Date: 2019-12-25 21:25:43 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 76 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 76
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:skmeans | 4 | 1.000 | 0.980 | 0.989 | ** | 2,3 |
| CV:skmeans | 4 | 1.000 | 0.977 | 0.984 | ** | 2,3 |
| MAD:skmeans | 3 | 1.000 | 0.945 | 0.980 | ** | |
| ATC:kmeans | 2 | 1.000 | 0.989 | 0.995 | ** | |
| ATC:skmeans | 4 | 1.000 | 0.967 | 0.978 | ** | 2 |
| ATC:pam | 6 | 1.000 | 0.965 | 0.986 | ** | 2,3,5 |
| ATC:NMF | 2 | 1.000 | 0.986 | 0.994 | ** | |
| MAD:mclust | 5 | 0.979 | 0.958 | 0.977 | ** | 2,3 |
| MAD:NMF | 4 | 0.963 | 0.918 | 0.968 | ** | 2,3 |
| SD:pam | 6 | 0.959 | 0.925 | 0.954 | ** | 3,4,5 |
| SD:mclust | 5 | 0.956 | 0.875 | 0.946 | ** | 2,3 |
| CV:NMF | 5 | 0.956 | 0.908 | 0.950 | ** | 3,4 |
| CV:pam | 6 | 0.955 | 0.945 | 0.965 | ** | 2,3,4,5 |
| CV:mclust | 5 | 0.955 | 0.903 | 0.957 | ** | 2,3 |
| SD:NMF | 5 | 0.940 | 0.898 | 0.946 | * | 3,4 |
| ATC:hclust | 2 | 0.918 | 0.941 | 0.975 | * | |
| MAD:pam | 6 | 0.908 | 0.844 | 0.919 | * | 2,3,4,5 |
| CV:hclust | 6 | 0.893 | 0.816 | 0.908 | ||
| SD:hclust | 6 | 0.848 | 0.790 | 0.904 | ||
| MAD:hclust | 5 | 0.848 | 0.778 | 0.891 | ||
| MAD:kmeans | 3 | 0.728 | 0.952 | 0.916 | ||
| CV:kmeans | 3 | 0.727 | 0.963 | 0.923 | ||
| ATC:mclust | 2 | 0.647 | 0.838 | 0.904 | ||
| SD:kmeans | 2 | 0.581 | 0.857 | 0.892 |
**: 1-PAC > 0.95, *: 1-PAC > 0.9
Cumulative distribution function curves of consensus matrix for all methods.
collect_plots(res_list, fun = plot_ecdf)
Consensus heatmaps for all methods. (What is a consensus heatmap?)
collect_plots(res_list, k = 2, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 3, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 4, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 5, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 6, fun = consensus_heatmap, mc.cores = 4)
Membership heatmaps for all methods. (What is a membership heatmap?)
collect_plots(res_list, k = 2, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 3, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 4, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 5, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 6, fun = membership_heatmap, mc.cores = 4)
Signature heatmaps for all methods. (What is a signature heatmap?)
Note in following heatmaps, rows are scaled.
collect_plots(res_list, k = 2, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 3, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 4, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 5, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 6, fun = get_signatures, mc.cores = 4)
The statistics used for measuring the stability of consensus partitioning. (How are they defined?)
get_stats(res_list, k = 2)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 2 0.728 0.896 0.943 0.487 0.494 0.494
#> CV:NMF 2 0.728 0.849 0.928 0.480 0.495 0.495
#> MAD:NMF 2 0.944 0.926 0.971 0.496 0.502 0.502
#> ATC:NMF 2 1.000 0.986 0.994 0.506 0.495 0.495
#> SD:skmeans 2 0.999 0.981 0.991 0.503 0.496 0.496
#> CV:skmeans 2 1.000 0.993 0.996 0.504 0.496 0.496
#> MAD:skmeans 2 0.872 0.956 0.979 0.499 0.502 0.502
#> ATC:skmeans 2 1.000 0.981 0.993 0.500 0.499 0.499
#> SD:mclust 2 1.000 1.000 1.000 0.428 0.572 0.572
#> CV:mclust 2 1.000 1.000 1.000 0.428 0.572 0.572
#> MAD:mclust 2 1.000 1.000 1.000 0.428 0.572 0.572
#> ATC:mclust 2 0.647 0.838 0.904 0.470 0.494 0.494
#> SD:kmeans 2 0.581 0.857 0.892 0.460 0.528 0.528
#> CV:kmeans 2 0.581 0.864 0.860 0.459 0.528 0.528
#> MAD:kmeans 2 0.581 0.853 0.899 0.465 0.522 0.522
#> ATC:kmeans 2 1.000 0.989 0.995 0.489 0.511 0.511
#> SD:pam 2 0.572 0.931 0.949 0.440 0.572 0.572
#> CV:pam 2 1.000 0.974 0.979 0.433 0.572 0.572
#> MAD:pam 2 1.000 0.991 0.996 0.485 0.516 0.516
#> ATC:pam 2 0.920 0.963 0.984 0.479 0.522 0.522
#> SD:hclust 2 0.500 0.673 0.856 0.462 0.499 0.499
#> CV:hclust 2 0.541 0.713 0.885 0.464 0.499 0.499
#> MAD:hclust 2 0.534 0.771 0.900 0.475 0.494 0.494
#> ATC:hclust 2 0.918 0.941 0.975 0.484 0.522 0.522
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 1.000 0.984 0.993 0.385 0.705 0.470
#> CV:NMF 3 1.000 0.991 0.996 0.405 0.704 0.469
#> MAD:NMF 3 1.000 0.960 0.985 0.359 0.716 0.490
#> ATC:NMF 3 0.762 0.789 0.893 0.271 0.821 0.649
#> SD:skmeans 3 1.000 0.958 0.985 0.338 0.742 0.522
#> CV:skmeans 3 1.000 0.964 0.986 0.336 0.728 0.504
#> MAD:skmeans 3 1.000 0.945 0.980 0.349 0.740 0.522
#> ATC:skmeans 3 0.782 0.917 0.917 0.296 0.828 0.661
#> SD:mclust 3 1.000 0.984 0.994 0.577 0.721 0.525
#> CV:mclust 3 1.000 0.984 0.994 0.577 0.720 0.524
#> MAD:mclust 3 1.000 0.984 0.994 0.576 0.721 0.525
#> ATC:mclust 3 0.561 0.492 0.755 0.357 0.720 0.503
#> SD:kmeans 3 0.654 0.923 0.866 0.386 0.762 0.565
#> CV:kmeans 3 0.727 0.963 0.923 0.423 0.762 0.565
#> MAD:kmeans 3 0.728 0.952 0.916 0.404 0.754 0.550
#> ATC:kmeans 3 0.660 0.736 0.868 0.332 0.828 0.670
#> SD:pam 3 1.000 0.993 0.997 0.533 0.754 0.571
#> CV:pam 3 1.000 0.985 0.992 0.556 0.754 0.571
#> MAD:pam 3 1.000 0.991 0.996 0.390 0.779 0.584
#> ATC:pam 3 1.000 0.952 0.978 0.381 0.788 0.606
#> SD:hclust 3 0.546 0.827 0.814 0.375 0.696 0.462
#> CV:hclust 3 0.615 0.813 0.851 0.386 0.696 0.462
#> MAD:hclust 3 0.663 0.658 0.837 0.344 0.814 0.639
#> ATC:hclust 3 0.772 0.764 0.885 0.259 0.915 0.837
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.964 0.947 0.978 0.1055 0.890 0.681
#> CV:NMF 4 1.000 0.949 0.979 0.1036 0.890 0.681
#> MAD:NMF 4 0.963 0.918 0.968 0.1020 0.883 0.664
#> ATC:NMF 4 0.794 0.787 0.888 0.1504 0.807 0.510
#> SD:skmeans 4 1.000 0.980 0.989 0.1056 0.908 0.727
#> CV:skmeans 4 1.000 0.977 0.984 0.1061 0.897 0.698
#> MAD:skmeans 4 0.862 0.929 0.932 0.1072 0.897 0.698
#> ATC:skmeans 4 1.000 0.967 0.978 0.0971 0.933 0.806
#> SD:mclust 4 0.897 0.797 0.896 0.0862 0.939 0.814
#> CV:mclust 4 0.886 0.892 0.936 0.0757 0.938 0.813
#> MAD:mclust 4 0.870 0.856 0.913 0.0790 0.939 0.814
#> ATC:mclust 4 0.723 0.755 0.869 0.1662 0.773 0.451
#> SD:kmeans 4 0.829 0.864 0.840 0.1325 0.914 0.745
#> CV:kmeans 4 0.811 0.718 0.819 0.1090 0.936 0.807
#> MAD:kmeans 4 0.827 0.831 0.801 0.1083 0.964 0.896
#> ATC:kmeans 4 0.687 0.411 0.669 0.1184 0.876 0.688
#> SD:pam 4 1.000 0.986 0.995 0.0953 0.934 0.799
#> CV:pam 4 1.000 0.969 0.989 0.0928 0.920 0.762
#> MAD:pam 4 1.000 0.988 0.995 0.0964 0.934 0.799
#> ATC:pam 4 0.743 0.733 0.792 0.1289 0.794 0.483
#> SD:hclust 4 0.684 0.814 0.895 0.1129 0.952 0.854
#> CV:hclust 4 0.713 0.805 0.873 0.0778 0.965 0.893
#> MAD:hclust 4 0.702 0.762 0.845 0.0947 0.793 0.501
#> ATC:hclust 4 0.785 0.755 0.875 0.0274 0.974 0.942
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.940 0.898 0.946 0.0425 0.921 0.716
#> CV:NMF 5 0.956 0.908 0.950 0.0434 0.921 0.716
#> MAD:NMF 5 0.889 0.866 0.916 0.0474 0.907 0.675
#> ATC:NMF 5 0.796 0.686 0.828 0.0508 0.954 0.824
#> SD:skmeans 5 0.883 0.845 0.916 0.0608 0.931 0.737
#> CV:skmeans 5 0.893 0.839 0.918 0.0593 0.938 0.761
#> MAD:skmeans 5 0.899 0.826 0.912 0.0604 0.931 0.737
#> ATC:skmeans 5 0.878 0.924 0.875 0.0774 0.924 0.735
#> SD:mclust 5 0.956 0.875 0.946 0.0621 0.907 0.686
#> CV:mclust 5 0.955 0.903 0.957 0.0729 0.915 0.707
#> MAD:mclust 5 0.979 0.958 0.977 0.0706 0.914 0.701
#> ATC:mclust 5 0.781 0.735 0.854 0.0519 0.927 0.723
#> SD:kmeans 5 0.796 0.768 0.814 0.0662 0.976 0.908
#> CV:kmeans 5 0.793 0.804 0.820 0.0610 0.940 0.797
#> MAD:kmeans 5 0.771 0.733 0.796 0.0648 0.909 0.723
#> ATC:kmeans 5 0.694 0.808 0.798 0.0704 0.818 0.469
#> SD:pam 5 1.000 0.992 0.998 0.0288 0.979 0.919
#> CV:pam 5 1.000 0.990 0.997 0.0312 0.968 0.881
#> MAD:pam 5 0.993 0.969 0.984 0.0281 0.982 0.930
#> ATC:pam 5 0.950 0.916 0.961 0.0796 0.850 0.493
#> SD:hclust 5 0.727 0.766 0.841 0.0768 0.914 0.709
#> CV:hclust 5 0.743 0.784 0.846 0.0869 0.933 0.769
#> MAD:hclust 5 0.848 0.778 0.891 0.0920 0.953 0.829
#> ATC:hclust 5 0.737 0.797 0.897 0.1074 0.820 0.597
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.876 0.809 0.892 0.0294 0.970 0.871
#> CV:NMF 6 0.894 0.811 0.887 0.0307 0.981 0.918
#> MAD:NMF 6 0.872 0.773 0.885 0.0283 0.980 0.913
#> ATC:NMF 6 0.784 0.717 0.824 0.0261 0.967 0.863
#> SD:skmeans 6 0.879 0.750 0.837 0.0301 0.964 0.828
#> CV:skmeans 6 0.888 0.710 0.865 0.0293 0.971 0.866
#> MAD:skmeans 6 0.884 0.713 0.873 0.0306 0.978 0.898
#> ATC:skmeans 6 0.863 0.901 0.863 0.0422 0.949 0.763
#> SD:mclust 6 0.873 0.688 0.855 0.0380 0.979 0.905
#> CV:mclust 6 0.883 0.852 0.874 0.0345 0.985 0.931
#> MAD:mclust 6 0.863 0.769 0.887 0.0420 0.972 0.873
#> ATC:mclust 6 0.809 0.712 0.874 0.0496 0.910 0.619
#> SD:kmeans 6 0.754 0.732 0.786 0.0430 0.959 0.834
#> CV:kmeans 6 0.733 0.438 0.752 0.0425 0.940 0.772
#> MAD:kmeans 6 0.735 0.540 0.794 0.0405 0.937 0.754
#> ATC:kmeans 6 0.755 0.858 0.835 0.0451 0.957 0.788
#> SD:pam 6 0.959 0.925 0.954 0.0185 0.977 0.907
#> CV:pam 6 0.955 0.945 0.965 0.0146 0.977 0.907
#> MAD:pam 6 0.908 0.844 0.919 0.0484 0.960 0.839
#> ATC:pam 6 1.000 0.965 0.986 0.0375 0.935 0.693
#> SD:hclust 6 0.848 0.790 0.904 0.0548 0.965 0.848
#> CV:hclust 6 0.893 0.816 0.908 0.0708 0.965 0.845
#> MAD:hclust 6 0.846 0.683 0.838 0.0434 0.921 0.696
#> ATC:hclust 6 0.815 0.716 0.881 0.0937 0.865 0.587
Following heatmap plots the partition for each combination of methods and the lightness correspond to the silhouette scores for samples in each method. On top the consensus subgroup is inferred from all methods by taking the mean silhouette scores as weight.
collect_stats(res_list, k = 2)
collect_stats(res_list, k = 3)
collect_stats(res_list, k = 4)
collect_stats(res_list, k = 5)
collect_stats(res_list, k = 6)
Collect partitions from all methods:
collect_classes(res_list, k = 2)
collect_classes(res_list, k = 3)
collect_classes(res_list, k = 4)
collect_classes(res_list, k = 5)
collect_classes(res_list, k = 6)
Overlap of top rows from different top-row methods:
top_rows_overlap(res_list, top_n = 1000, method = "euler")
top_rows_overlap(res_list, top_n = 2000, method = "euler")
top_rows_overlap(res_list, top_n = 3000, method = "euler")
top_rows_overlap(res_list, top_n = 4000, method = "euler")
top_rows_overlap(res_list, top_n = 5000, method = "euler")
Also visualize the correspondance of rankings between different top-row methods:
top_rows_overlap(res_list, top_n = 1000, method = "correspondance")
top_rows_overlap(res_list, top_n = 2000, method = "correspondance")
top_rows_overlap(res_list, top_n = 3000, method = "correspondance")
top_rows_overlap(res_list, top_n = 4000, method = "correspondance")
top_rows_overlap(res_list, top_n = 5000, method = "correspondance")
Heatmaps of the top rows:
top_rows_heatmap(res_list, top_n = 1000)
top_rows_heatmap(res_list, top_n = 2000)
top_rows_heatmap(res_list, top_n = 3000)
top_rows_heatmap(res_list, top_n = 4000)
top_rows_heatmap(res_list, top_n = 5000)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res_list, k = 2)
#> n tissue(p) genotype/variation(p) individual(p) k
#> SD:NMF 75 9.06e-07 7.59e-04 0.05134 2
#> CV:NMF 71 5.52e-07 3.65e-04 0.07133 2
#> MAD:NMF 73 2.16e-07 4.52e-03 0.05241 2
#> ATC:NMF 76 6.80e-07 5.88e-04 0.02667 2
#> SD:skmeans 76 4.99e-07 1.61e-03 0.08034 2
#> CV:skmeans 76 4.99e-07 1.61e-03 0.08034 2
#> MAD:skmeans 76 1.95e-07 1.24e-03 0.03728 2
#> ATC:skmeans 75 2.44e-07 6.76e-04 0.01807 2
#> SD:mclust 76 3.04e-12 1.17e-05 0.99018 2
#> CV:mclust 76 3.04e-12 1.17e-05 0.99018 2
#> MAD:mclust 76 3.04e-12 1.17e-05 0.99018 2
#> ATC:mclust 75 9.46e-07 2.26e-04 0.00555 2
#> SD:kmeans 76 2.17e-09 6.67e-03 0.08617 2
#> CV:kmeans 76 2.17e-09 6.67e-03 0.08617 2
#> MAD:kmeans 75 3.12e-09 6.64e-03 0.06583 2
#> ATC:kmeans 76 4.83e-08 9.05e-03 0.01639 2
#> SD:pam 76 3.04e-12 1.17e-05 0.99018 2
#> CV:pam 76 3.04e-12 1.17e-05 0.99018 2
#> MAD:pam 76 1.98e-08 5.13e-03 0.07094 2
#> ATC:pam 75 3.12e-09 7.87e-03 0.05269 2
#> SD:hclust 60 3.62e-09 4.36e-05 0.33194 2
#> CV:hclust 60 3.62e-09 4.36e-05 0.33194 2
#> MAD:hclust 67 5.18e-08 4.00e-03 0.05106 2
#> ATC:hclust 76 7.07e-09 1.08e-02 0.03990 2
test_to_known_factors(res_list, k = 3)
#> n tissue(p) genotype/variation(p) individual(p) k
#> SD:NMF 76 2.85e-20 4.94e-05 0.9774 3
#> CV:NMF 76 2.85e-20 4.94e-05 0.9774 3
#> MAD:NMF 75 8.78e-20 1.03e-04 0.9544 3
#> ATC:NMF 69 2.81e-11 2.74e-05 0.2811 3
#> SD:skmeans 74 1.34e-18 5.42e-06 0.9028 3
#> CV:skmeans 74 1.34e-18 5.42e-06 0.9460 3
#> MAD:skmeans 73 4.09e-19 1.27e-05 0.9240 3
#> ATC:skmeans 76 3.46e-15 4.51e-06 0.6508 3
#> SD:mclust 75 7.59e-20 1.17e-05 0.9573 3
#> CV:mclust 75 7.59e-20 1.17e-05 0.9573 3
#> MAD:mclust 75 7.59e-20 9.30e-06 0.9375 3
#> ATC:mclust 38 3.80e-05 7.26e-04 0.0730 3
#> SD:kmeans 76 2.85e-20 4.94e-05 0.9774 3
#> CV:kmeans 76 2.85e-20 4.94e-05 0.9774 3
#> MAD:kmeans 76 2.85e-20 4.94e-05 0.9774 3
#> ATC:kmeans 72 3.14e-09 4.42e-05 0.0659 3
#> SD:pam 76 1.53e-18 5.88e-06 0.8922 3
#> CV:pam 76 1.53e-18 5.88e-06 0.8922 3
#> MAD:pam 76 1.53e-18 5.88e-06 0.8922 3
#> ATC:pam 74 5.34e-09 2.94e-04 0.0275 3
#> SD:hclust 76 3.01e-21 5.75e-05 0.9916 3
#> CV:hclust 75 7.29e-21 3.97e-05 0.9850 3
#> MAD:hclust 56 2.05e-13 5.07e-04 0.7699 3
#> ATC:hclust 66 1.14e-06 1.17e-03 0.0758 3
test_to_known_factors(res_list, k = 4)
#> n tissue(p) genotype/variation(p) individual(p) k
#> SD:NMF 75 2.38e-19 2.57e-09 0.35834 4
#> CV:NMF 75 2.38e-19 2.57e-09 0.35834 4
#> MAD:NMF 72 1.27e-18 1.47e-09 0.43483 4
#> ATC:NMF 69 5.57e-12 1.44e-07 0.07401 4
#> SD:skmeans 76 2.32e-19 1.01e-09 0.19775 4
#> CV:skmeans 75 1.27e-19 7.10e-10 0.23558 4
#> MAD:skmeans 76 2.32e-19 1.01e-09 0.19775 4
#> ATC:skmeans 75 4.45e-13 8.70e-06 0.64634 4
#> SD:mclust 70 3.18e-21 5.89e-06 0.05217 4
#> CV:mclust 75 7.56e-19 1.95e-06 0.33661 4
#> MAD:mclust 74 1.89e-18 1.21e-06 0.30257 4
#> ATC:mclust 64 3.06e-13 1.80e-03 0.63962 4
#> SD:kmeans 74 3.63e-22 8.85e-09 0.40324 4
#> CV:kmeans 59 1.29e-20 2.34e-05 0.99777 4
#> MAD:kmeans 74 1.68e-19 2.77e-05 0.93779 4
#> ATC:kmeans 43 2.49e-07 1.70e-02 0.62474 4
#> SD:pam 75 1.05e-21 2.27e-09 0.35473 4
#> CV:pam 75 1.05e-21 2.27e-09 0.35473 4
#> MAD:pam 76 2.37e-21 6.19e-10 0.30079 4
#> ATC:pam 71 1.14e-09 4.02e-07 0.00123 4
#> SD:hclust 73 2.26e-20 7.84e-05 0.48736 4
#> CV:hclust 75 8.41e-21 7.24e-06 0.38164 4
#> MAD:hclust 63 7.21e-16 5.29e-06 0.08542 4
#> ATC:hclust 66 1.14e-06 1.17e-03 0.07584 4
test_to_known_factors(res_list, k = 5)
#> n tissue(p) genotype/variation(p) individual(p) k
#> SD:NMF 73 1.10e-15 1.63e-10 0.00382 5
#> CV:NMF 74 3.99e-16 2.12e-10 0.00344 5
#> MAD:NMF 73 2.39e-16 1.68e-10 0.00524 5
#> ATC:NMF 64 4.15e-12 6.46e-06 0.05676 5
#> SD:skmeans 72 1.53e-16 5.37e-08 0.30822 5
#> CV:skmeans 72 1.53e-16 2.67e-08 0.43016 5
#> MAD:skmeans 70 1.75e-15 6.17e-09 0.50003 5
#> ATC:skmeans 75 1.44e-15 8.32e-09 0.13567 5
#> SD:mclust 69 3.53e-21 6.70e-12 0.67679 5
#> CV:mclust 70 2.94e-20 4.72e-11 0.67366 5
#> MAD:mclust 76 2.61e-18 6.72e-11 0.21672 5
#> ATC:mclust 66 6.83e-11 2.24e-04 0.38834 5
#> SD:kmeans 71 4.64e-23 3.14e-09 0.37776 5
#> CV:kmeans 72 2.68e-22 1.67e-09 0.44843 5
#> MAD:kmeans 69 2.29e-18 8.80e-11 0.77692 5
#> ATC:kmeans 73 4.38e-16 3.16e-07 0.30648 5
#> SD:pam 76 1.33e-21 7.96e-12 0.01272 5
#> CV:pam 76 1.33e-21 7.96e-12 0.01272 5
#> MAD:pam 76 1.78e-21 4.53e-11 0.03977 5
#> ATC:pam 74 3.66e-13 5.00e-08 0.11876 5
#> SD:hclust 66 3.13e-14 1.39e-05 0.40926 5
#> CV:hclust 71 8.82e-16 4.97e-06 0.37955 5
#> MAD:hclust 69 4.90e-15 8.72e-06 0.34407 5
#> ATC:hclust 67 1.87e-08 1.50e-06 0.14910 5
test_to_known_factors(res_list, k = 6)
#> n tissue(p) genotype/variation(p) individual(p) k
#> SD:NMF 70 8.36e-15 7.54e-12 0.00195 6
#> CV:NMF 71 2.05e-15 6.30e-11 0.00141 6
#> MAD:NMF 70 6.20e-15 7.01e-11 0.00572 6
#> ATC:NMF 64 1.02e-12 4.42e-07 0.14454 6
#> SD:skmeans 65 7.63e-17 9.59e-09 0.02696 6
#> CV:skmeans 61 3.24e-16 1.74e-10 0.54070 6
#> MAD:skmeans 62 1.16e-16 2.11e-10 0.40770 6
#> ATC:skmeans 75 8.81e-13 5.80e-08 0.17147 6
#> SD:mclust 63 5.19e-13 3.51e-07 0.59266 6
#> CV:mclust 73 2.08e-21 4.96e-12 0.31037 6
#> MAD:mclust 67 2.82e-12 1.34e-08 0.22034 6
#> ATC:mclust 64 5.59e-14 8.52e-06 0.24640 6
#> SD:kmeans 65 7.31e-17 4.69e-08 0.70071 6
#> CV:kmeans 44 1.51e-08 7.26e-04 0.22722 6
#> MAD:kmeans 55 9.35e-13 1.28e-06 0.29751 6
#> ATC:kmeans 71 1.95e-14 2.53e-07 0.25106 6
#> SD:pam 74 1.82e-26 7.00e-12 0.02659 6
#> CV:pam 75 2.04e-24 1.54e-12 0.00838 6
#> MAD:pam 70 3.68e-20 1.67e-08 0.10086 6
#> ATC:pam 74 8.94e-15 7.17e-08 0.27272 6
#> SD:hclust 69 4.18e-18 1.04e-10 0.14865 6
#> CV:hclust 70 9.51e-19 6.55e-10 0.12403 6
#> MAD:hclust 60 1.39e-16 4.82e-13 0.22968 6
#> ATC:hclust 51 1.84e-08 3.77e-07 0.39669 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 76 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 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.500 0.673 0.856 0.4615 0.499 0.499
#> 3 3 0.546 0.827 0.814 0.3753 0.696 0.462
#> 4 4 0.684 0.814 0.895 0.1129 0.952 0.854
#> 5 5 0.727 0.766 0.841 0.0768 0.914 0.709
#> 6 6 0.848 0.790 0.904 0.0548 0.965 0.848
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM905004 1 0.949 0.4202 0.632 0.368
#> GSM905024 1 0.416 0.7944 0.916 0.084
#> GSM905038 1 0.871 0.5905 0.708 0.292
#> GSM905043 1 0.416 0.7944 0.916 0.084
#> GSM904986 2 0.983 0.3179 0.424 0.576
#> GSM904991 1 0.861 0.6038 0.716 0.284
#> GSM904994 2 0.983 0.3179 0.424 0.576
#> GSM904996 2 0.983 0.3179 0.424 0.576
#> GSM905007 1 0.861 0.6038 0.716 0.284
#> GSM905012 2 0.983 0.3179 0.424 0.576
#> GSM905022 1 0.998 0.0593 0.528 0.472
#> GSM905026 2 0.993 0.2287 0.452 0.548
#> GSM905027 1 0.990 0.1923 0.560 0.440
#> GSM905031 2 0.983 0.3179 0.424 0.576
#> GSM905036 1 0.866 0.5975 0.712 0.288
#> GSM905041 1 0.855 0.6093 0.720 0.280
#> GSM905044 2 0.991 0.2573 0.444 0.556
#> GSM904989 2 0.990 0.2701 0.440 0.560
#> GSM904999 1 0.985 0.2363 0.572 0.428
#> GSM905002 2 0.990 0.2705 0.440 0.560
#> GSM905009 2 0.983 0.3179 0.424 0.576
#> GSM905014 1 0.861 0.6038 0.716 0.284
#> GSM905017 1 0.985 0.2363 0.572 0.428
#> GSM905020 2 0.983 0.3179 0.424 0.576
#> GSM905023 1 0.866 0.5975 0.712 0.288
#> GSM905029 1 0.866 0.5975 0.712 0.288
#> GSM905032 1 0.855 0.6093 0.720 0.280
#> GSM905034 1 0.416 0.7944 0.916 0.084
#> GSM905040 1 0.000 0.8281 1.000 0.000
#> GSM904985 2 0.000 0.8011 0.000 1.000
#> GSM904988 2 0.000 0.8011 0.000 1.000
#> GSM904990 2 0.000 0.8011 0.000 1.000
#> GSM904992 2 0.000 0.8011 0.000 1.000
#> GSM904995 2 0.000 0.8011 0.000 1.000
#> GSM904998 2 0.000 0.8011 0.000 1.000
#> GSM905000 2 0.000 0.8011 0.000 1.000
#> GSM905003 2 0.000 0.8011 0.000 1.000
#> GSM905006 2 0.000 0.8011 0.000 1.000
#> GSM905008 2 0.000 0.8011 0.000 1.000
#> GSM905011 2 0.000 0.8011 0.000 1.000
#> GSM905013 2 0.000 0.8011 0.000 1.000
#> GSM905016 2 0.000 0.8011 0.000 1.000
#> GSM905018 2 0.000 0.8011 0.000 1.000
#> GSM905021 2 0.388 0.7638 0.076 0.924
#> GSM905025 2 0.000 0.8011 0.000 1.000
#> GSM905028 2 0.000 0.8011 0.000 1.000
#> GSM905030 2 0.000 0.8011 0.000 1.000
#> GSM905033 2 0.388 0.7638 0.076 0.924
#> GSM905035 2 0.000 0.8011 0.000 1.000
#> GSM905037 2 0.000 0.8011 0.000 1.000
#> GSM905039 2 0.000 0.8011 0.000 1.000
#> GSM905042 2 0.388 0.7638 0.076 0.924
#> GSM905046 1 0.000 0.8281 1.000 0.000
#> GSM905065 1 0.000 0.8281 1.000 0.000
#> GSM905049 1 0.204 0.8229 0.968 0.032
#> GSM905050 1 0.204 0.8229 0.968 0.032
#> GSM905064 1 0.204 0.8229 0.968 0.032
#> GSM905045 1 0.204 0.8229 0.968 0.032
#> GSM905051 1 0.204 0.8229 0.968 0.032
#> GSM905055 1 0.000 0.8281 1.000 0.000
#> GSM905058 1 0.000 0.8281 1.000 0.000
#> GSM905053 1 0.204 0.8229 0.968 0.032
#> GSM905061 1 0.204 0.8229 0.968 0.032
#> GSM905063 1 0.000 0.8281 1.000 0.000
#> GSM905054 1 0.204 0.8229 0.968 0.032
#> GSM905062 1 0.204 0.8229 0.968 0.032
#> GSM905052 1 0.204 0.8229 0.968 0.032
#> GSM905059 1 0.000 0.8281 1.000 0.000
#> GSM905047 1 0.000 0.8281 1.000 0.000
#> GSM905066 1 0.000 0.8281 1.000 0.000
#> GSM905056 1 0.000 0.8281 1.000 0.000
#> GSM905060 1 0.000 0.8281 1.000 0.000
#> GSM905048 1 0.000 0.8281 1.000 0.000
#> GSM905067 1 0.000 0.8281 1.000 0.000
#> GSM905057 1 0.000 0.8281 1.000 0.000
#> GSM905068 1 0.204 0.8229 0.968 0.032
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM905004 3 0.871 0.575 0.156 0.264 0.580
#> GSM905024 3 0.327 0.547 0.116 0.000 0.884
#> GSM905038 3 0.553 0.756 0.036 0.172 0.792
#> GSM905043 3 0.327 0.547 0.116 0.000 0.884
#> GSM904986 3 0.627 0.663 0.000 0.456 0.544
#> GSM904991 3 0.552 0.754 0.040 0.164 0.796
#> GSM904994 3 0.627 0.663 0.000 0.456 0.544
#> GSM904996 3 0.627 0.663 0.000 0.456 0.544
#> GSM905007 3 0.552 0.754 0.040 0.164 0.796
#> GSM905012 3 0.627 0.663 0.000 0.456 0.544
#> GSM905022 3 0.590 0.729 0.000 0.352 0.648
#> GSM905026 3 0.621 0.689 0.000 0.428 0.572
#> GSM905027 3 0.571 0.740 0.000 0.320 0.680
#> GSM905031 3 0.627 0.663 0.000 0.456 0.544
#> GSM905036 3 0.547 0.756 0.036 0.168 0.796
#> GSM905041 3 0.547 0.752 0.040 0.160 0.800
#> GSM905044 3 0.623 0.684 0.000 0.436 0.564
#> GSM904989 3 0.624 0.680 0.000 0.440 0.560
#> GSM904999 3 0.562 0.742 0.000 0.308 0.692
#> GSM905002 3 0.624 0.680 0.000 0.440 0.560
#> GSM905009 3 0.627 0.663 0.000 0.456 0.544
#> GSM905014 3 0.552 0.754 0.040 0.164 0.796
#> GSM905017 3 0.562 0.742 0.000 0.308 0.692
#> GSM905020 3 0.627 0.663 0.000 0.456 0.544
#> GSM905023 3 0.547 0.756 0.036 0.168 0.796
#> GSM905029 3 0.547 0.756 0.036 0.168 0.796
#> GSM905032 3 0.547 0.752 0.040 0.160 0.800
#> GSM905034 3 0.334 0.545 0.120 0.000 0.880
#> GSM905040 1 0.525 0.737 0.736 0.000 0.264
#> GSM904985 2 0.000 0.974 0.000 1.000 0.000
#> GSM904988 2 0.000 0.974 0.000 1.000 0.000
#> GSM904990 2 0.000 0.974 0.000 1.000 0.000
#> GSM904992 2 0.000 0.974 0.000 1.000 0.000
#> GSM904995 2 0.000 0.974 0.000 1.000 0.000
#> GSM904998 2 0.000 0.974 0.000 1.000 0.000
#> GSM905000 2 0.000 0.974 0.000 1.000 0.000
#> GSM905003 2 0.000 0.974 0.000 1.000 0.000
#> GSM905006 2 0.000 0.974 0.000 1.000 0.000
#> GSM905008 2 0.000 0.974 0.000 1.000 0.000
#> GSM905011 2 0.000 0.974 0.000 1.000 0.000
#> GSM905013 2 0.000 0.974 0.000 1.000 0.000
#> GSM905016 2 0.000 0.974 0.000 1.000 0.000
#> GSM905018 2 0.000 0.974 0.000 1.000 0.000
#> GSM905021 2 0.334 0.793 0.000 0.880 0.120
#> GSM905025 2 0.000 0.974 0.000 1.000 0.000
#> GSM905028 2 0.000 0.974 0.000 1.000 0.000
#> GSM905030 2 0.000 0.974 0.000 1.000 0.000
#> GSM905033 2 0.334 0.793 0.000 0.880 0.120
#> GSM905035 2 0.000 0.974 0.000 1.000 0.000
#> GSM905037 2 0.000 0.974 0.000 1.000 0.000
#> GSM905039 2 0.000 0.974 0.000 1.000 0.000
#> GSM905042 2 0.334 0.793 0.000 0.880 0.120
#> GSM905046 1 0.226 0.891 0.932 0.000 0.068
#> GSM905065 1 0.341 0.836 0.876 0.000 0.124
#> GSM905049 1 0.506 0.888 0.820 0.032 0.148
#> GSM905050 1 0.506 0.888 0.820 0.032 0.148
#> GSM905064 1 0.506 0.888 0.820 0.032 0.148
#> GSM905045 1 0.506 0.888 0.820 0.032 0.148
#> GSM905051 1 0.493 0.888 0.828 0.032 0.140
#> GSM905055 1 0.406 0.818 0.836 0.000 0.164
#> GSM905058 1 0.226 0.891 0.932 0.000 0.068
#> GSM905053 1 0.506 0.888 0.820 0.032 0.148
#> GSM905061 1 0.506 0.888 0.820 0.032 0.148
#> GSM905063 1 0.406 0.818 0.836 0.000 0.164
#> GSM905054 1 0.506 0.888 0.820 0.032 0.148
#> GSM905062 1 0.506 0.888 0.820 0.032 0.148
#> GSM905052 1 0.493 0.888 0.828 0.032 0.140
#> GSM905059 1 0.226 0.891 0.932 0.000 0.068
#> GSM905047 1 0.226 0.891 0.932 0.000 0.068
#> GSM905066 1 0.341 0.836 0.876 0.000 0.124
#> GSM905056 1 0.406 0.818 0.836 0.000 0.164
#> GSM905060 1 0.226 0.891 0.932 0.000 0.068
#> GSM905048 1 0.226 0.891 0.932 0.000 0.068
#> GSM905067 1 0.341 0.836 0.876 0.000 0.124
#> GSM905057 1 0.406 0.818 0.836 0.000 0.164
#> GSM905068 1 0.506 0.888 0.820 0.032 0.148
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM905004 3 0.7299 0.510 0.000 0.184 0.520 0.296
#> GSM905024 3 0.3649 0.575 0.204 0.000 0.796 0.000
#> GSM905038 3 0.0336 0.768 0.000 0.008 0.992 0.000
#> GSM905043 3 0.3649 0.575 0.204 0.000 0.796 0.000
#> GSM904986 3 0.4406 0.751 0.000 0.300 0.700 0.000
#> GSM904991 3 0.0000 0.764 0.000 0.000 1.000 0.000
#> GSM904994 3 0.4406 0.751 0.000 0.300 0.700 0.000
#> GSM904996 3 0.4406 0.751 0.000 0.300 0.700 0.000
#> GSM905007 3 0.0000 0.764 0.000 0.000 1.000 0.000
#> GSM905012 3 0.4406 0.751 0.000 0.300 0.700 0.000
#> GSM905022 3 0.3486 0.800 0.000 0.188 0.812 0.000
#> GSM905026 3 0.4164 0.773 0.000 0.264 0.736 0.000
#> GSM905027 3 0.3123 0.801 0.000 0.156 0.844 0.000
#> GSM905031 3 0.4406 0.751 0.000 0.300 0.700 0.000
#> GSM905036 3 0.0188 0.766 0.000 0.004 0.996 0.000
#> GSM905041 3 0.0188 0.762 0.004 0.000 0.996 0.000
#> GSM905044 3 0.4222 0.769 0.000 0.272 0.728 0.000
#> GSM904989 3 0.4304 0.763 0.000 0.284 0.716 0.000
#> GSM904999 3 0.3157 0.800 0.004 0.144 0.852 0.000
#> GSM905002 3 0.4304 0.763 0.000 0.284 0.716 0.000
#> GSM905009 3 0.4406 0.751 0.000 0.300 0.700 0.000
#> GSM905014 3 0.0000 0.764 0.000 0.000 1.000 0.000
#> GSM905017 3 0.3157 0.800 0.004 0.144 0.852 0.000
#> GSM905020 3 0.4406 0.751 0.000 0.300 0.700 0.000
#> GSM905023 3 0.0188 0.766 0.000 0.004 0.996 0.000
#> GSM905029 3 0.0188 0.766 0.000 0.004 0.996 0.000
#> GSM905032 3 0.0336 0.760 0.008 0.000 0.992 0.000
#> GSM905034 3 0.3688 0.572 0.208 0.000 0.792 0.000
#> GSM905040 1 0.2281 0.681 0.904 0.000 0.096 0.000
#> GSM904985 2 0.0000 0.977 0.000 1.000 0.000 0.000
#> GSM904988 2 0.0000 0.977 0.000 1.000 0.000 0.000
#> GSM904990 2 0.0000 0.977 0.000 1.000 0.000 0.000
#> GSM904992 2 0.0000 0.977 0.000 1.000 0.000 0.000
#> GSM904995 2 0.0000 0.977 0.000 1.000 0.000 0.000
#> GSM904998 2 0.0000 0.977 0.000 1.000 0.000 0.000
#> GSM905000 2 0.0000 0.977 0.000 1.000 0.000 0.000
#> GSM905003 2 0.0000 0.977 0.000 1.000 0.000 0.000
#> GSM905006 2 0.0000 0.977 0.000 1.000 0.000 0.000
#> GSM905008 2 0.0000 0.977 0.000 1.000 0.000 0.000
#> GSM905011 2 0.0000 0.977 0.000 1.000 0.000 0.000
#> GSM905013 2 0.0000 0.977 0.000 1.000 0.000 0.000
#> GSM905016 2 0.0000 0.977 0.000 1.000 0.000 0.000
#> GSM905018 2 0.0000 0.977 0.000 1.000 0.000 0.000
#> GSM905021 2 0.2814 0.821 0.000 0.868 0.132 0.000
#> GSM905025 2 0.0000 0.977 0.000 1.000 0.000 0.000
#> GSM905028 2 0.0000 0.977 0.000 1.000 0.000 0.000
#> GSM905030 2 0.0000 0.977 0.000 1.000 0.000 0.000
#> GSM905033 2 0.2814 0.821 0.000 0.868 0.132 0.000
#> GSM905035 2 0.0000 0.977 0.000 1.000 0.000 0.000
#> GSM905037 2 0.0000 0.977 0.000 1.000 0.000 0.000
#> GSM905039 2 0.0000 0.977 0.000 1.000 0.000 0.000
#> GSM905042 2 0.2814 0.821 0.000 0.868 0.132 0.000
#> GSM905046 4 0.3356 0.806 0.176 0.000 0.000 0.824
#> GSM905065 1 0.4977 0.257 0.540 0.000 0.000 0.460
#> GSM905049 4 0.0188 0.902 0.000 0.000 0.004 0.996
#> GSM905050 4 0.0188 0.902 0.000 0.000 0.004 0.996
#> GSM905064 4 0.0188 0.902 0.000 0.000 0.004 0.996
#> GSM905045 4 0.0188 0.902 0.000 0.000 0.004 0.996
#> GSM905051 4 0.0707 0.897 0.020 0.000 0.000 0.980
#> GSM905055 1 0.0188 0.745 0.996 0.000 0.000 0.004
#> GSM905058 4 0.3356 0.806 0.176 0.000 0.000 0.824
#> GSM905053 4 0.0188 0.902 0.000 0.000 0.004 0.996
#> GSM905061 4 0.0188 0.902 0.000 0.000 0.004 0.996
#> GSM905063 1 0.0188 0.745 0.996 0.000 0.000 0.004
#> GSM905054 4 0.0188 0.902 0.000 0.000 0.004 0.996
#> GSM905062 4 0.0188 0.902 0.000 0.000 0.004 0.996
#> GSM905052 4 0.0707 0.897 0.020 0.000 0.000 0.980
#> GSM905059 4 0.3356 0.806 0.176 0.000 0.000 0.824
#> GSM905047 4 0.3356 0.806 0.176 0.000 0.000 0.824
#> GSM905066 1 0.4977 0.257 0.540 0.000 0.000 0.460
#> GSM905056 1 0.0188 0.745 0.996 0.000 0.000 0.004
#> GSM905060 4 0.3356 0.806 0.176 0.000 0.000 0.824
#> GSM905048 4 0.3356 0.806 0.176 0.000 0.000 0.824
#> GSM905067 1 0.4977 0.257 0.540 0.000 0.000 0.460
#> GSM905057 1 0.0188 0.745 0.996 0.000 0.000 0.004
#> GSM905068 4 0.0188 0.902 0.000 0.000 0.004 0.996
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM905004 3 0.561 0.4245 0.000 0.104 0.600 0.296 0.000
#> GSM905024 5 0.143 0.6724 0.004 0.000 0.052 0.000 0.944
#> GSM905038 3 0.366 0.4224 0.000 0.000 0.724 0.000 0.276
#> GSM905043 5 0.143 0.6724 0.004 0.000 0.052 0.000 0.944
#> GSM904986 3 0.277 0.7960 0.000 0.164 0.836 0.000 0.000
#> GSM904991 5 0.380 0.7563 0.000 0.000 0.300 0.000 0.700
#> GSM904994 3 0.277 0.7960 0.000 0.164 0.836 0.000 0.000
#> GSM904996 3 0.277 0.7960 0.000 0.164 0.836 0.000 0.000
#> GSM905007 5 0.380 0.7563 0.000 0.000 0.300 0.000 0.700
#> GSM905012 3 0.277 0.7960 0.000 0.164 0.836 0.000 0.000
#> GSM905022 3 0.339 0.6936 0.000 0.060 0.840 0.000 0.100
#> GSM905026 3 0.287 0.7825 0.000 0.128 0.856 0.000 0.016
#> GSM905027 3 0.450 0.5543 0.000 0.060 0.732 0.000 0.208
#> GSM905031 3 0.277 0.7960 0.000 0.164 0.836 0.000 0.000
#> GSM905036 3 0.423 -0.0695 0.000 0.000 0.576 0.000 0.424
#> GSM905041 5 0.391 0.7586 0.004 0.000 0.292 0.000 0.704
#> GSM905044 3 0.275 0.7882 0.000 0.136 0.856 0.000 0.008
#> GSM904989 3 0.336 0.7900 0.000 0.164 0.816 0.000 0.020
#> GSM904999 5 0.542 0.4232 0.000 0.060 0.416 0.000 0.524
#> GSM905002 3 0.276 0.7935 0.000 0.148 0.848 0.000 0.004
#> GSM905009 3 0.277 0.7960 0.000 0.164 0.836 0.000 0.000
#> GSM905014 5 0.380 0.7563 0.000 0.000 0.300 0.000 0.700
#> GSM905017 5 0.542 0.4232 0.000 0.060 0.416 0.000 0.524
#> GSM905020 3 0.277 0.7960 0.000 0.164 0.836 0.000 0.000
#> GSM905023 3 0.413 0.1207 0.000 0.000 0.620 0.000 0.380
#> GSM905029 3 0.371 0.4060 0.000 0.000 0.716 0.000 0.284
#> GSM905032 5 0.364 0.7603 0.004 0.000 0.248 0.000 0.748
#> GSM905034 5 0.150 0.6696 0.004 0.000 0.056 0.000 0.940
#> GSM905040 1 0.247 0.8543 0.864 0.000 0.000 0.000 0.136
#> GSM904985 2 0.000 0.9651 0.000 1.000 0.000 0.000 0.000
#> GSM904988 2 0.000 0.9651 0.000 1.000 0.000 0.000 0.000
#> GSM904990 2 0.000 0.9651 0.000 1.000 0.000 0.000 0.000
#> GSM904992 2 0.000 0.9651 0.000 1.000 0.000 0.000 0.000
#> GSM904995 2 0.000 0.9651 0.000 1.000 0.000 0.000 0.000
#> GSM904998 2 0.000 0.9651 0.000 1.000 0.000 0.000 0.000
#> GSM905000 2 0.000 0.9651 0.000 1.000 0.000 0.000 0.000
#> GSM905003 2 0.000 0.9651 0.000 1.000 0.000 0.000 0.000
#> GSM905006 2 0.000 0.9651 0.000 1.000 0.000 0.000 0.000
#> GSM905008 2 0.000 0.9651 0.000 1.000 0.000 0.000 0.000
#> GSM905011 2 0.000 0.9651 0.000 1.000 0.000 0.000 0.000
#> GSM905013 2 0.000 0.9651 0.000 1.000 0.000 0.000 0.000
#> GSM905016 2 0.000 0.9651 0.000 1.000 0.000 0.000 0.000
#> GSM905018 2 0.000 0.9651 0.000 1.000 0.000 0.000 0.000
#> GSM905021 2 0.324 0.7034 0.000 0.784 0.216 0.000 0.000
#> GSM905025 2 0.000 0.9651 0.000 1.000 0.000 0.000 0.000
#> GSM905028 2 0.000 0.9651 0.000 1.000 0.000 0.000 0.000
#> GSM905030 2 0.000 0.9651 0.000 1.000 0.000 0.000 0.000
#> GSM905033 2 0.321 0.7099 0.000 0.788 0.212 0.000 0.000
#> GSM905035 2 0.000 0.9651 0.000 1.000 0.000 0.000 0.000
#> GSM905037 2 0.000 0.9651 0.000 1.000 0.000 0.000 0.000
#> GSM905039 2 0.000 0.9651 0.000 1.000 0.000 0.000 0.000
#> GSM905042 2 0.321 0.7099 0.000 0.788 0.212 0.000 0.000
#> GSM905046 4 0.566 0.7477 0.052 0.000 0.144 0.704 0.100
#> GSM905065 4 0.825 0.2766 0.300 0.000 0.132 0.352 0.216
#> GSM905049 4 0.000 0.8056 0.000 0.000 0.000 1.000 0.000
#> GSM905050 4 0.000 0.8056 0.000 0.000 0.000 1.000 0.000
#> GSM905064 4 0.000 0.8056 0.000 0.000 0.000 1.000 0.000
#> GSM905045 4 0.000 0.8056 0.000 0.000 0.000 1.000 0.000
#> GSM905051 4 0.162 0.8020 0.020 0.000 0.020 0.948 0.012
#> GSM905055 1 0.000 0.9671 1.000 0.000 0.000 0.000 0.000
#> GSM905058 4 0.566 0.7477 0.052 0.000 0.144 0.704 0.100
#> GSM905053 4 0.000 0.8056 0.000 0.000 0.000 1.000 0.000
#> GSM905061 4 0.000 0.8056 0.000 0.000 0.000 1.000 0.000
#> GSM905063 1 0.000 0.9671 1.000 0.000 0.000 0.000 0.000
#> GSM905054 4 0.000 0.8056 0.000 0.000 0.000 1.000 0.000
#> GSM905062 4 0.000 0.8056 0.000 0.000 0.000 1.000 0.000
#> GSM905052 4 0.162 0.8020 0.020 0.000 0.020 0.948 0.012
#> GSM905059 4 0.566 0.7477 0.052 0.000 0.144 0.704 0.100
#> GSM905047 4 0.566 0.7477 0.052 0.000 0.144 0.704 0.100
#> GSM905066 4 0.825 0.2766 0.300 0.000 0.132 0.352 0.216
#> GSM905056 1 0.000 0.9671 1.000 0.000 0.000 0.000 0.000
#> GSM905060 4 0.566 0.7477 0.052 0.000 0.144 0.704 0.100
#> GSM905048 4 0.566 0.7477 0.052 0.000 0.144 0.704 0.100
#> GSM905067 4 0.825 0.2766 0.300 0.000 0.132 0.352 0.216
#> GSM905057 1 0.000 0.9671 1.000 0.000 0.000 0.000 0.000
#> GSM905068 4 0.000 0.8056 0.000 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM905004 3 0.3634 0.462 0.000 0.008 0.696 0.296 0.000 0.000
#> GSM905024 5 0.0000 0.662 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM905038 3 0.3351 0.517 0.000 0.000 0.712 0.000 0.288 0.000
#> GSM905043 5 0.0000 0.662 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM904986 3 0.0260 0.821 0.000 0.008 0.992 0.000 0.000 0.000
#> GSM904991 5 0.3126 0.756 0.000 0.000 0.248 0.000 0.752 0.000
#> GSM904994 3 0.0260 0.821 0.000 0.008 0.992 0.000 0.000 0.000
#> GSM904996 3 0.0260 0.821 0.000 0.008 0.992 0.000 0.000 0.000
#> GSM905007 5 0.3126 0.756 0.000 0.000 0.248 0.000 0.752 0.000
#> GSM905012 3 0.0260 0.821 0.000 0.008 0.992 0.000 0.000 0.000
#> GSM905022 3 0.1957 0.747 0.000 0.000 0.888 0.000 0.112 0.000
#> GSM905026 3 0.0713 0.811 0.000 0.000 0.972 0.000 0.028 0.000
#> GSM905027 3 0.2941 0.609 0.000 0.000 0.780 0.000 0.220 0.000
#> GSM905031 3 0.0260 0.821 0.000 0.008 0.992 0.000 0.000 0.000
#> GSM905036 3 0.3823 0.070 0.000 0.000 0.564 0.000 0.436 0.000
#> GSM905041 5 0.3076 0.758 0.000 0.000 0.240 0.000 0.760 0.000
#> GSM905044 3 0.0547 0.815 0.000 0.000 0.980 0.000 0.020 0.000
#> GSM904989 3 0.0806 0.817 0.000 0.008 0.972 0.000 0.020 0.000
#> GSM904999 5 0.3854 0.347 0.000 0.000 0.464 0.000 0.536 0.000
#> GSM905002 3 0.0717 0.819 0.000 0.008 0.976 0.000 0.016 0.000
#> GSM905009 3 0.0260 0.821 0.000 0.008 0.992 0.000 0.000 0.000
#> GSM905014 5 0.3126 0.756 0.000 0.000 0.248 0.000 0.752 0.000
#> GSM905017 5 0.3854 0.347 0.000 0.000 0.464 0.000 0.536 0.000
#> GSM905020 3 0.0260 0.821 0.000 0.008 0.992 0.000 0.000 0.000
#> GSM905023 3 0.3737 0.242 0.000 0.000 0.608 0.000 0.392 0.000
#> GSM905029 3 0.3390 0.502 0.000 0.000 0.704 0.000 0.296 0.000
#> GSM905032 5 0.2762 0.760 0.000 0.000 0.196 0.000 0.804 0.000
#> GSM905034 5 0.0146 0.659 0.004 0.000 0.000 0.000 0.996 0.000
#> GSM905040 6 0.2219 0.842 0.000 0.000 0.000 0.000 0.136 0.864
#> GSM904985 2 0.0000 0.956 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM904988 2 0.0000 0.956 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM904990 2 0.0000 0.956 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM904992 2 0.0000 0.956 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM904995 2 0.0000 0.956 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM904998 2 0.0000 0.956 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905000 2 0.0000 0.956 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905003 2 0.0000 0.956 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905006 2 0.0000 0.956 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905008 2 0.0000 0.956 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905011 2 0.0000 0.956 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905013 2 0.0000 0.956 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905016 2 0.0000 0.956 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905018 2 0.0000 0.956 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905021 2 0.3266 0.655 0.000 0.728 0.272 0.000 0.000 0.000
#> GSM905025 2 0.0000 0.956 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905028 2 0.0000 0.956 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905030 2 0.0000 0.956 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905033 2 0.3244 0.660 0.000 0.732 0.268 0.000 0.000 0.000
#> GSM905035 2 0.0000 0.956 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905037 2 0.0000 0.956 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905039 2 0.0000 0.956 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905042 2 0.3244 0.660 0.000 0.732 0.268 0.000 0.000 0.000
#> GSM905046 1 0.0000 0.846 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM905065 1 0.5029 0.598 0.620 0.000 0.000 0.000 0.120 0.260
#> GSM905049 4 0.0000 0.901 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905050 4 0.0000 0.901 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905064 4 0.0000 0.901 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905045 4 0.0000 0.901 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905051 4 0.3843 0.337 0.452 0.000 0.000 0.548 0.000 0.000
#> GSM905055 6 0.0000 0.961 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM905058 1 0.0000 0.846 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM905053 4 0.0000 0.901 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905061 4 0.0000 0.901 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905063 6 0.0000 0.961 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM905054 4 0.0000 0.901 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905062 4 0.0000 0.901 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905052 4 0.3843 0.337 0.452 0.000 0.000 0.548 0.000 0.000
#> GSM905059 1 0.0000 0.846 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM905047 1 0.0000 0.846 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM905066 1 0.5029 0.598 0.620 0.000 0.000 0.000 0.120 0.260
#> GSM905056 6 0.0000 0.961 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM905060 1 0.0000 0.846 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM905048 1 0.0000 0.846 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM905067 1 0.5029 0.598 0.620 0.000 0.000 0.000 0.120 0.260
#> GSM905057 6 0.0000 0.961 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM905068 4 0.0000 0.901 0.000 0.000 0.000 1.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) genotype/variation(p) individual(p) k
#> SD:hclust 60 3.62e-09 4.36e-05 0.332 2
#> SD:hclust 76 3.01e-21 5.75e-05 0.992 3
#> SD:hclust 73 2.26e-20 7.84e-05 0.487 4
#> SD:hclust 66 3.13e-14 1.39e-05 0.409 5
#> SD:hclust 69 4.18e-18 1.04e-10 0.149 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 76 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.581 0.857 0.892 0.4596 0.528 0.528
#> 3 3 0.654 0.923 0.866 0.3861 0.762 0.565
#> 4 4 0.829 0.864 0.840 0.1325 0.914 0.745
#> 5 5 0.796 0.768 0.814 0.0662 0.976 0.908
#> 6 6 0.754 0.732 0.786 0.0430 0.959 0.834
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
#> GSM905004 2 0.9044 0.763 0.320 0.680
#> GSM905024 1 0.0672 0.991 0.992 0.008
#> GSM905038 2 0.9000 0.763 0.316 0.684
#> GSM905043 1 0.0672 0.991 0.992 0.008
#> GSM904986 2 0.8955 0.767 0.312 0.688
#> GSM904991 2 0.9044 0.759 0.320 0.680
#> GSM904994 2 0.8955 0.767 0.312 0.688
#> GSM904996 2 0.8955 0.767 0.312 0.688
#> GSM905007 2 0.9000 0.763 0.316 0.684
#> GSM905012 2 0.8955 0.767 0.312 0.688
#> GSM905022 2 0.8955 0.767 0.312 0.688
#> GSM905026 2 0.8955 0.767 0.312 0.688
#> GSM905027 2 0.8955 0.767 0.312 0.688
#> GSM905031 2 0.8955 0.767 0.312 0.688
#> GSM905036 2 0.9000 0.763 0.316 0.684
#> GSM905041 2 0.9922 0.529 0.448 0.552
#> GSM905044 2 0.8955 0.767 0.312 0.688
#> GSM904989 2 0.8955 0.767 0.312 0.688
#> GSM904999 2 0.8955 0.767 0.312 0.688
#> GSM905002 2 0.8955 0.767 0.312 0.688
#> GSM905009 2 0.8955 0.767 0.312 0.688
#> GSM905014 2 0.9000 0.763 0.316 0.684
#> GSM905017 2 0.8955 0.767 0.312 0.688
#> GSM905020 2 0.8955 0.767 0.312 0.688
#> GSM905023 2 0.9000 0.763 0.316 0.684
#> GSM905029 2 0.9000 0.763 0.316 0.684
#> GSM905032 2 0.9044 0.759 0.320 0.680
#> GSM905034 1 0.0672 0.991 0.992 0.008
#> GSM905040 1 0.0672 0.991 0.992 0.008
#> GSM904985 2 0.0672 0.798 0.008 0.992
#> GSM904988 2 0.0672 0.798 0.008 0.992
#> GSM904990 2 0.0672 0.798 0.008 0.992
#> GSM904992 2 0.0672 0.798 0.008 0.992
#> GSM904995 2 0.0672 0.798 0.008 0.992
#> GSM904998 2 0.0672 0.798 0.008 0.992
#> GSM905000 2 0.0672 0.798 0.008 0.992
#> GSM905003 2 0.0672 0.798 0.008 0.992
#> GSM905006 2 0.0672 0.798 0.008 0.992
#> GSM905008 2 0.0672 0.798 0.008 0.992
#> GSM905011 2 0.0672 0.798 0.008 0.992
#> GSM905013 2 0.0672 0.798 0.008 0.992
#> GSM905016 2 0.0672 0.798 0.008 0.992
#> GSM905018 2 0.0672 0.798 0.008 0.992
#> GSM905021 2 0.0672 0.798 0.008 0.992
#> GSM905025 2 0.0672 0.798 0.008 0.992
#> GSM905028 2 0.0672 0.798 0.008 0.992
#> GSM905030 2 0.0672 0.798 0.008 0.992
#> GSM905033 2 0.0672 0.798 0.008 0.992
#> GSM905035 2 0.0672 0.798 0.008 0.992
#> GSM905037 2 0.0672 0.798 0.008 0.992
#> GSM905039 2 0.0672 0.798 0.008 0.992
#> GSM905042 2 0.0672 0.798 0.008 0.992
#> GSM905046 1 0.0000 0.998 1.000 0.000
#> GSM905065 1 0.0000 0.998 1.000 0.000
#> GSM905049 1 0.0000 0.998 1.000 0.000
#> GSM905050 1 0.0000 0.998 1.000 0.000
#> GSM905064 1 0.0000 0.998 1.000 0.000
#> GSM905045 1 0.0000 0.998 1.000 0.000
#> GSM905051 1 0.0000 0.998 1.000 0.000
#> GSM905055 1 0.0000 0.998 1.000 0.000
#> GSM905058 1 0.0000 0.998 1.000 0.000
#> GSM905053 1 0.0000 0.998 1.000 0.000
#> GSM905061 1 0.0000 0.998 1.000 0.000
#> GSM905063 1 0.0000 0.998 1.000 0.000
#> GSM905054 1 0.0000 0.998 1.000 0.000
#> GSM905062 1 0.0000 0.998 1.000 0.000
#> GSM905052 1 0.0000 0.998 1.000 0.000
#> GSM905059 1 0.0000 0.998 1.000 0.000
#> GSM905047 1 0.0000 0.998 1.000 0.000
#> GSM905066 1 0.0000 0.998 1.000 0.000
#> GSM905056 1 0.0000 0.998 1.000 0.000
#> GSM905060 1 0.0000 0.998 1.000 0.000
#> GSM905048 1 0.0000 0.998 1.000 0.000
#> GSM905067 1 0.0000 0.998 1.000 0.000
#> GSM905057 1 0.0000 0.998 1.000 0.000
#> GSM905068 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
#> GSM905004 3 0.6363 0.804 0.136 0.096 0.768
#> GSM905024 3 0.3267 0.523 0.116 0.000 0.884
#> GSM905038 3 0.4931 0.954 0.000 0.232 0.768
#> GSM905043 3 0.3267 0.523 0.116 0.000 0.884
#> GSM904986 3 0.4931 0.954 0.000 0.232 0.768
#> GSM904991 3 0.4784 0.927 0.004 0.200 0.796
#> GSM904994 3 0.4931 0.954 0.000 0.232 0.768
#> GSM904996 3 0.4931 0.954 0.000 0.232 0.768
#> GSM905007 3 0.4931 0.954 0.000 0.232 0.768
#> GSM905012 3 0.4931 0.954 0.000 0.232 0.768
#> GSM905022 3 0.4931 0.954 0.000 0.232 0.768
#> GSM905026 3 0.4931 0.954 0.000 0.232 0.768
#> GSM905027 3 0.4931 0.954 0.000 0.232 0.768
#> GSM905031 3 0.4931 0.954 0.000 0.232 0.768
#> GSM905036 3 0.4931 0.954 0.000 0.232 0.768
#> GSM905041 3 0.4733 0.924 0.004 0.196 0.800
#> GSM905044 3 0.4931 0.954 0.000 0.232 0.768
#> GSM904989 3 0.4931 0.954 0.000 0.232 0.768
#> GSM904999 3 0.4931 0.954 0.000 0.232 0.768
#> GSM905002 3 0.4931 0.954 0.000 0.232 0.768
#> GSM905009 3 0.4931 0.954 0.000 0.232 0.768
#> GSM905014 3 0.4931 0.954 0.000 0.232 0.768
#> GSM905017 3 0.4931 0.954 0.000 0.232 0.768
#> GSM905020 3 0.4931 0.954 0.000 0.232 0.768
#> GSM905023 3 0.4931 0.954 0.000 0.232 0.768
#> GSM905029 3 0.4931 0.954 0.000 0.232 0.768
#> GSM905032 3 0.4555 0.927 0.000 0.200 0.800
#> GSM905034 1 0.5178 0.889 0.744 0.000 0.256
#> GSM905040 1 0.5327 0.884 0.728 0.000 0.272
#> GSM904985 2 0.1289 0.984 0.032 0.968 0.000
#> GSM904988 2 0.0237 0.988 0.004 0.996 0.000
#> GSM904990 2 0.0000 0.988 0.000 1.000 0.000
#> GSM904992 2 0.0237 0.988 0.004 0.996 0.000
#> GSM904995 2 0.1289 0.984 0.032 0.968 0.000
#> GSM904998 2 0.0237 0.988 0.004 0.996 0.000
#> GSM905000 2 0.0000 0.988 0.000 1.000 0.000
#> GSM905003 2 0.0592 0.987 0.012 0.988 0.000
#> GSM905006 2 0.0237 0.988 0.004 0.996 0.000
#> GSM905008 2 0.0237 0.988 0.004 0.996 0.000
#> GSM905011 2 0.0237 0.988 0.004 0.996 0.000
#> GSM905013 2 0.0000 0.988 0.000 1.000 0.000
#> GSM905016 2 0.1289 0.984 0.032 0.968 0.000
#> GSM905018 2 0.0000 0.988 0.000 1.000 0.000
#> GSM905021 2 0.1163 0.984 0.028 0.972 0.000
#> GSM905025 2 0.1163 0.984 0.028 0.972 0.000
#> GSM905028 2 0.0000 0.988 0.000 1.000 0.000
#> GSM905030 2 0.0237 0.988 0.004 0.996 0.000
#> GSM905033 2 0.1163 0.984 0.028 0.972 0.000
#> GSM905035 2 0.1289 0.984 0.032 0.968 0.000
#> GSM905037 2 0.0000 0.988 0.000 1.000 0.000
#> GSM905039 2 0.1163 0.984 0.028 0.972 0.000
#> GSM905042 2 0.1163 0.984 0.028 0.972 0.000
#> GSM905046 1 0.4796 0.899 0.780 0.000 0.220
#> GSM905065 1 0.4796 0.899 0.780 0.000 0.220
#> GSM905049 1 0.3116 0.847 0.892 0.000 0.108
#> GSM905050 1 0.3116 0.847 0.892 0.000 0.108
#> GSM905064 1 0.2356 0.862 0.928 0.000 0.072
#> GSM905045 1 0.3116 0.847 0.892 0.000 0.108
#> GSM905051 1 0.1753 0.869 0.952 0.000 0.048
#> GSM905055 1 0.5254 0.888 0.736 0.000 0.264
#> GSM905058 1 0.4796 0.899 0.780 0.000 0.220
#> GSM905053 1 0.3116 0.847 0.892 0.000 0.108
#> GSM905061 1 0.3116 0.847 0.892 0.000 0.108
#> GSM905063 1 0.5254 0.888 0.736 0.000 0.264
#> GSM905054 1 0.2959 0.851 0.900 0.000 0.100
#> GSM905062 1 0.3116 0.847 0.892 0.000 0.108
#> GSM905052 1 0.1753 0.869 0.952 0.000 0.048
#> GSM905059 1 0.4750 0.899 0.784 0.000 0.216
#> GSM905047 1 0.4750 0.899 0.784 0.000 0.216
#> GSM905066 1 0.4796 0.899 0.780 0.000 0.220
#> GSM905056 1 0.5254 0.888 0.736 0.000 0.264
#> GSM905060 1 0.4750 0.899 0.784 0.000 0.216
#> GSM905048 1 0.4796 0.899 0.780 0.000 0.220
#> GSM905067 1 0.4796 0.899 0.780 0.000 0.220
#> GSM905057 1 0.5254 0.888 0.736 0.000 0.264
#> GSM905068 1 0.3116 0.847 0.892 0.000 0.108
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM905004 3 0.3975 0.691 0.000 0.000 0.760 0.240
#> GSM905024 1 0.5614 0.143 0.592 0.020 0.384 0.004
#> GSM905038 3 0.0188 0.961 0.004 0.000 0.996 0.000
#> GSM905043 1 0.4855 0.236 0.644 0.000 0.352 0.004
#> GSM904986 3 0.0000 0.962 0.000 0.000 1.000 0.000
#> GSM904991 3 0.2654 0.910 0.108 0.000 0.888 0.004
#> GSM904994 3 0.0000 0.962 0.000 0.000 1.000 0.000
#> GSM904996 3 0.0000 0.962 0.000 0.000 1.000 0.000
#> GSM905007 3 0.1576 0.943 0.048 0.000 0.948 0.004
#> GSM905012 3 0.0000 0.962 0.000 0.000 1.000 0.000
#> GSM905022 3 0.0000 0.962 0.000 0.000 1.000 0.000
#> GSM905026 3 0.0000 0.962 0.000 0.000 1.000 0.000
#> GSM905027 3 0.0188 0.961 0.004 0.000 0.996 0.000
#> GSM905031 3 0.0000 0.962 0.000 0.000 1.000 0.000
#> GSM905036 3 0.0657 0.958 0.012 0.000 0.984 0.004
#> GSM905041 3 0.2799 0.908 0.108 0.000 0.884 0.008
#> GSM905044 3 0.0000 0.962 0.000 0.000 1.000 0.000
#> GSM904989 3 0.0000 0.962 0.000 0.000 1.000 0.000
#> GSM904999 3 0.3245 0.908 0.064 0.000 0.880 0.056
#> GSM905002 3 0.0000 0.962 0.000 0.000 1.000 0.000
#> GSM905009 3 0.0000 0.962 0.000 0.000 1.000 0.000
#> GSM905014 3 0.1637 0.938 0.060 0.000 0.940 0.000
#> GSM905017 3 0.3245 0.908 0.064 0.000 0.880 0.056
#> GSM905020 3 0.0000 0.962 0.000 0.000 1.000 0.000
#> GSM905023 3 0.0469 0.959 0.012 0.000 0.988 0.000
#> GSM905029 3 0.0188 0.961 0.004 0.000 0.996 0.000
#> GSM905032 3 0.4285 0.841 0.156 0.000 0.804 0.040
#> GSM905034 1 0.2744 0.660 0.912 0.024 0.012 0.052
#> GSM905040 1 0.0336 0.636 0.992 0.008 0.000 0.000
#> GSM904985 2 0.5136 0.878 0.000 0.728 0.048 0.224
#> GSM904988 2 0.1576 0.925 0.000 0.948 0.048 0.004
#> GSM904990 2 0.1389 0.925 0.000 0.952 0.048 0.000
#> GSM904992 2 0.1576 0.925 0.000 0.948 0.048 0.004
#> GSM904995 2 0.4919 0.885 0.000 0.752 0.048 0.200
#> GSM904998 2 0.1975 0.923 0.000 0.936 0.048 0.016
#> GSM905000 2 0.1389 0.925 0.000 0.952 0.048 0.000
#> GSM905003 2 0.2586 0.920 0.000 0.912 0.048 0.040
#> GSM905006 2 0.1576 0.925 0.000 0.948 0.048 0.004
#> GSM905008 2 0.2300 0.920 0.000 0.924 0.048 0.028
#> GSM905011 2 0.1576 0.925 0.000 0.948 0.048 0.004
#> GSM905013 2 0.1389 0.925 0.000 0.952 0.048 0.000
#> GSM905016 2 0.4919 0.885 0.000 0.752 0.048 0.200
#> GSM905018 2 0.1389 0.925 0.000 0.952 0.048 0.000
#> GSM905021 2 0.5623 0.837 0.000 0.660 0.048 0.292
#> GSM905025 2 0.4881 0.885 0.000 0.756 0.048 0.196
#> GSM905028 2 0.1389 0.925 0.000 0.952 0.048 0.000
#> GSM905030 2 0.1576 0.925 0.000 0.948 0.048 0.004
#> GSM905033 2 0.5416 0.858 0.000 0.692 0.048 0.260
#> GSM905035 2 0.4919 0.885 0.000 0.752 0.048 0.200
#> GSM905037 2 0.1389 0.925 0.000 0.952 0.048 0.000
#> GSM905039 2 0.4881 0.885 0.000 0.756 0.048 0.196
#> GSM905042 2 0.5416 0.858 0.000 0.692 0.048 0.260
#> GSM905046 1 0.4507 0.729 0.756 0.020 0.000 0.224
#> GSM905065 1 0.4018 0.730 0.772 0.004 0.000 0.224
#> GSM905049 4 0.5358 0.964 0.252 0.000 0.048 0.700
#> GSM905050 4 0.5358 0.964 0.252 0.000 0.048 0.700
#> GSM905064 4 0.5078 0.943 0.272 0.000 0.028 0.700
#> GSM905045 4 0.5358 0.964 0.252 0.000 0.048 0.700
#> GSM905051 4 0.5206 0.868 0.308 0.024 0.000 0.668
#> GSM905055 1 0.2737 0.722 0.888 0.008 0.000 0.104
#> GSM905058 1 0.4574 0.728 0.756 0.024 0.000 0.220
#> GSM905053 4 0.5358 0.964 0.252 0.000 0.048 0.700
#> GSM905061 4 0.5358 0.964 0.252 0.000 0.048 0.700
#> GSM905063 1 0.2737 0.722 0.888 0.008 0.000 0.104
#> GSM905054 4 0.5200 0.954 0.264 0.000 0.036 0.700
#> GSM905062 4 0.5358 0.964 0.252 0.000 0.048 0.700
#> GSM905052 4 0.5206 0.868 0.308 0.024 0.000 0.668
#> GSM905059 1 0.4644 0.719 0.748 0.024 0.000 0.228
#> GSM905047 1 0.4576 0.720 0.748 0.020 0.000 0.232
#> GSM905066 1 0.4018 0.730 0.772 0.004 0.000 0.224
#> GSM905056 1 0.2737 0.722 0.888 0.008 0.000 0.104
#> GSM905060 1 0.4644 0.719 0.748 0.024 0.000 0.228
#> GSM905048 1 0.4507 0.729 0.756 0.020 0.000 0.224
#> GSM905067 1 0.4018 0.730 0.772 0.004 0.000 0.224
#> GSM905057 1 0.2737 0.722 0.888 0.008 0.000 0.104
#> GSM905068 4 0.5358 0.964 0.252 0.000 0.048 0.700
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM905004 3 0.3635 0.543 0.000 0.000 0.748 0.248 0.004
#> GSM905024 5 0.6836 0.459 0.396 0.000 0.188 0.012 0.404
#> GSM905038 3 0.1043 0.868 0.000 0.000 0.960 0.000 0.040
#> GSM905043 5 0.6476 0.408 0.384 0.000 0.132 0.012 0.472
#> GSM904986 3 0.0000 0.878 0.000 0.000 1.000 0.000 0.000
#> GSM904991 3 0.3932 0.538 0.000 0.000 0.672 0.000 0.328
#> GSM904994 3 0.0000 0.878 0.000 0.000 1.000 0.000 0.000
#> GSM904996 3 0.0000 0.878 0.000 0.000 1.000 0.000 0.000
#> GSM905007 3 0.2891 0.767 0.000 0.000 0.824 0.000 0.176
#> GSM905012 3 0.0000 0.878 0.000 0.000 1.000 0.000 0.000
#> GSM905022 3 0.0000 0.878 0.000 0.000 1.000 0.000 0.000
#> GSM905026 3 0.0000 0.878 0.000 0.000 1.000 0.000 0.000
#> GSM905027 3 0.1043 0.868 0.000 0.000 0.960 0.000 0.040
#> GSM905031 3 0.0000 0.878 0.000 0.000 1.000 0.000 0.000
#> GSM905036 3 0.1851 0.844 0.000 0.000 0.912 0.000 0.088
#> GSM905041 3 0.3999 0.504 0.000 0.000 0.656 0.000 0.344
#> GSM905044 3 0.0000 0.878 0.000 0.000 1.000 0.000 0.000
#> GSM904989 3 0.0000 0.878 0.000 0.000 1.000 0.000 0.000
#> GSM904999 3 0.4752 0.523 0.000 0.000 0.648 0.036 0.316
#> GSM905002 3 0.0000 0.878 0.000 0.000 1.000 0.000 0.000
#> GSM905009 3 0.0000 0.878 0.000 0.000 1.000 0.000 0.000
#> GSM905014 3 0.3039 0.749 0.000 0.000 0.808 0.000 0.192
#> GSM905017 3 0.4752 0.523 0.000 0.000 0.648 0.036 0.316
#> GSM905020 3 0.0000 0.878 0.000 0.000 1.000 0.000 0.000
#> GSM905023 3 0.1792 0.847 0.000 0.000 0.916 0.000 0.084
#> GSM905029 3 0.1270 0.863 0.000 0.000 0.948 0.000 0.052
#> GSM905032 5 0.4443 -0.259 0.000 0.000 0.472 0.004 0.524
#> GSM905034 1 0.4791 -0.123 0.588 0.000 0.008 0.012 0.392
#> GSM905040 5 0.5291 -0.175 0.456 0.000 0.000 0.048 0.496
#> GSM904985 2 0.5747 0.764 0.000 0.636 0.004 0.200 0.160
#> GSM904988 2 0.0162 0.858 0.000 0.996 0.004 0.000 0.000
#> GSM904990 2 0.0451 0.858 0.000 0.988 0.004 0.008 0.000
#> GSM904992 2 0.0162 0.858 0.000 0.996 0.004 0.000 0.000
#> GSM904995 2 0.5497 0.775 0.000 0.664 0.004 0.196 0.136
#> GSM904998 2 0.0613 0.857 0.000 0.984 0.004 0.008 0.004
#> GSM905000 2 0.0451 0.858 0.000 0.988 0.004 0.008 0.000
#> GSM905003 2 0.2313 0.845 0.000 0.912 0.004 0.040 0.044
#> GSM905006 2 0.0162 0.858 0.000 0.996 0.004 0.000 0.000
#> GSM905008 2 0.1153 0.852 0.000 0.964 0.004 0.008 0.024
#> GSM905011 2 0.0162 0.858 0.000 0.996 0.004 0.000 0.000
#> GSM905013 2 0.0451 0.858 0.000 0.988 0.004 0.008 0.000
#> GSM905016 2 0.5497 0.775 0.000 0.664 0.004 0.196 0.136
#> GSM905018 2 0.0451 0.858 0.000 0.988 0.004 0.008 0.000
#> GSM905021 2 0.6414 0.645 0.000 0.504 0.004 0.168 0.324
#> GSM905025 2 0.5527 0.776 0.000 0.660 0.004 0.200 0.136
#> GSM905028 2 0.1892 0.848 0.000 0.916 0.004 0.080 0.000
#> GSM905030 2 0.0162 0.858 0.000 0.996 0.004 0.000 0.000
#> GSM905033 2 0.6054 0.713 0.000 0.572 0.004 0.140 0.284
#> GSM905035 2 0.5497 0.775 0.000 0.664 0.004 0.196 0.136
#> GSM905037 2 0.0451 0.858 0.000 0.988 0.004 0.008 0.000
#> GSM905039 2 0.5527 0.776 0.000 0.660 0.004 0.200 0.136
#> GSM905042 2 0.6054 0.713 0.000 0.572 0.004 0.140 0.284
#> GSM905046 1 0.0162 0.806 0.996 0.000 0.000 0.000 0.004
#> GSM905065 1 0.1732 0.801 0.920 0.000 0.000 0.000 0.080
#> GSM905049 4 0.4152 0.973 0.296 0.000 0.012 0.692 0.000
#> GSM905050 4 0.4152 0.973 0.296 0.000 0.012 0.692 0.000
#> GSM905064 4 0.4067 0.971 0.300 0.000 0.008 0.692 0.000
#> GSM905045 4 0.4305 0.973 0.296 0.000 0.012 0.688 0.004
#> GSM905051 4 0.5152 0.901 0.344 0.004 0.000 0.608 0.044
#> GSM905055 1 0.4477 0.655 0.708 0.000 0.000 0.040 0.252
#> GSM905058 1 0.0000 0.806 1.000 0.000 0.000 0.000 0.000
#> GSM905053 4 0.4152 0.973 0.296 0.000 0.012 0.692 0.000
#> GSM905061 4 0.4715 0.966 0.296 0.000 0.012 0.672 0.020
#> GSM905063 1 0.4352 0.661 0.720 0.000 0.000 0.036 0.244
#> GSM905054 4 0.4067 0.971 0.300 0.000 0.008 0.692 0.000
#> GSM905062 4 0.4715 0.966 0.296 0.000 0.012 0.672 0.020
#> GSM905052 4 0.5152 0.901 0.344 0.004 0.000 0.608 0.044
#> GSM905059 1 0.0510 0.800 0.984 0.000 0.000 0.016 0.000
#> GSM905047 1 0.0671 0.799 0.980 0.000 0.000 0.016 0.004
#> GSM905066 1 0.1732 0.801 0.920 0.000 0.000 0.000 0.080
#> GSM905056 1 0.4477 0.655 0.708 0.000 0.000 0.040 0.252
#> GSM905060 1 0.0510 0.800 0.984 0.000 0.000 0.016 0.000
#> GSM905048 1 0.0162 0.806 0.996 0.000 0.000 0.000 0.004
#> GSM905067 1 0.1732 0.801 0.920 0.000 0.000 0.000 0.080
#> GSM905057 1 0.4477 0.655 0.708 0.000 0.000 0.040 0.252
#> GSM905068 4 0.4305 0.973 0.296 0.000 0.012 0.688 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM905004 3 0.3485 0.568 0.000 0.000 0.772 0.204 0.004 NA
#> GSM905024 5 0.6203 0.441 0.300 0.000 0.052 0.012 0.548 NA
#> GSM905038 3 0.2312 0.799 0.000 0.000 0.876 0.000 0.112 NA
#> GSM905043 5 0.5826 0.406 0.256 0.000 0.028 0.012 0.600 NA
#> GSM904986 3 0.0000 0.866 0.000 0.000 1.000 0.000 0.000 NA
#> GSM904991 5 0.4205 0.226 0.000 0.000 0.420 0.000 0.564 NA
#> GSM904994 3 0.0000 0.866 0.000 0.000 1.000 0.000 0.000 NA
#> GSM904996 3 0.0000 0.866 0.000 0.000 1.000 0.000 0.000 NA
#> GSM905007 3 0.3984 0.459 0.000 0.000 0.648 0.000 0.336 NA
#> GSM905012 3 0.0000 0.866 0.000 0.000 1.000 0.000 0.000 NA
#> GSM905022 3 0.0000 0.866 0.000 0.000 1.000 0.000 0.000 NA
#> GSM905026 3 0.0000 0.866 0.000 0.000 1.000 0.000 0.000 NA
#> GSM905027 3 0.2278 0.788 0.000 0.000 0.868 0.000 0.128 NA
#> GSM905031 3 0.0000 0.866 0.000 0.000 1.000 0.000 0.000 NA
#> GSM905036 3 0.3420 0.662 0.000 0.000 0.748 0.000 0.240 NA
#> GSM905041 5 0.3899 0.277 0.000 0.000 0.404 0.000 0.592 NA
#> GSM905044 3 0.0000 0.866 0.000 0.000 1.000 0.000 0.000 NA
#> GSM904989 3 0.0260 0.863 0.000 0.000 0.992 0.000 0.000 NA
#> GSM904999 5 0.6402 0.283 0.000 0.000 0.368 0.056 0.452 NA
#> GSM905002 3 0.0000 0.866 0.000 0.000 1.000 0.000 0.000 NA
#> GSM905009 3 0.0260 0.863 0.000 0.000 0.992 0.000 0.000 NA
#> GSM905014 3 0.4076 0.381 0.000 0.000 0.620 0.000 0.364 NA
#> GSM905017 5 0.6402 0.283 0.000 0.000 0.368 0.056 0.452 NA
#> GSM905020 3 0.0000 0.866 0.000 0.000 1.000 0.000 0.000 NA
#> GSM905023 3 0.3420 0.662 0.000 0.000 0.748 0.000 0.240 NA
#> GSM905029 3 0.2805 0.758 0.000 0.000 0.828 0.000 0.160 NA
#> GSM905032 5 0.3457 0.504 0.016 0.000 0.232 0.000 0.752 NA
#> GSM905034 5 0.5521 0.310 0.360 0.000 0.000 0.016 0.532 NA
#> GSM905040 5 0.6105 0.150 0.288 0.000 0.000 0.012 0.484 NA
#> GSM904985 2 0.1864 0.658 0.000 0.924 0.000 0.004 0.032 NA
#> GSM904988 2 0.3854 0.792 0.000 0.536 0.000 0.000 0.000 NA
#> GSM904990 2 0.4103 0.792 0.000 0.544 0.000 0.004 0.004 NA
#> GSM904992 2 0.4114 0.792 0.000 0.532 0.000 0.004 0.004 NA
#> GSM904995 2 0.1194 0.670 0.000 0.956 0.000 0.004 0.032 NA
#> GSM904998 2 0.4381 0.790 0.000 0.524 0.000 0.004 0.016 NA
#> GSM905000 2 0.4103 0.792 0.000 0.544 0.000 0.004 0.004 NA
#> GSM905003 2 0.4678 0.784 0.000 0.544 0.000 0.012 0.024 NA
#> GSM905006 2 0.3854 0.792 0.000 0.536 0.000 0.000 0.000 NA
#> GSM905008 2 0.4389 0.787 0.000 0.512 0.000 0.004 0.016 NA
#> GSM905011 2 0.3854 0.792 0.000 0.536 0.000 0.000 0.000 NA
#> GSM905013 2 0.4204 0.793 0.000 0.540 0.000 0.004 0.008 NA
#> GSM905016 2 0.1194 0.670 0.000 0.956 0.000 0.004 0.032 NA
#> GSM905018 2 0.4103 0.792 0.000 0.544 0.000 0.004 0.004 NA
#> GSM905021 2 0.6188 0.377 0.000 0.580 0.000 0.068 0.192 NA
#> GSM905025 2 0.0291 0.671 0.000 0.992 0.000 0.000 0.004 NA
#> GSM905028 2 0.3844 0.773 0.000 0.676 0.000 0.004 0.008 NA
#> GSM905030 2 0.4178 0.793 0.000 0.560 0.000 0.004 0.008 NA
#> GSM905033 2 0.5022 0.548 0.000 0.712 0.000 0.060 0.140 NA
#> GSM905035 2 0.0508 0.668 0.000 0.984 0.000 0.004 0.012 NA
#> GSM905037 2 0.4158 0.792 0.000 0.572 0.000 0.004 0.008 NA
#> GSM905039 2 0.0405 0.672 0.000 0.988 0.000 0.000 0.004 NA
#> GSM905042 2 0.5022 0.548 0.000 0.712 0.000 0.060 0.140 NA
#> GSM905046 1 0.2020 0.832 0.896 0.000 0.000 0.096 0.008 NA
#> GSM905065 1 0.4028 0.832 0.796 0.000 0.000 0.096 0.056 NA
#> GSM905049 4 0.2048 0.969 0.120 0.000 0.000 0.880 0.000 NA
#> GSM905050 4 0.2048 0.969 0.120 0.000 0.000 0.880 0.000 NA
#> GSM905064 4 0.2048 0.969 0.120 0.000 0.000 0.880 0.000 NA
#> GSM905045 4 0.2662 0.965 0.120 0.000 0.000 0.856 0.000 NA
#> GSM905051 4 0.3542 0.894 0.184 0.000 0.000 0.784 0.016 NA
#> GSM905055 1 0.4403 0.707 0.708 0.000 0.000 0.000 0.096 NA
#> GSM905058 1 0.2476 0.829 0.880 0.000 0.000 0.092 0.024 NA
#> GSM905053 4 0.2048 0.969 0.120 0.000 0.000 0.880 0.000 NA
#> GSM905061 4 0.2815 0.962 0.120 0.000 0.000 0.848 0.000 NA
#> GSM905063 1 0.4434 0.704 0.712 0.000 0.000 0.000 0.116 NA
#> GSM905054 4 0.2048 0.969 0.120 0.000 0.000 0.880 0.000 NA
#> GSM905062 4 0.2815 0.962 0.120 0.000 0.000 0.848 0.000 NA
#> GSM905052 4 0.3542 0.894 0.184 0.000 0.000 0.784 0.016 NA
#> GSM905059 1 0.2669 0.821 0.864 0.000 0.000 0.108 0.024 NA
#> GSM905047 1 0.2212 0.823 0.880 0.000 0.000 0.112 0.008 NA
#> GSM905066 1 0.4028 0.832 0.796 0.000 0.000 0.096 0.056 NA
#> GSM905056 1 0.4403 0.707 0.708 0.000 0.000 0.000 0.096 NA
#> GSM905060 1 0.2669 0.821 0.864 0.000 0.000 0.108 0.024 NA
#> GSM905048 1 0.2020 0.832 0.896 0.000 0.000 0.096 0.008 NA
#> GSM905067 1 0.4028 0.832 0.796 0.000 0.000 0.096 0.056 NA
#> GSM905057 1 0.4403 0.707 0.708 0.000 0.000 0.000 0.096 NA
#> GSM905068 4 0.2662 0.965 0.120 0.000 0.000 0.856 0.000 NA
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) genotype/variation(p) individual(p) k
#> SD:kmeans 76 2.17e-09 6.67e-03 0.0862 2
#> SD:kmeans 76 2.85e-20 4.94e-05 0.9774 3
#> SD:kmeans 74 3.63e-22 8.85e-09 0.4032 4
#> SD:kmeans 71 4.64e-23 3.14e-09 0.3778 5
#> SD:kmeans 65 7.31e-17 4.69e-08 0.7007 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 76 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.999 0.981 0.991 0.5031 0.496 0.496
#> 3 3 1.000 0.958 0.985 0.3381 0.742 0.522
#> 4 4 1.000 0.980 0.989 0.1056 0.908 0.727
#> 5 5 0.883 0.845 0.916 0.0608 0.931 0.737
#> 6 6 0.879 0.750 0.837 0.0301 0.964 0.828
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
#> GSM905004 1 0.0000 0.988 1.000 0.000
#> GSM905024 1 0.0000 0.988 1.000 0.000
#> GSM905038 2 0.4298 0.907 0.088 0.912
#> GSM905043 1 0.0000 0.988 1.000 0.000
#> GSM904986 2 0.0000 0.993 0.000 1.000
#> GSM904991 1 0.0000 0.988 1.000 0.000
#> GSM904994 2 0.0000 0.993 0.000 1.000
#> GSM904996 2 0.0000 0.993 0.000 1.000
#> GSM905007 1 0.3733 0.920 0.928 0.072
#> GSM905012 2 0.0000 0.993 0.000 1.000
#> GSM905022 2 0.0000 0.993 0.000 1.000
#> GSM905026 2 0.0000 0.993 0.000 1.000
#> GSM905027 2 0.0938 0.983 0.012 0.988
#> GSM905031 2 0.0000 0.993 0.000 1.000
#> GSM905036 1 0.5294 0.866 0.880 0.120
#> GSM905041 1 0.0000 0.988 1.000 0.000
#> GSM905044 2 0.0000 0.993 0.000 1.000
#> GSM904989 2 0.0000 0.993 0.000 1.000
#> GSM904999 2 0.0000 0.993 0.000 1.000
#> GSM905002 2 0.0000 0.993 0.000 1.000
#> GSM905009 2 0.0000 0.993 0.000 1.000
#> GSM905014 1 0.7376 0.743 0.792 0.208
#> GSM905017 2 0.0000 0.993 0.000 1.000
#> GSM905020 2 0.0000 0.993 0.000 1.000
#> GSM905023 2 0.4298 0.907 0.088 0.912
#> GSM905029 2 0.4298 0.907 0.088 0.912
#> GSM905032 1 0.0000 0.988 1.000 0.000
#> GSM905034 1 0.0000 0.988 1.000 0.000
#> GSM905040 1 0.0000 0.988 1.000 0.000
#> GSM904985 2 0.0000 0.993 0.000 1.000
#> GSM904988 2 0.0000 0.993 0.000 1.000
#> GSM904990 2 0.0000 0.993 0.000 1.000
#> GSM904992 2 0.0000 0.993 0.000 1.000
#> GSM904995 2 0.0000 0.993 0.000 1.000
#> GSM904998 2 0.0000 0.993 0.000 1.000
#> GSM905000 2 0.0000 0.993 0.000 1.000
#> GSM905003 2 0.0000 0.993 0.000 1.000
#> GSM905006 2 0.0000 0.993 0.000 1.000
#> GSM905008 2 0.0000 0.993 0.000 1.000
#> GSM905011 2 0.0000 0.993 0.000 1.000
#> GSM905013 2 0.0000 0.993 0.000 1.000
#> GSM905016 2 0.0000 0.993 0.000 1.000
#> GSM905018 2 0.0000 0.993 0.000 1.000
#> GSM905021 2 0.0000 0.993 0.000 1.000
#> GSM905025 2 0.0000 0.993 0.000 1.000
#> GSM905028 2 0.0000 0.993 0.000 1.000
#> GSM905030 2 0.0000 0.993 0.000 1.000
#> GSM905033 2 0.0000 0.993 0.000 1.000
#> GSM905035 2 0.0000 0.993 0.000 1.000
#> GSM905037 2 0.0000 0.993 0.000 1.000
#> GSM905039 2 0.0000 0.993 0.000 1.000
#> GSM905042 2 0.0000 0.993 0.000 1.000
#> GSM905046 1 0.0000 0.988 1.000 0.000
#> GSM905065 1 0.0000 0.988 1.000 0.000
#> GSM905049 1 0.0000 0.988 1.000 0.000
#> GSM905050 1 0.0000 0.988 1.000 0.000
#> GSM905064 1 0.0000 0.988 1.000 0.000
#> GSM905045 1 0.0000 0.988 1.000 0.000
#> GSM905051 1 0.0000 0.988 1.000 0.000
#> GSM905055 1 0.0000 0.988 1.000 0.000
#> GSM905058 1 0.0000 0.988 1.000 0.000
#> GSM905053 1 0.0000 0.988 1.000 0.000
#> GSM905061 1 0.0000 0.988 1.000 0.000
#> GSM905063 1 0.0000 0.988 1.000 0.000
#> GSM905054 1 0.0000 0.988 1.000 0.000
#> GSM905062 1 0.0000 0.988 1.000 0.000
#> GSM905052 1 0.0000 0.988 1.000 0.000
#> GSM905059 1 0.0000 0.988 1.000 0.000
#> GSM905047 1 0.0000 0.988 1.000 0.000
#> GSM905066 1 0.0000 0.988 1.000 0.000
#> GSM905056 1 0.0000 0.988 1.000 0.000
#> GSM905060 1 0.0000 0.988 1.000 0.000
#> GSM905048 1 0.0000 0.988 1.000 0.000
#> GSM905067 1 0.0000 0.988 1.000 0.000
#> GSM905057 1 0.0000 0.988 1.000 0.000
#> GSM905068 1 0.0000 0.988 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM905004 3 0.631 -0.0314 0.492 0 0.508
#> GSM905024 1 0.593 0.4468 0.644 0 0.356
#> GSM905038 3 0.000 0.9784 0.000 0 1.000
#> GSM905043 1 0.559 0.5599 0.696 0 0.304
#> GSM904986 3 0.000 0.9784 0.000 0 1.000
#> GSM904991 3 0.000 0.9784 0.000 0 1.000
#> GSM904994 3 0.000 0.9784 0.000 0 1.000
#> GSM904996 3 0.000 0.9784 0.000 0 1.000
#> GSM905007 3 0.000 0.9784 0.000 0 1.000
#> GSM905012 3 0.000 0.9784 0.000 0 1.000
#> GSM905022 3 0.000 0.9784 0.000 0 1.000
#> GSM905026 3 0.000 0.9784 0.000 0 1.000
#> GSM905027 3 0.000 0.9784 0.000 0 1.000
#> GSM905031 3 0.000 0.9784 0.000 0 1.000
#> GSM905036 3 0.000 0.9784 0.000 0 1.000
#> GSM905041 3 0.000 0.9784 0.000 0 1.000
#> GSM905044 3 0.000 0.9784 0.000 0 1.000
#> GSM904989 3 0.000 0.9784 0.000 0 1.000
#> GSM904999 3 0.000 0.9784 0.000 0 1.000
#> GSM905002 3 0.000 0.9784 0.000 0 1.000
#> GSM905009 3 0.000 0.9784 0.000 0 1.000
#> GSM905014 3 0.000 0.9784 0.000 0 1.000
#> GSM905017 3 0.000 0.9784 0.000 0 1.000
#> GSM905020 3 0.000 0.9784 0.000 0 1.000
#> GSM905023 3 0.000 0.9784 0.000 0 1.000
#> GSM905029 3 0.000 0.9784 0.000 0 1.000
#> GSM905032 3 0.000 0.9784 0.000 0 1.000
#> GSM905034 1 0.000 0.9745 1.000 0 0.000
#> GSM905040 1 0.000 0.9745 1.000 0 0.000
#> GSM904985 2 0.000 1.0000 0.000 1 0.000
#> GSM904988 2 0.000 1.0000 0.000 1 0.000
#> GSM904990 2 0.000 1.0000 0.000 1 0.000
#> GSM904992 2 0.000 1.0000 0.000 1 0.000
#> GSM904995 2 0.000 1.0000 0.000 1 0.000
#> GSM904998 2 0.000 1.0000 0.000 1 0.000
#> GSM905000 2 0.000 1.0000 0.000 1 0.000
#> GSM905003 2 0.000 1.0000 0.000 1 0.000
#> GSM905006 2 0.000 1.0000 0.000 1 0.000
#> GSM905008 2 0.000 1.0000 0.000 1 0.000
#> GSM905011 2 0.000 1.0000 0.000 1 0.000
#> GSM905013 2 0.000 1.0000 0.000 1 0.000
#> GSM905016 2 0.000 1.0000 0.000 1 0.000
#> GSM905018 2 0.000 1.0000 0.000 1 0.000
#> GSM905021 2 0.000 1.0000 0.000 1 0.000
#> GSM905025 2 0.000 1.0000 0.000 1 0.000
#> GSM905028 2 0.000 1.0000 0.000 1 0.000
#> GSM905030 2 0.000 1.0000 0.000 1 0.000
#> GSM905033 2 0.000 1.0000 0.000 1 0.000
#> GSM905035 2 0.000 1.0000 0.000 1 0.000
#> GSM905037 2 0.000 1.0000 0.000 1 0.000
#> GSM905039 2 0.000 1.0000 0.000 1 0.000
#> GSM905042 2 0.000 1.0000 0.000 1 0.000
#> GSM905046 1 0.000 0.9745 1.000 0 0.000
#> GSM905065 1 0.000 0.9745 1.000 0 0.000
#> GSM905049 1 0.000 0.9745 1.000 0 0.000
#> GSM905050 1 0.000 0.9745 1.000 0 0.000
#> GSM905064 1 0.000 0.9745 1.000 0 0.000
#> GSM905045 1 0.000 0.9745 1.000 0 0.000
#> GSM905051 1 0.000 0.9745 1.000 0 0.000
#> GSM905055 1 0.000 0.9745 1.000 0 0.000
#> GSM905058 1 0.000 0.9745 1.000 0 0.000
#> GSM905053 1 0.000 0.9745 1.000 0 0.000
#> GSM905061 1 0.000 0.9745 1.000 0 0.000
#> GSM905063 1 0.000 0.9745 1.000 0 0.000
#> GSM905054 1 0.000 0.9745 1.000 0 0.000
#> GSM905062 1 0.000 0.9745 1.000 0 0.000
#> GSM905052 1 0.000 0.9745 1.000 0 0.000
#> GSM905059 1 0.000 0.9745 1.000 0 0.000
#> GSM905047 1 0.000 0.9745 1.000 0 0.000
#> GSM905066 1 0.000 0.9745 1.000 0 0.000
#> GSM905056 1 0.000 0.9745 1.000 0 0.000
#> GSM905060 1 0.000 0.9745 1.000 0 0.000
#> GSM905048 1 0.000 0.9745 1.000 0 0.000
#> GSM905067 1 0.000 0.9745 1.000 0 0.000
#> GSM905057 1 0.000 0.9745 1.000 0 0.000
#> GSM905068 1 0.000 0.9745 1.000 0 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM905004 4 0.3649 0.744 0.000 0 0.204 0.796
#> GSM905024 1 0.0000 0.964 1.000 0 0.000 0.000
#> GSM905038 3 0.0188 0.995 0.004 0 0.996 0.000
#> GSM905043 1 0.0000 0.964 1.000 0 0.000 0.000
#> GSM904986 3 0.0000 0.995 0.000 0 1.000 0.000
#> GSM904991 3 0.0592 0.990 0.016 0 0.984 0.000
#> GSM904994 3 0.0000 0.995 0.000 0 1.000 0.000
#> GSM904996 3 0.0000 0.995 0.000 0 1.000 0.000
#> GSM905007 3 0.0592 0.990 0.016 0 0.984 0.000
#> GSM905012 3 0.0000 0.995 0.000 0 1.000 0.000
#> GSM905022 3 0.0000 0.995 0.000 0 1.000 0.000
#> GSM905026 3 0.0000 0.995 0.000 0 1.000 0.000
#> GSM905027 3 0.0000 0.995 0.000 0 1.000 0.000
#> GSM905031 3 0.0000 0.995 0.000 0 1.000 0.000
#> GSM905036 3 0.0336 0.994 0.008 0 0.992 0.000
#> GSM905041 3 0.0707 0.987 0.020 0 0.980 0.000
#> GSM905044 3 0.0000 0.995 0.000 0 1.000 0.000
#> GSM904989 3 0.0000 0.995 0.000 0 1.000 0.000
#> GSM904999 3 0.0469 0.991 0.012 0 0.988 0.000
#> GSM905002 3 0.0000 0.995 0.000 0 1.000 0.000
#> GSM905009 3 0.0000 0.995 0.000 0 1.000 0.000
#> GSM905014 3 0.0592 0.990 0.016 0 0.984 0.000
#> GSM905017 3 0.0469 0.991 0.012 0 0.988 0.000
#> GSM905020 3 0.0000 0.995 0.000 0 1.000 0.000
#> GSM905023 3 0.0336 0.994 0.008 0 0.992 0.000
#> GSM905029 3 0.0188 0.995 0.004 0 0.996 0.000
#> GSM905032 1 0.4304 0.587 0.716 0 0.284 0.000
#> GSM905034 1 0.0000 0.964 1.000 0 0.000 0.000
#> GSM905040 1 0.0000 0.964 1.000 0 0.000 0.000
#> GSM904985 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM904988 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM904990 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM904992 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM904995 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM904998 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905000 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905003 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905006 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905008 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905011 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905013 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905016 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905018 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905021 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905025 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905028 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905030 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905033 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905035 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905037 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905039 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905042 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905046 1 0.0707 0.973 0.980 0 0.000 0.020
#> GSM905065 1 0.0707 0.973 0.980 0 0.000 0.020
#> GSM905049 4 0.0000 0.979 0.000 0 0.000 1.000
#> GSM905050 4 0.0000 0.979 0.000 0 0.000 1.000
#> GSM905064 4 0.0000 0.979 0.000 0 0.000 1.000
#> GSM905045 4 0.0000 0.979 0.000 0 0.000 1.000
#> GSM905051 4 0.0000 0.979 0.000 0 0.000 1.000
#> GSM905055 1 0.0592 0.973 0.984 0 0.000 0.016
#> GSM905058 1 0.0707 0.973 0.980 0 0.000 0.020
#> GSM905053 4 0.0000 0.979 0.000 0 0.000 1.000
#> GSM905061 4 0.0000 0.979 0.000 0 0.000 1.000
#> GSM905063 1 0.0592 0.973 0.984 0 0.000 0.016
#> GSM905054 4 0.0000 0.979 0.000 0 0.000 1.000
#> GSM905062 4 0.0000 0.979 0.000 0 0.000 1.000
#> GSM905052 4 0.0000 0.979 0.000 0 0.000 1.000
#> GSM905059 1 0.0707 0.973 0.980 0 0.000 0.020
#> GSM905047 1 0.0707 0.973 0.980 0 0.000 0.020
#> GSM905066 1 0.0707 0.973 0.980 0 0.000 0.020
#> GSM905056 1 0.0592 0.973 0.984 0 0.000 0.016
#> GSM905060 1 0.0707 0.973 0.980 0 0.000 0.020
#> GSM905048 1 0.0707 0.973 0.980 0 0.000 0.020
#> GSM905067 1 0.0707 0.973 0.980 0 0.000 0.020
#> GSM905057 1 0.0592 0.973 0.984 0 0.000 0.016
#> GSM905068 4 0.0000 0.979 0.000 0 0.000 1.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM905004 4 0.3521 0.681 0.000 0.000 0.232 0.764 0.004
#> GSM905024 5 0.3123 0.571 0.184 0.000 0.000 0.004 0.812
#> GSM905038 3 0.4273 -0.164 0.000 0.000 0.552 0.000 0.448
#> GSM905043 5 0.4118 0.233 0.336 0.000 0.000 0.004 0.660
#> GSM904986 3 0.0000 0.897 0.000 0.000 1.000 0.000 0.000
#> GSM904991 5 0.3177 0.741 0.000 0.000 0.208 0.000 0.792
#> GSM904994 3 0.0000 0.897 0.000 0.000 1.000 0.000 0.000
#> GSM904996 3 0.0000 0.897 0.000 0.000 1.000 0.000 0.000
#> GSM905007 5 0.3242 0.740 0.000 0.000 0.216 0.000 0.784
#> GSM905012 3 0.0000 0.897 0.000 0.000 1.000 0.000 0.000
#> GSM905022 3 0.0000 0.897 0.000 0.000 1.000 0.000 0.000
#> GSM905026 3 0.0510 0.887 0.000 0.000 0.984 0.000 0.016
#> GSM905027 3 0.4294 -0.272 0.000 0.000 0.532 0.000 0.468
#> GSM905031 3 0.0510 0.887 0.000 0.000 0.984 0.000 0.016
#> GSM905036 5 0.3983 0.615 0.000 0.000 0.340 0.000 0.660
#> GSM905041 5 0.2929 0.738 0.000 0.000 0.180 0.000 0.820
#> GSM905044 3 0.0510 0.887 0.000 0.000 0.984 0.000 0.016
#> GSM904989 3 0.0000 0.897 0.000 0.000 1.000 0.000 0.000
#> GSM904999 5 0.4402 0.624 0.000 0.000 0.352 0.012 0.636
#> GSM905002 3 0.0000 0.897 0.000 0.000 1.000 0.000 0.000
#> GSM905009 3 0.0000 0.897 0.000 0.000 1.000 0.000 0.000
#> GSM905014 5 0.3210 0.741 0.000 0.000 0.212 0.000 0.788
#> GSM905017 5 0.4402 0.624 0.000 0.000 0.352 0.012 0.636
#> GSM905020 3 0.0000 0.897 0.000 0.000 1.000 0.000 0.000
#> GSM905023 5 0.4030 0.598 0.000 0.000 0.352 0.000 0.648
#> GSM905029 5 0.4306 0.273 0.000 0.000 0.492 0.000 0.508
#> GSM905032 5 0.0613 0.647 0.008 0.000 0.004 0.004 0.984
#> GSM905034 1 0.3521 0.764 0.764 0.000 0.000 0.004 0.232
#> GSM905040 1 0.3969 0.750 0.692 0.000 0.000 0.004 0.304
#> GSM904985 2 0.0162 0.997 0.000 0.996 0.000 0.000 0.004
#> GSM904988 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM904990 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM904992 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM904995 2 0.0162 0.997 0.000 0.996 0.000 0.000 0.004
#> GSM904998 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM905000 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM905003 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM905006 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM905008 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM905011 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM905013 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM905016 2 0.0162 0.997 0.000 0.996 0.000 0.000 0.004
#> GSM905018 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM905021 2 0.0451 0.991 0.000 0.988 0.000 0.004 0.008
#> GSM905025 2 0.0162 0.997 0.000 0.996 0.000 0.000 0.004
#> GSM905028 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM905030 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM905033 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM905035 2 0.0162 0.997 0.000 0.996 0.000 0.000 0.004
#> GSM905037 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM905039 2 0.0162 0.997 0.000 0.996 0.000 0.000 0.004
#> GSM905042 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM905046 1 0.0162 0.917 0.996 0.000 0.000 0.004 0.000
#> GSM905065 1 0.0451 0.918 0.988 0.000 0.000 0.004 0.008
#> GSM905049 4 0.0404 0.932 0.012 0.000 0.000 0.988 0.000
#> GSM905050 4 0.0404 0.932 0.012 0.000 0.000 0.988 0.000
#> GSM905064 4 0.0404 0.932 0.012 0.000 0.000 0.988 0.000
#> GSM905045 4 0.0404 0.932 0.012 0.000 0.000 0.988 0.000
#> GSM905051 4 0.3395 0.743 0.236 0.000 0.000 0.764 0.000
#> GSM905055 1 0.2891 0.870 0.824 0.000 0.000 0.000 0.176
#> GSM905058 1 0.0162 0.917 0.996 0.000 0.000 0.004 0.000
#> GSM905053 4 0.0404 0.932 0.012 0.000 0.000 0.988 0.000
#> GSM905061 4 0.0566 0.931 0.012 0.000 0.000 0.984 0.004
#> GSM905063 1 0.2891 0.870 0.824 0.000 0.000 0.000 0.176
#> GSM905054 4 0.0404 0.932 0.012 0.000 0.000 0.988 0.000
#> GSM905062 4 0.0566 0.931 0.012 0.000 0.000 0.984 0.004
#> GSM905052 4 0.3395 0.743 0.236 0.000 0.000 0.764 0.000
#> GSM905059 1 0.0290 0.916 0.992 0.000 0.000 0.008 0.000
#> GSM905047 1 0.0290 0.916 0.992 0.000 0.000 0.008 0.000
#> GSM905066 1 0.0451 0.918 0.988 0.000 0.000 0.004 0.008
#> GSM905056 1 0.2891 0.870 0.824 0.000 0.000 0.000 0.176
#> GSM905060 1 0.0290 0.916 0.992 0.000 0.000 0.008 0.000
#> GSM905048 1 0.0162 0.917 0.996 0.000 0.000 0.004 0.000
#> GSM905067 1 0.0451 0.918 0.988 0.000 0.000 0.004 0.008
#> GSM905057 1 0.2891 0.870 0.824 0.000 0.000 0.000 0.176
#> GSM905068 4 0.0404 0.932 0.012 0.000 0.000 0.988 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM905004 4 0.4145 0.6460 0.044 0.000 0.208 0.736 0.012 0.000
#> GSM905024 5 0.5047 0.4827 0.236 0.000 0.000 0.000 0.628 0.136
#> GSM905038 5 0.4241 0.4637 0.024 0.000 0.368 0.000 0.608 0.000
#> GSM905043 5 0.5886 0.2209 0.236 0.000 0.000 0.000 0.472 0.292
#> GSM904986 3 0.0260 0.9804 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM904991 5 0.2325 0.7333 0.060 0.000 0.048 0.000 0.892 0.000
#> GSM904994 3 0.0000 0.9817 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM904996 3 0.0000 0.9817 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905007 5 0.2433 0.7428 0.044 0.000 0.072 0.000 0.884 0.000
#> GSM905012 3 0.0000 0.9817 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905022 3 0.0520 0.9779 0.008 0.000 0.984 0.000 0.008 0.000
#> GSM905026 3 0.1528 0.9416 0.016 0.000 0.936 0.000 0.048 0.000
#> GSM905027 5 0.4153 0.5329 0.024 0.000 0.340 0.000 0.636 0.000
#> GSM905031 3 0.0909 0.9681 0.012 0.000 0.968 0.000 0.020 0.000
#> GSM905036 5 0.2402 0.7279 0.012 0.000 0.120 0.000 0.868 0.000
#> GSM905041 5 0.1562 0.7297 0.024 0.000 0.032 0.000 0.940 0.004
#> GSM905044 3 0.1151 0.9609 0.012 0.000 0.956 0.000 0.032 0.000
#> GSM904989 3 0.0520 0.9748 0.008 0.000 0.984 0.000 0.008 0.000
#> GSM904999 5 0.5473 0.5922 0.240 0.000 0.192 0.000 0.568 0.000
#> GSM905002 3 0.0146 0.9811 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM905009 3 0.0260 0.9793 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM905014 5 0.2308 0.7417 0.040 0.000 0.068 0.000 0.892 0.000
#> GSM905017 5 0.5492 0.5914 0.244 0.000 0.192 0.000 0.564 0.000
#> GSM905020 3 0.0000 0.9817 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905023 5 0.2653 0.7173 0.012 0.000 0.144 0.000 0.844 0.000
#> GSM905029 5 0.3738 0.6101 0.016 0.000 0.280 0.000 0.704 0.000
#> GSM905032 5 0.5530 0.3646 0.140 0.000 0.000 0.000 0.496 0.364
#> GSM905034 1 0.5643 0.0657 0.476 0.000 0.000 0.000 0.156 0.368
#> GSM905040 6 0.3254 0.3757 0.124 0.000 0.000 0.000 0.056 0.820
#> GSM904985 2 0.1333 0.9601 0.048 0.944 0.000 0.000 0.008 0.000
#> GSM904988 2 0.0000 0.9740 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM904990 2 0.0000 0.9740 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM904992 2 0.0000 0.9740 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM904995 2 0.1333 0.9601 0.048 0.944 0.000 0.000 0.008 0.000
#> GSM904998 2 0.0000 0.9740 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905000 2 0.0000 0.9740 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905003 2 0.0000 0.9740 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905006 2 0.0000 0.9740 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905008 2 0.0000 0.9740 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905011 2 0.0000 0.9740 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905013 2 0.0000 0.9740 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905016 2 0.1333 0.9601 0.048 0.944 0.000 0.000 0.008 0.000
#> GSM905018 2 0.0000 0.9740 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905021 2 0.3409 0.8110 0.192 0.780 0.000 0.000 0.028 0.000
#> GSM905025 2 0.1333 0.9601 0.048 0.944 0.000 0.000 0.008 0.000
#> GSM905028 2 0.0000 0.9740 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905030 2 0.0000 0.9740 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905033 2 0.1411 0.9561 0.060 0.936 0.000 0.000 0.004 0.000
#> GSM905035 2 0.1333 0.9601 0.048 0.944 0.000 0.000 0.008 0.000
#> GSM905037 2 0.0000 0.9740 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905039 2 0.1333 0.9601 0.048 0.944 0.000 0.000 0.008 0.000
#> GSM905042 2 0.1411 0.9561 0.060 0.936 0.000 0.000 0.004 0.000
#> GSM905046 1 0.3868 0.8272 0.508 0.000 0.000 0.000 0.000 0.492
#> GSM905065 6 0.3823 -0.6600 0.436 0.000 0.000 0.000 0.000 0.564
#> GSM905049 4 0.0146 0.8850 0.004 0.000 0.000 0.996 0.000 0.000
#> GSM905050 4 0.0000 0.8852 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905064 4 0.0000 0.8852 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905045 4 0.0508 0.8839 0.012 0.000 0.000 0.984 0.004 0.000
#> GSM905051 4 0.5220 0.3760 0.348 0.000 0.000 0.556 0.004 0.092
#> GSM905055 6 0.0000 0.5441 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM905058 1 0.3868 0.8272 0.508 0.000 0.000 0.000 0.000 0.492
#> GSM905053 4 0.0000 0.8852 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905061 4 0.0603 0.8825 0.016 0.000 0.000 0.980 0.004 0.000
#> GSM905063 6 0.0000 0.5441 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM905054 4 0.0000 0.8852 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905062 4 0.0603 0.8825 0.016 0.000 0.000 0.980 0.004 0.000
#> GSM905052 4 0.5220 0.3760 0.348 0.000 0.000 0.556 0.004 0.092
#> GSM905059 1 0.3868 0.8272 0.508 0.000 0.000 0.000 0.000 0.492
#> GSM905047 1 0.3868 0.8272 0.508 0.000 0.000 0.000 0.000 0.492
#> GSM905066 6 0.3823 -0.6600 0.436 0.000 0.000 0.000 0.000 0.564
#> GSM905056 6 0.0000 0.5441 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM905060 1 0.3868 0.8272 0.508 0.000 0.000 0.000 0.000 0.492
#> GSM905048 1 0.3868 0.8272 0.508 0.000 0.000 0.000 0.000 0.492
#> GSM905067 6 0.3823 -0.6600 0.436 0.000 0.000 0.000 0.000 0.564
#> GSM905057 6 0.0000 0.5441 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM905068 4 0.0508 0.8835 0.012 0.000 0.000 0.984 0.004 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) genotype/variation(p) individual(p) k
#> SD:skmeans 76 4.99e-07 1.61e-03 0.0803 2
#> SD:skmeans 74 1.34e-18 5.42e-06 0.9028 3
#> SD:skmeans 76 2.32e-19 1.01e-09 0.1977 4
#> SD:skmeans 72 1.53e-16 5.37e-08 0.3082 5
#> SD:skmeans 65 7.63e-17 9.59e-09 0.0270 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 76 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 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.572 0.931 0.949 0.4395 0.572 0.572
#> 3 3 1.000 0.993 0.997 0.5330 0.754 0.571
#> 4 4 1.000 0.986 0.995 0.0953 0.934 0.799
#> 5 5 1.000 0.992 0.998 0.0288 0.979 0.919
#> 6 6 0.959 0.925 0.954 0.0185 0.977 0.907
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 3 4 5
There is also optional best \(k\) = 3 4 5 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
#> GSM905004 1 0.4939 0.897 0.892 0.108
#> GSM905024 1 0.0000 0.921 1.000 0.000
#> GSM905038 1 0.6801 0.870 0.820 0.180
#> GSM905043 1 0.0000 0.921 1.000 0.000
#> GSM904986 1 0.6801 0.870 0.820 0.180
#> GSM904991 1 0.0672 0.919 0.992 0.008
#> GSM904994 1 0.6801 0.870 0.820 0.180
#> GSM904996 1 0.6801 0.870 0.820 0.180
#> GSM905007 1 0.4939 0.897 0.892 0.108
#> GSM905012 1 0.6801 0.870 0.820 0.180
#> GSM905022 1 0.6801 0.870 0.820 0.180
#> GSM905026 1 0.6801 0.870 0.820 0.180
#> GSM905027 1 0.4939 0.897 0.892 0.108
#> GSM905031 1 0.6801 0.870 0.820 0.180
#> GSM905036 1 0.4939 0.897 0.892 0.108
#> GSM905041 1 0.0376 0.920 0.996 0.004
#> GSM905044 1 0.6801 0.870 0.820 0.180
#> GSM904989 1 0.6801 0.870 0.820 0.180
#> GSM904999 1 0.6801 0.870 0.820 0.180
#> GSM905002 1 0.6801 0.870 0.820 0.180
#> GSM905009 1 0.6801 0.870 0.820 0.180
#> GSM905014 1 0.6801 0.870 0.820 0.180
#> GSM905017 1 0.6801 0.870 0.820 0.180
#> GSM905020 1 0.6801 0.870 0.820 0.180
#> GSM905023 1 0.6801 0.870 0.820 0.180
#> GSM905029 1 0.6801 0.870 0.820 0.180
#> GSM905032 1 0.6801 0.870 0.820 0.180
#> GSM905034 1 0.0000 0.921 1.000 0.000
#> GSM905040 1 0.0000 0.921 1.000 0.000
#> GSM904985 2 0.0000 1.000 0.000 1.000
#> GSM904988 2 0.0000 1.000 0.000 1.000
#> GSM904990 2 0.0000 1.000 0.000 1.000
#> GSM904992 2 0.0000 1.000 0.000 1.000
#> GSM904995 2 0.0000 1.000 0.000 1.000
#> GSM904998 2 0.0000 1.000 0.000 1.000
#> GSM905000 2 0.0000 1.000 0.000 1.000
#> GSM905003 2 0.0000 1.000 0.000 1.000
#> GSM905006 2 0.0000 1.000 0.000 1.000
#> GSM905008 2 0.0000 1.000 0.000 1.000
#> GSM905011 2 0.0000 1.000 0.000 1.000
#> GSM905013 2 0.0000 1.000 0.000 1.000
#> GSM905016 2 0.0000 1.000 0.000 1.000
#> GSM905018 2 0.0000 1.000 0.000 1.000
#> GSM905021 2 0.0000 1.000 0.000 1.000
#> GSM905025 2 0.0000 1.000 0.000 1.000
#> GSM905028 2 0.0000 1.000 0.000 1.000
#> GSM905030 2 0.0000 1.000 0.000 1.000
#> GSM905033 2 0.0000 1.000 0.000 1.000
#> GSM905035 2 0.0000 1.000 0.000 1.000
#> GSM905037 2 0.0000 1.000 0.000 1.000
#> GSM905039 2 0.0000 1.000 0.000 1.000
#> GSM905042 2 0.0000 1.000 0.000 1.000
#> GSM905046 1 0.0000 0.921 1.000 0.000
#> GSM905065 1 0.0000 0.921 1.000 0.000
#> GSM905049 1 0.0000 0.921 1.000 0.000
#> GSM905050 1 0.0000 0.921 1.000 0.000
#> GSM905064 1 0.0000 0.921 1.000 0.000
#> GSM905045 1 0.0000 0.921 1.000 0.000
#> GSM905051 1 0.0000 0.921 1.000 0.000
#> GSM905055 1 0.0000 0.921 1.000 0.000
#> GSM905058 1 0.0000 0.921 1.000 0.000
#> GSM905053 1 0.0000 0.921 1.000 0.000
#> GSM905061 1 0.0000 0.921 1.000 0.000
#> GSM905063 1 0.0000 0.921 1.000 0.000
#> GSM905054 1 0.0000 0.921 1.000 0.000
#> GSM905062 1 0.0000 0.921 1.000 0.000
#> GSM905052 1 0.0000 0.921 1.000 0.000
#> GSM905059 1 0.0000 0.921 1.000 0.000
#> GSM905047 1 0.0000 0.921 1.000 0.000
#> GSM905066 1 0.0000 0.921 1.000 0.000
#> GSM905056 1 0.0000 0.921 1.000 0.000
#> GSM905060 1 0.0000 0.921 1.000 0.000
#> GSM905048 1 0.0000 0.921 1.000 0.000
#> GSM905067 1 0.0000 0.921 1.000 0.000
#> GSM905057 1 0.0000 0.921 1.000 0.000
#> GSM905068 1 0.0000 0.921 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM905004 3 0.0000 1.000 0.000 0 1.000
#> GSM905024 1 0.0237 0.987 0.996 0 0.004
#> GSM905038 3 0.0000 1.000 0.000 0 1.000
#> GSM905043 1 0.4346 0.778 0.816 0 0.184
#> GSM904986 3 0.0000 1.000 0.000 0 1.000
#> GSM904991 3 0.0000 1.000 0.000 0 1.000
#> GSM904994 3 0.0000 1.000 0.000 0 1.000
#> GSM904996 3 0.0000 1.000 0.000 0 1.000
#> GSM905007 3 0.0000 1.000 0.000 0 1.000
#> GSM905012 3 0.0000 1.000 0.000 0 1.000
#> GSM905022 3 0.0000 1.000 0.000 0 1.000
#> GSM905026 3 0.0000 1.000 0.000 0 1.000
#> GSM905027 3 0.0000 1.000 0.000 0 1.000
#> GSM905031 3 0.0000 1.000 0.000 0 1.000
#> GSM905036 3 0.0000 1.000 0.000 0 1.000
#> GSM905041 3 0.0000 1.000 0.000 0 1.000
#> GSM905044 3 0.0000 1.000 0.000 0 1.000
#> GSM904989 3 0.0000 1.000 0.000 0 1.000
#> GSM904999 3 0.0000 1.000 0.000 0 1.000
#> GSM905002 3 0.0000 1.000 0.000 0 1.000
#> GSM905009 3 0.0000 1.000 0.000 0 1.000
#> GSM905014 3 0.0000 1.000 0.000 0 1.000
#> GSM905017 3 0.0000 1.000 0.000 0 1.000
#> GSM905020 3 0.0000 1.000 0.000 0 1.000
#> GSM905023 3 0.0000 1.000 0.000 0 1.000
#> GSM905029 3 0.0000 1.000 0.000 0 1.000
#> GSM905032 3 0.0000 1.000 0.000 0 1.000
#> GSM905034 1 0.0000 0.991 1.000 0 0.000
#> GSM905040 1 0.0000 0.991 1.000 0 0.000
#> GSM904985 2 0.0000 1.000 0.000 1 0.000
#> GSM904988 2 0.0000 1.000 0.000 1 0.000
#> GSM904990 2 0.0000 1.000 0.000 1 0.000
#> GSM904992 2 0.0000 1.000 0.000 1 0.000
#> GSM904995 2 0.0000 1.000 0.000 1 0.000
#> GSM904998 2 0.0000 1.000 0.000 1 0.000
#> GSM905000 2 0.0000 1.000 0.000 1 0.000
#> GSM905003 2 0.0000 1.000 0.000 1 0.000
#> GSM905006 2 0.0000 1.000 0.000 1 0.000
#> GSM905008 2 0.0000 1.000 0.000 1 0.000
#> GSM905011 2 0.0000 1.000 0.000 1 0.000
#> GSM905013 2 0.0000 1.000 0.000 1 0.000
#> GSM905016 2 0.0000 1.000 0.000 1 0.000
#> GSM905018 2 0.0000 1.000 0.000 1 0.000
#> GSM905021 2 0.0000 1.000 0.000 1 0.000
#> GSM905025 2 0.0000 1.000 0.000 1 0.000
#> GSM905028 2 0.0000 1.000 0.000 1 0.000
#> GSM905030 2 0.0000 1.000 0.000 1 0.000
#> GSM905033 2 0.0000 1.000 0.000 1 0.000
#> GSM905035 2 0.0000 1.000 0.000 1 0.000
#> GSM905037 2 0.0000 1.000 0.000 1 0.000
#> GSM905039 2 0.0000 1.000 0.000 1 0.000
#> GSM905042 2 0.0000 1.000 0.000 1 0.000
#> GSM905046 1 0.0000 0.991 1.000 0 0.000
#> GSM905065 1 0.0000 0.991 1.000 0 0.000
#> GSM905049 1 0.0000 0.991 1.000 0 0.000
#> GSM905050 1 0.1753 0.947 0.952 0 0.048
#> GSM905064 1 0.0000 0.991 1.000 0 0.000
#> GSM905045 1 0.0000 0.991 1.000 0 0.000
#> GSM905051 1 0.0000 0.991 1.000 0 0.000
#> GSM905055 1 0.0000 0.991 1.000 0 0.000
#> GSM905058 1 0.0000 0.991 1.000 0 0.000
#> GSM905053 1 0.0000 0.991 1.000 0 0.000
#> GSM905061 1 0.0000 0.991 1.000 0 0.000
#> GSM905063 1 0.0000 0.991 1.000 0 0.000
#> GSM905054 1 0.0000 0.991 1.000 0 0.000
#> GSM905062 1 0.0000 0.991 1.000 0 0.000
#> GSM905052 1 0.0000 0.991 1.000 0 0.000
#> GSM905059 1 0.0000 0.991 1.000 0 0.000
#> GSM905047 1 0.0000 0.991 1.000 0 0.000
#> GSM905066 1 0.0000 0.991 1.000 0 0.000
#> GSM905056 1 0.0000 0.991 1.000 0 0.000
#> GSM905060 1 0.0000 0.991 1.000 0 0.000
#> GSM905048 1 0.0000 0.991 1.000 0 0.000
#> GSM905067 1 0.0000 0.991 1.000 0 0.000
#> GSM905057 1 0.0000 0.991 1.000 0 0.000
#> GSM905068 1 0.0747 0.977 0.984 0 0.016
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM905004 3 0.0000 1.000 0.000 0 1.000 0.000
#> GSM905024 1 0.4746 0.420 0.632 0 0.368 0.000
#> GSM905038 3 0.0000 1.000 0.000 0 1.000 0.000
#> GSM905043 1 0.0336 0.963 0.992 0 0.008 0.000
#> GSM904986 3 0.0000 1.000 0.000 0 1.000 0.000
#> GSM904991 3 0.0000 1.000 0.000 0 1.000 0.000
#> GSM904994 3 0.0000 1.000 0.000 0 1.000 0.000
#> GSM904996 3 0.0000 1.000 0.000 0 1.000 0.000
#> GSM905007 3 0.0000 1.000 0.000 0 1.000 0.000
#> GSM905012 3 0.0000 1.000 0.000 0 1.000 0.000
#> GSM905022 3 0.0000 1.000 0.000 0 1.000 0.000
#> GSM905026 3 0.0000 1.000 0.000 0 1.000 0.000
#> GSM905027 3 0.0000 1.000 0.000 0 1.000 0.000
#> GSM905031 3 0.0000 1.000 0.000 0 1.000 0.000
#> GSM905036 3 0.0000 1.000 0.000 0 1.000 0.000
#> GSM905041 3 0.0000 1.000 0.000 0 1.000 0.000
#> GSM905044 3 0.0000 1.000 0.000 0 1.000 0.000
#> GSM904989 3 0.0000 1.000 0.000 0 1.000 0.000
#> GSM904999 3 0.0000 1.000 0.000 0 1.000 0.000
#> GSM905002 3 0.0000 1.000 0.000 0 1.000 0.000
#> GSM905009 3 0.0000 1.000 0.000 0 1.000 0.000
#> GSM905014 3 0.0000 1.000 0.000 0 1.000 0.000
#> GSM905017 3 0.0000 1.000 0.000 0 1.000 0.000
#> GSM905020 3 0.0000 1.000 0.000 0 1.000 0.000
#> GSM905023 3 0.0000 1.000 0.000 0 1.000 0.000
#> GSM905029 3 0.0000 1.000 0.000 0 1.000 0.000
#> GSM905032 3 0.0000 1.000 0.000 0 1.000 0.000
#> GSM905034 1 0.0000 0.970 1.000 0 0.000 0.000
#> GSM905040 1 0.0000 0.970 1.000 0 0.000 0.000
#> GSM904985 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM904988 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM904990 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM904992 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM904995 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM904998 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905000 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905003 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905006 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905008 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905011 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905013 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905016 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905018 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905021 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905025 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905028 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905030 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905033 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905035 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905037 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905039 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905042 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905046 1 0.0000 0.970 1.000 0 0.000 0.000
#> GSM905065 1 0.0000 0.970 1.000 0 0.000 0.000
#> GSM905049 4 0.0000 1.000 0.000 0 0.000 1.000
#> GSM905050 4 0.0000 1.000 0.000 0 0.000 1.000
#> GSM905064 4 0.0000 1.000 0.000 0 0.000 1.000
#> GSM905045 4 0.0000 1.000 0.000 0 0.000 1.000
#> GSM905051 4 0.0000 1.000 0.000 0 0.000 1.000
#> GSM905055 1 0.0000 0.970 1.000 0 0.000 0.000
#> GSM905058 1 0.0000 0.970 1.000 0 0.000 0.000
#> GSM905053 4 0.0000 1.000 0.000 0 0.000 1.000
#> GSM905061 4 0.0000 1.000 0.000 0 0.000 1.000
#> GSM905063 1 0.0000 0.970 1.000 0 0.000 0.000
#> GSM905054 4 0.0000 1.000 0.000 0 0.000 1.000
#> GSM905062 4 0.0000 1.000 0.000 0 0.000 1.000
#> GSM905052 4 0.0000 1.000 0.000 0 0.000 1.000
#> GSM905059 1 0.0469 0.960 0.988 0 0.000 0.012
#> GSM905047 1 0.0000 0.970 1.000 0 0.000 0.000
#> GSM905066 1 0.0000 0.970 1.000 0 0.000 0.000
#> GSM905056 1 0.0000 0.970 1.000 0 0.000 0.000
#> GSM905060 1 0.0000 0.970 1.000 0 0.000 0.000
#> GSM905048 1 0.0000 0.970 1.000 0 0.000 0.000
#> GSM905067 1 0.0000 0.970 1.000 0 0.000 0.000
#> GSM905057 1 0.0000 0.970 1.000 0 0.000 0.000
#> GSM905068 4 0.0000 1.000 0.000 0 0.000 1.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM905004 3 0.0000 1.000 0.000 0 1.000 0 0
#> GSM905024 1 0.0162 0.970 0.996 0 0.004 0 0
#> GSM905038 3 0.0000 1.000 0.000 0 1.000 0 0
#> GSM905043 1 0.2966 0.704 0.816 0 0.184 0 0
#> GSM904986 3 0.0000 1.000 0.000 0 1.000 0 0
#> GSM904991 3 0.0000 1.000 0.000 0 1.000 0 0
#> GSM904994 3 0.0000 1.000 0.000 0 1.000 0 0
#> GSM904996 3 0.0000 1.000 0.000 0 1.000 0 0
#> GSM905007 3 0.0000 1.000 0.000 0 1.000 0 0
#> GSM905012 3 0.0000 1.000 0.000 0 1.000 0 0
#> GSM905022 3 0.0000 1.000 0.000 0 1.000 0 0
#> GSM905026 3 0.0000 1.000 0.000 0 1.000 0 0
#> GSM905027 3 0.0000 1.000 0.000 0 1.000 0 0
#> GSM905031 3 0.0000 1.000 0.000 0 1.000 0 0
#> GSM905036 3 0.0000 1.000 0.000 0 1.000 0 0
#> GSM905041 3 0.0000 1.000 0.000 0 1.000 0 0
#> GSM905044 3 0.0000 1.000 0.000 0 1.000 0 0
#> GSM904989 3 0.0000 1.000 0.000 0 1.000 0 0
#> GSM904999 3 0.0000 1.000 0.000 0 1.000 0 0
#> GSM905002 3 0.0000 1.000 0.000 0 1.000 0 0
#> GSM905009 3 0.0000 1.000 0.000 0 1.000 0 0
#> GSM905014 3 0.0000 1.000 0.000 0 1.000 0 0
#> GSM905017 3 0.0000 1.000 0.000 0 1.000 0 0
#> GSM905020 3 0.0000 1.000 0.000 0 1.000 0 0
#> GSM905023 3 0.0000 1.000 0.000 0 1.000 0 0
#> GSM905029 3 0.0000 1.000 0.000 0 1.000 0 0
#> GSM905032 3 0.0000 1.000 0.000 0 1.000 0 0
#> GSM905034 1 0.0000 0.975 1.000 0 0.000 0 0
#> GSM905040 5 0.0000 1.000 0.000 0 0.000 0 1
#> GSM904985 2 0.0000 1.000 0.000 1 0.000 0 0
#> GSM904988 2 0.0000 1.000 0.000 1 0.000 0 0
#> GSM904990 2 0.0000 1.000 0.000 1 0.000 0 0
#> GSM904992 2 0.0000 1.000 0.000 1 0.000 0 0
#> GSM904995 2 0.0000 1.000 0.000 1 0.000 0 0
#> GSM904998 2 0.0000 1.000 0.000 1 0.000 0 0
#> GSM905000 2 0.0000 1.000 0.000 1 0.000 0 0
#> GSM905003 2 0.0000 1.000 0.000 1 0.000 0 0
#> GSM905006 2 0.0000 1.000 0.000 1 0.000 0 0
#> GSM905008 2 0.0000 1.000 0.000 1 0.000 0 0
#> GSM905011 2 0.0000 1.000 0.000 1 0.000 0 0
#> GSM905013 2 0.0000 1.000 0.000 1 0.000 0 0
#> GSM905016 2 0.0000 1.000 0.000 1 0.000 0 0
#> GSM905018 2 0.0000 1.000 0.000 1 0.000 0 0
#> GSM905021 2 0.0000 1.000 0.000 1 0.000 0 0
#> GSM905025 2 0.0000 1.000 0.000 1 0.000 0 0
#> GSM905028 2 0.0000 1.000 0.000 1 0.000 0 0
#> GSM905030 2 0.0000 1.000 0.000 1 0.000 0 0
#> GSM905033 2 0.0000 1.000 0.000 1 0.000 0 0
#> GSM905035 2 0.0000 1.000 0.000 1 0.000 0 0
#> GSM905037 2 0.0000 1.000 0.000 1 0.000 0 0
#> GSM905039 2 0.0000 1.000 0.000 1 0.000 0 0
#> GSM905042 2 0.0000 1.000 0.000 1 0.000 0 0
#> GSM905046 1 0.0000 0.975 1.000 0 0.000 0 0
#> GSM905065 1 0.0000 0.975 1.000 0 0.000 0 0
#> GSM905049 4 0.0000 1.000 0.000 0 0.000 1 0
#> GSM905050 4 0.0000 1.000 0.000 0 0.000 1 0
#> GSM905064 4 0.0000 1.000 0.000 0 0.000 1 0
#> GSM905045 4 0.0000 1.000 0.000 0 0.000 1 0
#> GSM905051 4 0.0000 1.000 0.000 0 0.000 1 0
#> GSM905055 5 0.0000 1.000 0.000 0 0.000 0 1
#> GSM905058 1 0.0000 0.975 1.000 0 0.000 0 0
#> GSM905053 4 0.0000 1.000 0.000 0 0.000 1 0
#> GSM905061 4 0.0000 1.000 0.000 0 0.000 1 0
#> GSM905063 5 0.0000 1.000 0.000 0 0.000 0 1
#> GSM905054 4 0.0000 1.000 0.000 0 0.000 1 0
#> GSM905062 4 0.0000 1.000 0.000 0 0.000 1 0
#> GSM905052 4 0.0000 1.000 0.000 0 0.000 1 0
#> GSM905059 1 0.0000 0.975 1.000 0 0.000 0 0
#> GSM905047 1 0.0000 0.975 1.000 0 0.000 0 0
#> GSM905066 1 0.0000 0.975 1.000 0 0.000 0 0
#> GSM905056 5 0.0000 1.000 0.000 0 0.000 0 1
#> GSM905060 1 0.0000 0.975 1.000 0 0.000 0 0
#> GSM905048 1 0.0000 0.975 1.000 0 0.000 0 0
#> GSM905067 1 0.0000 0.975 1.000 0 0.000 0 0
#> GSM905057 5 0.0000 1.000 0.000 0 0.000 0 1
#> GSM905068 4 0.0000 1.000 0.000 0 0.000 1 0
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM905004 3 0.0000 0.947 0.000 0 1.000 0 0.000 0.000
#> GSM905024 3 0.3563 0.617 0.000 0 0.664 0 0.336 0.000
#> GSM905038 3 0.0000 0.947 0.000 0 1.000 0 0.000 0.000
#> GSM905043 1 0.3563 0.451 0.664 0 0.000 0 0.336 0.000
#> GSM904986 3 0.0000 0.947 0.000 0 1.000 0 0.000 0.000
#> GSM904991 3 0.3563 0.617 0.000 0 0.664 0 0.336 0.000
#> GSM904994 3 0.0000 0.947 0.000 0 1.000 0 0.000 0.000
#> GSM904996 3 0.0000 0.947 0.000 0 1.000 0 0.000 0.000
#> GSM905007 3 0.0146 0.945 0.000 0 0.996 0 0.004 0.000
#> GSM905012 3 0.0000 0.947 0.000 0 1.000 0 0.000 0.000
#> GSM905022 3 0.0000 0.947 0.000 0 1.000 0 0.000 0.000
#> GSM905026 3 0.0000 0.947 0.000 0 1.000 0 0.000 0.000
#> GSM905027 3 0.0000 0.947 0.000 0 1.000 0 0.000 0.000
#> GSM905031 3 0.0000 0.947 0.000 0 1.000 0 0.000 0.000
#> GSM905036 3 0.0146 0.945 0.000 0 0.996 0 0.004 0.000
#> GSM905041 3 0.3351 0.677 0.000 0 0.712 0 0.288 0.000
#> GSM905044 3 0.0000 0.947 0.000 0 1.000 0 0.000 0.000
#> GSM904989 3 0.0000 0.947 0.000 0 1.000 0 0.000 0.000
#> GSM904999 3 0.0000 0.947 0.000 0 1.000 0 0.000 0.000
#> GSM905002 3 0.0000 0.947 0.000 0 1.000 0 0.000 0.000
#> GSM905009 3 0.0000 0.947 0.000 0 1.000 0 0.000 0.000
#> GSM905014 3 0.0146 0.945 0.000 0 0.996 0 0.004 0.000
#> GSM905017 3 0.0000 0.947 0.000 0 1.000 0 0.000 0.000
#> GSM905020 3 0.0000 0.947 0.000 0 1.000 0 0.000 0.000
#> GSM905023 3 0.0146 0.945 0.000 0 0.996 0 0.004 0.000
#> GSM905029 3 0.0000 0.947 0.000 0 1.000 0 0.000 0.000
#> GSM905032 3 0.3531 0.628 0.000 0 0.672 0 0.328 0.000
#> GSM905034 5 0.0000 0.482 0.000 0 0.000 0 1.000 0.000
#> GSM905040 6 0.3547 0.595 0.000 0 0.000 0 0.332 0.668
#> GSM904985 2 0.0000 1.000 0.000 1 0.000 0 0.000 0.000
#> GSM904988 2 0.0000 1.000 0.000 1 0.000 0 0.000 0.000
#> GSM904990 2 0.0000 1.000 0.000 1 0.000 0 0.000 0.000
#> GSM904992 2 0.0000 1.000 0.000 1 0.000 0 0.000 0.000
#> GSM904995 2 0.0000 1.000 0.000 1 0.000 0 0.000 0.000
#> GSM904998 2 0.0000 1.000 0.000 1 0.000 0 0.000 0.000
#> GSM905000 2 0.0000 1.000 0.000 1 0.000 0 0.000 0.000
#> GSM905003 2 0.0000 1.000 0.000 1 0.000 0 0.000 0.000
#> GSM905006 2 0.0000 1.000 0.000 1 0.000 0 0.000 0.000
#> GSM905008 2 0.0000 1.000 0.000 1 0.000 0 0.000 0.000
#> GSM905011 2 0.0000 1.000 0.000 1 0.000 0 0.000 0.000
#> GSM905013 2 0.0000 1.000 0.000 1 0.000 0 0.000 0.000
#> GSM905016 2 0.0000 1.000 0.000 1 0.000 0 0.000 0.000
#> GSM905018 2 0.0000 1.000 0.000 1 0.000 0 0.000 0.000
#> GSM905021 2 0.0000 1.000 0.000 1 0.000 0 0.000 0.000
#> GSM905025 2 0.0000 1.000 0.000 1 0.000 0 0.000 0.000
#> GSM905028 2 0.0000 1.000 0.000 1 0.000 0 0.000 0.000
#> GSM905030 2 0.0000 1.000 0.000 1 0.000 0 0.000 0.000
#> GSM905033 2 0.0000 1.000 0.000 1 0.000 0 0.000 0.000
#> GSM905035 2 0.0000 1.000 0.000 1 0.000 0 0.000 0.000
#> GSM905037 2 0.0000 1.000 0.000 1 0.000 0 0.000 0.000
#> GSM905039 2 0.0000 1.000 0.000 1 0.000 0 0.000 0.000
#> GSM905042 2 0.0000 1.000 0.000 1 0.000 0 0.000 0.000
#> GSM905046 1 0.0458 0.862 0.984 0 0.000 0 0.016 0.000
#> GSM905065 1 0.0000 0.879 1.000 0 0.000 0 0.000 0.000
#> GSM905049 4 0.0000 1.000 0.000 0 0.000 1 0.000 0.000
#> GSM905050 4 0.0000 1.000 0.000 0 0.000 1 0.000 0.000
#> GSM905064 4 0.0000 1.000 0.000 0 0.000 1 0.000 0.000
#> GSM905045 4 0.0000 1.000 0.000 0 0.000 1 0.000 0.000
#> GSM905051 4 0.0000 1.000 0.000 0 0.000 1 0.000 0.000
#> GSM905055 6 0.0000 0.907 0.000 0 0.000 0 0.000 1.000
#> GSM905058 5 0.3563 0.851 0.336 0 0.000 0 0.664 0.000
#> GSM905053 4 0.0000 1.000 0.000 0 0.000 1 0.000 0.000
#> GSM905061 4 0.0000 1.000 0.000 0 0.000 1 0.000 0.000
#> GSM905063 6 0.0405 0.901 0.008 0 0.000 0 0.004 0.988
#> GSM905054 4 0.0000 1.000 0.000 0 0.000 1 0.000 0.000
#> GSM905062 4 0.0000 1.000 0.000 0 0.000 1 0.000 0.000
#> GSM905052 4 0.0000 1.000 0.000 0 0.000 1 0.000 0.000
#> GSM905059 5 0.3563 0.851 0.336 0 0.000 0 0.664 0.000
#> GSM905047 5 0.3563 0.851 0.336 0 0.000 0 0.664 0.000
#> GSM905066 1 0.0000 0.879 1.000 0 0.000 0 0.000 0.000
#> GSM905056 6 0.0000 0.907 0.000 0 0.000 0 0.000 1.000
#> GSM905060 5 0.3563 0.851 0.336 0 0.000 0 0.664 0.000
#> GSM905048 1 0.0000 0.879 1.000 0 0.000 0 0.000 0.000
#> GSM905067 1 0.0000 0.879 1.000 0 0.000 0 0.000 0.000
#> GSM905057 6 0.0000 0.907 0.000 0 0.000 0 0.000 1.000
#> GSM905068 4 0.0000 1.000 0.000 0 0.000 1 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) genotype/variation(p) individual(p) k
#> SD:pam 76 3.04e-12 1.17e-05 0.9902 2
#> SD:pam 76 1.53e-18 5.88e-06 0.8922 3
#> SD:pam 75 1.05e-21 2.27e-09 0.3547 4
#> SD:pam 76 1.33e-21 7.96e-12 0.0127 5
#> SD:pam 74 1.82e-26 7.00e-12 0.0266 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 76 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 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 1.000 1.000 0.4283 0.572 0.572
#> 3 3 1.000 0.984 0.994 0.5768 0.721 0.525
#> 4 4 0.897 0.797 0.896 0.0862 0.939 0.814
#> 5 5 0.956 0.875 0.946 0.0621 0.907 0.686
#> 6 6 0.873 0.688 0.855 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] 5
#> 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
#> GSM905004 1 0 1 1 0
#> GSM905024 1 0 1 1 0
#> GSM905038 1 0 1 1 0
#> GSM905043 1 0 1 1 0
#> GSM904986 1 0 1 1 0
#> GSM904991 1 0 1 1 0
#> GSM904994 1 0 1 1 0
#> GSM904996 1 0 1 1 0
#> GSM905007 1 0 1 1 0
#> GSM905012 1 0 1 1 0
#> GSM905022 1 0 1 1 0
#> GSM905026 1 0 1 1 0
#> GSM905027 1 0 1 1 0
#> GSM905031 1 0 1 1 0
#> GSM905036 1 0 1 1 0
#> GSM905041 1 0 1 1 0
#> GSM905044 1 0 1 1 0
#> GSM904989 1 0 1 1 0
#> GSM904999 1 0 1 1 0
#> GSM905002 1 0 1 1 0
#> GSM905009 1 0 1 1 0
#> GSM905014 1 0 1 1 0
#> GSM905017 1 0 1 1 0
#> GSM905020 1 0 1 1 0
#> GSM905023 1 0 1 1 0
#> GSM905029 1 0 1 1 0
#> GSM905032 1 0 1 1 0
#> GSM905034 1 0 1 1 0
#> GSM905040 1 0 1 1 0
#> GSM904985 2 0 1 0 1
#> GSM904988 2 0 1 0 1
#> GSM904990 2 0 1 0 1
#> GSM904992 2 0 1 0 1
#> GSM904995 2 0 1 0 1
#> GSM904998 2 0 1 0 1
#> GSM905000 2 0 1 0 1
#> GSM905003 2 0 1 0 1
#> GSM905006 2 0 1 0 1
#> GSM905008 2 0 1 0 1
#> GSM905011 2 0 1 0 1
#> GSM905013 2 0 1 0 1
#> GSM905016 2 0 1 0 1
#> GSM905018 2 0 1 0 1
#> GSM905021 2 0 1 0 1
#> GSM905025 2 0 1 0 1
#> GSM905028 2 0 1 0 1
#> GSM905030 2 0 1 0 1
#> GSM905033 2 0 1 0 1
#> GSM905035 2 0 1 0 1
#> GSM905037 2 0 1 0 1
#> GSM905039 2 0 1 0 1
#> GSM905042 2 0 1 0 1
#> GSM905046 1 0 1 1 0
#> GSM905065 1 0 1 1 0
#> GSM905049 1 0 1 1 0
#> GSM905050 1 0 1 1 0
#> GSM905064 1 0 1 1 0
#> GSM905045 1 0 1 1 0
#> GSM905051 1 0 1 1 0
#> GSM905055 1 0 1 1 0
#> GSM905058 1 0 1 1 0
#> GSM905053 1 0 1 1 0
#> GSM905061 1 0 1 1 0
#> GSM905063 1 0 1 1 0
#> GSM905054 1 0 1 1 0
#> GSM905062 1 0 1 1 0
#> GSM905052 1 0 1 1 0
#> GSM905059 1 0 1 1 0
#> GSM905047 1 0 1 1 0
#> GSM905066 1 0 1 1 0
#> GSM905056 1 0 1 1 0
#> GSM905060 1 0 1 1 0
#> GSM905048 1 0 1 1 0
#> GSM905067 1 0 1 1 0
#> GSM905057 1 0 1 1 0
#> GSM905068 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM905004 3 0.6079 0.369 0.388 0.000 0.612
#> GSM905024 3 0.0237 0.979 0.004 0.000 0.996
#> GSM905038 3 0.0000 0.982 0.000 0.000 1.000
#> GSM905043 3 0.0237 0.979 0.004 0.000 0.996
#> GSM904986 3 0.0000 0.982 0.000 0.000 1.000
#> GSM904991 3 0.0000 0.982 0.000 0.000 1.000
#> GSM904994 3 0.0000 0.982 0.000 0.000 1.000
#> GSM904996 3 0.0000 0.982 0.000 0.000 1.000
#> GSM905007 3 0.0000 0.982 0.000 0.000 1.000
#> GSM905012 3 0.0000 0.982 0.000 0.000 1.000
#> GSM905022 3 0.0000 0.982 0.000 0.000 1.000
#> GSM905026 3 0.0000 0.982 0.000 0.000 1.000
#> GSM905027 3 0.0000 0.982 0.000 0.000 1.000
#> GSM905031 3 0.0000 0.982 0.000 0.000 1.000
#> GSM905036 3 0.0000 0.982 0.000 0.000 1.000
#> GSM905041 3 0.0000 0.982 0.000 0.000 1.000
#> GSM905044 3 0.0000 0.982 0.000 0.000 1.000
#> GSM904989 3 0.0000 0.982 0.000 0.000 1.000
#> GSM904999 2 0.0237 0.996 0.004 0.996 0.000
#> GSM905002 3 0.0000 0.982 0.000 0.000 1.000
#> GSM905009 3 0.0000 0.982 0.000 0.000 1.000
#> GSM905014 3 0.0000 0.982 0.000 0.000 1.000
#> GSM905017 2 0.0237 0.996 0.004 0.996 0.000
#> GSM905020 3 0.0000 0.982 0.000 0.000 1.000
#> GSM905023 3 0.0000 0.982 0.000 0.000 1.000
#> GSM905029 3 0.0000 0.982 0.000 0.000 1.000
#> GSM905032 3 0.2400 0.918 0.004 0.064 0.932
#> GSM905034 3 0.0237 0.979 0.004 0.000 0.996
#> GSM905040 3 0.0237 0.979 0.004 0.000 0.996
#> GSM904985 2 0.0000 1.000 0.000 1.000 0.000
#> GSM904988 2 0.0000 1.000 0.000 1.000 0.000
#> GSM904990 2 0.0000 1.000 0.000 1.000 0.000
#> GSM904992 2 0.0000 1.000 0.000 1.000 0.000
#> GSM904995 2 0.0000 1.000 0.000 1.000 0.000
#> GSM904998 2 0.0000 1.000 0.000 1.000 0.000
#> GSM905000 2 0.0000 1.000 0.000 1.000 0.000
#> GSM905003 2 0.0000 1.000 0.000 1.000 0.000
#> GSM905006 2 0.0000 1.000 0.000 1.000 0.000
#> GSM905008 2 0.0000 1.000 0.000 1.000 0.000
#> GSM905011 2 0.0000 1.000 0.000 1.000 0.000
#> GSM905013 2 0.0000 1.000 0.000 1.000 0.000
#> GSM905016 2 0.0000 1.000 0.000 1.000 0.000
#> GSM905018 2 0.0000 1.000 0.000 1.000 0.000
#> GSM905021 2 0.0000 1.000 0.000 1.000 0.000
#> GSM905025 2 0.0000 1.000 0.000 1.000 0.000
#> GSM905028 2 0.0000 1.000 0.000 1.000 0.000
#> GSM905030 2 0.0000 1.000 0.000 1.000 0.000
#> GSM905033 2 0.0000 1.000 0.000 1.000 0.000
#> GSM905035 2 0.0000 1.000 0.000 1.000 0.000
#> GSM905037 2 0.0000 1.000 0.000 1.000 0.000
#> GSM905039 2 0.0000 1.000 0.000 1.000 0.000
#> GSM905042 2 0.0000 1.000 0.000 1.000 0.000
#> GSM905046 1 0.0000 1.000 1.000 0.000 0.000
#> GSM905065 1 0.0000 1.000 1.000 0.000 0.000
#> GSM905049 1 0.0000 1.000 1.000 0.000 0.000
#> GSM905050 1 0.0000 1.000 1.000 0.000 0.000
#> GSM905064 1 0.0000 1.000 1.000 0.000 0.000
#> GSM905045 1 0.0000 1.000 1.000 0.000 0.000
#> GSM905051 1 0.0000 1.000 1.000 0.000 0.000
#> GSM905055 1 0.0000 1.000 1.000 0.000 0.000
#> GSM905058 1 0.0000 1.000 1.000 0.000 0.000
#> GSM905053 1 0.0000 1.000 1.000 0.000 0.000
#> GSM905061 1 0.0000 1.000 1.000 0.000 0.000
#> GSM905063 1 0.0000 1.000 1.000 0.000 0.000
#> GSM905054 1 0.0000 1.000 1.000 0.000 0.000
#> GSM905062 1 0.0000 1.000 1.000 0.000 0.000
#> GSM905052 1 0.0000 1.000 1.000 0.000 0.000
#> GSM905059 1 0.0000 1.000 1.000 0.000 0.000
#> GSM905047 1 0.0000 1.000 1.000 0.000 0.000
#> GSM905066 1 0.0000 1.000 1.000 0.000 0.000
#> GSM905056 1 0.0000 1.000 1.000 0.000 0.000
#> GSM905060 1 0.0000 1.000 1.000 0.000 0.000
#> GSM905048 1 0.0000 1.000 1.000 0.000 0.000
#> GSM905067 1 0.0000 1.000 1.000 0.000 0.000
#> GSM905057 1 0.0000 1.000 1.000 0.000 0.000
#> GSM905068 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
#> GSM905004 1 0.7753 -0.3499 0.432 0.000 0.256 0.312
#> GSM905024 3 0.6273 0.5008 0.264 0.000 0.636 0.100
#> GSM905038 3 0.0000 0.9241 0.000 0.000 1.000 0.000
#> GSM905043 3 0.6436 0.4519 0.292 0.000 0.608 0.100
#> GSM904986 3 0.0000 0.9241 0.000 0.000 1.000 0.000
#> GSM904991 3 0.0000 0.9241 0.000 0.000 1.000 0.000
#> GSM904994 3 0.0000 0.9241 0.000 0.000 1.000 0.000
#> GSM904996 3 0.0000 0.9241 0.000 0.000 1.000 0.000
#> GSM905007 3 0.0000 0.9241 0.000 0.000 1.000 0.000
#> GSM905012 3 0.0000 0.9241 0.000 0.000 1.000 0.000
#> GSM905022 3 0.0000 0.9241 0.000 0.000 1.000 0.000
#> GSM905026 3 0.0000 0.9241 0.000 0.000 1.000 0.000
#> GSM905027 3 0.0000 0.9241 0.000 0.000 1.000 0.000
#> GSM905031 3 0.0000 0.9241 0.000 0.000 1.000 0.000
#> GSM905036 3 0.0000 0.9241 0.000 0.000 1.000 0.000
#> GSM905041 3 0.0000 0.9241 0.000 0.000 1.000 0.000
#> GSM905044 3 0.0000 0.9241 0.000 0.000 1.000 0.000
#> GSM904989 3 0.0000 0.9241 0.000 0.000 1.000 0.000
#> GSM904999 1 0.5893 0.3446 0.592 0.372 0.008 0.028
#> GSM905002 3 0.0000 0.9241 0.000 0.000 1.000 0.000
#> GSM905009 3 0.0000 0.9241 0.000 0.000 1.000 0.000
#> GSM905014 3 0.0000 0.9241 0.000 0.000 1.000 0.000
#> GSM905017 1 0.6038 0.2183 0.532 0.432 0.008 0.028
#> GSM905020 3 0.0000 0.9241 0.000 0.000 1.000 0.000
#> GSM905023 3 0.0376 0.9175 0.004 0.000 0.992 0.004
#> GSM905029 3 0.0000 0.9241 0.000 0.000 1.000 0.000
#> GSM905032 1 0.1256 0.3247 0.964 0.000 0.008 0.028
#> GSM905034 3 0.6273 0.5008 0.264 0.000 0.636 0.100
#> GSM905040 3 0.7568 -0.0635 0.400 0.000 0.408 0.192
#> GSM904985 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM904988 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM904990 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM904992 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM904995 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM904998 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM905000 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM905003 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM905006 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM905008 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM905011 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM905013 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM905016 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM905018 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM905021 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM905025 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM905028 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM905030 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM905033 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM905035 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM905037 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM905039 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM905042 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM905046 4 0.1867 0.7038 0.072 0.000 0.000 0.928
#> GSM905065 4 0.0000 0.6585 0.000 0.000 0.000 1.000
#> GSM905049 4 0.4907 0.7277 0.420 0.000 0.000 0.580
#> GSM905050 4 0.4907 0.7277 0.420 0.000 0.000 0.580
#> GSM905064 4 0.4761 0.7405 0.372 0.000 0.000 0.628
#> GSM905045 4 0.4898 0.7284 0.416 0.000 0.000 0.584
#> GSM905051 4 0.4661 0.7411 0.348 0.000 0.000 0.652
#> GSM905055 1 0.4933 0.5110 0.568 0.000 0.000 0.432
#> GSM905058 4 0.0000 0.6585 0.000 0.000 0.000 1.000
#> GSM905053 4 0.4907 0.7277 0.420 0.000 0.000 0.580
#> GSM905061 4 0.4907 0.7277 0.420 0.000 0.000 0.580
#> GSM905063 4 0.2216 0.5197 0.092 0.000 0.000 0.908
#> GSM905054 4 0.4776 0.7399 0.376 0.000 0.000 0.624
#> GSM905062 4 0.4907 0.7277 0.420 0.000 0.000 0.580
#> GSM905052 4 0.4661 0.7411 0.348 0.000 0.000 0.652
#> GSM905059 4 0.1867 0.7038 0.072 0.000 0.000 0.928
#> GSM905047 4 0.1867 0.7038 0.072 0.000 0.000 0.928
#> GSM905066 4 0.0000 0.6585 0.000 0.000 0.000 1.000
#> GSM905056 1 0.4933 0.5110 0.568 0.000 0.000 0.432
#> GSM905060 4 0.1867 0.7038 0.072 0.000 0.000 0.928
#> GSM905048 4 0.0000 0.6585 0.000 0.000 0.000 1.000
#> GSM905067 4 0.0000 0.6585 0.000 0.000 0.000 1.000
#> GSM905057 1 0.4933 0.5110 0.568 0.000 0.000 0.432
#> GSM905068 4 0.4907 0.7277 0.420 0.000 0.000 0.580
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM905004 4 0.504 0.4178 0.044 0 0.356 0.600 0.00
#> GSM905024 5 0.000 1.0000 0.000 0 0.000 0.000 1.00
#> GSM905038 3 0.000 1.0000 0.000 0 1.000 0.000 0.00
#> GSM905043 5 0.000 1.0000 0.000 0 0.000 0.000 1.00
#> GSM904986 3 0.000 1.0000 0.000 0 1.000 0.000 0.00
#> GSM904991 3 0.000 1.0000 0.000 0 1.000 0.000 0.00
#> GSM904994 3 0.000 1.0000 0.000 0 1.000 0.000 0.00
#> GSM904996 3 0.000 1.0000 0.000 0 1.000 0.000 0.00
#> GSM905007 3 0.000 1.0000 0.000 0 1.000 0.000 0.00
#> GSM905012 3 0.000 1.0000 0.000 0 1.000 0.000 0.00
#> GSM905022 3 0.000 1.0000 0.000 0 1.000 0.000 0.00
#> GSM905026 3 0.000 1.0000 0.000 0 1.000 0.000 0.00
#> GSM905027 3 0.000 1.0000 0.000 0 1.000 0.000 0.00
#> GSM905031 3 0.000 1.0000 0.000 0 1.000 0.000 0.00
#> GSM905036 3 0.000 1.0000 0.000 0 1.000 0.000 0.00
#> GSM905041 3 0.000 1.0000 0.000 0 1.000 0.000 0.00
#> GSM905044 3 0.000 1.0000 0.000 0 1.000 0.000 0.00
#> GSM904989 3 0.000 1.0000 0.000 0 1.000 0.000 0.00
#> GSM904999 5 0.000 1.0000 0.000 0 0.000 0.000 1.00
#> GSM905002 3 0.000 1.0000 0.000 0 1.000 0.000 0.00
#> GSM905009 3 0.000 1.0000 0.000 0 1.000 0.000 0.00
#> GSM905014 3 0.000 1.0000 0.000 0 1.000 0.000 0.00
#> GSM905017 5 0.000 1.0000 0.000 0 0.000 0.000 1.00
#> GSM905020 3 0.000 1.0000 0.000 0 1.000 0.000 0.00
#> GSM905023 3 0.000 1.0000 0.000 0 1.000 0.000 0.00
#> GSM905029 3 0.000 1.0000 0.000 0 1.000 0.000 0.00
#> GSM905032 5 0.000 1.0000 0.000 0 0.000 0.000 1.00
#> GSM905034 5 0.000 1.0000 0.000 0 0.000 0.000 1.00
#> GSM905040 5 0.000 1.0000 0.000 0 0.000 0.000 1.00
#> GSM904985 2 0.000 1.0000 0.000 1 0.000 0.000 0.00
#> GSM904988 2 0.000 1.0000 0.000 1 0.000 0.000 0.00
#> GSM904990 2 0.000 1.0000 0.000 1 0.000 0.000 0.00
#> GSM904992 2 0.000 1.0000 0.000 1 0.000 0.000 0.00
#> GSM904995 2 0.000 1.0000 0.000 1 0.000 0.000 0.00
#> GSM904998 2 0.000 1.0000 0.000 1 0.000 0.000 0.00
#> GSM905000 2 0.000 1.0000 0.000 1 0.000 0.000 0.00
#> GSM905003 2 0.000 1.0000 0.000 1 0.000 0.000 0.00
#> GSM905006 2 0.000 1.0000 0.000 1 0.000 0.000 0.00
#> GSM905008 2 0.000 1.0000 0.000 1 0.000 0.000 0.00
#> GSM905011 2 0.000 1.0000 0.000 1 0.000 0.000 0.00
#> GSM905013 2 0.000 1.0000 0.000 1 0.000 0.000 0.00
#> GSM905016 2 0.000 1.0000 0.000 1 0.000 0.000 0.00
#> GSM905018 2 0.000 1.0000 0.000 1 0.000 0.000 0.00
#> GSM905021 2 0.000 1.0000 0.000 1 0.000 0.000 0.00
#> GSM905025 2 0.000 1.0000 0.000 1 0.000 0.000 0.00
#> GSM905028 2 0.000 1.0000 0.000 1 0.000 0.000 0.00
#> GSM905030 2 0.000 1.0000 0.000 1 0.000 0.000 0.00
#> GSM905033 2 0.000 1.0000 0.000 1 0.000 0.000 0.00
#> GSM905035 2 0.000 1.0000 0.000 1 0.000 0.000 0.00
#> GSM905037 2 0.000 1.0000 0.000 1 0.000 0.000 0.00
#> GSM905039 2 0.000 1.0000 0.000 1 0.000 0.000 0.00
#> GSM905042 2 0.000 1.0000 0.000 1 0.000 0.000 0.00
#> GSM905046 1 0.167 0.6698 0.924 0 0.000 0.076 0.00
#> GSM905065 1 0.000 0.6857 1.000 0 0.000 0.000 0.00
#> GSM905049 4 0.000 0.9257 0.000 0 0.000 1.000 0.00
#> GSM905050 4 0.000 0.9257 0.000 0 0.000 1.000 0.00
#> GSM905064 4 0.112 0.8929 0.044 0 0.000 0.956 0.00
#> GSM905045 4 0.112 0.8929 0.044 0 0.000 0.956 0.00
#> GSM905051 1 0.407 0.4317 0.636 0 0.000 0.364 0.00
#> GSM905055 1 0.430 0.0748 0.520 0 0.000 0.000 0.48
#> GSM905058 1 0.000 0.6857 1.000 0 0.000 0.000 0.00
#> GSM905053 4 0.000 0.9257 0.000 0 0.000 1.000 0.00
#> GSM905061 4 0.000 0.9257 0.000 0 0.000 1.000 0.00
#> GSM905063 1 0.430 0.0748 0.520 0 0.000 0.000 0.48
#> GSM905054 4 0.000 0.9257 0.000 0 0.000 1.000 0.00
#> GSM905062 4 0.000 0.9257 0.000 0 0.000 1.000 0.00
#> GSM905052 1 0.407 0.4317 0.636 0 0.000 0.364 0.00
#> GSM905059 1 0.380 0.5245 0.700 0 0.000 0.300 0.00
#> GSM905047 1 0.380 0.5245 0.700 0 0.000 0.300 0.00
#> GSM905066 1 0.000 0.6857 1.000 0 0.000 0.000 0.00
#> GSM905056 1 0.430 0.0748 0.520 0 0.000 0.000 0.48
#> GSM905060 1 0.380 0.5245 0.700 0 0.000 0.300 0.00
#> GSM905048 1 0.000 0.6857 1.000 0 0.000 0.000 0.00
#> GSM905067 1 0.000 0.6857 1.000 0 0.000 0.000 0.00
#> GSM905057 1 0.430 0.0748 0.520 0 0.000 0.000 0.48
#> GSM905068 4 0.000 0.9257 0.000 0 0.000 1.000 0.00
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM905004 4 0.6240 0.549 0.024 0.000 0.176 0.608 0.044 0.148
#> GSM905024 5 0.0000 0.994 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM905038 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905043 5 0.0000 0.994 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM904986 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM904991 3 0.0632 0.976 0.000 0.000 0.976 0.000 0.024 0.000
#> GSM904994 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM904996 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905007 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905012 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905022 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905026 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905027 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905031 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905036 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905041 3 0.0865 0.964 0.000 0.000 0.964 0.000 0.036 0.000
#> GSM905044 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM904989 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM904999 5 0.0520 0.987 0.000 0.000 0.008 0.000 0.984 0.008
#> GSM905002 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905009 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905014 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905017 5 0.0520 0.987 0.000 0.000 0.008 0.000 0.984 0.008
#> GSM905020 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905023 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905029 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905032 5 0.0146 0.993 0.000 0.000 0.000 0.000 0.996 0.004
#> GSM905034 5 0.0000 0.994 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM905040 5 0.0000 0.994 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM904985 2 0.3797 -0.494 0.000 0.580 0.000 0.000 0.000 0.420
#> GSM904988 2 0.0000 0.632 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM904990 2 0.0000 0.632 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM904992 2 0.0000 0.632 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM904995 2 0.3634 -0.208 0.000 0.644 0.000 0.000 0.000 0.356
#> GSM904998 2 0.1007 0.595 0.000 0.956 0.000 0.000 0.000 0.044
#> GSM905000 2 0.0000 0.632 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905003 2 0.2416 0.427 0.000 0.844 0.000 0.000 0.000 0.156
#> GSM905006 2 0.0000 0.632 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905008 2 0.3860 -0.734 0.000 0.528 0.000 0.000 0.000 0.472
#> GSM905011 2 0.0000 0.632 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905013 2 0.0790 0.608 0.000 0.968 0.000 0.000 0.000 0.032
#> GSM905016 2 0.3634 -0.208 0.000 0.644 0.000 0.000 0.000 0.356
#> GSM905018 2 0.0000 0.632 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905021 6 0.3833 0.987 0.000 0.444 0.000 0.000 0.000 0.556
#> GSM905025 2 0.3634 -0.208 0.000 0.644 0.000 0.000 0.000 0.356
#> GSM905028 2 0.3634 -0.208 0.000 0.644 0.000 0.000 0.000 0.356
#> GSM905030 2 0.0713 0.612 0.000 0.972 0.000 0.000 0.000 0.028
#> GSM905033 6 0.3828 0.994 0.000 0.440 0.000 0.000 0.000 0.560
#> GSM905035 2 0.3634 -0.208 0.000 0.644 0.000 0.000 0.000 0.356
#> GSM905037 2 0.0000 0.632 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905039 2 0.3634 -0.208 0.000 0.644 0.000 0.000 0.000 0.356
#> GSM905042 6 0.3828 0.994 0.000 0.440 0.000 0.000 0.000 0.560
#> GSM905046 1 0.2830 0.643 0.836 0.000 0.000 0.144 0.000 0.020
#> GSM905065 1 0.0000 0.695 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM905049 4 0.0000 0.928 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905050 4 0.0000 0.928 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905064 4 0.1411 0.882 0.060 0.000 0.000 0.936 0.000 0.004
#> GSM905045 4 0.3275 0.790 0.032 0.000 0.000 0.820 0.008 0.140
#> GSM905051 1 0.5082 0.555 0.648 0.000 0.000 0.188 0.004 0.160
#> GSM905055 1 0.5994 0.217 0.440 0.000 0.000 0.000 0.284 0.276
#> GSM905058 1 0.0000 0.695 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM905053 4 0.0000 0.928 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905061 4 0.0000 0.928 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905063 1 0.5974 0.228 0.448 0.000 0.000 0.000 0.276 0.276
#> GSM905054 4 0.0000 0.928 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905062 4 0.0000 0.928 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905052 1 0.5055 0.560 0.652 0.000 0.000 0.184 0.004 0.160
#> GSM905059 1 0.4602 0.602 0.696 0.000 0.000 0.144 0.000 0.160
#> GSM905047 1 0.4602 0.602 0.696 0.000 0.000 0.144 0.000 0.160
#> GSM905066 1 0.0000 0.695 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM905056 1 0.5994 0.217 0.440 0.000 0.000 0.000 0.284 0.276
#> GSM905060 1 0.4602 0.602 0.696 0.000 0.000 0.144 0.000 0.160
#> GSM905048 1 0.0000 0.695 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM905067 1 0.0000 0.695 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM905057 1 0.5994 0.217 0.440 0.000 0.000 0.000 0.284 0.276
#> GSM905068 4 0.0000 0.928 0.000 0.000 0.000 1.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) genotype/variation(p) individual(p) k
#> SD:mclust 76 3.04e-12 1.17e-05 0.9902 2
#> SD:mclust 75 7.59e-20 1.17e-05 0.9573 3
#> SD:mclust 70 3.18e-21 5.89e-06 0.0522 4
#> SD:mclust 69 3.53e-21 6.70e-12 0.6768 5
#> SD:mclust 63 5.19e-13 3.51e-07 0.5927 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 76 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 5.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.728 0.896 0.943 0.4867 0.494 0.494
#> 3 3 1.000 0.984 0.993 0.3850 0.705 0.470
#> 4 4 0.964 0.947 0.978 0.1055 0.890 0.681
#> 5 5 0.940 0.898 0.946 0.0425 0.921 0.716
#> 6 6 0.876 0.809 0.892 0.0294 0.970 0.871
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] 3 4
There is also optional best \(k\) = 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
#> GSM905004 1 0.6887 0.721 0.816 0.184
#> GSM905024 1 0.0000 0.994 1.000 0.000
#> GSM905038 1 0.0376 0.990 0.996 0.004
#> GSM905043 1 0.0000 0.994 1.000 0.000
#> GSM904986 2 0.7950 0.751 0.240 0.760
#> GSM904991 1 0.0000 0.994 1.000 0.000
#> GSM904994 2 0.8713 0.702 0.292 0.708
#> GSM904996 2 0.8443 0.723 0.272 0.728
#> GSM905007 1 0.0000 0.994 1.000 0.000
#> GSM905012 2 0.8144 0.742 0.252 0.748
#> GSM905022 2 0.9608 0.558 0.384 0.616
#> GSM905026 2 0.9732 0.517 0.404 0.596
#> GSM905027 1 0.0672 0.985 0.992 0.008
#> GSM905031 2 0.8555 0.715 0.280 0.720
#> GSM905036 1 0.0000 0.994 1.000 0.000
#> GSM905041 1 0.0000 0.994 1.000 0.000
#> GSM905044 2 0.9248 0.636 0.340 0.660
#> GSM904989 2 0.9833 0.471 0.424 0.576
#> GSM904999 2 0.9248 0.636 0.340 0.660
#> GSM905002 2 0.9000 0.671 0.316 0.684
#> GSM905009 2 0.8608 0.711 0.284 0.716
#> GSM905014 1 0.0000 0.994 1.000 0.000
#> GSM905017 2 0.5946 0.815 0.144 0.856
#> GSM905020 2 0.6623 0.799 0.172 0.828
#> GSM905023 1 0.0376 0.990 0.996 0.004
#> GSM905029 1 0.0000 0.994 1.000 0.000
#> GSM905032 1 0.0000 0.994 1.000 0.000
#> GSM905034 1 0.0000 0.994 1.000 0.000
#> GSM905040 1 0.0000 0.994 1.000 0.000
#> GSM904985 2 0.0000 0.878 0.000 1.000
#> GSM904988 2 0.0000 0.878 0.000 1.000
#> GSM904990 2 0.0000 0.878 0.000 1.000
#> GSM904992 2 0.0000 0.878 0.000 1.000
#> GSM904995 2 0.0000 0.878 0.000 1.000
#> GSM904998 2 0.0000 0.878 0.000 1.000
#> GSM905000 2 0.0000 0.878 0.000 1.000
#> GSM905003 2 0.0000 0.878 0.000 1.000
#> GSM905006 2 0.0000 0.878 0.000 1.000
#> GSM905008 2 0.0000 0.878 0.000 1.000
#> GSM905011 2 0.0000 0.878 0.000 1.000
#> GSM905013 2 0.0000 0.878 0.000 1.000
#> GSM905016 2 0.0000 0.878 0.000 1.000
#> GSM905018 2 0.0000 0.878 0.000 1.000
#> GSM905021 2 0.0000 0.878 0.000 1.000
#> GSM905025 2 0.0000 0.878 0.000 1.000
#> GSM905028 2 0.0000 0.878 0.000 1.000
#> GSM905030 2 0.0000 0.878 0.000 1.000
#> GSM905033 2 0.0000 0.878 0.000 1.000
#> GSM905035 2 0.0000 0.878 0.000 1.000
#> GSM905037 2 0.0000 0.878 0.000 1.000
#> GSM905039 2 0.0000 0.878 0.000 1.000
#> GSM905042 2 0.0000 0.878 0.000 1.000
#> GSM905046 1 0.0000 0.994 1.000 0.000
#> GSM905065 1 0.0000 0.994 1.000 0.000
#> GSM905049 1 0.0000 0.994 1.000 0.000
#> GSM905050 1 0.0000 0.994 1.000 0.000
#> GSM905064 1 0.0000 0.994 1.000 0.000
#> GSM905045 1 0.0000 0.994 1.000 0.000
#> GSM905051 1 0.0000 0.994 1.000 0.000
#> GSM905055 1 0.0000 0.994 1.000 0.000
#> GSM905058 1 0.0000 0.994 1.000 0.000
#> GSM905053 1 0.0000 0.994 1.000 0.000
#> GSM905061 1 0.0000 0.994 1.000 0.000
#> GSM905063 1 0.0000 0.994 1.000 0.000
#> GSM905054 1 0.0000 0.994 1.000 0.000
#> GSM905062 1 0.0000 0.994 1.000 0.000
#> GSM905052 1 0.0000 0.994 1.000 0.000
#> GSM905059 1 0.0000 0.994 1.000 0.000
#> GSM905047 1 0.0000 0.994 1.000 0.000
#> GSM905066 1 0.0000 0.994 1.000 0.000
#> GSM905056 1 0.0000 0.994 1.000 0.000
#> GSM905060 1 0.0000 0.994 1.000 0.000
#> GSM905048 1 0.0000 0.994 1.000 0.000
#> GSM905067 1 0.0000 0.994 1.000 0.000
#> GSM905057 1 0.0000 0.994 1.000 0.000
#> GSM905068 1 0.0000 0.994 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM905004 3 0.000 0.994 0.000 0 1.000
#> GSM905024 3 0.271 0.904 0.088 0 0.912
#> GSM905038 3 0.000 0.994 0.000 0 1.000
#> GSM905043 3 0.207 0.936 0.060 0 0.940
#> GSM904986 3 0.000 0.994 0.000 0 1.000
#> GSM904991 3 0.000 0.994 0.000 0 1.000
#> GSM904994 3 0.000 0.994 0.000 0 1.000
#> GSM904996 3 0.000 0.994 0.000 0 1.000
#> GSM905007 3 0.000 0.994 0.000 0 1.000
#> GSM905012 3 0.000 0.994 0.000 0 1.000
#> GSM905022 3 0.000 0.994 0.000 0 1.000
#> GSM905026 3 0.000 0.994 0.000 0 1.000
#> GSM905027 3 0.000 0.994 0.000 0 1.000
#> GSM905031 3 0.000 0.994 0.000 0 1.000
#> GSM905036 3 0.000 0.994 0.000 0 1.000
#> GSM905041 3 0.000 0.994 0.000 0 1.000
#> GSM905044 3 0.000 0.994 0.000 0 1.000
#> GSM904989 3 0.000 0.994 0.000 0 1.000
#> GSM904999 3 0.000 0.994 0.000 0 1.000
#> GSM905002 3 0.000 0.994 0.000 0 1.000
#> GSM905009 3 0.000 0.994 0.000 0 1.000
#> GSM905014 3 0.000 0.994 0.000 0 1.000
#> GSM905017 3 0.000 0.994 0.000 0 1.000
#> GSM905020 3 0.000 0.994 0.000 0 1.000
#> GSM905023 3 0.000 0.994 0.000 0 1.000
#> GSM905029 3 0.000 0.994 0.000 0 1.000
#> GSM905032 3 0.000 0.994 0.000 0 1.000
#> GSM905034 1 0.207 0.926 0.940 0 0.060
#> GSM905040 1 0.573 0.520 0.676 0 0.324
#> GSM904985 2 0.000 1.000 0.000 1 0.000
#> GSM904988 2 0.000 1.000 0.000 1 0.000
#> GSM904990 2 0.000 1.000 0.000 1 0.000
#> GSM904992 2 0.000 1.000 0.000 1 0.000
#> GSM904995 2 0.000 1.000 0.000 1 0.000
#> GSM904998 2 0.000 1.000 0.000 1 0.000
#> GSM905000 2 0.000 1.000 0.000 1 0.000
#> GSM905003 2 0.000 1.000 0.000 1 0.000
#> GSM905006 2 0.000 1.000 0.000 1 0.000
#> GSM905008 2 0.000 1.000 0.000 1 0.000
#> GSM905011 2 0.000 1.000 0.000 1 0.000
#> GSM905013 2 0.000 1.000 0.000 1 0.000
#> GSM905016 2 0.000 1.000 0.000 1 0.000
#> GSM905018 2 0.000 1.000 0.000 1 0.000
#> GSM905021 2 0.000 1.000 0.000 1 0.000
#> GSM905025 2 0.000 1.000 0.000 1 0.000
#> GSM905028 2 0.000 1.000 0.000 1 0.000
#> GSM905030 2 0.000 1.000 0.000 1 0.000
#> GSM905033 2 0.000 1.000 0.000 1 0.000
#> GSM905035 2 0.000 1.000 0.000 1 0.000
#> GSM905037 2 0.000 1.000 0.000 1 0.000
#> GSM905039 2 0.000 1.000 0.000 1 0.000
#> GSM905042 2 0.000 1.000 0.000 1 0.000
#> GSM905046 1 0.000 0.984 1.000 0 0.000
#> GSM905065 1 0.000 0.984 1.000 0 0.000
#> GSM905049 1 0.000 0.984 1.000 0 0.000
#> GSM905050 1 0.000 0.984 1.000 0 0.000
#> GSM905064 1 0.000 0.984 1.000 0 0.000
#> GSM905045 1 0.000 0.984 1.000 0 0.000
#> GSM905051 1 0.000 0.984 1.000 0 0.000
#> GSM905055 1 0.000 0.984 1.000 0 0.000
#> GSM905058 1 0.000 0.984 1.000 0 0.000
#> GSM905053 1 0.000 0.984 1.000 0 0.000
#> GSM905061 1 0.000 0.984 1.000 0 0.000
#> GSM905063 1 0.000 0.984 1.000 0 0.000
#> GSM905054 1 0.000 0.984 1.000 0 0.000
#> GSM905062 1 0.000 0.984 1.000 0 0.000
#> GSM905052 1 0.000 0.984 1.000 0 0.000
#> GSM905059 1 0.000 0.984 1.000 0 0.000
#> GSM905047 1 0.000 0.984 1.000 0 0.000
#> GSM905066 1 0.000 0.984 1.000 0 0.000
#> GSM905056 1 0.000 0.984 1.000 0 0.000
#> GSM905060 1 0.000 0.984 1.000 0 0.000
#> GSM905048 1 0.000 0.984 1.000 0 0.000
#> GSM905067 1 0.000 0.984 1.000 0 0.000
#> GSM905057 1 0.000 0.984 1.000 0 0.000
#> GSM905068 1 0.000 0.984 1.000 0 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM905004 4 0.0000 0.948 0.000 0 0.000 1.000
#> GSM905024 1 0.4888 0.357 0.588 0 0.412 0.000
#> GSM905038 3 0.0000 0.986 0.000 0 1.000 0.000
#> GSM905043 1 0.4304 0.631 0.716 0 0.284 0.000
#> GSM904986 3 0.0000 0.986 0.000 0 1.000 0.000
#> GSM904991 3 0.0000 0.986 0.000 0 1.000 0.000
#> GSM904994 3 0.0000 0.986 0.000 0 1.000 0.000
#> GSM904996 3 0.0000 0.986 0.000 0 1.000 0.000
#> GSM905007 3 0.0000 0.986 0.000 0 1.000 0.000
#> GSM905012 4 0.4134 0.631 0.000 0 0.260 0.740
#> GSM905022 3 0.0000 0.986 0.000 0 1.000 0.000
#> GSM905026 3 0.0000 0.986 0.000 0 1.000 0.000
#> GSM905027 3 0.0000 0.986 0.000 0 1.000 0.000
#> GSM905031 3 0.2216 0.895 0.000 0 0.908 0.092
#> GSM905036 3 0.0000 0.986 0.000 0 1.000 0.000
#> GSM905041 3 0.0000 0.986 0.000 0 1.000 0.000
#> GSM905044 3 0.0000 0.986 0.000 0 1.000 0.000
#> GSM904989 3 0.0000 0.986 0.000 0 1.000 0.000
#> GSM904999 3 0.0000 0.986 0.000 0 1.000 0.000
#> GSM905002 3 0.0000 0.986 0.000 0 1.000 0.000
#> GSM905009 3 0.0592 0.972 0.000 0 0.984 0.016
#> GSM905014 3 0.0000 0.986 0.000 0 1.000 0.000
#> GSM905017 3 0.0000 0.986 0.000 0 1.000 0.000
#> GSM905020 3 0.3569 0.755 0.000 0 0.804 0.196
#> GSM905023 3 0.0000 0.986 0.000 0 1.000 0.000
#> GSM905029 3 0.0000 0.986 0.000 0 1.000 0.000
#> GSM905032 3 0.0000 0.986 0.000 0 1.000 0.000
#> GSM905034 1 0.0000 0.938 1.000 0 0.000 0.000
#> GSM905040 1 0.2589 0.832 0.884 0 0.116 0.000
#> GSM904985 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM904988 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM904990 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM904992 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM904995 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM904998 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905000 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905003 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905006 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905008 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905011 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905013 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905016 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905018 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905021 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905025 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905028 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905030 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905033 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905035 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905037 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905039 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905042 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905046 1 0.0000 0.938 1.000 0 0.000 0.000
#> GSM905065 1 0.0000 0.938 1.000 0 0.000 0.000
#> GSM905049 4 0.0000 0.948 0.000 0 0.000 1.000
#> GSM905050 4 0.0000 0.948 0.000 0 0.000 1.000
#> GSM905064 4 0.0000 0.948 0.000 0 0.000 1.000
#> GSM905045 4 0.0000 0.948 0.000 0 0.000 1.000
#> GSM905051 4 0.3726 0.734 0.212 0 0.000 0.788
#> GSM905055 1 0.0000 0.938 1.000 0 0.000 0.000
#> GSM905058 1 0.0000 0.938 1.000 0 0.000 0.000
#> GSM905053 4 0.0000 0.948 0.000 0 0.000 1.000
#> GSM905061 4 0.0000 0.948 0.000 0 0.000 1.000
#> GSM905063 1 0.0000 0.938 1.000 0 0.000 0.000
#> GSM905054 4 0.0000 0.948 0.000 0 0.000 1.000
#> GSM905062 4 0.0000 0.948 0.000 0 0.000 1.000
#> GSM905052 4 0.2345 0.868 0.100 0 0.000 0.900
#> GSM905059 1 0.0000 0.938 1.000 0 0.000 0.000
#> GSM905047 1 0.0469 0.928 0.988 0 0.000 0.012
#> GSM905066 1 0.0000 0.938 1.000 0 0.000 0.000
#> GSM905056 1 0.0000 0.938 1.000 0 0.000 0.000
#> GSM905060 1 0.0000 0.938 1.000 0 0.000 0.000
#> GSM905048 1 0.0000 0.938 1.000 0 0.000 0.000
#> GSM905067 1 0.0000 0.938 1.000 0 0.000 0.000
#> GSM905057 1 0.0000 0.938 1.000 0 0.000 0.000
#> GSM905068 4 0.0000 0.948 0.000 0 0.000 1.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM905004 4 0.1195 0.892 0.000 0.000 0.028 0.960 0.012
#> GSM905024 1 0.4546 0.495 0.668 0.000 0.304 0.000 0.028
#> GSM905038 3 0.0451 0.926 0.000 0.000 0.988 0.004 0.008
#> GSM905043 3 0.5113 0.250 0.380 0.000 0.576 0.000 0.044
#> GSM904986 3 0.1493 0.911 0.000 0.000 0.948 0.028 0.024
#> GSM904991 3 0.0404 0.924 0.000 0.000 0.988 0.000 0.012
#> GSM904994 3 0.1310 0.917 0.000 0.000 0.956 0.020 0.024
#> GSM904996 3 0.1211 0.919 0.000 0.000 0.960 0.016 0.024
#> GSM905007 3 0.0510 0.927 0.000 0.000 0.984 0.000 0.016
#> GSM905012 4 0.1579 0.882 0.000 0.000 0.032 0.944 0.024
#> GSM905022 3 0.0898 0.923 0.000 0.000 0.972 0.008 0.020
#> GSM905026 3 0.0693 0.925 0.000 0.000 0.980 0.008 0.012
#> GSM905027 3 0.0162 0.926 0.000 0.000 0.996 0.000 0.004
#> GSM905031 4 0.3550 0.728 0.000 0.000 0.184 0.796 0.020
#> GSM905036 3 0.0451 0.926 0.000 0.000 0.988 0.004 0.008
#> GSM905041 3 0.0609 0.920 0.000 0.000 0.980 0.000 0.020
#> GSM905044 3 0.0898 0.923 0.000 0.000 0.972 0.008 0.020
#> GSM904989 3 0.2300 0.873 0.000 0.000 0.904 0.072 0.024
#> GSM904999 3 0.0880 0.916 0.000 0.000 0.968 0.000 0.032
#> GSM905002 3 0.0898 0.923 0.000 0.000 0.972 0.008 0.020
#> GSM905009 3 0.4833 0.230 0.000 0.000 0.564 0.412 0.024
#> GSM905014 3 0.0510 0.925 0.000 0.000 0.984 0.000 0.016
#> GSM905017 3 0.0880 0.916 0.000 0.000 0.968 0.000 0.032
#> GSM905020 4 0.4292 0.600 0.000 0.000 0.272 0.704 0.024
#> GSM905023 3 0.0404 0.924 0.000 0.000 0.988 0.000 0.012
#> GSM905029 3 0.0000 0.927 0.000 0.000 1.000 0.000 0.000
#> GSM905032 5 0.3534 0.634 0.000 0.000 0.256 0.000 0.744
#> GSM905034 1 0.1386 0.880 0.952 0.000 0.032 0.000 0.016
#> GSM905040 5 0.1908 0.914 0.092 0.000 0.000 0.000 0.908
#> GSM904985 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM904988 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM904990 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM904992 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM904995 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM904998 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM905000 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM905003 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM905006 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM905008 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM905011 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM905013 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM905016 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM905018 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM905021 2 0.0162 0.996 0.000 0.996 0.000 0.000 0.004
#> GSM905025 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM905028 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM905030 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM905033 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM905035 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM905037 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM905039 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM905042 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM905046 1 0.0771 0.893 0.976 0.000 0.000 0.004 0.020
#> GSM905065 1 0.1608 0.870 0.928 0.000 0.000 0.000 0.072
#> GSM905049 4 0.1168 0.908 0.032 0.000 0.000 0.960 0.008
#> GSM905050 4 0.0510 0.914 0.016 0.000 0.000 0.984 0.000
#> GSM905064 4 0.2488 0.830 0.124 0.000 0.000 0.872 0.004
#> GSM905045 4 0.0955 0.911 0.028 0.000 0.000 0.968 0.004
#> GSM905051 1 0.2659 0.840 0.888 0.000 0.000 0.060 0.052
#> GSM905055 5 0.2020 0.920 0.100 0.000 0.000 0.000 0.900
#> GSM905058 1 0.0162 0.892 0.996 0.000 0.000 0.000 0.004
#> GSM905053 4 0.0771 0.913 0.020 0.000 0.000 0.976 0.004
#> GSM905061 4 0.0510 0.914 0.016 0.000 0.000 0.984 0.000
#> GSM905063 5 0.2127 0.916 0.108 0.000 0.000 0.000 0.892
#> GSM905054 4 0.1701 0.895 0.048 0.000 0.000 0.936 0.016
#> GSM905062 4 0.0404 0.913 0.012 0.000 0.000 0.988 0.000
#> GSM905052 1 0.3944 0.734 0.788 0.000 0.000 0.160 0.052
#> GSM905059 1 0.0794 0.890 0.972 0.000 0.000 0.028 0.000
#> GSM905047 1 0.0963 0.887 0.964 0.000 0.000 0.036 0.000
#> GSM905066 1 0.1671 0.868 0.924 0.000 0.000 0.000 0.076
#> GSM905056 5 0.1965 0.919 0.096 0.000 0.000 0.000 0.904
#> GSM905060 1 0.0794 0.890 0.972 0.000 0.000 0.028 0.000
#> GSM905048 1 0.0963 0.886 0.964 0.000 0.000 0.000 0.036
#> GSM905067 1 0.1608 0.870 0.928 0.000 0.000 0.000 0.072
#> GSM905057 5 0.2020 0.920 0.100 0.000 0.000 0.000 0.900
#> GSM905068 4 0.0290 0.912 0.008 0.000 0.000 0.992 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM905004 4 0.4482 0.5356 0.000 0.000 0.124 0.708 0.168 0.000
#> GSM905024 1 0.4669 0.5875 0.712 0.000 0.164 0.000 0.112 0.012
#> GSM905038 3 0.1444 0.8461 0.000 0.000 0.928 0.000 0.072 0.000
#> GSM905043 1 0.5587 0.2899 0.532 0.000 0.344 0.000 0.112 0.012
#> GSM904986 3 0.3637 0.7594 0.000 0.000 0.780 0.056 0.164 0.000
#> GSM904991 3 0.2402 0.8264 0.000 0.000 0.868 0.000 0.120 0.012
#> GSM904994 3 0.3053 0.7917 0.000 0.000 0.812 0.020 0.168 0.000
#> GSM904996 3 0.2968 0.7949 0.000 0.000 0.816 0.016 0.168 0.000
#> GSM905007 3 0.2070 0.8401 0.000 0.000 0.892 0.000 0.100 0.008
#> GSM905012 4 0.5039 0.5029 0.000 0.000 0.184 0.640 0.176 0.000
#> GSM905022 3 0.2300 0.8164 0.000 0.000 0.856 0.000 0.144 0.000
#> GSM905026 3 0.0790 0.8483 0.000 0.000 0.968 0.000 0.032 0.000
#> GSM905027 3 0.2212 0.8317 0.000 0.000 0.880 0.000 0.112 0.008
#> GSM905031 4 0.4454 0.5264 0.000 0.000 0.224 0.692 0.084 0.000
#> GSM905036 3 0.2656 0.8270 0.000 0.000 0.860 0.008 0.120 0.012
#> GSM905041 3 0.2402 0.8264 0.000 0.000 0.868 0.000 0.120 0.012
#> GSM905044 3 0.1411 0.8426 0.000 0.000 0.936 0.004 0.060 0.000
#> GSM904989 3 0.4918 0.5646 0.000 0.000 0.656 0.184 0.160 0.000
#> GSM904999 3 0.3518 0.7751 0.000 0.000 0.732 0.000 0.256 0.012
#> GSM905002 3 0.2416 0.8109 0.000 0.000 0.844 0.000 0.156 0.000
#> GSM905009 4 0.5573 0.3905 0.000 0.000 0.312 0.524 0.164 0.000
#> GSM905014 3 0.2489 0.8487 0.000 0.000 0.860 0.000 0.128 0.012
#> GSM905017 3 0.3171 0.8137 0.000 0.000 0.784 0.000 0.204 0.012
#> GSM905020 4 0.5420 0.4456 0.000 0.000 0.256 0.572 0.172 0.000
#> GSM905023 3 0.2402 0.8264 0.000 0.000 0.868 0.000 0.120 0.012
#> GSM905029 3 0.2006 0.8356 0.000 0.000 0.892 0.000 0.104 0.004
#> GSM905032 6 0.4226 0.6083 0.000 0.000 0.152 0.000 0.112 0.736
#> GSM905034 1 0.1500 0.8665 0.936 0.000 0.000 0.000 0.052 0.012
#> GSM905040 6 0.0260 0.9063 0.000 0.000 0.000 0.000 0.008 0.992
#> GSM904985 2 0.0000 0.9965 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM904988 2 0.0146 0.9958 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM904990 2 0.0146 0.9958 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM904992 2 0.0146 0.9958 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM904995 2 0.0000 0.9965 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM904998 2 0.0000 0.9965 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905000 2 0.0146 0.9958 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM905003 2 0.0000 0.9965 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905006 2 0.0146 0.9958 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM905008 2 0.0146 0.9958 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM905011 2 0.0146 0.9958 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM905013 2 0.0000 0.9965 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905016 2 0.0000 0.9965 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905018 2 0.0146 0.9958 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM905021 2 0.1082 0.9550 0.000 0.956 0.004 0.000 0.040 0.000
#> GSM905025 2 0.0000 0.9965 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905028 2 0.0000 0.9965 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905030 2 0.0146 0.9958 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM905033 2 0.0000 0.9965 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905035 2 0.0000 0.9965 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905037 2 0.0000 0.9965 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905039 2 0.0000 0.9965 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905042 2 0.0000 0.9965 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905046 1 0.0000 0.8798 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM905065 1 0.0405 0.8790 0.988 0.000 0.000 0.000 0.004 0.008
#> GSM905049 4 0.1908 0.5481 0.004 0.000 0.000 0.900 0.096 0.000
#> GSM905050 4 0.1010 0.5905 0.004 0.000 0.000 0.960 0.036 0.000
#> GSM905064 4 0.3834 0.2716 0.036 0.000 0.000 0.732 0.232 0.000
#> GSM905045 4 0.2964 0.3983 0.004 0.000 0.000 0.792 0.204 0.000
#> GSM905051 5 0.4911 0.9455 0.100 0.000 0.000 0.276 0.624 0.000
#> GSM905055 6 0.0363 0.9198 0.012 0.000 0.000 0.000 0.000 0.988
#> GSM905058 1 0.1141 0.8662 0.948 0.000 0.000 0.000 0.052 0.000
#> GSM905053 4 0.1908 0.5490 0.004 0.000 0.000 0.900 0.096 0.000
#> GSM905061 4 0.0405 0.6030 0.004 0.000 0.000 0.988 0.008 0.000
#> GSM905063 6 0.0363 0.9198 0.012 0.000 0.000 0.000 0.000 0.988
#> GSM905054 4 0.3714 0.0134 0.004 0.000 0.000 0.656 0.340 0.000
#> GSM905062 4 0.0458 0.6019 0.000 0.000 0.000 0.984 0.016 0.000
#> GSM905052 5 0.4720 0.9441 0.072 0.000 0.000 0.304 0.624 0.000
#> GSM905059 1 0.1327 0.8593 0.936 0.000 0.000 0.000 0.064 0.000
#> GSM905047 1 0.0291 0.8783 0.992 0.000 0.000 0.004 0.004 0.000
#> GSM905066 1 0.0603 0.8761 0.980 0.000 0.000 0.000 0.004 0.016
#> GSM905056 6 0.0363 0.9198 0.012 0.000 0.000 0.000 0.000 0.988
#> GSM905060 1 0.1267 0.8636 0.940 0.000 0.000 0.000 0.060 0.000
#> GSM905048 1 0.0146 0.8798 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM905067 1 0.0405 0.8790 0.988 0.000 0.000 0.000 0.004 0.008
#> GSM905057 6 0.0363 0.9198 0.012 0.000 0.000 0.000 0.000 0.988
#> GSM905068 4 0.0146 0.6022 0.000 0.000 0.000 0.996 0.004 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) genotype/variation(p) individual(p) k
#> SD:NMF 75 9.06e-07 7.59e-04 0.05134 2
#> SD:NMF 76 2.85e-20 4.94e-05 0.97745 3
#> SD:NMF 75 2.38e-19 2.57e-09 0.35834 4
#> SD:NMF 73 1.10e-15 1.63e-10 0.00382 5
#> SD:NMF 70 8.36e-15 7.54e-12 0.00195 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 76 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 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.541 0.713 0.885 0.4642 0.499 0.499
#> 3 3 0.615 0.813 0.851 0.3855 0.696 0.462
#> 4 4 0.713 0.805 0.873 0.0778 0.965 0.893
#> 5 5 0.743 0.784 0.846 0.0869 0.933 0.769
#> 6 6 0.893 0.816 0.908 0.0708 0.965 0.845
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM905004 1 0.9522 0.3379 0.628 0.372
#> GSM905024 1 0.4431 0.8483 0.908 0.092
#> GSM905038 1 0.5842 0.8124 0.860 0.140
#> GSM905043 1 0.4431 0.8483 0.908 0.092
#> GSM904986 2 0.9866 0.3182 0.432 0.568
#> GSM904991 1 0.5737 0.8165 0.864 0.136
#> GSM904994 2 0.9866 0.3182 0.432 0.568
#> GSM904996 2 0.9866 0.3182 0.432 0.568
#> GSM905007 1 0.5737 0.8165 0.864 0.136
#> GSM905012 2 0.9866 0.3182 0.432 0.568
#> GSM905022 1 0.9983 -0.0274 0.524 0.476
#> GSM905026 2 0.9996 0.1331 0.488 0.512
#> GSM905027 1 0.9963 0.0266 0.536 0.464
#> GSM905031 2 0.9866 0.3182 0.432 0.568
#> GSM905036 1 0.5737 0.8165 0.864 0.136
#> GSM905041 1 0.5408 0.8263 0.876 0.124
#> GSM905044 2 0.9996 0.1331 0.488 0.512
#> GSM904989 2 0.9866 0.3182 0.432 0.568
#> GSM904999 1 0.9954 0.0440 0.540 0.460
#> GSM905002 2 0.9933 0.2592 0.452 0.548
#> GSM905009 2 0.9866 0.3182 0.432 0.568
#> GSM905014 1 0.5737 0.8165 0.864 0.136
#> GSM905017 1 0.9954 0.0440 0.540 0.460
#> GSM905020 2 0.9866 0.3182 0.432 0.568
#> GSM905023 1 0.5737 0.8165 0.864 0.136
#> GSM905029 1 0.5737 0.8165 0.864 0.136
#> GSM905032 1 0.5178 0.8323 0.884 0.116
#> GSM905034 1 0.2043 0.8765 0.968 0.032
#> GSM905040 1 0.0000 0.8832 1.000 0.000
#> GSM904985 2 0.0000 0.8121 0.000 1.000
#> GSM904988 2 0.0000 0.8121 0.000 1.000
#> GSM904990 2 0.0000 0.8121 0.000 1.000
#> GSM904992 2 0.0000 0.8121 0.000 1.000
#> GSM904995 2 0.0000 0.8121 0.000 1.000
#> GSM904998 2 0.0000 0.8121 0.000 1.000
#> GSM905000 2 0.0000 0.8121 0.000 1.000
#> GSM905003 2 0.0000 0.8121 0.000 1.000
#> GSM905006 2 0.0000 0.8121 0.000 1.000
#> GSM905008 2 0.0000 0.8121 0.000 1.000
#> GSM905011 2 0.0000 0.8121 0.000 1.000
#> GSM905013 2 0.0000 0.8121 0.000 1.000
#> GSM905016 2 0.0000 0.8121 0.000 1.000
#> GSM905018 2 0.0000 0.8121 0.000 1.000
#> GSM905021 2 0.2778 0.7817 0.048 0.952
#> GSM905025 2 0.0000 0.8121 0.000 1.000
#> GSM905028 2 0.0000 0.8121 0.000 1.000
#> GSM905030 2 0.0000 0.8121 0.000 1.000
#> GSM905033 2 0.0000 0.8121 0.000 1.000
#> GSM905035 2 0.0000 0.8121 0.000 1.000
#> GSM905037 2 0.0000 0.8121 0.000 1.000
#> GSM905039 2 0.0000 0.8121 0.000 1.000
#> GSM905042 2 0.0000 0.8121 0.000 1.000
#> GSM905046 1 0.0000 0.8832 1.000 0.000
#> GSM905065 1 0.0000 0.8832 1.000 0.000
#> GSM905049 1 0.0938 0.8857 0.988 0.012
#> GSM905050 1 0.0938 0.8857 0.988 0.012
#> GSM905064 1 0.0938 0.8857 0.988 0.012
#> GSM905045 1 0.0938 0.8857 0.988 0.012
#> GSM905051 1 0.0938 0.8857 0.988 0.012
#> GSM905055 1 0.0000 0.8832 1.000 0.000
#> GSM905058 1 0.0000 0.8832 1.000 0.000
#> GSM905053 1 0.0938 0.8857 0.988 0.012
#> GSM905061 1 0.0938 0.8857 0.988 0.012
#> GSM905063 1 0.0000 0.8832 1.000 0.000
#> GSM905054 1 0.0938 0.8857 0.988 0.012
#> GSM905062 1 0.0938 0.8857 0.988 0.012
#> GSM905052 1 0.0938 0.8857 0.988 0.012
#> GSM905059 1 0.0000 0.8832 1.000 0.000
#> GSM905047 1 0.0000 0.8832 1.000 0.000
#> GSM905066 1 0.0000 0.8832 1.000 0.000
#> GSM905056 1 0.0000 0.8832 1.000 0.000
#> GSM905060 1 0.0000 0.8832 1.000 0.000
#> GSM905048 1 0.0000 0.8832 1.000 0.000
#> GSM905067 1 0.0000 0.8832 1.000 0.000
#> GSM905057 1 0.0000 0.8832 1.000 0.000
#> GSM905068 1 0.0938 0.8857 0.988 0.012
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM905004 3 0.7633 0.628 0.120 0.200 0.680
#> GSM905024 3 0.8260 0.624 0.172 0.192 0.636
#> GSM905038 3 0.7750 0.669 0.140 0.184 0.676
#> GSM905043 3 0.8260 0.624 0.172 0.192 0.636
#> GSM904986 3 0.3192 0.579 0.000 0.112 0.888
#> GSM904991 3 0.7702 0.668 0.140 0.180 0.680
#> GSM904994 3 0.3192 0.579 0.000 0.112 0.888
#> GSM904996 3 0.3192 0.579 0.000 0.112 0.888
#> GSM905007 3 0.7702 0.668 0.140 0.180 0.680
#> GSM905012 3 0.3192 0.579 0.000 0.112 0.888
#> GSM905022 3 0.0892 0.652 0.000 0.020 0.980
#> GSM905026 3 0.1964 0.631 0.000 0.056 0.944
#> GSM905027 3 0.0424 0.658 0.000 0.008 0.992
#> GSM905031 3 0.3192 0.579 0.000 0.112 0.888
#> GSM905036 3 0.7702 0.668 0.140 0.180 0.680
#> GSM905041 3 0.7843 0.658 0.140 0.192 0.668
#> GSM905044 3 0.1964 0.631 0.000 0.056 0.944
#> GSM904989 3 0.3192 0.579 0.000 0.112 0.888
#> GSM904999 3 0.0237 0.659 0.000 0.004 0.996
#> GSM905002 3 0.2796 0.600 0.000 0.092 0.908
#> GSM905009 3 0.3192 0.579 0.000 0.112 0.888
#> GSM905014 3 0.7702 0.668 0.140 0.180 0.680
#> GSM905017 3 0.0237 0.659 0.000 0.004 0.996
#> GSM905020 3 0.3192 0.579 0.000 0.112 0.888
#> GSM905023 3 0.7702 0.668 0.140 0.180 0.680
#> GSM905029 3 0.7702 0.668 0.140 0.180 0.680
#> GSM905032 3 0.7954 0.651 0.148 0.192 0.660
#> GSM905034 3 0.8242 0.483 0.336 0.092 0.572
#> GSM905040 1 0.4873 0.821 0.824 0.152 0.024
#> GSM904985 2 0.5810 0.978 0.000 0.664 0.336
#> GSM904988 2 0.5810 0.978 0.000 0.664 0.336
#> GSM904990 2 0.5810 0.978 0.000 0.664 0.336
#> GSM904992 2 0.5810 0.978 0.000 0.664 0.336
#> GSM904995 2 0.5810 0.978 0.000 0.664 0.336
#> GSM904998 2 0.5810 0.978 0.000 0.664 0.336
#> GSM905000 2 0.5810 0.978 0.000 0.664 0.336
#> GSM905003 2 0.5810 0.978 0.000 0.664 0.336
#> GSM905006 2 0.5810 0.978 0.000 0.664 0.336
#> GSM905008 2 0.5810 0.978 0.000 0.664 0.336
#> GSM905011 2 0.5810 0.978 0.000 0.664 0.336
#> GSM905013 2 0.5810 0.978 0.000 0.664 0.336
#> GSM905016 2 0.5810 0.978 0.000 0.664 0.336
#> GSM905018 2 0.5810 0.978 0.000 0.664 0.336
#> GSM905021 2 0.6308 0.736 0.000 0.508 0.492
#> GSM905025 2 0.5810 0.978 0.000 0.664 0.336
#> GSM905028 2 0.5810 0.978 0.000 0.664 0.336
#> GSM905030 2 0.5810 0.978 0.000 0.664 0.336
#> GSM905033 2 0.6204 0.864 0.000 0.576 0.424
#> GSM905035 2 0.5810 0.978 0.000 0.664 0.336
#> GSM905037 2 0.5810 0.978 0.000 0.664 0.336
#> GSM905039 2 0.5810 0.978 0.000 0.664 0.336
#> GSM905042 2 0.6204 0.864 0.000 0.576 0.424
#> GSM905046 1 0.0000 0.911 1.000 0.000 0.000
#> GSM905065 1 0.0000 0.911 1.000 0.000 0.000
#> GSM905049 1 0.3412 0.901 0.876 0.124 0.000
#> GSM905050 1 0.3412 0.901 0.876 0.124 0.000
#> GSM905064 1 0.3412 0.901 0.876 0.124 0.000
#> GSM905045 1 0.3412 0.901 0.876 0.124 0.000
#> GSM905051 1 0.3412 0.901 0.876 0.124 0.000
#> GSM905055 1 0.3879 0.832 0.848 0.152 0.000
#> GSM905058 1 0.0000 0.911 1.000 0.000 0.000
#> GSM905053 1 0.3412 0.901 0.876 0.124 0.000
#> GSM905061 1 0.3412 0.901 0.876 0.124 0.000
#> GSM905063 1 0.3879 0.832 0.848 0.152 0.000
#> GSM905054 1 0.3412 0.901 0.876 0.124 0.000
#> GSM905062 1 0.3412 0.901 0.876 0.124 0.000
#> GSM905052 1 0.3412 0.901 0.876 0.124 0.000
#> GSM905059 1 0.0000 0.911 1.000 0.000 0.000
#> GSM905047 1 0.0000 0.911 1.000 0.000 0.000
#> GSM905066 1 0.0000 0.911 1.000 0.000 0.000
#> GSM905056 1 0.3879 0.832 0.848 0.152 0.000
#> GSM905060 1 0.0000 0.911 1.000 0.000 0.000
#> GSM905048 1 0.0000 0.911 1.000 0.000 0.000
#> GSM905067 1 0.0000 0.911 1.000 0.000 0.000
#> GSM905057 1 0.3879 0.832 0.848 0.152 0.000
#> GSM905068 1 0.3412 0.901 0.876 0.124 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM905004 3 0.7662 0.556 0.008 0.272 0.512 0.208
#> GSM905024 3 0.1940 0.587 0.076 0.000 0.924 0.000
#> GSM905038 3 0.0376 0.632 0.004 0.004 0.992 0.000
#> GSM905043 3 0.1940 0.587 0.076 0.000 0.924 0.000
#> GSM904986 3 0.5229 0.597 0.008 0.428 0.564 0.000
#> GSM904991 3 0.1022 0.622 0.032 0.000 0.968 0.000
#> GSM904994 3 0.5229 0.597 0.008 0.428 0.564 0.000
#> GSM904996 3 0.5229 0.597 0.008 0.428 0.564 0.000
#> GSM905007 3 0.0921 0.624 0.028 0.000 0.972 0.000
#> GSM905012 3 0.5229 0.597 0.008 0.428 0.564 0.000
#> GSM905022 3 0.4917 0.668 0.008 0.336 0.656 0.000
#> GSM905026 3 0.5070 0.648 0.008 0.372 0.620 0.000
#> GSM905027 3 0.5311 0.671 0.024 0.328 0.648 0.000
#> GSM905031 3 0.5229 0.597 0.008 0.428 0.564 0.000
#> GSM905036 3 0.0707 0.627 0.020 0.000 0.980 0.000
#> GSM905041 3 0.1302 0.614 0.044 0.000 0.956 0.000
#> GSM905044 3 0.5070 0.648 0.008 0.372 0.620 0.000
#> GSM904989 3 0.5229 0.597 0.008 0.428 0.564 0.000
#> GSM904999 3 0.5173 0.671 0.020 0.320 0.660 0.000
#> GSM905002 3 0.5183 0.617 0.008 0.408 0.584 0.000
#> GSM905009 3 0.5229 0.597 0.008 0.428 0.564 0.000
#> GSM905014 3 0.1022 0.622 0.032 0.000 0.968 0.000
#> GSM905017 3 0.5173 0.671 0.020 0.320 0.660 0.000
#> GSM905020 3 0.5229 0.597 0.008 0.428 0.564 0.000
#> GSM905023 3 0.0707 0.627 0.020 0.000 0.980 0.000
#> GSM905029 3 0.0188 0.630 0.004 0.000 0.996 0.000
#> GSM905032 3 0.1474 0.608 0.052 0.000 0.948 0.000
#> GSM905034 3 0.5723 0.374 0.220 0.000 0.696 0.084
#> GSM905040 1 0.1798 0.967 0.944 0.000 0.016 0.040
#> GSM904985 2 0.0000 0.977 0.000 1.000 0.000 0.000
#> GSM904988 2 0.0000 0.977 0.000 1.000 0.000 0.000
#> GSM904990 2 0.0000 0.977 0.000 1.000 0.000 0.000
#> GSM904992 2 0.0000 0.977 0.000 1.000 0.000 0.000
#> GSM904995 2 0.0000 0.977 0.000 1.000 0.000 0.000
#> GSM904998 2 0.0000 0.977 0.000 1.000 0.000 0.000
#> GSM905000 2 0.0000 0.977 0.000 1.000 0.000 0.000
#> GSM905003 2 0.0000 0.977 0.000 1.000 0.000 0.000
#> GSM905006 2 0.0000 0.977 0.000 1.000 0.000 0.000
#> GSM905008 2 0.0000 0.977 0.000 1.000 0.000 0.000
#> GSM905011 2 0.0000 0.977 0.000 1.000 0.000 0.000
#> GSM905013 2 0.0000 0.977 0.000 1.000 0.000 0.000
#> GSM905016 2 0.0000 0.977 0.000 1.000 0.000 0.000
#> GSM905018 2 0.0000 0.977 0.000 1.000 0.000 0.000
#> GSM905021 2 0.3757 0.736 0.020 0.828 0.152 0.000
#> GSM905025 2 0.0000 0.977 0.000 1.000 0.000 0.000
#> GSM905028 2 0.0000 0.977 0.000 1.000 0.000 0.000
#> GSM905030 2 0.0000 0.977 0.000 1.000 0.000 0.000
#> GSM905033 2 0.2345 0.845 0.000 0.900 0.100 0.000
#> GSM905035 2 0.0000 0.977 0.000 1.000 0.000 0.000
#> GSM905037 2 0.0000 0.977 0.000 1.000 0.000 0.000
#> GSM905039 2 0.0000 0.977 0.000 1.000 0.000 0.000
#> GSM905042 2 0.2345 0.845 0.000 0.900 0.100 0.000
#> GSM905046 4 0.3486 0.842 0.188 0.000 0.000 0.812
#> GSM905065 4 0.3942 0.800 0.236 0.000 0.000 0.764
#> GSM905049 4 0.0000 0.885 0.000 0.000 0.000 1.000
#> GSM905050 4 0.0000 0.885 0.000 0.000 0.000 1.000
#> GSM905064 4 0.0000 0.885 0.000 0.000 0.000 1.000
#> GSM905045 4 0.0000 0.885 0.000 0.000 0.000 1.000
#> GSM905051 4 0.0000 0.885 0.000 0.000 0.000 1.000
#> GSM905055 1 0.1557 0.992 0.944 0.000 0.000 0.056
#> GSM905058 4 0.3486 0.842 0.188 0.000 0.000 0.812
#> GSM905053 4 0.0000 0.885 0.000 0.000 0.000 1.000
#> GSM905061 4 0.0000 0.885 0.000 0.000 0.000 1.000
#> GSM905063 1 0.1557 0.992 0.944 0.000 0.000 0.056
#> GSM905054 4 0.0000 0.885 0.000 0.000 0.000 1.000
#> GSM905062 4 0.0000 0.885 0.000 0.000 0.000 1.000
#> GSM905052 4 0.0000 0.885 0.000 0.000 0.000 1.000
#> GSM905059 4 0.3486 0.842 0.188 0.000 0.000 0.812
#> GSM905047 4 0.3486 0.842 0.188 0.000 0.000 0.812
#> GSM905066 4 0.3942 0.800 0.236 0.000 0.000 0.764
#> GSM905056 1 0.1557 0.992 0.944 0.000 0.000 0.056
#> GSM905060 4 0.3486 0.842 0.188 0.000 0.000 0.812
#> GSM905048 4 0.3486 0.842 0.188 0.000 0.000 0.812
#> GSM905067 4 0.3942 0.800 0.236 0.000 0.000 0.764
#> GSM905057 1 0.1557 0.992 0.944 0.000 0.000 0.056
#> GSM905068 4 0.0000 0.885 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
#> GSM905004 3 0.3073 0.5552 0.000 0.076 0.868 0.052 0.004
#> GSM905024 5 0.2208 0.7561 0.020 0.000 0.072 0.000 0.908
#> GSM905038 3 0.4262 -0.0867 0.000 0.000 0.560 0.000 0.440
#> GSM905043 5 0.2208 0.7561 0.020 0.000 0.072 0.000 0.908
#> GSM904986 3 0.3336 0.8394 0.000 0.228 0.772 0.000 0.000
#> GSM904991 5 0.2471 0.7738 0.000 0.000 0.136 0.000 0.864
#> GSM904994 3 0.3336 0.8394 0.000 0.228 0.772 0.000 0.000
#> GSM904996 3 0.3336 0.8394 0.000 0.228 0.772 0.000 0.000
#> GSM905007 5 0.2516 0.7719 0.000 0.000 0.140 0.000 0.860
#> GSM905012 3 0.3336 0.8394 0.000 0.228 0.772 0.000 0.000
#> GSM905022 3 0.5543 0.7372 0.000 0.224 0.640 0.000 0.136
#> GSM905026 3 0.4879 0.7993 0.000 0.228 0.696 0.000 0.076
#> GSM905027 3 0.6246 0.5994 0.000 0.224 0.544 0.000 0.232
#> GSM905031 3 0.3336 0.8394 0.000 0.228 0.772 0.000 0.000
#> GSM905036 5 0.4030 0.5331 0.000 0.000 0.352 0.000 0.648
#> GSM905041 5 0.2723 0.7742 0.012 0.000 0.124 0.000 0.864
#> GSM905044 3 0.4879 0.7993 0.000 0.228 0.696 0.000 0.076
#> GSM904989 3 0.3336 0.8394 0.000 0.228 0.772 0.000 0.000
#> GSM904999 5 0.6392 0.0529 0.000 0.220 0.268 0.000 0.512
#> GSM905002 3 0.3912 0.8321 0.000 0.228 0.752 0.000 0.020
#> GSM905009 3 0.3336 0.8394 0.000 0.228 0.772 0.000 0.000
#> GSM905014 5 0.2471 0.7738 0.000 0.000 0.136 0.000 0.864
#> GSM905017 5 0.6392 0.0529 0.000 0.220 0.268 0.000 0.512
#> GSM905020 3 0.3336 0.8394 0.000 0.228 0.772 0.000 0.000
#> GSM905023 5 0.4138 0.4702 0.000 0.000 0.384 0.000 0.616
#> GSM905029 3 0.4268 -0.0972 0.000 0.000 0.556 0.000 0.444
#> GSM905032 5 0.2519 0.7708 0.016 0.000 0.100 0.000 0.884
#> GSM905034 5 0.3977 0.5281 0.024 0.000 0.016 0.168 0.792
#> GSM905040 1 0.0703 0.9725 0.976 0.000 0.000 0.000 0.024
#> GSM904985 2 0.0000 0.9600 0.000 1.000 0.000 0.000 0.000
#> GSM904988 2 0.0000 0.9600 0.000 1.000 0.000 0.000 0.000
#> GSM904990 2 0.0000 0.9600 0.000 1.000 0.000 0.000 0.000
#> GSM904992 2 0.0000 0.9600 0.000 1.000 0.000 0.000 0.000
#> GSM904995 2 0.0000 0.9600 0.000 1.000 0.000 0.000 0.000
#> GSM904998 2 0.0000 0.9600 0.000 1.000 0.000 0.000 0.000
#> GSM905000 2 0.0000 0.9600 0.000 1.000 0.000 0.000 0.000
#> GSM905003 2 0.0000 0.9600 0.000 1.000 0.000 0.000 0.000
#> GSM905006 2 0.0000 0.9600 0.000 1.000 0.000 0.000 0.000
#> GSM905008 2 0.0000 0.9600 0.000 1.000 0.000 0.000 0.000
#> GSM905011 2 0.0000 0.9600 0.000 1.000 0.000 0.000 0.000
#> GSM905013 2 0.0000 0.9600 0.000 1.000 0.000 0.000 0.000
#> GSM905016 2 0.0000 0.9600 0.000 1.000 0.000 0.000 0.000
#> GSM905018 2 0.0000 0.9600 0.000 1.000 0.000 0.000 0.000
#> GSM905021 2 0.4141 0.5391 0.000 0.728 0.248 0.000 0.024
#> GSM905025 2 0.0000 0.9600 0.000 1.000 0.000 0.000 0.000
#> GSM905028 2 0.0000 0.9600 0.000 1.000 0.000 0.000 0.000
#> GSM905030 2 0.0000 0.9600 0.000 1.000 0.000 0.000 0.000
#> GSM905033 2 0.3109 0.6810 0.000 0.800 0.200 0.000 0.000
#> GSM905035 2 0.0000 0.9600 0.000 1.000 0.000 0.000 0.000
#> GSM905037 2 0.0000 0.9600 0.000 1.000 0.000 0.000 0.000
#> GSM905039 2 0.0000 0.9600 0.000 1.000 0.000 0.000 0.000
#> GSM905042 2 0.3109 0.6810 0.000 0.800 0.200 0.000 0.000
#> GSM905046 4 0.2927 0.7616 0.060 0.000 0.000 0.872 0.068
#> GSM905065 4 0.3767 0.7155 0.120 0.000 0.000 0.812 0.068
#> GSM905049 4 0.3461 0.8156 0.000 0.000 0.224 0.772 0.004
#> GSM905050 4 0.3461 0.8156 0.000 0.000 0.224 0.772 0.004
#> GSM905064 4 0.3461 0.8156 0.000 0.000 0.224 0.772 0.004
#> GSM905045 4 0.3461 0.8156 0.000 0.000 0.224 0.772 0.004
#> GSM905051 4 0.3109 0.8152 0.000 0.000 0.200 0.800 0.000
#> GSM905055 1 0.0000 0.9933 1.000 0.000 0.000 0.000 0.000
#> GSM905058 4 0.2927 0.7616 0.060 0.000 0.000 0.872 0.068
#> GSM905053 4 0.3461 0.8156 0.000 0.000 0.224 0.772 0.004
#> GSM905061 4 0.3461 0.8156 0.000 0.000 0.224 0.772 0.004
#> GSM905063 1 0.0000 0.9933 1.000 0.000 0.000 0.000 0.000
#> GSM905054 4 0.3461 0.8156 0.000 0.000 0.224 0.772 0.004
#> GSM905062 4 0.3461 0.8156 0.000 0.000 0.224 0.772 0.004
#> GSM905052 4 0.3109 0.8152 0.000 0.000 0.200 0.800 0.000
#> GSM905059 4 0.2927 0.7616 0.060 0.000 0.000 0.872 0.068
#> GSM905047 4 0.2927 0.7616 0.060 0.000 0.000 0.872 0.068
#> GSM905066 4 0.3767 0.7155 0.120 0.000 0.000 0.812 0.068
#> GSM905056 1 0.0000 0.9933 1.000 0.000 0.000 0.000 0.000
#> GSM905060 4 0.2927 0.7616 0.060 0.000 0.000 0.872 0.068
#> GSM905048 4 0.2927 0.7616 0.060 0.000 0.000 0.872 0.068
#> GSM905067 4 0.3767 0.7155 0.120 0.000 0.000 0.812 0.068
#> GSM905057 1 0.0000 0.9933 1.000 0.000 0.000 0.000 0.000
#> GSM905068 4 0.3461 0.8156 0.000 0.000 0.224 0.772 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM905004 3 0.3290 0.6252 0.000 0.016 0.776 0.208 0.000 0.000
#> GSM905024 5 0.0291 0.7472 0.004 0.000 0.000 0.000 0.992 0.004
#> GSM905038 3 0.3862 -0.0187 0.000 0.000 0.524 0.000 0.476 0.000
#> GSM905043 5 0.0291 0.7472 0.004 0.000 0.000 0.000 0.992 0.004
#> GSM904986 3 0.0458 0.8498 0.000 0.016 0.984 0.000 0.000 0.000
#> GSM904991 5 0.1556 0.7803 0.000 0.000 0.080 0.000 0.920 0.000
#> GSM904994 3 0.0458 0.8498 0.000 0.016 0.984 0.000 0.000 0.000
#> GSM904996 3 0.0458 0.8498 0.000 0.016 0.984 0.000 0.000 0.000
#> GSM905007 5 0.1610 0.7786 0.000 0.000 0.084 0.000 0.916 0.000
#> GSM905012 3 0.0458 0.8498 0.000 0.016 0.984 0.000 0.000 0.000
#> GSM905022 3 0.2664 0.7536 0.000 0.016 0.848 0.000 0.136 0.000
#> GSM905026 3 0.1951 0.8123 0.000 0.016 0.908 0.000 0.076 0.000
#> GSM905027 3 0.3534 0.6011 0.000 0.016 0.740 0.000 0.244 0.000
#> GSM905031 3 0.0458 0.8498 0.000 0.016 0.984 0.000 0.000 0.000
#> GSM905036 5 0.3428 0.5340 0.000 0.000 0.304 0.000 0.696 0.000
#> GSM905041 5 0.1387 0.7806 0.000 0.000 0.068 0.000 0.932 0.000
#> GSM905044 3 0.1951 0.8123 0.000 0.016 0.908 0.000 0.076 0.000
#> GSM904989 3 0.0458 0.8498 0.000 0.016 0.984 0.000 0.000 0.000
#> GSM904999 5 0.5547 0.2079 0.072 0.000 0.416 0.000 0.488 0.024
#> GSM905002 3 0.1003 0.8431 0.000 0.016 0.964 0.000 0.020 0.000
#> GSM905009 3 0.0458 0.8498 0.000 0.016 0.984 0.000 0.000 0.000
#> GSM905014 5 0.1556 0.7803 0.000 0.000 0.080 0.000 0.920 0.000
#> GSM905017 5 0.5547 0.2079 0.072 0.000 0.416 0.000 0.488 0.024
#> GSM905020 3 0.0458 0.8498 0.000 0.016 0.984 0.000 0.000 0.000
#> GSM905023 5 0.3563 0.4699 0.000 0.000 0.336 0.000 0.664 0.000
#> GSM905029 3 0.3864 -0.0307 0.000 0.000 0.520 0.000 0.480 0.000
#> GSM905032 5 0.0713 0.7667 0.000 0.000 0.028 0.000 0.972 0.000
#> GSM905034 5 0.3163 0.5663 0.232 0.000 0.000 0.000 0.764 0.004
#> GSM905040 6 0.1176 0.9706 0.020 0.000 0.000 0.000 0.024 0.956
#> GSM904985 2 0.0000 0.9397 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM904988 2 0.0000 0.9397 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM904990 2 0.0000 0.9397 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM904992 2 0.0000 0.9397 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM904995 2 0.0000 0.9397 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM904998 2 0.0000 0.9397 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905000 2 0.0000 0.9397 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905003 2 0.0000 0.9397 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905006 2 0.0000 0.9397 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905008 2 0.0000 0.9397 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905011 2 0.0000 0.9397 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905013 2 0.0000 0.9397 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905016 2 0.0000 0.9397 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905018 2 0.0000 0.9397 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905021 2 0.5524 0.2389 0.072 0.508 0.396 0.000 0.000 0.024
#> GSM905025 2 0.0000 0.9397 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905028 2 0.0000 0.9397 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905030 2 0.0000 0.9397 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905033 2 0.4134 0.5278 0.028 0.656 0.316 0.000 0.000 0.000
#> GSM905035 2 0.0000 0.9397 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905037 2 0.0000 0.9397 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905039 2 0.0000 0.9397 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905042 2 0.4134 0.5278 0.028 0.656 0.316 0.000 0.000 0.000
#> GSM905046 1 0.1501 0.9746 0.924 0.000 0.000 0.076 0.000 0.000
#> GSM905065 1 0.2512 0.9471 0.880 0.000 0.000 0.060 0.000 0.060
#> GSM905049 4 0.0000 0.9386 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905050 4 0.0000 0.9386 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905064 4 0.0000 0.9386 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905045 4 0.0000 0.9386 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905051 4 0.3266 0.6360 0.272 0.000 0.000 0.728 0.000 0.000
#> GSM905055 6 0.0713 0.9926 0.028 0.000 0.000 0.000 0.000 0.972
#> GSM905058 1 0.1501 0.9746 0.924 0.000 0.000 0.076 0.000 0.000
#> GSM905053 4 0.0000 0.9386 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905061 4 0.0000 0.9386 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905063 6 0.0713 0.9926 0.028 0.000 0.000 0.000 0.000 0.972
#> GSM905054 4 0.0000 0.9386 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905062 4 0.0000 0.9386 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905052 4 0.3266 0.6360 0.272 0.000 0.000 0.728 0.000 0.000
#> GSM905059 1 0.1501 0.9746 0.924 0.000 0.000 0.076 0.000 0.000
#> GSM905047 1 0.1501 0.9746 0.924 0.000 0.000 0.076 0.000 0.000
#> GSM905066 1 0.2512 0.9471 0.880 0.000 0.000 0.060 0.000 0.060
#> GSM905056 6 0.0713 0.9926 0.028 0.000 0.000 0.000 0.000 0.972
#> GSM905060 1 0.1501 0.9746 0.924 0.000 0.000 0.076 0.000 0.000
#> GSM905048 1 0.1501 0.9746 0.924 0.000 0.000 0.076 0.000 0.000
#> GSM905067 1 0.2512 0.9471 0.880 0.000 0.000 0.060 0.000 0.060
#> GSM905057 6 0.0713 0.9926 0.028 0.000 0.000 0.000 0.000 0.972
#> GSM905068 4 0.0000 0.9386 0.000 0.000 0.000 1.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) genotype/variation(p) individual(p) k
#> CV:hclust 60 3.62e-09 4.36e-05 0.332 2
#> CV:hclust 75 7.29e-21 3.97e-05 0.985 3
#> CV:hclust 75 8.41e-21 7.24e-06 0.382 4
#> CV:hclust 71 8.82e-16 4.97e-06 0.380 5
#> CV:hclust 70 9.51e-19 6.55e-10 0.124 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 76 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 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 0.581 0.864 0.860 0.4590 0.528 0.528
#> 3 3 0.727 0.963 0.923 0.4233 0.762 0.565
#> 4 4 0.811 0.718 0.819 0.1090 0.936 0.807
#> 5 5 0.793 0.804 0.820 0.0610 0.940 0.797
#> 6 6 0.733 0.438 0.752 0.0425 0.940 0.772
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
#> GSM905004 2 0.0672 0.769 0.008 0.992
#> GSM905024 1 0.9044 0.986 0.680 0.320
#> GSM905038 2 0.0000 0.775 0.000 1.000
#> GSM905043 1 0.9044 0.986 0.680 0.320
#> GSM904986 2 0.0000 0.775 0.000 1.000
#> GSM904991 2 0.0376 0.770 0.004 0.996
#> GSM904994 2 0.0000 0.775 0.000 1.000
#> GSM904996 2 0.0000 0.775 0.000 1.000
#> GSM905007 2 0.0000 0.775 0.000 1.000
#> GSM905012 2 0.0000 0.775 0.000 1.000
#> GSM905022 2 0.0000 0.775 0.000 1.000
#> GSM905026 2 0.0000 0.775 0.000 1.000
#> GSM905027 2 0.0000 0.775 0.000 1.000
#> GSM905031 2 0.0000 0.775 0.000 1.000
#> GSM905036 2 0.0000 0.775 0.000 1.000
#> GSM905041 2 0.1633 0.743 0.024 0.976
#> GSM905044 2 0.0000 0.775 0.000 1.000
#> GSM904989 2 0.0000 0.775 0.000 1.000
#> GSM904999 2 0.0000 0.775 0.000 1.000
#> GSM905002 2 0.0000 0.775 0.000 1.000
#> GSM905009 2 0.0000 0.775 0.000 1.000
#> GSM905014 2 0.0000 0.775 0.000 1.000
#> GSM905017 2 0.0000 0.775 0.000 1.000
#> GSM905020 2 0.0000 0.775 0.000 1.000
#> GSM905023 2 0.0000 0.775 0.000 1.000
#> GSM905029 2 0.0000 0.775 0.000 1.000
#> GSM905032 2 0.0376 0.770 0.004 0.996
#> GSM905034 1 0.9044 0.986 0.680 0.320
#> GSM905040 1 0.9044 0.986 0.680 0.320
#> GSM904985 2 0.9044 0.801 0.320 0.680
#> GSM904988 2 0.9044 0.801 0.320 0.680
#> GSM904990 2 0.9044 0.801 0.320 0.680
#> GSM904992 2 0.9044 0.801 0.320 0.680
#> GSM904995 2 0.9044 0.801 0.320 0.680
#> GSM904998 2 0.9044 0.801 0.320 0.680
#> GSM905000 2 0.9044 0.801 0.320 0.680
#> GSM905003 2 0.9044 0.801 0.320 0.680
#> GSM905006 2 0.9044 0.801 0.320 0.680
#> GSM905008 2 0.9044 0.801 0.320 0.680
#> GSM905011 2 0.9044 0.801 0.320 0.680
#> GSM905013 2 0.9044 0.801 0.320 0.680
#> GSM905016 2 0.9044 0.801 0.320 0.680
#> GSM905018 2 0.9044 0.801 0.320 0.680
#> GSM905021 2 0.9044 0.801 0.320 0.680
#> GSM905025 2 0.9044 0.801 0.320 0.680
#> GSM905028 2 0.9044 0.801 0.320 0.680
#> GSM905030 2 0.9044 0.801 0.320 0.680
#> GSM905033 2 0.9044 0.801 0.320 0.680
#> GSM905035 2 0.9044 0.801 0.320 0.680
#> GSM905037 2 0.9044 0.801 0.320 0.680
#> GSM905039 2 0.9044 0.801 0.320 0.680
#> GSM905042 2 0.9044 0.801 0.320 0.680
#> GSM905046 1 0.8909 0.998 0.692 0.308
#> GSM905065 1 0.8909 0.998 0.692 0.308
#> GSM905049 1 0.8909 0.998 0.692 0.308
#> GSM905050 1 0.8909 0.998 0.692 0.308
#> GSM905064 1 0.8909 0.998 0.692 0.308
#> GSM905045 1 0.8909 0.998 0.692 0.308
#> GSM905051 1 0.8909 0.998 0.692 0.308
#> GSM905055 1 0.8909 0.998 0.692 0.308
#> GSM905058 1 0.8909 0.998 0.692 0.308
#> GSM905053 1 0.8909 0.998 0.692 0.308
#> GSM905061 1 0.8909 0.998 0.692 0.308
#> GSM905063 1 0.8909 0.998 0.692 0.308
#> GSM905054 1 0.8909 0.998 0.692 0.308
#> GSM905062 1 0.8909 0.998 0.692 0.308
#> GSM905052 1 0.8909 0.998 0.692 0.308
#> GSM905059 1 0.8909 0.998 0.692 0.308
#> GSM905047 1 0.8909 0.998 0.692 0.308
#> GSM905066 1 0.8909 0.998 0.692 0.308
#> GSM905056 1 0.8909 0.998 0.692 0.308
#> GSM905060 1 0.8909 0.998 0.692 0.308
#> GSM905048 1 0.8909 0.998 0.692 0.308
#> GSM905067 1 0.8909 0.998 0.692 0.308
#> GSM905057 1 0.8909 0.998 0.692 0.308
#> GSM905068 1 0.8909 0.998 0.692 0.308
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM905004 3 0.2176 0.842 0.032 0.020 0.948
#> GSM905024 3 0.3038 0.827 0.104 0.000 0.896
#> GSM905038 3 0.3879 0.973 0.000 0.152 0.848
#> GSM905043 3 0.3038 0.827 0.104 0.000 0.896
#> GSM904986 3 0.3879 0.973 0.000 0.152 0.848
#> GSM904991 3 0.3192 0.943 0.000 0.112 0.888
#> GSM904994 3 0.3879 0.973 0.000 0.152 0.848
#> GSM904996 3 0.3879 0.973 0.000 0.152 0.848
#> GSM905007 3 0.3879 0.973 0.000 0.152 0.848
#> GSM905012 3 0.3879 0.973 0.000 0.152 0.848
#> GSM905022 3 0.3879 0.973 0.000 0.152 0.848
#> GSM905026 3 0.3879 0.973 0.000 0.152 0.848
#> GSM905027 3 0.3879 0.973 0.000 0.152 0.848
#> GSM905031 3 0.3879 0.973 0.000 0.152 0.848
#> GSM905036 3 0.3879 0.973 0.000 0.152 0.848
#> GSM905041 3 0.3116 0.940 0.000 0.108 0.892
#> GSM905044 3 0.3879 0.973 0.000 0.152 0.848
#> GSM904989 3 0.3879 0.973 0.000 0.152 0.848
#> GSM904999 3 0.3879 0.973 0.000 0.152 0.848
#> GSM905002 3 0.3879 0.973 0.000 0.152 0.848
#> GSM905009 3 0.3879 0.973 0.000 0.152 0.848
#> GSM905014 3 0.3879 0.973 0.000 0.152 0.848
#> GSM905017 3 0.3879 0.973 0.000 0.152 0.848
#> GSM905020 3 0.3879 0.973 0.000 0.152 0.848
#> GSM905023 3 0.3879 0.973 0.000 0.152 0.848
#> GSM905029 3 0.3879 0.973 0.000 0.152 0.848
#> GSM905032 3 0.3116 0.940 0.000 0.108 0.892
#> GSM905034 1 0.2165 0.943 0.936 0.000 0.064
#> GSM905040 1 0.2261 0.942 0.932 0.000 0.068
#> GSM904985 2 0.0592 0.993 0.012 0.988 0.000
#> GSM904988 2 0.0000 0.996 0.000 1.000 0.000
#> GSM904990 2 0.0000 0.996 0.000 1.000 0.000
#> GSM904992 2 0.0000 0.996 0.000 1.000 0.000
#> GSM904995 2 0.0592 0.993 0.012 0.988 0.000
#> GSM904998 2 0.0000 0.996 0.000 1.000 0.000
#> GSM905000 2 0.0000 0.996 0.000 1.000 0.000
#> GSM905003 2 0.0000 0.996 0.000 1.000 0.000
#> GSM905006 2 0.0000 0.996 0.000 1.000 0.000
#> GSM905008 2 0.0000 0.996 0.000 1.000 0.000
#> GSM905011 2 0.0000 0.996 0.000 1.000 0.000
#> GSM905013 2 0.0000 0.996 0.000 1.000 0.000
#> GSM905016 2 0.0592 0.993 0.012 0.988 0.000
#> GSM905018 2 0.0000 0.996 0.000 1.000 0.000
#> GSM905021 2 0.0747 0.993 0.016 0.984 0.000
#> GSM905025 2 0.0747 0.993 0.016 0.984 0.000
#> GSM905028 2 0.0237 0.995 0.004 0.996 0.000
#> GSM905030 2 0.0237 0.995 0.004 0.996 0.000
#> GSM905033 2 0.0592 0.994 0.012 0.988 0.000
#> GSM905035 2 0.0747 0.993 0.016 0.984 0.000
#> GSM905037 2 0.0237 0.995 0.004 0.996 0.000
#> GSM905039 2 0.0747 0.993 0.016 0.984 0.000
#> GSM905042 2 0.0592 0.994 0.012 0.988 0.000
#> GSM905046 1 0.1289 0.952 0.968 0.000 0.032
#> GSM905065 1 0.1289 0.952 0.968 0.000 0.032
#> GSM905049 1 0.3267 0.944 0.884 0.000 0.116
#> GSM905050 1 0.3267 0.944 0.884 0.000 0.116
#> GSM905064 1 0.3267 0.944 0.884 0.000 0.116
#> GSM905045 1 0.3267 0.944 0.884 0.000 0.116
#> GSM905051 1 0.3267 0.944 0.884 0.000 0.116
#> GSM905055 1 0.2261 0.942 0.932 0.000 0.068
#> GSM905058 1 0.1289 0.952 0.968 0.000 0.032
#> GSM905053 1 0.3267 0.944 0.884 0.000 0.116
#> GSM905061 1 0.3267 0.944 0.884 0.000 0.116
#> GSM905063 1 0.2261 0.942 0.932 0.000 0.068
#> GSM905054 1 0.3267 0.944 0.884 0.000 0.116
#> GSM905062 1 0.3267 0.944 0.884 0.000 0.116
#> GSM905052 1 0.3267 0.944 0.884 0.000 0.116
#> GSM905059 1 0.0747 0.953 0.984 0.000 0.016
#> GSM905047 1 0.0747 0.953 0.984 0.000 0.016
#> GSM905066 1 0.1289 0.952 0.968 0.000 0.032
#> GSM905056 1 0.2261 0.942 0.932 0.000 0.068
#> GSM905060 1 0.0747 0.953 0.984 0.000 0.016
#> GSM905048 1 0.1289 0.952 0.968 0.000 0.032
#> GSM905067 1 0.1289 0.952 0.968 0.000 0.032
#> GSM905057 1 0.2261 0.942 0.932 0.000 0.068
#> GSM905068 1 0.3267 0.944 0.884 0.000 0.116
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM905004 3 0.4406 0.5773 0.000 0.000 0.700 0.300
#> GSM905024 1 0.5558 0.0269 0.528 0.004 0.456 0.012
#> GSM905038 3 0.0469 0.9491 0.000 0.012 0.988 0.000
#> GSM905043 1 0.5290 0.1983 0.584 0.000 0.404 0.012
#> GSM904986 3 0.0469 0.9491 0.000 0.012 0.988 0.000
#> GSM904991 3 0.2921 0.8566 0.140 0.000 0.860 0.000
#> GSM904994 3 0.0469 0.9491 0.000 0.012 0.988 0.000
#> GSM904996 3 0.0469 0.9491 0.000 0.012 0.988 0.000
#> GSM905007 3 0.2101 0.9222 0.060 0.012 0.928 0.000
#> GSM905012 3 0.0469 0.9491 0.000 0.012 0.988 0.000
#> GSM905022 3 0.0469 0.9491 0.000 0.012 0.988 0.000
#> GSM905026 3 0.0469 0.9491 0.000 0.012 0.988 0.000
#> GSM905027 3 0.0469 0.9491 0.000 0.012 0.988 0.000
#> GSM905031 3 0.0469 0.9491 0.000 0.012 0.988 0.000
#> GSM905036 3 0.1059 0.9437 0.016 0.012 0.972 0.000
#> GSM905041 3 0.2921 0.8566 0.140 0.000 0.860 0.000
#> GSM905044 3 0.0469 0.9491 0.000 0.012 0.988 0.000
#> GSM904989 3 0.0469 0.9491 0.000 0.012 0.988 0.000
#> GSM904999 3 0.3217 0.8854 0.128 0.012 0.860 0.000
#> GSM905002 3 0.0469 0.9491 0.000 0.012 0.988 0.000
#> GSM905009 3 0.0469 0.9491 0.000 0.012 0.988 0.000
#> GSM905014 3 0.2329 0.9156 0.072 0.012 0.916 0.000
#> GSM905017 3 0.3217 0.8854 0.128 0.012 0.860 0.000
#> GSM905020 3 0.0469 0.9491 0.000 0.012 0.988 0.000
#> GSM905023 3 0.1059 0.9437 0.016 0.012 0.972 0.000
#> GSM905029 3 0.0469 0.9491 0.000 0.012 0.988 0.000
#> GSM905032 3 0.3893 0.7923 0.196 0.008 0.796 0.000
#> GSM905034 1 0.5464 0.3590 0.632 0.004 0.020 0.344
#> GSM905040 1 0.5047 0.4331 0.712 0.012 0.012 0.264
#> GSM904985 2 0.4182 0.9102 0.180 0.796 0.024 0.000
#> GSM904988 2 0.1629 0.9390 0.024 0.952 0.024 0.000
#> GSM904990 2 0.0817 0.9396 0.000 0.976 0.024 0.000
#> GSM904992 2 0.1629 0.9390 0.024 0.952 0.024 0.000
#> GSM904995 2 0.4095 0.9122 0.172 0.804 0.024 0.000
#> GSM904998 2 0.2111 0.9384 0.044 0.932 0.024 0.000
#> GSM905000 2 0.0817 0.9396 0.000 0.976 0.024 0.000
#> GSM905003 2 0.2197 0.9338 0.048 0.928 0.024 0.000
#> GSM905006 2 0.1629 0.9390 0.024 0.952 0.024 0.000
#> GSM905008 2 0.2111 0.9384 0.044 0.932 0.024 0.000
#> GSM905011 2 0.1629 0.9390 0.024 0.952 0.024 0.000
#> GSM905013 2 0.0817 0.9396 0.000 0.976 0.024 0.000
#> GSM905016 2 0.4095 0.9122 0.172 0.804 0.024 0.000
#> GSM905018 2 0.0817 0.9396 0.000 0.976 0.024 0.000
#> GSM905021 2 0.4644 0.8708 0.228 0.748 0.024 0.000
#> GSM905025 2 0.3659 0.9143 0.136 0.840 0.024 0.000
#> GSM905028 2 0.0817 0.9396 0.000 0.976 0.024 0.000
#> GSM905030 2 0.1629 0.9390 0.024 0.952 0.024 0.000
#> GSM905033 2 0.4225 0.8963 0.184 0.792 0.024 0.000
#> GSM905035 2 0.4095 0.9122 0.172 0.804 0.024 0.000
#> GSM905037 2 0.0817 0.9396 0.000 0.976 0.024 0.000
#> GSM905039 2 0.3659 0.9143 0.136 0.840 0.024 0.000
#> GSM905042 2 0.4225 0.8963 0.184 0.792 0.024 0.000
#> GSM905046 4 0.5273 0.1045 0.456 0.008 0.000 0.536
#> GSM905065 4 0.5147 0.0935 0.460 0.004 0.000 0.536
#> GSM905049 4 0.0469 0.6301 0.000 0.000 0.012 0.988
#> GSM905050 4 0.0469 0.6301 0.000 0.000 0.012 0.988
#> GSM905064 4 0.0188 0.6290 0.000 0.000 0.004 0.996
#> GSM905045 4 0.0469 0.6301 0.000 0.000 0.012 0.988
#> GSM905051 4 0.0188 0.6265 0.000 0.004 0.000 0.996
#> GSM905055 1 0.5809 0.3820 0.572 0.016 0.012 0.400
#> GSM905058 4 0.5277 0.0970 0.460 0.008 0.000 0.532
#> GSM905053 4 0.0469 0.6301 0.000 0.000 0.012 0.988
#> GSM905061 4 0.0469 0.6301 0.000 0.000 0.012 0.988
#> GSM905063 1 0.5809 0.3820 0.572 0.016 0.012 0.400
#> GSM905054 4 0.0336 0.6300 0.000 0.000 0.008 0.992
#> GSM905062 4 0.0469 0.6301 0.000 0.000 0.012 0.988
#> GSM905052 4 0.0188 0.6265 0.000 0.004 0.000 0.996
#> GSM905059 4 0.5257 0.1337 0.444 0.008 0.000 0.548
#> GSM905047 4 0.5250 0.1387 0.440 0.008 0.000 0.552
#> GSM905066 4 0.5147 0.0935 0.460 0.004 0.000 0.536
#> GSM905056 1 0.5809 0.3820 0.572 0.016 0.012 0.400
#> GSM905060 4 0.5257 0.1337 0.444 0.008 0.000 0.548
#> GSM905048 4 0.5273 0.1045 0.456 0.008 0.000 0.536
#> GSM905067 4 0.5147 0.0935 0.460 0.004 0.000 0.536
#> GSM905057 1 0.5809 0.3820 0.572 0.016 0.012 0.400
#> GSM905068 4 0.0469 0.6301 0.000 0.000 0.012 0.988
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM905004 3 0.4658 0.309 0.000 0.000 0.576 0.408 NA
#> GSM905024 1 0.6498 0.254 0.460 0.000 0.200 0.000 NA
#> GSM905038 3 0.1831 0.873 0.004 0.000 0.920 0.000 NA
#> GSM905043 1 0.6039 0.366 0.552 0.000 0.148 0.000 NA
#> GSM904986 3 0.0000 0.888 0.000 0.000 1.000 0.000 NA
#> GSM904991 3 0.5515 0.693 0.112 0.000 0.628 0.000 NA
#> GSM904994 3 0.0000 0.888 0.000 0.000 1.000 0.000 NA
#> GSM904996 3 0.0000 0.888 0.000 0.000 1.000 0.000 NA
#> GSM905007 3 0.3687 0.824 0.028 0.000 0.792 0.000 NA
#> GSM905012 3 0.0000 0.888 0.000 0.000 1.000 0.000 NA
#> GSM905022 3 0.0000 0.888 0.000 0.000 1.000 0.000 NA
#> GSM905026 3 0.0000 0.888 0.000 0.000 1.000 0.000 NA
#> GSM905027 3 0.0510 0.886 0.000 0.000 0.984 0.000 NA
#> GSM905031 3 0.0000 0.888 0.000 0.000 1.000 0.000 NA
#> GSM905036 3 0.2997 0.847 0.012 0.000 0.840 0.000 NA
#> GSM905041 3 0.5537 0.689 0.112 0.000 0.624 0.000 NA
#> GSM905044 3 0.0000 0.888 0.000 0.000 1.000 0.000 NA
#> GSM904989 3 0.0000 0.888 0.000 0.000 1.000 0.000 NA
#> GSM904999 3 0.4444 0.797 0.072 0.000 0.748 0.000 NA
#> GSM905002 3 0.0000 0.888 0.000 0.000 1.000 0.000 NA
#> GSM905009 3 0.0000 0.888 0.000 0.000 1.000 0.000 NA
#> GSM905014 3 0.3994 0.812 0.040 0.000 0.772 0.000 NA
#> GSM905017 3 0.4444 0.797 0.072 0.000 0.748 0.000 NA
#> GSM905020 3 0.0000 0.888 0.000 0.000 1.000 0.000 NA
#> GSM905023 3 0.2909 0.850 0.012 0.000 0.848 0.000 NA
#> GSM905029 3 0.1704 0.875 0.004 0.000 0.928 0.000 NA
#> GSM905032 3 0.6147 0.603 0.168 0.000 0.544 0.000 NA
#> GSM905034 1 0.5892 0.497 0.520 0.000 0.000 0.108 NA
#> GSM905040 1 0.5167 0.541 0.664 0.000 0.000 0.088 NA
#> GSM904985 2 0.4444 0.783 0.000 0.624 0.012 0.000 NA
#> GSM904988 2 0.0807 0.868 0.012 0.976 0.012 0.000 NA
#> GSM904990 2 0.0968 0.869 0.004 0.972 0.012 0.000 NA
#> GSM904992 2 0.0807 0.868 0.012 0.976 0.012 0.000 NA
#> GSM904995 2 0.4464 0.800 0.008 0.676 0.012 0.000 NA
#> GSM904998 2 0.2208 0.860 0.012 0.916 0.012 0.000 NA
#> GSM905000 2 0.0968 0.869 0.004 0.972 0.012 0.000 NA
#> GSM905003 2 0.3170 0.839 0.016 0.852 0.012 0.000 NA
#> GSM905006 2 0.0807 0.868 0.012 0.976 0.012 0.000 NA
#> GSM905008 2 0.2444 0.857 0.016 0.904 0.012 0.000 NA
#> GSM905011 2 0.0807 0.868 0.012 0.976 0.012 0.000 NA
#> GSM905013 2 0.0968 0.869 0.004 0.972 0.012 0.000 NA
#> GSM905016 2 0.4464 0.800 0.008 0.676 0.012 0.000 NA
#> GSM905018 2 0.0968 0.869 0.004 0.972 0.012 0.000 NA
#> GSM905021 2 0.5504 0.718 0.040 0.516 0.012 0.000 NA
#> GSM905025 2 0.4588 0.801 0.012 0.668 0.012 0.000 NA
#> GSM905028 2 0.1605 0.869 0.004 0.944 0.012 0.000 NA
#> GSM905030 2 0.0807 0.868 0.012 0.976 0.012 0.000 NA
#> GSM905033 2 0.5484 0.756 0.048 0.580 0.012 0.000 NA
#> GSM905035 2 0.4464 0.800 0.008 0.676 0.012 0.000 NA
#> GSM905037 2 0.0968 0.869 0.004 0.972 0.012 0.000 NA
#> GSM905039 2 0.4568 0.802 0.012 0.672 0.012 0.000 NA
#> GSM905042 2 0.5484 0.756 0.048 0.580 0.012 0.000 NA
#> GSM905046 1 0.5475 0.707 0.604 0.000 0.000 0.308 NA
#> GSM905065 1 0.4400 0.709 0.672 0.000 0.000 0.308 NA
#> GSM905049 4 0.0000 0.982 0.000 0.000 0.000 1.000 NA
#> GSM905050 4 0.0000 0.982 0.000 0.000 0.000 1.000 NA
#> GSM905064 4 0.0000 0.982 0.000 0.000 0.000 1.000 NA
#> GSM905045 4 0.0510 0.979 0.000 0.000 0.000 0.984 NA
#> GSM905051 4 0.1644 0.943 0.004 0.008 0.000 0.940 NA
#> GSM905055 1 0.5147 0.686 0.692 0.004 0.000 0.208 NA
#> GSM905058 1 0.5568 0.704 0.596 0.000 0.000 0.308 NA
#> GSM905053 4 0.0000 0.982 0.000 0.000 0.000 1.000 NA
#> GSM905061 4 0.0609 0.978 0.000 0.000 0.000 0.980 NA
#> GSM905063 1 0.4841 0.691 0.708 0.000 0.000 0.208 NA
#> GSM905054 4 0.0000 0.982 0.000 0.000 0.000 1.000 NA
#> GSM905062 4 0.0609 0.978 0.000 0.000 0.000 0.980 NA
#> GSM905052 4 0.1644 0.943 0.004 0.008 0.000 0.940 NA
#> GSM905059 1 0.5630 0.693 0.580 0.000 0.000 0.324 NA
#> GSM905047 1 0.5538 0.697 0.588 0.000 0.000 0.324 NA
#> GSM905066 1 0.4400 0.709 0.672 0.000 0.000 0.308 NA
#> GSM905056 1 0.5147 0.686 0.692 0.004 0.000 0.208 NA
#> GSM905060 1 0.5630 0.693 0.580 0.000 0.000 0.324 NA
#> GSM905048 1 0.5475 0.707 0.604 0.000 0.000 0.308 NA
#> GSM905067 1 0.4400 0.709 0.672 0.000 0.000 0.308 NA
#> GSM905057 1 0.5147 0.686 0.692 0.004 0.000 0.208 NA
#> GSM905068 4 0.0404 0.979 0.000 0.000 0.000 0.988 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM905004 3 0.5145 0.2390 0.000 0.000 0.556 0.372 0.016 0.056
#> GSM905024 5 0.6286 0.5273 0.260 0.000 0.096 0.008 0.564 0.072
#> GSM905038 3 0.3398 0.6409 0.000 0.000 0.768 0.004 0.216 0.012
#> GSM905043 5 0.5861 0.4968 0.228 0.000 0.064 0.008 0.620 0.080
#> GSM904986 3 0.0146 0.7882 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM904991 5 0.4285 0.0559 0.000 0.000 0.432 0.008 0.552 0.008
#> GSM904994 3 0.0000 0.7893 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM904996 3 0.0000 0.7893 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905007 3 0.4161 0.4127 0.000 0.000 0.612 0.008 0.372 0.008
#> GSM905012 3 0.0000 0.7893 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905022 3 0.0146 0.7882 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM905026 3 0.0146 0.7888 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM905027 3 0.2225 0.7437 0.000 0.000 0.892 0.008 0.092 0.008
#> GSM905031 3 0.0146 0.7888 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM905036 3 0.4044 0.5263 0.000 0.000 0.668 0.008 0.312 0.012
#> GSM905041 5 0.4172 0.0862 0.000 0.000 0.424 0.008 0.564 0.004
#> GSM905044 3 0.0291 0.7879 0.000 0.000 0.992 0.004 0.000 0.004
#> GSM904989 3 0.0291 0.7878 0.000 0.000 0.992 0.004 0.000 0.004
#> GSM904999 3 0.6076 0.2189 0.000 0.000 0.504 0.100 0.348 0.048
#> GSM905002 3 0.0000 0.7893 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905009 3 0.0146 0.7888 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM905014 3 0.4230 0.3437 0.000 0.000 0.584 0.008 0.400 0.008
#> GSM905017 3 0.6076 0.2189 0.000 0.000 0.504 0.100 0.348 0.048
#> GSM905020 3 0.0000 0.7893 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905023 3 0.4009 0.5391 0.000 0.000 0.676 0.008 0.304 0.012
#> GSM905029 3 0.3370 0.6490 0.000 0.000 0.772 0.004 0.212 0.012
#> GSM905032 5 0.3405 0.3582 0.000 0.000 0.272 0.000 0.724 0.004
#> GSM905034 5 0.5618 0.3080 0.364 0.000 0.004 0.012 0.524 0.096
#> GSM905040 5 0.6564 -0.0560 0.312 0.000 0.000 0.052 0.464 0.172
#> GSM904985 2 0.1983 0.2282 0.000 0.916 0.000 0.012 0.012 0.060
#> GSM904988 2 0.3862 -0.4944 0.000 0.524 0.000 0.000 0.000 0.476
#> GSM904990 2 0.3989 -0.4910 0.000 0.528 0.000 0.004 0.000 0.468
#> GSM904992 2 0.4089 -0.5148 0.000 0.524 0.000 0.000 0.008 0.468
#> GSM904995 2 0.0665 0.2576 0.000 0.980 0.000 0.008 0.004 0.008
#> GSM904998 2 0.4394 -0.7985 0.000 0.492 0.000 0.004 0.016 0.488
#> GSM905000 2 0.3989 -0.4910 0.000 0.528 0.000 0.004 0.000 0.468
#> GSM905003 6 0.5238 0.7514 0.000 0.464 0.000 0.024 0.044 0.468
#> GSM905006 2 0.3862 -0.4944 0.000 0.524 0.000 0.000 0.000 0.476
#> GSM905008 6 0.4537 0.7373 0.000 0.480 0.000 0.004 0.024 0.492
#> GSM905011 2 0.3862 -0.4944 0.000 0.524 0.000 0.000 0.000 0.476
#> GSM905013 2 0.3989 -0.4910 0.000 0.528 0.000 0.004 0.000 0.468
#> GSM905016 2 0.0665 0.2576 0.000 0.980 0.000 0.008 0.004 0.008
#> GSM905018 2 0.3989 -0.4910 0.000 0.528 0.000 0.004 0.000 0.468
#> GSM905021 2 0.5628 0.1404 0.000 0.660 0.000 0.084 0.124 0.132
#> GSM905025 2 0.0458 0.2543 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM905028 2 0.3861 -0.4131 0.000 0.640 0.000 0.008 0.000 0.352
#> GSM905030 2 0.4211 -0.5224 0.000 0.532 0.000 0.004 0.008 0.456
#> GSM905033 2 0.5563 0.1224 0.000 0.660 0.000 0.064 0.136 0.140
#> GSM905035 2 0.0405 0.2577 0.000 0.988 0.000 0.000 0.004 0.008
#> GSM905037 2 0.4080 -0.5001 0.000 0.536 0.000 0.008 0.000 0.456
#> GSM905039 2 0.0458 0.2543 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM905042 2 0.5563 0.1224 0.000 0.660 0.000 0.064 0.136 0.140
#> GSM905046 1 0.0653 0.8114 0.980 0.000 0.000 0.012 0.004 0.004
#> GSM905065 1 0.2806 0.8110 0.872 0.000 0.000 0.012 0.060 0.056
#> GSM905049 4 0.3081 0.9601 0.220 0.000 0.004 0.776 0.000 0.000
#> GSM905050 4 0.3081 0.9601 0.220 0.000 0.004 0.776 0.000 0.000
#> GSM905064 4 0.3081 0.9601 0.220 0.000 0.004 0.776 0.000 0.000
#> GSM905045 4 0.4072 0.9537 0.220 0.000 0.004 0.736 0.008 0.032
#> GSM905051 4 0.4341 0.8790 0.284 0.000 0.000 0.676 0.016 0.024
#> GSM905055 1 0.5978 0.6763 0.604 0.000 0.000 0.060 0.152 0.184
#> GSM905058 1 0.1642 0.7915 0.936 0.000 0.000 0.004 0.032 0.028
#> GSM905053 4 0.3081 0.9601 0.220 0.000 0.004 0.776 0.000 0.000
#> GSM905061 4 0.4168 0.9524 0.220 0.000 0.004 0.732 0.012 0.032
#> GSM905063 1 0.5846 0.6812 0.620 0.000 0.000 0.056 0.160 0.164
#> GSM905054 4 0.3081 0.9601 0.220 0.000 0.004 0.776 0.000 0.000
#> GSM905062 4 0.4168 0.9524 0.220 0.000 0.004 0.732 0.012 0.032
#> GSM905052 4 0.4341 0.8790 0.284 0.000 0.000 0.676 0.016 0.024
#> GSM905059 1 0.2038 0.7852 0.920 0.000 0.000 0.020 0.032 0.028
#> GSM905047 1 0.1003 0.8023 0.964 0.000 0.000 0.028 0.004 0.004
#> GSM905066 1 0.2806 0.8110 0.872 0.000 0.000 0.012 0.060 0.056
#> GSM905056 1 0.5978 0.6763 0.604 0.000 0.000 0.060 0.152 0.184
#> GSM905060 1 0.2038 0.7852 0.920 0.000 0.000 0.020 0.032 0.028
#> GSM905048 1 0.0653 0.8114 0.980 0.000 0.000 0.012 0.004 0.004
#> GSM905067 1 0.2806 0.8110 0.872 0.000 0.000 0.012 0.060 0.056
#> GSM905057 1 0.5978 0.6763 0.604 0.000 0.000 0.060 0.152 0.184
#> GSM905068 4 0.4072 0.9537 0.220 0.000 0.004 0.736 0.008 0.032
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) genotype/variation(p) individual(p) k
#> CV:kmeans 76 2.17e-09 6.67e-03 0.0862 2
#> CV:kmeans 76 2.85e-20 4.94e-05 0.9774 3
#> CV:kmeans 59 1.29e-20 2.34e-05 0.9978 4
#> CV:kmeans 72 2.68e-22 1.67e-09 0.4484 5
#> CV:kmeans 44 1.51e-08 7.26e-04 0.2272 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 76 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 0.993 0.996 0.5039 0.496 0.496
#> 3 3 1.000 0.964 0.986 0.3364 0.728 0.504
#> 4 4 1.000 0.977 0.984 0.1061 0.897 0.698
#> 5 5 0.893 0.839 0.918 0.0593 0.938 0.761
#> 6 6 0.888 0.710 0.865 0.0293 0.971 0.866
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
#> GSM905004 1 0.0000 0.997 1.000 0.000
#> GSM905024 1 0.0000 0.997 1.000 0.000
#> GSM905038 2 0.2778 0.952 0.048 0.952
#> GSM905043 1 0.0000 0.997 1.000 0.000
#> GSM904986 2 0.0000 0.996 0.000 1.000
#> GSM904991 1 0.0000 0.997 1.000 0.000
#> GSM904994 2 0.0000 0.996 0.000 1.000
#> GSM904996 2 0.0000 0.996 0.000 1.000
#> GSM905007 1 0.0000 0.997 1.000 0.000
#> GSM905012 2 0.0000 0.996 0.000 1.000
#> GSM905022 2 0.0000 0.996 0.000 1.000
#> GSM905026 2 0.0000 0.996 0.000 1.000
#> GSM905027 2 0.1633 0.975 0.024 0.976
#> GSM905031 2 0.0000 0.996 0.000 1.000
#> GSM905036 1 0.0672 0.990 0.992 0.008
#> GSM905041 1 0.0000 0.997 1.000 0.000
#> GSM905044 2 0.0000 0.996 0.000 1.000
#> GSM904989 2 0.0000 0.996 0.000 1.000
#> GSM904999 2 0.0000 0.996 0.000 1.000
#> GSM905002 2 0.0000 0.996 0.000 1.000
#> GSM905009 2 0.0000 0.996 0.000 1.000
#> GSM905014 1 0.4431 0.898 0.908 0.092
#> GSM905017 2 0.0000 0.996 0.000 1.000
#> GSM905020 2 0.0000 0.996 0.000 1.000
#> GSM905023 2 0.2778 0.952 0.048 0.952
#> GSM905029 2 0.2778 0.952 0.048 0.952
#> GSM905032 1 0.0000 0.997 1.000 0.000
#> GSM905034 1 0.0000 0.997 1.000 0.000
#> GSM905040 1 0.0000 0.997 1.000 0.000
#> GSM904985 2 0.0000 0.996 0.000 1.000
#> GSM904988 2 0.0000 0.996 0.000 1.000
#> GSM904990 2 0.0000 0.996 0.000 1.000
#> GSM904992 2 0.0000 0.996 0.000 1.000
#> GSM904995 2 0.0000 0.996 0.000 1.000
#> GSM904998 2 0.0000 0.996 0.000 1.000
#> GSM905000 2 0.0000 0.996 0.000 1.000
#> GSM905003 2 0.0000 0.996 0.000 1.000
#> GSM905006 2 0.0000 0.996 0.000 1.000
#> GSM905008 2 0.0000 0.996 0.000 1.000
#> GSM905011 2 0.0000 0.996 0.000 1.000
#> GSM905013 2 0.0000 0.996 0.000 1.000
#> GSM905016 2 0.0000 0.996 0.000 1.000
#> GSM905018 2 0.0000 0.996 0.000 1.000
#> GSM905021 2 0.0000 0.996 0.000 1.000
#> GSM905025 2 0.0000 0.996 0.000 1.000
#> GSM905028 2 0.0000 0.996 0.000 1.000
#> GSM905030 2 0.0000 0.996 0.000 1.000
#> GSM905033 2 0.0000 0.996 0.000 1.000
#> GSM905035 2 0.0000 0.996 0.000 1.000
#> GSM905037 2 0.0000 0.996 0.000 1.000
#> GSM905039 2 0.0000 0.996 0.000 1.000
#> GSM905042 2 0.0000 0.996 0.000 1.000
#> GSM905046 1 0.0000 0.997 1.000 0.000
#> GSM905065 1 0.0000 0.997 1.000 0.000
#> GSM905049 1 0.0000 0.997 1.000 0.000
#> GSM905050 1 0.0000 0.997 1.000 0.000
#> GSM905064 1 0.0000 0.997 1.000 0.000
#> GSM905045 1 0.0000 0.997 1.000 0.000
#> GSM905051 1 0.0000 0.997 1.000 0.000
#> GSM905055 1 0.0000 0.997 1.000 0.000
#> GSM905058 1 0.0000 0.997 1.000 0.000
#> GSM905053 1 0.0000 0.997 1.000 0.000
#> GSM905061 1 0.0000 0.997 1.000 0.000
#> GSM905063 1 0.0000 0.997 1.000 0.000
#> GSM905054 1 0.0000 0.997 1.000 0.000
#> GSM905062 1 0.0000 0.997 1.000 0.000
#> GSM905052 1 0.0000 0.997 1.000 0.000
#> GSM905059 1 0.0000 0.997 1.000 0.000
#> GSM905047 1 0.0000 0.997 1.000 0.000
#> GSM905066 1 0.0000 0.997 1.000 0.000
#> GSM905056 1 0.0000 0.997 1.000 0.000
#> GSM905060 1 0.0000 0.997 1.000 0.000
#> GSM905048 1 0.0000 0.997 1.000 0.000
#> GSM905067 1 0.0000 0.997 1.000 0.000
#> GSM905057 1 0.0000 0.997 1.000 0.000
#> GSM905068 1 0.0000 0.997 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM905004 1 0.475 0.707 0.784 0 0.216
#> GSM905024 3 0.617 0.312 0.412 0 0.588
#> GSM905038 3 0.000 0.965 0.000 0 1.000
#> GSM905043 3 0.618 0.301 0.416 0 0.584
#> GSM904986 3 0.000 0.965 0.000 0 1.000
#> GSM904991 3 0.000 0.965 0.000 0 1.000
#> GSM904994 3 0.000 0.965 0.000 0 1.000
#> GSM904996 3 0.000 0.965 0.000 0 1.000
#> GSM905007 3 0.000 0.965 0.000 0 1.000
#> GSM905012 3 0.000 0.965 0.000 0 1.000
#> GSM905022 3 0.000 0.965 0.000 0 1.000
#> GSM905026 3 0.000 0.965 0.000 0 1.000
#> GSM905027 3 0.000 0.965 0.000 0 1.000
#> GSM905031 3 0.000 0.965 0.000 0 1.000
#> GSM905036 3 0.000 0.965 0.000 0 1.000
#> GSM905041 3 0.000 0.965 0.000 0 1.000
#> GSM905044 3 0.000 0.965 0.000 0 1.000
#> GSM904989 3 0.000 0.965 0.000 0 1.000
#> GSM904999 3 0.000 0.965 0.000 0 1.000
#> GSM905002 3 0.000 0.965 0.000 0 1.000
#> GSM905009 3 0.000 0.965 0.000 0 1.000
#> GSM905014 3 0.000 0.965 0.000 0 1.000
#> GSM905017 3 0.000 0.965 0.000 0 1.000
#> GSM905020 3 0.000 0.965 0.000 0 1.000
#> GSM905023 3 0.000 0.965 0.000 0 1.000
#> GSM905029 3 0.000 0.965 0.000 0 1.000
#> GSM905032 3 0.000 0.965 0.000 0 1.000
#> GSM905034 1 0.000 0.991 1.000 0 0.000
#> GSM905040 1 0.000 0.991 1.000 0 0.000
#> GSM904985 2 0.000 1.000 0.000 1 0.000
#> GSM904988 2 0.000 1.000 0.000 1 0.000
#> GSM904990 2 0.000 1.000 0.000 1 0.000
#> GSM904992 2 0.000 1.000 0.000 1 0.000
#> GSM904995 2 0.000 1.000 0.000 1 0.000
#> GSM904998 2 0.000 1.000 0.000 1 0.000
#> GSM905000 2 0.000 1.000 0.000 1 0.000
#> GSM905003 2 0.000 1.000 0.000 1 0.000
#> GSM905006 2 0.000 1.000 0.000 1 0.000
#> GSM905008 2 0.000 1.000 0.000 1 0.000
#> GSM905011 2 0.000 1.000 0.000 1 0.000
#> GSM905013 2 0.000 1.000 0.000 1 0.000
#> GSM905016 2 0.000 1.000 0.000 1 0.000
#> GSM905018 2 0.000 1.000 0.000 1 0.000
#> GSM905021 2 0.000 1.000 0.000 1 0.000
#> GSM905025 2 0.000 1.000 0.000 1 0.000
#> GSM905028 2 0.000 1.000 0.000 1 0.000
#> GSM905030 2 0.000 1.000 0.000 1 0.000
#> GSM905033 2 0.000 1.000 0.000 1 0.000
#> GSM905035 2 0.000 1.000 0.000 1 0.000
#> GSM905037 2 0.000 1.000 0.000 1 0.000
#> GSM905039 2 0.000 1.000 0.000 1 0.000
#> GSM905042 2 0.000 1.000 0.000 1 0.000
#> GSM905046 1 0.000 0.991 1.000 0 0.000
#> GSM905065 1 0.000 0.991 1.000 0 0.000
#> GSM905049 1 0.000 0.991 1.000 0 0.000
#> GSM905050 1 0.000 0.991 1.000 0 0.000
#> GSM905064 1 0.000 0.991 1.000 0 0.000
#> GSM905045 1 0.000 0.991 1.000 0 0.000
#> GSM905051 1 0.000 0.991 1.000 0 0.000
#> GSM905055 1 0.000 0.991 1.000 0 0.000
#> GSM905058 1 0.000 0.991 1.000 0 0.000
#> GSM905053 1 0.000 0.991 1.000 0 0.000
#> GSM905061 1 0.000 0.991 1.000 0 0.000
#> GSM905063 1 0.000 0.991 1.000 0 0.000
#> GSM905054 1 0.000 0.991 1.000 0 0.000
#> GSM905062 1 0.000 0.991 1.000 0 0.000
#> GSM905052 1 0.000 0.991 1.000 0 0.000
#> GSM905059 1 0.000 0.991 1.000 0 0.000
#> GSM905047 1 0.000 0.991 1.000 0 0.000
#> GSM905066 1 0.000 0.991 1.000 0 0.000
#> GSM905056 1 0.000 0.991 1.000 0 0.000
#> GSM905060 1 0.000 0.991 1.000 0 0.000
#> GSM905048 1 0.000 0.991 1.000 0 0.000
#> GSM905067 1 0.000 0.991 1.000 0 0.000
#> GSM905057 1 0.000 0.991 1.000 0 0.000
#> GSM905068 1 0.000 0.991 1.000 0 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM905004 4 0.1022 0.961 0.000 0 0.032 0.968
#> GSM905024 1 0.0000 0.940 1.000 0 0.000 0.000
#> GSM905038 3 0.0336 0.987 0.008 0 0.992 0.000
#> GSM905043 1 0.0000 0.940 1.000 0 0.000 0.000
#> GSM904986 3 0.0000 0.989 0.000 0 1.000 0.000
#> GSM904991 3 0.1211 0.975 0.040 0 0.960 0.000
#> GSM904994 3 0.0000 0.989 0.000 0 1.000 0.000
#> GSM904996 3 0.0000 0.989 0.000 0 1.000 0.000
#> GSM905007 3 0.1211 0.975 0.040 0 0.960 0.000
#> GSM905012 3 0.0000 0.989 0.000 0 1.000 0.000
#> GSM905022 3 0.0000 0.989 0.000 0 1.000 0.000
#> GSM905026 3 0.0000 0.989 0.000 0 1.000 0.000
#> GSM905027 3 0.0000 0.989 0.000 0 1.000 0.000
#> GSM905031 3 0.0000 0.989 0.000 0 1.000 0.000
#> GSM905036 3 0.0707 0.984 0.020 0 0.980 0.000
#> GSM905041 3 0.1211 0.975 0.040 0 0.960 0.000
#> GSM905044 3 0.0000 0.989 0.000 0 1.000 0.000
#> GSM904989 3 0.0000 0.989 0.000 0 1.000 0.000
#> GSM904999 3 0.1022 0.978 0.032 0 0.968 0.000
#> GSM905002 3 0.0000 0.989 0.000 0 1.000 0.000
#> GSM905009 3 0.0000 0.989 0.000 0 1.000 0.000
#> GSM905014 3 0.1211 0.975 0.040 0 0.960 0.000
#> GSM905017 3 0.1022 0.978 0.032 0 0.968 0.000
#> GSM905020 3 0.0000 0.989 0.000 0 1.000 0.000
#> GSM905023 3 0.0707 0.984 0.020 0 0.980 0.000
#> GSM905029 3 0.0000 0.989 0.000 0 1.000 0.000
#> GSM905032 1 0.4713 0.388 0.640 0 0.360 0.000
#> GSM905034 1 0.0000 0.940 1.000 0 0.000 0.000
#> GSM905040 1 0.0000 0.940 1.000 0 0.000 0.000
#> GSM904985 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM904988 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM904990 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM904992 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM904995 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM904998 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905000 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905003 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905006 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905008 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905011 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905013 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905016 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905018 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905021 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905025 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905028 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905030 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905033 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905035 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905037 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905039 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905042 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905046 1 0.1211 0.962 0.960 0 0.000 0.040
#> GSM905065 1 0.1211 0.962 0.960 0 0.000 0.040
#> GSM905049 4 0.0000 0.996 0.000 0 0.000 1.000
#> GSM905050 4 0.0000 0.996 0.000 0 0.000 1.000
#> GSM905064 4 0.0000 0.996 0.000 0 0.000 1.000
#> GSM905045 4 0.0000 0.996 0.000 0 0.000 1.000
#> GSM905051 4 0.0000 0.996 0.000 0 0.000 1.000
#> GSM905055 1 0.1211 0.962 0.960 0 0.000 0.040
#> GSM905058 1 0.1211 0.962 0.960 0 0.000 0.040
#> GSM905053 4 0.0000 0.996 0.000 0 0.000 1.000
#> GSM905061 4 0.0000 0.996 0.000 0 0.000 1.000
#> GSM905063 1 0.1211 0.962 0.960 0 0.000 0.040
#> GSM905054 4 0.0000 0.996 0.000 0 0.000 1.000
#> GSM905062 4 0.0000 0.996 0.000 0 0.000 1.000
#> GSM905052 4 0.0000 0.996 0.000 0 0.000 1.000
#> GSM905059 1 0.1211 0.962 0.960 0 0.000 0.040
#> GSM905047 1 0.1211 0.962 0.960 0 0.000 0.040
#> GSM905066 1 0.1211 0.962 0.960 0 0.000 0.040
#> GSM905056 1 0.1211 0.962 0.960 0 0.000 0.040
#> GSM905060 1 0.1211 0.962 0.960 0 0.000 0.040
#> GSM905048 1 0.1211 0.962 0.960 0 0.000 0.040
#> GSM905067 1 0.1211 0.962 0.960 0 0.000 0.040
#> GSM905057 1 0.1211 0.962 0.960 0 0.000 0.040
#> GSM905068 4 0.0000 0.996 0.000 0 0.000 1.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM905004 4 0.2130 0.8780 0.000 0.000 0.080 0.908 0.012
#> GSM905024 5 0.2648 0.6396 0.152 0.000 0.000 0.000 0.848
#> GSM905038 3 0.4192 0.0631 0.000 0.000 0.596 0.000 0.404
#> GSM905043 5 0.3177 0.5570 0.208 0.000 0.000 0.000 0.792
#> GSM904986 3 0.0000 0.8618 0.000 0.000 1.000 0.000 0.000
#> GSM904991 5 0.3274 0.7393 0.000 0.000 0.220 0.000 0.780
#> GSM904994 3 0.0000 0.8618 0.000 0.000 1.000 0.000 0.000
#> GSM904996 3 0.0000 0.8618 0.000 0.000 1.000 0.000 0.000
#> GSM905007 5 0.3452 0.7283 0.000 0.000 0.244 0.000 0.756
#> GSM905012 3 0.0000 0.8618 0.000 0.000 1.000 0.000 0.000
#> GSM905022 3 0.0000 0.8618 0.000 0.000 1.000 0.000 0.000
#> GSM905026 3 0.0000 0.8618 0.000 0.000 1.000 0.000 0.000
#> GSM905027 3 0.3242 0.5828 0.000 0.000 0.784 0.000 0.216
#> GSM905031 3 0.0000 0.8618 0.000 0.000 1.000 0.000 0.000
#> GSM905036 5 0.4126 0.5506 0.000 0.000 0.380 0.000 0.620
#> GSM905041 5 0.3242 0.7395 0.000 0.000 0.216 0.000 0.784
#> GSM905044 3 0.0000 0.8618 0.000 0.000 1.000 0.000 0.000
#> GSM904989 3 0.0000 0.8618 0.000 0.000 1.000 0.000 0.000
#> GSM904999 5 0.4562 0.2157 0.000 0.000 0.496 0.008 0.496
#> GSM905002 3 0.0000 0.8618 0.000 0.000 1.000 0.000 0.000
#> GSM905009 3 0.0000 0.8618 0.000 0.000 1.000 0.000 0.000
#> GSM905014 5 0.3366 0.7355 0.000 0.000 0.232 0.000 0.768
#> GSM905017 3 0.4562 -0.3383 0.000 0.000 0.496 0.008 0.496
#> GSM905020 3 0.0000 0.8618 0.000 0.000 1.000 0.000 0.000
#> GSM905023 5 0.4171 0.5175 0.000 0.000 0.396 0.000 0.604
#> GSM905029 3 0.4114 0.1696 0.000 0.000 0.624 0.000 0.376
#> GSM905032 5 0.1205 0.6467 0.040 0.000 0.004 0.000 0.956
#> GSM905034 1 0.3586 0.7021 0.736 0.000 0.000 0.000 0.264
#> GSM905040 1 0.4030 0.6939 0.648 0.000 0.000 0.000 0.352
#> GSM904985 2 0.0510 0.9911 0.000 0.984 0.000 0.000 0.016
#> GSM904988 2 0.0000 0.9943 0.000 1.000 0.000 0.000 0.000
#> GSM904990 2 0.0000 0.9943 0.000 1.000 0.000 0.000 0.000
#> GSM904992 2 0.0000 0.9943 0.000 1.000 0.000 0.000 0.000
#> GSM904995 2 0.0510 0.9911 0.000 0.984 0.000 0.000 0.016
#> GSM904998 2 0.0000 0.9943 0.000 1.000 0.000 0.000 0.000
#> GSM905000 2 0.0000 0.9943 0.000 1.000 0.000 0.000 0.000
#> GSM905003 2 0.0000 0.9943 0.000 1.000 0.000 0.000 0.000
#> GSM905006 2 0.0000 0.9943 0.000 1.000 0.000 0.000 0.000
#> GSM905008 2 0.0000 0.9943 0.000 1.000 0.000 0.000 0.000
#> GSM905011 2 0.0000 0.9943 0.000 1.000 0.000 0.000 0.000
#> GSM905013 2 0.0000 0.9943 0.000 1.000 0.000 0.000 0.000
#> GSM905016 2 0.0510 0.9911 0.000 0.984 0.000 0.000 0.016
#> GSM905018 2 0.0000 0.9943 0.000 1.000 0.000 0.000 0.000
#> GSM905021 2 0.0609 0.9890 0.000 0.980 0.000 0.000 0.020
#> GSM905025 2 0.0510 0.9911 0.000 0.984 0.000 0.000 0.016
#> GSM905028 2 0.0000 0.9943 0.000 1.000 0.000 0.000 0.000
#> GSM905030 2 0.0000 0.9943 0.000 1.000 0.000 0.000 0.000
#> GSM905033 2 0.0510 0.9911 0.000 0.984 0.000 0.000 0.016
#> GSM905035 2 0.0510 0.9911 0.000 0.984 0.000 0.000 0.016
#> GSM905037 2 0.0000 0.9943 0.000 1.000 0.000 0.000 0.000
#> GSM905039 2 0.0510 0.9911 0.000 0.984 0.000 0.000 0.016
#> GSM905042 2 0.0510 0.9911 0.000 0.984 0.000 0.000 0.016
#> GSM905046 1 0.0290 0.9097 0.992 0.000 0.000 0.008 0.000
#> GSM905065 1 0.0451 0.9099 0.988 0.000 0.000 0.008 0.004
#> GSM905049 4 0.0290 0.9543 0.008 0.000 0.000 0.992 0.000
#> GSM905050 4 0.0290 0.9543 0.008 0.000 0.000 0.992 0.000
#> GSM905064 4 0.0290 0.9543 0.008 0.000 0.000 0.992 0.000
#> GSM905045 4 0.0451 0.9539 0.008 0.000 0.000 0.988 0.004
#> GSM905051 4 0.3123 0.8060 0.184 0.000 0.000 0.812 0.004
#> GSM905055 1 0.2966 0.8540 0.816 0.000 0.000 0.000 0.184
#> GSM905058 1 0.0451 0.9087 0.988 0.000 0.000 0.008 0.004
#> GSM905053 4 0.0290 0.9543 0.008 0.000 0.000 0.992 0.000
#> GSM905061 4 0.0693 0.9525 0.008 0.000 0.000 0.980 0.012
#> GSM905063 1 0.2966 0.8540 0.816 0.000 0.000 0.000 0.184
#> GSM905054 4 0.0290 0.9543 0.008 0.000 0.000 0.992 0.000
#> GSM905062 4 0.0693 0.9525 0.008 0.000 0.000 0.980 0.012
#> GSM905052 4 0.3086 0.8103 0.180 0.000 0.000 0.816 0.004
#> GSM905059 1 0.0451 0.9087 0.988 0.000 0.000 0.008 0.004
#> GSM905047 1 0.0290 0.9097 0.992 0.000 0.000 0.008 0.000
#> GSM905066 1 0.0451 0.9099 0.988 0.000 0.000 0.008 0.004
#> GSM905056 1 0.2966 0.8540 0.816 0.000 0.000 0.000 0.184
#> GSM905060 1 0.0451 0.9087 0.988 0.000 0.000 0.008 0.004
#> GSM905048 1 0.0290 0.9097 0.992 0.000 0.000 0.008 0.000
#> GSM905067 1 0.0451 0.9099 0.988 0.000 0.000 0.008 0.004
#> GSM905057 1 0.2966 0.8540 0.816 0.000 0.000 0.000 0.184
#> GSM905068 4 0.0693 0.9525 0.008 0.000 0.000 0.980 0.012
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM905004 4 0.2841 0.7948 0.000 0.000 0.092 0.864 0.012 0.032
#> GSM905024 5 0.4148 0.5055 0.108 0.000 0.000 0.000 0.744 0.148
#> GSM905038 5 0.4294 0.3288 0.000 0.000 0.428 0.000 0.552 0.020
#> GSM905043 5 0.4983 0.3582 0.148 0.000 0.000 0.000 0.644 0.208
#> GSM904986 3 0.0146 0.9437 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM904991 5 0.2106 0.6820 0.000 0.000 0.064 0.000 0.904 0.032
#> GSM904994 3 0.0000 0.9444 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM904996 3 0.0000 0.9444 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905007 5 0.1812 0.6890 0.000 0.000 0.080 0.000 0.912 0.008
#> GSM905012 3 0.0000 0.9444 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905022 3 0.0291 0.9429 0.000 0.000 0.992 0.000 0.004 0.004
#> GSM905026 3 0.1151 0.9186 0.000 0.000 0.956 0.000 0.032 0.012
#> GSM905027 3 0.4212 0.0381 0.000 0.000 0.560 0.000 0.424 0.016
#> GSM905031 3 0.0603 0.9345 0.000 0.000 0.980 0.000 0.016 0.004
#> GSM905036 5 0.2877 0.6790 0.000 0.000 0.168 0.000 0.820 0.012
#> GSM905041 5 0.1713 0.6733 0.000 0.000 0.044 0.000 0.928 0.028
#> GSM905044 3 0.0909 0.9293 0.000 0.000 0.968 0.000 0.020 0.012
#> GSM904989 3 0.0146 0.9428 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM904999 5 0.5984 0.4048 0.000 0.000 0.284 0.000 0.444 0.272
#> GSM905002 3 0.0291 0.9429 0.000 0.000 0.992 0.000 0.004 0.004
#> GSM905009 3 0.0000 0.9444 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905014 5 0.1701 0.6870 0.000 0.000 0.072 0.000 0.920 0.008
#> GSM905017 5 0.5984 0.4048 0.000 0.000 0.284 0.000 0.444 0.272
#> GSM905020 3 0.0000 0.9444 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905023 5 0.3104 0.6730 0.000 0.000 0.184 0.000 0.800 0.016
#> GSM905029 5 0.4224 0.3268 0.000 0.000 0.432 0.000 0.552 0.016
#> GSM905032 5 0.3868 0.0799 0.000 0.000 0.000 0.000 0.504 0.496
#> GSM905034 1 0.5117 0.0476 0.628 0.000 0.000 0.000 0.200 0.172
#> GSM905040 6 0.4950 0.0000 0.344 0.000 0.000 0.000 0.080 0.576
#> GSM904985 2 0.1471 0.9514 0.000 0.932 0.000 0.000 0.004 0.064
#> GSM904988 2 0.0000 0.9683 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM904990 2 0.0000 0.9683 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM904992 2 0.0000 0.9683 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM904995 2 0.1411 0.9525 0.000 0.936 0.000 0.000 0.004 0.060
#> GSM904998 2 0.0000 0.9683 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905000 2 0.0000 0.9683 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905003 2 0.0146 0.9676 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM905006 2 0.0000 0.9683 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905008 2 0.0146 0.9676 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM905011 2 0.0000 0.9683 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905013 2 0.0000 0.9683 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905016 2 0.1411 0.9525 0.000 0.936 0.000 0.000 0.004 0.060
#> GSM905018 2 0.0000 0.9683 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905021 2 0.3420 0.7751 0.000 0.748 0.000 0.000 0.012 0.240
#> GSM905025 2 0.1524 0.9518 0.000 0.932 0.000 0.000 0.008 0.060
#> GSM905028 2 0.0146 0.9678 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM905030 2 0.0146 0.9678 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM905033 2 0.1643 0.9482 0.000 0.924 0.000 0.000 0.008 0.068
#> GSM905035 2 0.1524 0.9518 0.000 0.932 0.000 0.000 0.008 0.060
#> GSM905037 2 0.0146 0.9678 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM905039 2 0.1524 0.9518 0.000 0.932 0.000 0.000 0.008 0.060
#> GSM905042 2 0.1701 0.9460 0.000 0.920 0.000 0.000 0.008 0.072
#> GSM905046 1 0.0291 0.6667 0.992 0.000 0.000 0.004 0.000 0.004
#> GSM905065 1 0.1219 0.6553 0.948 0.000 0.000 0.004 0.000 0.048
#> GSM905049 4 0.0000 0.8997 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905050 4 0.0000 0.8997 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905064 4 0.0000 0.8997 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905045 4 0.0363 0.8983 0.000 0.000 0.000 0.988 0.000 0.012
#> GSM905051 4 0.5092 0.4310 0.356 0.000 0.000 0.576 0.024 0.044
#> GSM905055 1 0.3986 -0.3769 0.532 0.000 0.000 0.000 0.004 0.464
#> GSM905058 1 0.1232 0.6548 0.956 0.000 0.000 0.004 0.016 0.024
#> GSM905053 4 0.0000 0.8997 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905061 4 0.0508 0.8963 0.000 0.000 0.000 0.984 0.004 0.012
#> GSM905063 1 0.3975 -0.3479 0.544 0.000 0.000 0.000 0.004 0.452
#> GSM905054 4 0.0000 0.8997 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905062 4 0.0508 0.8963 0.000 0.000 0.000 0.984 0.004 0.012
#> GSM905052 4 0.5092 0.4310 0.356 0.000 0.000 0.576 0.024 0.044
#> GSM905059 1 0.1232 0.6548 0.956 0.000 0.000 0.004 0.016 0.024
#> GSM905047 1 0.0291 0.6667 0.992 0.000 0.000 0.004 0.000 0.004
#> GSM905066 1 0.1219 0.6553 0.948 0.000 0.000 0.004 0.000 0.048
#> GSM905056 1 0.3986 -0.3769 0.532 0.000 0.000 0.000 0.004 0.464
#> GSM905060 1 0.1232 0.6548 0.956 0.000 0.000 0.004 0.016 0.024
#> GSM905048 1 0.0603 0.6663 0.980 0.000 0.000 0.004 0.000 0.016
#> GSM905067 1 0.1219 0.6553 0.948 0.000 0.000 0.004 0.000 0.048
#> GSM905057 1 0.3986 -0.3769 0.532 0.000 0.000 0.000 0.004 0.464
#> GSM905068 4 0.0260 0.8985 0.000 0.000 0.000 0.992 0.000 0.008
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) genotype/variation(p) individual(p) k
#> CV:skmeans 76 4.99e-07 1.61e-03 0.0803 2
#> CV:skmeans 74 1.34e-18 5.42e-06 0.9460 3
#> CV:skmeans 75 1.27e-19 7.10e-10 0.2356 4
#> CV:skmeans 72 1.53e-16 2.67e-08 0.4302 5
#> CV:skmeans 61 3.24e-16 1.74e-10 0.5407 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 76 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.974 0.979 0.4332 0.572 0.572
#> 3 3 1.000 0.985 0.992 0.5556 0.754 0.571
#> 4 4 1.000 0.969 0.989 0.0928 0.920 0.762
#> 5 5 1.000 0.990 0.997 0.0312 0.968 0.881
#> 6 6 0.955 0.945 0.965 0.0146 0.977 0.907
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2 3 4 5
There is also optional best \(k\) = 2 3 4 5 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
#> GSM905004 1 0.2043 0.964 0.968 0.032
#> GSM905024 1 0.0000 0.969 1.000 0.000
#> GSM905038 1 0.3879 0.950 0.924 0.076
#> GSM905043 1 0.0000 0.969 1.000 0.000
#> GSM904986 1 0.3879 0.950 0.924 0.076
#> GSM904991 1 0.0376 0.969 0.996 0.004
#> GSM904994 1 0.3879 0.950 0.924 0.076
#> GSM904996 1 0.3879 0.950 0.924 0.076
#> GSM905007 1 0.2043 0.964 0.968 0.032
#> GSM905012 1 0.3879 0.950 0.924 0.076
#> GSM905022 1 0.3879 0.950 0.924 0.076
#> GSM905026 1 0.3879 0.950 0.924 0.076
#> GSM905027 1 0.2043 0.964 0.968 0.032
#> GSM905031 1 0.3879 0.950 0.924 0.076
#> GSM905036 1 0.2043 0.964 0.968 0.032
#> GSM905041 1 0.0376 0.969 0.996 0.004
#> GSM905044 1 0.3879 0.950 0.924 0.076
#> GSM904989 1 0.3879 0.950 0.924 0.076
#> GSM904999 1 0.3879 0.950 0.924 0.076
#> GSM905002 1 0.3879 0.950 0.924 0.076
#> GSM905009 1 0.3879 0.950 0.924 0.076
#> GSM905014 1 0.3879 0.950 0.924 0.076
#> GSM905017 1 0.3879 0.950 0.924 0.076
#> GSM905020 1 0.3879 0.950 0.924 0.076
#> GSM905023 1 0.3879 0.950 0.924 0.076
#> GSM905029 1 0.3879 0.950 0.924 0.076
#> GSM905032 1 0.3879 0.950 0.924 0.076
#> GSM905034 1 0.0000 0.969 1.000 0.000
#> GSM905040 1 0.0000 0.969 1.000 0.000
#> GSM904985 2 0.0000 1.000 0.000 1.000
#> GSM904988 2 0.0000 1.000 0.000 1.000
#> GSM904990 2 0.0000 1.000 0.000 1.000
#> GSM904992 2 0.0000 1.000 0.000 1.000
#> GSM904995 2 0.0000 1.000 0.000 1.000
#> GSM904998 2 0.0000 1.000 0.000 1.000
#> GSM905000 2 0.0000 1.000 0.000 1.000
#> GSM905003 2 0.0000 1.000 0.000 1.000
#> GSM905006 2 0.0000 1.000 0.000 1.000
#> GSM905008 2 0.0000 1.000 0.000 1.000
#> GSM905011 2 0.0000 1.000 0.000 1.000
#> GSM905013 2 0.0000 1.000 0.000 1.000
#> GSM905016 2 0.0000 1.000 0.000 1.000
#> GSM905018 2 0.0000 1.000 0.000 1.000
#> GSM905021 2 0.0000 1.000 0.000 1.000
#> GSM905025 2 0.0000 1.000 0.000 1.000
#> GSM905028 2 0.0000 1.000 0.000 1.000
#> GSM905030 2 0.0000 1.000 0.000 1.000
#> GSM905033 2 0.0000 1.000 0.000 1.000
#> GSM905035 2 0.0000 1.000 0.000 1.000
#> GSM905037 2 0.0000 1.000 0.000 1.000
#> GSM905039 2 0.0000 1.000 0.000 1.000
#> GSM905042 2 0.0000 1.000 0.000 1.000
#> GSM905046 1 0.0000 0.969 1.000 0.000
#> GSM905065 1 0.0000 0.969 1.000 0.000
#> GSM905049 1 0.0000 0.969 1.000 0.000
#> GSM905050 1 0.0000 0.969 1.000 0.000
#> GSM905064 1 0.0000 0.969 1.000 0.000
#> GSM905045 1 0.0000 0.969 1.000 0.000
#> GSM905051 1 0.0000 0.969 1.000 0.000
#> GSM905055 1 0.0000 0.969 1.000 0.000
#> GSM905058 1 0.0000 0.969 1.000 0.000
#> GSM905053 1 0.0000 0.969 1.000 0.000
#> GSM905061 1 0.0000 0.969 1.000 0.000
#> GSM905063 1 0.0000 0.969 1.000 0.000
#> GSM905054 1 0.0000 0.969 1.000 0.000
#> GSM905062 1 0.0000 0.969 1.000 0.000
#> GSM905052 1 0.0000 0.969 1.000 0.000
#> GSM905059 1 0.0000 0.969 1.000 0.000
#> GSM905047 1 0.0000 0.969 1.000 0.000
#> GSM905066 1 0.0000 0.969 1.000 0.000
#> GSM905056 1 0.0000 0.969 1.000 0.000
#> GSM905060 1 0.0000 0.969 1.000 0.000
#> GSM905048 1 0.0000 0.969 1.000 0.000
#> GSM905067 1 0.0000 0.969 1.000 0.000
#> GSM905057 1 0.0000 0.969 1.000 0.000
#> GSM905068 1 0.0000 0.969 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM905004 3 0.0000 1.000 0.000 0 1.000
#> GSM905024 1 0.2066 0.932 0.940 0 0.060
#> GSM905038 3 0.0000 1.000 0.000 0 1.000
#> GSM905043 1 0.4452 0.782 0.808 0 0.192
#> GSM904986 3 0.0000 1.000 0.000 0 1.000
#> GSM904991 3 0.0000 1.000 0.000 0 1.000
#> GSM904994 3 0.0000 1.000 0.000 0 1.000
#> GSM904996 3 0.0000 1.000 0.000 0 1.000
#> GSM905007 3 0.0000 1.000 0.000 0 1.000
#> GSM905012 3 0.0000 1.000 0.000 0 1.000
#> GSM905022 3 0.0000 1.000 0.000 0 1.000
#> GSM905026 3 0.0000 1.000 0.000 0 1.000
#> GSM905027 3 0.0000 1.000 0.000 0 1.000
#> GSM905031 3 0.0000 1.000 0.000 0 1.000
#> GSM905036 3 0.0000 1.000 0.000 0 1.000
#> GSM905041 3 0.0000 1.000 0.000 0 1.000
#> GSM905044 3 0.0000 1.000 0.000 0 1.000
#> GSM904989 3 0.0000 1.000 0.000 0 1.000
#> GSM904999 3 0.0000 1.000 0.000 0 1.000
#> GSM905002 3 0.0000 1.000 0.000 0 1.000
#> GSM905009 3 0.0000 1.000 0.000 0 1.000
#> GSM905014 3 0.0000 1.000 0.000 0 1.000
#> GSM905017 3 0.0000 1.000 0.000 0 1.000
#> GSM905020 3 0.0000 1.000 0.000 0 1.000
#> GSM905023 3 0.0000 1.000 0.000 0 1.000
#> GSM905029 3 0.0000 1.000 0.000 0 1.000
#> GSM905032 3 0.0000 1.000 0.000 0 1.000
#> GSM905034 1 0.0237 0.976 0.996 0 0.004
#> GSM905040 1 0.0892 0.965 0.980 0 0.020
#> GSM904985 2 0.0000 1.000 0.000 1 0.000
#> GSM904988 2 0.0000 1.000 0.000 1 0.000
#> GSM904990 2 0.0000 1.000 0.000 1 0.000
#> GSM904992 2 0.0000 1.000 0.000 1 0.000
#> GSM904995 2 0.0000 1.000 0.000 1 0.000
#> GSM904998 2 0.0000 1.000 0.000 1 0.000
#> GSM905000 2 0.0000 1.000 0.000 1 0.000
#> GSM905003 2 0.0000 1.000 0.000 1 0.000
#> GSM905006 2 0.0000 1.000 0.000 1 0.000
#> GSM905008 2 0.0000 1.000 0.000 1 0.000
#> GSM905011 2 0.0000 1.000 0.000 1 0.000
#> GSM905013 2 0.0000 1.000 0.000 1 0.000
#> GSM905016 2 0.0000 1.000 0.000 1 0.000
#> GSM905018 2 0.0000 1.000 0.000 1 0.000
#> GSM905021 2 0.0000 1.000 0.000 1 0.000
#> GSM905025 2 0.0000 1.000 0.000 1 0.000
#> GSM905028 2 0.0000 1.000 0.000 1 0.000
#> GSM905030 2 0.0000 1.000 0.000 1 0.000
#> GSM905033 2 0.0000 1.000 0.000 1 0.000
#> GSM905035 2 0.0000 1.000 0.000 1 0.000
#> GSM905037 2 0.0000 1.000 0.000 1 0.000
#> GSM905039 2 0.0000 1.000 0.000 1 0.000
#> GSM905042 2 0.0000 1.000 0.000 1 0.000
#> GSM905046 1 0.0000 0.978 1.000 0 0.000
#> GSM905065 1 0.0000 0.978 1.000 0 0.000
#> GSM905049 1 0.0424 0.973 0.992 0 0.008
#> GSM905050 1 0.3551 0.857 0.868 0 0.132
#> GSM905064 1 0.0000 0.978 1.000 0 0.000
#> GSM905045 1 0.0000 0.978 1.000 0 0.000
#> GSM905051 1 0.0000 0.978 1.000 0 0.000
#> GSM905055 1 0.0000 0.978 1.000 0 0.000
#> GSM905058 1 0.0000 0.978 1.000 0 0.000
#> GSM905053 1 0.0000 0.978 1.000 0 0.000
#> GSM905061 1 0.0000 0.978 1.000 0 0.000
#> GSM905063 1 0.0000 0.978 1.000 0 0.000
#> GSM905054 1 0.0000 0.978 1.000 0 0.000
#> GSM905062 1 0.0000 0.978 1.000 0 0.000
#> GSM905052 1 0.0000 0.978 1.000 0 0.000
#> GSM905059 1 0.0000 0.978 1.000 0 0.000
#> GSM905047 1 0.0000 0.978 1.000 0 0.000
#> GSM905066 1 0.0000 0.978 1.000 0 0.000
#> GSM905056 1 0.0000 0.978 1.000 0 0.000
#> GSM905060 1 0.0000 0.978 1.000 0 0.000
#> GSM905048 1 0.0000 0.978 1.000 0 0.000
#> GSM905067 1 0.0000 0.978 1.000 0 0.000
#> GSM905057 1 0.0000 0.978 1.000 0 0.000
#> GSM905068 1 0.4062 0.816 0.836 0 0.164
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM905004 3 0.1389 0.9321 0.000 0 0.952 0.048
#> GSM905024 3 0.4981 0.0863 0.464 0 0.536 0.000
#> GSM905038 3 0.0000 0.9782 0.000 0 1.000 0.000
#> GSM905043 1 0.2589 0.8552 0.884 0 0.116 0.000
#> GSM904986 3 0.0000 0.9782 0.000 0 1.000 0.000
#> GSM904991 3 0.0000 0.9782 0.000 0 1.000 0.000
#> GSM904994 3 0.0000 0.9782 0.000 0 1.000 0.000
#> GSM904996 3 0.0000 0.9782 0.000 0 1.000 0.000
#> GSM905007 3 0.0000 0.9782 0.000 0 1.000 0.000
#> GSM905012 3 0.0000 0.9782 0.000 0 1.000 0.000
#> GSM905022 3 0.0000 0.9782 0.000 0 1.000 0.000
#> GSM905026 3 0.0000 0.9782 0.000 0 1.000 0.000
#> GSM905027 3 0.0000 0.9782 0.000 0 1.000 0.000
#> GSM905031 3 0.0000 0.9782 0.000 0 1.000 0.000
#> GSM905036 3 0.0000 0.9782 0.000 0 1.000 0.000
#> GSM905041 3 0.0000 0.9782 0.000 0 1.000 0.000
#> GSM905044 3 0.0000 0.9782 0.000 0 1.000 0.000
#> GSM904989 3 0.0000 0.9782 0.000 0 1.000 0.000
#> GSM904999 3 0.0000 0.9782 0.000 0 1.000 0.000
#> GSM905002 3 0.0000 0.9782 0.000 0 1.000 0.000
#> GSM905009 3 0.0000 0.9782 0.000 0 1.000 0.000
#> GSM905014 3 0.0000 0.9782 0.000 0 1.000 0.000
#> GSM905017 3 0.0000 0.9782 0.000 0 1.000 0.000
#> GSM905020 3 0.0000 0.9782 0.000 0 1.000 0.000
#> GSM905023 3 0.0000 0.9782 0.000 0 1.000 0.000
#> GSM905029 3 0.0000 0.9782 0.000 0 1.000 0.000
#> GSM905032 3 0.0000 0.9782 0.000 0 1.000 0.000
#> GSM905034 1 0.3569 0.7520 0.804 0 0.196 0.000
#> GSM905040 1 0.0592 0.9586 0.984 0 0.016 0.000
#> GSM904985 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM904988 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM904990 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM904992 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM904995 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM904998 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM905000 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM905003 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM905006 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM905008 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM905011 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM905013 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM905016 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM905018 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM905021 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM905025 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM905028 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM905030 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM905033 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM905035 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM905037 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM905039 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM905042 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM905046 1 0.0000 0.9709 1.000 0 0.000 0.000
#> GSM905065 1 0.0000 0.9709 1.000 0 0.000 0.000
#> GSM905049 4 0.0000 1.0000 0.000 0 0.000 1.000
#> GSM905050 4 0.0000 1.0000 0.000 0 0.000 1.000
#> GSM905064 4 0.0000 1.0000 0.000 0 0.000 1.000
#> GSM905045 4 0.0000 1.0000 0.000 0 0.000 1.000
#> GSM905051 4 0.0000 1.0000 0.000 0 0.000 1.000
#> GSM905055 1 0.0000 0.9709 1.000 0 0.000 0.000
#> GSM905058 1 0.0000 0.9709 1.000 0 0.000 0.000
#> GSM905053 4 0.0000 1.0000 0.000 0 0.000 1.000
#> GSM905061 4 0.0000 1.0000 0.000 0 0.000 1.000
#> GSM905063 1 0.0000 0.9709 1.000 0 0.000 0.000
#> GSM905054 4 0.0000 1.0000 0.000 0 0.000 1.000
#> GSM905062 4 0.0000 1.0000 0.000 0 0.000 1.000
#> GSM905052 4 0.0000 1.0000 0.000 0 0.000 1.000
#> GSM905059 1 0.1022 0.9468 0.968 0 0.000 0.032
#> GSM905047 1 0.0000 0.9709 1.000 0 0.000 0.000
#> GSM905066 1 0.0000 0.9709 1.000 0 0.000 0.000
#> GSM905056 1 0.0000 0.9709 1.000 0 0.000 0.000
#> GSM905060 1 0.0000 0.9709 1.000 0 0.000 0.000
#> GSM905048 1 0.0000 0.9709 1.000 0 0.000 0.000
#> GSM905067 1 0.0000 0.9709 1.000 0 0.000 0.000
#> GSM905057 1 0.0000 0.9709 1.000 0 0.000 0.000
#> GSM905068 4 0.0000 1.0000 0.000 0 0.000 1.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM905004 3 0.120 0.945 0.000 0 0.952 0.048 0
#> GSM905024 1 0.120 0.917 0.952 0 0.048 0.000 0
#> GSM905038 3 0.000 0.998 0.000 0 1.000 0.000 0
#> GSM905043 1 0.277 0.747 0.836 0 0.164 0.000 0
#> GSM904986 3 0.000 0.998 0.000 0 1.000 0.000 0
#> GSM904991 3 0.000 0.998 0.000 0 1.000 0.000 0
#> GSM904994 3 0.000 0.998 0.000 0 1.000 0.000 0
#> GSM904996 3 0.000 0.998 0.000 0 1.000 0.000 0
#> GSM905007 3 0.000 0.998 0.000 0 1.000 0.000 0
#> GSM905012 3 0.000 0.998 0.000 0 1.000 0.000 0
#> GSM905022 3 0.000 0.998 0.000 0 1.000 0.000 0
#> GSM905026 3 0.000 0.998 0.000 0 1.000 0.000 0
#> GSM905027 3 0.000 0.998 0.000 0 1.000 0.000 0
#> GSM905031 3 0.000 0.998 0.000 0 1.000 0.000 0
#> GSM905036 3 0.000 0.998 0.000 0 1.000 0.000 0
#> GSM905041 3 0.000 0.998 0.000 0 1.000 0.000 0
#> GSM905044 3 0.000 0.998 0.000 0 1.000 0.000 0
#> GSM904989 3 0.000 0.998 0.000 0 1.000 0.000 0
#> GSM904999 3 0.000 0.998 0.000 0 1.000 0.000 0
#> GSM905002 3 0.000 0.998 0.000 0 1.000 0.000 0
#> GSM905009 3 0.000 0.998 0.000 0 1.000 0.000 0
#> GSM905014 3 0.000 0.998 0.000 0 1.000 0.000 0
#> GSM905017 3 0.000 0.998 0.000 0 1.000 0.000 0
#> GSM905020 3 0.000 0.998 0.000 0 1.000 0.000 0
#> GSM905023 3 0.000 0.998 0.000 0 1.000 0.000 0
#> GSM905029 3 0.000 0.998 0.000 0 1.000 0.000 0
#> GSM905032 3 0.000 0.998 0.000 0 1.000 0.000 0
#> GSM905034 1 0.000 0.971 1.000 0 0.000 0.000 0
#> GSM905040 5 0.000 1.000 0.000 0 0.000 0.000 1
#> GSM904985 2 0.000 1.000 0.000 1 0.000 0.000 0
#> GSM904988 2 0.000 1.000 0.000 1 0.000 0.000 0
#> GSM904990 2 0.000 1.000 0.000 1 0.000 0.000 0
#> GSM904992 2 0.000 1.000 0.000 1 0.000 0.000 0
#> GSM904995 2 0.000 1.000 0.000 1 0.000 0.000 0
#> GSM904998 2 0.000 1.000 0.000 1 0.000 0.000 0
#> GSM905000 2 0.000 1.000 0.000 1 0.000 0.000 0
#> GSM905003 2 0.000 1.000 0.000 1 0.000 0.000 0
#> GSM905006 2 0.000 1.000 0.000 1 0.000 0.000 0
#> GSM905008 2 0.000 1.000 0.000 1 0.000 0.000 0
#> GSM905011 2 0.000 1.000 0.000 1 0.000 0.000 0
#> GSM905013 2 0.000 1.000 0.000 1 0.000 0.000 0
#> GSM905016 2 0.000 1.000 0.000 1 0.000 0.000 0
#> GSM905018 2 0.000 1.000 0.000 1 0.000 0.000 0
#> GSM905021 2 0.000 1.000 0.000 1 0.000 0.000 0
#> GSM905025 2 0.000 1.000 0.000 1 0.000 0.000 0
#> GSM905028 2 0.000 1.000 0.000 1 0.000 0.000 0
#> GSM905030 2 0.000 1.000 0.000 1 0.000 0.000 0
#> GSM905033 2 0.000 1.000 0.000 1 0.000 0.000 0
#> GSM905035 2 0.000 1.000 0.000 1 0.000 0.000 0
#> GSM905037 2 0.000 1.000 0.000 1 0.000 0.000 0
#> GSM905039 2 0.000 1.000 0.000 1 0.000 0.000 0
#> GSM905042 2 0.000 1.000 0.000 1 0.000 0.000 0
#> GSM905046 1 0.000 0.971 1.000 0 0.000 0.000 0
#> GSM905065 1 0.000 0.971 1.000 0 0.000 0.000 0
#> GSM905049 4 0.000 1.000 0.000 0 0.000 1.000 0
#> GSM905050 4 0.000 1.000 0.000 0 0.000 1.000 0
#> GSM905064 4 0.000 1.000 0.000 0 0.000 1.000 0
#> GSM905045 4 0.000 1.000 0.000 0 0.000 1.000 0
#> GSM905051 4 0.000 1.000 0.000 0 0.000 1.000 0
#> GSM905055 5 0.000 1.000 0.000 0 0.000 0.000 1
#> GSM905058 1 0.000 0.971 1.000 0 0.000 0.000 0
#> GSM905053 4 0.000 1.000 0.000 0 0.000 1.000 0
#> GSM905061 4 0.000 1.000 0.000 0 0.000 1.000 0
#> GSM905063 5 0.000 1.000 0.000 0 0.000 0.000 1
#> GSM905054 4 0.000 1.000 0.000 0 0.000 1.000 0
#> GSM905062 4 0.000 1.000 0.000 0 0.000 1.000 0
#> GSM905052 4 0.000 1.000 0.000 0 0.000 1.000 0
#> GSM905059 1 0.000 0.971 1.000 0 0.000 0.000 0
#> GSM905047 1 0.000 0.971 1.000 0 0.000 0.000 0
#> GSM905066 1 0.000 0.971 1.000 0 0.000 0.000 0
#> GSM905056 5 0.000 1.000 0.000 0 0.000 0.000 1
#> GSM905060 1 0.000 0.971 1.000 0 0.000 0.000 0
#> GSM905048 1 0.000 0.971 1.000 0 0.000 0.000 0
#> GSM905067 1 0.000 0.971 1.000 0 0.000 0.000 0
#> GSM905057 5 0.000 1.000 0.000 0 0.000 0.000 1
#> GSM905068 4 0.000 1.000 0.000 0 0.000 1.000 0
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM905004 3 0.107 0.923 0.000 0 0.952 0.048 0.000 0.000
#> GSM905024 3 0.322 0.721 0.000 0 0.736 0.000 0.264 0.000
#> GSM905038 3 0.000 0.965 0.000 0 1.000 0.000 0.000 0.000
#> GSM905043 1 0.299 0.736 0.824 0 0.024 0.000 0.152 0.000
#> GSM904986 3 0.000 0.965 0.000 0 1.000 0.000 0.000 0.000
#> GSM904991 3 0.238 0.852 0.000 0 0.848 0.000 0.152 0.000
#> GSM904994 3 0.000 0.965 0.000 0 1.000 0.000 0.000 0.000
#> GSM904996 3 0.000 0.965 0.000 0 1.000 0.000 0.000 0.000
#> GSM905007 3 0.000 0.965 0.000 0 1.000 0.000 0.000 0.000
#> GSM905012 3 0.000 0.965 0.000 0 1.000 0.000 0.000 0.000
#> GSM905022 3 0.000 0.965 0.000 0 1.000 0.000 0.000 0.000
#> GSM905026 3 0.000 0.965 0.000 0 1.000 0.000 0.000 0.000
#> GSM905027 3 0.000 0.965 0.000 0 1.000 0.000 0.000 0.000
#> GSM905031 3 0.000 0.965 0.000 0 1.000 0.000 0.000 0.000
#> GSM905036 3 0.000 0.965 0.000 0 1.000 0.000 0.000 0.000
#> GSM905041 3 0.238 0.852 0.000 0 0.848 0.000 0.152 0.000
#> GSM905044 3 0.000 0.965 0.000 0 1.000 0.000 0.000 0.000
#> GSM904989 3 0.000 0.965 0.000 0 1.000 0.000 0.000 0.000
#> GSM904999 3 0.000 0.965 0.000 0 1.000 0.000 0.000 0.000
#> GSM905002 3 0.000 0.965 0.000 0 1.000 0.000 0.000 0.000
#> GSM905009 3 0.000 0.965 0.000 0 1.000 0.000 0.000 0.000
#> GSM905014 3 0.218 0.870 0.000 0 0.868 0.000 0.132 0.000
#> GSM905017 3 0.000 0.965 0.000 0 1.000 0.000 0.000 0.000
#> GSM905020 3 0.000 0.965 0.000 0 1.000 0.000 0.000 0.000
#> GSM905023 3 0.000 0.965 0.000 0 1.000 0.000 0.000 0.000
#> GSM905029 3 0.000 0.965 0.000 0 1.000 0.000 0.000 0.000
#> GSM905032 3 0.226 0.864 0.000 0 0.860 0.000 0.140 0.000
#> GSM905034 5 0.000 0.747 0.000 0 0.000 0.000 1.000 0.000
#> GSM905040 6 0.238 0.750 0.000 0 0.000 0.000 0.152 0.848
#> GSM904985 2 0.000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM904988 2 0.000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM904990 2 0.000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM904992 2 0.000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM904995 2 0.000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM904998 2 0.000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM905000 2 0.000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM905003 2 0.000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM905006 2 0.000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM905008 2 0.000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM905011 2 0.000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM905013 2 0.000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM905016 2 0.000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM905018 2 0.000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM905021 2 0.000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM905025 2 0.000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM905028 2 0.000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM905030 2 0.000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM905033 2 0.000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM905035 2 0.000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM905037 2 0.000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM905039 2 0.000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM905042 2 0.000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM905046 1 0.079 0.914 0.968 0 0.000 0.000 0.032 0.000
#> GSM905065 1 0.000 0.941 1.000 0 0.000 0.000 0.000 0.000
#> GSM905049 4 0.000 1.000 0.000 0 0.000 1.000 0.000 0.000
#> GSM905050 4 0.000 1.000 0.000 0 0.000 1.000 0.000 0.000
#> GSM905064 4 0.000 1.000 0.000 0 0.000 1.000 0.000 0.000
#> GSM905045 4 0.000 1.000 0.000 0 0.000 1.000 0.000 0.000
#> GSM905051 4 0.000 1.000 0.000 0 0.000 1.000 0.000 0.000
#> GSM905055 6 0.000 0.854 0.000 0 0.000 0.000 0.000 1.000
#> GSM905058 5 0.238 0.906 0.152 0 0.000 0.000 0.848 0.000
#> GSM905053 4 0.000 1.000 0.000 0 0.000 1.000 0.000 0.000
#> GSM905061 4 0.000 1.000 0.000 0 0.000 1.000 0.000 0.000
#> GSM905063 6 0.490 0.439 0.304 0 0.000 0.000 0.088 0.608
#> GSM905054 4 0.000 1.000 0.000 0 0.000 1.000 0.000 0.000
#> GSM905062 4 0.000 1.000 0.000 0 0.000 1.000 0.000 0.000
#> GSM905052 4 0.000 1.000 0.000 0 0.000 1.000 0.000 0.000
#> GSM905059 5 0.238 0.906 0.152 0 0.000 0.000 0.848 0.000
#> GSM905047 5 0.327 0.789 0.272 0 0.000 0.000 0.728 0.000
#> GSM905066 1 0.000 0.941 1.000 0 0.000 0.000 0.000 0.000
#> GSM905056 6 0.000 0.854 0.000 0 0.000 0.000 0.000 1.000
#> GSM905060 5 0.238 0.906 0.152 0 0.000 0.000 0.848 0.000
#> GSM905048 1 0.000 0.941 1.000 0 0.000 0.000 0.000 0.000
#> GSM905067 1 0.000 0.941 1.000 0 0.000 0.000 0.000 0.000
#> GSM905057 6 0.000 0.854 0.000 0 0.000 0.000 0.000 1.000
#> GSM905068 4 0.000 1.000 0.000 0 0.000 1.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) genotype/variation(p) individual(p) k
#> CV:pam 76 3.04e-12 1.17e-05 0.99018 2
#> CV:pam 76 1.53e-18 5.88e-06 0.89219 3
#> CV:pam 75 1.05e-21 2.27e-09 0.35473 4
#> CV:pam 76 1.33e-21 7.96e-12 0.01272 5
#> CV:pam 75 2.04e-24 1.54e-12 0.00838 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 76 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 1.000 1.000 0.4283 0.572 0.572
#> 3 3 1.000 0.984 0.994 0.5772 0.720 0.524
#> 4 4 0.886 0.892 0.936 0.0757 0.938 0.813
#> 5 5 0.955 0.903 0.957 0.0729 0.915 0.707
#> 6 6 0.883 0.852 0.874 0.0345 0.985 0.931
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
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
#> GSM905004 1 0 1 1 0
#> GSM905024 1 0 1 1 0
#> GSM905038 1 0 1 1 0
#> GSM905043 1 0 1 1 0
#> GSM904986 1 0 1 1 0
#> GSM904991 1 0 1 1 0
#> GSM904994 1 0 1 1 0
#> GSM904996 1 0 1 1 0
#> GSM905007 1 0 1 1 0
#> GSM905012 1 0 1 1 0
#> GSM905022 1 0 1 1 0
#> GSM905026 1 0 1 1 0
#> GSM905027 1 0 1 1 0
#> GSM905031 1 0 1 1 0
#> GSM905036 1 0 1 1 0
#> GSM905041 1 0 1 1 0
#> GSM905044 1 0 1 1 0
#> GSM904989 1 0 1 1 0
#> GSM904999 1 0 1 1 0
#> GSM905002 1 0 1 1 0
#> GSM905009 1 0 1 1 0
#> GSM905014 1 0 1 1 0
#> GSM905017 1 0 1 1 0
#> GSM905020 1 0 1 1 0
#> GSM905023 1 0 1 1 0
#> GSM905029 1 0 1 1 0
#> GSM905032 1 0 1 1 0
#> GSM905034 1 0 1 1 0
#> GSM905040 1 0 1 1 0
#> GSM904985 2 0 1 0 1
#> GSM904988 2 0 1 0 1
#> GSM904990 2 0 1 0 1
#> GSM904992 2 0 1 0 1
#> GSM904995 2 0 1 0 1
#> GSM904998 2 0 1 0 1
#> GSM905000 2 0 1 0 1
#> GSM905003 2 0 1 0 1
#> GSM905006 2 0 1 0 1
#> GSM905008 2 0 1 0 1
#> GSM905011 2 0 1 0 1
#> GSM905013 2 0 1 0 1
#> GSM905016 2 0 1 0 1
#> GSM905018 2 0 1 0 1
#> GSM905021 2 0 1 0 1
#> GSM905025 2 0 1 0 1
#> GSM905028 2 0 1 0 1
#> GSM905030 2 0 1 0 1
#> GSM905033 2 0 1 0 1
#> GSM905035 2 0 1 0 1
#> GSM905037 2 0 1 0 1
#> GSM905039 2 0 1 0 1
#> GSM905042 2 0 1 0 1
#> GSM905046 1 0 1 1 0
#> GSM905065 1 0 1 1 0
#> GSM905049 1 0 1 1 0
#> GSM905050 1 0 1 1 0
#> GSM905064 1 0 1 1 0
#> GSM905045 1 0 1 1 0
#> GSM905051 1 0 1 1 0
#> GSM905055 1 0 1 1 0
#> GSM905058 1 0 1 1 0
#> GSM905053 1 0 1 1 0
#> GSM905061 1 0 1 1 0
#> GSM905063 1 0 1 1 0
#> GSM905054 1 0 1 1 0
#> GSM905062 1 0 1 1 0
#> GSM905052 1 0 1 1 0
#> GSM905059 1 0 1 1 0
#> GSM905047 1 0 1 1 0
#> GSM905066 1 0 1 1 0
#> GSM905056 1 0 1 1 0
#> GSM905060 1 0 1 1 0
#> GSM905048 1 0 1 1 0
#> GSM905067 1 0 1 1 0
#> GSM905057 1 0 1 1 0
#> GSM905068 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM905004 1 0.613 0.331 0.6 0.000 0.400
#> GSM905024 3 0.000 0.998 0.0 0.000 1.000
#> GSM905038 3 0.000 0.998 0.0 0.000 1.000
#> GSM905043 3 0.000 0.998 0.0 0.000 1.000
#> GSM904986 3 0.000 0.998 0.0 0.000 1.000
#> GSM904991 3 0.000 0.998 0.0 0.000 1.000
#> GSM904994 3 0.000 0.998 0.0 0.000 1.000
#> GSM904996 3 0.000 0.998 0.0 0.000 1.000
#> GSM905007 3 0.000 0.998 0.0 0.000 1.000
#> GSM905012 3 0.000 0.998 0.0 0.000 1.000
#> GSM905022 3 0.000 0.998 0.0 0.000 1.000
#> GSM905026 3 0.000 0.998 0.0 0.000 1.000
#> GSM905027 3 0.000 0.998 0.0 0.000 1.000
#> GSM905031 3 0.000 0.998 0.0 0.000 1.000
#> GSM905036 3 0.000 0.998 0.0 0.000 1.000
#> GSM905041 3 0.000 0.998 0.0 0.000 1.000
#> GSM905044 3 0.000 0.998 0.0 0.000 1.000
#> GSM904989 3 0.000 0.998 0.0 0.000 1.000
#> GSM904999 2 0.000 1.000 0.0 1.000 0.000
#> GSM905002 3 0.000 0.998 0.0 0.000 1.000
#> GSM905009 3 0.000 0.998 0.0 0.000 1.000
#> GSM905014 3 0.000 0.998 0.0 0.000 1.000
#> GSM905017 2 0.000 1.000 0.0 1.000 0.000
#> GSM905020 3 0.000 0.998 0.0 0.000 1.000
#> GSM905023 3 0.000 0.998 0.0 0.000 1.000
#> GSM905029 3 0.000 0.998 0.0 0.000 1.000
#> GSM905032 3 0.196 0.941 0.0 0.056 0.944
#> GSM905034 3 0.000 0.998 0.0 0.000 1.000
#> GSM905040 3 0.000 0.998 0.0 0.000 1.000
#> GSM904985 2 0.000 1.000 0.0 1.000 0.000
#> GSM904988 2 0.000 1.000 0.0 1.000 0.000
#> GSM904990 2 0.000 1.000 0.0 1.000 0.000
#> GSM904992 2 0.000 1.000 0.0 1.000 0.000
#> GSM904995 2 0.000 1.000 0.0 1.000 0.000
#> GSM904998 2 0.000 1.000 0.0 1.000 0.000
#> GSM905000 2 0.000 1.000 0.0 1.000 0.000
#> GSM905003 2 0.000 1.000 0.0 1.000 0.000
#> GSM905006 2 0.000 1.000 0.0 1.000 0.000
#> GSM905008 2 0.000 1.000 0.0 1.000 0.000
#> GSM905011 2 0.000 1.000 0.0 1.000 0.000
#> GSM905013 2 0.000 1.000 0.0 1.000 0.000
#> GSM905016 2 0.000 1.000 0.0 1.000 0.000
#> GSM905018 2 0.000 1.000 0.0 1.000 0.000
#> GSM905021 2 0.000 1.000 0.0 1.000 0.000
#> GSM905025 2 0.000 1.000 0.0 1.000 0.000
#> GSM905028 2 0.000 1.000 0.0 1.000 0.000
#> GSM905030 2 0.000 1.000 0.0 1.000 0.000
#> GSM905033 2 0.000 1.000 0.0 1.000 0.000
#> GSM905035 2 0.000 1.000 0.0 1.000 0.000
#> GSM905037 2 0.000 1.000 0.0 1.000 0.000
#> GSM905039 2 0.000 1.000 0.0 1.000 0.000
#> GSM905042 2 0.000 1.000 0.0 1.000 0.000
#> GSM905046 1 0.000 0.983 1.0 0.000 0.000
#> GSM905065 1 0.000 0.983 1.0 0.000 0.000
#> GSM905049 1 0.000 0.983 1.0 0.000 0.000
#> GSM905050 1 0.000 0.983 1.0 0.000 0.000
#> GSM905064 1 0.000 0.983 1.0 0.000 0.000
#> GSM905045 1 0.000 0.983 1.0 0.000 0.000
#> GSM905051 1 0.000 0.983 1.0 0.000 0.000
#> GSM905055 1 0.000 0.983 1.0 0.000 0.000
#> GSM905058 1 0.000 0.983 1.0 0.000 0.000
#> GSM905053 1 0.000 0.983 1.0 0.000 0.000
#> GSM905061 1 0.000 0.983 1.0 0.000 0.000
#> GSM905063 1 0.000 0.983 1.0 0.000 0.000
#> GSM905054 1 0.000 0.983 1.0 0.000 0.000
#> GSM905062 1 0.000 0.983 1.0 0.000 0.000
#> GSM905052 1 0.000 0.983 1.0 0.000 0.000
#> GSM905059 1 0.000 0.983 1.0 0.000 0.000
#> GSM905047 1 0.000 0.983 1.0 0.000 0.000
#> GSM905066 1 0.000 0.983 1.0 0.000 0.000
#> GSM905056 1 0.000 0.983 1.0 0.000 0.000
#> GSM905060 1 0.000 0.983 1.0 0.000 0.000
#> GSM905048 1 0.000 0.983 1.0 0.000 0.000
#> GSM905067 1 0.000 0.983 1.0 0.000 0.000
#> GSM905057 1 0.000 0.983 1.0 0.000 0.000
#> GSM905068 1 0.000 0.983 1.0 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM905004 4 0.5393 0.430 0.044 0.000 0.268 0.688
#> GSM905024 3 0.4222 0.642 0.272 0.000 0.728 0.000
#> GSM905038 3 0.0000 0.957 0.000 0.000 1.000 0.000
#> GSM905043 3 0.4522 0.558 0.320 0.000 0.680 0.000
#> GSM904986 3 0.0000 0.957 0.000 0.000 1.000 0.000
#> GSM904991 3 0.0000 0.957 0.000 0.000 1.000 0.000
#> GSM904994 3 0.0000 0.957 0.000 0.000 1.000 0.000
#> GSM904996 3 0.0000 0.957 0.000 0.000 1.000 0.000
#> GSM905007 3 0.0000 0.957 0.000 0.000 1.000 0.000
#> GSM905012 3 0.0000 0.957 0.000 0.000 1.000 0.000
#> GSM905022 3 0.0000 0.957 0.000 0.000 1.000 0.000
#> GSM905026 3 0.0000 0.957 0.000 0.000 1.000 0.000
#> GSM905027 3 0.0000 0.957 0.000 0.000 1.000 0.000
#> GSM905031 3 0.0000 0.957 0.000 0.000 1.000 0.000
#> GSM905036 3 0.0000 0.957 0.000 0.000 1.000 0.000
#> GSM905041 3 0.0592 0.942 0.016 0.000 0.984 0.000
#> GSM905044 3 0.0000 0.957 0.000 0.000 1.000 0.000
#> GSM904989 3 0.0000 0.957 0.000 0.000 1.000 0.000
#> GSM904999 1 0.4818 0.668 0.748 0.216 0.036 0.000
#> GSM905002 3 0.0000 0.957 0.000 0.000 1.000 0.000
#> GSM905009 3 0.0000 0.957 0.000 0.000 1.000 0.000
#> GSM905014 3 0.0000 0.957 0.000 0.000 1.000 0.000
#> GSM905017 1 0.5247 0.579 0.684 0.284 0.032 0.000
#> GSM905020 3 0.0000 0.957 0.000 0.000 1.000 0.000
#> GSM905023 3 0.0592 0.942 0.016 0.000 0.984 0.000
#> GSM905029 3 0.0000 0.957 0.000 0.000 1.000 0.000
#> GSM905032 1 0.4525 0.691 0.804 0.000 0.116 0.080
#> GSM905034 3 0.4331 0.619 0.288 0.000 0.712 0.000
#> GSM905040 1 0.3801 0.592 0.780 0.000 0.220 0.000
#> GSM904985 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM904988 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM904990 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM904992 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM904995 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM904998 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM905000 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM905003 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM905006 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM905008 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM905011 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM905013 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM905016 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM905018 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM905021 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM905025 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM905028 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM905030 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM905033 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM905035 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM905037 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM905039 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM905042 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM905046 4 0.3172 0.863 0.160 0.000 0.000 0.840
#> GSM905065 4 0.3266 0.859 0.168 0.000 0.000 0.832
#> GSM905049 4 0.0817 0.859 0.024 0.000 0.000 0.976
#> GSM905050 4 0.0817 0.859 0.024 0.000 0.000 0.976
#> GSM905064 4 0.0707 0.870 0.020 0.000 0.000 0.980
#> GSM905045 4 0.1302 0.865 0.044 0.000 0.000 0.956
#> GSM905051 4 0.1940 0.874 0.076 0.000 0.000 0.924
#> GSM905055 1 0.3266 0.684 0.832 0.000 0.000 0.168
#> GSM905058 4 0.3266 0.859 0.168 0.000 0.000 0.832
#> GSM905053 4 0.0817 0.859 0.024 0.000 0.000 0.976
#> GSM905061 4 0.0817 0.859 0.024 0.000 0.000 0.976
#> GSM905063 4 0.4661 0.616 0.348 0.000 0.000 0.652
#> GSM905054 4 0.0000 0.866 0.000 0.000 0.000 1.000
#> GSM905062 4 0.0817 0.859 0.024 0.000 0.000 0.976
#> GSM905052 4 0.1940 0.874 0.076 0.000 0.000 0.924
#> GSM905059 4 0.2973 0.868 0.144 0.000 0.000 0.856
#> GSM905047 4 0.2973 0.868 0.144 0.000 0.000 0.856
#> GSM905066 4 0.3266 0.859 0.168 0.000 0.000 0.832
#> GSM905056 1 0.3266 0.684 0.832 0.000 0.000 0.168
#> GSM905060 4 0.2973 0.868 0.144 0.000 0.000 0.856
#> GSM905048 4 0.3266 0.859 0.168 0.000 0.000 0.832
#> GSM905067 4 0.3266 0.859 0.168 0.000 0.000 0.832
#> GSM905057 1 0.3266 0.684 0.832 0.000 0.000 0.168
#> GSM905068 4 0.0817 0.859 0.024 0.000 0.000 0.976
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM905004 4 0.4618 0.649 0.068 0 0.208 0.724 0.000
#> GSM905024 5 0.0000 0.994 0.000 0 0.000 0.000 1.000
#> GSM905038 3 0.0000 1.000 0.000 0 1.000 0.000 0.000
#> GSM905043 5 0.0000 0.994 0.000 0 0.000 0.000 1.000
#> GSM904986 3 0.0000 1.000 0.000 0 1.000 0.000 0.000
#> GSM904991 3 0.0000 1.000 0.000 0 1.000 0.000 0.000
#> GSM904994 3 0.0000 1.000 0.000 0 1.000 0.000 0.000
#> GSM904996 3 0.0000 1.000 0.000 0 1.000 0.000 0.000
#> GSM905007 3 0.0000 1.000 0.000 0 1.000 0.000 0.000
#> GSM905012 3 0.0000 1.000 0.000 0 1.000 0.000 0.000
#> GSM905022 3 0.0000 1.000 0.000 0 1.000 0.000 0.000
#> GSM905026 3 0.0000 1.000 0.000 0 1.000 0.000 0.000
#> GSM905027 3 0.0000 1.000 0.000 0 1.000 0.000 0.000
#> GSM905031 3 0.0000 1.000 0.000 0 1.000 0.000 0.000
#> GSM905036 3 0.0000 1.000 0.000 0 1.000 0.000 0.000
#> GSM905041 3 0.0162 0.996 0.000 0 0.996 0.000 0.004
#> GSM905044 3 0.0000 1.000 0.000 0 1.000 0.000 0.000
#> GSM904989 3 0.0000 1.000 0.000 0 1.000 0.000 0.000
#> GSM904999 5 0.0404 0.984 0.000 0 0.012 0.000 0.988
#> GSM905002 3 0.0000 1.000 0.000 0 1.000 0.000 0.000
#> GSM905009 3 0.0000 1.000 0.000 0 1.000 0.000 0.000
#> GSM905014 3 0.0000 1.000 0.000 0 1.000 0.000 0.000
#> GSM905017 5 0.0404 0.984 0.000 0 0.012 0.000 0.988
#> GSM905020 3 0.0000 1.000 0.000 0 1.000 0.000 0.000
#> GSM905023 3 0.0000 1.000 0.000 0 1.000 0.000 0.000
#> GSM905029 3 0.0000 1.000 0.000 0 1.000 0.000 0.000
#> GSM905032 5 0.0000 0.994 0.000 0 0.000 0.000 1.000
#> GSM905034 5 0.0000 0.994 0.000 0 0.000 0.000 1.000
#> GSM905040 5 0.0000 0.994 0.000 0 0.000 0.000 1.000
#> GSM904985 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM904988 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM904990 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM904992 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM904995 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM904998 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM905000 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM905003 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM905006 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM905008 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM905011 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM905013 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM905016 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM905018 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM905021 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM905025 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM905028 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM905030 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM905033 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM905035 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM905037 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM905039 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM905042 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM905046 1 0.0162 0.764 0.996 0 0.000 0.004 0.000
#> GSM905065 1 0.0000 0.764 1.000 0 0.000 0.000 0.000
#> GSM905049 4 0.0000 0.946 0.000 0 0.000 1.000 0.000
#> GSM905050 4 0.0000 0.946 0.000 0 0.000 1.000 0.000
#> GSM905064 4 0.1608 0.896 0.072 0 0.000 0.928 0.000
#> GSM905045 4 0.1544 0.900 0.068 0 0.000 0.932 0.000
#> GSM905051 1 0.4126 0.350 0.620 0 0.000 0.380 0.000
#> GSM905055 1 0.4273 0.284 0.552 0 0.000 0.000 0.448
#> GSM905058 1 0.0000 0.764 1.000 0 0.000 0.000 0.000
#> GSM905053 4 0.0000 0.946 0.000 0 0.000 1.000 0.000
#> GSM905061 4 0.0000 0.946 0.000 0 0.000 1.000 0.000
#> GSM905063 1 0.4262 0.298 0.560 0 0.000 0.000 0.440
#> GSM905054 4 0.0000 0.946 0.000 0 0.000 1.000 0.000
#> GSM905062 4 0.0000 0.946 0.000 0 0.000 1.000 0.000
#> GSM905052 1 0.4126 0.350 0.620 0 0.000 0.380 0.000
#> GSM905059 1 0.2020 0.732 0.900 0 0.000 0.100 0.000
#> GSM905047 1 0.2127 0.726 0.892 0 0.000 0.108 0.000
#> GSM905066 1 0.0000 0.764 1.000 0 0.000 0.000 0.000
#> GSM905056 1 0.4273 0.284 0.552 0 0.000 0.000 0.448
#> GSM905060 1 0.2020 0.732 0.900 0 0.000 0.100 0.000
#> GSM905048 1 0.0000 0.764 1.000 0 0.000 0.000 0.000
#> GSM905067 1 0.0000 0.764 1.000 0 0.000 0.000 0.000
#> GSM905057 1 0.4273 0.284 0.552 0 0.000 0.000 0.448
#> GSM905068 4 0.0000 0.946 0.000 0 0.000 1.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM905004 4 0.8134 0.187 0.112 0.000 0.124 0.432 0.136 0.196
#> GSM905024 5 0.3592 0.986 0.000 0.000 0.000 0.000 0.656 0.344
#> GSM905038 3 0.0547 0.964 0.000 0.000 0.980 0.000 0.020 0.000
#> GSM905043 5 0.3592 0.986 0.000 0.000 0.000 0.000 0.656 0.344
#> GSM904986 3 0.0000 0.968 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM904991 3 0.2300 0.856 0.000 0.000 0.856 0.000 0.144 0.000
#> GSM904994 3 0.0000 0.968 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM904996 3 0.0000 0.968 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905007 3 0.1075 0.948 0.000 0.000 0.952 0.000 0.048 0.000
#> GSM905012 3 0.0000 0.968 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905022 3 0.0000 0.968 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905026 3 0.0000 0.968 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905027 3 0.0547 0.964 0.000 0.000 0.980 0.000 0.020 0.000
#> GSM905031 3 0.0000 0.968 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905036 3 0.0547 0.964 0.000 0.000 0.980 0.000 0.020 0.000
#> GSM905041 3 0.3189 0.732 0.000 0.000 0.760 0.000 0.236 0.004
#> GSM905044 3 0.0000 0.968 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM904989 3 0.0000 0.968 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM904999 5 0.3984 0.966 0.000 0.000 0.016 0.000 0.648 0.336
#> GSM905002 3 0.0363 0.964 0.000 0.000 0.988 0.000 0.012 0.000
#> GSM905009 3 0.0000 0.968 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905014 3 0.1075 0.948 0.000 0.000 0.952 0.000 0.048 0.000
#> GSM905017 5 0.3984 0.966 0.000 0.000 0.016 0.000 0.648 0.336
#> GSM905020 3 0.0000 0.968 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905023 3 0.1501 0.924 0.000 0.000 0.924 0.000 0.076 0.000
#> GSM905029 3 0.0547 0.964 0.000 0.000 0.980 0.000 0.020 0.000
#> GSM905032 5 0.3592 0.986 0.000 0.000 0.000 0.000 0.656 0.344
#> GSM905034 5 0.3592 0.986 0.000 0.000 0.000 0.000 0.656 0.344
#> GSM905040 5 0.3592 0.986 0.000 0.000 0.000 0.000 0.656 0.344
#> GSM904985 2 0.3254 0.841 0.048 0.816 0.000 0.000 0.136 0.000
#> GSM904988 2 0.0000 0.861 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM904990 2 0.0000 0.861 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM904992 2 0.0000 0.861 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM904995 2 0.3254 0.841 0.048 0.816 0.000 0.000 0.136 0.000
#> GSM904998 2 0.0000 0.861 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905000 2 0.0000 0.861 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905003 2 0.1267 0.858 0.000 0.940 0.000 0.000 0.060 0.000
#> GSM905006 2 0.0000 0.861 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905008 2 0.6302 0.593 0.048 0.488 0.000 0.000 0.332 0.132
#> GSM905011 2 0.0000 0.861 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905013 2 0.0000 0.861 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905016 2 0.3254 0.841 0.048 0.816 0.000 0.000 0.136 0.000
#> GSM905018 2 0.0000 0.861 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905021 2 0.6326 0.580 0.048 0.476 0.000 0.000 0.344 0.132
#> GSM905025 2 0.3254 0.841 0.048 0.816 0.000 0.000 0.136 0.000
#> GSM905028 2 0.3254 0.841 0.048 0.816 0.000 0.000 0.136 0.000
#> GSM905030 2 0.0000 0.861 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905033 2 0.6333 0.576 0.048 0.472 0.000 0.000 0.348 0.132
#> GSM905035 2 0.3254 0.841 0.048 0.816 0.000 0.000 0.136 0.000
#> GSM905037 2 0.0000 0.861 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905039 2 0.3254 0.841 0.048 0.816 0.000 0.000 0.136 0.000
#> GSM905042 2 0.6333 0.576 0.048 0.472 0.000 0.000 0.348 0.132
#> GSM905046 1 0.3360 0.720 0.732 0.000 0.000 0.004 0.000 0.264
#> GSM905065 1 0.3244 0.720 0.732 0.000 0.000 0.000 0.000 0.268
#> GSM905049 4 0.0000 0.910 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905050 4 0.0000 0.910 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905064 4 0.1141 0.878 0.052 0.000 0.000 0.948 0.000 0.000
#> GSM905045 4 0.3822 0.727 0.128 0.000 0.000 0.776 0.000 0.096
#> GSM905051 1 0.4314 0.481 0.712 0.000 0.000 0.220 0.004 0.064
#> GSM905055 6 0.2178 0.988 0.132 0.000 0.000 0.000 0.000 0.868
#> GSM905058 1 0.3244 0.720 0.732 0.000 0.000 0.000 0.000 0.268
#> GSM905053 4 0.0000 0.910 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905061 4 0.0000 0.910 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905063 6 0.2520 0.965 0.152 0.000 0.000 0.000 0.004 0.844
#> GSM905054 4 0.0000 0.910 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905062 4 0.0000 0.910 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905052 1 0.4314 0.481 0.712 0.000 0.000 0.220 0.004 0.064
#> GSM905059 1 0.1075 0.693 0.952 0.000 0.000 0.048 0.000 0.000
#> GSM905047 1 0.1075 0.693 0.952 0.000 0.000 0.048 0.000 0.000
#> GSM905066 1 0.3244 0.720 0.732 0.000 0.000 0.000 0.000 0.268
#> GSM905056 6 0.2178 0.988 0.132 0.000 0.000 0.000 0.000 0.868
#> GSM905060 1 0.1075 0.693 0.952 0.000 0.000 0.048 0.000 0.000
#> GSM905048 1 0.3244 0.720 0.732 0.000 0.000 0.000 0.000 0.268
#> GSM905067 1 0.3244 0.720 0.732 0.000 0.000 0.000 0.000 0.268
#> GSM905057 6 0.2178 0.988 0.132 0.000 0.000 0.000 0.000 0.868
#> GSM905068 4 0.0000 0.910 0.000 0.000 0.000 1.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) genotype/variation(p) individual(p) k
#> CV:mclust 76 3.04e-12 1.17e-05 0.990 2
#> CV:mclust 75 7.59e-20 1.17e-05 0.957 3
#> CV:mclust 75 7.56e-19 1.95e-06 0.337 4
#> CV:mclust 70 2.94e-20 4.72e-11 0.674 5
#> CV:mclust 73 2.08e-21 4.96e-12 0.310 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 76 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 5.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.728 0.849 0.928 0.4798 0.495 0.495
#> 3 3 1.000 0.991 0.996 0.4051 0.704 0.469
#> 4 4 1.000 0.949 0.979 0.1036 0.890 0.681
#> 5 5 0.956 0.908 0.950 0.0434 0.921 0.716
#> 6 6 0.894 0.811 0.887 0.0307 0.981 0.918
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] 3 4
There is also optional best \(k\) = 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
#> GSM905004 1 0.5629 0.800 0.868 0.132
#> GSM905024 1 0.0000 0.981 1.000 0.000
#> GSM905038 1 0.0672 0.973 0.992 0.008
#> GSM905043 1 0.0000 0.981 1.000 0.000
#> GSM904986 2 0.9323 0.599 0.348 0.652
#> GSM904991 1 0.0000 0.981 1.000 0.000
#> GSM904994 2 0.9635 0.540 0.388 0.612
#> GSM904996 2 0.9580 0.553 0.380 0.620
#> GSM905007 1 0.0000 0.981 1.000 0.000
#> GSM905012 2 0.9427 0.583 0.360 0.640
#> GSM905022 2 0.9977 0.350 0.472 0.528
#> GSM905026 2 0.9963 0.373 0.464 0.536
#> GSM905027 1 0.0672 0.973 0.992 0.008
#> GSM905031 2 0.9427 0.583 0.360 0.640
#> GSM905036 1 0.0000 0.981 1.000 0.000
#> GSM905041 1 0.0000 0.981 1.000 0.000
#> GSM905044 2 0.9795 0.487 0.416 0.584
#> GSM904989 1 0.9933 -0.132 0.548 0.452
#> GSM904999 2 0.9248 0.609 0.340 0.660
#> GSM905002 2 0.9850 0.461 0.428 0.572
#> GSM905009 2 0.9754 0.503 0.408 0.592
#> GSM905014 1 0.0000 0.981 1.000 0.000
#> GSM905017 2 0.7528 0.725 0.216 0.784
#> GSM905020 2 0.8144 0.696 0.252 0.748
#> GSM905023 1 0.0672 0.973 0.992 0.008
#> GSM905029 1 0.0000 0.981 1.000 0.000
#> GSM905032 1 0.0000 0.981 1.000 0.000
#> GSM905034 1 0.0000 0.981 1.000 0.000
#> GSM905040 1 0.0000 0.981 1.000 0.000
#> GSM904985 2 0.0000 0.850 0.000 1.000
#> GSM904988 2 0.0000 0.850 0.000 1.000
#> GSM904990 2 0.0000 0.850 0.000 1.000
#> GSM904992 2 0.0000 0.850 0.000 1.000
#> GSM904995 2 0.0000 0.850 0.000 1.000
#> GSM904998 2 0.0000 0.850 0.000 1.000
#> GSM905000 2 0.0000 0.850 0.000 1.000
#> GSM905003 2 0.0000 0.850 0.000 1.000
#> GSM905006 2 0.0000 0.850 0.000 1.000
#> GSM905008 2 0.0000 0.850 0.000 1.000
#> GSM905011 2 0.0000 0.850 0.000 1.000
#> GSM905013 2 0.0000 0.850 0.000 1.000
#> GSM905016 2 0.0000 0.850 0.000 1.000
#> GSM905018 2 0.0000 0.850 0.000 1.000
#> GSM905021 2 0.0000 0.850 0.000 1.000
#> GSM905025 2 0.0000 0.850 0.000 1.000
#> GSM905028 2 0.0000 0.850 0.000 1.000
#> GSM905030 2 0.0000 0.850 0.000 1.000
#> GSM905033 2 0.0000 0.850 0.000 1.000
#> GSM905035 2 0.0000 0.850 0.000 1.000
#> GSM905037 2 0.0000 0.850 0.000 1.000
#> GSM905039 2 0.0000 0.850 0.000 1.000
#> GSM905042 2 0.0000 0.850 0.000 1.000
#> GSM905046 1 0.0000 0.981 1.000 0.000
#> GSM905065 1 0.0000 0.981 1.000 0.000
#> GSM905049 1 0.0000 0.981 1.000 0.000
#> GSM905050 1 0.0000 0.981 1.000 0.000
#> GSM905064 1 0.0000 0.981 1.000 0.000
#> GSM905045 1 0.0000 0.981 1.000 0.000
#> GSM905051 1 0.0000 0.981 1.000 0.000
#> GSM905055 1 0.0000 0.981 1.000 0.000
#> GSM905058 1 0.0000 0.981 1.000 0.000
#> GSM905053 1 0.0000 0.981 1.000 0.000
#> GSM905061 1 0.0000 0.981 1.000 0.000
#> GSM905063 1 0.0000 0.981 1.000 0.000
#> GSM905054 1 0.0000 0.981 1.000 0.000
#> GSM905062 1 0.0000 0.981 1.000 0.000
#> GSM905052 1 0.0000 0.981 1.000 0.000
#> GSM905059 1 0.0000 0.981 1.000 0.000
#> GSM905047 1 0.0000 0.981 1.000 0.000
#> GSM905066 1 0.0000 0.981 1.000 0.000
#> GSM905056 1 0.0000 0.981 1.000 0.000
#> GSM905060 1 0.0000 0.981 1.000 0.000
#> GSM905048 1 0.0000 0.981 1.000 0.000
#> GSM905067 1 0.0000 0.981 1.000 0.000
#> GSM905057 1 0.0000 0.981 1.000 0.000
#> GSM905068 1 0.0000 0.981 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM905004 3 0.000 0.993 0.000 0 1.000
#> GSM905024 3 0.296 0.891 0.100 0 0.900
#> GSM905038 3 0.000 0.993 0.000 0 1.000
#> GSM905043 3 0.236 0.923 0.072 0 0.928
#> GSM904986 3 0.000 0.993 0.000 0 1.000
#> GSM904991 3 0.000 0.993 0.000 0 1.000
#> GSM904994 3 0.000 0.993 0.000 0 1.000
#> GSM904996 3 0.000 0.993 0.000 0 1.000
#> GSM905007 3 0.000 0.993 0.000 0 1.000
#> GSM905012 3 0.000 0.993 0.000 0 1.000
#> GSM905022 3 0.000 0.993 0.000 0 1.000
#> GSM905026 3 0.000 0.993 0.000 0 1.000
#> GSM905027 3 0.000 0.993 0.000 0 1.000
#> GSM905031 3 0.000 0.993 0.000 0 1.000
#> GSM905036 3 0.000 0.993 0.000 0 1.000
#> GSM905041 3 0.000 0.993 0.000 0 1.000
#> GSM905044 3 0.000 0.993 0.000 0 1.000
#> GSM904989 3 0.000 0.993 0.000 0 1.000
#> GSM904999 3 0.000 0.993 0.000 0 1.000
#> GSM905002 3 0.000 0.993 0.000 0 1.000
#> GSM905009 3 0.000 0.993 0.000 0 1.000
#> GSM905014 3 0.000 0.993 0.000 0 1.000
#> GSM905017 3 0.000 0.993 0.000 0 1.000
#> GSM905020 3 0.000 0.993 0.000 0 1.000
#> GSM905023 3 0.000 0.993 0.000 0 1.000
#> GSM905029 3 0.000 0.993 0.000 0 1.000
#> GSM905032 3 0.000 0.993 0.000 0 1.000
#> GSM905034 1 0.236 0.924 0.928 0 0.072
#> GSM905040 1 0.280 0.901 0.908 0 0.092
#> GSM904985 2 0.000 1.000 0.000 1 0.000
#> GSM904988 2 0.000 1.000 0.000 1 0.000
#> GSM904990 2 0.000 1.000 0.000 1 0.000
#> GSM904992 2 0.000 1.000 0.000 1 0.000
#> GSM904995 2 0.000 1.000 0.000 1 0.000
#> GSM904998 2 0.000 1.000 0.000 1 0.000
#> GSM905000 2 0.000 1.000 0.000 1 0.000
#> GSM905003 2 0.000 1.000 0.000 1 0.000
#> GSM905006 2 0.000 1.000 0.000 1 0.000
#> GSM905008 2 0.000 1.000 0.000 1 0.000
#> GSM905011 2 0.000 1.000 0.000 1 0.000
#> GSM905013 2 0.000 1.000 0.000 1 0.000
#> GSM905016 2 0.000 1.000 0.000 1 0.000
#> GSM905018 2 0.000 1.000 0.000 1 0.000
#> GSM905021 2 0.000 1.000 0.000 1 0.000
#> GSM905025 2 0.000 1.000 0.000 1 0.000
#> GSM905028 2 0.000 1.000 0.000 1 0.000
#> GSM905030 2 0.000 1.000 0.000 1 0.000
#> GSM905033 2 0.000 1.000 0.000 1 0.000
#> GSM905035 2 0.000 1.000 0.000 1 0.000
#> GSM905037 2 0.000 1.000 0.000 1 0.000
#> GSM905039 2 0.000 1.000 0.000 1 0.000
#> GSM905042 2 0.000 1.000 0.000 1 0.000
#> GSM905046 1 0.000 0.993 1.000 0 0.000
#> GSM905065 1 0.000 0.993 1.000 0 0.000
#> GSM905049 1 0.000 0.993 1.000 0 0.000
#> GSM905050 1 0.000 0.993 1.000 0 0.000
#> GSM905064 1 0.000 0.993 1.000 0 0.000
#> GSM905045 1 0.000 0.993 1.000 0 0.000
#> GSM905051 1 0.000 0.993 1.000 0 0.000
#> GSM905055 1 0.000 0.993 1.000 0 0.000
#> GSM905058 1 0.000 0.993 1.000 0 0.000
#> GSM905053 1 0.000 0.993 1.000 0 0.000
#> GSM905061 1 0.000 0.993 1.000 0 0.000
#> GSM905063 1 0.000 0.993 1.000 0 0.000
#> GSM905054 1 0.000 0.993 1.000 0 0.000
#> GSM905062 1 0.000 0.993 1.000 0 0.000
#> GSM905052 1 0.000 0.993 1.000 0 0.000
#> GSM905059 1 0.000 0.993 1.000 0 0.000
#> GSM905047 1 0.000 0.993 1.000 0 0.000
#> GSM905066 1 0.000 0.993 1.000 0 0.000
#> GSM905056 1 0.000 0.993 1.000 0 0.000
#> GSM905060 1 0.000 0.993 1.000 0 0.000
#> GSM905048 1 0.000 0.993 1.000 0 0.000
#> GSM905067 1 0.000 0.993 1.000 0 0.000
#> GSM905057 1 0.000 0.993 1.000 0 0.000
#> GSM905068 1 0.000 0.993 1.000 0 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM905004 4 0.0000 0.945 0.000 0 0.000 1.000
#> GSM905024 1 0.4977 0.204 0.540 0 0.460 0.000
#> GSM905038 3 0.0000 0.995 0.000 0 1.000 0.000
#> GSM905043 1 0.4564 0.535 0.672 0 0.328 0.000
#> GSM904986 3 0.0000 0.995 0.000 0 1.000 0.000
#> GSM904991 3 0.0000 0.995 0.000 0 1.000 0.000
#> GSM904994 3 0.0000 0.995 0.000 0 1.000 0.000
#> GSM904996 3 0.0000 0.995 0.000 0 1.000 0.000
#> GSM905007 3 0.0000 0.995 0.000 0 1.000 0.000
#> GSM905012 4 0.4477 0.541 0.000 0 0.312 0.688
#> GSM905022 3 0.0000 0.995 0.000 0 1.000 0.000
#> GSM905026 3 0.0000 0.995 0.000 0 1.000 0.000
#> GSM905027 3 0.0000 0.995 0.000 0 1.000 0.000
#> GSM905031 3 0.0469 0.985 0.000 0 0.988 0.012
#> GSM905036 3 0.0000 0.995 0.000 0 1.000 0.000
#> GSM905041 3 0.0000 0.995 0.000 0 1.000 0.000
#> GSM905044 3 0.0000 0.995 0.000 0 1.000 0.000
#> GSM904989 3 0.0188 0.992 0.000 0 0.996 0.004
#> GSM904999 3 0.0000 0.995 0.000 0 1.000 0.000
#> GSM905002 3 0.0000 0.995 0.000 0 1.000 0.000
#> GSM905009 3 0.0188 0.992 0.000 0 0.996 0.004
#> GSM905014 3 0.0000 0.995 0.000 0 1.000 0.000
#> GSM905017 3 0.0000 0.995 0.000 0 1.000 0.000
#> GSM905020 3 0.2149 0.900 0.000 0 0.912 0.088
#> GSM905023 3 0.0000 0.995 0.000 0 1.000 0.000
#> GSM905029 3 0.0000 0.995 0.000 0 1.000 0.000
#> GSM905032 3 0.0000 0.995 0.000 0 1.000 0.000
#> GSM905034 1 0.0921 0.914 0.972 0 0.028 0.000
#> GSM905040 1 0.0817 0.918 0.976 0 0.024 0.000
#> GSM904985 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM904988 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM904990 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM904992 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM904995 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM904998 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905000 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905003 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905006 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905008 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905011 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905013 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905016 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905018 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905021 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905025 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905028 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905030 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905033 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905035 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905037 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905039 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905042 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905046 1 0.0000 0.935 1.000 0 0.000 0.000
#> GSM905065 1 0.0000 0.935 1.000 0 0.000 0.000
#> GSM905049 4 0.0000 0.945 0.000 0 0.000 1.000
#> GSM905050 4 0.0000 0.945 0.000 0 0.000 1.000
#> GSM905064 4 0.0188 0.943 0.004 0 0.000 0.996
#> GSM905045 4 0.0000 0.945 0.000 0 0.000 1.000
#> GSM905051 4 0.3801 0.718 0.220 0 0.000 0.780
#> GSM905055 1 0.0000 0.935 1.000 0 0.000 0.000
#> GSM905058 1 0.0000 0.935 1.000 0 0.000 0.000
#> GSM905053 4 0.0000 0.945 0.000 0 0.000 1.000
#> GSM905061 4 0.0000 0.945 0.000 0 0.000 1.000
#> GSM905063 1 0.0000 0.935 1.000 0 0.000 0.000
#> GSM905054 4 0.0000 0.945 0.000 0 0.000 1.000
#> GSM905062 4 0.0000 0.945 0.000 0 0.000 1.000
#> GSM905052 4 0.1940 0.888 0.076 0 0.000 0.924
#> GSM905059 1 0.0000 0.935 1.000 0 0.000 0.000
#> GSM905047 1 0.0188 0.932 0.996 0 0.000 0.004
#> GSM905066 1 0.0000 0.935 1.000 0 0.000 0.000
#> GSM905056 1 0.0000 0.935 1.000 0 0.000 0.000
#> GSM905060 1 0.0000 0.935 1.000 0 0.000 0.000
#> GSM905048 1 0.0000 0.935 1.000 0 0.000 0.000
#> GSM905067 1 0.0000 0.935 1.000 0 0.000 0.000
#> GSM905057 1 0.0000 0.935 1.000 0 0.000 0.000
#> GSM905068 4 0.0000 0.945 0.000 0 0.000 1.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM905004 4 0.0912 0.890 0.000 0.000 0.012 0.972 0.016
#> GSM905024 1 0.4517 0.369 0.600 0.000 0.388 0.000 0.012
#> GSM905038 3 0.0404 0.941 0.000 0.000 0.988 0.000 0.012
#> GSM905043 3 0.5010 0.214 0.392 0.000 0.572 0.000 0.036
#> GSM904986 3 0.1485 0.929 0.000 0.000 0.948 0.020 0.032
#> GSM904991 3 0.0404 0.939 0.000 0.000 0.988 0.000 0.012
#> GSM904994 3 0.1579 0.926 0.000 0.000 0.944 0.024 0.032
#> GSM904996 3 0.1386 0.930 0.000 0.000 0.952 0.016 0.032
#> GSM905007 3 0.0771 0.941 0.000 0.000 0.976 0.004 0.020
#> GSM905012 4 0.1547 0.873 0.004 0.000 0.016 0.948 0.032
#> GSM905022 3 0.1168 0.934 0.000 0.000 0.960 0.008 0.032
#> GSM905026 3 0.0771 0.938 0.000 0.000 0.976 0.004 0.020
#> GSM905027 3 0.0162 0.941 0.000 0.000 0.996 0.000 0.004
#> GSM905031 4 0.4350 0.602 0.000 0.000 0.268 0.704 0.028
#> GSM905036 3 0.0404 0.939 0.000 0.000 0.988 0.000 0.012
#> GSM905041 3 0.0404 0.939 0.000 0.000 0.988 0.000 0.012
#> GSM905044 3 0.0992 0.936 0.000 0.000 0.968 0.008 0.024
#> GSM904989 3 0.1915 0.914 0.000 0.000 0.928 0.040 0.032
#> GSM904999 3 0.0290 0.940 0.000 0.000 0.992 0.000 0.008
#> GSM905002 3 0.1168 0.934 0.000 0.000 0.960 0.008 0.032
#> GSM905009 3 0.4099 0.709 0.004 0.000 0.764 0.200 0.032
#> GSM905014 3 0.0404 0.939 0.000 0.000 0.988 0.000 0.012
#> GSM905017 3 0.0290 0.940 0.000 0.000 0.992 0.000 0.008
#> GSM905020 4 0.4812 0.518 0.004 0.000 0.312 0.652 0.032
#> GSM905023 3 0.0404 0.939 0.000 0.000 0.988 0.000 0.012
#> GSM905029 3 0.0162 0.941 0.000 0.000 0.996 0.000 0.004
#> GSM905032 5 0.2561 0.797 0.000 0.000 0.144 0.000 0.856
#> GSM905034 1 0.1670 0.864 0.936 0.000 0.052 0.000 0.012
#> GSM905040 5 0.1952 0.951 0.084 0.000 0.004 0.000 0.912
#> GSM904985 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM904988 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM904990 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM904992 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM904995 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM904998 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM905000 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM905003 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM905006 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM905008 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM905011 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM905013 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM905016 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM905018 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM905021 2 0.0162 0.996 0.000 0.996 0.000 0.000 0.004
#> GSM905025 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM905028 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM905030 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM905033 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM905035 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM905037 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM905039 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM905042 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM905046 1 0.0451 0.892 0.988 0.000 0.000 0.008 0.004
#> GSM905065 1 0.1544 0.864 0.932 0.000 0.000 0.000 0.068
#> GSM905049 4 0.0703 0.905 0.024 0.000 0.000 0.976 0.000
#> GSM905050 4 0.0510 0.906 0.016 0.000 0.000 0.984 0.000
#> GSM905064 4 0.2020 0.842 0.100 0.000 0.000 0.900 0.000
#> GSM905045 4 0.0880 0.901 0.032 0.000 0.000 0.968 0.000
#> GSM905051 1 0.2504 0.852 0.896 0.000 0.000 0.064 0.040
#> GSM905055 5 0.1851 0.955 0.088 0.000 0.000 0.000 0.912
#> GSM905058 1 0.0162 0.892 0.996 0.000 0.000 0.004 0.000
#> GSM905053 4 0.0510 0.906 0.016 0.000 0.000 0.984 0.000
#> GSM905061 4 0.0404 0.906 0.012 0.000 0.000 0.988 0.000
#> GSM905063 5 0.1908 0.953 0.092 0.000 0.000 0.000 0.908
#> GSM905054 4 0.0880 0.901 0.032 0.000 0.000 0.968 0.000
#> GSM905062 4 0.0290 0.905 0.008 0.000 0.000 0.992 0.000
#> GSM905052 1 0.3432 0.787 0.828 0.000 0.000 0.132 0.040
#> GSM905059 1 0.0794 0.891 0.972 0.000 0.000 0.028 0.000
#> GSM905047 1 0.1121 0.884 0.956 0.000 0.000 0.044 0.000
#> GSM905066 1 0.1732 0.855 0.920 0.000 0.000 0.000 0.080
#> GSM905056 5 0.1851 0.955 0.088 0.000 0.000 0.000 0.912
#> GSM905060 1 0.0880 0.890 0.968 0.000 0.000 0.032 0.000
#> GSM905048 1 0.0404 0.889 0.988 0.000 0.000 0.000 0.012
#> GSM905067 1 0.1544 0.864 0.932 0.000 0.000 0.000 0.068
#> GSM905057 5 0.1851 0.955 0.088 0.000 0.000 0.000 0.912
#> GSM905068 4 0.0404 0.906 0.012 0.000 0.000 0.988 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM905004 4 0.3858 0.5916 0.000 0.000 0.216 0.740 0.044 0.000
#> GSM905024 1 0.5254 0.4044 0.608 0.000 0.196 0.000 0.196 0.000
#> GSM905038 3 0.2491 0.8116 0.000 0.000 0.836 0.000 0.164 0.000
#> GSM905043 1 0.6047 0.0234 0.448 0.000 0.320 0.000 0.228 0.004
#> GSM904986 3 0.1967 0.7596 0.000 0.000 0.904 0.012 0.084 0.000
#> GSM904991 3 0.3126 0.7927 0.000 0.000 0.752 0.000 0.248 0.000
#> GSM904994 3 0.1866 0.7621 0.000 0.000 0.908 0.008 0.084 0.000
#> GSM904996 3 0.1663 0.7649 0.000 0.000 0.912 0.000 0.088 0.000
#> GSM905007 3 0.1327 0.8099 0.000 0.000 0.936 0.000 0.064 0.000
#> GSM905012 4 0.4725 0.5144 0.000 0.000 0.264 0.648 0.088 0.000
#> GSM905022 3 0.1327 0.7753 0.000 0.000 0.936 0.000 0.064 0.000
#> GSM905026 3 0.1765 0.8105 0.000 0.000 0.904 0.000 0.096 0.000
#> GSM905027 3 0.3076 0.7970 0.000 0.000 0.760 0.000 0.240 0.000
#> GSM905031 4 0.3608 0.5691 0.000 0.000 0.272 0.716 0.012 0.000
#> GSM905036 3 0.3240 0.7959 0.000 0.000 0.752 0.004 0.244 0.000
#> GSM905041 3 0.3126 0.7927 0.000 0.000 0.752 0.000 0.248 0.000
#> GSM905044 3 0.0632 0.7979 0.000 0.000 0.976 0.000 0.024 0.000
#> GSM904989 3 0.3118 0.6889 0.000 0.000 0.836 0.092 0.072 0.000
#> GSM904999 3 0.3634 0.7335 0.000 0.000 0.644 0.000 0.356 0.000
#> GSM905002 3 0.1387 0.7736 0.000 0.000 0.932 0.000 0.068 0.000
#> GSM905009 3 0.5040 -0.1232 0.000 0.000 0.516 0.408 0.076 0.000
#> GSM905014 3 0.2527 0.8104 0.000 0.000 0.832 0.000 0.168 0.000
#> GSM905017 3 0.3563 0.7510 0.000 0.000 0.664 0.000 0.336 0.000
#> GSM905020 4 0.4932 0.4562 0.000 0.000 0.312 0.600 0.088 0.000
#> GSM905023 3 0.3151 0.7915 0.000 0.000 0.748 0.000 0.252 0.000
#> GSM905029 3 0.3023 0.7999 0.000 0.000 0.768 0.000 0.232 0.000
#> GSM905032 6 0.2778 0.7477 0.000 0.000 0.008 0.000 0.168 0.824
#> GSM905034 1 0.1556 0.8192 0.920 0.000 0.000 0.000 0.080 0.000
#> GSM905040 6 0.0291 0.9487 0.004 0.000 0.000 0.000 0.004 0.992
#> GSM904985 2 0.0146 0.9958 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM904988 2 0.0000 0.9968 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM904990 2 0.0000 0.9968 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM904992 2 0.0000 0.9968 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM904995 2 0.0146 0.9958 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM904998 2 0.0000 0.9968 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905000 2 0.0000 0.9968 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905003 2 0.0000 0.9968 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905006 2 0.0000 0.9968 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905008 2 0.0000 0.9968 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905011 2 0.0000 0.9968 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905013 2 0.0000 0.9968 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905016 2 0.0146 0.9958 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM905018 2 0.0000 0.9968 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905021 2 0.1007 0.9581 0.000 0.956 0.000 0.000 0.044 0.000
#> GSM905025 2 0.0146 0.9958 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM905028 2 0.0000 0.9968 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905030 2 0.0000 0.9968 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905033 2 0.0146 0.9958 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM905035 2 0.0146 0.9958 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM905037 2 0.0000 0.9968 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905039 2 0.0146 0.9958 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM905042 2 0.0146 0.9958 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM905046 1 0.0000 0.8371 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM905065 1 0.0632 0.8333 0.976 0.000 0.000 0.000 0.000 0.024
#> GSM905049 4 0.0790 0.7056 0.000 0.000 0.000 0.968 0.032 0.000
#> GSM905050 4 0.0146 0.7192 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM905064 4 0.3736 0.4544 0.068 0.000 0.000 0.776 0.156 0.000
#> GSM905045 4 0.2597 0.5501 0.000 0.000 0.000 0.824 0.176 0.000
#> GSM905051 5 0.4837 0.9567 0.088 0.000 0.000 0.288 0.624 0.000
#> GSM905055 6 0.0146 0.9511 0.004 0.000 0.000 0.000 0.000 0.996
#> GSM905058 1 0.1501 0.8198 0.924 0.000 0.000 0.000 0.076 0.000
#> GSM905053 4 0.0458 0.7151 0.000 0.000 0.000 0.984 0.016 0.000
#> GSM905061 4 0.0363 0.7189 0.000 0.000 0.000 0.988 0.012 0.000
#> GSM905063 6 0.0146 0.9511 0.004 0.000 0.000 0.000 0.000 0.996
#> GSM905054 4 0.2697 0.5258 0.000 0.000 0.000 0.812 0.188 0.000
#> GSM905062 4 0.0458 0.7182 0.000 0.000 0.000 0.984 0.016 0.000
#> GSM905052 5 0.4637 0.9558 0.064 0.000 0.000 0.308 0.628 0.000
#> GSM905059 1 0.1501 0.8198 0.924 0.000 0.000 0.000 0.076 0.000
#> GSM905047 1 0.0000 0.8371 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM905066 1 0.0790 0.8292 0.968 0.000 0.000 0.000 0.000 0.032
#> GSM905056 6 0.0146 0.9511 0.004 0.000 0.000 0.000 0.000 0.996
#> GSM905060 1 0.1501 0.8198 0.924 0.000 0.000 0.000 0.076 0.000
#> GSM905048 1 0.0146 0.8369 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM905067 1 0.0632 0.8333 0.976 0.000 0.000 0.000 0.000 0.024
#> GSM905057 6 0.0146 0.9511 0.004 0.000 0.000 0.000 0.000 0.996
#> GSM905068 4 0.0000 0.7196 0.000 0.000 0.000 1.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) genotype/variation(p) individual(p) k
#> CV:NMF 71 5.52e-07 3.65e-04 0.07133 2
#> CV:NMF 76 2.85e-20 4.94e-05 0.97745 3
#> CV:NMF 75 2.38e-19 2.57e-09 0.35834 4
#> CV:NMF 74 3.99e-16 2.12e-10 0.00344 5
#> CV:NMF 71 2.05e-15 6.30e-11 0.00141 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 76 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 5.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.534 0.771 0.900 0.4751 0.494 0.494
#> 3 3 0.663 0.658 0.837 0.3440 0.814 0.639
#> 4 4 0.702 0.762 0.845 0.0947 0.793 0.501
#> 5 5 0.848 0.778 0.891 0.0920 0.953 0.829
#> 6 6 0.846 0.683 0.838 0.0434 0.921 0.696
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM905004 2 0.871 0.646 0.292 0.708
#> GSM905024 1 0.456 0.789 0.904 0.096
#> GSM905038 1 0.999 0.102 0.516 0.484
#> GSM905043 1 0.456 0.789 0.904 0.096
#> GSM904986 2 0.634 0.840 0.160 0.840
#> GSM904991 1 0.994 0.202 0.544 0.456
#> GSM904994 2 0.634 0.840 0.160 0.840
#> GSM904996 2 0.634 0.840 0.160 0.840
#> GSM905007 1 0.994 0.202 0.544 0.456
#> GSM905012 2 0.634 0.840 0.160 0.840
#> GSM905022 2 0.714 0.798 0.196 0.804
#> GSM905026 2 0.634 0.840 0.160 0.840
#> GSM905027 2 0.714 0.798 0.196 0.804
#> GSM905031 2 0.634 0.840 0.160 0.840
#> GSM905036 1 0.997 0.162 0.532 0.468
#> GSM905041 1 0.990 0.246 0.560 0.440
#> GSM905044 2 0.634 0.840 0.160 0.840
#> GSM904989 2 0.634 0.840 0.160 0.840
#> GSM904999 2 0.871 0.633 0.292 0.708
#> GSM905002 2 0.634 0.840 0.160 0.840
#> GSM905009 2 0.634 0.840 0.160 0.840
#> GSM905014 1 0.994 0.202 0.544 0.456
#> GSM905017 2 0.871 0.633 0.292 0.708
#> GSM905020 2 0.634 0.840 0.160 0.840
#> GSM905023 1 0.997 0.162 0.532 0.468
#> GSM905029 1 0.999 0.102 0.516 0.484
#> GSM905032 1 0.980 0.306 0.584 0.416
#> GSM905034 1 0.456 0.789 0.904 0.096
#> GSM905040 1 0.358 0.809 0.932 0.068
#> GSM904985 2 0.000 0.897 0.000 1.000
#> GSM904988 2 0.000 0.897 0.000 1.000
#> GSM904990 2 0.000 0.897 0.000 1.000
#> GSM904992 2 0.000 0.897 0.000 1.000
#> GSM904995 2 0.000 0.897 0.000 1.000
#> GSM904998 2 0.000 0.897 0.000 1.000
#> GSM905000 2 0.000 0.897 0.000 1.000
#> GSM905003 2 0.000 0.897 0.000 1.000
#> GSM905006 2 0.000 0.897 0.000 1.000
#> GSM905008 2 0.000 0.897 0.000 1.000
#> GSM905011 2 0.000 0.897 0.000 1.000
#> GSM905013 2 0.000 0.897 0.000 1.000
#> GSM905016 2 0.000 0.897 0.000 1.000
#> GSM905018 2 0.000 0.897 0.000 1.000
#> GSM905021 2 0.430 0.870 0.088 0.912
#> GSM905025 2 0.000 0.897 0.000 1.000
#> GSM905028 2 0.000 0.897 0.000 1.000
#> GSM905030 2 0.000 0.897 0.000 1.000
#> GSM905033 2 0.000 0.897 0.000 1.000
#> GSM905035 2 0.000 0.897 0.000 1.000
#> GSM905037 2 0.000 0.897 0.000 1.000
#> GSM905039 2 0.000 0.897 0.000 1.000
#> GSM905042 2 0.000 0.897 0.000 1.000
#> GSM905046 1 0.000 0.850 1.000 0.000
#> GSM905065 1 0.000 0.850 1.000 0.000
#> GSM905049 1 0.000 0.850 1.000 0.000
#> GSM905050 1 0.000 0.850 1.000 0.000
#> GSM905064 1 0.000 0.850 1.000 0.000
#> GSM905045 1 0.000 0.850 1.000 0.000
#> GSM905051 1 0.000 0.850 1.000 0.000
#> GSM905055 1 0.000 0.850 1.000 0.000
#> GSM905058 1 0.000 0.850 1.000 0.000
#> GSM905053 1 0.000 0.850 1.000 0.000
#> GSM905061 1 0.000 0.850 1.000 0.000
#> GSM905063 1 0.000 0.850 1.000 0.000
#> GSM905054 1 0.000 0.850 1.000 0.000
#> GSM905062 1 0.000 0.850 1.000 0.000
#> GSM905052 1 0.000 0.850 1.000 0.000
#> GSM905059 1 0.000 0.850 1.000 0.000
#> GSM905047 1 0.000 0.850 1.000 0.000
#> GSM905066 1 0.000 0.850 1.000 0.000
#> GSM905056 1 0.000 0.850 1.000 0.000
#> GSM905060 1 0.000 0.850 1.000 0.000
#> GSM905048 1 0.000 0.850 1.000 0.000
#> GSM905067 1 0.000 0.850 1.000 0.000
#> GSM905057 1 0.000 0.850 1.000 0.000
#> GSM905068 1 0.000 0.850 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM905004 3 0.7969 0.1935 0.064 0.396 0.540
#> GSM905024 3 0.5431 0.3285 0.284 0.000 0.716
#> GSM905038 3 0.3715 0.7147 0.004 0.128 0.868
#> GSM905043 3 0.5431 0.3285 0.284 0.000 0.716
#> GSM904986 2 0.6299 0.1334 0.000 0.524 0.476
#> GSM904991 3 0.3375 0.7260 0.008 0.100 0.892
#> GSM904994 2 0.6299 0.1334 0.000 0.524 0.476
#> GSM904996 2 0.6299 0.1334 0.000 0.524 0.476
#> GSM905007 3 0.3375 0.7260 0.008 0.100 0.892
#> GSM905012 2 0.6299 0.1334 0.000 0.524 0.476
#> GSM905022 3 0.6280 0.0582 0.000 0.460 0.540
#> GSM905026 2 0.6299 0.1334 0.000 0.524 0.476
#> GSM905027 3 0.6280 0.0582 0.000 0.460 0.540
#> GSM905031 2 0.6299 0.1334 0.000 0.524 0.476
#> GSM905036 3 0.3607 0.7243 0.008 0.112 0.880
#> GSM905041 3 0.3502 0.7202 0.020 0.084 0.896
#> GSM905044 2 0.6299 0.1334 0.000 0.524 0.476
#> GSM904989 2 0.6299 0.1334 0.000 0.524 0.476
#> GSM904999 3 0.5905 0.3940 0.000 0.352 0.648
#> GSM905002 2 0.6299 0.1334 0.000 0.524 0.476
#> GSM905009 2 0.6299 0.1334 0.000 0.524 0.476
#> GSM905014 3 0.3375 0.7260 0.008 0.100 0.892
#> GSM905017 3 0.5905 0.3940 0.000 0.352 0.648
#> GSM905020 2 0.6299 0.1334 0.000 0.524 0.476
#> GSM905023 3 0.3607 0.7243 0.008 0.112 0.880
#> GSM905029 3 0.3715 0.7147 0.004 0.128 0.868
#> GSM905032 3 0.3181 0.7072 0.024 0.064 0.912
#> GSM905034 3 0.5431 0.3285 0.284 0.000 0.716
#> GSM905040 1 0.4399 0.8191 0.812 0.000 0.188
#> GSM904985 2 0.0000 0.7541 0.000 1.000 0.000
#> GSM904988 2 0.0000 0.7541 0.000 1.000 0.000
#> GSM904990 2 0.0000 0.7541 0.000 1.000 0.000
#> GSM904992 2 0.0000 0.7541 0.000 1.000 0.000
#> GSM904995 2 0.0000 0.7541 0.000 1.000 0.000
#> GSM904998 2 0.0000 0.7541 0.000 1.000 0.000
#> GSM905000 2 0.0000 0.7541 0.000 1.000 0.000
#> GSM905003 2 0.0000 0.7541 0.000 1.000 0.000
#> GSM905006 2 0.0000 0.7541 0.000 1.000 0.000
#> GSM905008 2 0.0000 0.7541 0.000 1.000 0.000
#> GSM905011 2 0.0000 0.7541 0.000 1.000 0.000
#> GSM905013 2 0.0000 0.7541 0.000 1.000 0.000
#> GSM905016 2 0.0000 0.7541 0.000 1.000 0.000
#> GSM905018 2 0.0000 0.7541 0.000 1.000 0.000
#> GSM905021 2 0.6126 0.2708 0.000 0.600 0.400
#> GSM905025 2 0.0000 0.7541 0.000 1.000 0.000
#> GSM905028 2 0.0000 0.7541 0.000 1.000 0.000
#> GSM905030 2 0.0000 0.7541 0.000 1.000 0.000
#> GSM905033 2 0.0424 0.7493 0.000 0.992 0.008
#> GSM905035 2 0.0000 0.7541 0.000 1.000 0.000
#> GSM905037 2 0.0000 0.7541 0.000 1.000 0.000
#> GSM905039 2 0.0000 0.7541 0.000 1.000 0.000
#> GSM905042 2 0.0424 0.7493 0.000 0.992 0.008
#> GSM905046 1 0.0000 0.9405 1.000 0.000 0.000
#> GSM905065 1 0.1289 0.9343 0.968 0.000 0.032
#> GSM905049 1 0.2878 0.9227 0.904 0.000 0.096
#> GSM905050 1 0.2878 0.9227 0.904 0.000 0.096
#> GSM905064 1 0.2878 0.9227 0.904 0.000 0.096
#> GSM905045 1 0.2878 0.9227 0.904 0.000 0.096
#> GSM905051 1 0.0000 0.9405 1.000 0.000 0.000
#> GSM905055 1 0.2796 0.9099 0.908 0.000 0.092
#> GSM905058 1 0.0000 0.9405 1.000 0.000 0.000
#> GSM905053 1 0.2878 0.9227 0.904 0.000 0.096
#> GSM905061 1 0.2878 0.9227 0.904 0.000 0.096
#> GSM905063 1 0.2796 0.9099 0.908 0.000 0.092
#> GSM905054 1 0.2878 0.9227 0.904 0.000 0.096
#> GSM905062 1 0.2878 0.9227 0.904 0.000 0.096
#> GSM905052 1 0.0000 0.9405 1.000 0.000 0.000
#> GSM905059 1 0.0000 0.9405 1.000 0.000 0.000
#> GSM905047 1 0.0000 0.9405 1.000 0.000 0.000
#> GSM905066 1 0.1289 0.9343 0.968 0.000 0.032
#> GSM905056 1 0.2796 0.9099 0.908 0.000 0.092
#> GSM905060 1 0.0000 0.9405 1.000 0.000 0.000
#> GSM905048 1 0.0000 0.9405 1.000 0.000 0.000
#> GSM905067 1 0.1289 0.9343 0.968 0.000 0.032
#> GSM905057 1 0.2796 0.9099 0.908 0.000 0.092
#> GSM905068 1 0.2878 0.9227 0.904 0.000 0.096
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM905004 3 0.4656 0.576 0.000 0.056 0.784 0.160
#> GSM905024 1 0.7732 0.412 0.392 0.380 0.228 0.000
#> GSM905038 3 0.4872 0.488 0.004 0.356 0.640 0.000
#> GSM905043 1 0.7732 0.412 0.392 0.380 0.228 0.000
#> GSM904986 3 0.1557 0.663 0.000 0.056 0.944 0.000
#> GSM904991 3 0.5428 0.446 0.020 0.380 0.600 0.000
#> GSM904994 3 0.1557 0.663 0.000 0.056 0.944 0.000
#> GSM904996 3 0.1557 0.663 0.000 0.056 0.944 0.000
#> GSM905007 3 0.5428 0.446 0.020 0.380 0.600 0.000
#> GSM905012 3 0.1557 0.663 0.000 0.056 0.944 0.000
#> GSM905022 3 0.0817 0.689 0.000 0.024 0.976 0.000
#> GSM905026 3 0.1557 0.663 0.000 0.056 0.944 0.000
#> GSM905027 3 0.0817 0.689 0.000 0.024 0.976 0.000
#> GSM905031 3 0.1557 0.663 0.000 0.056 0.944 0.000
#> GSM905036 3 0.4936 0.471 0.004 0.372 0.624 0.000
#> GSM905041 3 0.5781 0.423 0.036 0.380 0.584 0.000
#> GSM905044 3 0.1557 0.663 0.000 0.056 0.944 0.000
#> GSM904989 3 0.1557 0.663 0.000 0.056 0.944 0.000
#> GSM904999 3 0.2999 0.667 0.004 0.132 0.864 0.000
#> GSM905002 3 0.1557 0.663 0.000 0.056 0.944 0.000
#> GSM905009 3 0.1557 0.663 0.000 0.056 0.944 0.000
#> GSM905014 3 0.5428 0.446 0.020 0.380 0.600 0.000
#> GSM905017 3 0.2999 0.667 0.004 0.132 0.864 0.000
#> GSM905020 3 0.1557 0.663 0.000 0.056 0.944 0.000
#> GSM905023 3 0.4936 0.471 0.004 0.372 0.624 0.000
#> GSM905029 3 0.4872 0.488 0.004 0.356 0.640 0.000
#> GSM905032 3 0.6337 0.370 0.068 0.380 0.552 0.000
#> GSM905034 1 0.7732 0.412 0.392 0.380 0.228 0.000
#> GSM905040 1 0.2021 0.678 0.936 0.024 0.040 0.000
#> GSM904985 2 0.4790 0.998 0.000 0.620 0.380 0.000
#> GSM904988 2 0.4790 0.998 0.000 0.620 0.380 0.000
#> GSM904990 2 0.4790 0.998 0.000 0.620 0.380 0.000
#> GSM904992 2 0.4790 0.998 0.000 0.620 0.380 0.000
#> GSM904995 2 0.4790 0.998 0.000 0.620 0.380 0.000
#> GSM904998 2 0.4790 0.998 0.000 0.620 0.380 0.000
#> GSM905000 2 0.4790 0.998 0.000 0.620 0.380 0.000
#> GSM905003 2 0.4790 0.998 0.000 0.620 0.380 0.000
#> GSM905006 2 0.4790 0.998 0.000 0.620 0.380 0.000
#> GSM905008 2 0.4790 0.998 0.000 0.620 0.380 0.000
#> GSM905011 2 0.4790 0.998 0.000 0.620 0.380 0.000
#> GSM905013 2 0.4790 0.998 0.000 0.620 0.380 0.000
#> GSM905016 2 0.4790 0.998 0.000 0.620 0.380 0.000
#> GSM905018 2 0.4790 0.998 0.000 0.620 0.380 0.000
#> GSM905021 3 0.3074 0.394 0.000 0.152 0.848 0.000
#> GSM905025 2 0.4790 0.998 0.000 0.620 0.380 0.000
#> GSM905028 2 0.4790 0.998 0.000 0.620 0.380 0.000
#> GSM905030 2 0.4790 0.998 0.000 0.620 0.380 0.000
#> GSM905033 2 0.4830 0.983 0.000 0.608 0.392 0.000
#> GSM905035 2 0.4790 0.998 0.000 0.620 0.380 0.000
#> GSM905037 2 0.4790 0.998 0.000 0.620 0.380 0.000
#> GSM905039 2 0.4790 0.998 0.000 0.620 0.380 0.000
#> GSM905042 2 0.4830 0.983 0.000 0.608 0.392 0.000
#> GSM905046 4 0.3219 0.858 0.164 0.000 0.000 0.836
#> GSM905065 4 0.4855 0.584 0.400 0.000 0.000 0.600
#> GSM905049 4 0.0000 0.861 0.000 0.000 0.000 1.000
#> GSM905050 4 0.0000 0.861 0.000 0.000 0.000 1.000
#> GSM905064 4 0.0000 0.861 0.000 0.000 0.000 1.000
#> GSM905045 4 0.0000 0.861 0.000 0.000 0.000 1.000
#> GSM905051 4 0.2973 0.862 0.144 0.000 0.000 0.856
#> GSM905055 1 0.1022 0.673 0.968 0.000 0.000 0.032
#> GSM905058 4 0.3219 0.858 0.164 0.000 0.000 0.836
#> GSM905053 4 0.0000 0.861 0.000 0.000 0.000 1.000
#> GSM905061 4 0.0000 0.861 0.000 0.000 0.000 1.000
#> GSM905063 1 0.1022 0.673 0.968 0.000 0.000 0.032
#> GSM905054 4 0.0000 0.861 0.000 0.000 0.000 1.000
#> GSM905062 4 0.0000 0.861 0.000 0.000 0.000 1.000
#> GSM905052 4 0.2973 0.862 0.144 0.000 0.000 0.856
#> GSM905059 4 0.3219 0.858 0.164 0.000 0.000 0.836
#> GSM905047 4 0.3219 0.858 0.164 0.000 0.000 0.836
#> GSM905066 4 0.4855 0.584 0.400 0.000 0.000 0.600
#> GSM905056 1 0.1022 0.673 0.968 0.000 0.000 0.032
#> GSM905060 4 0.3219 0.858 0.164 0.000 0.000 0.836
#> GSM905048 4 0.3219 0.858 0.164 0.000 0.000 0.836
#> GSM905067 4 0.4855 0.584 0.400 0.000 0.000 0.600
#> GSM905057 1 0.1022 0.673 0.968 0.000 0.000 0.032
#> GSM905068 4 0.0000 0.861 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
#> GSM905004 3 0.4547 0.61763 0.112 0.056 0.788 0.044 0.000
#> GSM905024 5 0.0000 0.52593 0.000 0.000 0.000 0.000 1.000
#> GSM905038 3 0.4138 -0.00777 0.000 0.000 0.616 0.000 0.384
#> GSM905043 5 0.0000 0.52593 0.000 0.000 0.000 0.000 1.000
#> GSM904986 3 0.1410 0.77838 0.000 0.060 0.940 0.000 0.000
#> GSM904991 5 0.4249 0.57149 0.000 0.000 0.432 0.000 0.568
#> GSM904994 3 0.1410 0.77838 0.000 0.060 0.940 0.000 0.000
#> GSM904996 3 0.1410 0.77838 0.000 0.060 0.940 0.000 0.000
#> GSM905007 5 0.4249 0.57149 0.000 0.000 0.432 0.000 0.568
#> GSM905012 3 0.1410 0.77838 0.000 0.060 0.940 0.000 0.000
#> GSM905022 3 0.0865 0.72156 0.000 0.004 0.972 0.000 0.024
#> GSM905026 3 0.1571 0.77721 0.000 0.060 0.936 0.000 0.004
#> GSM905027 3 0.0955 0.72077 0.000 0.004 0.968 0.000 0.028
#> GSM905031 3 0.1571 0.77721 0.000 0.060 0.936 0.000 0.004
#> GSM905036 3 0.4235 -0.16342 0.000 0.000 0.576 0.000 0.424
#> GSM905041 5 0.4171 0.60293 0.000 0.000 0.396 0.000 0.604
#> GSM905044 3 0.1571 0.77721 0.000 0.060 0.936 0.000 0.004
#> GSM904989 3 0.1410 0.77838 0.000 0.060 0.940 0.000 0.000
#> GSM904999 3 0.3491 0.47742 0.000 0.004 0.768 0.000 0.228
#> GSM905002 3 0.1410 0.77838 0.000 0.060 0.940 0.000 0.000
#> GSM905009 3 0.1410 0.77838 0.000 0.060 0.940 0.000 0.000
#> GSM905014 5 0.4249 0.57149 0.000 0.000 0.432 0.000 0.568
#> GSM905017 3 0.3491 0.47742 0.000 0.004 0.768 0.000 0.228
#> GSM905020 3 0.1410 0.77838 0.000 0.060 0.940 0.000 0.000
#> GSM905023 3 0.4235 -0.16342 0.000 0.000 0.576 0.000 0.424
#> GSM905029 3 0.4138 -0.00777 0.000 0.000 0.616 0.000 0.384
#> GSM905032 5 0.4060 0.61915 0.000 0.000 0.360 0.000 0.640
#> GSM905034 5 0.0000 0.52593 0.000 0.000 0.000 0.000 1.000
#> GSM905040 1 0.4541 0.86806 0.752 0.000 0.000 0.112 0.136
#> GSM904985 2 0.0000 0.99809 0.000 1.000 0.000 0.000 0.000
#> GSM904988 2 0.0000 0.99809 0.000 1.000 0.000 0.000 0.000
#> GSM904990 2 0.0000 0.99809 0.000 1.000 0.000 0.000 0.000
#> GSM904992 2 0.0000 0.99809 0.000 1.000 0.000 0.000 0.000
#> GSM904995 2 0.0000 0.99809 0.000 1.000 0.000 0.000 0.000
#> GSM904998 2 0.0000 0.99809 0.000 1.000 0.000 0.000 0.000
#> GSM905000 2 0.0000 0.99809 0.000 1.000 0.000 0.000 0.000
#> GSM905003 2 0.0000 0.99809 0.000 1.000 0.000 0.000 0.000
#> GSM905006 2 0.0000 0.99809 0.000 1.000 0.000 0.000 0.000
#> GSM905008 2 0.0000 0.99809 0.000 1.000 0.000 0.000 0.000
#> GSM905011 2 0.0000 0.99809 0.000 1.000 0.000 0.000 0.000
#> GSM905013 2 0.0000 0.99809 0.000 1.000 0.000 0.000 0.000
#> GSM905016 2 0.0000 0.99809 0.000 1.000 0.000 0.000 0.000
#> GSM905018 2 0.0000 0.99809 0.000 1.000 0.000 0.000 0.000
#> GSM905021 3 0.3752 0.40264 0.000 0.292 0.708 0.000 0.000
#> GSM905025 2 0.0000 0.99809 0.000 1.000 0.000 0.000 0.000
#> GSM905028 2 0.0000 0.99809 0.000 1.000 0.000 0.000 0.000
#> GSM905030 2 0.0000 0.99809 0.000 1.000 0.000 0.000 0.000
#> GSM905033 2 0.0510 0.98073 0.000 0.984 0.016 0.000 0.000
#> GSM905035 2 0.0000 0.99809 0.000 1.000 0.000 0.000 0.000
#> GSM905037 2 0.0000 0.99809 0.000 1.000 0.000 0.000 0.000
#> GSM905039 2 0.0000 0.99809 0.000 1.000 0.000 0.000 0.000
#> GSM905042 2 0.0510 0.98073 0.000 0.984 0.016 0.000 0.000
#> GSM905046 4 0.0798 0.84620 0.008 0.000 0.000 0.976 0.016
#> GSM905065 4 0.4054 0.62467 0.020 0.000 0.000 0.732 0.248
#> GSM905049 4 0.2848 0.85262 0.156 0.000 0.004 0.840 0.000
#> GSM905050 4 0.2848 0.85262 0.156 0.000 0.004 0.840 0.000
#> GSM905064 4 0.2848 0.85262 0.156 0.000 0.004 0.840 0.000
#> GSM905045 4 0.2848 0.85262 0.156 0.000 0.004 0.840 0.000
#> GSM905051 4 0.0162 0.84911 0.000 0.000 0.000 0.996 0.004
#> GSM905055 1 0.2690 0.96979 0.844 0.000 0.000 0.156 0.000
#> GSM905058 4 0.0798 0.84620 0.008 0.000 0.000 0.976 0.016
#> GSM905053 4 0.2848 0.85262 0.156 0.000 0.004 0.840 0.000
#> GSM905061 4 0.2848 0.85262 0.156 0.000 0.004 0.840 0.000
#> GSM905063 1 0.2690 0.96979 0.844 0.000 0.000 0.156 0.000
#> GSM905054 4 0.2848 0.85262 0.156 0.000 0.004 0.840 0.000
#> GSM905062 4 0.2848 0.85262 0.156 0.000 0.004 0.840 0.000
#> GSM905052 4 0.0162 0.84911 0.000 0.000 0.000 0.996 0.004
#> GSM905059 4 0.0798 0.84620 0.008 0.000 0.000 0.976 0.016
#> GSM905047 4 0.0798 0.84620 0.008 0.000 0.000 0.976 0.016
#> GSM905066 4 0.4054 0.62467 0.020 0.000 0.000 0.732 0.248
#> GSM905056 1 0.2690 0.96979 0.844 0.000 0.000 0.156 0.000
#> GSM905060 4 0.0798 0.84620 0.008 0.000 0.000 0.976 0.016
#> GSM905048 4 0.0798 0.84620 0.008 0.000 0.000 0.976 0.016
#> GSM905067 4 0.4054 0.62467 0.020 0.000 0.000 0.732 0.248
#> GSM905057 1 0.2690 0.96979 0.844 0.000 0.000 0.156 0.000
#> GSM905068 4 0.2848 0.85262 0.156 0.000 0.004 0.840 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM905004 3 0.2454 0.6611 0.000 0.000 0.840 0.160 0.000 0.000
#> GSM905024 5 0.3499 0.3995 0.320 0.000 0.000 0.000 0.680 0.000
#> GSM905038 5 0.3647 0.4672 0.000 0.000 0.360 0.000 0.640 0.000
#> GSM905043 5 0.3499 0.3995 0.320 0.000 0.000 0.000 0.680 0.000
#> GSM904986 3 0.0000 0.8656 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM904991 5 0.3647 0.5390 0.000 0.000 0.360 0.000 0.640 0.000
#> GSM904994 3 0.0000 0.8656 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM904996 3 0.0000 0.8656 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905007 5 0.3647 0.5390 0.000 0.000 0.360 0.000 0.640 0.000
#> GSM905012 3 0.0000 0.8656 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905022 3 0.1714 0.7746 0.000 0.000 0.908 0.000 0.092 0.000
#> GSM905026 3 0.2730 0.7119 0.000 0.000 0.808 0.000 0.192 0.000
#> GSM905027 3 0.3330 0.5699 0.000 0.000 0.716 0.000 0.284 0.000
#> GSM905031 3 0.2730 0.7119 0.000 0.000 0.808 0.000 0.192 0.000
#> GSM905036 5 0.3499 0.5223 0.000 0.000 0.320 0.000 0.680 0.000
#> GSM905041 5 0.2402 0.6195 0.004 0.000 0.140 0.000 0.856 0.000
#> GSM905044 3 0.2730 0.7119 0.000 0.000 0.808 0.000 0.192 0.000
#> GSM904989 3 0.0000 0.8656 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM904999 5 0.6028 0.3024 0.316 0.000 0.264 0.000 0.420 0.000
#> GSM905002 3 0.0000 0.8656 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905009 3 0.0000 0.8656 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905014 5 0.3647 0.5390 0.000 0.000 0.360 0.000 0.640 0.000
#> GSM905017 5 0.6028 0.3024 0.316 0.000 0.264 0.000 0.420 0.000
#> GSM905020 3 0.0000 0.8656 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905023 5 0.3499 0.5223 0.000 0.000 0.320 0.000 0.680 0.000
#> GSM905029 5 0.3647 0.4672 0.000 0.000 0.360 0.000 0.640 0.000
#> GSM905032 5 0.2263 0.6207 0.016 0.000 0.100 0.000 0.884 0.000
#> GSM905034 5 0.3499 0.3995 0.320 0.000 0.000 0.000 0.680 0.000
#> GSM905040 6 0.2744 0.8711 0.064 0.000 0.000 0.000 0.072 0.864
#> GSM904985 2 0.0000 0.9651 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM904988 2 0.0000 0.9651 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM904990 2 0.0000 0.9651 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM904992 2 0.0000 0.9651 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM904995 2 0.0000 0.9651 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM904998 2 0.0000 0.9651 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905000 2 0.0000 0.9651 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905003 2 0.0000 0.9651 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905006 2 0.0000 0.9651 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905008 2 0.0000 0.9651 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905011 2 0.0000 0.9651 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905013 2 0.0000 0.9651 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905016 2 0.0000 0.9651 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905018 2 0.0000 0.9651 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905021 2 0.7704 -0.3561 0.244 0.288 0.212 0.000 0.256 0.000
#> GSM905025 2 0.0000 0.9651 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905028 2 0.0000 0.9651 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905030 2 0.0000 0.9651 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905033 2 0.0458 0.9524 0.016 0.984 0.000 0.000 0.000 0.000
#> GSM905035 2 0.0000 0.9651 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905037 2 0.0000 0.9651 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905039 2 0.0000 0.9651 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905042 2 0.0458 0.9524 0.016 0.984 0.000 0.000 0.000 0.000
#> GSM905046 4 0.4524 0.0199 0.376 0.000 0.000 0.584 0.000 0.040
#> GSM905065 1 0.6025 1.0000 0.452 0.000 0.000 0.416 0.080 0.052
#> GSM905049 4 0.0000 0.5859 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905050 4 0.0000 0.5859 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905064 4 0.0000 0.5859 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905045 4 0.0000 0.5859 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905051 4 0.4371 0.1044 0.344 0.000 0.000 0.620 0.000 0.036
#> GSM905055 6 0.0000 0.9699 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM905058 4 0.4524 0.0199 0.376 0.000 0.000 0.584 0.000 0.040
#> GSM905053 4 0.0000 0.5859 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905061 4 0.0000 0.5859 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905063 6 0.0000 0.9699 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM905054 4 0.0000 0.5859 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905062 4 0.0000 0.5859 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905052 4 0.4371 0.1044 0.344 0.000 0.000 0.620 0.000 0.036
#> GSM905059 4 0.4524 0.0199 0.376 0.000 0.000 0.584 0.000 0.040
#> GSM905047 4 0.4524 0.0199 0.376 0.000 0.000 0.584 0.000 0.040
#> GSM905066 1 0.6025 1.0000 0.452 0.000 0.000 0.416 0.080 0.052
#> GSM905056 6 0.0000 0.9699 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM905060 4 0.4524 0.0199 0.376 0.000 0.000 0.584 0.000 0.040
#> GSM905048 4 0.4524 0.0199 0.376 0.000 0.000 0.584 0.000 0.040
#> GSM905067 1 0.6025 1.0000 0.452 0.000 0.000 0.416 0.080 0.052
#> GSM905057 6 0.0000 0.9699 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM905068 4 0.0000 0.5859 0.000 0.000 0.000 1.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) genotype/variation(p) individual(p) k
#> MAD:hclust 67 5.18e-08 4.00e-03 0.0511 2
#> MAD:hclust 56 2.05e-13 5.07e-04 0.7699 3
#> MAD:hclust 63 7.21e-16 5.29e-06 0.0854 4
#> MAD:hclust 69 4.90e-15 8.72e-06 0.3441 5
#> MAD:hclust 60 1.39e-16 4.82e-13 0.2297 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 76 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 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 0.581 0.853 0.899 0.4645 0.522 0.522
#> 3 3 0.728 0.952 0.916 0.4035 0.754 0.550
#> 4 4 0.827 0.831 0.801 0.1083 0.964 0.896
#> 5 5 0.771 0.733 0.796 0.0648 0.909 0.723
#> 6 6 0.735 0.540 0.794 0.0405 0.937 0.754
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
#> GSM905004 2 0.876 0.782 0.296 0.704
#> GSM905024 1 0.224 0.938 0.964 0.036
#> GSM905038 2 0.827 0.795 0.260 0.740
#> GSM905043 1 0.224 0.938 0.964 0.036
#> GSM904986 2 0.808 0.805 0.248 0.752
#> GSM904991 2 0.850 0.777 0.276 0.724
#> GSM904994 2 0.808 0.805 0.248 0.752
#> GSM904996 2 0.808 0.805 0.248 0.752
#> GSM905007 2 0.827 0.795 0.260 0.740
#> GSM905012 2 0.808 0.805 0.248 0.752
#> GSM905022 2 0.808 0.805 0.248 0.752
#> GSM905026 2 0.808 0.805 0.248 0.752
#> GSM905027 2 0.827 0.795 0.260 0.740
#> GSM905031 2 0.808 0.805 0.248 0.752
#> GSM905036 2 0.850 0.777 0.276 0.724
#> GSM905041 1 1.000 -0.287 0.508 0.492
#> GSM905044 2 0.808 0.805 0.248 0.752
#> GSM904989 2 0.808 0.805 0.248 0.752
#> GSM904999 2 0.808 0.805 0.248 0.752
#> GSM905002 2 0.808 0.805 0.248 0.752
#> GSM905009 2 0.808 0.805 0.248 0.752
#> GSM905014 2 0.827 0.795 0.260 0.740
#> GSM905017 2 0.808 0.805 0.248 0.752
#> GSM905020 2 0.808 0.805 0.248 0.752
#> GSM905023 2 0.827 0.795 0.260 0.740
#> GSM905029 2 0.827 0.795 0.260 0.740
#> GSM905032 2 0.949 0.629 0.368 0.632
#> GSM905034 1 0.224 0.938 0.964 0.036
#> GSM905040 1 0.224 0.938 0.964 0.036
#> GSM904985 2 0.224 0.828 0.036 0.964
#> GSM904988 2 0.224 0.828 0.036 0.964
#> GSM904990 2 0.224 0.828 0.036 0.964
#> GSM904992 2 0.224 0.828 0.036 0.964
#> GSM904995 2 0.224 0.828 0.036 0.964
#> GSM904998 2 0.224 0.828 0.036 0.964
#> GSM905000 2 0.224 0.828 0.036 0.964
#> GSM905003 2 0.224 0.828 0.036 0.964
#> GSM905006 2 0.224 0.828 0.036 0.964
#> GSM905008 2 0.204 0.827 0.032 0.968
#> GSM905011 2 0.224 0.828 0.036 0.964
#> GSM905013 2 0.224 0.828 0.036 0.964
#> GSM905016 2 0.224 0.828 0.036 0.964
#> GSM905018 2 0.224 0.828 0.036 0.964
#> GSM905021 2 0.000 0.818 0.000 1.000
#> GSM905025 2 0.224 0.828 0.036 0.964
#> GSM905028 2 0.224 0.828 0.036 0.964
#> GSM905030 2 0.224 0.828 0.036 0.964
#> GSM905033 2 0.204 0.827 0.032 0.968
#> GSM905035 2 0.224 0.828 0.036 0.964
#> GSM905037 2 0.224 0.828 0.036 0.964
#> GSM905039 2 0.224 0.828 0.036 0.964
#> GSM905042 2 0.184 0.826 0.028 0.972
#> GSM905046 1 0.000 0.972 1.000 0.000
#> GSM905065 1 0.000 0.972 1.000 0.000
#> GSM905049 1 0.000 0.972 1.000 0.000
#> GSM905050 1 0.000 0.972 1.000 0.000
#> GSM905064 1 0.000 0.972 1.000 0.000
#> GSM905045 1 0.000 0.972 1.000 0.000
#> GSM905051 1 0.000 0.972 1.000 0.000
#> GSM905055 1 0.000 0.972 1.000 0.000
#> GSM905058 1 0.000 0.972 1.000 0.000
#> GSM905053 1 0.000 0.972 1.000 0.000
#> GSM905061 1 0.000 0.972 1.000 0.000
#> GSM905063 1 0.000 0.972 1.000 0.000
#> GSM905054 1 0.000 0.972 1.000 0.000
#> GSM905062 1 0.000 0.972 1.000 0.000
#> GSM905052 1 0.000 0.972 1.000 0.000
#> GSM905059 1 0.000 0.972 1.000 0.000
#> GSM905047 1 0.000 0.972 1.000 0.000
#> GSM905066 1 0.000 0.972 1.000 0.000
#> GSM905056 1 0.000 0.972 1.000 0.000
#> GSM905060 1 0.000 0.972 1.000 0.000
#> GSM905048 1 0.000 0.972 1.000 0.000
#> GSM905067 1 0.000 0.972 1.000 0.000
#> GSM905057 1 0.000 0.972 1.000 0.000
#> GSM905068 1 0.000 0.972 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM905004 3 0.1163 0.942 0.028 0.000 0.972
#> GSM905024 3 0.7097 0.646 0.128 0.148 0.724
#> GSM905038 3 0.0000 0.967 0.000 0.000 1.000
#> GSM905043 3 0.7097 0.646 0.128 0.148 0.724
#> GSM904986 3 0.0000 0.967 0.000 0.000 1.000
#> GSM904991 3 0.0747 0.954 0.000 0.016 0.984
#> GSM904994 3 0.0000 0.967 0.000 0.000 1.000
#> GSM904996 3 0.0000 0.967 0.000 0.000 1.000
#> GSM905007 3 0.0000 0.967 0.000 0.000 1.000
#> GSM905012 3 0.0000 0.967 0.000 0.000 1.000
#> GSM905022 3 0.0000 0.967 0.000 0.000 1.000
#> GSM905026 3 0.0000 0.967 0.000 0.000 1.000
#> GSM905027 3 0.0000 0.967 0.000 0.000 1.000
#> GSM905031 3 0.0000 0.967 0.000 0.000 1.000
#> GSM905036 3 0.0000 0.967 0.000 0.000 1.000
#> GSM905041 3 0.2446 0.908 0.012 0.052 0.936
#> GSM905044 3 0.0000 0.967 0.000 0.000 1.000
#> GSM904989 3 0.0000 0.967 0.000 0.000 1.000
#> GSM904999 3 0.0000 0.967 0.000 0.000 1.000
#> GSM905002 3 0.0000 0.967 0.000 0.000 1.000
#> GSM905009 3 0.0000 0.967 0.000 0.000 1.000
#> GSM905014 3 0.0000 0.967 0.000 0.000 1.000
#> GSM905017 3 0.0000 0.967 0.000 0.000 1.000
#> GSM905020 3 0.0000 0.967 0.000 0.000 1.000
#> GSM905023 3 0.0000 0.967 0.000 0.000 1.000
#> GSM905029 3 0.0000 0.967 0.000 0.000 1.000
#> GSM905032 3 0.1860 0.921 0.000 0.052 0.948
#> GSM905034 1 0.6968 0.839 0.732 0.148 0.120
#> GSM905040 1 0.6968 0.839 0.732 0.148 0.120
#> GSM904985 2 0.4002 0.998 0.000 0.840 0.160
#> GSM904988 2 0.4002 0.998 0.000 0.840 0.160
#> GSM904990 2 0.4002 0.998 0.000 0.840 0.160
#> GSM904992 2 0.4002 0.998 0.000 0.840 0.160
#> GSM904995 2 0.4002 0.998 0.000 0.840 0.160
#> GSM904998 2 0.4002 0.998 0.000 0.840 0.160
#> GSM905000 2 0.4002 0.998 0.000 0.840 0.160
#> GSM905003 2 0.4002 0.998 0.000 0.840 0.160
#> GSM905006 2 0.4002 0.998 0.000 0.840 0.160
#> GSM905008 2 0.4002 0.998 0.000 0.840 0.160
#> GSM905011 2 0.4002 0.998 0.000 0.840 0.160
#> GSM905013 2 0.4002 0.998 0.000 0.840 0.160
#> GSM905016 2 0.4002 0.998 0.000 0.840 0.160
#> GSM905018 2 0.4002 0.998 0.000 0.840 0.160
#> GSM905021 2 0.4002 0.998 0.000 0.840 0.160
#> GSM905025 2 0.4413 0.996 0.008 0.832 0.160
#> GSM905028 2 0.4413 0.996 0.008 0.832 0.160
#> GSM905030 2 0.4413 0.996 0.008 0.832 0.160
#> GSM905033 2 0.4413 0.996 0.008 0.832 0.160
#> GSM905035 2 0.4413 0.996 0.008 0.832 0.160
#> GSM905037 2 0.4413 0.996 0.008 0.832 0.160
#> GSM905039 2 0.4413 0.996 0.008 0.832 0.160
#> GSM905042 2 0.4413 0.996 0.008 0.832 0.160
#> GSM905046 1 0.4033 0.940 0.856 0.136 0.008
#> GSM905065 1 0.4033 0.940 0.856 0.136 0.008
#> GSM905049 1 0.0424 0.930 0.992 0.000 0.008
#> GSM905050 1 0.0424 0.930 0.992 0.000 0.008
#> GSM905064 1 0.0424 0.930 0.992 0.000 0.008
#> GSM905045 1 0.0424 0.930 0.992 0.000 0.008
#> GSM905051 1 0.0424 0.930 0.992 0.000 0.008
#> GSM905055 1 0.4413 0.934 0.832 0.160 0.008
#> GSM905058 1 0.4033 0.940 0.856 0.136 0.008
#> GSM905053 1 0.0424 0.930 0.992 0.000 0.008
#> GSM905061 1 0.0424 0.930 0.992 0.000 0.008
#> GSM905063 1 0.4228 0.936 0.844 0.148 0.008
#> GSM905054 1 0.0424 0.930 0.992 0.000 0.008
#> GSM905062 1 0.0424 0.930 0.992 0.000 0.008
#> GSM905052 1 0.0424 0.930 0.992 0.000 0.008
#> GSM905059 1 0.3896 0.940 0.864 0.128 0.008
#> GSM905047 1 0.3896 0.940 0.864 0.128 0.008
#> GSM905066 1 0.4033 0.940 0.856 0.136 0.008
#> GSM905056 1 0.4413 0.934 0.832 0.160 0.008
#> GSM905060 1 0.3896 0.940 0.864 0.128 0.008
#> GSM905048 1 0.4033 0.940 0.856 0.136 0.008
#> GSM905067 1 0.4033 0.940 0.856 0.136 0.008
#> GSM905057 1 0.4413 0.934 0.832 0.160 0.008
#> GSM905068 1 0.0424 0.930 0.992 0.000 0.008
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM905004 3 0.1109 0.930 0.000 0.004 0.968 NA
#> GSM905024 1 0.7833 -0.104 0.376 0.000 0.364 NA
#> GSM905038 3 0.1867 0.935 0.000 0.000 0.928 NA
#> GSM905043 1 0.7993 -0.104 0.372 0.004 0.364 NA
#> GSM904986 3 0.0000 0.946 0.000 0.000 1.000 NA
#> GSM904991 3 0.3486 0.882 0.000 0.000 0.812 NA
#> GSM904994 3 0.0000 0.946 0.000 0.000 1.000 NA
#> GSM904996 3 0.0000 0.946 0.000 0.000 1.000 NA
#> GSM905007 3 0.2281 0.929 0.000 0.000 0.904 NA
#> GSM905012 3 0.0000 0.946 0.000 0.000 1.000 NA
#> GSM905022 3 0.0000 0.946 0.000 0.000 1.000 NA
#> GSM905026 3 0.0000 0.946 0.000 0.000 1.000 NA
#> GSM905027 3 0.1474 0.940 0.000 0.000 0.948 NA
#> GSM905031 3 0.0000 0.946 0.000 0.000 1.000 NA
#> GSM905036 3 0.2814 0.915 0.000 0.000 0.868 NA
#> GSM905041 3 0.3486 0.882 0.000 0.000 0.812 NA
#> GSM905044 3 0.0000 0.946 0.000 0.000 1.000 NA
#> GSM904989 3 0.0000 0.946 0.000 0.000 1.000 NA
#> GSM904999 3 0.2814 0.915 0.000 0.000 0.868 NA
#> GSM905002 3 0.0000 0.946 0.000 0.000 1.000 NA
#> GSM905009 3 0.0000 0.946 0.000 0.000 1.000 NA
#> GSM905014 3 0.2281 0.929 0.000 0.000 0.904 NA
#> GSM905017 3 0.2814 0.915 0.000 0.000 0.868 NA
#> GSM905020 3 0.0000 0.946 0.000 0.000 1.000 NA
#> GSM905023 3 0.2704 0.919 0.000 0.000 0.876 NA
#> GSM905029 3 0.2530 0.924 0.000 0.000 0.888 NA
#> GSM905032 3 0.4372 0.808 0.000 0.004 0.728 NA
#> GSM905034 1 0.5652 0.587 0.688 0.008 0.044 NA
#> GSM905040 1 0.5865 0.572 0.644 0.016 0.028 NA
#> GSM904985 2 0.4552 0.912 0.000 0.784 0.044 NA
#> GSM904988 2 0.1302 0.942 0.000 0.956 0.044 NA
#> GSM904990 2 0.1302 0.942 0.000 0.956 0.044 NA
#> GSM904992 2 0.1302 0.942 0.000 0.956 0.044 NA
#> GSM904995 2 0.4224 0.919 0.000 0.812 0.044 NA
#> GSM904998 2 0.2408 0.939 0.000 0.920 0.044 NA
#> GSM905000 2 0.1302 0.942 0.000 0.956 0.044 NA
#> GSM905003 2 0.2500 0.938 0.000 0.916 0.044 NA
#> GSM905006 2 0.1302 0.942 0.000 0.956 0.044 NA
#> GSM905008 2 0.2500 0.938 0.000 0.916 0.044 NA
#> GSM905011 2 0.1302 0.942 0.000 0.956 0.044 NA
#> GSM905013 2 0.1302 0.942 0.000 0.956 0.044 NA
#> GSM905016 2 0.4224 0.919 0.000 0.812 0.044 NA
#> GSM905018 2 0.1302 0.942 0.000 0.956 0.044 NA
#> GSM905021 2 0.5156 0.882 0.000 0.720 0.044 NA
#> GSM905025 2 0.4370 0.916 0.000 0.800 0.044 NA
#> GSM905028 2 0.2002 0.941 0.000 0.936 0.044 NA
#> GSM905030 2 0.2002 0.941 0.000 0.936 0.044 NA
#> GSM905033 2 0.4800 0.906 0.000 0.760 0.044 NA
#> GSM905035 2 0.4462 0.915 0.000 0.792 0.044 NA
#> GSM905037 2 0.2002 0.941 0.000 0.936 0.044 NA
#> GSM905039 2 0.4370 0.916 0.000 0.800 0.044 NA
#> GSM905042 2 0.4800 0.906 0.000 0.760 0.044 NA
#> GSM905046 1 0.0000 0.766 1.000 0.000 0.000 NA
#> GSM905065 1 0.0188 0.766 0.996 0.004 0.000 NA
#> GSM905049 1 0.5112 0.715 0.560 0.004 0.000 NA
#> GSM905050 1 0.5112 0.715 0.560 0.004 0.000 NA
#> GSM905064 1 0.4948 0.715 0.560 0.000 0.000 NA
#> GSM905045 1 0.4948 0.715 0.560 0.000 0.000 NA
#> GSM905051 1 0.5161 0.720 0.592 0.008 0.000 NA
#> GSM905055 1 0.3552 0.727 0.848 0.024 0.000 NA
#> GSM905058 1 0.0336 0.766 0.992 0.008 0.000 NA
#> GSM905053 1 0.5112 0.715 0.560 0.004 0.000 NA
#> GSM905061 1 0.4948 0.715 0.560 0.000 0.000 NA
#> GSM905063 1 0.3280 0.728 0.860 0.016 0.000 NA
#> GSM905054 1 0.5112 0.715 0.560 0.004 0.000 NA
#> GSM905062 1 0.4948 0.715 0.560 0.000 0.000 NA
#> GSM905052 1 0.5161 0.720 0.592 0.008 0.000 NA
#> GSM905059 1 0.0336 0.766 0.992 0.008 0.000 NA
#> GSM905047 1 0.0000 0.766 1.000 0.000 0.000 NA
#> GSM905066 1 0.0188 0.766 0.996 0.004 0.000 NA
#> GSM905056 1 0.3552 0.727 0.848 0.024 0.000 NA
#> GSM905060 1 0.0336 0.766 0.992 0.008 0.000 NA
#> GSM905048 1 0.0000 0.766 1.000 0.000 0.000 NA
#> GSM905067 1 0.0188 0.766 0.996 0.004 0.000 NA
#> GSM905057 1 0.3552 0.727 0.848 0.024 0.000 NA
#> GSM905068 1 0.5112 0.715 0.560 0.004 0.000 NA
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM905004 3 0.0865 0.8324 0.000 0.000 0.972 0.024 0.004
#> GSM905024 5 0.6444 0.6772 0.260 0.000 0.176 0.012 0.552
#> GSM905038 3 0.3320 0.7775 0.000 0.004 0.820 0.012 0.164
#> GSM905043 5 0.6228 0.6781 0.220 0.000 0.176 0.012 0.592
#> GSM904986 3 0.0162 0.8500 0.000 0.004 0.996 0.000 0.000
#> GSM904991 3 0.4551 0.3226 0.000 0.004 0.556 0.004 0.436
#> GSM904994 3 0.0162 0.8500 0.000 0.004 0.996 0.000 0.000
#> GSM904996 3 0.0162 0.8500 0.000 0.004 0.996 0.000 0.000
#> GSM905007 3 0.3128 0.7784 0.000 0.004 0.824 0.004 0.168
#> GSM905012 3 0.0324 0.8497 0.000 0.004 0.992 0.004 0.000
#> GSM905022 3 0.0162 0.8500 0.000 0.004 0.996 0.000 0.000
#> GSM905026 3 0.0740 0.8486 0.000 0.004 0.980 0.008 0.008
#> GSM905027 3 0.2570 0.8158 0.000 0.004 0.880 0.008 0.108
#> GSM905031 3 0.0740 0.8486 0.000 0.004 0.980 0.008 0.008
#> GSM905036 3 0.4283 0.6456 0.000 0.004 0.692 0.012 0.292
#> GSM905041 3 0.4589 0.2210 0.000 0.004 0.520 0.004 0.472
#> GSM905044 3 0.0613 0.8491 0.000 0.004 0.984 0.004 0.008
#> GSM904989 3 0.0324 0.8497 0.000 0.004 0.992 0.004 0.000
#> GSM904999 3 0.4359 0.7301 0.000 0.004 0.756 0.052 0.188
#> GSM905002 3 0.0162 0.8500 0.000 0.004 0.996 0.000 0.000
#> GSM905009 3 0.0324 0.8497 0.000 0.004 0.992 0.004 0.000
#> GSM905014 3 0.3128 0.7784 0.000 0.004 0.824 0.004 0.168
#> GSM905017 3 0.4359 0.7301 0.000 0.004 0.756 0.052 0.188
#> GSM905020 3 0.0324 0.8497 0.000 0.004 0.992 0.004 0.000
#> GSM905023 3 0.4217 0.6627 0.000 0.004 0.704 0.012 0.280
#> GSM905029 3 0.3797 0.7240 0.000 0.004 0.756 0.008 0.232
#> GSM905032 5 0.4383 -0.0537 0.000 0.004 0.424 0.000 0.572
#> GSM905034 5 0.5205 0.4813 0.412 0.000 0.020 0.016 0.552
#> GSM905040 5 0.5629 0.2994 0.388 0.000 0.008 0.060 0.544
#> GSM904985 2 0.5572 0.7818 0.000 0.644 0.000 0.192 0.164
#> GSM904988 2 0.0000 0.8615 0.000 1.000 0.000 0.000 0.000
#> GSM904990 2 0.0000 0.8615 0.000 1.000 0.000 0.000 0.000
#> GSM904992 2 0.0162 0.8615 0.000 0.996 0.000 0.004 0.000
#> GSM904995 2 0.5273 0.7950 0.000 0.680 0.000 0.156 0.164
#> GSM904998 2 0.1830 0.8546 0.000 0.924 0.000 0.068 0.008
#> GSM905000 2 0.0000 0.8615 0.000 1.000 0.000 0.000 0.000
#> GSM905003 2 0.1894 0.8542 0.000 0.920 0.000 0.072 0.008
#> GSM905006 2 0.0000 0.8615 0.000 1.000 0.000 0.000 0.000
#> GSM905008 2 0.1956 0.8528 0.000 0.916 0.000 0.076 0.008
#> GSM905011 2 0.0000 0.8615 0.000 1.000 0.000 0.000 0.000
#> GSM905013 2 0.0162 0.8615 0.000 0.996 0.000 0.004 0.000
#> GSM905016 2 0.5273 0.7950 0.000 0.680 0.000 0.156 0.164
#> GSM905018 2 0.0000 0.8615 0.000 1.000 0.000 0.000 0.000
#> GSM905021 2 0.6155 0.7191 0.000 0.560 0.000 0.228 0.212
#> GSM905025 2 0.5354 0.7914 0.000 0.668 0.000 0.140 0.192
#> GSM905028 2 0.1741 0.8583 0.000 0.936 0.000 0.024 0.040
#> GSM905030 2 0.1485 0.8587 0.000 0.948 0.000 0.020 0.032
#> GSM905033 2 0.5700 0.7821 0.000 0.628 0.000 0.196 0.176
#> GSM905035 2 0.5460 0.7882 0.000 0.656 0.000 0.148 0.196
#> GSM905037 2 0.1386 0.8584 0.000 0.952 0.000 0.016 0.032
#> GSM905039 2 0.5314 0.7922 0.000 0.672 0.000 0.136 0.192
#> GSM905042 2 0.5700 0.7821 0.000 0.628 0.000 0.196 0.176
#> GSM905046 1 0.0000 0.7295 1.000 0.000 0.000 0.000 0.000
#> GSM905065 1 0.1270 0.7262 0.948 0.000 0.000 0.000 0.052
#> GSM905049 4 0.4201 0.9938 0.408 0.000 0.000 0.592 0.000
#> GSM905050 4 0.4201 0.9938 0.408 0.000 0.000 0.592 0.000
#> GSM905064 4 0.4350 0.9926 0.408 0.000 0.000 0.588 0.004
#> GSM905045 4 0.4499 0.9921 0.408 0.000 0.004 0.584 0.004
#> GSM905051 1 0.5137 -0.6660 0.536 0.000 0.000 0.424 0.040
#> GSM905055 1 0.5130 0.5579 0.680 0.000 0.000 0.100 0.220
#> GSM905058 1 0.0693 0.7265 0.980 0.000 0.000 0.008 0.012
#> GSM905053 4 0.4350 0.9926 0.408 0.000 0.000 0.588 0.004
#> GSM905061 4 0.4499 0.9921 0.408 0.000 0.004 0.584 0.004
#> GSM905063 1 0.5024 0.5494 0.692 0.000 0.000 0.096 0.212
#> GSM905054 4 0.4350 0.9926 0.408 0.000 0.000 0.588 0.004
#> GSM905062 4 0.4499 0.9921 0.408 0.000 0.004 0.584 0.004
#> GSM905052 1 0.5137 -0.6660 0.536 0.000 0.000 0.424 0.040
#> GSM905059 1 0.0807 0.7243 0.976 0.000 0.000 0.012 0.012
#> GSM905047 1 0.0162 0.7269 0.996 0.000 0.000 0.004 0.000
#> GSM905066 1 0.1270 0.7262 0.948 0.000 0.000 0.000 0.052
#> GSM905056 1 0.5130 0.5579 0.680 0.000 0.000 0.100 0.220
#> GSM905060 1 0.0807 0.7243 0.976 0.000 0.000 0.012 0.012
#> GSM905048 1 0.0000 0.7295 1.000 0.000 0.000 0.000 0.000
#> GSM905067 1 0.1270 0.7262 0.948 0.000 0.000 0.000 0.052
#> GSM905057 1 0.5130 0.5579 0.680 0.000 0.000 0.100 0.220
#> GSM905068 4 0.4350 0.9929 0.408 0.000 0.004 0.588 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM905004 3 0.2357 0.7306 0.008 0.000 0.908 0.032 0.016 0.036
#> GSM905024 5 0.5511 0.5602 0.192 0.000 0.100 0.000 0.652 0.056
#> GSM905038 3 0.4358 0.1944 0.008 0.000 0.596 0.000 0.380 0.016
#> GSM905043 5 0.5615 0.5608 0.208 0.000 0.100 0.000 0.636 0.056
#> GSM904986 3 0.0146 0.7824 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM904991 5 0.4417 0.3889 0.000 0.000 0.416 0.000 0.556 0.028
#> GSM904994 3 0.0000 0.7833 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM904996 3 0.0000 0.7833 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905007 3 0.4165 0.4049 0.004 0.000 0.676 0.000 0.292 0.028
#> GSM905012 3 0.0000 0.7833 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905022 3 0.0146 0.7824 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM905026 3 0.1610 0.7424 0.000 0.000 0.916 0.000 0.084 0.000
#> GSM905027 3 0.3565 0.4617 0.000 0.000 0.692 0.000 0.304 0.004
#> GSM905031 3 0.1327 0.7539 0.000 0.000 0.936 0.000 0.064 0.000
#> GSM905036 5 0.4312 0.1723 0.004 0.000 0.476 0.000 0.508 0.012
#> GSM905041 5 0.3508 0.5552 0.004 0.000 0.292 0.000 0.704 0.000
#> GSM905044 3 0.1471 0.7536 0.000 0.000 0.932 0.000 0.064 0.004
#> GSM904989 3 0.0862 0.7764 0.008 0.000 0.972 0.000 0.004 0.016
#> GSM904999 3 0.5815 0.3809 0.048 0.000 0.612 0.000 0.204 0.136
#> GSM905002 3 0.0000 0.7833 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905009 3 0.0405 0.7814 0.008 0.000 0.988 0.000 0.000 0.004
#> GSM905014 3 0.4165 0.4049 0.004 0.000 0.676 0.000 0.292 0.028
#> GSM905017 3 0.5815 0.3809 0.048 0.000 0.612 0.000 0.204 0.136
#> GSM905020 3 0.0000 0.7833 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905023 5 0.4313 0.1586 0.004 0.000 0.480 0.000 0.504 0.012
#> GSM905029 3 0.4199 -0.0218 0.004 0.000 0.544 0.000 0.444 0.008
#> GSM905032 5 0.3948 0.5724 0.012 0.000 0.272 0.000 0.704 0.012
#> GSM905034 5 0.5222 0.2626 0.264 0.000 0.004 0.020 0.636 0.076
#> GSM905040 1 0.5775 0.1161 0.468 0.000 0.000 0.020 0.408 0.104
#> GSM904985 2 0.4161 -0.3354 0.004 0.608 0.000 0.000 0.012 0.376
#> GSM904988 2 0.0146 0.6321 0.004 0.996 0.000 0.000 0.000 0.000
#> GSM904990 2 0.0146 0.6321 0.004 0.996 0.000 0.000 0.000 0.000
#> GSM904992 2 0.0436 0.6293 0.004 0.988 0.000 0.000 0.004 0.004
#> GSM904995 2 0.4347 -0.1357 0.012 0.660 0.000 0.000 0.024 0.304
#> GSM904998 2 0.2102 0.5733 0.012 0.908 0.000 0.000 0.012 0.068
#> GSM905000 2 0.0146 0.6321 0.004 0.996 0.000 0.000 0.000 0.000
#> GSM905003 2 0.2467 0.5467 0.012 0.884 0.000 0.000 0.016 0.088
#> GSM905006 2 0.0146 0.6321 0.004 0.996 0.000 0.000 0.000 0.000
#> GSM905008 2 0.2568 0.5357 0.012 0.876 0.000 0.000 0.016 0.096
#> GSM905011 2 0.0146 0.6321 0.004 0.996 0.000 0.000 0.000 0.000
#> GSM905013 2 0.0436 0.6293 0.004 0.988 0.000 0.000 0.004 0.004
#> GSM905016 2 0.4347 -0.1357 0.012 0.660 0.000 0.000 0.024 0.304
#> GSM905018 2 0.0146 0.6321 0.004 0.996 0.000 0.000 0.000 0.000
#> GSM905021 6 0.4924 0.0000 0.020 0.440 0.000 0.000 0.028 0.512
#> GSM905025 2 0.4497 -0.1932 0.012 0.600 0.000 0.000 0.020 0.368
#> GSM905028 2 0.2605 0.5590 0.012 0.876 0.000 0.000 0.020 0.092
#> GSM905030 2 0.1806 0.5823 0.000 0.908 0.000 0.000 0.004 0.088
#> GSM905033 2 0.4366 -0.4246 0.004 0.540 0.000 0.000 0.016 0.440
#> GSM905035 2 0.4528 -0.2291 0.012 0.588 0.000 0.000 0.020 0.380
#> GSM905037 2 0.1866 0.5809 0.000 0.908 0.000 0.000 0.008 0.084
#> GSM905039 2 0.4497 -0.1932 0.012 0.600 0.000 0.000 0.020 0.368
#> GSM905042 2 0.4366 -0.4246 0.004 0.540 0.000 0.000 0.016 0.440
#> GSM905046 1 0.4968 0.7866 0.688 0.000 0.000 0.208 0.044 0.060
#> GSM905065 1 0.3623 0.7873 0.764 0.000 0.000 0.208 0.020 0.008
#> GSM905049 4 0.0000 0.9090 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905050 4 0.0000 0.9090 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905064 4 0.0260 0.9082 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM905045 4 0.0909 0.9052 0.000 0.000 0.000 0.968 0.012 0.020
#> GSM905051 4 0.5717 0.5484 0.144 0.000 0.000 0.644 0.068 0.144
#> GSM905055 1 0.5545 0.6958 0.668 0.000 0.000 0.128 0.080 0.124
#> GSM905058 1 0.5278 0.7826 0.668 0.000 0.000 0.204 0.064 0.064
#> GSM905053 4 0.0363 0.9075 0.000 0.000 0.000 0.988 0.000 0.012
#> GSM905061 4 0.1176 0.9023 0.000 0.000 0.000 0.956 0.020 0.024
#> GSM905063 1 0.5073 0.7202 0.712 0.000 0.000 0.128 0.084 0.076
#> GSM905054 4 0.0363 0.9075 0.000 0.000 0.000 0.988 0.000 0.012
#> GSM905062 4 0.1176 0.9023 0.000 0.000 0.000 0.956 0.020 0.024
#> GSM905052 4 0.5717 0.5484 0.144 0.000 0.000 0.644 0.068 0.144
#> GSM905059 1 0.5278 0.7826 0.668 0.000 0.000 0.204 0.064 0.064
#> GSM905047 1 0.4968 0.7866 0.688 0.000 0.000 0.208 0.044 0.060
#> GSM905066 1 0.3623 0.7873 0.764 0.000 0.000 0.208 0.020 0.008
#> GSM905056 1 0.5545 0.6958 0.668 0.000 0.000 0.128 0.080 0.124
#> GSM905060 1 0.5278 0.7826 0.668 0.000 0.000 0.204 0.064 0.064
#> GSM905048 1 0.4968 0.7866 0.688 0.000 0.000 0.208 0.044 0.060
#> GSM905067 1 0.3623 0.7873 0.764 0.000 0.000 0.208 0.020 0.008
#> GSM905057 1 0.5545 0.6958 0.668 0.000 0.000 0.128 0.080 0.124
#> GSM905068 4 0.0806 0.9053 0.000 0.000 0.000 0.972 0.008 0.020
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) genotype/variation(p) individual(p) k
#> MAD:kmeans 75 3.12e-09 6.64e-03 0.0658 2
#> MAD:kmeans 76 2.85e-20 4.94e-05 0.9774 3
#> MAD:kmeans 74 1.68e-19 2.77e-05 0.9378 4
#> MAD:kmeans 69 2.29e-18 8.80e-11 0.7769 5
#> MAD:kmeans 55 9.35e-13 1.28e-06 0.2975 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 76 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.872 0.956 0.979 0.4993 0.502 0.502
#> 3 3 1.000 0.945 0.980 0.3487 0.740 0.522
#> 4 4 0.862 0.929 0.932 0.1072 0.897 0.698
#> 5 5 0.899 0.826 0.912 0.0604 0.931 0.737
#> 6 6 0.884 0.713 0.873 0.0306 0.978 0.898
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
#> GSM905004 1 0.0000 0.991 1.000 0.000
#> GSM905024 1 0.0000 0.991 1.000 0.000
#> GSM905038 2 0.7602 0.745 0.220 0.780
#> GSM905043 1 0.0000 0.991 1.000 0.000
#> GSM904986 2 0.0000 0.968 0.000 1.000
#> GSM904991 1 0.0376 0.988 0.996 0.004
#> GSM904994 2 0.0000 0.968 0.000 1.000
#> GSM904996 2 0.0000 0.968 0.000 1.000
#> GSM905007 2 0.8327 0.676 0.264 0.736
#> GSM905012 2 0.0000 0.968 0.000 1.000
#> GSM905022 2 0.0000 0.968 0.000 1.000
#> GSM905026 2 0.0000 0.968 0.000 1.000
#> GSM905027 2 0.6623 0.805 0.172 0.828
#> GSM905031 2 0.0000 0.968 0.000 1.000
#> GSM905036 1 0.7815 0.679 0.768 0.232
#> GSM905041 1 0.0000 0.991 1.000 0.000
#> GSM905044 2 0.0000 0.968 0.000 1.000
#> GSM904989 2 0.0000 0.968 0.000 1.000
#> GSM904999 2 0.0000 0.968 0.000 1.000
#> GSM905002 2 0.0000 0.968 0.000 1.000
#> GSM905009 2 0.0000 0.968 0.000 1.000
#> GSM905014 2 0.7219 0.771 0.200 0.800
#> GSM905017 2 0.0000 0.968 0.000 1.000
#> GSM905020 2 0.0000 0.968 0.000 1.000
#> GSM905023 2 0.7602 0.745 0.220 0.780
#> GSM905029 2 0.7602 0.745 0.220 0.780
#> GSM905032 1 0.1843 0.964 0.972 0.028
#> GSM905034 1 0.0000 0.991 1.000 0.000
#> GSM905040 1 0.0000 0.991 1.000 0.000
#> GSM904985 2 0.0000 0.968 0.000 1.000
#> GSM904988 2 0.0000 0.968 0.000 1.000
#> GSM904990 2 0.0000 0.968 0.000 1.000
#> GSM904992 2 0.0000 0.968 0.000 1.000
#> GSM904995 2 0.0000 0.968 0.000 1.000
#> GSM904998 2 0.0000 0.968 0.000 1.000
#> GSM905000 2 0.0000 0.968 0.000 1.000
#> GSM905003 2 0.0000 0.968 0.000 1.000
#> GSM905006 2 0.0000 0.968 0.000 1.000
#> GSM905008 2 0.0000 0.968 0.000 1.000
#> GSM905011 2 0.0000 0.968 0.000 1.000
#> GSM905013 2 0.0000 0.968 0.000 1.000
#> GSM905016 2 0.0000 0.968 0.000 1.000
#> GSM905018 2 0.0000 0.968 0.000 1.000
#> GSM905021 2 0.0000 0.968 0.000 1.000
#> GSM905025 2 0.0000 0.968 0.000 1.000
#> GSM905028 2 0.0000 0.968 0.000 1.000
#> GSM905030 2 0.0000 0.968 0.000 1.000
#> GSM905033 2 0.0000 0.968 0.000 1.000
#> GSM905035 2 0.0000 0.968 0.000 1.000
#> GSM905037 2 0.0000 0.968 0.000 1.000
#> GSM905039 2 0.0000 0.968 0.000 1.000
#> GSM905042 2 0.0000 0.968 0.000 1.000
#> GSM905046 1 0.0000 0.991 1.000 0.000
#> GSM905065 1 0.0000 0.991 1.000 0.000
#> GSM905049 1 0.0000 0.991 1.000 0.000
#> GSM905050 1 0.0000 0.991 1.000 0.000
#> GSM905064 1 0.0000 0.991 1.000 0.000
#> GSM905045 1 0.0000 0.991 1.000 0.000
#> GSM905051 1 0.0000 0.991 1.000 0.000
#> GSM905055 1 0.0000 0.991 1.000 0.000
#> GSM905058 1 0.0000 0.991 1.000 0.000
#> GSM905053 1 0.0000 0.991 1.000 0.000
#> GSM905061 1 0.0000 0.991 1.000 0.000
#> GSM905063 1 0.0000 0.991 1.000 0.000
#> GSM905054 1 0.0000 0.991 1.000 0.000
#> GSM905062 1 0.0000 0.991 1.000 0.000
#> GSM905052 1 0.0000 0.991 1.000 0.000
#> GSM905059 1 0.0000 0.991 1.000 0.000
#> GSM905047 1 0.0000 0.991 1.000 0.000
#> GSM905066 1 0.0000 0.991 1.000 0.000
#> GSM905056 1 0.0000 0.991 1.000 0.000
#> GSM905060 1 0.0000 0.991 1.000 0.000
#> GSM905048 1 0.0000 0.991 1.000 0.000
#> GSM905067 1 0.0000 0.991 1.000 0.000
#> GSM905057 1 0.0000 0.991 1.000 0.000
#> GSM905068 1 0.0000 0.991 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM905004 1 0.623 0.181 0.564 0 0.436
#> GSM905024 3 0.630 0.135 0.472 0 0.528
#> GSM905038 3 0.000 0.955 0.000 0 1.000
#> GSM905043 3 0.630 0.135 0.472 0 0.528
#> GSM904986 3 0.000 0.955 0.000 0 1.000
#> GSM904991 3 0.000 0.955 0.000 0 1.000
#> GSM904994 3 0.000 0.955 0.000 0 1.000
#> GSM904996 3 0.000 0.955 0.000 0 1.000
#> GSM905007 3 0.000 0.955 0.000 0 1.000
#> GSM905012 3 0.000 0.955 0.000 0 1.000
#> GSM905022 3 0.000 0.955 0.000 0 1.000
#> GSM905026 3 0.000 0.955 0.000 0 1.000
#> GSM905027 3 0.000 0.955 0.000 0 1.000
#> GSM905031 3 0.000 0.955 0.000 0 1.000
#> GSM905036 3 0.000 0.955 0.000 0 1.000
#> GSM905041 3 0.000 0.955 0.000 0 1.000
#> GSM905044 3 0.000 0.955 0.000 0 1.000
#> GSM904989 3 0.000 0.955 0.000 0 1.000
#> GSM904999 3 0.000 0.955 0.000 0 1.000
#> GSM905002 3 0.000 0.955 0.000 0 1.000
#> GSM905009 3 0.000 0.955 0.000 0 1.000
#> GSM905014 3 0.000 0.955 0.000 0 1.000
#> GSM905017 3 0.000 0.955 0.000 0 1.000
#> GSM905020 3 0.000 0.955 0.000 0 1.000
#> GSM905023 3 0.000 0.955 0.000 0 1.000
#> GSM905029 3 0.000 0.955 0.000 0 1.000
#> GSM905032 3 0.355 0.821 0.132 0 0.868
#> GSM905034 1 0.000 0.982 1.000 0 0.000
#> GSM905040 1 0.000 0.982 1.000 0 0.000
#> GSM904985 2 0.000 1.000 0.000 1 0.000
#> GSM904988 2 0.000 1.000 0.000 1 0.000
#> GSM904990 2 0.000 1.000 0.000 1 0.000
#> GSM904992 2 0.000 1.000 0.000 1 0.000
#> GSM904995 2 0.000 1.000 0.000 1 0.000
#> GSM904998 2 0.000 1.000 0.000 1 0.000
#> GSM905000 2 0.000 1.000 0.000 1 0.000
#> GSM905003 2 0.000 1.000 0.000 1 0.000
#> GSM905006 2 0.000 1.000 0.000 1 0.000
#> GSM905008 2 0.000 1.000 0.000 1 0.000
#> GSM905011 2 0.000 1.000 0.000 1 0.000
#> GSM905013 2 0.000 1.000 0.000 1 0.000
#> GSM905016 2 0.000 1.000 0.000 1 0.000
#> GSM905018 2 0.000 1.000 0.000 1 0.000
#> GSM905021 2 0.000 1.000 0.000 1 0.000
#> GSM905025 2 0.000 1.000 0.000 1 0.000
#> GSM905028 2 0.000 1.000 0.000 1 0.000
#> GSM905030 2 0.000 1.000 0.000 1 0.000
#> GSM905033 2 0.000 1.000 0.000 1 0.000
#> GSM905035 2 0.000 1.000 0.000 1 0.000
#> GSM905037 2 0.000 1.000 0.000 1 0.000
#> GSM905039 2 0.000 1.000 0.000 1 0.000
#> GSM905042 2 0.000 1.000 0.000 1 0.000
#> GSM905046 1 0.000 0.982 1.000 0 0.000
#> GSM905065 1 0.000 0.982 1.000 0 0.000
#> GSM905049 1 0.000 0.982 1.000 0 0.000
#> GSM905050 1 0.000 0.982 1.000 0 0.000
#> GSM905064 1 0.000 0.982 1.000 0 0.000
#> GSM905045 1 0.000 0.982 1.000 0 0.000
#> GSM905051 1 0.000 0.982 1.000 0 0.000
#> GSM905055 1 0.000 0.982 1.000 0 0.000
#> GSM905058 1 0.000 0.982 1.000 0 0.000
#> GSM905053 1 0.000 0.982 1.000 0 0.000
#> GSM905061 1 0.000 0.982 1.000 0 0.000
#> GSM905063 1 0.000 0.982 1.000 0 0.000
#> GSM905054 1 0.000 0.982 1.000 0 0.000
#> GSM905062 1 0.000 0.982 1.000 0 0.000
#> GSM905052 1 0.000 0.982 1.000 0 0.000
#> GSM905059 1 0.000 0.982 1.000 0 0.000
#> GSM905047 1 0.000 0.982 1.000 0 0.000
#> GSM905066 1 0.000 0.982 1.000 0 0.000
#> GSM905056 1 0.000 0.982 1.000 0 0.000
#> GSM905060 1 0.000 0.982 1.000 0 0.000
#> GSM905048 1 0.000 0.982 1.000 0 0.000
#> GSM905067 1 0.000 0.982 1.000 0 0.000
#> GSM905057 1 0.000 0.982 1.000 0 0.000
#> GSM905068 1 0.000 0.982 1.000 0 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM905004 4 0.3688 0.719 0.000 0 0.208 0.792
#> GSM905024 1 0.0000 0.773 1.000 0 0.000 0.000
#> GSM905038 3 0.1022 0.910 0.032 0 0.968 0.000
#> GSM905043 1 0.0000 0.773 1.000 0 0.000 0.000
#> GSM904986 3 0.0000 0.914 0.000 0 1.000 0.000
#> GSM904991 3 0.3764 0.872 0.216 0 0.784 0.000
#> GSM904994 3 0.0000 0.914 0.000 0 1.000 0.000
#> GSM904996 3 0.0000 0.914 0.000 0 1.000 0.000
#> GSM905007 3 0.3610 0.879 0.200 0 0.800 0.000
#> GSM905012 3 0.0000 0.914 0.000 0 1.000 0.000
#> GSM905022 3 0.0000 0.914 0.000 0 1.000 0.000
#> GSM905026 3 0.0000 0.914 0.000 0 1.000 0.000
#> GSM905027 3 0.2469 0.900 0.108 0 0.892 0.000
#> GSM905031 3 0.0000 0.914 0.000 0 1.000 0.000
#> GSM905036 3 0.3764 0.872 0.216 0 0.784 0.000
#> GSM905041 3 0.3837 0.867 0.224 0 0.776 0.000
#> GSM905044 3 0.0000 0.914 0.000 0 1.000 0.000
#> GSM904989 3 0.0000 0.914 0.000 0 1.000 0.000
#> GSM904999 3 0.3569 0.880 0.196 0 0.804 0.000
#> GSM905002 3 0.0000 0.914 0.000 0 1.000 0.000
#> GSM905009 3 0.0000 0.914 0.000 0 1.000 0.000
#> GSM905014 3 0.3610 0.879 0.200 0 0.800 0.000
#> GSM905017 3 0.3569 0.880 0.196 0 0.804 0.000
#> GSM905020 3 0.0000 0.914 0.000 0 1.000 0.000
#> GSM905023 3 0.3764 0.872 0.216 0 0.784 0.000
#> GSM905029 3 0.3764 0.872 0.216 0 0.784 0.000
#> GSM905032 1 0.1022 0.743 0.968 0 0.032 0.000
#> GSM905034 1 0.0000 0.773 1.000 0 0.000 0.000
#> GSM905040 1 0.0000 0.773 1.000 0 0.000 0.000
#> GSM904985 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM904988 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM904990 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM904992 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM904995 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM904998 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905000 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905003 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905006 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905008 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905011 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905013 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905016 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905018 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905021 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905025 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905028 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905030 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905033 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905035 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905037 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905039 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905042 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM905046 1 0.3837 0.903 0.776 0 0.000 0.224
#> GSM905065 1 0.3837 0.903 0.776 0 0.000 0.224
#> GSM905049 4 0.0000 0.972 0.000 0 0.000 1.000
#> GSM905050 4 0.0000 0.972 0.000 0 0.000 1.000
#> GSM905064 4 0.0000 0.972 0.000 0 0.000 1.000
#> GSM905045 4 0.0000 0.972 0.000 0 0.000 1.000
#> GSM905051 4 0.0188 0.969 0.004 0 0.000 0.996
#> GSM905055 1 0.3764 0.902 0.784 0 0.000 0.216
#> GSM905058 1 0.3837 0.903 0.776 0 0.000 0.224
#> GSM905053 4 0.0000 0.972 0.000 0 0.000 1.000
#> GSM905061 4 0.0000 0.972 0.000 0 0.000 1.000
#> GSM905063 1 0.3764 0.902 0.784 0 0.000 0.216
#> GSM905054 4 0.0000 0.972 0.000 0 0.000 1.000
#> GSM905062 4 0.0000 0.972 0.000 0 0.000 1.000
#> GSM905052 4 0.0188 0.969 0.004 0 0.000 0.996
#> GSM905059 1 0.3837 0.903 0.776 0 0.000 0.224
#> GSM905047 1 0.3837 0.903 0.776 0 0.000 0.224
#> GSM905066 1 0.3837 0.903 0.776 0 0.000 0.224
#> GSM905056 1 0.3764 0.902 0.784 0 0.000 0.216
#> GSM905060 1 0.3837 0.903 0.776 0 0.000 0.224
#> GSM905048 1 0.3837 0.903 0.776 0 0.000 0.224
#> GSM905067 1 0.3837 0.903 0.776 0 0.000 0.224
#> GSM905057 1 0.3764 0.902 0.784 0 0.000 0.216
#> GSM905068 4 0.0000 0.972 0.000 0 0.000 1.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM905004 4 0.2124 0.795 0.000 0.000 0.096 0.900 0.004
#> GSM905024 5 0.3992 0.532 0.268 0.000 0.000 0.012 0.720
#> GSM905038 5 0.3366 0.635 0.000 0.000 0.232 0.000 0.768
#> GSM905043 5 0.4063 0.515 0.280 0.000 0.000 0.012 0.708
#> GSM904986 3 0.0000 0.855 0.000 0.000 1.000 0.000 0.000
#> GSM904991 5 0.3928 0.613 0.000 0.000 0.296 0.004 0.700
#> GSM904994 3 0.0000 0.855 0.000 0.000 1.000 0.000 0.000
#> GSM904996 3 0.0000 0.855 0.000 0.000 1.000 0.000 0.000
#> GSM905007 5 0.4249 0.424 0.000 0.000 0.432 0.000 0.568
#> GSM905012 3 0.0000 0.855 0.000 0.000 1.000 0.000 0.000
#> GSM905022 3 0.0000 0.855 0.000 0.000 1.000 0.000 0.000
#> GSM905026 3 0.3452 0.629 0.000 0.000 0.756 0.000 0.244
#> GSM905027 5 0.3857 0.516 0.000 0.000 0.312 0.000 0.688
#> GSM905031 3 0.3274 0.661 0.000 0.000 0.780 0.000 0.220
#> GSM905036 5 0.1965 0.734 0.000 0.000 0.096 0.000 0.904
#> GSM905041 5 0.1270 0.729 0.000 0.000 0.052 0.000 0.948
#> GSM905044 3 0.3274 0.661 0.000 0.000 0.780 0.000 0.220
#> GSM904989 3 0.0000 0.855 0.000 0.000 1.000 0.000 0.000
#> GSM904999 3 0.4201 0.316 0.000 0.000 0.664 0.008 0.328
#> GSM905002 3 0.0000 0.855 0.000 0.000 1.000 0.000 0.000
#> GSM905009 3 0.0000 0.855 0.000 0.000 1.000 0.000 0.000
#> GSM905014 5 0.4227 0.446 0.000 0.000 0.420 0.000 0.580
#> GSM905017 3 0.4201 0.316 0.000 0.000 0.664 0.008 0.328
#> GSM905020 3 0.0000 0.855 0.000 0.000 1.000 0.000 0.000
#> GSM905023 5 0.2074 0.733 0.000 0.000 0.104 0.000 0.896
#> GSM905029 5 0.2471 0.721 0.000 0.000 0.136 0.000 0.864
#> GSM905032 5 0.2130 0.694 0.080 0.000 0.000 0.012 0.908
#> GSM905034 1 0.4063 0.624 0.708 0.000 0.000 0.012 0.280
#> GSM905040 1 0.3280 0.764 0.812 0.000 0.000 0.012 0.176
#> GSM904985 2 0.0290 0.992 0.000 0.992 0.000 0.000 0.008
#> GSM904988 2 0.0000 0.993 0.000 1.000 0.000 0.000 0.000
#> GSM904990 2 0.0000 0.993 0.000 1.000 0.000 0.000 0.000
#> GSM904992 2 0.0000 0.993 0.000 1.000 0.000 0.000 0.000
#> GSM904995 2 0.0290 0.992 0.000 0.992 0.000 0.000 0.008
#> GSM904998 2 0.0000 0.993 0.000 1.000 0.000 0.000 0.000
#> GSM905000 2 0.0000 0.993 0.000 1.000 0.000 0.000 0.000
#> GSM905003 2 0.0000 0.993 0.000 1.000 0.000 0.000 0.000
#> GSM905006 2 0.0000 0.993 0.000 1.000 0.000 0.000 0.000
#> GSM905008 2 0.0000 0.993 0.000 1.000 0.000 0.000 0.000
#> GSM905011 2 0.0000 0.993 0.000 1.000 0.000 0.000 0.000
#> GSM905013 2 0.0000 0.993 0.000 1.000 0.000 0.000 0.000
#> GSM905016 2 0.0290 0.992 0.000 0.992 0.000 0.000 0.008
#> GSM905018 2 0.0000 0.993 0.000 1.000 0.000 0.000 0.000
#> GSM905021 2 0.0798 0.984 0.000 0.976 0.000 0.008 0.016
#> GSM905025 2 0.0703 0.988 0.000 0.976 0.000 0.000 0.024
#> GSM905028 2 0.0404 0.991 0.000 0.988 0.000 0.000 0.012
#> GSM905030 2 0.0404 0.991 0.000 0.988 0.000 0.000 0.012
#> GSM905033 2 0.0703 0.988 0.000 0.976 0.000 0.000 0.024
#> GSM905035 2 0.0703 0.988 0.000 0.976 0.000 0.000 0.024
#> GSM905037 2 0.0404 0.991 0.000 0.988 0.000 0.000 0.012
#> GSM905039 2 0.0703 0.988 0.000 0.976 0.000 0.000 0.024
#> GSM905042 2 0.0703 0.988 0.000 0.976 0.000 0.000 0.024
#> GSM905046 1 0.1282 0.930 0.952 0.000 0.000 0.044 0.004
#> GSM905065 1 0.1121 0.931 0.956 0.000 0.000 0.044 0.000
#> GSM905049 4 0.0609 0.888 0.020 0.000 0.000 0.980 0.000
#> GSM905050 4 0.0609 0.888 0.020 0.000 0.000 0.980 0.000
#> GSM905064 4 0.0609 0.888 0.020 0.000 0.000 0.980 0.000
#> GSM905045 4 0.0771 0.888 0.020 0.000 0.000 0.976 0.004
#> GSM905051 4 0.4562 0.104 0.492 0.000 0.000 0.500 0.008
#> GSM905055 1 0.1121 0.906 0.956 0.000 0.000 0.000 0.044
#> GSM905058 1 0.1282 0.930 0.952 0.000 0.000 0.044 0.004
#> GSM905053 4 0.0609 0.888 0.020 0.000 0.000 0.980 0.000
#> GSM905061 4 0.0771 0.888 0.020 0.000 0.000 0.976 0.004
#> GSM905063 1 0.0963 0.909 0.964 0.000 0.000 0.000 0.036
#> GSM905054 4 0.0609 0.888 0.020 0.000 0.000 0.980 0.000
#> GSM905062 4 0.0771 0.888 0.020 0.000 0.000 0.976 0.004
#> GSM905052 4 0.4562 0.104 0.492 0.000 0.000 0.500 0.008
#> GSM905059 1 0.1357 0.929 0.948 0.000 0.000 0.048 0.004
#> GSM905047 1 0.1357 0.929 0.948 0.000 0.000 0.048 0.004
#> GSM905066 1 0.1121 0.931 0.956 0.000 0.000 0.044 0.000
#> GSM905056 1 0.1121 0.906 0.956 0.000 0.000 0.000 0.044
#> GSM905060 1 0.1357 0.929 0.948 0.000 0.000 0.048 0.004
#> GSM905048 1 0.1121 0.931 0.956 0.000 0.000 0.044 0.000
#> GSM905067 1 0.1121 0.931 0.956 0.000 0.000 0.044 0.000
#> GSM905057 1 0.1121 0.906 0.956 0.000 0.000 0.000 0.044
#> GSM905068 4 0.0771 0.888 0.020 0.000 0.000 0.976 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM905004 4 0.1829 0.918 0.000 0.000 0.056 0.920 0.000 0.024
#> GSM905024 5 0.5354 0.271 0.160 0.000 0.000 0.000 0.580 0.260
#> GSM905038 5 0.1757 0.658 0.000 0.000 0.076 0.000 0.916 0.008
#> GSM905043 5 0.5411 0.252 0.168 0.000 0.000 0.000 0.572 0.260
#> GSM904986 3 0.0458 0.811 0.000 0.000 0.984 0.000 0.000 0.016
#> GSM904991 5 0.4801 0.582 0.000 0.000 0.196 0.000 0.668 0.136
#> GSM904994 3 0.0000 0.814 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM904996 3 0.0000 0.814 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905007 5 0.4828 0.494 0.000 0.000 0.320 0.000 0.604 0.076
#> GSM905012 3 0.0000 0.814 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905022 3 0.0806 0.807 0.000 0.000 0.972 0.000 0.008 0.020
#> GSM905026 3 0.4300 0.516 0.000 0.000 0.640 0.000 0.324 0.036
#> GSM905027 5 0.3456 0.560 0.000 0.000 0.172 0.000 0.788 0.040
#> GSM905031 3 0.4087 0.575 0.000 0.000 0.688 0.000 0.276 0.036
#> GSM905036 5 0.1245 0.670 0.000 0.000 0.016 0.000 0.952 0.032
#> GSM905041 5 0.2191 0.641 0.000 0.000 0.004 0.000 0.876 0.120
#> GSM905044 3 0.4146 0.565 0.000 0.000 0.676 0.000 0.288 0.036
#> GSM904989 3 0.0260 0.812 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM904999 3 0.5951 0.126 0.000 0.000 0.456 0.000 0.272 0.272
#> GSM905002 3 0.0146 0.814 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM905009 3 0.0260 0.812 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM905014 5 0.4798 0.504 0.000 0.000 0.312 0.000 0.612 0.076
#> GSM905017 3 0.5951 0.126 0.000 0.000 0.456 0.000 0.272 0.272
#> GSM905020 3 0.0000 0.814 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905023 5 0.0777 0.671 0.000 0.000 0.024 0.000 0.972 0.004
#> GSM905029 5 0.1333 0.670 0.000 0.000 0.048 0.000 0.944 0.008
#> GSM905032 5 0.5587 0.319 0.240 0.000 0.000 0.000 0.548 0.212
#> GSM905034 6 0.5870 0.000 0.364 0.000 0.000 0.000 0.200 0.436
#> GSM905040 1 0.4044 -0.391 0.744 0.000 0.000 0.000 0.076 0.180
#> GSM904985 2 0.1267 0.949 0.000 0.940 0.000 0.000 0.000 0.060
#> GSM904988 2 0.0000 0.961 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM904990 2 0.0000 0.961 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM904992 2 0.0000 0.961 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM904995 2 0.1267 0.949 0.000 0.940 0.000 0.000 0.000 0.060
#> GSM904998 2 0.0000 0.961 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905000 2 0.0000 0.961 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905003 2 0.0146 0.961 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM905006 2 0.0000 0.961 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905008 2 0.0000 0.961 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905011 2 0.0000 0.961 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905013 2 0.0000 0.961 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905016 2 0.1267 0.949 0.000 0.940 0.000 0.000 0.000 0.060
#> GSM905018 2 0.0000 0.961 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905021 2 0.3244 0.752 0.000 0.732 0.000 0.000 0.000 0.268
#> GSM905025 2 0.1806 0.942 0.000 0.908 0.000 0.000 0.004 0.088
#> GSM905028 2 0.0935 0.955 0.000 0.964 0.000 0.000 0.004 0.032
#> GSM905030 2 0.0858 0.955 0.000 0.968 0.000 0.000 0.004 0.028
#> GSM905033 2 0.1958 0.937 0.000 0.896 0.000 0.000 0.004 0.100
#> GSM905035 2 0.1858 0.940 0.000 0.904 0.000 0.000 0.004 0.092
#> GSM905037 2 0.0858 0.955 0.000 0.968 0.000 0.000 0.004 0.028
#> GSM905039 2 0.1806 0.942 0.000 0.908 0.000 0.000 0.004 0.088
#> GSM905042 2 0.1958 0.937 0.000 0.896 0.000 0.000 0.004 0.100
#> GSM905046 1 0.3728 0.632 0.652 0.000 0.000 0.004 0.000 0.344
#> GSM905065 1 0.3668 0.631 0.668 0.000 0.000 0.004 0.000 0.328
#> GSM905049 4 0.0000 0.991 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905050 4 0.0000 0.991 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905064 4 0.0000 0.991 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905045 4 0.0000 0.991 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905051 1 0.5982 0.289 0.428 0.000 0.000 0.240 0.000 0.332
#> GSM905055 1 0.0520 0.319 0.984 0.000 0.000 0.000 0.008 0.008
#> GSM905058 1 0.3807 0.621 0.628 0.000 0.000 0.004 0.000 0.368
#> GSM905053 4 0.0000 0.991 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905061 4 0.0000 0.991 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905063 1 0.0146 0.330 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM905054 4 0.0000 0.991 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905062 4 0.0000 0.991 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905052 1 0.5982 0.289 0.428 0.000 0.000 0.240 0.000 0.332
#> GSM905059 1 0.3807 0.621 0.628 0.000 0.000 0.004 0.000 0.368
#> GSM905047 1 0.3742 0.631 0.648 0.000 0.000 0.004 0.000 0.348
#> GSM905066 1 0.3668 0.631 0.668 0.000 0.000 0.004 0.000 0.328
#> GSM905056 1 0.0520 0.319 0.984 0.000 0.000 0.000 0.008 0.008
#> GSM905060 1 0.3807 0.621 0.628 0.000 0.000 0.004 0.000 0.368
#> GSM905048 1 0.3728 0.632 0.652 0.000 0.000 0.004 0.000 0.344
#> GSM905067 1 0.3668 0.631 0.668 0.000 0.000 0.004 0.000 0.328
#> GSM905057 1 0.0520 0.319 0.984 0.000 0.000 0.000 0.008 0.008
#> GSM905068 4 0.0000 0.991 0.000 0.000 0.000 1.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) genotype/variation(p) individual(p) k
#> MAD:skmeans 76 1.95e-07 1.24e-03 0.0373 2
#> MAD:skmeans 73 4.09e-19 1.27e-05 0.9240 3
#> MAD:skmeans 76 2.32e-19 1.01e-09 0.1977 4
#> MAD:skmeans 70 1.75e-15 6.17e-09 0.5000 5
#> MAD:skmeans 62 1.16e-16 2.11e-10 0.4077 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 76 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 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.991 0.996 0.4845 0.516 0.516
#> 3 3 1.000 0.991 0.996 0.3900 0.779 0.584
#> 4 4 1.000 0.988 0.995 0.0964 0.934 0.799
#> 5 5 0.993 0.969 0.984 0.0281 0.982 0.930
#> 6 6 0.908 0.844 0.919 0.0484 0.960 0.839
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2 3 4 5
There is also optional best \(k\) = 2 3 4 5 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
#> GSM905004 2 0.204 0.965 0.032 0.968
#> GSM905024 1 0.000 0.994 1.000 0.000
#> GSM905038 2 0.000 0.996 0.000 1.000
#> GSM905043 1 0.000 0.994 1.000 0.000
#> GSM904986 2 0.000 0.996 0.000 1.000
#> GSM904991 1 0.653 0.796 0.832 0.168
#> GSM904994 2 0.000 0.996 0.000 1.000
#> GSM904996 2 0.000 0.996 0.000 1.000
#> GSM905007 2 0.000 0.996 0.000 1.000
#> GSM905012 2 0.000 0.996 0.000 1.000
#> GSM905022 2 0.000 0.996 0.000 1.000
#> GSM905026 2 0.000 0.996 0.000 1.000
#> GSM905027 2 0.000 0.996 0.000 1.000
#> GSM905031 2 0.000 0.996 0.000 1.000
#> GSM905036 2 0.541 0.858 0.124 0.876
#> GSM905041 1 0.000 0.994 1.000 0.000
#> GSM905044 2 0.000 0.996 0.000 1.000
#> GSM904989 2 0.000 0.996 0.000 1.000
#> GSM904999 2 0.000 0.996 0.000 1.000
#> GSM905002 2 0.000 0.996 0.000 1.000
#> GSM905009 2 0.000 0.996 0.000 1.000
#> GSM905014 2 0.000 0.996 0.000 1.000
#> GSM905017 2 0.000 0.996 0.000 1.000
#> GSM905020 2 0.000 0.996 0.000 1.000
#> GSM905023 2 0.000 0.996 0.000 1.000
#> GSM905029 2 0.000 0.996 0.000 1.000
#> GSM905032 2 0.000 0.996 0.000 1.000
#> GSM905034 1 0.000 0.994 1.000 0.000
#> GSM905040 1 0.000 0.994 1.000 0.000
#> GSM904985 2 0.000 0.996 0.000 1.000
#> GSM904988 2 0.000 0.996 0.000 1.000
#> GSM904990 2 0.000 0.996 0.000 1.000
#> GSM904992 2 0.000 0.996 0.000 1.000
#> GSM904995 2 0.000 0.996 0.000 1.000
#> GSM904998 2 0.000 0.996 0.000 1.000
#> GSM905000 2 0.000 0.996 0.000 1.000
#> GSM905003 2 0.000 0.996 0.000 1.000
#> GSM905006 2 0.000 0.996 0.000 1.000
#> GSM905008 2 0.000 0.996 0.000 1.000
#> GSM905011 2 0.000 0.996 0.000 1.000
#> GSM905013 2 0.000 0.996 0.000 1.000
#> GSM905016 2 0.000 0.996 0.000 1.000
#> GSM905018 2 0.000 0.996 0.000 1.000
#> GSM905021 2 0.000 0.996 0.000 1.000
#> GSM905025 2 0.000 0.996 0.000 1.000
#> GSM905028 2 0.000 0.996 0.000 1.000
#> GSM905030 2 0.000 0.996 0.000 1.000
#> GSM905033 2 0.000 0.996 0.000 1.000
#> GSM905035 2 0.000 0.996 0.000 1.000
#> GSM905037 2 0.000 0.996 0.000 1.000
#> GSM905039 2 0.000 0.996 0.000 1.000
#> GSM905042 2 0.000 0.996 0.000 1.000
#> GSM905046 1 0.000 0.994 1.000 0.000
#> GSM905065 1 0.000 0.994 1.000 0.000
#> GSM905049 1 0.000 0.994 1.000 0.000
#> GSM905050 1 0.000 0.994 1.000 0.000
#> GSM905064 1 0.000 0.994 1.000 0.000
#> GSM905045 1 0.000 0.994 1.000 0.000
#> GSM905051 1 0.000 0.994 1.000 0.000
#> GSM905055 1 0.000 0.994 1.000 0.000
#> GSM905058 1 0.000 0.994 1.000 0.000
#> GSM905053 1 0.000 0.994 1.000 0.000
#> GSM905061 1 0.000 0.994 1.000 0.000
#> GSM905063 1 0.000 0.994 1.000 0.000
#> GSM905054 1 0.000 0.994 1.000 0.000
#> GSM905062 1 0.000 0.994 1.000 0.000
#> GSM905052 1 0.000 0.994 1.000 0.000
#> GSM905059 1 0.000 0.994 1.000 0.000
#> GSM905047 1 0.000 0.994 1.000 0.000
#> GSM905066 1 0.000 0.994 1.000 0.000
#> GSM905056 1 0.000 0.994 1.000 0.000
#> GSM905060 1 0.000 0.994 1.000 0.000
#> GSM905048 1 0.000 0.994 1.000 0.000
#> GSM905067 1 0.000 0.994 1.000 0.000
#> GSM905057 1 0.000 0.994 1.000 0.000
#> GSM905068 1 0.000 0.994 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM905004 3 0.0000 1.000 0.000 0.000 1.000
#> GSM905024 1 0.0424 0.989 0.992 0.000 0.008
#> GSM905038 3 0.0000 1.000 0.000 0.000 1.000
#> GSM905043 1 0.2878 0.895 0.904 0.000 0.096
#> GSM904986 3 0.0000 1.000 0.000 0.000 1.000
#> GSM904991 3 0.0000 1.000 0.000 0.000 1.000
#> GSM904994 3 0.0000 1.000 0.000 0.000 1.000
#> GSM904996 3 0.0000 1.000 0.000 0.000 1.000
#> GSM905007 3 0.0000 1.000 0.000 0.000 1.000
#> GSM905012 3 0.0000 1.000 0.000 0.000 1.000
#> GSM905022 3 0.0000 1.000 0.000 0.000 1.000
#> GSM905026 3 0.0000 1.000 0.000 0.000 1.000
#> GSM905027 3 0.0000 1.000 0.000 0.000 1.000
#> GSM905031 3 0.0000 1.000 0.000 0.000 1.000
#> GSM905036 3 0.0000 1.000 0.000 0.000 1.000
#> GSM905041 3 0.0000 1.000 0.000 0.000 1.000
#> GSM905044 3 0.0000 1.000 0.000 0.000 1.000
#> GSM904989 3 0.0000 1.000 0.000 0.000 1.000
#> GSM904999 3 0.0000 1.000 0.000 0.000 1.000
#> GSM905002 3 0.0000 1.000 0.000 0.000 1.000
#> GSM905009 3 0.0000 1.000 0.000 0.000 1.000
#> GSM905014 3 0.0000 1.000 0.000 0.000 1.000
#> GSM905017 3 0.0000 1.000 0.000 0.000 1.000
#> GSM905020 3 0.0000 1.000 0.000 0.000 1.000
#> GSM905023 3 0.0000 1.000 0.000 0.000 1.000
#> GSM905029 3 0.0000 1.000 0.000 0.000 1.000
#> GSM905032 3 0.0000 1.000 0.000 0.000 1.000
#> GSM905034 1 0.0000 0.996 1.000 0.000 0.000
#> GSM905040 1 0.0237 0.993 0.996 0.000 0.004
#> GSM904985 2 0.0000 0.991 0.000 1.000 0.000
#> GSM904988 2 0.0000 0.991 0.000 1.000 0.000
#> GSM904990 2 0.0000 0.991 0.000 1.000 0.000
#> GSM904992 2 0.0000 0.991 0.000 1.000 0.000
#> GSM904995 2 0.0000 0.991 0.000 1.000 0.000
#> GSM904998 2 0.0000 0.991 0.000 1.000 0.000
#> GSM905000 2 0.0000 0.991 0.000 1.000 0.000
#> GSM905003 2 0.0000 0.991 0.000 1.000 0.000
#> GSM905006 2 0.0000 0.991 0.000 1.000 0.000
#> GSM905008 2 0.0000 0.991 0.000 1.000 0.000
#> GSM905011 2 0.0000 0.991 0.000 1.000 0.000
#> GSM905013 2 0.0000 0.991 0.000 1.000 0.000
#> GSM905016 2 0.0000 0.991 0.000 1.000 0.000
#> GSM905018 2 0.0000 0.991 0.000 1.000 0.000
#> GSM905021 2 0.4504 0.756 0.000 0.804 0.196
#> GSM905025 2 0.0000 0.991 0.000 1.000 0.000
#> GSM905028 2 0.0000 0.991 0.000 1.000 0.000
#> GSM905030 2 0.0000 0.991 0.000 1.000 0.000
#> GSM905033 2 0.0000 0.991 0.000 1.000 0.000
#> GSM905035 2 0.0000 0.991 0.000 1.000 0.000
#> GSM905037 2 0.0000 0.991 0.000 1.000 0.000
#> GSM905039 2 0.0000 0.991 0.000 1.000 0.000
#> GSM905042 2 0.0000 0.991 0.000 1.000 0.000
#> GSM905046 1 0.0000 0.996 1.000 0.000 0.000
#> GSM905065 1 0.0000 0.996 1.000 0.000 0.000
#> GSM905049 1 0.0000 0.996 1.000 0.000 0.000
#> GSM905050 1 0.0000 0.996 1.000 0.000 0.000
#> GSM905064 1 0.0000 0.996 1.000 0.000 0.000
#> GSM905045 1 0.0000 0.996 1.000 0.000 0.000
#> GSM905051 1 0.0000 0.996 1.000 0.000 0.000
#> GSM905055 1 0.0000 0.996 1.000 0.000 0.000
#> GSM905058 1 0.0000 0.996 1.000 0.000 0.000
#> GSM905053 1 0.0000 0.996 1.000 0.000 0.000
#> GSM905061 1 0.0000 0.996 1.000 0.000 0.000
#> GSM905063 1 0.0000 0.996 1.000 0.000 0.000
#> GSM905054 1 0.0000 0.996 1.000 0.000 0.000
#> GSM905062 1 0.0000 0.996 1.000 0.000 0.000
#> GSM905052 1 0.0000 0.996 1.000 0.000 0.000
#> GSM905059 1 0.0000 0.996 1.000 0.000 0.000
#> GSM905047 1 0.0000 0.996 1.000 0.000 0.000
#> GSM905066 1 0.0000 0.996 1.000 0.000 0.000
#> GSM905056 1 0.0000 0.996 1.000 0.000 0.000
#> GSM905060 1 0.0000 0.996 1.000 0.000 0.000
#> GSM905048 1 0.0000 0.996 1.000 0.000 0.000
#> GSM905067 1 0.0000 0.996 1.000 0.000 0.000
#> GSM905057 1 0.0000 0.996 1.000 0.000 0.000
#> GSM905068 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
#> GSM905004 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM905024 1 0.0469 0.981 0.988 0.000 0.012 0.000
#> GSM905038 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM905043 1 0.2281 0.878 0.904 0.000 0.096 0.000
#> GSM904986 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM904991 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM904994 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM904996 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM905007 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM905012 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM905022 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM905026 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM905027 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM905031 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM905036 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM905041 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM905044 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM904989 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM904999 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM905002 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM905009 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM905014 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM905017 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM905020 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM905023 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM905029 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM905032 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM905034 1 0.0188 0.988 0.996 0.000 0.004 0.000
#> GSM905040 1 0.0336 0.985 0.992 0.000 0.008 0.000
#> GSM904985 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM904988 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM904990 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM904992 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM904995 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM904998 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM905000 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM905003 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM905006 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM905008 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM905011 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM905013 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM905016 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM905018 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM905021 2 0.3569 0.738 0.000 0.804 0.196 0.000
#> GSM905025 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM905028 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM905030 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM905033 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM905035 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM905037 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM905039 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM905042 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM905046 1 0.0000 0.991 1.000 0.000 0.000 0.000
#> GSM905065 1 0.0000 0.991 1.000 0.000 0.000 0.000
#> GSM905049 4 0.0000 0.992 0.000 0.000 0.000 1.000
#> GSM905050 4 0.0000 0.992 0.000 0.000 0.000 1.000
#> GSM905064 4 0.0000 0.992 0.000 0.000 0.000 1.000
#> GSM905045 4 0.0000 0.992 0.000 0.000 0.000 1.000
#> GSM905051 4 0.1792 0.928 0.068 0.000 0.000 0.932
#> GSM905055 1 0.0000 0.991 1.000 0.000 0.000 0.000
#> GSM905058 1 0.0000 0.991 1.000 0.000 0.000 0.000
#> GSM905053 4 0.0000 0.992 0.000 0.000 0.000 1.000
#> GSM905061 4 0.0000 0.992 0.000 0.000 0.000 1.000
#> GSM905063 1 0.0000 0.991 1.000 0.000 0.000 0.000
#> GSM905054 4 0.0000 0.992 0.000 0.000 0.000 1.000
#> GSM905062 4 0.0000 0.992 0.000 0.000 0.000 1.000
#> GSM905052 4 0.0336 0.987 0.008 0.000 0.000 0.992
#> GSM905059 1 0.0000 0.991 1.000 0.000 0.000 0.000
#> GSM905047 1 0.0000 0.991 1.000 0.000 0.000 0.000
#> GSM905066 1 0.0000 0.991 1.000 0.000 0.000 0.000
#> GSM905056 1 0.0000 0.991 1.000 0.000 0.000 0.000
#> GSM905060 1 0.0000 0.991 1.000 0.000 0.000 0.000
#> GSM905048 1 0.0000 0.991 1.000 0.000 0.000 0.000
#> GSM905067 1 0.0000 0.991 1.000 0.000 0.000 0.000
#> GSM905057 1 0.0000 0.991 1.000 0.000 0.000 0.000
#> GSM905068 4 0.0000 0.992 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
#> GSM905004 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000
#> GSM905024 1 0.1892 0.902 0.916 0.000 0.004 0.000 0.080
#> GSM905038 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000
#> GSM905043 1 0.2754 0.865 0.880 0.000 0.040 0.000 0.080
#> GSM904986 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000
#> GSM904991 3 0.1732 0.924 0.000 0.000 0.920 0.000 0.080
#> GSM904994 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000
#> GSM904996 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000
#> GSM905007 3 0.0290 0.984 0.000 0.000 0.992 0.000 0.008
#> GSM905012 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000
#> GSM905022 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000
#> GSM905026 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000
#> GSM905027 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000
#> GSM905031 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000
#> GSM905036 3 0.0290 0.984 0.000 0.000 0.992 0.000 0.008
#> GSM905041 3 0.1732 0.924 0.000 0.000 0.920 0.000 0.080
#> GSM905044 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000
#> GSM904989 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000
#> GSM904999 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000
#> GSM905002 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000
#> GSM905009 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000
#> GSM905014 3 0.0290 0.984 0.000 0.000 0.992 0.000 0.008
#> GSM905017 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000
#> GSM905020 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000
#> GSM905023 3 0.0290 0.984 0.000 0.000 0.992 0.000 0.008
#> GSM905029 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000
#> GSM905032 3 0.2020 0.905 0.000 0.000 0.900 0.000 0.100
#> GSM905034 1 0.1732 0.904 0.920 0.000 0.000 0.000 0.080
#> GSM905040 5 0.0000 0.904 0.000 0.000 0.000 0.000 1.000
#> GSM904985 2 0.0000 0.988 0.000 1.000 0.000 0.000 0.000
#> GSM904988 2 0.0000 0.988 0.000 1.000 0.000 0.000 0.000
#> GSM904990 2 0.0000 0.988 0.000 1.000 0.000 0.000 0.000
#> GSM904992 2 0.0000 0.988 0.000 1.000 0.000 0.000 0.000
#> GSM904995 2 0.0000 0.988 0.000 1.000 0.000 0.000 0.000
#> GSM904998 2 0.0000 0.988 0.000 1.000 0.000 0.000 0.000
#> GSM905000 2 0.0000 0.988 0.000 1.000 0.000 0.000 0.000
#> GSM905003 2 0.0000 0.988 0.000 1.000 0.000 0.000 0.000
#> GSM905006 2 0.0000 0.988 0.000 1.000 0.000 0.000 0.000
#> GSM905008 2 0.0000 0.988 0.000 1.000 0.000 0.000 0.000
#> GSM905011 2 0.0000 0.988 0.000 1.000 0.000 0.000 0.000
#> GSM905013 2 0.0000 0.988 0.000 1.000 0.000 0.000 0.000
#> GSM905016 2 0.0000 0.988 0.000 1.000 0.000 0.000 0.000
#> GSM905018 2 0.0000 0.988 0.000 1.000 0.000 0.000 0.000
#> GSM905021 2 0.3039 0.703 0.000 0.808 0.192 0.000 0.000
#> GSM905025 2 0.0000 0.988 0.000 1.000 0.000 0.000 0.000
#> GSM905028 2 0.0000 0.988 0.000 1.000 0.000 0.000 0.000
#> GSM905030 2 0.0000 0.988 0.000 1.000 0.000 0.000 0.000
#> GSM905033 2 0.0000 0.988 0.000 1.000 0.000 0.000 0.000
#> GSM905035 2 0.0000 0.988 0.000 1.000 0.000 0.000 0.000
#> GSM905037 2 0.0000 0.988 0.000 1.000 0.000 0.000 0.000
#> GSM905039 2 0.0000 0.988 0.000 1.000 0.000 0.000 0.000
#> GSM905042 2 0.0000 0.988 0.000 1.000 0.000 0.000 0.000
#> GSM905046 1 0.0000 0.957 1.000 0.000 0.000 0.000 0.000
#> GSM905065 1 0.0000 0.957 1.000 0.000 0.000 0.000 0.000
#> GSM905049 4 0.0000 0.991 0.000 0.000 0.000 1.000 0.000
#> GSM905050 4 0.0000 0.991 0.000 0.000 0.000 1.000 0.000
#> GSM905064 4 0.0000 0.991 0.000 0.000 0.000 1.000 0.000
#> GSM905045 4 0.0000 0.991 0.000 0.000 0.000 1.000 0.000
#> GSM905051 4 0.1478 0.916 0.064 0.000 0.000 0.936 0.000
#> GSM905055 5 0.1732 0.967 0.080 0.000 0.000 0.000 0.920
#> GSM905058 1 0.0000 0.957 1.000 0.000 0.000 0.000 0.000
#> GSM905053 4 0.0000 0.991 0.000 0.000 0.000 1.000 0.000
#> GSM905061 4 0.0000 0.991 0.000 0.000 0.000 1.000 0.000
#> GSM905063 1 0.2813 0.779 0.832 0.000 0.000 0.000 0.168
#> GSM905054 4 0.0000 0.991 0.000 0.000 0.000 1.000 0.000
#> GSM905062 4 0.0000 0.991 0.000 0.000 0.000 1.000 0.000
#> GSM905052 4 0.0162 0.988 0.004 0.000 0.000 0.996 0.000
#> GSM905059 1 0.0000 0.957 1.000 0.000 0.000 0.000 0.000
#> GSM905047 1 0.0000 0.957 1.000 0.000 0.000 0.000 0.000
#> GSM905066 1 0.0000 0.957 1.000 0.000 0.000 0.000 0.000
#> GSM905056 5 0.1732 0.967 0.080 0.000 0.000 0.000 0.920
#> GSM905060 1 0.0000 0.957 1.000 0.000 0.000 0.000 0.000
#> GSM905048 1 0.0000 0.957 1.000 0.000 0.000 0.000 0.000
#> GSM905067 1 0.0000 0.957 1.000 0.000 0.000 0.000 0.000
#> GSM905057 5 0.1732 0.967 0.080 0.000 0.000 0.000 0.920
#> GSM905068 4 0.0000 0.991 0.000 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM905004 3 0.0000 0.822 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905024 5 0.4333 0.404 0.376 0.000 0.028 0.000 0.596 0.000
#> GSM905038 3 0.3578 0.643 0.000 0.000 0.660 0.000 0.340 0.000
#> GSM905043 5 0.3330 0.546 0.284 0.000 0.000 0.000 0.716 0.000
#> GSM904986 3 0.0000 0.822 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM904991 5 0.3828 0.309 0.000 0.000 0.440 0.000 0.560 0.000
#> GSM904994 3 0.0000 0.822 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM904996 3 0.0000 0.822 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905007 3 0.0458 0.812 0.000 0.000 0.984 0.000 0.016 0.000
#> GSM905012 3 0.0000 0.822 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905022 3 0.0000 0.822 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905026 3 0.3578 0.643 0.000 0.000 0.660 0.000 0.340 0.000
#> GSM905027 3 0.3774 0.569 0.000 0.000 0.592 0.000 0.408 0.000
#> GSM905031 3 0.3578 0.643 0.000 0.000 0.660 0.000 0.340 0.000
#> GSM905036 3 0.3851 0.493 0.000 0.000 0.540 0.000 0.460 0.000
#> GSM905041 5 0.1814 0.516 0.000 0.000 0.100 0.000 0.900 0.000
#> GSM905044 3 0.3578 0.643 0.000 0.000 0.660 0.000 0.340 0.000
#> GSM904989 3 0.0000 0.822 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM904999 3 0.0000 0.822 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905002 3 0.0000 0.822 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905009 3 0.0000 0.822 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905014 3 0.0458 0.812 0.000 0.000 0.984 0.000 0.016 0.000
#> GSM905017 3 0.0000 0.822 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905020 3 0.0000 0.822 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905023 3 0.3860 0.469 0.000 0.000 0.528 0.000 0.472 0.000
#> GSM905029 3 0.3774 0.569 0.000 0.000 0.592 0.000 0.408 0.000
#> GSM905032 5 0.1970 0.517 0.000 0.000 0.092 0.000 0.900 0.008
#> GSM905034 5 0.3578 0.367 0.340 0.000 0.000 0.000 0.660 0.000
#> GSM905040 5 0.3774 0.130 0.000 0.000 0.000 0.000 0.592 0.408
#> GSM904985 2 0.0000 0.988 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM904988 2 0.0000 0.988 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM904990 2 0.0000 0.988 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM904992 2 0.0000 0.988 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM904995 2 0.0000 0.988 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM904998 2 0.0000 0.988 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905000 2 0.0000 0.988 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905003 2 0.0000 0.988 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905006 2 0.0000 0.988 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905008 2 0.0000 0.988 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905011 2 0.0000 0.988 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905013 2 0.0000 0.988 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905016 2 0.0000 0.988 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905018 2 0.0000 0.988 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905021 2 0.2823 0.711 0.000 0.796 0.204 0.000 0.000 0.000
#> GSM905025 2 0.0000 0.988 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905028 2 0.0000 0.988 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905030 2 0.0000 0.988 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905033 2 0.0000 0.988 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905035 2 0.0000 0.988 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905037 2 0.0000 0.988 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905039 2 0.0000 0.988 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905042 2 0.0547 0.968 0.000 0.980 0.000 0.000 0.020 0.000
#> GSM905046 1 0.0000 0.928 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM905065 1 0.0000 0.928 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM905049 4 0.0000 0.990 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905050 4 0.0000 0.990 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905064 4 0.0000 0.990 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905045 4 0.0000 0.990 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905051 4 0.1471 0.916 0.064 0.000 0.000 0.932 0.004 0.000
#> GSM905055 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM905058 1 0.1814 0.907 0.900 0.000 0.000 0.000 0.100 0.000
#> GSM905053 4 0.0000 0.990 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905061 4 0.0000 0.990 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905063 1 0.3766 0.679 0.736 0.000 0.000 0.000 0.032 0.232
#> GSM905054 4 0.0000 0.990 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905062 4 0.0000 0.990 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905052 4 0.0405 0.981 0.008 0.000 0.000 0.988 0.004 0.000
#> GSM905059 1 0.1814 0.907 0.900 0.000 0.000 0.000 0.100 0.000
#> GSM905047 1 0.1267 0.916 0.940 0.000 0.000 0.000 0.060 0.000
#> GSM905066 1 0.0000 0.928 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM905056 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM905060 1 0.1814 0.907 0.900 0.000 0.000 0.000 0.100 0.000
#> GSM905048 1 0.0000 0.928 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM905067 1 0.0000 0.928 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM905057 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM905068 4 0.0000 0.990 0.000 0.000 0.000 1.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) genotype/variation(p) individual(p) k
#> MAD:pam 76 1.98e-08 5.13e-03 0.0709 2
#> MAD:pam 76 1.53e-18 5.88e-06 0.8922 3
#> MAD:pam 76 2.37e-21 6.19e-10 0.3008 4
#> MAD:pam 76 1.78e-21 4.53e-11 0.0398 5
#> MAD:pam 70 3.68e-20 1.67e-08 0.1009 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 76 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 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 1.000 1.000 0.4283 0.572 0.572
#> 3 3 1.000 0.984 0.994 0.5765 0.721 0.525
#> 4 4 0.870 0.856 0.913 0.0790 0.939 0.814
#> 5 5 0.979 0.958 0.977 0.0706 0.914 0.701
#> 6 6 0.863 0.769 0.887 0.0420 0.972 0.873
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
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
#> GSM905004 1 0 1 1 0
#> GSM905024 1 0 1 1 0
#> GSM905038 1 0 1 1 0
#> GSM905043 1 0 1 1 0
#> GSM904986 1 0 1 1 0
#> GSM904991 1 0 1 1 0
#> GSM904994 1 0 1 1 0
#> GSM904996 1 0 1 1 0
#> GSM905007 1 0 1 1 0
#> GSM905012 1 0 1 1 0
#> GSM905022 1 0 1 1 0
#> GSM905026 1 0 1 1 0
#> GSM905027 1 0 1 1 0
#> GSM905031 1 0 1 1 0
#> GSM905036 1 0 1 1 0
#> GSM905041 1 0 1 1 0
#> GSM905044 1 0 1 1 0
#> GSM904989 1 0 1 1 0
#> GSM904999 1 0 1 1 0
#> GSM905002 1 0 1 1 0
#> GSM905009 1 0 1 1 0
#> GSM905014 1 0 1 1 0
#> GSM905017 1 0 1 1 0
#> GSM905020 1 0 1 1 0
#> GSM905023 1 0 1 1 0
#> GSM905029 1 0 1 1 0
#> GSM905032 1 0 1 1 0
#> GSM905034 1 0 1 1 0
#> GSM905040 1 0 1 1 0
#> GSM904985 2 0 1 0 1
#> GSM904988 2 0 1 0 1
#> GSM904990 2 0 1 0 1
#> GSM904992 2 0 1 0 1
#> GSM904995 2 0 1 0 1
#> GSM904998 2 0 1 0 1
#> GSM905000 2 0 1 0 1
#> GSM905003 2 0 1 0 1
#> GSM905006 2 0 1 0 1
#> GSM905008 2 0 1 0 1
#> GSM905011 2 0 1 0 1
#> GSM905013 2 0 1 0 1
#> GSM905016 2 0 1 0 1
#> GSM905018 2 0 1 0 1
#> GSM905021 2 0 1 0 1
#> GSM905025 2 0 1 0 1
#> GSM905028 2 0 1 0 1
#> GSM905030 2 0 1 0 1
#> GSM905033 2 0 1 0 1
#> GSM905035 2 0 1 0 1
#> GSM905037 2 0 1 0 1
#> GSM905039 2 0 1 0 1
#> GSM905042 2 0 1 0 1
#> GSM905046 1 0 1 1 0
#> GSM905065 1 0 1 1 0
#> GSM905049 1 0 1 1 0
#> GSM905050 1 0 1 1 0
#> GSM905064 1 0 1 1 0
#> GSM905045 1 0 1 1 0
#> GSM905051 1 0 1 1 0
#> GSM905055 1 0 1 1 0
#> GSM905058 1 0 1 1 0
#> GSM905053 1 0 1 1 0
#> GSM905061 1 0 1 1 0
#> GSM905063 1 0 1 1 0
#> GSM905054 1 0 1 1 0
#> GSM905062 1 0 1 1 0
#> GSM905052 1 0 1 1 0
#> GSM905059 1 0 1 1 0
#> GSM905047 1 0 1 1 0
#> GSM905066 1 0 1 1 0
#> GSM905056 1 0 1 1 0
#> GSM905060 1 0 1 1 0
#> GSM905048 1 0 1 1 0
#> GSM905067 1 0 1 1 0
#> GSM905057 1 0 1 1 0
#> GSM905068 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM905004 3 0.1643 0.940 0.044 0.000 0.956
#> GSM905024 3 0.0000 0.983 0.000 0.000 1.000
#> GSM905038 3 0.0000 0.983 0.000 0.000 1.000
#> GSM905043 3 0.0000 0.983 0.000 0.000 1.000
#> GSM904986 3 0.0000 0.983 0.000 0.000 1.000
#> GSM904991 3 0.0000 0.983 0.000 0.000 1.000
#> GSM904994 3 0.0000 0.983 0.000 0.000 1.000
#> GSM904996 3 0.0000 0.983 0.000 0.000 1.000
#> GSM905007 3 0.0000 0.983 0.000 0.000 1.000
#> GSM905012 3 0.0000 0.983 0.000 0.000 1.000
#> GSM905022 3 0.0000 0.983 0.000 0.000 1.000
#> GSM905026 3 0.0000 0.983 0.000 0.000 1.000
#> GSM905027 3 0.0000 0.983 0.000 0.000 1.000
#> GSM905031 3 0.0000 0.983 0.000 0.000 1.000
#> GSM905036 3 0.0000 0.983 0.000 0.000 1.000
#> GSM905041 3 0.0000 0.983 0.000 0.000 1.000
#> GSM905044 3 0.0000 0.983 0.000 0.000 1.000
#> GSM904989 3 0.0000 0.983 0.000 0.000 1.000
#> GSM904999 2 0.0592 0.988 0.000 0.988 0.012
#> GSM905002 3 0.0000 0.983 0.000 0.000 1.000
#> GSM905009 3 0.0000 0.983 0.000 0.000 1.000
#> GSM905014 3 0.0000 0.983 0.000 0.000 1.000
#> GSM905017 2 0.0592 0.988 0.000 0.988 0.012
#> GSM905020 3 0.0000 0.983 0.000 0.000 1.000
#> GSM905023 3 0.0000 0.983 0.000 0.000 1.000
#> GSM905029 3 0.0000 0.983 0.000 0.000 1.000
#> GSM905032 3 0.6126 0.332 0.000 0.400 0.600
#> GSM905034 3 0.0000 0.983 0.000 0.000 1.000
#> GSM905040 3 0.0000 0.983 0.000 0.000 1.000
#> GSM904985 2 0.0000 0.999 0.000 1.000 0.000
#> GSM904988 2 0.0000 0.999 0.000 1.000 0.000
#> GSM904990 2 0.0000 0.999 0.000 1.000 0.000
#> GSM904992 2 0.0000 0.999 0.000 1.000 0.000
#> GSM904995 2 0.0000 0.999 0.000 1.000 0.000
#> GSM904998 2 0.0000 0.999 0.000 1.000 0.000
#> GSM905000 2 0.0000 0.999 0.000 1.000 0.000
#> GSM905003 2 0.0000 0.999 0.000 1.000 0.000
#> GSM905006 2 0.0000 0.999 0.000 1.000 0.000
#> GSM905008 2 0.0000 0.999 0.000 1.000 0.000
#> GSM905011 2 0.0000 0.999 0.000 1.000 0.000
#> GSM905013 2 0.0000 0.999 0.000 1.000 0.000
#> GSM905016 2 0.0000 0.999 0.000 1.000 0.000
#> GSM905018 2 0.0000 0.999 0.000 1.000 0.000
#> GSM905021 2 0.0000 0.999 0.000 1.000 0.000
#> GSM905025 2 0.0000 0.999 0.000 1.000 0.000
#> GSM905028 2 0.0000 0.999 0.000 1.000 0.000
#> GSM905030 2 0.0000 0.999 0.000 1.000 0.000
#> GSM905033 2 0.0000 0.999 0.000 1.000 0.000
#> GSM905035 2 0.0000 0.999 0.000 1.000 0.000
#> GSM905037 2 0.0000 0.999 0.000 1.000 0.000
#> GSM905039 2 0.0000 0.999 0.000 1.000 0.000
#> GSM905042 2 0.0000 0.999 0.000 1.000 0.000
#> GSM905046 1 0.0000 1.000 1.000 0.000 0.000
#> GSM905065 1 0.0000 1.000 1.000 0.000 0.000
#> GSM905049 1 0.0000 1.000 1.000 0.000 0.000
#> GSM905050 1 0.0000 1.000 1.000 0.000 0.000
#> GSM905064 1 0.0000 1.000 1.000 0.000 0.000
#> GSM905045 1 0.0000 1.000 1.000 0.000 0.000
#> GSM905051 1 0.0000 1.000 1.000 0.000 0.000
#> GSM905055 1 0.0000 1.000 1.000 0.000 0.000
#> GSM905058 1 0.0000 1.000 1.000 0.000 0.000
#> GSM905053 1 0.0000 1.000 1.000 0.000 0.000
#> GSM905061 1 0.0000 1.000 1.000 0.000 0.000
#> GSM905063 1 0.0000 1.000 1.000 0.000 0.000
#> GSM905054 1 0.0000 1.000 1.000 0.000 0.000
#> GSM905062 1 0.0000 1.000 1.000 0.000 0.000
#> GSM905052 1 0.0000 1.000 1.000 0.000 0.000
#> GSM905059 1 0.0000 1.000 1.000 0.000 0.000
#> GSM905047 1 0.0000 1.000 1.000 0.000 0.000
#> GSM905066 1 0.0000 1.000 1.000 0.000 0.000
#> GSM905056 1 0.0000 1.000 1.000 0.000 0.000
#> GSM905060 1 0.0000 1.000 1.000 0.000 0.000
#> GSM905048 1 0.0000 1.000 1.000 0.000 0.000
#> GSM905067 1 0.0000 1.000 1.000 0.000 0.000
#> GSM905057 1 0.0000 1.000 1.000 0.000 0.000
#> GSM905068 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
#> GSM905004 3 0.5636 0.342 0.024 0.000 0.552 0.424
#> GSM905024 3 0.3975 0.635 0.240 0.000 0.760 0.000
#> GSM905038 3 0.0000 0.926 0.000 0.000 1.000 0.000
#> GSM905043 3 0.4961 0.199 0.448 0.000 0.552 0.000
#> GSM904986 3 0.0000 0.926 0.000 0.000 1.000 0.000
#> GSM904991 3 0.0000 0.926 0.000 0.000 1.000 0.000
#> GSM904994 3 0.0000 0.926 0.000 0.000 1.000 0.000
#> GSM904996 3 0.0000 0.926 0.000 0.000 1.000 0.000
#> GSM905007 3 0.0000 0.926 0.000 0.000 1.000 0.000
#> GSM905012 3 0.0592 0.916 0.000 0.000 0.984 0.016
#> GSM905022 3 0.0000 0.926 0.000 0.000 1.000 0.000
#> GSM905026 3 0.0000 0.926 0.000 0.000 1.000 0.000
#> GSM905027 3 0.0000 0.926 0.000 0.000 1.000 0.000
#> GSM905031 3 0.0336 0.922 0.000 0.000 0.992 0.008
#> GSM905036 3 0.0000 0.926 0.000 0.000 1.000 0.000
#> GSM905041 3 0.0000 0.926 0.000 0.000 1.000 0.000
#> GSM905044 3 0.0000 0.926 0.000 0.000 1.000 0.000
#> GSM904989 3 0.0336 0.922 0.000 0.000 0.992 0.008
#> GSM904999 1 0.4406 0.717 0.780 0.192 0.028 0.000
#> GSM905002 3 0.0000 0.926 0.000 0.000 1.000 0.000
#> GSM905009 3 0.0336 0.922 0.000 0.000 0.992 0.008
#> GSM905014 3 0.0000 0.926 0.000 0.000 1.000 0.000
#> GSM905017 1 0.5343 0.584 0.656 0.316 0.028 0.000
#> GSM905020 3 0.0336 0.922 0.000 0.000 0.992 0.008
#> GSM905023 3 0.2589 0.808 0.116 0.000 0.884 0.000
#> GSM905029 3 0.0000 0.926 0.000 0.000 1.000 0.000
#> GSM905032 1 0.3182 0.752 0.876 0.000 0.028 0.096
#> GSM905034 3 0.4008 0.630 0.244 0.000 0.756 0.000
#> GSM905040 1 0.3266 0.699 0.832 0.000 0.168 0.000
#> GSM904985 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM904988 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM904990 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM904992 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM904995 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM904998 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM905000 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM905003 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM905006 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM905008 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM905011 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM905013 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM905016 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM905018 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM905021 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM905025 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM905028 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM905030 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM905033 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM905035 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM905037 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM905039 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM905042 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM905046 4 0.4643 0.772 0.344 0.000 0.000 0.656
#> GSM905065 4 0.4776 0.754 0.376 0.000 0.000 0.624
#> GSM905049 4 0.0000 0.732 0.000 0.000 0.000 1.000
#> GSM905050 4 0.0000 0.732 0.000 0.000 0.000 1.000
#> GSM905064 4 0.2216 0.761 0.092 0.000 0.000 0.908
#> GSM905045 4 0.2081 0.759 0.084 0.000 0.000 0.916
#> GSM905051 4 0.4134 0.775 0.260 0.000 0.000 0.740
#> GSM905055 1 0.0592 0.787 0.984 0.000 0.000 0.016
#> GSM905058 4 0.4713 0.764 0.360 0.000 0.000 0.640
#> GSM905053 4 0.0000 0.732 0.000 0.000 0.000 1.000
#> GSM905061 4 0.0000 0.732 0.000 0.000 0.000 1.000
#> GSM905063 4 0.4730 0.761 0.364 0.000 0.000 0.636
#> GSM905054 4 0.1022 0.743 0.032 0.000 0.000 0.968
#> GSM905062 4 0.0000 0.732 0.000 0.000 0.000 1.000
#> GSM905052 4 0.4134 0.775 0.260 0.000 0.000 0.740
#> GSM905059 4 0.4624 0.774 0.340 0.000 0.000 0.660
#> GSM905047 4 0.4624 0.774 0.340 0.000 0.000 0.660
#> GSM905066 4 0.4776 0.754 0.376 0.000 0.000 0.624
#> GSM905056 1 0.0592 0.787 0.984 0.000 0.000 0.016
#> GSM905060 4 0.4624 0.774 0.340 0.000 0.000 0.660
#> GSM905048 4 0.4730 0.762 0.364 0.000 0.000 0.636
#> GSM905067 4 0.4776 0.754 0.376 0.000 0.000 0.624
#> GSM905057 1 0.0592 0.787 0.984 0.000 0.000 0.016
#> GSM905068 4 0.0000 0.732 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
#> GSM905004 4 0.4169 0.637 0.016 0.000 0.256 0.724 0.004
#> GSM905024 5 0.1197 0.888 0.000 0.000 0.048 0.000 0.952
#> GSM905038 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM905043 5 0.1121 0.890 0.000 0.000 0.044 0.000 0.956
#> GSM904986 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM904991 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM904994 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM904996 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM905007 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM905012 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM905022 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM905026 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM905027 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM905031 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM905036 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM905041 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM905044 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM904989 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM904999 5 0.0000 0.902 0.000 0.000 0.000 0.000 1.000
#> GSM905002 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM905009 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM905014 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM905017 5 0.0000 0.902 0.000 0.000 0.000 0.000 1.000
#> GSM905020 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM905023 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM905029 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM905032 5 0.0000 0.902 0.000 0.000 0.000 0.000 1.000
#> GSM905034 5 0.1197 0.889 0.000 0.000 0.048 0.000 0.952
#> GSM905040 5 0.0000 0.902 0.000 0.000 0.000 0.000 1.000
#> GSM904985 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM904988 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM904990 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM904992 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM904995 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM904998 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM905000 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM905003 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM905006 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM905008 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM905011 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM905013 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM905016 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM905018 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM905021 2 0.0162 0.996 0.000 0.996 0.000 0.000 0.004
#> GSM905025 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM905028 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM905030 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM905033 2 0.0162 0.996 0.000 0.996 0.000 0.000 0.004
#> GSM905035 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM905037 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM905039 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM905042 2 0.0162 0.996 0.000 0.996 0.000 0.000 0.004
#> GSM905046 1 0.0000 0.978 1.000 0.000 0.000 0.000 0.000
#> GSM905065 1 0.0000 0.978 1.000 0.000 0.000 0.000 0.000
#> GSM905049 4 0.0000 0.915 0.000 0.000 0.000 1.000 0.000
#> GSM905050 4 0.0000 0.915 0.000 0.000 0.000 1.000 0.000
#> GSM905064 4 0.2377 0.822 0.128 0.000 0.000 0.872 0.000
#> GSM905045 4 0.3586 0.641 0.264 0.000 0.000 0.736 0.000
#> GSM905051 1 0.1043 0.970 0.960 0.000 0.000 0.040 0.000
#> GSM905055 5 0.2852 0.846 0.172 0.000 0.000 0.000 0.828
#> GSM905058 1 0.0000 0.978 1.000 0.000 0.000 0.000 0.000
#> GSM905053 4 0.0000 0.915 0.000 0.000 0.000 1.000 0.000
#> GSM905061 4 0.0000 0.915 0.000 0.000 0.000 1.000 0.000
#> GSM905063 5 0.3452 0.768 0.244 0.000 0.000 0.000 0.756
#> GSM905054 4 0.0162 0.913 0.004 0.000 0.000 0.996 0.000
#> GSM905062 4 0.0000 0.915 0.000 0.000 0.000 1.000 0.000
#> GSM905052 1 0.1043 0.970 0.960 0.000 0.000 0.040 0.000
#> GSM905059 1 0.0963 0.973 0.964 0.000 0.000 0.036 0.000
#> GSM905047 1 0.0963 0.973 0.964 0.000 0.000 0.036 0.000
#> GSM905066 1 0.0000 0.978 1.000 0.000 0.000 0.000 0.000
#> GSM905056 5 0.2852 0.846 0.172 0.000 0.000 0.000 0.828
#> GSM905060 1 0.0963 0.973 0.964 0.000 0.000 0.036 0.000
#> GSM905048 1 0.0000 0.978 1.000 0.000 0.000 0.000 0.000
#> GSM905067 1 0.0000 0.978 1.000 0.000 0.000 0.000 0.000
#> GSM905057 5 0.2852 0.846 0.172 0.000 0.000 0.000 0.828
#> GSM905068 4 0.0000 0.915 0.000 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM905004 4 0.4998 0.609 0.016 0.000 0.196 0.676 0.112 0.000
#> GSM905024 5 0.1610 0.815 0.000 0.000 0.000 0.000 0.916 0.084
#> GSM905038 3 0.2135 0.926 0.000 0.000 0.872 0.000 0.000 0.128
#> GSM905043 5 0.1610 0.815 0.000 0.000 0.000 0.000 0.916 0.084
#> GSM904986 3 0.0000 0.946 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM904991 3 0.2135 0.926 0.000 0.000 0.872 0.000 0.000 0.128
#> GSM904994 3 0.0000 0.946 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM904996 3 0.0000 0.946 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905007 3 0.2135 0.926 0.000 0.000 0.872 0.000 0.000 0.128
#> GSM905012 3 0.0000 0.946 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905022 3 0.0146 0.946 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM905026 3 0.0000 0.946 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905027 3 0.2135 0.926 0.000 0.000 0.872 0.000 0.000 0.128
#> GSM905031 3 0.0000 0.946 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905036 3 0.2135 0.926 0.000 0.000 0.872 0.000 0.000 0.128
#> GSM905041 3 0.2278 0.923 0.000 0.000 0.868 0.000 0.004 0.128
#> GSM905044 3 0.0146 0.946 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM904989 3 0.0000 0.946 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM904999 5 0.2996 0.740 0.000 0.000 0.000 0.000 0.772 0.228
#> GSM905002 3 0.0000 0.946 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905009 3 0.0000 0.946 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905014 3 0.2135 0.926 0.000 0.000 0.872 0.000 0.000 0.128
#> GSM905017 5 0.2996 0.740 0.000 0.000 0.000 0.000 0.772 0.228
#> GSM905020 3 0.0146 0.946 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM905023 3 0.1957 0.929 0.000 0.000 0.888 0.000 0.000 0.112
#> GSM905029 3 0.2135 0.926 0.000 0.000 0.872 0.000 0.000 0.128
#> GSM905032 5 0.1556 0.814 0.000 0.000 0.000 0.000 0.920 0.080
#> GSM905034 5 0.1075 0.825 0.000 0.000 0.000 0.000 0.952 0.048
#> GSM905040 5 0.0000 0.825 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM904985 2 0.3659 0.150 0.000 0.636 0.000 0.000 0.000 0.364
#> GSM904988 2 0.0000 0.703 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM904990 2 0.0000 0.703 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM904992 2 0.0000 0.703 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM904995 2 0.3659 0.150 0.000 0.636 0.000 0.000 0.000 0.364
#> GSM904998 2 0.0146 0.701 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM905000 2 0.0000 0.703 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905003 2 0.0146 0.701 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM905006 2 0.0000 0.703 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905008 2 0.3860 -0.415 0.000 0.528 0.000 0.000 0.000 0.472
#> GSM905011 2 0.0000 0.703 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905013 2 0.0146 0.701 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM905016 2 0.3659 0.150 0.000 0.636 0.000 0.000 0.000 0.364
#> GSM905018 2 0.0000 0.703 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905021 6 0.3765 0.800 0.000 0.404 0.000 0.000 0.000 0.596
#> GSM905025 2 0.3647 0.157 0.000 0.640 0.000 0.000 0.000 0.360
#> GSM905028 2 0.3647 0.157 0.000 0.640 0.000 0.000 0.000 0.360
#> GSM905030 2 0.0000 0.703 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905033 6 0.3547 0.913 0.000 0.332 0.000 0.000 0.000 0.668
#> GSM905035 2 0.3659 0.150 0.000 0.636 0.000 0.000 0.000 0.364
#> GSM905037 2 0.0000 0.703 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905039 2 0.3647 0.157 0.000 0.640 0.000 0.000 0.000 0.360
#> GSM905042 6 0.3547 0.913 0.000 0.332 0.000 0.000 0.000 0.668
#> GSM905046 1 0.0260 0.934 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM905065 1 0.0632 0.928 0.976 0.000 0.000 0.000 0.000 0.024
#> GSM905049 4 0.0000 0.947 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905050 4 0.0000 0.947 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905064 4 0.1866 0.867 0.084 0.000 0.000 0.908 0.000 0.008
#> GSM905045 1 0.5532 0.212 0.520 0.000 0.000 0.368 0.100 0.012
#> GSM905051 1 0.0870 0.932 0.972 0.000 0.000 0.012 0.004 0.012
#> GSM905055 5 0.4024 0.785 0.072 0.000 0.000 0.000 0.744 0.184
#> GSM905058 1 0.0363 0.931 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM905053 4 0.0000 0.947 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905061 4 0.0000 0.947 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905063 5 0.5454 0.589 0.252 0.000 0.000 0.000 0.568 0.180
#> GSM905054 4 0.0000 0.947 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905062 4 0.0000 0.947 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905052 1 0.0870 0.932 0.972 0.000 0.000 0.012 0.004 0.012
#> GSM905059 1 0.0725 0.933 0.976 0.000 0.000 0.012 0.000 0.012
#> GSM905047 1 0.0725 0.933 0.976 0.000 0.000 0.012 0.000 0.012
#> GSM905066 1 0.0865 0.920 0.964 0.000 0.000 0.000 0.000 0.036
#> GSM905056 5 0.4024 0.785 0.072 0.000 0.000 0.000 0.744 0.184
#> GSM905060 1 0.0725 0.933 0.976 0.000 0.000 0.012 0.000 0.012
#> GSM905048 1 0.0547 0.929 0.980 0.000 0.000 0.000 0.000 0.020
#> GSM905067 1 0.0632 0.928 0.976 0.000 0.000 0.000 0.000 0.024
#> GSM905057 5 0.4024 0.785 0.072 0.000 0.000 0.000 0.744 0.184
#> GSM905068 4 0.0000 0.947 0.000 0.000 0.000 1.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) genotype/variation(p) individual(p) k
#> MAD:mclust 76 3.04e-12 1.17e-05 0.990 2
#> MAD:mclust 75 7.59e-20 9.30e-06 0.938 3
#> MAD:mclust 74 1.89e-18 1.21e-06 0.303 4
#> MAD:mclust 76 2.61e-18 6.72e-11 0.217 5
#> MAD:mclust 67 2.82e-12 1.34e-08 0.220 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 76 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.944 0.926 0.971 0.4964 0.502 0.502
#> 3 3 1.000 0.960 0.985 0.3586 0.716 0.490
#> 4 4 0.963 0.918 0.968 0.1020 0.883 0.664
#> 5 5 0.889 0.866 0.916 0.0474 0.907 0.675
#> 6 6 0.872 0.773 0.885 0.0283 0.980 0.913
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 2 3
There is also optional best \(k\) = 2 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM905004 2 0.1414 0.954 0.020 0.980
#> GSM905024 1 0.0000 0.965 1.000 0.000
#> GSM905038 2 0.4161 0.891 0.084 0.916
#> GSM905043 1 0.0000 0.965 1.000 0.000
#> GSM904986 2 0.0000 0.970 0.000 1.000
#> GSM904991 1 0.4022 0.890 0.920 0.080
#> GSM904994 2 0.0000 0.970 0.000 1.000
#> GSM904996 2 0.0000 0.970 0.000 1.000
#> GSM905007 1 0.8861 0.562 0.696 0.304
#> GSM905012 2 0.0000 0.970 0.000 1.000
#> GSM905022 2 0.0000 0.970 0.000 1.000
#> GSM905026 2 0.0000 0.970 0.000 1.000
#> GSM905027 2 0.4298 0.887 0.088 0.912
#> GSM905031 2 0.0000 0.970 0.000 1.000
#> GSM905036 1 0.8016 0.672 0.756 0.244
#> GSM905041 1 0.0376 0.962 0.996 0.004
#> GSM905044 2 0.0000 0.970 0.000 1.000
#> GSM904989 2 0.0000 0.970 0.000 1.000
#> GSM904999 2 0.0000 0.970 0.000 1.000
#> GSM905002 2 0.0000 0.970 0.000 1.000
#> GSM905009 2 0.0000 0.970 0.000 1.000
#> GSM905014 1 0.9833 0.259 0.576 0.424
#> GSM905017 2 0.0000 0.970 0.000 1.000
#> GSM905020 2 0.0000 0.970 0.000 1.000
#> GSM905023 2 0.6343 0.799 0.160 0.840
#> GSM905029 2 0.9909 0.183 0.444 0.556
#> GSM905032 2 0.9608 0.366 0.384 0.616
#> GSM905034 1 0.0000 0.965 1.000 0.000
#> GSM905040 1 0.0000 0.965 1.000 0.000
#> GSM904985 2 0.0000 0.970 0.000 1.000
#> GSM904988 2 0.0000 0.970 0.000 1.000
#> GSM904990 2 0.0000 0.970 0.000 1.000
#> GSM904992 2 0.0000 0.970 0.000 1.000
#> GSM904995 2 0.0000 0.970 0.000 1.000
#> GSM904998 2 0.0000 0.970 0.000 1.000
#> GSM905000 2 0.0000 0.970 0.000 1.000
#> GSM905003 2 0.0000 0.970 0.000 1.000
#> GSM905006 2 0.0000 0.970 0.000 1.000
#> GSM905008 2 0.0000 0.970 0.000 1.000
#> GSM905011 2 0.0000 0.970 0.000 1.000
#> GSM905013 2 0.0000 0.970 0.000 1.000
#> GSM905016 2 0.0000 0.970 0.000 1.000
#> GSM905018 2 0.0000 0.970 0.000 1.000
#> GSM905021 2 0.0000 0.970 0.000 1.000
#> GSM905025 2 0.0000 0.970 0.000 1.000
#> GSM905028 2 0.0000 0.970 0.000 1.000
#> GSM905030 2 0.0000 0.970 0.000 1.000
#> GSM905033 2 0.0000 0.970 0.000 1.000
#> GSM905035 2 0.0000 0.970 0.000 1.000
#> GSM905037 2 0.0000 0.970 0.000 1.000
#> GSM905039 2 0.0000 0.970 0.000 1.000
#> GSM905042 2 0.0000 0.970 0.000 1.000
#> GSM905046 1 0.0000 0.965 1.000 0.000
#> GSM905065 1 0.0000 0.965 1.000 0.000
#> GSM905049 1 0.0000 0.965 1.000 0.000
#> GSM905050 1 0.0000 0.965 1.000 0.000
#> GSM905064 1 0.0000 0.965 1.000 0.000
#> GSM905045 1 0.0000 0.965 1.000 0.000
#> GSM905051 1 0.0000 0.965 1.000 0.000
#> GSM905055 1 0.0000 0.965 1.000 0.000
#> GSM905058 1 0.0000 0.965 1.000 0.000
#> GSM905053 1 0.0000 0.965 1.000 0.000
#> GSM905061 1 0.0000 0.965 1.000 0.000
#> GSM905063 1 0.0000 0.965 1.000 0.000
#> GSM905054 1 0.0000 0.965 1.000 0.000
#> GSM905062 1 0.0000 0.965 1.000 0.000
#> GSM905052 1 0.0000 0.965 1.000 0.000
#> GSM905059 1 0.0000 0.965 1.000 0.000
#> GSM905047 1 0.0000 0.965 1.000 0.000
#> GSM905066 1 0.0000 0.965 1.000 0.000
#> GSM905056 1 0.0000 0.965 1.000 0.000
#> GSM905060 1 0.0000 0.965 1.000 0.000
#> GSM905048 1 0.0000 0.965 1.000 0.000
#> GSM905067 1 0.0000 0.965 1.000 0.000
#> GSM905057 1 0.0000 0.965 1.000 0.000
#> GSM905068 1 0.0000 0.965 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM905004 2 0.6541 0.535841 0.024 0.672 0.304
#> GSM905024 3 0.0592 0.968559 0.012 0.000 0.988
#> GSM905038 3 0.0000 0.979023 0.000 0.000 1.000
#> GSM905043 3 0.0592 0.968559 0.012 0.000 0.988
#> GSM904986 3 0.0000 0.979023 0.000 0.000 1.000
#> GSM904991 3 0.0000 0.979023 0.000 0.000 1.000
#> GSM904994 3 0.0000 0.979023 0.000 0.000 1.000
#> GSM904996 3 0.0000 0.979023 0.000 0.000 1.000
#> GSM905007 3 0.0000 0.979023 0.000 0.000 1.000
#> GSM905012 3 0.0000 0.979023 0.000 0.000 1.000
#> GSM905022 3 0.0000 0.979023 0.000 0.000 1.000
#> GSM905026 3 0.0000 0.979023 0.000 0.000 1.000
#> GSM905027 3 0.0000 0.979023 0.000 0.000 1.000
#> GSM905031 3 0.0000 0.979023 0.000 0.000 1.000
#> GSM905036 3 0.0000 0.979023 0.000 0.000 1.000
#> GSM905041 3 0.0000 0.979023 0.000 0.000 1.000
#> GSM905044 3 0.0000 0.979023 0.000 0.000 1.000
#> GSM904989 3 0.0000 0.979023 0.000 0.000 1.000
#> GSM904999 3 0.0000 0.979023 0.000 0.000 1.000
#> GSM905002 3 0.0000 0.979023 0.000 0.000 1.000
#> GSM905009 3 0.0000 0.979023 0.000 0.000 1.000
#> GSM905014 3 0.0000 0.979023 0.000 0.000 1.000
#> GSM905017 3 0.0000 0.979023 0.000 0.000 1.000
#> GSM905020 3 0.0000 0.979023 0.000 0.000 1.000
#> GSM905023 3 0.0000 0.979023 0.000 0.000 1.000
#> GSM905029 3 0.0000 0.979023 0.000 0.000 1.000
#> GSM905032 3 0.0000 0.979023 0.000 0.000 1.000
#> GSM905034 1 0.4178 0.784600 0.828 0.000 0.172
#> GSM905040 3 0.6309 -0.000368 0.496 0.000 0.504
#> GSM904985 2 0.0000 0.980331 0.000 1.000 0.000
#> GSM904988 2 0.0000 0.980331 0.000 1.000 0.000
#> GSM904990 2 0.0000 0.980331 0.000 1.000 0.000
#> GSM904992 2 0.0000 0.980331 0.000 1.000 0.000
#> GSM904995 2 0.0000 0.980331 0.000 1.000 0.000
#> GSM904998 2 0.0000 0.980331 0.000 1.000 0.000
#> GSM905000 2 0.0000 0.980331 0.000 1.000 0.000
#> GSM905003 2 0.0000 0.980331 0.000 1.000 0.000
#> GSM905006 2 0.0000 0.980331 0.000 1.000 0.000
#> GSM905008 2 0.0000 0.980331 0.000 1.000 0.000
#> GSM905011 2 0.0000 0.980331 0.000 1.000 0.000
#> GSM905013 2 0.0000 0.980331 0.000 1.000 0.000
#> GSM905016 2 0.0000 0.980331 0.000 1.000 0.000
#> GSM905018 2 0.0000 0.980331 0.000 1.000 0.000
#> GSM905021 2 0.3412 0.853325 0.000 0.876 0.124
#> GSM905025 2 0.0000 0.980331 0.000 1.000 0.000
#> GSM905028 2 0.0000 0.980331 0.000 1.000 0.000
#> GSM905030 2 0.0000 0.980331 0.000 1.000 0.000
#> GSM905033 2 0.0000 0.980331 0.000 1.000 0.000
#> GSM905035 2 0.0000 0.980331 0.000 1.000 0.000
#> GSM905037 2 0.0000 0.980331 0.000 1.000 0.000
#> GSM905039 2 0.0000 0.980331 0.000 1.000 0.000
#> GSM905042 2 0.0000 0.980331 0.000 1.000 0.000
#> GSM905046 1 0.0000 0.992472 1.000 0.000 0.000
#> GSM905065 1 0.0000 0.992472 1.000 0.000 0.000
#> GSM905049 1 0.0000 0.992472 1.000 0.000 0.000
#> GSM905050 1 0.0000 0.992472 1.000 0.000 0.000
#> GSM905064 1 0.0000 0.992472 1.000 0.000 0.000
#> GSM905045 1 0.0000 0.992472 1.000 0.000 0.000
#> GSM905051 1 0.0000 0.992472 1.000 0.000 0.000
#> GSM905055 1 0.0000 0.992472 1.000 0.000 0.000
#> GSM905058 1 0.0000 0.992472 1.000 0.000 0.000
#> GSM905053 1 0.0000 0.992472 1.000 0.000 0.000
#> GSM905061 1 0.0000 0.992472 1.000 0.000 0.000
#> GSM905063 1 0.0000 0.992472 1.000 0.000 0.000
#> GSM905054 1 0.0000 0.992472 1.000 0.000 0.000
#> GSM905062 1 0.0000 0.992472 1.000 0.000 0.000
#> GSM905052 1 0.0000 0.992472 1.000 0.000 0.000
#> GSM905059 1 0.0000 0.992472 1.000 0.000 0.000
#> GSM905047 1 0.0000 0.992472 1.000 0.000 0.000
#> GSM905066 1 0.0000 0.992472 1.000 0.000 0.000
#> GSM905056 1 0.0000 0.992472 1.000 0.000 0.000
#> GSM905060 1 0.0000 0.992472 1.000 0.000 0.000
#> GSM905048 1 0.0000 0.992472 1.000 0.000 0.000
#> GSM905067 1 0.0000 0.992472 1.000 0.000 0.000
#> GSM905057 1 0.0000 0.992472 1.000 0.000 0.000
#> GSM905068 1 0.0000 0.992472 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM905004 4 0.0336 0.922 0.000 0.000 0.008 0.992
#> GSM905024 1 0.4992 0.127 0.524 0.000 0.476 0.000
#> GSM905038 3 0.0000 0.985 0.000 0.000 1.000 0.000
#> GSM905043 1 0.4776 0.407 0.624 0.000 0.376 0.000
#> GSM904986 3 0.0000 0.985 0.000 0.000 1.000 0.000
#> GSM904991 3 0.0000 0.985 0.000 0.000 1.000 0.000
#> GSM904994 3 0.0000 0.985 0.000 0.000 1.000 0.000
#> GSM904996 3 0.0000 0.985 0.000 0.000 1.000 0.000
#> GSM905007 3 0.0000 0.985 0.000 0.000 1.000 0.000
#> GSM905012 4 0.3356 0.756 0.000 0.000 0.176 0.824
#> GSM905022 3 0.0000 0.985 0.000 0.000 1.000 0.000
#> GSM905026 3 0.0000 0.985 0.000 0.000 1.000 0.000
#> GSM905027 3 0.0000 0.985 0.000 0.000 1.000 0.000
#> GSM905031 3 0.2408 0.887 0.000 0.000 0.896 0.104
#> GSM905036 3 0.0000 0.985 0.000 0.000 1.000 0.000
#> GSM905041 3 0.0000 0.985 0.000 0.000 1.000 0.000
#> GSM905044 3 0.0000 0.985 0.000 0.000 1.000 0.000
#> GSM904989 3 0.0000 0.985 0.000 0.000 1.000 0.000
#> GSM904999 3 0.0000 0.985 0.000 0.000 1.000 0.000
#> GSM905002 3 0.0000 0.985 0.000 0.000 1.000 0.000
#> GSM905009 3 0.0817 0.965 0.000 0.000 0.976 0.024
#> GSM905014 3 0.0000 0.985 0.000 0.000 1.000 0.000
#> GSM905017 3 0.0000 0.985 0.000 0.000 1.000 0.000
#> GSM905020 3 0.2647 0.864 0.000 0.000 0.880 0.120
#> GSM905023 3 0.0000 0.985 0.000 0.000 1.000 0.000
#> GSM905029 3 0.0000 0.985 0.000 0.000 1.000 0.000
#> GSM905032 3 0.1867 0.914 0.072 0.000 0.928 0.000
#> GSM905034 1 0.0817 0.884 0.976 0.000 0.024 0.000
#> GSM905040 1 0.0817 0.885 0.976 0.000 0.024 0.000
#> GSM904985 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM904988 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM904990 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM904992 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM904995 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM904998 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM905000 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM905003 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM905006 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM905008 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM905011 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM905013 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM905016 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM905018 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM905021 2 0.0188 0.995 0.000 0.996 0.004 0.000
#> GSM905025 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM905028 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM905030 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM905033 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM905035 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM905037 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM905039 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM905042 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM905046 1 0.0000 0.902 1.000 0.000 0.000 0.000
#> GSM905065 1 0.0000 0.902 1.000 0.000 0.000 0.000
#> GSM905049 4 0.0707 0.925 0.020 0.000 0.000 0.980
#> GSM905050 4 0.0000 0.923 0.000 0.000 0.000 1.000
#> GSM905064 4 0.1557 0.904 0.056 0.000 0.000 0.944
#> GSM905045 4 0.1022 0.921 0.032 0.000 0.000 0.968
#> GSM905051 1 0.4866 0.205 0.596 0.000 0.000 0.404
#> GSM905055 1 0.0000 0.902 1.000 0.000 0.000 0.000
#> GSM905058 1 0.0000 0.902 1.000 0.000 0.000 0.000
#> GSM905053 4 0.0336 0.926 0.008 0.000 0.000 0.992
#> GSM905061 4 0.0336 0.926 0.008 0.000 0.000 0.992
#> GSM905063 1 0.0000 0.902 1.000 0.000 0.000 0.000
#> GSM905054 4 0.1118 0.919 0.036 0.000 0.000 0.964
#> GSM905062 4 0.0336 0.926 0.008 0.000 0.000 0.992
#> GSM905052 4 0.4948 0.228 0.440 0.000 0.000 0.560
#> GSM905059 1 0.0000 0.902 1.000 0.000 0.000 0.000
#> GSM905047 1 0.0817 0.885 0.976 0.000 0.000 0.024
#> GSM905066 1 0.0000 0.902 1.000 0.000 0.000 0.000
#> GSM905056 1 0.0000 0.902 1.000 0.000 0.000 0.000
#> GSM905060 1 0.0336 0.897 0.992 0.000 0.000 0.008
#> GSM905048 1 0.0000 0.902 1.000 0.000 0.000 0.000
#> GSM905067 1 0.0000 0.902 1.000 0.000 0.000 0.000
#> GSM905057 1 0.0000 0.902 1.000 0.000 0.000 0.000
#> GSM905068 4 0.0000 0.923 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
#> GSM905004 4 0.3037 0.775 0.000 0.000 0.040 0.860 0.100
#> GSM905024 3 0.5519 0.228 0.412 0.000 0.520 0.000 0.068
#> GSM905038 3 0.1043 0.896 0.000 0.000 0.960 0.000 0.040
#> GSM905043 3 0.5163 0.530 0.296 0.000 0.636 0.000 0.068
#> GSM904986 3 0.1741 0.876 0.000 0.000 0.936 0.024 0.040
#> GSM904991 3 0.1270 0.895 0.000 0.000 0.948 0.000 0.052
#> GSM904994 3 0.2848 0.831 0.000 0.000 0.868 0.028 0.104
#> GSM904996 3 0.2624 0.833 0.000 0.000 0.872 0.012 0.116
#> GSM905007 3 0.1270 0.896 0.000 0.000 0.948 0.000 0.052
#> GSM905012 4 0.4010 0.735 0.000 0.000 0.072 0.792 0.136
#> GSM905022 3 0.0963 0.886 0.000 0.000 0.964 0.000 0.036
#> GSM905026 3 0.0963 0.897 0.000 0.000 0.964 0.000 0.036
#> GSM905027 3 0.0963 0.898 0.000 0.000 0.964 0.000 0.036
#> GSM905031 4 0.3919 0.691 0.000 0.000 0.188 0.776 0.036
#> GSM905036 3 0.1544 0.887 0.000 0.000 0.932 0.000 0.068
#> GSM905041 3 0.1544 0.887 0.000 0.000 0.932 0.000 0.068
#> GSM905044 3 0.1043 0.897 0.000 0.000 0.960 0.000 0.040
#> GSM904989 3 0.4410 0.715 0.000 0.000 0.764 0.112 0.124
#> GSM904999 3 0.0880 0.898 0.000 0.000 0.968 0.000 0.032
#> GSM905002 3 0.1544 0.873 0.000 0.000 0.932 0.000 0.068
#> GSM905009 4 0.6146 0.246 0.000 0.000 0.400 0.468 0.132
#> GSM905014 3 0.1197 0.896 0.000 0.000 0.952 0.000 0.048
#> GSM905017 3 0.0703 0.898 0.000 0.000 0.976 0.000 0.024
#> GSM905020 4 0.6016 0.461 0.000 0.000 0.312 0.548 0.140
#> GSM905023 3 0.1544 0.887 0.000 0.000 0.932 0.000 0.068
#> GSM905029 3 0.0880 0.897 0.000 0.000 0.968 0.000 0.032
#> GSM905032 5 0.3630 0.634 0.016 0.000 0.204 0.000 0.780
#> GSM905034 1 0.3055 0.783 0.864 0.000 0.072 0.000 0.064
#> GSM905040 5 0.3452 0.871 0.244 0.000 0.000 0.000 0.756
#> GSM904985 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM904988 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM904990 2 0.0162 0.995 0.000 0.996 0.000 0.000 0.004
#> GSM904992 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM904995 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM904998 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM905000 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM905003 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM905006 2 0.0162 0.995 0.000 0.996 0.000 0.000 0.004
#> GSM905008 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM905011 2 0.0162 0.995 0.000 0.996 0.000 0.000 0.004
#> GSM905013 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM905016 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM905018 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM905021 2 0.0992 0.966 0.000 0.968 0.024 0.000 0.008
#> GSM905025 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM905028 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM905030 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM905033 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM905035 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM905037 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM905039 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM905042 2 0.0162 0.994 0.000 0.996 0.000 0.000 0.004
#> GSM905046 1 0.0609 0.897 0.980 0.000 0.000 0.020 0.000
#> GSM905065 1 0.0290 0.890 0.992 0.000 0.000 0.000 0.008
#> GSM905049 4 0.0703 0.826 0.024 0.000 0.000 0.976 0.000
#> GSM905050 4 0.0290 0.830 0.008 0.000 0.000 0.992 0.000
#> GSM905064 4 0.3109 0.659 0.200 0.000 0.000 0.800 0.000
#> GSM905045 4 0.1608 0.801 0.072 0.000 0.000 0.928 0.000
#> GSM905051 1 0.2813 0.815 0.832 0.000 0.000 0.168 0.000
#> GSM905055 5 0.3242 0.889 0.216 0.000 0.000 0.000 0.784
#> GSM905058 1 0.0162 0.895 0.996 0.000 0.000 0.004 0.000
#> GSM905053 4 0.0290 0.830 0.008 0.000 0.000 0.992 0.000
#> GSM905061 4 0.0290 0.830 0.008 0.000 0.000 0.992 0.000
#> GSM905063 5 0.3837 0.815 0.308 0.000 0.000 0.000 0.692
#> GSM905054 4 0.1608 0.802 0.072 0.000 0.000 0.928 0.000
#> GSM905062 4 0.0290 0.830 0.008 0.000 0.000 0.992 0.000
#> GSM905052 1 0.3074 0.783 0.804 0.000 0.000 0.196 0.000
#> GSM905059 1 0.1410 0.892 0.940 0.000 0.000 0.060 0.000
#> GSM905047 1 0.2424 0.847 0.868 0.000 0.000 0.132 0.000
#> GSM905066 1 0.0290 0.890 0.992 0.000 0.000 0.000 0.008
#> GSM905056 5 0.3242 0.889 0.216 0.000 0.000 0.000 0.784
#> GSM905060 1 0.1544 0.889 0.932 0.000 0.000 0.068 0.000
#> GSM905048 1 0.0162 0.892 0.996 0.000 0.000 0.000 0.004
#> GSM905067 1 0.0290 0.890 0.992 0.000 0.000 0.000 0.008
#> GSM905057 5 0.3242 0.889 0.216 0.000 0.000 0.000 0.784
#> GSM905068 4 0.0162 0.829 0.004 0.000 0.000 0.996 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM905004 4 0.4192 -0.119 0.000 0.004 0.008 0.612 0.372 0.004
#> GSM905024 1 0.3862 0.157 0.524 0.000 0.476 0.000 0.000 0.000
#> GSM905038 3 0.0363 0.756 0.000 0.000 0.988 0.000 0.012 0.000
#> GSM905043 3 0.3892 0.320 0.352 0.000 0.640 0.000 0.004 0.004
#> GSM904986 3 0.3933 0.679 0.000 0.000 0.716 0.036 0.248 0.000
#> GSM904991 3 0.1387 0.767 0.000 0.000 0.932 0.000 0.068 0.000
#> GSM904994 3 0.4409 0.508 0.000 0.000 0.588 0.032 0.380 0.000
#> GSM904996 3 0.3782 0.512 0.000 0.000 0.588 0.000 0.412 0.000
#> GSM905007 3 0.2416 0.756 0.000 0.000 0.844 0.000 0.156 0.000
#> GSM905012 4 0.4762 -0.647 0.000 0.000 0.032 0.488 0.472 0.008
#> GSM905022 3 0.2941 0.727 0.000 0.000 0.780 0.000 0.220 0.000
#> GSM905026 3 0.1387 0.766 0.000 0.000 0.932 0.000 0.068 0.000
#> GSM905027 3 0.1007 0.765 0.000 0.000 0.956 0.000 0.044 0.000
#> GSM905031 4 0.3678 0.408 0.000 0.000 0.128 0.788 0.084 0.000
#> GSM905036 3 0.2234 0.652 0.000 0.000 0.872 0.124 0.004 0.000
#> GSM905041 3 0.0146 0.749 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM905044 3 0.1957 0.763 0.000 0.000 0.888 0.000 0.112 0.000
#> GSM904989 3 0.5850 -0.204 0.000 0.000 0.420 0.164 0.412 0.004
#> GSM904999 3 0.3918 0.583 0.000 0.004 0.632 0.000 0.360 0.004
#> GSM905002 3 0.3531 0.638 0.000 0.000 0.672 0.000 0.328 0.000
#> GSM905009 5 0.5951 0.767 0.000 0.000 0.192 0.356 0.448 0.004
#> GSM905014 3 0.2340 0.756 0.000 0.000 0.852 0.000 0.148 0.000
#> GSM905017 3 0.3329 0.716 0.000 0.004 0.756 0.000 0.236 0.004
#> GSM905020 5 0.5117 0.739 0.000 0.000 0.076 0.376 0.544 0.004
#> GSM905023 3 0.0717 0.746 0.000 0.000 0.976 0.016 0.008 0.000
#> GSM905029 3 0.0632 0.761 0.000 0.000 0.976 0.000 0.024 0.000
#> GSM905032 6 0.2772 0.794 0.000 0.000 0.180 0.000 0.004 0.816
#> GSM905034 1 0.1408 0.868 0.944 0.000 0.036 0.000 0.020 0.000
#> GSM905040 6 0.1708 0.927 0.024 0.000 0.040 0.000 0.004 0.932
#> GSM904985 2 0.0363 0.973 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM904988 2 0.0547 0.974 0.000 0.980 0.000 0.000 0.020 0.000
#> GSM904990 2 0.0632 0.973 0.000 0.976 0.000 0.000 0.024 0.000
#> GSM904992 2 0.0547 0.974 0.000 0.980 0.000 0.000 0.020 0.000
#> GSM904995 2 0.0363 0.973 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM904998 2 0.0000 0.976 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905000 2 0.0547 0.974 0.000 0.980 0.000 0.000 0.020 0.000
#> GSM905003 2 0.0000 0.976 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905006 2 0.0547 0.974 0.000 0.980 0.000 0.000 0.020 0.000
#> GSM905008 2 0.0458 0.975 0.000 0.984 0.000 0.000 0.016 0.000
#> GSM905011 2 0.0547 0.974 0.000 0.980 0.000 0.000 0.020 0.000
#> GSM905013 2 0.0547 0.974 0.000 0.980 0.000 0.000 0.020 0.000
#> GSM905016 2 0.0260 0.974 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM905018 2 0.0547 0.974 0.000 0.980 0.000 0.000 0.020 0.000
#> GSM905021 2 0.3828 0.637 0.000 0.696 0.004 0.000 0.288 0.012
#> GSM905025 2 0.0146 0.975 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM905028 2 0.0146 0.975 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM905030 2 0.0363 0.976 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM905033 2 0.0458 0.971 0.000 0.984 0.000 0.000 0.016 0.000
#> GSM905035 2 0.0363 0.973 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM905037 2 0.0146 0.976 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM905039 2 0.0146 0.975 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM905042 2 0.0603 0.969 0.000 0.980 0.004 0.000 0.016 0.000
#> GSM905046 1 0.0291 0.888 0.992 0.000 0.000 0.000 0.004 0.004
#> GSM905065 1 0.0291 0.888 0.992 0.000 0.000 0.000 0.004 0.004
#> GSM905049 4 0.0777 0.797 0.024 0.000 0.000 0.972 0.004 0.000
#> GSM905050 4 0.0458 0.798 0.016 0.000 0.000 0.984 0.000 0.000
#> GSM905064 4 0.2706 0.674 0.124 0.000 0.000 0.852 0.024 0.000
#> GSM905045 4 0.1297 0.789 0.040 0.000 0.000 0.948 0.012 0.000
#> GSM905051 1 0.4310 0.683 0.684 0.000 0.000 0.044 0.268 0.004
#> GSM905055 6 0.0632 0.945 0.024 0.000 0.000 0.000 0.000 0.976
#> GSM905058 1 0.0632 0.885 0.976 0.000 0.000 0.000 0.024 0.000
#> GSM905053 4 0.0777 0.797 0.024 0.000 0.000 0.972 0.004 0.000
#> GSM905061 4 0.0806 0.798 0.020 0.000 0.000 0.972 0.008 0.000
#> GSM905063 6 0.1007 0.936 0.044 0.000 0.000 0.000 0.000 0.956
#> GSM905054 4 0.1575 0.779 0.032 0.000 0.000 0.936 0.032 0.000
#> GSM905062 4 0.0717 0.791 0.008 0.000 0.000 0.976 0.016 0.000
#> GSM905052 1 0.4855 0.621 0.620 0.000 0.000 0.072 0.304 0.004
#> GSM905059 1 0.0632 0.885 0.976 0.000 0.000 0.000 0.024 0.000
#> GSM905047 1 0.0260 0.887 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM905066 1 0.0291 0.888 0.992 0.000 0.000 0.000 0.004 0.004
#> GSM905056 6 0.0547 0.943 0.020 0.000 0.000 0.000 0.000 0.980
#> GSM905060 1 0.0632 0.885 0.976 0.000 0.000 0.000 0.024 0.000
#> GSM905048 1 0.0291 0.888 0.992 0.000 0.000 0.000 0.004 0.004
#> GSM905067 1 0.0291 0.888 0.992 0.000 0.000 0.000 0.004 0.004
#> GSM905057 6 0.0632 0.945 0.024 0.000 0.000 0.000 0.000 0.976
#> GSM905068 4 0.0405 0.790 0.004 0.000 0.000 0.988 0.008 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) genotype/variation(p) individual(p) k
#> MAD:NMF 73 2.16e-07 4.52e-03 0.05241 2
#> MAD:NMF 75 8.78e-20 1.03e-04 0.95436 3
#> MAD:NMF 72 1.27e-18 1.47e-09 0.43483 4
#> MAD:NMF 73 2.39e-16 1.68e-10 0.00524 5
#> MAD:NMF 70 6.20e-15 7.01e-11 0.00572 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 76 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 0.918 0.941 0.975 0.4839 0.522 0.522
#> 3 3 0.772 0.764 0.885 0.2591 0.915 0.837
#> 4 4 0.785 0.755 0.875 0.0274 0.974 0.942
#> 5 5 0.737 0.797 0.897 0.1074 0.820 0.597
#> 6 6 0.815 0.716 0.881 0.0937 0.865 0.587
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
#> GSM905004 2 0.574 0.834 0.136 0.864
#> GSM905024 1 0.000 0.988 1.000 0.000
#> GSM905038 2 0.913 0.547 0.328 0.672
#> GSM905043 1 0.000 0.988 1.000 0.000
#> GSM904986 2 0.000 0.964 0.000 1.000
#> GSM904991 2 0.000 0.964 0.000 1.000
#> GSM904994 2 0.000 0.964 0.000 1.000
#> GSM904996 2 0.000 0.964 0.000 1.000
#> GSM905007 2 0.000 0.964 0.000 1.000
#> GSM905012 2 0.000 0.964 0.000 1.000
#> GSM905022 2 0.000 0.964 0.000 1.000
#> GSM905026 2 0.000 0.964 0.000 1.000
#> GSM905027 2 0.000 0.964 0.000 1.000
#> GSM905031 2 0.000 0.964 0.000 1.000
#> GSM905036 2 0.913 0.547 0.328 0.672
#> GSM905041 2 0.929 0.513 0.344 0.656
#> GSM905044 2 0.000 0.964 0.000 1.000
#> GSM904989 2 0.000 0.964 0.000 1.000
#> GSM904999 2 0.000 0.964 0.000 1.000
#> GSM905002 2 0.000 0.964 0.000 1.000
#> GSM905009 2 0.000 0.964 0.000 1.000
#> GSM905014 2 0.000 0.964 0.000 1.000
#> GSM905017 2 0.000 0.964 0.000 1.000
#> GSM905020 2 0.000 0.964 0.000 1.000
#> GSM905023 2 0.913 0.547 0.328 0.672
#> GSM905029 2 0.000 0.964 0.000 1.000
#> GSM905032 1 0.866 0.564 0.712 0.288
#> GSM905034 1 0.000 0.988 1.000 0.000
#> GSM905040 1 0.000 0.988 1.000 0.000
#> GSM904985 2 0.000 0.964 0.000 1.000
#> GSM904988 2 0.000 0.964 0.000 1.000
#> GSM904990 2 0.000 0.964 0.000 1.000
#> GSM904992 2 0.000 0.964 0.000 1.000
#> GSM904995 2 0.000 0.964 0.000 1.000
#> GSM904998 2 0.000 0.964 0.000 1.000
#> GSM905000 2 0.000 0.964 0.000 1.000
#> GSM905003 2 0.000 0.964 0.000 1.000
#> GSM905006 2 0.000 0.964 0.000 1.000
#> GSM905008 2 0.000 0.964 0.000 1.000
#> GSM905011 2 0.000 0.964 0.000 1.000
#> GSM905013 2 0.000 0.964 0.000 1.000
#> GSM905016 2 0.000 0.964 0.000 1.000
#> GSM905018 2 0.000 0.964 0.000 1.000
#> GSM905021 2 0.000 0.964 0.000 1.000
#> GSM905025 2 0.574 0.834 0.136 0.864
#> GSM905028 2 0.000 0.964 0.000 1.000
#> GSM905030 2 0.000 0.964 0.000 1.000
#> GSM905033 2 0.000 0.964 0.000 1.000
#> GSM905035 2 0.000 0.964 0.000 1.000
#> GSM905037 2 0.000 0.964 0.000 1.000
#> GSM905039 2 0.000 0.964 0.000 1.000
#> GSM905042 2 0.000 0.964 0.000 1.000
#> GSM905046 1 0.000 0.988 1.000 0.000
#> GSM905065 1 0.000 0.988 1.000 0.000
#> GSM905049 1 0.000 0.988 1.000 0.000
#> GSM905050 1 0.000 0.988 1.000 0.000
#> GSM905064 1 0.000 0.988 1.000 0.000
#> GSM905045 1 0.000 0.988 1.000 0.000
#> GSM905051 1 0.118 0.973 0.984 0.016
#> GSM905055 1 0.000 0.988 1.000 0.000
#> GSM905058 1 0.000 0.988 1.000 0.000
#> GSM905053 1 0.000 0.988 1.000 0.000
#> GSM905061 1 0.000 0.988 1.000 0.000
#> GSM905063 1 0.000 0.988 1.000 0.000
#> GSM905054 1 0.000 0.988 1.000 0.000
#> GSM905062 1 0.000 0.988 1.000 0.000
#> GSM905052 1 0.118 0.973 0.984 0.016
#> GSM905059 1 0.000 0.988 1.000 0.000
#> GSM905047 1 0.000 0.988 1.000 0.000
#> GSM905066 1 0.000 0.988 1.000 0.000
#> GSM905056 1 0.000 0.988 1.000 0.000
#> GSM905060 1 0.000 0.988 1.000 0.000
#> GSM905048 1 0.000 0.988 1.000 0.000
#> GSM905067 1 0.000 0.988 1.000 0.000
#> GSM905057 1 0.000 0.988 1.000 0.000
#> GSM905068 1 0.000 0.988 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM905004 3 0.4504 0.575 0.000 0.196 0.804
#> GSM905024 1 0.4452 0.780 0.808 0.000 0.192
#> GSM905038 3 0.0237 0.816 0.000 0.004 0.996
#> GSM905043 1 0.4452 0.780 0.808 0.000 0.192
#> GSM904986 2 0.0000 0.895 0.000 1.000 0.000
#> GSM904991 2 0.6126 0.443 0.000 0.600 0.400
#> GSM904994 2 0.0592 0.888 0.000 0.988 0.012
#> GSM904996 2 0.0000 0.895 0.000 1.000 0.000
#> GSM905007 2 0.6126 0.443 0.000 0.600 0.400
#> GSM905012 2 0.0592 0.888 0.000 0.988 0.012
#> GSM905022 2 0.0000 0.895 0.000 1.000 0.000
#> GSM905026 2 0.6267 0.345 0.000 0.548 0.452
#> GSM905027 2 0.6267 0.345 0.000 0.548 0.452
#> GSM905031 2 0.6267 0.345 0.000 0.548 0.452
#> GSM905036 3 0.0237 0.816 0.000 0.004 0.996
#> GSM905041 3 0.0747 0.804 0.016 0.000 0.984
#> GSM905044 2 0.6267 0.345 0.000 0.548 0.452
#> GSM904989 2 0.0592 0.888 0.000 0.988 0.012
#> GSM904999 2 0.0000 0.895 0.000 1.000 0.000
#> GSM905002 2 0.0000 0.895 0.000 1.000 0.000
#> GSM905009 2 0.0592 0.888 0.000 0.988 0.012
#> GSM905014 2 0.6126 0.443 0.000 0.600 0.400
#> GSM905017 2 0.0000 0.895 0.000 1.000 0.000
#> GSM905020 2 0.0000 0.895 0.000 1.000 0.000
#> GSM905023 3 0.0237 0.816 0.000 0.004 0.996
#> GSM905029 2 0.6305 0.269 0.000 0.516 0.484
#> GSM905032 3 0.6062 -0.131 0.384 0.000 0.616
#> GSM905034 1 0.4452 0.780 0.808 0.000 0.192
#> GSM905040 1 0.0237 0.808 0.996 0.000 0.004
#> GSM904985 2 0.0000 0.895 0.000 1.000 0.000
#> GSM904988 2 0.0000 0.895 0.000 1.000 0.000
#> GSM904990 2 0.0000 0.895 0.000 1.000 0.000
#> GSM904992 2 0.0000 0.895 0.000 1.000 0.000
#> GSM904995 2 0.0000 0.895 0.000 1.000 0.000
#> GSM904998 2 0.0000 0.895 0.000 1.000 0.000
#> GSM905000 2 0.0000 0.895 0.000 1.000 0.000
#> GSM905003 2 0.0000 0.895 0.000 1.000 0.000
#> GSM905006 2 0.0000 0.895 0.000 1.000 0.000
#> GSM905008 2 0.0000 0.895 0.000 1.000 0.000
#> GSM905011 2 0.0000 0.895 0.000 1.000 0.000
#> GSM905013 2 0.0000 0.895 0.000 1.000 0.000
#> GSM905016 2 0.0000 0.895 0.000 1.000 0.000
#> GSM905018 2 0.0000 0.895 0.000 1.000 0.000
#> GSM905021 2 0.0000 0.895 0.000 1.000 0.000
#> GSM905025 2 0.6154 0.277 0.000 0.592 0.408
#> GSM905028 2 0.0000 0.895 0.000 1.000 0.000
#> GSM905030 2 0.0000 0.895 0.000 1.000 0.000
#> GSM905033 2 0.0000 0.895 0.000 1.000 0.000
#> GSM905035 2 0.0000 0.895 0.000 1.000 0.000
#> GSM905037 2 0.0000 0.895 0.000 1.000 0.000
#> GSM905039 2 0.0000 0.895 0.000 1.000 0.000
#> GSM905042 2 0.0000 0.895 0.000 1.000 0.000
#> GSM905046 1 0.0000 0.808 1.000 0.000 0.000
#> GSM905065 1 0.0000 0.808 1.000 0.000 0.000
#> GSM905049 1 0.5760 0.726 0.672 0.000 0.328
#> GSM905050 1 0.5760 0.726 0.672 0.000 0.328
#> GSM905064 1 0.5760 0.726 0.672 0.000 0.328
#> GSM905045 1 0.5760 0.726 0.672 0.000 0.328
#> GSM905051 1 0.5859 0.707 0.656 0.000 0.344
#> GSM905055 1 0.0000 0.808 1.000 0.000 0.000
#> GSM905058 1 0.0000 0.808 1.000 0.000 0.000
#> GSM905053 1 0.5760 0.726 0.672 0.000 0.328
#> GSM905061 1 0.5760 0.726 0.672 0.000 0.328
#> GSM905063 1 0.0000 0.808 1.000 0.000 0.000
#> GSM905054 1 0.5760 0.726 0.672 0.000 0.328
#> GSM905062 1 0.5760 0.726 0.672 0.000 0.328
#> GSM905052 1 0.5859 0.707 0.656 0.000 0.344
#> GSM905059 1 0.0000 0.808 1.000 0.000 0.000
#> GSM905047 1 0.0000 0.808 1.000 0.000 0.000
#> GSM905066 1 0.0000 0.808 1.000 0.000 0.000
#> GSM905056 1 0.0000 0.808 1.000 0.000 0.000
#> GSM905060 1 0.0000 0.808 1.000 0.000 0.000
#> GSM905048 1 0.0000 0.808 1.000 0.000 0.000
#> GSM905067 1 0.0000 0.808 1.000 0.000 0.000
#> GSM905057 1 0.0000 0.808 1.000 0.000 0.000
#> GSM905068 1 0.5760 0.726 0.672 0.000 0.328
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM905004 3 0.6170 0.6309 0.136 0.000 0.672 0.192
#> GSM905024 1 0.2868 0.7526 0.864 0.000 0.136 0.000
#> GSM905038 3 0.4564 0.9162 0.328 0.000 0.672 0.000
#> GSM905043 1 0.2868 0.7526 0.864 0.000 0.136 0.000
#> GSM904986 2 0.0000 0.8924 0.000 1.000 0.000 0.000
#> GSM904991 2 0.4866 0.4453 0.000 0.596 0.404 0.000
#> GSM904994 2 0.0469 0.8874 0.000 0.988 0.012 0.000
#> GSM904996 2 0.0000 0.8924 0.000 1.000 0.000 0.000
#> GSM905007 2 0.4866 0.4453 0.000 0.596 0.404 0.000
#> GSM905012 2 0.0469 0.8874 0.000 0.988 0.012 0.000
#> GSM905022 2 0.0000 0.8924 0.000 1.000 0.000 0.000
#> GSM905026 2 0.5493 0.3169 0.000 0.528 0.456 0.016
#> GSM905027 2 0.5493 0.3169 0.000 0.528 0.456 0.016
#> GSM905031 2 0.5493 0.3169 0.000 0.528 0.456 0.016
#> GSM905036 3 0.4564 0.9162 0.328 0.000 0.672 0.000
#> GSM905041 3 0.4643 0.8938 0.344 0.000 0.656 0.000
#> GSM905044 2 0.5493 0.3169 0.000 0.528 0.456 0.016
#> GSM904989 2 0.0469 0.8874 0.000 0.988 0.012 0.000
#> GSM904999 2 0.0000 0.8924 0.000 1.000 0.000 0.000
#> GSM905002 2 0.0000 0.8924 0.000 1.000 0.000 0.000
#> GSM905009 2 0.0469 0.8874 0.000 0.988 0.012 0.000
#> GSM905014 2 0.4866 0.4453 0.000 0.596 0.404 0.000
#> GSM905017 2 0.0000 0.8924 0.000 1.000 0.000 0.000
#> GSM905020 2 0.0000 0.8924 0.000 1.000 0.000 0.000
#> GSM905023 3 0.4564 0.9162 0.328 0.000 0.672 0.000
#> GSM905029 2 0.4998 0.2637 0.000 0.512 0.488 0.000
#> GSM905032 1 0.4331 0.0451 0.712 0.000 0.288 0.000
#> GSM905034 1 0.2868 0.7526 0.864 0.000 0.136 0.000
#> GSM905040 1 0.5639 0.7716 0.636 0.000 0.324 0.040
#> GSM904985 2 0.0000 0.8924 0.000 1.000 0.000 0.000
#> GSM904988 2 0.0000 0.8924 0.000 1.000 0.000 0.000
#> GSM904990 2 0.0000 0.8924 0.000 1.000 0.000 0.000
#> GSM904992 2 0.0000 0.8924 0.000 1.000 0.000 0.000
#> GSM904995 2 0.0000 0.8924 0.000 1.000 0.000 0.000
#> GSM904998 2 0.0000 0.8924 0.000 1.000 0.000 0.000
#> GSM905000 2 0.0000 0.8924 0.000 1.000 0.000 0.000
#> GSM905003 2 0.0000 0.8924 0.000 1.000 0.000 0.000
#> GSM905006 2 0.0000 0.8924 0.000 1.000 0.000 0.000
#> GSM905008 2 0.0000 0.8924 0.000 1.000 0.000 0.000
#> GSM905011 2 0.0000 0.8924 0.000 1.000 0.000 0.000
#> GSM905013 2 0.0000 0.8924 0.000 1.000 0.000 0.000
#> GSM905016 2 0.0000 0.8924 0.000 1.000 0.000 0.000
#> GSM905018 2 0.0000 0.8924 0.000 1.000 0.000 0.000
#> GSM905021 2 0.0000 0.8924 0.000 1.000 0.000 0.000
#> GSM905025 4 0.1389 0.0000 0.000 0.048 0.000 0.952
#> GSM905028 2 0.0592 0.8866 0.000 0.984 0.000 0.016
#> GSM905030 2 0.0592 0.8866 0.000 0.984 0.000 0.016
#> GSM905033 2 0.0592 0.8866 0.000 0.984 0.000 0.016
#> GSM905035 2 0.0592 0.8866 0.000 0.984 0.000 0.016
#> GSM905037 2 0.0592 0.8866 0.000 0.984 0.000 0.016
#> GSM905039 2 0.0592 0.8866 0.000 0.984 0.000 0.016
#> GSM905042 2 0.0592 0.8866 0.000 0.984 0.000 0.016
#> GSM905046 1 0.5812 0.7714 0.624 0.000 0.328 0.048
#> GSM905065 1 0.5812 0.7714 0.624 0.000 0.328 0.048
#> GSM905049 1 0.0000 0.7085 1.000 0.000 0.000 0.000
#> GSM905050 1 0.0000 0.7085 1.000 0.000 0.000 0.000
#> GSM905064 1 0.0000 0.7085 1.000 0.000 0.000 0.000
#> GSM905045 1 0.0000 0.7085 1.000 0.000 0.000 0.000
#> GSM905051 1 0.0592 0.6921 0.984 0.000 0.016 0.000
#> GSM905055 1 0.5812 0.7714 0.624 0.000 0.328 0.048
#> GSM905058 1 0.5812 0.7714 0.624 0.000 0.328 0.048
#> GSM905053 1 0.0000 0.7085 1.000 0.000 0.000 0.000
#> GSM905061 1 0.0000 0.7085 1.000 0.000 0.000 0.000
#> GSM905063 1 0.5812 0.7714 0.624 0.000 0.328 0.048
#> GSM905054 1 0.0000 0.7085 1.000 0.000 0.000 0.000
#> GSM905062 1 0.0000 0.7085 1.000 0.000 0.000 0.000
#> GSM905052 1 0.0592 0.6921 0.984 0.000 0.016 0.000
#> GSM905059 1 0.5812 0.7714 0.624 0.000 0.328 0.048
#> GSM905047 1 0.5812 0.7714 0.624 0.000 0.328 0.048
#> GSM905066 1 0.5812 0.7714 0.624 0.000 0.328 0.048
#> GSM905056 1 0.5812 0.7714 0.624 0.000 0.328 0.048
#> GSM905060 1 0.5812 0.7714 0.624 0.000 0.328 0.048
#> GSM905048 1 0.5812 0.7714 0.624 0.000 0.328 0.048
#> GSM905067 1 0.5812 0.7714 0.624 0.000 0.328 0.048
#> GSM905057 1 0.5812 0.7714 0.624 0.000 0.328 0.048
#> GSM905068 1 0.0000 0.7085 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
#> GSM905004 3 0.2966 0.046 0.000 0.000 0.848 0.136 0.016
#> GSM905024 4 0.2471 0.799 0.136 0.000 0.000 0.864 0.000
#> GSM905038 3 0.3932 0.195 0.000 0.000 0.672 0.328 0.000
#> GSM905043 4 0.2471 0.799 0.136 0.000 0.000 0.864 0.000
#> GSM904986 2 0.2561 0.837 0.000 0.856 0.144 0.000 0.000
#> GSM904991 3 0.4268 0.434 0.000 0.444 0.556 0.000 0.000
#> GSM904994 2 0.2773 0.817 0.000 0.836 0.164 0.000 0.000
#> GSM904996 2 0.2648 0.830 0.000 0.848 0.152 0.000 0.000
#> GSM905007 3 0.4268 0.434 0.000 0.444 0.556 0.000 0.000
#> GSM905012 2 0.2773 0.817 0.000 0.836 0.164 0.000 0.000
#> GSM905022 2 0.2648 0.830 0.000 0.848 0.152 0.000 0.000
#> GSM905026 3 0.4651 0.560 0.000 0.372 0.608 0.000 0.020
#> GSM905027 3 0.4651 0.560 0.000 0.372 0.608 0.000 0.020
#> GSM905031 3 0.4651 0.560 0.000 0.372 0.608 0.000 0.020
#> GSM905036 3 0.3932 0.195 0.000 0.000 0.672 0.328 0.000
#> GSM905041 3 0.3999 0.180 0.000 0.000 0.656 0.344 0.000
#> GSM905044 3 0.4651 0.560 0.000 0.372 0.608 0.000 0.020
#> GSM904989 2 0.2773 0.817 0.000 0.836 0.164 0.000 0.000
#> GSM904999 2 0.2516 0.840 0.000 0.860 0.140 0.000 0.000
#> GSM905002 2 0.2648 0.830 0.000 0.848 0.152 0.000 0.000
#> GSM905009 2 0.2773 0.817 0.000 0.836 0.164 0.000 0.000
#> GSM905014 3 0.4268 0.434 0.000 0.444 0.556 0.000 0.000
#> GSM905017 2 0.2516 0.840 0.000 0.860 0.140 0.000 0.000
#> GSM905020 2 0.2648 0.830 0.000 0.848 0.152 0.000 0.000
#> GSM905023 3 0.3932 0.195 0.000 0.000 0.672 0.328 0.000
#> GSM905029 3 0.4060 0.567 0.000 0.360 0.640 0.000 0.000
#> GSM905032 4 0.3730 0.588 0.000 0.000 0.288 0.712 0.000
#> GSM905034 4 0.2561 0.790 0.144 0.000 0.000 0.856 0.000
#> GSM905040 1 0.3305 0.657 0.776 0.000 0.000 0.224 0.000
#> GSM904985 2 0.0000 0.919 0.000 1.000 0.000 0.000 0.000
#> GSM904988 2 0.0000 0.919 0.000 1.000 0.000 0.000 0.000
#> GSM904990 2 0.0000 0.919 0.000 1.000 0.000 0.000 0.000
#> GSM904992 2 0.0000 0.919 0.000 1.000 0.000 0.000 0.000
#> GSM904995 2 0.0000 0.919 0.000 1.000 0.000 0.000 0.000
#> GSM904998 2 0.0000 0.919 0.000 1.000 0.000 0.000 0.000
#> GSM905000 2 0.0000 0.919 0.000 1.000 0.000 0.000 0.000
#> GSM905003 2 0.0000 0.919 0.000 1.000 0.000 0.000 0.000
#> GSM905006 2 0.0000 0.919 0.000 1.000 0.000 0.000 0.000
#> GSM905008 2 0.0000 0.919 0.000 1.000 0.000 0.000 0.000
#> GSM905011 2 0.0000 0.919 0.000 1.000 0.000 0.000 0.000
#> GSM905013 2 0.0000 0.919 0.000 1.000 0.000 0.000 0.000
#> GSM905016 2 0.0000 0.919 0.000 1.000 0.000 0.000 0.000
#> GSM905018 2 0.0000 0.919 0.000 1.000 0.000 0.000 0.000
#> GSM905021 2 0.0000 0.919 0.000 1.000 0.000 0.000 0.000
#> GSM905025 5 0.0000 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM905028 2 0.0609 0.911 0.000 0.980 0.000 0.000 0.020
#> GSM905030 2 0.0609 0.911 0.000 0.980 0.000 0.000 0.020
#> GSM905033 2 0.0609 0.911 0.000 0.980 0.000 0.000 0.020
#> GSM905035 2 0.0609 0.911 0.000 0.980 0.000 0.000 0.020
#> GSM905037 2 0.0609 0.911 0.000 0.980 0.000 0.000 0.020
#> GSM905039 2 0.0609 0.911 0.000 0.980 0.000 0.000 0.020
#> GSM905042 2 0.0609 0.911 0.000 0.980 0.000 0.000 0.020
#> GSM905046 1 0.0290 0.976 0.992 0.000 0.000 0.008 0.000
#> GSM905065 1 0.0290 0.976 0.992 0.000 0.000 0.008 0.000
#> GSM905049 4 0.0000 0.922 0.000 0.000 0.000 1.000 0.000
#> GSM905050 4 0.0000 0.922 0.000 0.000 0.000 1.000 0.000
#> GSM905064 4 0.0000 0.922 0.000 0.000 0.000 1.000 0.000
#> GSM905045 4 0.0000 0.922 0.000 0.000 0.000 1.000 0.000
#> GSM905051 4 0.0510 0.915 0.000 0.000 0.016 0.984 0.000
#> GSM905055 1 0.0290 0.976 0.992 0.000 0.000 0.008 0.000
#> GSM905058 1 0.0290 0.976 0.992 0.000 0.000 0.008 0.000
#> GSM905053 4 0.0000 0.922 0.000 0.000 0.000 1.000 0.000
#> GSM905061 4 0.0963 0.904 0.036 0.000 0.000 0.964 0.000
#> GSM905063 1 0.0000 0.968 1.000 0.000 0.000 0.000 0.000
#> GSM905054 4 0.0000 0.922 0.000 0.000 0.000 1.000 0.000
#> GSM905062 4 0.0963 0.904 0.036 0.000 0.000 0.964 0.000
#> GSM905052 4 0.0510 0.915 0.000 0.000 0.016 0.984 0.000
#> GSM905059 1 0.0290 0.976 0.992 0.000 0.000 0.008 0.000
#> GSM905047 1 0.0290 0.976 0.992 0.000 0.000 0.008 0.000
#> GSM905066 1 0.0000 0.968 1.000 0.000 0.000 0.000 0.000
#> GSM905056 1 0.0290 0.976 0.992 0.000 0.000 0.008 0.000
#> GSM905060 1 0.0290 0.976 0.992 0.000 0.000 0.008 0.000
#> GSM905048 1 0.0290 0.976 0.992 0.000 0.000 0.008 0.000
#> GSM905067 1 0.0290 0.976 0.992 0.000 0.000 0.008 0.000
#> GSM905057 1 0.0290 0.976 0.992 0.000 0.000 0.008 0.000
#> GSM905068 4 0.0000 0.922 0.000 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM905004 6 0.4572 0.000 0.000 0.000 0.036 0.020 0.272 0.672
#> GSM905024 4 0.2362 0.795 0.136 0.000 0.000 0.860 0.000 0.004
#> GSM905038 3 0.6118 -0.350 0.000 0.000 0.364 0.328 0.308 0.000
#> GSM905043 4 0.2362 0.795 0.136 0.000 0.000 0.860 0.000 0.004
#> GSM904986 3 0.3843 0.408 0.000 0.452 0.548 0.000 0.000 0.000
#> GSM904991 3 0.0146 0.385 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM904994 3 0.3737 0.498 0.000 0.392 0.608 0.000 0.000 0.000
#> GSM904996 3 0.3765 0.488 0.000 0.404 0.596 0.000 0.000 0.000
#> GSM905007 3 0.0146 0.385 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM905012 3 0.3737 0.498 0.000 0.392 0.608 0.000 0.000 0.000
#> GSM905022 3 0.3774 0.482 0.000 0.408 0.592 0.000 0.000 0.000
#> GSM905026 3 0.1814 0.356 0.000 0.000 0.900 0.000 0.100 0.000
#> GSM905027 3 0.1814 0.356 0.000 0.000 0.900 0.000 0.100 0.000
#> GSM905031 3 0.1814 0.356 0.000 0.000 0.900 0.000 0.100 0.000
#> GSM905036 3 0.6118 -0.350 0.000 0.000 0.364 0.328 0.308 0.000
#> GSM905041 3 0.6123 -0.355 0.000 0.000 0.348 0.344 0.308 0.000
#> GSM905044 3 0.1814 0.356 0.000 0.000 0.900 0.000 0.100 0.000
#> GSM904989 3 0.3737 0.498 0.000 0.392 0.608 0.000 0.000 0.000
#> GSM904999 3 0.3868 0.314 0.000 0.496 0.504 0.000 0.000 0.000
#> GSM905002 3 0.3765 0.488 0.000 0.404 0.596 0.000 0.000 0.000
#> GSM905009 3 0.3737 0.498 0.000 0.392 0.608 0.000 0.000 0.000
#> GSM905014 3 0.0146 0.385 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM905017 3 0.3868 0.314 0.000 0.496 0.504 0.000 0.000 0.000
#> GSM905020 3 0.3765 0.488 0.000 0.404 0.596 0.000 0.000 0.000
#> GSM905023 3 0.6118 -0.350 0.000 0.000 0.364 0.328 0.308 0.000
#> GSM905029 3 0.1910 0.334 0.000 0.000 0.892 0.000 0.108 0.000
#> GSM905032 4 0.3351 0.528 0.000 0.000 0.000 0.712 0.288 0.000
#> GSM905034 4 0.2442 0.785 0.144 0.000 0.000 0.852 0.000 0.004
#> GSM905040 1 0.2969 0.656 0.776 0.000 0.000 0.224 0.000 0.000
#> GSM904985 2 0.0000 0.991 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM904988 2 0.0000 0.991 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM904990 2 0.0000 0.991 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM904992 2 0.0000 0.991 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM904995 2 0.0000 0.991 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM904998 2 0.0000 0.991 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905000 2 0.0000 0.991 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905003 2 0.0000 0.991 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905006 2 0.0000 0.991 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905008 2 0.0000 0.991 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905011 2 0.0000 0.991 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905013 2 0.0000 0.991 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905016 2 0.0000 0.991 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905018 2 0.0000 0.991 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905021 2 0.0146 0.987 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM905025 5 0.3565 0.000 0.000 0.000 0.004 0.000 0.692 0.304
#> GSM905028 2 0.0603 0.981 0.000 0.980 0.004 0.000 0.016 0.000
#> GSM905030 2 0.0603 0.981 0.000 0.980 0.004 0.000 0.016 0.000
#> GSM905033 2 0.0603 0.981 0.000 0.980 0.004 0.000 0.016 0.000
#> GSM905035 2 0.0603 0.981 0.000 0.980 0.004 0.000 0.016 0.000
#> GSM905037 2 0.0603 0.981 0.000 0.980 0.004 0.000 0.016 0.000
#> GSM905039 2 0.0603 0.981 0.000 0.980 0.004 0.000 0.016 0.000
#> GSM905042 2 0.0603 0.981 0.000 0.980 0.004 0.000 0.016 0.000
#> GSM905046 1 0.0260 0.972 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM905065 1 0.0260 0.972 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM905049 4 0.0000 0.919 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905050 4 0.0000 0.919 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905064 4 0.0000 0.919 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905045 4 0.0000 0.919 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905051 4 0.0458 0.912 0.000 0.000 0.000 0.984 0.016 0.000
#> GSM905055 1 0.0260 0.972 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM905058 1 0.0260 0.972 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM905053 4 0.0000 0.919 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905061 4 0.0865 0.900 0.036 0.000 0.000 0.964 0.000 0.000
#> GSM905063 1 0.0547 0.950 0.980 0.000 0.000 0.000 0.000 0.020
#> GSM905054 4 0.0000 0.919 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905062 4 0.0865 0.900 0.036 0.000 0.000 0.964 0.000 0.000
#> GSM905052 4 0.0458 0.912 0.000 0.000 0.000 0.984 0.016 0.000
#> GSM905059 1 0.0260 0.972 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM905047 1 0.0260 0.972 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM905066 1 0.0547 0.950 0.980 0.000 0.000 0.000 0.000 0.020
#> GSM905056 1 0.0260 0.972 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM905060 1 0.0260 0.972 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM905048 1 0.0260 0.972 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM905067 1 0.0260 0.972 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM905057 1 0.0260 0.972 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM905068 4 0.0000 0.919 0.000 0.000 0.000 1.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) genotype/variation(p) individual(p) k
#> ATC:hclust 76 7.07e-09 1.08e-02 0.0399 2
#> ATC:hclust 66 1.14e-06 1.17e-03 0.0758 3
#> ATC:hclust 66 1.14e-06 1.17e-03 0.0758 4
#> ATC:hclust 67 1.87e-08 1.50e-06 0.1491 5
#> ATC:hclust 51 1.84e-08 3.77e-07 0.3967 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 76 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.989 0.995 0.4889 0.511 0.511
#> 3 3 0.660 0.736 0.868 0.3317 0.828 0.670
#> 4 4 0.687 0.411 0.669 0.1184 0.876 0.688
#> 5 5 0.694 0.808 0.798 0.0704 0.818 0.469
#> 6 6 0.755 0.858 0.835 0.0451 0.957 0.788
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
#> GSM905004 2 0.0672 0.990 0.008 0.992
#> GSM905024 1 0.0000 0.991 1.000 0.000
#> GSM905038 2 0.0000 0.998 0.000 1.000
#> GSM905043 1 0.0000 0.991 1.000 0.000
#> GSM904986 2 0.0000 0.998 0.000 1.000
#> GSM904991 2 0.0000 0.998 0.000 1.000
#> GSM904994 2 0.0000 0.998 0.000 1.000
#> GSM904996 2 0.0000 0.998 0.000 1.000
#> GSM905007 2 0.0000 0.998 0.000 1.000
#> GSM905012 2 0.0000 0.998 0.000 1.000
#> GSM905022 2 0.0000 0.998 0.000 1.000
#> GSM905026 2 0.0000 0.998 0.000 1.000
#> GSM905027 2 0.0000 0.998 0.000 1.000
#> GSM905031 2 0.0000 0.998 0.000 1.000
#> GSM905036 1 0.8443 0.624 0.728 0.272
#> GSM905041 1 0.0000 0.991 1.000 0.000
#> GSM905044 2 0.0000 0.998 0.000 1.000
#> GSM904989 2 0.0000 0.998 0.000 1.000
#> GSM904999 2 0.0000 0.998 0.000 1.000
#> GSM905002 2 0.0000 0.998 0.000 1.000
#> GSM905009 2 0.0000 0.998 0.000 1.000
#> GSM905014 2 0.0000 0.998 0.000 1.000
#> GSM905017 2 0.0000 0.998 0.000 1.000
#> GSM905020 2 0.0000 0.998 0.000 1.000
#> GSM905023 2 0.4022 0.912 0.080 0.920
#> GSM905029 2 0.0000 0.998 0.000 1.000
#> GSM905032 1 0.0000 0.991 1.000 0.000
#> GSM905034 1 0.0000 0.991 1.000 0.000
#> GSM905040 1 0.0000 0.991 1.000 0.000
#> GSM904985 2 0.0000 0.998 0.000 1.000
#> GSM904988 2 0.0000 0.998 0.000 1.000
#> GSM904990 2 0.0000 0.998 0.000 1.000
#> GSM904992 2 0.0000 0.998 0.000 1.000
#> GSM904995 2 0.0000 0.998 0.000 1.000
#> GSM904998 2 0.0000 0.998 0.000 1.000
#> GSM905000 2 0.0000 0.998 0.000 1.000
#> GSM905003 2 0.0000 0.998 0.000 1.000
#> GSM905006 2 0.0000 0.998 0.000 1.000
#> GSM905008 2 0.0000 0.998 0.000 1.000
#> GSM905011 2 0.0000 0.998 0.000 1.000
#> GSM905013 2 0.0000 0.998 0.000 1.000
#> GSM905016 2 0.0000 0.998 0.000 1.000
#> GSM905018 2 0.0000 0.998 0.000 1.000
#> GSM905021 2 0.0000 0.998 0.000 1.000
#> GSM905025 2 0.0000 0.998 0.000 1.000
#> GSM905028 2 0.0000 0.998 0.000 1.000
#> GSM905030 2 0.0000 0.998 0.000 1.000
#> GSM905033 2 0.0000 0.998 0.000 1.000
#> GSM905035 2 0.0000 0.998 0.000 1.000
#> GSM905037 2 0.0000 0.998 0.000 1.000
#> GSM905039 2 0.0000 0.998 0.000 1.000
#> GSM905042 2 0.0000 0.998 0.000 1.000
#> GSM905046 1 0.0000 0.991 1.000 0.000
#> GSM905065 1 0.0000 0.991 1.000 0.000
#> GSM905049 1 0.0000 0.991 1.000 0.000
#> GSM905050 1 0.0000 0.991 1.000 0.000
#> GSM905064 1 0.0000 0.991 1.000 0.000
#> GSM905045 1 0.0000 0.991 1.000 0.000
#> GSM905051 1 0.0000 0.991 1.000 0.000
#> GSM905055 1 0.0000 0.991 1.000 0.000
#> GSM905058 1 0.0000 0.991 1.000 0.000
#> GSM905053 1 0.0000 0.991 1.000 0.000
#> GSM905061 1 0.0000 0.991 1.000 0.000
#> GSM905063 1 0.0000 0.991 1.000 0.000
#> GSM905054 1 0.0000 0.991 1.000 0.000
#> GSM905062 1 0.0000 0.991 1.000 0.000
#> GSM905052 1 0.0000 0.991 1.000 0.000
#> GSM905059 1 0.0000 0.991 1.000 0.000
#> GSM905047 1 0.0000 0.991 1.000 0.000
#> GSM905066 1 0.0000 0.991 1.000 0.000
#> GSM905056 1 0.0000 0.991 1.000 0.000
#> GSM905060 1 0.0000 0.991 1.000 0.000
#> GSM905048 1 0.0000 0.991 1.000 0.000
#> GSM905067 1 0.0000 0.991 1.000 0.000
#> GSM905057 1 0.0000 0.991 1.000 0.000
#> GSM905068 1 0.0000 0.991 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM905004 3 0.0000 0.800 0.000 0.000 1.000
#> GSM905024 1 0.5650 0.744 0.688 0.000 0.312
#> GSM905038 3 0.0000 0.800 0.000 0.000 1.000
#> GSM905043 1 0.5650 0.744 0.688 0.000 0.312
#> GSM904986 2 0.5882 0.581 0.000 0.652 0.348
#> GSM904991 3 0.2448 0.788 0.000 0.076 0.924
#> GSM904994 2 0.5882 0.581 0.000 0.652 0.348
#> GSM904996 2 0.5882 0.581 0.000 0.652 0.348
#> GSM905007 3 0.4452 0.712 0.000 0.192 0.808
#> GSM905012 2 0.5882 0.581 0.000 0.652 0.348
#> GSM905022 2 0.5882 0.581 0.000 0.652 0.348
#> GSM905026 3 0.4452 0.712 0.000 0.192 0.808
#> GSM905027 3 0.3412 0.767 0.000 0.124 0.876
#> GSM905031 3 0.4452 0.712 0.000 0.192 0.808
#> GSM905036 3 0.0000 0.800 0.000 0.000 1.000
#> GSM905041 3 0.3192 0.664 0.112 0.000 0.888
#> GSM905044 3 0.4452 0.712 0.000 0.192 0.808
#> GSM904989 2 0.5882 0.581 0.000 0.652 0.348
#> GSM904999 2 0.5882 0.581 0.000 0.652 0.348
#> GSM905002 2 0.5882 0.581 0.000 0.652 0.348
#> GSM905009 2 0.5882 0.581 0.000 0.652 0.348
#> GSM905014 3 0.5650 0.429 0.000 0.312 0.688
#> GSM905017 2 0.5882 0.581 0.000 0.652 0.348
#> GSM905020 2 0.5882 0.581 0.000 0.652 0.348
#> GSM905023 3 0.0000 0.800 0.000 0.000 1.000
#> GSM905029 3 0.0000 0.800 0.000 0.000 1.000
#> GSM905032 3 0.6062 -0.122 0.384 0.000 0.616
#> GSM905034 1 0.0000 0.870 1.000 0.000 0.000
#> GSM905040 1 0.0000 0.870 1.000 0.000 0.000
#> GSM904985 2 0.0000 0.812 0.000 1.000 0.000
#> GSM904988 2 0.0000 0.812 0.000 1.000 0.000
#> GSM904990 2 0.0000 0.812 0.000 1.000 0.000
#> GSM904992 2 0.0000 0.812 0.000 1.000 0.000
#> GSM904995 2 0.0000 0.812 0.000 1.000 0.000
#> GSM904998 2 0.0000 0.812 0.000 1.000 0.000
#> GSM905000 2 0.0000 0.812 0.000 1.000 0.000
#> GSM905003 2 0.0000 0.812 0.000 1.000 0.000
#> GSM905006 2 0.0000 0.812 0.000 1.000 0.000
#> GSM905008 2 0.0000 0.812 0.000 1.000 0.000
#> GSM905011 2 0.0000 0.812 0.000 1.000 0.000
#> GSM905013 2 0.0000 0.812 0.000 1.000 0.000
#> GSM905016 2 0.0000 0.812 0.000 1.000 0.000
#> GSM905018 2 0.0000 0.812 0.000 1.000 0.000
#> GSM905021 2 0.0000 0.812 0.000 1.000 0.000
#> GSM905025 2 0.6280 -0.100 0.000 0.540 0.460
#> GSM905028 2 0.0000 0.812 0.000 1.000 0.000
#> GSM905030 2 0.0237 0.810 0.000 0.996 0.004
#> GSM905033 2 0.1753 0.791 0.000 0.952 0.048
#> GSM905035 2 0.0237 0.810 0.000 0.996 0.004
#> GSM905037 2 0.0000 0.812 0.000 1.000 0.000
#> GSM905039 2 0.0237 0.810 0.000 0.996 0.004
#> GSM905042 2 0.6302 0.263 0.000 0.520 0.480
#> GSM905046 1 0.0000 0.870 1.000 0.000 0.000
#> GSM905065 1 0.0000 0.870 1.000 0.000 0.000
#> GSM905049 1 0.5650 0.744 0.688 0.000 0.312
#> GSM905050 1 0.6140 0.607 0.596 0.000 0.404
#> GSM905064 1 0.3816 0.835 0.852 0.000 0.148
#> GSM905045 1 0.5560 0.752 0.700 0.000 0.300
#> GSM905051 1 0.5650 0.744 0.688 0.000 0.312
#> GSM905055 1 0.0000 0.870 1.000 0.000 0.000
#> GSM905058 1 0.0000 0.870 1.000 0.000 0.000
#> GSM905053 1 0.5650 0.744 0.688 0.000 0.312
#> GSM905061 1 0.2448 0.855 0.924 0.000 0.076
#> GSM905063 1 0.0000 0.870 1.000 0.000 0.000
#> GSM905054 1 0.3816 0.835 0.852 0.000 0.148
#> GSM905062 1 0.3686 0.838 0.860 0.000 0.140
#> GSM905052 1 0.5650 0.744 0.688 0.000 0.312
#> GSM905059 1 0.0000 0.870 1.000 0.000 0.000
#> GSM905047 1 0.0000 0.870 1.000 0.000 0.000
#> GSM905066 1 0.0000 0.870 1.000 0.000 0.000
#> GSM905056 1 0.0000 0.870 1.000 0.000 0.000
#> GSM905060 1 0.0000 0.870 1.000 0.000 0.000
#> GSM905048 1 0.0000 0.870 1.000 0.000 0.000
#> GSM905067 1 0.0000 0.870 1.000 0.000 0.000
#> GSM905057 1 0.0000 0.870 1.000 0.000 0.000
#> GSM905068 1 0.5650 0.744 0.688 0.000 0.312
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM905004 3 0.1042 0.764 0.000 0.020 0.972 0.008
#> GSM905024 1 0.7456 0.630 0.508 0.000 0.256 0.236
#> GSM905038 3 0.3311 0.777 0.000 0.172 0.828 0.000
#> GSM905043 1 0.7456 0.630 0.508 0.000 0.256 0.236
#> GSM904986 2 0.1557 0.381 0.000 0.944 0.056 0.000
#> GSM904991 2 0.4999 -0.434 0.000 0.508 0.492 0.000
#> GSM904994 2 0.1637 0.380 0.000 0.940 0.060 0.000
#> GSM904996 2 0.1557 0.381 0.000 0.944 0.056 0.000
#> GSM905007 2 0.4985 -0.396 0.000 0.532 0.468 0.000
#> GSM905012 2 0.1637 0.380 0.000 0.940 0.060 0.000
#> GSM905022 2 0.1557 0.381 0.000 0.944 0.056 0.000
#> GSM905026 3 0.4630 0.763 0.000 0.196 0.768 0.036
#> GSM905027 3 0.3937 0.770 0.000 0.188 0.800 0.012
#> GSM905031 3 0.4630 0.763 0.000 0.196 0.768 0.036
#> GSM905036 3 0.0937 0.753 0.000 0.012 0.976 0.012
#> GSM905041 3 0.3272 0.665 0.032 0.008 0.884 0.076
#> GSM905044 3 0.4781 0.749 0.000 0.212 0.752 0.036
#> GSM904989 2 0.1637 0.380 0.000 0.940 0.060 0.000
#> GSM904999 2 0.1557 0.381 0.000 0.944 0.056 0.000
#> GSM905002 2 0.1557 0.381 0.000 0.944 0.056 0.000
#> GSM905009 2 0.1637 0.380 0.000 0.940 0.060 0.000
#> GSM905014 2 0.4977 -0.383 0.000 0.540 0.460 0.000
#> GSM905017 2 0.1557 0.381 0.000 0.944 0.056 0.000
#> GSM905020 2 0.1557 0.381 0.000 0.944 0.056 0.000
#> GSM905023 3 0.0469 0.760 0.000 0.012 0.988 0.000
#> GSM905029 3 0.3311 0.777 0.000 0.172 0.828 0.000
#> GSM905032 3 0.6618 0.169 0.124 0.000 0.604 0.272
#> GSM905034 1 0.0817 0.737 0.976 0.000 0.000 0.024
#> GSM905040 1 0.0592 0.738 0.984 0.000 0.000 0.016
#> GSM904985 2 0.4999 -0.338 0.000 0.508 0.000 0.492
#> GSM904988 2 0.5000 -0.349 0.000 0.504 0.000 0.496
#> GSM904990 2 0.5000 -0.349 0.000 0.504 0.000 0.496
#> GSM904992 2 0.5000 -0.349 0.000 0.504 0.000 0.496
#> GSM904995 2 0.4999 -0.338 0.000 0.508 0.000 0.492
#> GSM904998 2 0.4999 -0.338 0.000 0.508 0.000 0.492
#> GSM905000 2 0.4999 -0.338 0.000 0.508 0.000 0.492
#> GSM905003 2 0.4999 -0.338 0.000 0.508 0.000 0.492
#> GSM905006 2 0.5000 -0.349 0.000 0.504 0.000 0.496
#> GSM905008 2 0.4999 -0.338 0.000 0.508 0.000 0.492
#> GSM905011 2 0.5000 -0.349 0.000 0.504 0.000 0.496
#> GSM905013 2 0.4999 -0.338 0.000 0.508 0.000 0.492
#> GSM905016 2 0.4999 -0.338 0.000 0.508 0.000 0.492
#> GSM905018 2 0.4999 -0.338 0.000 0.508 0.000 0.492
#> GSM905021 2 0.4999 -0.338 0.000 0.508 0.000 0.492
#> GSM905025 3 0.5271 0.499 0.000 0.020 0.640 0.340
#> GSM905028 4 0.5322 0.910 0.000 0.312 0.028 0.660
#> GSM905030 4 0.5972 0.943 0.000 0.304 0.064 0.632
#> GSM905033 4 0.6156 0.861 0.000 0.344 0.064 0.592
#> GSM905035 4 0.5972 0.943 0.000 0.304 0.064 0.632
#> GSM905037 4 0.5322 0.910 0.000 0.312 0.028 0.660
#> GSM905039 4 0.5972 0.943 0.000 0.304 0.064 0.632
#> GSM905042 3 0.7476 0.395 0.000 0.236 0.504 0.260
#> GSM905046 1 0.0000 0.742 1.000 0.000 0.000 0.000
#> GSM905065 1 0.0188 0.742 0.996 0.000 0.000 0.004
#> GSM905049 1 0.7540 0.637 0.480 0.000 0.216 0.304
#> GSM905050 1 0.7902 0.480 0.368 0.000 0.328 0.304
#> GSM905064 1 0.7300 0.655 0.516 0.000 0.180 0.304
#> GSM905045 1 0.7540 0.637 0.480 0.000 0.216 0.304
#> GSM905051 1 0.7540 0.637 0.480 0.000 0.216 0.304
#> GSM905055 1 0.0336 0.741 0.992 0.000 0.000 0.008
#> GSM905058 1 0.0188 0.742 0.996 0.000 0.000 0.004
#> GSM905053 1 0.7540 0.637 0.480 0.000 0.216 0.304
#> GSM905061 1 0.7205 0.660 0.528 0.000 0.168 0.304
#> GSM905063 1 0.0817 0.737 0.976 0.000 0.000 0.024
#> GSM905054 1 0.7270 0.657 0.520 0.000 0.176 0.304
#> GSM905062 1 0.7270 0.657 0.520 0.000 0.176 0.304
#> GSM905052 1 0.7540 0.637 0.480 0.000 0.216 0.304
#> GSM905059 1 0.0188 0.742 0.996 0.000 0.000 0.004
#> GSM905047 1 0.0000 0.742 1.000 0.000 0.000 0.000
#> GSM905066 1 0.0817 0.737 0.976 0.000 0.000 0.024
#> GSM905056 1 0.0336 0.741 0.992 0.000 0.000 0.008
#> GSM905060 1 0.0188 0.742 0.996 0.000 0.000 0.004
#> GSM905048 1 0.0000 0.742 1.000 0.000 0.000 0.000
#> GSM905067 1 0.0188 0.742 0.996 0.000 0.000 0.004
#> GSM905057 1 0.0336 0.741 0.992 0.000 0.000 0.008
#> GSM905068 1 0.7563 0.633 0.476 0.000 0.220 0.304
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM905004 5 0.4114 0.701 0.000 0.000 0.024 0.244 0.732
#> GSM905024 4 0.7365 0.625 0.304 0.000 0.076 0.480 0.140
#> GSM905038 5 0.3759 0.775 0.000 0.000 0.136 0.056 0.808
#> GSM905043 4 0.7365 0.625 0.304 0.000 0.076 0.480 0.140
#> GSM904986 3 0.3750 0.907 0.000 0.232 0.756 0.012 0.000
#> GSM904991 3 0.4295 0.558 0.000 0.004 0.724 0.024 0.248
#> GSM904994 3 0.3366 0.910 0.000 0.232 0.768 0.000 0.000
#> GSM904996 3 0.3366 0.910 0.000 0.232 0.768 0.000 0.000
#> GSM905007 3 0.4096 0.584 0.000 0.004 0.744 0.020 0.232
#> GSM905012 3 0.3366 0.910 0.000 0.232 0.768 0.000 0.000
#> GSM905022 3 0.3750 0.907 0.000 0.232 0.756 0.012 0.000
#> GSM905026 5 0.3044 0.770 0.000 0.004 0.148 0.008 0.840
#> GSM905027 5 0.3170 0.764 0.000 0.004 0.160 0.008 0.828
#> GSM905031 5 0.3044 0.770 0.000 0.004 0.148 0.008 0.840
#> GSM905036 5 0.3663 0.702 0.000 0.000 0.016 0.208 0.776
#> GSM905041 5 0.5218 0.504 0.000 0.000 0.068 0.308 0.624
#> GSM905044 5 0.2970 0.756 0.000 0.004 0.168 0.000 0.828
#> GSM904989 3 0.3366 0.910 0.000 0.232 0.768 0.000 0.000
#> GSM904999 3 0.3750 0.907 0.000 0.232 0.756 0.012 0.000
#> GSM905002 3 0.3366 0.910 0.000 0.232 0.768 0.000 0.000
#> GSM905009 3 0.3366 0.910 0.000 0.232 0.768 0.000 0.000
#> GSM905014 3 0.4158 0.595 0.000 0.008 0.748 0.020 0.224
#> GSM905017 3 0.3750 0.907 0.000 0.232 0.756 0.012 0.000
#> GSM905020 3 0.3366 0.910 0.000 0.232 0.768 0.000 0.000
#> GSM905023 5 0.3596 0.709 0.000 0.000 0.016 0.200 0.784
#> GSM905029 5 0.3649 0.770 0.000 0.000 0.152 0.040 0.808
#> GSM905032 4 0.5115 0.283 0.012 0.000 0.028 0.608 0.352
#> GSM905034 1 0.3516 0.870 0.836 0.000 0.108 0.004 0.052
#> GSM905040 1 0.2103 0.933 0.920 0.000 0.056 0.004 0.020
#> GSM904985 2 0.0324 0.850 0.000 0.992 0.004 0.004 0.000
#> GSM904988 2 0.0000 0.851 0.000 1.000 0.000 0.000 0.000
#> GSM904990 2 0.0000 0.851 0.000 1.000 0.000 0.000 0.000
#> GSM904992 2 0.0000 0.851 0.000 1.000 0.000 0.000 0.000
#> GSM904995 2 0.0324 0.850 0.000 0.992 0.004 0.004 0.000
#> GSM904998 2 0.0162 0.851 0.000 0.996 0.004 0.000 0.000
#> GSM905000 2 0.0162 0.851 0.000 0.996 0.004 0.000 0.000
#> GSM905003 2 0.0162 0.851 0.000 0.996 0.004 0.000 0.000
#> GSM905006 2 0.0000 0.851 0.000 1.000 0.000 0.000 0.000
#> GSM905008 2 0.0162 0.851 0.000 0.996 0.004 0.000 0.000
#> GSM905011 2 0.0000 0.851 0.000 1.000 0.000 0.000 0.000
#> GSM905013 2 0.0162 0.851 0.000 0.996 0.004 0.000 0.000
#> GSM905016 2 0.0324 0.850 0.000 0.992 0.004 0.004 0.000
#> GSM905018 2 0.0162 0.851 0.000 0.996 0.004 0.000 0.000
#> GSM905021 2 0.1300 0.818 0.000 0.956 0.028 0.016 0.000
#> GSM905025 5 0.6566 0.480 0.000 0.104 0.084 0.192 0.620
#> GSM905028 2 0.6849 0.614 0.000 0.592 0.076 0.168 0.164
#> GSM905030 2 0.7081 0.580 0.000 0.560 0.076 0.168 0.196
#> GSM905033 2 0.7344 0.555 0.000 0.540 0.104 0.168 0.188
#> GSM905035 2 0.7081 0.580 0.000 0.560 0.076 0.168 0.196
#> GSM905037 2 0.6912 0.606 0.000 0.584 0.076 0.168 0.172
#> GSM905039 2 0.7081 0.580 0.000 0.560 0.076 0.168 0.196
#> GSM905042 5 0.7138 0.427 0.000 0.140 0.120 0.168 0.572
#> GSM905046 1 0.0807 0.951 0.976 0.000 0.012 0.000 0.012
#> GSM905065 1 0.0671 0.951 0.980 0.000 0.016 0.000 0.004
#> GSM905049 4 0.3424 0.886 0.240 0.000 0.000 0.760 0.000
#> GSM905050 4 0.4134 0.851 0.196 0.000 0.000 0.760 0.044
#> GSM905064 4 0.3766 0.872 0.268 0.000 0.000 0.728 0.004
#> GSM905045 4 0.3424 0.886 0.240 0.000 0.000 0.760 0.000
#> GSM905051 4 0.3579 0.886 0.240 0.000 0.004 0.756 0.000
#> GSM905055 1 0.0880 0.947 0.968 0.000 0.032 0.000 0.000
#> GSM905058 1 0.0912 0.951 0.972 0.000 0.012 0.000 0.016
#> GSM905053 4 0.3424 0.886 0.240 0.000 0.000 0.760 0.000
#> GSM905061 4 0.3814 0.865 0.276 0.000 0.000 0.720 0.004
#> GSM905063 1 0.2464 0.922 0.904 0.000 0.048 0.004 0.044
#> GSM905054 4 0.3661 0.867 0.276 0.000 0.000 0.724 0.000
#> GSM905062 4 0.3814 0.865 0.276 0.000 0.000 0.720 0.004
#> GSM905052 4 0.3579 0.886 0.240 0.000 0.004 0.756 0.000
#> GSM905059 1 0.0912 0.951 0.972 0.000 0.012 0.000 0.016
#> GSM905047 1 0.0807 0.951 0.976 0.000 0.012 0.000 0.012
#> GSM905066 1 0.2464 0.922 0.904 0.000 0.048 0.004 0.044
#> GSM905056 1 0.0880 0.947 0.968 0.000 0.032 0.000 0.000
#> GSM905060 1 0.1403 0.949 0.952 0.000 0.024 0.000 0.024
#> GSM905048 1 0.0579 0.953 0.984 0.000 0.008 0.000 0.008
#> GSM905067 1 0.0671 0.951 0.980 0.000 0.016 0.000 0.004
#> GSM905057 1 0.0880 0.947 0.968 0.000 0.032 0.000 0.000
#> GSM905068 4 0.3424 0.886 0.240 0.000 0.000 0.760 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM905004 5 0.4389 0.796 0.048 0.104 0.004 0.052 0.784 0.008
#> GSM905024 4 0.6936 0.448 0.108 0.248 0.000 0.500 0.136 0.008
#> GSM905038 5 0.1398 0.920 0.000 0.000 0.052 0.000 0.940 0.008
#> GSM905043 4 0.6936 0.448 0.108 0.248 0.000 0.500 0.136 0.008
#> GSM904986 3 0.0951 0.901 0.004 0.020 0.968 0.000 0.000 0.008
#> GSM904991 3 0.5233 0.531 0.028 0.076 0.632 0.000 0.264 0.000
#> GSM904994 3 0.0748 0.906 0.000 0.016 0.976 0.000 0.004 0.004
#> GSM904996 3 0.0146 0.907 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM905007 3 0.4710 0.664 0.028 0.076 0.716 0.000 0.180 0.000
#> GSM905012 3 0.0458 0.905 0.000 0.016 0.984 0.000 0.000 0.000
#> GSM905022 3 0.0951 0.901 0.004 0.020 0.968 0.000 0.000 0.008
#> GSM905026 5 0.1765 0.918 0.000 0.000 0.052 0.000 0.924 0.024
#> GSM905027 5 0.1738 0.920 0.000 0.004 0.052 0.000 0.928 0.016
#> GSM905031 5 0.1765 0.918 0.000 0.000 0.052 0.000 0.924 0.024
#> GSM905036 5 0.1471 0.889 0.000 0.000 0.004 0.064 0.932 0.000
#> GSM905041 5 0.4603 0.729 0.004 0.168 0.004 0.096 0.724 0.004
#> GSM905044 5 0.1909 0.918 0.000 0.004 0.052 0.000 0.920 0.024
#> GSM904989 3 0.0603 0.905 0.000 0.016 0.980 0.000 0.004 0.000
#> GSM904999 3 0.1036 0.900 0.004 0.024 0.964 0.000 0.000 0.008
#> GSM905002 3 0.0146 0.907 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM905009 3 0.0603 0.905 0.000 0.016 0.980 0.000 0.004 0.000
#> GSM905014 3 0.4547 0.688 0.028 0.076 0.736 0.000 0.160 0.000
#> GSM905017 3 0.1036 0.900 0.004 0.024 0.964 0.000 0.000 0.008
#> GSM905020 3 0.0146 0.907 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM905023 5 0.1429 0.896 0.000 0.000 0.004 0.052 0.940 0.004
#> GSM905029 5 0.1542 0.920 0.000 0.004 0.052 0.000 0.936 0.008
#> GSM905032 4 0.5067 0.443 0.004 0.080 0.000 0.612 0.300 0.004
#> GSM905034 1 0.5988 0.736 0.564 0.284 0.000 0.116 0.024 0.012
#> GSM905040 1 0.4384 0.895 0.760 0.104 0.000 0.116 0.008 0.012
#> GSM904985 2 0.6719 0.940 0.060 0.464 0.160 0.000 0.004 0.312
#> GSM904988 2 0.5498 0.950 0.000 0.528 0.148 0.000 0.000 0.324
#> GSM904990 2 0.5498 0.950 0.000 0.528 0.148 0.000 0.000 0.324
#> GSM904992 2 0.5498 0.950 0.000 0.528 0.148 0.000 0.000 0.324
#> GSM904995 2 0.6719 0.940 0.060 0.464 0.160 0.000 0.004 0.312
#> GSM904998 2 0.6337 0.949 0.040 0.488 0.160 0.000 0.000 0.312
#> GSM905000 2 0.5547 0.953 0.000 0.528 0.160 0.000 0.000 0.312
#> GSM905003 2 0.6382 0.947 0.044 0.488 0.160 0.000 0.000 0.308
#> GSM905006 2 0.5498 0.950 0.000 0.528 0.148 0.000 0.000 0.324
#> GSM905008 2 0.6392 0.948 0.044 0.484 0.160 0.000 0.000 0.312
#> GSM905011 2 0.5498 0.950 0.000 0.528 0.148 0.000 0.000 0.324
#> GSM905013 2 0.5547 0.953 0.000 0.528 0.160 0.000 0.000 0.312
#> GSM905016 2 0.6719 0.940 0.060 0.464 0.160 0.000 0.004 0.312
#> GSM905018 2 0.5547 0.953 0.000 0.528 0.160 0.000 0.000 0.312
#> GSM905021 2 0.6823 0.816 0.064 0.480 0.224 0.000 0.004 0.228
#> GSM905025 6 0.4452 0.394 0.004 0.040 0.000 0.000 0.312 0.644
#> GSM905028 6 0.1757 0.805 0.000 0.008 0.052 0.000 0.012 0.928
#> GSM905030 6 0.1682 0.814 0.000 0.000 0.052 0.000 0.020 0.928
#> GSM905033 6 0.2237 0.806 0.004 0.004 0.064 0.000 0.024 0.904
#> GSM905035 6 0.1765 0.816 0.000 0.000 0.052 0.000 0.024 0.924
#> GSM905037 6 0.1757 0.805 0.000 0.008 0.052 0.000 0.012 0.928
#> GSM905039 6 0.1765 0.816 0.000 0.000 0.052 0.000 0.024 0.924
#> GSM905042 6 0.4370 0.426 0.004 0.000 0.032 0.000 0.324 0.640
#> GSM905046 1 0.3251 0.927 0.828 0.040 0.000 0.124 0.000 0.008
#> GSM905065 1 0.2600 0.929 0.860 0.008 0.000 0.124 0.000 0.008
#> GSM905049 4 0.0000 0.894 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905050 4 0.0547 0.879 0.000 0.000 0.000 0.980 0.020 0.000
#> GSM905064 4 0.0000 0.894 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905045 4 0.0146 0.894 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM905051 4 0.0260 0.893 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM905055 1 0.3487 0.920 0.824 0.024 0.000 0.124 0.008 0.020
#> GSM905058 1 0.3491 0.926 0.820 0.040 0.000 0.124 0.004 0.012
#> GSM905053 4 0.0000 0.894 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905061 4 0.0146 0.894 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM905063 1 0.4965 0.895 0.740 0.080 0.000 0.120 0.028 0.032
#> GSM905054 4 0.0000 0.894 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905062 4 0.0146 0.894 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM905052 4 0.0260 0.893 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM905059 1 0.3491 0.926 0.820 0.040 0.000 0.124 0.004 0.012
#> GSM905047 1 0.3251 0.927 0.828 0.040 0.000 0.124 0.000 0.008
#> GSM905066 1 0.4965 0.895 0.740 0.080 0.000 0.120 0.028 0.032
#> GSM905056 1 0.3487 0.920 0.824 0.024 0.000 0.124 0.008 0.020
#> GSM905060 1 0.3924 0.925 0.788 0.076 0.000 0.124 0.004 0.008
#> GSM905048 1 0.3036 0.929 0.840 0.028 0.000 0.124 0.000 0.008
#> GSM905067 1 0.2600 0.929 0.860 0.008 0.000 0.124 0.000 0.008
#> GSM905057 1 0.3487 0.920 0.824 0.024 0.000 0.124 0.008 0.020
#> GSM905068 4 0.0000 0.894 0.000 0.000 0.000 1.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) genotype/variation(p) individual(p) k
#> ATC:kmeans 76 4.83e-08 9.05e-03 0.0164 2
#> ATC:kmeans 72 3.14e-09 4.42e-05 0.0659 3
#> ATC:kmeans 43 2.49e-07 1.70e-02 0.6247 4
#> ATC:kmeans 73 4.38e-16 3.16e-07 0.3065 5
#> ATC:kmeans 71 1.95e-14 2.53e-07 0.2511 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 76 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 0.981 0.993 0.5002 0.499 0.499
#> 3 3 0.782 0.917 0.917 0.2962 0.828 0.661
#> 4 4 1.000 0.967 0.978 0.0971 0.933 0.806
#> 5 5 0.878 0.924 0.875 0.0774 0.924 0.735
#> 6 6 0.863 0.901 0.863 0.0422 0.949 0.763
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
#> GSM905004 1 0.000 0.9855 1.000 0.000
#> GSM905024 1 0.000 0.9855 1.000 0.000
#> GSM905038 1 0.998 0.0919 0.524 0.476
#> GSM905043 1 0.000 0.9855 1.000 0.000
#> GSM904986 2 0.000 0.9991 0.000 1.000
#> GSM904991 2 0.000 0.9991 0.000 1.000
#> GSM904994 2 0.000 0.9991 0.000 1.000
#> GSM904996 2 0.000 0.9991 0.000 1.000
#> GSM905007 2 0.000 0.9991 0.000 1.000
#> GSM905012 2 0.000 0.9991 0.000 1.000
#> GSM905022 2 0.000 0.9991 0.000 1.000
#> GSM905026 2 0.000 0.9991 0.000 1.000
#> GSM905027 2 0.000 0.9991 0.000 1.000
#> GSM905031 2 0.000 0.9991 0.000 1.000
#> GSM905036 1 0.000 0.9855 1.000 0.000
#> GSM905041 1 0.000 0.9855 1.000 0.000
#> GSM905044 2 0.000 0.9991 0.000 1.000
#> GSM904989 2 0.000 0.9991 0.000 1.000
#> GSM904999 2 0.000 0.9991 0.000 1.000
#> GSM905002 2 0.000 0.9991 0.000 1.000
#> GSM905009 2 0.000 0.9991 0.000 1.000
#> GSM905014 2 0.000 0.9991 0.000 1.000
#> GSM905017 2 0.000 0.9991 0.000 1.000
#> GSM905020 2 0.000 0.9991 0.000 1.000
#> GSM905023 1 0.000 0.9855 1.000 0.000
#> GSM905029 2 0.224 0.9619 0.036 0.964
#> GSM905032 1 0.000 0.9855 1.000 0.000
#> GSM905034 1 0.000 0.9855 1.000 0.000
#> GSM905040 1 0.000 0.9855 1.000 0.000
#> GSM904985 2 0.000 0.9991 0.000 1.000
#> GSM904988 2 0.000 0.9991 0.000 1.000
#> GSM904990 2 0.000 0.9991 0.000 1.000
#> GSM904992 2 0.000 0.9991 0.000 1.000
#> GSM904995 2 0.000 0.9991 0.000 1.000
#> GSM904998 2 0.000 0.9991 0.000 1.000
#> GSM905000 2 0.000 0.9991 0.000 1.000
#> GSM905003 2 0.000 0.9991 0.000 1.000
#> GSM905006 2 0.000 0.9991 0.000 1.000
#> GSM905008 2 0.000 0.9991 0.000 1.000
#> GSM905011 2 0.000 0.9991 0.000 1.000
#> GSM905013 2 0.000 0.9991 0.000 1.000
#> GSM905016 2 0.000 0.9991 0.000 1.000
#> GSM905018 2 0.000 0.9991 0.000 1.000
#> GSM905021 2 0.000 0.9991 0.000 1.000
#> GSM905025 2 0.000 0.9991 0.000 1.000
#> GSM905028 2 0.000 0.9991 0.000 1.000
#> GSM905030 2 0.000 0.9991 0.000 1.000
#> GSM905033 2 0.000 0.9991 0.000 1.000
#> GSM905035 2 0.000 0.9991 0.000 1.000
#> GSM905037 2 0.000 0.9991 0.000 1.000
#> GSM905039 2 0.000 0.9991 0.000 1.000
#> GSM905042 2 0.000 0.9991 0.000 1.000
#> GSM905046 1 0.000 0.9855 1.000 0.000
#> GSM905065 1 0.000 0.9855 1.000 0.000
#> GSM905049 1 0.000 0.9855 1.000 0.000
#> GSM905050 1 0.000 0.9855 1.000 0.000
#> GSM905064 1 0.000 0.9855 1.000 0.000
#> GSM905045 1 0.000 0.9855 1.000 0.000
#> GSM905051 1 0.000 0.9855 1.000 0.000
#> GSM905055 1 0.000 0.9855 1.000 0.000
#> GSM905058 1 0.000 0.9855 1.000 0.000
#> GSM905053 1 0.000 0.9855 1.000 0.000
#> GSM905061 1 0.000 0.9855 1.000 0.000
#> GSM905063 1 0.000 0.9855 1.000 0.000
#> GSM905054 1 0.000 0.9855 1.000 0.000
#> GSM905062 1 0.000 0.9855 1.000 0.000
#> GSM905052 1 0.000 0.9855 1.000 0.000
#> GSM905059 1 0.000 0.9855 1.000 0.000
#> GSM905047 1 0.000 0.9855 1.000 0.000
#> GSM905066 1 0.000 0.9855 1.000 0.000
#> GSM905056 1 0.000 0.9855 1.000 0.000
#> GSM905060 1 0.000 0.9855 1.000 0.000
#> GSM905048 1 0.000 0.9855 1.000 0.000
#> GSM905067 1 0.000 0.9855 1.000 0.000
#> GSM905057 1 0.000 0.9855 1.000 0.000
#> GSM905068 1 0.000 0.9855 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM905004 1 0.0592 0.980 0.988 0.000 0.012
#> GSM905024 1 0.0000 0.990 1.000 0.000 0.000
#> GSM905038 3 0.4062 0.746 0.000 0.164 0.836
#> GSM905043 1 0.0000 0.990 1.000 0.000 0.000
#> GSM904986 3 0.3686 0.875 0.000 0.140 0.860
#> GSM904991 3 0.2625 0.848 0.000 0.084 0.916
#> GSM904994 3 0.3686 0.875 0.000 0.140 0.860
#> GSM904996 3 0.3686 0.875 0.000 0.140 0.860
#> GSM905007 3 0.3686 0.875 0.000 0.140 0.860
#> GSM905012 3 0.3686 0.875 0.000 0.140 0.860
#> GSM905022 3 0.3686 0.875 0.000 0.140 0.860
#> GSM905026 3 0.4178 0.743 0.000 0.172 0.828
#> GSM905027 3 0.4062 0.746 0.000 0.164 0.836
#> GSM905031 3 0.4178 0.743 0.000 0.172 0.828
#> GSM905036 1 0.3686 0.869 0.860 0.000 0.140
#> GSM905041 1 0.1964 0.946 0.944 0.000 0.056
#> GSM905044 3 0.4062 0.746 0.000 0.164 0.836
#> GSM904989 3 0.3686 0.875 0.000 0.140 0.860
#> GSM904999 3 0.3686 0.875 0.000 0.140 0.860
#> GSM905002 3 0.3686 0.875 0.000 0.140 0.860
#> GSM905009 3 0.3686 0.875 0.000 0.140 0.860
#> GSM905014 3 0.3686 0.875 0.000 0.140 0.860
#> GSM905017 3 0.3686 0.875 0.000 0.140 0.860
#> GSM905020 3 0.3686 0.875 0.000 0.140 0.860
#> GSM905023 1 0.3686 0.869 0.860 0.000 0.140
#> GSM905029 3 0.4002 0.746 0.000 0.160 0.840
#> GSM905032 1 0.0000 0.990 1.000 0.000 0.000
#> GSM905034 1 0.0000 0.990 1.000 0.000 0.000
#> GSM905040 1 0.0000 0.990 1.000 0.000 0.000
#> GSM904985 2 0.4002 0.920 0.000 0.840 0.160
#> GSM904988 2 0.4002 0.920 0.000 0.840 0.160
#> GSM904990 2 0.4002 0.920 0.000 0.840 0.160
#> GSM904992 2 0.4002 0.920 0.000 0.840 0.160
#> GSM904995 2 0.4002 0.920 0.000 0.840 0.160
#> GSM904998 2 0.4002 0.920 0.000 0.840 0.160
#> GSM905000 2 0.4002 0.920 0.000 0.840 0.160
#> GSM905003 2 0.4002 0.920 0.000 0.840 0.160
#> GSM905006 2 0.4002 0.920 0.000 0.840 0.160
#> GSM905008 2 0.4002 0.920 0.000 0.840 0.160
#> GSM905011 2 0.4002 0.920 0.000 0.840 0.160
#> GSM905013 2 0.4002 0.920 0.000 0.840 0.160
#> GSM905016 2 0.4002 0.920 0.000 0.840 0.160
#> GSM905018 2 0.4002 0.920 0.000 0.840 0.160
#> GSM905021 2 0.4002 0.920 0.000 0.840 0.160
#> GSM905025 2 0.0000 0.851 0.000 1.000 0.000
#> GSM905028 2 0.0000 0.851 0.000 1.000 0.000
#> GSM905030 2 0.0000 0.851 0.000 1.000 0.000
#> GSM905033 2 0.0000 0.851 0.000 1.000 0.000
#> GSM905035 2 0.0000 0.851 0.000 1.000 0.000
#> GSM905037 2 0.0000 0.851 0.000 1.000 0.000
#> GSM905039 2 0.0000 0.851 0.000 1.000 0.000
#> GSM905042 2 0.0000 0.851 0.000 1.000 0.000
#> GSM905046 1 0.0000 0.990 1.000 0.000 0.000
#> GSM905065 1 0.0000 0.990 1.000 0.000 0.000
#> GSM905049 1 0.0000 0.990 1.000 0.000 0.000
#> GSM905050 1 0.0000 0.990 1.000 0.000 0.000
#> GSM905064 1 0.0000 0.990 1.000 0.000 0.000
#> GSM905045 1 0.0000 0.990 1.000 0.000 0.000
#> GSM905051 1 0.0000 0.990 1.000 0.000 0.000
#> GSM905055 1 0.0000 0.990 1.000 0.000 0.000
#> GSM905058 1 0.0000 0.990 1.000 0.000 0.000
#> GSM905053 1 0.0000 0.990 1.000 0.000 0.000
#> GSM905061 1 0.0000 0.990 1.000 0.000 0.000
#> GSM905063 1 0.0000 0.990 1.000 0.000 0.000
#> GSM905054 1 0.0000 0.990 1.000 0.000 0.000
#> GSM905062 1 0.0000 0.990 1.000 0.000 0.000
#> GSM905052 1 0.0000 0.990 1.000 0.000 0.000
#> GSM905059 1 0.0000 0.990 1.000 0.000 0.000
#> GSM905047 1 0.0000 0.990 1.000 0.000 0.000
#> GSM905066 1 0.0000 0.990 1.000 0.000 0.000
#> GSM905056 1 0.0000 0.990 1.000 0.000 0.000
#> GSM905060 1 0.0000 0.990 1.000 0.000 0.000
#> GSM905048 1 0.0000 0.990 1.000 0.000 0.000
#> GSM905067 1 0.0000 0.990 1.000 0.000 0.000
#> GSM905057 1 0.0000 0.990 1.000 0.000 0.000
#> GSM905068 1 0.0000 0.990 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM905004 1 0.1284 0.972 0.964 0.000 0.024 0.012
#> GSM905024 1 0.0000 0.993 1.000 0.000 0.000 0.000
#> GSM905038 4 0.0469 0.917 0.000 0.000 0.012 0.988
#> GSM905043 1 0.0000 0.993 1.000 0.000 0.000 0.000
#> GSM904986 3 0.0188 0.999 0.000 0.004 0.996 0.000
#> GSM904991 3 0.0469 0.985 0.000 0.000 0.988 0.012
#> GSM904994 3 0.0188 0.999 0.000 0.004 0.996 0.000
#> GSM904996 3 0.0188 0.999 0.000 0.004 0.996 0.000
#> GSM905007 3 0.0188 0.999 0.000 0.004 0.996 0.000
#> GSM905012 3 0.0188 0.999 0.000 0.004 0.996 0.000
#> GSM905022 3 0.0188 0.999 0.000 0.004 0.996 0.000
#> GSM905026 4 0.1584 0.919 0.000 0.036 0.012 0.952
#> GSM905027 4 0.1584 0.919 0.000 0.036 0.012 0.952
#> GSM905031 4 0.1584 0.919 0.000 0.036 0.012 0.952
#> GSM905036 4 0.0469 0.916 0.012 0.000 0.000 0.988
#> GSM905041 4 0.4790 0.392 0.380 0.000 0.000 0.620
#> GSM905044 4 0.1584 0.919 0.000 0.036 0.012 0.952
#> GSM904989 3 0.0188 0.999 0.000 0.004 0.996 0.000
#> GSM904999 3 0.0188 0.999 0.000 0.004 0.996 0.000
#> GSM905002 3 0.0188 0.999 0.000 0.004 0.996 0.000
#> GSM905009 3 0.0188 0.999 0.000 0.004 0.996 0.000
#> GSM905014 3 0.0188 0.999 0.000 0.004 0.996 0.000
#> GSM905017 3 0.0188 0.999 0.000 0.004 0.996 0.000
#> GSM905020 3 0.0188 0.999 0.000 0.004 0.996 0.000
#> GSM905023 4 0.0469 0.916 0.012 0.000 0.000 0.988
#> GSM905029 4 0.0469 0.917 0.000 0.000 0.012 0.988
#> GSM905032 1 0.0000 0.993 1.000 0.000 0.000 0.000
#> GSM905034 1 0.0000 0.993 1.000 0.000 0.000 0.000
#> GSM905040 1 0.0000 0.993 1.000 0.000 0.000 0.000
#> GSM904985 2 0.1118 0.974 0.000 0.964 0.036 0.000
#> GSM904988 2 0.1118 0.974 0.000 0.964 0.036 0.000
#> GSM904990 2 0.1118 0.974 0.000 0.964 0.036 0.000
#> GSM904992 2 0.1118 0.974 0.000 0.964 0.036 0.000
#> GSM904995 2 0.1118 0.974 0.000 0.964 0.036 0.000
#> GSM904998 2 0.1118 0.974 0.000 0.964 0.036 0.000
#> GSM905000 2 0.1118 0.974 0.000 0.964 0.036 0.000
#> GSM905003 2 0.1118 0.974 0.000 0.964 0.036 0.000
#> GSM905006 2 0.1118 0.974 0.000 0.964 0.036 0.000
#> GSM905008 2 0.1118 0.974 0.000 0.964 0.036 0.000
#> GSM905011 2 0.1118 0.974 0.000 0.964 0.036 0.000
#> GSM905013 2 0.1118 0.974 0.000 0.964 0.036 0.000
#> GSM905016 2 0.1118 0.974 0.000 0.964 0.036 0.000
#> GSM905018 2 0.1118 0.974 0.000 0.964 0.036 0.000
#> GSM905021 2 0.4072 0.704 0.000 0.748 0.252 0.000
#> GSM905025 2 0.0000 0.961 0.000 1.000 0.000 0.000
#> GSM905028 2 0.0000 0.961 0.000 1.000 0.000 0.000
#> GSM905030 2 0.0000 0.961 0.000 1.000 0.000 0.000
#> GSM905033 2 0.0000 0.961 0.000 1.000 0.000 0.000
#> GSM905035 2 0.0000 0.961 0.000 1.000 0.000 0.000
#> GSM905037 2 0.0000 0.961 0.000 1.000 0.000 0.000
#> GSM905039 2 0.0000 0.961 0.000 1.000 0.000 0.000
#> GSM905042 2 0.0000 0.961 0.000 1.000 0.000 0.000
#> GSM905046 1 0.0000 0.993 1.000 0.000 0.000 0.000
#> GSM905065 1 0.0000 0.993 1.000 0.000 0.000 0.000
#> GSM905049 1 0.0657 0.990 0.984 0.000 0.004 0.012
#> GSM905050 1 0.0657 0.990 0.984 0.000 0.004 0.012
#> GSM905064 1 0.0657 0.990 0.984 0.000 0.004 0.012
#> GSM905045 1 0.0657 0.990 0.984 0.000 0.004 0.012
#> GSM905051 1 0.0469 0.991 0.988 0.000 0.000 0.012
#> GSM905055 1 0.0000 0.993 1.000 0.000 0.000 0.000
#> GSM905058 1 0.0000 0.993 1.000 0.000 0.000 0.000
#> GSM905053 1 0.0657 0.990 0.984 0.000 0.004 0.012
#> GSM905061 1 0.0657 0.990 0.984 0.000 0.004 0.012
#> GSM905063 1 0.0000 0.993 1.000 0.000 0.000 0.000
#> GSM905054 1 0.0657 0.990 0.984 0.000 0.004 0.012
#> GSM905062 1 0.0657 0.990 0.984 0.000 0.004 0.012
#> GSM905052 1 0.0469 0.991 0.988 0.000 0.000 0.012
#> GSM905059 1 0.0000 0.993 1.000 0.000 0.000 0.000
#> GSM905047 1 0.0000 0.993 1.000 0.000 0.000 0.000
#> GSM905066 1 0.0000 0.993 1.000 0.000 0.000 0.000
#> GSM905056 1 0.0000 0.993 1.000 0.000 0.000 0.000
#> GSM905060 1 0.0000 0.993 1.000 0.000 0.000 0.000
#> GSM905048 1 0.0000 0.993 1.000 0.000 0.000 0.000
#> GSM905067 1 0.0000 0.993 1.000 0.000 0.000 0.000
#> GSM905057 1 0.0000 0.993 1.000 0.000 0.000 0.000
#> GSM905068 1 0.0657 0.990 0.984 0.000 0.004 0.012
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM905004 4 0.2409 0.821 0.068 0.000 0.032 0.900 0.000
#> GSM905024 1 0.4192 0.945 0.596 0.000 0.000 0.404 0.000
#> GSM905038 5 0.0703 0.882 0.024 0.000 0.000 0.000 0.976
#> GSM905043 1 0.4192 0.945 0.596 0.000 0.000 0.404 0.000
#> GSM904986 3 0.0880 0.989 0.000 0.032 0.968 0.000 0.000
#> GSM904991 3 0.0771 0.950 0.020 0.000 0.976 0.000 0.004
#> GSM904994 3 0.0880 0.989 0.000 0.032 0.968 0.000 0.000
#> GSM904996 3 0.0880 0.989 0.000 0.032 0.968 0.000 0.000
#> GSM905007 3 0.0404 0.959 0.012 0.000 0.988 0.000 0.000
#> GSM905012 3 0.0880 0.989 0.000 0.032 0.968 0.000 0.000
#> GSM905022 3 0.0880 0.989 0.000 0.032 0.968 0.000 0.000
#> GSM905026 5 0.2583 0.883 0.132 0.004 0.000 0.000 0.864
#> GSM905027 5 0.2488 0.884 0.124 0.004 0.000 0.000 0.872
#> GSM905031 5 0.2583 0.883 0.132 0.004 0.000 0.000 0.864
#> GSM905036 5 0.1478 0.875 0.064 0.000 0.000 0.000 0.936
#> GSM905041 5 0.5987 0.355 0.304 0.000 0.000 0.140 0.556
#> GSM905044 5 0.2583 0.883 0.132 0.004 0.000 0.000 0.864
#> GSM904989 3 0.0880 0.989 0.000 0.032 0.968 0.000 0.000
#> GSM904999 3 0.0880 0.989 0.000 0.032 0.968 0.000 0.000
#> GSM905002 3 0.0880 0.989 0.000 0.032 0.968 0.000 0.000
#> GSM905009 3 0.0880 0.989 0.000 0.032 0.968 0.000 0.000
#> GSM905014 3 0.0000 0.965 0.000 0.000 1.000 0.000 0.000
#> GSM905017 3 0.0880 0.989 0.000 0.032 0.968 0.000 0.000
#> GSM905020 3 0.0880 0.989 0.000 0.032 0.968 0.000 0.000
#> GSM905023 5 0.1544 0.874 0.068 0.000 0.000 0.000 0.932
#> GSM905029 5 0.0566 0.883 0.012 0.000 0.004 0.000 0.984
#> GSM905032 1 0.4227 0.966 0.580 0.000 0.000 0.420 0.000
#> GSM905034 1 0.4201 0.951 0.592 0.000 0.000 0.408 0.000
#> GSM905040 1 0.4249 0.979 0.568 0.000 0.000 0.432 0.000
#> GSM904985 2 0.0162 0.909 0.000 0.996 0.004 0.000 0.000
#> GSM904988 2 0.0162 0.909 0.000 0.996 0.004 0.000 0.000
#> GSM904990 2 0.0162 0.909 0.000 0.996 0.004 0.000 0.000
#> GSM904992 2 0.0162 0.909 0.000 0.996 0.004 0.000 0.000
#> GSM904995 2 0.0162 0.909 0.000 0.996 0.004 0.000 0.000
#> GSM904998 2 0.0162 0.909 0.000 0.996 0.004 0.000 0.000
#> GSM905000 2 0.0162 0.909 0.000 0.996 0.004 0.000 0.000
#> GSM905003 2 0.0162 0.909 0.000 0.996 0.004 0.000 0.000
#> GSM905006 2 0.0162 0.909 0.000 0.996 0.004 0.000 0.000
#> GSM905008 2 0.0162 0.909 0.000 0.996 0.004 0.000 0.000
#> GSM905011 2 0.0162 0.909 0.000 0.996 0.004 0.000 0.000
#> GSM905013 2 0.0162 0.909 0.000 0.996 0.004 0.000 0.000
#> GSM905016 2 0.0162 0.909 0.000 0.996 0.004 0.000 0.000
#> GSM905018 2 0.0162 0.909 0.000 0.996 0.004 0.000 0.000
#> GSM905021 2 0.3003 0.722 0.000 0.812 0.188 0.000 0.000
#> GSM905025 2 0.3612 0.804 0.268 0.732 0.000 0.000 0.000
#> GSM905028 2 0.3366 0.830 0.232 0.768 0.000 0.000 0.000
#> GSM905030 2 0.3366 0.830 0.232 0.768 0.000 0.000 0.000
#> GSM905033 2 0.3109 0.842 0.200 0.800 0.000 0.000 0.000
#> GSM905035 2 0.3366 0.830 0.232 0.768 0.000 0.000 0.000
#> GSM905037 2 0.3366 0.830 0.232 0.768 0.000 0.000 0.000
#> GSM905039 2 0.3366 0.830 0.232 0.768 0.000 0.000 0.000
#> GSM905042 2 0.3366 0.830 0.232 0.768 0.000 0.000 0.000
#> GSM905046 1 0.4262 0.986 0.560 0.000 0.000 0.440 0.000
#> GSM905065 1 0.4262 0.986 0.560 0.000 0.000 0.440 0.000
#> GSM905049 4 0.0000 0.970 0.000 0.000 0.000 1.000 0.000
#> GSM905050 4 0.0000 0.970 0.000 0.000 0.000 1.000 0.000
#> GSM905064 4 0.0404 0.958 0.012 0.000 0.000 0.988 0.000
#> GSM905045 4 0.0000 0.970 0.000 0.000 0.000 1.000 0.000
#> GSM905051 4 0.0963 0.926 0.036 0.000 0.000 0.964 0.000
#> GSM905055 1 0.4262 0.986 0.560 0.000 0.000 0.440 0.000
#> GSM905058 1 0.4262 0.986 0.560 0.000 0.000 0.440 0.000
#> GSM905053 4 0.0000 0.970 0.000 0.000 0.000 1.000 0.000
#> GSM905061 4 0.0000 0.970 0.000 0.000 0.000 1.000 0.000
#> GSM905063 1 0.4262 0.986 0.560 0.000 0.000 0.440 0.000
#> GSM905054 4 0.0000 0.970 0.000 0.000 0.000 1.000 0.000
#> GSM905062 4 0.0000 0.970 0.000 0.000 0.000 1.000 0.000
#> GSM905052 4 0.0963 0.926 0.036 0.000 0.000 0.964 0.000
#> GSM905059 1 0.4262 0.986 0.560 0.000 0.000 0.440 0.000
#> GSM905047 1 0.4262 0.986 0.560 0.000 0.000 0.440 0.000
#> GSM905066 1 0.4262 0.986 0.560 0.000 0.000 0.440 0.000
#> GSM905056 1 0.4262 0.986 0.560 0.000 0.000 0.440 0.000
#> GSM905060 1 0.4262 0.986 0.560 0.000 0.000 0.440 0.000
#> GSM905048 1 0.4262 0.986 0.560 0.000 0.000 0.440 0.000
#> GSM905067 1 0.4262 0.986 0.560 0.000 0.000 0.440 0.000
#> GSM905057 1 0.4262 0.986 0.560 0.000 0.000 0.440 0.000
#> GSM905068 4 0.0000 0.970 0.000 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM905004 4 0.3469 0.683 0.104 0.088 0.000 0.808 0.000 0.000
#> GSM905024 1 0.1745 0.871 0.924 0.020 0.000 0.056 0.000 0.000
#> GSM905038 6 0.4212 0.811 0.000 0.264 0.000 0.048 0.000 0.688
#> GSM905043 1 0.1745 0.871 0.924 0.020 0.000 0.056 0.000 0.000
#> GSM904986 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM904991 3 0.1682 0.940 0.000 0.020 0.928 0.052 0.000 0.000
#> GSM904994 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM904996 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905007 3 0.1480 0.948 0.000 0.020 0.940 0.040 0.000 0.000
#> GSM905012 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905022 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905026 6 0.1141 0.846 0.000 0.000 0.000 0.000 0.052 0.948
#> GSM905027 6 0.1075 0.847 0.000 0.000 0.000 0.000 0.048 0.952
#> GSM905031 6 0.1141 0.846 0.000 0.000 0.000 0.000 0.052 0.948
#> GSM905036 6 0.5042 0.773 0.000 0.332 0.000 0.092 0.000 0.576
#> GSM905041 1 0.7253 -0.228 0.380 0.232 0.000 0.104 0.000 0.284
#> GSM905044 6 0.1075 0.847 0.000 0.000 0.000 0.000 0.048 0.952
#> GSM904989 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM904999 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905002 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905009 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905014 3 0.0993 0.962 0.000 0.012 0.964 0.024 0.000 0.000
#> GSM905017 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905020 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905023 6 0.5047 0.769 0.000 0.348 0.000 0.088 0.000 0.564
#> GSM905029 6 0.2911 0.838 0.000 0.144 0.000 0.024 0.000 0.832
#> GSM905032 1 0.1633 0.884 0.932 0.024 0.000 0.044 0.000 0.000
#> GSM905034 1 0.1124 0.899 0.956 0.008 0.000 0.036 0.000 0.000
#> GSM905040 1 0.0458 0.917 0.984 0.000 0.000 0.016 0.000 0.000
#> GSM904985 2 0.4439 0.978 0.000 0.540 0.028 0.000 0.432 0.000
#> GSM904988 2 0.4377 0.983 0.000 0.540 0.024 0.000 0.436 0.000
#> GSM904990 2 0.4377 0.983 0.000 0.540 0.024 0.000 0.436 0.000
#> GSM904992 2 0.4377 0.983 0.000 0.540 0.024 0.000 0.436 0.000
#> GSM904995 2 0.4377 0.983 0.000 0.540 0.024 0.000 0.436 0.000
#> GSM904998 2 0.4377 0.983 0.000 0.540 0.024 0.000 0.436 0.000
#> GSM905000 2 0.4377 0.983 0.000 0.540 0.024 0.000 0.436 0.000
#> GSM905003 2 0.4439 0.978 0.000 0.540 0.028 0.000 0.432 0.000
#> GSM905006 2 0.4377 0.983 0.000 0.540 0.024 0.000 0.436 0.000
#> GSM905008 2 0.4439 0.978 0.000 0.540 0.028 0.000 0.432 0.000
#> GSM905011 2 0.4377 0.983 0.000 0.540 0.024 0.000 0.436 0.000
#> GSM905013 2 0.4377 0.983 0.000 0.540 0.024 0.000 0.436 0.000
#> GSM905016 2 0.4377 0.983 0.000 0.540 0.024 0.000 0.436 0.000
#> GSM905018 2 0.4377 0.983 0.000 0.540 0.024 0.000 0.436 0.000
#> GSM905021 2 0.5300 0.787 0.000 0.540 0.116 0.000 0.344 0.000
#> GSM905025 5 0.2527 0.778 0.000 0.064 0.000 0.048 0.884 0.004
#> GSM905028 5 0.0000 0.926 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM905030 5 0.0000 0.926 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM905033 5 0.2219 0.668 0.000 0.136 0.000 0.000 0.864 0.000
#> GSM905035 5 0.0000 0.926 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM905037 5 0.0000 0.926 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM905039 5 0.0000 0.926 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM905042 5 0.0790 0.890 0.000 0.032 0.000 0.000 0.968 0.000
#> GSM905046 1 0.0458 0.926 0.984 0.000 0.000 0.016 0.000 0.000
#> GSM905065 1 0.0260 0.927 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM905049 4 0.3126 0.927 0.248 0.000 0.000 0.752 0.000 0.000
#> GSM905050 4 0.3126 0.927 0.248 0.000 0.000 0.752 0.000 0.000
#> GSM905064 4 0.3515 0.861 0.324 0.000 0.000 0.676 0.000 0.000
#> GSM905045 4 0.3126 0.927 0.248 0.000 0.000 0.752 0.000 0.000
#> GSM905051 4 0.3899 0.750 0.404 0.004 0.000 0.592 0.000 0.000
#> GSM905055 1 0.0000 0.926 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM905058 1 0.0458 0.926 0.984 0.000 0.000 0.016 0.000 0.000
#> GSM905053 4 0.3126 0.927 0.248 0.000 0.000 0.752 0.000 0.000
#> GSM905061 4 0.3126 0.927 0.248 0.000 0.000 0.752 0.000 0.000
#> GSM905063 1 0.0458 0.926 0.984 0.000 0.000 0.016 0.000 0.000
#> GSM905054 4 0.3126 0.927 0.248 0.000 0.000 0.752 0.000 0.000
#> GSM905062 4 0.3126 0.927 0.248 0.000 0.000 0.752 0.000 0.000
#> GSM905052 4 0.3899 0.750 0.404 0.004 0.000 0.592 0.000 0.000
#> GSM905059 1 0.0458 0.926 0.984 0.000 0.000 0.016 0.000 0.000
#> GSM905047 1 0.0458 0.926 0.984 0.000 0.000 0.016 0.000 0.000
#> GSM905066 1 0.0458 0.926 0.984 0.000 0.000 0.016 0.000 0.000
#> GSM905056 1 0.0000 0.926 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM905060 1 0.0458 0.926 0.984 0.000 0.000 0.016 0.000 0.000
#> GSM905048 1 0.0458 0.926 0.984 0.000 0.000 0.016 0.000 0.000
#> GSM905067 1 0.0260 0.927 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM905057 1 0.0000 0.926 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM905068 4 0.3126 0.927 0.248 0.000 0.000 0.752 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) genotype/variation(p) individual(p) k
#> ATC:skmeans 75 2.44e-07 6.76e-04 0.0181 2
#> ATC:skmeans 76 3.46e-15 4.51e-06 0.6508 3
#> ATC:skmeans 75 4.45e-13 8.70e-06 0.6463 4
#> ATC:skmeans 75 1.44e-15 8.32e-09 0.1357 5
#> ATC:skmeans 75 8.81e-13 5.80e-08 0.1715 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 76 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.920 0.963 0.984 0.4793 0.522 0.522
#> 3 3 1.000 0.952 0.978 0.3805 0.788 0.606
#> 4 4 0.743 0.733 0.792 0.1289 0.794 0.483
#> 5 5 0.950 0.916 0.961 0.0796 0.850 0.493
#> 6 6 1.000 0.965 0.986 0.0375 0.935 0.693
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2 3 5
There is also optional best \(k\) = 2 3 5 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
#> GSM905004 2 0.5946 0.844 0.144 0.856
#> GSM905024 1 0.0000 0.984 1.000 0.000
#> GSM905038 2 0.1414 0.968 0.020 0.980
#> GSM905043 1 0.0000 0.984 1.000 0.000
#> GSM904986 2 0.0000 0.983 0.000 1.000
#> GSM904991 2 0.0672 0.977 0.008 0.992
#> GSM904994 2 0.0000 0.983 0.000 1.000
#> GSM904996 2 0.0000 0.983 0.000 1.000
#> GSM905007 2 0.0376 0.980 0.004 0.996
#> GSM905012 2 0.0000 0.983 0.000 1.000
#> GSM905022 2 0.0000 0.983 0.000 1.000
#> GSM905026 2 0.0376 0.980 0.004 0.996
#> GSM905027 2 0.0376 0.980 0.004 0.996
#> GSM905031 2 0.0376 0.980 0.004 0.996
#> GSM905036 2 0.5842 0.849 0.140 0.860
#> GSM905041 2 0.6623 0.808 0.172 0.828
#> GSM905044 2 0.0376 0.980 0.004 0.996
#> GSM904989 2 0.0000 0.983 0.000 1.000
#> GSM904999 2 0.0000 0.983 0.000 1.000
#> GSM905002 2 0.0000 0.983 0.000 1.000
#> GSM905009 2 0.0000 0.983 0.000 1.000
#> GSM905014 2 0.0000 0.983 0.000 1.000
#> GSM905017 2 0.0000 0.983 0.000 1.000
#> GSM905020 2 0.0000 0.983 0.000 1.000
#> GSM905023 2 0.5842 0.849 0.140 0.860
#> GSM905029 2 0.5737 0.854 0.136 0.864
#> GSM905032 1 0.9881 0.183 0.564 0.436
#> GSM905034 1 0.0000 0.984 1.000 0.000
#> GSM905040 1 0.0000 0.984 1.000 0.000
#> GSM904985 2 0.0000 0.983 0.000 1.000
#> GSM904988 2 0.0000 0.983 0.000 1.000
#> GSM904990 2 0.0000 0.983 0.000 1.000
#> GSM904992 2 0.0000 0.983 0.000 1.000
#> GSM904995 2 0.0000 0.983 0.000 1.000
#> GSM904998 2 0.0000 0.983 0.000 1.000
#> GSM905000 2 0.0000 0.983 0.000 1.000
#> GSM905003 2 0.0000 0.983 0.000 1.000
#> GSM905006 2 0.0000 0.983 0.000 1.000
#> GSM905008 2 0.0000 0.983 0.000 1.000
#> GSM905011 2 0.0000 0.983 0.000 1.000
#> GSM905013 2 0.0000 0.983 0.000 1.000
#> GSM905016 2 0.0000 0.983 0.000 1.000
#> GSM905018 2 0.0000 0.983 0.000 1.000
#> GSM905021 2 0.0000 0.983 0.000 1.000
#> GSM905025 2 0.0000 0.983 0.000 1.000
#> GSM905028 2 0.0000 0.983 0.000 1.000
#> GSM905030 2 0.0000 0.983 0.000 1.000
#> GSM905033 2 0.0000 0.983 0.000 1.000
#> GSM905035 2 0.0000 0.983 0.000 1.000
#> GSM905037 2 0.0000 0.983 0.000 1.000
#> GSM905039 2 0.0000 0.983 0.000 1.000
#> GSM905042 2 0.0000 0.983 0.000 1.000
#> GSM905046 1 0.0000 0.984 1.000 0.000
#> GSM905065 1 0.0000 0.984 1.000 0.000
#> GSM905049 1 0.0000 0.984 1.000 0.000
#> GSM905050 1 0.0000 0.984 1.000 0.000
#> GSM905064 1 0.0000 0.984 1.000 0.000
#> GSM905045 1 0.0000 0.984 1.000 0.000
#> GSM905051 1 0.0000 0.984 1.000 0.000
#> GSM905055 1 0.0000 0.984 1.000 0.000
#> GSM905058 1 0.0000 0.984 1.000 0.000
#> GSM905053 1 0.0000 0.984 1.000 0.000
#> GSM905061 1 0.0000 0.984 1.000 0.000
#> GSM905063 1 0.0000 0.984 1.000 0.000
#> GSM905054 1 0.0000 0.984 1.000 0.000
#> GSM905062 1 0.0000 0.984 1.000 0.000
#> GSM905052 1 0.0000 0.984 1.000 0.000
#> GSM905059 1 0.0000 0.984 1.000 0.000
#> GSM905047 1 0.0000 0.984 1.000 0.000
#> GSM905066 1 0.0000 0.984 1.000 0.000
#> GSM905056 1 0.0000 0.984 1.000 0.000
#> GSM905060 1 0.0000 0.984 1.000 0.000
#> GSM905048 1 0.0000 0.984 1.000 0.000
#> GSM905067 1 0.0000 0.984 1.000 0.000
#> GSM905057 1 0.0000 0.984 1.000 0.000
#> GSM905068 1 0.0000 0.984 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM905004 3 0.0237 0.973 0.004 0.000 0.996
#> GSM905024 1 0.0000 0.986 1.000 0.000 0.000
#> GSM905038 3 0.0000 0.976 0.000 0.000 1.000
#> GSM905043 1 0.5760 0.494 0.672 0.000 0.328
#> GSM904986 2 0.1860 0.945 0.000 0.948 0.052
#> GSM904991 3 0.0000 0.976 0.000 0.000 1.000
#> GSM904994 2 0.3192 0.889 0.000 0.888 0.112
#> GSM904996 2 0.0000 0.971 0.000 1.000 0.000
#> GSM905007 3 0.0000 0.976 0.000 0.000 1.000
#> GSM905012 2 0.0000 0.971 0.000 1.000 0.000
#> GSM905022 2 0.0000 0.971 0.000 1.000 0.000
#> GSM905026 3 0.0000 0.976 0.000 0.000 1.000
#> GSM905027 3 0.0000 0.976 0.000 0.000 1.000
#> GSM905031 3 0.0000 0.976 0.000 0.000 1.000
#> GSM905036 3 0.0000 0.976 0.000 0.000 1.000
#> GSM905041 3 0.0000 0.976 0.000 0.000 1.000
#> GSM905044 3 0.0000 0.976 0.000 0.000 1.000
#> GSM904989 2 0.6192 0.315 0.000 0.580 0.420
#> GSM904999 2 0.0000 0.971 0.000 1.000 0.000
#> GSM905002 2 0.0000 0.971 0.000 1.000 0.000
#> GSM905009 2 0.1411 0.949 0.000 0.964 0.036
#> GSM905014 3 0.0000 0.976 0.000 0.000 1.000
#> GSM905017 2 0.0000 0.971 0.000 1.000 0.000
#> GSM905020 2 0.0000 0.971 0.000 1.000 0.000
#> GSM905023 3 0.0000 0.976 0.000 0.000 1.000
#> GSM905029 3 0.0000 0.976 0.000 0.000 1.000
#> GSM905032 3 0.0892 0.960 0.020 0.000 0.980
#> GSM905034 1 0.0000 0.986 1.000 0.000 0.000
#> GSM905040 1 0.0000 0.986 1.000 0.000 0.000
#> GSM904985 2 0.0000 0.971 0.000 1.000 0.000
#> GSM904988 2 0.0000 0.971 0.000 1.000 0.000
#> GSM904990 2 0.0000 0.971 0.000 1.000 0.000
#> GSM904992 2 0.0000 0.971 0.000 1.000 0.000
#> GSM904995 2 0.0000 0.971 0.000 1.000 0.000
#> GSM904998 2 0.0000 0.971 0.000 1.000 0.000
#> GSM905000 2 0.0000 0.971 0.000 1.000 0.000
#> GSM905003 2 0.0000 0.971 0.000 1.000 0.000
#> GSM905006 2 0.0000 0.971 0.000 1.000 0.000
#> GSM905008 2 0.0000 0.971 0.000 1.000 0.000
#> GSM905011 2 0.0000 0.971 0.000 1.000 0.000
#> GSM905013 2 0.0000 0.971 0.000 1.000 0.000
#> GSM905016 2 0.0000 0.971 0.000 1.000 0.000
#> GSM905018 2 0.0000 0.971 0.000 1.000 0.000
#> GSM905021 2 0.0000 0.971 0.000 1.000 0.000
#> GSM905025 3 0.0000 0.976 0.000 0.000 1.000
#> GSM905028 2 0.1289 0.956 0.000 0.968 0.032
#> GSM905030 2 0.1860 0.944 0.000 0.948 0.052
#> GSM905033 2 0.1964 0.941 0.000 0.944 0.056
#> GSM905035 2 0.2261 0.932 0.000 0.932 0.068
#> GSM905037 2 0.1289 0.956 0.000 0.968 0.032
#> GSM905039 2 0.2066 0.938 0.000 0.940 0.060
#> GSM905042 3 0.0000 0.976 0.000 0.000 1.000
#> GSM905046 1 0.0000 0.986 1.000 0.000 0.000
#> GSM905065 1 0.0000 0.986 1.000 0.000 0.000
#> GSM905049 1 0.0000 0.986 1.000 0.000 0.000
#> GSM905050 3 0.5560 0.573 0.300 0.000 0.700
#> GSM905064 1 0.0000 0.986 1.000 0.000 0.000
#> GSM905045 1 0.0000 0.986 1.000 0.000 0.000
#> GSM905051 1 0.0000 0.986 1.000 0.000 0.000
#> GSM905055 1 0.0000 0.986 1.000 0.000 0.000
#> GSM905058 1 0.0000 0.986 1.000 0.000 0.000
#> GSM905053 1 0.0000 0.986 1.000 0.000 0.000
#> GSM905061 1 0.0000 0.986 1.000 0.000 0.000
#> GSM905063 1 0.0000 0.986 1.000 0.000 0.000
#> GSM905054 1 0.0000 0.986 1.000 0.000 0.000
#> GSM905062 1 0.0000 0.986 1.000 0.000 0.000
#> GSM905052 1 0.0237 0.982 0.996 0.000 0.004
#> GSM905059 1 0.0000 0.986 1.000 0.000 0.000
#> GSM905047 1 0.0000 0.986 1.000 0.000 0.000
#> GSM905066 1 0.0000 0.986 1.000 0.000 0.000
#> GSM905056 1 0.0000 0.986 1.000 0.000 0.000
#> GSM905060 1 0.0000 0.986 1.000 0.000 0.000
#> GSM905048 1 0.0000 0.986 1.000 0.000 0.000
#> GSM905067 1 0.0000 0.986 1.000 0.000 0.000
#> GSM905057 1 0.0000 0.986 1.000 0.000 0.000
#> GSM905068 3 0.2261 0.912 0.068 0.000 0.932
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM905004 4 0.2469 0.197 0.000 0.000 0.108 0.892
#> GSM905024 1 0.1474 0.893 0.948 0.000 0.000 0.052
#> GSM905038 3 0.4933 0.728 0.000 0.000 0.568 0.432
#> GSM905043 1 0.4477 0.411 0.688 0.000 0.000 0.312
#> GSM904986 3 0.0000 0.603 0.000 0.000 1.000 0.000
#> GSM904991 3 0.1557 0.635 0.000 0.000 0.944 0.056
#> GSM904994 3 0.0000 0.603 0.000 0.000 1.000 0.000
#> GSM904996 2 0.4933 0.642 0.000 0.568 0.432 0.000
#> GSM905007 3 0.0000 0.603 0.000 0.000 1.000 0.000
#> GSM905012 2 0.4933 0.642 0.000 0.568 0.432 0.000
#> GSM905022 2 0.4933 0.642 0.000 0.568 0.432 0.000
#> GSM905026 3 0.4933 0.728 0.000 0.000 0.568 0.432
#> GSM905027 3 0.4933 0.728 0.000 0.000 0.568 0.432
#> GSM905031 3 0.4933 0.728 0.000 0.000 0.568 0.432
#> GSM905036 3 0.4933 0.728 0.000 0.000 0.568 0.432
#> GSM905041 4 0.2216 0.240 0.000 0.000 0.092 0.908
#> GSM905044 3 0.4933 0.728 0.000 0.000 0.568 0.432
#> GSM904989 3 0.0469 0.589 0.000 0.012 0.988 0.000
#> GSM904999 2 0.4941 0.638 0.000 0.564 0.436 0.000
#> GSM905002 2 0.4933 0.642 0.000 0.568 0.432 0.000
#> GSM905009 2 0.4955 0.629 0.000 0.556 0.444 0.000
#> GSM905014 3 0.0000 0.603 0.000 0.000 1.000 0.000
#> GSM905017 2 0.4933 0.642 0.000 0.568 0.432 0.000
#> GSM905020 2 0.4933 0.642 0.000 0.568 0.432 0.000
#> GSM905023 3 0.4933 0.728 0.000 0.000 0.568 0.432
#> GSM905029 3 0.4933 0.728 0.000 0.000 0.568 0.432
#> GSM905032 4 0.0000 0.404 0.000 0.000 0.000 1.000
#> GSM905034 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> GSM905040 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> GSM904985 2 0.0000 0.805 0.000 1.000 0.000 0.000
#> GSM904988 2 0.0000 0.805 0.000 1.000 0.000 0.000
#> GSM904990 2 0.0000 0.805 0.000 1.000 0.000 0.000
#> GSM904992 2 0.0000 0.805 0.000 1.000 0.000 0.000
#> GSM904995 2 0.0000 0.805 0.000 1.000 0.000 0.000
#> GSM904998 2 0.0000 0.805 0.000 1.000 0.000 0.000
#> GSM905000 2 0.0000 0.805 0.000 1.000 0.000 0.000
#> GSM905003 2 0.0000 0.805 0.000 1.000 0.000 0.000
#> GSM905006 2 0.0000 0.805 0.000 1.000 0.000 0.000
#> GSM905008 2 0.0000 0.805 0.000 1.000 0.000 0.000
#> GSM905011 2 0.0000 0.805 0.000 1.000 0.000 0.000
#> GSM905013 2 0.0000 0.805 0.000 1.000 0.000 0.000
#> GSM905016 2 0.0000 0.805 0.000 1.000 0.000 0.000
#> GSM905018 2 0.0000 0.805 0.000 1.000 0.000 0.000
#> GSM905021 2 0.4008 0.717 0.000 0.756 0.244 0.000
#> GSM905025 3 0.4933 0.728 0.000 0.000 0.568 0.432
#> GSM905028 3 0.4941 0.497 0.000 0.436 0.564 0.000
#> GSM905030 3 0.4933 0.504 0.000 0.432 0.568 0.000
#> GSM905033 3 0.6896 0.636 0.000 0.292 0.568 0.140
#> GSM905035 3 0.7039 0.660 0.000 0.256 0.568 0.176
#> GSM905037 3 0.4933 0.504 0.000 0.432 0.568 0.000
#> GSM905039 3 0.4933 0.504 0.000 0.432 0.568 0.000
#> GSM905042 3 0.4933 0.728 0.000 0.000 0.568 0.432
#> GSM905046 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> GSM905065 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> GSM905049 4 0.4933 0.713 0.432 0.000 0.000 0.568
#> GSM905050 4 0.4406 0.663 0.300 0.000 0.000 0.700
#> GSM905064 4 0.4933 0.713 0.432 0.000 0.000 0.568
#> GSM905045 4 0.4933 0.713 0.432 0.000 0.000 0.568
#> GSM905051 4 0.4933 0.713 0.432 0.000 0.000 0.568
#> GSM905055 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> GSM905058 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> GSM905053 4 0.4933 0.713 0.432 0.000 0.000 0.568
#> GSM905061 4 0.4933 0.713 0.432 0.000 0.000 0.568
#> GSM905063 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> GSM905054 4 0.4933 0.713 0.432 0.000 0.000 0.568
#> GSM905062 4 0.4933 0.713 0.432 0.000 0.000 0.568
#> GSM905052 4 0.4925 0.712 0.428 0.000 0.000 0.572
#> GSM905059 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> GSM905047 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> GSM905066 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> GSM905056 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> GSM905060 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> GSM905048 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> GSM905067 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> GSM905057 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> GSM905068 4 0.3356 0.605 0.176 0.000 0.000 0.824
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM905004 5 0.4114 0.404 0.000 0.000 0.000 0.376 0.624
#> GSM905024 1 0.1270 0.941 0.948 0.000 0.000 0.052 0.000
#> GSM905038 5 0.0000 0.926 0.000 0.000 0.000 0.000 1.000
#> GSM905043 1 0.2886 0.824 0.844 0.000 0.000 0.148 0.008
#> GSM904986 3 0.0000 0.956 0.000 0.000 1.000 0.000 0.000
#> GSM904991 3 0.1121 0.921 0.000 0.000 0.956 0.000 0.044
#> GSM904994 3 0.0000 0.956 0.000 0.000 1.000 0.000 0.000
#> GSM904996 3 0.0000 0.956 0.000 0.000 1.000 0.000 0.000
#> GSM905007 3 0.0609 0.940 0.000 0.000 0.980 0.000 0.020
#> GSM905012 3 0.0000 0.956 0.000 0.000 1.000 0.000 0.000
#> GSM905022 3 0.0000 0.956 0.000 0.000 1.000 0.000 0.000
#> GSM905026 5 0.0000 0.926 0.000 0.000 0.000 0.000 1.000
#> GSM905027 5 0.0000 0.926 0.000 0.000 0.000 0.000 1.000
#> GSM905031 5 0.0000 0.926 0.000 0.000 0.000 0.000 1.000
#> GSM905036 5 0.0000 0.926 0.000 0.000 0.000 0.000 1.000
#> GSM905041 5 0.3305 0.679 0.000 0.000 0.000 0.224 0.776
#> GSM905044 5 0.0000 0.926 0.000 0.000 0.000 0.000 1.000
#> GSM904989 3 0.0000 0.956 0.000 0.000 1.000 0.000 0.000
#> GSM904999 3 0.0000 0.956 0.000 0.000 1.000 0.000 0.000
#> GSM905002 3 0.0000 0.956 0.000 0.000 1.000 0.000 0.000
#> GSM905009 3 0.0000 0.956 0.000 0.000 1.000 0.000 0.000
#> GSM905014 3 0.0609 0.940 0.000 0.000 0.980 0.000 0.020
#> GSM905017 3 0.0000 0.956 0.000 0.000 1.000 0.000 0.000
#> GSM905020 3 0.0000 0.956 0.000 0.000 1.000 0.000 0.000
#> GSM905023 5 0.0000 0.926 0.000 0.000 0.000 0.000 1.000
#> GSM905029 5 0.0000 0.926 0.000 0.000 0.000 0.000 1.000
#> GSM905032 4 0.1121 0.952 0.000 0.000 0.000 0.956 0.044
#> GSM905034 1 0.0000 0.987 1.000 0.000 0.000 0.000 0.000
#> GSM905040 1 0.0000 0.987 1.000 0.000 0.000 0.000 0.000
#> GSM904985 2 0.0609 0.933 0.000 0.980 0.020 0.000 0.000
#> GSM904988 2 0.0609 0.933 0.000 0.980 0.020 0.000 0.000
#> GSM904990 2 0.0609 0.933 0.000 0.980 0.020 0.000 0.000
#> GSM904992 2 0.0609 0.933 0.000 0.980 0.020 0.000 0.000
#> GSM904995 2 0.0609 0.933 0.000 0.980 0.020 0.000 0.000
#> GSM904998 2 0.0609 0.933 0.000 0.980 0.020 0.000 0.000
#> GSM905000 2 0.0609 0.933 0.000 0.980 0.020 0.000 0.000
#> GSM905003 2 0.0609 0.933 0.000 0.980 0.020 0.000 0.000
#> GSM905006 2 0.0609 0.933 0.000 0.980 0.020 0.000 0.000
#> GSM905008 2 0.0609 0.933 0.000 0.980 0.020 0.000 0.000
#> GSM905011 2 0.0609 0.933 0.000 0.980 0.020 0.000 0.000
#> GSM905013 2 0.0609 0.933 0.000 0.980 0.020 0.000 0.000
#> GSM905016 2 0.0609 0.933 0.000 0.980 0.020 0.000 0.000
#> GSM905018 2 0.0609 0.933 0.000 0.980 0.020 0.000 0.000
#> GSM905021 3 0.4300 0.093 0.000 0.476 0.524 0.000 0.000
#> GSM905025 5 0.0609 0.918 0.000 0.020 0.000 0.000 0.980
#> GSM905028 2 0.3395 0.710 0.000 0.764 0.000 0.000 0.236
#> GSM905030 2 0.3480 0.696 0.000 0.752 0.000 0.000 0.248
#> GSM905033 5 0.3727 0.672 0.000 0.216 0.016 0.000 0.768
#> GSM905035 5 0.1121 0.903 0.000 0.044 0.000 0.000 0.956
#> GSM905037 2 0.3480 0.696 0.000 0.752 0.000 0.000 0.248
#> GSM905039 2 0.3480 0.696 0.000 0.752 0.000 0.000 0.248
#> GSM905042 5 0.0609 0.918 0.000 0.020 0.000 0.000 0.980
#> GSM905046 1 0.0000 0.987 1.000 0.000 0.000 0.000 0.000
#> GSM905065 1 0.0000 0.987 1.000 0.000 0.000 0.000 0.000
#> GSM905049 4 0.0000 0.996 0.000 0.000 0.000 1.000 0.000
#> GSM905050 4 0.0000 0.996 0.000 0.000 0.000 1.000 0.000
#> GSM905064 4 0.0000 0.996 0.000 0.000 0.000 1.000 0.000
#> GSM905045 4 0.0000 0.996 0.000 0.000 0.000 1.000 0.000
#> GSM905051 4 0.0000 0.996 0.000 0.000 0.000 1.000 0.000
#> GSM905055 1 0.0000 0.987 1.000 0.000 0.000 0.000 0.000
#> GSM905058 1 0.0000 0.987 1.000 0.000 0.000 0.000 0.000
#> GSM905053 4 0.0000 0.996 0.000 0.000 0.000 1.000 0.000
#> GSM905061 4 0.0000 0.996 0.000 0.000 0.000 1.000 0.000
#> GSM905063 1 0.0000 0.987 1.000 0.000 0.000 0.000 0.000
#> GSM905054 4 0.0000 0.996 0.000 0.000 0.000 1.000 0.000
#> GSM905062 4 0.0000 0.996 0.000 0.000 0.000 1.000 0.000
#> GSM905052 4 0.0000 0.996 0.000 0.000 0.000 1.000 0.000
#> GSM905059 1 0.0000 0.987 1.000 0.000 0.000 0.000 0.000
#> GSM905047 1 0.0000 0.987 1.000 0.000 0.000 0.000 0.000
#> GSM905066 1 0.0000 0.987 1.000 0.000 0.000 0.000 0.000
#> GSM905056 1 0.0000 0.987 1.000 0.000 0.000 0.000 0.000
#> GSM905060 1 0.0000 0.987 1.000 0.000 0.000 0.000 0.000
#> GSM905048 1 0.0000 0.987 1.000 0.000 0.000 0.000 0.000
#> GSM905067 1 0.0000 0.987 1.000 0.000 0.000 0.000 0.000
#> GSM905057 1 0.0000 0.987 1.000 0.000 0.000 0.000 0.000
#> GSM905068 4 0.0000 0.996 0.000 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM905004 5 0.0000 0.960 0.000 0.000 0.000 0.000 1.000 0
#> GSM905024 1 0.1141 0.918 0.948 0.000 0.000 0.052 0.000 0
#> GSM905038 5 0.0000 0.960 0.000 0.000 0.000 0.000 1.000 0
#> GSM905043 1 0.5528 0.248 0.508 0.000 0.000 0.144 0.348 0
#> GSM904986 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0
#> GSM904991 5 0.3717 0.369 0.000 0.000 0.384 0.000 0.616 0
#> GSM904994 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0
#> GSM904996 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0
#> GSM905007 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0
#> GSM905012 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0
#> GSM905022 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0
#> GSM905026 5 0.0000 0.960 0.000 0.000 0.000 0.000 1.000 0
#> GSM905027 5 0.0000 0.960 0.000 0.000 0.000 0.000 1.000 0
#> GSM905031 5 0.0000 0.960 0.000 0.000 0.000 0.000 1.000 0
#> GSM905036 5 0.0000 0.960 0.000 0.000 0.000 0.000 1.000 0
#> GSM905041 5 0.0000 0.960 0.000 0.000 0.000 0.000 1.000 0
#> GSM905044 5 0.0000 0.960 0.000 0.000 0.000 0.000 1.000 0
#> GSM904989 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0
#> GSM904999 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0
#> GSM905002 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0
#> GSM905009 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0
#> GSM905014 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0
#> GSM905017 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0
#> GSM905020 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0
#> GSM905023 5 0.0000 0.960 0.000 0.000 0.000 0.000 1.000 0
#> GSM905029 5 0.0000 0.960 0.000 0.000 0.000 0.000 1.000 0
#> GSM905032 5 0.0146 0.956 0.000 0.000 0.000 0.004 0.996 0
#> GSM905034 1 0.0000 0.966 1.000 0.000 0.000 0.000 0.000 0
#> GSM905040 1 0.0000 0.966 1.000 0.000 0.000 0.000 0.000 0
#> GSM904985 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000 0
#> GSM904988 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000 0
#> GSM904990 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000 0
#> GSM904992 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000 0
#> GSM904995 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000 0
#> GSM904998 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000 0
#> GSM905000 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000 0
#> GSM905003 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000 0
#> GSM905006 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000 0
#> GSM905008 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000 0
#> GSM905011 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000 0
#> GSM905013 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000 0
#> GSM905016 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000 0
#> GSM905018 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000 0
#> GSM905021 2 0.1765 0.888 0.000 0.904 0.096 0.000 0.000 0
#> GSM905025 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1
#> GSM905028 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1
#> GSM905030 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1
#> GSM905033 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1
#> GSM905035 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1
#> GSM905037 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1
#> GSM905039 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1
#> GSM905042 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1
#> GSM905046 1 0.0000 0.966 1.000 0.000 0.000 0.000 0.000 0
#> GSM905065 1 0.0000 0.966 1.000 0.000 0.000 0.000 0.000 0
#> GSM905049 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0
#> GSM905050 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0
#> GSM905064 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0
#> GSM905045 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0
#> GSM905051 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0
#> GSM905055 1 0.0000 0.966 1.000 0.000 0.000 0.000 0.000 0
#> GSM905058 1 0.0000 0.966 1.000 0.000 0.000 0.000 0.000 0
#> GSM905053 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0
#> GSM905061 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0
#> GSM905063 1 0.0000 0.966 1.000 0.000 0.000 0.000 0.000 0
#> GSM905054 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0
#> GSM905062 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0
#> GSM905052 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0
#> GSM905059 1 0.0000 0.966 1.000 0.000 0.000 0.000 0.000 0
#> GSM905047 1 0.0000 0.966 1.000 0.000 0.000 0.000 0.000 0
#> GSM905066 1 0.0000 0.966 1.000 0.000 0.000 0.000 0.000 0
#> GSM905056 1 0.0000 0.966 1.000 0.000 0.000 0.000 0.000 0
#> GSM905060 1 0.0000 0.966 1.000 0.000 0.000 0.000 0.000 0
#> GSM905048 1 0.0000 0.966 1.000 0.000 0.000 0.000 0.000 0
#> GSM905067 1 0.0000 0.966 1.000 0.000 0.000 0.000 0.000 0
#> GSM905057 1 0.0000 0.966 1.000 0.000 0.000 0.000 0.000 0
#> GSM905068 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) genotype/variation(p) individual(p) k
#> ATC:pam 75 3.12e-09 7.87e-03 0.05269 2
#> ATC:pam 74 5.34e-09 2.94e-04 0.02753 3
#> ATC:pam 71 1.14e-09 4.02e-07 0.00123 4
#> ATC:pam 74 3.66e-13 5.00e-08 0.11876 5
#> ATC:pam 74 8.94e-15 7.17e-08 0.27272 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 76 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 0.647 0.838 0.904 0.4697 0.494 0.494
#> 3 3 0.561 0.492 0.755 0.3572 0.720 0.503
#> 4 4 0.723 0.755 0.869 0.1662 0.773 0.451
#> 5 5 0.781 0.735 0.854 0.0519 0.927 0.723
#> 6 6 0.809 0.712 0.874 0.0496 0.910 0.619
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
#> GSM905004 1 0.0376 0.830 0.996 0.004
#> GSM905024 1 0.9129 0.642 0.672 0.328
#> GSM905038 1 0.9286 0.618 0.656 0.344
#> GSM905043 1 0.9129 0.642 0.672 0.328
#> GSM904986 2 0.1843 0.939 0.028 0.972
#> GSM904991 2 0.7950 0.687 0.240 0.760
#> GSM904994 2 0.3584 0.945 0.068 0.932
#> GSM904996 2 0.1843 0.939 0.028 0.972
#> GSM905007 2 0.6531 0.767 0.168 0.832
#> GSM905012 2 0.1843 0.939 0.028 0.972
#> GSM905022 2 0.1843 0.939 0.028 0.972
#> GSM905026 1 0.9686 0.525 0.604 0.396
#> GSM905027 1 0.9635 0.543 0.612 0.388
#> GSM905031 1 0.9775 0.487 0.588 0.412
#> GSM905036 1 0.9170 0.637 0.668 0.332
#> GSM905041 1 0.9170 0.637 0.668 0.332
#> GSM905044 1 0.9686 0.525 0.604 0.396
#> GSM904989 2 0.1843 0.939 0.028 0.972
#> GSM904999 2 0.1843 0.939 0.028 0.972
#> GSM905002 2 0.1843 0.939 0.028 0.972
#> GSM905009 2 0.1843 0.939 0.028 0.972
#> GSM905014 2 0.5519 0.833 0.128 0.872
#> GSM905017 2 0.1843 0.939 0.028 0.972
#> GSM905020 2 0.1843 0.939 0.028 0.972
#> GSM905023 1 0.9170 0.637 0.668 0.332
#> GSM905029 1 0.9580 0.555 0.620 0.380
#> GSM905032 1 0.9129 0.642 0.672 0.328
#> GSM905034 1 0.9129 0.642 0.672 0.328
#> GSM905040 1 0.9129 0.642 0.672 0.328
#> GSM904985 2 0.2603 0.963 0.044 0.956
#> GSM904988 2 0.2603 0.963 0.044 0.956
#> GSM904990 2 0.2603 0.963 0.044 0.956
#> GSM904992 2 0.2603 0.963 0.044 0.956
#> GSM904995 2 0.2603 0.963 0.044 0.956
#> GSM904998 2 0.2603 0.963 0.044 0.956
#> GSM905000 2 0.2603 0.963 0.044 0.956
#> GSM905003 2 0.2603 0.963 0.044 0.956
#> GSM905006 2 0.2603 0.963 0.044 0.956
#> GSM905008 2 0.2603 0.963 0.044 0.956
#> GSM905011 2 0.2603 0.963 0.044 0.956
#> GSM905013 2 0.2603 0.963 0.044 0.956
#> GSM905016 2 0.2603 0.963 0.044 0.956
#> GSM905018 2 0.2603 0.963 0.044 0.956
#> GSM905021 2 0.2603 0.963 0.044 0.956
#> GSM905025 2 0.2603 0.963 0.044 0.956
#> GSM905028 2 0.2603 0.963 0.044 0.956
#> GSM905030 2 0.2603 0.963 0.044 0.956
#> GSM905033 2 0.2603 0.963 0.044 0.956
#> GSM905035 2 0.2603 0.963 0.044 0.956
#> GSM905037 2 0.2603 0.963 0.044 0.956
#> GSM905039 2 0.2603 0.963 0.044 0.956
#> GSM905042 2 0.2603 0.963 0.044 0.956
#> GSM905046 1 0.0000 0.832 1.000 0.000
#> GSM905065 1 0.0000 0.832 1.000 0.000
#> GSM905049 1 0.0000 0.832 1.000 0.000
#> GSM905050 1 0.9087 0.645 0.676 0.324
#> GSM905064 1 0.0000 0.832 1.000 0.000
#> GSM905045 1 0.0000 0.832 1.000 0.000
#> GSM905051 1 0.0000 0.832 1.000 0.000
#> GSM905055 1 0.0000 0.832 1.000 0.000
#> GSM905058 1 0.0000 0.832 1.000 0.000
#> GSM905053 1 0.0000 0.832 1.000 0.000
#> GSM905061 1 0.0000 0.832 1.000 0.000
#> GSM905063 1 0.5737 0.772 0.864 0.136
#> GSM905054 1 0.0000 0.832 1.000 0.000
#> GSM905062 1 0.0000 0.832 1.000 0.000
#> GSM905052 1 0.0000 0.832 1.000 0.000
#> GSM905059 1 0.0000 0.832 1.000 0.000
#> GSM905047 1 0.0000 0.832 1.000 0.000
#> GSM905066 1 0.0000 0.832 1.000 0.000
#> GSM905056 1 0.0000 0.832 1.000 0.000
#> GSM905060 1 0.0000 0.832 1.000 0.000
#> GSM905048 1 0.0000 0.832 1.000 0.000
#> GSM905067 1 0.0000 0.832 1.000 0.000
#> GSM905057 1 0.0000 0.832 1.000 0.000
#> GSM905068 1 0.0000 0.832 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM905004 1 0.6587 0.53454 0.752 0.092 0.156
#> GSM905024 1 0.6302 0.28620 0.520 0.000 0.480
#> GSM905038 3 0.6180 -0.07614 0.416 0.000 0.584
#> GSM905043 1 0.6302 0.28620 0.520 0.000 0.480
#> GSM904986 3 0.6235 0.00236 0.000 0.436 0.564
#> GSM904991 3 0.6235 0.00236 0.000 0.436 0.564
#> GSM904994 3 0.6451 0.00132 0.004 0.436 0.560
#> GSM904996 3 0.6235 0.00236 0.000 0.436 0.564
#> GSM905007 3 0.6451 0.00132 0.004 0.436 0.560
#> GSM905012 3 0.6235 0.00236 0.000 0.436 0.564
#> GSM905022 3 0.6235 0.00236 0.000 0.436 0.564
#> GSM905026 3 0.6180 -0.07614 0.416 0.000 0.584
#> GSM905027 3 0.6180 -0.07614 0.416 0.000 0.584
#> GSM905031 3 0.6180 -0.07614 0.416 0.000 0.584
#> GSM905036 3 0.6180 -0.07614 0.416 0.000 0.584
#> GSM905041 3 0.6180 -0.07614 0.416 0.000 0.584
#> GSM905044 3 0.6180 -0.07614 0.416 0.000 0.584
#> GSM904989 3 0.6235 0.00236 0.000 0.436 0.564
#> GSM904999 3 0.6235 0.00236 0.000 0.436 0.564
#> GSM905002 3 0.6235 0.00236 0.000 0.436 0.564
#> GSM905009 3 0.6235 0.00236 0.000 0.436 0.564
#> GSM905014 3 0.6235 0.00236 0.000 0.436 0.564
#> GSM905017 3 0.6235 0.00236 0.000 0.436 0.564
#> GSM905020 3 0.6235 0.00236 0.000 0.436 0.564
#> GSM905023 3 0.6180 -0.07614 0.416 0.000 0.584
#> GSM905029 3 0.6180 -0.07614 0.416 0.000 0.584
#> GSM905032 1 0.6235 0.37047 0.564 0.000 0.436
#> GSM905034 1 0.6235 0.37047 0.564 0.000 0.436
#> GSM905040 1 0.6235 0.37047 0.564 0.000 0.436
#> GSM904985 2 0.0000 0.97923 0.000 1.000 0.000
#> GSM904988 2 0.0000 0.97923 0.000 1.000 0.000
#> GSM904990 2 0.0000 0.97923 0.000 1.000 0.000
#> GSM904992 2 0.0000 0.97923 0.000 1.000 0.000
#> GSM904995 2 0.0000 0.97923 0.000 1.000 0.000
#> GSM904998 2 0.0000 0.97923 0.000 1.000 0.000
#> GSM905000 2 0.0000 0.97923 0.000 1.000 0.000
#> GSM905003 2 0.0000 0.97923 0.000 1.000 0.000
#> GSM905006 2 0.0000 0.97923 0.000 1.000 0.000
#> GSM905008 2 0.0000 0.97923 0.000 1.000 0.000
#> GSM905011 2 0.0000 0.97923 0.000 1.000 0.000
#> GSM905013 2 0.0000 0.97923 0.000 1.000 0.000
#> GSM905016 2 0.0000 0.97923 0.000 1.000 0.000
#> GSM905018 2 0.0000 0.97923 0.000 1.000 0.000
#> GSM905021 2 0.4887 0.66662 0.000 0.772 0.228
#> GSM905025 3 0.9850 0.18132 0.252 0.356 0.392
#> GSM905028 3 0.9614 0.22828 0.208 0.356 0.436
#> GSM905030 3 0.9614 0.22828 0.208 0.356 0.436
#> GSM905033 3 0.9614 0.22828 0.208 0.356 0.436
#> GSM905035 3 0.9614 0.22828 0.208 0.356 0.436
#> GSM905037 3 0.9614 0.22828 0.208 0.356 0.436
#> GSM905039 3 0.9614 0.22828 0.208 0.356 0.436
#> GSM905042 3 0.9614 0.22828 0.208 0.356 0.436
#> GSM905046 1 0.0000 0.85306 1.000 0.000 0.000
#> GSM905065 1 0.0000 0.85306 1.000 0.000 0.000
#> GSM905049 1 0.0000 0.85306 1.000 0.000 0.000
#> GSM905050 1 0.6079 0.43901 0.612 0.000 0.388
#> GSM905064 1 0.0000 0.85306 1.000 0.000 0.000
#> GSM905045 1 0.0424 0.84737 0.992 0.000 0.008
#> GSM905051 1 0.0000 0.85306 1.000 0.000 0.000
#> GSM905055 1 0.0000 0.85306 1.000 0.000 0.000
#> GSM905058 1 0.0000 0.85306 1.000 0.000 0.000
#> GSM905053 1 0.0000 0.85306 1.000 0.000 0.000
#> GSM905061 1 0.0000 0.85306 1.000 0.000 0.000
#> GSM905063 1 0.6062 0.44447 0.616 0.000 0.384
#> GSM905054 1 0.0000 0.85306 1.000 0.000 0.000
#> GSM905062 1 0.0000 0.85306 1.000 0.000 0.000
#> GSM905052 1 0.0000 0.85306 1.000 0.000 0.000
#> GSM905059 1 0.0000 0.85306 1.000 0.000 0.000
#> GSM905047 1 0.0000 0.85306 1.000 0.000 0.000
#> GSM905066 1 0.0000 0.85306 1.000 0.000 0.000
#> GSM905056 1 0.0000 0.85306 1.000 0.000 0.000
#> GSM905060 1 0.0000 0.85306 1.000 0.000 0.000
#> GSM905048 1 0.0000 0.85306 1.000 0.000 0.000
#> GSM905067 1 0.0000 0.85306 1.000 0.000 0.000
#> GSM905057 1 0.0000 0.85306 1.000 0.000 0.000
#> GSM905068 1 0.0000 0.85306 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM905004 4 0.6468 0.5978 0.088 0.008 0.272 0.632
#> GSM905024 1 0.2589 0.8191 0.884 0.000 0.000 0.116
#> GSM905038 1 0.2222 0.8577 0.924 0.000 0.060 0.016
#> GSM905043 1 0.2469 0.8235 0.892 0.000 0.000 0.108
#> GSM904986 3 0.0336 0.9328 0.000 0.008 0.992 0.000
#> GSM904991 3 0.0937 0.9187 0.012 0.012 0.976 0.000
#> GSM904994 3 0.0188 0.9314 0.000 0.004 0.996 0.000
#> GSM904996 3 0.0469 0.9322 0.000 0.012 0.988 0.000
#> GSM905007 3 0.0937 0.9187 0.012 0.012 0.976 0.000
#> GSM905012 3 0.0336 0.9324 0.000 0.008 0.992 0.000
#> GSM905022 3 0.0336 0.9328 0.000 0.008 0.992 0.000
#> GSM905026 1 0.1978 0.8538 0.928 0.000 0.068 0.004
#> GSM905027 1 0.1978 0.8538 0.928 0.000 0.068 0.004
#> GSM905031 1 0.1978 0.8538 0.928 0.000 0.068 0.004
#> GSM905036 1 0.2222 0.8577 0.924 0.000 0.060 0.016
#> GSM905041 1 0.2521 0.8571 0.912 0.000 0.064 0.024
#> GSM905044 1 0.1978 0.8538 0.928 0.000 0.068 0.004
#> GSM904989 3 0.0469 0.9322 0.000 0.012 0.988 0.000
#> GSM904999 3 0.0336 0.9328 0.000 0.008 0.992 0.000
#> GSM905002 3 0.0469 0.9322 0.000 0.012 0.988 0.000
#> GSM905009 3 0.0336 0.9324 0.000 0.008 0.992 0.000
#> GSM905014 3 0.0469 0.9256 0.000 0.012 0.988 0.000
#> GSM905017 3 0.0336 0.9328 0.000 0.008 0.992 0.000
#> GSM905020 3 0.0469 0.9322 0.000 0.012 0.988 0.000
#> GSM905023 1 0.2222 0.8577 0.924 0.000 0.060 0.016
#> GSM905029 1 0.2255 0.8563 0.920 0.000 0.068 0.012
#> GSM905032 1 0.0921 0.8231 0.972 0.000 0.000 0.028
#> GSM905034 1 0.2647 0.8180 0.880 0.000 0.000 0.120
#> GSM905040 1 0.2814 0.8128 0.868 0.000 0.000 0.132
#> GSM904985 2 0.3942 0.6067 0.000 0.764 0.236 0.000
#> GSM904988 2 0.0336 0.7887 0.000 0.992 0.008 0.000
#> GSM904990 2 0.0336 0.7887 0.000 0.992 0.008 0.000
#> GSM904992 2 0.0336 0.7887 0.000 0.992 0.008 0.000
#> GSM904995 2 0.3528 0.6668 0.000 0.808 0.192 0.000
#> GSM904998 2 0.0336 0.7887 0.000 0.992 0.008 0.000
#> GSM905000 2 0.0336 0.7887 0.000 0.992 0.008 0.000
#> GSM905003 3 0.4948 0.1541 0.000 0.440 0.560 0.000
#> GSM905006 2 0.0336 0.7887 0.000 0.992 0.008 0.000
#> GSM905008 2 0.1474 0.7688 0.000 0.948 0.052 0.000
#> GSM905011 2 0.0336 0.7887 0.000 0.992 0.008 0.000
#> GSM905013 2 0.0336 0.7887 0.000 0.992 0.008 0.000
#> GSM905016 2 0.3528 0.6668 0.000 0.808 0.192 0.000
#> GSM905018 2 0.0336 0.7887 0.000 0.992 0.008 0.000
#> GSM905021 3 0.4605 0.4314 0.000 0.336 0.664 0.000
#> GSM905025 2 0.5392 0.4116 0.424 0.564 0.008 0.004
#> GSM905028 2 0.5337 0.4140 0.424 0.564 0.012 0.000
#> GSM905030 2 0.5337 0.4140 0.424 0.564 0.012 0.000
#> GSM905033 1 0.5911 0.0834 0.584 0.372 0.044 0.000
#> GSM905035 2 0.5337 0.4140 0.424 0.564 0.012 0.000
#> GSM905037 2 0.5337 0.4140 0.424 0.564 0.012 0.000
#> GSM905039 2 0.5337 0.4140 0.424 0.564 0.012 0.000
#> GSM905042 1 0.6794 0.2555 0.584 0.280 0.136 0.000
#> GSM905046 4 0.0817 0.8504 0.024 0.000 0.000 0.976
#> GSM905065 4 0.0000 0.8506 0.000 0.000 0.000 1.000
#> GSM905049 4 0.3907 0.8306 0.232 0.000 0.000 0.768
#> GSM905050 1 0.4746 0.1817 0.632 0.000 0.000 0.368
#> GSM905064 4 0.3837 0.8324 0.224 0.000 0.000 0.776
#> GSM905045 4 0.3907 0.8306 0.232 0.000 0.000 0.768
#> GSM905051 4 0.3837 0.8324 0.224 0.000 0.000 0.776
#> GSM905055 4 0.0000 0.8506 0.000 0.000 0.000 1.000
#> GSM905058 4 0.0000 0.8506 0.000 0.000 0.000 1.000
#> GSM905053 4 0.3907 0.8306 0.232 0.000 0.000 0.768
#> GSM905061 4 0.3907 0.8306 0.232 0.000 0.000 0.768
#> GSM905063 4 0.4817 0.0584 0.388 0.000 0.000 0.612
#> GSM905054 4 0.3907 0.8306 0.232 0.000 0.000 0.768
#> GSM905062 4 0.3907 0.8306 0.232 0.000 0.000 0.768
#> GSM905052 4 0.3837 0.8324 0.224 0.000 0.000 0.776
#> GSM905059 4 0.0000 0.8506 0.000 0.000 0.000 1.000
#> GSM905047 4 0.2868 0.8347 0.136 0.000 0.000 0.864
#> GSM905066 4 0.0000 0.8506 0.000 0.000 0.000 1.000
#> GSM905056 4 0.0000 0.8506 0.000 0.000 0.000 1.000
#> GSM905060 4 0.0000 0.8506 0.000 0.000 0.000 1.000
#> GSM905048 4 0.0000 0.8506 0.000 0.000 0.000 1.000
#> GSM905067 4 0.0000 0.8506 0.000 0.000 0.000 1.000
#> GSM905057 4 0.0000 0.8506 0.000 0.000 0.000 1.000
#> GSM905068 4 0.3907 0.8306 0.232 0.000 0.000 0.768
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM905004 1 0.6218 0.4610 0.516 0.028 0.052 0.008 0.396
#> GSM905024 4 0.6234 0.1067 0.160 0.000 0.000 0.508 0.332
#> GSM905038 4 0.2286 0.8202 0.000 0.000 0.004 0.888 0.108
#> GSM905043 4 0.5489 0.3944 0.136 0.000 0.000 0.648 0.216
#> GSM904986 3 0.0290 0.9753 0.000 0.008 0.992 0.000 0.000
#> GSM904991 3 0.0290 0.9700 0.000 0.000 0.992 0.008 0.000
#> GSM904994 3 0.0290 0.9753 0.000 0.008 0.992 0.000 0.000
#> GSM904996 3 0.0290 0.9753 0.000 0.008 0.992 0.000 0.000
#> GSM905007 3 0.0290 0.9700 0.000 0.000 0.992 0.008 0.000
#> GSM905012 3 0.0000 0.9729 0.000 0.000 1.000 0.000 0.000
#> GSM905022 3 0.0290 0.9753 0.000 0.008 0.992 0.000 0.000
#> GSM905026 4 0.0162 0.8254 0.000 0.000 0.004 0.996 0.000
#> GSM905027 4 0.0162 0.8254 0.000 0.000 0.004 0.996 0.000
#> GSM905031 4 0.0162 0.8254 0.000 0.000 0.004 0.996 0.000
#> GSM905036 4 0.2389 0.8139 0.000 0.000 0.004 0.880 0.116
#> GSM905041 4 0.1894 0.8352 0.000 0.000 0.008 0.920 0.072
#> GSM905044 4 0.0162 0.8254 0.000 0.000 0.004 0.996 0.000
#> GSM904989 3 0.0000 0.9729 0.000 0.000 1.000 0.000 0.000
#> GSM904999 3 0.0290 0.9753 0.000 0.008 0.992 0.000 0.000
#> GSM905002 3 0.0290 0.9753 0.000 0.008 0.992 0.000 0.000
#> GSM905009 3 0.0000 0.9729 0.000 0.000 1.000 0.000 0.000
#> GSM905014 3 0.0162 0.9718 0.000 0.000 0.996 0.004 0.000
#> GSM905017 3 0.0290 0.9753 0.000 0.008 0.992 0.000 0.000
#> GSM905020 3 0.0290 0.9753 0.000 0.008 0.992 0.000 0.000
#> GSM905023 4 0.1831 0.8353 0.000 0.000 0.004 0.920 0.076
#> GSM905029 4 0.2011 0.8314 0.000 0.000 0.004 0.908 0.088
#> GSM905032 5 0.5828 0.2485 0.100 0.000 0.000 0.380 0.520
#> GSM905034 5 0.6527 0.2194 0.196 0.000 0.000 0.376 0.428
#> GSM905040 5 0.6465 0.3023 0.208 0.000 0.000 0.308 0.484
#> GSM904985 2 0.3452 0.7380 0.000 0.756 0.244 0.000 0.000
#> GSM904988 2 0.0000 0.8929 0.000 1.000 0.000 0.000 0.000
#> GSM904990 2 0.0000 0.8929 0.000 1.000 0.000 0.000 0.000
#> GSM904992 2 0.0000 0.8929 0.000 1.000 0.000 0.000 0.000
#> GSM904995 2 0.3671 0.7430 0.000 0.756 0.236 0.000 0.008
#> GSM904998 2 0.0290 0.8949 0.000 0.992 0.008 0.000 0.000
#> GSM905000 2 0.0290 0.8949 0.000 0.992 0.008 0.000 0.000
#> GSM905003 2 0.4030 0.5536 0.000 0.648 0.352 0.000 0.000
#> GSM905006 2 0.0000 0.8929 0.000 1.000 0.000 0.000 0.000
#> GSM905008 2 0.1197 0.8784 0.000 0.952 0.048 0.000 0.000
#> GSM905011 2 0.0000 0.8929 0.000 1.000 0.000 0.000 0.000
#> GSM905013 2 0.0290 0.8949 0.000 0.992 0.008 0.000 0.000
#> GSM905016 2 0.3452 0.7380 0.000 0.756 0.244 0.000 0.000
#> GSM905018 2 0.0290 0.8949 0.000 0.992 0.008 0.000 0.000
#> GSM905021 3 0.3424 0.6332 0.000 0.240 0.760 0.000 0.000
#> GSM905025 5 0.1410 0.6604 0.000 0.060 0.000 0.000 0.940
#> GSM905028 5 0.1983 0.6630 0.000 0.060 0.008 0.008 0.924
#> GSM905030 5 0.2199 0.6613 0.000 0.060 0.008 0.016 0.916
#> GSM905033 5 0.6643 0.3936 0.000 0.060 0.084 0.308 0.548
#> GSM905035 5 0.4642 0.5647 0.000 0.060 0.008 0.192 0.740
#> GSM905037 5 0.1983 0.6630 0.000 0.060 0.008 0.008 0.924
#> GSM905039 5 0.1983 0.6630 0.000 0.060 0.008 0.008 0.924
#> GSM905042 5 0.6541 0.2672 0.000 0.036 0.088 0.396 0.480
#> GSM905046 1 0.1357 0.7513 0.948 0.000 0.000 0.004 0.048
#> GSM905065 1 0.0000 0.7461 1.000 0.000 0.000 0.000 0.000
#> GSM905049 1 0.4967 0.7136 0.660 0.000 0.000 0.060 0.280
#> GSM905050 5 0.5316 0.2036 0.284 0.000 0.000 0.084 0.632
#> GSM905064 1 0.5083 0.7080 0.652 0.000 0.000 0.068 0.280
#> GSM905045 1 0.5009 0.7067 0.652 0.000 0.000 0.060 0.288
#> GSM905051 1 0.5026 0.7116 0.656 0.000 0.000 0.064 0.280
#> GSM905055 1 0.0000 0.7461 1.000 0.000 0.000 0.000 0.000
#> GSM905058 1 0.0000 0.7461 1.000 0.000 0.000 0.000 0.000
#> GSM905053 1 0.5026 0.7116 0.656 0.000 0.000 0.064 0.280
#> GSM905061 1 0.4967 0.7136 0.660 0.000 0.000 0.060 0.280
#> GSM905063 1 0.4906 -0.0721 0.496 0.000 0.000 0.024 0.480
#> GSM905054 1 0.4967 0.7136 0.660 0.000 0.000 0.060 0.280
#> GSM905062 1 0.4967 0.7136 0.660 0.000 0.000 0.060 0.280
#> GSM905052 1 0.5026 0.7116 0.656 0.000 0.000 0.064 0.280
#> GSM905059 1 0.0000 0.7461 1.000 0.000 0.000 0.000 0.000
#> GSM905047 1 0.3602 0.7339 0.796 0.000 0.000 0.024 0.180
#> GSM905066 1 0.0000 0.7461 1.000 0.000 0.000 0.000 0.000
#> GSM905056 1 0.0000 0.7461 1.000 0.000 0.000 0.000 0.000
#> GSM905060 1 0.1121 0.7509 0.956 0.000 0.000 0.000 0.044
#> GSM905048 1 0.0404 0.7480 0.988 0.000 0.000 0.000 0.012
#> GSM905067 1 0.0000 0.7461 1.000 0.000 0.000 0.000 0.000
#> GSM905057 1 0.0000 0.7461 1.000 0.000 0.000 0.000 0.000
#> GSM905068 1 0.5083 0.7080 0.652 0.000 0.000 0.068 0.280
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM905004 4 0.4580 0.4978 0.008 0.000 0.048 0.744 0.036 0.164
#> GSM905024 4 0.5562 0.0937 0.016 0.000 0.000 0.484 0.412 0.088
#> GSM905038 5 0.1556 0.8707 0.000 0.000 0.000 0.000 0.920 0.080
#> GSM905043 5 0.5292 -0.0815 0.016 0.000 0.000 0.452 0.472 0.060
#> GSM904986 3 0.0000 0.9733 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM904991 3 0.0937 0.9476 0.000 0.000 0.960 0.000 0.040 0.000
#> GSM904994 3 0.0000 0.9733 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM904996 3 0.0000 0.9733 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905007 3 0.0937 0.9476 0.000 0.000 0.960 0.000 0.040 0.000
#> GSM905012 3 0.0000 0.9733 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905022 3 0.0000 0.9733 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905026 5 0.0000 0.8705 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM905027 5 0.0000 0.8705 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM905031 5 0.0363 0.8749 0.000 0.000 0.000 0.000 0.988 0.012
#> GSM905036 5 0.1444 0.8758 0.000 0.000 0.000 0.000 0.928 0.072
#> GSM905041 5 0.1462 0.8786 0.000 0.000 0.000 0.008 0.936 0.056
#> GSM905044 5 0.0000 0.8705 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM904989 3 0.0000 0.9733 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM904999 3 0.0000 0.9733 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905002 3 0.0000 0.9733 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905009 3 0.0000 0.9733 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905014 3 0.0865 0.9504 0.000 0.000 0.964 0.000 0.036 0.000
#> GSM905017 3 0.0000 0.9733 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905020 3 0.0000 0.9733 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM905023 5 0.1204 0.8796 0.000 0.000 0.000 0.000 0.944 0.056
#> GSM905029 5 0.1556 0.8707 0.000 0.000 0.000 0.000 0.920 0.080
#> GSM905032 4 0.5285 0.0323 0.000 0.000 0.000 0.480 0.420 0.100
#> GSM905034 4 0.5622 0.2500 0.028 0.000 0.000 0.528 0.364 0.080
#> GSM905040 4 0.6125 0.2846 0.060 0.000 0.000 0.512 0.336 0.092
#> GSM904985 2 0.3050 0.7661 0.000 0.764 0.236 0.000 0.000 0.000
#> GSM904988 2 0.0000 0.8925 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM904990 2 0.0000 0.8925 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM904992 2 0.0000 0.8925 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM904995 2 0.3245 0.7709 0.000 0.764 0.228 0.000 0.000 0.008
#> GSM904998 2 0.0000 0.8925 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905000 2 0.0000 0.8925 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905003 2 0.3911 0.7172 0.000 0.712 0.256 0.000 0.000 0.032
#> GSM905006 2 0.0000 0.8925 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905008 2 0.2378 0.8250 0.000 0.848 0.152 0.000 0.000 0.000
#> GSM905011 2 0.0000 0.8925 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905013 2 0.0000 0.8925 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905016 2 0.3050 0.7661 0.000 0.764 0.236 0.000 0.000 0.000
#> GSM905018 2 0.0000 0.8925 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM905021 3 0.3523 0.7081 0.000 0.180 0.780 0.000 0.000 0.040
#> GSM905025 6 0.0000 0.8649 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM905028 6 0.0000 0.8649 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM905030 6 0.0000 0.8649 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM905033 6 0.5113 0.5469 0.000 0.000 0.204 0.000 0.168 0.628
#> GSM905035 6 0.1267 0.8250 0.000 0.000 0.000 0.000 0.060 0.940
#> GSM905037 6 0.0000 0.8649 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM905039 6 0.0000 0.8649 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM905042 6 0.5254 0.2175 0.000 0.000 0.100 0.000 0.392 0.508
#> GSM905046 4 0.3817 -0.2531 0.432 0.000 0.000 0.568 0.000 0.000
#> GSM905065 1 0.3409 0.6628 0.700 0.000 0.000 0.300 0.000 0.000
#> GSM905049 4 0.0000 0.6816 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905050 4 0.5100 0.4634 0.000 0.000 0.000 0.612 0.128 0.260
#> GSM905064 4 0.0603 0.6777 0.016 0.000 0.000 0.980 0.004 0.000
#> GSM905045 4 0.0000 0.6816 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905051 4 0.0405 0.6808 0.008 0.000 0.000 0.988 0.004 0.000
#> GSM905055 1 0.0000 0.6829 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM905058 1 0.3823 0.5527 0.564 0.000 0.000 0.436 0.000 0.000
#> GSM905053 4 0.0260 0.6806 0.008 0.000 0.000 0.992 0.000 0.000
#> GSM905061 4 0.0146 0.6808 0.004 0.000 0.000 0.996 0.000 0.000
#> GSM905063 4 0.6792 0.3911 0.124 0.000 0.000 0.492 0.124 0.260
#> GSM905054 4 0.0000 0.6816 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905062 4 0.0000 0.6816 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM905052 4 0.0508 0.6796 0.012 0.000 0.000 0.984 0.004 0.000
#> GSM905059 1 0.3797 0.5732 0.580 0.000 0.000 0.420 0.000 0.000
#> GSM905047 4 0.2883 0.4508 0.212 0.000 0.000 0.788 0.000 0.000
#> GSM905066 4 0.3864 -0.4164 0.480 0.000 0.000 0.520 0.000 0.000
#> GSM905056 1 0.0000 0.6829 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM905060 1 0.3838 0.5227 0.552 0.000 0.000 0.448 0.000 0.000
#> GSM905048 1 0.3563 0.6450 0.664 0.000 0.000 0.336 0.000 0.000
#> GSM905067 1 0.0000 0.6829 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM905057 1 0.0000 0.6829 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM905068 4 0.0260 0.6806 0.008 0.000 0.000 0.992 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) genotype/variation(p) individual(p) k
#> ATC:mclust 75 9.46e-07 2.26e-04 0.00555 2
#> ATC:mclust 38 3.80e-05 7.26e-04 0.07302 3
#> ATC:mclust 64 3.06e-13 1.80e-03 0.63962 4
#> ATC:mclust 66 6.83e-11 2.24e-04 0.38834 5
#> ATC:mclust 64 5.59e-14 8.52e-06 0.24640 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 76 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.986 0.994 0.5056 0.495 0.495
#> 3 3 0.762 0.789 0.893 0.2712 0.821 0.649
#> 4 4 0.794 0.787 0.888 0.1504 0.807 0.510
#> 5 5 0.796 0.686 0.828 0.0508 0.954 0.824
#> 6 6 0.784 0.717 0.824 0.0261 0.967 0.863
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
#> GSM905004 1 0.0000 0.994 1.000 0.000
#> GSM905024 1 0.0000 0.994 1.000 0.000
#> GSM905038 1 0.1184 0.979 0.984 0.016
#> GSM905043 1 0.0000 0.994 1.000 0.000
#> GSM904986 2 0.0000 0.993 0.000 1.000
#> GSM904991 1 0.4815 0.887 0.896 0.104
#> GSM904994 2 0.0000 0.993 0.000 1.000
#> GSM904996 2 0.0000 0.993 0.000 1.000
#> GSM905007 2 0.0672 0.986 0.008 0.992
#> GSM905012 2 0.0000 0.993 0.000 1.000
#> GSM905022 2 0.0000 0.993 0.000 1.000
#> GSM905026 2 0.0376 0.990 0.004 0.996
#> GSM905027 2 0.8016 0.674 0.244 0.756
#> GSM905031 2 0.0376 0.990 0.004 0.996
#> GSM905036 1 0.0000 0.994 1.000 0.000
#> GSM905041 1 0.0000 0.994 1.000 0.000
#> GSM905044 2 0.0000 0.993 0.000 1.000
#> GSM904989 2 0.0000 0.993 0.000 1.000
#> GSM904999 2 0.0000 0.993 0.000 1.000
#> GSM905002 2 0.0000 0.993 0.000 1.000
#> GSM905009 2 0.0000 0.993 0.000 1.000
#> GSM905014 2 0.0000 0.993 0.000 1.000
#> GSM905017 2 0.0000 0.993 0.000 1.000
#> GSM905020 2 0.0000 0.993 0.000 1.000
#> GSM905023 1 0.0000 0.994 1.000 0.000
#> GSM905029 1 0.4690 0.892 0.900 0.100
#> GSM905032 1 0.0000 0.994 1.000 0.000
#> GSM905034 1 0.0000 0.994 1.000 0.000
#> GSM905040 1 0.0000 0.994 1.000 0.000
#> GSM904985 2 0.0000 0.993 0.000 1.000
#> GSM904988 2 0.0000 0.993 0.000 1.000
#> GSM904990 2 0.0000 0.993 0.000 1.000
#> GSM904992 2 0.0000 0.993 0.000 1.000
#> GSM904995 2 0.0000 0.993 0.000 1.000
#> GSM904998 2 0.0000 0.993 0.000 1.000
#> GSM905000 2 0.0000 0.993 0.000 1.000
#> GSM905003 2 0.0000 0.993 0.000 1.000
#> GSM905006 2 0.0000 0.993 0.000 1.000
#> GSM905008 2 0.0000 0.993 0.000 1.000
#> GSM905011 2 0.0000 0.993 0.000 1.000
#> GSM905013 2 0.0000 0.993 0.000 1.000
#> GSM905016 2 0.0000 0.993 0.000 1.000
#> GSM905018 2 0.0000 0.993 0.000 1.000
#> GSM905021 2 0.0000 0.993 0.000 1.000
#> GSM905025 2 0.0000 0.993 0.000 1.000
#> GSM905028 2 0.0000 0.993 0.000 1.000
#> GSM905030 2 0.0000 0.993 0.000 1.000
#> GSM905033 2 0.0000 0.993 0.000 1.000
#> GSM905035 2 0.0000 0.993 0.000 1.000
#> GSM905037 2 0.0000 0.993 0.000 1.000
#> GSM905039 2 0.0000 0.993 0.000 1.000
#> GSM905042 2 0.0000 0.993 0.000 1.000
#> GSM905046 1 0.0000 0.994 1.000 0.000
#> GSM905065 1 0.0000 0.994 1.000 0.000
#> GSM905049 1 0.0000 0.994 1.000 0.000
#> GSM905050 1 0.0000 0.994 1.000 0.000
#> GSM905064 1 0.0000 0.994 1.000 0.000
#> GSM905045 1 0.0000 0.994 1.000 0.000
#> GSM905051 1 0.0000 0.994 1.000 0.000
#> GSM905055 1 0.0000 0.994 1.000 0.000
#> GSM905058 1 0.0000 0.994 1.000 0.000
#> GSM905053 1 0.0000 0.994 1.000 0.000
#> GSM905061 1 0.0000 0.994 1.000 0.000
#> GSM905063 1 0.0000 0.994 1.000 0.000
#> GSM905054 1 0.0000 0.994 1.000 0.000
#> GSM905062 1 0.0000 0.994 1.000 0.000
#> GSM905052 1 0.0000 0.994 1.000 0.000
#> GSM905059 1 0.0000 0.994 1.000 0.000
#> GSM905047 1 0.0000 0.994 1.000 0.000
#> GSM905066 1 0.0000 0.994 1.000 0.000
#> GSM905056 1 0.0000 0.994 1.000 0.000
#> GSM905060 1 0.0000 0.994 1.000 0.000
#> GSM905048 1 0.0000 0.994 1.000 0.000
#> GSM905067 1 0.0000 0.994 1.000 0.000
#> GSM905057 1 0.0000 0.994 1.000 0.000
#> GSM905068 1 0.0000 0.994 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM905004 1 0.1529 0.955 0.960 0.040 0.000
#> GSM905024 1 0.0000 0.978 1.000 0.000 0.000
#> GSM905038 1 0.4702 0.716 0.788 0.000 0.212
#> GSM905043 1 0.0000 0.978 1.000 0.000 0.000
#> GSM904986 3 0.0000 0.784 0.000 0.000 1.000
#> GSM904991 3 0.5733 0.478 0.324 0.000 0.676
#> GSM904994 3 0.0000 0.784 0.000 0.000 1.000
#> GSM904996 3 0.0000 0.784 0.000 0.000 1.000
#> GSM905007 3 0.3551 0.676 0.132 0.000 0.868
#> GSM905012 3 0.0000 0.784 0.000 0.000 1.000
#> GSM905022 3 0.0000 0.784 0.000 0.000 1.000
#> GSM905026 3 0.5988 0.464 0.000 0.368 0.632
#> GSM905027 3 0.6567 0.613 0.088 0.160 0.752
#> GSM905031 3 0.6215 0.369 0.000 0.428 0.572
#> GSM905036 1 0.0747 0.971 0.984 0.016 0.000
#> GSM905041 1 0.1753 0.937 0.952 0.000 0.048
#> GSM905044 3 0.0000 0.784 0.000 0.000 1.000
#> GSM904989 3 0.0000 0.784 0.000 0.000 1.000
#> GSM904999 3 0.0000 0.784 0.000 0.000 1.000
#> GSM905002 3 0.0000 0.784 0.000 0.000 1.000
#> GSM905009 3 0.0000 0.784 0.000 0.000 1.000
#> GSM905014 3 0.1163 0.765 0.028 0.000 0.972
#> GSM905017 3 0.0000 0.784 0.000 0.000 1.000
#> GSM905020 3 0.0000 0.784 0.000 0.000 1.000
#> GSM905023 1 0.0000 0.978 1.000 0.000 0.000
#> GSM905029 3 0.5988 0.384 0.368 0.000 0.632
#> GSM905032 1 0.0592 0.973 0.988 0.012 0.000
#> GSM905034 1 0.0000 0.978 1.000 0.000 0.000
#> GSM905040 1 0.0000 0.978 1.000 0.000 0.000
#> GSM904985 3 0.6309 -0.484 0.000 0.496 0.504
#> GSM904988 2 0.4974 0.816 0.000 0.764 0.236
#> GSM904990 2 0.4931 0.816 0.000 0.768 0.232
#> GSM904992 2 0.5529 0.801 0.000 0.704 0.296
#> GSM904995 2 0.5760 0.781 0.000 0.672 0.328
#> GSM904998 2 0.6111 0.697 0.000 0.604 0.396
#> GSM905000 2 0.5835 0.770 0.000 0.660 0.340
#> GSM905003 3 0.6140 -0.203 0.000 0.404 0.596
#> GSM905006 2 0.4702 0.813 0.000 0.788 0.212
#> GSM905008 3 0.6274 -0.370 0.000 0.456 0.544
#> GSM905011 2 0.4842 0.815 0.000 0.776 0.224
#> GSM905013 2 0.5988 0.741 0.000 0.632 0.368
#> GSM905016 2 0.6026 0.730 0.000 0.624 0.376
#> GSM905018 2 0.6008 0.735 0.000 0.628 0.372
#> GSM905021 3 0.0000 0.784 0.000 0.000 1.000
#> GSM905025 2 0.0000 0.712 0.000 1.000 0.000
#> GSM905028 2 0.1529 0.744 0.000 0.960 0.040
#> GSM905030 2 0.1411 0.742 0.000 0.964 0.036
#> GSM905033 2 0.5529 0.801 0.000 0.704 0.296
#> GSM905035 2 0.0892 0.731 0.000 0.980 0.020
#> GSM905037 2 0.1289 0.739 0.000 0.968 0.032
#> GSM905039 2 0.0892 0.731 0.000 0.980 0.020
#> GSM905042 2 0.5291 0.811 0.000 0.732 0.268
#> GSM905046 1 0.0000 0.978 1.000 0.000 0.000
#> GSM905065 1 0.0000 0.978 1.000 0.000 0.000
#> GSM905049 1 0.2356 0.931 0.928 0.072 0.000
#> GSM905050 1 0.5098 0.737 0.752 0.248 0.000
#> GSM905064 1 0.0000 0.978 1.000 0.000 0.000
#> GSM905045 1 0.1529 0.957 0.960 0.040 0.000
#> GSM905051 1 0.0000 0.978 1.000 0.000 0.000
#> GSM905055 1 0.0000 0.978 1.000 0.000 0.000
#> GSM905058 1 0.0000 0.978 1.000 0.000 0.000
#> GSM905053 1 0.0000 0.978 1.000 0.000 0.000
#> GSM905061 1 0.1163 0.964 0.972 0.028 0.000
#> GSM905063 1 0.0592 0.973 0.988 0.012 0.000
#> GSM905054 1 0.0237 0.976 0.996 0.004 0.000
#> GSM905062 1 0.1289 0.962 0.968 0.032 0.000
#> GSM905052 1 0.0000 0.978 1.000 0.000 0.000
#> GSM905059 1 0.0000 0.978 1.000 0.000 0.000
#> GSM905047 1 0.0000 0.978 1.000 0.000 0.000
#> GSM905066 1 0.0000 0.978 1.000 0.000 0.000
#> GSM905056 1 0.0000 0.978 1.000 0.000 0.000
#> GSM905060 1 0.0000 0.978 1.000 0.000 0.000
#> GSM905048 1 0.0000 0.978 1.000 0.000 0.000
#> GSM905067 1 0.0000 0.978 1.000 0.000 0.000
#> GSM905057 1 0.0000 0.978 1.000 0.000 0.000
#> GSM905068 1 0.0000 0.978 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM905004 4 0.5633 0.5318 0.380 0.008 0.016 0.596
#> GSM905024 1 0.0336 0.9235 0.992 0.000 0.000 0.008
#> GSM905038 3 0.4963 0.5378 0.020 0.000 0.696 0.284
#> GSM905043 1 0.2021 0.8533 0.936 0.000 0.040 0.024
#> GSM904986 3 0.1398 0.8869 0.000 0.040 0.956 0.004
#> GSM904991 3 0.1302 0.8588 0.044 0.000 0.956 0.000
#> GSM904994 3 0.1576 0.8840 0.000 0.048 0.948 0.004
#> GSM904996 3 0.1902 0.8796 0.000 0.064 0.932 0.004
#> GSM905007 3 0.1339 0.8841 0.008 0.024 0.964 0.004
#> GSM905012 3 0.4387 0.7512 0.000 0.200 0.776 0.024
#> GSM905022 3 0.1305 0.8871 0.000 0.036 0.960 0.004
#> GSM905026 4 0.3355 0.6000 0.000 0.004 0.160 0.836
#> GSM905027 3 0.2048 0.8466 0.000 0.008 0.928 0.064
#> GSM905031 4 0.2924 0.6360 0.000 0.016 0.100 0.884
#> GSM905036 4 0.3176 0.6607 0.036 0.000 0.084 0.880
#> GSM905041 3 0.5933 0.1206 0.464 0.000 0.500 0.036
#> GSM905044 3 0.1706 0.8658 0.000 0.016 0.948 0.036
#> GSM904989 3 0.2610 0.8593 0.000 0.088 0.900 0.012
#> GSM904999 3 0.1305 0.8871 0.000 0.036 0.960 0.004
#> GSM905002 3 0.1211 0.8867 0.000 0.040 0.960 0.000
#> GSM905009 3 0.4406 0.7579 0.000 0.192 0.780 0.028
#> GSM905014 3 0.1256 0.8861 0.008 0.028 0.964 0.000
#> GSM905017 3 0.1305 0.8871 0.000 0.036 0.960 0.004
#> GSM905020 3 0.3324 0.8275 0.000 0.136 0.852 0.012
#> GSM905023 4 0.6087 0.1870 0.048 0.000 0.412 0.540
#> GSM905029 3 0.2261 0.8600 0.024 0.008 0.932 0.036
#> GSM905032 4 0.5404 0.0801 0.476 0.000 0.012 0.512
#> GSM905034 1 0.0376 0.9272 0.992 0.000 0.004 0.004
#> GSM905040 1 0.0188 0.9276 0.996 0.000 0.000 0.004
#> GSM904985 2 0.1118 0.9239 0.000 0.964 0.036 0.000
#> GSM904988 2 0.0188 0.9311 0.000 0.996 0.004 0.000
#> GSM904990 2 0.0000 0.9302 0.000 1.000 0.000 0.000
#> GSM904992 2 0.0188 0.9311 0.000 0.996 0.004 0.000
#> GSM904995 2 0.0592 0.9318 0.000 0.984 0.016 0.000
#> GSM904998 2 0.0592 0.9318 0.000 0.984 0.016 0.000
#> GSM905000 2 0.0469 0.9318 0.000 0.988 0.012 0.000
#> GSM905003 2 0.1398 0.9201 0.000 0.956 0.040 0.004
#> GSM905006 2 0.0524 0.9255 0.000 0.988 0.004 0.008
#> GSM905008 2 0.1305 0.9225 0.000 0.960 0.036 0.004
#> GSM905011 2 0.0000 0.9302 0.000 1.000 0.000 0.000
#> GSM905013 2 0.0592 0.9318 0.000 0.984 0.016 0.000
#> GSM905016 2 0.0592 0.9318 0.000 0.984 0.016 0.000
#> GSM905018 2 0.0592 0.9318 0.000 0.984 0.016 0.000
#> GSM905021 2 0.3791 0.7616 0.000 0.796 0.200 0.004
#> GSM905025 4 0.2593 0.6305 0.000 0.104 0.004 0.892
#> GSM905028 2 0.1489 0.9109 0.000 0.952 0.004 0.044
#> GSM905030 2 0.1867 0.8988 0.000 0.928 0.000 0.072
#> GSM905033 2 0.3523 0.8521 0.000 0.856 0.112 0.032
#> GSM905035 2 0.4690 0.7025 0.000 0.712 0.012 0.276
#> GSM905037 2 0.2125 0.8992 0.000 0.920 0.004 0.076
#> GSM905039 2 0.3402 0.8269 0.000 0.832 0.004 0.164
#> GSM905042 2 0.5834 0.6998 0.000 0.704 0.172 0.124
#> GSM905046 1 0.0000 0.9289 1.000 0.000 0.000 0.000
#> GSM905065 1 0.0188 0.9289 0.996 0.000 0.004 0.000
#> GSM905049 4 0.4631 0.6489 0.260 0.004 0.008 0.728
#> GSM905050 4 0.1743 0.6835 0.056 0.000 0.004 0.940
#> GSM905064 1 0.0336 0.9254 0.992 0.000 0.000 0.008
#> GSM905045 4 0.4401 0.6459 0.272 0.004 0.000 0.724
#> GSM905051 1 0.0927 0.9121 0.976 0.000 0.008 0.016
#> GSM905055 1 0.0000 0.9289 1.000 0.000 0.000 0.000
#> GSM905058 1 0.0188 0.9289 0.996 0.000 0.004 0.000
#> GSM905053 4 0.5365 0.4966 0.412 0.004 0.008 0.576
#> GSM905061 1 0.5168 -0.3299 0.504 0.000 0.004 0.492
#> GSM905063 1 0.1635 0.8858 0.948 0.000 0.008 0.044
#> GSM905054 1 0.5055 0.0985 0.624 0.000 0.008 0.368
#> GSM905062 4 0.5203 0.4930 0.416 0.000 0.008 0.576
#> GSM905052 1 0.0804 0.9159 0.980 0.000 0.008 0.012
#> GSM905059 1 0.0188 0.9289 0.996 0.000 0.004 0.000
#> GSM905047 1 0.0188 0.9277 0.996 0.000 0.000 0.004
#> GSM905066 1 0.0188 0.9289 0.996 0.000 0.004 0.000
#> GSM905056 1 0.0000 0.9289 1.000 0.000 0.000 0.000
#> GSM905060 1 0.0188 0.9289 0.996 0.000 0.004 0.000
#> GSM905048 1 0.0000 0.9289 1.000 0.000 0.000 0.000
#> GSM905067 1 0.0188 0.9289 0.996 0.000 0.004 0.000
#> GSM905057 1 0.0000 0.9289 1.000 0.000 0.000 0.000
#> GSM905068 4 0.5172 0.5135 0.404 0.000 0.008 0.588
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM905004 4 0.2674 0.3075 0.004 0.000 0.140 0.856 0.000
#> GSM905024 1 0.0955 0.8848 0.968 0.000 0.004 0.000 0.028
#> GSM905038 5 0.4287 0.5722 0.000 0.000 0.460 0.000 0.540
#> GSM905043 1 0.2719 0.7790 0.852 0.000 0.004 0.000 0.144
#> GSM904986 3 0.2130 0.5774 0.000 0.012 0.908 0.000 0.080
#> GSM904991 3 0.1410 0.6926 0.000 0.000 0.940 0.060 0.000
#> GSM904994 3 0.3282 0.7055 0.000 0.008 0.804 0.188 0.000
#> GSM904996 3 0.3339 0.7101 0.000 0.040 0.836 0.124 0.000
#> GSM905007 3 0.3774 0.6676 0.000 0.000 0.704 0.296 0.000
#> GSM905012 3 0.5320 0.6012 0.000 0.060 0.572 0.368 0.000
#> GSM905022 3 0.1743 0.6386 0.000 0.028 0.940 0.004 0.028
#> GSM905026 5 0.4030 0.6494 0.000 0.000 0.352 0.000 0.648
#> GSM905027 5 0.4305 0.5352 0.000 0.000 0.488 0.000 0.512
#> GSM905031 5 0.3055 0.4284 0.000 0.000 0.072 0.064 0.864
#> GSM905036 5 0.1914 0.4846 0.000 0.000 0.060 0.016 0.924
#> GSM905041 5 0.5778 0.5025 0.088 0.000 0.452 0.000 0.460
#> GSM905044 3 0.4448 -0.5590 0.000 0.004 0.516 0.000 0.480
#> GSM904989 3 0.4201 0.6507 0.000 0.008 0.664 0.328 0.000
#> GSM904999 3 0.1300 0.6461 0.000 0.028 0.956 0.000 0.016
#> GSM905002 3 0.2674 0.7124 0.000 0.012 0.868 0.120 0.000
#> GSM905009 3 0.4599 0.5948 0.000 0.016 0.600 0.384 0.000
#> GSM905014 3 0.2230 0.7093 0.000 0.000 0.884 0.116 0.000
#> GSM905017 3 0.1818 0.6304 0.000 0.044 0.932 0.000 0.024
#> GSM905020 3 0.5087 0.6482 0.000 0.064 0.644 0.292 0.000
#> GSM905023 5 0.4088 0.6471 0.000 0.000 0.368 0.000 0.632
#> GSM905029 3 0.4151 -0.1953 0.000 0.004 0.652 0.000 0.344
#> GSM905032 5 0.2903 0.2896 0.080 0.000 0.000 0.048 0.872
#> GSM905034 1 0.1502 0.8701 0.940 0.000 0.004 0.000 0.056
#> GSM905040 1 0.1282 0.8765 0.952 0.000 0.004 0.000 0.044
#> GSM904985 2 0.0290 0.9285 0.000 0.992 0.008 0.000 0.000
#> GSM904988 2 0.0000 0.9315 0.000 1.000 0.000 0.000 0.000
#> GSM904990 2 0.0162 0.9303 0.000 0.996 0.000 0.004 0.000
#> GSM904992 2 0.0000 0.9315 0.000 1.000 0.000 0.000 0.000
#> GSM904995 2 0.0000 0.9315 0.000 1.000 0.000 0.000 0.000
#> GSM904998 2 0.0000 0.9315 0.000 1.000 0.000 0.000 0.000
#> GSM905000 2 0.0000 0.9315 0.000 1.000 0.000 0.000 0.000
#> GSM905003 2 0.0290 0.9285 0.000 0.992 0.008 0.000 0.000
#> GSM905006 2 0.0162 0.9303 0.000 0.996 0.000 0.004 0.000
#> GSM905008 2 0.0290 0.9285 0.000 0.992 0.008 0.000 0.000
#> GSM905011 2 0.0162 0.9303 0.000 0.996 0.000 0.004 0.000
#> GSM905013 2 0.0000 0.9315 0.000 1.000 0.000 0.000 0.000
#> GSM905016 2 0.0000 0.9315 0.000 1.000 0.000 0.000 0.000
#> GSM905018 2 0.0000 0.9315 0.000 1.000 0.000 0.000 0.000
#> GSM905021 2 0.2561 0.8032 0.000 0.856 0.144 0.000 0.000
#> GSM905025 4 0.5044 0.4448 0.000 0.032 0.000 0.504 0.464
#> GSM905028 2 0.0162 0.9305 0.000 0.996 0.000 0.004 0.000
#> GSM905030 2 0.1522 0.9029 0.000 0.944 0.000 0.044 0.012
#> GSM905033 2 0.3317 0.8063 0.000 0.840 0.044 0.000 0.116
#> GSM905035 2 0.4639 0.6612 0.000 0.708 0.000 0.056 0.236
#> GSM905037 2 0.1408 0.9054 0.000 0.948 0.000 0.044 0.008
#> GSM905039 2 0.2592 0.8668 0.000 0.892 0.000 0.052 0.056
#> GSM905042 2 0.5778 -0.0502 0.000 0.460 0.088 0.000 0.452
#> GSM905046 1 0.0162 0.8934 0.996 0.000 0.004 0.000 0.000
#> GSM905065 1 0.0162 0.8934 0.996 0.000 0.004 0.000 0.000
#> GSM905049 4 0.4562 0.5553 0.032 0.000 0.000 0.676 0.292
#> GSM905050 4 0.4283 0.4807 0.000 0.000 0.000 0.544 0.456
#> GSM905064 1 0.1106 0.8774 0.964 0.000 0.000 0.024 0.012
#> GSM905045 4 0.6738 0.5027 0.256 0.000 0.000 0.376 0.368
#> GSM905051 1 0.2629 0.7860 0.860 0.000 0.004 0.136 0.000
#> GSM905055 1 0.0000 0.8936 1.000 0.000 0.000 0.000 0.000
#> GSM905058 1 0.0162 0.8934 0.996 0.000 0.004 0.000 0.000
#> GSM905053 4 0.5236 0.3275 0.380 0.000 0.000 0.568 0.052
#> GSM905061 1 0.6407 -0.0813 0.512 0.000 0.000 0.244 0.244
#> GSM905063 1 0.1798 0.8664 0.928 0.000 0.004 0.004 0.064
#> GSM905054 1 0.3593 0.7337 0.824 0.000 0.000 0.116 0.060
#> GSM905062 1 0.6817 -0.4918 0.348 0.000 0.000 0.344 0.308
#> GSM905052 1 0.2488 0.7996 0.872 0.000 0.004 0.124 0.000
#> GSM905059 1 0.0324 0.8934 0.992 0.000 0.004 0.004 0.000
#> GSM905047 1 0.0324 0.8934 0.992 0.000 0.004 0.004 0.000
#> GSM905066 1 0.0162 0.8934 0.996 0.000 0.004 0.000 0.000
#> GSM905056 1 0.0000 0.8936 1.000 0.000 0.000 0.000 0.000
#> GSM905060 1 0.0324 0.8934 0.992 0.000 0.004 0.004 0.000
#> GSM905048 1 0.0000 0.8936 1.000 0.000 0.000 0.000 0.000
#> GSM905067 1 0.0000 0.8936 1.000 0.000 0.000 0.000 0.000
#> GSM905057 1 0.0000 0.8936 1.000 0.000 0.000 0.000 0.000
#> GSM905068 4 0.5853 0.5297 0.252 0.000 0.036 0.640 0.072
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM905004 3 0.6784 -0.0225 0.052 0.000 0.400 0.336 0.000 NA
#> GSM905024 1 0.1480 0.8163 0.940 0.000 0.000 0.000 0.040 NA
#> GSM905038 5 0.4042 0.6271 0.000 0.000 0.020 0.180 0.760 NA
#> GSM905043 1 0.1471 0.8008 0.932 0.000 0.000 0.000 0.064 NA
#> GSM904986 3 0.4039 0.6801 0.000 0.000 0.732 0.000 0.208 NA
#> GSM904991 3 0.2510 0.7841 0.000 0.000 0.872 0.000 0.100 NA
#> GSM904994 3 0.1078 0.8144 0.000 0.000 0.964 0.008 0.016 NA
#> GSM904996 3 0.2653 0.8076 0.000 0.024 0.896 0.036 0.024 NA
#> GSM905007 3 0.1542 0.8157 0.000 0.000 0.944 0.016 0.024 NA
#> GSM905012 3 0.3830 0.7280 0.000 0.020 0.788 0.148 0.000 NA
#> GSM905022 3 0.3359 0.7579 0.000 0.008 0.820 0.000 0.128 NA
#> GSM905026 5 0.3412 0.6681 0.000 0.000 0.064 0.128 0.808 NA
#> GSM905027 5 0.2418 0.6495 0.000 0.000 0.092 0.008 0.884 NA
#> GSM905031 5 0.4468 0.4995 0.000 0.000 0.028 0.316 0.644 NA
#> GSM905036 5 0.3641 0.6213 0.000 0.000 0.028 0.224 0.748 NA
#> GSM905041 5 0.5127 0.4683 0.156 0.000 0.112 0.000 0.692 NA
#> GSM905044 5 0.3098 0.6056 0.000 0.000 0.164 0.000 0.812 NA
#> GSM904989 3 0.3000 0.7637 0.000 0.000 0.840 0.124 0.004 NA
#> GSM904999 3 0.3874 0.7318 0.000 0.008 0.776 0.000 0.156 NA
#> GSM905002 3 0.1837 0.8128 0.000 0.004 0.932 0.032 0.020 NA
#> GSM905009 3 0.3511 0.7360 0.000 0.004 0.800 0.148 0.000 NA
#> GSM905014 3 0.1268 0.8136 0.000 0.000 0.952 0.008 0.036 NA
#> GSM905017 3 0.4100 0.7081 0.000 0.008 0.752 0.000 0.176 NA
#> GSM905020 3 0.3707 0.7493 0.000 0.044 0.808 0.120 0.000 NA
#> GSM905023 5 0.3764 0.6635 0.012 0.000 0.056 0.140 0.792 NA
#> GSM905029 5 0.4524 0.3585 0.000 0.000 0.320 0.000 0.628 NA
#> GSM905032 5 0.5200 0.4819 0.044 0.000 0.000 0.076 0.668 NA
#> GSM905034 1 0.0891 0.8188 0.968 0.000 0.000 0.000 0.008 NA
#> GSM905040 1 0.0806 0.8237 0.972 0.000 0.000 0.000 0.008 NA
#> GSM904985 2 0.0363 0.9351 0.000 0.988 0.012 0.000 0.000 NA
#> GSM904988 2 0.0000 0.9361 0.000 1.000 0.000 0.000 0.000 NA
#> GSM904990 2 0.0000 0.9361 0.000 1.000 0.000 0.000 0.000 NA
#> GSM904992 2 0.0146 0.9370 0.000 0.996 0.004 0.000 0.000 NA
#> GSM904995 2 0.0260 0.9364 0.000 0.992 0.008 0.000 0.000 NA
#> GSM904998 2 0.0260 0.9364 0.000 0.992 0.008 0.000 0.000 NA
#> GSM905000 2 0.0146 0.9370 0.000 0.996 0.004 0.000 0.000 NA
#> GSM905003 2 0.0622 0.9315 0.000 0.980 0.012 0.000 0.000 NA
#> GSM905006 2 0.0000 0.9361 0.000 1.000 0.000 0.000 0.000 NA
#> GSM905008 2 0.0622 0.9313 0.000 0.980 0.012 0.000 0.000 NA
#> GSM905011 2 0.0146 0.9370 0.000 0.996 0.004 0.000 0.000 NA
#> GSM905013 2 0.0146 0.9370 0.000 0.996 0.004 0.000 0.000 NA
#> GSM905016 2 0.0260 0.9364 0.000 0.992 0.008 0.000 0.000 NA
#> GSM905018 2 0.0146 0.9370 0.000 0.996 0.004 0.000 0.000 NA
#> GSM905021 2 0.4305 0.4959 0.000 0.656 0.312 0.000 0.012 NA
#> GSM905025 4 0.5427 0.4229 0.000 0.036 0.000 0.520 0.048 NA
#> GSM905028 2 0.0837 0.9249 0.000 0.972 0.000 0.004 0.020 NA
#> GSM905030 2 0.1938 0.8956 0.000 0.920 0.000 0.036 0.040 NA
#> GSM905033 2 0.3352 0.7692 0.000 0.800 0.000 0.012 0.172 NA
#> GSM905035 2 0.4176 0.6778 0.000 0.732 0.000 0.064 0.200 NA
#> GSM905037 2 0.1909 0.8947 0.000 0.920 0.000 0.024 0.052 NA
#> GSM905039 2 0.2649 0.8620 0.000 0.876 0.000 0.068 0.052 NA
#> GSM905042 5 0.5072 0.3560 0.000 0.308 0.000 0.044 0.616 NA
#> GSM905046 1 0.0692 0.8244 0.976 0.000 0.000 0.004 0.000 NA
#> GSM905065 1 0.0547 0.8245 0.980 0.000 0.000 0.000 0.000 NA
#> GSM905049 4 0.3372 0.6123 0.076 0.000 0.032 0.848 0.036 NA
#> GSM905050 4 0.5160 0.4459 0.008 0.000 0.000 0.648 0.184 NA
#> GSM905064 1 0.3168 0.7559 0.804 0.000 0.000 0.024 0.000 NA
#> GSM905045 4 0.5846 0.4835 0.288 0.000 0.000 0.568 0.100 NA
#> GSM905051 1 0.4529 0.6958 0.740 0.000 0.032 0.052 0.004 NA
#> GSM905055 1 0.3782 0.5947 0.636 0.000 0.000 0.004 0.000 NA
#> GSM905058 1 0.0146 0.8224 0.996 0.000 0.000 0.000 0.000 NA
#> GSM905053 4 0.6448 0.5411 0.224 0.000 0.036 0.568 0.028 NA
#> GSM905061 1 0.5364 0.4199 0.624 0.000 0.000 0.216 0.012 NA
#> GSM905063 1 0.2851 0.7396 0.844 0.000 0.000 0.020 0.004 NA
#> GSM905054 1 0.4520 0.5680 0.688 0.000 0.000 0.248 0.012 NA
#> GSM905062 1 0.5928 -0.1369 0.456 0.000 0.000 0.416 0.036 NA
#> GSM905052 1 0.4610 0.6931 0.732 0.000 0.032 0.044 0.008 NA
#> GSM905059 1 0.0146 0.8224 0.996 0.000 0.000 0.000 0.000 NA
#> GSM905047 1 0.0935 0.8239 0.964 0.000 0.000 0.004 0.000 NA
#> GSM905066 1 0.1010 0.8159 0.960 0.000 0.000 0.004 0.000 NA
#> GSM905056 1 0.3954 0.5764 0.620 0.000 0.000 0.004 0.004 NA
#> GSM905060 1 0.0291 0.8226 0.992 0.000 0.000 0.004 0.000 NA
#> GSM905048 1 0.1082 0.8229 0.956 0.000 0.000 0.004 0.000 NA
#> GSM905067 1 0.1141 0.8210 0.948 0.000 0.000 0.000 0.000 NA
#> GSM905057 1 0.3769 0.5999 0.640 0.000 0.000 0.004 0.000 NA
#> GSM905068 4 0.6158 0.5444 0.044 0.000 0.064 0.628 0.064 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 tissue(p) genotype/variation(p) individual(p) k
#> ATC:NMF 76 6.80e-07 5.88e-04 0.0267 2
#> ATC:NMF 69 2.81e-11 2.74e-05 0.2811 3
#> ATC:NMF 69 5.57e-12 1.44e-07 0.0740 4
#> ATC:NMF 64 4.15e-12 6.46e-06 0.0568 5
#> ATC:NMF 64 1.02e-12 4.42e-07 0.1445 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