.6291 0.362 0.000 0.532 0.468
#> GSM372328 2 0.6045 0.520 0.000 0.620 0.380
#> GSM372330 2 0.0000 0.781 0.000 1.000 0.000
#> GSM372332 3 0.4399 0.630 0.188 0.000 0.812
#> GSM372335 2 0.6225 0.437 0.000 0.568 0.432
#> GSM372337 3 0.3038 0.719 0.000 0.104 0.896
#> GSM372339 3 0.4121 0.675 0.000 0.168 0.832
#> GSM372341 3 0.4121 0.675 0.000 0.168 0.832
#> GSM372343 2 0.6291 0.362 0.000 0.532 0.468
#> GSM372345 3 0.3038 0.719 0.000 0.104 0.896
#> GSM372347 3 0.3038 0.719 0.000 0.104 0.896
#> GSM372349 3 0.0424 0.699 0.000 0.008 0.992
#> GSM372351 2 0.6026 0.526 0.000 0.624 0.376
#> GSM372353 2 0.6225 0.437 0.000 0.568 0.432
#> GSM372355 2 0.1031 0.776 0.000 0.976 0.024
#> GSM372357 2 0.4452 0.690 0.000 0.808 0.192
#> GSM372359 2 0.6225 0.437 0.000 0.568 0.432
#> GSM372361 2 0.0747 0.778 0.000 0.984 0.016
#> GSM372363 2 0.0000 0.781 0.000 1.000 0.000
#> GSM372308 1 0.3551 0.869 0.868 0.000 0.132
#> GSM372310 1 0.3551 0.869 0.868 0.000 0.132
#> GSM372312 3 0.6026 0.262 0.376 0.000 0.624
#> GSM372314 1 0.3192 0.886 0.888 0.000 0.112
#> GSM372316 1 0.0000 0.956 1.000 0.000 0.000
#> GSM372318 1 0.0000 0.956 1.000 0.000 0.000
#> GSM372320 1 0.0000 0.956 1.000 0.000 0.000
#> GSM372322 1 0.0000 0.956 1.000 0.000 0.000
#> GSM372324 1 0.2537 0.909 0.920 0.000 0.080
#> GSM372325 1 0.3551 0.869 0.868 0.000 0.132
#> GSM372327 1 0.0000 0.956 1.000 0.000 0.000
#> GSM372329 1 0.0000 0.956 1.000 0.000 0.000
#> GSM372331 1 0.3551 0.869 0.868 0.000 0.132
#> GSM372333 1 0.6260 0.281 0.552 0.000 0.448
#> GSM372334 1 0.0000 0.956 1.000 0.000 0.000
#> GSM372336 1 0.0000 0.956 1.000 0.000 0.000
#> GSM372338 1 0.0000 0.956 1.000 0.000 0.000
#> GSM372340 1 0.0000 0.956 1.000 0.000 0.000
#> GSM372342 1 0.0000 0.956 1.000 0.000 0.000
#> GSM372344 1 0.0000 0.956 1.000 0.000 0.000
#> GSM372346 1 0.0000 0.956 1.000 0.000 0.000
#> GSM372348 1 0.0000 0.956 1.000 0.000 0.000
#> GSM372350 3 0.6168 0.175 0.412 0.000 0.588
#> GSM372352 3 0.2959 0.719 0.000 0.100 0.900
#> GSM372354 1 0.0000 0.956 1.000 0.000 0.000
#> GSM372356 1 0.1031 0.944 0.976 0.000 0.024
#> GSM372358 1 0.0000 0.956 1.000 0.000 0.000
#> GSM372360 1 0.0000 0.956 1.000 0.000 0.000
#> GSM372362 1 0.0000 0.956 1.000 0.000 0.000
#> GSM372364 1 0.0000 0.956 1.000 0.000 0.000
#> GSM372365 1 0.1031 0.944 0.976 0.000 0.024
#> GSM372366 1 0.0000 0.956 1.000 0.000 0.000
#> GSM372367 1 0.1031 0.944 0.976 0.000 0.024
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM372286 2 0.0469 0.8889 0.000 0.988 0.012 0.000
#> GSM372287 2 0.0000 0.8981 0.000 1.000 0.000 0.000
#> GSM372288 2 0.0000 0.8981 0.000 1.000 0.000 0.000
#> GSM372289 2 0.0000 0.8981 0.000 1.000 0.000 0.000
#> GSM372290 2 0.0000 0.8981 0.000 1.000 0.000 0.000
#> GSM372291 4 0.5769 0.6293 0.036 0.000 0.376 0.588
#> GSM372292 3 0.4989 0.3774 0.000 0.472 0.528 0.000
#> GSM372293 3 0.2345 0.5742 0.000 0.100 0.900 0.000
#> GSM372294 3 0.7096 0.0175 0.000 0.332 0.524 0.144
#> GSM372295 3 0.6149 0.2102 0.000 0.180 0.676 0.144
#> GSM372296 2 0.0000 0.8981 0.000 1.000 0.000 0.000
#> GSM372297 2 0.0000 0.8981 0.000 1.000 0.000 0.000
#> GSM372298 2 0.0000 0.8981 0.000 1.000 0.000 0.000
#> GSM372299 3 0.5256 0.5101 0.000 0.392 0.596 0.012
#> GSM372300 3 0.2345 0.5742 0.000 0.100 0.900 0.000
#> GSM372301 3 0.4972 0.4121 0.000 0.456 0.544 0.000
#> GSM372302 2 0.0000 0.8981 0.000 1.000 0.000 0.000
#> GSM372303 3 0.0336 0.4668 0.000 0.000 0.992 0.008
#> GSM372304 2 0.0000 0.8981 0.000 1.000 0.000 0.000
#> GSM372305 2 0.0000 0.8981 0.000 1.000 0.000 0.000
#> GSM372306 2 0.4888 -0.0428 0.000 0.588 0.412 0.000
#> GSM372307 2 0.0000 0.8981 0.000 1.000 0.000 0.000
#> GSM372309 2 0.4888 -0.0428 0.000 0.588 0.412 0.000
#> GSM372311 2 0.0000 0.8981 0.000 1.000 0.000 0.000
#> GSM372313 2 0.2760 0.7494 0.000 0.872 0.128 0.000
#> GSM372315 2 0.0000 0.8981 0.000 1.000 0.000 0.000
#> GSM372317 2 0.4431 0.3555 0.000 0.696 0.304 0.000
#> GSM372319 2 0.0000 0.8981 0.000 1.000 0.000 0.000
#> GSM372321 2 0.0000 0.8981 0.000 1.000 0.000 0.000
#> GSM372323 3 0.4817 0.5188 0.000 0.388 0.612 0.000
#> GSM372326 3 0.4817 0.5188 0.000 0.388 0.612 0.000
#> GSM372328 3 0.4998 0.3371 0.000 0.488 0.512 0.000
#> GSM372330 2 0.0000 0.8981 0.000 1.000 0.000 0.000
#> GSM372332 3 0.6005 -0.3070 0.040 0.000 0.500 0.460
#> GSM372335 3 0.4916 0.4749 0.000 0.424 0.576 0.000
#> GSM372337 3 0.4581 0.4829 0.000 0.080 0.800 0.120
#> GSM372339 3 0.1004 0.5025 0.000 0.024 0.972 0.004
#> GSM372341 3 0.1004 0.5025 0.000 0.024 0.972 0.004
#> GSM372343 3 0.4817 0.5184 0.000 0.388 0.612 0.000
#> GSM372345 3 0.4581 0.4829 0.000 0.080 0.800 0.120
#> GSM372347 3 0.4581 0.4829 0.000 0.080 0.800 0.120
#> GSM372349 3 0.3356 0.2650 0.000 0.000 0.824 0.176
#> GSM372351 3 0.4994 0.3553 0.000 0.480 0.520 0.000
#> GSM372353 3 0.4916 0.4749 0.000 0.424 0.576 0.000
#> GSM372355 2 0.1474 0.8498 0.000 0.948 0.052 0.000
#> GSM372357 2 0.4454 0.3679 0.000 0.692 0.308 0.000
#> GSM372359 3 0.4916 0.4749 0.000 0.424 0.576 0.000
#> GSM372361 2 0.0592 0.8856 0.000 0.984 0.016 0.000
#> GSM372363 2 0.0000 0.8981 0.000 1.000 0.000 0.000
#> GSM372308 1 0.4831 0.6229 0.704 0.000 0.016 0.280
#> GSM372310 1 0.4831 0.6229 0.704 0.000 0.016 0.280
#> GSM372312 4 0.4553 0.7422 0.040 0.000 0.180 0.780
#> GSM372314 1 0.4630 0.6648 0.732 0.000 0.016 0.252
#> GSM372316 1 0.1022 0.8915 0.968 0.000 0.000 0.032
#> GSM372318 1 0.0921 0.8923 0.972 0.000 0.000 0.028
#> GSM372320 1 0.1118 0.8898 0.964 0.000 0.000 0.036
#> GSM372322 1 0.1022 0.8915 0.968 0.000 0.000 0.032
#> GSM372324 1 0.4086 0.7211 0.776 0.000 0.008 0.216
#> GSM372325 1 0.4831 0.6229 0.704 0.000 0.016 0.280
#> GSM372327 1 0.0000 0.8949 1.000 0.000 0.000 0.000
#> GSM372329 1 0.0000 0.8949 1.000 0.000 0.000 0.000
#> GSM372331 1 0.4831 0.6229 0.704 0.000 0.016 0.280
#> GSM372333 4 0.7085 0.5046 0.300 0.000 0.156 0.544
#> GSM372334 1 0.1118 0.8898 0.964 0.000 0.000 0.036
#> GSM372336 1 0.0336 0.8945 0.992 0.000 0.000 0.008
#> GSM372338 1 0.1118 0.8898 0.964 0.000 0.000 0.036
#> GSM372340 1 0.1118 0.8898 0.964 0.000 0.000 0.036
#> GSM372342 1 0.0336 0.8945 0.992 0.000 0.000 0.008
#> GSM372344 1 0.1118 0.8898 0.964 0.000 0.000 0.036
#> GSM372346 1 0.1022 0.8915 0.968 0.000 0.000 0.032
#> GSM372348 1 0.0336 0.8945 0.992 0.000 0.000 0.008
#> GSM372350 4 0.1211 0.7119 0.040 0.000 0.000 0.960
#> GSM372352 3 0.4513 0.4770 0.000 0.076 0.804 0.120
#> GSM372354 1 0.1022 0.8915 0.968 0.000 0.000 0.032
#> GSM372356 1 0.2589 0.8338 0.884 0.000 0.000 0.116
#> GSM372358 1 0.0469 0.8935 0.988 0.000 0.000 0.012
#> GSM372360 1 0.0336 0.8945 0.992 0.000 0.000 0.008
#> GSM372362 1 0.0336 0.8945 0.992 0.000 0.000 0.008
#> GSM372364 1 0.0469 0.8935 0.988 0.000 0.000 0.012
#> GSM372365 1 0.2589 0.8338 0.884 0.000 0.000 0.116
#> GSM372366 1 0.1022 0.8915 0.968 0.000 0.000 0.032
#> GSM372367 1 0.2589 0.8338 0.884 0.000 0.000 0.116
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM372286 2 0.4060 0.9675 0.000 0.640 0.360 0.000 0.000
#> GSM372287 2 0.3999 0.9800 0.000 0.656 0.344 0.000 0.000
#> GSM372288 2 0.3999 0.9800 0.000 0.656 0.344 0.000 0.000
#> GSM372289 2 0.3999 0.9800 0.000 0.656 0.344 0.000 0.000
#> GSM372290 2 0.3999 0.9800 0.000 0.656 0.344 0.000 0.000
#> GSM372291 4 0.3452 0.5074 0.000 0.032 0.000 0.820 0.148
#> GSM372292 3 0.1732 0.5743 0.000 0.080 0.920 0.000 0.000
#> GSM372293 3 0.4165 0.3172 0.000 0.000 0.672 0.320 0.008
#> GSM372294 4 0.6181 0.2263 0.000 0.328 0.136 0.532 0.004
#> GSM372295 4 0.6351 0.1642 0.000 0.176 0.288 0.532 0.004
#> GSM372296 2 0.3999 0.9800 0.000 0.656 0.344 0.000 0.000
#> GSM372297 2 0.3999 0.9800 0.000 0.656 0.344 0.000 0.000
#> GSM372298 2 0.4030 0.9752 0.000 0.648 0.352 0.000 0.000
#> GSM372299 3 0.0609 0.6265 0.000 0.000 0.980 0.000 0.020
#> GSM372300 3 0.4165 0.3172 0.000 0.000 0.672 0.320 0.008
#> GSM372301 3 0.1704 0.5927 0.000 0.068 0.928 0.004 0.000
#> GSM372302 2 0.3999 0.9800 0.000 0.656 0.344 0.000 0.000
#> GSM372303 3 0.4533 0.1077 0.000 0.000 0.544 0.448 0.008
#> GSM372304 2 0.3999 0.9800 0.000 0.656 0.344 0.000 0.000
#> GSM372305 2 0.4015 0.9778 0.000 0.652 0.348 0.000 0.000
#> GSM372306 3 0.3274 0.2860 0.000 0.220 0.780 0.000 0.000
#> GSM372307 2 0.3999 0.9800 0.000 0.656 0.344 0.000 0.000
#> GSM372309 3 0.3274 0.2860 0.000 0.220 0.780 0.000 0.000
#> GSM372311 2 0.3999 0.9800 0.000 0.656 0.344 0.000 0.000
#> GSM372313 2 0.4304 0.7530 0.000 0.516 0.484 0.000 0.000
#> GSM372315 2 0.4030 0.9752 0.000 0.648 0.352 0.000 0.000
#> GSM372317 3 0.3966 -0.1838 0.000 0.336 0.664 0.000 0.000
#> GSM372319 2 0.3999 0.9800 0.000 0.656 0.344 0.000 0.000
#> GSM372321 2 0.3999 0.9800 0.000 0.656 0.344 0.000 0.000
#> GSM372323 3 0.0510 0.6284 0.000 0.000 0.984 0.016 0.000
#> GSM372326 3 0.0510 0.6284 0.000 0.000 0.984 0.016 0.000
#> GSM372328 3 0.2124 0.5513 0.000 0.096 0.900 0.004 0.000
#> GSM372330 2 0.4030 0.9752 0.000 0.648 0.352 0.000 0.000
#> GSM372332 4 0.7923 0.3906 0.048 0.200 0.284 0.444 0.024
#> GSM372335 3 0.0880 0.6243 0.000 0.032 0.968 0.000 0.000
#> GSM372337 3 0.4294 0.1383 0.000 0.000 0.532 0.468 0.000
#> GSM372339 3 0.4138 0.1937 0.000 0.000 0.616 0.384 0.000
#> GSM372341 3 0.4138 0.1937 0.000 0.000 0.616 0.384 0.000
#> GSM372343 3 0.0510 0.6284 0.000 0.000 0.984 0.016 0.000
#> GSM372345 3 0.4294 0.1383 0.000 0.000 0.532 0.468 0.000
#> GSM372347 3 0.4294 0.1383 0.000 0.000 0.532 0.468 0.000
#> GSM372349 4 0.4565 0.0537 0.000 0.012 0.408 0.580 0.000
#> GSM372351 3 0.2127 0.5350 0.000 0.108 0.892 0.000 0.000
#> GSM372353 3 0.0880 0.6243 0.000 0.032 0.968 0.000 0.000
#> GSM372355 2 0.4201 0.9005 0.000 0.592 0.408 0.000 0.000
#> GSM372357 3 0.3966 -0.2493 0.000 0.336 0.664 0.000 0.000
#> GSM372359 3 0.0880 0.6243 0.000 0.032 0.968 0.000 0.000
#> GSM372361 2 0.4074 0.9630 0.000 0.636 0.364 0.000 0.000
#> GSM372363 2 0.3999 0.9800 0.000 0.656 0.344 0.000 0.000
#> GSM372308 1 0.5033 0.5921 0.716 0.000 0.004 0.156 0.124
#> GSM372310 1 0.5033 0.5921 0.716 0.000 0.004 0.156 0.124
#> GSM372312 4 0.6986 0.4763 0.048 0.224 0.016 0.584 0.128
#> GSM372314 1 0.4743 0.6101 0.744 0.000 0.004 0.136 0.116
#> GSM372316 1 0.1732 0.6282 0.920 0.000 0.000 0.000 0.080
#> GSM372318 1 0.4138 -0.2708 0.616 0.000 0.000 0.000 0.384
#> GSM372320 5 0.4074 1.0000 0.364 0.000 0.000 0.000 0.636
#> GSM372322 1 0.4219 -0.3825 0.584 0.000 0.000 0.000 0.416
#> GSM372324 1 0.4117 0.6337 0.788 0.000 0.000 0.116 0.096
#> GSM372325 1 0.5033 0.5921 0.716 0.000 0.004 0.156 0.124
#> GSM372327 1 0.3966 -0.1046 0.664 0.000 0.000 0.000 0.336
#> GSM372329 1 0.3966 -0.1046 0.664 0.000 0.000 0.000 0.336
#> GSM372331 1 0.5033 0.5921 0.716 0.000 0.004 0.156 0.124
#> GSM372333 4 0.8360 0.0812 0.308 0.200 0.004 0.352 0.136
#> GSM372334 5 0.4074 1.0000 0.364 0.000 0.000 0.000 0.636
#> GSM372336 1 0.0162 0.6944 0.996 0.000 0.000 0.000 0.004
#> GSM372338 5 0.4074 1.0000 0.364 0.000 0.000 0.000 0.636
#> GSM372340 5 0.4074 1.0000 0.364 0.000 0.000 0.000 0.636
#> GSM372342 1 0.0162 0.6944 0.996 0.000 0.000 0.000 0.004
#> GSM372344 5 0.4074 1.0000 0.364 0.000 0.000 0.000 0.636
#> GSM372346 1 0.4219 -0.3825 0.584 0.000 0.000 0.000 0.416
#> GSM372348 1 0.0162 0.6944 0.996 0.000 0.000 0.000 0.004
#> GSM372350 4 0.6736 0.3474 0.000 0.344 0.000 0.396 0.260
#> GSM372352 3 0.4297 0.1298 0.000 0.000 0.528 0.472 0.000
#> GSM372354 1 0.1732 0.6282 0.920 0.000 0.000 0.000 0.080
#> GSM372356 1 0.2305 0.6858 0.896 0.000 0.000 0.012 0.092
#> GSM372358 1 0.0000 0.6953 1.000 0.000 0.000 0.000 0.000
#> GSM372360 1 0.0162 0.6944 0.996 0.000 0.000 0.000 0.004
#> GSM372362 1 0.0162 0.6944 0.996 0.000 0.000 0.000 0.004
#> GSM372364 1 0.0000 0.6953 1.000 0.000 0.000 0.000 0.000
#> GSM372365 1 0.2305 0.6858 0.896 0.000 0.000 0.012 0.092
#> GSM372366 1 0.1732 0.6282 0.920 0.000 0.000 0.000 0.080
#> GSM372367 1 0.2305 0.6858 0.896 0.000 0.000 0.012 0.092
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM372286 4 0.1444 0.9020 0.000 0.072 0.000 0.928 0.000 0.000
#> GSM372287 4 0.0000 0.9331 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM372288 4 0.0000 0.9331 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM372289 4 0.0000 0.9331 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM372290 4 0.0000 0.9331 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM372291 6 0.4926 0.4009 0.068 0.000 0.392 0.000 0.000 0.540
#> GSM372292 2 0.1674 0.6800 0.004 0.924 0.004 0.068 0.000 0.000
#> GSM372293 2 0.4444 -0.3606 0.028 0.536 0.436 0.000 0.000 0.000
#> GSM372294 3 0.5054 -0.0696 0.068 0.052 0.692 0.188 0.000 0.000
#> GSM372295 3 0.4920 0.1019 0.068 0.204 0.692 0.036 0.000 0.000
#> GSM372296 4 0.0000 0.9331 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM372297 4 0.0000 0.9331 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM372298 4 0.0458 0.9293 0.000 0.016 0.000 0.984 0.000 0.000
#> GSM372299 2 0.1440 0.6636 0.004 0.948 0.032 0.004 0.012 0.000
#> GSM372300 2 0.4444 -0.3606 0.028 0.536 0.436 0.000 0.000 0.000
#> GSM372301 2 0.1644 0.6841 0.004 0.932 0.012 0.052 0.000 0.000
#> GSM372302 4 0.0000 0.9331 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM372303 3 0.4682 0.4680 0.048 0.396 0.556 0.000 0.000 0.000
#> GSM372304 4 0.0000 0.9331 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM372305 4 0.1075 0.9176 0.000 0.048 0.000 0.952 0.000 0.000
#> GSM372306 2 0.2912 0.5401 0.000 0.784 0.000 0.216 0.000 0.000
#> GSM372307 4 0.0000 0.9331 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM372309 2 0.2912 0.5401 0.000 0.784 0.000 0.216 0.000 0.000
#> GSM372311 4 0.0000 0.9331 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM372313 4 0.3101 0.7097 0.000 0.244 0.000 0.756 0.000 0.000
#> GSM372315 4 0.0937 0.9233 0.000 0.040 0.000 0.960 0.000 0.000
#> GSM372317 2 0.3578 0.3749 0.000 0.660 0.000 0.340 0.000 0.000
#> GSM372319 4 0.0632 0.9287 0.000 0.024 0.000 0.976 0.000 0.000
#> GSM372321 4 0.0632 0.9287 0.000 0.024 0.000 0.976 0.000 0.000
#> GSM372323 2 0.1007 0.6571 0.000 0.956 0.044 0.000 0.000 0.000
#> GSM372326 2 0.1007 0.6571 0.000 0.956 0.044 0.000 0.000 0.000
#> GSM372328 2 0.1700 0.6706 0.000 0.916 0.004 0.080 0.000 0.000
#> GSM372330 4 0.0937 0.9233 0.000 0.040 0.000 0.960 0.000 0.000
#> GSM372332 3 0.6805 -0.0253 0.004 0.204 0.448 0.000 0.052 0.292
#> GSM372335 2 0.0458 0.6866 0.000 0.984 0.000 0.016 0.000 0.000
#> GSM372337 3 0.4123 0.5913 0.000 0.420 0.568 0.000 0.012 0.000
#> GSM372339 2 0.3797 -0.2000 0.000 0.580 0.420 0.000 0.000 0.000
#> GSM372341 2 0.3797 -0.2000 0.000 0.580 0.420 0.000 0.000 0.000
#> GSM372343 2 0.1219 0.6589 0.000 0.948 0.048 0.004 0.000 0.000
#> GSM372345 3 0.4123 0.5913 0.000 0.420 0.568 0.000 0.012 0.000
#> GSM372347 3 0.4123 0.5913 0.000 0.420 0.568 0.000 0.012 0.000
#> GSM372349 3 0.4776 0.5857 0.000 0.300 0.636 0.000 0.012 0.052
#> GSM372351 2 0.1765 0.6592 0.000 0.904 0.000 0.096 0.000 0.000
#> GSM372353 2 0.0458 0.6866 0.000 0.984 0.000 0.016 0.000 0.000
#> GSM372355 4 0.2664 0.7923 0.000 0.184 0.000 0.816 0.000 0.000
#> GSM372357 4 0.3843 0.2418 0.000 0.452 0.000 0.548 0.000 0.000
#> GSM372359 2 0.0458 0.6866 0.000 0.984 0.000 0.016 0.000 0.000
#> GSM372361 4 0.1663 0.8894 0.000 0.088 0.000 0.912 0.000 0.000
#> GSM372363 4 0.0000 0.9331 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM372308 5 0.3475 0.6339 0.052 0.004 0.124 0.000 0.816 0.004
#> GSM372310 5 0.3475 0.6339 0.052 0.004 0.124 0.000 0.816 0.004
#> GSM372312 6 0.6794 0.4613 0.052 0.020 0.320 0.000 0.132 0.476
#> GSM372314 5 0.3375 0.6488 0.060 0.004 0.104 0.000 0.828 0.004
#> GSM372316 5 0.3023 0.5638 0.232 0.000 0.000 0.000 0.768 0.000
#> GSM372318 1 0.3823 0.5277 0.564 0.000 0.000 0.000 0.436 0.000
#> GSM372320 1 0.2527 0.8289 0.832 0.000 0.000 0.000 0.168 0.000
#> GSM372322 1 0.3756 0.6128 0.600 0.000 0.000 0.000 0.400 0.000
#> GSM372324 5 0.3176 0.6665 0.084 0.000 0.084 0.000 0.832 0.000
#> GSM372325 5 0.3475 0.6339 0.052 0.004 0.124 0.000 0.816 0.004
#> GSM372327 5 0.3869 -0.4353 0.500 0.000 0.000 0.000 0.500 0.000
#> GSM372329 5 0.3869 -0.4353 0.500 0.000 0.000 0.000 0.500 0.000
#> GSM372331 5 0.3475 0.6339 0.052 0.004 0.124 0.000 0.816 0.004
#> GSM372333 5 0.7040 -0.2650 0.052 0.008 0.284 0.000 0.408 0.248
#> GSM372334 1 0.2527 0.8289 0.832 0.000 0.000 0.000 0.168 0.000
#> GSM372336 5 0.2135 0.6841 0.128 0.000 0.000 0.000 0.872 0.000
#> GSM372338 1 0.2527 0.8289 0.832 0.000 0.000 0.000 0.168 0.000
#> GSM372340 1 0.2527 0.8289 0.832 0.000 0.000 0.000 0.168 0.000
#> GSM372342 5 0.2219 0.6799 0.136 0.000 0.000 0.000 0.864 0.000
#> GSM372344 1 0.2527 0.8289 0.832 0.000 0.000 0.000 0.168 0.000
#> GSM372346 1 0.3756 0.6128 0.600 0.000 0.000 0.000 0.400 0.000
#> GSM372348 5 0.2135 0.6841 0.128 0.000 0.000 0.000 0.872 0.000
#> GSM372350 6 0.0000 0.5335 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM372352 3 0.4116 0.5939 0.000 0.416 0.572 0.000 0.012 0.000
#> GSM372354 5 0.3023 0.5638 0.232 0.000 0.000 0.000 0.768 0.000
#> GSM372356 5 0.0000 0.7008 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM372358 5 0.1863 0.6928 0.104 0.000 0.000 0.000 0.896 0.000
#> GSM372360 5 0.2135 0.6846 0.128 0.000 0.000 0.000 0.872 0.000
#> GSM372362 5 0.2135 0.6846 0.128 0.000 0.000 0.000 0.872 0.000
#> GSM372364 5 0.1863 0.6928 0.104 0.000 0.000 0.000 0.896 0.000
#> GSM372365 5 0.0000 0.7008 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM372366 5 0.3023 0.5638 0.232 0.000 0.000 0.000 0.768 0.000
#> GSM372367 5 0.0000 0.7008 0.000 0.000 0.000 0.000 1.000 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) specimen(p) individual(p) k
#> ATC:hclust 78 0.000126 8.92e-17 0.998 2
#> ATC:hclust 69 0.000191 1.74e-13 0.876 3
#> ATC:hclust 62 0.000257 3.33e-11 0.693 4
#> ATC:hclust 57 0.000886 1.64e-10 0.395 5
#> ATC:hclust 67 0.000840 3.20e-11 0.969 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 51941 rows and 82 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 0.4919 0.509 0.509
#> 3 3 0.890 0.911 0.961 0.3685 0.741 0.526
#> 4 4 0.786 0.769 0.844 0.0981 0.854 0.594
#> 5 5 0.733 0.728 0.816 0.0568 0.913 0.687
#> 6 6 0.754 0.637 0.791 0.0380 0.979 0.905
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
#> GSM372286 2 0 1 0 1
#> GSM372287 2 0 1 0 1
#> GSM372288 2 0 1 0 1
#> GSM372289 2 0 1 0 1
#> GSM372290 2 0 1 0 1
#> GSM372291 1 0 1 1 0
#> GSM372292 2 0 1 0 1
#> GSM372293 2 0 1 0 1
#> GSM372294 2 0 1 0 1
#> GSM372295 2 0 1 0 1
#> GSM372296 2 0 1 0 1
#> GSM372297 2 0 1 0 1
#> GSM372298 2 0 1 0 1
#> GSM372299 2 0 1 0 1
#> GSM372300 2 0 1 0 1
#> GSM372301 2 0 1 0 1
#> GSM372302 2 0 1 0 1
#> GSM372303 2 0 1 0 1
#> GSM372304 2 0 1 0 1
#> GSM372305 2 0 1 0 1
#> GSM372306 2 0 1 0 1
#> GSM372307 2 0 1 0 1
#> GSM372309 2 0 1 0 1
#> GSM372311 2 0 1 0 1
#> GSM372313 2 0 1 0 1
#> GSM372315 2 0 1 0 1
#> GSM372317 2 0 1 0 1
#> GSM372319 2 0 1 0 1
#> GSM372321 2 0 1 0 1
#> GSM372323 2 0 1 0 1
#> GSM372326 2 0 1 0 1
#> GSM372328 2 0 1 0 1
#> GSM372330 2 0 1 0 1
#> GSM372332 1 0 1 1 0
#> GSM372335 2 0 1 0 1
#> GSM372337 2 0 1 0 1
#> GSM372339 2 0 1 0 1
#> GSM372341 2 0 1 0 1
#> GSM372343 2 0 1 0 1
#> GSM372345 2 0 1 0 1
#> GSM372347 2 0 1 0 1
#> GSM372349 2 0 1 0 1
#> GSM372351 2 0 1 0 1
#> GSM372353 2 0 1 0 1
#> GSM372355 2 0 1 0 1
#> GSM372357 2 0 1 0 1
#> GSM372359 2 0 1 0 1
#> GSM372361 2 0 1 0 1
#> GSM372363 2 0 1 0 1
#> GSM372308 1 0 1 1 0
#> GSM372310 1 0 1 1 0
#> GSM372312 1 0 1 1 0
#> GSM372314 1 0 1 1 0
#> GSM372316 1 0 1 1 0
#> GSM372318 1 0 1 1 0
#> GSM372320 1 0 1 1 0
#> GSM372322 1 0 1 1 0
#> GSM372324 1 0 1 1 0
#> GSM372325 1 0 1 1 0
#> GSM372327 1 0 1 1 0
#> GSM372329 1 0 1 1 0
#> GSM372331 1 0 1 1 0
#> GSM372333 1 0 1 1 0
#> GSM372334 1 0 1 1 0
#> GSM372336 1 0 1 1 0
#> GSM372338 1 0 1 1 0
#> GSM372340 1 0 1 1 0
#> GSM372342 1 0 1 1 0
#> GSM372344 1 0 1 1 0
#> GSM372346 1 0 1 1 0
#> GSM372348 1 0 1 1 0
#> GSM372350 1 0 1 1 0
#> GSM372352 2 0 1 0 1
#> GSM372354 1 0 1 1 0
#> GSM372356 1 0 1 1 0
#> GSM372358 1 0 1 1 0
#> GSM372360 1 0 1 1 0
#> GSM372362 1 0 1 1 0
#> GSM372364 1 0 1 1 0
#> GSM372365 1 0 1 1 0
#> GSM372366 1 0 1 1 0
#> GSM372367 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM372286 2 0.0000 0.9687 0.000 1.000 0.000
#> GSM372287 2 0.0000 0.9687 0.000 1.000 0.000
#> GSM372288 2 0.0000 0.9687 0.000 1.000 0.000
#> GSM372289 2 0.0000 0.9687 0.000 1.000 0.000
#> GSM372290 2 0.0000 0.9687 0.000 1.000 0.000
#> GSM372291 3 0.4605 0.7484 0.204 0.000 0.796
#> GSM372292 2 0.0000 0.9687 0.000 1.000 0.000
#> GSM372293 3 0.0000 0.9181 0.000 0.000 1.000
#> GSM372294 3 0.5591 0.5774 0.000 0.304 0.696
#> GSM372295 3 0.0237 0.9166 0.000 0.004 0.996
#> GSM372296 2 0.0000 0.9687 0.000 1.000 0.000
#> GSM372297 2 0.0000 0.9687 0.000 1.000 0.000
#> GSM372298 2 0.0000 0.9687 0.000 1.000 0.000
#> GSM372299 3 0.0000 0.9181 0.000 0.000 1.000
#> GSM372300 3 0.0000 0.9181 0.000 0.000 1.000
#> GSM372301 3 0.0237 0.9166 0.000 0.004 0.996
#> GSM372302 2 0.0000 0.9687 0.000 1.000 0.000
#> GSM372303 3 0.0000 0.9181 0.000 0.000 1.000
#> GSM372304 2 0.0000 0.9687 0.000 1.000 0.000
#> GSM372305 2 0.0000 0.9687 0.000 1.000 0.000
#> GSM372306 2 0.0237 0.9654 0.000 0.996 0.004
#> GSM372307 2 0.0000 0.9687 0.000 1.000 0.000
#> GSM372309 3 0.4750 0.6937 0.000 0.216 0.784
#> GSM372311 2 0.0000 0.9687 0.000 1.000 0.000
#> GSM372313 2 0.0000 0.9687 0.000 1.000 0.000
#> GSM372315 2 0.0000 0.9687 0.000 1.000 0.000
#> GSM372317 2 0.0000 0.9687 0.000 1.000 0.000
#> GSM372319 2 0.0000 0.9687 0.000 1.000 0.000
#> GSM372321 2 0.0000 0.9687 0.000 1.000 0.000
#> GSM372323 3 0.0000 0.9181 0.000 0.000 1.000
#> GSM372326 3 0.0237 0.9166 0.000 0.004 0.996
#> GSM372328 2 0.4605 0.7525 0.000 0.796 0.204
#> GSM372330 2 0.0000 0.9687 0.000 1.000 0.000
#> GSM372332 3 0.0000 0.9181 0.000 0.000 1.000
#> GSM372335 3 0.0237 0.9166 0.000 0.004 0.996
#> GSM372337 3 0.0000 0.9181 0.000 0.000 1.000
#> GSM372339 3 0.0237 0.9166 0.000 0.004 0.996
#> GSM372341 3 0.0000 0.9181 0.000 0.000 1.000
#> GSM372343 3 0.0000 0.9181 0.000 0.000 1.000
#> GSM372345 3 0.0000 0.9181 0.000 0.000 1.000
#> GSM372347 3 0.0000 0.9181 0.000 0.000 1.000
#> GSM372349 3 0.0000 0.9181 0.000 0.000 1.000
#> GSM372351 2 0.5621 0.5849 0.000 0.692 0.308
#> GSM372353 3 0.0000 0.9181 0.000 0.000 1.000
#> GSM372355 2 0.0000 0.9687 0.000 1.000 0.000
#> GSM372357 2 0.5291 0.6561 0.000 0.732 0.268
#> GSM372359 3 0.4702 0.6986 0.000 0.212 0.788
#> GSM372361 2 0.0000 0.9687 0.000 1.000 0.000
#> GSM372363 2 0.0000 0.9687 0.000 1.000 0.000
#> GSM372308 1 0.6260 0.0723 0.552 0.000 0.448
#> GSM372310 1 0.0237 0.9783 0.996 0.000 0.004
#> GSM372312 3 0.4605 0.7484 0.204 0.000 0.796
#> GSM372314 1 0.0237 0.9783 0.996 0.000 0.004
#> GSM372316 1 0.0000 0.9811 1.000 0.000 0.000
#> GSM372318 1 0.0000 0.9811 1.000 0.000 0.000
#> GSM372320 1 0.0000 0.9811 1.000 0.000 0.000
#> GSM372322 1 0.0000 0.9811 1.000 0.000 0.000
#> GSM372324 1 0.0000 0.9811 1.000 0.000 0.000
#> GSM372325 3 0.5058 0.6992 0.244 0.000 0.756
#> GSM372327 1 0.0000 0.9811 1.000 0.000 0.000
#> GSM372329 1 0.0000 0.9811 1.000 0.000 0.000
#> GSM372331 1 0.0237 0.9783 0.996 0.000 0.004
#> GSM372333 3 0.5058 0.6992 0.244 0.000 0.756
#> GSM372334 1 0.0000 0.9811 1.000 0.000 0.000
#> GSM372336 1 0.0000 0.9811 1.000 0.000 0.000
#> GSM372338 1 0.0000 0.9811 1.000 0.000 0.000
#> GSM372340 1 0.0000 0.9811 1.000 0.000 0.000
#> GSM372342 1 0.0000 0.9811 1.000 0.000 0.000
#> GSM372344 1 0.0000 0.9811 1.000 0.000 0.000
#> GSM372346 1 0.0000 0.9811 1.000 0.000 0.000
#> GSM372348 1 0.0000 0.9811 1.000 0.000 0.000
#> GSM372350 3 0.5621 0.5892 0.308 0.000 0.692
#> GSM372352 3 0.0000 0.9181 0.000 0.000 1.000
#> GSM372354 1 0.0000 0.9811 1.000 0.000 0.000
#> GSM372356 1 0.0000 0.9811 1.000 0.000 0.000
#> GSM372358 1 0.0000 0.9811 1.000 0.000 0.000
#> GSM372360 1 0.0000 0.9811 1.000 0.000 0.000
#> GSM372362 1 0.0000 0.9811 1.000 0.000 0.000
#> GSM372364 1 0.0000 0.9811 1.000 0.000 0.000
#> GSM372365 1 0.0237 0.9783 0.996 0.000 0.004
#> GSM372366 1 0.0000 0.9811 1.000 0.000 0.000
#> GSM372367 1 0.0000 0.9811 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM372286 2 0.0707 0.9627 0.000 0.980 0.000 0.020
#> GSM372287 2 0.0188 0.9660 0.000 0.996 0.000 0.004
#> GSM372288 2 0.0188 0.9660 0.000 0.996 0.000 0.004
#> GSM372289 2 0.0188 0.9660 0.000 0.996 0.000 0.004
#> GSM372290 2 0.0188 0.9660 0.000 0.996 0.000 0.004
#> GSM372291 4 0.4807 0.3548 0.024 0.000 0.248 0.728
#> GSM372292 2 0.2385 0.9186 0.000 0.920 0.052 0.028
#> GSM372293 3 0.0336 0.8494 0.000 0.000 0.992 0.008
#> GSM372294 3 0.7596 0.3954 0.000 0.212 0.456 0.332
#> GSM372295 3 0.4543 0.6568 0.000 0.000 0.676 0.324
#> GSM372296 2 0.0707 0.9607 0.000 0.980 0.000 0.020
#> GSM372297 2 0.0592 0.9622 0.000 0.984 0.000 0.016
#> GSM372298 2 0.1109 0.9603 0.000 0.968 0.004 0.028
#> GSM372299 3 0.0817 0.8423 0.000 0.000 0.976 0.024
#> GSM372300 3 0.0592 0.8485 0.000 0.000 0.984 0.016
#> GSM372301 3 0.0469 0.8481 0.000 0.000 0.988 0.012
#> GSM372302 2 0.1398 0.9573 0.000 0.956 0.004 0.040
#> GSM372303 3 0.2868 0.7988 0.000 0.000 0.864 0.136
#> GSM372304 2 0.0592 0.9622 0.000 0.984 0.000 0.016
#> GSM372305 2 0.0000 0.9664 0.000 1.000 0.000 0.000
#> GSM372306 2 0.5508 0.2214 0.000 0.572 0.408 0.020
#> GSM372307 2 0.0188 0.9660 0.000 0.996 0.000 0.004
#> GSM372309 3 0.3708 0.7445 0.000 0.148 0.832 0.020
#> GSM372311 2 0.0000 0.9664 0.000 1.000 0.000 0.000
#> GSM372313 2 0.1174 0.9577 0.000 0.968 0.012 0.020
#> GSM372315 2 0.0000 0.9664 0.000 1.000 0.000 0.000
#> GSM372317 2 0.1174 0.9577 0.000 0.968 0.012 0.020
#> GSM372319 2 0.0000 0.9664 0.000 1.000 0.000 0.000
#> GSM372321 2 0.0000 0.9664 0.000 1.000 0.000 0.000
#> GSM372323 3 0.0188 0.8491 0.000 0.000 0.996 0.004
#> GSM372326 3 0.0000 0.8489 0.000 0.000 1.000 0.000
#> GSM372328 3 0.4910 0.5934 0.000 0.276 0.704 0.020
#> GSM372330 2 0.0895 0.9613 0.000 0.976 0.004 0.020
#> GSM372332 4 0.4888 0.0338 0.000 0.000 0.412 0.588
#> GSM372335 3 0.0000 0.8489 0.000 0.000 1.000 0.000
#> GSM372337 3 0.0469 0.8488 0.000 0.000 0.988 0.012
#> GSM372339 3 0.2760 0.8032 0.000 0.000 0.872 0.128
#> GSM372341 3 0.2868 0.7988 0.000 0.000 0.864 0.136
#> GSM372343 3 0.0188 0.8491 0.000 0.000 0.996 0.004
#> GSM372345 3 0.0469 0.8488 0.000 0.000 0.988 0.012
#> GSM372347 3 0.0469 0.8488 0.000 0.000 0.988 0.012
#> GSM372349 3 0.4382 0.6696 0.000 0.000 0.704 0.296
#> GSM372351 3 0.4826 0.6126 0.000 0.264 0.716 0.020
#> GSM372353 3 0.0707 0.8418 0.000 0.000 0.980 0.020
#> GSM372355 2 0.0895 0.9613 0.000 0.976 0.004 0.020
#> GSM372357 3 0.5558 0.2368 0.000 0.432 0.548 0.020
#> GSM372359 3 0.3024 0.7545 0.000 0.148 0.852 0.000
#> GSM372361 2 0.0707 0.9627 0.000 0.980 0.000 0.020
#> GSM372363 2 0.0000 0.9664 0.000 1.000 0.000 0.000
#> GSM372308 4 0.5085 0.6697 0.260 0.000 0.032 0.708
#> GSM372310 4 0.5149 0.6463 0.336 0.000 0.016 0.648
#> GSM372312 4 0.4574 0.4046 0.024 0.000 0.220 0.756
#> GSM372314 4 0.5149 0.6463 0.336 0.000 0.016 0.648
#> GSM372316 1 0.0336 0.8863 0.992 0.000 0.000 0.008
#> GSM372318 1 0.0000 0.8886 1.000 0.000 0.000 0.000
#> GSM372320 1 0.0000 0.8886 1.000 0.000 0.000 0.000
#> GSM372322 1 0.0000 0.8886 1.000 0.000 0.000 0.000
#> GSM372324 4 0.4679 0.6287 0.352 0.000 0.000 0.648
#> GSM372325 4 0.5056 0.6658 0.224 0.000 0.044 0.732
#> GSM372327 1 0.0000 0.8886 1.000 0.000 0.000 0.000
#> GSM372329 1 0.0336 0.8863 0.992 0.000 0.000 0.008
#> GSM372331 4 0.4883 0.6646 0.288 0.000 0.016 0.696
#> GSM372333 4 0.5056 0.6658 0.224 0.000 0.044 0.732
#> GSM372334 1 0.0000 0.8886 1.000 0.000 0.000 0.000
#> GSM372336 4 0.4989 0.3291 0.472 0.000 0.000 0.528
#> GSM372338 1 0.0000 0.8886 1.000 0.000 0.000 0.000
#> GSM372340 1 0.0000 0.8886 1.000 0.000 0.000 0.000
#> GSM372342 1 0.2216 0.8184 0.908 0.000 0.000 0.092
#> GSM372344 1 0.0000 0.8886 1.000 0.000 0.000 0.000
#> GSM372346 1 0.0000 0.8886 1.000 0.000 0.000 0.000
#> GSM372348 1 0.4817 0.1713 0.612 0.000 0.000 0.388
#> GSM372350 4 0.4635 0.4120 0.028 0.000 0.216 0.756
#> GSM372352 3 0.2345 0.8114 0.000 0.000 0.900 0.100
#> GSM372354 1 0.0000 0.8886 1.000 0.000 0.000 0.000
#> GSM372356 4 0.4679 0.6287 0.352 0.000 0.000 0.648
#> GSM372358 1 0.4164 0.5543 0.736 0.000 0.000 0.264
#> GSM372360 1 0.3400 0.7067 0.820 0.000 0.000 0.180
#> GSM372362 1 0.1716 0.8449 0.936 0.000 0.000 0.064
#> GSM372364 1 0.4907 0.0425 0.580 0.000 0.000 0.420
#> GSM372365 4 0.5149 0.6463 0.336 0.000 0.016 0.648
#> GSM372366 1 0.0336 0.8863 0.992 0.000 0.000 0.008
#> GSM372367 4 0.4679 0.6287 0.352 0.000 0.000 0.648
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM372286 2 0.2068 0.878 0.004 0.904 0.000 0.092 0.000
#> GSM372287 2 0.1393 0.892 0.024 0.956 0.000 0.008 0.012
#> GSM372288 2 0.1393 0.892 0.024 0.956 0.000 0.008 0.012
#> GSM372289 2 0.1393 0.892 0.024 0.956 0.000 0.008 0.012
#> GSM372290 2 0.1200 0.893 0.016 0.964 0.000 0.008 0.012
#> GSM372291 4 0.4704 0.571 0.012 0.000 0.036 0.712 0.240
#> GSM372292 2 0.5808 0.721 0.072 0.680 0.060 0.188 0.000
#> GSM372293 3 0.1267 0.768 0.012 0.000 0.960 0.024 0.004
#> GSM372294 4 0.5758 0.443 0.008 0.108 0.192 0.676 0.016
#> GSM372295 4 0.4829 0.335 0.008 0.000 0.372 0.604 0.016
#> GSM372296 2 0.2589 0.873 0.044 0.900 0.000 0.048 0.008
#> GSM372297 2 0.2359 0.878 0.044 0.912 0.000 0.036 0.008
#> GSM372298 2 0.3926 0.856 0.052 0.808 0.000 0.132 0.008
#> GSM372299 3 0.2597 0.762 0.040 0.000 0.904 0.036 0.020
#> GSM372300 3 0.1799 0.761 0.012 0.000 0.940 0.028 0.020
#> GSM372301 3 0.1787 0.771 0.016 0.004 0.936 0.044 0.000
#> GSM372302 2 0.4668 0.827 0.052 0.744 0.004 0.192 0.008
#> GSM372303 3 0.3787 0.619 0.012 0.000 0.800 0.168 0.020
#> GSM372304 2 0.2359 0.878 0.044 0.912 0.000 0.036 0.008
#> GSM372305 2 0.0451 0.897 0.000 0.988 0.000 0.008 0.004
#> GSM372306 3 0.7021 0.330 0.052 0.236 0.540 0.172 0.000
#> GSM372307 2 0.1200 0.893 0.016 0.964 0.000 0.008 0.012
#> GSM372309 3 0.4964 0.625 0.052 0.040 0.744 0.164 0.000
#> GSM372311 2 0.0162 0.897 0.000 0.996 0.000 0.000 0.004
#> GSM372313 2 0.4609 0.787 0.056 0.756 0.016 0.172 0.000
#> GSM372315 2 0.0162 0.899 0.004 0.996 0.000 0.000 0.000
#> GSM372317 2 0.4609 0.787 0.056 0.756 0.016 0.172 0.000
#> GSM372319 2 0.0451 0.897 0.000 0.988 0.000 0.008 0.004
#> GSM372321 2 0.0451 0.897 0.000 0.988 0.000 0.008 0.004
#> GSM372323 3 0.0579 0.774 0.008 0.000 0.984 0.008 0.000
#> GSM372326 3 0.0798 0.774 0.008 0.000 0.976 0.016 0.000
#> GSM372328 3 0.5237 0.603 0.044 0.060 0.724 0.172 0.000
#> GSM372330 2 0.3723 0.828 0.044 0.804 0.000 0.152 0.000
#> GSM372332 3 0.6812 -0.347 0.008 0.000 0.408 0.380 0.204
#> GSM372335 3 0.2304 0.754 0.044 0.000 0.908 0.048 0.000
#> GSM372337 3 0.0898 0.769 0.000 0.000 0.972 0.008 0.020
#> GSM372339 3 0.3362 0.635 0.008 0.000 0.824 0.156 0.012
#> GSM372341 3 0.3516 0.629 0.008 0.000 0.820 0.152 0.020
#> GSM372343 3 0.0324 0.773 0.000 0.000 0.992 0.004 0.004
#> GSM372345 3 0.0898 0.769 0.000 0.000 0.972 0.008 0.020
#> GSM372347 3 0.1106 0.770 0.000 0.000 0.964 0.012 0.024
#> GSM372349 4 0.5160 0.177 0.008 0.000 0.476 0.492 0.024
#> GSM372351 3 0.5371 0.596 0.052 0.060 0.716 0.172 0.000
#> GSM372353 3 0.2151 0.763 0.040 0.000 0.924 0.016 0.020
#> GSM372355 2 0.3681 0.830 0.044 0.808 0.000 0.148 0.000
#> GSM372357 3 0.7287 0.220 0.052 0.304 0.472 0.172 0.000
#> GSM372359 3 0.3744 0.715 0.048 0.024 0.844 0.080 0.004
#> GSM372361 2 0.2741 0.862 0.004 0.860 0.000 0.132 0.004
#> GSM372363 2 0.0451 0.897 0.000 0.988 0.000 0.008 0.004
#> GSM372308 5 0.3018 0.760 0.012 0.000 0.012 0.116 0.860
#> GSM372310 5 0.3366 0.775 0.032 0.000 0.008 0.116 0.844
#> GSM372312 4 0.4731 0.568 0.012 0.000 0.036 0.708 0.244
#> GSM372314 5 0.3366 0.775 0.032 0.000 0.008 0.116 0.844
#> GSM372316 1 0.4026 0.843 0.736 0.000 0.000 0.020 0.244
#> GSM372318 1 0.2660 0.907 0.864 0.000 0.000 0.008 0.128
#> GSM372320 1 0.2536 0.908 0.868 0.000 0.000 0.004 0.128
#> GSM372322 1 0.2377 0.908 0.872 0.000 0.000 0.000 0.128
#> GSM372324 5 0.3192 0.777 0.040 0.000 0.000 0.112 0.848
#> GSM372325 5 0.3214 0.709 0.000 0.000 0.036 0.120 0.844
#> GSM372327 1 0.2377 0.908 0.872 0.000 0.000 0.000 0.128
#> GSM372329 1 0.4223 0.834 0.724 0.000 0.000 0.028 0.248
#> GSM372331 5 0.3010 0.764 0.016 0.000 0.008 0.116 0.860
#> GSM372333 5 0.3214 0.709 0.000 0.000 0.036 0.120 0.844
#> GSM372334 1 0.2536 0.908 0.868 0.000 0.000 0.004 0.128
#> GSM372336 5 0.2900 0.720 0.108 0.000 0.000 0.028 0.864
#> GSM372338 1 0.2536 0.908 0.868 0.000 0.000 0.004 0.128
#> GSM372340 1 0.2536 0.908 0.868 0.000 0.000 0.004 0.128
#> GSM372342 1 0.4787 0.658 0.608 0.000 0.000 0.028 0.364
#> GSM372344 1 0.2536 0.908 0.868 0.000 0.000 0.004 0.128
#> GSM372346 1 0.2377 0.908 0.872 0.000 0.000 0.000 0.128
#> GSM372348 5 0.4563 0.527 0.244 0.000 0.000 0.048 0.708
#> GSM372350 4 0.4731 0.568 0.012 0.000 0.036 0.708 0.244
#> GSM372352 3 0.1830 0.753 0.000 0.000 0.932 0.040 0.028
#> GSM372354 1 0.3488 0.886 0.808 0.000 0.000 0.024 0.168
#> GSM372356 5 0.1043 0.785 0.040 0.000 0.000 0.000 0.960
#> GSM372358 5 0.4703 0.233 0.340 0.000 0.000 0.028 0.632
#> GSM372360 5 0.4937 -0.144 0.428 0.000 0.000 0.028 0.544
#> GSM372362 1 0.4655 0.731 0.644 0.000 0.000 0.028 0.328
#> GSM372364 5 0.3327 0.676 0.144 0.000 0.000 0.028 0.828
#> GSM372365 5 0.1168 0.784 0.032 0.000 0.008 0.000 0.960
#> GSM372366 1 0.4374 0.812 0.700 0.000 0.000 0.028 0.272
#> GSM372367 5 0.1043 0.785 0.040 0.000 0.000 0.000 0.960
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM372286 4 0.2300 0.7952 0.000 0.144 0.000 0.856 0.000 0.000
#> GSM372287 4 0.1167 0.8169 0.000 0.020 0.000 0.960 0.012 0.008
#> GSM372288 4 0.1053 0.8175 0.000 0.020 0.000 0.964 0.012 0.004
#> GSM372289 4 0.1053 0.8175 0.000 0.020 0.000 0.964 0.012 0.004
#> GSM372290 4 0.0748 0.8194 0.000 0.016 0.000 0.976 0.004 0.004
#> GSM372291 6 0.3225 0.6983 0.000 0.016 0.016 0.000 0.148 0.820
#> GSM372292 4 0.5608 0.1929 0.000 0.436 0.056 0.476 0.024 0.008
#> GSM372293 3 0.2537 0.6361 0.000 0.088 0.880 0.000 0.008 0.024
#> GSM372294 6 0.6373 0.5539 0.000 0.232 0.096 0.076 0.016 0.580
#> GSM372295 6 0.5762 0.5704 0.000 0.208 0.200 0.000 0.016 0.576
#> GSM372296 4 0.4026 0.7483 0.000 0.092 0.000 0.796 0.044 0.068
#> GSM372297 4 0.2582 0.7984 0.000 0.060 0.000 0.888 0.032 0.020
#> GSM372298 4 0.3631 0.7620 0.000 0.168 0.000 0.788 0.032 0.012
#> GSM372299 3 0.3813 0.4769 0.000 0.224 0.744 0.000 0.008 0.024
#> GSM372300 3 0.2563 0.6353 0.000 0.084 0.880 0.000 0.008 0.028
#> GSM372301 3 0.3352 0.6185 0.000 0.144 0.816 0.000 0.016 0.024
#> GSM372302 4 0.5126 0.6792 0.000 0.216 0.000 0.672 0.044 0.068
#> GSM372303 3 0.4126 0.5453 0.000 0.112 0.764 0.000 0.008 0.116
#> GSM372304 4 0.2582 0.7984 0.000 0.060 0.000 0.888 0.032 0.020
#> GSM372305 4 0.1219 0.8242 0.000 0.048 0.000 0.948 0.000 0.004
#> GSM372306 2 0.5654 0.8721 0.000 0.444 0.404 0.152 0.000 0.000
#> GSM372307 4 0.0964 0.8194 0.000 0.016 0.000 0.968 0.004 0.012
#> GSM372309 3 0.4018 -0.3068 0.000 0.412 0.580 0.008 0.000 0.000
#> GSM372311 4 0.1196 0.8247 0.000 0.040 0.000 0.952 0.000 0.008
#> GSM372313 4 0.3817 0.4213 0.000 0.432 0.000 0.568 0.000 0.000
#> GSM372315 4 0.1267 0.8260 0.000 0.060 0.000 0.940 0.000 0.000
#> GSM372317 4 0.3817 0.4213 0.000 0.432 0.000 0.568 0.000 0.000
#> GSM372319 4 0.1340 0.8246 0.000 0.040 0.000 0.948 0.004 0.008
#> GSM372321 4 0.1340 0.8246 0.000 0.040 0.000 0.948 0.004 0.008
#> GSM372323 3 0.1610 0.6296 0.000 0.084 0.916 0.000 0.000 0.000
#> GSM372326 3 0.1957 0.6111 0.000 0.112 0.888 0.000 0.000 0.000
#> GSM372328 3 0.4151 -0.3430 0.000 0.412 0.576 0.008 0.004 0.000
#> GSM372330 4 0.3565 0.6481 0.000 0.304 0.000 0.692 0.000 0.004
#> GSM372332 3 0.6544 -0.1060 0.000 0.044 0.476 0.000 0.268 0.212
#> GSM372335 3 0.3360 0.3715 0.000 0.264 0.732 0.000 0.000 0.004
#> GSM372337 3 0.0146 0.6631 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM372339 3 0.2923 0.5939 0.000 0.052 0.848 0.000 0.000 0.100
#> GSM372341 3 0.2728 0.5946 0.000 0.040 0.860 0.000 0.000 0.100
#> GSM372343 3 0.0458 0.6624 0.000 0.016 0.984 0.000 0.000 0.000
#> GSM372345 3 0.0146 0.6631 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM372347 3 0.0881 0.6602 0.000 0.012 0.972 0.000 0.008 0.008
#> GSM372349 6 0.5125 0.4478 0.000 0.080 0.360 0.000 0.004 0.556
#> GSM372351 3 0.4178 -0.3878 0.000 0.428 0.560 0.008 0.004 0.000
#> GSM372353 3 0.3213 0.4772 0.000 0.204 0.784 0.000 0.008 0.004
#> GSM372355 4 0.3409 0.6513 0.000 0.300 0.000 0.700 0.000 0.000
#> GSM372357 2 0.5631 0.8702 0.000 0.444 0.408 0.148 0.000 0.000
#> GSM372359 3 0.3733 0.2674 0.000 0.288 0.700 0.000 0.008 0.004
#> GSM372361 4 0.2491 0.7799 0.000 0.164 0.000 0.836 0.000 0.000
#> GSM372363 4 0.1265 0.8242 0.000 0.044 0.000 0.948 0.000 0.008
#> GSM372308 5 0.2259 0.7779 0.040 0.000 0.020 0.000 0.908 0.032
#> GSM372310 5 0.2046 0.7918 0.060 0.000 0.000 0.000 0.908 0.032
#> GSM372312 6 0.2948 0.6749 0.000 0.000 0.008 0.000 0.188 0.804
#> GSM372314 5 0.2046 0.7918 0.060 0.000 0.000 0.000 0.908 0.032
#> GSM372316 1 0.3263 0.7708 0.800 0.176 0.000 0.000 0.020 0.004
#> GSM372318 1 0.1745 0.8154 0.924 0.056 0.000 0.000 0.000 0.020
#> GSM372320 1 0.0806 0.8155 0.972 0.020 0.000 0.000 0.000 0.008
#> GSM372322 1 0.0000 0.8207 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372324 5 0.2393 0.7927 0.064 0.004 0.000 0.000 0.892 0.040
#> GSM372325 5 0.2563 0.7548 0.028 0.000 0.036 0.000 0.892 0.044
#> GSM372327 1 0.0622 0.8203 0.980 0.008 0.000 0.000 0.000 0.012
#> GSM372329 1 0.4282 0.7357 0.736 0.200 0.000 0.000 0.036 0.028
#> GSM372331 5 0.2046 0.7918 0.060 0.000 0.000 0.000 0.908 0.032
#> GSM372333 5 0.2563 0.7548 0.028 0.000 0.036 0.000 0.892 0.044
#> GSM372334 1 0.0806 0.8155 0.972 0.020 0.000 0.000 0.000 0.008
#> GSM372336 5 0.5306 0.6787 0.112 0.208 0.000 0.000 0.652 0.028
#> GSM372338 1 0.0806 0.8155 0.972 0.020 0.000 0.000 0.000 0.008
#> GSM372340 1 0.0806 0.8155 0.972 0.020 0.000 0.000 0.000 0.008
#> GSM372342 1 0.5928 0.5271 0.556 0.268 0.000 0.000 0.148 0.028
#> GSM372344 1 0.0806 0.8155 0.972 0.020 0.000 0.000 0.000 0.008
#> GSM372346 1 0.0000 0.8207 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372348 5 0.5792 0.5726 0.188 0.200 0.000 0.000 0.588 0.024
#> GSM372350 6 0.2631 0.6965 0.000 0.000 0.008 0.000 0.152 0.840
#> GSM372352 3 0.1334 0.6603 0.000 0.032 0.948 0.000 0.000 0.020
#> GSM372354 1 0.2320 0.7983 0.864 0.132 0.000 0.000 0.004 0.000
#> GSM372356 5 0.3783 0.7795 0.060 0.136 0.000 0.000 0.792 0.012
#> GSM372358 5 0.6420 0.3769 0.240 0.288 0.000 0.000 0.448 0.024
#> GSM372360 1 0.6531 -0.0553 0.364 0.288 0.000 0.000 0.328 0.020
#> GSM372362 1 0.5400 0.5952 0.596 0.284 0.000 0.000 0.104 0.016
#> GSM372364 5 0.5528 0.6452 0.100 0.288 0.000 0.000 0.588 0.024
#> GSM372365 5 0.3783 0.7795 0.060 0.136 0.000 0.000 0.792 0.012
#> GSM372366 1 0.4575 0.6835 0.668 0.276 0.000 0.000 0.040 0.016
#> GSM372367 5 0.3783 0.7795 0.060 0.136 0.000 0.000 0.792 0.012
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) specimen(p) individual(p) k
#> ATC:kmeans 82 0.000214 5.97e-16 0.998 2
#> ATC:kmeans 81 0.000250 2.61e-13 0.911 3
#> ATC:kmeans 72 0.000416 1.57e-13 0.842 4
#> ATC:kmeans 74 0.000849 1.26e-12 0.683 5
#> ATC:kmeans 68 0.000737 3.37e-10 0.341 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 51941 rows and 82 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 0.988 0.995 0.4934 0.509 0.509
#> 3 3 0.944 0.882 0.954 0.3007 0.851 0.707
#> 4 4 0.946 0.919 0.948 0.0647 0.933 0.817
#> 5 5 0.867 0.871 0.913 0.0506 0.980 0.935
#> 6 6 0.849 0.751 0.869 0.0455 0.991 0.969
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
#> GSM372286 2 0.000 0.992 0.00 1.00
#> GSM372287 2 0.000 0.992 0.00 1.00
#> GSM372288 2 0.000 0.992 0.00 1.00
#> GSM372289 2 0.000 0.992 0.00 1.00
#> GSM372290 2 0.000 0.992 0.00 1.00
#> GSM372291 1 0.000 1.000 1.00 0.00
#> GSM372292 2 0.000 0.992 0.00 1.00
#> GSM372293 2 0.000 0.992 0.00 1.00
#> GSM372294 2 0.000 0.992 0.00 1.00
#> GSM372295 2 0.000 0.992 0.00 1.00
#> GSM372296 2 0.000 0.992 0.00 1.00
#> GSM372297 2 0.000 0.992 0.00 1.00
#> GSM372298 2 0.000 0.992 0.00 1.00
#> GSM372299 2 0.000 0.992 0.00 1.00
#> GSM372300 2 0.000 0.992 0.00 1.00
#> GSM372301 2 0.000 0.992 0.00 1.00
#> GSM372302 2 0.000 0.992 0.00 1.00
#> GSM372303 2 0.000 0.992 0.00 1.00
#> GSM372304 2 0.000 0.992 0.00 1.00
#> GSM372305 2 0.000 0.992 0.00 1.00
#> GSM372306 2 0.000 0.992 0.00 1.00
#> GSM372307 2 0.000 0.992 0.00 1.00
#> GSM372309 2 0.000 0.992 0.00 1.00
#> GSM372311 2 0.000 0.992 0.00 1.00
#> GSM372313 2 0.000 0.992 0.00 1.00
#> GSM372315 2 0.000 0.992 0.00 1.00
#> GSM372317 2 0.000 0.992 0.00 1.00
#> GSM372319 2 0.000 0.992 0.00 1.00
#> GSM372321 2 0.000 0.992 0.00 1.00
#> GSM372323 2 0.000 0.992 0.00 1.00
#> GSM372326 2 0.000 0.992 0.00 1.00
#> GSM372328 2 0.000 0.992 0.00 1.00
#> GSM372330 2 0.000 0.992 0.00 1.00
#> GSM372332 1 0.000 1.000 1.00 0.00
#> GSM372335 2 0.000 0.992 0.00 1.00
#> GSM372337 2 0.000 0.992 0.00 1.00
#> GSM372339 2 0.000 0.992 0.00 1.00
#> GSM372341 2 0.000 0.992 0.00 1.00
#> GSM372343 2 0.000 0.992 0.00 1.00
#> GSM372345 2 0.000 0.992 0.00 1.00
#> GSM372347 2 0.000 0.992 0.00 1.00
#> GSM372349 2 0.000 0.992 0.00 1.00
#> GSM372351 2 0.000 0.992 0.00 1.00
#> GSM372353 2 0.000 0.992 0.00 1.00
#> GSM372355 2 0.000 0.992 0.00 1.00
#> GSM372357 2 0.000 0.992 0.00 1.00
#> GSM372359 2 0.000 0.992 0.00 1.00
#> GSM372361 2 0.000 0.992 0.00 1.00
#> GSM372363 2 0.000 0.992 0.00 1.00
#> GSM372308 1 0.000 1.000 1.00 0.00
#> GSM372310 1 0.000 1.000 1.00 0.00
#> GSM372312 1 0.000 1.000 1.00 0.00
#> GSM372314 1 0.000 1.000 1.00 0.00
#> GSM372316 1 0.000 1.000 1.00 0.00
#> GSM372318 1 0.000 1.000 1.00 0.00
#> GSM372320 1 0.000 1.000 1.00 0.00
#> GSM372322 1 0.000 1.000 1.00 0.00
#> GSM372324 1 0.000 1.000 1.00 0.00
#> GSM372325 1 0.000 1.000 1.00 0.00
#> GSM372327 1 0.000 1.000 1.00 0.00
#> GSM372329 1 0.000 1.000 1.00 0.00
#> GSM372331 1 0.000 1.000 1.00 0.00
#> GSM372333 1 0.000 1.000 1.00 0.00
#> GSM372334 1 0.000 1.000 1.00 0.00
#> GSM372336 1 0.000 1.000 1.00 0.00
#> GSM372338 1 0.000 1.000 1.00 0.00
#> GSM372340 1 0.000 1.000 1.00 0.00
#> GSM372342 1 0.000 1.000 1.00 0.00
#> GSM372344 1 0.000 1.000 1.00 0.00
#> GSM372346 1 0.000 1.000 1.00 0.00
#> GSM372348 1 0.000 1.000 1.00 0.00
#> GSM372350 1 0.000 1.000 1.00 0.00
#> GSM372352 2 0.958 0.387 0.38 0.62
#> GSM372354 1 0.000 1.000 1.00 0.00
#> GSM372356 1 0.000 1.000 1.00 0.00
#> GSM372358 1 0.000 1.000 1.00 0.00
#> GSM372360 1 0.000 1.000 1.00 0.00
#> GSM372362 1 0.000 1.000 1.00 0.00
#> GSM372364 1 0.000 1.000 1.00 0.00
#> GSM372365 1 0.000 1.000 1.00 0.00
#> GSM372366 1 0.000 1.000 1.00 0.00
#> GSM372367 1 0.000 1.000 1.00 0.00
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM372286 2 0.000 0.9827 0.000 1.000 0.000
#> GSM372287 2 0.000 0.9827 0.000 1.000 0.000
#> GSM372288 2 0.000 0.9827 0.000 1.000 0.000
#> GSM372289 2 0.000 0.9827 0.000 1.000 0.000
#> GSM372290 2 0.000 0.9827 0.000 1.000 0.000
#> GSM372291 1 0.613 0.4162 0.600 0.000 0.400
#> GSM372292 2 0.000 0.9827 0.000 1.000 0.000
#> GSM372293 3 0.000 0.8656 0.000 0.000 1.000
#> GSM372294 3 0.629 0.2199 0.000 0.468 0.532
#> GSM372295 3 0.615 0.3724 0.000 0.408 0.592
#> GSM372296 2 0.000 0.9827 0.000 1.000 0.000
#> GSM372297 2 0.000 0.9827 0.000 1.000 0.000
#> GSM372298 2 0.000 0.9827 0.000 1.000 0.000
#> GSM372299 2 0.000 0.9827 0.000 1.000 0.000
#> GSM372300 3 0.000 0.8656 0.000 0.000 1.000
#> GSM372301 2 0.630 -0.0846 0.000 0.520 0.480
#> GSM372302 2 0.000 0.9827 0.000 1.000 0.000
#> GSM372303 3 0.000 0.8656 0.000 0.000 1.000
#> GSM372304 2 0.000 0.9827 0.000 1.000 0.000
#> GSM372305 2 0.000 0.9827 0.000 1.000 0.000
#> GSM372306 2 0.000 0.9827 0.000 1.000 0.000
#> GSM372307 2 0.000 0.9827 0.000 1.000 0.000
#> GSM372309 2 0.000 0.9827 0.000 1.000 0.000
#> GSM372311 2 0.000 0.9827 0.000 1.000 0.000
#> GSM372313 2 0.000 0.9827 0.000 1.000 0.000
#> GSM372315 2 0.000 0.9827 0.000 1.000 0.000
#> GSM372317 2 0.000 0.9827 0.000 1.000 0.000
#> GSM372319 2 0.000 0.9827 0.000 1.000 0.000
#> GSM372321 2 0.000 0.9827 0.000 1.000 0.000
#> GSM372323 3 0.613 0.3577 0.000 0.400 0.600
#> GSM372326 3 0.613 0.3577 0.000 0.400 0.600
#> GSM372328 2 0.000 0.9827 0.000 1.000 0.000
#> GSM372330 2 0.000 0.9827 0.000 1.000 0.000
#> GSM372332 1 0.614 0.4073 0.596 0.000 0.404
#> GSM372335 2 0.000 0.9827 0.000 1.000 0.000
#> GSM372337 3 0.000 0.8656 0.000 0.000 1.000
#> GSM372339 3 0.000 0.8656 0.000 0.000 1.000
#> GSM372341 3 0.000 0.8656 0.000 0.000 1.000
#> GSM372343 3 0.000 0.8656 0.000 0.000 1.000
#> GSM372345 3 0.000 0.8656 0.000 0.000 1.000
#> GSM372347 3 0.000 0.8656 0.000 0.000 1.000
#> GSM372349 3 0.000 0.8656 0.000 0.000 1.000
#> GSM372351 2 0.000 0.9827 0.000 1.000 0.000
#> GSM372353 2 0.000 0.9827 0.000 1.000 0.000
#> GSM372355 2 0.000 0.9827 0.000 1.000 0.000
#> GSM372357 2 0.000 0.9827 0.000 1.000 0.000
#> GSM372359 2 0.000 0.9827 0.000 1.000 0.000
#> GSM372361 2 0.000 0.9827 0.000 1.000 0.000
#> GSM372363 2 0.000 0.9827 0.000 1.000 0.000
#> GSM372308 1 0.000 0.9490 1.000 0.000 0.000
#> GSM372310 1 0.000 0.9490 1.000 0.000 0.000
#> GSM372312 1 0.613 0.4162 0.600 0.000 0.400
#> GSM372314 1 0.000 0.9490 1.000 0.000 0.000
#> GSM372316 1 0.000 0.9490 1.000 0.000 0.000
#> GSM372318 1 0.000 0.9490 1.000 0.000 0.000
#> GSM372320 1 0.000 0.9490 1.000 0.000 0.000
#> GSM372322 1 0.000 0.9490 1.000 0.000 0.000
#> GSM372324 1 0.000 0.9490 1.000 0.000 0.000
#> GSM372325 1 0.000 0.9490 1.000 0.000 0.000
#> GSM372327 1 0.000 0.9490 1.000 0.000 0.000
#> GSM372329 1 0.000 0.9490 1.000 0.000 0.000
#> GSM372331 1 0.000 0.9490 1.000 0.000 0.000
#> GSM372333 1 0.000 0.9490 1.000 0.000 0.000
#> GSM372334 1 0.000 0.9490 1.000 0.000 0.000
#> GSM372336 1 0.000 0.9490 1.000 0.000 0.000
#> GSM372338 1 0.000 0.9490 1.000 0.000 0.000
#> GSM372340 1 0.000 0.9490 1.000 0.000 0.000
#> GSM372342 1 0.000 0.9490 1.000 0.000 0.000
#> GSM372344 1 0.000 0.9490 1.000 0.000 0.000
#> GSM372346 1 0.000 0.9490 1.000 0.000 0.000
#> GSM372348 1 0.000 0.9490 1.000 0.000 0.000
#> GSM372350 1 0.613 0.4162 0.600 0.000 0.400
#> GSM372352 3 0.000 0.8656 0.000 0.000 1.000
#> GSM372354 1 0.000 0.9490 1.000 0.000 0.000
#> GSM372356 1 0.000 0.9490 1.000 0.000 0.000
#> GSM372358 1 0.000 0.9490 1.000 0.000 0.000
#> GSM372360 1 0.000 0.9490 1.000 0.000 0.000
#> GSM372362 1 0.000 0.9490 1.000 0.000 0.000
#> GSM372364 1 0.000 0.9490 1.000 0.000 0.000
#> GSM372365 1 0.000 0.9490 1.000 0.000 0.000
#> GSM372366 1 0.000 0.9490 1.000 0.000 0.000
#> GSM372367 1 0.000 0.9490 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM372286 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM372287 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM372288 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM372289 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM372290 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM372291 4 0.3873 0.674 0.228 0.000 0.000 0.772
#> GSM372292 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM372293 3 0.4072 0.812 0.000 0.000 0.748 0.252
#> GSM372294 4 0.5430 0.496 0.000 0.300 0.036 0.664
#> GSM372295 4 0.5466 0.500 0.000 0.292 0.040 0.668
#> GSM372296 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM372297 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM372298 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM372299 2 0.4122 0.687 0.000 0.760 0.004 0.236
#> GSM372300 3 0.4072 0.812 0.000 0.000 0.748 0.252
#> GSM372301 3 0.4599 0.801 0.000 0.016 0.736 0.248
#> GSM372302 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM372303 3 0.4134 0.808 0.000 0.000 0.740 0.260
#> GSM372304 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM372305 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM372306 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM372307 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM372309 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM372311 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM372313 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM372315 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM372317 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM372319 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM372321 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM372323 3 0.0000 0.907 0.000 0.000 1.000 0.000
#> GSM372326 3 0.0469 0.898 0.000 0.012 0.988 0.000
#> GSM372328 2 0.0817 0.966 0.000 0.976 0.024 0.000
#> GSM372330 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM372332 4 0.5125 0.453 0.388 0.000 0.008 0.604
#> GSM372335 2 0.0188 0.986 0.000 0.996 0.004 0.000
#> GSM372337 3 0.0000 0.907 0.000 0.000 1.000 0.000
#> GSM372339 3 0.0188 0.905 0.000 0.000 0.996 0.004
#> GSM372341 3 0.0188 0.905 0.000 0.000 0.996 0.004
#> GSM372343 3 0.0000 0.907 0.000 0.000 1.000 0.000
#> GSM372345 3 0.0000 0.907 0.000 0.000 1.000 0.000
#> GSM372347 3 0.0000 0.907 0.000 0.000 1.000 0.000
#> GSM372349 4 0.4331 0.457 0.000 0.000 0.288 0.712
#> GSM372351 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM372353 2 0.0707 0.970 0.000 0.980 0.020 0.000
#> GSM372355 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM372357 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM372359 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM372361 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM372363 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM372308 1 0.0188 0.975 0.996 0.000 0.000 0.004
#> GSM372310 1 0.0188 0.975 0.996 0.000 0.000 0.004
#> GSM372312 4 0.4008 0.674 0.244 0.000 0.000 0.756
#> GSM372314 1 0.0188 0.975 0.996 0.000 0.000 0.004
#> GSM372316 1 0.0188 0.976 0.996 0.000 0.000 0.004
#> GSM372318 1 0.1302 0.970 0.956 0.000 0.000 0.044
#> GSM372320 1 0.1302 0.970 0.956 0.000 0.000 0.044
#> GSM372322 1 0.1302 0.970 0.956 0.000 0.000 0.044
#> GSM372324 1 0.1302 0.970 0.956 0.000 0.000 0.044
#> GSM372325 1 0.1389 0.969 0.952 0.000 0.000 0.048
#> GSM372327 1 0.1302 0.970 0.956 0.000 0.000 0.044
#> GSM372329 1 0.0188 0.976 0.996 0.000 0.000 0.004
#> GSM372331 1 0.0188 0.975 0.996 0.000 0.000 0.004
#> GSM372333 1 0.1389 0.969 0.952 0.000 0.000 0.048
#> GSM372334 1 0.1302 0.970 0.956 0.000 0.000 0.044
#> GSM372336 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM372338 1 0.1302 0.970 0.956 0.000 0.000 0.044
#> GSM372340 1 0.1302 0.970 0.956 0.000 0.000 0.044
#> GSM372342 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM372344 1 0.1302 0.970 0.956 0.000 0.000 0.044
#> GSM372346 1 0.1302 0.970 0.956 0.000 0.000 0.044
#> GSM372348 1 0.1302 0.970 0.956 0.000 0.000 0.044
#> GSM372350 4 0.4040 0.673 0.248 0.000 0.000 0.752
#> GSM372352 4 0.4072 0.471 0.000 0.000 0.252 0.748
#> GSM372354 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM372356 1 0.0188 0.975 0.996 0.000 0.000 0.004
#> GSM372358 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM372360 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM372362 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM372364 1 0.0188 0.975 0.996 0.000 0.000 0.004
#> GSM372365 1 0.0188 0.975 0.996 0.000 0.000 0.004
#> GSM372366 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM372367 1 0.0188 0.975 0.996 0.000 0.000 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM372286 2 0.0000 0.962 0.000 1.000 0.000 0.000 0.000
#> GSM372287 2 0.0000 0.962 0.000 1.000 0.000 0.000 0.000
#> GSM372288 2 0.0000 0.962 0.000 1.000 0.000 0.000 0.000
#> GSM372289 2 0.0000 0.962 0.000 1.000 0.000 0.000 0.000
#> GSM372290 2 0.0000 0.962 0.000 1.000 0.000 0.000 0.000
#> GSM372291 5 0.1704 0.699 0.068 0.000 0.000 0.004 0.928
#> GSM372292 2 0.0000 0.962 0.000 1.000 0.000 0.000 0.000
#> GSM372293 4 0.4555 0.800 0.000 0.000 0.344 0.636 0.020
#> GSM372294 5 0.3796 0.487 0.000 0.300 0.000 0.000 0.700
#> GSM372295 5 0.3928 0.490 0.000 0.296 0.000 0.004 0.700
#> GSM372296 2 0.0000 0.962 0.000 1.000 0.000 0.000 0.000
#> GSM372297 2 0.0000 0.962 0.000 1.000 0.000 0.000 0.000
#> GSM372298 2 0.0000 0.962 0.000 1.000 0.000 0.000 0.000
#> GSM372299 4 0.3489 0.411 0.000 0.208 0.004 0.784 0.004
#> GSM372300 4 0.4555 0.800 0.000 0.000 0.344 0.636 0.020
#> GSM372301 4 0.4691 0.799 0.000 0.004 0.340 0.636 0.020
#> GSM372302 2 0.0000 0.962 0.000 1.000 0.000 0.000 0.000
#> GSM372303 4 0.4624 0.800 0.000 0.000 0.340 0.636 0.024
#> GSM372304 2 0.0000 0.962 0.000 1.000 0.000 0.000 0.000
#> GSM372305 2 0.0000 0.962 0.000 1.000 0.000 0.000 0.000
#> GSM372306 2 0.0324 0.959 0.000 0.992 0.000 0.004 0.004
#> GSM372307 2 0.0000 0.962 0.000 1.000 0.000 0.000 0.000
#> GSM372309 2 0.0451 0.957 0.000 0.988 0.000 0.008 0.004
#> GSM372311 2 0.0000 0.962 0.000 1.000 0.000 0.000 0.000
#> GSM372313 2 0.0451 0.957 0.000 0.988 0.000 0.008 0.004
#> GSM372315 2 0.0000 0.962 0.000 1.000 0.000 0.000 0.000
#> GSM372317 2 0.0162 0.961 0.000 0.996 0.000 0.000 0.004
#> GSM372319 2 0.0000 0.962 0.000 1.000 0.000 0.000 0.000
#> GSM372321 2 0.0000 0.962 0.000 1.000 0.000 0.000 0.000
#> GSM372323 3 0.0162 0.972 0.000 0.000 0.996 0.004 0.000
#> GSM372326 3 0.0486 0.964 0.000 0.004 0.988 0.004 0.004
#> GSM372328 2 0.3395 0.683 0.000 0.764 0.236 0.000 0.000
#> GSM372330 2 0.0324 0.959 0.000 0.992 0.000 0.004 0.004
#> GSM372332 5 0.4420 0.285 0.448 0.000 0.000 0.004 0.548
#> GSM372335 2 0.1717 0.918 0.000 0.936 0.004 0.052 0.008
#> GSM372337 3 0.0703 0.965 0.000 0.000 0.976 0.000 0.024
#> GSM372339 3 0.0162 0.972 0.000 0.000 0.996 0.004 0.000
#> GSM372341 3 0.0290 0.971 0.000 0.000 0.992 0.000 0.008
#> GSM372343 3 0.0162 0.972 0.000 0.000 0.996 0.004 0.000
#> GSM372345 3 0.0703 0.965 0.000 0.000 0.976 0.000 0.024
#> GSM372347 3 0.1992 0.914 0.000 0.000 0.924 0.032 0.044
#> GSM372349 5 0.1732 0.649 0.000 0.000 0.080 0.000 0.920
#> GSM372351 2 0.0960 0.947 0.000 0.972 0.016 0.008 0.004
#> GSM372353 2 0.5993 0.558 0.000 0.652 0.148 0.172 0.028
#> GSM372355 2 0.0324 0.959 0.000 0.992 0.000 0.004 0.004
#> GSM372357 2 0.3399 0.797 0.000 0.812 0.004 0.172 0.012
#> GSM372359 2 0.3769 0.779 0.000 0.796 0.004 0.172 0.028
#> GSM372361 2 0.0000 0.962 0.000 1.000 0.000 0.000 0.000
#> GSM372363 2 0.0000 0.962 0.000 1.000 0.000 0.000 0.000
#> GSM372308 1 0.3224 0.883 0.824 0.000 0.000 0.160 0.016
#> GSM372310 1 0.3456 0.873 0.800 0.000 0.000 0.184 0.016
#> GSM372312 5 0.1965 0.700 0.096 0.000 0.000 0.000 0.904
#> GSM372314 1 0.3183 0.884 0.828 0.000 0.000 0.156 0.016
#> GSM372316 1 0.1732 0.901 0.920 0.000 0.000 0.080 0.000
#> GSM372318 1 0.0609 0.900 0.980 0.000 0.000 0.000 0.020
#> GSM372320 1 0.0609 0.900 0.980 0.000 0.000 0.000 0.020
#> GSM372322 1 0.0609 0.900 0.980 0.000 0.000 0.000 0.020
#> GSM372324 1 0.0771 0.899 0.976 0.000 0.000 0.004 0.020
#> GSM372325 1 0.0771 0.899 0.976 0.000 0.000 0.004 0.020
#> GSM372327 1 0.0609 0.900 0.980 0.000 0.000 0.000 0.020
#> GSM372329 1 0.0000 0.902 1.000 0.000 0.000 0.000 0.000
#> GSM372331 1 0.3098 0.886 0.836 0.000 0.000 0.148 0.016
#> GSM372333 1 0.1012 0.898 0.968 0.000 0.000 0.012 0.020
#> GSM372334 1 0.0609 0.900 0.980 0.000 0.000 0.000 0.020
#> GSM372336 1 0.2179 0.899 0.896 0.000 0.000 0.100 0.004
#> GSM372338 1 0.0609 0.900 0.980 0.000 0.000 0.000 0.020
#> GSM372340 1 0.0609 0.900 0.980 0.000 0.000 0.000 0.020
#> GSM372342 1 0.2648 0.890 0.848 0.000 0.000 0.152 0.000
#> GSM372344 1 0.0609 0.900 0.980 0.000 0.000 0.000 0.020
#> GSM372346 1 0.0609 0.900 0.980 0.000 0.000 0.000 0.020
#> GSM372348 1 0.0609 0.900 0.980 0.000 0.000 0.000 0.020
#> GSM372350 5 0.1965 0.700 0.096 0.000 0.000 0.000 0.904
#> GSM372352 5 0.1484 0.655 0.000 0.000 0.048 0.008 0.944
#> GSM372354 1 0.0510 0.903 0.984 0.000 0.000 0.016 0.000
#> GSM372356 1 0.3419 0.874 0.804 0.000 0.000 0.180 0.016
#> GSM372358 1 0.3419 0.874 0.804 0.000 0.000 0.180 0.016
#> GSM372360 1 0.3419 0.874 0.804 0.000 0.000 0.180 0.016
#> GSM372362 1 0.3381 0.876 0.808 0.000 0.000 0.176 0.016
#> GSM372364 1 0.3419 0.874 0.804 0.000 0.000 0.180 0.016
#> GSM372365 1 0.3419 0.874 0.804 0.000 0.000 0.180 0.016
#> GSM372366 1 0.2020 0.899 0.900 0.000 0.000 0.100 0.000
#> GSM372367 1 0.3419 0.874 0.804 0.000 0.000 0.180 0.016
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM372286 2 0.0146 0.8898 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM372287 2 0.0363 0.8867 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM372288 2 0.0363 0.8867 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM372289 2 0.0146 0.8898 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM372290 2 0.0146 0.8898 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM372291 4 0.1285 0.7088 0.052 0.000 0.000 0.944 0.004 0.000
#> GSM372292 2 0.0458 0.8898 0.000 0.984 0.000 0.000 0.016 0.000
#> GSM372293 6 0.2362 0.8694 0.000 0.000 0.136 0.004 0.000 0.860
#> GSM372294 4 0.4724 0.3827 0.000 0.288 0.000 0.648 0.052 0.012
#> GSM372295 4 0.4769 0.4150 0.000 0.272 0.000 0.652 0.068 0.008
#> GSM372296 2 0.0458 0.8843 0.000 0.984 0.000 0.000 0.016 0.000
#> GSM372297 2 0.0458 0.8843 0.000 0.984 0.000 0.000 0.016 0.000
#> GSM372298 2 0.0363 0.8898 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM372299 6 0.4763 0.3914 0.000 0.044 0.000 0.016 0.304 0.636
#> GSM372300 6 0.2489 0.8735 0.000 0.000 0.128 0.012 0.000 0.860
#> GSM372301 6 0.2531 0.8700 0.000 0.008 0.128 0.004 0.000 0.860
#> GSM372302 2 0.0458 0.8843 0.000 0.984 0.000 0.000 0.016 0.000
#> GSM372303 6 0.2538 0.8722 0.000 0.000 0.124 0.016 0.000 0.860
#> GSM372304 2 0.0458 0.8843 0.000 0.984 0.000 0.000 0.016 0.000
#> GSM372305 2 0.0260 0.8889 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM372306 2 0.1265 0.8578 0.000 0.948 0.000 0.000 0.044 0.008
#> GSM372307 2 0.0146 0.8898 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM372309 2 0.1542 0.8443 0.000 0.936 0.000 0.004 0.052 0.008
#> GSM372311 2 0.0363 0.8875 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM372313 2 0.1542 0.8443 0.000 0.936 0.000 0.004 0.052 0.008
#> GSM372315 2 0.0363 0.8875 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM372317 2 0.0547 0.8831 0.000 0.980 0.000 0.000 0.020 0.000
#> GSM372319 2 0.0000 0.8901 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM372321 2 0.0000 0.8901 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM372323 3 0.0508 0.9625 0.000 0.000 0.984 0.000 0.012 0.004
#> GSM372326 3 0.0909 0.9581 0.000 0.000 0.968 0.000 0.020 0.012
#> GSM372328 2 0.4088 0.0971 0.000 0.668 0.308 0.000 0.020 0.004
#> GSM372330 2 0.0632 0.8804 0.000 0.976 0.000 0.000 0.024 0.000
#> GSM372332 4 0.5778 0.2786 0.420 0.000 0.008 0.476 0.072 0.024
#> GSM372335 2 0.2946 0.6905 0.000 0.848 0.004 0.004 0.120 0.024
#> GSM372337 3 0.0692 0.9533 0.000 0.000 0.976 0.020 0.004 0.000
#> GSM372339 3 0.0909 0.9596 0.000 0.000 0.968 0.000 0.012 0.020
#> GSM372341 3 0.0692 0.9597 0.000 0.000 0.976 0.004 0.000 0.020
#> GSM372343 3 0.0725 0.9620 0.000 0.000 0.976 0.000 0.012 0.012
#> GSM372345 3 0.0692 0.9533 0.000 0.000 0.976 0.020 0.004 0.000
#> GSM372347 3 0.2614 0.8859 0.000 0.000 0.888 0.036 0.052 0.024
#> GSM372349 4 0.2586 0.6655 0.000 0.000 0.080 0.880 0.032 0.008
#> GSM372351 2 0.1644 0.8378 0.000 0.932 0.012 0.004 0.052 0.000
#> GSM372353 5 0.7224 0.0000 0.000 0.372 0.096 0.024 0.396 0.112
#> GSM372355 2 0.1152 0.8617 0.000 0.952 0.000 0.000 0.044 0.004
#> GSM372357 2 0.5639 -0.6044 0.000 0.528 0.004 0.008 0.348 0.112
#> GSM372359 2 0.5959 -0.7713 0.000 0.468 0.004 0.020 0.396 0.112
#> GSM372361 2 0.0000 0.8901 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM372363 2 0.0260 0.8889 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM372308 1 0.3737 0.7387 0.608 0.000 0.000 0.000 0.392 0.000
#> GSM372310 1 0.3828 0.7101 0.560 0.000 0.000 0.000 0.440 0.000
#> GSM372312 4 0.1500 0.7079 0.052 0.000 0.000 0.936 0.012 0.000
#> GSM372314 1 0.3607 0.7577 0.652 0.000 0.000 0.000 0.348 0.000
#> GSM372316 1 0.2135 0.8106 0.872 0.000 0.000 0.000 0.128 0.000
#> GSM372318 1 0.0000 0.8126 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372320 1 0.0000 0.8126 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372322 1 0.0000 0.8126 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372324 1 0.0458 0.8072 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM372325 1 0.1701 0.7852 0.920 0.000 0.000 0.000 0.072 0.008
#> GSM372327 1 0.0000 0.8126 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372329 1 0.0146 0.8132 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM372331 1 0.3547 0.7631 0.668 0.000 0.000 0.000 0.332 0.000
#> GSM372333 1 0.2890 0.7295 0.848 0.000 0.000 0.012 0.124 0.016
#> GSM372334 1 0.0000 0.8126 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372336 1 0.2454 0.8077 0.840 0.000 0.000 0.000 0.160 0.000
#> GSM372338 1 0.0000 0.8126 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372340 1 0.0000 0.8126 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372342 1 0.3151 0.7861 0.748 0.000 0.000 0.000 0.252 0.000
#> GSM372344 1 0.0000 0.8126 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372346 1 0.0000 0.8126 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372348 1 0.0000 0.8126 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372350 4 0.1462 0.7084 0.056 0.000 0.000 0.936 0.008 0.000
#> GSM372352 4 0.2313 0.6735 0.000 0.000 0.016 0.904 0.044 0.036
#> GSM372354 1 0.0790 0.8149 0.968 0.000 0.000 0.000 0.032 0.000
#> GSM372356 1 0.3817 0.7126 0.568 0.000 0.000 0.000 0.432 0.000
#> GSM372358 1 0.3765 0.7274 0.596 0.000 0.000 0.000 0.404 0.000
#> GSM372360 1 0.3756 0.7297 0.600 0.000 0.000 0.000 0.400 0.000
#> GSM372362 1 0.3684 0.7429 0.628 0.000 0.000 0.000 0.372 0.000
#> GSM372364 1 0.3817 0.7126 0.568 0.000 0.000 0.000 0.432 0.000
#> GSM372365 1 0.3817 0.7126 0.568 0.000 0.000 0.000 0.432 0.000
#> GSM372366 1 0.2562 0.8062 0.828 0.000 0.000 0.000 0.172 0.000
#> GSM372367 1 0.3817 0.7126 0.568 0.000 0.000 0.000 0.432 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) specimen(p) individual(p) k
#> ATC:skmeans 81 1.71e-04 1.32e-16 0.998 2
#> ATC:skmeans 73 2.36e-04 2.01e-14 0.946 3
#> ATC:skmeans 78 5.67e-04 1.54e-14 0.699 4
#> ATC:skmeans 78 3.10e-06 1.21e-16 0.417 5
#> ATC:skmeans 74 1.18e-06 4.55e-16 0.480 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 51941 rows and 82 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 5.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.970 0.988 0.4979 0.505 0.505
#> 3 3 0.833 0.916 0.960 0.3476 0.720 0.496
#> 4 4 1.000 0.962 0.983 0.1192 0.850 0.585
#> 5 5 0.901 0.853 0.910 0.0407 0.945 0.788
#> 6 6 0.899 0.811 0.911 0.0365 0.951 0.786
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
#> attr(,"optional")
#> [1] 2 4
There is also optional best \(k\) = 2 4 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM372286 2 0.000 0.980 0.000 1.000
#> GSM372287 2 0.000 0.980 0.000 1.000
#> GSM372288 2 0.000 0.980 0.000 1.000
#> GSM372289 2 0.000 0.980 0.000 1.000
#> GSM372290 2 0.000 0.980 0.000 1.000
#> GSM372291 1 0.000 0.996 1.000 0.000
#> GSM372292 2 0.000 0.980 0.000 1.000
#> GSM372293 2 0.000 0.980 0.000 1.000
#> GSM372294 2 0.000 0.980 0.000 1.000
#> GSM372295 2 0.000 0.980 0.000 1.000
#> GSM372296 2 0.000 0.980 0.000 1.000
#> GSM372297 2 0.000 0.980 0.000 1.000
#> GSM372298 2 0.000 0.980 0.000 1.000
#> GSM372299 2 0.000 0.980 0.000 1.000
#> GSM372300 2 0.955 0.410 0.376 0.624
#> GSM372301 2 0.000 0.980 0.000 1.000
#> GSM372302 2 0.000 0.980 0.000 1.000
#> GSM372303 2 0.971 0.349 0.400 0.600
#> GSM372304 2 0.000 0.980 0.000 1.000
#> GSM372305 2 0.000 0.980 0.000 1.000
#> GSM372306 2 0.000 0.980 0.000 1.000
#> GSM372307 2 0.000 0.980 0.000 1.000
#> GSM372309 2 0.000 0.980 0.000 1.000
#> GSM372311 2 0.000 0.980 0.000 1.000
#> GSM372313 2 0.000 0.980 0.000 1.000
#> GSM372315 2 0.000 0.980 0.000 1.000
#> GSM372317 2 0.000 0.980 0.000 1.000
#> GSM372319 2 0.000 0.980 0.000 1.000
#> GSM372321 2 0.000 0.980 0.000 1.000
#> GSM372323 2 0.000 0.980 0.000 1.000
#> GSM372326 2 0.000 0.980 0.000 1.000
#> GSM372328 2 0.000 0.980 0.000 1.000
#> GSM372330 2 0.000 0.980 0.000 1.000
#> GSM372332 1 0.242 0.957 0.960 0.040
#> GSM372335 2 0.000 0.980 0.000 1.000
#> GSM372337 2 0.000 0.980 0.000 1.000
#> GSM372339 2 0.000 0.980 0.000 1.000
#> GSM372341 2 0.000 0.980 0.000 1.000
#> GSM372343 2 0.000 0.980 0.000 1.000
#> GSM372345 2 0.000 0.980 0.000 1.000
#> GSM372347 2 0.506 0.863 0.112 0.888
#> GSM372349 2 0.000 0.980 0.000 1.000
#> GSM372351 2 0.000 0.980 0.000 1.000
#> GSM372353 2 0.000 0.980 0.000 1.000
#> GSM372355 2 0.000 0.980 0.000 1.000
#> GSM372357 2 0.000 0.980 0.000 1.000
#> GSM372359 2 0.000 0.980 0.000 1.000
#> GSM372361 2 0.000 0.980 0.000 1.000
#> GSM372363 2 0.000 0.980 0.000 1.000
#> GSM372308 1 0.000 0.996 1.000 0.000
#> GSM372310 1 0.000 0.996 1.000 0.000
#> GSM372312 1 0.000 0.996 1.000 0.000
#> GSM372314 1 0.000 0.996 1.000 0.000
#> GSM372316 1 0.000 0.996 1.000 0.000
#> GSM372318 1 0.000 0.996 1.000 0.000
#> GSM372320 1 0.000 0.996 1.000 0.000
#> GSM372322 1 0.000 0.996 1.000 0.000
#> GSM372324 1 0.000 0.996 1.000 0.000
#> GSM372325 1 0.000 0.996 1.000 0.000
#> GSM372327 1 0.000 0.996 1.000 0.000
#> GSM372329 1 0.000 0.996 1.000 0.000
#> GSM372331 1 0.000 0.996 1.000 0.000
#> GSM372333 1 0.000 0.996 1.000 0.000
#> GSM372334 1 0.000 0.996 1.000 0.000
#> GSM372336 1 0.000 0.996 1.000 0.000
#> GSM372338 1 0.000 0.996 1.000 0.000
#> GSM372340 1 0.000 0.996 1.000 0.000
#> GSM372342 1 0.000 0.996 1.000 0.000
#> GSM372344 1 0.000 0.996 1.000 0.000
#> GSM372346 1 0.000 0.996 1.000 0.000
#> GSM372348 1 0.000 0.996 1.000 0.000
#> GSM372350 1 0.000 0.996 1.000 0.000
#> GSM372352 1 0.402 0.912 0.920 0.080
#> GSM372354 1 0.000 0.996 1.000 0.000
#> GSM372356 1 0.000 0.996 1.000 0.000
#> GSM372358 1 0.000 0.996 1.000 0.000
#> GSM372360 1 0.000 0.996 1.000 0.000
#> GSM372362 1 0.000 0.996 1.000 0.000
#> GSM372364 1 0.000 0.996 1.000 0.000
#> GSM372365 1 0.000 0.996 1.000 0.000
#> GSM372366 1 0.000 0.996 1.000 0.000
#> GSM372367 1 0.000 0.996 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM372286 2 0.0000 0.984 0.000 1.000 0.000
#> GSM372287 2 0.0000 0.984 0.000 1.000 0.000
#> GSM372288 2 0.0000 0.984 0.000 1.000 0.000
#> GSM372289 2 0.0000 0.984 0.000 1.000 0.000
#> GSM372290 2 0.0000 0.984 0.000 1.000 0.000
#> GSM372291 3 0.0592 0.938 0.012 0.000 0.988
#> GSM372292 2 0.3267 0.868 0.000 0.884 0.116
#> GSM372293 3 0.0592 0.945 0.000 0.012 0.988
#> GSM372294 2 0.3686 0.830 0.000 0.860 0.140
#> GSM372295 3 0.0592 0.945 0.000 0.012 0.988
#> GSM372296 2 0.0000 0.984 0.000 1.000 0.000
#> GSM372297 2 0.0000 0.984 0.000 1.000 0.000
#> GSM372298 2 0.0000 0.984 0.000 1.000 0.000
#> GSM372299 3 0.1753 0.928 0.000 0.048 0.952
#> GSM372300 3 0.0000 0.945 0.000 0.000 1.000
#> GSM372301 3 0.1753 0.928 0.000 0.048 0.952
#> GSM372302 2 0.0000 0.984 0.000 1.000 0.000
#> GSM372303 3 0.0000 0.945 0.000 0.000 1.000
#> GSM372304 2 0.0000 0.984 0.000 1.000 0.000
#> GSM372305 2 0.0000 0.984 0.000 1.000 0.000
#> GSM372306 2 0.0000 0.984 0.000 1.000 0.000
#> GSM372307 2 0.0000 0.984 0.000 1.000 0.000
#> GSM372309 3 0.1529 0.933 0.000 0.040 0.960
#> GSM372311 2 0.0000 0.984 0.000 1.000 0.000
#> GSM372313 2 0.0000 0.984 0.000 1.000 0.000
#> GSM372315 2 0.0000 0.984 0.000 1.000 0.000
#> GSM372317 2 0.0000 0.984 0.000 1.000 0.000
#> GSM372319 2 0.0000 0.984 0.000 1.000 0.000
#> GSM372321 2 0.0000 0.984 0.000 1.000 0.000
#> GSM372323 3 0.0592 0.945 0.000 0.012 0.988
#> GSM372326 3 0.0592 0.945 0.000 0.012 0.988
#> GSM372328 3 0.5497 0.588 0.000 0.292 0.708
#> GSM372330 2 0.0000 0.984 0.000 1.000 0.000
#> GSM372332 3 0.0000 0.945 0.000 0.000 1.000
#> GSM372335 3 0.1753 0.928 0.000 0.048 0.952
#> GSM372337 3 0.0000 0.945 0.000 0.000 1.000
#> GSM372339 3 0.0592 0.945 0.000 0.012 0.988
#> GSM372341 3 0.0000 0.945 0.000 0.000 1.000
#> GSM372343 3 0.0592 0.945 0.000 0.012 0.988
#> GSM372345 3 0.0000 0.945 0.000 0.000 1.000
#> GSM372347 3 0.0000 0.945 0.000 0.000 1.000
#> GSM372349 3 0.0000 0.945 0.000 0.000 1.000
#> GSM372351 3 0.6286 0.158 0.000 0.464 0.536
#> GSM372353 3 0.1529 0.933 0.000 0.040 0.960
#> GSM372355 2 0.0000 0.984 0.000 1.000 0.000
#> GSM372357 2 0.3482 0.853 0.000 0.872 0.128
#> GSM372359 3 0.1753 0.928 0.000 0.048 0.952
#> GSM372361 2 0.0000 0.984 0.000 1.000 0.000
#> GSM372363 2 0.0000 0.984 0.000 1.000 0.000
#> GSM372308 3 0.3192 0.834 0.112 0.000 0.888
#> GSM372310 1 0.5098 0.732 0.752 0.000 0.248
#> GSM372312 3 0.0000 0.945 0.000 0.000 1.000
#> GSM372314 1 0.5098 0.732 0.752 0.000 0.248
#> GSM372316 1 0.0000 0.939 1.000 0.000 0.000
#> GSM372318 1 0.0000 0.939 1.000 0.000 0.000
#> GSM372320 1 0.0000 0.939 1.000 0.000 0.000
#> GSM372322 1 0.0000 0.939 1.000 0.000 0.000
#> GSM372324 1 0.0592 0.933 0.988 0.000 0.012
#> GSM372325 3 0.0000 0.945 0.000 0.000 1.000
#> GSM372327 1 0.0000 0.939 1.000 0.000 0.000
#> GSM372329 1 0.0000 0.939 1.000 0.000 0.000
#> GSM372331 1 0.5098 0.732 0.752 0.000 0.248
#> GSM372333 3 0.0000 0.945 0.000 0.000 1.000
#> GSM372334 1 0.0000 0.939 1.000 0.000 0.000
#> GSM372336 1 0.0237 0.937 0.996 0.000 0.004
#> GSM372338 1 0.0000 0.939 1.000 0.000 0.000
#> GSM372340 1 0.0000 0.939 1.000 0.000 0.000
#> GSM372342 1 0.0000 0.939 1.000 0.000 0.000
#> GSM372344 1 0.0000 0.939 1.000 0.000 0.000
#> GSM372346 1 0.0000 0.939 1.000 0.000 0.000
#> GSM372348 1 0.0000 0.939 1.000 0.000 0.000
#> GSM372350 3 0.4121 0.757 0.168 0.000 0.832
#> GSM372352 3 0.0000 0.945 0.000 0.000 1.000
#> GSM372354 1 0.0000 0.939 1.000 0.000 0.000
#> GSM372356 1 0.5098 0.732 0.752 0.000 0.248
#> GSM372358 1 0.0000 0.939 1.000 0.000 0.000
#> GSM372360 1 0.0000 0.939 1.000 0.000 0.000
#> GSM372362 1 0.0000 0.939 1.000 0.000 0.000
#> GSM372364 1 0.0424 0.935 0.992 0.000 0.008
#> GSM372365 1 0.5098 0.732 0.752 0.000 0.248
#> GSM372366 1 0.0000 0.939 1.000 0.000 0.000
#> GSM372367 1 0.5058 0.737 0.756 0.000 0.244
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM372286 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM372287 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM372288 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM372289 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM372290 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM372291 4 0.0469 0.947 0.000 0.000 0.012 0.988
#> GSM372292 3 0.0469 0.972 0.000 0.012 0.988 0.000
#> GSM372293 3 0.0000 0.974 0.000 0.000 1.000 0.000
#> GSM372294 2 0.1118 0.963 0.000 0.964 0.036 0.000
#> GSM372295 3 0.0000 0.974 0.000 0.000 1.000 0.000
#> GSM372296 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM372297 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM372298 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM372299 3 0.0469 0.972 0.000 0.012 0.988 0.000
#> GSM372300 3 0.0000 0.974 0.000 0.000 1.000 0.000
#> GSM372301 3 0.0469 0.972 0.000 0.012 0.988 0.000
#> GSM372302 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM372303 3 0.0000 0.974 0.000 0.000 1.000 0.000
#> GSM372304 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM372305 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM372306 2 0.1118 0.963 0.000 0.964 0.036 0.000
#> GSM372307 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM372309 3 0.0469 0.972 0.000 0.012 0.988 0.000
#> GSM372311 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM372313 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM372315 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM372317 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM372319 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM372321 2 0.0592 0.982 0.000 0.984 0.016 0.000
#> GSM372323 3 0.0000 0.974 0.000 0.000 1.000 0.000
#> GSM372326 3 0.0000 0.974 0.000 0.000 1.000 0.000
#> GSM372328 3 0.0469 0.972 0.000 0.012 0.988 0.000
#> GSM372330 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM372332 4 0.4040 0.676 0.000 0.000 0.248 0.752
#> GSM372335 3 0.0469 0.972 0.000 0.012 0.988 0.000
#> GSM372337 3 0.0000 0.974 0.000 0.000 1.000 0.000
#> GSM372339 3 0.0000 0.974 0.000 0.000 1.000 0.000
#> GSM372341 3 0.0000 0.974 0.000 0.000 1.000 0.000
#> GSM372343 3 0.0000 0.974 0.000 0.000 1.000 0.000
#> GSM372345 3 0.0000 0.974 0.000 0.000 1.000 0.000
#> GSM372347 3 0.0000 0.974 0.000 0.000 1.000 0.000
#> GSM372349 3 0.0000 0.974 0.000 0.000 1.000 0.000
#> GSM372351 3 0.0469 0.972 0.000 0.012 0.988 0.000
#> GSM372353 3 0.0469 0.972 0.000 0.012 0.988 0.000
#> GSM372355 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM372357 3 0.4830 0.361 0.000 0.392 0.608 0.000
#> GSM372359 3 0.0469 0.972 0.000 0.012 0.988 0.000
#> GSM372361 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM372363 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM372308 4 0.0000 0.954 0.000 0.000 0.000 1.000
#> GSM372310 4 0.0000 0.954 0.000 0.000 0.000 1.000
#> GSM372312 4 0.0469 0.947 0.000 0.000 0.012 0.988
#> GSM372314 4 0.0000 0.954 0.000 0.000 0.000 1.000
#> GSM372316 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM372318 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM372320 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM372322 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM372324 4 0.0000 0.954 0.000 0.000 0.000 1.000
#> GSM372325 4 0.0000 0.954 0.000 0.000 0.000 1.000
#> GSM372327 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM372329 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM372331 4 0.0000 0.954 0.000 0.000 0.000 1.000
#> GSM372333 4 0.0000 0.954 0.000 0.000 0.000 1.000
#> GSM372334 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM372336 4 0.0000 0.954 0.000 0.000 0.000 1.000
#> GSM372338 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM372340 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM372342 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM372344 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM372346 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM372348 4 0.3801 0.725 0.220 0.000 0.000 0.780
#> GSM372350 4 0.0000 0.954 0.000 0.000 0.000 1.000
#> GSM372352 3 0.1022 0.948 0.000 0.000 0.968 0.032
#> GSM372354 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM372356 4 0.0000 0.954 0.000 0.000 0.000 1.000
#> GSM372358 4 0.4193 0.641 0.268 0.000 0.000 0.732
#> GSM372360 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM372362 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM372364 4 0.0000 0.954 0.000 0.000 0.000 1.000
#> GSM372365 4 0.0000 0.954 0.000 0.000 0.000 1.000
#> GSM372366 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM372367 4 0.0000 0.954 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
#> GSM372286 2 0.0162 0.9831 0.004 0.996 0.000 0.000 0.000
#> GSM372287 2 0.0000 0.9836 0.000 1.000 0.000 0.000 0.000
#> GSM372288 2 0.0000 0.9836 0.000 1.000 0.000 0.000 0.000
#> GSM372289 2 0.0000 0.9836 0.000 1.000 0.000 0.000 0.000
#> GSM372290 2 0.0000 0.9836 0.000 1.000 0.000 0.000 0.000
#> GSM372291 5 0.3579 0.7408 0.240 0.000 0.004 0.000 0.756
#> GSM372292 3 0.0290 0.9434 0.008 0.000 0.992 0.000 0.000
#> GSM372293 3 0.0000 0.9436 0.000 0.000 1.000 0.000 0.000
#> GSM372294 2 0.4141 0.7000 0.248 0.728 0.024 0.000 0.000
#> GSM372295 3 0.3452 0.7326 0.244 0.000 0.756 0.000 0.000
#> GSM372296 2 0.0000 0.9836 0.000 1.000 0.000 0.000 0.000
#> GSM372297 2 0.0000 0.9836 0.000 1.000 0.000 0.000 0.000
#> GSM372298 2 0.0162 0.9831 0.004 0.996 0.000 0.000 0.000
#> GSM372299 3 0.0290 0.9434 0.008 0.000 0.992 0.000 0.000
#> GSM372300 3 0.0000 0.9436 0.000 0.000 1.000 0.000 0.000
#> GSM372301 3 0.0290 0.9434 0.008 0.000 0.992 0.000 0.000
#> GSM372302 2 0.0290 0.9812 0.008 0.992 0.000 0.000 0.000
#> GSM372303 3 0.0000 0.9436 0.000 0.000 1.000 0.000 0.000
#> GSM372304 2 0.0000 0.9836 0.000 1.000 0.000 0.000 0.000
#> GSM372305 2 0.0162 0.9831 0.004 0.996 0.000 0.000 0.000
#> GSM372306 2 0.1331 0.9421 0.008 0.952 0.040 0.000 0.000
#> GSM372307 2 0.0000 0.9836 0.000 1.000 0.000 0.000 0.000
#> GSM372309 3 0.0290 0.9434 0.008 0.000 0.992 0.000 0.000
#> GSM372311 2 0.0000 0.9836 0.000 1.000 0.000 0.000 0.000
#> GSM372313 2 0.0290 0.9812 0.008 0.992 0.000 0.000 0.000
#> GSM372315 2 0.0162 0.9831 0.004 0.996 0.000 0.000 0.000
#> GSM372317 2 0.0324 0.9808 0.004 0.992 0.004 0.000 0.000
#> GSM372319 2 0.0000 0.9836 0.000 1.000 0.000 0.000 0.000
#> GSM372321 2 0.0771 0.9662 0.004 0.976 0.020 0.000 0.000
#> GSM372323 3 0.0000 0.9436 0.000 0.000 1.000 0.000 0.000
#> GSM372326 3 0.0000 0.9436 0.000 0.000 1.000 0.000 0.000
#> GSM372328 3 0.0290 0.9434 0.008 0.000 0.992 0.000 0.000
#> GSM372330 2 0.0162 0.9831 0.004 0.996 0.000 0.000 0.000
#> GSM372332 5 0.4083 0.7538 0.132 0.000 0.080 0.000 0.788
#> GSM372335 3 0.0290 0.9434 0.008 0.000 0.992 0.000 0.000
#> GSM372337 3 0.0000 0.9436 0.000 0.000 1.000 0.000 0.000
#> GSM372339 3 0.0000 0.9436 0.000 0.000 1.000 0.000 0.000
#> GSM372341 3 0.0000 0.9436 0.000 0.000 1.000 0.000 0.000
#> GSM372343 3 0.0000 0.9436 0.000 0.000 1.000 0.000 0.000
#> GSM372345 3 0.0000 0.9436 0.000 0.000 1.000 0.000 0.000
#> GSM372347 3 0.3177 0.7061 0.000 0.000 0.792 0.000 0.208
#> GSM372349 3 0.3424 0.7330 0.240 0.000 0.760 0.000 0.000
#> GSM372351 3 0.0290 0.9434 0.008 0.000 0.992 0.000 0.000
#> GSM372353 3 0.0290 0.9434 0.008 0.000 0.992 0.000 0.000
#> GSM372355 2 0.0162 0.9831 0.004 0.996 0.000 0.000 0.000
#> GSM372357 3 0.4403 0.3864 0.008 0.384 0.608 0.000 0.000
#> GSM372359 3 0.0290 0.9434 0.008 0.000 0.992 0.000 0.000
#> GSM372361 2 0.0000 0.9836 0.000 1.000 0.000 0.000 0.000
#> GSM372363 2 0.0000 0.9836 0.000 1.000 0.000 0.000 0.000
#> GSM372308 5 0.0000 0.8467 0.000 0.000 0.000 0.000 1.000
#> GSM372310 5 0.0000 0.8467 0.000 0.000 0.000 0.000 1.000
#> GSM372312 5 0.3579 0.7408 0.240 0.000 0.004 0.000 0.756
#> GSM372314 5 0.0000 0.8467 0.000 0.000 0.000 0.000 1.000
#> GSM372316 1 0.4278 0.4587 0.548 0.000 0.000 0.452 0.000
#> GSM372318 4 0.4219 -0.0399 0.416 0.000 0.000 0.584 0.000
#> GSM372320 4 0.0000 0.9315 0.000 0.000 0.000 1.000 0.000
#> GSM372322 4 0.0000 0.9315 0.000 0.000 0.000 1.000 0.000
#> GSM372324 5 0.0000 0.8467 0.000 0.000 0.000 0.000 1.000
#> GSM372325 5 0.0000 0.8467 0.000 0.000 0.000 0.000 1.000
#> GSM372327 4 0.0000 0.9315 0.000 0.000 0.000 1.000 0.000
#> GSM372329 1 0.3534 0.7793 0.744 0.000 0.000 0.256 0.000
#> GSM372331 5 0.0000 0.8467 0.000 0.000 0.000 0.000 1.000
#> GSM372333 5 0.0000 0.8467 0.000 0.000 0.000 0.000 1.000
#> GSM372334 4 0.0000 0.9315 0.000 0.000 0.000 1.000 0.000
#> GSM372336 1 0.4182 0.4394 0.600 0.000 0.000 0.000 0.400
#> GSM372338 4 0.0000 0.9315 0.000 0.000 0.000 1.000 0.000
#> GSM372340 4 0.0000 0.9315 0.000 0.000 0.000 1.000 0.000
#> GSM372342 1 0.3534 0.7793 0.744 0.000 0.000 0.256 0.000
#> GSM372344 4 0.0000 0.9315 0.000 0.000 0.000 1.000 0.000
#> GSM372346 4 0.0000 0.9315 0.000 0.000 0.000 1.000 0.000
#> GSM372348 1 0.5532 0.6996 0.648 0.000 0.000 0.156 0.196
#> GSM372350 5 0.3424 0.7427 0.240 0.000 0.000 0.000 0.760
#> GSM372352 5 0.4291 0.1699 0.000 0.000 0.464 0.000 0.536
#> GSM372354 1 0.3534 0.7793 0.744 0.000 0.000 0.256 0.000
#> GSM372356 5 0.3242 0.6039 0.216 0.000 0.000 0.000 0.784
#> GSM372358 1 0.3607 0.6784 0.752 0.000 0.000 0.004 0.244
#> GSM372360 1 0.3480 0.7816 0.752 0.000 0.000 0.248 0.000
#> GSM372362 1 0.3480 0.7816 0.752 0.000 0.000 0.248 0.000
#> GSM372364 1 0.3480 0.6733 0.752 0.000 0.000 0.000 0.248
#> GSM372365 5 0.2852 0.6760 0.172 0.000 0.000 0.000 0.828
#> GSM372366 1 0.3508 0.7810 0.748 0.000 0.000 0.252 0.000
#> GSM372367 5 0.0290 0.8431 0.008 0.000 0.000 0.000 0.992
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM372286 2 0.0363 0.987 0.012 0.988 0.000 0.000 0.000 0.000
#> GSM372287 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM372288 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM372289 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM372290 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM372291 4 0.3634 0.454 0.000 0.000 0.000 0.644 0.356 0.000
#> GSM372292 3 0.0363 0.847 0.012 0.000 0.988 0.000 0.000 0.000
#> GSM372293 3 0.0458 0.851 0.000 0.000 0.984 0.016 0.000 0.000
#> GSM372294 4 0.4049 0.362 0.000 0.332 0.020 0.648 0.000 0.000
#> GSM372295 4 0.3023 0.506 0.000 0.000 0.232 0.768 0.000 0.000
#> GSM372296 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM372297 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM372298 2 0.0363 0.987 0.012 0.988 0.000 0.000 0.000 0.000
#> GSM372299 3 0.0291 0.851 0.004 0.000 0.992 0.004 0.000 0.000
#> GSM372300 3 0.3592 0.624 0.000 0.000 0.656 0.344 0.000 0.000
#> GSM372301 3 0.0146 0.850 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM372302 2 0.0820 0.976 0.012 0.972 0.016 0.000 0.000 0.000
#> GSM372303 3 0.0458 0.851 0.000 0.000 0.984 0.016 0.000 0.000
#> GSM372304 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM372305 2 0.0363 0.987 0.012 0.988 0.000 0.000 0.000 0.000
#> GSM372306 2 0.1411 0.928 0.004 0.936 0.060 0.000 0.000 0.000
#> GSM372307 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM372309 3 0.0146 0.850 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM372311 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM372313 2 0.0820 0.976 0.012 0.972 0.016 0.000 0.000 0.000
#> GSM372315 2 0.0363 0.987 0.012 0.988 0.000 0.000 0.000 0.000
#> GSM372317 2 0.0508 0.985 0.012 0.984 0.004 0.000 0.000 0.000
#> GSM372319 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM372321 2 0.0909 0.970 0.012 0.968 0.020 0.000 0.000 0.000
#> GSM372323 3 0.2219 0.789 0.000 0.000 0.864 0.136 0.000 0.000
#> GSM372326 3 0.0363 0.851 0.000 0.000 0.988 0.012 0.000 0.000
#> GSM372328 3 0.0146 0.850 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM372330 2 0.0363 0.987 0.012 0.988 0.000 0.000 0.000 0.000
#> GSM372332 5 0.3684 0.476 0.000 0.000 0.004 0.332 0.664 0.000
#> GSM372335 3 0.0146 0.850 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM372337 3 0.3620 0.616 0.000 0.000 0.648 0.352 0.000 0.000
#> GSM372339 3 0.0458 0.851 0.000 0.000 0.984 0.016 0.000 0.000
#> GSM372341 3 0.3607 0.619 0.000 0.000 0.652 0.348 0.000 0.000
#> GSM372343 3 0.0458 0.851 0.000 0.000 0.984 0.016 0.000 0.000
#> GSM372345 3 0.3620 0.616 0.000 0.000 0.648 0.352 0.000 0.000
#> GSM372347 3 0.3756 0.612 0.000 0.000 0.644 0.352 0.004 0.000
#> GSM372349 4 0.0146 0.506 0.000 0.000 0.004 0.996 0.000 0.000
#> GSM372351 3 0.0146 0.850 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM372353 3 0.1531 0.828 0.004 0.000 0.928 0.068 0.000 0.000
#> GSM372355 2 0.0363 0.987 0.012 0.988 0.000 0.000 0.000 0.000
#> GSM372357 3 0.4026 0.244 0.012 0.376 0.612 0.000 0.000 0.000
#> GSM372359 3 0.0508 0.847 0.012 0.000 0.984 0.004 0.000 0.000
#> GSM372361 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM372363 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM372308 5 0.0000 0.867 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM372310 5 0.0000 0.867 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM372312 4 0.3634 0.454 0.000 0.000 0.000 0.644 0.356 0.000
#> GSM372314 5 0.0000 0.867 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM372316 1 0.3464 0.631 0.688 0.000 0.000 0.000 0.000 0.312
#> GSM372318 6 0.3797 0.121 0.420 0.000 0.000 0.000 0.000 0.580
#> GSM372320 6 0.0000 0.939 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM372322 6 0.0000 0.939 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM372324 5 0.0000 0.867 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM372325 5 0.0000 0.867 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM372327 6 0.0000 0.939 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM372329 1 0.2003 0.897 0.884 0.000 0.000 0.000 0.000 0.116
#> GSM372331 5 0.0000 0.867 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM372333 5 0.0000 0.867 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM372334 6 0.0000 0.939 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM372336 5 0.2941 0.682 0.220 0.000 0.000 0.000 0.780 0.000
#> GSM372338 6 0.0000 0.939 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM372340 6 0.0000 0.939 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM372342 1 0.2003 0.897 0.884 0.000 0.000 0.000 0.000 0.116
#> GSM372344 6 0.0000 0.939 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM372346 6 0.0000 0.939 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM372348 5 0.4002 0.491 0.320 0.000 0.000 0.000 0.660 0.020
#> GSM372350 4 0.3620 0.456 0.000 0.000 0.000 0.648 0.352 0.000
#> GSM372352 4 0.4097 -0.422 0.000 0.000 0.488 0.504 0.008 0.000
#> GSM372354 1 0.2003 0.897 0.884 0.000 0.000 0.000 0.000 0.116
#> GSM372356 5 0.1910 0.820 0.108 0.000 0.000 0.000 0.892 0.000
#> GSM372358 1 0.0363 0.884 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM372360 1 0.0363 0.890 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM372362 1 0.0632 0.895 0.976 0.000 0.000 0.000 0.000 0.024
#> GSM372364 1 0.0363 0.884 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM372365 5 0.1863 0.822 0.104 0.000 0.000 0.000 0.896 0.000
#> GSM372366 1 0.1957 0.898 0.888 0.000 0.000 0.000 0.000 0.112
#> GSM372367 5 0.1863 0.822 0.104 0.000 0.000 0.000 0.896 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) specimen(p) individual(p) k
#> ATC:pam 80 0.000309 2.07e-16 0.999 2
#> ATC:pam 81 0.000045 2.60e-13 0.909 3
#> ATC:pam 81 0.000196 7.74e-14 0.864 4
#> ATC:pam 77 0.001120 1.01e-12 0.908 5
#> ATC:pam 73 0.002113 2.34e-12 0.658 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 51941 rows and 82 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.983 0.990 0.4736 0.530 0.530
#> 3 3 0.753 0.801 0.877 0.2832 0.874 0.761
#> 4 4 0.898 0.881 0.947 0.1605 0.833 0.612
#> 5 5 0.723 0.726 0.805 0.0855 0.926 0.750
#> 6 6 0.823 0.831 0.908 0.0671 0.896 0.594
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
#> GSM372286 2 0.0000 0.984 0.000 1.000
#> GSM372287 2 0.0000 0.984 0.000 1.000
#> GSM372288 2 0.0000 0.984 0.000 1.000
#> GSM372289 2 0.0000 0.984 0.000 1.000
#> GSM372290 2 0.0000 0.984 0.000 1.000
#> GSM372291 2 0.4431 0.915 0.092 0.908
#> GSM372292 2 0.0000 0.984 0.000 1.000
#> GSM372293 2 0.0000 0.984 0.000 1.000
#> GSM372294 2 0.4431 0.915 0.092 0.908
#> GSM372295 2 0.4431 0.915 0.092 0.908
#> GSM372296 2 0.0000 0.984 0.000 1.000
#> GSM372297 2 0.0000 0.984 0.000 1.000
#> GSM372298 2 0.0000 0.984 0.000 1.000
#> GSM372299 2 0.4022 0.927 0.080 0.920
#> GSM372300 2 0.0000 0.984 0.000 1.000
#> GSM372301 2 0.0000 0.984 0.000 1.000
#> GSM372302 2 0.0000 0.984 0.000 1.000
#> GSM372303 2 0.0000 0.984 0.000 1.000
#> GSM372304 2 0.0000 0.984 0.000 1.000
#> GSM372305 2 0.0000 0.984 0.000 1.000
#> GSM372306 2 0.0000 0.984 0.000 1.000
#> GSM372307 2 0.0000 0.984 0.000 1.000
#> GSM372309 2 0.0000 0.984 0.000 1.000
#> GSM372311 2 0.0000 0.984 0.000 1.000
#> GSM372313 2 0.0000 0.984 0.000 1.000
#> GSM372315 2 0.0000 0.984 0.000 1.000
#> GSM372317 2 0.0000 0.984 0.000 1.000
#> GSM372319 2 0.0000 0.984 0.000 1.000
#> GSM372321 2 0.0000 0.984 0.000 1.000
#> GSM372323 2 0.0000 0.984 0.000 1.000
#> GSM372326 2 0.0000 0.984 0.000 1.000
#> GSM372328 2 0.0000 0.984 0.000 1.000
#> GSM372330 2 0.0000 0.984 0.000 1.000
#> GSM372332 2 0.4022 0.926 0.080 0.920
#> GSM372335 2 0.0000 0.984 0.000 1.000
#> GSM372337 2 0.0000 0.984 0.000 1.000
#> GSM372339 2 0.0000 0.984 0.000 1.000
#> GSM372341 2 0.0000 0.984 0.000 1.000
#> GSM372343 2 0.0000 0.984 0.000 1.000
#> GSM372345 2 0.0000 0.984 0.000 1.000
#> GSM372347 2 0.0672 0.979 0.008 0.992
#> GSM372349 2 0.4022 0.926 0.080 0.920
#> GSM372351 2 0.0000 0.984 0.000 1.000
#> GSM372353 2 0.0672 0.979 0.008 0.992
#> GSM372355 2 0.0000 0.984 0.000 1.000
#> GSM372357 2 0.0672 0.979 0.008 0.992
#> GSM372359 2 0.0672 0.979 0.008 0.992
#> GSM372361 2 0.0000 0.984 0.000 1.000
#> GSM372363 2 0.0000 0.984 0.000 1.000
#> GSM372308 1 0.0000 1.000 1.000 0.000
#> GSM372310 1 0.0000 1.000 1.000 0.000
#> GSM372312 2 0.4431 0.915 0.092 0.908
#> GSM372314 1 0.0000 1.000 1.000 0.000
#> GSM372316 1 0.0000 1.000 1.000 0.000
#> GSM372318 1 0.0000 1.000 1.000 0.000
#> GSM372320 1 0.0000 1.000 1.000 0.000
#> GSM372322 1 0.0000 1.000 1.000 0.000
#> GSM372324 1 0.0000 1.000 1.000 0.000
#> GSM372325 1 0.0000 1.000 1.000 0.000
#> GSM372327 1 0.0000 1.000 1.000 0.000
#> GSM372329 1 0.0000 1.000 1.000 0.000
#> GSM372331 1 0.0000 1.000 1.000 0.000
#> GSM372333 1 0.0000 1.000 1.000 0.000
#> GSM372334 1 0.0000 1.000 1.000 0.000
#> GSM372336 1 0.0000 1.000 1.000 0.000
#> GSM372338 1 0.0000 1.000 1.000 0.000
#> GSM372340 1 0.0000 1.000 1.000 0.000
#> GSM372342 1 0.0000 1.000 1.000 0.000
#> GSM372344 1 0.0000 1.000 1.000 0.000
#> GSM372346 1 0.0000 1.000 1.000 0.000
#> GSM372348 1 0.0000 1.000 1.000 0.000
#> GSM372350 2 0.4431 0.915 0.092 0.908
#> GSM372352 2 0.4022 0.926 0.080 0.920
#> GSM372354 1 0.0000 1.000 1.000 0.000
#> GSM372356 1 0.0000 1.000 1.000 0.000
#> GSM372358 1 0.0000 1.000 1.000 0.000
#> GSM372360 1 0.0000 1.000 1.000 0.000
#> GSM372362 1 0.0000 1.000 1.000 0.000
#> GSM372364 1 0.0000 1.000 1.000 0.000
#> GSM372365 1 0.0000 1.000 1.000 0.000
#> GSM372366 1 0.0000 1.000 1.000 0.000
#> GSM372367 1 0.0000 1.000 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM372286 2 0.4178 0.8100 0.000 0.828 0.172
#> GSM372287 2 0.6299 0.2817 0.000 0.524 0.476
#> GSM372288 2 0.6280 0.3296 0.000 0.540 0.460
#> GSM372289 2 0.5810 0.6049 0.000 0.664 0.336
#> GSM372290 2 0.4235 0.8074 0.000 0.824 0.176
#> GSM372291 3 0.1964 0.7556 0.056 0.000 0.944
#> GSM372292 2 0.4062 0.8133 0.000 0.836 0.164
#> GSM372293 2 0.0424 0.8072 0.000 0.992 0.008
#> GSM372294 3 0.1031 0.7538 0.024 0.000 0.976
#> GSM372295 3 0.1031 0.7538 0.024 0.000 0.976
#> GSM372296 3 0.6235 -0.0676 0.000 0.436 0.564
#> GSM372297 2 0.6286 0.3183 0.000 0.536 0.464
#> GSM372298 2 0.4062 0.8133 0.000 0.836 0.164
#> GSM372299 2 0.6398 0.0299 0.416 0.580 0.004
#> GSM372300 2 0.0424 0.8072 0.000 0.992 0.008
#> GSM372301 2 0.0424 0.8072 0.000 0.992 0.008
#> GSM372302 3 0.6280 -0.1534 0.000 0.460 0.540
#> GSM372303 2 0.0892 0.7998 0.000 0.980 0.020
#> GSM372304 2 0.6308 0.2285 0.000 0.508 0.492
#> GSM372305 2 0.4178 0.8100 0.000 0.828 0.172
#> GSM372306 2 0.3752 0.8148 0.000 0.856 0.144
#> GSM372307 2 0.6026 0.5298 0.000 0.624 0.376
#> GSM372309 2 0.4062 0.8133 0.000 0.836 0.164
#> GSM372311 2 0.4178 0.8100 0.000 0.828 0.172
#> GSM372313 2 0.4062 0.8133 0.000 0.836 0.164
#> GSM372315 2 0.4178 0.8100 0.000 0.828 0.172
#> GSM372317 2 0.4062 0.8133 0.000 0.836 0.164
#> GSM372319 2 0.4178 0.8100 0.000 0.828 0.172
#> GSM372321 2 0.4235 0.8074 0.000 0.824 0.176
#> GSM372323 2 0.0000 0.8092 0.000 1.000 0.000
#> GSM372326 2 0.0424 0.8072 0.000 0.992 0.008
#> GSM372328 2 0.0424 0.8072 0.000 0.992 0.008
#> GSM372330 2 0.4062 0.8133 0.000 0.836 0.164
#> GSM372332 3 0.9498 0.4542 0.216 0.300 0.484
#> GSM372335 2 0.0000 0.8092 0.000 1.000 0.000
#> GSM372337 2 0.0424 0.8072 0.000 0.992 0.008
#> GSM372339 2 0.0892 0.7998 0.000 0.980 0.020
#> GSM372341 2 0.0892 0.7998 0.000 0.980 0.020
#> GSM372343 2 0.0592 0.8049 0.000 0.988 0.012
#> GSM372345 2 0.0424 0.8072 0.000 0.992 0.008
#> GSM372347 2 0.0000 0.8092 0.000 1.000 0.000
#> GSM372349 3 0.1453 0.7514 0.024 0.008 0.968
#> GSM372351 2 0.0892 0.8114 0.000 0.980 0.020
#> GSM372353 2 0.0000 0.8092 0.000 1.000 0.000
#> GSM372355 2 0.4062 0.8133 0.000 0.836 0.164
#> GSM372357 2 0.0000 0.8092 0.000 1.000 0.000
#> GSM372359 2 0.0000 0.8092 0.000 1.000 0.000
#> GSM372361 2 0.4178 0.8100 0.000 0.828 0.172
#> GSM372363 2 0.4178 0.8100 0.000 0.828 0.172
#> GSM372308 1 0.0592 0.9875 0.988 0.012 0.000
#> GSM372310 1 0.0424 0.9908 0.992 0.008 0.000
#> GSM372312 3 0.1964 0.7556 0.056 0.000 0.944
#> GSM372314 1 0.0592 0.9875 0.988 0.012 0.000
#> GSM372316 1 0.0000 0.9944 1.000 0.000 0.000
#> GSM372318 1 0.0000 0.9944 1.000 0.000 0.000
#> GSM372320 1 0.0000 0.9944 1.000 0.000 0.000
#> GSM372322 1 0.0000 0.9944 1.000 0.000 0.000
#> GSM372324 1 0.0424 0.9908 0.992 0.008 0.000
#> GSM372325 1 0.1289 0.9658 0.968 0.032 0.000
#> GSM372327 1 0.0000 0.9944 1.000 0.000 0.000
#> GSM372329 1 0.0000 0.9944 1.000 0.000 0.000
#> GSM372331 1 0.0424 0.9908 0.992 0.008 0.000
#> GSM372333 1 0.1289 0.9658 0.968 0.032 0.000
#> GSM372334 1 0.0000 0.9944 1.000 0.000 0.000
#> GSM372336 1 0.0000 0.9944 1.000 0.000 0.000
#> GSM372338 1 0.0000 0.9944 1.000 0.000 0.000
#> GSM372340 1 0.0000 0.9944 1.000 0.000 0.000
#> GSM372342 1 0.0000 0.9944 1.000 0.000 0.000
#> GSM372344 1 0.0000 0.9944 1.000 0.000 0.000
#> GSM372346 1 0.0000 0.9944 1.000 0.000 0.000
#> GSM372348 1 0.0000 0.9944 1.000 0.000 0.000
#> GSM372350 3 0.1964 0.7556 0.056 0.000 0.944
#> GSM372352 3 0.9187 0.5124 0.272 0.196 0.532
#> GSM372354 1 0.0000 0.9944 1.000 0.000 0.000
#> GSM372356 1 0.0424 0.9908 0.992 0.008 0.000
#> GSM372358 1 0.0000 0.9944 1.000 0.000 0.000
#> GSM372360 1 0.0000 0.9944 1.000 0.000 0.000
#> GSM372362 1 0.0000 0.9944 1.000 0.000 0.000
#> GSM372364 1 0.0000 0.9944 1.000 0.000 0.000
#> GSM372365 1 0.0424 0.9908 0.992 0.008 0.000
#> GSM372366 1 0.0000 0.9944 1.000 0.000 0.000
#> GSM372367 1 0.0424 0.9908 0.992 0.008 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM372286 2 0.0000 0.867 0.000 1.000 0.000 0.00
#> GSM372287 2 0.0000 0.867 0.000 1.000 0.000 0.00
#> GSM372288 2 0.0000 0.867 0.000 1.000 0.000 0.00
#> GSM372289 2 0.0000 0.867 0.000 1.000 0.000 0.00
#> GSM372290 2 0.0000 0.867 0.000 1.000 0.000 0.00
#> GSM372291 4 0.0000 0.939 0.000 0.000 0.000 1.00
#> GSM372292 2 0.4977 0.236 0.000 0.540 0.460 0.00
#> GSM372293 3 0.0000 0.909 0.000 0.000 1.000 0.00
#> GSM372294 4 0.0000 0.939 0.000 0.000 0.000 1.00
#> GSM372295 4 0.0000 0.939 0.000 0.000 0.000 1.00
#> GSM372296 2 0.0000 0.867 0.000 1.000 0.000 0.00
#> GSM372297 2 0.0000 0.867 0.000 1.000 0.000 0.00
#> GSM372298 2 0.4304 0.635 0.000 0.716 0.284 0.00
#> GSM372299 3 0.0657 0.911 0.004 0.012 0.984 0.00
#> GSM372300 3 0.0000 0.909 0.000 0.000 1.000 0.00
#> GSM372301 3 0.1557 0.884 0.000 0.056 0.944 0.00
#> GSM372302 2 0.0000 0.867 0.000 1.000 0.000 0.00
#> GSM372303 3 0.0000 0.909 0.000 0.000 1.000 0.00
#> GSM372304 2 0.0000 0.867 0.000 1.000 0.000 0.00
#> GSM372305 2 0.0000 0.867 0.000 1.000 0.000 0.00
#> GSM372306 3 0.4406 0.575 0.000 0.300 0.700 0.00
#> GSM372307 2 0.0000 0.867 0.000 1.000 0.000 0.00
#> GSM372309 3 0.4406 0.575 0.000 0.300 0.700 0.00
#> GSM372311 2 0.0000 0.867 0.000 1.000 0.000 0.00
#> GSM372313 2 0.4222 0.646 0.000 0.728 0.272 0.00
#> GSM372315 2 0.1474 0.843 0.000 0.948 0.052 0.00
#> GSM372317 2 0.4543 0.573 0.000 0.676 0.324 0.00
#> GSM372319 2 0.1557 0.840 0.000 0.944 0.056 0.00
#> GSM372321 2 0.1716 0.836 0.000 0.936 0.064 0.00
#> GSM372323 3 0.0336 0.911 0.000 0.008 0.992 0.00
#> GSM372326 3 0.0000 0.909 0.000 0.000 1.000 0.00
#> GSM372328 3 0.0000 0.909 0.000 0.000 1.000 0.00
#> GSM372330 2 0.4585 0.561 0.000 0.668 0.332 0.00
#> GSM372332 3 0.0469 0.912 0.000 0.012 0.988 0.00
#> GSM372335 3 0.2011 0.879 0.000 0.080 0.920 0.00
#> GSM372337 3 0.0469 0.912 0.000 0.012 0.988 0.00
#> GSM372339 3 0.0188 0.911 0.000 0.004 0.996 0.00
#> GSM372341 3 0.0188 0.911 0.000 0.004 0.996 0.00
#> GSM372343 3 0.0000 0.909 0.000 0.000 1.000 0.00
#> GSM372345 3 0.0469 0.912 0.000 0.012 0.988 0.00
#> GSM372347 3 0.0469 0.912 0.000 0.012 0.988 0.00
#> GSM372349 4 0.6689 0.619 0.000 0.184 0.196 0.62
#> GSM372351 3 0.4304 0.603 0.000 0.284 0.716 0.00
#> GSM372353 3 0.1940 0.881 0.000 0.076 0.924 0.00
#> GSM372355 2 0.4543 0.573 0.000 0.676 0.324 0.00
#> GSM372357 3 0.2216 0.869 0.000 0.092 0.908 0.00
#> GSM372359 3 0.2216 0.869 0.000 0.092 0.908 0.00
#> GSM372361 2 0.0000 0.867 0.000 1.000 0.000 0.00
#> GSM372363 2 0.0000 0.867 0.000 1.000 0.000 0.00
#> GSM372308 1 0.1867 0.924 0.928 0.000 0.072 0.00
#> GSM372310 1 0.0336 0.983 0.992 0.000 0.008 0.00
#> GSM372312 4 0.0000 0.939 0.000 0.000 0.000 1.00
#> GSM372314 1 0.0592 0.976 0.984 0.000 0.016 0.00
#> GSM372316 1 0.0000 0.989 1.000 0.000 0.000 0.00
#> GSM372318 1 0.0000 0.989 1.000 0.000 0.000 0.00
#> GSM372320 1 0.0000 0.989 1.000 0.000 0.000 0.00
#> GSM372322 1 0.0000 0.989 1.000 0.000 0.000 0.00
#> GSM372324 1 0.0000 0.989 1.000 0.000 0.000 0.00
#> GSM372325 1 0.1867 0.924 0.928 0.000 0.072 0.00
#> GSM372327 1 0.0000 0.989 1.000 0.000 0.000 0.00
#> GSM372329 1 0.0000 0.989 1.000 0.000 0.000 0.00
#> GSM372331 1 0.1474 0.944 0.948 0.000 0.052 0.00
#> GSM372333 1 0.1867 0.924 0.928 0.000 0.072 0.00
#> GSM372334 1 0.0000 0.989 1.000 0.000 0.000 0.00
#> GSM372336 1 0.0000 0.989 1.000 0.000 0.000 0.00
#> GSM372338 1 0.0000 0.989 1.000 0.000 0.000 0.00
#> GSM372340 1 0.0000 0.989 1.000 0.000 0.000 0.00
#> GSM372342 1 0.0000 0.989 1.000 0.000 0.000 0.00
#> GSM372344 1 0.0000 0.989 1.000 0.000 0.000 0.00
#> GSM372346 1 0.0000 0.989 1.000 0.000 0.000 0.00
#> GSM372348 1 0.0000 0.989 1.000 0.000 0.000 0.00
#> GSM372350 4 0.0000 0.939 0.000 0.000 0.000 1.00
#> GSM372352 3 0.4206 0.722 0.136 0.048 0.816 0.00
#> GSM372354 1 0.0000 0.989 1.000 0.000 0.000 0.00
#> GSM372356 1 0.0000 0.989 1.000 0.000 0.000 0.00
#> GSM372358 1 0.0000 0.989 1.000 0.000 0.000 0.00
#> GSM372360 1 0.0000 0.989 1.000 0.000 0.000 0.00
#> GSM372362 1 0.0000 0.989 1.000 0.000 0.000 0.00
#> GSM372364 1 0.0000 0.989 1.000 0.000 0.000 0.00
#> GSM372365 1 0.0000 0.989 1.000 0.000 0.000 0.00
#> GSM372366 1 0.0000 0.989 1.000 0.000 0.000 0.00
#> GSM372367 1 0.0000 0.989 1.000 0.000 0.000 0.00
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM372286 2 0.0000 0.8131 0.000 1.000 0.000 0.000 0.000
#> GSM372287 2 0.2719 0.7840 0.000 0.852 0.000 0.004 0.144
#> GSM372288 2 0.2719 0.7840 0.000 0.852 0.000 0.004 0.144
#> GSM372289 2 0.2719 0.7840 0.000 0.852 0.000 0.004 0.144
#> GSM372290 2 0.0162 0.8128 0.000 0.996 0.004 0.000 0.000
#> GSM372291 4 0.0000 0.9250 0.000 0.000 0.000 1.000 0.000
#> GSM372292 3 0.5530 0.3504 0.000 0.368 0.556 0.000 0.076
#> GSM372293 3 0.3177 0.7907 0.000 0.000 0.792 0.000 0.208
#> GSM372294 4 0.0000 0.9250 0.000 0.000 0.000 1.000 0.000
#> GSM372295 4 0.0162 0.9235 0.000 0.000 0.000 0.996 0.004
#> GSM372296 2 0.2719 0.7840 0.000 0.852 0.000 0.004 0.144
#> GSM372297 2 0.2719 0.7840 0.000 0.852 0.000 0.004 0.144
#> GSM372298 2 0.4235 0.5338 0.000 0.656 0.336 0.000 0.008
#> GSM372299 3 0.2304 0.7614 0.008 0.100 0.892 0.000 0.000
#> GSM372300 3 0.3177 0.7907 0.000 0.000 0.792 0.000 0.208
#> GSM372301 3 0.3455 0.7901 0.000 0.008 0.784 0.000 0.208
#> GSM372302 2 0.2719 0.7840 0.000 0.852 0.000 0.004 0.144
#> GSM372303 3 0.3177 0.7907 0.000 0.000 0.792 0.000 0.208
#> GSM372304 2 0.2719 0.7840 0.000 0.852 0.000 0.004 0.144
#> GSM372305 2 0.0000 0.8131 0.000 1.000 0.000 0.000 0.000
#> GSM372306 3 0.3210 0.6300 0.000 0.212 0.788 0.000 0.000
#> GSM372307 2 0.2719 0.7840 0.000 0.852 0.000 0.004 0.144
#> GSM372309 3 0.3913 0.4577 0.000 0.324 0.676 0.000 0.000
#> GSM372311 2 0.0162 0.8128 0.000 0.996 0.004 0.000 0.000
#> GSM372313 2 0.3999 0.5368 0.000 0.656 0.344 0.000 0.000
#> GSM372315 2 0.1732 0.7858 0.000 0.920 0.080 0.000 0.000
#> GSM372317 2 0.4045 0.5152 0.000 0.644 0.356 0.000 0.000
#> GSM372319 2 0.1410 0.7953 0.000 0.940 0.060 0.000 0.000
#> GSM372321 2 0.1732 0.7935 0.000 0.920 0.080 0.000 0.000
#> GSM372323 3 0.2966 0.7948 0.000 0.000 0.816 0.000 0.184
#> GSM372326 3 0.3177 0.7907 0.000 0.000 0.792 0.000 0.208
#> GSM372328 3 0.3333 0.7907 0.000 0.004 0.788 0.000 0.208
#> GSM372330 2 0.4074 0.4982 0.000 0.636 0.364 0.000 0.000
#> GSM372332 3 0.3687 0.6727 0.180 0.028 0.792 0.000 0.000
#> GSM372335 3 0.0963 0.7991 0.000 0.036 0.964 0.000 0.000
#> GSM372337 3 0.0609 0.8044 0.000 0.000 0.980 0.000 0.020
#> GSM372339 3 0.3177 0.7907 0.000 0.000 0.792 0.000 0.208
#> GSM372341 3 0.3177 0.7907 0.000 0.000 0.792 0.000 0.208
#> GSM372343 3 0.3177 0.7907 0.000 0.000 0.792 0.000 0.208
#> GSM372345 3 0.1270 0.8049 0.000 0.000 0.948 0.000 0.052
#> GSM372347 3 0.0794 0.8004 0.000 0.028 0.972 0.000 0.000
#> GSM372349 4 0.7598 0.5212 0.004 0.164 0.160 0.532 0.140
#> GSM372351 3 0.1341 0.7890 0.000 0.056 0.944 0.000 0.000
#> GSM372353 3 0.0880 0.7998 0.000 0.032 0.968 0.000 0.000
#> GSM372355 2 0.4030 0.5229 0.000 0.648 0.352 0.000 0.000
#> GSM372357 3 0.0963 0.7992 0.000 0.036 0.964 0.000 0.000
#> GSM372359 3 0.0880 0.7998 0.000 0.032 0.968 0.000 0.000
#> GSM372361 2 0.0000 0.8131 0.000 1.000 0.000 0.000 0.000
#> GSM372363 2 0.0000 0.8131 0.000 1.000 0.000 0.000 0.000
#> GSM372308 1 0.0000 0.7344 1.000 0.000 0.000 0.000 0.000
#> GSM372310 1 0.0000 0.7344 1.000 0.000 0.000 0.000 0.000
#> GSM372312 4 0.0000 0.9250 0.000 0.000 0.000 1.000 0.000
#> GSM372314 1 0.0000 0.7344 1.000 0.000 0.000 0.000 0.000
#> GSM372316 1 0.4138 -0.0198 0.616 0.000 0.000 0.000 0.384
#> GSM372318 5 0.4249 0.8229 0.432 0.000 0.000 0.000 0.568
#> GSM372320 5 0.4030 0.9620 0.352 0.000 0.000 0.000 0.648
#> GSM372322 5 0.4030 0.9620 0.352 0.000 0.000 0.000 0.648
#> GSM372324 1 0.1478 0.6807 0.936 0.000 0.000 0.000 0.064
#> GSM372325 1 0.0963 0.7111 0.964 0.000 0.000 0.000 0.036
#> GSM372327 5 0.4030 0.9620 0.352 0.000 0.000 0.000 0.648
#> GSM372329 1 0.3913 0.3047 0.676 0.000 0.000 0.000 0.324
#> GSM372331 1 0.0000 0.7344 1.000 0.000 0.000 0.000 0.000
#> GSM372333 1 0.0880 0.7143 0.968 0.000 0.000 0.000 0.032
#> GSM372334 5 0.4030 0.9620 0.352 0.000 0.000 0.000 0.648
#> GSM372336 1 0.2605 0.6419 0.852 0.000 0.000 0.000 0.148
#> GSM372338 5 0.4030 0.9620 0.352 0.000 0.000 0.000 0.648
#> GSM372340 5 0.4030 0.9620 0.352 0.000 0.000 0.000 0.648
#> GSM372342 1 0.4030 0.1771 0.648 0.000 0.000 0.000 0.352
#> GSM372344 5 0.4088 0.9426 0.368 0.000 0.000 0.000 0.632
#> GSM372346 5 0.4030 0.9620 0.352 0.000 0.000 0.000 0.648
#> GSM372348 1 0.3774 0.3905 0.704 0.000 0.000 0.000 0.296
#> GSM372350 4 0.0000 0.9250 0.000 0.000 0.000 1.000 0.000
#> GSM372352 3 0.6097 0.5350 0.180 0.144 0.644 0.000 0.032
#> GSM372354 5 0.4210 0.8675 0.412 0.000 0.000 0.000 0.588
#> GSM372356 1 0.0000 0.7344 1.000 0.000 0.000 0.000 0.000
#> GSM372358 1 0.2074 0.6906 0.896 0.000 0.000 0.000 0.104
#> GSM372360 1 0.3752 0.4018 0.708 0.000 0.000 0.000 0.292
#> GSM372362 1 0.3816 0.3701 0.696 0.000 0.000 0.000 0.304
#> GSM372364 1 0.1965 0.6961 0.904 0.000 0.000 0.000 0.096
#> GSM372365 1 0.0000 0.7344 1.000 0.000 0.000 0.000 0.000
#> GSM372366 1 0.3913 0.3047 0.676 0.000 0.000 0.000 0.324
#> GSM372367 1 0.0000 0.7344 1.000 0.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM372286 4 0.3050 0.8090 0.000 0.236 0.000 0.764 0.000 0.000
#> GSM372287 4 0.0000 0.8570 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM372288 4 0.0000 0.8570 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM372289 4 0.0000 0.8570 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM372290 4 0.2996 0.8131 0.000 0.228 0.000 0.772 0.000 0.000
#> GSM372291 6 0.0000 0.9434 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM372292 2 0.2260 0.8065 0.000 0.860 0.140 0.000 0.000 0.000
#> GSM372293 3 0.0000 0.9425 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372294 6 0.0000 0.9434 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM372295 6 0.0000 0.9434 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM372296 4 0.0000 0.8570 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM372297 4 0.0000 0.8570 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM372298 2 0.2450 0.7304 0.000 0.868 0.016 0.116 0.000 0.000
#> GSM372299 2 0.2762 0.7744 0.000 0.804 0.196 0.000 0.000 0.000
#> GSM372300 3 0.0000 0.9425 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372301 3 0.1267 0.9005 0.000 0.060 0.940 0.000 0.000 0.000
#> GSM372302 4 0.0000 0.8570 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM372303 3 0.0000 0.9425 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372304 4 0.0000 0.8570 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM372305 4 0.3050 0.8050 0.000 0.236 0.000 0.764 0.000 0.000
#> GSM372306 2 0.0790 0.8176 0.000 0.968 0.032 0.000 0.000 0.000
#> GSM372307 4 0.0000 0.8570 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM372309 2 0.0547 0.8170 0.000 0.980 0.020 0.000 0.000 0.000
#> GSM372311 4 0.2969 0.8162 0.000 0.224 0.000 0.776 0.000 0.000
#> GSM372313 2 0.1610 0.7494 0.000 0.916 0.000 0.084 0.000 0.000
#> GSM372315 4 0.3464 0.7184 0.000 0.312 0.000 0.688 0.000 0.000
#> GSM372317 2 0.0146 0.8108 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM372319 2 0.3797 0.0616 0.000 0.580 0.000 0.420 0.000 0.000
#> GSM372321 2 0.3515 0.3782 0.000 0.676 0.000 0.324 0.000 0.000
#> GSM372323 3 0.1141 0.9452 0.000 0.052 0.948 0.000 0.000 0.000
#> GSM372326 3 0.0790 0.9494 0.000 0.032 0.968 0.000 0.000 0.000
#> GSM372328 3 0.1610 0.9272 0.000 0.084 0.916 0.000 0.000 0.000
#> GSM372330 2 0.0363 0.8146 0.000 0.988 0.012 0.000 0.000 0.000
#> GSM372332 3 0.2905 0.8889 0.000 0.084 0.852 0.000 0.064 0.000
#> GSM372335 2 0.2454 0.7879 0.000 0.840 0.160 0.000 0.000 0.000
#> GSM372337 3 0.1556 0.9321 0.000 0.080 0.920 0.000 0.000 0.000
#> GSM372339 3 0.0713 0.9497 0.000 0.028 0.972 0.000 0.000 0.000
#> GSM372341 3 0.0547 0.9488 0.000 0.020 0.980 0.000 0.000 0.000
#> GSM372343 3 0.0000 0.9425 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM372345 3 0.1556 0.9321 0.000 0.080 0.920 0.000 0.000 0.000
#> GSM372347 3 0.1765 0.9188 0.000 0.096 0.904 0.000 0.000 0.000
#> GSM372349 6 0.4102 0.6776 0.000 0.000 0.216 0.028 0.020 0.736
#> GSM372351 2 0.2378 0.8016 0.000 0.848 0.152 0.000 0.000 0.000
#> GSM372353 2 0.2631 0.7861 0.000 0.820 0.180 0.000 0.000 0.000
#> GSM372355 2 0.0260 0.8130 0.000 0.992 0.008 0.000 0.000 0.000
#> GSM372357 2 0.1957 0.8076 0.000 0.888 0.112 0.000 0.000 0.000
#> GSM372359 2 0.2597 0.7886 0.000 0.824 0.176 0.000 0.000 0.000
#> GSM372361 4 0.2969 0.8162 0.000 0.224 0.000 0.776 0.000 0.000
#> GSM372363 4 0.2941 0.8180 0.000 0.220 0.000 0.780 0.000 0.000
#> GSM372308 5 0.0363 0.9053 0.012 0.000 0.000 0.000 0.988 0.000
#> GSM372310 5 0.0363 0.9053 0.012 0.000 0.000 0.000 0.988 0.000
#> GSM372312 6 0.0000 0.9434 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM372314 5 0.0363 0.9053 0.012 0.000 0.000 0.000 0.988 0.000
#> GSM372316 5 0.3309 0.7130 0.280 0.000 0.000 0.000 0.720 0.000
#> GSM372318 1 0.3737 0.1652 0.608 0.000 0.000 0.000 0.392 0.000
#> GSM372320 1 0.0000 0.9279 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372322 1 0.0000 0.9279 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372324 5 0.0458 0.9060 0.016 0.000 0.000 0.000 0.984 0.000
#> GSM372325 5 0.0363 0.9053 0.012 0.000 0.000 0.000 0.988 0.000
#> GSM372327 1 0.0260 0.9199 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM372329 5 0.2378 0.8596 0.152 0.000 0.000 0.000 0.848 0.000
#> GSM372331 5 0.0363 0.9053 0.012 0.000 0.000 0.000 0.988 0.000
#> GSM372333 5 0.0363 0.9053 0.012 0.000 0.000 0.000 0.988 0.000
#> GSM372334 1 0.0000 0.9279 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372336 5 0.1610 0.8923 0.084 0.000 0.000 0.000 0.916 0.000
#> GSM372338 1 0.0000 0.9279 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372340 1 0.0000 0.9279 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372342 5 0.3175 0.7290 0.256 0.000 0.000 0.000 0.744 0.000
#> GSM372344 1 0.0000 0.9279 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372346 1 0.0000 0.9279 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372348 5 0.2300 0.8653 0.144 0.000 0.000 0.000 0.856 0.000
#> GSM372350 6 0.0000 0.9434 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM372352 2 0.4911 0.2020 0.000 0.524 0.412 0.000 0.064 0.000
#> GSM372354 5 0.3804 0.3643 0.424 0.000 0.000 0.000 0.576 0.000
#> GSM372356 5 0.0146 0.9022 0.004 0.000 0.000 0.000 0.996 0.000
#> GSM372358 5 0.1007 0.9012 0.044 0.000 0.000 0.000 0.956 0.000
#> GSM372360 5 0.1957 0.8770 0.112 0.000 0.000 0.000 0.888 0.000
#> GSM372362 5 0.1957 0.8770 0.112 0.000 0.000 0.000 0.888 0.000
#> GSM372364 5 0.0632 0.9035 0.024 0.000 0.000 0.000 0.976 0.000
#> GSM372365 5 0.0146 0.9022 0.004 0.000 0.000 0.000 0.996 0.000
#> GSM372366 5 0.2416 0.8568 0.156 0.000 0.000 0.000 0.844 0.000
#> GSM372367 5 0.0458 0.9058 0.016 0.000 0.000 0.000 0.984 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) specimen(p) individual(p) k
#> ATC:mclust 82 0.000161 5.58e-16 0.998 2
#> ATC:mclust 74 0.001995 1.61e-14 0.767 3
#> ATC:mclust 81 0.000215 1.09e-14 0.489 4
#> ATC:mclust 72 0.002248 1.43e-11 0.617 5
#> ATC:mclust 77 0.000235 1.52e-13 0.503 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 51941 rows and 82 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.949 0.943 0.976 0.5014 0.499 0.499
#> 3 3 0.848 0.862 0.937 0.3054 0.755 0.552
#> 4 4 0.863 0.872 0.925 0.0958 0.845 0.609
#> 5 5 0.831 0.804 0.892 0.0531 0.932 0.773
#> 6 6 0.803 0.778 0.859 0.0551 0.927 0.718
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
#> GSM372286 2 0.0000 0.969 0.000 1.000
#> GSM372287 2 0.0000 0.969 0.000 1.000
#> GSM372288 2 0.0000 0.969 0.000 1.000
#> GSM372289 2 0.0000 0.969 0.000 1.000
#> GSM372290 2 0.0000 0.969 0.000 1.000
#> GSM372291 1 0.0000 0.982 1.000 0.000
#> GSM372292 2 0.0000 0.969 0.000 1.000
#> GSM372293 2 0.0000 0.969 0.000 1.000
#> GSM372294 2 0.0000 0.969 0.000 1.000
#> GSM372295 2 0.0000 0.969 0.000 1.000
#> GSM372296 2 0.0000 0.969 0.000 1.000
#> GSM372297 2 0.0000 0.969 0.000 1.000
#> GSM372298 2 0.0000 0.969 0.000 1.000
#> GSM372299 2 0.9896 0.239 0.440 0.560
#> GSM372300 1 0.9710 0.295 0.600 0.400
#> GSM372301 2 0.0000 0.969 0.000 1.000
#> GSM372302 2 0.0000 0.969 0.000 1.000
#> GSM372303 2 0.6343 0.814 0.160 0.840
#> GSM372304 2 0.0000 0.969 0.000 1.000
#> GSM372305 2 0.0000 0.969 0.000 1.000
#> GSM372306 2 0.0000 0.969 0.000 1.000
#> GSM372307 2 0.0000 0.969 0.000 1.000
#> GSM372309 2 0.0000 0.969 0.000 1.000
#> GSM372311 2 0.0000 0.969 0.000 1.000
#> GSM372313 2 0.0000 0.969 0.000 1.000
#> GSM372315 2 0.0000 0.969 0.000 1.000
#> GSM372317 2 0.0000 0.969 0.000 1.000
#> GSM372319 2 0.0000 0.969 0.000 1.000
#> GSM372321 2 0.0000 0.969 0.000 1.000
#> GSM372323 2 0.0000 0.969 0.000 1.000
#> GSM372326 2 0.0000 0.969 0.000 1.000
#> GSM372328 2 0.0000 0.969 0.000 1.000
#> GSM372330 2 0.0000 0.969 0.000 1.000
#> GSM372332 1 0.0000 0.982 1.000 0.000
#> GSM372335 2 0.0000 0.969 0.000 1.000
#> GSM372337 2 0.2603 0.934 0.044 0.956
#> GSM372339 2 0.0000 0.969 0.000 1.000
#> GSM372341 2 0.4022 0.902 0.080 0.920
#> GSM372343 2 0.0000 0.969 0.000 1.000
#> GSM372345 2 0.7376 0.749 0.208 0.792
#> GSM372347 1 0.7528 0.707 0.784 0.216
#> GSM372349 2 0.8144 0.679 0.252 0.748
#> GSM372351 2 0.0000 0.969 0.000 1.000
#> GSM372353 2 0.5408 0.856 0.124 0.876
#> GSM372355 2 0.0000 0.969 0.000 1.000
#> GSM372357 2 0.0000 0.969 0.000 1.000
#> GSM372359 2 0.0000 0.969 0.000 1.000
#> GSM372361 2 0.0000 0.969 0.000 1.000
#> GSM372363 2 0.0000 0.969 0.000 1.000
#> GSM372308 1 0.0000 0.982 1.000 0.000
#> GSM372310 1 0.0000 0.982 1.000 0.000
#> GSM372312 1 0.0000 0.982 1.000 0.000
#> GSM372314 1 0.0000 0.982 1.000 0.000
#> GSM372316 1 0.0000 0.982 1.000 0.000
#> GSM372318 1 0.0000 0.982 1.000 0.000
#> GSM372320 1 0.0000 0.982 1.000 0.000
#> GSM372322 1 0.0000 0.982 1.000 0.000
#> GSM372324 1 0.0000 0.982 1.000 0.000
#> GSM372325 1 0.0000 0.982 1.000 0.000
#> GSM372327 1 0.0000 0.982 1.000 0.000
#> GSM372329 1 0.0000 0.982 1.000 0.000
#> GSM372331 1 0.0000 0.982 1.000 0.000
#> GSM372333 1 0.0000 0.982 1.000 0.000
#> GSM372334 1 0.0000 0.982 1.000 0.000
#> GSM372336 1 0.0000 0.982 1.000 0.000
#> GSM372338 1 0.0000 0.982 1.000 0.000
#> GSM372340 1 0.0000 0.982 1.000 0.000
#> GSM372342 1 0.0000 0.982 1.000 0.000
#> GSM372344 1 0.0000 0.982 1.000 0.000
#> GSM372346 1 0.0000 0.982 1.000 0.000
#> GSM372348 1 0.0000 0.982 1.000 0.000
#> GSM372350 1 0.0000 0.982 1.000 0.000
#> GSM372352 1 0.0938 0.970 0.988 0.012
#> GSM372354 1 0.0000 0.982 1.000 0.000
#> GSM372356 1 0.0000 0.982 1.000 0.000
#> GSM372358 1 0.0000 0.982 1.000 0.000
#> GSM372360 1 0.0000 0.982 1.000 0.000
#> GSM372362 1 0.0000 0.982 1.000 0.000
#> GSM372364 1 0.0000 0.982 1.000 0.000
#> GSM372365 1 0.0000 0.982 1.000 0.000
#> GSM372366 1 0.0000 0.982 1.000 0.000
#> GSM372367 1 0.0000 0.982 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM372286 2 0.0237 0.908 0.000 0.996 0.004
#> GSM372287 2 0.0237 0.908 0.000 0.996 0.004
#> GSM372288 2 0.0237 0.908 0.000 0.996 0.004
#> GSM372289 2 0.0237 0.908 0.000 0.996 0.004
#> GSM372290 2 0.0237 0.908 0.000 0.996 0.004
#> GSM372291 3 0.2261 0.862 0.068 0.000 0.932
#> GSM372292 2 0.5621 0.633 0.000 0.692 0.308
#> GSM372293 3 0.0592 0.886 0.000 0.012 0.988
#> GSM372294 3 0.4605 0.730 0.000 0.204 0.796
#> GSM372295 3 0.4504 0.739 0.000 0.196 0.804
#> GSM372296 2 0.0424 0.906 0.000 0.992 0.008
#> GSM372297 2 0.0237 0.908 0.000 0.996 0.004
#> GSM372298 2 0.1643 0.890 0.000 0.956 0.044
#> GSM372299 1 0.6758 0.625 0.728 0.072 0.200
#> GSM372300 3 0.0237 0.889 0.004 0.000 0.996
#> GSM372301 3 0.5835 0.336 0.000 0.340 0.660
#> GSM372302 2 0.4178 0.772 0.000 0.828 0.172
#> GSM372303 3 0.0000 0.889 0.000 0.000 1.000
#> GSM372304 2 0.0237 0.908 0.000 0.996 0.004
#> GSM372305 2 0.0000 0.907 0.000 1.000 0.000
#> GSM372306 2 0.0237 0.907 0.000 0.996 0.004
#> GSM372307 2 0.0237 0.908 0.000 0.996 0.004
#> GSM372309 2 0.0592 0.904 0.000 0.988 0.012
#> GSM372311 2 0.0237 0.908 0.000 0.996 0.004
#> GSM372313 2 0.0000 0.907 0.000 1.000 0.000
#> GSM372315 2 0.0237 0.908 0.000 0.996 0.004
#> GSM372317 2 0.0237 0.907 0.000 0.996 0.004
#> GSM372319 2 0.0237 0.908 0.000 0.996 0.004
#> GSM372321 2 0.0237 0.908 0.000 0.996 0.004
#> GSM372323 2 0.6062 0.498 0.000 0.616 0.384
#> GSM372326 2 0.6045 0.507 0.000 0.620 0.380
#> GSM372328 2 0.5948 0.547 0.000 0.640 0.360
#> GSM372330 2 0.2448 0.867 0.000 0.924 0.076
#> GSM372332 3 0.2165 0.866 0.064 0.000 0.936
#> GSM372335 2 0.3482 0.829 0.000 0.872 0.128
#> GSM372337 3 0.0592 0.887 0.000 0.012 0.988
#> GSM372339 3 0.0237 0.889 0.000 0.004 0.996
#> GSM372341 3 0.0000 0.889 0.000 0.000 1.000
#> GSM372343 3 0.1753 0.861 0.000 0.048 0.952
#> GSM372345 3 0.0237 0.889 0.004 0.000 0.996
#> GSM372347 2 0.8581 0.142 0.096 0.460 0.444
#> GSM372349 3 0.0592 0.888 0.000 0.012 0.988
#> GSM372351 2 0.4346 0.777 0.000 0.816 0.184
#> GSM372353 1 0.8271 0.153 0.520 0.400 0.080
#> GSM372355 2 0.0000 0.907 0.000 1.000 0.000
#> GSM372357 2 0.0237 0.907 0.000 0.996 0.004
#> GSM372359 2 0.3816 0.813 0.000 0.852 0.148
#> GSM372361 2 0.0000 0.907 0.000 1.000 0.000
#> GSM372363 2 0.0000 0.907 0.000 1.000 0.000
#> GSM372308 1 0.0000 0.970 1.000 0.000 0.000
#> GSM372310 1 0.0000 0.970 1.000 0.000 0.000
#> GSM372312 3 0.5948 0.439 0.360 0.000 0.640
#> GSM372314 1 0.0000 0.970 1.000 0.000 0.000
#> GSM372316 1 0.0000 0.970 1.000 0.000 0.000
#> GSM372318 1 0.0000 0.970 1.000 0.000 0.000
#> GSM372320 1 0.1163 0.947 0.972 0.000 0.028
#> GSM372322 1 0.0000 0.970 1.000 0.000 0.000
#> GSM372324 1 0.0000 0.970 1.000 0.000 0.000
#> GSM372325 1 0.0237 0.967 0.996 0.000 0.004
#> GSM372327 1 0.0000 0.970 1.000 0.000 0.000
#> GSM372329 1 0.0000 0.970 1.000 0.000 0.000
#> GSM372331 1 0.0237 0.967 0.996 0.004 0.000
#> GSM372333 1 0.0000 0.970 1.000 0.000 0.000
#> GSM372334 1 0.0592 0.961 0.988 0.000 0.012
#> GSM372336 1 0.0000 0.970 1.000 0.000 0.000
#> GSM372338 1 0.0747 0.958 0.984 0.000 0.016
#> GSM372340 1 0.0000 0.970 1.000 0.000 0.000
#> GSM372342 1 0.0000 0.970 1.000 0.000 0.000
#> GSM372344 1 0.0747 0.958 0.984 0.000 0.016
#> GSM372346 1 0.0000 0.970 1.000 0.000 0.000
#> GSM372348 1 0.0000 0.970 1.000 0.000 0.000
#> GSM372350 3 0.4121 0.773 0.168 0.000 0.832
#> GSM372352 3 0.0592 0.888 0.012 0.000 0.988
#> GSM372354 1 0.0000 0.970 1.000 0.000 0.000
#> GSM372356 1 0.0000 0.970 1.000 0.000 0.000
#> GSM372358 1 0.0000 0.970 1.000 0.000 0.000
#> GSM372360 1 0.0000 0.970 1.000 0.000 0.000
#> GSM372362 1 0.0000 0.970 1.000 0.000 0.000
#> GSM372364 1 0.0000 0.970 1.000 0.000 0.000
#> GSM372365 1 0.0000 0.970 1.000 0.000 0.000
#> GSM372366 1 0.0000 0.970 1.000 0.000 0.000
#> GSM372367 1 0.0000 0.970 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM372286 2 0.0000 0.927 0.000 1.000 0.000 0.000
#> GSM372287 2 0.0000 0.927 0.000 1.000 0.000 0.000
#> GSM372288 2 0.0000 0.927 0.000 1.000 0.000 0.000
#> GSM372289 2 0.0000 0.927 0.000 1.000 0.000 0.000
#> GSM372290 2 0.0000 0.927 0.000 1.000 0.000 0.000
#> GSM372291 4 0.2300 0.894 0.028 0.000 0.048 0.924
#> GSM372292 3 0.3552 0.840 0.000 0.128 0.848 0.024
#> GSM372293 3 0.1867 0.847 0.000 0.000 0.928 0.072
#> GSM372294 4 0.3004 0.879 0.000 0.060 0.048 0.892
#> GSM372295 4 0.3110 0.889 0.004 0.048 0.056 0.892
#> GSM372296 2 0.3946 0.740 0.000 0.812 0.020 0.168
#> GSM372297 2 0.0921 0.910 0.000 0.972 0.000 0.028
#> GSM372298 2 0.1022 0.906 0.000 0.968 0.032 0.000
#> GSM372299 1 0.6726 0.481 0.636 0.032 0.264 0.068
#> GSM372300 3 0.2281 0.834 0.000 0.000 0.904 0.096
#> GSM372301 3 0.2859 0.823 0.000 0.008 0.880 0.112
#> GSM372302 2 0.5472 0.518 0.000 0.676 0.044 0.280
#> GSM372303 3 0.4072 0.660 0.000 0.000 0.748 0.252
#> GSM372304 2 0.1022 0.906 0.000 0.968 0.000 0.032
#> GSM372305 2 0.0336 0.925 0.000 0.992 0.008 0.000
#> GSM372306 3 0.3726 0.783 0.000 0.212 0.788 0.000
#> GSM372307 2 0.0000 0.927 0.000 1.000 0.000 0.000
#> GSM372309 3 0.3710 0.799 0.000 0.192 0.804 0.004
#> GSM372311 2 0.0000 0.927 0.000 1.000 0.000 0.000
#> GSM372313 2 0.0707 0.919 0.000 0.980 0.020 0.000
#> GSM372315 2 0.0000 0.927 0.000 1.000 0.000 0.000
#> GSM372317 3 0.4343 0.734 0.000 0.264 0.732 0.004
#> GSM372319 2 0.0592 0.921 0.000 0.984 0.016 0.000
#> GSM372321 2 0.5163 -0.184 0.000 0.516 0.480 0.004
#> GSM372323 3 0.0707 0.855 0.000 0.000 0.980 0.020
#> GSM372326 3 0.0524 0.859 0.000 0.004 0.988 0.008
#> GSM372328 3 0.1854 0.862 0.000 0.048 0.940 0.012
#> GSM372330 3 0.4072 0.752 0.000 0.252 0.748 0.000
#> GSM372332 3 0.3751 0.755 0.004 0.000 0.800 0.196
#> GSM372335 3 0.2408 0.848 0.000 0.104 0.896 0.000
#> GSM372337 3 0.1302 0.855 0.000 0.000 0.956 0.044
#> GSM372339 3 0.1637 0.853 0.000 0.000 0.940 0.060
#> GSM372341 3 0.1716 0.851 0.000 0.000 0.936 0.064
#> GSM372343 3 0.1118 0.856 0.000 0.000 0.964 0.036
#> GSM372345 3 0.1118 0.856 0.000 0.000 0.964 0.036
#> GSM372347 3 0.2124 0.841 0.008 0.000 0.924 0.068
#> GSM372349 4 0.2704 0.871 0.000 0.000 0.124 0.876
#> GSM372351 3 0.2814 0.835 0.000 0.132 0.868 0.000
#> GSM372353 3 0.3953 0.815 0.040 0.028 0.860 0.072
#> GSM372355 2 0.0592 0.921 0.000 0.984 0.016 0.000
#> GSM372357 3 0.4937 0.605 0.004 0.332 0.660 0.004
#> GSM372359 3 0.4191 0.824 0.024 0.060 0.848 0.068
#> GSM372361 2 0.0000 0.927 0.000 1.000 0.000 0.000
#> GSM372363 2 0.0336 0.925 0.000 0.992 0.008 0.000
#> GSM372308 1 0.0336 0.966 0.992 0.000 0.000 0.008
#> GSM372310 1 0.0188 0.965 0.996 0.000 0.000 0.004
#> GSM372312 4 0.3688 0.735 0.208 0.000 0.000 0.792
#> GSM372314 1 0.1398 0.947 0.956 0.000 0.004 0.040
#> GSM372316 1 0.0469 0.966 0.988 0.000 0.000 0.012
#> GSM372318 1 0.0707 0.965 0.980 0.000 0.000 0.020
#> GSM372320 1 0.1022 0.959 0.968 0.000 0.000 0.032
#> GSM372322 1 0.0707 0.965 0.980 0.000 0.000 0.020
#> GSM372324 1 0.1256 0.953 0.964 0.000 0.008 0.028
#> GSM372325 1 0.1256 0.953 0.964 0.000 0.008 0.028
#> GSM372327 1 0.0592 0.966 0.984 0.000 0.000 0.016
#> GSM372329 1 0.0707 0.965 0.980 0.000 0.000 0.020
#> GSM372331 1 0.0592 0.966 0.984 0.000 0.000 0.016
#> GSM372333 1 0.2048 0.925 0.928 0.000 0.008 0.064
#> GSM372334 1 0.0921 0.961 0.972 0.000 0.000 0.028
#> GSM372336 1 0.0469 0.966 0.988 0.000 0.000 0.012
#> GSM372338 1 0.1022 0.959 0.968 0.000 0.000 0.032
#> GSM372340 1 0.0707 0.965 0.980 0.000 0.000 0.020
#> GSM372342 1 0.0188 0.966 0.996 0.000 0.000 0.004
#> GSM372344 1 0.1118 0.957 0.964 0.000 0.000 0.036
#> GSM372346 1 0.0592 0.966 0.984 0.000 0.000 0.016
#> GSM372348 1 0.0707 0.965 0.980 0.000 0.000 0.020
#> GSM372350 4 0.2222 0.881 0.060 0.000 0.016 0.924
#> GSM372352 4 0.3105 0.858 0.004 0.000 0.140 0.856
#> GSM372354 1 0.0336 0.964 0.992 0.000 0.000 0.008
#> GSM372356 1 0.1118 0.953 0.964 0.000 0.000 0.036
#> GSM372358 1 0.0817 0.959 0.976 0.000 0.000 0.024
#> GSM372360 1 0.0336 0.964 0.992 0.000 0.000 0.008
#> GSM372362 1 0.0336 0.964 0.992 0.000 0.000 0.008
#> GSM372364 1 0.0921 0.957 0.972 0.000 0.000 0.028
#> GSM372365 1 0.0921 0.957 0.972 0.000 0.000 0.028
#> GSM372366 1 0.0592 0.966 0.984 0.000 0.000 0.016
#> GSM372367 1 0.0469 0.963 0.988 0.000 0.000 0.012
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM372286 2 0.0000 0.8544 0.000 1.000 0.000 0.000 0.000
#> GSM372287 2 0.0000 0.8544 0.000 1.000 0.000 0.000 0.000
#> GSM372288 2 0.0000 0.8544 0.000 1.000 0.000 0.000 0.000
#> GSM372289 2 0.0000 0.8544 0.000 1.000 0.000 0.000 0.000
#> GSM372290 2 0.0000 0.8544 0.000 1.000 0.000 0.000 0.000
#> GSM372291 5 0.3650 0.7091 0.028 0.000 0.000 0.176 0.796
#> GSM372292 4 0.5633 0.6905 0.000 0.232 0.096 0.656 0.016
#> GSM372293 4 0.4634 0.7277 0.000 0.004 0.100 0.752 0.144
#> GSM372294 5 0.2879 0.7951 0.000 0.080 0.032 0.008 0.880
#> GSM372295 5 0.1924 0.8316 0.000 0.008 0.064 0.004 0.924
#> GSM372296 2 0.2722 0.7689 0.000 0.868 0.004 0.008 0.120
#> GSM372297 2 0.3370 0.7121 0.000 0.824 0.000 0.148 0.028
#> GSM372298 4 0.4552 0.5315 0.000 0.352 0.012 0.632 0.004
#> GSM372299 4 0.4171 0.6549 0.108 0.072 0.016 0.804 0.000
#> GSM372300 4 0.3627 0.7511 0.000 0.008 0.064 0.836 0.092
#> GSM372301 4 0.4894 0.7652 0.000 0.076 0.052 0.768 0.104
#> GSM372302 2 0.5025 0.5945 0.000 0.724 0.008 0.116 0.152
#> GSM372303 4 0.3988 0.6985 0.000 0.000 0.036 0.768 0.196
#> GSM372304 2 0.2597 0.7764 0.000 0.884 0.000 0.092 0.024
#> GSM372305 2 0.1952 0.8130 0.000 0.912 0.084 0.004 0.000
#> GSM372306 3 0.2966 0.7702 0.000 0.136 0.848 0.016 0.000
#> GSM372307 2 0.0000 0.8544 0.000 1.000 0.000 0.000 0.000
#> GSM372309 3 0.3035 0.7840 0.000 0.112 0.856 0.032 0.000
#> GSM372311 2 0.0290 0.8531 0.000 0.992 0.008 0.000 0.000
#> GSM372313 2 0.2193 0.8233 0.000 0.912 0.060 0.028 0.000
#> GSM372315 2 0.0000 0.8544 0.000 1.000 0.000 0.000 0.000
#> GSM372317 3 0.2997 0.7595 0.000 0.148 0.840 0.012 0.000
#> GSM372319 2 0.4283 0.0394 0.000 0.544 0.456 0.000 0.000
#> GSM372321 3 0.3488 0.7200 0.000 0.180 0.804 0.008 0.008
#> GSM372323 3 0.0794 0.8088 0.000 0.000 0.972 0.028 0.000
#> GSM372326 3 0.1952 0.7991 0.000 0.004 0.912 0.084 0.000
#> GSM372328 3 0.2060 0.8083 0.000 0.016 0.924 0.052 0.008
#> GSM372330 2 0.6684 -0.3336 0.000 0.392 0.236 0.372 0.000
#> GSM372332 3 0.3519 0.6484 0.000 0.000 0.776 0.008 0.216
#> GSM372335 3 0.5599 0.1016 0.000 0.072 0.484 0.444 0.000
#> GSM372337 3 0.1270 0.8015 0.000 0.000 0.948 0.000 0.052
#> GSM372339 3 0.1872 0.8033 0.000 0.000 0.928 0.020 0.052
#> GSM372341 3 0.1892 0.7908 0.000 0.000 0.916 0.004 0.080
#> GSM372343 3 0.2305 0.7935 0.000 0.000 0.896 0.092 0.012
#> GSM372345 3 0.1270 0.8016 0.000 0.000 0.948 0.000 0.052
#> GSM372347 3 0.1251 0.8082 0.000 0.000 0.956 0.036 0.008
#> GSM372349 5 0.2848 0.7724 0.000 0.000 0.156 0.004 0.840
#> GSM372351 3 0.3532 0.7701 0.000 0.048 0.824 0.128 0.000
#> GSM372353 3 0.4449 0.7099 0.028 0.000 0.772 0.164 0.036
#> GSM372355 2 0.1012 0.8488 0.000 0.968 0.020 0.012 0.000
#> GSM372357 3 0.5974 0.3912 0.000 0.320 0.548 0.132 0.000
#> GSM372359 3 0.5661 0.2207 0.008 0.020 0.512 0.436 0.024
#> GSM372361 2 0.1597 0.8356 0.000 0.940 0.048 0.012 0.000
#> GSM372363 2 0.1831 0.8193 0.000 0.920 0.076 0.004 0.000
#> GSM372308 1 0.0000 0.9782 1.000 0.000 0.000 0.000 0.000
#> GSM372310 1 0.0162 0.9780 0.996 0.000 0.000 0.000 0.004
#> GSM372312 5 0.3527 0.6393 0.192 0.000 0.000 0.016 0.792
#> GSM372314 1 0.1538 0.9581 0.948 0.000 0.008 0.008 0.036
#> GSM372316 1 0.0290 0.9780 0.992 0.000 0.000 0.008 0.000
#> GSM372318 1 0.0451 0.9769 0.988 0.000 0.000 0.008 0.004
#> GSM372320 1 0.1186 0.9662 0.964 0.000 0.008 0.008 0.020
#> GSM372322 1 0.0451 0.9769 0.988 0.000 0.000 0.008 0.004
#> GSM372324 1 0.1106 0.9682 0.964 0.000 0.012 0.000 0.024
#> GSM372325 1 0.2515 0.9231 0.908 0.000 0.032 0.020 0.040
#> GSM372327 1 0.0162 0.9782 0.996 0.000 0.000 0.000 0.004
#> GSM372329 1 0.0324 0.9779 0.992 0.000 0.000 0.004 0.004
#> GSM372331 1 0.0566 0.9761 0.984 0.000 0.000 0.012 0.004
#> GSM372333 1 0.3331 0.8771 0.864 0.000 0.068 0.024 0.044
#> GSM372334 1 0.0613 0.9764 0.984 0.000 0.004 0.008 0.004
#> GSM372336 1 0.0162 0.9780 0.996 0.000 0.000 0.000 0.004
#> GSM372338 1 0.0579 0.9755 0.984 0.000 0.000 0.008 0.008
#> GSM372340 1 0.0451 0.9769 0.988 0.000 0.000 0.008 0.004
#> GSM372342 1 0.0290 0.9780 0.992 0.000 0.000 0.008 0.000
#> GSM372344 1 0.0992 0.9669 0.968 0.000 0.000 0.008 0.024
#> GSM372346 1 0.0162 0.9782 0.996 0.000 0.000 0.000 0.004
#> GSM372348 1 0.0451 0.9769 0.988 0.000 0.000 0.008 0.004
#> GSM372350 5 0.1386 0.8286 0.032 0.000 0.016 0.000 0.952
#> GSM372352 5 0.2790 0.8082 0.000 0.000 0.052 0.068 0.880
#> GSM372354 1 0.0162 0.9780 0.996 0.000 0.000 0.000 0.004
#> GSM372356 1 0.1243 0.9656 0.960 0.000 0.004 0.008 0.028
#> GSM372358 1 0.0992 0.9697 0.968 0.000 0.000 0.008 0.024
#> GSM372360 1 0.0579 0.9760 0.984 0.000 0.000 0.008 0.008
#> GSM372362 1 0.0579 0.9760 0.984 0.000 0.000 0.008 0.008
#> GSM372364 1 0.1243 0.9656 0.960 0.000 0.004 0.008 0.028
#> GSM372365 1 0.0992 0.9697 0.968 0.000 0.000 0.008 0.024
#> GSM372366 1 0.0000 0.9782 1.000 0.000 0.000 0.000 0.000
#> GSM372367 1 0.0404 0.9767 0.988 0.000 0.000 0.000 0.012
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM372286 4 0.1152 0.8286 0.000 0.044 0.000 0.952 0.004 0.000
#> GSM372287 4 0.0622 0.8382 0.000 0.008 0.000 0.980 0.012 0.000
#> GSM372288 4 0.0146 0.8385 0.000 0.000 0.004 0.996 0.000 0.000
#> GSM372289 4 0.0547 0.8380 0.000 0.020 0.000 0.980 0.000 0.000
#> GSM372290 4 0.0458 0.8388 0.000 0.000 0.016 0.984 0.000 0.000
#> GSM372291 5 0.3534 0.5876 0.008 0.000 0.000 0.000 0.716 0.276
#> GSM372292 6 0.3983 0.7180 0.000 0.000 0.056 0.208 0.000 0.736
#> GSM372293 6 0.2450 0.7896 0.000 0.012 0.064 0.004 0.024 0.896
#> GSM372294 5 0.1956 0.8513 0.000 0.032 0.008 0.016 0.928 0.016
#> GSM372295 5 0.2220 0.8492 0.004 0.008 0.016 0.012 0.916 0.044
#> GSM372296 4 0.3683 0.6908 0.000 0.000 0.004 0.784 0.160 0.052
#> GSM372297 4 0.3990 0.5246 0.000 0.000 0.000 0.688 0.028 0.284
#> GSM372298 6 0.4214 0.5491 0.000 0.004 0.012 0.320 0.008 0.656
#> GSM372299 6 0.5804 0.6843 0.072 0.092 0.040 0.088 0.008 0.700
#> GSM372300 6 0.1913 0.7913 0.000 0.016 0.044 0.000 0.016 0.924
#> GSM372301 6 0.2339 0.8051 0.000 0.004 0.036 0.028 0.024 0.908
#> GSM372302 4 0.4834 0.5180 0.000 0.000 0.000 0.660 0.128 0.212
#> GSM372303 6 0.2209 0.7683 0.000 0.004 0.024 0.000 0.072 0.900
#> GSM372304 4 0.3027 0.7199 0.000 0.000 0.000 0.824 0.028 0.148
#> GSM372305 4 0.0972 0.8345 0.000 0.028 0.008 0.964 0.000 0.000
#> GSM372306 2 0.5882 0.6037 0.000 0.584 0.220 0.164 0.000 0.032
#> GSM372307 4 0.0363 0.8387 0.000 0.000 0.012 0.988 0.000 0.000
#> GSM372309 2 0.5576 0.6510 0.000 0.660 0.152 0.148 0.016 0.024
#> GSM372311 4 0.0692 0.8379 0.000 0.000 0.020 0.976 0.000 0.004
#> GSM372313 2 0.4032 0.5099 0.000 0.696 0.004 0.280 0.012 0.008
#> GSM372315 4 0.0436 0.8394 0.000 0.004 0.004 0.988 0.000 0.004
#> GSM372317 3 0.2814 0.7395 0.000 0.008 0.820 0.172 0.000 0.000
#> GSM372319 3 0.3659 0.4770 0.000 0.000 0.636 0.364 0.000 0.000
#> GSM372321 3 0.2805 0.7273 0.000 0.004 0.812 0.184 0.000 0.000
#> GSM372323 3 0.2039 0.8198 0.000 0.020 0.904 0.000 0.000 0.076
#> GSM372326 3 0.2383 0.8103 0.000 0.024 0.880 0.000 0.000 0.096
#> GSM372328 3 0.1434 0.8291 0.000 0.000 0.940 0.012 0.000 0.048
#> GSM372330 4 0.6584 0.1674 0.000 0.208 0.064 0.508 0.000 0.220
#> GSM372332 3 0.4233 0.6883 0.004 0.056 0.768 0.000 0.148 0.024
#> GSM372335 2 0.6674 0.4175 0.000 0.496 0.144 0.072 0.004 0.284
#> GSM372337 3 0.2808 0.7894 0.000 0.048 0.868 0.000 0.076 0.008
#> GSM372339 3 0.1092 0.8267 0.000 0.000 0.960 0.000 0.020 0.020
#> GSM372341 3 0.1500 0.8156 0.000 0.000 0.936 0.000 0.052 0.012
#> GSM372343 3 0.2170 0.8147 0.000 0.012 0.888 0.000 0.000 0.100
#> GSM372345 3 0.3300 0.7683 0.000 0.076 0.840 0.000 0.068 0.016
#> GSM372347 2 0.4516 0.6322 0.000 0.704 0.220 0.000 0.012 0.064
#> GSM372349 5 0.2214 0.8389 0.000 0.012 0.092 0.000 0.892 0.004
#> GSM372351 3 0.2850 0.7991 0.000 0.016 0.856 0.016 0.000 0.112
#> GSM372353 2 0.5223 0.6043 0.016 0.664 0.192 0.000 0.004 0.124
#> GSM372355 4 0.4083 0.0105 0.000 0.460 0.008 0.532 0.000 0.000
#> GSM372357 2 0.5812 0.6268 0.000 0.640 0.116 0.152 0.000 0.092
#> GSM372359 2 0.5034 0.6090 0.012 0.700 0.100 0.016 0.000 0.172
#> GSM372361 4 0.1053 0.8364 0.000 0.020 0.012 0.964 0.004 0.000
#> GSM372363 4 0.1007 0.8278 0.000 0.000 0.044 0.956 0.000 0.000
#> GSM372308 1 0.1493 0.9461 0.936 0.056 0.000 0.000 0.004 0.004
#> GSM372310 1 0.1411 0.9466 0.936 0.060 0.000 0.000 0.000 0.004
#> GSM372312 5 0.2610 0.8431 0.036 0.020 0.048 0.000 0.892 0.004
#> GSM372314 1 0.3352 0.7798 0.776 0.208 0.008 0.000 0.000 0.008
#> GSM372316 1 0.0146 0.9604 0.996 0.004 0.000 0.000 0.000 0.000
#> GSM372318 1 0.0260 0.9599 0.992 0.008 0.000 0.000 0.000 0.000
#> GSM372320 1 0.1409 0.9460 0.948 0.032 0.000 0.000 0.012 0.008
#> GSM372322 1 0.0146 0.9604 0.996 0.004 0.000 0.000 0.000 0.000
#> GSM372324 1 0.3123 0.8544 0.824 0.152 0.012 0.000 0.004 0.008
#> GSM372325 2 0.6113 0.3461 0.144 0.576 0.044 0.000 0.232 0.004
#> GSM372327 1 0.1353 0.9528 0.952 0.024 0.012 0.000 0.000 0.012
#> GSM372329 1 0.0000 0.9605 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372331 2 0.4178 0.4461 0.292 0.680 0.000 0.004 0.016 0.008
#> GSM372333 2 0.6133 0.4542 0.156 0.628 0.088 0.000 0.116 0.012
#> GSM372334 1 0.1578 0.9399 0.936 0.048 0.000 0.000 0.012 0.004
#> GSM372336 1 0.0000 0.9605 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM372338 1 0.1194 0.9500 0.956 0.032 0.000 0.000 0.008 0.004
#> GSM372340 1 0.0458 0.9592 0.984 0.016 0.000 0.000 0.000 0.000
#> GSM372342 1 0.0260 0.9600 0.992 0.008 0.000 0.000 0.000 0.000
#> GSM372344 1 0.0692 0.9572 0.976 0.020 0.000 0.000 0.004 0.000
#> GSM372346 1 0.1007 0.9545 0.956 0.044 0.000 0.000 0.000 0.000
#> GSM372348 1 0.0260 0.9611 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM372350 5 0.1942 0.8605 0.020 0.004 0.028 0.000 0.928 0.020
#> GSM372352 5 0.3737 0.7107 0.000 0.184 0.036 0.000 0.772 0.008
#> GSM372354 1 0.0508 0.9617 0.984 0.012 0.004 0.000 0.000 0.000
#> GSM372356 1 0.1268 0.9548 0.952 0.036 0.008 0.000 0.000 0.004
#> GSM372358 1 0.1003 0.9583 0.964 0.028 0.004 0.000 0.000 0.004
#> GSM372360 1 0.0790 0.9591 0.968 0.032 0.000 0.000 0.000 0.000
#> GSM372362 1 0.0547 0.9607 0.980 0.020 0.000 0.000 0.000 0.000
#> GSM372364 1 0.1410 0.9519 0.944 0.044 0.008 0.000 0.000 0.004
#> GSM372365 1 0.1155 0.9560 0.956 0.036 0.004 0.000 0.000 0.004
#> GSM372366 1 0.0363 0.9616 0.988 0.012 0.000 0.000 0.000 0.000
#> GSM372367 1 0.1728 0.9406 0.924 0.064 0.008 0.000 0.000 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) specimen(p) individual(p) k
#> ATC:NMF 80 1.97e-04 1.23e-15 0.997 2
#> ATC:NMF 77 9.19e-04 1.50e-13 0.876 3
#> ATC:NMF 80 6.06e-05 9.14e-16 0.626 4
#> ATC:NMF 77 1.10e-08 3.37e-19 0.349 5
#> ATC:NMF 75 1.04e-08 9.09e-19 0.445 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