Date: 2019-12-25 20:49:21 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 7758 rows and 79 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] 7758 79
The density distribution for each sample is visualized as in one column in the following heatmap. The clustering is based on the distance which is the Kolmogorov-Smirnov statistic between two distributions.
library(ComplexHeatmap)
densityHeatmap(mat, top_annotation = HeatmapAnnotation(df = get_anno(res_list),
col = get_anno_col(res_list)), ylab = "value", cluster_columns = TRUE, show_column_names = FALSE,
mc.cores = 4)
Folowing table shows the best k (number of partitions) for each combination
of top-value methods and partition methods. Clicking on the method name in
the table goes to the section for a single combination of methods.
The cola vignette explains the definition of the metrics used for determining the best number of partitions.
suggest_best_k(res_list)
| The best k | 1-PAC | Mean silhouette | Concordance | Optional k | ||
|---|---|---|---|---|---|---|
| SD:kmeans | 3 | 1.000 | 0.986 | 0.991 | ** | |
| CV:kmeans | 3 | 1.000 | 0.969 | 0.979 | ** | |
| CV:NMF | 2 | 1.000 | 0.967 | 0.986 | ** | |
| MAD:skmeans | 3 | 1.000 | 0.954 | 0.982 | ** | 2 |
| ATC:kmeans | 2 | 1.000 | 0.955 | 0.973 | ** | |
| ATC:mclust | 2 | 1.000 | 0.970 | 0.969 | ** | |
| CV:skmeans | 3 | 0.999 | 0.955 | 0.981 | ** | 2 |
| MAD:NMF | 2 | 0.973 | 0.941 | 0.978 | ** | |
| MAD:kmeans | 3 | 0.954 | 0.960 | 0.975 | ** | 2 |
| ATC:pam | 6 | 0.937 | 0.859 | 0.941 | * | 4,5 |
| ATC:NMF | 2 | 0.922 | 0.926 | 0.972 | * | |
| SD:NMF | 3 | 0.920 | 0.928 | 0.960 | * | 2 |
| ATC:skmeans | 6 | 0.911 | 0.902 | 0.919 | * | 2,3,4,5 |
| SD:skmeans | 4 | 0.902 | 0.894 | 0.940 | * | 2,3 |
| MAD:pam | 4 | 0.901 | 0.865 | 0.941 | * | |
| SD:mclust | 5 | 0.810 | 0.843 | 0.885 | ||
| ATC:hclust | 6 | 0.803 | 0.836 | 0.887 | ||
| CV:mclust | 4 | 0.761 | 0.846 | 0.908 | ||
| SD:hclust | 2 | 0.679 | 0.854 | 0.927 | ||
| MAD:hclust | 2 | 0.625 | 0.876 | 0.937 | ||
| CV:hclust | 2 | 0.622 | 0.838 | 0.901 | ||
| CV:pam | 2 | 0.616 | 0.875 | 0.926 | ||
| SD:pam | 2 | 0.558 | 0.729 | 0.896 | ||
| MAD:mclust | 2 | 0.531 | 0.930 | 0.930 |
**: 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 0.973 0.944 0.979 0.502 0.498 0.498
#> CV:NMF 2 1.000 0.967 0.986 0.504 0.498 0.498
#> MAD:NMF 2 0.973 0.941 0.978 0.503 0.496 0.496
#> ATC:NMF 2 0.922 0.926 0.972 0.502 0.498 0.498
#> SD:skmeans 2 1.000 0.987 0.995 0.504 0.498 0.498
#> CV:skmeans 2 1.000 0.988 0.995 0.504 0.498 0.498
#> MAD:skmeans 2 1.000 0.986 0.994 0.504 0.496 0.496
#> ATC:skmeans 2 1.000 0.990 0.996 0.507 0.494 0.494
#> SD:mclust 2 0.293 0.718 0.821 0.362 0.705 0.705
#> CV:mclust 2 0.610 0.850 0.916 0.384 0.562 0.562
#> MAD:mclust 2 0.531 0.930 0.930 0.465 0.498 0.498
#> ATC:mclust 2 1.000 0.970 0.969 0.489 0.496 0.496
#> SD:kmeans 2 0.528 0.926 0.935 0.493 0.498 0.498
#> CV:kmeans 2 0.514 0.898 0.914 0.491 0.498 0.498
#> MAD:kmeans 2 1.000 0.964 0.968 0.498 0.498 0.498
#> ATC:kmeans 2 1.000 0.955 0.973 0.503 0.494 0.494
#> SD:pam 2 0.558 0.729 0.896 0.486 0.498 0.498
#> CV:pam 2 0.616 0.875 0.926 0.475 0.529 0.529
#> MAD:pam 2 0.637 0.790 0.915 0.498 0.496 0.496
#> ATC:pam 2 0.846 0.908 0.962 0.505 0.494 0.494
#> SD:hclust 2 0.679 0.854 0.927 0.494 0.496 0.496
#> CV:hclust 2 0.622 0.838 0.901 0.479 0.507 0.507
#> MAD:hclust 2 0.625 0.876 0.937 0.492 0.498 0.498
#> ATC:hclust 2 0.322 0.781 0.853 0.458 0.500 0.500
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 0.920 0.928 0.960 0.317 0.784 0.590
#> CV:NMF 3 0.786 0.861 0.920 0.310 0.765 0.562
#> MAD:NMF 3 0.892 0.913 0.957 0.317 0.776 0.576
#> ATC:NMF 3 0.871 0.876 0.948 0.308 0.736 0.518
#> SD:skmeans 3 0.983 0.955 0.982 0.311 0.784 0.590
#> CV:skmeans 3 0.999 0.955 0.981 0.313 0.775 0.577
#> MAD:skmeans 3 1.000 0.954 0.982 0.309 0.776 0.578
#> ATC:skmeans 3 0.982 0.960 0.983 0.310 0.756 0.544
#> SD:mclust 3 0.526 0.764 0.877 0.704 0.603 0.461
#> CV:mclust 3 0.819 0.821 0.901 0.702 0.679 0.474
#> MAD:mclust 3 0.537 0.722 0.870 0.281 0.620 0.395
#> ATC:mclust 3 0.885 0.958 0.963 0.331 0.771 0.569
#> SD:kmeans 3 1.000 0.986 0.991 0.328 0.794 0.607
#> CV:kmeans 3 1.000 0.969 0.979 0.335 0.794 0.607
#> MAD:kmeans 3 0.954 0.960 0.975 0.321 0.794 0.607
#> ATC:kmeans 3 0.833 0.936 0.949 0.314 0.774 0.572
#> SD:pam 3 0.481 0.555 0.778 0.334 0.791 0.603
#> CV:pam 3 0.520 0.749 0.851 0.351 0.804 0.643
#> MAD:pam 3 0.598 0.692 0.792 0.309 0.764 0.566
#> ATC:pam 3 0.686 0.838 0.926 0.285 0.741 0.527
#> SD:hclust 3 0.702 0.706 0.874 0.180 0.869 0.749
#> CV:hclust 3 0.671 0.747 0.872 0.182 0.962 0.926
#> MAD:hclust 3 0.632 0.805 0.900 0.209 0.903 0.805
#> ATC:hclust 3 0.486 0.825 0.874 0.356 0.825 0.656
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.623 0.655 0.821 0.1280 0.829 0.551
#> CV:NMF 4 0.596 0.616 0.795 0.1165 0.931 0.803
#> MAD:NMF 4 0.645 0.661 0.825 0.1272 0.819 0.530
#> ATC:NMF 4 0.602 0.655 0.824 0.1040 0.821 0.548
#> SD:skmeans 4 0.902 0.894 0.940 0.1258 0.895 0.699
#> CV:skmeans 4 0.703 0.433 0.797 0.1191 0.952 0.868
#> MAD:skmeans 4 0.892 0.923 0.954 0.1291 0.894 0.698
#> ATC:skmeans 4 0.947 0.955 0.970 0.1257 0.903 0.715
#> SD:mclust 4 0.729 0.804 0.845 0.1788 0.769 0.461
#> CV:mclust 4 0.761 0.846 0.908 0.1014 0.890 0.700
#> MAD:mclust 4 0.815 0.881 0.933 0.2440 0.783 0.487
#> ATC:mclust 4 0.732 0.731 0.883 0.1304 0.774 0.443
#> SD:kmeans 4 0.725 0.644 0.809 0.1114 0.969 0.913
#> CV:kmeans 4 0.743 0.775 0.851 0.1033 0.938 0.823
#> MAD:kmeans 4 0.743 0.700 0.793 0.1111 0.930 0.797
#> ATC:kmeans 4 0.746 0.681 0.835 0.1117 0.931 0.797
#> SD:pam 4 0.694 0.737 0.878 0.1562 0.830 0.557
#> CV:pam 4 0.629 0.665 0.826 0.1613 0.811 0.535
#> MAD:pam 4 0.901 0.865 0.941 0.1554 0.873 0.652
#> ATC:pam 4 0.928 0.932 0.967 0.1654 0.793 0.477
#> SD:hclust 4 0.675 0.776 0.888 0.0782 0.925 0.826
#> CV:hclust 4 0.697 0.754 0.869 0.1033 0.886 0.763
#> MAD:hclust 4 0.626 0.755 0.874 0.0672 0.968 0.922
#> ATC:hclust 4 0.766 0.801 0.853 0.0941 0.986 0.960
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.622 0.580 0.774 0.0603 0.920 0.704
#> CV:NMF 5 0.631 0.545 0.773 0.0778 0.813 0.450
#> MAD:NMF 5 0.611 0.592 0.768 0.0602 0.928 0.731
#> ATC:NMF 5 0.634 0.541 0.720 0.0584 0.870 0.608
#> SD:skmeans 5 0.774 0.784 0.877 0.0668 0.947 0.795
#> CV:skmeans 5 0.698 0.677 0.831 0.0754 0.836 0.536
#> MAD:skmeans 5 0.822 0.836 0.903 0.0619 0.943 0.779
#> ATC:skmeans 5 0.965 0.920 0.961 0.0625 0.932 0.741
#> SD:mclust 5 0.810 0.843 0.885 0.0735 0.872 0.572
#> CV:mclust 5 0.751 0.723 0.811 0.0622 0.990 0.965
#> MAD:mclust 5 0.884 0.828 0.916 0.0646 0.897 0.636
#> ATC:mclust 5 0.690 0.752 0.818 0.0609 0.957 0.830
#> SD:kmeans 5 0.676 0.676 0.799 0.0755 0.845 0.549
#> CV:kmeans 5 0.672 0.598 0.762 0.0768 0.932 0.769
#> MAD:kmeans 5 0.706 0.766 0.821 0.0744 0.884 0.617
#> ATC:kmeans 5 0.757 0.762 0.822 0.0675 0.882 0.602
#> SD:pam 5 0.728 0.730 0.848 0.0527 0.895 0.629
#> CV:pam 5 0.676 0.673 0.786 0.0480 0.911 0.684
#> MAD:pam 5 0.835 0.822 0.908 0.0501 0.914 0.682
#> ATC:pam 5 0.905 0.848 0.933 0.0494 0.950 0.800
#> SD:hclust 5 0.628 0.664 0.831 0.1465 0.930 0.810
#> CV:hclust 5 0.638 0.702 0.842 0.1268 0.940 0.840
#> MAD:hclust 5 0.618 0.568 0.760 0.1397 0.880 0.698
#> ATC:hclust 5 0.833 0.773 0.874 0.0675 0.964 0.888
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.631 0.521 0.740 0.0461 0.863 0.467
#> CV:NMF 6 0.619 0.452 0.693 0.0397 0.925 0.668
#> MAD:NMF 6 0.619 0.481 0.701 0.0461 0.882 0.524
#> ATC:NMF 6 0.637 0.498 0.736 0.0480 0.868 0.561
#> SD:skmeans 6 0.728 0.686 0.792 0.0410 0.993 0.968
#> CV:skmeans 6 0.689 0.593 0.751 0.0411 0.980 0.904
#> MAD:skmeans 6 0.765 0.724 0.805 0.0405 0.985 0.929
#> ATC:skmeans 6 0.911 0.902 0.919 0.0408 0.954 0.776
#> SD:mclust 6 0.736 0.697 0.833 0.0425 0.952 0.784
#> CV:mclust 6 0.725 0.464 0.752 0.0580 0.895 0.652
#> MAD:mclust 6 0.805 0.701 0.839 0.0353 0.920 0.653
#> ATC:mclust 6 0.868 0.826 0.924 0.0615 0.918 0.643
#> SD:kmeans 6 0.694 0.637 0.746 0.0456 0.949 0.767
#> CV:kmeans 6 0.664 0.466 0.713 0.0463 0.917 0.672
#> MAD:kmeans 6 0.730 0.583 0.764 0.0460 0.968 0.851
#> ATC:kmeans 6 0.820 0.728 0.804 0.0438 0.975 0.879
#> SD:pam 6 0.725 0.555 0.747 0.0394 0.967 0.847
#> CV:pam 6 0.685 0.568 0.784 0.0321 0.969 0.870
#> MAD:pam 6 0.805 0.670 0.802 0.0387 0.939 0.718
#> ATC:pam 6 0.937 0.859 0.941 0.0447 0.943 0.735
#> SD:hclust 6 0.663 0.647 0.783 0.0427 0.994 0.980
#> CV:hclust 6 0.621 0.652 0.826 0.0413 0.993 0.978
#> MAD:hclust 6 0.680 0.617 0.767 0.0557 0.919 0.758
#> ATC:hclust 6 0.803 0.836 0.887 0.0244 0.980 0.932
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 = 776, method = "euler")
top_rows_overlap(res_list, top_n = 1552, method = "euler")
top_rows_overlap(res_list, top_n = 2328, method = "euler")
top_rows_overlap(res_list, top_n = 3103, method = "euler")
top_rows_overlap(res_list, top_n = 3879, method = "euler")
Also visualize the correspondance of rankings between different top-row methods:
top_rows_overlap(res_list, top_n = 776, method = "correspondance")
top_rows_overlap(res_list, top_n = 1552, method = "correspondance")
top_rows_overlap(res_list, top_n = 2328, method = "correspondance")
top_rows_overlap(res_list, top_n = 3103, method = "correspondance")
top_rows_overlap(res_list, top_n = 3879, method = "correspondance")
Heatmaps of the top rows:
top_rows_heatmap(res_list, top_n = 776)
top_rows_heatmap(res_list, top_n = 1552)
top_rows_heatmap(res_list, top_n = 2328)
top_rows_heatmap(res_list, top_n = 3103)
top_rows_heatmap(res_list, top_n = 3879)
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 time(p) k
#> SD:NMF 77 6.27e-07 2
#> CV:NMF 77 5.70e-07 2
#> MAD:NMF 75 1.02e-06 2
#> ATC:NMF 76 9.68e-07 2
#> SD:skmeans 78 3.66e-07 2
#> CV:skmeans 79 3.41e-07 2
#> MAD:skmeans 78 3.66e-07 2
#> ATC:skmeans 79 6.81e-06 2
#> SD:mclust 73 1.53e-02 2
#> CV:mclust 75 4.38e-04 2
#> MAD:mclust 79 3.41e-07 2
#> ATC:mclust 79 3.90e-07 2
#> SD:kmeans 79 3.41e-07 2
#> CV:kmeans 79 3.41e-07 2
#> MAD:kmeans 79 3.41e-07 2
#> ATC:kmeans 78 2.73e-06 2
#> SD:pam 65 7.62e-05 2
#> CV:pam 77 6.31e-02 2
#> MAD:pam 71 7.38e-06 2
#> ATC:pam 75 2.20e-04 2
#> SD:hclust 72 2.53e-07 2
#> CV:hclust 73 2.65e-07 2
#> MAD:hclust 75 3.82e-07 2
#> ATC:hclust 70 1.24e-07 2
test_to_known_factors(res_list, k = 3)
#> n time(p) k
#> SD:NMF 78 2.67e-05 3
#> CV:NMF 76 3.48e-05 3
#> MAD:NMF 75 4.07e-05 3
#> ATC:NMF 72 1.22e-05 3
#> SD:skmeans 78 2.67e-05 3
#> CV:skmeans 77 2.91e-05 3
#> MAD:skmeans 77 2.19e-05 3
#> ATC:skmeans 78 9.67e-06 3
#> SD:mclust 73 7.00e-03 3
#> CV:mclust 71 5.49e-05 3
#> MAD:mclust 70 2.12e-02 3
#> ATC:mclust 79 2.39e-06 3
#> SD:kmeans 79 1.69e-05 3
#> CV:kmeans 78 1.71e-05 3
#> MAD:kmeans 79 1.69e-05 3
#> ATC:kmeans 79 9.57e-06 3
#> SD:pam 51 5.28e-05 3
#> CV:pam 74 7.17e-07 3
#> MAD:pam 69 2.65e-07 3
#> ATC:pam 72 4.32e-06 3
#> SD:hclust 63 7.31e-06 3
#> CV:hclust 64 1.94e-04 3
#> MAD:hclust 72 2.14e-09 3
#> ATC:hclust 79 2.39e-06 3
test_to_known_factors(res_list, k = 4)
#> n time(p) k
#> SD:NMF 64 3.55e-04 4
#> CV:NMF 63 1.58e-03 4
#> MAD:NMF 64 3.55e-04 4
#> ATC:NMF 64 5.08e-04 4
#> SD:skmeans 78 3.11e-05 4
#> CV:skmeans 44 8.32e-02 4
#> MAD:skmeans 77 3.99e-05 4
#> ATC:skmeans 79 1.58e-05 4
#> SD:mclust 72 1.16e-03 4
#> CV:mclust 76 2.12e-08 4
#> MAD:mclust 77 5.62e-04 4
#> ATC:mclust 68 9.53e-06 4
#> SD:kmeans 64 1.86e-04 4
#> CV:kmeans 68 6.39e-04 4
#> MAD:kmeans 67 3.93e-04 4
#> ATC:kmeans 69 2.16e-04 4
#> SD:pam 67 1.18e-04 4
#> CV:pam 65 2.76e-05 4
#> MAD:pam 73 3.63e-04 4
#> ATC:pam 78 1.19e-06 4
#> SD:hclust 69 1.35e-07 4
#> CV:hclust 68 1.68e-08 4
#> MAD:hclust 70 1.24e-07 4
#> ATC:hclust 69 5.91e-06 4
test_to_known_factors(res_list, k = 5)
#> n time(p) k
#> SD:NMF 61 3.46e-04 5
#> CV:NMF 55 1.09e-03 5
#> MAD:NMF 59 9.64e-05 5
#> ATC:NMF 49 1.13e-02 5
#> SD:skmeans 72 3.03e-05 5
#> CV:skmeans 67 5.27e-07 5
#> MAD:skmeans 74 1.86e-05 5
#> ATC:skmeans 76 3.32e-06 5
#> SD:mclust 75 4.54e-06 5
#> CV:mclust 71 5.57e-08 5
#> MAD:mclust 72 2.19e-05 5
#> ATC:mclust 74 4.48e-06 5
#> SD:kmeans 68 4.99e-05 5
#> CV:kmeans 62 1.84e-06 5
#> MAD:kmeans 74 1.92e-05 5
#> ATC:kmeans 75 2.03e-06 5
#> SD:pam 68 1.96e-04 5
#> CV:pam 66 1.30e-05 5
#> MAD:pam 73 2.54e-05 5
#> ATC:pam 72 6.62e-06 5
#> SD:hclust 65 4.36e-07 5
#> CV:hclust 68 7.03e-08 5
#> MAD:hclust 53 1.32e-05 5
#> ATC:hclust 70 1.74e-05 5
test_to_known_factors(res_list, k = 6)
#> n time(p) k
#> SD:NMF 49 2.57e-03 6
#> CV:NMF 41 4.42e-05 6
#> MAD:NMF 46 1.46e-03 6
#> ATC:NMF 48 1.92e-05 6
#> SD:skmeans 71 1.71e-05 6
#> CV:skmeans 61 1.21e-05 6
#> MAD:skmeans 73 1.17e-05 6
#> ATC:skmeans 76 1.94e-05 6
#> SD:mclust 70 4.23e-05 6
#> CV:mclust 44 4.67e-04 6
#> MAD:mclust 61 5.94e-05 6
#> ATC:mclust 73 1.32e-05 6
#> SD:kmeans 67 1.42e-07 6
#> CV:kmeans 50 1.07e-01 6
#> MAD:kmeans 59 1.43e-04 6
#> ATC:kmeans 61 1.20e-05 6
#> SD:pam 52 8.95e-04 6
#> CV:pam 58 1.59e-05 6
#> MAD:pam 66 1.70e-05 6
#> ATC:pam 72 8.78e-05 6
#> SD:hclust 66 3.59e-09 6
#> CV:hclust 60 1.25e-08 6
#> MAD:hclust 62 1.01e-06 6
#> ATC:hclust 75 6.20e-06 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 7758 rows and 79 columns.
#> Top rows (776, 1552, 2328, 3103, 3879) are extracted by 'SD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.679 0.854 0.927 0.4937 0.496 0.496
#> 3 3 0.702 0.706 0.874 0.1800 0.869 0.749
#> 4 4 0.675 0.776 0.888 0.0782 0.925 0.826
#> 5 5 0.628 0.664 0.831 0.1465 0.930 0.810
#> 6 6 0.663 0.647 0.783 0.0427 0.994 0.980
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
#> GSM35441 2 0.0938 0.903 0.012 0.988
#> GSM35446 2 0.5408 0.843 0.124 0.876
#> GSM35449 2 0.0938 0.903 0.012 0.988
#> GSM35455 2 0.0938 0.903 0.012 0.988
#> GSM35458 2 0.2948 0.896 0.052 0.948
#> GSM35460 2 0.5408 0.843 0.124 0.876
#> GSM35461 2 0.9922 0.254 0.448 0.552
#> GSM35463 2 0.0938 0.903 0.012 0.988
#> GSM35472 2 0.9850 0.316 0.428 0.572
#> GSM35475 2 0.2236 0.899 0.036 0.964
#> GSM35483 2 0.0938 0.903 0.012 0.988
#> GSM35496 1 0.0938 0.936 0.988 0.012
#> GSM35497 2 0.0938 0.903 0.012 0.988
#> GSM35504 2 0.3879 0.885 0.076 0.924
#> GSM35508 2 0.0938 0.902 0.012 0.988
#> GSM35511 2 0.2236 0.899 0.036 0.964
#> GSM35512 2 0.9491 0.469 0.368 0.632
#> GSM35515 2 0.2948 0.896 0.052 0.948
#> GSM35519 2 0.9491 0.469 0.368 0.632
#> GSM35527 2 0.0938 0.902 0.012 0.988
#> GSM35532 2 0.2423 0.898 0.040 0.960
#> GSM35439 2 0.0938 0.903 0.012 0.988
#> GSM35443 1 0.0672 0.940 0.992 0.008
#> GSM35445 1 0.0672 0.940 0.992 0.008
#> GSM35448 2 0.4562 0.869 0.096 0.904
#> GSM35451 1 0.2236 0.928 0.964 0.036
#> GSM35454 1 0.2603 0.923 0.956 0.044
#> GSM35457 2 0.0938 0.903 0.012 0.988
#> GSM35465 2 0.3431 0.890 0.064 0.936
#> GSM35468 1 0.0000 0.940 1.000 0.000
#> GSM35471 1 0.3584 0.902 0.932 0.068
#> GSM35473 1 0.0376 0.939 0.996 0.004
#> GSM35477 1 0.2236 0.928 0.964 0.036
#> GSM35480 1 0.0000 0.940 1.000 0.000
#> GSM35482 1 0.0672 0.938 0.992 0.008
#> GSM35485 2 0.0938 0.903 0.012 0.988
#> GSM35489 2 0.4161 0.882 0.084 0.916
#> GSM35492 1 0.0000 0.940 1.000 0.000
#> GSM35495 2 0.9881 0.278 0.436 0.564
#> GSM35499 2 0.1633 0.903 0.024 0.976
#> GSM35502 1 0.0000 0.940 1.000 0.000
#> GSM35505 1 0.2603 0.923 0.956 0.044
#> GSM35507 1 0.8713 0.594 0.708 0.292
#> GSM35510 2 0.1633 0.903 0.024 0.976
#> GSM35514 1 0.0000 0.940 1.000 0.000
#> GSM35517 2 0.0938 0.903 0.012 0.988
#> GSM35520 2 0.3879 0.888 0.076 0.924
#> GSM35523 1 0.6148 0.814 0.848 0.152
#> GSM35529 2 0.0938 0.903 0.012 0.988
#> GSM35531 2 0.4161 0.882 0.084 0.916
#> GSM35534 2 0.0938 0.903 0.012 0.988
#> GSM35536 1 0.0376 0.940 0.996 0.004
#> GSM35538 1 0.0938 0.939 0.988 0.012
#> GSM35539 1 0.0376 0.940 0.996 0.004
#> GSM35540 2 0.2778 0.898 0.048 0.952
#> GSM35541 2 0.0938 0.903 0.012 0.988
#> GSM35442 1 0.0672 0.940 0.992 0.008
#> GSM35447 1 0.2603 0.923 0.956 0.044
#> GSM35450 1 0.1843 0.932 0.972 0.028
#> GSM35453 1 0.0376 0.939 0.996 0.004
#> GSM35456 1 0.6048 0.823 0.852 0.148
#> GSM35464 1 0.9323 0.473 0.652 0.348
#> GSM35467 1 0.0000 0.940 1.000 0.000
#> GSM35470 1 0.0672 0.938 0.992 0.008
#> GSM35479 1 0.0938 0.936 0.988 0.012
#> GSM35484 1 0.1414 0.936 0.980 0.020
#> GSM35488 1 0.0672 0.940 0.992 0.008
#> GSM35491 1 0.0000 0.940 1.000 0.000
#> GSM35494 1 0.0938 0.936 0.988 0.012
#> GSM35498 1 0.9323 0.473 0.652 0.348
#> GSM35501 1 0.0000 0.940 1.000 0.000
#> GSM35509 1 0.9044 0.518 0.680 0.320
#> GSM35513 1 0.0000 0.940 1.000 0.000
#> GSM35516 2 0.8386 0.660 0.268 0.732
#> GSM35522 1 0.6148 0.814 0.848 0.152
#> GSM35525 1 0.0000 0.940 1.000 0.000
#> GSM35528 1 0.0672 0.940 0.992 0.008
#> GSM35533 1 0.1414 0.936 0.980 0.020
#> GSM35537 1 0.0672 0.940 0.992 0.008
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM35441 2 0.0475 0.804 0.004 0.992 0.004
#> GSM35446 3 0.0424 0.594 0.000 0.008 0.992
#> GSM35449 2 0.0829 0.801 0.004 0.984 0.012
#> GSM35455 2 0.0829 0.801 0.004 0.984 0.012
#> GSM35458 3 0.7029 0.470 0.020 0.440 0.540
#> GSM35460 3 0.0424 0.594 0.000 0.008 0.992
#> GSM35461 1 0.9864 -0.187 0.416 0.296 0.288
#> GSM35463 2 0.1525 0.792 0.004 0.964 0.032
#> GSM35472 1 0.9921 -0.239 0.396 0.308 0.296
#> GSM35475 3 0.6215 0.494 0.000 0.428 0.572
#> GSM35483 2 0.1525 0.792 0.004 0.964 0.032
#> GSM35496 1 0.2261 0.877 0.932 0.000 0.068
#> GSM35497 2 0.0829 0.801 0.004 0.984 0.012
#> GSM35504 3 0.5291 0.504 0.000 0.268 0.732
#> GSM35508 2 0.6140 -0.119 0.000 0.596 0.404
#> GSM35511 3 0.6215 0.494 0.000 0.428 0.572
#> GSM35512 2 0.9996 -0.199 0.328 0.348 0.324
#> GSM35515 3 0.7029 0.470 0.020 0.440 0.540
#> GSM35519 2 0.9996 -0.199 0.328 0.348 0.324
#> GSM35527 2 0.6140 -0.119 0.000 0.596 0.404
#> GSM35532 3 0.6204 0.498 0.000 0.424 0.576
#> GSM35439 2 0.0237 0.804 0.004 0.996 0.000
#> GSM35443 1 0.0747 0.902 0.984 0.000 0.016
#> GSM35445 1 0.0592 0.903 0.988 0.000 0.012
#> GSM35448 3 0.1643 0.600 0.000 0.044 0.956
#> GSM35451 1 0.1411 0.894 0.964 0.036 0.000
#> GSM35454 1 0.2096 0.884 0.944 0.004 0.052
#> GSM35457 2 0.0661 0.804 0.004 0.988 0.008
#> GSM35465 2 0.2550 0.764 0.056 0.932 0.012
#> GSM35468 1 0.0000 0.903 1.000 0.000 0.000
#> GSM35471 1 0.2651 0.872 0.928 0.060 0.012
#> GSM35473 1 0.0424 0.903 0.992 0.000 0.008
#> GSM35477 1 0.1411 0.894 0.964 0.036 0.000
#> GSM35480 1 0.0000 0.903 1.000 0.000 0.000
#> GSM35482 1 0.1163 0.897 0.972 0.000 0.028
#> GSM35485 2 0.0237 0.804 0.004 0.996 0.000
#> GSM35489 2 0.4095 0.728 0.064 0.880 0.056
#> GSM35492 1 0.0000 0.903 1.000 0.000 0.000
#> GSM35495 3 0.5882 0.267 0.348 0.000 0.652
#> GSM35499 2 0.1774 0.797 0.016 0.960 0.024
#> GSM35502 1 0.0000 0.903 1.000 0.000 0.000
#> GSM35505 1 0.2096 0.884 0.944 0.004 0.052
#> GSM35507 1 0.6019 0.595 0.700 0.288 0.012
#> GSM35510 2 0.1774 0.797 0.016 0.960 0.024
#> GSM35514 1 0.0000 0.903 1.000 0.000 0.000
#> GSM35517 2 0.0237 0.804 0.004 0.996 0.000
#> GSM35520 2 0.5276 0.656 0.052 0.820 0.128
#> GSM35523 1 0.4110 0.789 0.844 0.152 0.004
#> GSM35529 2 0.0475 0.804 0.004 0.992 0.004
#> GSM35531 2 0.4095 0.728 0.064 0.880 0.056
#> GSM35534 2 0.0237 0.804 0.004 0.996 0.000
#> GSM35536 1 0.0237 0.903 0.996 0.004 0.000
#> GSM35538 1 0.0592 0.903 0.988 0.012 0.000
#> GSM35539 1 0.0237 0.903 0.996 0.004 0.000
#> GSM35540 2 0.2269 0.781 0.040 0.944 0.016
#> GSM35541 2 0.0237 0.804 0.004 0.996 0.000
#> GSM35442 1 0.0747 0.902 0.984 0.000 0.016
#> GSM35447 1 0.2096 0.884 0.944 0.004 0.052
#> GSM35450 1 0.1163 0.897 0.972 0.028 0.000
#> GSM35453 1 0.0424 0.903 0.992 0.000 0.008
#> GSM35456 1 0.4411 0.794 0.844 0.140 0.016
#> GSM35464 1 0.6404 0.494 0.644 0.344 0.012
#> GSM35467 1 0.0000 0.903 1.000 0.000 0.000
#> GSM35470 1 0.1163 0.897 0.972 0.000 0.028
#> GSM35479 1 0.2356 0.875 0.928 0.000 0.072
#> GSM35484 1 0.0983 0.901 0.980 0.016 0.004
#> GSM35488 1 0.0424 0.903 0.992 0.008 0.000
#> GSM35491 1 0.0000 0.903 1.000 0.000 0.000
#> GSM35494 1 0.2165 0.879 0.936 0.000 0.064
#> GSM35498 1 0.6404 0.494 0.644 0.344 0.012
#> GSM35501 1 0.0000 0.903 1.000 0.000 0.000
#> GSM35509 1 0.6140 0.398 0.596 0.000 0.404
#> GSM35513 1 0.0000 0.903 1.000 0.000 0.000
#> GSM35516 2 0.5881 0.419 0.256 0.728 0.016
#> GSM35522 1 0.4110 0.789 0.844 0.152 0.004
#> GSM35525 1 0.0000 0.903 1.000 0.000 0.000
#> GSM35528 1 0.0424 0.903 0.992 0.008 0.000
#> GSM35533 1 0.0983 0.901 0.980 0.016 0.004
#> GSM35537 1 0.0829 0.903 0.984 0.004 0.012
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM35441 2 0.2714 0.846 0.000 0.884 0.112 0.004
#> GSM35446 4 0.0921 0.741 0.000 0.000 0.028 0.972
#> GSM35449 2 0.4088 0.736 0.000 0.764 0.232 0.004
#> GSM35455 2 0.4088 0.736 0.000 0.764 0.232 0.004
#> GSM35458 3 0.2775 0.596 0.020 0.084 0.896 0.000
#> GSM35460 4 0.0921 0.741 0.000 0.000 0.028 0.972
#> GSM35461 3 0.5993 0.396 0.408 0.028 0.556 0.008
#> GSM35463 2 0.1406 0.865 0.000 0.960 0.016 0.024
#> GSM35472 3 0.5822 0.413 0.392 0.028 0.576 0.004
#> GSM35475 3 0.1302 0.591 0.000 0.044 0.956 0.000
#> GSM35483 2 0.1520 0.863 0.000 0.956 0.020 0.024
#> GSM35496 1 0.2965 0.866 0.892 0.000 0.036 0.072
#> GSM35497 2 0.4088 0.736 0.000 0.764 0.232 0.004
#> GSM35504 4 0.5448 0.511 0.000 0.244 0.056 0.700
#> GSM35508 3 0.4720 0.343 0.000 0.324 0.672 0.004
#> GSM35511 3 0.1302 0.591 0.000 0.044 0.956 0.000
#> GSM35512 3 0.5560 0.476 0.324 0.028 0.644 0.004
#> GSM35515 3 0.2775 0.596 0.020 0.084 0.896 0.000
#> GSM35519 3 0.5560 0.476 0.324 0.028 0.644 0.004
#> GSM35527 3 0.4720 0.343 0.000 0.324 0.672 0.004
#> GSM35532 3 0.1211 0.588 0.000 0.040 0.960 0.000
#> GSM35439 2 0.0188 0.874 0.000 0.996 0.004 0.000
#> GSM35443 1 0.1284 0.909 0.964 0.000 0.024 0.012
#> GSM35445 1 0.0927 0.912 0.976 0.000 0.016 0.008
#> GSM35448 4 0.1837 0.735 0.000 0.028 0.028 0.944
#> GSM35451 1 0.1305 0.905 0.960 0.036 0.004 0.000
#> GSM35454 1 0.2076 0.891 0.932 0.004 0.056 0.008
#> GSM35457 2 0.2266 0.863 0.000 0.912 0.084 0.004
#> GSM35465 2 0.2901 0.854 0.040 0.908 0.036 0.016
#> GSM35468 1 0.0336 0.914 0.992 0.000 0.008 0.000
#> GSM35471 1 0.2287 0.881 0.924 0.060 0.012 0.004
#> GSM35473 1 0.0804 0.911 0.980 0.000 0.012 0.008
#> GSM35477 1 0.1305 0.905 0.960 0.036 0.004 0.000
#> GSM35480 1 0.0188 0.914 0.996 0.000 0.004 0.000
#> GSM35482 1 0.2124 0.893 0.932 0.000 0.028 0.040
#> GSM35485 2 0.0188 0.874 0.000 0.996 0.004 0.000
#> GSM35489 2 0.4198 0.786 0.052 0.828 0.116 0.004
#> GSM35492 1 0.0524 0.913 0.988 0.000 0.008 0.004
#> GSM35495 4 0.5492 0.325 0.328 0.000 0.032 0.640
#> GSM35499 2 0.2275 0.872 0.004 0.928 0.048 0.020
#> GSM35502 1 0.0188 0.913 0.996 0.000 0.004 0.000
#> GSM35505 1 0.2076 0.891 0.932 0.004 0.056 0.008
#> GSM35507 1 0.5182 0.566 0.692 0.284 0.012 0.012
#> GSM35510 2 0.2360 0.872 0.004 0.924 0.052 0.020
#> GSM35514 1 0.0188 0.913 0.996 0.000 0.004 0.000
#> GSM35517 2 0.0376 0.873 0.004 0.992 0.004 0.000
#> GSM35520 2 0.4973 0.706 0.040 0.752 0.204 0.004
#> GSM35523 1 0.3780 0.779 0.832 0.148 0.004 0.016
#> GSM35529 2 0.2334 0.859 0.000 0.908 0.088 0.004
#> GSM35531 2 0.4198 0.786 0.052 0.828 0.116 0.004
#> GSM35534 2 0.0188 0.874 0.000 0.996 0.004 0.000
#> GSM35536 1 0.0376 0.914 0.992 0.004 0.004 0.000
#> GSM35538 1 0.0657 0.913 0.984 0.012 0.004 0.000
#> GSM35539 1 0.0524 0.914 0.988 0.008 0.000 0.004
#> GSM35540 2 0.2694 0.865 0.024 0.916 0.044 0.016
#> GSM35541 2 0.0188 0.874 0.000 0.996 0.004 0.000
#> GSM35442 1 0.1284 0.909 0.964 0.000 0.024 0.012
#> GSM35447 1 0.2076 0.891 0.932 0.004 0.056 0.008
#> GSM35450 1 0.1109 0.908 0.968 0.028 0.004 0.000
#> GSM35453 1 0.0804 0.911 0.980 0.000 0.012 0.008
#> GSM35456 1 0.3873 0.791 0.832 0.144 0.016 0.008
#> GSM35464 1 0.5793 0.448 0.628 0.336 0.020 0.016
#> GSM35467 1 0.0188 0.913 0.996 0.000 0.004 0.000
#> GSM35470 1 0.2124 0.893 0.932 0.000 0.028 0.040
#> GSM35479 1 0.2949 0.862 0.888 0.000 0.024 0.088
#> GSM35484 1 0.0927 0.912 0.976 0.016 0.008 0.000
#> GSM35488 1 0.0524 0.914 0.988 0.008 0.004 0.000
#> GSM35491 1 0.0524 0.913 0.988 0.000 0.008 0.004
#> GSM35494 1 0.2845 0.869 0.896 0.000 0.028 0.076
#> GSM35498 1 0.5793 0.448 0.628 0.336 0.020 0.016
#> GSM35501 1 0.0188 0.913 0.996 0.000 0.004 0.000
#> GSM35509 1 0.5756 0.259 0.568 0.000 0.032 0.400
#> GSM35513 1 0.0188 0.913 0.996 0.000 0.004 0.000
#> GSM35516 2 0.4886 0.519 0.244 0.732 0.016 0.008
#> GSM35522 1 0.3780 0.779 0.832 0.148 0.004 0.016
#> GSM35525 1 0.0376 0.914 0.992 0.004 0.000 0.004
#> GSM35528 1 0.0524 0.914 0.988 0.008 0.004 0.000
#> GSM35533 1 0.0927 0.912 0.976 0.016 0.008 0.000
#> GSM35537 1 0.1262 0.912 0.968 0.008 0.008 0.016
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM35441 2 0.2952 0.834 0.000 0.868 0.020 0.008 0.104
#> GSM35446 4 0.1282 0.795 0.000 0.000 0.044 0.952 0.004
#> GSM35449 2 0.4542 0.698 0.000 0.724 0.036 0.008 0.232
#> GSM35455 2 0.4542 0.698 0.000 0.724 0.036 0.008 0.232
#> GSM35458 5 0.1960 0.690 0.020 0.048 0.004 0.000 0.928
#> GSM35460 4 0.1282 0.795 0.000 0.000 0.044 0.952 0.004
#> GSM35461 5 0.5274 0.432 0.056 0.000 0.372 0.000 0.572
#> GSM35463 2 0.2478 0.827 0.000 0.904 0.060 0.028 0.008
#> GSM35472 5 0.5068 0.466 0.044 0.000 0.364 0.000 0.592
#> GSM35475 5 0.0451 0.695 0.000 0.008 0.004 0.000 0.988
#> GSM35483 2 0.2629 0.822 0.000 0.896 0.064 0.032 0.008
#> GSM35496 3 0.3289 0.756 0.172 0.000 0.816 0.004 0.008
#> GSM35497 2 0.4542 0.698 0.000 0.724 0.036 0.008 0.232
#> GSM35504 4 0.4879 0.577 0.000 0.212 0.052 0.720 0.016
#> GSM35508 5 0.5295 0.414 0.000 0.280 0.064 0.008 0.648
#> GSM35511 5 0.0290 0.695 0.000 0.008 0.000 0.000 0.992
#> GSM35512 5 0.4697 0.556 0.036 0.000 0.304 0.000 0.660
#> GSM35515 5 0.1960 0.690 0.020 0.048 0.004 0.000 0.928
#> GSM35519 5 0.4697 0.556 0.036 0.000 0.304 0.000 0.660
#> GSM35527 5 0.5295 0.414 0.000 0.280 0.064 0.008 0.648
#> GSM35532 5 0.0162 0.693 0.000 0.004 0.000 0.000 0.996
#> GSM35439 2 0.0451 0.858 0.000 0.988 0.008 0.000 0.004
#> GSM35443 1 0.3910 0.509 0.720 0.000 0.272 0.000 0.008
#> GSM35445 1 0.3231 0.647 0.800 0.000 0.196 0.000 0.004
#> GSM35448 4 0.0693 0.785 0.000 0.008 0.012 0.980 0.000
#> GSM35451 1 0.1364 0.784 0.952 0.036 0.012 0.000 0.000
#> GSM35454 1 0.5112 -0.225 0.496 0.000 0.468 0.000 0.036
#> GSM35457 2 0.2429 0.851 0.000 0.900 0.020 0.004 0.076
#> GSM35465 2 0.3070 0.840 0.008 0.872 0.088 0.004 0.028
#> GSM35468 1 0.1341 0.775 0.944 0.000 0.056 0.000 0.000
#> GSM35471 1 0.2529 0.766 0.900 0.056 0.040 0.000 0.004
#> GSM35473 1 0.3039 0.647 0.808 0.000 0.192 0.000 0.000
#> GSM35477 1 0.1364 0.784 0.952 0.036 0.012 0.000 0.000
#> GSM35480 1 0.1270 0.782 0.948 0.000 0.052 0.000 0.000
#> GSM35482 3 0.3684 0.721 0.280 0.000 0.720 0.000 0.000
#> GSM35485 2 0.0451 0.858 0.000 0.988 0.008 0.000 0.004
#> GSM35489 2 0.3957 0.788 0.028 0.820 0.040 0.000 0.112
#> GSM35492 1 0.1410 0.773 0.940 0.000 0.060 0.000 0.000
#> GSM35495 4 0.5304 0.333 0.052 0.000 0.352 0.592 0.004
#> GSM35499 2 0.2705 0.855 0.004 0.900 0.048 0.012 0.036
#> GSM35502 1 0.0000 0.790 1.000 0.000 0.000 0.000 0.000
#> GSM35505 1 0.5112 -0.225 0.496 0.000 0.468 0.000 0.036
#> GSM35507 1 0.5416 0.468 0.656 0.256 0.080 0.004 0.004
#> GSM35510 2 0.2784 0.856 0.004 0.896 0.048 0.012 0.040
#> GSM35514 1 0.0162 0.790 0.996 0.000 0.004 0.000 0.000
#> GSM35517 2 0.0613 0.858 0.004 0.984 0.008 0.000 0.004
#> GSM35520 2 0.4551 0.705 0.012 0.744 0.044 0.000 0.200
#> GSM35523 1 0.4592 0.628 0.756 0.100 0.140 0.004 0.000
#> GSM35529 2 0.2490 0.847 0.000 0.896 0.020 0.004 0.080
#> GSM35531 2 0.3957 0.788 0.028 0.820 0.040 0.000 0.112
#> GSM35534 2 0.0613 0.858 0.000 0.984 0.008 0.004 0.004
#> GSM35536 1 0.0865 0.790 0.972 0.004 0.024 0.000 0.000
#> GSM35538 1 0.0807 0.790 0.976 0.012 0.012 0.000 0.000
#> GSM35539 1 0.1697 0.781 0.932 0.008 0.060 0.000 0.000
#> GSM35540 2 0.2934 0.847 0.004 0.880 0.076 0.004 0.036
#> GSM35541 2 0.0451 0.858 0.000 0.988 0.008 0.000 0.004
#> GSM35442 1 0.4046 0.459 0.696 0.000 0.296 0.000 0.008
#> GSM35447 1 0.5112 -0.225 0.496 0.000 0.468 0.000 0.036
#> GSM35450 1 0.1195 0.787 0.960 0.028 0.012 0.000 0.000
#> GSM35453 1 0.3143 0.632 0.796 0.000 0.204 0.000 0.000
#> GSM35456 1 0.3793 0.684 0.820 0.132 0.036 0.004 0.008
#> GSM35464 1 0.6020 0.362 0.588 0.304 0.092 0.004 0.012
#> GSM35467 1 0.0000 0.790 1.000 0.000 0.000 0.000 0.000
#> GSM35470 3 0.4278 0.330 0.452 0.000 0.548 0.000 0.000
#> GSM35479 3 0.3203 0.754 0.168 0.000 0.820 0.012 0.000
#> GSM35484 1 0.1179 0.792 0.964 0.016 0.016 0.000 0.004
#> GSM35488 1 0.0451 0.791 0.988 0.008 0.004 0.000 0.000
#> GSM35491 1 0.1410 0.773 0.940 0.000 0.060 0.000 0.000
#> GSM35494 3 0.3048 0.761 0.176 0.000 0.820 0.004 0.000
#> GSM35498 1 0.6020 0.362 0.588 0.304 0.092 0.004 0.012
#> GSM35501 1 0.0000 0.790 1.000 0.000 0.000 0.000 0.000
#> GSM35509 3 0.5969 0.198 0.108 0.000 0.544 0.344 0.004
#> GSM35513 1 0.0000 0.790 1.000 0.000 0.000 0.000 0.000
#> GSM35516 2 0.4597 0.559 0.240 0.720 0.028 0.004 0.008
#> GSM35522 1 0.4592 0.628 0.756 0.100 0.140 0.004 0.000
#> GSM35525 1 0.1638 0.778 0.932 0.004 0.064 0.000 0.000
#> GSM35528 1 0.0579 0.791 0.984 0.008 0.008 0.000 0.000
#> GSM35533 1 0.1179 0.792 0.964 0.016 0.016 0.000 0.004
#> GSM35537 1 0.3010 0.707 0.824 0.004 0.172 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM35441 2 0.3424 0.6736 0.000 0.772 0.000 0.204 0.024 0.000
#> GSM35446 6 0.0865 0.7814 0.000 0.000 0.036 0.000 0.000 0.964
#> GSM35449 2 0.4687 0.4149 0.000 0.604 0.000 0.336 0.060 0.000
#> GSM35455 2 0.4687 0.4149 0.000 0.604 0.000 0.336 0.060 0.000
#> GSM35458 5 0.4280 0.5860 0.020 0.040 0.000 0.212 0.728 0.000
#> GSM35460 6 0.0865 0.7814 0.000 0.000 0.036 0.000 0.000 0.964
#> GSM35461 5 0.3171 0.6033 0.012 0.000 0.204 0.000 0.784 0.000
#> GSM35463 2 0.3852 0.5525 0.000 0.732 0.016 0.240 0.000 0.012
#> GSM35472 5 0.2933 0.6181 0.000 0.000 0.200 0.000 0.796 0.004
#> GSM35475 5 0.2964 0.6398 0.000 0.004 0.000 0.204 0.792 0.000
#> GSM35483 2 0.4035 0.5281 0.000 0.712 0.016 0.256 0.000 0.016
#> GSM35496 3 0.1332 0.6773 0.028 0.000 0.952 0.000 0.012 0.008
#> GSM35497 2 0.4687 0.4149 0.000 0.604 0.000 0.336 0.060 0.000
#> GSM35504 6 0.4545 0.5143 0.000 0.184 0.004 0.092 0.004 0.716
#> GSM35508 4 0.5173 1.0000 0.000 0.160 0.000 0.616 0.224 0.000
#> GSM35511 5 0.2994 0.6371 0.000 0.004 0.000 0.208 0.788 0.000
#> GSM35512 5 0.2135 0.6559 0.000 0.000 0.128 0.000 0.872 0.000
#> GSM35515 5 0.4280 0.5860 0.020 0.040 0.000 0.212 0.728 0.000
#> GSM35519 5 0.2135 0.6559 0.000 0.000 0.128 0.000 0.872 0.000
#> GSM35527 4 0.5173 1.0000 0.000 0.160 0.000 0.616 0.224 0.000
#> GSM35532 5 0.2994 0.6382 0.000 0.000 0.000 0.208 0.788 0.004
#> GSM35439 2 0.0146 0.7508 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM35443 1 0.4470 0.5776 0.696 0.000 0.228 0.004 0.072 0.000
#> GSM35445 1 0.3183 0.6841 0.788 0.000 0.200 0.004 0.008 0.000
#> GSM35448 6 0.0653 0.7697 0.000 0.004 0.004 0.012 0.000 0.980
#> GSM35451 1 0.1382 0.7976 0.948 0.036 0.008 0.008 0.000 0.000
#> GSM35454 1 0.6047 0.0174 0.448 0.000 0.320 0.004 0.228 0.000
#> GSM35457 2 0.2877 0.7179 0.000 0.820 0.000 0.168 0.012 0.000
#> GSM35465 2 0.3152 0.7146 0.000 0.792 0.008 0.196 0.004 0.000
#> GSM35468 1 0.1572 0.7918 0.936 0.000 0.028 0.000 0.036 0.000
#> GSM35471 1 0.2449 0.7842 0.896 0.056 0.024 0.024 0.000 0.000
#> GSM35473 1 0.2933 0.6842 0.796 0.000 0.200 0.000 0.004 0.000
#> GSM35477 1 0.1382 0.7976 0.948 0.036 0.008 0.008 0.000 0.000
#> GSM35480 1 0.1434 0.7961 0.940 0.000 0.048 0.012 0.000 0.000
#> GSM35482 3 0.3279 0.6201 0.148 0.000 0.816 0.008 0.028 0.000
#> GSM35485 2 0.0458 0.7481 0.000 0.984 0.000 0.016 0.000 0.000
#> GSM35489 2 0.3616 0.6720 0.020 0.808 0.004 0.028 0.140 0.000
#> GSM35492 1 0.1649 0.7902 0.932 0.000 0.032 0.000 0.036 0.000
#> GSM35495 6 0.3881 0.2877 0.004 0.000 0.396 0.000 0.000 0.600
#> GSM35499 2 0.2833 0.7401 0.000 0.836 0.000 0.148 0.004 0.012
#> GSM35502 1 0.0000 0.8026 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35505 1 0.6047 0.0174 0.448 0.000 0.320 0.004 0.228 0.000
#> GSM35507 1 0.5526 0.4929 0.616 0.232 0.024 0.128 0.000 0.000
#> GSM35510 2 0.2872 0.7394 0.000 0.832 0.000 0.152 0.004 0.012
#> GSM35514 1 0.0146 0.8026 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM35517 2 0.0260 0.7508 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM35520 2 0.4232 0.5677 0.004 0.732 0.004 0.056 0.204 0.000
#> GSM35523 1 0.4890 0.6192 0.700 0.048 0.056 0.196 0.000 0.000
#> GSM35529 2 0.2912 0.7115 0.000 0.816 0.000 0.172 0.012 0.000
#> GSM35531 2 0.3616 0.6720 0.020 0.808 0.004 0.028 0.140 0.000
#> GSM35534 2 0.0777 0.7451 0.000 0.972 0.000 0.024 0.000 0.004
#> GSM35536 1 0.0862 0.8033 0.972 0.004 0.008 0.000 0.016 0.000
#> GSM35538 1 0.0767 0.8025 0.976 0.012 0.008 0.004 0.000 0.000
#> GSM35539 1 0.2263 0.7885 0.900 0.004 0.060 0.036 0.000 0.000
#> GSM35540 2 0.2979 0.7249 0.000 0.804 0.004 0.188 0.004 0.000
#> GSM35541 2 0.0146 0.7508 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM35442 1 0.4632 0.5356 0.668 0.000 0.256 0.004 0.072 0.000
#> GSM35447 1 0.6047 0.0174 0.448 0.000 0.320 0.004 0.228 0.000
#> GSM35450 1 0.1116 0.8006 0.960 0.028 0.008 0.004 0.000 0.000
#> GSM35453 1 0.3023 0.6719 0.784 0.000 0.212 0.000 0.004 0.000
#> GSM35456 1 0.3982 0.6952 0.784 0.120 0.016 0.080 0.000 0.000
#> GSM35464 1 0.5905 0.3965 0.552 0.272 0.024 0.152 0.000 0.000
#> GSM35467 1 0.0000 0.8026 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35470 3 0.4735 0.2133 0.392 0.000 0.564 0.008 0.036 0.000
#> GSM35479 3 0.1003 0.6700 0.020 0.000 0.964 0.000 0.000 0.016
#> GSM35484 1 0.1109 0.8050 0.964 0.016 0.012 0.004 0.004 0.000
#> GSM35488 1 0.0405 0.8032 0.988 0.008 0.000 0.004 0.000 0.000
#> GSM35491 1 0.1649 0.7902 0.932 0.000 0.032 0.000 0.036 0.000
#> GSM35494 3 0.0858 0.6805 0.028 0.000 0.968 0.000 0.000 0.004
#> GSM35498 1 0.5905 0.3965 0.552 0.272 0.024 0.152 0.000 0.000
#> GSM35501 1 0.0000 0.8026 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35509 3 0.3861 0.1095 0.008 0.000 0.640 0.000 0.000 0.352
#> GSM35513 1 0.0000 0.8026 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35516 2 0.4337 0.4742 0.224 0.712 0.008 0.056 0.000 0.000
#> GSM35522 1 0.4890 0.6192 0.700 0.048 0.056 0.196 0.000 0.000
#> GSM35525 1 0.2179 0.7862 0.900 0.000 0.064 0.036 0.000 0.000
#> GSM35528 1 0.0665 0.8035 0.980 0.008 0.004 0.008 0.000 0.000
#> GSM35533 1 0.1109 0.8050 0.964 0.016 0.012 0.004 0.004 0.000
#> GSM35537 1 0.3927 0.6919 0.756 0.000 0.172 0.072 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 time(p) k
#> SD:hclust 72 2.53e-07 2
#> SD:hclust 63 7.31e-06 3
#> SD:hclust 69 1.35e-07 4
#> SD:hclust 65 4.36e-07 5
#> SD:hclust 66 3.59e-09 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 7758 rows and 79 columns.
#> Top rows (776, 1552, 2328, 3103, 3879) 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 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 0.528 0.926 0.935 0.4934 0.498 0.498
#> 3 3 1.000 0.986 0.991 0.3283 0.794 0.607
#> 4 4 0.725 0.644 0.809 0.1114 0.969 0.913
#> 5 5 0.676 0.676 0.799 0.0755 0.845 0.549
#> 6 6 0.694 0.637 0.746 0.0456 0.949 0.767
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
#> GSM35441 2 0.6048 0.934 0.148 0.852
#> GSM35446 2 0.0376 0.893 0.004 0.996
#> GSM35449 2 0.6048 0.934 0.148 0.852
#> GSM35455 2 0.6048 0.934 0.148 0.852
#> GSM35458 2 0.5519 0.933 0.128 0.872
#> GSM35460 2 0.0376 0.893 0.004 0.996
#> GSM35461 1 0.5946 0.876 0.856 0.144
#> GSM35463 2 0.5946 0.933 0.144 0.856
#> GSM35472 2 0.4161 0.848 0.084 0.916
#> GSM35475 2 0.1843 0.908 0.028 0.972
#> GSM35483 2 0.4815 0.928 0.104 0.896
#> GSM35496 1 0.5946 0.876 0.856 0.144
#> GSM35497 2 0.6048 0.934 0.148 0.852
#> GSM35504 2 0.0376 0.898 0.004 0.996
#> GSM35508 2 0.1843 0.908 0.028 0.972
#> GSM35511 2 0.0672 0.894 0.008 0.992
#> GSM35512 2 0.2043 0.886 0.032 0.968
#> GSM35515 2 0.5519 0.933 0.128 0.872
#> GSM35519 2 0.0672 0.894 0.008 0.992
#> GSM35527 2 0.1843 0.908 0.028 0.972
#> GSM35532 2 0.0672 0.894 0.008 0.992
#> GSM35439 2 0.6048 0.934 0.148 0.852
#> GSM35443 1 0.0376 0.953 0.996 0.004
#> GSM35445 1 0.1843 0.944 0.972 0.028
#> GSM35448 2 0.0376 0.893 0.004 0.996
#> GSM35451 1 0.0376 0.953 0.996 0.004
#> GSM35454 1 0.6048 0.875 0.852 0.148
#> GSM35457 2 0.6048 0.934 0.148 0.852
#> GSM35465 2 0.6048 0.934 0.148 0.852
#> GSM35468 1 0.0376 0.953 0.996 0.004
#> GSM35471 1 0.0672 0.952 0.992 0.008
#> GSM35473 1 0.1633 0.945 0.976 0.024
#> GSM35477 1 0.0376 0.953 0.996 0.004
#> GSM35480 1 0.1414 0.947 0.980 0.020
#> GSM35482 1 0.6048 0.875 0.852 0.148
#> GSM35485 2 0.5946 0.933 0.144 0.856
#> GSM35489 2 0.6048 0.934 0.148 0.852
#> GSM35492 1 0.0376 0.953 0.996 0.004
#> GSM35495 1 0.6247 0.870 0.844 0.156
#> GSM35499 2 0.5946 0.933 0.144 0.856
#> GSM35502 1 0.0376 0.953 0.996 0.004
#> GSM35505 1 0.6048 0.875 0.852 0.148
#> GSM35507 1 0.0376 0.953 0.996 0.004
#> GSM35510 2 0.5946 0.933 0.144 0.856
#> GSM35514 1 0.0376 0.953 0.996 0.004
#> GSM35517 2 0.6048 0.934 0.148 0.852
#> GSM35520 2 0.1633 0.906 0.024 0.976
#> GSM35523 1 0.0376 0.953 0.996 0.004
#> GSM35529 2 0.6048 0.934 0.148 0.852
#> GSM35531 2 0.6048 0.934 0.148 0.852
#> GSM35534 2 0.5946 0.933 0.144 0.856
#> GSM35536 1 0.0376 0.953 0.996 0.004
#> GSM35538 1 0.0376 0.953 0.996 0.004
#> GSM35539 1 0.0376 0.953 0.996 0.004
#> GSM35540 2 0.1633 0.906 0.024 0.976
#> GSM35541 2 0.6048 0.934 0.148 0.852
#> GSM35442 1 0.3879 0.919 0.924 0.076
#> GSM35447 1 0.6048 0.875 0.852 0.148
#> GSM35450 1 0.0376 0.953 0.996 0.004
#> GSM35453 1 0.2778 0.935 0.952 0.048
#> GSM35456 1 0.0672 0.952 0.992 0.008
#> GSM35464 2 0.6048 0.934 0.148 0.852
#> GSM35467 1 0.0376 0.953 0.996 0.004
#> GSM35470 1 0.2423 0.938 0.960 0.040
#> GSM35479 1 0.6048 0.875 0.852 0.148
#> GSM35484 1 0.0672 0.952 0.992 0.008
#> GSM35488 1 0.0376 0.953 0.996 0.004
#> GSM35491 1 0.0376 0.953 0.996 0.004
#> GSM35494 1 0.6048 0.875 0.852 0.148
#> GSM35498 1 0.0376 0.953 0.996 0.004
#> GSM35501 1 0.0376 0.953 0.996 0.004
#> GSM35509 1 0.6048 0.875 0.852 0.148
#> GSM35513 1 0.0376 0.953 0.996 0.004
#> GSM35516 2 0.6048 0.934 0.148 0.852
#> GSM35522 1 0.0376 0.953 0.996 0.004
#> GSM35525 1 0.0376 0.953 0.996 0.004
#> GSM35528 1 0.0376 0.953 0.996 0.004
#> GSM35533 1 0.0672 0.952 0.992 0.008
#> GSM35537 1 0.1184 0.948 0.984 0.016
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM35441 2 0.0000 0.997 0.000 1.000 0.000
#> GSM35446 3 0.0592 0.973 0.000 0.012 0.988
#> GSM35449 2 0.0237 0.996 0.000 0.996 0.004
#> GSM35455 2 0.0237 0.996 0.000 0.996 0.004
#> GSM35458 2 0.0592 0.990 0.000 0.988 0.012
#> GSM35460 3 0.0592 0.973 0.000 0.012 0.988
#> GSM35461 3 0.2356 0.915 0.072 0.000 0.928
#> GSM35463 2 0.0000 0.997 0.000 1.000 0.000
#> GSM35472 3 0.0424 0.973 0.000 0.008 0.992
#> GSM35475 2 0.1031 0.979 0.000 0.976 0.024
#> GSM35483 2 0.0000 0.997 0.000 1.000 0.000
#> GSM35496 3 0.0237 0.977 0.004 0.000 0.996
#> GSM35497 2 0.0237 0.996 0.000 0.996 0.004
#> GSM35504 2 0.0000 0.997 0.000 1.000 0.000
#> GSM35508 2 0.0237 0.996 0.000 0.996 0.004
#> GSM35511 3 0.4796 0.725 0.000 0.220 0.780
#> GSM35512 3 0.0000 0.975 0.000 0.000 1.000
#> GSM35515 2 0.0592 0.990 0.000 0.988 0.012
#> GSM35519 3 0.0747 0.970 0.000 0.016 0.984
#> GSM35527 2 0.0237 0.996 0.000 0.996 0.004
#> GSM35532 3 0.0747 0.970 0.000 0.016 0.984
#> GSM35439 2 0.0000 0.997 0.000 1.000 0.000
#> GSM35443 1 0.0424 0.995 0.992 0.000 0.008
#> GSM35445 1 0.0424 0.995 0.992 0.000 0.008
#> GSM35448 3 0.0892 0.969 0.000 0.020 0.980
#> GSM35451 1 0.0000 0.994 1.000 0.000 0.000
#> GSM35454 3 0.0237 0.977 0.004 0.000 0.996
#> GSM35457 2 0.0000 0.997 0.000 1.000 0.000
#> GSM35465 2 0.0000 0.997 0.000 1.000 0.000
#> GSM35468 1 0.0424 0.995 0.992 0.000 0.008
#> GSM35471 1 0.0237 0.993 0.996 0.000 0.004
#> GSM35473 1 0.0424 0.995 0.992 0.000 0.008
#> GSM35477 1 0.0000 0.994 1.000 0.000 0.000
#> GSM35480 1 0.0424 0.995 0.992 0.000 0.008
#> GSM35482 3 0.0237 0.977 0.004 0.000 0.996
#> GSM35485 2 0.0000 0.997 0.000 1.000 0.000
#> GSM35489 2 0.0000 0.997 0.000 1.000 0.000
#> GSM35492 1 0.0424 0.995 0.992 0.000 0.008
#> GSM35495 3 0.0237 0.977 0.004 0.000 0.996
#> GSM35499 2 0.0000 0.997 0.000 1.000 0.000
#> GSM35502 1 0.0424 0.995 0.992 0.000 0.008
#> GSM35505 3 0.0237 0.977 0.004 0.000 0.996
#> GSM35507 1 0.0000 0.994 1.000 0.000 0.000
#> GSM35510 2 0.0000 0.997 0.000 1.000 0.000
#> GSM35514 1 0.0424 0.995 0.992 0.000 0.008
#> GSM35517 2 0.0000 0.997 0.000 1.000 0.000
#> GSM35520 2 0.0424 0.992 0.000 0.992 0.008
#> GSM35523 1 0.0424 0.991 0.992 0.000 0.008
#> GSM35529 2 0.0000 0.997 0.000 1.000 0.000
#> GSM35531 2 0.0000 0.997 0.000 1.000 0.000
#> GSM35534 2 0.0000 0.997 0.000 1.000 0.000
#> GSM35536 1 0.0424 0.995 0.992 0.000 0.008
#> GSM35538 1 0.0000 0.994 1.000 0.000 0.000
#> GSM35539 1 0.0000 0.994 1.000 0.000 0.000
#> GSM35540 2 0.0000 0.997 0.000 1.000 0.000
#> GSM35541 2 0.0000 0.997 0.000 1.000 0.000
#> GSM35442 1 0.1411 0.973 0.964 0.000 0.036
#> GSM35447 3 0.0237 0.977 0.004 0.000 0.996
#> GSM35450 1 0.0000 0.994 1.000 0.000 0.000
#> GSM35453 1 0.0424 0.995 0.992 0.000 0.008
#> GSM35456 1 0.0000 0.994 1.000 0.000 0.000
#> GSM35464 2 0.0424 0.991 0.008 0.992 0.000
#> GSM35467 1 0.0424 0.995 0.992 0.000 0.008
#> GSM35470 1 0.0747 0.991 0.984 0.000 0.016
#> GSM35479 3 0.0237 0.977 0.004 0.000 0.996
#> GSM35484 1 0.0424 0.995 0.992 0.000 0.008
#> GSM35488 1 0.0000 0.994 1.000 0.000 0.000
#> GSM35491 1 0.0424 0.995 0.992 0.000 0.008
#> GSM35494 3 0.0237 0.977 0.004 0.000 0.996
#> GSM35498 1 0.0424 0.991 0.992 0.000 0.008
#> GSM35501 1 0.0424 0.995 0.992 0.000 0.008
#> GSM35509 3 0.0237 0.977 0.004 0.000 0.996
#> GSM35513 1 0.0424 0.995 0.992 0.000 0.008
#> GSM35516 2 0.0000 0.997 0.000 1.000 0.000
#> GSM35522 1 0.0424 0.991 0.992 0.000 0.008
#> GSM35525 1 0.0000 0.994 1.000 0.000 0.000
#> GSM35528 1 0.0000 0.994 1.000 0.000 0.000
#> GSM35533 1 0.0424 0.995 0.992 0.000 0.008
#> GSM35537 1 0.0424 0.991 0.992 0.000 0.008
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM35441 2 0.2623 0.852 0.000 0.908 0.028 0.064
#> GSM35446 3 0.4697 0.690 0.000 0.000 0.644 0.356
#> GSM35449 2 0.4727 0.807 0.000 0.792 0.100 0.108
#> GSM35455 2 0.3840 0.831 0.000 0.844 0.052 0.104
#> GSM35458 2 0.6575 0.481 0.000 0.508 0.412 0.080
#> GSM35460 3 0.4713 0.690 0.000 0.000 0.640 0.360
#> GSM35461 3 0.3638 0.588 0.032 0.000 0.848 0.120
#> GSM35463 2 0.1584 0.853 0.000 0.952 0.012 0.036
#> GSM35472 3 0.4134 0.680 0.000 0.000 0.740 0.260
#> GSM35475 3 0.6477 -0.361 0.000 0.420 0.508 0.072
#> GSM35483 2 0.1488 0.854 0.000 0.956 0.012 0.032
#> GSM35496 3 0.4907 0.652 0.000 0.000 0.580 0.420
#> GSM35497 2 0.4669 0.808 0.000 0.796 0.100 0.104
#> GSM35504 2 0.2402 0.855 0.000 0.912 0.012 0.076
#> GSM35508 2 0.6352 0.684 0.000 0.632 0.260 0.108
#> GSM35511 3 0.4499 0.394 0.000 0.124 0.804 0.072
#> GSM35512 3 0.4134 0.680 0.000 0.000 0.740 0.260
#> GSM35515 2 0.6575 0.481 0.000 0.508 0.412 0.080
#> GSM35519 3 0.0188 0.548 0.000 0.004 0.996 0.000
#> GSM35527 2 0.6245 0.699 0.000 0.648 0.244 0.108
#> GSM35532 3 0.0376 0.546 0.000 0.004 0.992 0.004
#> GSM35439 2 0.0000 0.860 0.000 1.000 0.000 0.000
#> GSM35443 1 0.1406 0.758 0.960 0.000 0.024 0.016
#> GSM35445 1 0.0000 0.777 1.000 0.000 0.000 0.000
#> GSM35448 3 0.5511 0.671 0.000 0.028 0.620 0.352
#> GSM35451 1 0.4564 0.601 0.672 0.000 0.000 0.328
#> GSM35454 3 0.4989 0.608 0.000 0.000 0.528 0.472
#> GSM35457 2 0.2255 0.855 0.000 0.920 0.012 0.068
#> GSM35465 2 0.3271 0.838 0.000 0.856 0.012 0.132
#> GSM35468 1 0.0592 0.773 0.984 0.000 0.000 0.016
#> GSM35471 1 0.4967 0.406 0.548 0.000 0.000 0.452
#> GSM35473 1 0.0000 0.777 1.000 0.000 0.000 0.000
#> GSM35477 1 0.4564 0.601 0.672 0.000 0.000 0.328
#> GSM35480 1 0.2345 0.745 0.900 0.000 0.000 0.100
#> GSM35482 4 0.4989 -0.770 0.000 0.000 0.472 0.528
#> GSM35485 2 0.1284 0.856 0.000 0.964 0.012 0.024
#> GSM35489 2 0.0524 0.861 0.000 0.988 0.004 0.008
#> GSM35492 1 0.0592 0.773 0.984 0.000 0.000 0.016
#> GSM35495 3 0.4948 0.646 0.000 0.000 0.560 0.440
#> GSM35499 2 0.2714 0.838 0.000 0.884 0.004 0.112
#> GSM35502 1 0.0000 0.777 1.000 0.000 0.000 0.000
#> GSM35505 3 0.4761 0.685 0.000 0.000 0.628 0.372
#> GSM35507 1 0.6380 0.335 0.500 0.064 0.000 0.436
#> GSM35510 2 0.1743 0.858 0.000 0.940 0.004 0.056
#> GSM35514 1 0.0000 0.777 1.000 0.000 0.000 0.000
#> GSM35517 2 0.0000 0.860 0.000 1.000 0.000 0.000
#> GSM35520 2 0.5220 0.471 0.000 0.568 0.424 0.008
#> GSM35523 1 0.5168 0.314 0.504 0.000 0.004 0.492
#> GSM35529 2 0.2179 0.855 0.000 0.924 0.012 0.064
#> GSM35531 2 0.1624 0.856 0.000 0.952 0.028 0.020
#> GSM35534 2 0.1488 0.854 0.000 0.956 0.012 0.032
#> GSM35536 1 0.0000 0.777 1.000 0.000 0.000 0.000
#> GSM35538 1 0.3873 0.684 0.772 0.000 0.000 0.228
#> GSM35539 1 0.4277 0.647 0.720 0.000 0.000 0.280
#> GSM35540 2 0.3217 0.840 0.000 0.860 0.012 0.128
#> GSM35541 2 0.0469 0.859 0.000 0.988 0.000 0.012
#> GSM35442 1 0.3198 0.693 0.880 0.000 0.040 0.080
#> GSM35447 3 0.4679 0.689 0.000 0.000 0.648 0.352
#> GSM35450 1 0.4040 0.671 0.752 0.000 0.000 0.248
#> GSM35453 1 0.2198 0.719 0.920 0.000 0.008 0.072
#> GSM35456 1 0.4866 0.499 0.596 0.000 0.000 0.404
#> GSM35464 2 0.5537 0.486 0.016 0.588 0.004 0.392
#> GSM35467 1 0.0000 0.777 1.000 0.000 0.000 0.000
#> GSM35470 1 0.5497 0.387 0.524 0.000 0.016 0.460
#> GSM35479 3 0.5000 0.577 0.000 0.000 0.504 0.496
#> GSM35484 1 0.0000 0.777 1.000 0.000 0.000 0.000
#> GSM35488 1 0.0592 0.773 0.984 0.000 0.000 0.016
#> GSM35491 1 0.0592 0.773 0.984 0.000 0.000 0.016
#> GSM35494 3 0.5000 0.577 0.000 0.000 0.504 0.496
#> GSM35498 1 0.4989 0.371 0.528 0.000 0.000 0.472
#> GSM35501 1 0.0000 0.777 1.000 0.000 0.000 0.000
#> GSM35509 3 0.5000 0.583 0.000 0.000 0.504 0.496
#> GSM35513 1 0.0000 0.777 1.000 0.000 0.000 0.000
#> GSM35516 2 0.1389 0.852 0.000 0.952 0.000 0.048
#> GSM35522 4 0.5163 -0.633 0.480 0.000 0.004 0.516
#> GSM35525 1 0.3356 0.718 0.824 0.000 0.000 0.176
#> GSM35528 1 0.4356 0.647 0.708 0.000 0.000 0.292
#> GSM35533 1 0.0000 0.777 1.000 0.000 0.000 0.000
#> GSM35537 1 0.5137 0.411 0.544 0.000 0.004 0.452
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM35441 2 0.4073 0.7499 0.000 0.792 0.000 0.104 0.104
#> GSM35446 3 0.3409 0.7602 0.000 0.000 0.836 0.052 0.112
#> GSM35449 2 0.5223 0.6309 0.000 0.672 0.000 0.108 0.220
#> GSM35455 2 0.4918 0.6687 0.000 0.708 0.000 0.100 0.192
#> GSM35458 5 0.3224 0.6156 0.000 0.160 0.000 0.016 0.824
#> GSM35460 3 0.3307 0.7660 0.000 0.000 0.844 0.052 0.104
#> GSM35461 5 0.5842 0.0861 0.032 0.000 0.392 0.040 0.536
#> GSM35463 2 0.3247 0.7712 0.000 0.864 0.012 0.052 0.072
#> GSM35472 3 0.4482 0.4109 0.000 0.000 0.612 0.012 0.376
#> GSM35475 5 0.2511 0.6446 0.000 0.080 0.028 0.000 0.892
#> GSM35483 2 0.3316 0.7689 0.000 0.860 0.012 0.056 0.072
#> GSM35496 3 0.2983 0.7799 0.000 0.000 0.868 0.076 0.056
#> GSM35497 2 0.5130 0.6332 0.000 0.680 0.000 0.100 0.220
#> GSM35504 2 0.3704 0.7764 0.000 0.832 0.020 0.112 0.036
#> GSM35508 5 0.5968 -0.2027 0.000 0.444 0.000 0.108 0.448
#> GSM35511 5 0.2966 0.5877 0.000 0.016 0.136 0.000 0.848
#> GSM35512 3 0.4547 0.3617 0.000 0.000 0.588 0.012 0.400
#> GSM35515 5 0.3224 0.6156 0.000 0.160 0.000 0.016 0.824
#> GSM35519 5 0.4003 0.4319 0.000 0.000 0.288 0.008 0.704
#> GSM35527 2 0.5964 0.1379 0.000 0.464 0.000 0.108 0.428
#> GSM35532 5 0.3835 0.4615 0.000 0.000 0.260 0.008 0.732
#> GSM35439 2 0.1725 0.7982 0.000 0.936 0.000 0.020 0.044
#> GSM35443 1 0.2673 0.8223 0.892 0.000 0.004 0.044 0.060
#> GSM35445 1 0.1815 0.8410 0.940 0.000 0.016 0.024 0.020
#> GSM35448 3 0.5261 0.6864 0.000 0.048 0.736 0.084 0.132
#> GSM35451 4 0.4510 0.6330 0.432 0.000 0.000 0.560 0.008
#> GSM35454 3 0.2506 0.7921 0.008 0.000 0.904 0.052 0.036
#> GSM35457 2 0.3731 0.7652 0.000 0.816 0.000 0.112 0.072
#> GSM35465 2 0.4444 0.7405 0.000 0.748 0.000 0.180 0.072
#> GSM35468 1 0.1911 0.8455 0.932 0.000 0.004 0.028 0.036
#> GSM35471 4 0.4141 0.7493 0.248 0.000 0.024 0.728 0.000
#> GSM35473 1 0.1405 0.8481 0.956 0.000 0.008 0.016 0.020
#> GSM35477 4 0.4510 0.6330 0.432 0.000 0.000 0.560 0.008
#> GSM35480 1 0.3409 0.7402 0.844 0.000 0.016 0.116 0.024
#> GSM35482 3 0.2890 0.7547 0.000 0.000 0.836 0.160 0.004
#> GSM35485 2 0.2722 0.7836 0.000 0.892 0.008 0.040 0.060
#> GSM35489 2 0.2074 0.7982 0.000 0.920 0.000 0.036 0.044
#> GSM35492 1 0.1996 0.8438 0.928 0.000 0.004 0.032 0.036
#> GSM35495 3 0.1965 0.7985 0.000 0.000 0.924 0.052 0.024
#> GSM35499 2 0.2548 0.7921 0.000 0.876 0.004 0.116 0.004
#> GSM35502 1 0.0162 0.8582 0.996 0.000 0.000 0.004 0.000
#> GSM35505 3 0.2647 0.7884 0.008 0.000 0.892 0.024 0.076
#> GSM35507 4 0.4466 0.7007 0.176 0.076 0.000 0.748 0.000
#> GSM35510 2 0.2017 0.7979 0.000 0.912 0.000 0.080 0.008
#> GSM35514 1 0.0162 0.8582 0.996 0.000 0.000 0.004 0.000
#> GSM35517 2 0.1282 0.8007 0.000 0.952 0.000 0.004 0.044
#> GSM35520 5 0.4963 0.3991 0.000 0.352 0.040 0.000 0.608
#> GSM35523 4 0.4784 0.7385 0.204 0.000 0.056 0.728 0.012
#> GSM35529 2 0.3731 0.7652 0.000 0.816 0.000 0.112 0.072
#> GSM35531 2 0.3301 0.7723 0.000 0.864 0.024 0.036 0.076
#> GSM35534 2 0.3247 0.7712 0.000 0.864 0.012 0.052 0.072
#> GSM35536 1 0.0579 0.8558 0.984 0.000 0.000 0.008 0.008
#> GSM35538 1 0.4538 -0.4555 0.540 0.000 0.000 0.452 0.008
#> GSM35539 4 0.4542 0.5983 0.456 0.000 0.000 0.536 0.008
#> GSM35540 2 0.4289 0.7475 0.000 0.760 0.000 0.176 0.064
#> GSM35541 2 0.1597 0.7981 0.000 0.940 0.000 0.012 0.048
#> GSM35442 1 0.5231 0.6513 0.740 0.000 0.132 0.064 0.064
#> GSM35447 3 0.2990 0.7815 0.008 0.000 0.868 0.024 0.100
#> GSM35450 4 0.4560 0.5434 0.484 0.000 0.000 0.508 0.008
#> GSM35453 1 0.3674 0.7246 0.832 0.000 0.116 0.032 0.020
#> GSM35456 4 0.4127 0.7279 0.312 0.008 0.000 0.680 0.000
#> GSM35464 4 0.3944 0.3412 0.004 0.272 0.000 0.720 0.004
#> GSM35467 1 0.0162 0.8582 0.996 0.000 0.000 0.004 0.000
#> GSM35470 4 0.6003 0.6623 0.176 0.000 0.164 0.640 0.020
#> GSM35479 3 0.2753 0.7676 0.000 0.000 0.856 0.136 0.008
#> GSM35484 1 0.1772 0.8466 0.940 0.000 0.008 0.032 0.020
#> GSM35488 1 0.1750 0.8454 0.936 0.000 0.000 0.036 0.028
#> GSM35491 1 0.1996 0.8438 0.928 0.000 0.004 0.032 0.036
#> GSM35494 3 0.2488 0.7737 0.000 0.000 0.872 0.124 0.004
#> GSM35498 4 0.4192 0.7505 0.232 0.000 0.032 0.736 0.000
#> GSM35501 1 0.0162 0.8582 0.996 0.000 0.000 0.004 0.000
#> GSM35509 3 0.2179 0.7845 0.000 0.000 0.888 0.112 0.000
#> GSM35513 1 0.0162 0.8582 0.996 0.000 0.000 0.004 0.000
#> GSM35516 2 0.2514 0.7895 0.000 0.896 0.000 0.060 0.044
#> GSM35522 4 0.4524 0.7203 0.164 0.004 0.052 0.768 0.012
#> GSM35525 1 0.4109 0.2533 0.700 0.000 0.000 0.288 0.012
#> GSM35528 4 0.4886 0.5861 0.448 0.000 0.000 0.528 0.024
#> GSM35533 1 0.1934 0.8435 0.932 0.000 0.008 0.040 0.020
#> GSM35537 4 0.5693 0.7001 0.196 0.000 0.124 0.664 0.016
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM35441 2 0.4984 -0.283 0.000 0.512 0.000 0.020 0.032 0.436
#> GSM35446 3 0.3865 0.698 0.000 0.004 0.800 0.016 0.116 0.064
#> GSM35449 6 0.5695 0.719 0.000 0.356 0.000 0.016 0.112 0.516
#> GSM35455 6 0.5300 0.597 0.000 0.404 0.000 0.016 0.064 0.516
#> GSM35458 5 0.4621 0.564 0.000 0.088 0.000 0.016 0.716 0.180
#> GSM35460 3 0.3865 0.698 0.000 0.004 0.800 0.016 0.116 0.064
#> GSM35461 5 0.5059 0.571 0.016 0.000 0.188 0.032 0.704 0.060
#> GSM35463 2 0.2562 0.632 0.000 0.892 0.008 0.024 0.012 0.064
#> GSM35472 5 0.4303 0.290 0.000 0.000 0.392 0.012 0.588 0.008
#> GSM35475 5 0.2592 0.700 0.000 0.020 0.012 0.004 0.884 0.080
#> GSM35483 2 0.2562 0.632 0.000 0.892 0.008 0.024 0.012 0.064
#> GSM35496 3 0.5140 0.688 0.000 0.000 0.708 0.112 0.104 0.076
#> GSM35497 6 0.5695 0.719 0.000 0.356 0.000 0.016 0.112 0.516
#> GSM35504 2 0.5485 0.419 0.000 0.620 0.052 0.032 0.016 0.280
#> GSM35508 6 0.5514 0.679 0.000 0.176 0.000 0.000 0.272 0.552
#> GSM35511 5 0.2364 0.712 0.000 0.004 0.032 0.000 0.892 0.072
#> GSM35512 5 0.4077 0.458 0.000 0.000 0.320 0.012 0.660 0.008
#> GSM35515 5 0.4621 0.564 0.000 0.088 0.000 0.016 0.716 0.180
#> GSM35519 5 0.2191 0.698 0.000 0.000 0.120 0.000 0.876 0.004
#> GSM35527 6 0.5515 0.691 0.000 0.184 0.000 0.000 0.260 0.556
#> GSM35532 5 0.2070 0.712 0.000 0.000 0.092 0.000 0.896 0.012
#> GSM35439 2 0.0363 0.666 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM35443 1 0.3469 0.820 0.828 0.000 0.000 0.032 0.036 0.104
#> GSM35445 1 0.3075 0.813 0.856 0.000 0.016 0.032 0.004 0.092
#> GSM35448 3 0.5539 0.613 0.000 0.028 0.692 0.040 0.116 0.124
#> GSM35451 4 0.4665 0.748 0.260 0.012 0.000 0.676 0.004 0.048
#> GSM35454 3 0.4163 0.732 0.012 0.000 0.800 0.060 0.044 0.084
#> GSM35457 2 0.4305 -0.114 0.000 0.544 0.000 0.020 0.000 0.436
#> GSM35465 2 0.5218 -0.217 0.000 0.480 0.000 0.092 0.000 0.428
#> GSM35468 1 0.3104 0.824 0.852 0.000 0.000 0.028 0.028 0.092
#> GSM35471 4 0.3248 0.791 0.136 0.016 0.016 0.828 0.000 0.004
#> GSM35473 1 0.2858 0.819 0.868 0.000 0.012 0.028 0.004 0.088
#> GSM35477 4 0.4665 0.748 0.260 0.012 0.000 0.676 0.004 0.048
#> GSM35480 1 0.3862 0.780 0.800 0.000 0.012 0.100 0.004 0.084
#> GSM35482 3 0.5069 0.673 0.000 0.000 0.680 0.200 0.032 0.088
#> GSM35485 2 0.1232 0.657 0.000 0.956 0.004 0.016 0.000 0.024
#> GSM35489 2 0.0891 0.664 0.000 0.968 0.000 0.008 0.000 0.024
#> GSM35492 1 0.3249 0.825 0.840 0.000 0.000 0.028 0.028 0.104
#> GSM35495 3 0.2477 0.746 0.000 0.000 0.896 0.024 0.032 0.048
#> GSM35499 2 0.3247 0.553 0.000 0.808 0.000 0.036 0.000 0.156
#> GSM35502 1 0.0603 0.852 0.980 0.000 0.000 0.016 0.000 0.004
#> GSM35505 3 0.4969 0.700 0.012 0.000 0.736 0.052 0.116 0.084
#> GSM35507 4 0.3528 0.766 0.076 0.048 0.000 0.832 0.000 0.044
#> GSM35510 2 0.3541 0.453 0.000 0.748 0.000 0.020 0.000 0.232
#> GSM35514 1 0.0603 0.852 0.980 0.000 0.000 0.016 0.000 0.004
#> GSM35517 2 0.0547 0.666 0.000 0.980 0.000 0.000 0.000 0.020
#> GSM35520 5 0.4078 0.474 0.000 0.320 0.024 0.000 0.656 0.000
#> GSM35523 4 0.3832 0.769 0.096 0.004 0.016 0.816 0.008 0.060
#> GSM35529 2 0.4300 -0.114 0.000 0.548 0.000 0.020 0.000 0.432
#> GSM35531 2 0.1363 0.649 0.000 0.952 0.012 0.004 0.028 0.004
#> GSM35534 2 0.2116 0.636 0.000 0.912 0.004 0.024 0.004 0.056
#> GSM35536 1 0.1924 0.837 0.920 0.000 0.000 0.028 0.004 0.048
#> GSM35538 4 0.4845 0.591 0.384 0.000 0.000 0.560 0.004 0.052
#> GSM35539 4 0.4449 0.742 0.272 0.000 0.000 0.672 0.004 0.052
#> GSM35540 2 0.5218 -0.207 0.000 0.480 0.000 0.092 0.000 0.428
#> GSM35541 2 0.0458 0.666 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM35442 1 0.6715 0.627 0.596 0.000 0.096 0.092 0.052 0.164
#> GSM35447 3 0.5165 0.688 0.012 0.000 0.716 0.052 0.136 0.084
#> GSM35450 4 0.4602 0.687 0.320 0.000 0.000 0.628 0.004 0.048
#> GSM35453 1 0.4343 0.748 0.780 0.000 0.064 0.056 0.004 0.096
#> GSM35456 4 0.3722 0.780 0.192 0.024 0.008 0.772 0.000 0.004
#> GSM35464 4 0.4265 0.610 0.012 0.112 0.000 0.756 0.000 0.120
#> GSM35467 1 0.0603 0.852 0.980 0.000 0.000 0.016 0.000 0.004
#> GSM35470 4 0.6507 0.489 0.076 0.000 0.172 0.576 0.012 0.164
#> GSM35479 3 0.4031 0.722 0.000 0.000 0.772 0.124 0.008 0.096
#> GSM35484 1 0.2492 0.837 0.888 0.000 0.008 0.020 0.004 0.080
#> GSM35488 1 0.3179 0.820 0.848 0.000 0.000 0.032 0.028 0.092
#> GSM35491 1 0.3249 0.825 0.840 0.000 0.000 0.028 0.028 0.104
#> GSM35494 3 0.3716 0.734 0.000 0.000 0.792 0.128 0.004 0.076
#> GSM35498 4 0.3288 0.786 0.104 0.016 0.016 0.844 0.000 0.020
#> GSM35501 1 0.0603 0.852 0.980 0.000 0.000 0.016 0.000 0.004
#> GSM35509 3 0.2451 0.757 0.000 0.000 0.884 0.060 0.000 0.056
#> GSM35513 1 0.0603 0.852 0.980 0.000 0.000 0.016 0.000 0.004
#> GSM35516 2 0.0777 0.661 0.000 0.972 0.000 0.024 0.000 0.004
#> GSM35522 4 0.3907 0.758 0.080 0.004 0.016 0.812 0.008 0.080
#> GSM35525 1 0.4476 0.449 0.680 0.000 0.000 0.256 0.004 0.060
#> GSM35528 4 0.4972 0.730 0.256 0.000 0.000 0.656 0.024 0.064
#> GSM35533 1 0.2492 0.837 0.888 0.000 0.008 0.020 0.004 0.080
#> GSM35537 4 0.5549 0.611 0.076 0.000 0.128 0.688 0.012 0.096
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 time(p) k
#> SD:kmeans 79 3.41e-07 2
#> SD:kmeans 79 1.69e-05 3
#> SD:kmeans 64 1.86e-04 4
#> SD:kmeans 68 4.99e-05 5
#> SD:kmeans 67 1.42e-07 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "skmeans"]
# you can also extract it by
# res = res_list["SD:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 7758 rows and 79 columns.
#> Top rows (776, 1552, 2328, 3103, 3879) are extracted by 'SD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.987 0.995 0.5037 0.498 0.498
#> 3 3 0.983 0.955 0.982 0.3109 0.784 0.590
#> 4 4 0.902 0.894 0.940 0.1258 0.895 0.699
#> 5 5 0.774 0.784 0.877 0.0668 0.947 0.795
#> 6 6 0.728 0.686 0.792 0.0410 0.993 0.968
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
#> GSM35441 2 0.0000 1.000 0.000 1.000
#> GSM35446 2 0.0000 1.000 0.000 1.000
#> GSM35449 2 0.0000 1.000 0.000 1.000
#> GSM35455 2 0.0000 1.000 0.000 1.000
#> GSM35458 2 0.0000 1.000 0.000 1.000
#> GSM35460 2 0.0000 1.000 0.000 1.000
#> GSM35461 1 0.0000 0.990 1.000 0.000
#> GSM35463 2 0.0000 1.000 0.000 1.000
#> GSM35472 2 0.0376 0.996 0.004 0.996
#> GSM35475 2 0.0000 1.000 0.000 1.000
#> GSM35483 2 0.0000 1.000 0.000 1.000
#> GSM35496 1 0.0000 0.990 1.000 0.000
#> GSM35497 2 0.0000 1.000 0.000 1.000
#> GSM35504 2 0.0000 1.000 0.000 1.000
#> GSM35508 2 0.0000 1.000 0.000 1.000
#> GSM35511 2 0.0000 1.000 0.000 1.000
#> GSM35512 2 0.0000 1.000 0.000 1.000
#> GSM35515 2 0.0000 1.000 0.000 1.000
#> GSM35519 2 0.0000 1.000 0.000 1.000
#> GSM35527 2 0.0000 1.000 0.000 1.000
#> GSM35532 2 0.0000 1.000 0.000 1.000
#> GSM35439 2 0.0000 1.000 0.000 1.000
#> GSM35443 1 0.0000 0.990 1.000 0.000
#> GSM35445 1 0.0000 0.990 1.000 0.000
#> GSM35448 2 0.0000 1.000 0.000 1.000
#> GSM35451 1 0.0000 0.990 1.000 0.000
#> GSM35454 1 0.0000 0.990 1.000 0.000
#> GSM35457 2 0.0000 1.000 0.000 1.000
#> GSM35465 2 0.0000 1.000 0.000 1.000
#> GSM35468 1 0.0000 0.990 1.000 0.000
#> GSM35471 1 0.0000 0.990 1.000 0.000
#> GSM35473 1 0.0000 0.990 1.000 0.000
#> GSM35477 1 0.0000 0.990 1.000 0.000
#> GSM35480 1 0.0000 0.990 1.000 0.000
#> GSM35482 1 0.0000 0.990 1.000 0.000
#> GSM35485 2 0.0000 1.000 0.000 1.000
#> GSM35489 2 0.0000 1.000 0.000 1.000
#> GSM35492 1 0.0000 0.990 1.000 0.000
#> GSM35495 1 0.9491 0.422 0.632 0.368
#> GSM35499 2 0.0000 1.000 0.000 1.000
#> GSM35502 1 0.0000 0.990 1.000 0.000
#> GSM35505 1 0.0000 0.990 1.000 0.000
#> GSM35507 1 0.0000 0.990 1.000 0.000
#> GSM35510 2 0.0000 1.000 0.000 1.000
#> GSM35514 1 0.0000 0.990 1.000 0.000
#> GSM35517 2 0.0000 1.000 0.000 1.000
#> GSM35520 2 0.0000 1.000 0.000 1.000
#> GSM35523 1 0.0000 0.990 1.000 0.000
#> GSM35529 2 0.0000 1.000 0.000 1.000
#> GSM35531 2 0.0000 1.000 0.000 1.000
#> GSM35534 2 0.0000 1.000 0.000 1.000
#> GSM35536 1 0.0000 0.990 1.000 0.000
#> GSM35538 1 0.0000 0.990 1.000 0.000
#> GSM35539 1 0.0000 0.990 1.000 0.000
#> GSM35540 2 0.0000 1.000 0.000 1.000
#> GSM35541 2 0.0000 1.000 0.000 1.000
#> GSM35442 1 0.0000 0.990 1.000 0.000
#> GSM35447 1 0.2603 0.947 0.956 0.044
#> GSM35450 1 0.0000 0.990 1.000 0.000
#> GSM35453 1 0.0000 0.990 1.000 0.000
#> GSM35456 1 0.0000 0.990 1.000 0.000
#> GSM35464 2 0.0000 1.000 0.000 1.000
#> GSM35467 1 0.0000 0.990 1.000 0.000
#> GSM35470 1 0.0000 0.990 1.000 0.000
#> GSM35479 1 0.0000 0.990 1.000 0.000
#> GSM35484 1 0.0000 0.990 1.000 0.000
#> GSM35488 1 0.0000 0.990 1.000 0.000
#> GSM35491 1 0.0000 0.990 1.000 0.000
#> GSM35494 1 0.0000 0.990 1.000 0.000
#> GSM35498 1 0.0000 0.990 1.000 0.000
#> GSM35501 1 0.0000 0.990 1.000 0.000
#> GSM35509 1 0.0938 0.979 0.988 0.012
#> GSM35513 1 0.0000 0.990 1.000 0.000
#> GSM35516 2 0.0000 1.000 0.000 1.000
#> GSM35522 1 0.0000 0.990 1.000 0.000
#> GSM35525 1 0.0000 0.990 1.000 0.000
#> GSM35528 1 0.0000 0.990 1.000 0.000
#> GSM35533 1 0.0000 0.990 1.000 0.000
#> GSM35537 1 0.0000 0.990 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM35441 2 0.0000 0.988 0.000 1.000 0.000
#> GSM35446 3 0.0000 0.960 0.000 0.000 1.000
#> GSM35449 2 0.0000 0.988 0.000 1.000 0.000
#> GSM35455 2 0.0000 0.988 0.000 1.000 0.000
#> GSM35458 2 0.0000 0.988 0.000 1.000 0.000
#> GSM35460 3 0.0000 0.960 0.000 0.000 1.000
#> GSM35461 3 0.0000 0.960 0.000 0.000 1.000
#> GSM35463 2 0.0000 0.988 0.000 1.000 0.000
#> GSM35472 3 0.0000 0.960 0.000 0.000 1.000
#> GSM35475 2 0.5529 0.571 0.000 0.704 0.296
#> GSM35483 2 0.0000 0.988 0.000 1.000 0.000
#> GSM35496 3 0.0000 0.960 0.000 0.000 1.000
#> GSM35497 2 0.0000 0.988 0.000 1.000 0.000
#> GSM35504 2 0.0000 0.988 0.000 1.000 0.000
#> GSM35508 2 0.0000 0.988 0.000 1.000 0.000
#> GSM35511 3 0.4750 0.697 0.000 0.216 0.784
#> GSM35512 3 0.0000 0.960 0.000 0.000 1.000
#> GSM35515 2 0.0000 0.988 0.000 1.000 0.000
#> GSM35519 3 0.0000 0.960 0.000 0.000 1.000
#> GSM35527 2 0.0000 0.988 0.000 1.000 0.000
#> GSM35532 3 0.0000 0.960 0.000 0.000 1.000
#> GSM35439 2 0.0000 0.988 0.000 1.000 0.000
#> GSM35443 1 0.0000 0.985 1.000 0.000 0.000
#> GSM35445 1 0.0000 0.985 1.000 0.000 0.000
#> GSM35448 3 0.0000 0.960 0.000 0.000 1.000
#> GSM35451 1 0.0000 0.985 1.000 0.000 0.000
#> GSM35454 3 0.0000 0.960 0.000 0.000 1.000
#> GSM35457 2 0.0000 0.988 0.000 1.000 0.000
#> GSM35465 2 0.0000 0.988 0.000 1.000 0.000
#> GSM35468 1 0.0000 0.985 1.000 0.000 0.000
#> GSM35471 1 0.0000 0.985 1.000 0.000 0.000
#> GSM35473 1 0.0000 0.985 1.000 0.000 0.000
#> GSM35477 1 0.0000 0.985 1.000 0.000 0.000
#> GSM35480 1 0.0000 0.985 1.000 0.000 0.000
#> GSM35482 3 0.0000 0.960 0.000 0.000 1.000
#> GSM35485 2 0.0000 0.988 0.000 1.000 0.000
#> GSM35489 2 0.0000 0.988 0.000 1.000 0.000
#> GSM35492 1 0.0000 0.985 1.000 0.000 0.000
#> GSM35495 3 0.0000 0.960 0.000 0.000 1.000
#> GSM35499 2 0.0000 0.988 0.000 1.000 0.000
#> GSM35502 1 0.0000 0.985 1.000 0.000 0.000
#> GSM35505 3 0.0000 0.960 0.000 0.000 1.000
#> GSM35507 1 0.4842 0.711 0.776 0.224 0.000
#> GSM35510 2 0.0000 0.988 0.000 1.000 0.000
#> GSM35514 1 0.0000 0.985 1.000 0.000 0.000
#> GSM35517 2 0.0000 0.988 0.000 1.000 0.000
#> GSM35520 2 0.0747 0.973 0.000 0.984 0.016
#> GSM35523 1 0.0000 0.985 1.000 0.000 0.000
#> GSM35529 2 0.0000 0.988 0.000 1.000 0.000
#> GSM35531 2 0.0000 0.988 0.000 1.000 0.000
#> GSM35534 2 0.0000 0.988 0.000 1.000 0.000
#> GSM35536 1 0.0000 0.985 1.000 0.000 0.000
#> GSM35538 1 0.0000 0.985 1.000 0.000 0.000
#> GSM35539 1 0.0000 0.985 1.000 0.000 0.000
#> GSM35540 2 0.0000 0.988 0.000 1.000 0.000
#> GSM35541 2 0.0000 0.988 0.000 1.000 0.000
#> GSM35442 3 0.6280 0.126 0.460 0.000 0.540
#> GSM35447 3 0.0000 0.960 0.000 0.000 1.000
#> GSM35450 1 0.0000 0.985 1.000 0.000 0.000
#> GSM35453 1 0.2537 0.907 0.920 0.000 0.080
#> GSM35456 1 0.0000 0.985 1.000 0.000 0.000
#> GSM35464 2 0.0000 0.988 0.000 1.000 0.000
#> GSM35467 1 0.0000 0.985 1.000 0.000 0.000
#> GSM35470 1 0.3192 0.869 0.888 0.000 0.112
#> GSM35479 3 0.0000 0.960 0.000 0.000 1.000
#> GSM35484 1 0.0000 0.985 1.000 0.000 0.000
#> GSM35488 1 0.0000 0.985 1.000 0.000 0.000
#> GSM35491 1 0.0000 0.985 1.000 0.000 0.000
#> GSM35494 3 0.0000 0.960 0.000 0.000 1.000
#> GSM35498 1 0.0000 0.985 1.000 0.000 0.000
#> GSM35501 1 0.0000 0.985 1.000 0.000 0.000
#> GSM35509 3 0.0000 0.960 0.000 0.000 1.000
#> GSM35513 1 0.0000 0.985 1.000 0.000 0.000
#> GSM35516 2 0.0000 0.988 0.000 1.000 0.000
#> GSM35522 1 0.0000 0.985 1.000 0.000 0.000
#> GSM35525 1 0.0000 0.985 1.000 0.000 0.000
#> GSM35528 1 0.0000 0.985 1.000 0.000 0.000
#> GSM35533 1 0.0000 0.985 1.000 0.000 0.000
#> GSM35537 1 0.0000 0.985 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM35441 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM35446 3 0.0000 0.956 0.000 0.000 1.000 0.000
#> GSM35449 2 0.0188 0.965 0.000 0.996 0.000 0.004
#> GSM35455 2 0.0188 0.965 0.000 0.996 0.000 0.004
#> GSM35458 2 0.2408 0.920 0.000 0.920 0.044 0.036
#> GSM35460 3 0.0188 0.956 0.000 0.000 0.996 0.004
#> GSM35461 3 0.1584 0.944 0.012 0.000 0.952 0.036
#> GSM35463 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM35472 3 0.0707 0.951 0.000 0.000 0.980 0.020
#> GSM35475 2 0.5200 0.621 0.000 0.700 0.264 0.036
#> GSM35483 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM35496 3 0.0921 0.952 0.000 0.000 0.972 0.028
#> GSM35497 2 0.0188 0.965 0.000 0.996 0.000 0.004
#> GSM35504 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM35508 2 0.0804 0.959 0.000 0.980 0.008 0.012
#> GSM35511 3 0.4707 0.701 0.000 0.204 0.760 0.036
#> GSM35512 3 0.0817 0.950 0.000 0.000 0.976 0.024
#> GSM35515 2 0.2494 0.917 0.000 0.916 0.048 0.036
#> GSM35519 3 0.1305 0.943 0.000 0.004 0.960 0.036
#> GSM35527 2 0.0336 0.964 0.000 0.992 0.000 0.008
#> GSM35532 3 0.1118 0.945 0.000 0.000 0.964 0.036
#> GSM35439 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM35443 1 0.0707 0.927 0.980 0.000 0.000 0.020
#> GSM35445 1 0.0000 0.941 1.000 0.000 0.000 0.000
#> GSM35448 3 0.0188 0.956 0.000 0.000 0.996 0.004
#> GSM35451 4 0.3873 0.802 0.228 0.000 0.000 0.772
#> GSM35454 3 0.1211 0.948 0.000 0.000 0.960 0.040
#> GSM35457 2 0.0336 0.964 0.000 0.992 0.000 0.008
#> GSM35465 2 0.2011 0.915 0.000 0.920 0.000 0.080
#> GSM35468 1 0.0188 0.940 0.996 0.000 0.000 0.004
#> GSM35471 4 0.1302 0.860 0.044 0.000 0.000 0.956
#> GSM35473 1 0.0000 0.941 1.000 0.000 0.000 0.000
#> GSM35477 4 0.3764 0.811 0.216 0.000 0.000 0.784
#> GSM35480 1 0.2345 0.852 0.900 0.000 0.000 0.100
#> GSM35482 3 0.2216 0.915 0.000 0.000 0.908 0.092
#> GSM35485 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM35489 2 0.0336 0.964 0.000 0.992 0.000 0.008
#> GSM35492 1 0.0188 0.940 0.996 0.000 0.000 0.004
#> GSM35495 3 0.0817 0.953 0.000 0.000 0.976 0.024
#> GSM35499 2 0.1389 0.941 0.000 0.952 0.000 0.048
#> GSM35502 1 0.0000 0.941 1.000 0.000 0.000 0.000
#> GSM35505 3 0.0000 0.956 0.000 0.000 1.000 0.000
#> GSM35507 4 0.2111 0.843 0.024 0.044 0.000 0.932
#> GSM35510 2 0.0469 0.962 0.000 0.988 0.000 0.012
#> GSM35514 1 0.0000 0.941 1.000 0.000 0.000 0.000
#> GSM35517 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM35520 2 0.3082 0.887 0.000 0.884 0.084 0.032
#> GSM35523 4 0.1118 0.858 0.036 0.000 0.000 0.964
#> GSM35529 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM35531 2 0.1256 0.949 0.000 0.964 0.028 0.008
#> GSM35534 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM35536 1 0.0000 0.941 1.000 0.000 0.000 0.000
#> GSM35538 1 0.4989 -0.216 0.528 0.000 0.000 0.472
#> GSM35539 4 0.4040 0.783 0.248 0.000 0.000 0.752
#> GSM35540 2 0.1792 0.926 0.000 0.932 0.000 0.068
#> GSM35541 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM35442 1 0.2739 0.855 0.904 0.000 0.060 0.036
#> GSM35447 3 0.0000 0.956 0.000 0.000 1.000 0.000
#> GSM35450 4 0.4661 0.639 0.348 0.000 0.000 0.652
#> GSM35453 1 0.1398 0.902 0.956 0.000 0.040 0.004
#> GSM35456 4 0.2021 0.860 0.056 0.012 0.000 0.932
#> GSM35464 4 0.2345 0.802 0.000 0.100 0.000 0.900
#> GSM35467 1 0.0000 0.941 1.000 0.000 0.000 0.000
#> GSM35470 4 0.5639 0.564 0.324 0.000 0.040 0.636
#> GSM35479 3 0.1557 0.941 0.000 0.000 0.944 0.056
#> GSM35484 1 0.0000 0.941 1.000 0.000 0.000 0.000
#> GSM35488 1 0.0188 0.940 0.996 0.000 0.000 0.004
#> GSM35491 1 0.0188 0.940 0.996 0.000 0.000 0.004
#> GSM35494 3 0.1557 0.941 0.000 0.000 0.944 0.056
#> GSM35498 4 0.1211 0.860 0.040 0.000 0.000 0.960
#> GSM35501 1 0.0000 0.941 1.000 0.000 0.000 0.000
#> GSM35509 3 0.1557 0.941 0.000 0.000 0.944 0.056
#> GSM35513 1 0.0000 0.941 1.000 0.000 0.000 0.000
#> GSM35516 2 0.0817 0.956 0.000 0.976 0.000 0.024
#> GSM35522 4 0.1209 0.857 0.032 0.004 0.000 0.964
#> GSM35525 1 0.3219 0.748 0.836 0.000 0.000 0.164
#> GSM35528 4 0.3873 0.801 0.228 0.000 0.000 0.772
#> GSM35533 1 0.0000 0.941 1.000 0.000 0.000 0.000
#> GSM35537 4 0.2466 0.849 0.096 0.000 0.004 0.900
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM35441 2 0.2561 0.8286 0.000 0.856 0.000 0.000 0.144
#> GSM35446 3 0.1851 0.8527 0.000 0.000 0.912 0.000 0.088
#> GSM35449 2 0.3857 0.6635 0.000 0.688 0.000 0.000 0.312
#> GSM35455 2 0.3305 0.7673 0.000 0.776 0.000 0.000 0.224
#> GSM35458 5 0.1732 0.7825 0.000 0.080 0.000 0.000 0.920
#> GSM35460 3 0.1197 0.8737 0.000 0.000 0.952 0.000 0.048
#> GSM35461 5 0.4757 0.3540 0.024 0.000 0.380 0.000 0.596
#> GSM35463 2 0.1202 0.8583 0.000 0.960 0.004 0.004 0.032
#> GSM35472 3 0.4166 0.4325 0.004 0.000 0.648 0.000 0.348
#> GSM35475 5 0.2304 0.7963 0.000 0.048 0.044 0.000 0.908
#> GSM35483 2 0.1644 0.8552 0.000 0.940 0.008 0.004 0.048
#> GSM35496 3 0.1605 0.8703 0.004 0.000 0.944 0.012 0.040
#> GSM35497 2 0.3857 0.6680 0.000 0.688 0.000 0.000 0.312
#> GSM35504 2 0.2032 0.8598 0.000 0.924 0.020 0.004 0.052
#> GSM35508 2 0.4307 0.2635 0.000 0.504 0.000 0.000 0.496
#> GSM35511 5 0.2818 0.7774 0.000 0.012 0.132 0.000 0.856
#> GSM35512 3 0.4359 0.2596 0.004 0.000 0.584 0.000 0.412
#> GSM35515 5 0.1732 0.7825 0.000 0.080 0.000 0.000 0.920
#> GSM35519 5 0.3143 0.7336 0.000 0.000 0.204 0.000 0.796
#> GSM35527 2 0.4161 0.5283 0.000 0.608 0.000 0.000 0.392
#> GSM35532 5 0.3210 0.7253 0.000 0.000 0.212 0.000 0.788
#> GSM35439 2 0.1124 0.8584 0.000 0.960 0.004 0.000 0.036
#> GSM35443 1 0.1544 0.8883 0.932 0.000 0.000 0.000 0.068
#> GSM35445 1 0.1117 0.9089 0.964 0.000 0.020 0.000 0.016
#> GSM35448 3 0.2569 0.8402 0.000 0.032 0.896 0.004 0.068
#> GSM35451 4 0.3769 0.7814 0.180 0.000 0.000 0.788 0.032
#> GSM35454 3 0.0898 0.8743 0.000 0.000 0.972 0.008 0.020
#> GSM35457 2 0.1892 0.8525 0.000 0.916 0.000 0.004 0.080
#> GSM35465 2 0.3410 0.8248 0.000 0.840 0.000 0.068 0.092
#> GSM35468 1 0.0955 0.9143 0.968 0.000 0.000 0.004 0.028
#> GSM35471 4 0.0162 0.8123 0.004 0.000 0.000 0.996 0.000
#> GSM35473 1 0.0566 0.9175 0.984 0.000 0.000 0.004 0.012
#> GSM35477 4 0.3694 0.7861 0.172 0.000 0.000 0.796 0.032
#> GSM35480 1 0.3122 0.8299 0.860 0.000 0.016 0.108 0.016
#> GSM35482 3 0.1731 0.8558 0.004 0.000 0.932 0.060 0.004
#> GSM35485 2 0.1205 0.8580 0.000 0.956 0.004 0.000 0.040
#> GSM35489 2 0.0880 0.8620 0.000 0.968 0.000 0.000 0.032
#> GSM35492 1 0.0794 0.9132 0.972 0.000 0.000 0.000 0.028
#> GSM35495 3 0.0404 0.8785 0.000 0.000 0.988 0.000 0.012
#> GSM35499 2 0.1403 0.8564 0.000 0.952 0.000 0.024 0.024
#> GSM35502 1 0.0162 0.9193 0.996 0.000 0.000 0.004 0.000
#> GSM35505 3 0.1270 0.8763 0.000 0.000 0.948 0.000 0.052
#> GSM35507 4 0.1597 0.8071 0.008 0.020 0.000 0.948 0.024
#> GSM35510 2 0.1282 0.8598 0.000 0.952 0.000 0.004 0.044
#> GSM35514 1 0.0162 0.9193 0.996 0.000 0.000 0.004 0.000
#> GSM35517 2 0.0880 0.8623 0.000 0.968 0.000 0.000 0.032
#> GSM35520 5 0.4192 0.6699 0.000 0.232 0.032 0.000 0.736
#> GSM35523 4 0.0324 0.8120 0.004 0.000 0.000 0.992 0.004
#> GSM35529 2 0.1908 0.8495 0.000 0.908 0.000 0.000 0.092
#> GSM35531 2 0.3080 0.7818 0.000 0.852 0.020 0.004 0.124
#> GSM35534 2 0.1492 0.8560 0.000 0.948 0.008 0.004 0.040
#> GSM35536 1 0.0451 0.9178 0.988 0.000 0.000 0.004 0.008
#> GSM35538 1 0.4736 0.0834 0.576 0.000 0.000 0.404 0.020
#> GSM35539 4 0.3863 0.7122 0.248 0.000 0.000 0.740 0.012
#> GSM35540 2 0.3165 0.8338 0.000 0.848 0.000 0.036 0.116
#> GSM35541 2 0.1124 0.8584 0.000 0.960 0.004 0.000 0.036
#> GSM35442 1 0.3919 0.7868 0.816 0.000 0.100 0.008 0.076
#> GSM35447 3 0.1908 0.8605 0.000 0.000 0.908 0.000 0.092
#> GSM35450 4 0.4697 0.4718 0.388 0.000 0.000 0.592 0.020
#> GSM35453 1 0.2519 0.8425 0.884 0.000 0.100 0.000 0.016
#> GSM35456 4 0.1668 0.8161 0.032 0.000 0.000 0.940 0.028
#> GSM35464 4 0.2824 0.7425 0.000 0.096 0.000 0.872 0.032
#> GSM35467 1 0.0162 0.9193 0.996 0.000 0.000 0.004 0.000
#> GSM35470 4 0.7028 0.3235 0.256 0.000 0.280 0.448 0.016
#> GSM35479 3 0.1205 0.8681 0.000 0.000 0.956 0.040 0.004
#> GSM35484 1 0.0566 0.9184 0.984 0.000 0.000 0.004 0.012
#> GSM35488 1 0.0898 0.9166 0.972 0.000 0.000 0.008 0.020
#> GSM35491 1 0.0794 0.9132 0.972 0.000 0.000 0.000 0.028
#> GSM35494 3 0.1331 0.8670 0.000 0.000 0.952 0.040 0.008
#> GSM35498 4 0.0451 0.8114 0.004 0.000 0.000 0.988 0.008
#> GSM35501 1 0.0162 0.9193 0.996 0.000 0.000 0.004 0.000
#> GSM35509 3 0.0510 0.8769 0.000 0.000 0.984 0.016 0.000
#> GSM35513 1 0.0162 0.9193 0.996 0.000 0.000 0.004 0.000
#> GSM35516 2 0.1914 0.8445 0.000 0.924 0.000 0.016 0.060
#> GSM35522 4 0.0324 0.8120 0.004 0.000 0.000 0.992 0.004
#> GSM35525 1 0.3579 0.6329 0.756 0.000 0.000 0.240 0.004
#> GSM35528 4 0.3757 0.7549 0.208 0.000 0.000 0.772 0.020
#> GSM35533 1 0.0771 0.9165 0.976 0.000 0.000 0.004 0.020
#> GSM35537 4 0.3512 0.7650 0.088 0.000 0.068 0.840 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM35441 2 0.1584 0.7111 0.000 0.928 0.000 0.000 0.064 NA
#> GSM35446 3 0.2263 0.8058 0.000 0.000 0.884 0.000 0.100 NA
#> GSM35449 2 0.3658 0.5887 0.000 0.752 0.000 0.000 0.216 NA
#> GSM35455 2 0.2909 0.6630 0.000 0.836 0.000 0.000 0.136 NA
#> GSM35458 5 0.2000 0.7906 0.004 0.032 0.000 0.000 0.916 NA
#> GSM35460 3 0.1265 0.8374 0.000 0.000 0.948 0.000 0.044 NA
#> GSM35461 5 0.5339 0.5717 0.028 0.000 0.180 0.000 0.656 NA
#> GSM35463 2 0.3756 0.6881 0.000 0.600 0.000 0.000 0.000 NA
#> GSM35472 3 0.4591 0.2049 0.000 0.000 0.552 0.000 0.408 NA
#> GSM35475 5 0.1218 0.7992 0.000 0.028 0.004 0.000 0.956 NA
#> GSM35483 2 0.4319 0.6784 0.000 0.576 0.000 0.000 0.024 NA
#> GSM35496 3 0.3324 0.7971 0.000 0.000 0.824 0.004 0.060 NA
#> GSM35497 2 0.3558 0.5945 0.000 0.760 0.000 0.000 0.212 NA
#> GSM35504 2 0.3736 0.7255 0.000 0.788 0.020 0.000 0.032 NA
#> GSM35508 2 0.4241 0.3665 0.000 0.608 0.000 0.000 0.368 NA
#> GSM35511 5 0.0972 0.8013 0.000 0.008 0.028 0.000 0.964 NA
#> GSM35512 5 0.4517 0.0707 0.000 0.000 0.444 0.000 0.524 NA
#> GSM35515 5 0.2000 0.7906 0.004 0.032 0.000 0.000 0.916 NA
#> GSM35519 5 0.2263 0.7762 0.000 0.000 0.100 0.000 0.884 NA
#> GSM35527 2 0.4065 0.4787 0.000 0.672 0.000 0.000 0.300 NA
#> GSM35532 5 0.1918 0.7862 0.000 0.000 0.088 0.000 0.904 NA
#> GSM35439 2 0.3819 0.7119 0.000 0.652 0.000 0.000 0.008 NA
#> GSM35443 1 0.3695 0.7556 0.776 0.000 0.000 0.000 0.060 NA
#> GSM35445 1 0.2862 0.7935 0.864 0.000 0.048 0.000 0.008 NA
#> GSM35448 3 0.3972 0.7299 0.000 0.016 0.784 0.000 0.076 NA
#> GSM35451 4 0.4584 0.6711 0.196 0.000 0.000 0.700 0.004 NA
#> GSM35454 3 0.1946 0.8258 0.004 0.000 0.912 0.000 0.012 NA
#> GSM35457 2 0.1074 0.7203 0.000 0.960 0.000 0.000 0.028 NA
#> GSM35465 2 0.3851 0.6547 0.000 0.804 0.000 0.096 0.028 NA
#> GSM35468 1 0.2357 0.8088 0.872 0.000 0.000 0.000 0.012 NA
#> GSM35471 4 0.1204 0.7314 0.000 0.000 0.000 0.944 0.000 NA
#> GSM35473 1 0.1524 0.8249 0.932 0.000 0.000 0.000 0.008 NA
#> GSM35477 4 0.4584 0.6694 0.196 0.000 0.000 0.700 0.004 NA
#> GSM35480 1 0.4681 0.6726 0.732 0.000 0.032 0.140 0.000 NA
#> GSM35482 3 0.3686 0.7665 0.000 0.000 0.796 0.060 0.008 NA
#> GSM35485 2 0.3872 0.6920 0.000 0.604 0.000 0.000 0.004 NA
#> GSM35489 2 0.3383 0.7333 0.000 0.728 0.000 0.000 0.004 NA
#> GSM35492 1 0.2572 0.8011 0.852 0.000 0.000 0.000 0.012 NA
#> GSM35495 3 0.0363 0.8439 0.000 0.000 0.988 0.000 0.012 NA
#> GSM35499 2 0.3017 0.7358 0.000 0.816 0.000 0.020 0.000 NA
#> GSM35502 1 0.0000 0.8342 1.000 0.000 0.000 0.000 0.000 NA
#> GSM35505 3 0.2575 0.8220 0.004 0.000 0.880 0.000 0.044 NA
#> GSM35507 4 0.2933 0.7135 0.008 0.032 0.000 0.860 0.004 NA
#> GSM35510 2 0.1327 0.7351 0.000 0.936 0.000 0.000 0.000 NA
#> GSM35514 1 0.0000 0.8342 1.000 0.000 0.000 0.000 0.000 NA
#> GSM35517 2 0.3151 0.7334 0.000 0.748 0.000 0.000 0.000 NA
#> GSM35520 5 0.4787 0.6049 0.000 0.104 0.020 0.000 0.708 NA
#> GSM35523 4 0.2135 0.7183 0.000 0.000 0.000 0.872 0.000 NA
#> GSM35529 2 0.1124 0.7175 0.000 0.956 0.000 0.000 0.036 NA
#> GSM35531 2 0.5522 0.5960 0.000 0.492 0.008 0.004 0.088 NA
#> GSM35534 2 0.4212 0.6719 0.000 0.560 0.000 0.000 0.016 NA
#> GSM35536 1 0.0458 0.8339 0.984 0.000 0.000 0.000 0.000 NA
#> GSM35538 1 0.5033 -0.1790 0.476 0.000 0.000 0.452 0.000 NA
#> GSM35539 4 0.4381 0.6270 0.236 0.000 0.000 0.692 0.000 NA
#> GSM35540 2 0.4389 0.6325 0.000 0.772 0.000 0.084 0.068 NA
#> GSM35541 2 0.3515 0.7148 0.000 0.676 0.000 0.000 0.000 NA
#> GSM35442 1 0.6017 0.5836 0.592 0.000 0.116 0.000 0.068 NA
#> GSM35447 3 0.3382 0.7852 0.004 0.000 0.820 0.000 0.112 NA
#> GSM35450 4 0.4855 0.4887 0.328 0.000 0.000 0.596 0.000 NA
#> GSM35453 1 0.4342 0.6868 0.740 0.000 0.152 0.000 0.008 NA
#> GSM35456 4 0.3863 0.7174 0.092 0.008 0.000 0.796 0.004 NA
#> GSM35464 4 0.4824 0.5901 0.000 0.180 0.000 0.680 0.004 NA
#> GSM35467 1 0.0000 0.8342 1.000 0.000 0.000 0.000 0.000 NA
#> GSM35470 4 0.7660 0.1275 0.124 0.000 0.292 0.308 0.008 NA
#> GSM35479 3 0.2301 0.8201 0.000 0.000 0.884 0.020 0.000 NA
#> GSM35484 1 0.1655 0.8236 0.932 0.000 0.000 0.008 0.008 NA
#> GSM35488 1 0.3263 0.7866 0.832 0.000 0.000 0.040 0.012 NA
#> GSM35491 1 0.2489 0.8044 0.860 0.000 0.000 0.000 0.012 NA
#> GSM35494 3 0.1946 0.8314 0.000 0.000 0.912 0.012 0.004 NA
#> GSM35498 4 0.2520 0.7134 0.000 0.000 0.000 0.844 0.004 NA
#> GSM35501 1 0.0146 0.8340 0.996 0.000 0.000 0.000 0.000 NA
#> GSM35509 3 0.0777 0.8432 0.000 0.000 0.972 0.004 0.000 NA
#> GSM35513 1 0.0146 0.8343 0.996 0.000 0.000 0.000 0.000 NA
#> GSM35516 2 0.4341 0.6942 0.000 0.616 0.000 0.024 0.004 NA
#> GSM35522 4 0.2135 0.7183 0.000 0.000 0.000 0.872 0.000 NA
#> GSM35525 1 0.4814 0.3575 0.616 0.000 0.000 0.304 0.000 NA
#> GSM35528 4 0.5112 0.6423 0.196 0.000 0.000 0.652 0.008 NA
#> GSM35533 1 0.2182 0.8153 0.904 0.000 0.000 0.020 0.008 NA
#> GSM35537 4 0.5488 0.6058 0.032 0.000 0.100 0.640 0.004 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 time(p) k
#> SD:skmeans 78 3.66e-07 2
#> SD:skmeans 78 2.67e-05 3
#> SD:skmeans 78 3.11e-05 4
#> SD:skmeans 72 3.03e-05 5
#> SD:skmeans 71 1.71e-05 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 7758 rows and 79 columns.
#> Top rows (776, 1552, 2328, 3103, 3879) are extracted by 'SD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.558 0.729 0.896 0.4864 0.498 0.498
#> 3 3 0.481 0.555 0.778 0.3343 0.791 0.603
#> 4 4 0.694 0.737 0.878 0.1562 0.830 0.557
#> 5 5 0.728 0.730 0.848 0.0527 0.895 0.629
#> 6 6 0.725 0.555 0.747 0.0394 0.967 0.847
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
#> GSM35441 2 0.0000 0.84779 0.000 1.000
#> GSM35446 2 0.9427 0.46385 0.360 0.640
#> GSM35449 2 0.0376 0.84667 0.004 0.996
#> GSM35455 2 0.0000 0.84779 0.000 1.000
#> GSM35458 1 1.0000 -0.13907 0.504 0.496
#> GSM35460 2 0.9608 0.41779 0.384 0.616
#> GSM35461 1 0.8267 0.56331 0.740 0.260
#> GSM35463 2 0.0000 0.84779 0.000 1.000
#> GSM35472 2 0.9710 0.38315 0.400 0.600
#> GSM35475 2 0.9933 0.26238 0.452 0.548
#> GSM35483 2 0.0000 0.84779 0.000 1.000
#> GSM35496 1 0.0000 0.88958 1.000 0.000
#> GSM35497 2 0.0000 0.84779 0.000 1.000
#> GSM35504 2 0.0000 0.84779 0.000 1.000
#> GSM35508 2 0.0000 0.84779 0.000 1.000
#> GSM35511 2 0.6531 0.72924 0.168 0.832
#> GSM35512 2 0.9970 0.22131 0.468 0.532
#> GSM35515 1 0.9922 0.03963 0.552 0.448
#> GSM35519 2 0.9815 0.34201 0.420 0.580
#> GSM35527 2 0.0000 0.84779 0.000 1.000
#> GSM35532 2 0.7950 0.65111 0.240 0.760
#> GSM35439 2 0.0000 0.84779 0.000 1.000
#> GSM35443 1 0.0000 0.88958 1.000 0.000
#> GSM35445 1 0.0000 0.88958 1.000 0.000
#> GSM35448 2 0.1184 0.84326 0.016 0.984
#> GSM35451 1 0.3114 0.85687 0.944 0.056
#> GSM35454 2 0.9998 0.10728 0.492 0.508
#> GSM35457 2 0.0376 0.84667 0.004 0.996
#> GSM35465 2 0.0938 0.84455 0.012 0.988
#> GSM35468 1 0.0000 0.88958 1.000 0.000
#> GSM35471 1 0.4815 0.81777 0.896 0.104
#> GSM35473 1 0.0000 0.88958 1.000 0.000
#> GSM35477 1 0.0000 0.88958 1.000 0.000
#> GSM35480 1 0.0000 0.88958 1.000 0.000
#> GSM35482 1 0.3733 0.84542 0.928 0.072
#> GSM35485 2 0.0000 0.84779 0.000 1.000
#> GSM35489 2 0.0376 0.84710 0.004 0.996
#> GSM35492 1 0.0000 0.88958 1.000 0.000
#> GSM35495 1 0.9977 0.00291 0.528 0.472
#> GSM35499 2 0.2423 0.83254 0.040 0.960
#> GSM35502 1 0.0000 0.88958 1.000 0.000
#> GSM35505 1 0.9993 -0.06335 0.516 0.484
#> GSM35507 1 0.6148 0.76989 0.848 0.152
#> GSM35510 2 0.0000 0.84779 0.000 1.000
#> GSM35514 1 0.0000 0.88958 1.000 0.000
#> GSM35517 2 0.0000 0.84779 0.000 1.000
#> GSM35520 2 0.9358 0.47770 0.352 0.648
#> GSM35523 1 0.4562 0.81922 0.904 0.096
#> GSM35529 2 0.0000 0.84779 0.000 1.000
#> GSM35531 2 0.4815 0.78996 0.104 0.896
#> GSM35534 2 0.0000 0.84779 0.000 1.000
#> GSM35536 1 0.0000 0.88958 1.000 0.000
#> GSM35538 1 0.0000 0.88958 1.000 0.000
#> GSM35539 1 0.0000 0.88958 1.000 0.000
#> GSM35540 2 0.1843 0.83856 0.028 0.972
#> GSM35541 2 0.0000 0.84779 0.000 1.000
#> GSM35442 1 0.0000 0.88958 1.000 0.000
#> GSM35447 1 0.9815 0.13806 0.580 0.420
#> GSM35450 1 0.0000 0.88958 1.000 0.000
#> GSM35453 1 0.0000 0.88958 1.000 0.000
#> GSM35456 1 0.5629 0.79208 0.868 0.132
#> GSM35464 2 0.3114 0.82384 0.056 0.944
#> GSM35467 1 0.0000 0.88958 1.000 0.000
#> GSM35470 1 0.0000 0.88958 1.000 0.000
#> GSM35479 1 0.0376 0.88761 0.996 0.004
#> GSM35484 1 0.5059 0.79625 0.888 0.112
#> GSM35488 1 0.0000 0.88958 1.000 0.000
#> GSM35491 1 0.0000 0.88958 1.000 0.000
#> GSM35494 1 0.2423 0.86714 0.960 0.040
#> GSM35498 1 0.8909 0.51031 0.692 0.308
#> GSM35501 1 0.0000 0.88958 1.000 0.000
#> GSM35509 1 0.4562 0.82524 0.904 0.096
#> GSM35513 1 0.0000 0.88958 1.000 0.000
#> GSM35516 2 0.0000 0.84779 0.000 1.000
#> GSM35522 2 0.9993 0.02235 0.484 0.516
#> GSM35525 1 0.0000 0.88958 1.000 0.000
#> GSM35528 1 0.0000 0.88958 1.000 0.000
#> GSM35533 1 0.0000 0.88958 1.000 0.000
#> GSM35537 1 0.0000 0.88958 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM35441 2 0.0000 0.8930 0.000 1.000 0.000
#> GSM35446 3 0.4842 0.5042 0.000 0.224 0.776
#> GSM35449 2 0.1411 0.8749 0.000 0.964 0.036
#> GSM35455 2 0.0000 0.8930 0.000 1.000 0.000
#> GSM35458 1 0.8318 0.2057 0.600 0.284 0.116
#> GSM35460 3 0.3879 0.5495 0.000 0.152 0.848
#> GSM35461 3 0.5760 0.4075 0.328 0.000 0.672
#> GSM35463 2 0.0000 0.8930 0.000 1.000 0.000
#> GSM35472 3 0.6438 0.5376 0.136 0.100 0.764
#> GSM35475 3 0.9243 0.4039 0.192 0.288 0.520
#> GSM35483 2 0.0592 0.8899 0.000 0.988 0.012
#> GSM35496 3 0.5650 0.4193 0.312 0.000 0.688
#> GSM35497 2 0.0000 0.8930 0.000 1.000 0.000
#> GSM35504 2 0.1031 0.8855 0.000 0.976 0.024
#> GSM35508 2 0.0000 0.8930 0.000 1.000 0.000
#> GSM35511 3 0.6936 0.1103 0.016 0.460 0.524
#> GSM35512 3 0.7027 0.4432 0.296 0.044 0.660
#> GSM35515 1 0.8468 0.1416 0.576 0.308 0.116
#> GSM35519 3 0.8753 0.4831 0.188 0.224 0.588
#> GSM35527 2 0.0237 0.8921 0.000 0.996 0.004
#> GSM35532 3 0.7123 0.3135 0.032 0.364 0.604
#> GSM35439 2 0.0000 0.8930 0.000 1.000 0.000
#> GSM35443 1 0.4062 0.6140 0.836 0.000 0.164
#> GSM35445 1 0.4702 0.6157 0.788 0.000 0.212
#> GSM35448 3 0.5529 0.4224 0.000 0.296 0.704
#> GSM35451 1 0.6204 0.5123 0.576 0.000 0.424
#> GSM35454 3 0.6680 -0.4640 0.484 0.008 0.508
#> GSM35457 2 0.1411 0.8749 0.000 0.964 0.036
#> GSM35465 2 0.3412 0.7975 0.000 0.876 0.124
#> GSM35468 1 0.1411 0.6541 0.964 0.000 0.036
#> GSM35471 1 0.6274 0.4826 0.544 0.000 0.456
#> GSM35473 1 0.1411 0.6523 0.964 0.000 0.036
#> GSM35477 1 0.6215 0.5093 0.572 0.000 0.428
#> GSM35480 1 0.6126 0.5215 0.600 0.000 0.400
#> GSM35482 3 0.6295 -0.4527 0.472 0.000 0.528
#> GSM35485 2 0.0424 0.8904 0.000 0.992 0.008
#> GSM35489 2 0.0424 0.8904 0.000 0.992 0.008
#> GSM35492 1 0.1289 0.6529 0.968 0.000 0.032
#> GSM35495 3 0.1315 0.4862 0.008 0.020 0.972
#> GSM35499 2 0.6260 0.2300 0.000 0.552 0.448
#> GSM35502 1 0.0000 0.6646 1.000 0.000 0.000
#> GSM35505 3 0.8410 0.1144 0.360 0.096 0.544
#> GSM35507 1 0.6793 0.4722 0.536 0.012 0.452
#> GSM35510 2 0.3116 0.7999 0.000 0.892 0.108
#> GSM35514 1 0.0592 0.6624 0.988 0.000 0.012
#> GSM35517 2 0.0000 0.8930 0.000 1.000 0.000
#> GSM35520 2 0.9258 0.0232 0.256 0.528 0.216
#> GSM35523 1 0.6267 0.4867 0.548 0.000 0.452
#> GSM35529 2 0.0000 0.8930 0.000 1.000 0.000
#> GSM35531 2 0.7180 0.5461 0.116 0.716 0.168
#> GSM35534 2 0.0424 0.8904 0.000 0.992 0.008
#> GSM35536 1 0.0000 0.6646 1.000 0.000 0.000
#> GSM35538 1 0.0237 0.6652 0.996 0.000 0.004
#> GSM35539 1 0.5859 0.5490 0.656 0.000 0.344
#> GSM35540 2 0.3879 0.7667 0.000 0.848 0.152
#> GSM35541 2 0.0000 0.8930 0.000 1.000 0.000
#> GSM35442 1 0.2066 0.6388 0.940 0.000 0.060
#> GSM35447 1 0.6730 0.2164 0.680 0.036 0.284
#> GSM35450 1 0.5529 0.5635 0.704 0.000 0.296
#> GSM35453 1 0.1529 0.6535 0.960 0.000 0.040
#> GSM35456 1 0.6274 0.4826 0.544 0.000 0.456
#> GSM35464 2 0.4178 0.7433 0.000 0.828 0.172
#> GSM35467 1 0.0237 0.6641 0.996 0.000 0.004
#> GSM35470 1 0.6267 0.4867 0.548 0.000 0.452
#> GSM35479 3 0.5098 0.1446 0.248 0.000 0.752
#> GSM35484 1 0.3502 0.6415 0.896 0.020 0.084
#> GSM35488 1 0.1289 0.6529 0.968 0.000 0.032
#> GSM35491 1 0.2796 0.6490 0.908 0.000 0.092
#> GSM35494 1 0.6309 0.4352 0.504 0.000 0.496
#> GSM35498 3 0.9014 -0.2887 0.408 0.132 0.460
#> GSM35501 1 0.0237 0.6652 0.996 0.000 0.004
#> GSM35509 3 0.1529 0.4544 0.040 0.000 0.960
#> GSM35513 1 0.0747 0.6611 0.984 0.000 0.016
#> GSM35516 2 0.2116 0.8626 0.012 0.948 0.040
#> GSM35522 3 0.9725 0.0022 0.272 0.276 0.452
#> GSM35525 1 0.4750 0.6126 0.784 0.000 0.216
#> GSM35528 1 0.4062 0.6153 0.836 0.000 0.164
#> GSM35533 1 0.6180 0.5175 0.584 0.000 0.416
#> GSM35537 1 0.6267 0.4867 0.548 0.000 0.452
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM35441 2 0.0000 0.9149 0.000 1.000 0.000 0.000
#> GSM35446 3 0.0188 0.8663 0.000 0.000 0.996 0.004
#> GSM35449 2 0.0000 0.9149 0.000 1.000 0.000 0.000
#> GSM35455 2 0.0000 0.9149 0.000 1.000 0.000 0.000
#> GSM35458 1 0.4070 0.7407 0.836 0.016 0.124 0.024
#> GSM35460 3 0.0188 0.8663 0.000 0.000 0.996 0.004
#> GSM35461 3 0.6888 0.1067 0.448 0.000 0.448 0.104
#> GSM35463 2 0.0000 0.9149 0.000 1.000 0.000 0.000
#> GSM35472 3 0.3051 0.8343 0.028 0.000 0.884 0.088
#> GSM35475 3 0.2816 0.8513 0.064 0.036 0.900 0.000
#> GSM35483 2 0.2976 0.8418 0.000 0.872 0.120 0.008
#> GSM35496 3 0.3966 0.8133 0.072 0.000 0.840 0.088
#> GSM35497 2 0.0000 0.9149 0.000 1.000 0.000 0.000
#> GSM35504 2 0.0336 0.9114 0.000 0.992 0.008 0.000
#> GSM35508 2 0.0000 0.9149 0.000 1.000 0.000 0.000
#> GSM35511 3 0.2385 0.8575 0.028 0.052 0.920 0.000
#> GSM35512 3 0.0921 0.8682 0.028 0.000 0.972 0.000
#> GSM35515 1 0.3958 0.7500 0.844 0.016 0.116 0.024
#> GSM35519 3 0.2456 0.8640 0.040 0.028 0.924 0.008
#> GSM35527 2 0.0000 0.9149 0.000 1.000 0.000 0.000
#> GSM35532 3 0.2023 0.8671 0.028 0.028 0.940 0.004
#> GSM35439 2 0.0000 0.9149 0.000 1.000 0.000 0.000
#> GSM35443 1 0.2773 0.7749 0.880 0.000 0.004 0.116
#> GSM35445 4 0.6733 0.2409 0.416 0.000 0.092 0.492
#> GSM35448 3 0.0469 0.8663 0.000 0.012 0.988 0.000
#> GSM35451 4 0.1302 0.7982 0.044 0.000 0.000 0.956
#> GSM35454 4 0.6684 0.3203 0.336 0.000 0.104 0.560
#> GSM35457 2 0.0000 0.9149 0.000 1.000 0.000 0.000
#> GSM35465 2 0.0921 0.9018 0.000 0.972 0.000 0.028
#> GSM35468 1 0.0779 0.8438 0.980 0.000 0.004 0.016
#> GSM35471 4 0.0188 0.8033 0.004 0.000 0.000 0.996
#> GSM35473 1 0.1211 0.8365 0.960 0.000 0.040 0.000
#> GSM35477 4 0.2345 0.7730 0.100 0.000 0.000 0.900
#> GSM35480 4 0.1211 0.7998 0.040 0.000 0.000 0.960
#> GSM35482 4 0.3128 0.7669 0.076 0.000 0.040 0.884
#> GSM35485 2 0.2647 0.8444 0.000 0.880 0.120 0.000
#> GSM35489 2 0.2345 0.8595 0.000 0.900 0.100 0.000
#> GSM35492 1 0.0188 0.8437 0.996 0.000 0.004 0.000
#> GSM35495 3 0.2408 0.8161 0.000 0.000 0.896 0.104
#> GSM35499 2 0.5168 0.1554 0.000 0.504 0.004 0.492
#> GSM35502 1 0.4697 0.3471 0.644 0.000 0.000 0.356
#> GSM35505 3 0.2593 0.8080 0.104 0.000 0.892 0.004
#> GSM35507 4 0.0000 0.8032 0.000 0.000 0.000 1.000
#> GSM35510 2 0.0000 0.9149 0.000 1.000 0.000 0.000
#> GSM35514 1 0.0921 0.8411 0.972 0.000 0.000 0.028
#> GSM35517 2 0.0000 0.9149 0.000 1.000 0.000 0.000
#> GSM35520 3 0.6413 0.6351 0.104 0.216 0.668 0.012
#> GSM35523 4 0.0000 0.8032 0.000 0.000 0.000 1.000
#> GSM35529 2 0.0000 0.9149 0.000 1.000 0.000 0.000
#> GSM35531 2 0.7717 0.4388 0.020 0.548 0.212 0.220
#> GSM35534 2 0.2647 0.8444 0.000 0.880 0.120 0.000
#> GSM35536 1 0.1022 0.8399 0.968 0.000 0.000 0.032
#> GSM35538 4 0.5000 0.0154 0.500 0.000 0.000 0.500
#> GSM35539 4 0.2469 0.7678 0.108 0.000 0.000 0.892
#> GSM35540 2 0.2530 0.8462 0.000 0.888 0.000 0.112
#> GSM35541 2 0.0000 0.9149 0.000 1.000 0.000 0.000
#> GSM35442 1 0.1151 0.8389 0.968 0.000 0.024 0.008
#> GSM35447 1 0.4746 0.3962 0.632 0.000 0.368 0.000
#> GSM35450 4 0.2868 0.7456 0.136 0.000 0.000 0.864
#> GSM35453 1 0.5535 0.5969 0.720 0.000 0.088 0.192
#> GSM35456 4 0.0000 0.8032 0.000 0.000 0.000 1.000
#> GSM35464 2 0.2868 0.8251 0.000 0.864 0.000 0.136
#> GSM35467 1 0.0817 0.8429 0.976 0.000 0.000 0.024
#> GSM35470 4 0.0000 0.8032 0.000 0.000 0.000 1.000
#> GSM35479 4 0.2011 0.7785 0.000 0.000 0.080 0.920
#> GSM35484 1 0.2060 0.8330 0.932 0.000 0.016 0.052
#> GSM35488 1 0.0188 0.8444 0.996 0.000 0.000 0.004
#> GSM35491 1 0.1305 0.8374 0.960 0.000 0.004 0.036
#> GSM35494 4 0.2466 0.7688 0.004 0.000 0.096 0.900
#> GSM35498 4 0.4907 0.2171 0.420 0.000 0.000 0.580
#> GSM35501 1 0.4999 -0.0833 0.508 0.000 0.000 0.492
#> GSM35509 4 0.5000 -0.0137 0.000 0.000 0.496 0.504
#> GSM35513 1 0.0707 0.8439 0.980 0.000 0.000 0.020
#> GSM35516 2 0.2868 0.8093 0.000 0.864 0.000 0.136
#> GSM35522 4 0.0000 0.8032 0.000 0.000 0.000 1.000
#> GSM35525 4 0.4331 0.5713 0.288 0.000 0.000 0.712
#> GSM35528 4 0.4655 0.4269 0.312 0.000 0.004 0.684
#> GSM35533 4 0.1557 0.7951 0.056 0.000 0.000 0.944
#> GSM35537 4 0.0000 0.8032 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
#> GSM35441 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000
#> GSM35446 5 0.4161 0.231 0.000 0.000 0.392 0.000 0.608
#> GSM35449 2 0.0404 0.925 0.000 0.988 0.012 0.000 0.000
#> GSM35455 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000
#> GSM35458 1 0.4429 0.753 0.764 0.000 0.060 0.008 0.168
#> GSM35460 3 0.4249 0.130 0.000 0.000 0.568 0.000 0.432
#> GSM35461 1 0.4821 0.236 0.516 0.000 0.000 0.020 0.464
#> GSM35463 2 0.2020 0.896 0.000 0.900 0.100 0.000 0.000
#> GSM35472 5 0.1717 0.780 0.004 0.000 0.052 0.008 0.936
#> GSM35475 5 0.1831 0.777 0.004 0.000 0.076 0.000 0.920
#> GSM35483 2 0.3617 0.850 0.000 0.824 0.128 0.004 0.044
#> GSM35496 5 0.6021 0.373 0.104 0.000 0.268 0.020 0.608
#> GSM35497 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000
#> GSM35504 2 0.0963 0.919 0.000 0.964 0.036 0.000 0.000
#> GSM35508 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000
#> GSM35511 5 0.0794 0.812 0.000 0.000 0.028 0.000 0.972
#> GSM35512 5 0.0162 0.803 0.004 0.000 0.000 0.000 0.996
#> GSM35515 1 0.4248 0.765 0.780 0.000 0.056 0.008 0.156
#> GSM35519 5 0.0794 0.812 0.000 0.000 0.028 0.000 0.972
#> GSM35527 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000
#> GSM35532 5 0.0794 0.812 0.000 0.000 0.028 0.000 0.972
#> GSM35439 2 0.1608 0.908 0.000 0.928 0.072 0.000 0.000
#> GSM35443 1 0.3134 0.808 0.848 0.000 0.000 0.032 0.120
#> GSM35445 3 0.5747 0.567 0.212 0.000 0.620 0.168 0.000
#> GSM35448 3 0.3210 0.502 0.000 0.000 0.788 0.000 0.212
#> GSM35451 4 0.1410 0.834 0.060 0.000 0.000 0.940 0.000
#> GSM35454 3 0.3639 0.625 0.024 0.000 0.792 0.184 0.000
#> GSM35457 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000
#> GSM35465 2 0.0703 0.917 0.000 0.976 0.000 0.024 0.000
#> GSM35468 1 0.2873 0.813 0.860 0.000 0.000 0.020 0.120
#> GSM35471 4 0.0992 0.836 0.008 0.000 0.024 0.968 0.000
#> GSM35473 1 0.1121 0.798 0.956 0.000 0.044 0.000 0.000
#> GSM35477 4 0.1908 0.825 0.092 0.000 0.000 0.908 0.000
#> GSM35480 4 0.1907 0.838 0.028 0.000 0.044 0.928 0.000
#> GSM35482 4 0.5557 0.328 0.020 0.000 0.368 0.572 0.040
#> GSM35485 2 0.3460 0.852 0.000 0.828 0.128 0.000 0.044
#> GSM35489 2 0.3322 0.868 0.000 0.848 0.104 0.004 0.044
#> GSM35492 1 0.2280 0.817 0.880 0.000 0.000 0.000 0.120
#> GSM35495 3 0.4276 0.510 0.000 0.000 0.716 0.028 0.256
#> GSM35499 2 0.4960 0.624 0.000 0.688 0.080 0.232 0.000
#> GSM35502 1 0.4114 0.206 0.624 0.000 0.000 0.376 0.000
#> GSM35505 3 0.4808 0.544 0.108 0.000 0.724 0.000 0.168
#> GSM35507 4 0.1544 0.826 0.000 0.000 0.068 0.932 0.000
#> GSM35510 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000
#> GSM35514 1 0.0162 0.813 0.996 0.000 0.000 0.004 0.000
#> GSM35517 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000
#> GSM35520 5 0.5431 0.609 0.036 0.092 0.144 0.004 0.724
#> GSM35523 4 0.2127 0.814 0.000 0.000 0.108 0.892 0.000
#> GSM35529 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000
#> GSM35531 3 0.7567 0.153 0.020 0.336 0.464 0.128 0.052
#> GSM35534 2 0.3460 0.852 0.000 0.828 0.128 0.000 0.044
#> GSM35536 1 0.0290 0.812 0.992 0.000 0.000 0.008 0.000
#> GSM35538 4 0.3424 0.697 0.240 0.000 0.000 0.760 0.000
#> GSM35539 4 0.1908 0.825 0.092 0.000 0.000 0.908 0.000
#> GSM35540 2 0.2628 0.857 0.000 0.884 0.028 0.088 0.000
#> GSM35541 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000
#> GSM35442 1 0.2583 0.812 0.864 0.000 0.000 0.004 0.132
#> GSM35447 3 0.4944 0.555 0.208 0.000 0.700 0.000 0.092
#> GSM35450 4 0.2127 0.817 0.108 0.000 0.000 0.892 0.000
#> GSM35453 3 0.4620 0.415 0.392 0.000 0.592 0.016 0.000
#> GSM35456 4 0.1544 0.826 0.000 0.000 0.068 0.932 0.000
#> GSM35464 2 0.3130 0.832 0.000 0.856 0.048 0.096 0.000
#> GSM35467 1 0.0162 0.813 0.996 0.000 0.000 0.004 0.000
#> GSM35470 4 0.2286 0.814 0.000 0.000 0.108 0.888 0.004
#> GSM35479 3 0.4074 0.331 0.000 0.000 0.636 0.364 0.000
#> GSM35484 1 0.2507 0.787 0.900 0.000 0.016 0.072 0.012
#> GSM35488 1 0.1041 0.820 0.964 0.000 0.000 0.004 0.032
#> GSM35491 1 0.2439 0.817 0.876 0.000 0.000 0.004 0.120
#> GSM35494 3 0.2929 0.606 0.000 0.000 0.820 0.180 0.000
#> GSM35498 1 0.5513 0.223 0.524 0.000 0.068 0.408 0.000
#> GSM35501 4 0.4101 0.497 0.372 0.000 0.000 0.628 0.000
#> GSM35509 3 0.3639 0.612 0.000 0.000 0.812 0.144 0.044
#> GSM35513 1 0.0162 0.813 0.996 0.000 0.000 0.004 0.000
#> GSM35516 2 0.3375 0.842 0.000 0.840 0.056 0.104 0.000
#> GSM35522 4 0.2127 0.814 0.000 0.000 0.108 0.892 0.000
#> GSM35525 4 0.2813 0.773 0.168 0.000 0.000 0.832 0.000
#> GSM35528 4 0.3960 0.766 0.100 0.000 0.032 0.824 0.044
#> GSM35533 4 0.1478 0.834 0.064 0.000 0.000 0.936 0.000
#> GSM35537 4 0.2127 0.814 0.000 0.000 0.108 0.892 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM35441 2 0.0000 0.83015 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM35446 5 0.3717 0.22346 0.000 0.000 0.384 0.000 0.616 0.000
#> GSM35449 2 0.1663 0.80918 0.000 0.912 0.000 0.000 0.000 0.088
#> GSM35455 2 0.0000 0.83015 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM35458 1 0.5383 0.61399 0.684 0.000 0.076 0.000 0.120 0.120
#> GSM35460 3 0.3515 0.39968 0.000 0.000 0.676 0.000 0.324 0.000
#> GSM35461 1 0.3371 0.47924 0.708 0.000 0.000 0.000 0.292 0.000
#> GSM35463 2 0.3885 0.69761 0.000 0.684 0.012 0.000 0.004 0.300
#> GSM35472 5 0.3272 0.70410 0.080 0.000 0.076 0.008 0.836 0.000
#> GSM35475 5 0.5413 0.64277 0.100 0.000 0.064 0.000 0.672 0.164
#> GSM35483 2 0.5454 0.60047 0.000 0.576 0.012 0.000 0.112 0.300
#> GSM35496 5 0.7321 0.32240 0.172 0.000 0.176 0.232 0.420 0.000
#> GSM35497 2 0.0000 0.83015 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM35504 2 0.1296 0.82042 0.000 0.952 0.012 0.000 0.004 0.032
#> GSM35508 2 0.0000 0.83015 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM35511 5 0.0146 0.74698 0.004 0.000 0.000 0.000 0.996 0.000
#> GSM35512 5 0.2527 0.73671 0.084 0.000 0.000 0.000 0.876 0.040
#> GSM35515 1 0.5223 0.62532 0.700 0.000 0.076 0.000 0.108 0.116
#> GSM35519 5 0.1196 0.74276 0.008 0.000 0.000 0.000 0.952 0.040
#> GSM35527 2 0.0146 0.83009 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM35532 5 0.0260 0.74545 0.000 0.000 0.000 0.000 0.992 0.008
#> GSM35439 2 0.3672 0.71518 0.000 0.712 0.008 0.000 0.004 0.276
#> GSM35443 1 0.0806 0.81148 0.972 0.000 0.000 0.008 0.020 0.000
#> GSM35445 3 0.4853 0.68115 0.120 0.000 0.728 0.052 0.000 0.100
#> GSM35448 3 0.4074 0.63569 0.000 0.000 0.752 0.000 0.140 0.108
#> GSM35451 4 0.4384 -0.23566 0.016 0.000 0.004 0.520 0.000 0.460
#> GSM35454 3 0.3748 0.74226 0.028 0.000 0.812 0.092 0.000 0.068
#> GSM35457 2 0.0000 0.83015 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM35465 2 0.0260 0.82746 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM35468 1 0.0547 0.81455 0.980 0.000 0.000 0.000 0.020 0.000
#> GSM35471 4 0.3774 0.00162 0.000 0.000 0.000 0.592 0.000 0.408
#> GSM35473 1 0.2624 0.81208 0.856 0.000 0.020 0.000 0.000 0.124
#> GSM35477 4 0.4529 -0.26729 0.024 0.000 0.004 0.512 0.000 0.460
#> GSM35480 4 0.3758 0.13555 0.008 0.000 0.000 0.668 0.000 0.324
#> GSM35482 4 0.4478 0.24417 0.076 0.000 0.192 0.720 0.012 0.000
#> GSM35485 2 0.5454 0.60047 0.000 0.576 0.012 0.000 0.112 0.300
#> GSM35489 2 0.5654 0.63458 0.000 0.604 0.004 0.036 0.088 0.268
#> GSM35492 1 0.0547 0.81455 0.980 0.000 0.000 0.000 0.020 0.000
#> GSM35495 3 0.1765 0.71197 0.000 0.000 0.904 0.000 0.096 0.000
#> GSM35499 2 0.4981 0.51617 0.000 0.584 0.004 0.340 0.000 0.072
#> GSM35502 1 0.5878 0.25628 0.504 0.000 0.008 0.176 0.000 0.312
#> GSM35505 3 0.4090 0.72542 0.068 0.000 0.792 0.000 0.048 0.092
#> GSM35507 4 0.2996 0.35271 0.000 0.000 0.000 0.772 0.000 0.228
#> GSM35510 2 0.0000 0.83015 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM35514 1 0.2402 0.81452 0.856 0.000 0.004 0.000 0.000 0.140
#> GSM35517 2 0.0458 0.82950 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM35520 5 0.5022 0.52645 0.012 0.008 0.044 0.000 0.604 0.332
#> GSM35523 4 0.0000 0.44763 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM35529 2 0.0000 0.83015 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM35531 6 0.6219 -0.01461 0.028 0.080 0.144 0.000 0.112 0.636
#> GSM35534 2 0.5454 0.60047 0.000 0.576 0.012 0.000 0.112 0.300
#> GSM35536 1 0.2872 0.80631 0.832 0.000 0.004 0.012 0.000 0.152
#> GSM35538 6 0.5287 0.33114 0.076 0.000 0.008 0.424 0.000 0.492
#> GSM35539 4 0.4468 -0.36768 0.020 0.000 0.004 0.488 0.000 0.488
#> GSM35540 2 0.2631 0.74275 0.000 0.840 0.000 0.152 0.000 0.008
#> GSM35541 2 0.0547 0.82939 0.000 0.980 0.000 0.000 0.000 0.020
#> GSM35442 1 0.0713 0.81061 0.972 0.000 0.000 0.000 0.028 0.000
#> GSM35447 3 0.3674 0.71092 0.160 0.000 0.792 0.004 0.036 0.008
#> GSM35450 6 0.4467 0.19807 0.020 0.000 0.004 0.480 0.000 0.496
#> GSM35453 3 0.4499 0.63038 0.216 0.000 0.704 0.008 0.000 0.072
#> GSM35456 4 0.3217 0.35256 0.008 0.000 0.000 0.768 0.000 0.224
#> GSM35464 2 0.3606 0.63890 0.000 0.728 0.000 0.256 0.000 0.016
#> GSM35467 1 0.2402 0.81452 0.856 0.000 0.004 0.000 0.000 0.140
#> GSM35470 4 0.0000 0.44763 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM35479 3 0.3860 0.34883 0.000 0.000 0.528 0.472 0.000 0.000
#> GSM35484 1 0.4304 0.67227 0.704 0.000 0.020 0.028 0.000 0.248
#> GSM35488 1 0.1806 0.82193 0.908 0.000 0.000 0.000 0.004 0.088
#> GSM35491 1 0.0547 0.81455 0.980 0.000 0.000 0.000 0.020 0.000
#> GSM35494 3 0.1863 0.73814 0.000 0.000 0.896 0.104 0.000 0.000
#> GSM35498 4 0.3999 -0.18072 0.496 0.000 0.000 0.500 0.000 0.004
#> GSM35501 6 0.5341 0.31437 0.108 0.000 0.008 0.304 0.000 0.580
#> GSM35509 3 0.1814 0.73863 0.000 0.000 0.900 0.100 0.000 0.000
#> GSM35513 1 0.2402 0.81452 0.856 0.000 0.004 0.000 0.000 0.140
#> GSM35516 2 0.4589 0.41993 0.000 0.504 0.000 0.036 0.000 0.460
#> GSM35522 4 0.0000 0.44763 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM35525 6 0.4877 0.28026 0.040 0.000 0.008 0.464 0.000 0.488
#> GSM35528 4 0.4865 0.20416 0.096 0.000 0.000 0.652 0.004 0.248
#> GSM35533 4 0.4461 -0.25980 0.020 0.000 0.004 0.512 0.000 0.464
#> GSM35537 4 0.0000 0.44763 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 time(p) k
#> SD:pam 65 7.62e-05 2
#> SD:pam 51 5.28e-05 3
#> SD:pam 67 1.18e-04 4
#> SD:pam 68 1.96e-04 5
#> SD:pam 52 8.95e-04 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 7758 rows and 79 columns.
#> Top rows (776, 1552, 2328, 3103, 3879) 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 0.293 0.718 0.821 0.3619 0.705 0.705
#> 3 3 0.526 0.764 0.877 0.7037 0.603 0.461
#> 4 4 0.729 0.804 0.845 0.1788 0.769 0.461
#> 5 5 0.810 0.843 0.885 0.0735 0.872 0.572
#> 6 6 0.736 0.697 0.833 0.0425 0.952 0.784
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
#> GSM35441 2 0.644 0.7285 0.164 0.836
#> GSM35446 2 0.000 0.7849 0.000 1.000
#> GSM35449 2 0.644 0.7285 0.164 0.836
#> GSM35455 2 0.644 0.7285 0.164 0.836
#> GSM35458 2 0.000 0.7849 0.000 1.000
#> GSM35460 2 0.000 0.7849 0.000 1.000
#> GSM35461 2 0.595 0.7442 0.144 0.856
#> GSM35463 2 0.644 0.7285 0.164 0.836
#> GSM35472 2 0.311 0.7757 0.056 0.944
#> GSM35475 2 0.000 0.7849 0.000 1.000
#> GSM35483 2 0.644 0.7285 0.164 0.836
#> GSM35496 2 0.595 0.7442 0.144 0.856
#> GSM35497 2 0.644 0.7285 0.164 0.836
#> GSM35504 2 0.000 0.7849 0.000 1.000
#> GSM35508 2 0.634 0.7306 0.160 0.840
#> GSM35511 2 0.000 0.7849 0.000 1.000
#> GSM35512 2 0.224 0.7804 0.036 0.964
#> GSM35515 2 0.000 0.7849 0.000 1.000
#> GSM35519 2 0.000 0.7849 0.000 1.000
#> GSM35527 2 0.644 0.7285 0.164 0.836
#> GSM35532 2 0.000 0.7849 0.000 1.000
#> GSM35439 2 0.595 0.7378 0.144 0.856
#> GSM35443 1 0.904 0.7873 0.680 0.320
#> GSM35445 2 0.929 0.4138 0.344 0.656
#> GSM35448 2 0.000 0.7849 0.000 1.000
#> GSM35451 2 0.808 0.6202 0.248 0.752
#> GSM35454 2 0.595 0.7442 0.144 0.856
#> GSM35457 2 0.644 0.7285 0.164 0.836
#> GSM35465 2 0.644 0.7285 0.164 0.836
#> GSM35468 1 0.738 0.9360 0.792 0.208
#> GSM35471 2 0.595 0.7442 0.144 0.856
#> GSM35473 1 0.788 0.9119 0.764 0.236
#> GSM35477 2 0.855 0.5632 0.280 0.720
#> GSM35480 2 0.866 0.5472 0.288 0.712
#> GSM35482 2 0.595 0.7442 0.144 0.856
#> GSM35485 2 0.644 0.7285 0.164 0.836
#> GSM35489 2 0.644 0.7285 0.164 0.836
#> GSM35492 1 0.745 0.9337 0.788 0.212
#> GSM35495 2 0.574 0.7480 0.136 0.864
#> GSM35499 2 0.295 0.7721 0.052 0.948
#> GSM35502 1 0.644 0.9309 0.836 0.164
#> GSM35505 2 0.595 0.7442 0.144 0.856
#> GSM35507 2 0.595 0.7442 0.144 0.856
#> GSM35510 2 0.634 0.7306 0.160 0.840
#> GSM35514 1 0.644 0.9309 0.836 0.164
#> GSM35517 2 0.644 0.7285 0.164 0.836
#> GSM35520 2 0.000 0.7849 0.000 1.000
#> GSM35523 2 0.738 0.6778 0.208 0.792
#> GSM35529 2 0.644 0.7285 0.164 0.836
#> GSM35531 2 0.000 0.7849 0.000 1.000
#> GSM35534 2 0.644 0.7285 0.164 0.836
#> GSM35536 1 0.644 0.9309 0.836 0.164
#> GSM35538 2 1.000 -0.1447 0.496 0.504
#> GSM35539 2 0.992 0.0859 0.448 0.552
#> GSM35540 2 0.204 0.7779 0.032 0.968
#> GSM35541 2 0.644 0.7285 0.164 0.836
#> GSM35442 2 0.595 0.7442 0.144 0.856
#> GSM35447 2 0.584 0.7462 0.140 0.860
#> GSM35450 2 0.994 0.0466 0.456 0.544
#> GSM35453 2 0.745 0.6721 0.212 0.788
#> GSM35456 2 0.595 0.7442 0.144 0.856
#> GSM35464 2 0.184 0.7820 0.028 0.972
#> GSM35467 1 0.644 0.9309 0.836 0.164
#> GSM35470 2 0.775 0.6503 0.228 0.772
#> GSM35479 2 0.595 0.7442 0.144 0.856
#> GSM35484 1 0.767 0.9245 0.776 0.224
#> GSM35488 1 0.738 0.9360 0.792 0.208
#> GSM35491 1 0.738 0.9360 0.792 0.208
#> GSM35494 2 0.595 0.7442 0.144 0.856
#> GSM35498 2 0.605 0.7409 0.148 0.852
#> GSM35501 1 0.644 0.9309 0.836 0.164
#> GSM35509 2 0.595 0.7442 0.144 0.856
#> GSM35513 1 0.644 0.9309 0.836 0.164
#> GSM35516 2 0.563 0.7427 0.132 0.868
#> GSM35522 2 0.625 0.7340 0.156 0.844
#> GSM35525 2 0.997 -0.0103 0.468 0.532
#> GSM35528 2 0.981 0.1594 0.420 0.580
#> GSM35533 1 0.891 0.7963 0.692 0.308
#> GSM35537 2 0.821 0.6067 0.256 0.744
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM35441 2 0.0000 0.9175 0.000 1.000 0.000
#> GSM35446 3 0.0237 0.8217 0.000 0.004 0.996
#> GSM35449 2 0.0000 0.9175 0.000 1.000 0.000
#> GSM35455 2 0.0000 0.9175 0.000 1.000 0.000
#> GSM35458 3 0.3879 0.7935 0.000 0.152 0.848
#> GSM35460 3 0.0237 0.8217 0.000 0.004 0.996
#> GSM35461 3 0.3359 0.8031 0.084 0.016 0.900
#> GSM35463 2 0.0747 0.9193 0.000 0.984 0.016
#> GSM35472 3 0.0892 0.8192 0.000 0.020 0.980
#> GSM35475 3 0.3879 0.7935 0.000 0.152 0.848
#> GSM35483 2 0.1289 0.9138 0.000 0.968 0.032
#> GSM35496 3 0.0747 0.8191 0.000 0.016 0.984
#> GSM35497 2 0.0000 0.9175 0.000 1.000 0.000
#> GSM35504 3 0.3619 0.7942 0.000 0.136 0.864
#> GSM35508 3 0.6286 0.2726 0.000 0.464 0.536
#> GSM35511 3 0.3116 0.8089 0.000 0.108 0.892
#> GSM35512 3 0.0747 0.8191 0.000 0.016 0.984
#> GSM35515 3 0.3879 0.7935 0.000 0.152 0.848
#> GSM35519 3 0.1411 0.8205 0.000 0.036 0.964
#> GSM35527 2 0.6008 0.2906 0.000 0.628 0.372
#> GSM35532 3 0.0892 0.8192 0.000 0.020 0.980
#> GSM35439 2 0.1337 0.9168 0.012 0.972 0.016
#> GSM35443 1 0.5167 0.7579 0.792 0.016 0.192
#> GSM35445 1 0.6192 0.2834 0.580 0.000 0.420
#> GSM35448 3 0.0237 0.8217 0.000 0.004 0.996
#> GSM35451 3 0.5733 0.5998 0.324 0.000 0.676
#> GSM35454 3 0.0592 0.8218 0.012 0.000 0.988
#> GSM35457 2 0.0829 0.9205 0.012 0.984 0.004
#> GSM35465 2 0.3618 0.8293 0.012 0.884 0.104
#> GSM35468 1 0.0747 0.8546 0.984 0.016 0.000
#> GSM35471 3 0.5431 0.6477 0.284 0.000 0.716
#> GSM35473 1 0.2625 0.8481 0.916 0.000 0.084
#> GSM35477 1 0.5926 0.4525 0.644 0.000 0.356
#> GSM35480 3 0.6291 0.1492 0.468 0.000 0.532
#> GSM35482 3 0.0592 0.8210 0.012 0.000 0.988
#> GSM35485 2 0.0747 0.9193 0.000 0.984 0.016
#> GSM35489 2 0.0829 0.9205 0.012 0.984 0.004
#> GSM35492 1 0.1337 0.8563 0.972 0.016 0.012
#> GSM35495 3 0.0000 0.8216 0.000 0.000 1.000
#> GSM35499 3 0.5678 0.6135 0.000 0.316 0.684
#> GSM35502 1 0.0000 0.8579 1.000 0.000 0.000
#> GSM35505 3 0.0000 0.8216 0.000 0.000 1.000
#> GSM35507 3 0.5953 0.6587 0.280 0.012 0.708
#> GSM35510 2 0.6252 0.0348 0.000 0.556 0.444
#> GSM35514 1 0.0000 0.8579 1.000 0.000 0.000
#> GSM35517 2 0.0829 0.9205 0.012 0.984 0.004
#> GSM35520 3 0.4805 0.7669 0.012 0.176 0.812
#> GSM35523 3 0.5591 0.6310 0.304 0.000 0.696
#> GSM35529 2 0.0829 0.9205 0.012 0.984 0.004
#> GSM35531 3 0.5406 0.7278 0.012 0.224 0.764
#> GSM35534 2 0.0747 0.9193 0.000 0.984 0.016
#> GSM35536 1 0.0000 0.8579 1.000 0.000 0.000
#> GSM35538 1 0.4121 0.7914 0.832 0.000 0.168
#> GSM35539 1 0.5216 0.6703 0.740 0.000 0.260
#> GSM35540 3 0.5812 0.6804 0.012 0.264 0.724
#> GSM35541 2 0.0829 0.9205 0.012 0.984 0.004
#> GSM35442 3 0.4277 0.7810 0.132 0.016 0.852
#> GSM35447 3 0.0000 0.8216 0.000 0.000 1.000
#> GSM35450 1 0.4555 0.7611 0.800 0.000 0.200
#> GSM35453 3 0.4121 0.7580 0.168 0.000 0.832
#> GSM35456 3 0.5327 0.6627 0.272 0.000 0.728
#> GSM35464 3 0.7084 0.5635 0.036 0.336 0.628
#> GSM35467 1 0.0000 0.8579 1.000 0.000 0.000
#> GSM35470 3 0.5178 0.6884 0.256 0.000 0.744
#> GSM35479 3 0.0000 0.8216 0.000 0.000 1.000
#> GSM35484 1 0.1860 0.8562 0.948 0.000 0.052
#> GSM35488 1 0.0747 0.8546 0.984 0.016 0.000
#> GSM35491 1 0.0237 0.8579 0.996 0.004 0.000
#> GSM35494 3 0.0000 0.8216 0.000 0.000 1.000
#> GSM35498 3 0.5621 0.6247 0.308 0.000 0.692
#> GSM35501 1 0.0000 0.8579 1.000 0.000 0.000
#> GSM35509 3 0.0000 0.8216 0.000 0.000 1.000
#> GSM35513 1 0.0000 0.8579 1.000 0.000 0.000
#> GSM35516 2 0.1399 0.9138 0.004 0.968 0.028
#> GSM35522 3 0.5431 0.6592 0.284 0.000 0.716
#> GSM35525 1 0.4452 0.7690 0.808 0.000 0.192
#> GSM35528 1 0.5219 0.7613 0.788 0.016 0.196
#> GSM35533 1 0.3267 0.8355 0.884 0.000 0.116
#> GSM35537 3 0.5621 0.6247 0.308 0.000 0.692
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM35441 2 0.0817 0.927 0.024 0.976 0.000 0.000
#> GSM35446 3 0.0000 0.831 0.000 0.000 1.000 0.000
#> GSM35449 2 0.0817 0.927 0.024 0.976 0.000 0.000
#> GSM35455 2 0.0817 0.927 0.024 0.976 0.000 0.000
#> GSM35458 3 0.5152 0.800 0.316 0.020 0.664 0.000
#> GSM35460 3 0.0000 0.831 0.000 0.000 1.000 0.000
#> GSM35461 3 0.4836 0.802 0.320 0.000 0.672 0.008
#> GSM35463 2 0.0336 0.933 0.000 0.992 0.008 0.000
#> GSM35472 3 0.3837 0.822 0.224 0.000 0.776 0.000
#> GSM35475 3 0.4564 0.804 0.328 0.000 0.672 0.000
#> GSM35483 2 0.0188 0.933 0.000 0.996 0.004 0.000
#> GSM35496 3 0.2973 0.829 0.144 0.000 0.856 0.000
#> GSM35497 2 0.0817 0.927 0.024 0.976 0.000 0.000
#> GSM35504 3 0.4994 0.114 0.000 0.480 0.520 0.000
#> GSM35508 2 0.5530 0.405 0.032 0.632 0.336 0.000
#> GSM35511 3 0.4564 0.804 0.328 0.000 0.672 0.000
#> GSM35512 3 0.4522 0.806 0.320 0.000 0.680 0.000
#> GSM35515 3 0.4957 0.802 0.320 0.012 0.668 0.000
#> GSM35519 3 0.4564 0.804 0.328 0.000 0.672 0.000
#> GSM35527 2 0.3441 0.816 0.024 0.856 0.120 0.000
#> GSM35532 3 0.4564 0.804 0.328 0.000 0.672 0.000
#> GSM35439 2 0.0336 0.933 0.000 0.992 0.000 0.008
#> GSM35443 1 0.6819 0.757 0.564 0.000 0.124 0.312
#> GSM35445 4 0.4372 0.675 0.056 0.012 0.104 0.828
#> GSM35448 3 0.0000 0.831 0.000 0.000 1.000 0.000
#> GSM35451 4 0.0188 0.873 0.000 0.004 0.000 0.996
#> GSM35454 3 0.0000 0.831 0.000 0.000 1.000 0.000
#> GSM35457 2 0.0336 0.933 0.000 0.992 0.000 0.008
#> GSM35465 2 0.0336 0.933 0.000 0.992 0.000 0.008
#> GSM35468 1 0.4477 0.936 0.688 0.000 0.000 0.312
#> GSM35471 4 0.0657 0.868 0.000 0.012 0.004 0.984
#> GSM35473 1 0.7200 0.701 0.500 0.008 0.112 0.380
#> GSM35477 4 0.0188 0.873 0.000 0.004 0.000 0.996
#> GSM35480 4 0.0657 0.868 0.000 0.012 0.004 0.984
#> GSM35482 3 0.1824 0.809 0.000 0.004 0.936 0.060
#> GSM35485 2 0.0188 0.933 0.000 0.996 0.004 0.000
#> GSM35489 2 0.0336 0.933 0.000 0.992 0.000 0.008
#> GSM35492 1 0.4477 0.936 0.688 0.000 0.000 0.312
#> GSM35495 3 0.0000 0.831 0.000 0.000 1.000 0.000
#> GSM35499 2 0.0469 0.930 0.000 0.988 0.012 0.000
#> GSM35502 1 0.4564 0.943 0.672 0.000 0.000 0.328
#> GSM35505 3 0.0336 0.830 0.000 0.008 0.992 0.000
#> GSM35507 4 0.0707 0.856 0.000 0.020 0.000 0.980
#> GSM35510 2 0.0188 0.933 0.000 0.996 0.004 0.000
#> GSM35514 1 0.4564 0.943 0.672 0.000 0.000 0.328
#> GSM35517 2 0.0188 0.933 0.000 0.996 0.000 0.004
#> GSM35520 3 0.6418 0.719 0.140 0.180 0.672 0.008
#> GSM35523 4 0.0376 0.873 0.000 0.004 0.004 0.992
#> GSM35529 2 0.0336 0.933 0.000 0.992 0.000 0.008
#> GSM35531 2 0.3577 0.776 0.000 0.832 0.156 0.012
#> GSM35534 2 0.0188 0.933 0.000 0.996 0.004 0.000
#> GSM35536 1 0.4564 0.943 0.672 0.000 0.000 0.328
#> GSM35538 4 0.0592 0.861 0.016 0.000 0.000 0.984
#> GSM35539 4 0.0188 0.873 0.000 0.004 0.000 0.996
#> GSM35540 2 0.5099 0.322 0.000 0.612 0.380 0.008
#> GSM35541 2 0.0188 0.933 0.000 0.996 0.000 0.004
#> GSM35442 3 0.5026 0.502 0.016 0.000 0.672 0.312
#> GSM35447 3 0.0672 0.829 0.000 0.008 0.984 0.008
#> GSM35450 4 0.0188 0.873 0.000 0.004 0.000 0.996
#> GSM35453 3 0.4792 0.500 0.000 0.008 0.680 0.312
#> GSM35456 4 0.0657 0.868 0.000 0.012 0.004 0.984
#> GSM35464 2 0.2647 0.844 0.000 0.880 0.000 0.120
#> GSM35467 1 0.4564 0.943 0.672 0.000 0.000 0.328
#> GSM35470 4 0.4905 0.256 0.000 0.004 0.364 0.632
#> GSM35479 3 0.0188 0.830 0.000 0.004 0.996 0.000
#> GSM35484 4 0.5459 -0.573 0.476 0.008 0.004 0.512
#> GSM35488 1 0.4477 0.936 0.688 0.000 0.000 0.312
#> GSM35491 1 0.4522 0.941 0.680 0.000 0.000 0.320
#> GSM35494 3 0.0188 0.830 0.000 0.004 0.996 0.000
#> GSM35498 4 0.0188 0.873 0.000 0.004 0.000 0.996
#> GSM35501 1 0.4564 0.943 0.672 0.000 0.000 0.328
#> GSM35509 3 0.0000 0.831 0.000 0.000 1.000 0.000
#> GSM35513 1 0.4564 0.943 0.672 0.000 0.000 0.328
#> GSM35516 2 0.0188 0.933 0.000 0.996 0.004 0.000
#> GSM35522 4 0.0376 0.873 0.000 0.004 0.004 0.992
#> GSM35525 4 0.0188 0.869 0.004 0.000 0.000 0.996
#> GSM35528 4 0.0921 0.855 0.028 0.000 0.000 0.972
#> GSM35533 4 0.4755 0.333 0.260 0.012 0.004 0.724
#> GSM35537 4 0.0376 0.873 0.000 0.004 0.004 0.992
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM35441 2 0.3027 0.8821 0.000 0.876 0.012 0.072 0.040
#> GSM35446 3 0.4142 0.7343 0.000 0.012 0.752 0.016 0.220
#> GSM35449 2 0.3103 0.8817 0.000 0.872 0.012 0.072 0.044
#> GSM35455 2 0.3027 0.8821 0.000 0.876 0.012 0.072 0.040
#> GSM35458 5 0.2054 0.8786 0.000 0.004 0.008 0.072 0.916
#> GSM35460 3 0.2378 0.8168 0.000 0.012 0.908 0.016 0.064
#> GSM35461 5 0.3906 0.7316 0.068 0.000 0.132 0.000 0.800
#> GSM35463 2 0.0000 0.9458 0.000 1.000 0.000 0.000 0.000
#> GSM35472 3 0.4803 0.3909 0.020 0.000 0.536 0.000 0.444
#> GSM35475 5 0.1894 0.8789 0.000 0.000 0.008 0.072 0.920
#> GSM35483 2 0.0000 0.9458 0.000 1.000 0.000 0.000 0.000
#> GSM35496 3 0.3365 0.7727 0.044 0.000 0.836 0.000 0.120
#> GSM35497 2 0.3027 0.8821 0.000 0.876 0.012 0.072 0.040
#> GSM35504 2 0.0798 0.9386 0.000 0.976 0.000 0.008 0.016
#> GSM35508 2 0.3709 0.8532 0.000 0.840 0.020 0.072 0.068
#> GSM35511 5 0.1942 0.8798 0.000 0.000 0.012 0.068 0.920
#> GSM35512 5 0.3659 0.6039 0.012 0.000 0.220 0.000 0.768
#> GSM35515 5 0.2054 0.8786 0.000 0.004 0.008 0.072 0.916
#> GSM35519 5 0.0404 0.8678 0.000 0.000 0.012 0.000 0.988
#> GSM35527 2 0.3316 0.8758 0.000 0.860 0.012 0.072 0.056
#> GSM35532 5 0.0404 0.8678 0.000 0.000 0.012 0.000 0.988
#> GSM35439 2 0.0000 0.9458 0.000 1.000 0.000 0.000 0.000
#> GSM35443 1 0.0404 0.8960 0.988 0.000 0.000 0.000 0.012
#> GSM35445 1 0.2424 0.8570 0.868 0.000 0.000 0.132 0.000
#> GSM35448 3 0.4301 0.7245 0.000 0.016 0.740 0.016 0.228
#> GSM35451 4 0.1908 0.9149 0.092 0.000 0.000 0.908 0.000
#> GSM35454 3 0.1205 0.8360 0.000 0.000 0.956 0.040 0.004
#> GSM35457 2 0.0290 0.9450 0.000 0.992 0.000 0.000 0.008
#> GSM35465 2 0.0290 0.9450 0.000 0.992 0.000 0.000 0.008
#> GSM35468 1 0.0404 0.8960 0.988 0.000 0.000 0.000 0.012
#> GSM35471 4 0.1851 0.9152 0.088 0.000 0.000 0.912 0.000
#> GSM35473 1 0.1478 0.9037 0.936 0.000 0.000 0.064 0.000
#> GSM35477 4 0.1908 0.9149 0.092 0.000 0.000 0.908 0.000
#> GSM35480 4 0.4300 0.1730 0.476 0.000 0.000 0.524 0.000
#> GSM35482 3 0.2297 0.8129 0.020 0.000 0.912 0.060 0.008
#> GSM35485 2 0.0000 0.9458 0.000 1.000 0.000 0.000 0.000
#> GSM35489 2 0.0000 0.9458 0.000 1.000 0.000 0.000 0.000
#> GSM35492 1 0.0404 0.8960 0.988 0.000 0.000 0.000 0.012
#> GSM35495 3 0.0510 0.8347 0.000 0.000 0.984 0.016 0.000
#> GSM35499 2 0.0290 0.9450 0.000 0.992 0.000 0.000 0.008
#> GSM35502 1 0.1043 0.9111 0.960 0.000 0.000 0.040 0.000
#> GSM35505 3 0.3921 0.7791 0.000 0.000 0.784 0.044 0.172
#> GSM35507 4 0.2011 0.9137 0.088 0.004 0.000 0.908 0.000
#> GSM35510 2 0.0290 0.9450 0.000 0.992 0.000 0.000 0.008
#> GSM35514 1 0.1043 0.9111 0.960 0.000 0.000 0.040 0.000
#> GSM35517 2 0.0000 0.9458 0.000 1.000 0.000 0.000 0.000
#> GSM35520 5 0.3013 0.7416 0.000 0.160 0.008 0.000 0.832
#> GSM35523 4 0.1851 0.9152 0.088 0.000 0.000 0.912 0.000
#> GSM35529 2 0.0290 0.9450 0.000 0.992 0.000 0.000 0.008
#> GSM35531 2 0.0404 0.9412 0.000 0.988 0.000 0.000 0.012
#> GSM35534 2 0.0000 0.9458 0.000 1.000 0.000 0.000 0.000
#> GSM35536 1 0.1043 0.9111 0.960 0.000 0.000 0.040 0.000
#> GSM35538 1 0.2074 0.8757 0.896 0.000 0.000 0.104 0.000
#> GSM35539 4 0.2280 0.9034 0.120 0.000 0.000 0.880 0.000
#> GSM35540 2 0.0510 0.9417 0.000 0.984 0.000 0.000 0.016
#> GSM35541 2 0.0000 0.9458 0.000 1.000 0.000 0.000 0.000
#> GSM35442 1 0.2775 0.8224 0.884 0.000 0.076 0.004 0.036
#> GSM35447 3 0.4588 0.7341 0.000 0.000 0.720 0.060 0.220
#> GSM35450 4 0.3242 0.8130 0.216 0.000 0.000 0.784 0.000
#> GSM35453 1 0.2754 0.8833 0.884 0.000 0.032 0.080 0.004
#> GSM35456 4 0.2248 0.9068 0.088 0.012 0.000 0.900 0.000
#> GSM35464 2 0.3983 0.4940 0.000 0.660 0.000 0.340 0.000
#> GSM35467 1 0.1043 0.9111 0.960 0.000 0.000 0.040 0.000
#> GSM35470 4 0.4338 0.6965 0.280 0.000 0.024 0.696 0.000
#> GSM35479 3 0.0703 0.8361 0.000 0.000 0.976 0.024 0.000
#> GSM35484 1 0.2424 0.8538 0.868 0.000 0.000 0.132 0.000
#> GSM35488 1 0.0404 0.8960 0.988 0.000 0.000 0.000 0.012
#> GSM35491 1 0.0566 0.8981 0.984 0.000 0.000 0.004 0.012
#> GSM35494 3 0.1410 0.8260 0.000 0.000 0.940 0.060 0.000
#> GSM35498 4 0.1851 0.9152 0.088 0.000 0.000 0.912 0.000
#> GSM35501 1 0.1043 0.9111 0.960 0.000 0.000 0.040 0.000
#> GSM35509 3 0.0609 0.8346 0.000 0.000 0.980 0.020 0.000
#> GSM35513 1 0.1043 0.9111 0.960 0.000 0.000 0.040 0.000
#> GSM35516 2 0.0000 0.9458 0.000 1.000 0.000 0.000 0.000
#> GSM35522 4 0.1851 0.9152 0.088 0.000 0.000 0.912 0.000
#> GSM35525 1 0.1410 0.9049 0.940 0.000 0.000 0.060 0.000
#> GSM35528 1 0.4617 -0.0827 0.552 0.000 0.000 0.436 0.012
#> GSM35533 1 0.3242 0.7378 0.784 0.000 0.000 0.216 0.000
#> GSM35537 4 0.2424 0.8941 0.132 0.000 0.000 0.868 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM35441 2 0.2838 0.5850 0.000 0.808 0.000 0.000 0.004 0.188
#> GSM35446 3 0.5786 0.6109 0.000 0.012 0.604 0.028 0.256 0.100
#> GSM35449 2 0.2871 0.5815 0.000 0.804 0.000 0.000 0.004 0.192
#> GSM35455 2 0.2838 0.5850 0.000 0.808 0.000 0.000 0.004 0.188
#> GSM35458 5 0.4072 0.7207 0.004 0.040 0.000 0.004 0.736 0.216
#> GSM35460 3 0.4498 0.7385 0.000 0.012 0.768 0.028 0.096 0.096
#> GSM35461 5 0.3531 0.6813 0.032 0.000 0.152 0.008 0.804 0.004
#> GSM35463 2 0.1141 0.7264 0.000 0.948 0.000 0.000 0.000 0.052
#> GSM35472 5 0.4274 -0.1617 0.004 0.000 0.432 0.000 0.552 0.012
#> GSM35475 5 0.2902 0.7631 0.000 0.004 0.000 0.000 0.800 0.196
#> GSM35483 2 0.1663 0.7406 0.000 0.912 0.000 0.000 0.000 0.088
#> GSM35496 3 0.3194 0.7038 0.012 0.000 0.808 0.004 0.172 0.004
#> GSM35497 2 0.2838 0.5850 0.000 0.808 0.000 0.000 0.004 0.188
#> GSM35504 6 0.3756 0.6467 0.000 0.352 0.000 0.004 0.000 0.644
#> GSM35508 6 0.4189 0.5045 0.000 0.376 0.000 0.000 0.020 0.604
#> GSM35511 5 0.0865 0.7778 0.000 0.000 0.000 0.000 0.964 0.036
#> GSM35512 5 0.2809 0.6206 0.004 0.000 0.168 0.000 0.824 0.004
#> GSM35515 5 0.3332 0.7507 0.004 0.004 0.000 0.004 0.772 0.216
#> GSM35519 5 0.0260 0.7743 0.000 0.000 0.000 0.000 0.992 0.008
#> GSM35527 6 0.3872 0.4917 0.000 0.392 0.000 0.000 0.004 0.604
#> GSM35532 5 0.0146 0.7720 0.000 0.000 0.000 0.000 0.996 0.004
#> GSM35439 2 0.1267 0.7479 0.000 0.940 0.000 0.000 0.000 0.060
#> GSM35443 1 0.0653 0.8422 0.980 0.000 0.012 0.004 0.004 0.000
#> GSM35445 1 0.3891 0.8154 0.768 0.004 0.064 0.164 0.000 0.000
#> GSM35448 3 0.5889 0.6019 0.000 0.016 0.596 0.028 0.260 0.100
#> GSM35451 4 0.1082 0.8611 0.040 0.004 0.000 0.956 0.000 0.000
#> GSM35454 3 0.0547 0.8118 0.000 0.000 0.980 0.020 0.000 0.000
#> GSM35457 2 0.1863 0.6407 0.000 0.896 0.000 0.000 0.000 0.104
#> GSM35465 2 0.2793 0.4589 0.000 0.800 0.000 0.000 0.000 0.200
#> GSM35468 1 0.0653 0.8422 0.980 0.000 0.012 0.004 0.004 0.000
#> GSM35471 4 0.1296 0.8594 0.032 0.012 0.004 0.952 0.000 0.000
#> GSM35473 1 0.2714 0.8626 0.848 0.004 0.012 0.136 0.000 0.000
#> GSM35477 4 0.1082 0.8611 0.040 0.004 0.000 0.956 0.000 0.000
#> GSM35480 4 0.4191 0.2326 0.388 0.004 0.012 0.596 0.000 0.000
#> GSM35482 3 0.1700 0.7733 0.000 0.004 0.916 0.080 0.000 0.000
#> GSM35485 2 0.1556 0.7462 0.000 0.920 0.000 0.000 0.000 0.080
#> GSM35489 2 0.1700 0.7462 0.000 0.916 0.004 0.000 0.000 0.080
#> GSM35492 1 0.0653 0.8422 0.980 0.000 0.012 0.004 0.004 0.000
#> GSM35495 3 0.2221 0.8065 0.000 0.000 0.896 0.032 0.000 0.072
#> GSM35499 2 0.3847 -0.4382 0.000 0.544 0.000 0.000 0.000 0.456
#> GSM35502 1 0.1957 0.8773 0.888 0.000 0.000 0.112 0.000 0.000
#> GSM35505 3 0.3098 0.7374 0.000 0.000 0.812 0.024 0.164 0.000
#> GSM35507 4 0.1151 0.8598 0.032 0.012 0.000 0.956 0.000 0.000
#> GSM35510 6 0.3862 0.4983 0.000 0.476 0.000 0.000 0.000 0.524
#> GSM35514 1 0.1863 0.8787 0.896 0.000 0.000 0.104 0.000 0.000
#> GSM35517 2 0.0146 0.7379 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM35520 5 0.4375 0.6661 0.000 0.120 0.004 0.000 0.732 0.144
#> GSM35523 4 0.0935 0.8618 0.032 0.004 0.000 0.964 0.000 0.000
#> GSM35529 2 0.2631 0.4770 0.000 0.820 0.000 0.000 0.000 0.180
#> GSM35531 2 0.3032 0.6979 0.000 0.852 0.004 0.020 0.016 0.108
#> GSM35534 2 0.1714 0.7404 0.000 0.908 0.000 0.000 0.000 0.092
#> GSM35536 1 0.1863 0.8787 0.896 0.000 0.000 0.104 0.000 0.000
#> GSM35538 1 0.2135 0.8717 0.872 0.000 0.000 0.128 0.000 0.000
#> GSM35539 4 0.2135 0.8048 0.128 0.000 0.000 0.872 0.000 0.000
#> GSM35540 6 0.3795 0.6520 0.000 0.364 0.004 0.000 0.000 0.632
#> GSM35541 2 0.0146 0.7379 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM35442 1 0.3434 0.7434 0.820 0.000 0.132 0.012 0.032 0.004
#> GSM35447 3 0.3949 0.6811 0.000 0.004 0.748 0.036 0.208 0.004
#> GSM35450 4 0.2558 0.7769 0.156 0.004 0.000 0.840 0.000 0.000
#> GSM35453 1 0.4530 0.7677 0.716 0.004 0.144 0.136 0.000 0.000
#> GSM35456 4 0.1296 0.8594 0.032 0.012 0.004 0.952 0.000 0.000
#> GSM35464 4 0.4097 -0.1138 0.000 0.488 0.000 0.504 0.000 0.008
#> GSM35467 1 0.1863 0.8787 0.896 0.000 0.000 0.104 0.000 0.000
#> GSM35470 4 0.4800 0.6441 0.124 0.004 0.192 0.680 0.000 0.000
#> GSM35479 3 0.0717 0.8135 0.000 0.000 0.976 0.016 0.000 0.008
#> GSM35484 1 0.2879 0.8379 0.816 0.004 0.004 0.176 0.000 0.000
#> GSM35488 1 0.0653 0.8422 0.980 0.000 0.012 0.004 0.004 0.000
#> GSM35491 1 0.0767 0.8435 0.976 0.000 0.012 0.008 0.004 0.000
#> GSM35494 3 0.0632 0.8109 0.000 0.000 0.976 0.024 0.000 0.000
#> GSM35498 4 0.0935 0.8618 0.032 0.004 0.000 0.964 0.000 0.000
#> GSM35501 1 0.2003 0.8762 0.884 0.000 0.000 0.116 0.000 0.000
#> GSM35509 3 0.2039 0.8082 0.000 0.000 0.904 0.020 0.000 0.076
#> GSM35513 1 0.1863 0.8787 0.896 0.000 0.000 0.104 0.000 0.000
#> GSM35516 2 0.1701 0.7454 0.000 0.920 0.000 0.008 0.000 0.072
#> GSM35522 4 0.1049 0.8611 0.032 0.008 0.000 0.960 0.000 0.000
#> GSM35525 1 0.2003 0.8762 0.884 0.000 0.000 0.116 0.000 0.000
#> GSM35528 1 0.4218 0.0995 0.584 0.000 0.012 0.400 0.004 0.000
#> GSM35533 1 0.3521 0.7287 0.724 0.004 0.004 0.268 0.000 0.000
#> GSM35537 4 0.2600 0.8247 0.084 0.004 0.036 0.876 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 time(p) k
#> SD:mclust 73 1.53e-02 2
#> SD:mclust 73 7.00e-03 3
#> SD:mclust 72 1.16e-03 4
#> SD:mclust 75 4.54e-06 5
#> SD:mclust 70 4.23e-05 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 7758 rows and 79 columns.
#> Top rows (776, 1552, 2328, 3103, 3879) are extracted by 'SD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.973 0.944 0.979 0.5021 0.498 0.498
#> 3 3 0.920 0.928 0.960 0.3166 0.784 0.590
#> 4 4 0.623 0.655 0.821 0.1280 0.829 0.551
#> 5 5 0.622 0.580 0.774 0.0603 0.920 0.704
#> 6 6 0.631 0.521 0.740 0.0461 0.863 0.467
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
#> attr(,"optional")
#> [1] 2
There is also optional best \(k\) = 2 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM35441 2 0.0000 0.9767 0.000 1.000
#> GSM35446 2 0.0000 0.9767 0.000 1.000
#> GSM35449 2 0.0000 0.9767 0.000 1.000
#> GSM35455 2 0.0000 0.9767 0.000 1.000
#> GSM35458 2 0.0000 0.9767 0.000 1.000
#> GSM35460 2 0.0000 0.9767 0.000 1.000
#> GSM35461 1 0.0000 0.9781 1.000 0.000
#> GSM35463 2 0.0000 0.9767 0.000 1.000
#> GSM35472 2 0.8813 0.5557 0.300 0.700
#> GSM35475 2 0.0000 0.9767 0.000 1.000
#> GSM35483 2 0.0000 0.9767 0.000 1.000
#> GSM35496 1 0.0000 0.9781 1.000 0.000
#> GSM35497 2 0.0000 0.9767 0.000 1.000
#> GSM35504 2 0.0000 0.9767 0.000 1.000
#> GSM35508 2 0.0000 0.9767 0.000 1.000
#> GSM35511 2 0.0000 0.9767 0.000 1.000
#> GSM35512 2 0.9988 0.0456 0.480 0.520
#> GSM35515 2 0.0000 0.9767 0.000 1.000
#> GSM35519 2 0.0000 0.9767 0.000 1.000
#> GSM35527 2 0.0000 0.9767 0.000 1.000
#> GSM35532 2 0.0000 0.9767 0.000 1.000
#> GSM35439 2 0.0000 0.9767 0.000 1.000
#> GSM35443 1 0.0000 0.9781 1.000 0.000
#> GSM35445 1 0.0000 0.9781 1.000 0.000
#> GSM35448 2 0.0000 0.9767 0.000 1.000
#> GSM35451 1 0.0000 0.9781 1.000 0.000
#> GSM35454 1 0.0000 0.9781 1.000 0.000
#> GSM35457 2 0.0000 0.9767 0.000 1.000
#> GSM35465 2 0.0000 0.9767 0.000 1.000
#> GSM35468 1 0.0000 0.9781 1.000 0.000
#> GSM35471 1 0.0000 0.9781 1.000 0.000
#> GSM35473 1 0.0000 0.9781 1.000 0.000
#> GSM35477 1 0.0000 0.9781 1.000 0.000
#> GSM35480 1 0.0000 0.9781 1.000 0.000
#> GSM35482 1 0.0000 0.9781 1.000 0.000
#> GSM35485 2 0.0000 0.9767 0.000 1.000
#> GSM35489 2 0.0000 0.9767 0.000 1.000
#> GSM35492 1 0.0000 0.9781 1.000 0.000
#> GSM35495 1 0.9608 0.3716 0.616 0.384
#> GSM35499 2 0.0000 0.9767 0.000 1.000
#> GSM35502 1 0.0000 0.9781 1.000 0.000
#> GSM35505 1 0.0000 0.9781 1.000 0.000
#> GSM35507 1 0.6712 0.7789 0.824 0.176
#> GSM35510 2 0.0000 0.9767 0.000 1.000
#> GSM35514 1 0.0000 0.9781 1.000 0.000
#> GSM35517 2 0.0000 0.9767 0.000 1.000
#> GSM35520 2 0.0000 0.9767 0.000 1.000
#> GSM35523 1 0.0000 0.9781 1.000 0.000
#> GSM35529 2 0.0000 0.9767 0.000 1.000
#> GSM35531 2 0.0000 0.9767 0.000 1.000
#> GSM35534 2 0.0000 0.9767 0.000 1.000
#> GSM35536 1 0.0000 0.9781 1.000 0.000
#> GSM35538 1 0.0000 0.9781 1.000 0.000
#> GSM35539 1 0.0000 0.9781 1.000 0.000
#> GSM35540 2 0.0000 0.9767 0.000 1.000
#> GSM35541 2 0.0000 0.9767 0.000 1.000
#> GSM35442 1 0.0000 0.9781 1.000 0.000
#> GSM35447 1 0.0000 0.9781 1.000 0.000
#> GSM35450 1 0.0000 0.9781 1.000 0.000
#> GSM35453 1 0.0000 0.9781 1.000 0.000
#> GSM35456 1 0.0000 0.9781 1.000 0.000
#> GSM35464 2 0.0376 0.9730 0.004 0.996
#> GSM35467 1 0.0000 0.9781 1.000 0.000
#> GSM35470 1 0.0000 0.9781 1.000 0.000
#> GSM35479 1 0.0000 0.9781 1.000 0.000
#> GSM35484 1 0.0000 0.9781 1.000 0.000
#> GSM35488 1 0.0000 0.9781 1.000 0.000
#> GSM35491 1 0.0000 0.9781 1.000 0.000
#> GSM35494 1 0.0000 0.9781 1.000 0.000
#> GSM35498 1 0.0000 0.9781 1.000 0.000
#> GSM35501 1 0.0000 0.9781 1.000 0.000
#> GSM35509 1 0.9044 0.5250 0.680 0.320
#> GSM35513 1 0.0000 0.9781 1.000 0.000
#> GSM35516 2 0.0000 0.9767 0.000 1.000
#> GSM35522 1 0.0376 0.9745 0.996 0.004
#> GSM35525 1 0.0000 0.9781 1.000 0.000
#> GSM35528 1 0.0000 0.9781 1.000 0.000
#> GSM35533 1 0.0000 0.9781 1.000 0.000
#> GSM35537 1 0.0000 0.9781 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM35441 2 0.0000 0.971 0.000 1.000 0.000
#> GSM35446 3 0.1163 0.926 0.000 0.028 0.972
#> GSM35449 2 0.0237 0.971 0.000 0.996 0.004
#> GSM35455 2 0.0000 0.971 0.000 1.000 0.000
#> GSM35458 2 0.0592 0.968 0.000 0.988 0.012
#> GSM35460 3 0.0892 0.930 0.000 0.020 0.980
#> GSM35461 3 0.3267 0.857 0.116 0.000 0.884
#> GSM35463 2 0.0475 0.969 0.004 0.992 0.004
#> GSM35472 3 0.0661 0.934 0.004 0.008 0.988
#> GSM35475 2 0.4605 0.768 0.000 0.796 0.204
#> GSM35483 2 0.0592 0.968 0.000 0.988 0.012
#> GSM35496 3 0.0747 0.935 0.016 0.000 0.984
#> GSM35497 2 0.0237 0.971 0.000 0.996 0.004
#> GSM35504 2 0.1964 0.941 0.000 0.944 0.056
#> GSM35508 2 0.2066 0.939 0.000 0.940 0.060
#> GSM35511 3 0.3816 0.815 0.000 0.148 0.852
#> GSM35512 3 0.0592 0.933 0.000 0.012 0.988
#> GSM35515 2 0.1031 0.963 0.000 0.976 0.024
#> GSM35519 3 0.1163 0.927 0.000 0.028 0.972
#> GSM35527 2 0.1289 0.958 0.000 0.968 0.032
#> GSM35532 3 0.1411 0.922 0.000 0.036 0.964
#> GSM35439 2 0.0983 0.962 0.016 0.980 0.004
#> GSM35443 1 0.1163 0.955 0.972 0.000 0.028
#> GSM35445 1 0.1163 0.955 0.972 0.000 0.028
#> GSM35448 3 0.4002 0.799 0.000 0.160 0.840
#> GSM35451 1 0.1267 0.946 0.972 0.024 0.004
#> GSM35454 3 0.1964 0.914 0.056 0.000 0.944
#> GSM35457 2 0.0000 0.971 0.000 1.000 0.000
#> GSM35465 2 0.0000 0.971 0.000 1.000 0.000
#> GSM35468 1 0.0747 0.960 0.984 0.000 0.016
#> GSM35471 1 0.0661 0.956 0.988 0.008 0.004
#> GSM35473 1 0.1031 0.957 0.976 0.000 0.024
#> GSM35477 1 0.0983 0.952 0.980 0.016 0.004
#> GSM35480 1 0.0592 0.961 0.988 0.000 0.012
#> GSM35482 3 0.1031 0.933 0.024 0.000 0.976
#> GSM35485 2 0.0237 0.971 0.000 0.996 0.004
#> GSM35489 2 0.0424 0.969 0.008 0.992 0.000
#> GSM35492 1 0.0892 0.959 0.980 0.000 0.020
#> GSM35495 3 0.0237 0.935 0.004 0.000 0.996
#> GSM35499 2 0.0000 0.971 0.000 1.000 0.000
#> GSM35502 1 0.0424 0.961 0.992 0.000 0.008
#> GSM35505 3 0.0892 0.934 0.020 0.000 0.980
#> GSM35507 1 0.5365 0.674 0.744 0.252 0.004
#> GSM35510 2 0.0237 0.971 0.000 0.996 0.004
#> GSM35514 1 0.0424 0.961 0.992 0.000 0.008
#> GSM35517 2 0.0475 0.969 0.004 0.992 0.004
#> GSM35520 2 0.3752 0.852 0.000 0.856 0.144
#> GSM35523 1 0.0661 0.961 0.988 0.004 0.008
#> GSM35529 2 0.0237 0.971 0.000 0.996 0.004
#> GSM35531 2 0.0237 0.971 0.004 0.996 0.000
#> GSM35534 2 0.0000 0.971 0.000 1.000 0.000
#> GSM35536 1 0.0592 0.961 0.988 0.000 0.012
#> GSM35538 1 0.0237 0.960 0.996 0.004 0.000
#> GSM35539 1 0.0000 0.961 1.000 0.000 0.000
#> GSM35540 2 0.2796 0.911 0.000 0.908 0.092
#> GSM35541 2 0.0661 0.967 0.008 0.988 0.004
#> GSM35442 3 0.6045 0.381 0.380 0.000 0.620
#> GSM35447 3 0.0592 0.935 0.012 0.000 0.988
#> GSM35450 1 0.0424 0.958 0.992 0.008 0.000
#> GSM35453 1 0.4399 0.779 0.812 0.000 0.188
#> GSM35456 1 0.2200 0.920 0.940 0.056 0.004
#> GSM35464 2 0.1525 0.950 0.032 0.964 0.004
#> GSM35467 1 0.0592 0.961 0.988 0.000 0.012
#> GSM35470 1 0.4974 0.705 0.764 0.000 0.236
#> GSM35479 3 0.1163 0.931 0.028 0.000 0.972
#> GSM35484 1 0.0424 0.961 0.992 0.000 0.008
#> GSM35488 1 0.0237 0.961 0.996 0.000 0.004
#> GSM35491 1 0.0892 0.959 0.980 0.000 0.020
#> GSM35494 3 0.1529 0.926 0.040 0.000 0.960
#> GSM35498 1 0.0592 0.956 0.988 0.012 0.000
#> GSM35501 1 0.0592 0.961 0.988 0.000 0.012
#> GSM35509 3 0.0237 0.935 0.004 0.000 0.996
#> GSM35513 1 0.0424 0.961 0.992 0.000 0.008
#> GSM35516 2 0.1267 0.956 0.024 0.972 0.004
#> GSM35522 1 0.2301 0.916 0.936 0.060 0.004
#> GSM35525 1 0.0592 0.961 0.988 0.000 0.012
#> GSM35528 1 0.0475 0.961 0.992 0.004 0.004
#> GSM35533 1 0.0424 0.961 0.992 0.000 0.008
#> GSM35537 1 0.1964 0.933 0.944 0.000 0.056
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM35441 2 0.1022 0.7801 0.000 0.968 0.000 0.032
#> GSM35446 3 0.0895 0.7869 0.000 0.020 0.976 0.004
#> GSM35449 2 0.1211 0.7781 0.000 0.960 0.000 0.040
#> GSM35455 2 0.1211 0.7781 0.000 0.960 0.000 0.040
#> GSM35458 2 0.5507 0.6418 0.096 0.780 0.060 0.064
#> GSM35460 3 0.1722 0.7912 0.000 0.008 0.944 0.048
#> GSM35461 3 0.6830 0.2014 0.420 0.012 0.500 0.068
#> GSM35463 2 0.4941 0.0460 0.000 0.564 0.000 0.436
#> GSM35472 3 0.3030 0.7706 0.024 0.036 0.904 0.036
#> GSM35475 2 0.6381 0.5901 0.096 0.724 0.116 0.064
#> GSM35483 2 0.0469 0.7815 0.000 0.988 0.000 0.012
#> GSM35496 3 0.1837 0.7904 0.028 0.000 0.944 0.028
#> GSM35497 2 0.0592 0.7814 0.000 0.984 0.000 0.016
#> GSM35504 4 0.6705 0.1659 0.000 0.440 0.088 0.472
#> GSM35508 2 0.1182 0.7776 0.000 0.968 0.016 0.016
#> GSM35511 2 0.6042 0.2919 0.000 0.580 0.368 0.052
#> GSM35512 3 0.4842 0.7255 0.048 0.088 0.816 0.048
#> GSM35515 2 0.5780 0.6269 0.100 0.764 0.072 0.064
#> GSM35519 2 0.7450 0.0414 0.048 0.476 0.416 0.060
#> GSM35527 2 0.1042 0.7811 0.000 0.972 0.008 0.020
#> GSM35532 3 0.6032 0.2653 0.004 0.380 0.576 0.040
#> GSM35439 2 0.1022 0.7786 0.000 0.968 0.000 0.032
#> GSM35443 1 0.3323 0.7790 0.876 0.000 0.064 0.060
#> GSM35445 1 0.2796 0.8535 0.892 0.000 0.016 0.092
#> GSM35448 3 0.4163 0.7612 0.000 0.076 0.828 0.096
#> GSM35451 4 0.5112 0.0769 0.436 0.004 0.000 0.560
#> GSM35454 3 0.4054 0.7465 0.016 0.000 0.796 0.188
#> GSM35457 2 0.4898 0.1254 0.000 0.584 0.000 0.416
#> GSM35465 4 0.4866 0.3662 0.000 0.404 0.000 0.596
#> GSM35468 1 0.1109 0.8528 0.968 0.000 0.004 0.028
#> GSM35471 4 0.2081 0.6619 0.084 0.000 0.000 0.916
#> GSM35473 1 0.1004 0.8711 0.972 0.000 0.004 0.024
#> GSM35477 1 0.4655 0.6234 0.684 0.004 0.000 0.312
#> GSM35480 1 0.5184 0.6557 0.672 0.000 0.024 0.304
#> GSM35482 3 0.2714 0.7839 0.004 0.000 0.884 0.112
#> GSM35485 2 0.0921 0.7802 0.000 0.972 0.000 0.028
#> GSM35489 2 0.2589 0.7199 0.000 0.884 0.000 0.116
#> GSM35492 1 0.2002 0.8321 0.936 0.000 0.020 0.044
#> GSM35495 3 0.2647 0.7811 0.000 0.000 0.880 0.120
#> GSM35499 4 0.4647 0.5221 0.000 0.288 0.008 0.704
#> GSM35502 1 0.1211 0.8696 0.960 0.000 0.000 0.040
#> GSM35505 3 0.3037 0.7637 0.076 0.000 0.888 0.036
#> GSM35507 4 0.4440 0.6718 0.136 0.060 0.000 0.804
#> GSM35510 4 0.4991 0.3777 0.000 0.388 0.004 0.608
#> GSM35514 1 0.0817 0.8677 0.976 0.000 0.000 0.024
#> GSM35517 2 0.1474 0.7688 0.000 0.948 0.000 0.052
#> GSM35520 2 0.3056 0.7225 0.000 0.888 0.072 0.040
#> GSM35523 4 0.2662 0.6505 0.084 0.000 0.016 0.900
#> GSM35529 2 0.4040 0.5445 0.000 0.752 0.000 0.248
#> GSM35531 2 0.0844 0.7750 0.004 0.980 0.012 0.004
#> GSM35534 2 0.0000 0.7796 0.000 1.000 0.000 0.000
#> GSM35536 1 0.0000 0.8677 1.000 0.000 0.000 0.000
#> GSM35538 1 0.2281 0.8549 0.904 0.000 0.000 0.096
#> GSM35539 1 0.4584 0.6555 0.696 0.000 0.004 0.300
#> GSM35540 4 0.6968 0.3079 0.000 0.392 0.116 0.492
#> GSM35541 2 0.2760 0.7046 0.000 0.872 0.000 0.128
#> GSM35442 1 0.5848 0.3263 0.616 0.000 0.336 0.048
#> GSM35447 3 0.4830 0.7184 0.124 0.024 0.804 0.048
#> GSM35450 1 0.3764 0.7670 0.784 0.000 0.000 0.216
#> GSM35453 1 0.4171 0.7943 0.824 0.000 0.116 0.060
#> GSM35456 4 0.3743 0.6431 0.160 0.016 0.000 0.824
#> GSM35464 4 0.5062 0.5485 0.024 0.284 0.000 0.692
#> GSM35467 1 0.0707 0.8667 0.980 0.000 0.000 0.020
#> GSM35470 3 0.7188 0.3902 0.204 0.000 0.552 0.244
#> GSM35479 3 0.3710 0.7460 0.004 0.000 0.804 0.192
#> GSM35484 1 0.1118 0.8690 0.964 0.000 0.000 0.036
#> GSM35488 1 0.0592 0.8708 0.984 0.000 0.000 0.016
#> GSM35491 1 0.0592 0.8623 0.984 0.000 0.000 0.016
#> GSM35494 3 0.3257 0.7701 0.004 0.000 0.844 0.152
#> GSM35498 4 0.3768 0.6189 0.184 0.008 0.000 0.808
#> GSM35501 1 0.1557 0.8667 0.944 0.000 0.000 0.056
#> GSM35509 3 0.3528 0.7489 0.000 0.000 0.808 0.192
#> GSM35513 1 0.0817 0.8653 0.976 0.000 0.000 0.024
#> GSM35516 2 0.4776 0.2365 0.000 0.624 0.000 0.376
#> GSM35522 4 0.2088 0.6585 0.064 0.004 0.004 0.928
#> GSM35525 1 0.3306 0.8190 0.840 0.000 0.004 0.156
#> GSM35528 1 0.3172 0.8183 0.840 0.000 0.000 0.160
#> GSM35533 1 0.2345 0.8541 0.900 0.000 0.000 0.100
#> GSM35537 4 0.7031 0.1612 0.152 0.000 0.296 0.552
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM35441 5 0.3151 0.6875 0.000 0.020 0.000 0.144 0.836
#> GSM35446 3 0.2676 0.7372 0.000 0.080 0.884 0.000 0.036
#> GSM35449 5 0.3300 0.6538 0.000 0.004 0.000 0.204 0.792
#> GSM35455 5 0.3016 0.6905 0.000 0.020 0.000 0.132 0.848
#> GSM35458 5 0.2429 0.6564 0.076 0.004 0.020 0.000 0.900
#> GSM35460 3 0.2228 0.7403 0.000 0.076 0.908 0.004 0.012
#> GSM35461 3 0.6874 0.2938 0.332 0.000 0.460 0.016 0.192
#> GSM35463 2 0.3085 0.6958 0.000 0.852 0.000 0.032 0.116
#> GSM35472 3 0.2605 0.7007 0.000 0.000 0.852 0.000 0.148
#> GSM35475 5 0.3275 0.6324 0.068 0.008 0.064 0.000 0.860
#> GSM35483 2 0.3957 0.6696 0.000 0.712 0.000 0.008 0.280
#> GSM35496 3 0.2012 0.7337 0.000 0.000 0.920 0.020 0.060
#> GSM35497 5 0.2411 0.7011 0.000 0.008 0.000 0.108 0.884
#> GSM35504 2 0.5104 0.6782 0.000 0.748 0.044 0.084 0.124
#> GSM35508 5 0.2450 0.6986 0.000 0.000 0.028 0.076 0.896
#> GSM35511 5 0.3489 0.5345 0.004 0.004 0.208 0.000 0.784
#> GSM35512 3 0.3719 0.6621 0.012 0.004 0.776 0.000 0.208
#> GSM35515 5 0.2670 0.6498 0.080 0.004 0.028 0.000 0.888
#> GSM35519 5 0.5053 0.2993 0.048 0.004 0.304 0.000 0.644
#> GSM35527 5 0.2389 0.7005 0.000 0.000 0.004 0.116 0.880
#> GSM35532 3 0.4306 0.1707 0.000 0.000 0.508 0.000 0.492
#> GSM35439 5 0.4238 0.5454 0.004 0.228 0.000 0.028 0.740
#> GSM35443 1 0.2842 0.7748 0.888 0.000 0.044 0.012 0.056
#> GSM35445 1 0.5079 0.6416 0.700 0.232 0.028 0.040 0.000
#> GSM35448 2 0.4292 0.3055 0.000 0.704 0.272 0.000 0.024
#> GSM35451 4 0.5019 0.0523 0.436 0.032 0.000 0.532 0.000
#> GSM35454 3 0.5111 0.4242 0.000 0.408 0.552 0.040 0.000
#> GSM35457 4 0.4803 -0.0648 0.000 0.020 0.000 0.536 0.444
#> GSM35465 4 0.3081 0.5799 0.000 0.012 0.000 0.832 0.156
#> GSM35468 1 0.1503 0.8142 0.952 0.000 0.008 0.020 0.020
#> GSM35471 4 0.3584 0.6353 0.056 0.060 0.032 0.852 0.000
#> GSM35473 1 0.1278 0.8137 0.960 0.016 0.004 0.020 0.000
#> GSM35477 1 0.4152 0.5877 0.692 0.012 0.000 0.296 0.000
#> GSM35480 1 0.5406 0.6285 0.680 0.060 0.028 0.232 0.000
#> GSM35482 3 0.3004 0.7149 0.000 0.008 0.864 0.108 0.020
#> GSM35485 2 0.4387 0.5963 0.004 0.652 0.000 0.008 0.336
#> GSM35489 5 0.4887 0.5865 0.000 0.132 0.000 0.148 0.720
#> GSM35492 1 0.1787 0.8072 0.940 0.000 0.012 0.016 0.032
#> GSM35495 3 0.3229 0.7201 0.000 0.128 0.840 0.032 0.000
#> GSM35499 2 0.4701 0.5121 0.000 0.712 0.004 0.232 0.052
#> GSM35502 1 0.0880 0.8149 0.968 0.000 0.000 0.032 0.000
#> GSM35505 3 0.5024 0.4892 0.032 0.368 0.596 0.000 0.004
#> GSM35507 4 0.2125 0.6627 0.024 0.004 0.000 0.920 0.052
#> GSM35510 4 0.6495 -0.1222 0.000 0.328 0.000 0.468 0.204
#> GSM35514 1 0.0771 0.8128 0.976 0.004 0.000 0.000 0.020
#> GSM35517 5 0.4433 0.5679 0.000 0.200 0.000 0.060 0.740
#> GSM35520 5 0.2992 0.6518 0.008 0.072 0.044 0.000 0.876
#> GSM35523 4 0.2027 0.6695 0.040 0.000 0.008 0.928 0.024
#> GSM35529 5 0.4451 0.4673 0.000 0.016 0.000 0.340 0.644
#> GSM35531 5 0.5711 -0.2395 0.032 0.468 0.020 0.004 0.476
#> GSM35534 2 0.4003 0.6600 0.008 0.704 0.000 0.000 0.288
#> GSM35536 1 0.0727 0.8171 0.980 0.000 0.004 0.012 0.004
#> GSM35538 1 0.2648 0.7580 0.848 0.000 0.000 0.152 0.000
#> GSM35539 4 0.4688 -0.0831 0.456 0.008 0.004 0.532 0.000
#> GSM35540 4 0.4837 0.5258 0.000 0.016 0.076 0.744 0.164
#> GSM35541 5 0.4863 0.4403 0.000 0.272 0.000 0.056 0.672
#> GSM35442 1 0.5434 0.4517 0.644 0.000 0.276 0.012 0.068
#> GSM35447 3 0.6165 0.6080 0.100 0.196 0.648 0.000 0.056
#> GSM35450 1 0.3578 0.7053 0.784 0.008 0.004 0.204 0.000
#> GSM35453 1 0.4044 0.7302 0.804 0.028 0.140 0.028 0.000
#> GSM35456 4 0.5611 0.4998 0.152 0.212 0.000 0.636 0.000
#> GSM35464 4 0.2511 0.6376 0.004 0.016 0.000 0.892 0.088
#> GSM35467 1 0.0566 0.8144 0.984 0.004 0.000 0.000 0.012
#> GSM35470 4 0.6253 0.2327 0.136 0.004 0.356 0.504 0.000
#> GSM35479 3 0.3691 0.6647 0.000 0.040 0.804 0.156 0.000
#> GSM35484 1 0.2516 0.7492 0.860 0.140 0.000 0.000 0.000
#> GSM35488 1 0.1443 0.8140 0.948 0.000 0.004 0.044 0.004
#> GSM35491 1 0.1186 0.8162 0.964 0.000 0.008 0.020 0.008
#> GSM35494 3 0.2450 0.7312 0.000 0.048 0.900 0.052 0.000
#> GSM35498 4 0.1914 0.6680 0.060 0.000 0.000 0.924 0.016
#> GSM35501 1 0.0703 0.8152 0.976 0.000 0.000 0.024 0.000
#> GSM35509 3 0.3051 0.7229 0.000 0.076 0.864 0.060 0.000
#> GSM35513 1 0.0693 0.8138 0.980 0.008 0.000 0.000 0.012
#> GSM35516 2 0.5617 0.5568 0.008 0.592 0.000 0.072 0.328
#> GSM35522 4 0.1750 0.6675 0.028 0.000 0.000 0.936 0.036
#> GSM35525 1 0.4283 0.6071 0.692 0.004 0.012 0.292 0.000
#> GSM35528 1 0.4802 0.1306 0.504 0.000 0.004 0.480 0.012
#> GSM35533 1 0.5426 0.2781 0.496 0.456 0.008 0.040 0.000
#> GSM35537 4 0.5029 0.5302 0.080 0.008 0.204 0.708 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM35441 5 0.4905 0.58449 0.000 0.080 0.000 0.200 0.692 0.028
#> GSM35446 3 0.3240 0.71073 0.000 0.056 0.840 0.000 0.012 0.092
#> GSM35449 5 0.4695 0.42418 0.000 0.016 0.000 0.336 0.616 0.032
#> GSM35455 5 0.2622 0.68140 0.000 0.024 0.000 0.104 0.868 0.004
#> GSM35458 5 0.2793 0.66710 0.044 0.020 0.000 0.000 0.876 0.060
#> GSM35460 3 0.1793 0.74497 0.000 0.032 0.928 0.000 0.004 0.036
#> GSM35461 6 0.4624 0.54628 0.044 0.000 0.124 0.004 0.076 0.752
#> GSM35463 2 0.2716 0.53545 0.000 0.868 0.000 0.028 0.096 0.008
#> GSM35472 3 0.4434 0.07985 0.000 0.000 0.544 0.000 0.028 0.428
#> GSM35475 5 0.4289 0.46753 0.012 0.004 0.008 0.000 0.636 0.340
#> GSM35483 2 0.4539 0.41562 0.000 0.644 0.004 0.000 0.304 0.048
#> GSM35496 3 0.2963 0.66131 0.000 0.004 0.828 0.000 0.016 0.152
#> GSM35497 5 0.2255 0.69053 0.000 0.004 0.000 0.088 0.892 0.016
#> GSM35504 2 0.6690 0.37372 0.000 0.476 0.296 0.016 0.180 0.032
#> GSM35508 5 0.2596 0.68080 0.000 0.016 0.008 0.024 0.892 0.060
#> GSM35511 5 0.3898 0.62609 0.000 0.012 0.060 0.000 0.780 0.148
#> GSM35512 6 0.4396 0.29628 0.000 0.000 0.352 0.000 0.036 0.612
#> GSM35515 5 0.2614 0.66953 0.044 0.012 0.000 0.000 0.884 0.060
#> GSM35519 6 0.4528 0.48395 0.000 0.004 0.132 0.000 0.148 0.716
#> GSM35527 5 0.3266 0.67661 0.000 0.016 0.004 0.096 0.844 0.040
#> GSM35532 5 0.5725 0.25300 0.000 0.000 0.280 0.000 0.512 0.208
#> GSM35439 5 0.3699 0.58532 0.012 0.176 0.000 0.000 0.780 0.032
#> GSM35443 6 0.3303 0.53863 0.212 0.000 0.004 0.004 0.004 0.776
#> GSM35445 1 0.4926 0.57842 0.656 0.268 0.012 0.008 0.000 0.056
#> GSM35448 2 0.5524 0.17168 0.000 0.532 0.372 0.000 0.064 0.032
#> GSM35451 4 0.3931 0.64887 0.088 0.052 0.000 0.804 0.000 0.056
#> GSM35454 3 0.5342 0.30502 0.012 0.396 0.516 0.000 0.000 0.076
#> GSM35457 4 0.4093 0.54601 0.000 0.056 0.000 0.736 0.204 0.004
#> GSM35465 4 0.1621 0.71057 0.000 0.008 0.004 0.936 0.048 0.004
#> GSM35468 1 0.3081 0.64594 0.776 0.000 0.000 0.000 0.004 0.220
#> GSM35471 4 0.2875 0.69887 0.052 0.032 0.028 0.880 0.000 0.008
#> GSM35473 1 0.1562 0.77246 0.940 0.024 0.000 0.000 0.004 0.032
#> GSM35477 4 0.5497 0.46320 0.204 0.024 0.000 0.628 0.000 0.144
#> GSM35480 1 0.3288 0.73770 0.860 0.028 0.036 0.020 0.000 0.056
#> GSM35482 3 0.2525 0.73547 0.004 0.012 0.904 0.028 0.016 0.036
#> GSM35485 2 0.4002 0.39384 0.000 0.660 0.000 0.000 0.320 0.020
#> GSM35489 4 0.7121 0.15967 0.000 0.208 0.000 0.464 0.164 0.164
#> GSM35492 6 0.3850 0.34314 0.340 0.004 0.000 0.004 0.000 0.652
#> GSM35495 3 0.2058 0.73911 0.000 0.036 0.908 0.000 0.000 0.056
#> GSM35499 2 0.4517 -0.05120 0.000 0.528 0.000 0.444 0.024 0.004
#> GSM35502 1 0.0964 0.77116 0.968 0.004 0.000 0.000 0.012 0.016
#> GSM35505 6 0.5373 0.40825 0.004 0.152 0.248 0.000 0.000 0.596
#> GSM35507 4 0.0717 0.72142 0.000 0.000 0.000 0.976 0.016 0.008
#> GSM35510 4 0.5426 0.30266 0.000 0.312 0.008 0.576 0.100 0.004
#> GSM35514 1 0.1974 0.76938 0.920 0.012 0.000 0.000 0.020 0.048
#> GSM35517 5 0.3837 0.60395 0.000 0.180 0.000 0.044 0.768 0.008
#> GSM35520 5 0.5161 0.52345 0.000 0.112 0.012 0.000 0.640 0.236
#> GSM35523 4 0.4094 0.65857 0.100 0.020 0.056 0.804 0.016 0.004
#> GSM35529 5 0.4593 0.43801 0.000 0.040 0.000 0.352 0.604 0.004
#> GSM35531 6 0.5912 0.16322 0.004 0.292 0.000 0.060 0.072 0.572
#> GSM35534 2 0.4234 0.37763 0.000 0.644 0.000 0.000 0.324 0.032
#> GSM35536 1 0.1732 0.76207 0.920 0.004 0.000 0.004 0.000 0.072
#> GSM35538 1 0.3967 0.70858 0.776 0.008 0.000 0.084 0.000 0.132
#> GSM35539 1 0.3462 0.67810 0.792 0.004 0.016 0.180 0.000 0.008
#> GSM35540 4 0.3834 0.65872 0.000 0.020 0.116 0.804 0.056 0.004
#> GSM35541 5 0.4488 0.41073 0.000 0.304 0.000 0.012 0.652 0.032
#> GSM35442 6 0.5596 0.51948 0.228 0.000 0.164 0.004 0.008 0.596
#> GSM35447 6 0.6113 0.19522 0.008 0.184 0.340 0.000 0.004 0.464
#> GSM35450 1 0.4988 0.63757 0.688 0.024 0.000 0.184 0.000 0.104
#> GSM35453 1 0.1887 0.76261 0.924 0.016 0.048 0.000 0.000 0.012
#> GSM35456 1 0.7070 0.25771 0.448 0.196 0.004 0.264 0.000 0.088
#> GSM35464 4 0.0862 0.71986 0.000 0.008 0.000 0.972 0.016 0.004
#> GSM35467 1 0.1692 0.77067 0.932 0.008 0.000 0.000 0.012 0.048
#> GSM35470 3 0.5888 0.33428 0.264 0.008 0.568 0.148 0.004 0.008
#> GSM35479 3 0.2193 0.72285 0.036 0.004 0.916 0.032 0.004 0.008
#> GSM35484 1 0.6137 0.24134 0.424 0.312 0.000 0.004 0.000 0.260
#> GSM35488 1 0.3571 0.65082 0.760 0.004 0.000 0.020 0.000 0.216
#> GSM35491 6 0.4550 0.00583 0.448 0.008 0.000 0.020 0.000 0.524
#> GSM35494 3 0.2050 0.72471 0.048 0.008 0.920 0.012 0.000 0.012
#> GSM35498 4 0.1026 0.72130 0.008 0.008 0.012 0.968 0.000 0.004
#> GSM35501 1 0.0653 0.77125 0.980 0.004 0.000 0.000 0.004 0.012
#> GSM35509 3 0.0964 0.74794 0.000 0.004 0.968 0.012 0.000 0.016
#> GSM35513 1 0.2282 0.76639 0.900 0.020 0.000 0.000 0.012 0.068
#> GSM35516 2 0.5382 0.28415 0.000 0.612 0.000 0.284 0.060 0.044
#> GSM35522 4 0.3227 0.69454 0.060 0.016 0.040 0.864 0.016 0.004
#> GSM35525 1 0.2210 0.74884 0.908 0.004 0.016 0.064 0.004 0.004
#> GSM35528 4 0.4815 -0.00191 0.452 0.008 0.004 0.512 0.004 0.020
#> GSM35533 2 0.5370 -0.22668 0.420 0.492 0.000 0.012 0.000 0.076
#> GSM35537 1 0.6604 0.18140 0.468 0.012 0.300 0.200 0.008 0.012
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n time(p) k
#> SD:NMF 77 6.27e-07 2
#> SD:NMF 78 2.67e-05 3
#> SD:NMF 64 3.55e-04 4
#> SD:NMF 61 3.46e-04 5
#> SD:NMF 49 2.57e-03 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 7758 rows and 79 columns.
#> Top rows (776, 1552, 2328, 3103, 3879) are extracted by 'CV' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.622 0.838 0.901 0.4786 0.507 0.507
#> 3 3 0.671 0.747 0.872 0.1817 0.962 0.926
#> 4 4 0.697 0.754 0.869 0.1033 0.886 0.763
#> 5 5 0.638 0.702 0.842 0.1268 0.940 0.840
#> 6 6 0.621 0.652 0.826 0.0413 0.993 0.978
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
#> GSM35441 2 0.3879 0.9430 0.076 0.924
#> GSM35446 2 0.6247 0.8306 0.156 0.844
#> GSM35449 2 0.3733 0.9429 0.072 0.928
#> GSM35455 2 0.3733 0.9429 0.072 0.928
#> GSM35458 2 0.6148 0.8750 0.152 0.848
#> GSM35460 2 0.6247 0.8306 0.156 0.844
#> GSM35461 1 0.9993 0.0984 0.516 0.484
#> GSM35463 2 0.3431 0.9410 0.064 0.936
#> GSM35472 1 0.9983 0.1195 0.524 0.476
#> GSM35475 2 0.3114 0.9263 0.056 0.944
#> GSM35483 2 0.3584 0.9414 0.068 0.932
#> GSM35496 1 0.3584 0.8542 0.932 0.068
#> GSM35497 2 0.3733 0.9429 0.072 0.928
#> GSM35504 2 0.3733 0.9420 0.072 0.928
#> GSM35508 2 0.2948 0.9311 0.052 0.948
#> GSM35511 2 0.3114 0.9263 0.056 0.944
#> GSM35512 1 0.9998 0.0666 0.508 0.492
#> GSM35515 2 0.6148 0.8750 0.152 0.848
#> GSM35519 1 0.9998 0.0666 0.508 0.492
#> GSM35527 2 0.2948 0.9311 0.052 0.948
#> GSM35532 2 0.3431 0.9196 0.064 0.936
#> GSM35439 2 0.3584 0.9414 0.068 0.932
#> GSM35443 1 0.1633 0.8959 0.976 0.024
#> GSM35445 1 0.0938 0.8989 0.988 0.012
#> GSM35448 2 0.6531 0.8596 0.168 0.832
#> GSM35451 1 0.1843 0.8971 0.972 0.028
#> GSM35454 1 0.1414 0.8916 0.980 0.020
#> GSM35457 2 0.4022 0.9425 0.080 0.920
#> GSM35465 2 0.6973 0.8483 0.188 0.812
#> GSM35468 1 0.1184 0.9001 0.984 0.016
#> GSM35471 1 0.4161 0.8600 0.916 0.084
#> GSM35473 1 0.0938 0.8989 0.988 0.012
#> GSM35477 1 0.1843 0.8971 0.972 0.028
#> GSM35480 1 0.0938 0.8989 0.988 0.012
#> GSM35482 1 0.3114 0.8700 0.944 0.056
#> GSM35485 2 0.3584 0.9414 0.068 0.932
#> GSM35489 2 0.4022 0.9412 0.080 0.920
#> GSM35492 1 0.1184 0.9001 0.984 0.016
#> GSM35495 2 0.8955 0.5473 0.312 0.688
#> GSM35499 2 0.4022 0.9414 0.080 0.920
#> GSM35502 1 0.1184 0.9001 0.984 0.016
#> GSM35505 1 0.1414 0.8916 0.980 0.020
#> GSM35507 1 0.9087 0.5239 0.676 0.324
#> GSM35510 2 0.3733 0.9429 0.072 0.928
#> GSM35514 1 0.1184 0.9001 0.984 0.016
#> GSM35517 2 0.3733 0.9424 0.072 0.928
#> GSM35520 2 0.4161 0.9397 0.084 0.916
#> GSM35523 1 0.3733 0.8703 0.928 0.072
#> GSM35529 2 0.4022 0.9425 0.080 0.920
#> GSM35531 2 0.4022 0.9412 0.080 0.920
#> GSM35534 2 0.3431 0.9410 0.064 0.936
#> GSM35536 1 0.1184 0.9001 0.984 0.016
#> GSM35538 1 0.1184 0.9001 0.984 0.016
#> GSM35539 1 0.1184 0.9001 0.984 0.016
#> GSM35540 2 0.6887 0.8538 0.184 0.816
#> GSM35541 2 0.3584 0.9414 0.068 0.932
#> GSM35442 1 0.1633 0.8959 0.976 0.024
#> GSM35447 1 0.1843 0.8904 0.972 0.028
#> GSM35450 1 0.1184 0.9001 0.984 0.016
#> GSM35453 1 0.0376 0.8961 0.996 0.004
#> GSM35456 1 0.4298 0.8614 0.912 0.088
#> GSM35464 1 0.9552 0.4026 0.624 0.376
#> GSM35467 1 0.1184 0.9001 0.984 0.016
#> GSM35470 1 0.1633 0.8921 0.976 0.024
#> GSM35479 1 0.3733 0.8542 0.928 0.072
#> GSM35484 1 0.1414 0.8991 0.980 0.020
#> GSM35488 1 0.1184 0.9001 0.984 0.016
#> GSM35491 1 0.1184 0.9001 0.984 0.016
#> GSM35494 1 0.3733 0.8542 0.928 0.072
#> GSM35498 1 0.9552 0.4026 0.624 0.376
#> GSM35501 1 0.1184 0.9001 0.984 0.016
#> GSM35509 1 0.8327 0.6798 0.736 0.264
#> GSM35513 1 0.1184 0.9001 0.984 0.016
#> GSM35516 2 0.4161 0.9403 0.084 0.916
#> GSM35522 1 0.3733 0.8703 0.928 0.072
#> GSM35525 1 0.1184 0.9001 0.984 0.016
#> GSM35528 1 0.1184 0.9001 0.984 0.016
#> GSM35533 1 0.1414 0.8991 0.980 0.020
#> GSM35537 1 0.3274 0.8793 0.940 0.060
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM35441 2 0.1765 0.820 0.040 0.956 0.004
#> GSM35446 3 0.0747 0.882 0.000 0.016 0.984
#> GSM35449 2 0.2297 0.819 0.036 0.944 0.020
#> GSM35455 2 0.2297 0.819 0.036 0.944 0.020
#> GSM35458 2 0.8765 0.325 0.116 0.504 0.380
#> GSM35460 3 0.0747 0.882 0.000 0.016 0.984
#> GSM35461 1 0.9306 0.161 0.480 0.348 0.172
#> GSM35463 2 0.3846 0.758 0.016 0.876 0.108
#> GSM35472 1 0.9306 0.168 0.488 0.336 0.176
#> GSM35475 2 0.6647 0.451 0.012 0.592 0.396
#> GSM35483 2 0.3910 0.760 0.020 0.876 0.104
#> GSM35496 1 0.3272 0.828 0.904 0.016 0.080
#> GSM35497 2 0.2297 0.819 0.036 0.944 0.020
#> GSM35504 2 0.5335 0.675 0.008 0.760 0.232
#> GSM35508 2 0.6737 0.477 0.016 0.600 0.384
#> GSM35511 2 0.6661 0.444 0.012 0.588 0.400
#> GSM35512 1 0.9379 0.142 0.472 0.348 0.180
#> GSM35515 2 0.8765 0.325 0.116 0.504 0.380
#> GSM35519 1 0.9379 0.142 0.472 0.348 0.180
#> GSM35527 2 0.6737 0.477 0.016 0.600 0.384
#> GSM35532 2 0.6924 0.418 0.020 0.580 0.400
#> GSM35439 2 0.1525 0.818 0.032 0.964 0.004
#> GSM35443 1 0.1170 0.875 0.976 0.016 0.008
#> GSM35445 1 0.0829 0.880 0.984 0.004 0.012
#> GSM35448 3 0.2682 0.832 0.004 0.076 0.920
#> GSM35451 1 0.0892 0.879 0.980 0.020 0.000
#> GSM35454 1 0.1411 0.869 0.964 0.000 0.036
#> GSM35457 2 0.2063 0.820 0.044 0.948 0.008
#> GSM35465 2 0.3879 0.716 0.152 0.848 0.000
#> GSM35468 1 0.0424 0.882 0.992 0.008 0.000
#> GSM35471 1 0.2537 0.838 0.920 0.080 0.000
#> GSM35473 1 0.0829 0.880 0.984 0.004 0.012
#> GSM35477 1 0.0892 0.879 0.980 0.020 0.000
#> GSM35480 1 0.0237 0.881 0.996 0.004 0.000
#> GSM35482 1 0.2773 0.850 0.928 0.024 0.048
#> GSM35485 2 0.2031 0.817 0.032 0.952 0.016
#> GSM35489 2 0.1878 0.819 0.044 0.952 0.004
#> GSM35492 1 0.0424 0.882 0.992 0.008 0.000
#> GSM35495 3 0.5292 0.727 0.172 0.028 0.800
#> GSM35499 2 0.1878 0.818 0.044 0.952 0.004
#> GSM35502 1 0.0424 0.882 0.992 0.008 0.000
#> GSM35505 1 0.1411 0.869 0.964 0.000 0.036
#> GSM35507 1 0.5859 0.494 0.656 0.344 0.000
#> GSM35510 2 0.1647 0.819 0.036 0.960 0.004
#> GSM35514 1 0.0424 0.882 0.992 0.008 0.000
#> GSM35517 2 0.1765 0.821 0.040 0.956 0.004
#> GSM35520 2 0.6007 0.705 0.044 0.764 0.192
#> GSM35523 1 0.2165 0.853 0.936 0.064 0.000
#> GSM35529 2 0.2063 0.820 0.044 0.948 0.008
#> GSM35531 2 0.1878 0.819 0.044 0.952 0.004
#> GSM35534 2 0.3461 0.785 0.024 0.900 0.076
#> GSM35536 1 0.0424 0.882 0.992 0.008 0.000
#> GSM35538 1 0.0424 0.882 0.992 0.008 0.000
#> GSM35539 1 0.0424 0.882 0.992 0.008 0.000
#> GSM35540 2 0.4047 0.719 0.148 0.848 0.004
#> GSM35541 2 0.1525 0.818 0.032 0.964 0.004
#> GSM35442 1 0.1170 0.875 0.976 0.016 0.008
#> GSM35447 1 0.1765 0.868 0.956 0.004 0.040
#> GSM35450 1 0.0424 0.882 0.992 0.008 0.000
#> GSM35453 1 0.0892 0.876 0.980 0.000 0.020
#> GSM35456 1 0.2537 0.844 0.920 0.080 0.000
#> GSM35464 1 0.6111 0.375 0.604 0.396 0.000
#> GSM35467 1 0.0424 0.882 0.992 0.008 0.000
#> GSM35470 1 0.1482 0.871 0.968 0.020 0.012
#> GSM35479 1 0.3445 0.822 0.896 0.016 0.088
#> GSM35484 1 0.0661 0.881 0.988 0.008 0.004
#> GSM35488 1 0.0424 0.882 0.992 0.008 0.000
#> GSM35491 1 0.0424 0.882 0.992 0.008 0.000
#> GSM35494 1 0.3359 0.825 0.900 0.016 0.084
#> GSM35498 1 0.6111 0.375 0.604 0.396 0.000
#> GSM35501 1 0.0424 0.882 0.992 0.008 0.000
#> GSM35509 1 0.6629 0.421 0.624 0.016 0.360
#> GSM35513 1 0.0424 0.882 0.992 0.008 0.000
#> GSM35516 2 0.1860 0.818 0.052 0.948 0.000
#> GSM35522 1 0.2165 0.853 0.936 0.064 0.000
#> GSM35525 1 0.0424 0.882 0.992 0.008 0.000
#> GSM35528 1 0.0424 0.882 0.992 0.008 0.000
#> GSM35533 1 0.0661 0.881 0.988 0.008 0.004
#> GSM35537 1 0.1860 0.862 0.948 0.052 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM35441 2 0.3893 0.745 0.008 0.796 0.196 0.000
#> GSM35446 4 0.1004 0.878 0.000 0.004 0.024 0.972
#> GSM35449 2 0.4977 0.385 0.000 0.540 0.460 0.000
#> GSM35455 2 0.4977 0.385 0.000 0.540 0.460 0.000
#> GSM35458 3 0.4224 0.562 0.100 0.076 0.824 0.000
#> GSM35460 4 0.1004 0.878 0.000 0.004 0.024 0.972
#> GSM35461 3 0.5976 0.339 0.452 0.024 0.516 0.008
#> GSM35463 2 0.3486 0.729 0.000 0.864 0.044 0.092
#> GSM35472 3 0.6096 0.318 0.460 0.024 0.504 0.012
#> GSM35475 3 0.1940 0.559 0.000 0.076 0.924 0.000
#> GSM35483 2 0.3734 0.728 0.004 0.856 0.044 0.096
#> GSM35496 1 0.3301 0.842 0.876 0.000 0.048 0.076
#> GSM35497 2 0.4967 0.399 0.000 0.548 0.452 0.000
#> GSM35504 2 0.5363 0.597 0.000 0.720 0.064 0.216
#> GSM35508 3 0.2921 0.538 0.000 0.140 0.860 0.000
#> GSM35511 3 0.2125 0.558 0.000 0.076 0.920 0.004
#> GSM35512 3 0.6082 0.358 0.444 0.024 0.520 0.012
#> GSM35515 3 0.4224 0.562 0.100 0.076 0.824 0.000
#> GSM35519 3 0.6082 0.358 0.444 0.024 0.520 0.012
#> GSM35527 3 0.2921 0.538 0.000 0.140 0.860 0.000
#> GSM35532 3 0.2234 0.556 0.004 0.064 0.924 0.008
#> GSM35439 2 0.0524 0.813 0.008 0.988 0.004 0.000
#> GSM35443 1 0.1305 0.904 0.960 0.000 0.036 0.004
#> GSM35445 1 0.0657 0.913 0.984 0.000 0.012 0.004
#> GSM35448 4 0.2089 0.840 0.000 0.048 0.020 0.932
#> GSM35451 1 0.0592 0.913 0.984 0.016 0.000 0.000
#> GSM35454 1 0.1510 0.903 0.956 0.000 0.016 0.028
#> GSM35457 2 0.3636 0.760 0.008 0.820 0.172 0.000
#> GSM35465 2 0.5121 0.690 0.116 0.764 0.120 0.000
#> GSM35468 1 0.0188 0.917 0.996 0.004 0.000 0.000
#> GSM35471 1 0.1940 0.866 0.924 0.076 0.000 0.000
#> GSM35473 1 0.0657 0.913 0.984 0.000 0.012 0.004
#> GSM35477 1 0.0592 0.913 0.984 0.016 0.000 0.000
#> GSM35480 1 0.0000 0.916 1.000 0.000 0.000 0.000
#> GSM35482 1 0.2759 0.869 0.904 0.000 0.052 0.044
#> GSM35485 2 0.0992 0.811 0.008 0.976 0.012 0.004
#> GSM35489 2 0.1042 0.815 0.020 0.972 0.008 0.000
#> GSM35492 1 0.0188 0.917 0.996 0.004 0.000 0.000
#> GSM35495 4 0.4485 0.674 0.152 0.000 0.052 0.796
#> GSM35499 2 0.1411 0.816 0.020 0.960 0.020 0.000
#> GSM35502 1 0.0188 0.917 0.996 0.004 0.000 0.000
#> GSM35505 1 0.1510 0.903 0.956 0.000 0.016 0.028
#> GSM35507 1 0.5925 0.408 0.648 0.284 0.068 0.000
#> GSM35510 2 0.1284 0.816 0.012 0.964 0.024 0.000
#> GSM35514 1 0.0188 0.917 0.996 0.004 0.000 0.000
#> GSM35517 2 0.1151 0.814 0.024 0.968 0.008 0.000
#> GSM35520 2 0.5184 0.579 0.024 0.672 0.304 0.000
#> GSM35523 1 0.2131 0.876 0.932 0.032 0.036 0.000
#> GSM35529 2 0.3636 0.760 0.008 0.820 0.172 0.000
#> GSM35531 2 0.1042 0.815 0.020 0.972 0.008 0.000
#> GSM35534 2 0.2443 0.771 0.000 0.916 0.024 0.060
#> GSM35536 1 0.0188 0.917 0.996 0.004 0.000 0.000
#> GSM35538 1 0.0188 0.917 0.996 0.004 0.000 0.000
#> GSM35539 1 0.0188 0.917 0.996 0.004 0.000 0.000
#> GSM35540 2 0.5266 0.684 0.108 0.752 0.140 0.000
#> GSM35541 2 0.0524 0.813 0.008 0.988 0.004 0.000
#> GSM35442 1 0.1305 0.904 0.960 0.000 0.036 0.004
#> GSM35447 1 0.1733 0.900 0.948 0.000 0.024 0.028
#> GSM35450 1 0.0188 0.917 0.996 0.004 0.000 0.000
#> GSM35453 1 0.1059 0.909 0.972 0.000 0.012 0.016
#> GSM35456 1 0.2334 0.856 0.908 0.088 0.004 0.000
#> GSM35464 1 0.6519 0.262 0.584 0.320 0.096 0.000
#> GSM35467 1 0.0188 0.917 0.996 0.004 0.000 0.000
#> GSM35470 1 0.1576 0.898 0.948 0.000 0.048 0.004
#> GSM35479 1 0.3439 0.834 0.868 0.000 0.048 0.084
#> GSM35484 1 0.0376 0.916 0.992 0.004 0.000 0.004
#> GSM35488 1 0.0188 0.917 0.996 0.004 0.000 0.000
#> GSM35491 1 0.0188 0.917 0.996 0.004 0.000 0.000
#> GSM35494 1 0.3370 0.838 0.872 0.000 0.048 0.080
#> GSM35498 1 0.6519 0.262 0.584 0.320 0.096 0.000
#> GSM35501 1 0.0188 0.917 0.996 0.004 0.000 0.000
#> GSM35509 1 0.5855 0.398 0.600 0.000 0.044 0.356
#> GSM35513 1 0.0188 0.917 0.996 0.004 0.000 0.000
#> GSM35516 2 0.1452 0.810 0.036 0.956 0.008 0.000
#> GSM35522 1 0.2131 0.876 0.932 0.032 0.036 0.000
#> GSM35525 1 0.0188 0.917 0.996 0.004 0.000 0.000
#> GSM35528 1 0.0188 0.917 0.996 0.004 0.000 0.000
#> GSM35533 1 0.0376 0.916 0.992 0.004 0.000 0.004
#> GSM35537 1 0.1837 0.888 0.944 0.028 0.028 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM35441 2 0.3565 0.744 0.000 0.800 0.024 0.000 0.176
#> GSM35446 4 0.1608 0.894 0.000 0.000 0.072 0.928 0.000
#> GSM35449 2 0.4655 0.318 0.000 0.512 0.012 0.000 0.476
#> GSM35455 2 0.4653 0.326 0.000 0.516 0.012 0.000 0.472
#> GSM35458 5 0.2965 0.660 0.084 0.028 0.012 0.000 0.876
#> GSM35460 4 0.1608 0.894 0.000 0.000 0.072 0.928 0.000
#> GSM35461 5 0.6349 0.343 0.212 0.000 0.268 0.000 0.520
#> GSM35463 2 0.4214 0.696 0.000 0.788 0.088 0.120 0.004
#> GSM35472 5 0.6380 0.326 0.204 0.000 0.288 0.000 0.508
#> GSM35475 5 0.0404 0.666 0.000 0.012 0.000 0.000 0.988
#> GSM35483 2 0.4519 0.676 0.000 0.764 0.120 0.112 0.004
#> GSM35496 3 0.2970 0.819 0.168 0.000 0.828 0.000 0.004
#> GSM35497 2 0.4641 0.357 0.000 0.532 0.012 0.000 0.456
#> GSM35504 2 0.5724 0.527 0.000 0.640 0.076 0.260 0.024
#> GSM35508 5 0.2077 0.640 0.000 0.084 0.008 0.000 0.908
#> GSM35511 5 0.0566 0.666 0.000 0.012 0.004 0.000 0.984
#> GSM35512 5 0.6319 0.357 0.204 0.000 0.272 0.000 0.524
#> GSM35515 5 0.2965 0.660 0.084 0.028 0.012 0.000 0.876
#> GSM35519 5 0.6319 0.357 0.204 0.000 0.272 0.000 0.524
#> GSM35527 5 0.2077 0.640 0.000 0.084 0.008 0.000 0.908
#> GSM35532 5 0.0798 0.666 0.000 0.008 0.016 0.000 0.976
#> GSM35439 2 0.0486 0.804 0.000 0.988 0.004 0.004 0.004
#> GSM35443 1 0.3496 0.717 0.788 0.000 0.200 0.000 0.012
#> GSM35445 1 0.2284 0.809 0.896 0.000 0.096 0.004 0.004
#> GSM35448 4 0.0162 0.852 0.000 0.000 0.004 0.996 0.000
#> GSM35451 1 0.0566 0.844 0.984 0.012 0.004 0.000 0.000
#> GSM35454 1 0.4305 0.541 0.688 0.000 0.296 0.004 0.012
#> GSM35457 2 0.3398 0.763 0.004 0.828 0.024 0.000 0.144
#> GSM35465 2 0.4810 0.724 0.056 0.776 0.080 0.000 0.088
#> GSM35468 1 0.1410 0.836 0.940 0.000 0.060 0.000 0.000
#> GSM35471 1 0.2172 0.802 0.908 0.076 0.016 0.000 0.000
#> GSM35473 1 0.2052 0.819 0.912 0.000 0.080 0.004 0.004
#> GSM35477 1 0.0566 0.844 0.984 0.012 0.004 0.000 0.000
#> GSM35480 1 0.0162 0.844 0.996 0.000 0.004 0.000 0.000
#> GSM35482 3 0.4456 0.642 0.320 0.000 0.660 0.000 0.020
#> GSM35485 2 0.0671 0.802 0.000 0.980 0.016 0.004 0.000
#> GSM35489 2 0.1016 0.806 0.012 0.972 0.004 0.004 0.008
#> GSM35492 1 0.1671 0.828 0.924 0.000 0.076 0.000 0.000
#> GSM35495 4 0.3970 0.692 0.020 0.000 0.236 0.744 0.000
#> GSM35499 2 0.0960 0.806 0.008 0.972 0.016 0.000 0.004
#> GSM35502 1 0.0162 0.844 0.996 0.000 0.004 0.000 0.000
#> GSM35505 1 0.4305 0.541 0.688 0.000 0.296 0.004 0.012
#> GSM35507 1 0.6229 0.348 0.588 0.292 0.080 0.000 0.040
#> GSM35510 2 0.0854 0.806 0.004 0.976 0.012 0.000 0.008
#> GSM35514 1 0.0000 0.843 1.000 0.000 0.000 0.000 0.000
#> GSM35517 2 0.0510 0.805 0.016 0.984 0.000 0.000 0.000
#> GSM35520 2 0.4280 0.555 0.008 0.676 0.004 0.000 0.312
#> GSM35523 1 0.3161 0.773 0.860 0.032 0.100 0.000 0.008
#> GSM35529 2 0.3398 0.763 0.004 0.828 0.024 0.000 0.144
#> GSM35531 2 0.1016 0.806 0.012 0.972 0.004 0.004 0.008
#> GSM35534 2 0.3033 0.754 0.000 0.864 0.052 0.084 0.000
#> GSM35536 1 0.0510 0.846 0.984 0.000 0.016 0.000 0.000
#> GSM35538 1 0.0404 0.844 0.988 0.000 0.012 0.000 0.000
#> GSM35539 1 0.0162 0.844 0.996 0.000 0.004 0.000 0.000
#> GSM35540 2 0.4972 0.719 0.044 0.760 0.088 0.000 0.108
#> GSM35541 2 0.0486 0.804 0.000 0.988 0.004 0.004 0.004
#> GSM35442 1 0.3628 0.695 0.772 0.000 0.216 0.000 0.012
#> GSM35447 1 0.4492 0.526 0.680 0.000 0.296 0.004 0.020
#> GSM35450 1 0.0162 0.844 0.996 0.000 0.004 0.000 0.000
#> GSM35453 1 0.2877 0.766 0.848 0.000 0.144 0.004 0.004
#> GSM35456 1 0.2170 0.793 0.904 0.088 0.004 0.000 0.004
#> GSM35464 1 0.6818 0.218 0.516 0.332 0.088 0.000 0.064
#> GSM35467 1 0.0162 0.844 0.996 0.000 0.004 0.000 0.000
#> GSM35470 1 0.4213 0.532 0.680 0.000 0.308 0.000 0.012
#> GSM35479 3 0.3250 0.818 0.168 0.000 0.820 0.008 0.004
#> GSM35484 1 0.1116 0.841 0.964 0.004 0.028 0.004 0.000
#> GSM35488 1 0.1197 0.841 0.952 0.000 0.048 0.000 0.000
#> GSM35491 1 0.1671 0.828 0.924 0.000 0.076 0.000 0.000
#> GSM35494 3 0.3128 0.819 0.168 0.000 0.824 0.004 0.004
#> GSM35498 1 0.6818 0.218 0.516 0.332 0.088 0.000 0.064
#> GSM35501 1 0.0162 0.844 0.996 0.000 0.004 0.000 0.000
#> GSM35509 3 0.5192 0.394 0.076 0.000 0.644 0.280 0.000
#> GSM35513 1 0.0162 0.844 0.996 0.000 0.004 0.000 0.000
#> GSM35516 2 0.0794 0.801 0.028 0.972 0.000 0.000 0.000
#> GSM35522 1 0.3161 0.773 0.860 0.032 0.100 0.000 0.008
#> GSM35525 1 0.0510 0.845 0.984 0.000 0.016 0.000 0.000
#> GSM35528 1 0.1197 0.841 0.952 0.000 0.048 0.000 0.000
#> GSM35533 1 0.1116 0.841 0.964 0.004 0.028 0.004 0.000
#> GSM35537 1 0.3023 0.782 0.868 0.028 0.096 0.000 0.008
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM35441 2 0.3332 0.6792 0.000 0.808 0.000 0.048 0.144 0.000
#> GSM35446 6 0.0937 0.8820 0.000 0.000 0.040 0.000 0.000 0.960
#> GSM35449 2 0.4705 0.3517 0.000 0.520 0.000 0.036 0.440 0.004
#> GSM35455 2 0.4701 0.3598 0.000 0.524 0.000 0.036 0.436 0.004
#> GSM35458 5 0.2770 0.6339 0.068 0.024 0.004 0.024 0.880 0.000
#> GSM35460 6 0.0937 0.8820 0.000 0.000 0.040 0.000 0.000 0.960
#> GSM35461 5 0.6274 0.3849 0.168 0.000 0.292 0.036 0.504 0.000
#> GSM35463 2 0.4076 0.0585 0.000 0.592 0.000 0.396 0.000 0.012
#> GSM35472 5 0.6270 0.3654 0.160 0.000 0.308 0.036 0.496 0.000
#> GSM35475 5 0.0260 0.6428 0.000 0.008 0.000 0.000 0.992 0.000
#> GSM35483 4 0.3012 0.0000 0.000 0.196 0.000 0.796 0.000 0.008
#> GSM35496 3 0.1528 0.8001 0.012 0.000 0.944 0.016 0.000 0.028
#> GSM35497 2 0.4682 0.3898 0.000 0.540 0.000 0.036 0.420 0.004
#> GSM35504 2 0.5988 -0.2613 0.000 0.488 0.000 0.340 0.016 0.156
#> GSM35508 5 0.2579 0.5858 0.000 0.088 0.000 0.032 0.876 0.004
#> GSM35511 5 0.0146 0.6427 0.000 0.004 0.000 0.000 0.996 0.000
#> GSM35512 5 0.6223 0.3930 0.160 0.000 0.292 0.036 0.512 0.000
#> GSM35515 5 0.2770 0.6339 0.068 0.024 0.004 0.024 0.880 0.000
#> GSM35519 5 0.6223 0.3930 0.160 0.000 0.292 0.036 0.512 0.000
#> GSM35527 5 0.2579 0.5858 0.000 0.088 0.000 0.032 0.876 0.004
#> GSM35532 5 0.0508 0.6428 0.000 0.000 0.012 0.004 0.984 0.000
#> GSM35439 2 0.0363 0.7219 0.000 0.988 0.000 0.012 0.000 0.000
#> GSM35443 1 0.3878 0.7082 0.736 0.000 0.228 0.032 0.004 0.000
#> GSM35445 1 0.2983 0.7880 0.832 0.000 0.136 0.032 0.000 0.000
#> GSM35448 6 0.1007 0.8208 0.000 0.000 0.000 0.044 0.000 0.956
#> GSM35451 1 0.0725 0.8369 0.976 0.012 0.000 0.012 0.000 0.000
#> GSM35454 1 0.5033 0.4746 0.572 0.000 0.364 0.052 0.008 0.004
#> GSM35457 2 0.3078 0.6963 0.000 0.836 0.000 0.056 0.108 0.000
#> GSM35465 2 0.4481 0.6484 0.032 0.784 0.040 0.092 0.052 0.000
#> GSM35468 1 0.2088 0.8209 0.904 0.000 0.068 0.028 0.000 0.000
#> GSM35471 1 0.2395 0.8079 0.892 0.076 0.012 0.020 0.000 0.000
#> GSM35473 1 0.2633 0.8066 0.864 0.000 0.104 0.032 0.000 0.000
#> GSM35477 1 0.0725 0.8369 0.976 0.012 0.000 0.012 0.000 0.000
#> GSM35480 1 0.0717 0.8359 0.976 0.000 0.008 0.016 0.000 0.000
#> GSM35482 3 0.3385 0.5703 0.172 0.000 0.796 0.028 0.004 0.000
#> GSM35485 2 0.0937 0.7133 0.000 0.960 0.000 0.040 0.000 0.000
#> GSM35489 2 0.1007 0.7224 0.008 0.968 0.004 0.016 0.004 0.000
#> GSM35492 1 0.2309 0.8129 0.888 0.000 0.084 0.028 0.000 0.000
#> GSM35495 6 0.3161 0.6920 0.000 0.000 0.216 0.008 0.000 0.776
#> GSM35499 2 0.1065 0.7241 0.008 0.964 0.008 0.020 0.000 0.000
#> GSM35502 1 0.0291 0.8365 0.992 0.000 0.004 0.004 0.000 0.000
#> GSM35505 1 0.5033 0.4746 0.572 0.000 0.364 0.052 0.008 0.004
#> GSM35507 1 0.6125 0.4189 0.564 0.296 0.040 0.076 0.024 0.000
#> GSM35510 2 0.0837 0.7245 0.004 0.972 0.004 0.020 0.000 0.000
#> GSM35514 1 0.0146 0.8356 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM35517 2 0.0717 0.7218 0.016 0.976 0.000 0.008 0.000 0.000
#> GSM35520 2 0.4052 0.4319 0.004 0.676 0.008 0.008 0.304 0.000
#> GSM35523 1 0.3504 0.7626 0.832 0.032 0.060 0.076 0.000 0.000
#> GSM35529 2 0.3078 0.6963 0.000 0.836 0.000 0.056 0.108 0.000
#> GSM35531 2 0.1007 0.7224 0.008 0.968 0.004 0.016 0.004 0.000
#> GSM35534 2 0.2980 0.5596 0.000 0.800 0.000 0.192 0.000 0.008
#> GSM35536 1 0.0820 0.8386 0.972 0.000 0.016 0.012 0.000 0.000
#> GSM35538 1 0.0622 0.8372 0.980 0.000 0.008 0.012 0.000 0.000
#> GSM35539 1 0.0405 0.8369 0.988 0.000 0.004 0.008 0.000 0.000
#> GSM35540 2 0.4664 0.6483 0.020 0.768 0.048 0.092 0.072 0.000
#> GSM35541 2 0.0458 0.7208 0.000 0.984 0.000 0.016 0.000 0.000
#> GSM35442 1 0.3979 0.6901 0.720 0.000 0.244 0.032 0.004 0.000
#> GSM35447 1 0.5206 0.4599 0.564 0.000 0.364 0.052 0.016 0.004
#> GSM35450 1 0.0363 0.8356 0.988 0.000 0.000 0.012 0.000 0.000
#> GSM35453 1 0.3621 0.7353 0.772 0.000 0.192 0.032 0.000 0.004
#> GSM35456 1 0.2432 0.8054 0.888 0.080 0.008 0.024 0.000 0.000
#> GSM35464 1 0.6694 0.2871 0.488 0.340 0.048 0.084 0.040 0.000
#> GSM35467 1 0.0291 0.8365 0.992 0.000 0.004 0.004 0.000 0.000
#> GSM35470 1 0.4495 0.4773 0.580 0.000 0.388 0.028 0.004 0.000
#> GSM35479 3 0.1750 0.7978 0.012 0.000 0.932 0.016 0.000 0.040
#> GSM35484 1 0.1793 0.8311 0.928 0.004 0.032 0.036 0.000 0.000
#> GSM35488 1 0.1845 0.8267 0.920 0.000 0.052 0.028 0.000 0.000
#> GSM35491 1 0.2309 0.8129 0.888 0.000 0.084 0.028 0.000 0.000
#> GSM35494 3 0.1605 0.8008 0.012 0.000 0.940 0.016 0.000 0.032
#> GSM35498 1 0.6694 0.2871 0.488 0.340 0.048 0.084 0.040 0.000
#> GSM35501 1 0.0405 0.8372 0.988 0.000 0.004 0.008 0.000 0.000
#> GSM35509 3 0.3707 0.4563 0.000 0.000 0.680 0.008 0.000 0.312
#> GSM35513 1 0.0291 0.8365 0.992 0.000 0.004 0.004 0.000 0.000
#> GSM35516 2 0.1074 0.7149 0.028 0.960 0.000 0.012 0.000 0.000
#> GSM35522 1 0.3504 0.7626 0.832 0.032 0.060 0.076 0.000 0.000
#> GSM35525 1 0.0603 0.8367 0.980 0.000 0.016 0.004 0.000 0.000
#> GSM35528 1 0.1845 0.8267 0.920 0.000 0.052 0.028 0.000 0.000
#> GSM35533 1 0.1793 0.8311 0.928 0.004 0.032 0.036 0.000 0.000
#> GSM35537 1 0.3378 0.7691 0.840 0.028 0.064 0.068 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 time(p) k
#> CV:hclust 73 2.65e-07 2
#> CV:hclust 64 1.94e-04 3
#> CV:hclust 68 1.68e-08 4
#> CV:hclust 68 7.03e-08 5
#> CV:hclust 60 1.25e-08 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 7758 rows and 79 columns.
#> Top rows (776, 1552, 2328, 3103, 3879) 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 0.514 0.898 0.914 0.4911 0.498 0.498
#> 3 3 1.000 0.969 0.979 0.3353 0.794 0.607
#> 4 4 0.743 0.775 0.851 0.1033 0.938 0.823
#> 5 5 0.672 0.598 0.762 0.0768 0.932 0.769
#> 6 6 0.664 0.466 0.713 0.0463 0.917 0.672
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
#> GSM35441 2 0.7299 0.903 0.204 0.796
#> GSM35446 2 0.0000 0.859 0.000 1.000
#> GSM35449 2 0.7299 0.903 0.204 0.796
#> GSM35455 2 0.7299 0.903 0.204 0.796
#> GSM35458 2 0.7219 0.904 0.200 0.800
#> GSM35460 2 0.0000 0.859 0.000 1.000
#> GSM35461 1 0.7056 0.826 0.808 0.192
#> GSM35463 2 0.6973 0.904 0.188 0.812
#> GSM35472 2 0.1414 0.859 0.020 0.980
#> GSM35475 2 0.2236 0.873 0.036 0.964
#> GSM35483 2 0.4022 0.888 0.080 0.920
#> GSM35496 1 0.7056 0.826 0.808 0.192
#> GSM35497 2 0.7299 0.903 0.204 0.796
#> GSM35504 2 0.0376 0.861 0.004 0.996
#> GSM35508 2 0.2236 0.873 0.036 0.964
#> GSM35511 2 0.0938 0.861 0.012 0.988
#> GSM35512 2 0.1414 0.859 0.020 0.980
#> GSM35515 2 0.6712 0.903 0.176 0.824
#> GSM35519 2 0.0938 0.861 0.012 0.988
#> GSM35527 2 0.2603 0.876 0.044 0.956
#> GSM35532 2 0.0938 0.861 0.012 0.988
#> GSM35439 2 0.7219 0.903 0.200 0.800
#> GSM35443 1 0.0000 0.935 1.000 0.000
#> GSM35445 1 0.2603 0.923 0.956 0.044
#> GSM35448 2 0.0000 0.859 0.000 1.000
#> GSM35451 1 0.0376 0.935 0.996 0.004
#> GSM35454 1 0.7219 0.828 0.800 0.200
#> GSM35457 2 0.7219 0.903 0.200 0.800
#> GSM35465 2 0.7219 0.903 0.200 0.800
#> GSM35468 1 0.0000 0.935 1.000 0.000
#> GSM35471 1 0.0672 0.933 0.992 0.008
#> GSM35473 1 0.2603 0.923 0.956 0.044
#> GSM35477 1 0.0376 0.935 0.996 0.004
#> GSM35480 1 0.1633 0.930 0.976 0.024
#> GSM35482 1 0.7139 0.827 0.804 0.196
#> GSM35485 2 0.7056 0.904 0.192 0.808
#> GSM35489 2 0.7219 0.903 0.200 0.800
#> GSM35492 1 0.0000 0.935 1.000 0.000
#> GSM35495 1 0.7299 0.825 0.796 0.204
#> GSM35499 2 0.7056 0.904 0.192 0.808
#> GSM35502 1 0.0000 0.935 1.000 0.000
#> GSM35505 1 0.7299 0.825 0.796 0.204
#> GSM35507 1 0.0376 0.935 0.996 0.004
#> GSM35510 2 0.7056 0.904 0.192 0.808
#> GSM35514 1 0.0000 0.935 1.000 0.000
#> GSM35517 2 0.7139 0.904 0.196 0.804
#> GSM35520 2 0.2236 0.875 0.036 0.964
#> GSM35523 1 0.0376 0.935 0.996 0.004
#> GSM35529 2 0.7219 0.903 0.200 0.800
#> GSM35531 2 0.7139 0.904 0.196 0.804
#> GSM35534 2 0.6973 0.904 0.188 0.812
#> GSM35536 1 0.0000 0.935 1.000 0.000
#> GSM35538 1 0.0000 0.935 1.000 0.000
#> GSM35539 1 0.0376 0.935 0.996 0.004
#> GSM35540 2 0.2603 0.877 0.044 0.956
#> GSM35541 2 0.7139 0.904 0.196 0.804
#> GSM35442 1 0.4815 0.887 0.896 0.104
#> GSM35447 1 0.7376 0.823 0.792 0.208
#> GSM35450 1 0.0376 0.935 0.996 0.004
#> GSM35453 1 0.4298 0.902 0.912 0.088
#> GSM35456 1 0.0938 0.932 0.988 0.012
#> GSM35464 2 0.7815 0.875 0.232 0.768
#> GSM35467 1 0.0000 0.935 1.000 0.000
#> GSM35470 1 0.2948 0.917 0.948 0.052
#> GSM35479 1 0.7299 0.825 0.796 0.204
#> GSM35484 1 0.0938 0.932 0.988 0.012
#> GSM35488 1 0.0000 0.935 1.000 0.000
#> GSM35491 1 0.0000 0.935 1.000 0.000
#> GSM35494 1 0.7299 0.825 0.796 0.204
#> GSM35498 1 0.0376 0.935 0.996 0.004
#> GSM35501 1 0.0000 0.935 1.000 0.000
#> GSM35509 1 0.7299 0.825 0.796 0.204
#> GSM35513 1 0.0000 0.935 1.000 0.000
#> GSM35516 2 0.7139 0.904 0.196 0.804
#> GSM35522 1 0.0376 0.935 0.996 0.004
#> GSM35525 1 0.0000 0.935 1.000 0.000
#> GSM35528 1 0.0000 0.935 1.000 0.000
#> GSM35533 1 0.0938 0.932 0.988 0.012
#> GSM35537 1 0.1414 0.931 0.980 0.020
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM35441 2 0.0424 0.981 0.000 0.992 0.008
#> GSM35446 3 0.0892 0.963 0.000 0.020 0.980
#> GSM35449 2 0.1031 0.976 0.000 0.976 0.024
#> GSM35455 2 0.0892 0.977 0.000 0.980 0.020
#> GSM35458 2 0.1031 0.976 0.000 0.976 0.024
#> GSM35460 3 0.0892 0.963 0.000 0.020 0.980
#> GSM35461 3 0.2187 0.960 0.028 0.024 0.948
#> GSM35463 2 0.1289 0.974 0.000 0.968 0.032
#> GSM35472 3 0.1289 0.960 0.000 0.032 0.968
#> GSM35475 2 0.1163 0.974 0.000 0.972 0.028
#> GSM35483 2 0.1289 0.974 0.000 0.968 0.032
#> GSM35496 3 0.1585 0.963 0.028 0.008 0.964
#> GSM35497 2 0.1031 0.976 0.000 0.976 0.024
#> GSM35504 2 0.1411 0.972 0.000 0.964 0.036
#> GSM35508 2 0.1031 0.976 0.000 0.976 0.024
#> GSM35511 3 0.2625 0.922 0.000 0.084 0.916
#> GSM35512 3 0.1289 0.960 0.000 0.032 0.968
#> GSM35515 2 0.1031 0.976 0.000 0.976 0.024
#> GSM35519 3 0.1529 0.957 0.000 0.040 0.960
#> GSM35527 2 0.1031 0.976 0.000 0.976 0.024
#> GSM35532 3 0.1289 0.960 0.000 0.032 0.968
#> GSM35439 2 0.0424 0.982 0.000 0.992 0.008
#> GSM35443 1 0.0000 0.985 1.000 0.000 0.000
#> GSM35445 1 0.0000 0.985 1.000 0.000 0.000
#> GSM35448 3 0.1031 0.962 0.000 0.024 0.976
#> GSM35451 1 0.0000 0.985 1.000 0.000 0.000
#> GSM35454 3 0.1129 0.968 0.020 0.004 0.976
#> GSM35457 2 0.0237 0.982 0.000 0.996 0.004
#> GSM35465 2 0.0237 0.982 0.000 0.996 0.004
#> GSM35468 1 0.0000 0.985 1.000 0.000 0.000
#> GSM35471 1 0.0000 0.985 1.000 0.000 0.000
#> GSM35473 1 0.0000 0.985 1.000 0.000 0.000
#> GSM35477 1 0.0000 0.985 1.000 0.000 0.000
#> GSM35480 1 0.0000 0.985 1.000 0.000 0.000
#> GSM35482 3 0.1964 0.952 0.056 0.000 0.944
#> GSM35485 2 0.1289 0.974 0.000 0.968 0.032
#> GSM35489 2 0.0237 0.982 0.000 0.996 0.004
#> GSM35492 1 0.0000 0.985 1.000 0.000 0.000
#> GSM35495 3 0.1170 0.966 0.008 0.016 0.976
#> GSM35499 2 0.1289 0.974 0.000 0.968 0.032
#> GSM35502 1 0.0000 0.985 1.000 0.000 0.000
#> GSM35505 3 0.1129 0.968 0.020 0.004 0.976
#> GSM35507 1 0.5988 0.411 0.632 0.368 0.000
#> GSM35510 2 0.1289 0.974 0.000 0.968 0.032
#> GSM35514 1 0.0000 0.985 1.000 0.000 0.000
#> GSM35517 2 0.0592 0.981 0.000 0.988 0.012
#> GSM35520 2 0.0592 0.981 0.000 0.988 0.012
#> GSM35523 1 0.0000 0.985 1.000 0.000 0.000
#> GSM35529 2 0.0237 0.982 0.000 0.996 0.004
#> GSM35531 2 0.0747 0.980 0.000 0.984 0.016
#> GSM35534 2 0.1289 0.974 0.000 0.968 0.032
#> GSM35536 1 0.0000 0.985 1.000 0.000 0.000
#> GSM35538 1 0.0000 0.985 1.000 0.000 0.000
#> GSM35539 1 0.0000 0.985 1.000 0.000 0.000
#> GSM35540 2 0.0237 0.982 0.000 0.996 0.004
#> GSM35541 2 0.0592 0.981 0.000 0.988 0.012
#> GSM35442 1 0.1031 0.964 0.976 0.000 0.024
#> GSM35447 3 0.1129 0.968 0.020 0.004 0.976
#> GSM35450 1 0.0000 0.985 1.000 0.000 0.000
#> GSM35453 1 0.0747 0.972 0.984 0.000 0.016
#> GSM35456 1 0.0000 0.985 1.000 0.000 0.000
#> GSM35464 2 0.0747 0.975 0.016 0.984 0.000
#> GSM35467 1 0.0000 0.985 1.000 0.000 0.000
#> GSM35470 1 0.0592 0.975 0.988 0.000 0.012
#> GSM35479 3 0.1964 0.952 0.056 0.000 0.944
#> GSM35484 1 0.0000 0.985 1.000 0.000 0.000
#> GSM35488 1 0.0000 0.985 1.000 0.000 0.000
#> GSM35491 1 0.0000 0.985 1.000 0.000 0.000
#> GSM35494 3 0.1964 0.952 0.056 0.000 0.944
#> GSM35498 1 0.0000 0.985 1.000 0.000 0.000
#> GSM35501 1 0.0000 0.985 1.000 0.000 0.000
#> GSM35509 3 0.1170 0.967 0.016 0.008 0.976
#> GSM35513 1 0.0000 0.985 1.000 0.000 0.000
#> GSM35516 2 0.0747 0.980 0.000 0.984 0.016
#> GSM35522 1 0.0000 0.985 1.000 0.000 0.000
#> GSM35525 1 0.0000 0.985 1.000 0.000 0.000
#> GSM35528 1 0.0000 0.985 1.000 0.000 0.000
#> GSM35533 1 0.0000 0.985 1.000 0.000 0.000
#> GSM35537 1 0.0000 0.985 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM35441 2 0.2011 0.831 0.000 0.920 0.000 0.080
#> GSM35446 3 0.1118 0.916 0.000 0.000 0.964 0.036
#> GSM35449 2 0.4477 0.460 0.000 0.688 0.000 0.312
#> GSM35455 2 0.4134 0.580 0.000 0.740 0.000 0.260
#> GSM35458 4 0.5070 0.462 0.000 0.416 0.004 0.580
#> GSM35460 3 0.1022 0.917 0.000 0.000 0.968 0.032
#> GSM35461 4 0.5873 0.163 0.036 0.000 0.416 0.548
#> GSM35463 2 0.2124 0.828 0.000 0.924 0.008 0.068
#> GSM35472 3 0.3870 0.739 0.000 0.004 0.788 0.208
#> GSM35475 4 0.5386 0.509 0.000 0.368 0.020 0.612
#> GSM35483 2 0.2124 0.828 0.000 0.924 0.008 0.068
#> GSM35496 3 0.2401 0.881 0.004 0.000 0.904 0.092
#> GSM35497 2 0.4477 0.460 0.000 0.688 0.000 0.312
#> GSM35504 2 0.3542 0.778 0.000 0.864 0.060 0.076
#> GSM35508 4 0.5070 0.445 0.000 0.416 0.004 0.580
#> GSM35511 4 0.5955 0.403 0.000 0.056 0.328 0.616
#> GSM35512 3 0.3870 0.739 0.000 0.004 0.788 0.208
#> GSM35515 4 0.5070 0.462 0.000 0.416 0.004 0.580
#> GSM35519 4 0.5535 0.234 0.000 0.020 0.420 0.560
#> GSM35527 4 0.4972 0.342 0.000 0.456 0.000 0.544
#> GSM35532 4 0.5119 0.173 0.000 0.004 0.440 0.556
#> GSM35439 2 0.0188 0.857 0.000 0.996 0.000 0.004
#> GSM35443 1 0.2198 0.860 0.920 0.000 0.008 0.072
#> GSM35445 1 0.2739 0.861 0.904 0.000 0.036 0.060
#> GSM35448 3 0.2480 0.876 0.000 0.008 0.904 0.088
#> GSM35451 1 0.3486 0.854 0.812 0.000 0.000 0.188
#> GSM35454 3 0.1305 0.914 0.000 0.004 0.960 0.036
#> GSM35457 2 0.1940 0.833 0.000 0.924 0.000 0.076
#> GSM35465 2 0.2704 0.820 0.000 0.876 0.000 0.124
#> GSM35468 1 0.1022 0.879 0.968 0.000 0.000 0.032
#> GSM35471 1 0.4353 0.828 0.756 0.000 0.012 0.232
#> GSM35473 1 0.1661 0.875 0.944 0.000 0.004 0.052
#> GSM35477 1 0.3486 0.854 0.812 0.000 0.000 0.188
#> GSM35480 1 0.1716 0.880 0.936 0.000 0.000 0.064
#> GSM35482 3 0.1743 0.911 0.004 0.000 0.940 0.056
#> GSM35485 2 0.1824 0.836 0.000 0.936 0.004 0.060
#> GSM35489 2 0.0469 0.857 0.000 0.988 0.000 0.012
#> GSM35492 1 0.1022 0.879 0.968 0.000 0.000 0.032
#> GSM35495 3 0.0336 0.921 0.000 0.000 0.992 0.008
#> GSM35499 2 0.1978 0.837 0.000 0.928 0.004 0.068
#> GSM35502 1 0.1118 0.879 0.964 0.000 0.000 0.036
#> GSM35505 3 0.1396 0.918 0.004 0.004 0.960 0.032
#> GSM35507 1 0.8000 0.334 0.436 0.308 0.008 0.248
#> GSM35510 2 0.0895 0.856 0.000 0.976 0.004 0.020
#> GSM35514 1 0.1118 0.879 0.964 0.000 0.000 0.036
#> GSM35517 2 0.0188 0.857 0.000 0.996 0.000 0.004
#> GSM35520 2 0.3355 0.693 0.000 0.836 0.004 0.160
#> GSM35523 1 0.4642 0.821 0.740 0.000 0.020 0.240
#> GSM35529 2 0.1940 0.833 0.000 0.924 0.000 0.076
#> GSM35531 2 0.0592 0.856 0.000 0.984 0.000 0.016
#> GSM35534 2 0.1824 0.836 0.000 0.936 0.004 0.060
#> GSM35536 1 0.0707 0.881 0.980 0.000 0.000 0.020
#> GSM35538 1 0.2921 0.867 0.860 0.000 0.000 0.140
#> GSM35539 1 0.3172 0.862 0.840 0.000 0.000 0.160
#> GSM35540 2 0.2831 0.820 0.000 0.876 0.004 0.120
#> GSM35541 2 0.0336 0.857 0.000 0.992 0.000 0.008
#> GSM35442 1 0.2984 0.844 0.888 0.000 0.028 0.084
#> GSM35447 3 0.1675 0.917 0.004 0.004 0.948 0.044
#> GSM35450 1 0.3074 0.865 0.848 0.000 0.000 0.152
#> GSM35453 1 0.3858 0.814 0.844 0.000 0.100 0.056
#> GSM35456 1 0.5833 0.796 0.676 0.052 0.008 0.264
#> GSM35464 2 0.5640 0.529 0.052 0.688 0.004 0.256
#> GSM35467 1 0.1118 0.879 0.964 0.000 0.000 0.036
#> GSM35470 1 0.4720 0.843 0.768 0.000 0.044 0.188
#> GSM35479 3 0.1305 0.914 0.004 0.000 0.960 0.036
#> GSM35484 1 0.1902 0.877 0.932 0.004 0.000 0.064
#> GSM35488 1 0.0592 0.881 0.984 0.000 0.000 0.016
#> GSM35491 1 0.1022 0.879 0.968 0.000 0.000 0.032
#> GSM35494 3 0.1209 0.916 0.004 0.000 0.964 0.032
#> GSM35498 1 0.4599 0.822 0.736 0.000 0.016 0.248
#> GSM35501 1 0.1118 0.879 0.964 0.000 0.000 0.036
#> GSM35509 3 0.0817 0.919 0.000 0.000 0.976 0.024
#> GSM35513 1 0.1118 0.879 0.964 0.000 0.000 0.036
#> GSM35516 2 0.0592 0.857 0.000 0.984 0.000 0.016
#> GSM35522 1 0.4642 0.821 0.740 0.000 0.020 0.240
#> GSM35525 1 0.1867 0.881 0.928 0.000 0.000 0.072
#> GSM35528 1 0.3266 0.862 0.832 0.000 0.000 0.168
#> GSM35533 1 0.1902 0.877 0.932 0.004 0.000 0.064
#> GSM35537 1 0.4711 0.826 0.740 0.000 0.024 0.236
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM35441 2 0.4002 0.7525 0.000 0.796 0.000 0.084 0.120
#> GSM35446 3 0.2448 0.8395 0.000 0.000 0.892 0.088 0.020
#> GSM35449 2 0.5483 0.2855 0.000 0.512 0.000 0.064 0.424
#> GSM35455 2 0.5396 0.3985 0.000 0.560 0.000 0.064 0.376
#> GSM35458 5 0.3241 0.7726 0.000 0.144 0.000 0.024 0.832
#> GSM35460 3 0.2208 0.8404 0.000 0.000 0.908 0.072 0.020
#> GSM35461 5 0.5252 0.4953 0.008 0.000 0.272 0.064 0.656
#> GSM35463 2 0.3564 0.7288 0.000 0.820 0.008 0.148 0.024
#> GSM35472 3 0.4477 0.6622 0.000 0.000 0.708 0.040 0.252
#> GSM35475 5 0.1952 0.7999 0.000 0.084 0.004 0.000 0.912
#> GSM35483 2 0.4037 0.7058 0.000 0.784 0.012 0.176 0.028
#> GSM35496 3 0.3688 0.8042 0.000 0.000 0.816 0.060 0.124
#> GSM35497 2 0.5478 0.2912 0.000 0.516 0.000 0.064 0.420
#> GSM35504 2 0.5331 0.6630 0.000 0.712 0.064 0.184 0.040
#> GSM35508 5 0.3569 0.7679 0.000 0.104 0.000 0.068 0.828
#> GSM35511 5 0.2824 0.7726 0.000 0.008 0.088 0.024 0.880
#> GSM35512 3 0.4552 0.6444 0.000 0.000 0.696 0.040 0.264
#> GSM35515 5 0.3241 0.7726 0.000 0.144 0.000 0.024 0.832
#> GSM35519 5 0.4186 0.6771 0.000 0.004 0.184 0.044 0.768
#> GSM35527 5 0.4277 0.6982 0.000 0.156 0.000 0.076 0.768
#> GSM35532 5 0.3732 0.6886 0.000 0.000 0.176 0.032 0.792
#> GSM35439 2 0.0693 0.8078 0.000 0.980 0.000 0.008 0.012
#> GSM35443 1 0.4754 0.5471 0.736 0.000 0.008 0.184 0.072
#> GSM35445 1 0.3275 0.5894 0.860 0.000 0.064 0.068 0.008
#> GSM35448 3 0.4219 0.7462 0.000 0.020 0.772 0.184 0.024
#> GSM35451 1 0.4774 -0.2218 0.540 0.012 0.000 0.444 0.004
#> GSM35454 3 0.2747 0.8473 0.016 0.000 0.884 0.088 0.012
#> GSM35457 2 0.3865 0.7577 0.000 0.808 0.000 0.092 0.100
#> GSM35465 2 0.4761 0.7136 0.000 0.728 0.000 0.168 0.104
#> GSM35468 1 0.3612 0.5861 0.800 0.000 0.000 0.172 0.028
#> GSM35471 4 0.4837 0.4734 0.424 0.016 0.004 0.556 0.000
#> GSM35473 1 0.2339 0.6264 0.912 0.000 0.028 0.052 0.008
#> GSM35477 1 0.4783 -0.2388 0.532 0.012 0.000 0.452 0.004
#> GSM35480 1 0.2609 0.6203 0.896 0.000 0.028 0.068 0.008
#> GSM35482 3 0.2813 0.8457 0.000 0.000 0.868 0.108 0.024
#> GSM35485 2 0.2006 0.7857 0.000 0.916 0.000 0.072 0.012
#> GSM35489 2 0.1697 0.8045 0.000 0.932 0.000 0.060 0.008
#> GSM35492 1 0.3612 0.5861 0.800 0.000 0.000 0.172 0.028
#> GSM35495 3 0.0963 0.8586 0.000 0.000 0.964 0.036 0.000
#> GSM35499 2 0.1522 0.8075 0.000 0.944 0.000 0.044 0.012
#> GSM35502 1 0.0000 0.6541 1.000 0.000 0.000 0.000 0.000
#> GSM35505 3 0.2850 0.8477 0.016 0.000 0.880 0.088 0.016
#> GSM35507 4 0.6462 0.4769 0.168 0.240 0.000 0.572 0.020
#> GSM35510 2 0.1281 0.8091 0.000 0.956 0.000 0.032 0.012
#> GSM35514 1 0.0162 0.6536 0.996 0.000 0.000 0.004 0.000
#> GSM35517 2 0.0404 0.8085 0.000 0.988 0.000 0.000 0.012
#> GSM35520 2 0.3722 0.6909 0.000 0.796 0.004 0.024 0.176
#> GSM35523 4 0.5173 0.6096 0.348 0.012 0.004 0.612 0.024
#> GSM35529 2 0.3912 0.7570 0.000 0.804 0.000 0.088 0.108
#> GSM35531 2 0.0794 0.8063 0.000 0.972 0.000 0.028 0.000
#> GSM35534 2 0.2873 0.7564 0.000 0.860 0.000 0.120 0.020
#> GSM35536 1 0.1041 0.6492 0.964 0.000 0.000 0.032 0.004
#> GSM35538 1 0.4251 0.0844 0.624 0.000 0.000 0.372 0.004
#> GSM35539 1 0.4331 -0.0119 0.596 0.000 0.000 0.400 0.004
#> GSM35540 2 0.4797 0.7102 0.000 0.724 0.000 0.172 0.104
#> GSM35541 2 0.0798 0.8063 0.000 0.976 0.000 0.016 0.008
#> GSM35442 1 0.6396 0.4302 0.620 0.000 0.076 0.224 0.080
#> GSM35447 3 0.2850 0.8477 0.016 0.000 0.880 0.088 0.016
#> GSM35450 1 0.4288 0.0490 0.612 0.000 0.000 0.384 0.004
#> GSM35453 1 0.4326 0.5037 0.784 0.000 0.124 0.084 0.008
#> GSM35456 1 0.6127 -0.3182 0.484 0.076 0.012 0.424 0.004
#> GSM35464 4 0.5411 0.0841 0.012 0.380 0.000 0.568 0.040
#> GSM35467 1 0.0000 0.6541 1.000 0.000 0.000 0.000 0.000
#> GSM35470 4 0.6434 0.2021 0.404 0.000 0.072 0.484 0.040
#> GSM35479 3 0.1877 0.8561 0.000 0.000 0.924 0.064 0.012
#> GSM35484 1 0.2647 0.6297 0.892 0.000 0.024 0.076 0.008
#> GSM35488 1 0.3409 0.5818 0.816 0.000 0.000 0.160 0.024
#> GSM35491 1 0.3612 0.5861 0.800 0.000 0.000 0.172 0.028
#> GSM35494 3 0.1410 0.8604 0.000 0.000 0.940 0.060 0.000
#> GSM35498 4 0.5061 0.6096 0.340 0.020 0.004 0.624 0.012
#> GSM35501 1 0.0000 0.6541 1.000 0.000 0.000 0.000 0.000
#> GSM35509 3 0.0880 0.8637 0.000 0.000 0.968 0.032 0.000
#> GSM35513 1 0.0162 0.6536 0.996 0.000 0.000 0.004 0.000
#> GSM35516 2 0.0771 0.8076 0.000 0.976 0.000 0.020 0.004
#> GSM35522 4 0.5144 0.6132 0.340 0.012 0.004 0.620 0.024
#> GSM35525 1 0.3550 0.4560 0.760 0.000 0.000 0.236 0.004
#> GSM35528 1 0.4827 -0.2567 0.504 0.000 0.000 0.476 0.020
#> GSM35533 1 0.2734 0.6331 0.888 0.000 0.028 0.076 0.008
#> GSM35537 4 0.5215 0.5059 0.380 0.000 0.016 0.580 0.024
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM35441 2 0.4351 0.5520 0.000 0.676 0.000 0.044 0.276 0.004
#> GSM35446 3 0.2701 0.6139 0.000 0.000 0.864 0.028 0.004 0.104
#> GSM35449 5 0.4481 0.0291 0.000 0.416 0.000 0.024 0.556 0.004
#> GSM35455 5 0.4504 -0.0237 0.000 0.432 0.000 0.024 0.540 0.004
#> GSM35458 5 0.4354 0.3142 0.008 0.044 0.000 0.020 0.748 0.180
#> GSM35460 3 0.2701 0.6139 0.000 0.000 0.864 0.028 0.004 0.104
#> GSM35461 6 0.6105 0.0000 0.004 0.000 0.192 0.008 0.316 0.480
#> GSM35463 2 0.4834 0.5589 0.000 0.672 0.008 0.076 0.004 0.240
#> GSM35472 3 0.5740 -0.3948 0.000 0.000 0.436 0.000 0.168 0.396
#> GSM35475 5 0.3874 0.0431 0.000 0.012 0.008 0.000 0.704 0.276
#> GSM35483 2 0.5465 0.4922 0.000 0.600 0.020 0.088 0.004 0.288
#> GSM35496 3 0.5218 0.3719 0.000 0.000 0.624 0.044 0.048 0.284
#> GSM35497 5 0.4487 0.0172 0.000 0.420 0.000 0.024 0.552 0.004
#> GSM35504 2 0.6942 0.4148 0.000 0.488 0.076 0.096 0.032 0.308
#> GSM35508 5 0.1390 0.3842 0.000 0.032 0.000 0.004 0.948 0.016
#> GSM35511 5 0.4047 -0.0112 0.000 0.000 0.036 0.004 0.716 0.244
#> GSM35512 3 0.5764 -0.4234 0.000 0.000 0.424 0.000 0.172 0.404
#> GSM35515 5 0.4354 0.3142 0.008 0.044 0.000 0.020 0.748 0.180
#> GSM35519 5 0.5274 -0.5831 0.000 0.000 0.100 0.000 0.492 0.408
#> GSM35527 5 0.1946 0.4059 0.000 0.072 0.000 0.004 0.912 0.012
#> GSM35532 5 0.5077 -0.4351 0.000 0.000 0.088 0.000 0.552 0.360
#> GSM35439 2 0.1010 0.7380 0.000 0.960 0.000 0.004 0.036 0.000
#> GSM35443 1 0.5095 0.5763 0.676 0.000 0.004 0.132 0.012 0.176
#> GSM35445 1 0.4605 0.6114 0.760 0.000 0.096 0.056 0.004 0.084
#> GSM35448 3 0.5696 0.3538 0.000 0.036 0.572 0.076 0.004 0.312
#> GSM35451 4 0.4361 0.5252 0.424 0.000 0.000 0.552 0.000 0.024
#> GSM35454 3 0.4832 0.5883 0.048 0.008 0.740 0.052 0.004 0.148
#> GSM35457 2 0.4327 0.5615 0.000 0.688 0.000 0.048 0.260 0.004
#> GSM35465 2 0.5456 0.4913 0.000 0.596 0.000 0.152 0.244 0.008
#> GSM35468 1 0.4546 0.6017 0.728 0.000 0.000 0.128 0.012 0.132
#> GSM35471 4 0.3831 0.6507 0.244 0.008 0.004 0.732 0.000 0.012
#> GSM35473 1 0.3471 0.6573 0.840 0.000 0.040 0.040 0.004 0.076
#> GSM35477 4 0.4361 0.5252 0.424 0.000 0.000 0.552 0.000 0.024
#> GSM35480 1 0.4258 0.6309 0.776 0.000 0.028 0.120 0.004 0.072
#> GSM35482 3 0.4482 0.5521 0.000 0.000 0.708 0.124 0.000 0.168
#> GSM35485 2 0.2152 0.7095 0.000 0.904 0.000 0.024 0.004 0.068
#> GSM35489 2 0.2003 0.7283 0.000 0.912 0.000 0.044 0.044 0.000
#> GSM35492 1 0.4621 0.6031 0.720 0.000 0.000 0.128 0.012 0.140
#> GSM35495 3 0.1524 0.6395 0.000 0.000 0.932 0.008 0.000 0.060
#> GSM35499 2 0.1760 0.7372 0.000 0.928 0.000 0.048 0.004 0.020
#> GSM35502 1 0.1003 0.6932 0.964 0.000 0.000 0.028 0.004 0.004
#> GSM35505 3 0.4853 0.5814 0.044 0.008 0.728 0.044 0.004 0.172
#> GSM35507 4 0.5000 0.5392 0.060 0.180 0.000 0.700 0.060 0.000
#> GSM35510 2 0.1857 0.7374 0.000 0.928 0.000 0.028 0.032 0.012
#> GSM35514 1 0.1003 0.6932 0.964 0.000 0.000 0.028 0.004 0.004
#> GSM35517 2 0.1080 0.7388 0.000 0.960 0.000 0.004 0.032 0.004
#> GSM35520 2 0.4643 0.4862 0.000 0.700 0.004 0.000 0.176 0.120
#> GSM35523 4 0.3732 0.6670 0.180 0.012 0.000 0.776 0.000 0.032
#> GSM35529 2 0.4289 0.5594 0.000 0.688 0.000 0.044 0.264 0.004
#> GSM35531 2 0.1180 0.7397 0.000 0.960 0.000 0.016 0.012 0.012
#> GSM35534 2 0.4203 0.5945 0.000 0.720 0.000 0.056 0.004 0.220
#> GSM35536 1 0.1913 0.6682 0.908 0.000 0.000 0.080 0.000 0.012
#> GSM35538 1 0.4331 -0.4252 0.516 0.000 0.000 0.464 0.000 0.020
#> GSM35539 4 0.4322 0.4956 0.452 0.000 0.000 0.528 0.000 0.020
#> GSM35540 2 0.5572 0.4774 0.000 0.580 0.000 0.168 0.244 0.008
#> GSM35541 2 0.1036 0.7395 0.000 0.964 0.000 0.008 0.024 0.004
#> GSM35442 1 0.6847 0.4198 0.508 0.000 0.084 0.136 0.012 0.260
#> GSM35447 3 0.4509 0.5875 0.044 0.000 0.744 0.040 0.004 0.168
#> GSM35450 4 0.4325 0.4707 0.456 0.000 0.000 0.524 0.000 0.020
#> GSM35453 1 0.5160 0.5423 0.700 0.000 0.160 0.048 0.004 0.088
#> GSM35456 4 0.5255 0.5104 0.328 0.028 0.008 0.596 0.000 0.040
#> GSM35464 4 0.4836 0.2982 0.000 0.268 0.000 0.644 0.084 0.004
#> GSM35467 1 0.1003 0.6932 0.964 0.000 0.000 0.028 0.004 0.004
#> GSM35470 4 0.6767 0.3583 0.208 0.000 0.100 0.508 0.000 0.184
#> GSM35479 3 0.2733 0.6379 0.000 0.000 0.864 0.080 0.000 0.056
#> GSM35484 1 0.4259 0.6359 0.784 0.000 0.040 0.092 0.004 0.080
#> GSM35488 1 0.4454 0.5944 0.736 0.000 0.000 0.144 0.012 0.108
#> GSM35491 1 0.4621 0.6031 0.720 0.000 0.000 0.128 0.012 0.140
#> GSM35494 3 0.3052 0.6422 0.004 0.000 0.848 0.068 0.000 0.080
#> GSM35498 4 0.3642 0.6655 0.160 0.016 0.000 0.796 0.004 0.024
#> GSM35501 1 0.1003 0.6932 0.964 0.000 0.000 0.028 0.004 0.004
#> GSM35509 3 0.0993 0.6546 0.000 0.000 0.964 0.024 0.000 0.012
#> GSM35513 1 0.1003 0.6932 0.964 0.000 0.000 0.028 0.004 0.004
#> GSM35516 2 0.1346 0.7382 0.000 0.952 0.000 0.024 0.008 0.016
#> GSM35522 4 0.3732 0.6670 0.180 0.012 0.000 0.776 0.000 0.032
#> GSM35525 1 0.4066 0.3132 0.692 0.000 0.000 0.272 0.000 0.036
#> GSM35528 4 0.5305 0.4242 0.400 0.000 0.000 0.516 0.012 0.072
#> GSM35533 1 0.4357 0.6342 0.776 0.000 0.040 0.096 0.004 0.084
#> GSM35537 4 0.4661 0.6280 0.176 0.000 0.036 0.724 0.000 0.064
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 time(p) k
#> CV:kmeans 79 3.41e-07 2
#> CV:kmeans 78 1.71e-05 3
#> CV:kmeans 68 6.39e-04 4
#> CV:kmeans 62 1.84e-06 5
#> CV:kmeans 50 1.07e-01 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 7758 rows and 79 columns.
#> Top rows (776, 1552, 2328, 3103, 3879) 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 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.988 0.995 0.5037 0.498 0.498
#> 3 3 0.999 0.955 0.981 0.3132 0.775 0.577
#> 4 4 0.703 0.433 0.797 0.1191 0.952 0.868
#> 5 5 0.698 0.677 0.831 0.0754 0.836 0.536
#> 6 6 0.689 0.593 0.751 0.0411 0.980 0.904
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
#> attr(,"optional")
#> [1] 2
There is also optional best \(k\) = 2 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM35441 2 0.0000 1.000 0.000 1.000
#> GSM35446 2 0.0000 1.000 0.000 1.000
#> GSM35449 2 0.0000 1.000 0.000 1.000
#> GSM35455 2 0.0000 1.000 0.000 1.000
#> GSM35458 2 0.0000 1.000 0.000 1.000
#> GSM35460 2 0.0000 1.000 0.000 1.000
#> GSM35461 1 0.0000 0.990 1.000 0.000
#> GSM35463 2 0.0000 1.000 0.000 1.000
#> GSM35472 2 0.0000 1.000 0.000 1.000
#> GSM35475 2 0.0000 1.000 0.000 1.000
#> GSM35483 2 0.0000 1.000 0.000 1.000
#> GSM35496 1 0.0000 0.990 1.000 0.000
#> GSM35497 2 0.0000 1.000 0.000 1.000
#> GSM35504 2 0.0000 1.000 0.000 1.000
#> GSM35508 2 0.0000 1.000 0.000 1.000
#> GSM35511 2 0.0000 1.000 0.000 1.000
#> GSM35512 2 0.0000 1.000 0.000 1.000
#> GSM35515 2 0.0000 1.000 0.000 1.000
#> GSM35519 2 0.0000 1.000 0.000 1.000
#> GSM35527 2 0.0000 1.000 0.000 1.000
#> GSM35532 2 0.0000 1.000 0.000 1.000
#> GSM35439 2 0.0000 1.000 0.000 1.000
#> GSM35443 1 0.0000 0.990 1.000 0.000
#> GSM35445 1 0.0000 0.990 1.000 0.000
#> GSM35448 2 0.0000 1.000 0.000 1.000
#> GSM35451 1 0.0000 0.990 1.000 0.000
#> GSM35454 1 0.0000 0.990 1.000 0.000
#> GSM35457 2 0.0000 1.000 0.000 1.000
#> GSM35465 2 0.0000 1.000 0.000 1.000
#> GSM35468 1 0.0000 0.990 1.000 0.000
#> GSM35471 1 0.0000 0.990 1.000 0.000
#> GSM35473 1 0.0000 0.990 1.000 0.000
#> GSM35477 1 0.0000 0.990 1.000 0.000
#> GSM35480 1 0.0000 0.990 1.000 0.000
#> GSM35482 1 0.0000 0.990 1.000 0.000
#> GSM35485 2 0.0000 1.000 0.000 1.000
#> GSM35489 2 0.0000 1.000 0.000 1.000
#> GSM35492 1 0.0000 0.990 1.000 0.000
#> GSM35495 1 0.7376 0.744 0.792 0.208
#> GSM35499 2 0.0000 1.000 0.000 1.000
#> GSM35502 1 0.0000 0.990 1.000 0.000
#> GSM35505 1 0.0000 0.990 1.000 0.000
#> GSM35507 1 0.6048 0.829 0.852 0.148
#> GSM35510 2 0.0000 1.000 0.000 1.000
#> GSM35514 1 0.0000 0.990 1.000 0.000
#> GSM35517 2 0.0000 1.000 0.000 1.000
#> GSM35520 2 0.0000 1.000 0.000 1.000
#> GSM35523 1 0.0000 0.990 1.000 0.000
#> GSM35529 2 0.0000 1.000 0.000 1.000
#> GSM35531 2 0.0000 1.000 0.000 1.000
#> GSM35534 2 0.0000 1.000 0.000 1.000
#> GSM35536 1 0.0000 0.990 1.000 0.000
#> GSM35538 1 0.0000 0.990 1.000 0.000
#> GSM35539 1 0.0000 0.990 1.000 0.000
#> GSM35540 2 0.0000 1.000 0.000 1.000
#> GSM35541 2 0.0000 1.000 0.000 1.000
#> GSM35442 1 0.0000 0.990 1.000 0.000
#> GSM35447 1 0.2948 0.942 0.948 0.052
#> GSM35450 1 0.0000 0.990 1.000 0.000
#> GSM35453 1 0.0000 0.990 1.000 0.000
#> GSM35456 1 0.0000 0.990 1.000 0.000
#> GSM35464 2 0.0376 0.996 0.004 0.996
#> GSM35467 1 0.0000 0.990 1.000 0.000
#> GSM35470 1 0.0000 0.990 1.000 0.000
#> GSM35479 1 0.0000 0.990 1.000 0.000
#> GSM35484 1 0.0000 0.990 1.000 0.000
#> GSM35488 1 0.0000 0.990 1.000 0.000
#> GSM35491 1 0.0000 0.990 1.000 0.000
#> GSM35494 1 0.0000 0.990 1.000 0.000
#> GSM35498 1 0.0000 0.990 1.000 0.000
#> GSM35501 1 0.0000 0.990 1.000 0.000
#> GSM35509 1 0.1414 0.973 0.980 0.020
#> GSM35513 1 0.0000 0.990 1.000 0.000
#> GSM35516 2 0.0000 1.000 0.000 1.000
#> GSM35522 1 0.0000 0.990 1.000 0.000
#> GSM35525 1 0.0000 0.990 1.000 0.000
#> GSM35528 1 0.0000 0.990 1.000 0.000
#> GSM35533 1 0.0000 0.990 1.000 0.000
#> GSM35537 1 0.0000 0.990 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM35441 2 0.0000 0.973 0.000 1.000 0.000
#> GSM35446 3 0.0000 0.995 0.000 0.000 1.000
#> GSM35449 2 0.0000 0.973 0.000 1.000 0.000
#> GSM35455 2 0.0000 0.973 0.000 1.000 0.000
#> GSM35458 2 0.0000 0.973 0.000 1.000 0.000
#> GSM35460 3 0.0000 0.995 0.000 0.000 1.000
#> GSM35461 3 0.0000 0.995 0.000 0.000 1.000
#> GSM35463 2 0.0000 0.973 0.000 1.000 0.000
#> GSM35472 3 0.0000 0.995 0.000 0.000 1.000
#> GSM35475 2 0.6126 0.334 0.000 0.600 0.400
#> GSM35483 2 0.0000 0.973 0.000 1.000 0.000
#> GSM35496 3 0.0000 0.995 0.000 0.000 1.000
#> GSM35497 2 0.0000 0.973 0.000 1.000 0.000
#> GSM35504 2 0.0747 0.961 0.000 0.984 0.016
#> GSM35508 2 0.0237 0.970 0.000 0.996 0.004
#> GSM35511 3 0.2537 0.908 0.000 0.080 0.920
#> GSM35512 3 0.0000 0.995 0.000 0.000 1.000
#> GSM35515 2 0.0592 0.964 0.000 0.988 0.012
#> GSM35519 3 0.0000 0.995 0.000 0.000 1.000
#> GSM35527 2 0.0000 0.973 0.000 1.000 0.000
#> GSM35532 3 0.0000 0.995 0.000 0.000 1.000
#> GSM35439 2 0.0000 0.973 0.000 1.000 0.000
#> GSM35443 1 0.0237 0.975 0.996 0.000 0.004
#> GSM35445 1 0.1643 0.942 0.956 0.000 0.044
#> GSM35448 3 0.0000 0.995 0.000 0.000 1.000
#> GSM35451 1 0.0000 0.978 1.000 0.000 0.000
#> GSM35454 3 0.0000 0.995 0.000 0.000 1.000
#> GSM35457 2 0.0000 0.973 0.000 1.000 0.000
#> GSM35465 2 0.0000 0.973 0.000 1.000 0.000
#> GSM35468 1 0.0000 0.978 1.000 0.000 0.000
#> GSM35471 1 0.0000 0.978 1.000 0.000 0.000
#> GSM35473 1 0.0237 0.975 0.996 0.000 0.004
#> GSM35477 1 0.0000 0.978 1.000 0.000 0.000
#> GSM35480 1 0.0000 0.978 1.000 0.000 0.000
#> GSM35482 3 0.0000 0.995 0.000 0.000 1.000
#> GSM35485 2 0.0000 0.973 0.000 1.000 0.000
#> GSM35489 2 0.0000 0.973 0.000 1.000 0.000
#> GSM35492 1 0.0000 0.978 1.000 0.000 0.000
#> GSM35495 3 0.0000 0.995 0.000 0.000 1.000
#> GSM35499 2 0.0000 0.973 0.000 1.000 0.000
#> GSM35502 1 0.0000 0.978 1.000 0.000 0.000
#> GSM35505 3 0.0000 0.995 0.000 0.000 1.000
#> GSM35507 2 0.5016 0.681 0.240 0.760 0.000
#> GSM35510 2 0.0000 0.973 0.000 1.000 0.000
#> GSM35514 1 0.0000 0.978 1.000 0.000 0.000
#> GSM35517 2 0.0000 0.973 0.000 1.000 0.000
#> GSM35520 2 0.1643 0.935 0.000 0.956 0.044
#> GSM35523 1 0.0000 0.978 1.000 0.000 0.000
#> GSM35529 2 0.0000 0.973 0.000 1.000 0.000
#> GSM35531 2 0.0000 0.973 0.000 1.000 0.000
#> GSM35534 2 0.0000 0.973 0.000 1.000 0.000
#> GSM35536 1 0.0000 0.978 1.000 0.000 0.000
#> GSM35538 1 0.0000 0.978 1.000 0.000 0.000
#> GSM35539 1 0.0000 0.978 1.000 0.000 0.000
#> GSM35540 2 0.0000 0.973 0.000 1.000 0.000
#> GSM35541 2 0.0000 0.973 0.000 1.000 0.000
#> GSM35442 1 0.6154 0.338 0.592 0.000 0.408
#> GSM35447 3 0.0000 0.995 0.000 0.000 1.000
#> GSM35450 1 0.0000 0.978 1.000 0.000 0.000
#> GSM35453 1 0.2878 0.892 0.904 0.000 0.096
#> GSM35456 1 0.0892 0.960 0.980 0.020 0.000
#> GSM35464 2 0.0000 0.973 0.000 1.000 0.000
#> GSM35467 1 0.0000 0.978 1.000 0.000 0.000
#> GSM35470 1 0.3192 0.874 0.888 0.000 0.112
#> GSM35479 3 0.0000 0.995 0.000 0.000 1.000
#> GSM35484 1 0.0000 0.978 1.000 0.000 0.000
#> GSM35488 1 0.0000 0.978 1.000 0.000 0.000
#> GSM35491 1 0.0000 0.978 1.000 0.000 0.000
#> GSM35494 3 0.0000 0.995 0.000 0.000 1.000
#> GSM35498 1 0.0000 0.978 1.000 0.000 0.000
#> GSM35501 1 0.0000 0.978 1.000 0.000 0.000
#> GSM35509 3 0.0000 0.995 0.000 0.000 1.000
#> GSM35513 1 0.0000 0.978 1.000 0.000 0.000
#> GSM35516 2 0.0000 0.973 0.000 1.000 0.000
#> GSM35522 1 0.0000 0.978 1.000 0.000 0.000
#> GSM35525 1 0.0000 0.978 1.000 0.000 0.000
#> GSM35528 1 0.0000 0.978 1.000 0.000 0.000
#> GSM35533 1 0.0000 0.978 1.000 0.000 0.000
#> GSM35537 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
#> GSM35441 2 0.1940 0.8816 0.000 0.924 0.000 0.076
#> GSM35446 3 0.0376 0.8997 0.000 0.004 0.992 0.004
#> GSM35449 2 0.3907 0.8264 0.000 0.768 0.000 0.232
#> GSM35455 2 0.3356 0.8504 0.000 0.824 0.000 0.176
#> GSM35458 2 0.4836 0.7528 0.000 0.672 0.008 0.320
#> GSM35460 3 0.0188 0.9002 0.000 0.000 0.996 0.004
#> GSM35461 3 0.4193 0.7863 0.000 0.000 0.732 0.268
#> GSM35463 2 0.0524 0.8863 0.000 0.988 0.004 0.008
#> GSM35472 3 0.3024 0.8549 0.000 0.000 0.852 0.148
#> GSM35475 2 0.7344 0.4826 0.000 0.504 0.180 0.316
#> GSM35483 2 0.1510 0.8812 0.000 0.956 0.028 0.016
#> GSM35496 3 0.1867 0.8842 0.000 0.000 0.928 0.072
#> GSM35497 2 0.3801 0.8300 0.000 0.780 0.000 0.220
#> GSM35504 2 0.2255 0.8625 0.000 0.920 0.068 0.012
#> GSM35508 2 0.4980 0.7633 0.000 0.680 0.016 0.304
#> GSM35511 3 0.6634 0.6189 0.000 0.108 0.580 0.312
#> GSM35512 3 0.3074 0.8535 0.000 0.000 0.848 0.152
#> GSM35515 2 0.4957 0.7488 0.000 0.668 0.012 0.320
#> GSM35519 3 0.4718 0.7676 0.000 0.012 0.708 0.280
#> GSM35527 2 0.4193 0.8022 0.000 0.732 0.000 0.268
#> GSM35532 3 0.4483 0.7709 0.000 0.004 0.712 0.284
#> GSM35439 2 0.0000 0.8869 0.000 1.000 0.000 0.000
#> GSM35443 1 0.5353 -0.5168 0.556 0.000 0.012 0.432
#> GSM35445 1 0.7483 -0.6817 0.456 0.000 0.184 0.360
#> GSM35448 3 0.0895 0.8934 0.000 0.020 0.976 0.004
#> GSM35451 1 0.3123 0.2718 0.844 0.000 0.000 0.156
#> GSM35454 3 0.0921 0.8850 0.000 0.000 0.972 0.028
#> GSM35457 2 0.1637 0.8838 0.000 0.940 0.000 0.060
#> GSM35465 2 0.3486 0.8189 0.000 0.812 0.000 0.188
#> GSM35468 1 0.4761 -0.2695 0.628 0.000 0.000 0.372
#> GSM35471 1 0.4428 0.2711 0.720 0.004 0.000 0.276
#> GSM35473 1 0.6290 -0.4538 0.568 0.000 0.068 0.364
#> GSM35477 1 0.3266 0.2725 0.832 0.000 0.000 0.168
#> GSM35480 1 0.5929 -0.3926 0.596 0.000 0.048 0.356
#> GSM35482 3 0.0707 0.8988 0.000 0.000 0.980 0.020
#> GSM35485 2 0.0188 0.8866 0.000 0.996 0.000 0.004
#> GSM35489 2 0.0921 0.8872 0.000 0.972 0.000 0.028
#> GSM35492 1 0.4761 -0.2695 0.628 0.000 0.000 0.372
#> GSM35495 3 0.0000 0.8997 0.000 0.000 1.000 0.000
#> GSM35499 2 0.2888 0.8328 0.000 0.872 0.004 0.124
#> GSM35502 1 0.4713 -0.2560 0.640 0.000 0.000 0.360
#> GSM35505 3 0.0469 0.8966 0.000 0.000 0.988 0.012
#> GSM35507 1 0.7591 0.1666 0.452 0.208 0.000 0.340
#> GSM35510 2 0.0707 0.8855 0.000 0.980 0.000 0.020
#> GSM35514 1 0.4713 -0.2560 0.640 0.000 0.000 0.360
#> GSM35517 2 0.0188 0.8869 0.000 0.996 0.000 0.004
#> GSM35520 2 0.4417 0.8215 0.000 0.796 0.044 0.160
#> GSM35523 1 0.4500 0.2664 0.684 0.000 0.000 0.316
#> GSM35529 2 0.1474 0.8840 0.000 0.948 0.000 0.052
#> GSM35531 2 0.0188 0.8866 0.000 0.996 0.000 0.004
#> GSM35534 2 0.0188 0.8866 0.000 0.996 0.000 0.004
#> GSM35536 1 0.4679 -0.2498 0.648 0.000 0.000 0.352
#> GSM35538 1 0.1557 0.1357 0.944 0.000 0.000 0.056
#> GSM35539 1 0.1389 0.2288 0.952 0.000 0.000 0.048
#> GSM35540 2 0.3528 0.8306 0.000 0.808 0.000 0.192
#> GSM35541 2 0.0000 0.8869 0.000 1.000 0.000 0.000
#> GSM35442 4 0.7221 0.0000 0.428 0.000 0.140 0.432
#> GSM35447 3 0.0336 0.9000 0.000 0.000 0.992 0.008
#> GSM35450 1 0.0336 0.2028 0.992 0.000 0.000 0.008
#> GSM35453 1 0.7768 -0.6885 0.400 0.000 0.240 0.360
#> GSM35456 1 0.7334 0.2067 0.552 0.140 0.012 0.296
#> GSM35464 1 0.7924 -0.0626 0.340 0.332 0.000 0.328
#> GSM35467 1 0.4713 -0.2560 0.640 0.000 0.000 0.360
#> GSM35470 1 0.6620 -0.3734 0.576 0.000 0.104 0.320
#> GSM35479 3 0.0188 0.8992 0.000 0.000 0.996 0.004
#> GSM35484 1 0.6335 -0.4392 0.572 0.004 0.060 0.364
#> GSM35488 1 0.4746 -0.2663 0.632 0.000 0.000 0.368
#> GSM35491 1 0.4761 -0.2695 0.628 0.000 0.000 0.372
#> GSM35494 3 0.0336 0.8984 0.000 0.000 0.992 0.008
#> GSM35498 1 0.5090 0.2593 0.660 0.016 0.000 0.324
#> GSM35501 1 0.4697 -0.2521 0.644 0.000 0.000 0.356
#> GSM35509 3 0.0000 0.8997 0.000 0.000 1.000 0.000
#> GSM35513 1 0.4713 -0.2560 0.640 0.000 0.000 0.360
#> GSM35516 2 0.1398 0.8794 0.004 0.956 0.000 0.040
#> GSM35522 1 0.4814 0.2649 0.676 0.008 0.000 0.316
#> GSM35525 1 0.4304 -0.1846 0.716 0.000 0.000 0.284
#> GSM35528 1 0.2814 0.2520 0.868 0.000 0.000 0.132
#> GSM35533 1 0.5957 -0.3997 0.588 0.000 0.048 0.364
#> GSM35537 1 0.4882 0.2171 0.708 0.000 0.020 0.272
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM35441 2 0.4248 0.6809 0.000 0.728 0.000 0.032 0.240
#> GSM35446 3 0.0771 0.8986 0.000 0.004 0.976 0.000 0.020
#> GSM35449 5 0.4538 0.3610 0.000 0.364 0.000 0.016 0.620
#> GSM35455 2 0.4627 0.1785 0.000 0.544 0.000 0.012 0.444
#> GSM35458 5 0.2166 0.7513 0.004 0.072 0.000 0.012 0.912
#> GSM35460 3 0.0290 0.9010 0.000 0.000 0.992 0.000 0.008
#> GSM35461 5 0.5092 0.4284 0.008 0.000 0.276 0.052 0.664
#> GSM35463 2 0.0566 0.8505 0.000 0.984 0.012 0.000 0.004
#> GSM35472 3 0.4288 0.5464 0.000 0.000 0.664 0.012 0.324
#> GSM35475 5 0.2228 0.7550 0.000 0.048 0.040 0.000 0.912
#> GSM35483 2 0.2230 0.8152 0.000 0.912 0.044 0.000 0.044
#> GSM35496 3 0.2653 0.8489 0.000 0.000 0.880 0.024 0.096
#> GSM35497 5 0.4537 0.2763 0.000 0.396 0.000 0.012 0.592
#> GSM35504 2 0.3270 0.7743 0.000 0.852 0.100 0.004 0.044
#> GSM35508 5 0.2645 0.7405 0.000 0.096 0.008 0.012 0.884
#> GSM35511 5 0.2358 0.7185 0.000 0.008 0.104 0.000 0.888
#> GSM35512 3 0.4201 0.5341 0.000 0.000 0.664 0.008 0.328
#> GSM35515 5 0.2102 0.7513 0.004 0.068 0.000 0.012 0.916
#> GSM35519 5 0.3282 0.6368 0.000 0.000 0.188 0.008 0.804
#> GSM35527 5 0.3123 0.6913 0.000 0.160 0.000 0.012 0.828
#> GSM35532 5 0.3551 0.6001 0.000 0.000 0.220 0.008 0.772
#> GSM35439 2 0.1364 0.8574 0.000 0.952 0.000 0.012 0.036
#> GSM35443 1 0.4509 0.6642 0.752 0.000 0.000 0.152 0.096
#> GSM35445 1 0.2989 0.7006 0.852 0.000 0.132 0.008 0.008
#> GSM35448 3 0.2761 0.8168 0.000 0.104 0.872 0.000 0.024
#> GSM35451 4 0.4547 0.4480 0.400 0.000 0.000 0.588 0.012
#> GSM35454 3 0.0902 0.8955 0.008 0.004 0.976 0.004 0.008
#> GSM35457 2 0.3714 0.7944 0.000 0.812 0.000 0.056 0.132
#> GSM35465 2 0.5341 0.6664 0.000 0.664 0.000 0.212 0.124
#> GSM35468 1 0.3413 0.7124 0.832 0.000 0.000 0.124 0.044
#> GSM35471 4 0.3132 0.7226 0.172 0.000 0.000 0.820 0.008
#> GSM35473 1 0.1788 0.7447 0.932 0.000 0.056 0.004 0.008
#> GSM35477 4 0.4564 0.4909 0.372 0.000 0.000 0.612 0.016
#> GSM35480 1 0.3257 0.7149 0.860 0.000 0.052 0.080 0.008
#> GSM35482 3 0.2914 0.8537 0.000 0.000 0.872 0.076 0.052
#> GSM35485 2 0.0404 0.8536 0.000 0.988 0.000 0.000 0.012
#> GSM35489 2 0.2359 0.8431 0.000 0.904 0.000 0.036 0.060
#> GSM35492 1 0.3622 0.7070 0.816 0.000 0.000 0.136 0.048
#> GSM35495 3 0.0000 0.9010 0.000 0.000 1.000 0.000 0.000
#> GSM35499 2 0.2291 0.8357 0.000 0.908 0.008 0.072 0.012
#> GSM35502 1 0.0566 0.7557 0.984 0.000 0.000 0.012 0.004
#> GSM35505 3 0.1095 0.8941 0.012 0.008 0.968 0.000 0.012
#> GSM35507 4 0.3120 0.7233 0.032 0.064 0.000 0.876 0.028
#> GSM35510 2 0.1493 0.8564 0.000 0.948 0.000 0.028 0.024
#> GSM35514 1 0.0324 0.7558 0.992 0.000 0.000 0.004 0.004
#> GSM35517 2 0.1124 0.8579 0.000 0.960 0.000 0.004 0.036
#> GSM35520 5 0.5296 0.1740 0.000 0.468 0.048 0.000 0.484
#> GSM35523 4 0.1764 0.7473 0.064 0.000 0.000 0.928 0.008
#> GSM35529 2 0.3573 0.7856 0.000 0.812 0.000 0.036 0.152
#> GSM35531 2 0.1087 0.8525 0.000 0.968 0.008 0.008 0.016
#> GSM35534 2 0.0693 0.8492 0.000 0.980 0.012 0.000 0.008
#> GSM35536 1 0.0404 0.7566 0.988 0.000 0.000 0.012 0.000
#> GSM35538 1 0.4555 0.2539 0.636 0.000 0.000 0.344 0.020
#> GSM35539 1 0.4747 -0.2369 0.496 0.000 0.000 0.488 0.016
#> GSM35540 2 0.5902 0.5747 0.000 0.600 0.000 0.192 0.208
#> GSM35541 2 0.0898 0.8571 0.000 0.972 0.000 0.008 0.020
#> GSM35442 1 0.6425 0.5576 0.644 0.000 0.140 0.132 0.084
#> GSM35447 3 0.0865 0.9004 0.004 0.000 0.972 0.000 0.024
#> GSM35450 1 0.4708 -0.0596 0.548 0.000 0.000 0.436 0.016
#> GSM35453 1 0.4070 0.5751 0.728 0.000 0.256 0.004 0.012
#> GSM35456 4 0.5939 0.6216 0.236 0.116 0.004 0.632 0.012
#> GSM35464 4 0.3807 0.6159 0.004 0.176 0.000 0.792 0.028
#> GSM35467 1 0.0566 0.7570 0.984 0.000 0.000 0.012 0.004
#> GSM35470 1 0.7454 0.0443 0.376 0.000 0.208 0.372 0.044
#> GSM35479 3 0.1485 0.8896 0.000 0.000 0.948 0.032 0.020
#> GSM35484 1 0.2569 0.7424 0.912 0.012 0.032 0.028 0.016
#> GSM35488 1 0.3321 0.7165 0.832 0.000 0.000 0.136 0.032
#> GSM35491 1 0.3460 0.7112 0.828 0.000 0.000 0.128 0.044
#> GSM35494 3 0.0912 0.8986 0.000 0.000 0.972 0.016 0.012
#> GSM35498 4 0.0451 0.7359 0.008 0.000 0.000 0.988 0.004
#> GSM35501 1 0.0451 0.7565 0.988 0.000 0.000 0.008 0.004
#> GSM35509 3 0.0451 0.9008 0.000 0.000 0.988 0.004 0.008
#> GSM35513 1 0.0162 0.7561 0.996 0.000 0.000 0.004 0.000
#> GSM35516 2 0.1082 0.8559 0.000 0.964 0.000 0.028 0.008
#> GSM35522 4 0.1628 0.7490 0.056 0.000 0.000 0.936 0.008
#> GSM35525 1 0.3967 0.5027 0.724 0.000 0.000 0.264 0.012
#> GSM35528 4 0.4661 0.4527 0.312 0.000 0.000 0.656 0.032
#> GSM35533 1 0.2452 0.7370 0.908 0.000 0.028 0.052 0.012
#> GSM35537 4 0.4707 0.6330 0.184 0.000 0.040 0.748 0.028
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM35441 2 0.5650 0.507 0.000 0.588 0.000 0.016 0.236 NA
#> GSM35446 3 0.1700 0.842 0.000 0.000 0.928 0.000 0.024 NA
#> GSM35449 5 0.5216 0.423 0.000 0.256 0.000 0.004 0.612 NA
#> GSM35455 5 0.5484 0.075 0.000 0.392 0.000 0.000 0.480 NA
#> GSM35458 5 0.0972 0.710 0.000 0.008 0.000 0.000 0.964 NA
#> GSM35460 3 0.0891 0.847 0.000 0.000 0.968 0.000 0.008 NA
#> GSM35461 5 0.6407 0.256 0.020 0.000 0.220 0.012 0.512 NA
#> GSM35463 2 0.2455 0.734 0.000 0.872 0.012 0.000 0.004 NA
#> GSM35472 3 0.5271 0.509 0.000 0.000 0.592 0.004 0.284 NA
#> GSM35475 5 0.1511 0.709 0.000 0.012 0.012 0.000 0.944 NA
#> GSM35483 2 0.4121 0.676 0.000 0.772 0.032 0.000 0.048 NA
#> GSM35496 3 0.3714 0.796 0.000 0.000 0.800 0.020 0.044 NA
#> GSM35497 5 0.5085 0.404 0.000 0.272 0.000 0.000 0.608 NA
#> GSM35504 2 0.5561 0.636 0.000 0.664 0.088 0.004 0.068 NA
#> GSM35508 5 0.2221 0.692 0.000 0.032 0.000 0.000 0.896 NA
#> GSM35511 5 0.1921 0.691 0.000 0.000 0.052 0.000 0.916 NA
#> GSM35512 3 0.5049 0.551 0.000 0.000 0.624 0.004 0.268 NA
#> GSM35515 5 0.0972 0.710 0.000 0.008 0.000 0.000 0.964 NA
#> GSM35519 5 0.4100 0.587 0.000 0.004 0.148 0.004 0.764 NA
#> GSM35527 5 0.3520 0.639 0.000 0.100 0.000 0.000 0.804 NA
#> GSM35532 5 0.3566 0.593 0.000 0.000 0.156 0.000 0.788 NA
#> GSM35439 2 0.2129 0.767 0.000 0.904 0.000 0.000 0.040 NA
#> GSM35443 1 0.5222 0.550 0.616 0.000 0.004 0.052 0.028 NA
#> GSM35445 1 0.4840 0.534 0.680 0.000 0.152 0.004 0.000 NA
#> GSM35448 3 0.4251 0.724 0.000 0.116 0.768 0.000 0.024 NA
#> GSM35451 4 0.5495 0.224 0.404 0.000 0.000 0.468 0.000 NA
#> GSM35454 3 0.2695 0.808 0.004 0.008 0.844 0.000 0.000 NA
#> GSM35457 2 0.5547 0.616 0.000 0.640 0.000 0.036 0.148 NA
#> GSM35465 2 0.7078 0.440 0.000 0.448 0.000 0.228 0.108 NA
#> GSM35468 1 0.4593 0.596 0.680 0.000 0.000 0.048 0.016 NA
#> GSM35471 4 0.3274 0.629 0.096 0.000 0.000 0.824 0.000 NA
#> GSM35473 1 0.2848 0.660 0.856 0.000 0.036 0.004 0.000 NA
#> GSM35477 4 0.5523 0.307 0.360 0.000 0.000 0.500 0.000 NA
#> GSM35480 1 0.4999 0.536 0.704 0.000 0.036 0.144 0.000 NA
#> GSM35482 3 0.3702 0.800 0.000 0.000 0.808 0.072 0.016 NA
#> GSM35485 2 0.1524 0.758 0.000 0.932 0.000 0.000 0.008 NA
#> GSM35489 2 0.3694 0.743 0.000 0.804 0.000 0.016 0.056 NA
#> GSM35492 1 0.4615 0.593 0.676 0.000 0.000 0.048 0.016 NA
#> GSM35495 3 0.0603 0.849 0.000 0.004 0.980 0.000 0.000 NA
#> GSM35499 2 0.3541 0.752 0.000 0.812 0.008 0.044 0.004 NA
#> GSM35502 1 0.0363 0.681 0.988 0.000 0.000 0.012 0.000 NA
#> GSM35505 3 0.2420 0.821 0.004 0.004 0.864 0.000 0.000 NA
#> GSM35507 4 0.4324 0.632 0.016 0.044 0.000 0.760 0.016 NA
#> GSM35510 2 0.3121 0.756 0.000 0.824 0.000 0.008 0.020 NA
#> GSM35514 1 0.0603 0.682 0.980 0.000 0.000 0.004 0.000 NA
#> GSM35517 2 0.2164 0.768 0.000 0.908 0.000 0.008 0.028 NA
#> GSM35520 5 0.5489 0.179 0.000 0.412 0.032 0.000 0.500 NA
#> GSM35523 4 0.1341 0.659 0.024 0.000 0.000 0.948 0.000 NA
#> GSM35529 2 0.5228 0.607 0.000 0.648 0.000 0.012 0.172 NA
#> GSM35531 2 0.2203 0.759 0.000 0.896 0.004 0.000 0.016 NA
#> GSM35534 2 0.1970 0.745 0.000 0.900 0.000 0.000 0.008 NA
#> GSM35536 1 0.1845 0.678 0.920 0.000 0.000 0.028 0.000 NA
#> GSM35538 1 0.4887 0.313 0.624 0.000 0.000 0.280 0.000 NA
#> GSM35539 1 0.5226 -0.149 0.460 0.000 0.000 0.448 0.000 NA
#> GSM35540 2 0.7431 0.347 0.000 0.392 0.000 0.232 0.164 NA
#> GSM35541 2 0.1863 0.768 0.000 0.920 0.000 0.000 0.036 NA
#> GSM35442 1 0.6706 0.380 0.456 0.000 0.108 0.048 0.024 NA
#> GSM35447 3 0.2680 0.828 0.004 0.000 0.856 0.000 0.016 NA
#> GSM35450 1 0.5290 0.109 0.544 0.000 0.000 0.340 0.000 NA
#> GSM35453 1 0.5287 0.404 0.588 0.000 0.288 0.004 0.000 NA
#> GSM35456 4 0.6792 0.447 0.248 0.080 0.000 0.480 0.000 NA
#> GSM35464 4 0.5118 0.507 0.000 0.108 0.000 0.688 0.036 NA
#> GSM35467 1 0.0520 0.683 0.984 0.000 0.000 0.008 0.000 NA
#> GSM35470 4 0.7950 0.116 0.176 0.000 0.220 0.304 0.016 NA
#> GSM35479 3 0.2365 0.830 0.000 0.000 0.888 0.040 0.000 NA
#> GSM35484 1 0.4178 0.607 0.748 0.012 0.020 0.020 0.000 NA
#> GSM35488 1 0.4594 0.604 0.700 0.000 0.000 0.072 0.012 NA
#> GSM35491 1 0.4615 0.593 0.676 0.000 0.000 0.048 0.016 NA
#> GSM35494 3 0.1867 0.843 0.000 0.000 0.916 0.020 0.000 NA
#> GSM35498 4 0.1858 0.651 0.004 0.000 0.000 0.904 0.000 NA
#> GSM35501 1 0.0508 0.680 0.984 0.000 0.000 0.012 0.000 NA
#> GSM35509 3 0.0777 0.849 0.000 0.000 0.972 0.004 0.000 NA
#> GSM35513 1 0.0458 0.683 0.984 0.000 0.000 0.000 0.000 NA
#> GSM35516 2 0.2933 0.753 0.000 0.852 0.000 0.032 0.008 NA
#> GSM35522 4 0.1245 0.659 0.016 0.000 0.000 0.952 0.000 NA
#> GSM35525 1 0.4212 0.452 0.688 0.000 0.000 0.264 0.000 NA
#> GSM35528 4 0.5771 0.294 0.252 0.000 0.000 0.532 0.004 NA
#> GSM35533 1 0.4279 0.616 0.752 0.004 0.016 0.056 0.000 NA
#> GSM35537 4 0.4924 0.565 0.096 0.000 0.076 0.728 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 time(p) k
#> CV:skmeans 79 3.41e-07 2
#> CV:skmeans 77 2.91e-05 3
#> CV:skmeans 44 8.32e-02 4
#> CV:skmeans 67 5.27e-07 5
#> CV:skmeans 61 1.21e-05 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "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 7758 rows and 79 columns.
#> Top rows (776, 1552, 2328, 3103, 3879) are extracted by 'CV' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.616 0.875 0.926 0.4746 0.529 0.529
#> 3 3 0.520 0.749 0.851 0.3512 0.804 0.643
#> 4 4 0.629 0.665 0.826 0.1613 0.811 0.535
#> 5 5 0.676 0.673 0.786 0.0480 0.911 0.684
#> 6 6 0.685 0.568 0.784 0.0321 0.969 0.870
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
#> GSM35441 2 0.0938 0.945 0.012 0.988
#> GSM35446 1 0.9323 0.601 0.652 0.348
#> GSM35449 2 0.1184 0.945 0.016 0.984
#> GSM35455 2 0.0000 0.945 0.000 1.000
#> GSM35458 1 0.9044 0.634 0.680 0.320
#> GSM35460 1 0.7674 0.787 0.776 0.224
#> GSM35461 1 0.3879 0.899 0.924 0.076
#> GSM35463 2 0.0672 0.944 0.008 0.992
#> GSM35472 1 0.6712 0.828 0.824 0.176
#> GSM35475 1 0.9248 0.615 0.660 0.340
#> GSM35483 2 0.0376 0.945 0.004 0.996
#> GSM35496 1 0.2043 0.913 0.968 0.032
#> GSM35497 2 0.0000 0.945 0.000 1.000
#> GSM35504 2 0.2778 0.926 0.048 0.952
#> GSM35508 2 0.0376 0.946 0.004 0.996
#> GSM35511 2 0.4022 0.896 0.080 0.920
#> GSM35512 1 0.7139 0.815 0.804 0.196
#> GSM35515 1 0.7376 0.797 0.792 0.208
#> GSM35519 1 0.7528 0.795 0.784 0.216
#> GSM35527 2 0.0376 0.946 0.004 0.996
#> GSM35532 2 0.9000 0.490 0.316 0.684
#> GSM35439 2 0.0938 0.945 0.012 0.988
#> GSM35443 1 0.2043 0.913 0.968 0.032
#> GSM35445 1 0.0376 0.910 0.996 0.004
#> GSM35448 2 0.4815 0.873 0.104 0.896
#> GSM35451 1 0.2236 0.910 0.964 0.036
#> GSM35454 1 0.5946 0.855 0.856 0.144
#> GSM35457 2 0.1184 0.944 0.016 0.984
#> GSM35465 2 0.1633 0.942 0.024 0.976
#> GSM35468 1 0.1414 0.913 0.980 0.020
#> GSM35471 1 0.4022 0.897 0.920 0.080
#> GSM35473 1 0.0376 0.910 0.996 0.004
#> GSM35477 1 0.1843 0.911 0.972 0.028
#> GSM35480 1 0.1633 0.914 0.976 0.024
#> GSM35482 1 0.3274 0.907 0.940 0.060
#> GSM35485 2 0.0672 0.944 0.008 0.992
#> GSM35489 2 0.0938 0.945 0.012 0.988
#> GSM35492 1 0.0000 0.910 1.000 0.000
#> GSM35495 1 0.7056 0.821 0.808 0.192
#> GSM35499 2 0.3584 0.916 0.068 0.932
#> GSM35502 1 0.0000 0.910 1.000 0.000
#> GSM35505 1 0.3733 0.894 0.928 0.072
#> GSM35507 1 0.9170 0.559 0.668 0.332
#> GSM35510 2 0.0376 0.945 0.004 0.996
#> GSM35514 1 0.0000 0.910 1.000 0.000
#> GSM35517 2 0.0000 0.945 0.000 1.000
#> GSM35520 1 0.9983 0.293 0.524 0.476
#> GSM35523 1 0.6531 0.834 0.832 0.168
#> GSM35529 2 0.0376 0.946 0.004 0.996
#> GSM35531 2 0.3733 0.911 0.072 0.928
#> GSM35534 2 0.0000 0.945 0.000 1.000
#> GSM35536 1 0.0000 0.910 1.000 0.000
#> GSM35538 1 0.0376 0.911 0.996 0.004
#> GSM35539 1 0.1184 0.913 0.984 0.016
#> GSM35540 2 0.3431 0.919 0.064 0.936
#> GSM35541 2 0.0672 0.944 0.008 0.992
#> GSM35442 1 0.1843 0.913 0.972 0.028
#> GSM35447 1 0.4939 0.885 0.892 0.108
#> GSM35450 1 0.0000 0.910 1.000 0.000
#> GSM35453 1 0.0000 0.910 1.000 0.000
#> GSM35456 1 0.5946 0.851 0.856 0.144
#> GSM35464 2 0.3733 0.914 0.072 0.928
#> GSM35467 1 0.0000 0.910 1.000 0.000
#> GSM35470 1 0.2236 0.913 0.964 0.036
#> GSM35479 1 0.2236 0.913 0.964 0.036
#> GSM35484 1 0.2043 0.913 0.968 0.032
#> GSM35488 1 0.0000 0.910 1.000 0.000
#> GSM35491 1 0.1414 0.913 0.980 0.020
#> GSM35494 1 0.2778 0.912 0.952 0.048
#> GSM35498 2 0.8081 0.684 0.248 0.752
#> GSM35501 1 0.0000 0.910 1.000 0.000
#> GSM35509 1 0.3584 0.905 0.932 0.068
#> GSM35513 1 0.0000 0.910 1.000 0.000
#> GSM35516 2 0.0672 0.944 0.008 0.992
#> GSM35522 2 0.6712 0.808 0.176 0.824
#> GSM35525 1 0.0000 0.910 1.000 0.000
#> GSM35528 1 0.2043 0.914 0.968 0.032
#> GSM35533 1 0.2043 0.912 0.968 0.032
#> GSM35537 1 0.2603 0.911 0.956 0.044
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM35441 2 0.0747 0.8745 0.000 0.984 0.016
#> GSM35446 3 0.1031 0.7984 0.000 0.024 0.976
#> GSM35449 2 0.0237 0.8767 0.000 0.996 0.004
#> GSM35455 2 0.0000 0.8763 0.000 1.000 0.000
#> GSM35458 1 0.8546 0.4407 0.588 0.276 0.136
#> GSM35460 3 0.1129 0.8006 0.004 0.020 0.976
#> GSM35461 3 0.4521 0.7713 0.180 0.004 0.816
#> GSM35463 2 0.1964 0.8632 0.000 0.944 0.056
#> GSM35472 3 0.3213 0.8057 0.092 0.008 0.900
#> GSM35475 3 0.7880 0.7007 0.164 0.168 0.668
#> GSM35483 2 0.2261 0.8527 0.000 0.932 0.068
#> GSM35496 3 0.4062 0.7813 0.164 0.000 0.836
#> GSM35497 2 0.0000 0.8763 0.000 1.000 0.000
#> GSM35504 2 0.3686 0.8009 0.000 0.860 0.140
#> GSM35508 2 0.0237 0.8755 0.000 0.996 0.004
#> GSM35511 3 0.6416 0.5693 0.020 0.304 0.676
#> GSM35512 3 0.4475 0.7950 0.144 0.016 0.840
#> GSM35515 1 0.7899 0.6186 0.664 0.144 0.192
#> GSM35519 3 0.5060 0.7889 0.156 0.028 0.816
#> GSM35527 2 0.0000 0.8763 0.000 1.000 0.000
#> GSM35532 3 0.4446 0.7874 0.032 0.112 0.856
#> GSM35439 2 0.0237 0.8766 0.000 0.996 0.004
#> GSM35443 1 0.4834 0.7530 0.792 0.004 0.204
#> GSM35445 1 0.2625 0.8098 0.916 0.000 0.084
#> GSM35448 3 0.4291 0.6953 0.000 0.180 0.820
#> GSM35451 1 0.4178 0.7860 0.828 0.000 0.172
#> GSM35454 1 0.6836 0.6461 0.572 0.016 0.412
#> GSM35457 2 0.0592 0.8754 0.000 0.988 0.012
#> GSM35465 2 0.1289 0.8696 0.000 0.968 0.032
#> GSM35468 1 0.3619 0.7909 0.864 0.000 0.136
#> GSM35471 1 0.5706 0.7264 0.680 0.000 0.320
#> GSM35473 1 0.0892 0.8058 0.980 0.000 0.020
#> GSM35477 1 0.3941 0.7913 0.844 0.000 0.156
#> GSM35480 1 0.4887 0.7799 0.772 0.000 0.228
#> GSM35482 1 0.6264 0.6997 0.616 0.004 0.380
#> GSM35485 2 0.0892 0.8746 0.000 0.980 0.020
#> GSM35489 2 0.0747 0.8758 0.000 0.984 0.016
#> GSM35492 1 0.2066 0.7932 0.940 0.000 0.060
#> GSM35495 3 0.1491 0.7952 0.016 0.016 0.968
#> GSM35499 2 0.5650 0.5864 0.000 0.688 0.312
#> GSM35502 1 0.0237 0.8073 0.996 0.000 0.004
#> GSM35505 1 0.5315 0.7209 0.772 0.012 0.216
#> GSM35507 1 0.9133 0.5159 0.528 0.176 0.296
#> GSM35510 2 0.1031 0.8737 0.000 0.976 0.024
#> GSM35514 1 0.0424 0.8071 0.992 0.000 0.008
#> GSM35517 2 0.1031 0.8737 0.000 0.976 0.024
#> GSM35520 2 0.8140 -0.1675 0.456 0.476 0.068
#> GSM35523 1 0.7367 0.6923 0.648 0.060 0.292
#> GSM35529 2 0.0000 0.8763 0.000 1.000 0.000
#> GSM35531 2 0.4189 0.8146 0.056 0.876 0.068
#> GSM35534 2 0.1031 0.8737 0.000 0.976 0.024
#> GSM35536 1 0.0237 0.8064 0.996 0.000 0.004
#> GSM35538 1 0.0424 0.8089 0.992 0.000 0.008
#> GSM35539 1 0.4062 0.7910 0.836 0.000 0.164
#> GSM35540 2 0.3752 0.7792 0.000 0.856 0.144
#> GSM35541 2 0.0000 0.8763 0.000 1.000 0.000
#> GSM35442 1 0.4399 0.7672 0.812 0.000 0.188
#> GSM35447 1 0.5681 0.6951 0.748 0.016 0.236
#> GSM35450 1 0.3619 0.7917 0.864 0.000 0.136
#> GSM35453 1 0.1289 0.8097 0.968 0.000 0.032
#> GSM35456 1 0.6172 0.7274 0.680 0.012 0.308
#> GSM35464 2 0.4178 0.7440 0.000 0.828 0.172
#> GSM35467 1 0.0237 0.8064 0.996 0.000 0.004
#> GSM35470 1 0.4842 0.7718 0.776 0.000 0.224
#> GSM35479 3 0.6126 -0.0216 0.400 0.000 0.600
#> GSM35484 1 0.3965 0.8056 0.860 0.008 0.132
#> GSM35488 1 0.1753 0.7953 0.952 0.000 0.048
#> GSM35491 1 0.3267 0.7952 0.884 0.000 0.116
#> GSM35494 1 0.6033 0.7159 0.660 0.004 0.336
#> GSM35498 2 0.9135 0.3074 0.208 0.544 0.248
#> GSM35501 1 0.0237 0.8073 0.996 0.000 0.004
#> GSM35509 3 0.1878 0.7667 0.044 0.004 0.952
#> GSM35513 1 0.0237 0.8064 0.996 0.000 0.004
#> GSM35516 2 0.1529 0.8701 0.000 0.960 0.040
#> GSM35522 2 0.9111 0.2993 0.176 0.532 0.292
#> GSM35525 1 0.2959 0.8021 0.900 0.000 0.100
#> GSM35528 1 0.4172 0.7863 0.840 0.004 0.156
#> GSM35533 1 0.4605 0.7797 0.796 0.000 0.204
#> GSM35537 1 0.5722 0.7400 0.704 0.004 0.292
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM35441 2 0.0188 0.9300 0.000 0.996 0.004 0.000
#> GSM35446 3 0.0524 0.8333 0.000 0.004 0.988 0.008
#> GSM35449 2 0.0188 0.9300 0.000 0.996 0.004 0.000
#> GSM35455 2 0.0188 0.9300 0.000 0.996 0.004 0.000
#> GSM35458 1 0.5126 0.6381 0.792 0.116 0.028 0.064
#> GSM35460 3 0.0524 0.8333 0.000 0.004 0.988 0.008
#> GSM35461 1 0.6626 0.1545 0.544 0.000 0.364 0.092
#> GSM35463 2 0.3051 0.8808 0.000 0.884 0.028 0.088
#> GSM35472 3 0.2915 0.8412 0.080 0.000 0.892 0.028
#> GSM35475 3 0.3557 0.8241 0.108 0.036 0.856 0.000
#> GSM35483 2 0.4387 0.8083 0.000 0.804 0.052 0.144
#> GSM35496 3 0.3612 0.8250 0.100 0.000 0.856 0.044
#> GSM35497 2 0.0188 0.9300 0.000 0.996 0.004 0.000
#> GSM35504 2 0.4940 0.7884 0.000 0.776 0.128 0.096
#> GSM35508 2 0.0564 0.9290 0.004 0.988 0.004 0.004
#> GSM35511 3 0.3858 0.8014 0.056 0.100 0.844 0.000
#> GSM35512 3 0.2376 0.8458 0.068 0.000 0.916 0.016
#> GSM35515 1 0.4149 0.6901 0.840 0.032 0.020 0.108
#> GSM35519 3 0.3700 0.8300 0.096 0.008 0.860 0.036
#> GSM35527 2 0.0376 0.9295 0.000 0.992 0.004 0.004
#> GSM35532 3 0.3161 0.8434 0.056 0.028 0.896 0.020
#> GSM35439 2 0.0000 0.9297 0.000 1.000 0.000 0.000
#> GSM35443 1 0.3196 0.6939 0.856 0.000 0.008 0.136
#> GSM35445 1 0.5979 0.5400 0.692 0.000 0.136 0.172
#> GSM35448 3 0.2319 0.8160 0.000 0.040 0.924 0.036
#> GSM35451 4 0.2814 0.6762 0.132 0.000 0.000 0.868
#> GSM35454 4 0.7648 -0.1135 0.392 0.008 0.160 0.440
#> GSM35457 2 0.0336 0.9293 0.000 0.992 0.000 0.008
#> GSM35465 2 0.0817 0.9248 0.000 0.976 0.000 0.024
#> GSM35468 1 0.2546 0.7161 0.900 0.000 0.008 0.092
#> GSM35471 4 0.0376 0.7007 0.004 0.000 0.004 0.992
#> GSM35473 1 0.1936 0.7224 0.940 0.000 0.032 0.028
#> GSM35477 4 0.4776 0.4042 0.376 0.000 0.000 0.624
#> GSM35480 4 0.2670 0.7033 0.072 0.000 0.024 0.904
#> GSM35482 1 0.6082 0.0891 0.480 0.000 0.044 0.476
#> GSM35485 2 0.0376 0.9287 0.000 0.992 0.004 0.004
#> GSM35489 2 0.0469 0.9290 0.000 0.988 0.000 0.012
#> GSM35492 1 0.0672 0.7241 0.984 0.000 0.008 0.008
#> GSM35495 3 0.1675 0.8286 0.004 0.004 0.948 0.044
#> GSM35499 4 0.5296 -0.2376 0.000 0.496 0.008 0.496
#> GSM35502 1 0.4994 -0.1367 0.520 0.000 0.000 0.480
#> GSM35505 3 0.5349 0.2590 0.368 0.004 0.616 0.012
#> GSM35507 4 0.1109 0.6958 0.004 0.028 0.000 0.968
#> GSM35510 2 0.0376 0.9287 0.000 0.992 0.004 0.004
#> GSM35514 1 0.2216 0.6973 0.908 0.000 0.000 0.092
#> GSM35517 2 0.0376 0.9287 0.000 0.992 0.004 0.004
#> GSM35520 2 0.6186 0.6268 0.196 0.692 0.100 0.012
#> GSM35523 4 0.1389 0.6953 0.048 0.000 0.000 0.952
#> GSM35529 2 0.0188 0.9300 0.000 0.996 0.004 0.000
#> GSM35531 2 0.5460 0.7862 0.032 0.768 0.060 0.140
#> GSM35534 2 0.1305 0.9165 0.000 0.960 0.036 0.004
#> GSM35536 1 0.1867 0.7109 0.928 0.000 0.000 0.072
#> GSM35538 4 0.4999 0.1268 0.492 0.000 0.000 0.508
#> GSM35539 4 0.4193 0.5721 0.268 0.000 0.000 0.732
#> GSM35540 2 0.2814 0.8521 0.000 0.868 0.000 0.132
#> GSM35541 2 0.0188 0.9300 0.000 0.996 0.004 0.000
#> GSM35442 1 0.3032 0.7005 0.868 0.000 0.008 0.124
#> GSM35447 1 0.4675 0.6291 0.736 0.000 0.244 0.020
#> GSM35450 4 0.3266 0.6591 0.168 0.000 0.000 0.832
#> GSM35453 1 0.6327 0.4535 0.652 0.000 0.132 0.216
#> GSM35456 4 0.0657 0.7028 0.012 0.000 0.004 0.984
#> GSM35464 2 0.3074 0.8317 0.000 0.848 0.000 0.152
#> GSM35467 1 0.1474 0.7166 0.948 0.000 0.000 0.052
#> GSM35470 4 0.4428 0.5019 0.276 0.000 0.004 0.720
#> GSM35479 4 0.3229 0.6669 0.072 0.000 0.048 0.880
#> GSM35484 1 0.4098 0.6716 0.784 0.000 0.012 0.204
#> GSM35488 1 0.0336 0.7230 0.992 0.000 0.000 0.008
#> GSM35491 1 0.1807 0.7258 0.940 0.000 0.008 0.052
#> GSM35494 4 0.5619 0.5847 0.124 0.000 0.152 0.724
#> GSM35498 1 0.5636 0.2522 0.544 0.016 0.004 0.436
#> GSM35501 1 0.4985 -0.1289 0.532 0.000 0.000 0.468
#> GSM35509 3 0.5158 0.1929 0.000 0.004 0.524 0.472
#> GSM35513 1 0.1637 0.7156 0.940 0.000 0.000 0.060
#> GSM35516 2 0.3404 0.8685 0.000 0.864 0.032 0.104
#> GSM35522 4 0.0657 0.6993 0.004 0.012 0.000 0.984
#> GSM35525 4 0.4866 0.3573 0.404 0.000 0.000 0.596
#> GSM35528 4 0.5203 0.1956 0.416 0.000 0.008 0.576
#> GSM35533 4 0.2860 0.6891 0.100 0.004 0.008 0.888
#> GSM35537 4 0.1474 0.6958 0.052 0.000 0.000 0.948
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM35441 2 0.0162 0.895 0.000 0.996 0.000 0.000 0.004
#> GSM35446 5 0.4126 0.373 0.000 0.000 0.380 0.000 0.620
#> GSM35449 2 0.0162 0.895 0.000 0.996 0.000 0.000 0.004
#> GSM35455 2 0.0162 0.895 0.000 0.996 0.000 0.000 0.004
#> GSM35458 1 0.6024 0.618 0.668 0.016 0.196 0.024 0.096
#> GSM35460 5 0.3949 0.505 0.000 0.000 0.332 0.000 0.668
#> GSM35461 1 0.5720 0.442 0.596 0.000 0.020 0.060 0.324
#> GSM35463 2 0.3275 0.850 0.000 0.860 0.064 0.068 0.008
#> GSM35472 5 0.1701 0.831 0.016 0.000 0.028 0.012 0.944
#> GSM35475 5 0.3495 0.713 0.032 0.000 0.152 0.000 0.816
#> GSM35483 2 0.4747 0.762 0.000 0.764 0.116 0.100 0.020
#> GSM35496 5 0.2522 0.815 0.028 0.000 0.056 0.012 0.904
#> GSM35497 2 0.0162 0.895 0.000 0.996 0.000 0.000 0.004
#> GSM35504 2 0.5360 0.623 0.000 0.676 0.244 0.052 0.028
#> GSM35508 2 0.2032 0.872 0.000 0.924 0.052 0.004 0.020
#> GSM35511 5 0.1808 0.812 0.004 0.020 0.040 0.000 0.936
#> GSM35512 5 0.1644 0.834 0.012 0.004 0.028 0.008 0.948
#> GSM35515 1 0.5833 0.625 0.676 0.004 0.192 0.032 0.096
#> GSM35519 5 0.1383 0.833 0.012 0.008 0.012 0.008 0.960
#> GSM35527 2 0.0854 0.892 0.000 0.976 0.012 0.004 0.008
#> GSM35532 5 0.0566 0.830 0.004 0.000 0.012 0.000 0.984
#> GSM35439 2 0.0404 0.894 0.000 0.988 0.012 0.000 0.000
#> GSM35443 1 0.3275 0.752 0.860 0.000 0.008 0.068 0.064
#> GSM35445 3 0.5656 0.484 0.316 0.000 0.592 0.088 0.004
#> GSM35448 3 0.4511 0.257 0.000 0.000 0.628 0.016 0.356
#> GSM35451 4 0.2624 0.683 0.116 0.000 0.012 0.872 0.000
#> GSM35454 3 0.5808 0.560 0.064 0.004 0.600 0.316 0.016
#> GSM35457 2 0.0290 0.895 0.000 0.992 0.000 0.008 0.000
#> GSM35465 2 0.0865 0.891 0.000 0.972 0.000 0.024 0.004
#> GSM35468 1 0.2369 0.774 0.908 0.000 0.004 0.032 0.056
#> GSM35471 4 0.0798 0.678 0.016 0.000 0.008 0.976 0.000
#> GSM35473 1 0.2206 0.743 0.912 0.000 0.068 0.016 0.004
#> GSM35477 4 0.4735 0.610 0.284 0.000 0.044 0.672 0.000
#> GSM35480 4 0.3651 0.669 0.060 0.000 0.108 0.828 0.004
#> GSM35482 4 0.7123 0.124 0.368 0.000 0.220 0.392 0.020
#> GSM35485 2 0.0880 0.891 0.000 0.968 0.032 0.000 0.000
#> GSM35489 2 0.0955 0.893 0.000 0.968 0.028 0.004 0.000
#> GSM35492 1 0.1764 0.774 0.928 0.000 0.008 0.000 0.064
#> GSM35495 3 0.4564 0.234 0.000 0.000 0.612 0.016 0.372
#> GSM35499 2 0.5582 0.445 0.000 0.564 0.060 0.368 0.008
#> GSM35502 4 0.5243 0.466 0.412 0.000 0.048 0.540 0.000
#> GSM35505 3 0.5794 0.543 0.228 0.004 0.624 0.000 0.144
#> GSM35507 4 0.1989 0.659 0.004 0.032 0.028 0.932 0.004
#> GSM35510 2 0.0510 0.894 0.000 0.984 0.016 0.000 0.000
#> GSM35514 1 0.2770 0.704 0.880 0.000 0.044 0.076 0.000
#> GSM35517 2 0.0404 0.895 0.000 0.988 0.012 0.000 0.000
#> GSM35520 2 0.6470 0.555 0.168 0.644 0.076 0.004 0.108
#> GSM35523 4 0.3523 0.639 0.048 0.000 0.096 0.844 0.012
#> GSM35529 2 0.0162 0.895 0.000 0.996 0.000 0.000 0.004
#> GSM35531 2 0.6272 0.650 0.036 0.668 0.096 0.176 0.024
#> GSM35534 2 0.1914 0.878 0.000 0.924 0.060 0.000 0.016
#> GSM35536 1 0.2708 0.715 0.884 0.000 0.044 0.072 0.000
#> GSM35538 4 0.5022 0.567 0.332 0.000 0.048 0.620 0.000
#> GSM35539 4 0.4028 0.664 0.192 0.000 0.040 0.768 0.000
#> GSM35540 2 0.3161 0.827 0.000 0.860 0.032 0.100 0.008
#> GSM35541 2 0.0000 0.895 0.000 1.000 0.000 0.000 0.000
#> GSM35442 1 0.2938 0.763 0.880 0.000 0.008 0.048 0.064
#> GSM35447 3 0.5331 0.458 0.344 0.000 0.600 0.008 0.048
#> GSM35450 4 0.2966 0.680 0.136 0.000 0.016 0.848 0.000
#> GSM35453 1 0.5891 -0.219 0.476 0.000 0.448 0.060 0.016
#> GSM35456 4 0.1492 0.668 0.008 0.000 0.040 0.948 0.004
#> GSM35464 2 0.3510 0.801 0.000 0.832 0.032 0.128 0.008
#> GSM35467 1 0.0693 0.761 0.980 0.000 0.008 0.012 0.000
#> GSM35470 4 0.5611 0.585 0.236 0.000 0.092 0.656 0.016
#> GSM35479 4 0.4972 0.531 0.060 0.000 0.196 0.724 0.020
#> GSM35484 1 0.3280 0.700 0.812 0.000 0.012 0.176 0.000
#> GSM35488 1 0.1331 0.774 0.952 0.000 0.008 0.000 0.040
#> GSM35491 1 0.2199 0.775 0.916 0.000 0.008 0.016 0.060
#> GSM35494 3 0.5721 0.535 0.084 0.000 0.640 0.256 0.020
#> GSM35498 1 0.5308 0.447 0.628 0.004 0.044 0.316 0.008
#> GSM35501 4 0.5255 0.522 0.388 0.000 0.052 0.560 0.000
#> GSM35509 3 0.5422 0.464 0.000 0.000 0.580 0.348 0.072
#> GSM35513 1 0.1992 0.737 0.924 0.000 0.044 0.032 0.000
#> GSM35516 2 0.3325 0.838 0.000 0.852 0.032 0.104 0.012
#> GSM35522 4 0.2679 0.646 0.004 0.004 0.096 0.884 0.012
#> GSM35525 4 0.4822 0.608 0.288 0.000 0.048 0.664 0.000
#> GSM35528 4 0.5336 0.291 0.428 0.000 0.008 0.528 0.036
#> GSM35533 4 0.2853 0.681 0.076 0.004 0.040 0.880 0.000
#> GSM35537 4 0.3661 0.640 0.056 0.000 0.096 0.836 0.012
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM35441 2 0.0000 0.8450 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM35446 3 0.3997 -0.0992 0.000 0.000 0.508 0.000 0.488 0.004
#> GSM35449 2 0.0260 0.8454 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM35455 2 0.0000 0.8450 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM35458 1 0.4999 0.2883 0.500 0.008 0.000 0.004 0.040 0.448
#> GSM35460 5 0.4338 0.0173 0.000 0.000 0.484 0.000 0.496 0.020
#> GSM35461 1 0.4945 0.3864 0.636 0.000 0.004 0.020 0.296 0.044
#> GSM35463 2 0.5315 0.7591 0.000 0.704 0.100 0.044 0.016 0.136
#> GSM35472 5 0.1749 0.7881 0.024 0.000 0.036 0.000 0.932 0.008
#> GSM35475 5 0.4435 0.5304 0.024 0.000 0.004 0.000 0.580 0.392
#> GSM35483 2 0.5873 0.7092 0.000 0.652 0.148 0.056 0.016 0.128
#> GSM35496 5 0.3296 0.7408 0.044 0.000 0.044 0.000 0.848 0.064
#> GSM35497 2 0.0000 0.8450 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM35504 2 0.5561 0.5852 0.000 0.632 0.240 0.020 0.016 0.092
#> GSM35508 2 0.4584 0.7043 0.000 0.736 0.068 0.000 0.036 0.160
#> GSM35511 5 0.3701 0.7175 0.012 0.000 0.072 0.000 0.804 0.112
#> GSM35512 5 0.1708 0.7915 0.024 0.000 0.040 0.000 0.932 0.004
#> GSM35515 1 0.4772 0.2912 0.504 0.000 0.000 0.004 0.040 0.452
#> GSM35519 5 0.1313 0.7933 0.028 0.000 0.016 0.000 0.952 0.004
#> GSM35527 2 0.3155 0.7839 0.000 0.840 0.068 0.004 0.000 0.088
#> GSM35532 5 0.1218 0.7888 0.012 0.000 0.004 0.000 0.956 0.028
#> GSM35439 2 0.2145 0.8347 0.000 0.900 0.028 0.000 0.000 0.072
#> GSM35443 1 0.1976 0.6819 0.924 0.000 0.004 0.032 0.032 0.008
#> GSM35445 3 0.4703 0.5451 0.236 0.000 0.684 0.064 0.000 0.016
#> GSM35448 3 0.3094 0.5495 0.000 0.000 0.824 0.000 0.140 0.036
#> GSM35451 4 0.1075 0.6178 0.048 0.000 0.000 0.952 0.000 0.000
#> GSM35454 3 0.4451 0.5611 0.056 0.000 0.744 0.164 0.000 0.036
#> GSM35457 2 0.0146 0.8446 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM35465 2 0.0717 0.8420 0.000 0.976 0.000 0.008 0.000 0.016
#> GSM35468 1 0.0922 0.7046 0.968 0.000 0.004 0.004 0.024 0.000
#> GSM35471 4 0.0993 0.5980 0.000 0.000 0.012 0.964 0.000 0.024
#> GSM35473 1 0.2045 0.6813 0.920 0.000 0.024 0.028 0.000 0.028
#> GSM35477 4 0.2872 0.5592 0.152 0.000 0.004 0.832 0.000 0.012
#> GSM35480 4 0.4194 0.5242 0.048 0.000 0.048 0.776 0.000 0.128
#> GSM35482 6 0.7927 0.0000 0.276 0.000 0.140 0.256 0.020 0.308
#> GSM35485 2 0.2563 0.8309 0.000 0.880 0.040 0.004 0.000 0.076
#> GSM35489 2 0.2688 0.8250 0.000 0.868 0.064 0.000 0.000 0.068
#> GSM35492 1 0.1194 0.7022 0.956 0.000 0.004 0.000 0.032 0.008
#> GSM35495 3 0.3263 0.5466 0.000 0.000 0.800 0.004 0.176 0.020
#> GSM35499 2 0.6062 0.4860 0.000 0.564 0.036 0.192 0.000 0.208
#> GSM35502 4 0.4217 0.3497 0.296 0.000 0.008 0.672 0.000 0.024
#> GSM35505 3 0.4225 0.6184 0.152 0.000 0.768 0.004 0.048 0.028
#> GSM35507 4 0.4080 0.4553 0.004 0.080 0.016 0.784 0.000 0.116
#> GSM35510 2 0.0436 0.8456 0.000 0.988 0.004 0.004 0.000 0.004
#> GSM35514 1 0.2734 0.6366 0.864 0.000 0.008 0.104 0.000 0.024
#> GSM35517 2 0.1194 0.8442 0.000 0.956 0.008 0.004 0.000 0.032
#> GSM35520 2 0.7408 0.5153 0.088 0.532 0.088 0.004 0.096 0.192
#> GSM35523 4 0.4657 0.2815 0.016 0.000 0.032 0.656 0.004 0.292
#> GSM35529 2 0.0000 0.8450 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM35531 2 0.7285 0.4177 0.036 0.488 0.124 0.276 0.008 0.068
#> GSM35534 2 0.4436 0.7832 0.000 0.752 0.096 0.004 0.016 0.132
#> GSM35536 1 0.3219 0.5887 0.808 0.000 0.008 0.168 0.000 0.016
#> GSM35538 4 0.3197 0.5298 0.176 0.000 0.008 0.804 0.000 0.012
#> GSM35539 4 0.2112 0.6076 0.088 0.000 0.000 0.896 0.000 0.016
#> GSM35540 2 0.2932 0.7729 0.000 0.836 0.004 0.020 0.000 0.140
#> GSM35541 2 0.0000 0.8450 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM35442 1 0.1647 0.6939 0.940 0.000 0.004 0.016 0.032 0.008
#> GSM35447 3 0.4378 0.5715 0.252 0.000 0.700 0.008 0.008 0.032
#> GSM35450 4 0.1349 0.6179 0.056 0.000 0.000 0.940 0.000 0.004
#> GSM35453 3 0.5574 0.2823 0.392 0.000 0.504 0.084 0.000 0.020
#> GSM35456 4 0.2971 0.5138 0.004 0.000 0.020 0.832 0.000 0.144
#> GSM35464 2 0.3304 0.7446 0.000 0.816 0.004 0.040 0.000 0.140
#> GSM35467 1 0.1370 0.6942 0.948 0.000 0.004 0.036 0.000 0.012
#> GSM35470 4 0.6250 -0.0134 0.176 0.000 0.024 0.532 0.008 0.260
#> GSM35479 4 0.6751 -0.2461 0.048 0.000 0.148 0.480 0.016 0.308
#> GSM35484 1 0.3349 0.5104 0.748 0.000 0.008 0.244 0.000 0.000
#> GSM35488 1 0.1007 0.7048 0.968 0.000 0.004 0.016 0.008 0.004
#> GSM35491 1 0.1116 0.7035 0.960 0.000 0.004 0.000 0.028 0.008
#> GSM35494 3 0.5770 0.4163 0.052 0.000 0.656 0.136 0.012 0.144
#> GSM35498 1 0.5456 0.1515 0.656 0.004 0.028 0.168 0.000 0.144
#> GSM35501 4 0.4012 0.4402 0.256 0.000 0.008 0.712 0.000 0.024
#> GSM35509 3 0.5484 0.3637 0.000 0.000 0.644 0.172 0.032 0.152
#> GSM35513 1 0.2588 0.6568 0.876 0.000 0.008 0.092 0.000 0.024
#> GSM35516 2 0.4251 0.7765 0.000 0.768 0.012 0.136 0.008 0.076
#> GSM35522 4 0.4235 0.3112 0.000 0.000 0.032 0.672 0.004 0.292
#> GSM35525 4 0.3183 0.5509 0.164 0.000 0.008 0.812 0.000 0.016
#> GSM35528 1 0.4862 -0.2917 0.480 0.000 0.004 0.480 0.020 0.016
#> GSM35533 4 0.1750 0.6130 0.040 0.000 0.016 0.932 0.000 0.012
#> GSM35537 4 0.4813 0.2756 0.024 0.000 0.032 0.648 0.004 0.292
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 time(p) k
#> CV:pam 77 6.31e-02 2
#> CV:pam 74 7.17e-07 3
#> CV:pam 65 2.76e-05 4
#> CV:pam 66 1.30e-05 5
#> CV:pam 58 1.59e-05 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "mclust"]
# you can also extract it by
# res = res_list["CV:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 7758 rows and 79 columns.
#> Top rows (776, 1552, 2328, 3103, 3879) are extracted by 'CV' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.610 0.850 0.916 0.3839 0.562 0.562
#> 3 3 0.819 0.821 0.901 0.7017 0.679 0.474
#> 4 4 0.761 0.846 0.908 0.1014 0.890 0.700
#> 5 5 0.751 0.723 0.811 0.0622 0.990 0.965
#> 6 6 0.725 0.464 0.752 0.0580 0.895 0.652
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM35441 2 0.0000 0.9589 0.000 1.000
#> GSM35446 2 0.0000 0.9589 0.000 1.000
#> GSM35449 2 0.0000 0.9589 0.000 1.000
#> GSM35455 2 0.0000 0.9589 0.000 1.000
#> GSM35458 2 0.0000 0.9589 0.000 1.000
#> GSM35460 2 0.0000 0.9589 0.000 1.000
#> GSM35461 2 0.1184 0.9498 0.016 0.984
#> GSM35463 2 0.0000 0.9589 0.000 1.000
#> GSM35472 2 0.0000 0.9589 0.000 1.000
#> GSM35475 2 0.0000 0.9589 0.000 1.000
#> GSM35483 2 0.0000 0.9589 0.000 1.000
#> GSM35496 2 0.1184 0.9498 0.016 0.984
#> GSM35497 2 0.0000 0.9589 0.000 1.000
#> GSM35504 2 0.0000 0.9589 0.000 1.000
#> GSM35508 2 0.0000 0.9589 0.000 1.000
#> GSM35511 2 0.0000 0.9589 0.000 1.000
#> GSM35512 2 0.0000 0.9589 0.000 1.000
#> GSM35515 2 0.0000 0.9589 0.000 1.000
#> GSM35519 2 0.0000 0.9589 0.000 1.000
#> GSM35527 2 0.0000 0.9589 0.000 1.000
#> GSM35532 2 0.0000 0.9589 0.000 1.000
#> GSM35439 2 0.0000 0.9589 0.000 1.000
#> GSM35443 1 0.9993 0.4126 0.516 0.484
#> GSM35445 2 0.9580 0.1022 0.380 0.620
#> GSM35448 2 0.0000 0.9589 0.000 1.000
#> GSM35451 1 0.9608 0.6555 0.616 0.384
#> GSM35454 2 0.1184 0.9498 0.016 0.984
#> GSM35457 2 0.0000 0.9589 0.000 1.000
#> GSM35465 2 0.0000 0.9589 0.000 1.000
#> GSM35468 1 0.6712 0.8101 0.824 0.176
#> GSM35471 2 0.9522 0.1338 0.372 0.628
#> GSM35473 1 0.8909 0.7504 0.692 0.308
#> GSM35477 1 0.8861 0.7531 0.696 0.304
#> GSM35480 1 0.9209 0.7247 0.664 0.336
#> GSM35482 2 0.1184 0.9498 0.016 0.984
#> GSM35485 2 0.0000 0.9589 0.000 1.000
#> GSM35489 2 0.0000 0.9589 0.000 1.000
#> GSM35492 1 0.6887 0.8084 0.816 0.184
#> GSM35495 2 0.0938 0.9522 0.012 0.988
#> GSM35499 2 0.0000 0.9589 0.000 1.000
#> GSM35502 1 0.0000 0.7717 1.000 0.000
#> GSM35505 2 0.1184 0.9498 0.016 0.984
#> GSM35507 2 0.1184 0.9498 0.016 0.984
#> GSM35510 2 0.0000 0.9589 0.000 1.000
#> GSM35514 1 0.5737 0.8076 0.864 0.136
#> GSM35517 2 0.0000 0.9589 0.000 1.000
#> GSM35520 2 0.0000 0.9589 0.000 1.000
#> GSM35523 1 0.9491 0.6814 0.632 0.368
#> GSM35529 2 0.0000 0.9589 0.000 1.000
#> GSM35531 2 0.0000 0.9589 0.000 1.000
#> GSM35534 2 0.0000 0.9589 0.000 1.000
#> GSM35536 1 0.0000 0.7717 1.000 0.000
#> GSM35538 1 0.1184 0.7777 0.984 0.016
#> GSM35539 1 0.3431 0.7874 0.936 0.064
#> GSM35540 2 0.0000 0.9589 0.000 1.000
#> GSM35541 2 0.0000 0.9589 0.000 1.000
#> GSM35442 2 0.2043 0.9335 0.032 0.968
#> GSM35447 2 0.1184 0.9498 0.016 0.984
#> GSM35450 1 0.6438 0.7968 0.836 0.164
#> GSM35453 2 0.3879 0.8788 0.076 0.924
#> GSM35456 2 0.1184 0.9498 0.016 0.984
#> GSM35464 2 0.0000 0.9589 0.000 1.000
#> GSM35467 1 0.0000 0.7717 1.000 0.000
#> GSM35470 1 0.9850 0.5683 0.572 0.428
#> GSM35479 2 0.1184 0.9498 0.016 0.984
#> GSM35484 1 0.9491 0.6835 0.632 0.368
#> GSM35488 1 0.6623 0.8106 0.828 0.172
#> GSM35491 1 0.6623 0.8106 0.828 0.172
#> GSM35494 2 0.1184 0.9498 0.016 0.984
#> GSM35498 2 0.7674 0.6039 0.224 0.776
#> GSM35501 1 0.0000 0.7717 1.000 0.000
#> GSM35509 2 0.1184 0.9498 0.016 0.984
#> GSM35513 1 0.0000 0.7717 1.000 0.000
#> GSM35516 2 0.0000 0.9589 0.000 1.000
#> GSM35522 2 0.9635 0.0755 0.388 0.612
#> GSM35525 1 0.0000 0.7717 1.000 0.000
#> GSM35528 1 0.7815 0.7933 0.768 0.232
#> GSM35533 1 0.9491 0.6831 0.632 0.368
#> GSM35537 1 0.9087 0.7370 0.676 0.324
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM35441 2 0.1163 0.8205 0.000 0.972 0.028
#> GSM35446 3 0.1031 0.9153 0.000 0.024 0.976
#> GSM35449 2 0.1289 0.8215 0.000 0.968 0.032
#> GSM35455 2 0.1163 0.8205 0.000 0.972 0.028
#> GSM35458 2 0.6280 0.3243 0.000 0.540 0.460
#> GSM35460 3 0.1031 0.9153 0.000 0.024 0.976
#> GSM35461 3 0.3805 0.8392 0.092 0.024 0.884
#> GSM35463 2 0.2537 0.8145 0.000 0.920 0.080
#> GSM35472 3 0.1031 0.9030 0.000 0.024 0.976
#> GSM35475 2 0.6291 0.3045 0.000 0.532 0.468
#> GSM35483 2 0.2796 0.8085 0.000 0.908 0.092
#> GSM35496 3 0.1267 0.9042 0.004 0.024 0.972
#> GSM35497 2 0.1163 0.8205 0.000 0.972 0.028
#> GSM35504 2 0.6308 0.2380 0.000 0.508 0.492
#> GSM35508 2 0.6280 0.3243 0.000 0.540 0.460
#> GSM35511 3 0.4178 0.7397 0.000 0.172 0.828
#> GSM35512 3 0.1031 0.9030 0.000 0.024 0.976
#> GSM35515 2 0.6280 0.3243 0.000 0.540 0.460
#> GSM35519 3 0.2878 0.8490 0.000 0.096 0.904
#> GSM35527 2 0.6235 0.3553 0.000 0.564 0.436
#> GSM35532 3 0.1529 0.8977 0.000 0.040 0.960
#> GSM35439 2 0.1832 0.8270 0.036 0.956 0.008
#> GSM35443 1 0.3181 0.9369 0.912 0.024 0.064
#> GSM35445 1 0.3752 0.9190 0.884 0.020 0.096
#> GSM35448 3 0.1031 0.9153 0.000 0.024 0.976
#> GSM35451 1 0.1832 0.9490 0.956 0.008 0.036
#> GSM35454 3 0.1315 0.9155 0.008 0.020 0.972
#> GSM35457 2 0.1647 0.8255 0.036 0.960 0.004
#> GSM35465 2 0.1999 0.8272 0.036 0.952 0.012
#> GSM35468 1 0.2879 0.9400 0.924 0.024 0.052
#> GSM35471 1 0.3141 0.9370 0.912 0.020 0.068
#> GSM35473 1 0.3587 0.9255 0.892 0.020 0.088
#> GSM35477 1 0.1832 0.9490 0.956 0.008 0.036
#> GSM35480 1 0.3325 0.9333 0.904 0.020 0.076
#> GSM35482 3 0.1529 0.8992 0.040 0.000 0.960
#> GSM35485 2 0.1529 0.8253 0.000 0.960 0.040
#> GSM35489 2 0.1832 0.8270 0.036 0.956 0.008
#> GSM35492 1 0.2982 0.9392 0.920 0.024 0.056
#> GSM35495 3 0.1129 0.9169 0.004 0.020 0.976
#> GSM35499 2 0.2356 0.8169 0.000 0.928 0.072
#> GSM35502 1 0.0000 0.9391 1.000 0.000 0.000
#> GSM35505 3 0.1129 0.9169 0.004 0.020 0.976
#> GSM35507 2 0.6606 0.6250 0.236 0.716 0.048
#> GSM35510 2 0.1411 0.8257 0.000 0.964 0.036
#> GSM35514 1 0.1031 0.9481 0.976 0.000 0.024
#> GSM35517 2 0.1453 0.8290 0.024 0.968 0.008
#> GSM35520 2 0.7438 0.3600 0.036 0.536 0.428
#> GSM35523 1 0.1765 0.9494 0.956 0.004 0.040
#> GSM35529 2 0.1999 0.8251 0.036 0.952 0.012
#> GSM35531 2 0.2810 0.8251 0.036 0.928 0.036
#> GSM35534 2 0.1643 0.8253 0.000 0.956 0.044
#> GSM35536 1 0.0000 0.9391 1.000 0.000 0.000
#> GSM35538 1 0.0000 0.9391 1.000 0.000 0.000
#> GSM35539 1 0.0237 0.9406 0.996 0.000 0.004
#> GSM35540 2 0.5111 0.7682 0.036 0.820 0.144
#> GSM35541 2 0.1620 0.8290 0.024 0.964 0.012
#> GSM35442 3 0.7188 -0.0302 0.484 0.024 0.492
#> GSM35447 3 0.1129 0.9169 0.004 0.020 0.976
#> GSM35450 1 0.1015 0.9448 0.980 0.008 0.012
#> GSM35453 1 0.6627 0.5095 0.644 0.020 0.336
#> GSM35456 1 0.3325 0.9334 0.904 0.020 0.076
#> GSM35464 2 0.2269 0.8276 0.040 0.944 0.016
#> GSM35467 1 0.0000 0.9391 1.000 0.000 0.000
#> GSM35470 1 0.2537 0.9395 0.920 0.000 0.080
#> GSM35479 3 0.1647 0.9027 0.036 0.004 0.960
#> GSM35484 1 0.3234 0.9353 0.908 0.020 0.072
#> GSM35488 1 0.2879 0.9400 0.924 0.024 0.052
#> GSM35491 1 0.1529 0.9492 0.960 0.000 0.040
#> GSM35494 3 0.1129 0.9169 0.004 0.020 0.976
#> GSM35498 1 0.1860 0.9487 0.948 0.000 0.052
#> GSM35501 1 0.0000 0.9391 1.000 0.000 0.000
#> GSM35509 3 0.1129 0.9169 0.004 0.020 0.976
#> GSM35513 1 0.0000 0.9391 1.000 0.000 0.000
#> GSM35516 2 0.1643 0.8253 0.000 0.956 0.044
#> GSM35522 1 0.1989 0.9486 0.948 0.004 0.048
#> GSM35525 1 0.0000 0.9391 1.000 0.000 0.000
#> GSM35528 1 0.2879 0.9400 0.924 0.024 0.052
#> GSM35533 1 0.3234 0.9353 0.908 0.020 0.072
#> GSM35537 1 0.1753 0.9492 0.952 0.000 0.048
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM35441 2 0.3907 0.686 0.000 0.768 0.000 0.232
#> GSM35446 3 0.0469 0.908 0.000 0.000 0.988 0.012
#> GSM35449 4 0.4955 0.215 0.000 0.444 0.000 0.556
#> GSM35455 2 0.4406 0.556 0.000 0.700 0.000 0.300
#> GSM35458 4 0.3550 0.838 0.000 0.044 0.096 0.860
#> GSM35460 3 0.0469 0.908 0.000 0.000 0.988 0.012
#> GSM35461 4 0.4832 0.711 0.056 0.000 0.176 0.768
#> GSM35463 2 0.0469 0.923 0.000 0.988 0.012 0.000
#> GSM35472 3 0.4406 0.582 0.000 0.000 0.700 0.300
#> GSM35475 4 0.2805 0.835 0.000 0.012 0.100 0.888
#> GSM35483 2 0.0707 0.919 0.000 0.980 0.020 0.000
#> GSM35496 3 0.3837 0.707 0.000 0.000 0.776 0.224
#> GSM35497 4 0.4888 0.310 0.000 0.412 0.000 0.588
#> GSM35504 2 0.3893 0.716 0.000 0.796 0.196 0.008
#> GSM35508 4 0.3279 0.840 0.000 0.032 0.096 0.872
#> GSM35511 4 0.2530 0.831 0.000 0.004 0.100 0.896
#> GSM35512 3 0.3907 0.696 0.000 0.000 0.768 0.232
#> GSM35515 4 0.3372 0.840 0.000 0.036 0.096 0.868
#> GSM35519 4 0.3105 0.828 0.000 0.012 0.120 0.868
#> GSM35527 4 0.4362 0.810 0.000 0.088 0.096 0.816
#> GSM35532 4 0.2831 0.819 0.000 0.004 0.120 0.876
#> GSM35439 2 0.0336 0.924 0.008 0.992 0.000 0.000
#> GSM35443 1 0.4072 0.784 0.748 0.000 0.000 0.252
#> GSM35445 1 0.3157 0.835 0.852 0.004 0.144 0.000
#> GSM35448 3 0.0469 0.908 0.000 0.000 0.988 0.012
#> GSM35451 1 0.0000 0.918 1.000 0.000 0.000 0.000
#> GSM35454 3 0.0000 0.910 0.000 0.000 1.000 0.000
#> GSM35457 2 0.0524 0.922 0.004 0.988 0.000 0.008
#> GSM35465 2 0.0895 0.917 0.004 0.976 0.000 0.020
#> GSM35468 1 0.2408 0.906 0.896 0.000 0.000 0.104
#> GSM35471 1 0.0779 0.915 0.980 0.004 0.016 0.000
#> GSM35473 1 0.2714 0.863 0.884 0.004 0.112 0.000
#> GSM35477 1 0.0000 0.918 1.000 0.000 0.000 0.000
#> GSM35480 1 0.2053 0.892 0.924 0.004 0.072 0.000
#> GSM35482 3 0.3822 0.775 0.120 0.004 0.844 0.032
#> GSM35485 2 0.0188 0.925 0.000 0.996 0.004 0.000
#> GSM35489 2 0.0188 0.923 0.004 0.996 0.000 0.000
#> GSM35492 1 0.2973 0.887 0.856 0.000 0.000 0.144
#> GSM35495 3 0.0000 0.910 0.000 0.000 1.000 0.000
#> GSM35499 2 0.0336 0.923 0.000 0.992 0.008 0.000
#> GSM35502 1 0.2345 0.906 0.900 0.000 0.000 0.100
#> GSM35505 3 0.0188 0.910 0.000 0.004 0.996 0.000
#> GSM35507 1 0.4624 0.475 0.660 0.340 0.000 0.000
#> GSM35510 2 0.0188 0.925 0.000 0.996 0.004 0.000
#> GSM35514 1 0.2281 0.907 0.904 0.000 0.000 0.096
#> GSM35517 2 0.0188 0.924 0.004 0.996 0.000 0.000
#> GSM35520 2 0.3556 0.793 0.004 0.864 0.096 0.036
#> GSM35523 1 0.0188 0.918 0.996 0.004 0.000 0.000
#> GSM35529 2 0.1743 0.893 0.004 0.940 0.000 0.056
#> GSM35531 2 0.0336 0.924 0.008 0.992 0.000 0.000
#> GSM35534 2 0.0188 0.925 0.000 0.996 0.004 0.000
#> GSM35536 1 0.2345 0.906 0.900 0.000 0.000 0.100
#> GSM35538 1 0.0000 0.918 1.000 0.000 0.000 0.000
#> GSM35539 1 0.0000 0.918 1.000 0.000 0.000 0.000
#> GSM35540 2 0.4434 0.706 0.004 0.772 0.016 0.208
#> GSM35541 2 0.0188 0.924 0.004 0.996 0.000 0.000
#> GSM35442 1 0.5257 0.720 0.752 0.000 0.104 0.144
#> GSM35447 3 0.0188 0.910 0.000 0.004 0.996 0.000
#> GSM35450 1 0.0000 0.918 1.000 0.000 0.000 0.000
#> GSM35453 1 0.4456 0.693 0.716 0.004 0.280 0.000
#> GSM35456 1 0.2845 0.869 0.896 0.076 0.028 0.000
#> GSM35464 2 0.1042 0.913 0.020 0.972 0.000 0.008
#> GSM35467 1 0.2345 0.906 0.900 0.000 0.000 0.100
#> GSM35470 1 0.0779 0.918 0.980 0.004 0.016 0.000
#> GSM35479 3 0.0657 0.904 0.012 0.004 0.984 0.000
#> GSM35484 1 0.1209 0.911 0.964 0.004 0.032 0.000
#> GSM35488 1 0.2408 0.906 0.896 0.000 0.000 0.104
#> GSM35491 1 0.2466 0.907 0.900 0.004 0.000 0.096
#> GSM35494 3 0.0188 0.910 0.000 0.004 0.996 0.000
#> GSM35498 1 0.0188 0.918 0.996 0.004 0.000 0.000
#> GSM35501 1 0.2216 0.909 0.908 0.000 0.000 0.092
#> GSM35509 3 0.0188 0.910 0.000 0.004 0.996 0.000
#> GSM35513 1 0.2345 0.906 0.900 0.000 0.000 0.100
#> GSM35516 2 0.0188 0.925 0.000 0.996 0.004 0.000
#> GSM35522 1 0.0336 0.918 0.992 0.008 0.000 0.000
#> GSM35525 1 0.1398 0.918 0.956 0.004 0.000 0.040
#> GSM35528 1 0.1211 0.917 0.960 0.000 0.000 0.040
#> GSM35533 1 0.1209 0.911 0.964 0.004 0.032 0.000
#> GSM35537 1 0.0188 0.918 0.996 0.004 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM35441 2 0.4434 0.269 0.000 0.536 0.000 NA 0.460
#> GSM35446 3 0.4227 0.858 0.000 0.000 0.580 NA 0.000
#> GSM35449 5 0.4251 0.164 0.000 0.372 0.000 NA 0.624
#> GSM35455 5 0.4451 -0.242 0.000 0.492 0.000 NA 0.504
#> GSM35458 5 0.0671 0.686 0.000 0.016 0.004 NA 0.980
#> GSM35460 3 0.4227 0.858 0.000 0.000 0.580 NA 0.000
#> GSM35461 5 0.5380 0.405 0.004 0.000 0.464 NA 0.488
#> GSM35463 2 0.1197 0.839 0.000 0.952 0.000 NA 0.000
#> GSM35472 3 0.2280 0.458 0.000 0.000 0.880 NA 0.120
#> GSM35475 5 0.0963 0.682 0.000 0.000 0.036 NA 0.964
#> GSM35483 2 0.1608 0.830 0.000 0.928 0.000 NA 0.000
#> GSM35496 3 0.1430 0.558 0.000 0.000 0.944 NA 0.052
#> GSM35497 5 0.4166 0.228 0.000 0.348 0.000 NA 0.648
#> GSM35504 2 0.1956 0.824 0.000 0.916 0.008 NA 0.000
#> GSM35508 5 0.0324 0.689 0.000 0.004 0.000 NA 0.992
#> GSM35511 5 0.4060 0.540 0.000 0.000 0.360 NA 0.640
#> GSM35512 3 0.1608 0.535 0.000 0.000 0.928 NA 0.072
#> GSM35515 5 0.0451 0.689 0.000 0.008 0.004 NA 0.988
#> GSM35519 5 0.4262 0.473 0.000 0.000 0.440 NA 0.560
#> GSM35527 5 0.0451 0.688 0.000 0.008 0.000 NA 0.988
#> GSM35532 5 0.4210 0.501 0.000 0.000 0.412 NA 0.588
#> GSM35439 2 0.0727 0.836 0.004 0.980 0.000 NA 0.012
#> GSM35443 1 0.2353 0.824 0.908 0.000 0.004 NA 0.028
#> GSM35445 1 0.3427 0.814 0.796 0.000 0.012 NA 0.000
#> GSM35448 3 0.4227 0.858 0.000 0.000 0.580 NA 0.000
#> GSM35451 1 0.4030 0.742 0.648 0.000 0.000 NA 0.000
#> GSM35454 3 0.4210 0.859 0.000 0.000 0.588 NA 0.000
#> GSM35457 2 0.3579 0.681 0.000 0.756 0.000 NA 0.240
#> GSM35465 2 0.3210 0.715 0.000 0.788 0.000 NA 0.212
#> GSM35468 1 0.1697 0.831 0.932 0.000 0.008 NA 0.000
#> GSM35471 1 0.4101 0.732 0.628 0.000 0.000 NA 0.000
#> GSM35473 1 0.2079 0.833 0.916 0.000 0.020 NA 0.000
#> GSM35477 1 0.3796 0.770 0.700 0.000 0.000 NA 0.000
#> GSM35480 1 0.3455 0.815 0.784 0.000 0.008 NA 0.000
#> GSM35482 3 0.3142 0.633 0.048 0.004 0.876 NA 0.012
#> GSM35485 2 0.1270 0.838 0.000 0.948 0.000 NA 0.000
#> GSM35489 2 0.1732 0.810 0.000 0.920 0.000 NA 0.080
#> GSM35492 1 0.1857 0.830 0.928 0.000 0.008 NA 0.004
#> GSM35495 3 0.4192 0.861 0.000 0.000 0.596 NA 0.000
#> GSM35499 2 0.1270 0.838 0.000 0.948 0.000 NA 0.000
#> GSM35502 1 0.1410 0.832 0.940 0.000 0.000 NA 0.000
#> GSM35505 3 0.4182 0.861 0.000 0.000 0.600 NA 0.000
#> GSM35507 1 0.6474 0.512 0.528 0.284 0.008 NA 0.000
#> GSM35510 2 0.1270 0.838 0.000 0.948 0.000 NA 0.000
#> GSM35514 1 0.0451 0.838 0.988 0.000 0.004 NA 0.000
#> GSM35517 2 0.0290 0.840 0.000 0.992 0.000 NA 0.000
#> GSM35520 2 0.3048 0.721 0.000 0.820 0.004 NA 0.176
#> GSM35523 1 0.3741 0.795 0.732 0.004 0.000 NA 0.000
#> GSM35529 2 0.4066 0.560 0.000 0.672 0.000 NA 0.324
#> GSM35531 2 0.0703 0.841 0.000 0.976 0.000 NA 0.000
#> GSM35534 2 0.1270 0.838 0.000 0.948 0.000 NA 0.000
#> GSM35536 1 0.0290 0.838 0.992 0.000 0.000 NA 0.000
#> GSM35538 1 0.1341 0.841 0.944 0.000 0.000 NA 0.000
#> GSM35539 1 0.3210 0.807 0.788 0.000 0.000 NA 0.000
#> GSM35540 2 0.4425 0.275 0.000 0.544 0.004 NA 0.452
#> GSM35541 2 0.0566 0.840 0.004 0.984 0.000 NA 0.000
#> GSM35442 1 0.4294 0.729 0.780 0.000 0.148 NA 0.008
#> GSM35447 3 0.4182 0.861 0.000 0.000 0.600 NA 0.000
#> GSM35450 1 0.3913 0.759 0.676 0.000 0.000 NA 0.000
#> GSM35453 1 0.3297 0.798 0.848 0.000 0.068 NA 0.000
#> GSM35456 1 0.6515 0.509 0.440 0.196 0.000 NA 0.000
#> GSM35464 2 0.3607 0.738 0.008 0.804 0.008 NA 0.176
#> GSM35467 1 0.1341 0.831 0.944 0.000 0.000 NA 0.000
#> GSM35470 1 0.2650 0.827 0.892 0.004 0.036 NA 0.000
#> GSM35479 3 0.4150 0.851 0.000 0.000 0.612 NA 0.000
#> GSM35484 1 0.3999 0.757 0.656 0.000 0.000 NA 0.000
#> GSM35488 1 0.1408 0.835 0.948 0.000 0.008 NA 0.000
#> GSM35491 1 0.1443 0.835 0.948 0.004 0.004 NA 0.000
#> GSM35494 3 0.4161 0.859 0.000 0.000 0.608 NA 0.000
#> GSM35498 1 0.4088 0.787 0.712 0.004 0.008 NA 0.000
#> GSM35501 1 0.1270 0.835 0.948 0.000 0.000 NA 0.000
#> GSM35509 3 0.4182 0.861 0.000 0.000 0.600 NA 0.000
#> GSM35513 1 0.1341 0.831 0.944 0.000 0.000 NA 0.000
#> GSM35516 2 0.0865 0.842 0.004 0.972 0.000 NA 0.000
#> GSM35522 1 0.4066 0.761 0.672 0.004 0.000 NA 0.000
#> GSM35525 1 0.1270 0.834 0.948 0.000 0.000 NA 0.000
#> GSM35528 1 0.1764 0.838 0.928 0.000 0.008 NA 0.000
#> GSM35533 1 0.4264 0.737 0.620 0.000 0.004 NA 0.000
#> GSM35537 1 0.1928 0.840 0.920 0.004 0.004 NA 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM35441 6 0.1556 0.5949 0.000 0.080 0.000 0.000 0.000 0.920
#> GSM35446 3 0.1908 0.8543 0.000 0.000 0.900 0.096 0.000 0.004
#> GSM35449 6 0.1116 0.6228 0.000 0.028 0.000 0.004 0.008 0.960
#> GSM35455 6 0.1204 0.6087 0.000 0.056 0.000 0.000 0.000 0.944
#> GSM35458 6 0.3782 0.4874 0.000 0.000 0.000 0.004 0.360 0.636
#> GSM35460 3 0.1908 0.8543 0.000 0.000 0.900 0.096 0.000 0.004
#> GSM35461 5 0.3328 0.6748 0.000 0.000 0.064 0.120 0.816 0.000
#> GSM35463 2 0.0291 0.7572 0.000 0.992 0.004 0.000 0.000 0.004
#> GSM35472 5 0.3584 0.5554 0.000 0.000 0.308 0.004 0.688 0.000
#> GSM35475 6 0.3937 0.3992 0.000 0.000 0.000 0.004 0.424 0.572
#> GSM35483 2 0.0291 0.7572 0.000 0.992 0.004 0.000 0.000 0.004
#> GSM35496 5 0.3782 0.4619 0.000 0.000 0.360 0.004 0.636 0.000
#> GSM35497 6 0.1059 0.6258 0.000 0.016 0.000 0.004 0.016 0.964
#> GSM35504 2 0.0858 0.7472 0.000 0.968 0.028 0.004 0.000 0.000
#> GSM35508 6 0.3819 0.4752 0.000 0.000 0.000 0.004 0.372 0.624
#> GSM35511 5 0.1588 0.6344 0.000 0.000 0.000 0.004 0.924 0.072
#> GSM35512 5 0.3714 0.5068 0.000 0.000 0.340 0.004 0.656 0.000
#> GSM35515 6 0.3807 0.4803 0.000 0.000 0.000 0.004 0.368 0.628
#> GSM35519 5 0.1720 0.6950 0.000 0.000 0.032 0.000 0.928 0.040
#> GSM35527 6 0.3930 0.4796 0.000 0.004 0.000 0.004 0.364 0.628
#> GSM35532 5 0.1461 0.6821 0.000 0.000 0.016 0.000 0.940 0.044
#> GSM35439 2 0.3807 0.5931 0.000 0.628 0.000 0.004 0.000 0.368
#> GSM35443 1 0.3288 0.4720 0.724 0.000 0.000 0.276 0.000 0.000
#> GSM35445 1 0.4044 0.3320 0.744 0.000 0.076 0.180 0.000 0.000
#> GSM35448 3 0.1908 0.8543 0.000 0.000 0.900 0.096 0.000 0.004
#> GSM35451 1 0.3979 -0.6547 0.540 0.000 0.004 0.456 0.000 0.000
#> GSM35454 3 0.1082 0.8813 0.000 0.000 0.956 0.004 0.040 0.000
#> GSM35457 6 0.3684 0.1824 0.000 0.332 0.000 0.004 0.000 0.664
#> GSM35465 6 0.3756 0.1723 0.000 0.352 0.000 0.004 0.000 0.644
#> GSM35468 1 0.3288 0.4720 0.724 0.000 0.000 0.276 0.000 0.000
#> GSM35471 1 0.3998 -0.6489 0.504 0.000 0.004 0.492 0.000 0.000
#> GSM35473 1 0.2858 0.4409 0.844 0.000 0.032 0.124 0.000 0.000
#> GSM35477 1 0.3833 -0.6385 0.556 0.000 0.000 0.444 0.000 0.000
#> GSM35480 1 0.3572 0.3242 0.764 0.000 0.032 0.204 0.000 0.000
#> GSM35482 3 0.4692 -0.0789 0.000 0.004 0.532 0.036 0.428 0.000
#> GSM35485 2 0.1958 0.7499 0.000 0.896 0.004 0.000 0.000 0.100
#> GSM35489 2 0.3982 0.3807 0.000 0.536 0.000 0.004 0.000 0.460
#> GSM35492 1 0.3288 0.4720 0.724 0.000 0.000 0.276 0.000 0.000
#> GSM35495 3 0.1141 0.8718 0.000 0.000 0.948 0.052 0.000 0.000
#> GSM35499 2 0.0146 0.7555 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM35502 1 0.1267 0.5162 0.940 0.000 0.000 0.060 0.000 0.000
#> GSM35505 3 0.0937 0.8832 0.000 0.000 0.960 0.000 0.040 0.000
#> GSM35507 4 0.6010 0.6543 0.408 0.048 0.000 0.460 0.000 0.084
#> GSM35510 2 0.0146 0.7555 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM35514 1 0.0000 0.5113 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35517 2 0.3850 0.6327 0.000 0.652 0.004 0.004 0.000 0.340
#> GSM35520 2 0.6098 0.2385 0.000 0.516 0.028 0.000 0.300 0.156
#> GSM35523 1 0.3982 -0.5853 0.536 0.004 0.000 0.460 0.000 0.000
#> GSM35529 6 0.2793 0.4684 0.000 0.200 0.000 0.000 0.000 0.800
#> GSM35531 2 0.4709 0.6087 0.024 0.696 0.000 0.220 0.000 0.060
#> GSM35534 2 0.0692 0.7591 0.000 0.976 0.004 0.000 0.000 0.020
#> GSM35536 1 0.0000 0.5113 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35538 1 0.0865 0.4875 0.964 0.000 0.000 0.036 0.000 0.000
#> GSM35539 1 0.2135 0.3574 0.872 0.000 0.000 0.128 0.000 0.000
#> GSM35540 6 0.4317 0.5337 0.000 0.252 0.000 0.000 0.060 0.688
#> GSM35541 2 0.3850 0.6327 0.000 0.652 0.004 0.004 0.000 0.340
#> GSM35442 1 0.5514 0.3889 0.608 0.000 0.056 0.276 0.060 0.000
#> GSM35447 3 0.0937 0.8832 0.000 0.000 0.960 0.000 0.040 0.000
#> GSM35450 1 0.3807 -0.4753 0.628 0.000 0.004 0.368 0.000 0.000
#> GSM35453 1 0.4912 0.3053 0.696 0.000 0.168 0.116 0.020 0.000
#> GSM35456 4 0.5777 0.5754 0.372 0.156 0.004 0.468 0.000 0.000
#> GSM35464 6 0.5986 -0.0350 0.012 0.356 0.000 0.164 0.000 0.468
#> GSM35467 1 0.1267 0.5162 0.940 0.000 0.000 0.060 0.000 0.000
#> GSM35470 1 0.3848 0.4649 0.692 0.004 0.000 0.292 0.012 0.000
#> GSM35479 3 0.0865 0.8836 0.000 0.000 0.964 0.000 0.036 0.000
#> GSM35484 1 0.4002 -0.3891 0.588 0.000 0.008 0.404 0.000 0.000
#> GSM35488 1 0.3221 0.4780 0.736 0.000 0.000 0.264 0.000 0.000
#> GSM35491 1 0.3215 0.4849 0.756 0.004 0.000 0.240 0.000 0.000
#> GSM35494 3 0.0937 0.8832 0.000 0.000 0.960 0.000 0.040 0.000
#> GSM35498 4 0.3996 0.5346 0.484 0.004 0.000 0.512 0.000 0.000
#> GSM35501 1 0.1141 0.5163 0.948 0.000 0.000 0.052 0.000 0.000
#> GSM35509 3 0.0363 0.8787 0.000 0.000 0.988 0.012 0.000 0.000
#> GSM35513 1 0.1204 0.5173 0.944 0.000 0.000 0.056 0.000 0.000
#> GSM35516 2 0.3834 0.6899 0.000 0.728 0.004 0.024 0.000 0.244
#> GSM35522 4 0.3999 0.6312 0.496 0.004 0.000 0.500 0.000 0.000
#> GSM35525 1 0.1444 0.5143 0.928 0.000 0.000 0.072 0.000 0.000
#> GSM35528 1 0.3330 0.4745 0.716 0.000 0.000 0.284 0.000 0.000
#> GSM35533 1 0.4238 -0.4425 0.540 0.000 0.016 0.444 0.000 0.000
#> GSM35537 1 0.2805 0.4907 0.812 0.004 0.000 0.184 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 time(p) k
#> CV:mclust 75 4.38e-04 2
#> CV:mclust 71 5.49e-05 3
#> CV:mclust 76 2.12e-08 4
#> CV:mclust 71 5.57e-08 5
#> CV:mclust 44 4.67e-04 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "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 7758 rows and 79 columns.
#> Top rows (776, 1552, 2328, 3103, 3879) are extracted by 'CV' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.967 0.986 0.5043 0.498 0.498
#> 3 3 0.786 0.861 0.920 0.3105 0.765 0.562
#> 4 4 0.596 0.616 0.795 0.1165 0.931 0.803
#> 5 5 0.631 0.545 0.773 0.0778 0.813 0.450
#> 6 6 0.619 0.452 0.693 0.0397 0.925 0.668
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
#> GSM35441 2 0.0000 0.998 0.000 1.000
#> GSM35446 2 0.0000 0.998 0.000 1.000
#> GSM35449 2 0.0000 0.998 0.000 1.000
#> GSM35455 2 0.0000 0.998 0.000 1.000
#> GSM35458 2 0.0000 0.998 0.000 1.000
#> GSM35460 2 0.0000 0.998 0.000 1.000
#> GSM35461 1 0.0000 0.975 1.000 0.000
#> GSM35463 2 0.0000 0.998 0.000 1.000
#> GSM35472 2 0.1184 0.984 0.016 0.984
#> GSM35475 2 0.0000 0.998 0.000 1.000
#> GSM35483 2 0.0000 0.998 0.000 1.000
#> GSM35496 1 0.0000 0.975 1.000 0.000
#> GSM35497 2 0.0000 0.998 0.000 1.000
#> GSM35504 2 0.0000 0.998 0.000 1.000
#> GSM35508 2 0.0000 0.998 0.000 1.000
#> GSM35511 2 0.0000 0.998 0.000 1.000
#> GSM35512 2 0.1184 0.984 0.016 0.984
#> GSM35515 2 0.0000 0.998 0.000 1.000
#> GSM35519 2 0.0000 0.998 0.000 1.000
#> GSM35527 2 0.0000 0.998 0.000 1.000
#> GSM35532 2 0.0000 0.998 0.000 1.000
#> GSM35439 2 0.0000 0.998 0.000 1.000
#> GSM35443 1 0.0000 0.975 1.000 0.000
#> GSM35445 1 0.0000 0.975 1.000 0.000
#> GSM35448 2 0.0000 0.998 0.000 1.000
#> GSM35451 1 0.0000 0.975 1.000 0.000
#> GSM35454 1 0.0000 0.975 1.000 0.000
#> GSM35457 2 0.0000 0.998 0.000 1.000
#> GSM35465 2 0.0000 0.998 0.000 1.000
#> GSM35468 1 0.0000 0.975 1.000 0.000
#> GSM35471 1 0.0000 0.975 1.000 0.000
#> GSM35473 1 0.0000 0.975 1.000 0.000
#> GSM35477 1 0.0000 0.975 1.000 0.000
#> GSM35480 1 0.0000 0.975 1.000 0.000
#> GSM35482 1 0.0376 0.972 0.996 0.004
#> GSM35485 2 0.0000 0.998 0.000 1.000
#> GSM35489 2 0.0000 0.998 0.000 1.000
#> GSM35492 1 0.0000 0.975 1.000 0.000
#> GSM35495 1 0.9775 0.326 0.588 0.412
#> GSM35499 2 0.0000 0.998 0.000 1.000
#> GSM35502 1 0.0000 0.975 1.000 0.000
#> GSM35505 1 0.0000 0.975 1.000 0.000
#> GSM35507 1 0.7815 0.702 0.768 0.232
#> GSM35510 2 0.0000 0.998 0.000 1.000
#> GSM35514 1 0.0000 0.975 1.000 0.000
#> GSM35517 2 0.0000 0.998 0.000 1.000
#> GSM35520 2 0.0000 0.998 0.000 1.000
#> GSM35523 1 0.0000 0.975 1.000 0.000
#> GSM35529 2 0.0000 0.998 0.000 1.000
#> GSM35531 2 0.0672 0.991 0.008 0.992
#> GSM35534 2 0.0000 0.998 0.000 1.000
#> GSM35536 1 0.0000 0.975 1.000 0.000
#> GSM35538 1 0.0000 0.975 1.000 0.000
#> GSM35539 1 0.0000 0.975 1.000 0.000
#> GSM35540 2 0.0000 0.998 0.000 1.000
#> GSM35541 2 0.0000 0.998 0.000 1.000
#> GSM35442 1 0.0000 0.975 1.000 0.000
#> GSM35447 1 0.1414 0.958 0.980 0.020
#> GSM35450 1 0.0000 0.975 1.000 0.000
#> GSM35453 1 0.0000 0.975 1.000 0.000
#> GSM35456 1 0.0000 0.975 1.000 0.000
#> GSM35464 2 0.1414 0.980 0.020 0.980
#> GSM35467 1 0.0000 0.975 1.000 0.000
#> GSM35470 1 0.0000 0.975 1.000 0.000
#> GSM35479 1 0.0000 0.975 1.000 0.000
#> GSM35484 1 0.0000 0.975 1.000 0.000
#> GSM35488 1 0.0000 0.975 1.000 0.000
#> GSM35491 1 0.0000 0.975 1.000 0.000
#> GSM35494 1 0.0000 0.975 1.000 0.000
#> GSM35498 1 0.0000 0.975 1.000 0.000
#> GSM35501 1 0.0000 0.975 1.000 0.000
#> GSM35509 1 0.9427 0.457 0.640 0.360
#> GSM35513 1 0.0000 0.975 1.000 0.000
#> GSM35516 2 0.0000 0.998 0.000 1.000
#> GSM35522 1 0.0000 0.975 1.000 0.000
#> GSM35525 1 0.0000 0.975 1.000 0.000
#> GSM35528 1 0.0000 0.975 1.000 0.000
#> GSM35533 1 0.0000 0.975 1.000 0.000
#> GSM35537 1 0.0000 0.975 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM35441 2 0.0237 0.9215 0.000 0.996 0.004
#> GSM35446 3 0.2711 0.8485 0.000 0.088 0.912
#> GSM35449 2 0.0892 0.9201 0.000 0.980 0.020
#> GSM35455 2 0.0424 0.9215 0.000 0.992 0.008
#> GSM35458 2 0.0892 0.9211 0.000 0.980 0.020
#> GSM35460 3 0.2261 0.8582 0.000 0.068 0.932
#> GSM35461 3 0.3038 0.8606 0.104 0.000 0.896
#> GSM35463 2 0.1905 0.9043 0.016 0.956 0.028
#> GSM35472 3 0.2173 0.8689 0.008 0.048 0.944
#> GSM35475 2 0.6062 0.3967 0.000 0.616 0.384
#> GSM35483 2 0.1411 0.9147 0.000 0.964 0.036
#> GSM35496 3 0.2261 0.8779 0.068 0.000 0.932
#> GSM35497 2 0.0892 0.9201 0.000 0.980 0.020
#> GSM35504 2 0.3551 0.8477 0.000 0.868 0.132
#> GSM35508 2 0.3752 0.8314 0.000 0.856 0.144
#> GSM35511 3 0.5098 0.6608 0.000 0.248 0.752
#> GSM35512 3 0.2301 0.8645 0.004 0.060 0.936
#> GSM35515 2 0.1753 0.9093 0.000 0.952 0.048
#> GSM35519 3 0.3340 0.8265 0.000 0.120 0.880
#> GSM35527 2 0.2165 0.8996 0.000 0.936 0.064
#> GSM35532 3 0.3267 0.8300 0.000 0.116 0.884
#> GSM35439 2 0.2550 0.8897 0.040 0.936 0.024
#> GSM35443 1 0.2711 0.9049 0.912 0.000 0.088
#> GSM35445 1 0.2448 0.9184 0.924 0.000 0.076
#> GSM35448 3 0.4796 0.7087 0.000 0.220 0.780
#> GSM35451 1 0.2903 0.9007 0.924 0.048 0.028
#> GSM35454 3 0.4291 0.7755 0.180 0.000 0.820
#> GSM35457 2 0.0000 0.9212 0.000 1.000 0.000
#> GSM35465 2 0.0000 0.9212 0.000 1.000 0.000
#> GSM35468 1 0.1643 0.9324 0.956 0.000 0.044
#> GSM35471 1 0.2564 0.9126 0.936 0.028 0.036
#> GSM35473 1 0.1753 0.9307 0.952 0.000 0.048
#> GSM35477 1 0.2793 0.9041 0.928 0.044 0.028
#> GSM35480 1 0.1163 0.9389 0.972 0.000 0.028
#> GSM35482 3 0.2356 0.8761 0.072 0.000 0.928
#> GSM35485 2 0.1453 0.9112 0.008 0.968 0.024
#> GSM35489 2 0.0592 0.9186 0.012 0.988 0.000
#> GSM35492 1 0.1753 0.9311 0.952 0.000 0.048
#> GSM35495 3 0.1525 0.8799 0.032 0.004 0.964
#> GSM35499 2 0.1525 0.9210 0.004 0.964 0.032
#> GSM35502 1 0.0747 0.9392 0.984 0.000 0.016
#> GSM35505 3 0.2448 0.8732 0.076 0.000 0.924
#> GSM35507 2 0.7188 -0.0219 0.488 0.488 0.024
#> GSM35510 2 0.1031 0.9189 0.000 0.976 0.024
#> GSM35514 1 0.1031 0.9385 0.976 0.000 0.024
#> GSM35517 2 0.0237 0.9207 0.000 0.996 0.004
#> GSM35520 2 0.3816 0.8265 0.000 0.852 0.148
#> GSM35523 1 0.1491 0.9385 0.968 0.016 0.016
#> GSM35529 2 0.0892 0.9201 0.000 0.980 0.020
#> GSM35531 2 0.0747 0.9176 0.016 0.984 0.000
#> GSM35534 2 0.0592 0.9222 0.000 0.988 0.012
#> GSM35536 1 0.1289 0.9366 0.968 0.000 0.032
#> GSM35538 1 0.1170 0.9346 0.976 0.016 0.008
#> GSM35539 1 0.0424 0.9369 0.992 0.008 0.000
#> GSM35540 2 0.2796 0.8792 0.000 0.908 0.092
#> GSM35541 2 0.1337 0.9126 0.012 0.972 0.016
#> GSM35442 3 0.6274 0.1560 0.456 0.000 0.544
#> GSM35447 3 0.1964 0.8792 0.056 0.000 0.944
#> GSM35450 1 0.1919 0.9219 0.956 0.024 0.020
#> GSM35453 1 0.5138 0.6826 0.748 0.000 0.252
#> GSM35456 1 0.4636 0.8278 0.848 0.116 0.036
#> GSM35464 2 0.2846 0.8796 0.056 0.924 0.020
#> GSM35467 1 0.0892 0.9390 0.980 0.000 0.020
#> GSM35470 1 0.5465 0.6122 0.712 0.000 0.288
#> GSM35479 3 0.3267 0.8513 0.116 0.000 0.884
#> GSM35484 1 0.2031 0.9208 0.952 0.016 0.032
#> GSM35488 1 0.1453 0.9397 0.968 0.008 0.024
#> GSM35491 1 0.1643 0.9324 0.956 0.000 0.044
#> GSM35494 3 0.3340 0.8477 0.120 0.000 0.880
#> GSM35498 1 0.1453 0.9344 0.968 0.024 0.008
#> GSM35501 1 0.0892 0.9390 0.980 0.000 0.020
#> GSM35509 3 0.1647 0.8801 0.036 0.004 0.960
#> GSM35513 1 0.0747 0.9393 0.984 0.000 0.016
#> GSM35516 2 0.2806 0.8845 0.040 0.928 0.032
#> GSM35522 1 0.2772 0.8899 0.916 0.080 0.004
#> GSM35525 1 0.1289 0.9366 0.968 0.000 0.032
#> GSM35528 1 0.1774 0.9368 0.960 0.024 0.016
#> GSM35533 1 0.1878 0.9290 0.952 0.004 0.044
#> GSM35537 1 0.2711 0.9034 0.912 0.000 0.088
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM35441 2 0.0707 0.7417 0.000 0.980 0.000 0.020
#> GSM35446 3 0.2773 0.7574 0.000 0.004 0.880 0.116
#> GSM35449 2 0.0844 0.7369 0.004 0.980 0.004 0.012
#> GSM35455 2 0.0592 0.7408 0.000 0.984 0.000 0.016
#> GSM35458 2 0.3550 0.6740 0.040 0.880 0.056 0.024
#> GSM35460 3 0.2654 0.7625 0.000 0.004 0.888 0.108
#> GSM35461 3 0.5984 0.5380 0.248 0.048 0.684 0.020
#> GSM35463 4 0.4164 0.5508 0.000 0.264 0.000 0.736
#> GSM35472 3 0.1890 0.7514 0.000 0.056 0.936 0.008
#> GSM35475 2 0.5620 0.5065 0.028 0.732 0.200 0.040
#> GSM35483 2 0.4898 0.1728 0.000 0.584 0.000 0.416
#> GSM35496 3 0.1631 0.7606 0.016 0.008 0.956 0.020
#> GSM35497 2 0.0524 0.7373 0.000 0.988 0.004 0.008
#> GSM35504 4 0.6182 0.4865 0.000 0.276 0.088 0.636
#> GSM35508 2 0.2256 0.7088 0.000 0.924 0.056 0.020
#> GSM35511 3 0.5493 0.2477 0.000 0.456 0.528 0.016
#> GSM35512 3 0.3253 0.7268 0.008 0.100 0.876 0.016
#> GSM35515 2 0.3550 0.6740 0.040 0.880 0.056 0.024
#> GSM35519 3 0.5581 0.4892 0.008 0.340 0.632 0.020
#> GSM35527 2 0.1174 0.7314 0.000 0.968 0.020 0.012
#> GSM35532 3 0.4857 0.5693 0.000 0.284 0.700 0.016
#> GSM35439 2 0.2676 0.7305 0.012 0.896 0.000 0.092
#> GSM35443 1 0.3432 0.7342 0.860 0.012 0.120 0.008
#> GSM35445 1 0.6111 0.3866 0.556 0.000 0.052 0.392
#> GSM35448 3 0.5768 0.3798 0.000 0.028 0.516 0.456
#> GSM35451 1 0.5062 0.5860 0.680 0.020 0.000 0.300
#> GSM35454 3 0.4992 0.4159 0.000 0.000 0.524 0.476
#> GSM35457 2 0.3355 0.6808 0.004 0.836 0.000 0.160
#> GSM35465 2 0.4053 0.6066 0.004 0.768 0.000 0.228
#> GSM35468 1 0.1356 0.7883 0.960 0.000 0.032 0.008
#> GSM35471 4 0.4188 0.3367 0.244 0.004 0.000 0.752
#> GSM35473 1 0.1733 0.7947 0.948 0.000 0.028 0.024
#> GSM35477 1 0.3591 0.7378 0.824 0.008 0.000 0.168
#> GSM35480 1 0.5247 0.6516 0.684 0.000 0.032 0.284
#> GSM35482 3 0.1489 0.7643 0.004 0.000 0.952 0.044
#> GSM35485 2 0.4072 0.5892 0.000 0.748 0.000 0.252
#> GSM35489 2 0.3448 0.6933 0.004 0.828 0.000 0.168
#> GSM35492 1 0.1722 0.7828 0.944 0.000 0.048 0.008
#> GSM35495 3 0.4008 0.6971 0.000 0.000 0.756 0.244
#> GSM35499 4 0.3356 0.6043 0.000 0.176 0.000 0.824
#> GSM35502 1 0.0657 0.7942 0.984 0.000 0.004 0.012
#> GSM35505 3 0.4387 0.6998 0.012 0.000 0.752 0.236
#> GSM35507 2 0.7916 -0.2471 0.316 0.356 0.000 0.328
#> GSM35510 4 0.4996 -0.0732 0.000 0.484 0.000 0.516
#> GSM35514 1 0.0672 0.7929 0.984 0.000 0.008 0.008
#> GSM35517 2 0.2216 0.7310 0.000 0.908 0.000 0.092
#> GSM35520 2 0.3464 0.7011 0.000 0.868 0.056 0.076
#> GSM35523 1 0.5762 0.5053 0.608 0.040 0.000 0.352
#> GSM35529 2 0.2081 0.7317 0.000 0.916 0.000 0.084
#> GSM35531 2 0.4630 0.6119 0.016 0.732 0.000 0.252
#> GSM35534 2 0.4543 0.4453 0.000 0.676 0.000 0.324
#> GSM35536 1 0.0524 0.7942 0.988 0.000 0.008 0.004
#> GSM35538 1 0.1022 0.7930 0.968 0.000 0.000 0.032
#> GSM35539 1 0.2973 0.7613 0.856 0.000 0.000 0.144
#> GSM35540 2 0.4290 0.6590 0.000 0.800 0.036 0.164
#> GSM35541 2 0.3528 0.6883 0.000 0.808 0.000 0.192
#> GSM35442 1 0.5463 0.0482 0.500 0.004 0.488 0.008
#> GSM35447 3 0.2515 0.7677 0.012 0.004 0.912 0.072
#> GSM35450 1 0.2921 0.7622 0.860 0.000 0.000 0.140
#> GSM35453 1 0.5690 0.6444 0.700 0.000 0.216 0.084
#> GSM35456 4 0.4761 0.5092 0.184 0.048 0.000 0.768
#> GSM35464 2 0.4910 0.5095 0.020 0.704 0.000 0.276
#> GSM35467 1 0.0188 0.7939 0.996 0.000 0.004 0.000
#> GSM35470 1 0.6791 0.3714 0.508 0.000 0.392 0.100
#> GSM35479 3 0.2081 0.7585 0.000 0.000 0.916 0.084
#> GSM35484 1 0.3831 0.6770 0.792 0.000 0.004 0.204
#> GSM35488 1 0.0937 0.7954 0.976 0.000 0.012 0.012
#> GSM35491 1 0.1305 0.7887 0.960 0.000 0.036 0.004
#> GSM35494 3 0.2081 0.7614 0.000 0.000 0.916 0.084
#> GSM35498 1 0.5775 0.5724 0.660 0.048 0.004 0.288
#> GSM35501 1 0.1209 0.7931 0.964 0.000 0.004 0.032
#> GSM35509 3 0.3311 0.7413 0.000 0.000 0.828 0.172
#> GSM35513 1 0.0672 0.7939 0.984 0.000 0.008 0.008
#> GSM35516 2 0.5298 0.3580 0.016 0.612 0.000 0.372
#> GSM35522 1 0.6324 0.4267 0.572 0.072 0.000 0.356
#> GSM35525 1 0.1890 0.7907 0.936 0.000 0.008 0.056
#> GSM35528 1 0.2820 0.7857 0.904 0.020 0.008 0.068
#> GSM35533 1 0.5408 0.1928 0.500 0.000 0.012 0.488
#> GSM35537 1 0.6506 0.6259 0.652 0.004 0.200 0.144
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM35441 2 0.2416 0.73109 0.000 0.888 0.000 0.100 0.012
#> GSM35446 3 0.3002 0.72327 0.000 0.028 0.856 0.000 0.116
#> GSM35449 2 0.3123 0.67668 0.000 0.812 0.000 0.184 0.004
#> GSM35455 2 0.2248 0.73595 0.000 0.900 0.000 0.088 0.012
#> GSM35458 2 0.2075 0.71257 0.040 0.924 0.032 0.000 0.004
#> GSM35460 3 0.2748 0.73129 0.000 0.008 0.880 0.016 0.096
#> GSM35461 3 0.6233 0.53626 0.208 0.156 0.616 0.016 0.004
#> GSM35463 5 0.2969 0.55560 0.000 0.128 0.000 0.020 0.852
#> GSM35472 3 0.3088 0.70894 0.012 0.108 0.864 0.008 0.008
#> GSM35475 2 0.2853 0.68424 0.040 0.880 0.076 0.000 0.004
#> GSM35483 5 0.4118 0.34067 0.000 0.336 0.000 0.004 0.660
#> GSM35496 3 0.2450 0.73776 0.016 0.024 0.916 0.036 0.008
#> GSM35497 2 0.1544 0.73959 0.000 0.932 0.000 0.068 0.000
#> GSM35504 5 0.3880 0.57062 0.000 0.096 0.052 0.024 0.828
#> GSM35508 2 0.2529 0.73141 0.000 0.900 0.040 0.056 0.004
#> GSM35511 2 0.4064 0.50272 0.000 0.716 0.272 0.004 0.008
#> GSM35512 3 0.3613 0.68063 0.016 0.160 0.812 0.000 0.012
#> GSM35515 2 0.2313 0.70639 0.040 0.912 0.044 0.000 0.004
#> GSM35519 2 0.4726 0.34378 0.024 0.644 0.328 0.000 0.004
#> GSM35527 2 0.2295 0.73609 0.000 0.900 0.008 0.088 0.004
#> GSM35532 3 0.4562 0.22769 0.004 0.444 0.548 0.000 0.004
#> GSM35439 2 0.3299 0.67624 0.004 0.828 0.000 0.016 0.152
#> GSM35443 1 0.2623 0.77275 0.900 0.048 0.044 0.004 0.004
#> GSM35445 1 0.5972 0.22960 0.480 0.000 0.036 0.040 0.444
#> GSM35448 5 0.5018 0.28535 0.000 0.052 0.284 0.004 0.660
#> GSM35451 4 0.5324 0.39371 0.340 0.004 0.000 0.600 0.056
#> GSM35454 5 0.4906 -0.00240 0.004 0.000 0.380 0.024 0.592
#> GSM35457 4 0.4974 -0.09335 0.000 0.464 0.000 0.508 0.028
#> GSM35465 4 0.3779 0.52042 0.000 0.200 0.000 0.776 0.024
#> GSM35468 1 0.1334 0.81894 0.960 0.012 0.004 0.020 0.004
#> GSM35471 4 0.4423 0.57753 0.048 0.000 0.024 0.780 0.148
#> GSM35473 1 0.0671 0.82087 0.980 0.000 0.000 0.016 0.004
#> GSM35477 4 0.4576 0.12607 0.456 0.004 0.000 0.536 0.004
#> GSM35480 1 0.7172 0.31718 0.460 0.000 0.040 0.172 0.328
#> GSM35482 3 0.2396 0.73300 0.004 0.008 0.900 0.084 0.004
#> GSM35485 2 0.4306 -0.01373 0.000 0.508 0.000 0.000 0.492
#> GSM35489 2 0.4509 0.64325 0.000 0.752 0.000 0.152 0.096
#> GSM35492 1 0.1664 0.80635 0.948 0.020 0.020 0.008 0.004
#> GSM35495 3 0.3400 0.70846 0.000 0.000 0.828 0.036 0.136
#> GSM35499 5 0.3304 0.55943 0.000 0.052 0.004 0.092 0.852
#> GSM35502 1 0.1043 0.81489 0.960 0.000 0.000 0.040 0.000
#> GSM35505 3 0.5431 0.23378 0.048 0.004 0.500 0.000 0.448
#> GSM35507 4 0.1770 0.65702 0.008 0.048 0.000 0.936 0.008
#> GSM35510 5 0.6597 0.28901 0.000 0.244 0.000 0.296 0.460
#> GSM35514 1 0.0727 0.81921 0.980 0.012 0.000 0.004 0.004
#> GSM35517 2 0.3193 0.68535 0.000 0.840 0.000 0.028 0.132
#> GSM35520 2 0.2228 0.72194 0.008 0.916 0.020 0.000 0.056
#> GSM35523 4 0.1130 0.66342 0.012 0.004 0.012 0.968 0.004
#> GSM35529 2 0.4138 0.57231 0.000 0.708 0.000 0.276 0.016
#> GSM35531 2 0.5049 0.00481 0.024 0.500 0.004 0.000 0.472
#> GSM35534 5 0.4235 0.14856 0.000 0.424 0.000 0.000 0.576
#> GSM35536 1 0.0566 0.82100 0.984 0.004 0.000 0.012 0.000
#> GSM35538 1 0.2424 0.75502 0.868 0.000 0.000 0.132 0.000
#> GSM35539 4 0.4613 0.23895 0.408 0.000 0.004 0.580 0.008
#> GSM35540 4 0.5447 0.45803 0.000 0.200 0.128 0.668 0.004
#> GSM35541 2 0.4073 0.59920 0.000 0.752 0.000 0.032 0.216
#> GSM35442 1 0.5258 0.40654 0.628 0.040 0.320 0.008 0.004
#> GSM35447 3 0.5377 0.63038 0.056 0.044 0.704 0.000 0.196
#> GSM35450 1 0.3582 0.64368 0.768 0.000 0.000 0.224 0.008
#> GSM35453 1 0.4891 0.64999 0.732 0.000 0.196 0.036 0.036
#> GSM35456 5 0.5733 -0.07933 0.060 0.004 0.004 0.436 0.496
#> GSM35464 4 0.2597 0.62740 0.000 0.092 0.000 0.884 0.024
#> GSM35467 1 0.0613 0.81952 0.984 0.008 0.000 0.004 0.004
#> GSM35470 3 0.6489 -0.01500 0.144 0.000 0.444 0.404 0.008
#> GSM35479 3 0.2953 0.71617 0.004 0.000 0.868 0.100 0.028
#> GSM35484 1 0.3741 0.61578 0.732 0.000 0.000 0.004 0.264
#> GSM35488 1 0.1430 0.81243 0.944 0.004 0.000 0.052 0.000
#> GSM35491 1 0.0865 0.82115 0.972 0.004 0.000 0.024 0.000
#> GSM35494 3 0.2075 0.73889 0.004 0.000 0.924 0.040 0.032
#> GSM35498 4 0.1280 0.66771 0.024 0.008 0.008 0.960 0.000
#> GSM35501 1 0.0794 0.81886 0.972 0.000 0.000 0.028 0.000
#> GSM35509 3 0.2843 0.73025 0.000 0.000 0.876 0.048 0.076
#> GSM35513 1 0.0579 0.81879 0.984 0.008 0.000 0.000 0.008
#> GSM35516 5 0.5296 -0.02220 0.000 0.468 0.000 0.048 0.484
#> GSM35522 4 0.0451 0.66337 0.004 0.008 0.000 0.988 0.000
#> GSM35525 1 0.4302 0.44352 0.648 0.000 0.004 0.344 0.004
#> GSM35528 4 0.4183 0.44450 0.324 0.008 0.000 0.668 0.000
#> GSM35533 5 0.4722 0.07402 0.368 0.000 0.000 0.024 0.608
#> GSM35537 4 0.4253 0.53970 0.032 0.000 0.204 0.756 0.008
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM35441 5 0.6787 0.4134 0.000 0.076 0.000 0.264 0.472 0.188
#> GSM35446 3 0.3224 0.6208 0.000 0.084 0.848 0.000 0.036 0.032
#> GSM35449 5 0.3930 0.5931 0.000 0.004 0.000 0.156 0.768 0.072
#> GSM35455 5 0.2094 0.6791 0.000 0.008 0.000 0.068 0.908 0.016
#> GSM35458 5 0.2973 0.6506 0.024 0.000 0.000 0.004 0.836 0.136
#> GSM35460 3 0.1760 0.6393 0.000 0.048 0.928 0.000 0.004 0.020
#> GSM35461 6 0.7122 0.2227 0.076 0.000 0.276 0.008 0.204 0.436
#> GSM35463 2 0.3180 0.4600 0.000 0.852 0.004 0.012 0.072 0.060
#> GSM35472 3 0.4270 0.4720 0.000 0.004 0.724 0.008 0.044 0.220
#> GSM35475 5 0.3318 0.6133 0.020 0.000 0.024 0.000 0.824 0.132
#> GSM35483 2 0.4531 0.3923 0.000 0.692 0.012 0.000 0.240 0.056
#> GSM35496 3 0.3100 0.6058 0.000 0.004 0.848 0.012 0.028 0.108
#> GSM35497 5 0.2670 0.6802 0.000 0.020 0.000 0.052 0.884 0.044
#> GSM35504 2 0.5906 0.4150 0.000 0.652 0.128 0.012 0.132 0.076
#> GSM35508 5 0.2734 0.6272 0.000 0.000 0.008 0.024 0.864 0.104
#> GSM35511 5 0.3268 0.5767 0.000 0.000 0.076 0.000 0.824 0.100
#> GSM35512 3 0.4438 0.3061 0.000 0.000 0.628 0.000 0.044 0.328
#> GSM35515 5 0.2128 0.6550 0.032 0.000 0.000 0.004 0.908 0.056
#> GSM35519 6 0.6120 0.2097 0.000 0.008 0.308 0.000 0.228 0.456
#> GSM35527 5 0.2979 0.6359 0.000 0.000 0.004 0.056 0.852 0.088
#> GSM35532 3 0.5439 -0.0494 0.000 0.000 0.472 0.000 0.408 0.120
#> GSM35439 5 0.6079 0.4420 0.004 0.188 0.000 0.024 0.556 0.228
#> GSM35443 1 0.5005 0.2220 0.488 0.000 0.040 0.004 0.008 0.460
#> GSM35445 2 0.5938 -0.0280 0.400 0.480 0.020 0.012 0.000 0.088
#> GSM35448 2 0.5921 0.0285 0.000 0.508 0.372 0.004 0.072 0.044
#> GSM35451 4 0.4979 0.5178 0.248 0.040 0.000 0.664 0.000 0.048
#> GSM35454 3 0.5000 0.2728 0.000 0.432 0.512 0.012 0.000 0.044
#> GSM35457 4 0.5461 0.4244 0.000 0.076 0.000 0.664 0.180 0.080
#> GSM35465 4 0.3067 0.6229 0.000 0.016 0.004 0.852 0.104 0.024
#> GSM35468 1 0.3500 0.6755 0.768 0.000 0.000 0.028 0.000 0.204
#> GSM35471 4 0.3760 0.6248 0.032 0.096 0.024 0.824 0.000 0.024
#> GSM35473 1 0.1296 0.7533 0.952 0.012 0.000 0.004 0.000 0.032
#> GSM35477 4 0.4585 0.3749 0.324 0.016 0.000 0.632 0.000 0.028
#> GSM35480 1 0.6355 0.3233 0.552 0.256 0.012 0.044 0.000 0.136
#> GSM35482 3 0.2067 0.6303 0.000 0.004 0.916 0.048 0.004 0.028
#> GSM35485 2 0.5418 0.2595 0.000 0.596 0.004 0.008 0.280 0.112
#> GSM35489 4 0.7376 0.0520 0.000 0.204 0.000 0.408 0.164 0.224
#> GSM35492 1 0.4024 0.4468 0.592 0.000 0.004 0.004 0.000 0.400
#> GSM35495 3 0.1983 0.6398 0.000 0.060 0.916 0.012 0.000 0.012
#> GSM35499 2 0.5122 0.2675 0.000 0.628 0.016 0.292 0.008 0.056
#> GSM35502 1 0.1219 0.7481 0.948 0.000 0.000 0.004 0.000 0.048
#> GSM35505 3 0.6148 0.0398 0.020 0.164 0.452 0.000 0.000 0.364
#> GSM35507 4 0.1979 0.6573 0.008 0.004 0.004 0.924 0.048 0.012
#> GSM35510 4 0.6097 0.0737 0.000 0.404 0.004 0.464 0.080 0.048
#> GSM35514 1 0.3222 0.6991 0.844 0.012 0.000 0.004 0.040 0.100
#> GSM35517 5 0.4911 0.5700 0.000 0.156 0.000 0.040 0.712 0.092
#> GSM35520 5 0.5690 0.4589 0.000 0.152 0.012 0.000 0.560 0.276
#> GSM35523 4 0.3769 0.6316 0.100 0.000 0.044 0.816 0.004 0.036
#> GSM35529 5 0.5907 0.1864 0.000 0.032 0.000 0.420 0.452 0.096
#> GSM35531 6 0.6929 -0.2387 0.004 0.312 0.004 0.072 0.152 0.456
#> GSM35534 2 0.6102 0.1158 0.000 0.492 0.004 0.008 0.292 0.204
#> GSM35536 1 0.1049 0.7556 0.960 0.000 0.000 0.008 0.000 0.032
#> GSM35538 1 0.2206 0.7468 0.904 0.008 0.000 0.064 0.000 0.024
#> GSM35539 1 0.4616 0.3329 0.596 0.000 0.004 0.360 0.000 0.040
#> GSM35540 4 0.4527 0.6034 0.000 0.024 0.100 0.772 0.080 0.024
#> GSM35541 5 0.6862 0.2345 0.000 0.292 0.000 0.072 0.440 0.196
#> GSM35442 6 0.6217 0.0866 0.208 0.000 0.380 0.012 0.000 0.400
#> GSM35447 3 0.5994 0.3574 0.020 0.144 0.576 0.000 0.012 0.248
#> GSM35450 1 0.4253 0.6694 0.752 0.016 0.004 0.176 0.000 0.052
#> GSM35453 1 0.4287 0.6535 0.772 0.024 0.136 0.008 0.000 0.060
#> GSM35456 2 0.7113 0.1393 0.316 0.444 0.008 0.068 0.008 0.156
#> GSM35464 4 0.1929 0.6516 0.004 0.008 0.000 0.924 0.048 0.016
#> GSM35467 1 0.0547 0.7525 0.980 0.000 0.000 0.000 0.000 0.020
#> GSM35470 3 0.5786 0.2894 0.108 0.000 0.600 0.244 0.000 0.048
#> GSM35479 3 0.2641 0.6021 0.000 0.004 0.876 0.072 0.000 0.048
#> GSM35484 1 0.5372 0.2761 0.528 0.364 0.000 0.004 0.000 0.104
#> GSM35488 1 0.2979 0.7327 0.840 0.000 0.000 0.044 0.000 0.116
#> GSM35491 1 0.4163 0.5633 0.656 0.008 0.000 0.016 0.000 0.320
#> GSM35494 3 0.3176 0.6222 0.016 0.024 0.856 0.008 0.004 0.092
#> GSM35498 4 0.1657 0.6588 0.012 0.000 0.040 0.936 0.000 0.012
#> GSM35501 1 0.0713 0.7528 0.972 0.000 0.000 0.000 0.000 0.028
#> GSM35509 3 0.1710 0.6378 0.000 0.020 0.936 0.028 0.000 0.016
#> GSM35513 1 0.0858 0.7532 0.968 0.000 0.000 0.000 0.004 0.028
#> GSM35516 2 0.6456 0.3468 0.020 0.592 0.000 0.132 0.184 0.072
#> GSM35522 4 0.3613 0.6458 0.076 0.004 0.036 0.840 0.012 0.032
#> GSM35525 1 0.3706 0.6579 0.772 0.000 0.000 0.172 0.000 0.056
#> GSM35528 4 0.4768 0.1305 0.416 0.000 0.000 0.532 0.000 0.052
#> GSM35533 2 0.5227 -0.1652 0.460 0.480 0.008 0.020 0.000 0.032
#> GSM35537 4 0.6675 0.3279 0.204 0.004 0.264 0.480 0.000 0.048
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 time(p) k
#> CV:NMF 77 5.70e-07 2
#> CV:NMF 76 3.48e-05 3
#> CV:NMF 63 1.58e-03 4
#> CV:NMF 55 1.09e-03 5
#> CV:NMF 41 4.42e-05 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 7758 rows and 79 columns.
#> Top rows (776, 1552, 2328, 3103, 3879) are extracted by 'MAD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.625 0.876 0.937 0.4917 0.498 0.498
#> 3 3 0.632 0.805 0.900 0.2088 0.903 0.805
#> 4 4 0.626 0.755 0.874 0.0672 0.968 0.922
#> 5 5 0.618 0.568 0.760 0.1397 0.880 0.698
#> 6 6 0.680 0.617 0.767 0.0557 0.919 0.758
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
#> GSM35441 2 0.0000 0.913 0.000 1.000
#> GSM35446 2 0.4815 0.877 0.104 0.896
#> GSM35449 2 0.0000 0.913 0.000 1.000
#> GSM35455 2 0.0000 0.913 0.000 1.000
#> GSM35458 2 0.4161 0.893 0.084 0.916
#> GSM35460 2 0.4815 0.877 0.104 0.896
#> GSM35461 1 0.8661 0.606 0.712 0.288
#> GSM35463 2 0.0000 0.913 0.000 1.000
#> GSM35472 2 0.9866 0.289 0.432 0.568
#> GSM35475 2 0.3879 0.897 0.076 0.924
#> GSM35483 2 0.0000 0.913 0.000 1.000
#> GSM35496 1 0.0000 0.943 1.000 0.000
#> GSM35497 2 0.0000 0.913 0.000 1.000
#> GSM35504 2 0.3879 0.896 0.076 0.924
#> GSM35508 2 0.0000 0.913 0.000 1.000
#> GSM35511 2 0.3584 0.898 0.068 0.932
#> GSM35512 2 0.9661 0.401 0.392 0.608
#> GSM35515 2 0.4161 0.893 0.084 0.916
#> GSM35519 2 0.9661 0.401 0.392 0.608
#> GSM35527 2 0.0000 0.913 0.000 1.000
#> GSM35532 2 0.4161 0.891 0.084 0.916
#> GSM35439 2 0.0000 0.913 0.000 1.000
#> GSM35443 1 0.2043 0.931 0.968 0.032
#> GSM35445 1 0.0000 0.943 1.000 0.000
#> GSM35448 2 0.4431 0.887 0.092 0.908
#> GSM35451 1 0.1414 0.939 0.980 0.020
#> GSM35454 1 0.6343 0.817 0.840 0.160
#> GSM35457 2 0.0000 0.913 0.000 1.000
#> GSM35465 2 0.2236 0.906 0.036 0.964
#> GSM35468 1 0.0672 0.942 0.992 0.008
#> GSM35471 1 0.2236 0.930 0.964 0.036
#> GSM35473 1 0.0000 0.943 1.000 0.000
#> GSM35477 1 0.1414 0.939 0.980 0.020
#> GSM35480 1 0.0000 0.943 1.000 0.000
#> GSM35482 1 0.0376 0.943 0.996 0.004
#> GSM35485 2 0.0376 0.914 0.004 0.996
#> GSM35489 2 0.4690 0.874 0.100 0.900
#> GSM35492 1 0.0672 0.942 0.992 0.008
#> GSM35495 2 0.9661 0.410 0.392 0.608
#> GSM35499 2 0.0376 0.914 0.004 0.996
#> GSM35502 1 0.0000 0.943 1.000 0.000
#> GSM35505 1 0.6343 0.817 0.840 0.160
#> GSM35507 1 0.7376 0.761 0.792 0.208
#> GSM35510 2 0.0376 0.914 0.004 0.996
#> GSM35514 1 0.0000 0.943 1.000 0.000
#> GSM35517 2 0.0000 0.913 0.000 1.000
#> GSM35520 2 0.4815 0.871 0.104 0.896
#> GSM35523 1 0.5519 0.852 0.872 0.128
#> GSM35529 2 0.0000 0.913 0.000 1.000
#> GSM35531 2 0.4690 0.874 0.100 0.900
#> GSM35534 2 0.0938 0.913 0.012 0.988
#> GSM35536 1 0.0000 0.943 1.000 0.000
#> GSM35538 1 0.0000 0.943 1.000 0.000
#> GSM35539 1 0.0000 0.943 1.000 0.000
#> GSM35540 2 0.0376 0.914 0.004 0.996
#> GSM35541 2 0.0000 0.913 0.000 1.000
#> GSM35442 1 0.2043 0.931 0.968 0.032
#> GSM35447 1 0.6343 0.817 0.840 0.160
#> GSM35450 1 0.1414 0.939 0.980 0.020
#> GSM35453 1 0.0000 0.943 1.000 0.000
#> GSM35456 1 0.3274 0.916 0.940 0.060
#> GSM35464 1 0.7528 0.749 0.784 0.216
#> GSM35467 1 0.0000 0.943 1.000 0.000
#> GSM35470 1 0.0000 0.943 1.000 0.000
#> GSM35479 1 0.0376 0.943 0.996 0.004
#> GSM35484 1 0.1184 0.940 0.984 0.016
#> GSM35488 1 0.0000 0.943 1.000 0.000
#> GSM35491 1 0.0672 0.942 0.992 0.008
#> GSM35494 1 0.0376 0.943 0.996 0.004
#> GSM35498 1 0.7528 0.749 0.784 0.216
#> GSM35501 1 0.0000 0.943 1.000 0.000
#> GSM35509 1 0.7376 0.749 0.792 0.208
#> GSM35513 1 0.0000 0.943 1.000 0.000
#> GSM35516 2 0.3584 0.896 0.068 0.932
#> GSM35522 1 0.5519 0.852 0.872 0.128
#> GSM35525 1 0.0000 0.943 1.000 0.000
#> GSM35528 1 0.0000 0.943 1.000 0.000
#> GSM35533 1 0.1184 0.940 0.984 0.016
#> GSM35537 1 0.0000 0.943 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM35441 2 0.0592 0.896 0.000 0.988 0.012
#> GSM35446 3 0.0237 0.671 0.000 0.004 0.996
#> GSM35449 2 0.0592 0.896 0.000 0.988 0.012
#> GSM35455 2 0.0592 0.896 0.000 0.988 0.012
#> GSM35458 3 0.5731 0.663 0.020 0.228 0.752
#> GSM35460 3 0.0237 0.671 0.000 0.004 0.996
#> GSM35461 1 0.7084 0.403 0.628 0.036 0.336
#> GSM35463 2 0.0000 0.895 0.000 1.000 0.000
#> GSM35472 3 0.8857 0.486 0.344 0.132 0.524
#> GSM35475 3 0.5493 0.657 0.012 0.232 0.756
#> GSM35483 2 0.0000 0.895 0.000 1.000 0.000
#> GSM35496 1 0.2796 0.872 0.908 0.000 0.092
#> GSM35497 2 0.0592 0.896 0.000 0.988 0.012
#> GSM35504 3 0.6154 0.194 0.000 0.408 0.592
#> GSM35508 2 0.5882 0.433 0.000 0.652 0.348
#> GSM35511 3 0.4842 0.657 0.000 0.224 0.776
#> GSM35512 3 0.8793 0.556 0.308 0.140 0.552
#> GSM35515 3 0.5731 0.663 0.020 0.228 0.752
#> GSM35519 3 0.8793 0.556 0.308 0.140 0.552
#> GSM35527 2 0.5882 0.433 0.000 0.652 0.348
#> GSM35532 3 0.4883 0.669 0.004 0.208 0.788
#> GSM35439 2 0.0000 0.895 0.000 1.000 0.000
#> GSM35443 1 0.1751 0.910 0.960 0.012 0.028
#> GSM35445 1 0.0000 0.924 1.000 0.000 0.000
#> GSM35448 3 0.0747 0.671 0.000 0.016 0.984
#> GSM35451 1 0.0892 0.920 0.980 0.020 0.000
#> GSM35454 1 0.4741 0.785 0.828 0.020 0.152
#> GSM35457 2 0.0592 0.896 0.000 0.988 0.012
#> GSM35465 2 0.2434 0.866 0.036 0.940 0.024
#> GSM35468 1 0.0424 0.923 0.992 0.008 0.000
#> GSM35471 1 0.1411 0.912 0.964 0.036 0.000
#> GSM35473 1 0.0000 0.924 1.000 0.000 0.000
#> GSM35477 1 0.0892 0.920 0.980 0.020 0.000
#> GSM35480 1 0.0000 0.924 1.000 0.000 0.000
#> GSM35482 1 0.2496 0.890 0.928 0.004 0.068
#> GSM35485 2 0.0237 0.893 0.004 0.996 0.000
#> GSM35489 2 0.6299 0.655 0.096 0.772 0.132
#> GSM35492 1 0.0424 0.923 0.992 0.008 0.000
#> GSM35495 3 0.5591 0.497 0.304 0.000 0.696
#> GSM35499 2 0.1765 0.884 0.004 0.956 0.040
#> GSM35502 1 0.0000 0.924 1.000 0.000 0.000
#> GSM35505 1 0.4741 0.785 0.828 0.020 0.152
#> GSM35507 1 0.4654 0.729 0.792 0.208 0.000
#> GSM35510 2 0.1765 0.884 0.004 0.956 0.040
#> GSM35514 1 0.0000 0.924 1.000 0.000 0.000
#> GSM35517 2 0.0000 0.895 0.000 1.000 0.000
#> GSM35520 2 0.7782 0.450 0.100 0.652 0.248
#> GSM35523 1 0.3482 0.825 0.872 0.128 0.000
#> GSM35529 2 0.0592 0.896 0.000 0.988 0.012
#> GSM35531 2 0.6299 0.655 0.096 0.772 0.132
#> GSM35534 2 0.0983 0.889 0.004 0.980 0.016
#> GSM35536 1 0.0000 0.924 1.000 0.000 0.000
#> GSM35538 1 0.0000 0.924 1.000 0.000 0.000
#> GSM35539 1 0.0000 0.924 1.000 0.000 0.000
#> GSM35540 2 0.1765 0.884 0.004 0.956 0.040
#> GSM35541 2 0.0000 0.895 0.000 1.000 0.000
#> GSM35442 1 0.1751 0.910 0.960 0.012 0.028
#> GSM35447 1 0.4741 0.785 0.828 0.020 0.152
#> GSM35450 1 0.0892 0.920 0.980 0.020 0.000
#> GSM35453 1 0.0000 0.924 1.000 0.000 0.000
#> GSM35456 1 0.2066 0.897 0.940 0.060 0.000
#> GSM35464 1 0.4750 0.717 0.784 0.216 0.000
#> GSM35467 1 0.0000 0.924 1.000 0.000 0.000
#> GSM35470 1 0.0592 0.922 0.988 0.000 0.012
#> GSM35479 1 0.2796 0.873 0.908 0.000 0.092
#> GSM35484 1 0.0747 0.921 0.984 0.016 0.000
#> GSM35488 1 0.0000 0.924 1.000 0.000 0.000
#> GSM35491 1 0.0424 0.923 0.992 0.008 0.000
#> GSM35494 1 0.2796 0.873 0.908 0.000 0.092
#> GSM35498 1 0.4750 0.717 0.784 0.216 0.000
#> GSM35501 1 0.0000 0.924 1.000 0.000 0.000
#> GSM35509 1 0.5529 0.596 0.704 0.000 0.296
#> GSM35513 1 0.0000 0.924 1.000 0.000 0.000
#> GSM35516 2 0.2261 0.828 0.068 0.932 0.000
#> GSM35522 1 0.3482 0.825 0.872 0.128 0.000
#> GSM35525 1 0.0000 0.924 1.000 0.000 0.000
#> GSM35528 1 0.0000 0.924 1.000 0.000 0.000
#> GSM35533 1 0.0747 0.921 0.984 0.016 0.000
#> GSM35537 1 0.0424 0.923 0.992 0.000 0.008
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM35441 2 0.2149 0.864 0.000 0.912 0.088 0.000
#> GSM35446 4 0.2530 0.694 0.000 0.000 0.112 0.888
#> GSM35449 2 0.2868 0.841 0.000 0.864 0.136 0.000
#> GSM35455 2 0.2868 0.841 0.000 0.864 0.136 0.000
#> GSM35458 3 0.1767 0.562 0.012 0.044 0.944 0.000
#> GSM35460 4 0.2530 0.694 0.000 0.000 0.112 0.888
#> GSM35461 1 0.5756 0.352 0.568 0.000 0.400 0.032
#> GSM35463 2 0.1022 0.860 0.000 0.968 0.000 0.032
#> GSM35472 3 0.5827 0.314 0.316 0.000 0.632 0.052
#> GSM35475 3 0.1489 0.559 0.004 0.044 0.952 0.000
#> GSM35483 2 0.1022 0.860 0.000 0.968 0.000 0.032
#> GSM35496 1 0.4100 0.837 0.832 0.000 0.092 0.076
#> GSM35497 2 0.2868 0.841 0.000 0.864 0.136 0.000
#> GSM35504 4 0.7002 0.226 0.000 0.352 0.128 0.520
#> GSM35508 3 0.5778 -0.125 0.000 0.472 0.500 0.028
#> GSM35511 3 0.1677 0.550 0.000 0.040 0.948 0.012
#> GSM35512 3 0.5417 0.359 0.284 0.000 0.676 0.040
#> GSM35515 3 0.1767 0.562 0.012 0.044 0.944 0.000
#> GSM35519 3 0.5417 0.359 0.284 0.000 0.676 0.040
#> GSM35527 3 0.5778 -0.125 0.000 0.472 0.500 0.028
#> GSM35532 3 0.1284 0.541 0.000 0.024 0.964 0.012
#> GSM35439 2 0.1022 0.860 0.000 0.968 0.000 0.032
#> GSM35443 1 0.2363 0.887 0.920 0.000 0.056 0.024
#> GSM35445 1 0.1042 0.902 0.972 0.000 0.008 0.020
#> GSM35448 4 0.2988 0.690 0.000 0.012 0.112 0.876
#> GSM35451 1 0.1247 0.900 0.968 0.012 0.004 0.016
#> GSM35454 1 0.4805 0.760 0.780 0.004 0.164 0.052
#> GSM35457 2 0.2216 0.863 0.000 0.908 0.092 0.000
#> GSM35465 2 0.3202 0.851 0.024 0.888 0.076 0.012
#> GSM35468 1 0.1629 0.900 0.952 0.000 0.024 0.024
#> GSM35471 1 0.1920 0.893 0.944 0.028 0.004 0.024
#> GSM35473 1 0.1042 0.902 0.972 0.000 0.008 0.020
#> GSM35477 1 0.1247 0.900 0.968 0.012 0.004 0.016
#> GSM35480 1 0.0469 0.905 0.988 0.000 0.000 0.012
#> GSM35482 1 0.3667 0.858 0.856 0.000 0.056 0.088
#> GSM35485 2 0.1209 0.859 0.004 0.964 0.000 0.032
#> GSM35489 2 0.6070 0.637 0.076 0.712 0.188 0.024
#> GSM35492 1 0.1629 0.900 0.952 0.000 0.024 0.024
#> GSM35495 4 0.6112 0.342 0.248 0.000 0.096 0.656
#> GSM35499 2 0.2799 0.857 0.000 0.884 0.108 0.008
#> GSM35502 1 0.0000 0.905 1.000 0.000 0.000 0.000
#> GSM35505 1 0.4805 0.760 0.780 0.004 0.164 0.052
#> GSM35507 1 0.5036 0.712 0.760 0.192 0.012 0.036
#> GSM35510 2 0.2799 0.857 0.000 0.884 0.108 0.008
#> GSM35514 1 0.0000 0.905 1.000 0.000 0.000 0.000
#> GSM35517 2 0.1022 0.860 0.000 0.968 0.000 0.032
#> GSM35520 2 0.6705 0.413 0.080 0.592 0.316 0.012
#> GSM35523 1 0.4059 0.804 0.832 0.124 0.004 0.040
#> GSM35529 2 0.2216 0.863 0.000 0.908 0.092 0.000
#> GSM35531 2 0.6070 0.637 0.076 0.712 0.188 0.024
#> GSM35534 2 0.1576 0.852 0.004 0.948 0.000 0.048
#> GSM35536 1 0.0000 0.905 1.000 0.000 0.000 0.000
#> GSM35538 1 0.0000 0.905 1.000 0.000 0.000 0.000
#> GSM35539 1 0.0592 0.904 0.984 0.000 0.000 0.016
#> GSM35540 2 0.2799 0.857 0.000 0.884 0.108 0.008
#> GSM35541 2 0.1022 0.860 0.000 0.968 0.000 0.032
#> GSM35442 1 0.2363 0.887 0.920 0.000 0.056 0.024
#> GSM35447 1 0.4805 0.760 0.780 0.004 0.164 0.052
#> GSM35450 1 0.1247 0.900 0.968 0.012 0.004 0.016
#> GSM35453 1 0.1042 0.902 0.972 0.000 0.008 0.020
#> GSM35456 1 0.2467 0.880 0.920 0.052 0.004 0.024
#> GSM35464 1 0.5114 0.700 0.752 0.200 0.012 0.036
#> GSM35467 1 0.0000 0.905 1.000 0.000 0.000 0.000
#> GSM35470 1 0.1938 0.897 0.936 0.000 0.012 0.052
#> GSM35479 1 0.3803 0.837 0.836 0.000 0.032 0.132
#> GSM35484 1 0.1640 0.903 0.956 0.012 0.012 0.020
#> GSM35488 1 0.0000 0.905 1.000 0.000 0.000 0.000
#> GSM35491 1 0.1629 0.900 0.952 0.000 0.024 0.024
#> GSM35494 1 0.3803 0.837 0.836 0.000 0.032 0.132
#> GSM35498 1 0.5114 0.700 0.752 0.200 0.012 0.036
#> GSM35501 1 0.0000 0.905 1.000 0.000 0.000 0.000
#> GSM35509 1 0.5657 0.560 0.644 0.000 0.044 0.312
#> GSM35513 1 0.0000 0.905 1.000 0.000 0.000 0.000
#> GSM35516 2 0.2816 0.807 0.064 0.900 0.000 0.036
#> GSM35522 1 0.4059 0.804 0.832 0.124 0.004 0.040
#> GSM35525 1 0.0592 0.904 0.984 0.000 0.000 0.016
#> GSM35528 1 0.0000 0.905 1.000 0.000 0.000 0.000
#> GSM35533 1 0.1640 0.903 0.956 0.012 0.012 0.020
#> GSM35537 1 0.1474 0.900 0.948 0.000 0.000 0.052
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM35441 2 0.2388 0.714 0.000 0.900 0.000 0.028 0.072
#> GSM35446 3 0.4169 0.338 0.000 0.000 0.732 0.240 0.028
#> GSM35449 2 0.3323 0.658 0.000 0.844 0.000 0.056 0.100
#> GSM35455 2 0.3323 0.658 0.000 0.844 0.000 0.056 0.100
#> GSM35458 5 0.4370 0.259 0.008 0.004 0.000 0.332 0.656
#> GSM35460 3 0.4169 0.338 0.000 0.000 0.732 0.240 0.028
#> GSM35461 5 0.5532 0.226 0.224 0.000 0.092 0.016 0.668
#> GSM35463 2 0.2471 0.719 0.000 0.864 0.000 0.136 0.000
#> GSM35472 5 0.1948 0.398 0.024 0.000 0.036 0.008 0.932
#> GSM35475 5 0.4370 0.252 0.004 0.008 0.000 0.332 0.656
#> GSM35483 2 0.2516 0.716 0.000 0.860 0.000 0.140 0.000
#> GSM35496 5 0.7944 -0.234 0.316 0.000 0.264 0.076 0.344
#> GSM35497 2 0.3323 0.658 0.000 0.844 0.000 0.056 0.100
#> GSM35504 4 0.7646 0.172 0.000 0.320 0.312 0.324 0.044
#> GSM35508 4 0.6460 0.570 0.000 0.404 0.000 0.416 0.180
#> GSM35511 5 0.4253 0.246 0.000 0.004 0.004 0.332 0.660
#> GSM35512 5 0.1093 0.400 0.020 0.004 0.004 0.004 0.968
#> GSM35515 5 0.4370 0.259 0.008 0.004 0.000 0.332 0.656
#> GSM35519 5 0.1093 0.400 0.020 0.004 0.004 0.004 0.968
#> GSM35527 4 0.6460 0.570 0.000 0.404 0.000 0.416 0.180
#> GSM35532 5 0.4181 0.261 0.000 0.004 0.004 0.316 0.676
#> GSM35439 2 0.2127 0.732 0.000 0.892 0.000 0.108 0.000
#> GSM35443 1 0.4377 0.715 0.796 0.000 0.088 0.024 0.092
#> GSM35445 1 0.2605 0.794 0.900 0.000 0.060 0.024 0.016
#> GSM35448 3 0.4276 0.328 0.000 0.000 0.716 0.256 0.028
#> GSM35451 1 0.1573 0.815 0.948 0.008 0.004 0.036 0.004
#> GSM35454 5 0.6462 0.115 0.428 0.004 0.084 0.024 0.460
#> GSM35457 2 0.2069 0.720 0.000 0.912 0.000 0.012 0.076
#> GSM35465 2 0.3384 0.666 0.000 0.848 0.004 0.088 0.060
#> GSM35468 1 0.3169 0.778 0.868 0.000 0.084 0.024 0.024
#> GSM35471 1 0.3739 0.771 0.844 0.020 0.060 0.072 0.004
#> GSM35473 1 0.2502 0.796 0.904 0.000 0.060 0.024 0.012
#> GSM35477 1 0.1573 0.815 0.948 0.008 0.004 0.036 0.004
#> GSM35480 1 0.2104 0.809 0.916 0.000 0.060 0.024 0.000
#> GSM35482 1 0.8033 -0.300 0.328 0.000 0.280 0.084 0.308
#> GSM35485 2 0.2286 0.731 0.004 0.888 0.000 0.108 0.000
#> GSM35489 2 0.5367 0.495 0.024 0.672 0.000 0.056 0.248
#> GSM35492 1 0.3313 0.772 0.860 0.000 0.088 0.024 0.028
#> GSM35495 3 0.2632 0.406 0.040 0.000 0.888 0.000 0.072
#> GSM35499 2 0.3062 0.693 0.000 0.868 0.004 0.048 0.080
#> GSM35502 1 0.0162 0.823 0.996 0.000 0.000 0.004 0.000
#> GSM35505 5 0.6462 0.115 0.428 0.004 0.084 0.024 0.460
#> GSM35507 1 0.6939 0.527 0.616 0.132 0.084 0.156 0.012
#> GSM35510 2 0.3062 0.693 0.000 0.868 0.004 0.048 0.080
#> GSM35514 1 0.0162 0.823 0.996 0.000 0.000 0.004 0.000
#> GSM35517 2 0.2127 0.732 0.000 0.892 0.000 0.108 0.000
#> GSM35520 2 0.6270 0.211 0.028 0.568 0.000 0.096 0.308
#> GSM35523 1 0.6682 0.541 0.620 0.068 0.136 0.172 0.004
#> GSM35529 2 0.2069 0.720 0.000 0.912 0.000 0.012 0.076
#> GSM35531 2 0.5367 0.495 0.024 0.672 0.000 0.056 0.248
#> GSM35534 2 0.2646 0.722 0.004 0.868 0.004 0.124 0.000
#> GSM35536 1 0.0000 0.823 1.000 0.000 0.000 0.000 0.000
#> GSM35538 1 0.0000 0.823 1.000 0.000 0.000 0.000 0.000
#> GSM35539 1 0.2676 0.783 0.884 0.000 0.080 0.036 0.000
#> GSM35540 2 0.3062 0.693 0.000 0.868 0.004 0.048 0.080
#> GSM35541 2 0.2127 0.732 0.000 0.892 0.000 0.108 0.000
#> GSM35442 1 0.4377 0.715 0.796 0.000 0.088 0.024 0.092
#> GSM35447 5 0.6462 0.115 0.428 0.004 0.084 0.024 0.460
#> GSM35450 1 0.1573 0.815 0.948 0.008 0.004 0.036 0.004
#> GSM35453 1 0.2605 0.794 0.900 0.000 0.060 0.024 0.016
#> GSM35456 1 0.4325 0.749 0.812 0.036 0.076 0.072 0.004
#> GSM35464 1 0.7013 0.515 0.608 0.140 0.084 0.156 0.012
#> GSM35467 1 0.0162 0.823 0.996 0.000 0.000 0.004 0.000
#> GSM35470 1 0.6798 0.450 0.596 0.000 0.200 0.088 0.116
#> GSM35479 3 0.7964 0.143 0.304 0.000 0.336 0.076 0.284
#> GSM35484 1 0.2599 0.814 0.908 0.008 0.032 0.040 0.012
#> GSM35488 1 0.0000 0.823 1.000 0.000 0.000 0.000 0.000
#> GSM35491 1 0.3313 0.772 0.860 0.000 0.088 0.024 0.028
#> GSM35494 3 0.7964 0.143 0.304 0.000 0.336 0.076 0.284
#> GSM35498 1 0.7013 0.515 0.608 0.140 0.084 0.156 0.012
#> GSM35501 1 0.0162 0.823 0.996 0.000 0.000 0.004 0.000
#> GSM35509 3 0.6747 0.262 0.172 0.000 0.540 0.028 0.260
#> GSM35513 1 0.0162 0.823 0.996 0.000 0.000 0.004 0.000
#> GSM35516 2 0.3493 0.674 0.060 0.832 0.000 0.108 0.000
#> GSM35522 1 0.6682 0.541 0.620 0.068 0.136 0.172 0.004
#> GSM35525 1 0.2676 0.783 0.884 0.000 0.080 0.036 0.000
#> GSM35528 1 0.0000 0.823 1.000 0.000 0.000 0.000 0.000
#> GSM35533 1 0.2599 0.814 0.908 0.008 0.032 0.040 0.012
#> GSM35537 1 0.5632 0.639 0.704 0.000 0.156 0.084 0.056
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM35441 2 0.1838 0.76753 0.000 0.916 0.000 0.000 0.068 NA
#> GSM35446 4 0.0458 0.74211 0.000 0.000 0.016 0.984 0.000 NA
#> GSM35449 2 0.2747 0.73040 0.000 0.860 0.004 0.000 0.108 NA
#> GSM35455 2 0.2747 0.73040 0.000 0.860 0.004 0.000 0.108 NA
#> GSM35458 5 0.0436 0.64464 0.004 0.004 0.000 0.000 0.988 NA
#> GSM35460 4 0.0458 0.74211 0.000 0.000 0.016 0.984 0.000 NA
#> GSM35461 5 0.7529 0.14980 0.188 0.000 0.192 0.000 0.360 NA
#> GSM35463 2 0.3468 0.72442 0.000 0.712 0.000 0.004 0.000 NA
#> GSM35472 5 0.5591 0.52478 0.000 0.000 0.116 0.028 0.604 NA
#> GSM35475 5 0.0405 0.64414 0.000 0.008 0.000 0.000 0.988 NA
#> GSM35483 2 0.3595 0.71960 0.000 0.704 0.000 0.008 0.000 NA
#> GSM35496 3 0.1938 0.72230 0.020 0.000 0.920 0.000 0.052 NA
#> GSM35497 2 0.2747 0.73040 0.000 0.860 0.004 0.000 0.108 NA
#> GSM35504 4 0.5538 0.32356 0.000 0.332 0.004 0.568 0.028 NA
#> GSM35508 5 0.6088 0.05287 0.000 0.404 0.012 0.000 0.408 NA
#> GSM35511 5 0.0551 0.64010 0.000 0.004 0.000 0.008 0.984 NA
#> GSM35512 5 0.5277 0.54670 0.000 0.004 0.076 0.024 0.636 NA
#> GSM35515 5 0.0436 0.64464 0.004 0.004 0.000 0.000 0.988 NA
#> GSM35519 5 0.5277 0.54670 0.000 0.004 0.076 0.024 0.636 NA
#> GSM35527 5 0.6088 0.05287 0.000 0.404 0.012 0.000 0.408 NA
#> GSM35532 5 0.1026 0.63865 0.000 0.004 0.012 0.008 0.968 NA
#> GSM35439 2 0.2823 0.76139 0.000 0.796 0.000 0.000 0.000 NA
#> GSM35443 1 0.4443 0.64939 0.756 0.000 0.136 0.000 0.044 NA
#> GSM35445 1 0.2510 0.73174 0.872 0.000 0.100 0.000 0.000 NA
#> GSM35448 4 0.0000 0.73820 0.000 0.000 0.000 1.000 0.000 NA
#> GSM35451 1 0.1787 0.75986 0.920 0.000 0.008 0.000 0.004 NA
#> GSM35454 1 0.7716 0.00895 0.380 0.000 0.172 0.020 0.140 NA
#> GSM35457 2 0.1398 0.76890 0.000 0.940 0.000 0.000 0.052 NA
#> GSM35465 2 0.2745 0.73147 0.000 0.860 0.008 0.000 0.020 NA
#> GSM35468 1 0.3167 0.71306 0.836 0.000 0.120 0.000 0.012 NA
#> GSM35471 1 0.3896 0.69163 0.780 0.008 0.052 0.000 0.004 NA
#> GSM35473 1 0.2432 0.73357 0.876 0.000 0.100 0.000 0.000 NA
#> GSM35477 1 0.1787 0.75986 0.920 0.000 0.008 0.000 0.004 NA
#> GSM35480 1 0.2331 0.74867 0.888 0.000 0.032 0.000 0.000 NA
#> GSM35482 3 0.2077 0.73589 0.040 0.000 0.920 0.008 0.024 NA
#> GSM35485 2 0.3023 0.75234 0.000 0.768 0.000 0.000 0.000 NA
#> GSM35489 2 0.5982 0.58524 0.016 0.568 0.008 0.000 0.180 NA
#> GSM35492 1 0.3281 0.70882 0.828 0.000 0.124 0.000 0.012 NA
#> GSM35495 4 0.3607 0.30177 0.000 0.000 0.348 0.652 0.000 NA
#> GSM35499 2 0.2476 0.75214 0.000 0.892 0.004 0.004 0.040 NA
#> GSM35502 1 0.0000 0.76771 1.000 0.000 0.000 0.000 0.000 NA
#> GSM35505 1 0.7716 0.00895 0.380 0.000 0.172 0.020 0.140 NA
#> GSM35507 1 0.6276 0.44835 0.548 0.116 0.060 0.000 0.004 NA
#> GSM35510 2 0.2476 0.75214 0.000 0.892 0.004 0.004 0.040 NA
#> GSM35514 1 0.0000 0.76771 1.000 0.000 0.000 0.000 0.000 NA
#> GSM35517 2 0.2823 0.76139 0.000 0.796 0.000 0.000 0.000 NA
#> GSM35520 2 0.6379 0.37136 0.016 0.472 0.008 0.000 0.304 NA
#> GSM35523 1 0.6302 0.40545 0.532 0.056 0.144 0.000 0.000 NA
#> GSM35529 2 0.1398 0.76890 0.000 0.940 0.000 0.000 0.052 NA
#> GSM35531 2 0.5982 0.58524 0.016 0.568 0.008 0.000 0.180 NA
#> GSM35534 2 0.3514 0.74659 0.000 0.752 0.000 0.020 0.000 NA
#> GSM35536 1 0.0260 0.76767 0.992 0.000 0.000 0.000 0.000 NA
#> GSM35538 1 0.0603 0.76700 0.980 0.000 0.004 0.000 0.000 NA
#> GSM35539 1 0.3297 0.70389 0.820 0.000 0.068 0.000 0.000 NA
#> GSM35540 2 0.2476 0.75214 0.000 0.892 0.004 0.004 0.040 NA
#> GSM35541 2 0.2823 0.76139 0.000 0.796 0.000 0.000 0.000 NA
#> GSM35442 1 0.4443 0.64939 0.756 0.000 0.136 0.000 0.044 NA
#> GSM35447 1 0.7716 0.00895 0.380 0.000 0.172 0.020 0.140 NA
#> GSM35450 1 0.1787 0.75986 0.920 0.000 0.008 0.000 0.004 NA
#> GSM35453 1 0.2510 0.73174 0.872 0.000 0.100 0.000 0.000 NA
#> GSM35456 1 0.4309 0.66290 0.744 0.020 0.044 0.000 0.004 NA
#> GSM35464 1 0.6344 0.43696 0.540 0.124 0.060 0.000 0.004 NA
#> GSM35467 1 0.0000 0.76771 1.000 0.000 0.000 0.000 0.000 NA
#> GSM35470 3 0.4905 0.21699 0.344 0.000 0.580 0.000 0.000 NA
#> GSM35479 3 0.1549 0.74268 0.020 0.000 0.936 0.044 0.000 NA
#> GSM35484 1 0.2461 0.75877 0.888 0.000 0.044 0.000 0.004 NA
#> GSM35488 1 0.0603 0.76700 0.980 0.000 0.004 0.000 0.000 NA
#> GSM35491 1 0.3281 0.70882 0.828 0.000 0.124 0.000 0.012 NA
#> GSM35494 3 0.1549 0.74268 0.020 0.000 0.936 0.044 0.000 NA
#> GSM35498 1 0.6344 0.43696 0.540 0.124 0.060 0.000 0.004 NA
#> GSM35501 1 0.0000 0.76771 1.000 0.000 0.000 0.000 0.000 NA
#> GSM35509 3 0.3265 0.48319 0.004 0.000 0.748 0.248 0.000 NA
#> GSM35513 1 0.0000 0.76771 1.000 0.000 0.000 0.000 0.000 NA
#> GSM35516 2 0.4003 0.73354 0.048 0.740 0.004 0.000 0.000 NA
#> GSM35522 1 0.6302 0.40545 0.532 0.056 0.144 0.000 0.000 NA
#> GSM35525 1 0.3297 0.70389 0.820 0.000 0.068 0.000 0.000 NA
#> GSM35528 1 0.0603 0.76700 0.980 0.000 0.004 0.000 0.000 NA
#> GSM35533 1 0.2461 0.75877 0.888 0.000 0.044 0.000 0.004 NA
#> GSM35537 1 0.5432 0.18034 0.480 0.000 0.400 0.000 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 time(p) k
#> MAD:hclust 75 3.82e-07 2
#> MAD:hclust 72 2.14e-09 3
#> MAD:hclust 70 1.24e-07 4
#> MAD:hclust 53 1.32e-05 5
#> MAD:hclust 62 1.01e-06 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "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 7758 rows and 79 columns.
#> Top rows (776, 1552, 2328, 3103, 3879) 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 1.000 0.964 0.968 0.4981 0.498 0.498
#> 3 3 0.954 0.960 0.975 0.3208 0.794 0.607
#> 4 4 0.743 0.700 0.793 0.1111 0.930 0.797
#> 5 5 0.706 0.766 0.821 0.0744 0.884 0.617
#> 6 6 0.730 0.583 0.764 0.0460 0.968 0.851
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
#> attr(,"optional")
#> [1] 2
There is also optional best \(k\) = 2 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM35441 2 0.3431 0.970 0.064 0.936
#> GSM35446 2 0.0376 0.949 0.004 0.996
#> GSM35449 2 0.3431 0.970 0.064 0.936
#> GSM35455 2 0.3431 0.970 0.064 0.936
#> GSM35458 2 0.3431 0.970 0.064 0.936
#> GSM35460 2 0.0376 0.949 0.004 0.996
#> GSM35461 1 0.3431 0.944 0.936 0.064
#> GSM35463 2 0.3431 0.970 0.064 0.936
#> GSM35472 2 0.4690 0.878 0.100 0.900
#> GSM35475 2 0.0938 0.955 0.012 0.988
#> GSM35483 2 0.3114 0.968 0.056 0.944
#> GSM35496 1 0.3431 0.944 0.936 0.064
#> GSM35497 2 0.3431 0.970 0.064 0.936
#> GSM35504 2 0.0376 0.949 0.004 0.996
#> GSM35508 2 0.0672 0.954 0.008 0.992
#> GSM35511 2 0.0376 0.949 0.004 0.996
#> GSM35512 2 0.4690 0.878 0.100 0.900
#> GSM35515 2 0.3274 0.969 0.060 0.940
#> GSM35519 2 0.0376 0.949 0.004 0.996
#> GSM35527 2 0.0938 0.955 0.012 0.988
#> GSM35532 2 0.0376 0.949 0.004 0.996
#> GSM35439 2 0.3431 0.970 0.064 0.936
#> GSM35443 1 0.0376 0.980 0.996 0.004
#> GSM35445 1 0.0376 0.977 0.996 0.004
#> GSM35448 2 0.0376 0.949 0.004 0.996
#> GSM35451 1 0.0376 0.980 0.996 0.004
#> GSM35454 1 0.3431 0.944 0.936 0.064
#> GSM35457 2 0.3431 0.970 0.064 0.936
#> GSM35465 2 0.3431 0.970 0.064 0.936
#> GSM35468 1 0.0376 0.980 0.996 0.004
#> GSM35471 1 0.0376 0.980 0.996 0.004
#> GSM35473 1 0.0000 0.978 1.000 0.000
#> GSM35477 1 0.0376 0.980 0.996 0.004
#> GSM35480 1 0.0000 0.978 1.000 0.000
#> GSM35482 1 0.3431 0.944 0.936 0.064
#> GSM35485 2 0.3431 0.970 0.064 0.936
#> GSM35489 2 0.3431 0.970 0.064 0.936
#> GSM35492 1 0.0376 0.980 0.996 0.004
#> GSM35495 1 0.6247 0.862 0.844 0.156
#> GSM35499 2 0.3431 0.970 0.064 0.936
#> GSM35502 1 0.0376 0.980 0.996 0.004
#> GSM35505 1 0.3431 0.944 0.936 0.064
#> GSM35507 1 0.0376 0.980 0.996 0.004
#> GSM35510 2 0.3431 0.970 0.064 0.936
#> GSM35514 1 0.0376 0.980 0.996 0.004
#> GSM35517 2 0.3431 0.970 0.064 0.936
#> GSM35520 2 0.0000 0.951 0.000 1.000
#> GSM35523 1 0.0376 0.980 0.996 0.004
#> GSM35529 2 0.3431 0.970 0.064 0.936
#> GSM35531 2 0.3431 0.970 0.064 0.936
#> GSM35534 2 0.3431 0.970 0.064 0.936
#> GSM35536 1 0.0376 0.980 0.996 0.004
#> GSM35538 1 0.0376 0.980 0.996 0.004
#> GSM35539 1 0.0376 0.980 0.996 0.004
#> GSM35540 2 0.0376 0.949 0.004 0.996
#> GSM35541 2 0.3431 0.970 0.064 0.936
#> GSM35442 1 0.1633 0.968 0.976 0.024
#> GSM35447 1 0.3431 0.944 0.936 0.064
#> GSM35450 1 0.0376 0.980 0.996 0.004
#> GSM35453 1 0.0938 0.974 0.988 0.012
#> GSM35456 1 0.0376 0.980 0.996 0.004
#> GSM35464 2 0.3431 0.970 0.064 0.936
#> GSM35467 1 0.0376 0.980 0.996 0.004
#> GSM35470 1 0.0938 0.974 0.988 0.012
#> GSM35479 1 0.3431 0.944 0.936 0.064
#> GSM35484 1 0.0376 0.980 0.996 0.004
#> GSM35488 1 0.0376 0.980 0.996 0.004
#> GSM35491 1 0.0376 0.980 0.996 0.004
#> GSM35494 1 0.3431 0.944 0.936 0.064
#> GSM35498 1 0.0376 0.980 0.996 0.004
#> GSM35501 1 0.0376 0.980 0.996 0.004
#> GSM35509 1 0.3431 0.944 0.936 0.064
#> GSM35513 1 0.0376 0.980 0.996 0.004
#> GSM35516 2 0.3431 0.970 0.064 0.936
#> GSM35522 1 0.0376 0.980 0.996 0.004
#> GSM35525 1 0.0376 0.980 0.996 0.004
#> GSM35528 1 0.0376 0.980 0.996 0.004
#> GSM35533 1 0.0376 0.980 0.996 0.004
#> GSM35537 1 0.0672 0.975 0.992 0.008
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM35441 2 0.0237 0.966 0.000 0.996 0.004
#> GSM35446 3 0.1163 0.965 0.000 0.028 0.972
#> GSM35449 2 0.0237 0.966 0.000 0.996 0.004
#> GSM35455 2 0.0237 0.966 0.000 0.996 0.004
#> GSM35458 2 0.4235 0.803 0.000 0.824 0.176
#> GSM35460 3 0.1031 0.968 0.000 0.024 0.976
#> GSM35461 3 0.0592 0.975 0.012 0.000 0.988
#> GSM35463 2 0.0237 0.966 0.000 0.996 0.004
#> GSM35472 3 0.0892 0.970 0.000 0.020 0.980
#> GSM35475 2 0.5016 0.711 0.000 0.760 0.240
#> GSM35483 2 0.0237 0.966 0.000 0.996 0.004
#> GSM35496 3 0.0424 0.976 0.008 0.000 0.992
#> GSM35497 2 0.0237 0.966 0.000 0.996 0.004
#> GSM35504 2 0.0237 0.966 0.000 0.996 0.004
#> GSM35508 2 0.0237 0.966 0.000 0.996 0.004
#> GSM35511 3 0.4178 0.793 0.000 0.172 0.828
#> GSM35512 3 0.0424 0.974 0.000 0.008 0.992
#> GSM35515 2 0.4235 0.803 0.000 0.824 0.176
#> GSM35519 3 0.1163 0.965 0.000 0.028 0.972
#> GSM35527 2 0.0237 0.966 0.000 0.996 0.004
#> GSM35532 3 0.1163 0.965 0.000 0.028 0.972
#> GSM35439 2 0.0237 0.966 0.000 0.996 0.004
#> GSM35443 1 0.0892 0.985 0.980 0.000 0.020
#> GSM35445 1 0.0892 0.985 0.980 0.000 0.020
#> GSM35448 3 0.1163 0.965 0.000 0.028 0.972
#> GSM35451 1 0.0237 0.982 0.996 0.000 0.004
#> GSM35454 3 0.0424 0.976 0.008 0.000 0.992
#> GSM35457 2 0.0237 0.966 0.000 0.996 0.004
#> GSM35465 2 0.0237 0.966 0.000 0.996 0.004
#> GSM35468 1 0.0892 0.985 0.980 0.000 0.020
#> GSM35471 1 0.0592 0.980 0.988 0.000 0.012
#> GSM35473 1 0.0892 0.985 0.980 0.000 0.020
#> GSM35477 1 0.0237 0.982 0.996 0.000 0.004
#> GSM35480 1 0.0892 0.985 0.980 0.000 0.020
#> GSM35482 3 0.0424 0.976 0.008 0.000 0.992
#> GSM35485 2 0.0237 0.966 0.000 0.996 0.004
#> GSM35489 2 0.0237 0.966 0.000 0.996 0.004
#> GSM35492 1 0.0892 0.985 0.980 0.000 0.020
#> GSM35495 3 0.0424 0.976 0.008 0.000 0.992
#> GSM35499 2 0.0237 0.966 0.000 0.996 0.004
#> GSM35502 1 0.0892 0.985 0.980 0.000 0.020
#> GSM35505 3 0.0592 0.975 0.012 0.000 0.988
#> GSM35507 1 0.1525 0.957 0.964 0.032 0.004
#> GSM35510 2 0.0237 0.966 0.000 0.996 0.004
#> GSM35514 1 0.0892 0.985 0.980 0.000 0.020
#> GSM35517 2 0.0237 0.966 0.000 0.996 0.004
#> GSM35520 2 0.4346 0.788 0.000 0.816 0.184
#> GSM35523 1 0.0592 0.980 0.988 0.000 0.012
#> GSM35529 2 0.0237 0.966 0.000 0.996 0.004
#> GSM35531 2 0.0237 0.966 0.000 0.996 0.004
#> GSM35534 2 0.0237 0.966 0.000 0.996 0.004
#> GSM35536 1 0.0892 0.985 0.980 0.000 0.020
#> GSM35538 1 0.0000 0.982 1.000 0.000 0.000
#> GSM35539 1 0.0237 0.982 0.996 0.000 0.004
#> GSM35540 2 0.0237 0.966 0.000 0.996 0.004
#> GSM35541 2 0.0237 0.966 0.000 0.996 0.004
#> GSM35442 1 0.3879 0.846 0.848 0.000 0.152
#> GSM35447 3 0.0592 0.975 0.012 0.000 0.988
#> GSM35450 1 0.0000 0.982 1.000 0.000 0.000
#> GSM35453 1 0.0892 0.985 0.980 0.000 0.020
#> GSM35456 1 0.0237 0.982 0.996 0.000 0.004
#> GSM35464 2 0.1315 0.948 0.020 0.972 0.008
#> GSM35467 1 0.0892 0.985 0.980 0.000 0.020
#> GSM35470 1 0.1163 0.981 0.972 0.000 0.028
#> GSM35479 3 0.0424 0.976 0.008 0.000 0.992
#> GSM35484 1 0.0892 0.985 0.980 0.000 0.020
#> GSM35488 1 0.0237 0.983 0.996 0.000 0.004
#> GSM35491 1 0.0892 0.985 0.980 0.000 0.020
#> GSM35494 3 0.0424 0.976 0.008 0.000 0.992
#> GSM35498 1 0.0592 0.980 0.988 0.000 0.012
#> GSM35501 1 0.0892 0.985 0.980 0.000 0.020
#> GSM35509 3 0.0424 0.976 0.008 0.000 0.992
#> GSM35513 1 0.0892 0.985 0.980 0.000 0.020
#> GSM35516 2 0.0237 0.966 0.000 0.996 0.004
#> GSM35522 1 0.0592 0.980 0.988 0.000 0.012
#> GSM35525 1 0.0000 0.982 1.000 0.000 0.000
#> GSM35528 1 0.0237 0.982 0.996 0.000 0.004
#> GSM35533 1 0.0892 0.985 0.980 0.000 0.020
#> GSM35537 1 0.0592 0.980 0.988 0.000 0.012
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM35441 2 0.0921 0.869 0.000 0.972 0.000 0.028
#> GSM35446 3 0.0592 0.833 0.000 0.000 0.984 0.016
#> GSM35449 2 0.1557 0.864 0.000 0.944 0.000 0.056
#> GSM35455 2 0.1118 0.868 0.000 0.964 0.000 0.036
#> GSM35458 2 0.7581 0.339 0.000 0.424 0.196 0.380
#> GSM35460 3 0.0336 0.834 0.000 0.000 0.992 0.008
#> GSM35461 3 0.3591 0.808 0.008 0.000 0.824 0.168
#> GSM35463 2 0.2149 0.868 0.000 0.912 0.000 0.088
#> GSM35472 3 0.2149 0.816 0.000 0.000 0.912 0.088
#> GSM35475 4 0.7887 -0.355 0.000 0.292 0.332 0.376
#> GSM35483 2 0.2149 0.868 0.000 0.912 0.000 0.088
#> GSM35496 3 0.3569 0.797 0.000 0.000 0.804 0.196
#> GSM35497 2 0.1474 0.865 0.000 0.948 0.000 0.052
#> GSM35504 2 0.0336 0.871 0.000 0.992 0.000 0.008
#> GSM35508 2 0.3688 0.773 0.000 0.792 0.000 0.208
#> GSM35511 3 0.6058 0.617 0.000 0.068 0.624 0.308
#> GSM35512 3 0.2760 0.800 0.000 0.000 0.872 0.128
#> GSM35515 2 0.7581 0.339 0.000 0.424 0.196 0.380
#> GSM35519 3 0.4483 0.703 0.000 0.004 0.712 0.284
#> GSM35527 2 0.3219 0.806 0.000 0.836 0.000 0.164
#> GSM35532 3 0.4483 0.703 0.000 0.004 0.712 0.284
#> GSM35439 2 0.2149 0.868 0.000 0.912 0.000 0.088
#> GSM35443 1 0.0592 0.793 0.984 0.000 0.000 0.016
#> GSM35445 1 0.0000 0.810 1.000 0.000 0.000 0.000
#> GSM35448 3 0.0927 0.832 0.000 0.008 0.976 0.016
#> GSM35451 1 0.4624 0.220 0.660 0.000 0.000 0.340
#> GSM35454 3 0.3528 0.792 0.000 0.000 0.808 0.192
#> GSM35457 2 0.0817 0.869 0.000 0.976 0.000 0.024
#> GSM35465 2 0.1211 0.866 0.000 0.960 0.000 0.040
#> GSM35468 1 0.0000 0.810 1.000 0.000 0.000 0.000
#> GSM35471 4 0.5509 0.657 0.424 0.004 0.012 0.560
#> GSM35473 1 0.0000 0.810 1.000 0.000 0.000 0.000
#> GSM35477 1 0.4624 0.220 0.660 0.000 0.000 0.340
#> GSM35480 1 0.2216 0.711 0.908 0.000 0.000 0.092
#> GSM35482 3 0.4072 0.757 0.000 0.000 0.748 0.252
#> GSM35485 2 0.2081 0.868 0.000 0.916 0.000 0.084
#> GSM35489 2 0.2011 0.869 0.000 0.920 0.000 0.080
#> GSM35492 1 0.0000 0.810 1.000 0.000 0.000 0.000
#> GSM35495 3 0.2973 0.810 0.000 0.000 0.856 0.144
#> GSM35499 2 0.0921 0.870 0.000 0.972 0.000 0.028
#> GSM35502 1 0.0000 0.810 1.000 0.000 0.000 0.000
#> GSM35505 3 0.0817 0.834 0.000 0.000 0.976 0.024
#> GSM35507 4 0.6857 0.534 0.404 0.104 0.000 0.492
#> GSM35510 2 0.0000 0.871 0.000 1.000 0.000 0.000
#> GSM35514 1 0.0000 0.810 1.000 0.000 0.000 0.000
#> GSM35517 2 0.1867 0.871 0.000 0.928 0.000 0.072
#> GSM35520 2 0.7896 0.134 0.000 0.360 0.292 0.348
#> GSM35523 4 0.5500 0.663 0.420 0.004 0.012 0.564
#> GSM35529 2 0.0921 0.869 0.000 0.972 0.000 0.028
#> GSM35531 2 0.3796 0.835 0.000 0.848 0.056 0.096
#> GSM35534 2 0.2149 0.868 0.000 0.912 0.000 0.088
#> GSM35536 1 0.0000 0.810 1.000 0.000 0.000 0.000
#> GSM35538 1 0.4431 0.322 0.696 0.000 0.000 0.304
#> GSM35539 1 0.4564 0.258 0.672 0.000 0.000 0.328
#> GSM35540 2 0.1211 0.866 0.000 0.960 0.000 0.040
#> GSM35541 2 0.2011 0.870 0.000 0.920 0.000 0.080
#> GSM35442 1 0.2996 0.677 0.892 0.000 0.044 0.064
#> GSM35447 3 0.0000 0.834 0.000 0.000 1.000 0.000
#> GSM35450 1 0.4543 0.271 0.676 0.000 0.000 0.324
#> GSM35453 1 0.1545 0.757 0.952 0.000 0.008 0.040
#> GSM35456 1 0.5155 -0.391 0.528 0.004 0.000 0.468
#> GSM35464 2 0.4776 0.409 0.000 0.624 0.000 0.376
#> GSM35467 1 0.0000 0.810 1.000 0.000 0.000 0.000
#> GSM35470 4 0.5571 0.629 0.396 0.000 0.024 0.580
#> GSM35479 3 0.4072 0.757 0.000 0.000 0.748 0.252
#> GSM35484 1 0.0000 0.810 1.000 0.000 0.000 0.000
#> GSM35488 1 0.0000 0.810 1.000 0.000 0.000 0.000
#> GSM35491 1 0.0000 0.810 1.000 0.000 0.000 0.000
#> GSM35494 3 0.4072 0.757 0.000 0.000 0.748 0.252
#> GSM35498 4 0.5500 0.663 0.420 0.004 0.012 0.564
#> GSM35501 1 0.0000 0.810 1.000 0.000 0.000 0.000
#> GSM35509 3 0.4040 0.759 0.000 0.000 0.752 0.248
#> GSM35513 1 0.0000 0.810 1.000 0.000 0.000 0.000
#> GSM35516 2 0.2081 0.869 0.000 0.916 0.000 0.084
#> GSM35522 4 0.5500 0.663 0.420 0.004 0.012 0.564
#> GSM35525 1 0.1716 0.756 0.936 0.000 0.000 0.064
#> GSM35528 1 0.4564 0.258 0.672 0.000 0.000 0.328
#> GSM35533 1 0.0000 0.810 1.000 0.000 0.000 0.000
#> GSM35537 4 0.5300 0.641 0.408 0.000 0.012 0.580
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM35441 2 0.1943 0.786 0.000 0.924 0.000 0.020 0.056
#> GSM35446 3 0.3958 0.711 0.000 0.000 0.776 0.040 0.184
#> GSM35449 2 0.2850 0.759 0.000 0.872 0.000 0.036 0.092
#> GSM35455 2 0.2359 0.778 0.000 0.904 0.000 0.036 0.060
#> GSM35458 5 0.2856 0.750 0.000 0.104 0.008 0.016 0.872
#> GSM35460 3 0.3810 0.723 0.000 0.000 0.792 0.040 0.168
#> GSM35461 3 0.5087 0.195 0.016 0.000 0.516 0.012 0.456
#> GSM35463 2 0.5159 0.745 0.000 0.704 0.004 0.156 0.136
#> GSM35472 3 0.4505 0.459 0.000 0.000 0.604 0.012 0.384
#> GSM35475 5 0.2221 0.771 0.000 0.052 0.036 0.000 0.912
#> GSM35483 2 0.5196 0.743 0.000 0.700 0.004 0.160 0.136
#> GSM35496 3 0.2592 0.756 0.000 0.000 0.892 0.056 0.052
#> GSM35497 2 0.2850 0.759 0.000 0.872 0.000 0.036 0.092
#> GSM35504 2 0.2830 0.774 0.000 0.884 0.016 0.080 0.020
#> GSM35508 2 0.5063 0.425 0.000 0.632 0.000 0.056 0.312
#> GSM35511 5 0.3594 0.687 0.000 0.020 0.172 0.004 0.804
#> GSM35512 3 0.4659 0.162 0.000 0.000 0.496 0.012 0.492
#> GSM35515 5 0.2856 0.750 0.000 0.104 0.008 0.016 0.872
#> GSM35519 5 0.3835 0.590 0.000 0.000 0.244 0.012 0.744
#> GSM35527 2 0.4885 0.501 0.000 0.668 0.000 0.056 0.276
#> GSM35532 5 0.3550 0.608 0.000 0.000 0.236 0.004 0.760
#> GSM35439 2 0.4364 0.771 0.000 0.768 0.000 0.112 0.120
#> GSM35443 1 0.2351 0.918 0.916 0.000 0.028 0.020 0.036
#> GSM35445 1 0.1569 0.931 0.944 0.000 0.044 0.008 0.004
#> GSM35448 3 0.5196 0.667 0.000 0.016 0.712 0.092 0.180
#> GSM35451 4 0.4235 0.794 0.336 0.000 0.000 0.656 0.008
#> GSM35454 3 0.1471 0.760 0.004 0.000 0.952 0.024 0.020
#> GSM35457 2 0.1872 0.787 0.000 0.928 0.000 0.020 0.052
#> GSM35465 2 0.2291 0.784 0.000 0.908 0.000 0.036 0.056
#> GSM35468 1 0.1267 0.936 0.960 0.000 0.004 0.012 0.024
#> GSM35471 4 0.4337 0.829 0.196 0.000 0.056 0.748 0.000
#> GSM35473 1 0.1041 0.935 0.964 0.000 0.032 0.000 0.004
#> GSM35477 4 0.4235 0.794 0.336 0.000 0.000 0.656 0.008
#> GSM35480 1 0.2694 0.862 0.892 0.000 0.032 0.068 0.008
#> GSM35482 3 0.2573 0.734 0.000 0.000 0.880 0.104 0.016
#> GSM35485 2 0.4877 0.758 0.000 0.732 0.004 0.136 0.128
#> GSM35489 2 0.4210 0.776 0.000 0.780 0.000 0.096 0.124
#> GSM35492 1 0.1612 0.934 0.948 0.000 0.012 0.016 0.024
#> GSM35495 3 0.1907 0.764 0.000 0.000 0.928 0.044 0.028
#> GSM35499 2 0.1408 0.795 0.000 0.948 0.000 0.044 0.008
#> GSM35502 1 0.0324 0.940 0.992 0.000 0.000 0.004 0.004
#> GSM35505 3 0.2597 0.746 0.004 0.000 0.872 0.004 0.120
#> GSM35507 4 0.5253 0.778 0.140 0.100 0.024 0.732 0.004
#> GSM35510 2 0.0566 0.796 0.000 0.984 0.000 0.012 0.004
#> GSM35514 1 0.0324 0.940 0.992 0.000 0.000 0.004 0.004
#> GSM35517 2 0.4111 0.777 0.000 0.788 0.000 0.092 0.120
#> GSM35520 5 0.3310 0.736 0.000 0.136 0.024 0.004 0.836
#> GSM35523 4 0.4845 0.822 0.188 0.000 0.076 0.728 0.008
#> GSM35529 2 0.1965 0.786 0.000 0.924 0.000 0.024 0.052
#> GSM35531 2 0.5076 0.710 0.000 0.692 0.000 0.108 0.200
#> GSM35534 2 0.5159 0.745 0.000 0.704 0.004 0.156 0.136
#> GSM35536 1 0.0404 0.938 0.988 0.000 0.000 0.012 0.000
#> GSM35538 4 0.4331 0.716 0.400 0.000 0.000 0.596 0.004
#> GSM35539 4 0.4252 0.792 0.340 0.000 0.000 0.652 0.008
#> GSM35540 2 0.2209 0.786 0.000 0.912 0.000 0.032 0.056
#> GSM35541 2 0.4361 0.773 0.000 0.768 0.000 0.108 0.124
#> GSM35442 1 0.3904 0.815 0.820 0.000 0.116 0.020 0.044
#> GSM35447 3 0.2964 0.734 0.004 0.000 0.840 0.004 0.152
#> GSM35450 4 0.4211 0.773 0.360 0.000 0.000 0.636 0.004
#> GSM35453 1 0.2233 0.868 0.892 0.000 0.104 0.000 0.004
#> GSM35456 4 0.4243 0.826 0.244 0.004 0.016 0.732 0.004
#> GSM35464 4 0.4108 0.453 0.000 0.308 0.000 0.684 0.008
#> GSM35467 1 0.0324 0.940 0.992 0.000 0.000 0.004 0.004
#> GSM35470 4 0.5963 0.732 0.152 0.000 0.196 0.636 0.016
#> GSM35479 3 0.2573 0.738 0.000 0.000 0.880 0.104 0.016
#> GSM35484 1 0.1280 0.939 0.960 0.000 0.024 0.008 0.008
#> GSM35488 1 0.0912 0.936 0.972 0.000 0.000 0.016 0.012
#> GSM35491 1 0.1507 0.935 0.952 0.000 0.012 0.012 0.024
#> GSM35494 3 0.2305 0.738 0.000 0.000 0.896 0.092 0.012
#> GSM35498 4 0.4359 0.828 0.188 0.000 0.052 0.756 0.004
#> GSM35501 1 0.0324 0.940 0.992 0.000 0.000 0.004 0.004
#> GSM35509 3 0.2124 0.747 0.000 0.000 0.900 0.096 0.004
#> GSM35513 1 0.0324 0.940 0.992 0.000 0.000 0.004 0.004
#> GSM35516 2 0.4361 0.774 0.000 0.768 0.000 0.108 0.124
#> GSM35522 4 0.4965 0.821 0.184 0.004 0.076 0.728 0.008
#> GSM35525 1 0.2416 0.817 0.888 0.000 0.000 0.100 0.012
#> GSM35528 4 0.4283 0.786 0.348 0.000 0.000 0.644 0.008
#> GSM35533 1 0.1280 0.939 0.960 0.000 0.024 0.008 0.008
#> GSM35537 4 0.5680 0.776 0.176 0.000 0.160 0.656 0.008
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM35441 2 0.0405 0.5077 0.000 0.988 0.000 0.000 0.004 0.008
#> GSM35446 3 0.5319 0.6065 0.000 0.000 0.616 0.008 0.236 0.140
#> GSM35449 2 0.2388 0.4936 0.000 0.904 0.004 0.016 0.036 0.040
#> GSM35455 2 0.2076 0.4987 0.000 0.920 0.004 0.016 0.020 0.040
#> GSM35458 5 0.4489 0.6774 0.008 0.104 0.000 0.000 0.724 0.164
#> GSM35460 3 0.5161 0.6253 0.000 0.000 0.640 0.008 0.220 0.132
#> GSM35461 5 0.5330 0.3525 0.012 0.000 0.320 0.000 0.576 0.092
#> GSM35463 6 0.3955 0.9504 0.000 0.436 0.000 0.004 0.000 0.560
#> GSM35472 3 0.4264 0.1340 0.000 0.000 0.496 0.000 0.488 0.016
#> GSM35475 5 0.2507 0.7464 0.000 0.040 0.004 0.000 0.884 0.072
#> GSM35483 6 0.4056 0.9653 0.000 0.416 0.000 0.004 0.004 0.576
#> GSM35496 3 0.3155 0.6907 0.008 0.000 0.864 0.056 0.040 0.032
#> GSM35497 2 0.2388 0.4936 0.000 0.904 0.004 0.016 0.036 0.040
#> GSM35504 2 0.4070 0.0718 0.000 0.672 0.008 0.008 0.004 0.308
#> GSM35508 2 0.5101 0.3094 0.000 0.668 0.004 0.024 0.228 0.076
#> GSM35511 5 0.2558 0.7381 0.000 0.036 0.040 0.004 0.896 0.024
#> GSM35512 5 0.4026 0.2923 0.000 0.000 0.348 0.000 0.636 0.016
#> GSM35515 5 0.4489 0.6774 0.008 0.104 0.000 0.000 0.724 0.164
#> GSM35519 5 0.2212 0.7043 0.000 0.000 0.112 0.000 0.880 0.008
#> GSM35527 2 0.4577 0.3743 0.000 0.740 0.004 0.024 0.156 0.076
#> GSM35532 5 0.1714 0.7186 0.000 0.000 0.092 0.000 0.908 0.000
#> GSM35439 2 0.4262 -0.5237 0.000 0.560 0.000 0.004 0.012 0.424
#> GSM35443 1 0.3454 0.8742 0.836 0.000 0.016 0.012 0.036 0.100
#> GSM35445 1 0.3091 0.8742 0.856 0.000 0.044 0.012 0.004 0.084
#> GSM35448 3 0.6035 0.5178 0.000 0.000 0.504 0.012 0.212 0.272
#> GSM35451 4 0.3139 0.8239 0.152 0.000 0.000 0.816 0.000 0.032
#> GSM35454 3 0.3983 0.6911 0.012 0.000 0.796 0.012 0.064 0.116
#> GSM35457 2 0.0291 0.5045 0.000 0.992 0.000 0.004 0.000 0.004
#> GSM35465 2 0.1672 0.4907 0.000 0.932 0.000 0.048 0.004 0.016
#> GSM35468 1 0.2545 0.8901 0.888 0.000 0.000 0.020 0.024 0.068
#> GSM35471 4 0.1718 0.8269 0.044 0.000 0.016 0.932 0.000 0.008
#> GSM35473 1 0.1969 0.8955 0.920 0.000 0.020 0.004 0.004 0.052
#> GSM35477 4 0.3139 0.8239 0.152 0.000 0.000 0.816 0.000 0.032
#> GSM35480 1 0.3676 0.8446 0.828 0.000 0.040 0.068 0.004 0.060
#> GSM35482 3 0.2933 0.6790 0.008 0.000 0.860 0.096 0.004 0.032
#> GSM35485 2 0.4226 -0.7294 0.000 0.504 0.000 0.004 0.008 0.484
#> GSM35489 2 0.4364 -0.5153 0.000 0.556 0.000 0.008 0.012 0.424
#> GSM35492 1 0.2422 0.8899 0.892 0.000 0.000 0.012 0.024 0.072
#> GSM35495 3 0.3787 0.7056 0.000 0.000 0.804 0.020 0.072 0.104
#> GSM35499 2 0.3660 0.2672 0.000 0.772 0.000 0.036 0.004 0.188
#> GSM35502 1 0.0622 0.9058 0.980 0.000 0.000 0.012 0.008 0.000
#> GSM35505 3 0.5126 0.6362 0.012 0.000 0.668 0.004 0.196 0.120
#> GSM35507 4 0.2919 0.8075 0.032 0.056 0.008 0.880 0.004 0.020
#> GSM35510 2 0.2234 0.3801 0.000 0.872 0.000 0.004 0.000 0.124
#> GSM35514 1 0.0622 0.9058 0.980 0.000 0.000 0.012 0.008 0.000
#> GSM35517 2 0.4041 -0.4778 0.000 0.584 0.000 0.004 0.004 0.408
#> GSM35520 5 0.3421 0.7174 0.000 0.044 0.016 0.000 0.824 0.116
#> GSM35523 4 0.3018 0.8144 0.040 0.000 0.032 0.876 0.016 0.036
#> GSM35529 2 0.0000 0.5066 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM35531 2 0.5022 -0.6186 0.000 0.496 0.000 0.004 0.060 0.440
#> GSM35534 6 0.3930 0.9675 0.000 0.420 0.000 0.000 0.004 0.576
#> GSM35536 1 0.1148 0.9034 0.960 0.000 0.000 0.020 0.004 0.016
#> GSM35538 4 0.4022 0.7100 0.272 0.000 0.000 0.700 0.008 0.020
#> GSM35539 4 0.3651 0.8208 0.160 0.000 0.000 0.792 0.016 0.032
#> GSM35540 2 0.1245 0.5022 0.000 0.952 0.000 0.032 0.000 0.016
#> GSM35541 2 0.3930 -0.5060 0.000 0.576 0.000 0.000 0.004 0.420
#> GSM35442 1 0.5503 0.7585 0.692 0.000 0.116 0.024 0.040 0.128
#> GSM35447 3 0.5173 0.6185 0.008 0.000 0.648 0.004 0.224 0.116
#> GSM35450 4 0.3550 0.7998 0.188 0.000 0.000 0.780 0.008 0.024
#> GSM35453 1 0.3275 0.8588 0.848 0.000 0.068 0.016 0.004 0.064
#> GSM35456 4 0.2729 0.8321 0.080 0.000 0.008 0.876 0.004 0.032
#> GSM35464 4 0.3129 0.7278 0.000 0.152 0.000 0.820 0.004 0.024
#> GSM35467 1 0.0622 0.9058 0.980 0.000 0.000 0.012 0.008 0.000
#> GSM35470 4 0.5989 0.4221 0.032 0.000 0.324 0.548 0.016 0.080
#> GSM35479 3 0.3292 0.6739 0.008 0.000 0.840 0.088 0.004 0.060
#> GSM35484 1 0.2849 0.8942 0.872 0.000 0.016 0.020 0.008 0.084
#> GSM35488 1 0.2449 0.8928 0.896 0.000 0.000 0.024 0.024 0.056
#> GSM35491 1 0.2422 0.8899 0.892 0.000 0.000 0.012 0.024 0.072
#> GSM35494 3 0.2763 0.6849 0.008 0.000 0.868 0.088 0.000 0.036
#> GSM35498 4 0.1988 0.8233 0.040 0.000 0.016 0.924 0.004 0.016
#> GSM35501 1 0.0622 0.9058 0.980 0.000 0.000 0.012 0.008 0.000
#> GSM35509 3 0.2645 0.7023 0.000 0.000 0.880 0.056 0.008 0.056
#> GSM35513 1 0.0622 0.9058 0.980 0.000 0.000 0.012 0.008 0.000
#> GSM35516 2 0.4887 -0.4936 0.000 0.536 0.000 0.044 0.008 0.412
#> GSM35522 4 0.3018 0.8144 0.040 0.000 0.032 0.876 0.016 0.036
#> GSM35525 1 0.3422 0.8038 0.832 0.000 0.008 0.112 0.016 0.032
#> GSM35528 4 0.3735 0.8111 0.172 0.000 0.000 0.780 0.012 0.036
#> GSM35533 1 0.2952 0.8924 0.864 0.000 0.016 0.020 0.008 0.092
#> GSM35537 4 0.5573 0.5177 0.024 0.000 0.284 0.608 0.016 0.068
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 time(p) k
#> MAD:kmeans 79 3.41e-07 2
#> MAD:kmeans 79 1.69e-05 3
#> MAD:kmeans 67 3.93e-04 4
#> MAD:kmeans 74 1.92e-05 5
#> MAD:kmeans 59 1.43e-04 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 7758 rows and 79 columns.
#> Top rows (776, 1552, 2328, 3103, 3879) are extracted by 'MAD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.986 0.994 0.5043 0.496 0.496
#> 3 3 1.000 0.954 0.982 0.3086 0.776 0.578
#> 4 4 0.892 0.923 0.954 0.1291 0.894 0.698
#> 5 5 0.822 0.836 0.903 0.0619 0.943 0.779
#> 6 6 0.765 0.724 0.805 0.0405 0.985 0.929
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
#> attr(,"optional")
#> [1] 2
There is also optional best \(k\) = 2 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM35441 2 0.0000 0.990 0.000 1.000
#> GSM35446 2 0.0000 0.990 0.000 1.000
#> GSM35449 2 0.0000 0.990 0.000 1.000
#> GSM35455 2 0.0000 0.990 0.000 1.000
#> GSM35458 2 0.0000 0.990 0.000 1.000
#> GSM35460 2 0.0000 0.990 0.000 1.000
#> GSM35461 1 0.0000 0.997 1.000 0.000
#> GSM35463 2 0.0000 0.990 0.000 1.000
#> GSM35472 2 0.0000 0.990 0.000 1.000
#> GSM35475 2 0.0000 0.990 0.000 1.000
#> GSM35483 2 0.0000 0.990 0.000 1.000
#> GSM35496 1 0.0000 0.997 1.000 0.000
#> GSM35497 2 0.0000 0.990 0.000 1.000
#> GSM35504 2 0.0000 0.990 0.000 1.000
#> GSM35508 2 0.0000 0.990 0.000 1.000
#> GSM35511 2 0.0000 0.990 0.000 1.000
#> GSM35512 2 0.0000 0.990 0.000 1.000
#> GSM35515 2 0.0000 0.990 0.000 1.000
#> GSM35519 2 0.0000 0.990 0.000 1.000
#> GSM35527 2 0.0000 0.990 0.000 1.000
#> GSM35532 2 0.0000 0.990 0.000 1.000
#> GSM35439 2 0.0000 0.990 0.000 1.000
#> GSM35443 1 0.0000 0.997 1.000 0.000
#> GSM35445 1 0.0000 0.997 1.000 0.000
#> GSM35448 2 0.0000 0.990 0.000 1.000
#> GSM35451 1 0.0000 0.997 1.000 0.000
#> GSM35454 1 0.0000 0.997 1.000 0.000
#> GSM35457 2 0.0000 0.990 0.000 1.000
#> GSM35465 2 0.0000 0.990 0.000 1.000
#> GSM35468 1 0.0000 0.997 1.000 0.000
#> GSM35471 1 0.0000 0.997 1.000 0.000
#> GSM35473 1 0.0000 0.997 1.000 0.000
#> GSM35477 1 0.0000 0.997 1.000 0.000
#> GSM35480 1 0.0000 0.997 1.000 0.000
#> GSM35482 1 0.0000 0.997 1.000 0.000
#> GSM35485 2 0.0000 0.990 0.000 1.000
#> GSM35489 2 0.0000 0.990 0.000 1.000
#> GSM35492 1 0.0000 0.997 1.000 0.000
#> GSM35495 2 0.9358 0.453 0.352 0.648
#> GSM35499 2 0.0000 0.990 0.000 1.000
#> GSM35502 1 0.0000 0.997 1.000 0.000
#> GSM35505 1 0.0000 0.997 1.000 0.000
#> GSM35507 1 0.0376 0.994 0.996 0.004
#> GSM35510 2 0.0000 0.990 0.000 1.000
#> GSM35514 1 0.0000 0.997 1.000 0.000
#> GSM35517 2 0.0000 0.990 0.000 1.000
#> GSM35520 2 0.0000 0.990 0.000 1.000
#> GSM35523 1 0.0000 0.997 1.000 0.000
#> GSM35529 2 0.0000 0.990 0.000 1.000
#> GSM35531 2 0.0000 0.990 0.000 1.000
#> GSM35534 2 0.0000 0.990 0.000 1.000
#> GSM35536 1 0.0000 0.997 1.000 0.000
#> GSM35538 1 0.0000 0.997 1.000 0.000
#> GSM35539 1 0.0000 0.997 1.000 0.000
#> GSM35540 2 0.0000 0.990 0.000 1.000
#> GSM35541 2 0.0000 0.990 0.000 1.000
#> GSM35442 1 0.0000 0.997 1.000 0.000
#> GSM35447 1 0.4298 0.902 0.912 0.088
#> GSM35450 1 0.0000 0.997 1.000 0.000
#> GSM35453 1 0.0000 0.997 1.000 0.000
#> GSM35456 1 0.0000 0.997 1.000 0.000
#> GSM35464 2 0.0000 0.990 0.000 1.000
#> GSM35467 1 0.0000 0.997 1.000 0.000
#> GSM35470 1 0.0000 0.997 1.000 0.000
#> GSM35479 1 0.0000 0.997 1.000 0.000
#> GSM35484 1 0.0000 0.997 1.000 0.000
#> GSM35488 1 0.0000 0.997 1.000 0.000
#> GSM35491 1 0.0000 0.997 1.000 0.000
#> GSM35494 1 0.0000 0.997 1.000 0.000
#> GSM35498 1 0.0000 0.997 1.000 0.000
#> GSM35501 1 0.0000 0.997 1.000 0.000
#> GSM35509 1 0.1184 0.982 0.984 0.016
#> GSM35513 1 0.0000 0.997 1.000 0.000
#> GSM35516 2 0.0000 0.990 0.000 1.000
#> GSM35522 1 0.0000 0.997 1.000 0.000
#> GSM35525 1 0.0000 0.997 1.000 0.000
#> GSM35528 1 0.0000 0.997 1.000 0.000
#> GSM35533 1 0.0000 0.997 1.000 0.000
#> GSM35537 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
#> GSM35441 2 0.0000 0.964 0.000 1.000 0.000
#> GSM35446 3 0.0000 0.992 0.000 0.000 1.000
#> GSM35449 2 0.0000 0.964 0.000 1.000 0.000
#> GSM35455 2 0.0000 0.964 0.000 1.000 0.000
#> GSM35458 2 0.0237 0.960 0.000 0.996 0.004
#> GSM35460 3 0.0000 0.992 0.000 0.000 1.000
#> GSM35461 3 0.0000 0.992 0.000 0.000 1.000
#> GSM35463 2 0.0000 0.964 0.000 1.000 0.000
#> GSM35472 3 0.0000 0.992 0.000 0.000 1.000
#> GSM35475 2 0.6215 0.244 0.000 0.572 0.428
#> GSM35483 2 0.0000 0.964 0.000 1.000 0.000
#> GSM35496 3 0.0000 0.992 0.000 0.000 1.000
#> GSM35497 2 0.0000 0.964 0.000 1.000 0.000
#> GSM35504 2 0.0000 0.964 0.000 1.000 0.000
#> GSM35508 2 0.0000 0.964 0.000 1.000 0.000
#> GSM35511 3 0.3551 0.841 0.000 0.132 0.868
#> GSM35512 3 0.0000 0.992 0.000 0.000 1.000
#> GSM35515 2 0.0237 0.960 0.000 0.996 0.004
#> GSM35519 3 0.0000 0.992 0.000 0.000 1.000
#> GSM35527 2 0.0000 0.964 0.000 1.000 0.000
#> GSM35532 3 0.0000 0.992 0.000 0.000 1.000
#> GSM35439 2 0.0000 0.964 0.000 1.000 0.000
#> GSM35443 1 0.0000 0.989 1.000 0.000 0.000
#> GSM35445 1 0.0000 0.989 1.000 0.000 0.000
#> GSM35448 3 0.0000 0.992 0.000 0.000 1.000
#> GSM35451 1 0.0000 0.989 1.000 0.000 0.000
#> GSM35454 3 0.0000 0.992 0.000 0.000 1.000
#> GSM35457 2 0.0000 0.964 0.000 1.000 0.000
#> GSM35465 2 0.0000 0.964 0.000 1.000 0.000
#> GSM35468 1 0.0000 0.989 1.000 0.000 0.000
#> GSM35471 1 0.0000 0.989 1.000 0.000 0.000
#> GSM35473 1 0.0000 0.989 1.000 0.000 0.000
#> GSM35477 1 0.0000 0.989 1.000 0.000 0.000
#> GSM35480 1 0.0000 0.989 1.000 0.000 0.000
#> GSM35482 3 0.0000 0.992 0.000 0.000 1.000
#> GSM35485 2 0.0000 0.964 0.000 1.000 0.000
#> GSM35489 2 0.0000 0.964 0.000 1.000 0.000
#> GSM35492 1 0.0000 0.989 1.000 0.000 0.000
#> GSM35495 3 0.0000 0.992 0.000 0.000 1.000
#> GSM35499 2 0.0000 0.964 0.000 1.000 0.000
#> GSM35502 1 0.0000 0.989 1.000 0.000 0.000
#> GSM35505 3 0.0000 0.992 0.000 0.000 1.000
#> GSM35507 2 0.6180 0.283 0.416 0.584 0.000
#> GSM35510 2 0.0000 0.964 0.000 1.000 0.000
#> GSM35514 1 0.0000 0.989 1.000 0.000 0.000
#> GSM35517 2 0.0000 0.964 0.000 1.000 0.000
#> GSM35520 2 0.2711 0.877 0.000 0.912 0.088
#> GSM35523 1 0.0000 0.989 1.000 0.000 0.000
#> GSM35529 2 0.0000 0.964 0.000 1.000 0.000
#> GSM35531 2 0.0000 0.964 0.000 1.000 0.000
#> GSM35534 2 0.0000 0.964 0.000 1.000 0.000
#> GSM35536 1 0.0000 0.989 1.000 0.000 0.000
#> GSM35538 1 0.0000 0.989 1.000 0.000 0.000
#> GSM35539 1 0.0000 0.989 1.000 0.000 0.000
#> GSM35540 2 0.0000 0.964 0.000 1.000 0.000
#> GSM35541 2 0.0000 0.964 0.000 1.000 0.000
#> GSM35442 1 0.5560 0.576 0.700 0.000 0.300
#> GSM35447 3 0.0000 0.992 0.000 0.000 1.000
#> GSM35450 1 0.0000 0.989 1.000 0.000 0.000
#> GSM35453 1 0.0000 0.989 1.000 0.000 0.000
#> GSM35456 1 0.0000 0.989 1.000 0.000 0.000
#> GSM35464 2 0.0000 0.964 0.000 1.000 0.000
#> GSM35467 1 0.0000 0.989 1.000 0.000 0.000
#> GSM35470 1 0.1163 0.963 0.972 0.000 0.028
#> GSM35479 3 0.0000 0.992 0.000 0.000 1.000
#> GSM35484 1 0.0000 0.989 1.000 0.000 0.000
#> GSM35488 1 0.0000 0.989 1.000 0.000 0.000
#> GSM35491 1 0.0000 0.989 1.000 0.000 0.000
#> GSM35494 3 0.0000 0.992 0.000 0.000 1.000
#> GSM35498 1 0.0000 0.989 1.000 0.000 0.000
#> GSM35501 1 0.0000 0.989 1.000 0.000 0.000
#> GSM35509 3 0.0000 0.992 0.000 0.000 1.000
#> GSM35513 1 0.0000 0.989 1.000 0.000 0.000
#> GSM35516 2 0.0000 0.964 0.000 1.000 0.000
#> GSM35522 1 0.0000 0.989 1.000 0.000 0.000
#> GSM35525 1 0.0000 0.989 1.000 0.000 0.000
#> GSM35528 1 0.0000 0.989 1.000 0.000 0.000
#> GSM35533 1 0.0000 0.989 1.000 0.000 0.000
#> GSM35537 1 0.0000 0.989 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM35441 2 0.0188 0.968 0.000 0.996 0.000 0.004
#> GSM35446 3 0.0000 0.950 0.000 0.000 1.000 0.000
#> GSM35449 2 0.0188 0.968 0.000 0.996 0.000 0.004
#> GSM35455 2 0.0188 0.968 0.000 0.996 0.000 0.004
#> GSM35458 2 0.2281 0.895 0.000 0.904 0.096 0.000
#> GSM35460 3 0.0000 0.950 0.000 0.000 1.000 0.000
#> GSM35461 3 0.1059 0.943 0.016 0.000 0.972 0.012
#> GSM35463 2 0.0000 0.968 0.000 1.000 0.000 0.000
#> GSM35472 3 0.0000 0.950 0.000 0.000 1.000 0.000
#> GSM35475 2 0.4804 0.424 0.000 0.616 0.384 0.000
#> GSM35483 2 0.0000 0.968 0.000 1.000 0.000 0.000
#> GSM35496 3 0.2011 0.932 0.000 0.000 0.920 0.080
#> GSM35497 2 0.0188 0.968 0.000 0.996 0.000 0.004
#> GSM35504 2 0.0188 0.968 0.000 0.996 0.000 0.004
#> GSM35508 2 0.0188 0.968 0.000 0.996 0.000 0.004
#> GSM35511 3 0.2760 0.814 0.000 0.128 0.872 0.000
#> GSM35512 3 0.0000 0.950 0.000 0.000 1.000 0.000
#> GSM35515 2 0.2281 0.895 0.000 0.904 0.096 0.000
#> GSM35519 3 0.0000 0.950 0.000 0.000 1.000 0.000
#> GSM35527 2 0.0188 0.968 0.000 0.996 0.000 0.004
#> GSM35532 3 0.0000 0.950 0.000 0.000 1.000 0.000
#> GSM35439 2 0.0000 0.968 0.000 1.000 0.000 0.000
#> GSM35443 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM35445 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM35448 3 0.0000 0.950 0.000 0.000 1.000 0.000
#> GSM35451 4 0.2704 0.863 0.124 0.000 0.000 0.876
#> GSM35454 3 0.2081 0.930 0.000 0.000 0.916 0.084
#> GSM35457 2 0.0188 0.968 0.000 0.996 0.000 0.004
#> GSM35465 2 0.0592 0.960 0.000 0.984 0.000 0.016
#> GSM35468 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM35471 4 0.0188 0.864 0.004 0.000 0.000 0.996
#> GSM35473 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM35477 4 0.2704 0.863 0.124 0.000 0.000 0.876
#> GSM35480 1 0.1637 0.928 0.940 0.000 0.000 0.060
#> GSM35482 3 0.2647 0.910 0.000 0.000 0.880 0.120
#> GSM35485 2 0.0000 0.968 0.000 1.000 0.000 0.000
#> GSM35489 2 0.0000 0.968 0.000 1.000 0.000 0.000
#> GSM35492 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM35495 3 0.1716 0.937 0.000 0.000 0.936 0.064
#> GSM35499 2 0.0188 0.968 0.000 0.996 0.000 0.004
#> GSM35502 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM35505 3 0.0000 0.950 0.000 0.000 1.000 0.000
#> GSM35507 4 0.1867 0.847 0.000 0.072 0.000 0.928
#> GSM35510 2 0.0188 0.968 0.000 0.996 0.000 0.004
#> GSM35514 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM35517 2 0.0188 0.968 0.000 0.996 0.000 0.004
#> GSM35520 2 0.2868 0.857 0.000 0.864 0.136 0.000
#> GSM35523 4 0.0188 0.864 0.004 0.000 0.000 0.996
#> GSM35529 2 0.0188 0.968 0.000 0.996 0.000 0.004
#> GSM35531 2 0.1302 0.938 0.000 0.956 0.044 0.000
#> GSM35534 2 0.0000 0.968 0.000 1.000 0.000 0.000
#> GSM35536 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM35538 4 0.4898 0.457 0.416 0.000 0.000 0.584
#> GSM35539 4 0.3219 0.843 0.164 0.000 0.000 0.836
#> GSM35540 2 0.0188 0.968 0.000 0.996 0.000 0.004
#> GSM35541 2 0.0000 0.968 0.000 1.000 0.000 0.000
#> GSM35442 1 0.0336 0.984 0.992 0.000 0.008 0.000
#> GSM35447 3 0.0000 0.950 0.000 0.000 1.000 0.000
#> GSM35450 4 0.3726 0.801 0.212 0.000 0.000 0.788
#> GSM35453 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM35456 4 0.2174 0.874 0.052 0.020 0.000 0.928
#> GSM35464 4 0.2704 0.814 0.000 0.124 0.000 0.876
#> GSM35467 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM35470 4 0.4509 0.622 0.288 0.000 0.004 0.708
#> GSM35479 3 0.2647 0.910 0.000 0.000 0.880 0.120
#> GSM35484 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM35488 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM35491 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM35494 3 0.2647 0.910 0.000 0.000 0.880 0.120
#> GSM35498 4 0.0188 0.864 0.004 0.000 0.000 0.996
#> GSM35501 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM35509 3 0.2469 0.917 0.000 0.000 0.892 0.108
#> GSM35513 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM35516 2 0.0000 0.968 0.000 1.000 0.000 0.000
#> GSM35522 4 0.0000 0.862 0.000 0.000 0.000 1.000
#> GSM35525 1 0.1557 0.932 0.944 0.000 0.000 0.056
#> GSM35528 4 0.3074 0.850 0.152 0.000 0.000 0.848
#> GSM35533 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM35537 4 0.1022 0.867 0.032 0.000 0.000 0.968
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM35441 2 0.0703 0.923 0.000 0.976 0.000 0.000 0.024
#> GSM35446 3 0.3210 0.745 0.000 0.000 0.788 0.000 0.212
#> GSM35449 2 0.1732 0.899 0.000 0.920 0.000 0.000 0.080
#> GSM35455 2 0.1043 0.919 0.000 0.960 0.000 0.000 0.040
#> GSM35458 5 0.1732 0.755 0.000 0.080 0.000 0.000 0.920
#> GSM35460 3 0.2127 0.833 0.000 0.000 0.892 0.000 0.108
#> GSM35461 5 0.4915 0.326 0.020 0.000 0.420 0.004 0.556
#> GSM35463 2 0.1894 0.917 0.000 0.920 0.000 0.008 0.072
#> GSM35472 3 0.4060 0.423 0.000 0.000 0.640 0.000 0.360
#> GSM35475 5 0.1750 0.777 0.000 0.036 0.028 0.000 0.936
#> GSM35483 2 0.2295 0.911 0.000 0.900 0.004 0.008 0.088
#> GSM35496 3 0.1216 0.852 0.000 0.000 0.960 0.020 0.020
#> GSM35497 2 0.2020 0.884 0.000 0.900 0.000 0.000 0.100
#> GSM35504 2 0.0912 0.923 0.000 0.972 0.016 0.000 0.012
#> GSM35508 2 0.3857 0.585 0.000 0.688 0.000 0.000 0.312
#> GSM35511 5 0.2660 0.767 0.000 0.008 0.128 0.000 0.864
#> GSM35512 5 0.4287 0.139 0.000 0.000 0.460 0.000 0.540
#> GSM35515 5 0.1732 0.755 0.000 0.080 0.000 0.000 0.920
#> GSM35519 5 0.2605 0.759 0.000 0.000 0.148 0.000 0.852
#> GSM35527 2 0.2516 0.848 0.000 0.860 0.000 0.000 0.140
#> GSM35532 5 0.2561 0.761 0.000 0.000 0.144 0.000 0.856
#> GSM35439 2 0.1956 0.916 0.000 0.916 0.000 0.008 0.076
#> GSM35443 1 0.0771 0.962 0.976 0.000 0.000 0.004 0.020
#> GSM35445 1 0.0324 0.974 0.992 0.000 0.004 0.000 0.004
#> GSM35448 3 0.3914 0.729 0.000 0.016 0.760 0.004 0.220
#> GSM35451 4 0.2179 0.827 0.100 0.000 0.000 0.896 0.004
#> GSM35454 3 0.0798 0.854 0.008 0.000 0.976 0.000 0.016
#> GSM35457 2 0.0404 0.924 0.000 0.988 0.000 0.000 0.012
#> GSM35465 2 0.1493 0.914 0.000 0.948 0.000 0.024 0.028
#> GSM35468 1 0.0162 0.976 0.996 0.000 0.000 0.004 0.000
#> GSM35471 4 0.0693 0.826 0.000 0.000 0.012 0.980 0.008
#> GSM35473 1 0.0162 0.976 0.996 0.000 0.000 0.000 0.004
#> GSM35477 4 0.2068 0.829 0.092 0.000 0.000 0.904 0.004
#> GSM35480 1 0.1952 0.902 0.912 0.000 0.000 0.084 0.004
#> GSM35482 3 0.1408 0.838 0.000 0.000 0.948 0.044 0.008
#> GSM35485 2 0.2017 0.915 0.000 0.912 0.000 0.008 0.080
#> GSM35489 2 0.1408 0.924 0.000 0.948 0.000 0.008 0.044
#> GSM35492 1 0.0162 0.976 0.996 0.000 0.000 0.004 0.000
#> GSM35495 3 0.0703 0.856 0.000 0.000 0.976 0.000 0.024
#> GSM35499 2 0.0703 0.922 0.000 0.976 0.000 0.000 0.024
#> GSM35502 1 0.0000 0.976 1.000 0.000 0.000 0.000 0.000
#> GSM35505 3 0.2127 0.836 0.000 0.000 0.892 0.000 0.108
#> GSM35507 4 0.1485 0.818 0.000 0.032 0.000 0.948 0.020
#> GSM35510 2 0.0290 0.924 0.000 0.992 0.000 0.000 0.008
#> GSM35514 1 0.0000 0.976 1.000 0.000 0.000 0.000 0.000
#> GSM35517 2 0.1197 0.926 0.000 0.952 0.000 0.000 0.048
#> GSM35520 5 0.2006 0.764 0.000 0.072 0.012 0.000 0.916
#> GSM35523 4 0.1310 0.823 0.000 0.000 0.024 0.956 0.020
#> GSM35529 2 0.0404 0.924 0.000 0.988 0.000 0.000 0.012
#> GSM35531 2 0.3443 0.835 0.000 0.816 0.012 0.008 0.164
#> GSM35534 2 0.2463 0.904 0.000 0.888 0.004 0.008 0.100
#> GSM35536 1 0.0000 0.976 1.000 0.000 0.000 0.000 0.000
#> GSM35538 4 0.4375 0.405 0.420 0.000 0.000 0.576 0.004
#> GSM35539 4 0.2843 0.812 0.144 0.000 0.000 0.848 0.008
#> GSM35540 2 0.1408 0.918 0.000 0.948 0.000 0.008 0.044
#> GSM35541 2 0.1764 0.919 0.000 0.928 0.000 0.008 0.064
#> GSM35442 1 0.2032 0.917 0.924 0.000 0.052 0.004 0.020
#> GSM35447 3 0.2891 0.786 0.000 0.000 0.824 0.000 0.176
#> GSM35450 4 0.3266 0.775 0.200 0.000 0.000 0.796 0.004
#> GSM35453 1 0.0566 0.970 0.984 0.000 0.012 0.000 0.004
#> GSM35456 4 0.1503 0.829 0.020 0.008 0.000 0.952 0.020
#> GSM35464 4 0.3106 0.730 0.000 0.140 0.000 0.840 0.020
#> GSM35467 1 0.0000 0.976 1.000 0.000 0.000 0.000 0.000
#> GSM35470 4 0.7121 0.318 0.240 0.000 0.308 0.432 0.020
#> GSM35479 3 0.1549 0.834 0.000 0.000 0.944 0.040 0.016
#> GSM35484 1 0.0162 0.976 0.996 0.000 0.000 0.000 0.004
#> GSM35488 1 0.0290 0.974 0.992 0.000 0.000 0.008 0.000
#> GSM35491 1 0.0162 0.976 0.996 0.000 0.000 0.004 0.000
#> GSM35494 3 0.1331 0.840 0.000 0.000 0.952 0.040 0.008
#> GSM35498 4 0.1106 0.824 0.000 0.000 0.012 0.964 0.024
#> GSM35501 1 0.0000 0.976 1.000 0.000 0.000 0.000 0.000
#> GSM35509 3 0.0404 0.853 0.000 0.000 0.988 0.012 0.000
#> GSM35513 1 0.0000 0.976 1.000 0.000 0.000 0.000 0.000
#> GSM35516 2 0.1914 0.921 0.000 0.924 0.000 0.016 0.060
#> GSM35522 4 0.1310 0.823 0.000 0.000 0.024 0.956 0.020
#> GSM35525 1 0.2886 0.801 0.844 0.000 0.000 0.148 0.008
#> GSM35528 4 0.2806 0.808 0.152 0.000 0.000 0.844 0.004
#> GSM35533 1 0.0162 0.976 0.996 0.000 0.000 0.000 0.004
#> GSM35537 4 0.4697 0.732 0.068 0.000 0.152 0.760 0.020
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM35441 2 0.0632 0.7791 0.000 0.976 0.000 0.000 0.024 NA
#> GSM35446 3 0.4312 0.5305 0.000 0.000 0.676 0.000 0.272 NA
#> GSM35449 2 0.2384 0.7346 0.000 0.884 0.000 0.000 0.084 NA
#> GSM35455 2 0.1856 0.7633 0.000 0.920 0.000 0.000 0.048 NA
#> GSM35458 5 0.2445 0.7448 0.000 0.020 0.000 0.000 0.872 NA
#> GSM35460 3 0.3279 0.6543 0.000 0.000 0.796 0.000 0.176 NA
#> GSM35461 5 0.5719 0.5110 0.032 0.000 0.224 0.004 0.616 NA
#> GSM35463 2 0.3961 0.7015 0.000 0.556 0.000 0.000 0.004 NA
#> GSM35472 5 0.4703 -0.0426 0.000 0.000 0.464 0.000 0.492 NA
#> GSM35475 5 0.1124 0.7715 0.000 0.008 0.000 0.000 0.956 NA
#> GSM35483 2 0.4314 0.6891 0.000 0.536 0.000 0.000 0.020 NA
#> GSM35496 3 0.3224 0.7057 0.000 0.000 0.824 0.004 0.040 NA
#> GSM35497 2 0.2436 0.7373 0.000 0.880 0.000 0.000 0.088 NA
#> GSM35504 2 0.2778 0.7779 0.000 0.824 0.008 0.000 0.000 NA
#> GSM35508 2 0.3782 0.5791 0.000 0.740 0.000 0.000 0.224 NA
#> GSM35511 5 0.0713 0.7755 0.000 0.000 0.028 0.000 0.972 NA
#> GSM35512 5 0.4180 0.3592 0.000 0.000 0.348 0.000 0.628 NA
#> GSM35515 5 0.2445 0.7448 0.000 0.020 0.000 0.000 0.872 NA
#> GSM35519 5 0.1196 0.7700 0.000 0.000 0.040 0.000 0.952 NA
#> GSM35527 2 0.2798 0.7114 0.000 0.852 0.000 0.000 0.112 NA
#> GSM35532 5 0.0713 0.7757 0.000 0.000 0.028 0.000 0.972 NA
#> GSM35439 2 0.4064 0.7306 0.000 0.624 0.000 0.000 0.016 NA
#> GSM35443 1 0.2398 0.8876 0.888 0.000 0.004 0.004 0.016 NA
#> GSM35445 1 0.2364 0.8888 0.892 0.000 0.032 0.004 0.000 NA
#> GSM35448 3 0.5405 0.4905 0.000 0.008 0.612 0.000 0.208 NA
#> GSM35451 4 0.2630 0.7854 0.064 0.000 0.000 0.872 0.000 NA
#> GSM35454 3 0.2315 0.7122 0.008 0.000 0.892 0.000 0.016 NA
#> GSM35457 2 0.0146 0.7814 0.000 0.996 0.000 0.000 0.000 NA
#> GSM35465 2 0.1765 0.7638 0.000 0.924 0.000 0.024 0.000 NA
#> GSM35468 1 0.1411 0.9075 0.936 0.000 0.000 0.004 0.000 NA
#> GSM35471 4 0.1010 0.7860 0.000 0.000 0.004 0.960 0.000 NA
#> GSM35473 1 0.1196 0.9112 0.952 0.000 0.008 0.000 0.000 NA
#> GSM35477 4 0.2629 0.7856 0.060 0.000 0.000 0.872 0.000 NA
#> GSM35480 1 0.3627 0.8171 0.808 0.000 0.008 0.092 0.000 NA
#> GSM35482 3 0.3219 0.7003 0.000 0.000 0.820 0.012 0.020 NA
#> GSM35485 2 0.4123 0.7068 0.000 0.568 0.000 0.000 0.012 NA
#> GSM35489 2 0.3383 0.7671 0.000 0.728 0.000 0.000 0.004 NA
#> GSM35492 1 0.1471 0.9063 0.932 0.000 0.000 0.004 0.000 NA
#> GSM35495 3 0.1196 0.7262 0.000 0.000 0.952 0.000 0.040 NA
#> GSM35499 2 0.2320 0.7868 0.000 0.864 0.000 0.004 0.000 NA
#> GSM35502 1 0.0363 0.9174 0.988 0.000 0.000 0.000 0.000 NA
#> GSM35505 3 0.3936 0.6633 0.008 0.000 0.780 0.000 0.124 NA
#> GSM35507 4 0.2122 0.7746 0.000 0.024 0.000 0.900 0.000 NA
#> GSM35510 2 0.1141 0.7876 0.000 0.948 0.000 0.000 0.000 NA
#> GSM35514 1 0.0146 0.9177 0.996 0.000 0.000 0.000 0.000 NA
#> GSM35517 2 0.3081 0.7770 0.000 0.776 0.000 0.000 0.004 NA
#> GSM35520 5 0.2491 0.7249 0.000 0.020 0.000 0.000 0.868 NA
#> GSM35523 4 0.3029 0.7561 0.000 0.000 0.036 0.840 0.004 NA
#> GSM35529 2 0.0146 0.7812 0.000 0.996 0.000 0.000 0.004 NA
#> GSM35531 2 0.4895 0.6449 0.000 0.496 0.000 0.000 0.060 NA
#> GSM35534 2 0.4453 0.6821 0.000 0.528 0.000 0.000 0.028 NA
#> GSM35536 1 0.0458 0.9171 0.984 0.000 0.000 0.000 0.000 NA
#> GSM35538 4 0.4783 0.2861 0.428 0.000 0.000 0.520 0.000 NA
#> GSM35539 4 0.3644 0.7599 0.120 0.000 0.000 0.792 0.000 NA
#> GSM35540 2 0.1851 0.7672 0.000 0.924 0.004 0.004 0.012 NA
#> GSM35541 2 0.3756 0.7390 0.000 0.644 0.000 0.000 0.004 NA
#> GSM35442 1 0.4729 0.7480 0.720 0.000 0.092 0.008 0.012 NA
#> GSM35447 3 0.4746 0.5412 0.008 0.000 0.672 0.000 0.240 NA
#> GSM35450 4 0.4117 0.6792 0.228 0.000 0.000 0.716 0.000 NA
#> GSM35453 1 0.2499 0.8802 0.880 0.000 0.048 0.000 0.000 NA
#> GSM35456 4 0.2001 0.7774 0.004 0.004 0.000 0.900 0.000 NA
#> GSM35464 4 0.4787 0.6058 0.000 0.220 0.000 0.672 0.004 NA
#> GSM35467 1 0.0000 0.9175 1.000 0.000 0.000 0.000 0.000 NA
#> GSM35470 3 0.7594 -0.0631 0.136 0.000 0.340 0.264 0.004 NA
#> GSM35479 3 0.2876 0.7092 0.000 0.000 0.844 0.016 0.008 NA
#> GSM35484 1 0.1542 0.9098 0.936 0.000 0.004 0.008 0.000 NA
#> GSM35488 1 0.2201 0.8921 0.896 0.000 0.000 0.028 0.000 NA
#> GSM35491 1 0.1349 0.9086 0.940 0.000 0.000 0.004 0.000 NA
#> GSM35494 3 0.2784 0.7109 0.000 0.000 0.848 0.012 0.008 NA
#> GSM35498 4 0.2906 0.7675 0.000 0.004 0.016 0.844 0.004 NA
#> GSM35501 1 0.0363 0.9174 0.988 0.000 0.000 0.000 0.000 NA
#> GSM35509 3 0.1616 0.7294 0.000 0.000 0.932 0.000 0.020 NA
#> GSM35513 1 0.0000 0.9175 1.000 0.000 0.000 0.000 0.000 NA
#> GSM35516 2 0.4428 0.7366 0.000 0.624 0.000 0.032 0.004 NA
#> GSM35522 4 0.2882 0.7596 0.000 0.000 0.028 0.848 0.004 NA
#> GSM35525 1 0.4186 0.6496 0.728 0.000 0.000 0.192 0.000 NA
#> GSM35528 4 0.4032 0.7509 0.140 0.000 0.000 0.764 0.004 NA
#> GSM35533 1 0.1923 0.9029 0.916 0.000 0.004 0.016 0.000 NA
#> GSM35537 4 0.6806 0.3752 0.064 0.000 0.220 0.484 0.004 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 time(p) k
#> MAD:skmeans 78 3.66e-07 2
#> MAD:skmeans 77 2.19e-05 3
#> MAD:skmeans 77 3.99e-05 4
#> MAD:skmeans 74 1.86e-05 5
#> MAD:skmeans 73 1.17e-05 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 7758 rows and 79 columns.
#> Top rows (776, 1552, 2328, 3103, 3879) are extracted by 'MAD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.637 0.790 0.915 0.4976 0.496 0.496
#> 3 3 0.598 0.692 0.792 0.3094 0.764 0.566
#> 4 4 0.901 0.865 0.941 0.1554 0.873 0.652
#> 5 5 0.835 0.822 0.908 0.0501 0.914 0.682
#> 6 6 0.805 0.670 0.802 0.0387 0.939 0.718
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM35441 2 0.0000 0.9012 0.000 1.000
#> GSM35446 2 0.6438 0.7847 0.164 0.836
#> GSM35449 2 0.0000 0.9012 0.000 1.000
#> GSM35455 2 0.0000 0.9012 0.000 1.000
#> GSM35458 1 0.9954 0.0660 0.540 0.460
#> GSM35460 2 0.6973 0.7593 0.188 0.812
#> GSM35461 1 0.2043 0.8779 0.968 0.032
#> GSM35463 2 0.0000 0.9012 0.000 1.000
#> GSM35472 2 0.7453 0.7303 0.212 0.788
#> GSM35475 2 0.9881 0.2741 0.436 0.564
#> GSM35483 2 0.0000 0.9012 0.000 1.000
#> GSM35496 1 0.0000 0.8976 1.000 0.000
#> GSM35497 2 0.0000 0.9012 0.000 1.000
#> GSM35504 2 0.0000 0.9012 0.000 1.000
#> GSM35508 2 0.0000 0.9012 0.000 1.000
#> GSM35511 2 0.4562 0.8433 0.096 0.904
#> GSM35512 2 0.9248 0.5303 0.340 0.660
#> GSM35515 1 0.9775 0.2323 0.588 0.412
#> GSM35519 2 0.7950 0.6973 0.240 0.760
#> GSM35527 2 0.0000 0.9012 0.000 1.000
#> GSM35532 2 0.4431 0.8465 0.092 0.908
#> GSM35439 2 0.0000 0.9012 0.000 1.000
#> GSM35443 1 0.0000 0.8976 1.000 0.000
#> GSM35445 1 0.0000 0.8976 1.000 0.000
#> GSM35448 2 0.1184 0.8937 0.016 0.984
#> GSM35451 1 0.3879 0.8459 0.924 0.076
#> GSM35454 2 0.9933 0.1862 0.452 0.548
#> GSM35457 2 0.0000 0.9012 0.000 1.000
#> GSM35465 2 0.0000 0.9012 0.000 1.000
#> GSM35468 1 0.0000 0.8976 1.000 0.000
#> GSM35471 1 0.8327 0.6147 0.736 0.264
#> GSM35473 1 0.0000 0.8976 1.000 0.000
#> GSM35477 1 0.0672 0.8955 0.992 0.008
#> GSM35480 1 0.0376 0.8971 0.996 0.004
#> GSM35482 1 0.3733 0.8490 0.928 0.072
#> GSM35485 2 0.0000 0.9012 0.000 1.000
#> GSM35489 2 0.0000 0.9012 0.000 1.000
#> GSM35492 1 0.0000 0.8976 1.000 0.000
#> GSM35495 2 0.8207 0.6700 0.256 0.744
#> GSM35499 2 0.0000 0.9012 0.000 1.000
#> GSM35502 1 0.0000 0.8976 1.000 0.000
#> GSM35505 1 0.9996 -0.0171 0.512 0.488
#> GSM35507 1 0.8955 0.5416 0.688 0.312
#> GSM35510 2 0.0000 0.9012 0.000 1.000
#> GSM35514 1 0.0000 0.8976 1.000 0.000
#> GSM35517 2 0.0000 0.9012 0.000 1.000
#> GSM35520 2 0.6343 0.7866 0.160 0.840
#> GSM35523 1 0.1843 0.8842 0.972 0.028
#> GSM35529 2 0.0000 0.9012 0.000 1.000
#> GSM35531 2 0.0938 0.8958 0.012 0.988
#> GSM35534 2 0.0000 0.9012 0.000 1.000
#> GSM35536 1 0.0000 0.8976 1.000 0.000
#> GSM35538 1 0.0000 0.8976 1.000 0.000
#> GSM35539 1 0.0672 0.8955 0.992 0.008
#> GSM35540 2 0.0000 0.9012 0.000 1.000
#> GSM35541 2 0.0000 0.9012 0.000 1.000
#> GSM35442 1 0.0000 0.8976 1.000 0.000
#> GSM35447 1 0.9635 0.2973 0.612 0.388
#> GSM35450 1 0.0376 0.8971 0.996 0.004
#> GSM35453 1 0.0000 0.8976 1.000 0.000
#> GSM35456 1 0.8327 0.6170 0.736 0.264
#> GSM35464 2 0.1184 0.8925 0.016 0.984
#> GSM35467 1 0.0000 0.8976 1.000 0.000
#> GSM35470 1 0.0376 0.8971 0.996 0.004
#> GSM35479 1 0.0376 0.8971 0.996 0.004
#> GSM35484 1 0.0938 0.8921 0.988 0.012
#> GSM35488 1 0.0000 0.8976 1.000 0.000
#> GSM35491 1 0.0000 0.8976 1.000 0.000
#> GSM35494 1 0.1633 0.8861 0.976 0.024
#> GSM35498 1 0.9933 0.1714 0.548 0.452
#> GSM35501 1 0.0000 0.8976 1.000 0.000
#> GSM35509 1 0.8555 0.5888 0.720 0.280
#> GSM35513 1 0.0000 0.8976 1.000 0.000
#> GSM35516 2 0.0000 0.9012 0.000 1.000
#> GSM35522 2 0.9795 0.1976 0.416 0.584
#> GSM35525 1 0.0000 0.8976 1.000 0.000
#> GSM35528 1 0.0376 0.8971 0.996 0.004
#> GSM35533 1 0.0376 0.8971 0.996 0.004
#> GSM35537 1 0.0376 0.8971 0.996 0.004
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM35441 2 0.0000 0.964 0.000 1.000 0.000
#> GSM35446 3 0.8310 0.622 0.184 0.184 0.632
#> GSM35449 2 0.0000 0.964 0.000 1.000 0.000
#> GSM35455 2 0.0000 0.964 0.000 1.000 0.000
#> GSM35458 3 0.9757 -0.125 0.324 0.244 0.432
#> GSM35460 3 0.8042 0.612 0.248 0.116 0.636
#> GSM35461 3 0.0747 0.549 0.016 0.000 0.984
#> GSM35463 2 0.0000 0.964 0.000 1.000 0.000
#> GSM35472 3 0.6044 0.661 0.056 0.172 0.772
#> GSM35475 3 0.5318 0.636 0.016 0.204 0.780
#> GSM35483 2 0.0000 0.964 0.000 1.000 0.000
#> GSM35496 3 0.0424 0.560 0.008 0.000 0.992
#> GSM35497 2 0.0000 0.964 0.000 1.000 0.000
#> GSM35504 2 0.1411 0.932 0.036 0.964 0.000
#> GSM35508 2 0.0000 0.964 0.000 1.000 0.000
#> GSM35511 3 0.6079 0.423 0.000 0.388 0.612
#> GSM35512 3 0.1643 0.598 0.000 0.044 0.956
#> GSM35515 3 0.9598 -0.105 0.304 0.228 0.468
#> GSM35519 3 0.4861 0.644 0.008 0.192 0.800
#> GSM35527 2 0.0000 0.964 0.000 1.000 0.000
#> GSM35532 3 0.6470 0.473 0.012 0.356 0.632
#> GSM35439 2 0.0000 0.964 0.000 1.000 0.000
#> GSM35443 1 0.6026 0.685 0.624 0.000 0.376
#> GSM35445 1 0.4887 0.690 0.772 0.000 0.228
#> GSM35448 3 0.8303 0.618 0.172 0.196 0.632
#> GSM35451 1 0.0237 0.690 0.996 0.000 0.004
#> GSM35454 1 0.4121 0.515 0.832 0.000 0.168
#> GSM35457 2 0.0000 0.964 0.000 1.000 0.000
#> GSM35465 2 0.0661 0.955 0.008 0.988 0.004
#> GSM35468 1 0.5968 0.693 0.636 0.000 0.364
#> GSM35471 1 0.0892 0.681 0.980 0.000 0.020
#> GSM35473 1 0.6079 0.679 0.612 0.000 0.388
#> GSM35477 1 0.0237 0.690 0.996 0.000 0.004
#> GSM35480 1 0.0747 0.683 0.984 0.000 0.016
#> GSM35482 1 0.1860 0.666 0.948 0.000 0.052
#> GSM35485 2 0.0000 0.964 0.000 1.000 0.000
#> GSM35489 2 0.0000 0.964 0.000 1.000 0.000
#> GSM35492 1 0.5968 0.693 0.636 0.000 0.364
#> GSM35495 3 0.6318 0.518 0.356 0.008 0.636
#> GSM35499 2 0.4465 0.750 0.176 0.820 0.004
#> GSM35502 1 0.5948 0.695 0.640 0.000 0.360
#> GSM35505 3 0.6848 0.330 0.416 0.016 0.568
#> GSM35507 1 0.1878 0.655 0.952 0.044 0.004
#> GSM35510 2 0.3482 0.819 0.128 0.872 0.000
#> GSM35514 1 0.5968 0.693 0.636 0.000 0.364
#> GSM35517 2 0.0000 0.964 0.000 1.000 0.000
#> GSM35520 3 0.8097 0.443 0.072 0.388 0.540
#> GSM35523 1 0.0237 0.690 0.996 0.000 0.004
#> GSM35529 2 0.0000 0.964 0.000 1.000 0.000
#> GSM35531 2 0.2486 0.897 0.008 0.932 0.060
#> GSM35534 2 0.0000 0.964 0.000 1.000 0.000
#> GSM35536 1 0.5948 0.695 0.640 0.000 0.360
#> GSM35538 1 0.5926 0.696 0.644 0.000 0.356
#> GSM35539 1 0.0237 0.690 0.996 0.000 0.004
#> GSM35540 2 0.0983 0.949 0.016 0.980 0.004
#> GSM35541 2 0.0000 0.964 0.000 1.000 0.000
#> GSM35442 1 0.6168 0.648 0.588 0.000 0.412
#> GSM35447 3 0.6019 0.128 0.288 0.012 0.700
#> GSM35450 1 0.0000 0.690 1.000 0.000 0.000
#> GSM35453 1 0.6140 0.672 0.596 0.000 0.404
#> GSM35456 1 0.1015 0.682 0.980 0.008 0.012
#> GSM35464 2 0.4110 0.785 0.152 0.844 0.004
#> GSM35467 1 0.5968 0.693 0.636 0.000 0.364
#> GSM35470 1 0.0237 0.690 0.996 0.000 0.004
#> GSM35479 1 0.5650 0.165 0.688 0.000 0.312
#> GSM35484 1 0.6079 0.679 0.612 0.000 0.388
#> GSM35488 1 0.5968 0.693 0.636 0.000 0.364
#> GSM35491 1 0.5968 0.693 0.636 0.000 0.364
#> GSM35494 1 0.1643 0.668 0.956 0.000 0.044
#> GSM35498 1 0.3425 0.566 0.884 0.112 0.004
#> GSM35501 1 0.5926 0.696 0.644 0.000 0.356
#> GSM35509 3 0.6204 0.442 0.424 0.000 0.576
#> GSM35513 1 0.5968 0.693 0.636 0.000 0.364
#> GSM35516 2 0.0237 0.961 0.004 0.996 0.000
#> GSM35522 1 0.5690 0.258 0.708 0.288 0.004
#> GSM35525 1 0.5098 0.703 0.752 0.000 0.248
#> GSM35528 1 0.5882 0.697 0.652 0.000 0.348
#> GSM35533 1 0.0592 0.685 0.988 0.000 0.012
#> GSM35537 1 0.0237 0.690 0.996 0.000 0.004
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM35441 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM35446 3 0.0000 0.927 0.000 0.000 1.000 0.000
#> GSM35449 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM35455 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM35458 1 0.0657 0.925 0.984 0.004 0.012 0.000
#> GSM35460 3 0.0000 0.927 0.000 0.000 1.000 0.000
#> GSM35461 3 0.4790 0.409 0.380 0.000 0.620 0.000
#> GSM35463 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM35472 3 0.0000 0.927 0.000 0.000 1.000 0.000
#> GSM35475 3 0.1256 0.915 0.028 0.008 0.964 0.000
#> GSM35483 2 0.0336 0.977 0.000 0.992 0.008 0.000
#> GSM35496 3 0.1022 0.917 0.032 0.000 0.968 0.000
#> GSM35497 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM35504 2 0.0188 0.979 0.000 0.996 0.004 0.000
#> GSM35508 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM35511 3 0.0592 0.922 0.000 0.016 0.984 0.000
#> GSM35512 3 0.0000 0.927 0.000 0.000 1.000 0.000
#> GSM35515 1 0.0469 0.928 0.988 0.000 0.012 0.000
#> GSM35519 3 0.0336 0.926 0.000 0.008 0.992 0.000
#> GSM35527 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM35532 3 0.0336 0.926 0.000 0.008 0.992 0.000
#> GSM35439 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM35443 1 0.0000 0.936 1.000 0.000 0.000 0.000
#> GSM35445 4 0.5933 0.312 0.408 0.000 0.040 0.552
#> GSM35448 3 0.0000 0.927 0.000 0.000 1.000 0.000
#> GSM35451 4 0.0000 0.884 0.000 0.000 0.000 1.000
#> GSM35454 1 0.7013 0.214 0.516 0.000 0.128 0.356
#> GSM35457 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM35465 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM35468 1 0.0000 0.936 1.000 0.000 0.000 0.000
#> GSM35471 4 0.0000 0.884 0.000 0.000 0.000 1.000
#> GSM35473 1 0.0000 0.936 1.000 0.000 0.000 0.000
#> GSM35477 4 0.0469 0.879 0.012 0.000 0.000 0.988
#> GSM35480 4 0.0000 0.884 0.000 0.000 0.000 1.000
#> GSM35482 4 0.2830 0.832 0.040 0.000 0.060 0.900
#> GSM35485 2 0.0336 0.977 0.000 0.992 0.008 0.000
#> GSM35489 2 0.0188 0.980 0.000 0.996 0.004 0.000
#> GSM35492 1 0.0000 0.936 1.000 0.000 0.000 0.000
#> GSM35495 3 0.1637 0.893 0.000 0.000 0.940 0.060
#> GSM35499 2 0.2216 0.897 0.000 0.908 0.000 0.092
#> GSM35502 1 0.4730 0.305 0.636 0.000 0.000 0.364
#> GSM35505 3 0.1211 0.911 0.040 0.000 0.960 0.000
#> GSM35507 4 0.0000 0.884 0.000 0.000 0.000 1.000
#> GSM35510 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM35514 1 0.0000 0.936 1.000 0.000 0.000 0.000
#> GSM35517 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM35520 3 0.1520 0.916 0.024 0.020 0.956 0.000
#> GSM35523 4 0.0000 0.884 0.000 0.000 0.000 1.000
#> GSM35529 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM35531 2 0.4365 0.744 0.000 0.784 0.188 0.028
#> GSM35534 2 0.0336 0.977 0.000 0.992 0.008 0.000
#> GSM35536 1 0.0000 0.936 1.000 0.000 0.000 0.000
#> GSM35538 4 0.4382 0.597 0.296 0.000 0.000 0.704
#> GSM35539 4 0.0000 0.884 0.000 0.000 0.000 1.000
#> GSM35540 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM35541 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM35442 1 0.0000 0.936 1.000 0.000 0.000 0.000
#> GSM35447 3 0.2888 0.836 0.124 0.000 0.872 0.004
#> GSM35450 4 0.0000 0.884 0.000 0.000 0.000 1.000
#> GSM35453 1 0.2036 0.887 0.936 0.000 0.032 0.032
#> GSM35456 4 0.0188 0.883 0.004 0.000 0.000 0.996
#> GSM35464 2 0.0188 0.979 0.000 0.996 0.000 0.004
#> GSM35467 1 0.0000 0.936 1.000 0.000 0.000 0.000
#> GSM35470 4 0.0000 0.884 0.000 0.000 0.000 1.000
#> GSM35479 4 0.1022 0.868 0.000 0.000 0.032 0.968
#> GSM35484 1 0.0000 0.936 1.000 0.000 0.000 0.000
#> GSM35488 1 0.0000 0.936 1.000 0.000 0.000 0.000
#> GSM35491 1 0.0000 0.936 1.000 0.000 0.000 0.000
#> GSM35494 4 0.1209 0.868 0.004 0.000 0.032 0.964
#> GSM35498 4 0.4972 0.127 0.456 0.000 0.000 0.544
#> GSM35501 4 0.4776 0.451 0.376 0.000 0.000 0.624
#> GSM35509 3 0.4406 0.576 0.000 0.000 0.700 0.300
#> GSM35513 1 0.0000 0.936 1.000 0.000 0.000 0.000
#> GSM35516 2 0.1867 0.918 0.000 0.928 0.000 0.072
#> GSM35522 4 0.0000 0.884 0.000 0.000 0.000 1.000
#> GSM35525 4 0.3610 0.725 0.200 0.000 0.000 0.800
#> GSM35528 4 0.4134 0.648 0.260 0.000 0.000 0.740
#> GSM35533 4 0.0000 0.884 0.000 0.000 0.000 1.000
#> GSM35537 4 0.0000 0.884 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
#> GSM35441 2 0.0000 0.9586 0.000 1.000 0.000 0.000 0.000
#> GSM35446 5 0.2690 0.7220 0.000 0.000 0.156 0.000 0.844
#> GSM35449 2 0.0290 0.9577 0.000 0.992 0.008 0.000 0.000
#> GSM35455 2 0.0000 0.9586 0.000 1.000 0.000 0.000 0.000
#> GSM35458 1 0.1117 0.9156 0.964 0.000 0.016 0.000 0.020
#> GSM35460 3 0.4088 0.4191 0.000 0.000 0.632 0.000 0.368
#> GSM35461 1 0.4088 0.3779 0.632 0.000 0.000 0.000 0.368
#> GSM35463 2 0.2377 0.9029 0.000 0.872 0.128 0.000 0.000
#> GSM35472 5 0.0609 0.8641 0.000 0.000 0.020 0.000 0.980
#> GSM35475 5 0.0609 0.8624 0.000 0.000 0.020 0.000 0.980
#> GSM35483 2 0.3098 0.8766 0.000 0.836 0.148 0.000 0.016
#> GSM35496 5 0.6390 -0.0563 0.168 0.000 0.396 0.000 0.436
#> GSM35497 2 0.0000 0.9586 0.000 1.000 0.000 0.000 0.000
#> GSM35504 2 0.1851 0.9239 0.000 0.912 0.088 0.000 0.000
#> GSM35508 2 0.0000 0.9586 0.000 1.000 0.000 0.000 0.000
#> GSM35511 5 0.0000 0.8702 0.000 0.000 0.000 0.000 1.000
#> GSM35512 5 0.0404 0.8671 0.000 0.000 0.012 0.000 0.988
#> GSM35515 1 0.1549 0.9003 0.944 0.000 0.016 0.000 0.040
#> GSM35519 5 0.0000 0.8702 0.000 0.000 0.000 0.000 1.000
#> GSM35527 2 0.0000 0.9586 0.000 1.000 0.000 0.000 0.000
#> GSM35532 5 0.0000 0.8702 0.000 0.000 0.000 0.000 1.000
#> GSM35439 2 0.2230 0.9104 0.000 0.884 0.116 0.000 0.000
#> GSM35443 1 0.0000 0.9354 1.000 0.000 0.000 0.000 0.000
#> GSM35445 3 0.4444 0.7144 0.088 0.000 0.756 0.156 0.000
#> GSM35448 3 0.2230 0.6783 0.000 0.000 0.884 0.000 0.116
#> GSM35451 4 0.0000 0.8974 0.000 0.000 0.000 1.000 0.000
#> GSM35454 3 0.3474 0.7447 0.020 0.000 0.824 0.148 0.008
#> GSM35457 2 0.0000 0.9586 0.000 1.000 0.000 0.000 0.000
#> GSM35465 2 0.0324 0.9561 0.000 0.992 0.004 0.004 0.000
#> GSM35468 1 0.0000 0.9354 1.000 0.000 0.000 0.000 0.000
#> GSM35471 4 0.0162 0.8975 0.000 0.000 0.004 0.996 0.000
#> GSM35473 1 0.0162 0.9352 0.996 0.000 0.004 0.000 0.000
#> GSM35477 4 0.0000 0.8974 0.000 0.000 0.000 1.000 0.000
#> GSM35480 4 0.1043 0.8903 0.000 0.000 0.040 0.960 0.000
#> GSM35482 3 0.3728 0.6700 0.008 0.000 0.748 0.244 0.000
#> GSM35485 2 0.2873 0.8920 0.000 0.856 0.128 0.000 0.016
#> GSM35489 2 0.0865 0.9514 0.000 0.972 0.024 0.000 0.004
#> GSM35492 1 0.0000 0.9354 1.000 0.000 0.000 0.000 0.000
#> GSM35495 3 0.3282 0.6829 0.000 0.000 0.804 0.008 0.188
#> GSM35499 2 0.1774 0.9170 0.000 0.932 0.016 0.052 0.000
#> GSM35502 1 0.4238 0.3231 0.628 0.000 0.004 0.368 0.000
#> GSM35505 3 0.3727 0.6669 0.016 0.000 0.768 0.000 0.216
#> GSM35507 4 0.0510 0.8961 0.000 0.000 0.016 0.984 0.000
#> GSM35510 2 0.0000 0.9586 0.000 1.000 0.000 0.000 0.000
#> GSM35514 1 0.0162 0.9352 0.996 0.000 0.004 0.000 0.000
#> GSM35517 2 0.0000 0.9586 0.000 1.000 0.000 0.000 0.000
#> GSM35520 5 0.2787 0.7555 0.004 0.004 0.136 0.000 0.856
#> GSM35523 4 0.1197 0.8878 0.000 0.000 0.048 0.952 0.000
#> GSM35529 2 0.0000 0.9586 0.000 1.000 0.000 0.000 0.000
#> GSM35531 3 0.6084 0.2673 0.000 0.336 0.568 0.048 0.048
#> GSM35534 2 0.2873 0.8920 0.000 0.856 0.128 0.000 0.016
#> GSM35536 1 0.0162 0.9352 0.996 0.000 0.004 0.000 0.000
#> GSM35538 4 0.2536 0.8046 0.128 0.000 0.004 0.868 0.000
#> GSM35539 4 0.0000 0.8974 0.000 0.000 0.000 1.000 0.000
#> GSM35540 2 0.0324 0.9561 0.000 0.992 0.004 0.004 0.000
#> GSM35541 2 0.0000 0.9586 0.000 1.000 0.000 0.000 0.000
#> GSM35442 1 0.0000 0.9354 1.000 0.000 0.000 0.000 0.000
#> GSM35447 3 0.4042 0.6694 0.032 0.000 0.756 0.000 0.212
#> GSM35450 4 0.0162 0.8963 0.000 0.000 0.004 0.996 0.000
#> GSM35453 3 0.3612 0.5837 0.268 0.000 0.732 0.000 0.000
#> GSM35456 4 0.0510 0.8961 0.000 0.000 0.016 0.984 0.000
#> GSM35464 2 0.0693 0.9500 0.000 0.980 0.012 0.008 0.000
#> GSM35467 1 0.0162 0.9352 0.996 0.000 0.004 0.000 0.000
#> GSM35470 4 0.1197 0.8878 0.000 0.000 0.048 0.952 0.000
#> GSM35479 3 0.3366 0.6860 0.000 0.000 0.768 0.232 0.000
#> GSM35484 1 0.0324 0.9332 0.992 0.000 0.004 0.004 0.000
#> GSM35488 1 0.0000 0.9354 1.000 0.000 0.000 0.000 0.000
#> GSM35491 1 0.0000 0.9354 1.000 0.000 0.000 0.000 0.000
#> GSM35494 3 0.2605 0.7365 0.000 0.000 0.852 0.148 0.000
#> GSM35498 4 0.4747 0.0272 0.484 0.000 0.016 0.500 0.000
#> GSM35501 4 0.3884 0.5946 0.288 0.000 0.004 0.708 0.000
#> GSM35509 3 0.2969 0.7407 0.000 0.000 0.852 0.128 0.020
#> GSM35513 1 0.0162 0.9352 0.996 0.000 0.004 0.000 0.000
#> GSM35516 2 0.1872 0.9272 0.000 0.928 0.020 0.052 0.000
#> GSM35522 4 0.1197 0.8878 0.000 0.000 0.048 0.952 0.000
#> GSM35525 4 0.2179 0.8317 0.100 0.000 0.004 0.896 0.000
#> GSM35528 4 0.2389 0.8213 0.116 0.000 0.004 0.880 0.000
#> GSM35533 4 0.0000 0.8974 0.000 0.000 0.000 1.000 0.000
#> GSM35537 4 0.1197 0.8878 0.000 0.000 0.048 0.952 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM35441 6 0.3867 0.934 0.000 0.488 0.000 0.000 0.000 0.512
#> GSM35446 5 0.2664 0.674 0.000 0.000 0.184 0.000 0.816 0.000
#> GSM35449 2 0.3804 -0.705 0.000 0.576 0.000 0.000 0.000 0.424
#> GSM35455 6 0.3867 0.934 0.000 0.488 0.000 0.000 0.000 0.512
#> GSM35458 1 0.4617 0.686 0.720 0.020 0.016 0.000 0.036 0.208
#> GSM35460 3 0.3828 0.125 0.000 0.000 0.560 0.000 0.440 0.000
#> GSM35461 1 0.3797 0.241 0.580 0.000 0.000 0.000 0.420 0.000
#> GSM35463 2 0.0000 0.529 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM35472 5 0.0713 0.814 0.000 0.000 0.028 0.000 0.972 0.000
#> GSM35475 5 0.3794 0.722 0.000 0.128 0.016 0.000 0.796 0.060
#> GSM35483 2 0.0622 0.526 0.000 0.980 0.012 0.000 0.008 0.000
#> GSM35496 5 0.6447 0.427 0.096 0.000 0.176 0.000 0.560 0.168
#> GSM35497 6 0.3867 0.934 0.000 0.488 0.000 0.000 0.000 0.512
#> GSM35504 2 0.3672 -0.529 0.000 0.632 0.000 0.000 0.000 0.368
#> GSM35508 6 0.3869 0.917 0.000 0.500 0.000 0.000 0.000 0.500
#> GSM35511 5 0.0000 0.820 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM35512 5 0.0458 0.818 0.000 0.000 0.016 0.000 0.984 0.000
#> GSM35515 1 0.4295 0.693 0.728 0.000 0.016 0.000 0.048 0.208
#> GSM35519 5 0.0260 0.820 0.000 0.008 0.000 0.000 0.992 0.000
#> GSM35527 2 0.3869 -0.930 0.000 0.500 0.000 0.000 0.000 0.500
#> GSM35532 5 0.0000 0.820 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM35439 2 0.1075 0.514 0.000 0.952 0.000 0.000 0.000 0.048
#> GSM35443 1 0.0000 0.865 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35445 3 0.2052 0.816 0.028 0.000 0.912 0.056 0.000 0.004
#> GSM35448 3 0.3422 0.720 0.000 0.168 0.792 0.000 0.040 0.000
#> GSM35451 4 0.0000 0.889 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM35454 3 0.1458 0.826 0.016 0.016 0.948 0.020 0.000 0.000
#> GSM35457 6 0.3867 0.934 0.000 0.488 0.000 0.000 0.000 0.512
#> GSM35465 6 0.3860 0.917 0.000 0.472 0.000 0.000 0.000 0.528
#> GSM35468 1 0.0000 0.865 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35471 4 0.1245 0.888 0.000 0.000 0.016 0.952 0.000 0.032
#> GSM35473 1 0.0603 0.865 0.980 0.000 0.004 0.000 0.000 0.016
#> GSM35477 4 0.0000 0.889 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM35480 4 0.3351 0.832 0.004 0.000 0.028 0.800 0.000 0.168
#> GSM35482 3 0.5286 0.537 0.008 0.000 0.608 0.120 0.000 0.264
#> GSM35485 2 0.0260 0.531 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM35489 2 0.2632 0.332 0.000 0.832 0.000 0.000 0.004 0.164
#> GSM35492 1 0.0000 0.865 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35495 3 0.1226 0.817 0.000 0.000 0.952 0.004 0.040 0.004
#> GSM35499 6 0.4356 0.727 0.000 0.432 0.016 0.004 0.000 0.548
#> GSM35502 1 0.4370 0.181 0.536 0.000 0.004 0.444 0.000 0.016
#> GSM35505 3 0.2089 0.816 0.020 0.020 0.916 0.000 0.044 0.000
#> GSM35507 4 0.2094 0.878 0.000 0.000 0.020 0.900 0.000 0.080
#> GSM35510 6 0.3867 0.934 0.000 0.488 0.000 0.000 0.000 0.512
#> GSM35514 1 0.0603 0.865 0.980 0.000 0.004 0.000 0.000 0.016
#> GSM35517 2 0.3869 -0.930 0.000 0.500 0.000 0.000 0.000 0.500
#> GSM35520 5 0.4855 0.383 0.000 0.460 0.000 0.000 0.484 0.056
#> GSM35523 4 0.3789 0.800 0.000 0.000 0.024 0.716 0.000 0.260
#> GSM35529 6 0.3867 0.934 0.000 0.488 0.000 0.000 0.000 0.512
#> GSM35531 2 0.5614 0.161 0.000 0.632 0.164 0.168 0.036 0.000
#> GSM35534 2 0.0260 0.531 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM35536 1 0.0748 0.864 0.976 0.000 0.004 0.004 0.000 0.016
#> GSM35538 4 0.0748 0.880 0.016 0.000 0.004 0.976 0.000 0.004
#> GSM35539 4 0.0000 0.889 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM35540 6 0.3854 0.903 0.000 0.464 0.000 0.000 0.000 0.536
#> GSM35541 6 0.3869 0.917 0.000 0.500 0.000 0.000 0.000 0.500
#> GSM35442 1 0.0000 0.865 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35447 3 0.2125 0.811 0.016 0.004 0.908 0.000 0.068 0.004
#> GSM35450 4 0.0291 0.887 0.000 0.000 0.004 0.992 0.000 0.004
#> GSM35453 3 0.2312 0.773 0.112 0.000 0.876 0.000 0.000 0.012
#> GSM35456 4 0.2094 0.878 0.000 0.000 0.020 0.900 0.000 0.080
#> GSM35464 6 0.3923 0.794 0.000 0.416 0.004 0.000 0.000 0.580
#> GSM35467 1 0.0603 0.865 0.980 0.000 0.004 0.000 0.000 0.016
#> GSM35470 4 0.3789 0.800 0.000 0.000 0.024 0.716 0.000 0.260
#> GSM35479 3 0.4474 0.635 0.000 0.000 0.704 0.108 0.000 0.188
#> GSM35484 1 0.1218 0.853 0.956 0.000 0.004 0.028 0.000 0.012
#> GSM35488 1 0.0291 0.865 0.992 0.000 0.000 0.004 0.000 0.004
#> GSM35491 1 0.0000 0.865 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35494 3 0.0993 0.822 0.000 0.000 0.964 0.024 0.000 0.012
#> GSM35498 1 0.5488 0.256 0.548 0.000 0.020 0.348 0.000 0.084
#> GSM35501 4 0.2765 0.764 0.132 0.000 0.004 0.848 0.000 0.016
#> GSM35509 3 0.0692 0.824 0.000 0.000 0.976 0.020 0.000 0.004
#> GSM35513 1 0.0603 0.865 0.980 0.000 0.004 0.000 0.000 0.016
#> GSM35516 2 0.3803 0.384 0.000 0.780 0.004 0.068 0.000 0.148
#> GSM35522 4 0.3789 0.800 0.000 0.000 0.024 0.716 0.000 0.260
#> GSM35525 4 0.1148 0.884 0.016 0.000 0.004 0.960 0.000 0.020
#> GSM35528 4 0.2176 0.863 0.080 0.000 0.000 0.896 0.000 0.024
#> GSM35533 4 0.0146 0.890 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM35537 4 0.3789 0.800 0.000 0.000 0.024 0.716 0.000 0.260
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 time(p) k
#> MAD:pam 71 7.38e-06 2
#> MAD:pam 69 2.65e-07 3
#> MAD:pam 73 3.63e-04 4
#> MAD:pam 73 2.54e-05 5
#> MAD:pam 66 1.70e-05 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 7758 rows and 79 columns.
#> Top rows (776, 1552, 2328, 3103, 3879) 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 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 0.531 0.930 0.930 0.4653 0.498 0.498
#> 3 3 0.537 0.722 0.870 0.2812 0.620 0.395
#> 4 4 0.815 0.881 0.933 0.2440 0.783 0.487
#> 5 5 0.884 0.828 0.916 0.0646 0.897 0.636
#> 6 6 0.805 0.701 0.839 0.0353 0.920 0.653
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
#> GSM35441 2 0.0000 0.966 0.000 1.000
#> GSM35446 2 0.2778 0.958 0.048 0.952
#> GSM35449 2 0.0000 0.966 0.000 1.000
#> GSM35455 2 0.0000 0.966 0.000 1.000
#> GSM35458 2 0.2778 0.958 0.048 0.952
#> GSM35460 2 0.2778 0.958 0.048 0.952
#> GSM35461 1 0.6148 0.933 0.848 0.152
#> GSM35463 2 0.0000 0.966 0.000 1.000
#> GSM35472 2 0.2948 0.955 0.052 0.948
#> GSM35475 2 0.2778 0.958 0.048 0.952
#> GSM35483 2 0.0000 0.966 0.000 1.000
#> GSM35496 1 0.6148 0.933 0.848 0.152
#> GSM35497 2 0.0000 0.966 0.000 1.000
#> GSM35504 2 0.2778 0.958 0.048 0.952
#> GSM35508 2 0.0000 0.966 0.000 1.000
#> GSM35511 2 0.2778 0.958 0.048 0.952
#> GSM35512 2 0.2948 0.955 0.052 0.948
#> GSM35515 2 0.2778 0.958 0.048 0.952
#> GSM35519 2 0.2778 0.958 0.048 0.952
#> GSM35527 2 0.0000 0.966 0.000 1.000
#> GSM35532 2 0.2778 0.958 0.048 0.952
#> GSM35439 2 0.0000 0.966 0.000 1.000
#> GSM35443 1 0.1843 0.890 0.972 0.028
#> GSM35445 1 0.5629 0.931 0.868 0.132
#> GSM35448 2 0.2778 0.958 0.048 0.952
#> GSM35451 1 0.6048 0.934 0.852 0.148
#> GSM35454 1 0.6148 0.933 0.848 0.152
#> GSM35457 2 0.0000 0.966 0.000 1.000
#> GSM35465 2 0.0000 0.966 0.000 1.000
#> GSM35468 1 0.0000 0.878 1.000 0.000
#> GSM35471 1 0.6148 0.933 0.848 0.152
#> GSM35473 1 0.0000 0.878 1.000 0.000
#> GSM35477 1 0.5946 0.935 0.856 0.144
#> GSM35480 1 0.5946 0.935 0.856 0.144
#> GSM35482 1 0.6148 0.933 0.848 0.152
#> GSM35485 2 0.0000 0.966 0.000 1.000
#> GSM35489 2 0.0000 0.966 0.000 1.000
#> GSM35492 1 0.0000 0.878 1.000 0.000
#> GSM35495 1 0.6148 0.933 0.848 0.152
#> GSM35499 2 0.1414 0.964 0.020 0.980
#> GSM35502 1 0.0000 0.878 1.000 0.000
#> GSM35505 1 0.6887 0.901 0.816 0.184
#> GSM35507 1 0.6148 0.933 0.848 0.152
#> GSM35510 2 0.0376 0.966 0.004 0.996
#> GSM35514 1 0.0000 0.878 1.000 0.000
#> GSM35517 2 0.0000 0.966 0.000 1.000
#> GSM35520 2 0.2778 0.958 0.048 0.952
#> GSM35523 1 0.6148 0.933 0.848 0.152
#> GSM35529 2 0.0000 0.966 0.000 1.000
#> GSM35531 2 0.2778 0.958 0.048 0.952
#> GSM35534 2 0.0000 0.966 0.000 1.000
#> GSM35536 1 0.0000 0.878 1.000 0.000
#> GSM35538 1 0.5946 0.935 0.856 0.144
#> GSM35539 1 0.5946 0.935 0.856 0.144
#> GSM35540 2 0.2423 0.960 0.040 0.960
#> GSM35541 2 0.0000 0.966 0.000 1.000
#> GSM35442 1 0.6048 0.934 0.852 0.148
#> GSM35447 2 0.8608 0.564 0.284 0.716
#> GSM35450 1 0.5946 0.935 0.856 0.144
#> GSM35453 1 0.5946 0.935 0.856 0.144
#> GSM35456 1 0.6148 0.933 0.848 0.152
#> GSM35464 1 0.8443 0.781 0.728 0.272
#> GSM35467 1 0.0000 0.878 1.000 0.000
#> GSM35470 1 0.6048 0.934 0.852 0.148
#> GSM35479 1 0.6148 0.933 0.848 0.152
#> GSM35484 1 0.0672 0.882 0.992 0.008
#> GSM35488 1 0.0000 0.878 1.000 0.000
#> GSM35491 1 0.0000 0.878 1.000 0.000
#> GSM35494 1 0.6148 0.933 0.848 0.152
#> GSM35498 1 0.6148 0.933 0.848 0.152
#> GSM35501 1 0.0000 0.878 1.000 0.000
#> GSM35509 1 0.6148 0.933 0.848 0.152
#> GSM35513 1 0.0000 0.878 1.000 0.000
#> GSM35516 2 0.0000 0.966 0.000 1.000
#> GSM35522 1 0.6148 0.933 0.848 0.152
#> GSM35525 1 0.5946 0.935 0.856 0.144
#> GSM35528 1 0.5946 0.935 0.856 0.144
#> GSM35533 1 0.2603 0.898 0.956 0.044
#> GSM35537 1 0.5946 0.935 0.856 0.144
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM35441 2 0.0000 0.9086 0.000 1.000 0.000
#> GSM35446 3 0.0592 0.7972 0.000 0.012 0.988
#> GSM35449 2 0.0000 0.9086 0.000 1.000 0.000
#> GSM35455 2 0.0000 0.9086 0.000 1.000 0.000
#> GSM35458 3 0.5016 0.6968 0.000 0.240 0.760
#> GSM35460 3 0.0592 0.7972 0.000 0.012 0.988
#> GSM35461 3 0.0000 0.7977 0.000 0.000 1.000
#> GSM35463 2 0.0000 0.9086 0.000 1.000 0.000
#> GSM35472 3 0.0592 0.7972 0.000 0.012 0.988
#> GSM35475 3 0.4842 0.7071 0.000 0.224 0.776
#> GSM35483 2 0.1529 0.8930 0.000 0.960 0.040
#> GSM35496 3 0.0000 0.7977 0.000 0.000 1.000
#> GSM35497 2 0.0000 0.9086 0.000 1.000 0.000
#> GSM35504 3 0.5016 0.6968 0.000 0.240 0.760
#> GSM35508 2 0.5733 0.5078 0.000 0.676 0.324
#> GSM35511 3 0.0592 0.7972 0.000 0.012 0.988
#> GSM35512 3 0.0592 0.7972 0.000 0.012 0.988
#> GSM35515 3 0.5016 0.6968 0.000 0.240 0.760
#> GSM35519 3 0.0747 0.7967 0.000 0.016 0.984
#> GSM35527 2 0.4235 0.7780 0.000 0.824 0.176
#> GSM35532 3 0.0592 0.7972 0.000 0.012 0.988
#> GSM35439 2 0.1289 0.8978 0.000 0.968 0.032
#> GSM35443 1 0.5905 0.4214 0.648 0.000 0.352
#> GSM35445 3 0.6192 0.3312 0.420 0.000 0.580
#> GSM35448 3 0.0592 0.7972 0.000 0.012 0.988
#> GSM35451 3 0.5098 0.7108 0.248 0.000 0.752
#> GSM35454 3 0.0000 0.7977 0.000 0.000 1.000
#> GSM35457 2 0.0000 0.9086 0.000 1.000 0.000
#> GSM35465 2 0.3816 0.8071 0.000 0.852 0.148
#> GSM35468 1 0.0000 0.7782 1.000 0.000 0.000
#> GSM35471 3 0.5016 0.7178 0.240 0.000 0.760
#> GSM35473 1 0.2878 0.7375 0.904 0.000 0.096
#> GSM35477 3 0.5216 0.6969 0.260 0.000 0.740
#> GSM35480 3 0.5948 0.4958 0.360 0.000 0.640
#> GSM35482 3 0.0000 0.7977 0.000 0.000 1.000
#> GSM35485 2 0.0000 0.9086 0.000 1.000 0.000
#> GSM35489 2 0.0000 0.9086 0.000 1.000 0.000
#> GSM35492 1 0.0592 0.7761 0.988 0.000 0.012
#> GSM35495 3 0.0000 0.7977 0.000 0.000 1.000
#> GSM35499 2 0.5988 0.3987 0.000 0.632 0.368
#> GSM35502 1 0.0000 0.7782 1.000 0.000 0.000
#> GSM35505 3 0.0237 0.7980 0.000 0.004 0.996
#> GSM35507 3 0.5201 0.7199 0.236 0.004 0.760
#> GSM35510 2 0.4452 0.7488 0.000 0.808 0.192
#> GSM35514 1 0.0000 0.7782 1.000 0.000 0.000
#> GSM35517 2 0.0000 0.9086 0.000 1.000 0.000
#> GSM35520 3 0.5016 0.6968 0.000 0.240 0.760
#> GSM35523 3 0.5098 0.7108 0.248 0.000 0.752
#> GSM35529 2 0.0000 0.9086 0.000 1.000 0.000
#> GSM35531 3 0.5016 0.6968 0.000 0.240 0.760
#> GSM35534 2 0.1753 0.8884 0.000 0.952 0.048
#> GSM35536 1 0.0000 0.7782 1.000 0.000 0.000
#> GSM35538 1 0.6260 0.1540 0.552 0.000 0.448
#> GSM35539 3 0.5760 0.5783 0.328 0.000 0.672
#> GSM35540 3 0.5098 0.6898 0.000 0.248 0.752
#> GSM35541 2 0.0000 0.9086 0.000 1.000 0.000
#> GSM35442 3 0.4974 0.7230 0.236 0.000 0.764
#> GSM35447 3 0.0237 0.7980 0.000 0.004 0.996
#> GSM35450 1 0.6299 0.0617 0.524 0.000 0.476
#> GSM35453 3 0.5138 0.7102 0.252 0.000 0.748
#> GSM35456 3 0.5058 0.7144 0.244 0.000 0.756
#> GSM35464 3 0.6168 0.7183 0.224 0.036 0.740
#> GSM35467 1 0.0000 0.7782 1.000 0.000 0.000
#> GSM35470 3 0.5016 0.7178 0.240 0.000 0.760
#> GSM35479 3 0.0000 0.7977 0.000 0.000 1.000
#> GSM35484 1 0.3551 0.7120 0.868 0.000 0.132
#> GSM35488 1 0.0000 0.7782 1.000 0.000 0.000
#> GSM35491 1 0.0000 0.7782 1.000 0.000 0.000
#> GSM35494 3 0.0000 0.7977 0.000 0.000 1.000
#> GSM35498 3 0.5098 0.7108 0.248 0.000 0.752
#> GSM35501 1 0.0000 0.7782 1.000 0.000 0.000
#> GSM35509 3 0.0000 0.7977 0.000 0.000 1.000
#> GSM35513 1 0.0000 0.7782 1.000 0.000 0.000
#> GSM35516 2 0.0592 0.9047 0.000 0.988 0.012
#> GSM35522 3 0.5098 0.7108 0.248 0.000 0.752
#> GSM35525 1 0.6299 0.0600 0.524 0.000 0.476
#> GSM35528 1 0.6308 -0.0190 0.508 0.000 0.492
#> GSM35533 1 0.6026 0.3660 0.624 0.000 0.376
#> GSM35537 3 0.5098 0.7108 0.248 0.000 0.752
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM35441 2 0.0000 0.941 0.000 1.000 0.000 0.000
#> GSM35446 3 0.0336 0.918 0.008 0.000 0.992 0.000
#> GSM35449 2 0.0000 0.941 0.000 1.000 0.000 0.000
#> GSM35455 2 0.0000 0.941 0.000 1.000 0.000 0.000
#> GSM35458 3 0.0804 0.917 0.008 0.012 0.980 0.000
#> GSM35460 3 0.0336 0.918 0.008 0.000 0.992 0.000
#> GSM35461 3 0.3351 0.884 0.148 0.000 0.844 0.008
#> GSM35463 2 0.0000 0.941 0.000 1.000 0.000 0.000
#> GSM35472 3 0.0188 0.918 0.004 0.000 0.996 0.000
#> GSM35475 3 0.0804 0.917 0.008 0.012 0.980 0.000
#> GSM35483 2 0.0188 0.941 0.000 0.996 0.004 0.000
#> GSM35496 3 0.3324 0.889 0.136 0.000 0.852 0.012
#> GSM35497 2 0.0000 0.941 0.000 1.000 0.000 0.000
#> GSM35504 2 0.4382 0.592 0.000 0.704 0.296 0.000
#> GSM35508 2 0.0188 0.940 0.000 0.996 0.004 0.000
#> GSM35511 3 0.0657 0.917 0.012 0.004 0.984 0.000
#> GSM35512 3 0.0469 0.917 0.012 0.000 0.988 0.000
#> GSM35515 3 0.0804 0.917 0.008 0.012 0.980 0.000
#> GSM35519 3 0.0657 0.917 0.012 0.004 0.984 0.000
#> GSM35527 2 0.0000 0.941 0.000 1.000 0.000 0.000
#> GSM35532 3 0.0657 0.917 0.012 0.004 0.984 0.000
#> GSM35439 2 0.0188 0.941 0.000 0.996 0.004 0.000
#> GSM35443 1 0.2924 0.839 0.884 0.000 0.100 0.016
#> GSM35445 1 0.7566 0.311 0.480 0.000 0.228 0.292
#> GSM35448 3 0.0927 0.916 0.008 0.016 0.976 0.000
#> GSM35451 4 0.0188 0.925 0.004 0.000 0.000 0.996
#> GSM35454 3 0.3674 0.896 0.116 0.000 0.848 0.036
#> GSM35457 2 0.0000 0.941 0.000 1.000 0.000 0.000
#> GSM35465 2 0.0188 0.939 0.000 0.996 0.004 0.000
#> GSM35468 1 0.0707 0.928 0.980 0.000 0.000 0.020
#> GSM35471 4 0.0000 0.924 0.000 0.000 0.000 1.000
#> GSM35473 1 0.1724 0.907 0.948 0.000 0.032 0.020
#> GSM35477 4 0.0592 0.921 0.016 0.000 0.000 0.984
#> GSM35480 4 0.2530 0.832 0.112 0.000 0.000 0.888
#> GSM35482 3 0.3674 0.896 0.116 0.000 0.848 0.036
#> GSM35485 2 0.0188 0.941 0.000 0.996 0.004 0.000
#> GSM35489 2 0.0188 0.941 0.000 0.996 0.004 0.000
#> GSM35492 1 0.0895 0.926 0.976 0.000 0.004 0.020
#> GSM35495 3 0.3674 0.896 0.116 0.000 0.848 0.036
#> GSM35499 2 0.0817 0.926 0.000 0.976 0.024 0.000
#> GSM35502 1 0.0707 0.928 0.980 0.000 0.000 0.020
#> GSM35505 3 0.2675 0.908 0.100 0.000 0.892 0.008
#> GSM35507 4 0.0376 0.923 0.004 0.004 0.000 0.992
#> GSM35510 2 0.0188 0.939 0.000 0.996 0.004 0.000
#> GSM35514 1 0.0707 0.928 0.980 0.000 0.000 0.020
#> GSM35517 2 0.0000 0.941 0.000 1.000 0.000 0.000
#> GSM35520 3 0.0927 0.916 0.008 0.016 0.976 0.000
#> GSM35523 4 0.0000 0.924 0.000 0.000 0.000 1.000
#> GSM35529 2 0.0000 0.941 0.000 1.000 0.000 0.000
#> GSM35531 2 0.4564 0.560 0.000 0.672 0.328 0.000
#> GSM35534 2 0.0188 0.941 0.000 0.996 0.004 0.000
#> GSM35536 1 0.0707 0.928 0.980 0.000 0.000 0.020
#> GSM35538 4 0.2081 0.883 0.084 0.000 0.000 0.916
#> GSM35539 4 0.0000 0.924 0.000 0.000 0.000 1.000
#> GSM35540 2 0.4040 0.676 0.000 0.752 0.248 0.000
#> GSM35541 2 0.0000 0.941 0.000 1.000 0.000 0.000
#> GSM35442 3 0.3479 0.876 0.148 0.000 0.840 0.012
#> GSM35447 3 0.1211 0.919 0.040 0.000 0.960 0.000
#> GSM35450 4 0.1118 0.911 0.036 0.000 0.000 0.964
#> GSM35453 3 0.3711 0.872 0.140 0.000 0.836 0.024
#> GSM35456 4 0.0188 0.925 0.004 0.000 0.000 0.996
#> GSM35464 2 0.4560 0.569 0.004 0.700 0.000 0.296
#> GSM35467 1 0.0707 0.928 0.980 0.000 0.000 0.020
#> GSM35470 4 0.6717 0.279 0.108 0.000 0.332 0.560
#> GSM35479 3 0.3674 0.896 0.116 0.000 0.848 0.036
#> GSM35484 1 0.2048 0.899 0.928 0.000 0.008 0.064
#> GSM35488 1 0.0707 0.928 0.980 0.000 0.000 0.020
#> GSM35491 1 0.0707 0.928 0.980 0.000 0.000 0.020
#> GSM35494 3 0.3674 0.896 0.116 0.000 0.848 0.036
#> GSM35498 4 0.0188 0.925 0.004 0.000 0.000 0.996
#> GSM35501 1 0.0707 0.928 0.980 0.000 0.000 0.020
#> GSM35509 3 0.3674 0.896 0.116 0.000 0.848 0.036
#> GSM35513 1 0.0707 0.928 0.980 0.000 0.000 0.020
#> GSM35516 2 0.0188 0.941 0.000 0.996 0.004 0.000
#> GSM35522 4 0.0000 0.924 0.000 0.000 0.000 1.000
#> GSM35525 4 0.2921 0.819 0.140 0.000 0.000 0.860
#> GSM35528 4 0.1557 0.903 0.056 0.000 0.000 0.944
#> GSM35533 1 0.4882 0.629 0.708 0.000 0.020 0.272
#> GSM35537 4 0.1474 0.894 0.052 0.000 0.000 0.948
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM35441 2 0.0000 0.9590 0.000 1.000 0.000 0.000 0.000
#> GSM35446 5 0.2648 0.7953 0.000 0.000 0.152 0.000 0.848
#> GSM35449 2 0.1608 0.9525 0.000 0.928 0.072 0.000 0.000
#> GSM35455 2 0.0162 0.9589 0.000 0.996 0.004 0.000 0.000
#> GSM35458 5 0.0000 0.8684 0.000 0.000 0.000 0.000 1.000
#> GSM35460 5 0.4302 0.0805 0.000 0.000 0.480 0.000 0.520
#> GSM35461 3 0.6700 0.2688 0.252 0.000 0.416 0.000 0.332
#> GSM35463 2 0.0000 0.9590 0.000 1.000 0.000 0.000 0.000
#> GSM35472 5 0.2605 0.7986 0.000 0.000 0.148 0.000 0.852
#> GSM35475 5 0.0000 0.8684 0.000 0.000 0.000 0.000 1.000
#> GSM35483 2 0.0000 0.9590 0.000 1.000 0.000 0.000 0.000
#> GSM35496 3 0.1792 0.8646 0.000 0.000 0.916 0.000 0.084
#> GSM35497 2 0.0000 0.9590 0.000 1.000 0.000 0.000 0.000
#> GSM35504 2 0.1851 0.9488 0.000 0.912 0.088 0.000 0.000
#> GSM35508 2 0.1892 0.9501 0.000 0.916 0.080 0.000 0.004
#> GSM35511 5 0.0162 0.8702 0.000 0.000 0.004 0.000 0.996
#> GSM35512 5 0.0963 0.8605 0.000 0.000 0.036 0.000 0.964
#> GSM35515 5 0.0000 0.8684 0.000 0.000 0.000 0.000 1.000
#> GSM35519 5 0.0162 0.8702 0.000 0.000 0.004 0.000 0.996
#> GSM35527 2 0.1792 0.9504 0.000 0.916 0.084 0.000 0.000
#> GSM35532 5 0.0162 0.8702 0.000 0.000 0.004 0.000 0.996
#> GSM35439 2 0.0000 0.9590 0.000 1.000 0.000 0.000 0.000
#> GSM35443 1 0.1197 0.8785 0.952 0.000 0.048 0.000 0.000
#> GSM35445 1 0.0955 0.8988 0.968 0.000 0.004 0.028 0.000
#> GSM35448 5 0.2648 0.7953 0.000 0.000 0.152 0.000 0.848
#> GSM35451 4 0.0000 0.8913 0.000 0.000 0.000 1.000 0.000
#> GSM35454 3 0.1792 0.8646 0.000 0.000 0.916 0.000 0.084
#> GSM35457 2 0.1792 0.9504 0.000 0.916 0.084 0.000 0.000
#> GSM35465 2 0.1792 0.9504 0.000 0.916 0.084 0.000 0.000
#> GSM35468 1 0.0000 0.9118 1.000 0.000 0.000 0.000 0.000
#> GSM35471 4 0.0000 0.8913 0.000 0.000 0.000 1.000 0.000
#> GSM35473 1 0.0000 0.9118 1.000 0.000 0.000 0.000 0.000
#> GSM35477 4 0.0000 0.8913 0.000 0.000 0.000 1.000 0.000
#> GSM35480 1 0.3661 0.6094 0.724 0.000 0.000 0.276 0.000
#> GSM35482 3 0.1792 0.8646 0.000 0.000 0.916 0.000 0.084
#> GSM35485 2 0.0000 0.9590 0.000 1.000 0.000 0.000 0.000
#> GSM35489 2 0.0000 0.9590 0.000 1.000 0.000 0.000 0.000
#> GSM35492 1 0.0000 0.9118 1.000 0.000 0.000 0.000 0.000
#> GSM35495 3 0.1792 0.8646 0.000 0.000 0.916 0.000 0.084
#> GSM35499 2 0.1792 0.9504 0.000 0.916 0.084 0.000 0.000
#> GSM35502 1 0.0000 0.9118 1.000 0.000 0.000 0.000 0.000
#> GSM35505 3 0.4283 0.1652 0.000 0.000 0.544 0.000 0.456
#> GSM35507 4 0.0000 0.8913 0.000 0.000 0.000 1.000 0.000
#> GSM35510 2 0.1792 0.9504 0.000 0.916 0.084 0.000 0.000
#> GSM35514 1 0.0000 0.9118 1.000 0.000 0.000 0.000 0.000
#> GSM35517 2 0.0000 0.9590 0.000 1.000 0.000 0.000 0.000
#> GSM35520 5 0.0162 0.8702 0.000 0.000 0.004 0.000 0.996
#> GSM35523 4 0.0000 0.8913 0.000 0.000 0.000 1.000 0.000
#> GSM35529 2 0.1792 0.9504 0.000 0.916 0.084 0.000 0.000
#> GSM35531 2 0.2813 0.7956 0.000 0.832 0.000 0.000 0.168
#> GSM35534 2 0.0162 0.9570 0.000 0.996 0.000 0.000 0.004
#> GSM35536 1 0.0000 0.9118 1.000 0.000 0.000 0.000 0.000
#> GSM35538 1 0.4268 0.1866 0.556 0.000 0.000 0.444 0.000
#> GSM35539 4 0.0290 0.8883 0.008 0.000 0.000 0.992 0.000
#> GSM35540 2 0.1851 0.9488 0.000 0.912 0.088 0.000 0.000
#> GSM35541 2 0.0000 0.9590 0.000 1.000 0.000 0.000 0.000
#> GSM35442 1 0.5654 0.1135 0.536 0.000 0.380 0.000 0.084
#> GSM35447 5 0.3816 0.5311 0.000 0.000 0.304 0.000 0.696
#> GSM35450 4 0.0963 0.8725 0.036 0.000 0.000 0.964 0.000
#> GSM35453 1 0.1952 0.8320 0.912 0.000 0.004 0.000 0.084
#> GSM35456 4 0.0000 0.8913 0.000 0.000 0.000 1.000 0.000
#> GSM35464 4 0.3949 0.4691 0.000 0.332 0.000 0.668 0.000
#> GSM35467 1 0.0000 0.9118 1.000 0.000 0.000 0.000 0.000
#> GSM35470 4 0.6299 0.0327 0.416 0.000 0.152 0.432 0.000
#> GSM35479 3 0.1792 0.8646 0.000 0.000 0.916 0.000 0.084
#> GSM35484 1 0.0162 0.9102 0.996 0.000 0.000 0.004 0.000
#> GSM35488 1 0.0000 0.9118 1.000 0.000 0.000 0.000 0.000
#> GSM35491 1 0.0000 0.9118 1.000 0.000 0.000 0.000 0.000
#> GSM35494 3 0.1792 0.8646 0.000 0.000 0.916 0.000 0.084
#> GSM35498 4 0.0000 0.8913 0.000 0.000 0.000 1.000 0.000
#> GSM35501 1 0.0000 0.9118 1.000 0.000 0.000 0.000 0.000
#> GSM35509 3 0.1792 0.8646 0.000 0.000 0.916 0.000 0.084
#> GSM35513 1 0.0000 0.9118 1.000 0.000 0.000 0.000 0.000
#> GSM35516 2 0.0000 0.9590 0.000 1.000 0.000 0.000 0.000
#> GSM35522 4 0.0000 0.8913 0.000 0.000 0.000 1.000 0.000
#> GSM35525 1 0.2179 0.8259 0.888 0.000 0.000 0.112 0.000
#> GSM35528 4 0.2377 0.7920 0.128 0.000 0.000 0.872 0.000
#> GSM35533 1 0.1121 0.8889 0.956 0.000 0.000 0.044 0.000
#> GSM35537 4 0.2471 0.7838 0.136 0.000 0.000 0.864 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM35441 2 0.3330 0.71769 0.000 0.716 0.000 0.000 0.000 0.284
#> GSM35446 5 0.2542 0.84144 0.000 0.000 0.080 0.000 0.876 0.044
#> GSM35449 2 0.3126 0.73644 0.000 0.752 0.000 0.000 0.000 0.248
#> GSM35455 2 0.3330 0.71769 0.000 0.716 0.000 0.000 0.000 0.284
#> GSM35458 6 0.3634 0.25075 0.000 0.000 0.000 0.000 0.356 0.644
#> GSM35460 5 0.4530 0.38652 0.000 0.000 0.356 0.000 0.600 0.044
#> GSM35461 3 0.5990 0.30931 0.224 0.000 0.500 0.000 0.268 0.008
#> GSM35463 2 0.3390 0.69660 0.000 0.704 0.000 0.000 0.000 0.296
#> GSM35472 5 0.1714 0.84838 0.000 0.000 0.092 0.000 0.908 0.000
#> GSM35475 6 0.3782 0.15425 0.000 0.000 0.000 0.000 0.412 0.588
#> GSM35483 6 0.3706 0.31312 0.000 0.380 0.000 0.000 0.000 0.620
#> GSM35496 3 0.0551 0.78700 0.004 0.000 0.984 0.000 0.004 0.008
#> GSM35497 2 0.3330 0.71769 0.000 0.716 0.000 0.000 0.000 0.284
#> GSM35504 2 0.2266 0.67242 0.000 0.880 0.000 0.000 0.012 0.108
#> GSM35508 2 0.0363 0.76790 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM35511 5 0.1625 0.83159 0.000 0.000 0.012 0.000 0.928 0.060
#> GSM35512 5 0.0790 0.85885 0.000 0.000 0.032 0.000 0.968 0.000
#> GSM35515 6 0.3774 0.16406 0.000 0.000 0.000 0.000 0.408 0.592
#> GSM35519 5 0.2070 0.80802 0.000 0.000 0.012 0.000 0.896 0.092
#> GSM35527 2 0.0146 0.76745 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM35532 5 0.0363 0.85456 0.000 0.000 0.012 0.000 0.988 0.000
#> GSM35439 6 0.3482 0.44622 0.000 0.316 0.000 0.000 0.000 0.684
#> GSM35443 1 0.0405 0.93223 0.988 0.000 0.000 0.000 0.004 0.008
#> GSM35445 1 0.1471 0.89787 0.932 0.000 0.064 0.004 0.000 0.000
#> GSM35448 5 0.2608 0.83975 0.000 0.000 0.080 0.000 0.872 0.048
#> GSM35451 4 0.0000 0.85158 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM35454 3 0.0000 0.79124 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM35457 2 0.2092 0.77188 0.000 0.876 0.000 0.000 0.000 0.124
#> GSM35465 2 0.0865 0.77623 0.000 0.964 0.000 0.000 0.000 0.036
#> GSM35468 1 0.0000 0.93558 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35471 4 0.0000 0.85158 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM35473 1 0.0146 0.93520 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM35477 4 0.0260 0.84853 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM35480 1 0.3493 0.67198 0.756 0.000 0.008 0.228 0.000 0.008
#> GSM35482 3 0.0000 0.79124 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM35485 6 0.3634 0.38248 0.000 0.356 0.000 0.000 0.000 0.644
#> GSM35489 6 0.3592 0.40348 0.000 0.344 0.000 0.000 0.000 0.656
#> GSM35492 1 0.0000 0.93558 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35495 3 0.0632 0.78130 0.000 0.000 0.976 0.000 0.000 0.024
#> GSM35499 2 0.0790 0.75063 0.000 0.968 0.000 0.000 0.000 0.032
#> GSM35502 1 0.0146 0.93520 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM35505 3 0.4100 0.31548 0.004 0.000 0.600 0.000 0.388 0.008
#> GSM35507 4 0.0146 0.84853 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM35510 2 0.1327 0.72802 0.000 0.936 0.000 0.000 0.000 0.064
#> GSM35514 1 0.0000 0.93558 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35517 2 0.3330 0.71355 0.000 0.716 0.000 0.000 0.000 0.284
#> GSM35520 6 0.3907 0.15254 0.000 0.000 0.004 0.000 0.408 0.588
#> GSM35523 4 0.0000 0.85158 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM35529 2 0.1204 0.77798 0.000 0.944 0.000 0.000 0.000 0.056
#> GSM35531 6 0.2608 0.52424 0.000 0.080 0.000 0.000 0.048 0.872
#> GSM35534 6 0.3409 0.45801 0.000 0.300 0.000 0.000 0.000 0.700
#> GSM35536 1 0.0000 0.93558 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35538 1 0.1196 0.90970 0.952 0.000 0.000 0.040 0.000 0.008
#> GSM35539 4 0.3945 0.36407 0.380 0.000 0.000 0.612 0.000 0.008
#> GSM35540 2 0.1802 0.71176 0.000 0.916 0.000 0.000 0.012 0.072
#> GSM35541 2 0.3351 0.70860 0.000 0.712 0.000 0.000 0.000 0.288
#> GSM35442 1 0.2573 0.82697 0.856 0.000 0.132 0.000 0.004 0.008
#> GSM35447 3 0.4269 0.28909 0.004 0.000 0.580 0.004 0.404 0.008
#> GSM35450 4 0.4051 0.22740 0.432 0.000 0.000 0.560 0.000 0.008
#> GSM35453 1 0.2191 0.84713 0.876 0.000 0.120 0.004 0.000 0.000
#> GSM35456 4 0.0000 0.85158 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM35464 4 0.3555 0.58212 0.000 0.176 0.000 0.780 0.000 0.044
#> GSM35467 1 0.0000 0.93558 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35470 3 0.4989 0.42195 0.100 0.000 0.632 0.264 0.000 0.004
#> GSM35479 3 0.0000 0.79124 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM35484 1 0.0146 0.93520 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM35488 1 0.0000 0.93558 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35491 1 0.0000 0.93558 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35494 3 0.0000 0.79124 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM35498 4 0.0000 0.85158 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM35501 1 0.0146 0.93520 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM35509 3 0.0547 0.78359 0.000 0.000 0.980 0.000 0.000 0.020
#> GSM35513 1 0.0000 0.93558 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35516 6 0.3620 0.39380 0.000 0.352 0.000 0.000 0.000 0.648
#> GSM35522 4 0.0000 0.85158 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM35525 1 0.0806 0.92496 0.972 0.000 0.000 0.020 0.000 0.008
#> GSM35528 1 0.4080 -0.00281 0.536 0.000 0.000 0.456 0.000 0.008
#> GSM35533 1 0.0937 0.91616 0.960 0.000 0.000 0.040 0.000 0.000
#> GSM35537 4 0.3419 0.73134 0.116 0.000 0.056 0.820 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 time(p) k
#> MAD:mclust 79 3.41e-07 2
#> MAD:mclust 70 2.12e-02 3
#> MAD:mclust 77 5.62e-04 4
#> MAD:mclust 72 2.19e-05 5
#> MAD:mclust 61 5.94e-05 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 7758 rows and 79 columns.
#> Top rows (776, 1552, 2328, 3103, 3879) are extracted by 'MAD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.973 0.941 0.978 0.5030 0.496 0.496
#> 3 3 0.892 0.913 0.957 0.3169 0.776 0.576
#> 4 4 0.645 0.661 0.825 0.1272 0.819 0.530
#> 5 5 0.611 0.592 0.768 0.0602 0.928 0.731
#> 6 6 0.619 0.481 0.701 0.0461 0.882 0.524
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
#> GSM35441 2 0.0000 0.968 0.000 1.000
#> GSM35446 2 0.0000 0.968 0.000 1.000
#> GSM35449 2 0.0000 0.968 0.000 1.000
#> GSM35455 2 0.0000 0.968 0.000 1.000
#> GSM35458 2 0.1414 0.952 0.020 0.980
#> GSM35460 2 0.0000 0.968 0.000 1.000
#> GSM35461 1 0.0000 0.983 1.000 0.000
#> GSM35463 2 0.0000 0.968 0.000 1.000
#> GSM35472 2 0.6623 0.779 0.172 0.828
#> GSM35475 2 0.0000 0.968 0.000 1.000
#> GSM35483 2 0.0000 0.968 0.000 1.000
#> GSM35496 1 0.0000 0.983 1.000 0.000
#> GSM35497 2 0.0000 0.968 0.000 1.000
#> GSM35504 2 0.0000 0.968 0.000 1.000
#> GSM35508 2 0.0000 0.968 0.000 1.000
#> GSM35511 2 0.0000 0.968 0.000 1.000
#> GSM35512 2 0.9954 0.157 0.460 0.540
#> GSM35515 2 0.1414 0.952 0.020 0.980
#> GSM35519 2 0.0000 0.968 0.000 1.000
#> GSM35527 2 0.0000 0.968 0.000 1.000
#> GSM35532 2 0.0000 0.968 0.000 1.000
#> GSM35439 2 0.0000 0.968 0.000 1.000
#> GSM35443 1 0.0000 0.983 1.000 0.000
#> GSM35445 1 0.0000 0.983 1.000 0.000
#> GSM35448 2 0.0000 0.968 0.000 1.000
#> GSM35451 1 0.0000 0.983 1.000 0.000
#> GSM35454 1 0.0000 0.983 1.000 0.000
#> GSM35457 2 0.0000 0.968 0.000 1.000
#> GSM35465 2 0.0000 0.968 0.000 1.000
#> GSM35468 1 0.0000 0.983 1.000 0.000
#> GSM35471 1 0.0000 0.983 1.000 0.000
#> GSM35473 1 0.0000 0.983 1.000 0.000
#> GSM35477 1 0.0000 0.983 1.000 0.000
#> GSM35480 1 0.0000 0.983 1.000 0.000
#> GSM35482 1 0.0000 0.983 1.000 0.000
#> GSM35485 2 0.0000 0.968 0.000 1.000
#> GSM35489 2 0.0000 0.968 0.000 1.000
#> GSM35492 1 0.0000 0.983 1.000 0.000
#> GSM35495 2 0.9850 0.260 0.428 0.572
#> GSM35499 2 0.0000 0.968 0.000 1.000
#> GSM35502 1 0.0000 0.983 1.000 0.000
#> GSM35505 1 0.0000 0.983 1.000 0.000
#> GSM35507 1 0.9129 0.496 0.672 0.328
#> GSM35510 2 0.0000 0.968 0.000 1.000
#> GSM35514 1 0.0000 0.983 1.000 0.000
#> GSM35517 2 0.0000 0.968 0.000 1.000
#> GSM35520 2 0.0000 0.968 0.000 1.000
#> GSM35523 1 0.0000 0.983 1.000 0.000
#> GSM35529 2 0.0000 0.968 0.000 1.000
#> GSM35531 2 0.0000 0.968 0.000 1.000
#> GSM35534 2 0.0000 0.968 0.000 1.000
#> GSM35536 1 0.0000 0.983 1.000 0.000
#> GSM35538 1 0.0000 0.983 1.000 0.000
#> GSM35539 1 0.0000 0.983 1.000 0.000
#> GSM35540 2 0.0000 0.968 0.000 1.000
#> GSM35541 2 0.0000 0.968 0.000 1.000
#> GSM35442 1 0.0000 0.983 1.000 0.000
#> GSM35447 1 0.0000 0.983 1.000 0.000
#> GSM35450 1 0.0000 0.983 1.000 0.000
#> GSM35453 1 0.0000 0.983 1.000 0.000
#> GSM35456 1 0.0000 0.983 1.000 0.000
#> GSM35464 2 0.0376 0.965 0.004 0.996
#> GSM35467 1 0.0000 0.983 1.000 0.000
#> GSM35470 1 0.0000 0.983 1.000 0.000
#> GSM35479 1 0.0000 0.983 1.000 0.000
#> GSM35484 1 0.0000 0.983 1.000 0.000
#> GSM35488 1 0.0000 0.983 1.000 0.000
#> GSM35491 1 0.0000 0.983 1.000 0.000
#> GSM35494 1 0.0000 0.983 1.000 0.000
#> GSM35498 1 0.0000 0.983 1.000 0.000
#> GSM35501 1 0.0000 0.983 1.000 0.000
#> GSM35509 1 0.9286 0.454 0.656 0.344
#> GSM35513 1 0.0000 0.983 1.000 0.000
#> GSM35516 2 0.0000 0.968 0.000 1.000
#> GSM35522 1 0.0000 0.983 1.000 0.000
#> GSM35525 1 0.0000 0.983 1.000 0.000
#> GSM35528 1 0.0000 0.983 1.000 0.000
#> GSM35533 1 0.0000 0.983 1.000 0.000
#> GSM35537 1 0.0000 0.983 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM35441 2 0.0237 0.961 0.000 0.996 0.004
#> GSM35446 3 0.0424 0.918 0.000 0.008 0.992
#> GSM35449 2 0.0237 0.961 0.000 0.996 0.004
#> GSM35455 2 0.0237 0.961 0.000 0.996 0.004
#> GSM35458 2 0.2269 0.936 0.016 0.944 0.040
#> GSM35460 3 0.0237 0.920 0.000 0.004 0.996
#> GSM35461 3 0.3686 0.844 0.140 0.000 0.860
#> GSM35463 2 0.0237 0.959 0.004 0.996 0.000
#> GSM35472 3 0.0237 0.920 0.000 0.004 0.996
#> GSM35475 3 0.5810 0.437 0.000 0.336 0.664
#> GSM35483 2 0.0424 0.960 0.000 0.992 0.008
#> GSM35496 3 0.1753 0.911 0.048 0.000 0.952
#> GSM35497 2 0.0237 0.961 0.000 0.996 0.004
#> GSM35504 2 0.2878 0.902 0.000 0.904 0.096
#> GSM35508 2 0.3038 0.895 0.000 0.896 0.104
#> GSM35511 3 0.0747 0.914 0.000 0.016 0.984
#> GSM35512 3 0.0000 0.921 0.000 0.000 1.000
#> GSM35515 2 0.3851 0.860 0.004 0.860 0.136
#> GSM35519 3 0.0237 0.920 0.000 0.004 0.996
#> GSM35527 2 0.1753 0.937 0.000 0.952 0.048
#> GSM35532 3 0.0237 0.920 0.000 0.004 0.996
#> GSM35439 2 0.0237 0.959 0.004 0.996 0.000
#> GSM35443 1 0.0424 0.965 0.992 0.000 0.008
#> GSM35445 1 0.0424 0.965 0.992 0.000 0.008
#> GSM35448 3 0.2448 0.865 0.000 0.076 0.924
#> GSM35451 1 0.1860 0.930 0.948 0.052 0.000
#> GSM35454 3 0.2959 0.882 0.100 0.000 0.900
#> GSM35457 2 0.0000 0.961 0.000 1.000 0.000
#> GSM35465 2 0.0000 0.961 0.000 1.000 0.000
#> GSM35468 1 0.0424 0.965 0.992 0.000 0.008
#> GSM35471 1 0.0892 0.956 0.980 0.020 0.000
#> GSM35473 1 0.0424 0.965 0.992 0.000 0.008
#> GSM35477 1 0.1289 0.947 0.968 0.032 0.000
#> GSM35480 1 0.0237 0.966 0.996 0.000 0.004
#> GSM35482 3 0.1860 0.909 0.052 0.000 0.948
#> GSM35485 2 0.0000 0.961 0.000 1.000 0.000
#> GSM35489 2 0.0237 0.959 0.004 0.996 0.000
#> GSM35492 1 0.0424 0.965 0.992 0.000 0.008
#> GSM35495 3 0.0237 0.921 0.004 0.000 0.996
#> GSM35499 2 0.0237 0.961 0.000 0.996 0.004
#> GSM35502 1 0.0237 0.966 0.996 0.000 0.004
#> GSM35505 3 0.0747 0.920 0.016 0.000 0.984
#> GSM35507 1 0.6111 0.379 0.604 0.396 0.000
#> GSM35510 2 0.0237 0.961 0.000 0.996 0.004
#> GSM35514 1 0.0237 0.966 0.996 0.000 0.004
#> GSM35517 2 0.0000 0.961 0.000 1.000 0.000
#> GSM35520 2 0.6008 0.455 0.000 0.628 0.372
#> GSM35523 1 0.0237 0.965 0.996 0.004 0.000
#> GSM35529 2 0.0237 0.961 0.000 0.996 0.004
#> GSM35531 2 0.0237 0.959 0.004 0.996 0.000
#> GSM35534 2 0.0424 0.960 0.000 0.992 0.008
#> GSM35536 1 0.0237 0.966 0.996 0.000 0.004
#> GSM35538 1 0.0237 0.965 0.996 0.004 0.000
#> GSM35539 1 0.0237 0.965 0.996 0.004 0.000
#> GSM35540 2 0.3619 0.866 0.000 0.864 0.136
#> GSM35541 2 0.0237 0.959 0.004 0.996 0.000
#> GSM35442 3 0.6045 0.432 0.380 0.000 0.620
#> GSM35447 3 0.0592 0.921 0.012 0.000 0.988
#> GSM35450 1 0.0237 0.965 0.996 0.004 0.000
#> GSM35453 1 0.1753 0.933 0.952 0.000 0.048
#> GSM35456 1 0.3116 0.875 0.892 0.108 0.000
#> GSM35464 2 0.0592 0.954 0.012 0.988 0.000
#> GSM35467 1 0.0237 0.966 0.996 0.000 0.004
#> GSM35470 1 0.3038 0.872 0.896 0.000 0.104
#> GSM35479 3 0.2356 0.900 0.072 0.000 0.928
#> GSM35484 1 0.0000 0.965 1.000 0.000 0.000
#> GSM35488 1 0.0000 0.965 1.000 0.000 0.000
#> GSM35491 1 0.0424 0.965 0.992 0.000 0.008
#> GSM35494 3 0.3116 0.875 0.108 0.000 0.892
#> GSM35498 1 0.1031 0.953 0.976 0.024 0.000
#> GSM35501 1 0.0237 0.966 0.996 0.000 0.004
#> GSM35509 3 0.0237 0.921 0.004 0.000 0.996
#> GSM35513 1 0.0237 0.966 0.996 0.000 0.004
#> GSM35516 2 0.0424 0.957 0.008 0.992 0.000
#> GSM35522 1 0.2625 0.901 0.916 0.084 0.000
#> GSM35525 1 0.0237 0.966 0.996 0.000 0.004
#> GSM35528 1 0.0237 0.965 0.996 0.004 0.000
#> GSM35533 1 0.0000 0.965 1.000 0.000 0.000
#> GSM35537 1 0.0747 0.960 0.984 0.000 0.016
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM35441 2 0.1902 0.7595 0.000 0.932 0.004 0.064
#> GSM35446 3 0.1545 0.7605 0.000 0.040 0.952 0.008
#> GSM35449 2 0.2868 0.7063 0.000 0.864 0.000 0.136
#> GSM35455 2 0.1792 0.7562 0.000 0.932 0.000 0.068
#> GSM35458 2 0.5756 0.5888 0.176 0.728 0.084 0.012
#> GSM35460 3 0.1637 0.7684 0.000 0.000 0.940 0.060
#> GSM35461 3 0.5811 0.1380 0.468 0.012 0.508 0.012
#> GSM35463 2 0.4776 0.2562 0.000 0.624 0.000 0.376
#> GSM35472 3 0.1575 0.7587 0.012 0.028 0.956 0.004
#> GSM35475 2 0.6019 0.5835 0.128 0.716 0.144 0.012
#> GSM35483 2 0.0657 0.7671 0.000 0.984 0.004 0.012
#> GSM35496 3 0.1807 0.7712 0.008 0.000 0.940 0.052
#> GSM35497 2 0.0895 0.7677 0.000 0.976 0.004 0.020
#> GSM35504 2 0.6330 -0.1147 0.000 0.492 0.060 0.448
#> GSM35508 2 0.1488 0.7612 0.000 0.956 0.032 0.012
#> GSM35511 2 0.5919 0.2316 0.020 0.564 0.404 0.012
#> GSM35512 3 0.3909 0.7233 0.052 0.080 0.856 0.012
#> GSM35515 2 0.5981 0.5831 0.164 0.716 0.108 0.012
#> GSM35519 2 0.6746 0.1380 0.064 0.520 0.404 0.012
#> GSM35527 2 0.1211 0.7659 0.000 0.960 0.000 0.040
#> GSM35532 3 0.6012 0.1919 0.024 0.404 0.560 0.012
#> GSM35439 2 0.0921 0.7668 0.000 0.972 0.000 0.028
#> GSM35443 1 0.1890 0.8300 0.936 0.000 0.056 0.008
#> GSM35445 1 0.2589 0.8625 0.884 0.000 0.000 0.116
#> GSM35448 3 0.3706 0.7334 0.000 0.112 0.848 0.040
#> GSM35451 4 0.4883 0.4188 0.288 0.016 0.000 0.696
#> GSM35454 3 0.3658 0.7539 0.020 0.000 0.836 0.144
#> GSM35457 4 0.4994 0.1732 0.000 0.480 0.000 0.520
#> GSM35465 4 0.4454 0.5480 0.000 0.308 0.000 0.692
#> GSM35468 1 0.0188 0.8754 0.996 0.000 0.004 0.000
#> GSM35471 4 0.1585 0.6924 0.040 0.004 0.004 0.952
#> GSM35473 1 0.0707 0.8851 0.980 0.000 0.000 0.020
#> GSM35477 1 0.4661 0.6161 0.652 0.000 0.000 0.348
#> GSM35480 1 0.4576 0.7487 0.728 0.000 0.012 0.260
#> GSM35482 3 0.3172 0.7477 0.000 0.000 0.840 0.160
#> GSM35485 2 0.0707 0.7672 0.000 0.980 0.000 0.020
#> GSM35489 2 0.2216 0.7419 0.000 0.908 0.000 0.092
#> GSM35492 1 0.0469 0.8709 0.988 0.000 0.012 0.000
#> GSM35495 3 0.2647 0.7597 0.000 0.000 0.880 0.120
#> GSM35499 4 0.4713 0.4679 0.000 0.360 0.000 0.640
#> GSM35502 1 0.1302 0.8848 0.956 0.000 0.000 0.044
#> GSM35505 3 0.4305 0.6977 0.160 0.020 0.808 0.012
#> GSM35507 4 0.2563 0.7104 0.020 0.072 0.000 0.908
#> GSM35510 4 0.4761 0.4465 0.000 0.372 0.000 0.628
#> GSM35514 1 0.0592 0.8840 0.984 0.000 0.000 0.016
#> GSM35517 2 0.2011 0.7496 0.000 0.920 0.000 0.080
#> GSM35520 2 0.3623 0.6896 0.016 0.856 0.116 0.012
#> GSM35523 4 0.1629 0.6674 0.024 0.000 0.024 0.952
#> GSM35529 2 0.4164 0.5235 0.000 0.736 0.000 0.264
#> GSM35531 2 0.1139 0.7609 0.008 0.972 0.012 0.008
#> GSM35534 2 0.0188 0.7648 0.000 0.996 0.004 0.000
#> GSM35536 1 0.0921 0.8857 0.972 0.000 0.000 0.028
#> GSM35538 1 0.2647 0.8575 0.880 0.000 0.000 0.120
#> GSM35539 1 0.4790 0.5806 0.620 0.000 0.000 0.380
#> GSM35540 4 0.6876 0.4748 0.000 0.288 0.140 0.572
#> GSM35541 2 0.2469 0.7298 0.000 0.892 0.000 0.108
#> GSM35442 1 0.4382 0.4777 0.704 0.000 0.296 0.000
#> GSM35447 3 0.5767 0.6331 0.220 0.060 0.708 0.012
#> GSM35450 1 0.4008 0.7659 0.756 0.000 0.000 0.244
#> GSM35453 1 0.2996 0.8573 0.892 0.000 0.044 0.064
#> GSM35456 4 0.3080 0.6926 0.096 0.024 0.000 0.880
#> GSM35464 4 0.3831 0.6475 0.004 0.204 0.000 0.792
#> GSM35467 1 0.0592 0.8839 0.984 0.000 0.000 0.016
#> GSM35470 3 0.7367 0.2652 0.160 0.000 0.436 0.404
#> GSM35479 3 0.3942 0.6911 0.000 0.000 0.764 0.236
#> GSM35484 1 0.0921 0.8861 0.972 0.000 0.000 0.028
#> GSM35488 1 0.1211 0.8865 0.960 0.000 0.000 0.040
#> GSM35491 1 0.0524 0.8799 0.988 0.000 0.004 0.008
#> GSM35494 3 0.3649 0.7222 0.000 0.000 0.796 0.204
#> GSM35498 4 0.2048 0.6941 0.064 0.008 0.000 0.928
#> GSM35501 1 0.1474 0.8842 0.948 0.000 0.000 0.052
#> GSM35509 3 0.3486 0.7315 0.000 0.000 0.812 0.188
#> GSM35513 1 0.0188 0.8797 0.996 0.000 0.000 0.004
#> GSM35516 2 0.4790 0.2437 0.000 0.620 0.000 0.380
#> GSM35522 4 0.0967 0.6905 0.016 0.004 0.004 0.976
#> GSM35525 1 0.3726 0.7989 0.788 0.000 0.000 0.212
#> GSM35528 1 0.3907 0.7800 0.768 0.000 0.000 0.232
#> GSM35533 1 0.1557 0.8837 0.944 0.000 0.000 0.056
#> GSM35537 4 0.6726 0.0884 0.124 0.000 0.292 0.584
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM35441 5 0.3958 0.5667 0.000 0.040 0.000 0.184 0.776
#> GSM35446 3 0.2491 0.7673 0.000 0.036 0.896 0.000 0.068
#> GSM35449 5 0.3966 0.4248 0.000 0.000 0.000 0.336 0.664
#> GSM35455 5 0.3745 0.5692 0.000 0.024 0.000 0.196 0.780
#> GSM35458 5 0.3733 0.5308 0.160 0.004 0.032 0.000 0.804
#> GSM35460 3 0.1597 0.7772 0.000 0.024 0.948 0.008 0.020
#> GSM35461 3 0.6927 0.2036 0.372 0.000 0.384 0.008 0.236
#> GSM35463 2 0.3003 0.7457 0.000 0.864 0.000 0.044 0.092
#> GSM35472 3 0.2439 0.7407 0.004 0.000 0.876 0.000 0.120
#> GSM35475 5 0.3812 0.5391 0.128 0.008 0.048 0.000 0.816
#> GSM35483 2 0.3003 0.7504 0.000 0.812 0.000 0.000 0.188
#> GSM35496 3 0.1662 0.7709 0.004 0.000 0.936 0.004 0.056
#> GSM35497 5 0.2824 0.5954 0.000 0.020 0.000 0.116 0.864
#> GSM35504 2 0.5244 0.7051 0.000 0.740 0.048 0.100 0.112
#> GSM35508 5 0.2586 0.6022 0.000 0.012 0.012 0.084 0.892
#> GSM35511 5 0.4003 0.4266 0.008 0.000 0.288 0.000 0.704
#> GSM35512 3 0.3890 0.6127 0.012 0.000 0.736 0.000 0.252
#> GSM35515 5 0.3835 0.5274 0.156 0.000 0.048 0.000 0.796
#> GSM35519 5 0.5029 0.3316 0.060 0.000 0.292 0.000 0.648
#> GSM35527 5 0.3289 0.5865 0.000 0.008 0.004 0.172 0.816
#> GSM35532 5 0.4517 0.0490 0.008 0.000 0.436 0.000 0.556
#> GSM35439 5 0.4491 0.2668 0.000 0.328 0.000 0.020 0.652
#> GSM35443 1 0.2450 0.7711 0.896 0.000 0.028 0.000 0.076
#> GSM35445 1 0.5744 0.6596 0.652 0.228 0.020 0.100 0.000
#> GSM35448 2 0.3901 0.5273 0.000 0.776 0.196 0.004 0.024
#> GSM35451 4 0.5338 0.0869 0.392 0.040 0.000 0.560 0.008
#> GSM35454 3 0.6269 0.4210 0.012 0.364 0.512 0.112 0.000
#> GSM35457 4 0.4822 0.3303 0.000 0.032 0.000 0.616 0.352
#> GSM35465 4 0.3438 0.6252 0.000 0.020 0.000 0.808 0.172
#> GSM35468 1 0.0865 0.8222 0.972 0.000 0.000 0.004 0.024
#> GSM35471 4 0.3954 0.6230 0.060 0.048 0.060 0.832 0.000
#> GSM35473 1 0.2291 0.8225 0.908 0.036 0.000 0.056 0.000
#> GSM35477 1 0.4244 0.6734 0.712 0.016 0.000 0.268 0.004
#> GSM35480 1 0.5093 0.7298 0.732 0.060 0.036 0.172 0.000
#> GSM35482 3 0.2005 0.7723 0.000 0.004 0.924 0.056 0.016
#> GSM35485 2 0.3814 0.6874 0.000 0.720 0.000 0.004 0.276
#> GSM35489 5 0.5091 0.3905 0.000 0.236 0.000 0.088 0.676
#> GSM35492 1 0.1443 0.8101 0.948 0.000 0.004 0.004 0.044
#> GSM35495 3 0.2654 0.7599 0.000 0.084 0.884 0.032 0.000
#> GSM35499 2 0.4714 0.6645 0.000 0.724 0.000 0.192 0.084
#> GSM35502 1 0.0771 0.8297 0.976 0.004 0.000 0.020 0.000
#> GSM35505 3 0.5680 0.5446 0.016 0.340 0.596 0.012 0.036
#> GSM35507 4 0.2488 0.6748 0.004 0.000 0.000 0.872 0.124
#> GSM35510 4 0.6478 -0.1636 0.000 0.368 0.000 0.444 0.188
#> GSM35514 1 0.0451 0.8274 0.988 0.004 0.000 0.000 0.008
#> GSM35517 5 0.4990 0.2424 0.000 0.324 0.000 0.048 0.628
#> GSM35520 5 0.3543 0.5231 0.008 0.124 0.036 0.000 0.832
#> GSM35523 4 0.2703 0.6899 0.024 0.000 0.020 0.896 0.060
#> GSM35529 5 0.4987 0.3968 0.000 0.044 0.000 0.340 0.616
#> GSM35531 2 0.4806 0.4757 0.008 0.600 0.008 0.004 0.380
#> GSM35534 2 0.3074 0.7481 0.000 0.804 0.000 0.000 0.196
#> GSM35536 1 0.0451 0.8294 0.988 0.004 0.000 0.008 0.000
#> GSM35538 1 0.1908 0.8166 0.908 0.000 0.000 0.092 0.000
#> GSM35539 1 0.4713 0.3712 0.544 0.016 0.000 0.440 0.000
#> GSM35540 4 0.4957 0.5946 0.000 0.008 0.092 0.724 0.176
#> GSM35541 5 0.5216 -0.1354 0.000 0.436 0.000 0.044 0.520
#> GSM35442 1 0.4971 0.5362 0.704 0.000 0.212 0.004 0.080
#> GSM35447 3 0.6683 0.6145 0.076 0.204 0.624 0.012 0.084
#> GSM35450 1 0.3326 0.7812 0.824 0.024 0.000 0.152 0.000
#> GSM35453 1 0.4001 0.7902 0.820 0.024 0.056 0.100 0.000
#> GSM35456 4 0.4478 0.5916 0.144 0.088 0.000 0.764 0.004
#> GSM35464 4 0.2864 0.6615 0.000 0.012 0.000 0.852 0.136
#> GSM35467 1 0.0451 0.8274 0.988 0.004 0.000 0.000 0.008
#> GSM35470 4 0.6504 0.1293 0.196 0.000 0.356 0.448 0.000
#> GSM35479 3 0.2777 0.7335 0.000 0.016 0.864 0.120 0.000
#> GSM35484 1 0.3171 0.7499 0.816 0.176 0.000 0.008 0.000
#> GSM35488 1 0.0798 0.8294 0.976 0.000 0.000 0.016 0.008
#> GSM35491 1 0.0798 0.8281 0.976 0.000 0.000 0.008 0.016
#> GSM35494 3 0.3073 0.7357 0.004 0.024 0.856 0.116 0.000
#> GSM35498 4 0.2770 0.6933 0.044 0.000 0.000 0.880 0.076
#> GSM35501 1 0.1697 0.8241 0.932 0.008 0.000 0.060 0.000
#> GSM35509 3 0.2438 0.7611 0.000 0.040 0.900 0.060 0.000
#> GSM35513 1 0.0451 0.8274 0.988 0.004 0.000 0.000 0.008
#> GSM35516 2 0.5628 0.6575 0.000 0.624 0.000 0.132 0.244
#> GSM35522 4 0.2577 0.6911 0.016 0.000 0.008 0.892 0.084
#> GSM35525 1 0.3427 0.7609 0.796 0.012 0.000 0.192 0.000
#> GSM35528 1 0.5002 0.4385 0.612 0.000 0.000 0.344 0.044
#> GSM35533 1 0.5850 0.3570 0.476 0.428 0.000 0.096 0.000
#> GSM35537 4 0.6082 0.4276 0.140 0.020 0.216 0.624 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM35441 5 0.5260 0.51835 0.000 0.064 0.000 0.304 0.604 0.028
#> GSM35446 3 0.3997 0.68752 0.000 0.108 0.776 0.000 0.008 0.108
#> GSM35449 4 0.4684 -0.06568 0.000 0.008 0.000 0.520 0.444 0.028
#> GSM35455 5 0.2833 0.68362 0.000 0.012 0.000 0.148 0.836 0.004
#> GSM35458 5 0.2649 0.68111 0.036 0.012 0.000 0.000 0.880 0.072
#> GSM35460 3 0.2095 0.77029 0.000 0.016 0.904 0.000 0.004 0.076
#> GSM35461 6 0.4468 0.50868 0.060 0.000 0.076 0.000 0.100 0.764
#> GSM35463 2 0.2189 0.54165 0.000 0.904 0.000 0.032 0.060 0.004
#> GSM35472 3 0.4868 0.24492 0.000 0.008 0.560 0.004 0.036 0.392
#> GSM35475 5 0.3452 0.58461 0.004 0.004 0.000 0.000 0.736 0.256
#> GSM35483 2 0.4160 0.42409 0.008 0.684 0.000 0.000 0.284 0.024
#> GSM35496 3 0.2944 0.72072 0.000 0.012 0.832 0.000 0.008 0.148
#> GSM35497 5 0.2426 0.70122 0.000 0.012 0.000 0.092 0.884 0.012
#> GSM35504 2 0.6508 0.49451 0.000 0.556 0.236 0.056 0.136 0.016
#> GSM35508 5 0.3508 0.68783 0.000 0.016 0.004 0.100 0.828 0.052
#> GSM35511 5 0.3525 0.63744 0.000 0.004 0.068 0.000 0.808 0.120
#> GSM35512 6 0.4993 0.14711 0.000 0.000 0.360 0.000 0.080 0.560
#> GSM35515 5 0.2402 0.68369 0.032 0.012 0.000 0.000 0.896 0.060
#> GSM35519 6 0.5083 0.36349 0.000 0.004 0.120 0.000 0.244 0.632
#> GSM35527 5 0.3757 0.66800 0.000 0.016 0.000 0.164 0.784 0.036
#> GSM35532 5 0.5587 0.34418 0.000 0.004 0.252 0.000 0.564 0.180
#> GSM35439 5 0.4392 0.57631 0.024 0.188 0.000 0.012 0.744 0.032
#> GSM35443 6 0.3668 0.41281 0.256 0.008 0.000 0.000 0.008 0.728
#> GSM35445 1 0.6133 0.35584 0.484 0.352 0.016 0.008 0.000 0.140
#> GSM35448 2 0.4962 0.32882 0.000 0.608 0.320 0.000 0.060 0.012
#> GSM35451 4 0.5204 0.52720 0.128 0.072 0.000 0.700 0.000 0.100
#> GSM35454 2 0.5227 -0.15583 0.000 0.456 0.452 0.000 0.000 0.092
#> GSM35457 4 0.3395 0.54782 0.000 0.056 0.000 0.816 0.124 0.004
#> GSM35465 4 0.1498 0.61162 0.000 0.032 0.000 0.940 0.028 0.000
#> GSM35468 1 0.3818 0.58968 0.720 0.004 0.000 0.012 0.004 0.260
#> GSM35471 4 0.3625 0.61274 0.064 0.024 0.044 0.840 0.000 0.028
#> GSM35473 1 0.1644 0.74225 0.932 0.028 0.000 0.000 0.000 0.040
#> GSM35477 4 0.5928 0.39653 0.216 0.028 0.000 0.572 0.000 0.184
#> GSM35480 1 0.3467 0.68952 0.848 0.028 0.056 0.016 0.000 0.052
#> GSM35482 3 0.2073 0.77054 0.004 0.016 0.920 0.008 0.004 0.048
#> GSM35485 2 0.4064 0.29620 0.000 0.624 0.000 0.000 0.360 0.016
#> GSM35489 4 0.7115 0.09808 0.000 0.244 0.000 0.452 0.140 0.164
#> GSM35492 6 0.4353 0.20211 0.360 0.012 0.000 0.008 0.004 0.616
#> GSM35495 3 0.2190 0.76946 0.000 0.040 0.900 0.000 0.000 0.060
#> GSM35499 2 0.4837 0.03890 0.000 0.528 0.000 0.428 0.016 0.028
#> GSM35502 1 0.0405 0.74272 0.988 0.000 0.000 0.000 0.004 0.008
#> GSM35505 6 0.5438 0.25999 0.000 0.160 0.280 0.000 0.000 0.560
#> GSM35507 4 0.0924 0.62545 0.004 0.008 0.008 0.972 0.008 0.000
#> GSM35510 4 0.4993 0.26142 0.000 0.316 0.004 0.600 0.080 0.000
#> GSM35514 1 0.2089 0.73974 0.916 0.020 0.000 0.000 0.020 0.044
#> GSM35517 5 0.4871 0.55445 0.000 0.184 0.000 0.108 0.692 0.016
#> GSM35520 5 0.4497 0.60203 0.000 0.100 0.004 0.000 0.712 0.184
#> GSM35523 4 0.5824 0.49521 0.140 0.012 0.144 0.656 0.004 0.044
#> GSM35529 5 0.4514 0.46386 0.000 0.040 0.000 0.372 0.588 0.000
#> GSM35531 6 0.6115 0.02338 0.008 0.340 0.000 0.060 0.068 0.524
#> GSM35534 2 0.4550 0.40181 0.008 0.652 0.000 0.000 0.296 0.044
#> GSM35536 1 0.2211 0.73449 0.900 0.008 0.000 0.008 0.004 0.080
#> GSM35538 1 0.3613 0.66295 0.772 0.008 0.000 0.024 0.000 0.196
#> GSM35539 1 0.3686 0.67458 0.816 0.004 0.020 0.108 0.000 0.052
#> GSM35540 4 0.4585 0.50236 0.000 0.028 0.208 0.720 0.036 0.008
#> GSM35541 5 0.5082 0.40985 0.000 0.296 0.000 0.048 0.624 0.032
#> GSM35442 6 0.5331 0.46784 0.252 0.004 0.128 0.000 0.004 0.612
#> GSM35447 6 0.6585 0.08654 0.008 0.244 0.324 0.000 0.016 0.408
#> GSM35450 1 0.5042 0.60814 0.684 0.020 0.000 0.152 0.000 0.144
#> GSM35453 1 0.2015 0.73450 0.916 0.012 0.056 0.000 0.000 0.016
#> GSM35456 4 0.6715 0.06711 0.388 0.160 0.004 0.396 0.000 0.052
#> GSM35464 4 0.0909 0.61974 0.000 0.020 0.000 0.968 0.012 0.000
#> GSM35467 1 0.1599 0.74201 0.940 0.024 0.000 0.000 0.008 0.028
#> GSM35470 3 0.6433 0.21197 0.304 0.004 0.508 0.128 0.000 0.056
#> GSM35479 3 0.1396 0.75211 0.012 0.004 0.952 0.008 0.000 0.024
#> GSM35484 1 0.6133 0.17251 0.416 0.248 0.000 0.004 0.000 0.332
#> GSM35488 1 0.3916 0.53322 0.680 0.000 0.000 0.020 0.000 0.300
#> GSM35491 6 0.4605 -0.00682 0.416 0.016 0.000 0.016 0.000 0.552
#> GSM35494 3 0.0862 0.76921 0.008 0.004 0.972 0.000 0.000 0.016
#> GSM35498 4 0.1901 0.62896 0.024 0.016 0.012 0.932 0.000 0.016
#> GSM35501 1 0.0551 0.74250 0.984 0.004 0.000 0.000 0.004 0.008
#> GSM35509 3 0.0748 0.77792 0.000 0.004 0.976 0.004 0.000 0.016
#> GSM35513 1 0.2146 0.73772 0.908 0.024 0.000 0.000 0.008 0.060
#> GSM35516 2 0.6124 0.01989 0.008 0.464 0.000 0.408 0.068 0.052
#> GSM35522 4 0.4194 0.58539 0.072 0.012 0.068 0.804 0.004 0.040
#> GSM35525 1 0.3165 0.70114 0.860 0.004 0.028 0.056 0.000 0.052
#> GSM35528 4 0.5468 -0.04513 0.448 0.004 0.008 0.460 0.000 0.080
#> GSM35533 1 0.5243 0.27172 0.460 0.456 0.000 0.004 0.000 0.080
#> GSM35537 1 0.6760 0.24242 0.496 0.008 0.272 0.172 0.004 0.048
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 time(p) k
#> MAD:NMF 75 1.02e-06 2
#> MAD:NMF 75 4.07e-05 3
#> MAD:NMF 64 3.55e-04 4
#> MAD:NMF 59 9.64e-05 5
#> MAD:NMF 46 1.46e-03 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 7758 rows and 79 columns.
#> Top rows (776, 1552, 2328, 3103, 3879) 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 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 0.322 0.781 0.853 0.4580 0.500 0.500
#> 3 3 0.486 0.825 0.874 0.3563 0.825 0.656
#> 4 4 0.766 0.801 0.853 0.0941 0.986 0.960
#> 5 5 0.833 0.773 0.874 0.0675 0.964 0.888
#> 6 6 0.803 0.836 0.887 0.0244 0.980 0.932
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
#> GSM35441 2 0.6148 0.772 0.152 0.848
#> GSM35446 2 0.0000 0.710 0.000 1.000
#> GSM35449 2 0.6148 0.772 0.152 0.848
#> GSM35455 2 0.6148 0.772 0.152 0.848
#> GSM35458 2 0.9358 0.670 0.352 0.648
#> GSM35460 2 0.0000 0.710 0.000 1.000
#> GSM35461 1 0.9970 -0.367 0.532 0.468
#> GSM35463 2 0.8443 0.732 0.272 0.728
#> GSM35472 2 0.9922 0.538 0.448 0.552
#> GSM35475 2 0.9358 0.670 0.352 0.648
#> GSM35483 2 0.8443 0.732 0.272 0.728
#> GSM35496 2 0.9850 0.329 0.428 0.572
#> GSM35497 2 0.6148 0.772 0.152 0.848
#> GSM35504 2 0.6148 0.772 0.152 0.848
#> GSM35508 2 0.0000 0.710 0.000 1.000
#> GSM35511 2 0.0000 0.710 0.000 1.000
#> GSM35512 2 0.9922 0.538 0.448 0.552
#> GSM35515 2 0.9358 0.670 0.352 0.648
#> GSM35519 2 0.9922 0.538 0.448 0.552
#> GSM35527 2 0.0000 0.710 0.000 1.000
#> GSM35532 2 0.0000 0.710 0.000 1.000
#> GSM35439 2 0.8443 0.732 0.272 0.728
#> GSM35443 1 0.0000 0.980 1.000 0.000
#> GSM35445 1 0.0000 0.980 1.000 0.000
#> GSM35448 2 0.1414 0.720 0.020 0.980
#> GSM35451 1 0.0000 0.980 1.000 0.000
#> GSM35454 2 0.9983 0.488 0.476 0.524
#> GSM35457 2 0.6148 0.772 0.152 0.848
#> GSM35465 2 0.6148 0.772 0.152 0.848
#> GSM35468 1 0.0000 0.980 1.000 0.000
#> GSM35471 1 0.0000 0.980 1.000 0.000
#> GSM35473 1 0.0000 0.980 1.000 0.000
#> GSM35477 1 0.0000 0.980 1.000 0.000
#> GSM35480 1 0.0000 0.980 1.000 0.000
#> GSM35482 2 0.9850 0.329 0.428 0.572
#> GSM35485 2 0.8443 0.732 0.272 0.728
#> GSM35489 2 0.8443 0.732 0.272 0.728
#> GSM35492 1 0.0000 0.980 1.000 0.000
#> GSM35495 2 0.9427 0.473 0.360 0.640
#> GSM35499 2 0.6148 0.772 0.152 0.848
#> GSM35502 1 0.0000 0.980 1.000 0.000
#> GSM35505 2 0.9983 0.488 0.476 0.524
#> GSM35507 1 0.0000 0.980 1.000 0.000
#> GSM35510 2 0.6148 0.772 0.152 0.848
#> GSM35514 1 0.0000 0.980 1.000 0.000
#> GSM35517 2 0.8443 0.732 0.272 0.728
#> GSM35520 2 0.9358 0.670 0.352 0.648
#> GSM35523 1 0.0000 0.980 1.000 0.000
#> GSM35529 2 0.6148 0.772 0.152 0.848
#> GSM35531 2 0.8443 0.732 0.272 0.728
#> GSM35534 2 0.8443 0.732 0.272 0.728
#> GSM35536 1 0.0000 0.980 1.000 0.000
#> GSM35538 1 0.0000 0.980 1.000 0.000
#> GSM35539 1 0.0000 0.980 1.000 0.000
#> GSM35540 2 0.6148 0.772 0.152 0.848
#> GSM35541 2 0.8443 0.732 0.272 0.728
#> GSM35442 1 0.0000 0.980 1.000 0.000
#> GSM35447 2 0.9970 0.504 0.468 0.532
#> GSM35450 1 0.0000 0.980 1.000 0.000
#> GSM35453 1 0.0000 0.980 1.000 0.000
#> GSM35456 1 0.0000 0.980 1.000 0.000
#> GSM35464 1 0.0376 0.974 0.996 0.004
#> GSM35467 1 0.0000 0.980 1.000 0.000
#> GSM35470 1 0.0000 0.980 1.000 0.000
#> GSM35479 2 0.9850 0.329 0.428 0.572
#> GSM35484 1 0.0000 0.980 1.000 0.000
#> GSM35488 1 0.0000 0.980 1.000 0.000
#> GSM35491 1 0.0000 0.980 1.000 0.000
#> GSM35494 2 0.9850 0.329 0.428 0.572
#> GSM35498 1 0.0000 0.980 1.000 0.000
#> GSM35501 1 0.0000 0.980 1.000 0.000
#> GSM35509 2 0.9580 0.436 0.380 0.620
#> GSM35513 1 0.0000 0.980 1.000 0.000
#> GSM35516 2 0.9323 0.683 0.348 0.652
#> GSM35522 1 0.0000 0.980 1.000 0.000
#> GSM35525 1 0.0000 0.980 1.000 0.000
#> GSM35528 1 0.0000 0.980 1.000 0.000
#> GSM35533 1 0.0000 0.980 1.000 0.000
#> GSM35537 1 0.0000 0.980 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM35441 2 0.000 0.865 0.000 1.000 0.000
#> GSM35446 3 0.388 0.548 0.000 0.152 0.848
#> GSM35449 2 0.000 0.865 0.000 1.000 0.000
#> GSM35455 2 0.000 0.865 0.000 1.000 0.000
#> GSM35458 3 0.723 0.653 0.080 0.228 0.692
#> GSM35460 3 0.388 0.548 0.000 0.152 0.848
#> GSM35461 3 0.928 0.660 0.328 0.176 0.496
#> GSM35463 2 0.334 0.844 0.120 0.880 0.000
#> GSM35472 3 0.835 0.705 0.176 0.196 0.628
#> GSM35475 3 0.723 0.653 0.080 0.228 0.692
#> GSM35483 2 0.685 0.731 0.120 0.740 0.140
#> GSM35496 3 0.593 0.587 0.356 0.000 0.644
#> GSM35497 2 0.000 0.865 0.000 1.000 0.000
#> GSM35504 2 0.341 0.785 0.000 0.876 0.124
#> GSM35508 2 0.586 0.508 0.000 0.656 0.344
#> GSM35511 3 0.418 0.545 0.000 0.172 0.828
#> GSM35512 3 0.835 0.705 0.176 0.196 0.628
#> GSM35515 3 0.723 0.653 0.080 0.228 0.692
#> GSM35519 3 0.835 0.705 0.176 0.196 0.628
#> GSM35527 2 0.586 0.508 0.000 0.656 0.344
#> GSM35532 3 0.418 0.545 0.000 0.172 0.828
#> GSM35439 2 0.334 0.844 0.120 0.880 0.000
#> GSM35443 1 0.000 0.963 1.000 0.000 0.000
#> GSM35445 1 0.000 0.963 1.000 0.000 0.000
#> GSM35448 3 0.440 0.538 0.000 0.188 0.812
#> GSM35451 1 0.196 0.955 0.944 0.000 0.056
#> GSM35454 3 0.865 0.698 0.204 0.196 0.600
#> GSM35457 2 0.000 0.865 0.000 1.000 0.000
#> GSM35465 2 0.000 0.865 0.000 1.000 0.000
#> GSM35468 1 0.000 0.963 1.000 0.000 0.000
#> GSM35471 1 0.196 0.955 0.944 0.000 0.056
#> GSM35473 1 0.000 0.963 1.000 0.000 0.000
#> GSM35477 1 0.196 0.955 0.944 0.000 0.056
#> GSM35480 1 0.000 0.963 1.000 0.000 0.000
#> GSM35482 3 0.593 0.587 0.356 0.000 0.644
#> GSM35485 2 0.334 0.844 0.120 0.880 0.000
#> GSM35489 2 0.334 0.844 0.120 0.880 0.000
#> GSM35492 1 0.000 0.963 1.000 0.000 0.000
#> GSM35495 3 0.536 0.688 0.220 0.012 0.768
#> GSM35499 2 0.000 0.865 0.000 1.000 0.000
#> GSM35502 1 0.000 0.963 1.000 0.000 0.000
#> GSM35505 3 0.865 0.698 0.204 0.196 0.600
#> GSM35507 1 0.196 0.955 0.944 0.000 0.056
#> GSM35510 2 0.000 0.865 0.000 1.000 0.000
#> GSM35514 1 0.000 0.963 1.000 0.000 0.000
#> GSM35517 2 0.334 0.844 0.120 0.880 0.000
#> GSM35520 3 0.723 0.653 0.080 0.228 0.692
#> GSM35523 1 0.220 0.953 0.940 0.004 0.056
#> GSM35529 2 0.000 0.865 0.000 1.000 0.000
#> GSM35531 2 0.334 0.844 0.120 0.880 0.000
#> GSM35534 2 0.334 0.844 0.120 0.880 0.000
#> GSM35536 1 0.000 0.963 1.000 0.000 0.000
#> GSM35538 1 0.196 0.955 0.944 0.000 0.056
#> GSM35539 1 0.196 0.955 0.944 0.000 0.056
#> GSM35540 2 0.000 0.865 0.000 1.000 0.000
#> GSM35541 2 0.334 0.844 0.120 0.880 0.000
#> GSM35442 1 0.000 0.963 1.000 0.000 0.000
#> GSM35447 3 0.857 0.701 0.196 0.196 0.608
#> GSM35450 1 0.196 0.955 0.944 0.000 0.056
#> GSM35453 1 0.000 0.963 1.000 0.000 0.000
#> GSM35456 1 0.196 0.955 0.944 0.000 0.056
#> GSM35464 1 0.220 0.953 0.940 0.004 0.056
#> GSM35467 1 0.000 0.963 1.000 0.000 0.000
#> GSM35470 1 0.141 0.936 0.964 0.000 0.036
#> GSM35479 3 0.593 0.587 0.356 0.000 0.644
#> GSM35484 1 0.196 0.955 0.944 0.000 0.056
#> GSM35488 1 0.000 0.963 1.000 0.000 0.000
#> GSM35491 1 0.000 0.963 1.000 0.000 0.000
#> GSM35494 3 0.593 0.587 0.356 0.000 0.644
#> GSM35498 1 0.196 0.955 0.944 0.000 0.056
#> GSM35501 1 0.000 0.963 1.000 0.000 0.000
#> GSM35509 3 0.558 0.672 0.240 0.012 0.748
#> GSM35513 1 0.000 0.963 1.000 0.000 0.000
#> GSM35516 2 0.557 0.752 0.140 0.804 0.056
#> GSM35522 1 0.220 0.953 0.940 0.004 0.056
#> GSM35525 1 0.000 0.963 1.000 0.000 0.000
#> GSM35528 1 0.196 0.955 0.944 0.000 0.056
#> GSM35533 1 0.196 0.955 0.944 0.000 0.056
#> GSM35537 1 0.141 0.936 0.964 0.000 0.036
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM35441 2 0.2011 0.866 0.000 0.920 0.000 0.080
#> GSM35446 3 0.4624 0.368 0.000 0.000 0.660 0.340
#> GSM35449 2 0.2011 0.866 0.000 0.920 0.000 0.080
#> GSM35455 2 0.2011 0.866 0.000 0.920 0.000 0.080
#> GSM35458 3 0.6109 0.609 0.004 0.224 0.676 0.096
#> GSM35460 3 0.4624 0.368 0.000 0.000 0.660 0.340
#> GSM35461 3 0.6971 0.598 0.128 0.188 0.652 0.032
#> GSM35463 2 0.1716 0.859 0.064 0.936 0.000 0.000
#> GSM35472 3 0.4458 0.656 0.008 0.196 0.780 0.016
#> GSM35475 3 0.6109 0.609 0.004 0.224 0.676 0.096
#> GSM35483 2 0.5334 0.706 0.064 0.792 0.072 0.072
#> GSM35496 3 0.5758 0.493 0.128 0.000 0.712 0.160
#> GSM35497 2 0.2011 0.866 0.000 0.920 0.000 0.080
#> GSM35504 2 0.5339 0.266 0.000 0.600 0.016 0.384
#> GSM35508 4 0.3803 1.000 0.000 0.132 0.032 0.836
#> GSM35511 3 0.4985 0.228 0.000 0.000 0.532 0.468
#> GSM35512 3 0.4458 0.656 0.008 0.196 0.780 0.016
#> GSM35515 3 0.6109 0.609 0.004 0.224 0.676 0.096
#> GSM35519 3 0.4458 0.656 0.008 0.196 0.780 0.016
#> GSM35527 4 0.3803 1.000 0.000 0.132 0.032 0.836
#> GSM35532 3 0.4985 0.228 0.000 0.000 0.532 0.468
#> GSM35439 2 0.1716 0.859 0.064 0.936 0.000 0.000
#> GSM35443 1 0.0336 0.954 0.992 0.000 0.008 0.000
#> GSM35445 1 0.0336 0.954 0.992 0.000 0.008 0.000
#> GSM35448 3 0.5639 0.390 0.000 0.040 0.636 0.324
#> GSM35451 1 0.1792 0.950 0.932 0.000 0.068 0.000
#> GSM35454 3 0.4348 0.653 0.024 0.196 0.780 0.000
#> GSM35457 2 0.2011 0.866 0.000 0.920 0.000 0.080
#> GSM35465 2 0.2011 0.866 0.000 0.920 0.000 0.080
#> GSM35468 1 0.0000 0.957 1.000 0.000 0.000 0.000
#> GSM35471 1 0.1792 0.950 0.932 0.000 0.068 0.000
#> GSM35473 1 0.0000 0.957 1.000 0.000 0.000 0.000
#> GSM35477 1 0.1792 0.950 0.932 0.000 0.068 0.000
#> GSM35480 1 0.0000 0.957 1.000 0.000 0.000 0.000
#> GSM35482 3 0.5758 0.493 0.128 0.000 0.712 0.160
#> GSM35485 2 0.1716 0.859 0.064 0.936 0.000 0.000
#> GSM35489 2 0.1716 0.859 0.064 0.936 0.000 0.000
#> GSM35492 1 0.0000 0.957 1.000 0.000 0.000 0.000
#> GSM35495 3 0.2466 0.582 0.004 0.000 0.900 0.096
#> GSM35499 2 0.2011 0.866 0.000 0.920 0.000 0.080
#> GSM35502 1 0.0000 0.957 1.000 0.000 0.000 0.000
#> GSM35505 3 0.4348 0.653 0.024 0.196 0.780 0.000
#> GSM35507 1 0.1792 0.950 0.932 0.000 0.068 0.000
#> GSM35510 2 0.2011 0.866 0.000 0.920 0.000 0.080
#> GSM35514 1 0.0000 0.957 1.000 0.000 0.000 0.000
#> GSM35517 2 0.2048 0.859 0.064 0.928 0.000 0.008
#> GSM35520 3 0.6109 0.609 0.004 0.224 0.676 0.096
#> GSM35523 1 0.1978 0.948 0.928 0.004 0.068 0.000
#> GSM35529 2 0.2011 0.866 0.000 0.920 0.000 0.080
#> GSM35531 2 0.1716 0.859 0.064 0.936 0.000 0.000
#> GSM35534 2 0.1716 0.859 0.064 0.936 0.000 0.000
#> GSM35536 1 0.0000 0.957 1.000 0.000 0.000 0.000
#> GSM35538 1 0.1792 0.950 0.932 0.000 0.068 0.000
#> GSM35539 1 0.1792 0.950 0.932 0.000 0.068 0.000
#> GSM35540 2 0.2011 0.866 0.000 0.920 0.000 0.080
#> GSM35541 2 0.1716 0.859 0.064 0.936 0.000 0.000
#> GSM35442 1 0.0336 0.954 0.992 0.000 0.008 0.000
#> GSM35447 3 0.4136 0.655 0.016 0.196 0.788 0.000
#> GSM35450 1 0.1792 0.950 0.932 0.000 0.068 0.000
#> GSM35453 1 0.0336 0.954 0.992 0.000 0.008 0.000
#> GSM35456 1 0.1792 0.950 0.932 0.000 0.068 0.000
#> GSM35464 1 0.1978 0.948 0.928 0.004 0.068 0.000
#> GSM35467 1 0.0000 0.957 1.000 0.000 0.000 0.000
#> GSM35470 1 0.1854 0.915 0.940 0.000 0.048 0.012
#> GSM35479 3 0.5758 0.493 0.128 0.000 0.712 0.160
#> GSM35484 1 0.1792 0.950 0.932 0.000 0.068 0.000
#> GSM35488 1 0.0000 0.957 1.000 0.000 0.000 0.000
#> GSM35491 1 0.0000 0.957 1.000 0.000 0.000 0.000
#> GSM35494 3 0.5758 0.493 0.128 0.000 0.712 0.160
#> GSM35498 1 0.1792 0.950 0.932 0.000 0.068 0.000
#> GSM35501 1 0.0000 0.957 1.000 0.000 0.000 0.000
#> GSM35509 3 0.3479 0.554 0.012 0.000 0.840 0.148
#> GSM35513 1 0.0000 0.957 1.000 0.000 0.000 0.000
#> GSM35516 2 0.3621 0.770 0.072 0.860 0.068 0.000
#> GSM35522 1 0.1978 0.948 0.928 0.004 0.068 0.000
#> GSM35525 1 0.0000 0.957 1.000 0.000 0.000 0.000
#> GSM35528 1 0.1792 0.950 0.932 0.000 0.068 0.000
#> GSM35533 1 0.1792 0.950 0.932 0.000 0.068 0.000
#> GSM35537 1 0.1854 0.915 0.940 0.000 0.048 0.012
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM35441 2 0.0000 0.8786 0.000 1.000 0.000 0.000 0.000
#> GSM35446 3 0.5736 0.0567 0.000 0.000 0.512 0.088 0.400
#> GSM35449 2 0.0000 0.8786 0.000 1.000 0.000 0.000 0.000
#> GSM35455 2 0.0000 0.8786 0.000 1.000 0.000 0.000 0.000
#> GSM35458 5 0.2642 0.7014 0.004 0.024 0.084 0.000 0.888
#> GSM35460 3 0.5736 0.0567 0.000 0.000 0.512 0.088 0.400
#> GSM35461 5 0.5263 0.2314 0.100 0.000 0.240 0.000 0.660
#> GSM35463 2 0.2648 0.8696 0.000 0.848 0.000 0.152 0.000
#> GSM35472 5 0.0324 0.7204 0.004 0.000 0.004 0.000 0.992
#> GSM35475 5 0.2642 0.7014 0.004 0.024 0.084 0.000 0.888
#> GSM35483 2 0.5983 0.6854 0.000 0.680 0.072 0.152 0.096
#> GSM35496 3 0.4322 0.5663 0.088 0.000 0.768 0.000 0.144
#> GSM35497 2 0.0000 0.8786 0.000 1.000 0.000 0.000 0.000
#> GSM35504 2 0.6405 0.1758 0.000 0.620 0.148 0.188 0.044
#> GSM35508 4 0.4955 1.0000 0.000 0.148 0.124 0.724 0.004
#> GSM35511 5 0.6540 0.1352 0.000 0.000 0.300 0.228 0.472
#> GSM35512 5 0.0324 0.7204 0.004 0.000 0.004 0.000 0.992
#> GSM35515 5 0.2642 0.7014 0.004 0.024 0.084 0.000 0.888
#> GSM35519 5 0.0324 0.7204 0.004 0.000 0.004 0.000 0.992
#> GSM35527 4 0.4955 1.0000 0.000 0.148 0.124 0.724 0.004
#> GSM35532 5 0.6540 0.1352 0.000 0.000 0.300 0.228 0.472
#> GSM35439 2 0.2648 0.8696 0.000 0.848 0.000 0.152 0.000
#> GSM35443 1 0.0290 0.9413 0.992 0.000 0.008 0.000 0.000
#> GSM35445 1 0.0290 0.9413 0.992 0.000 0.008 0.000 0.000
#> GSM35448 3 0.5785 -0.0374 0.000 0.004 0.484 0.076 0.436
#> GSM35451 1 0.2068 0.9300 0.904 0.000 0.004 0.092 0.000
#> GSM35454 5 0.1399 0.7014 0.020 0.000 0.028 0.000 0.952
#> GSM35457 2 0.0000 0.8786 0.000 1.000 0.000 0.000 0.000
#> GSM35465 2 0.0000 0.8786 0.000 1.000 0.000 0.000 0.000
#> GSM35468 1 0.0000 0.9446 1.000 0.000 0.000 0.000 0.000
#> GSM35471 1 0.2124 0.9286 0.900 0.000 0.004 0.096 0.000
#> GSM35473 1 0.0000 0.9446 1.000 0.000 0.000 0.000 0.000
#> GSM35477 1 0.2068 0.9300 0.904 0.000 0.004 0.092 0.000
#> GSM35480 1 0.0000 0.9446 1.000 0.000 0.000 0.000 0.000
#> GSM35482 3 0.4322 0.5663 0.088 0.000 0.768 0.000 0.144
#> GSM35485 2 0.2648 0.8696 0.000 0.848 0.000 0.152 0.000
#> GSM35489 2 0.2648 0.8696 0.000 0.848 0.000 0.152 0.000
#> GSM35492 1 0.0000 0.9446 1.000 0.000 0.000 0.000 0.000
#> GSM35495 5 0.4307 -0.2764 0.000 0.000 0.500 0.000 0.500
#> GSM35499 2 0.0000 0.8786 0.000 1.000 0.000 0.000 0.000
#> GSM35502 1 0.0000 0.9446 1.000 0.000 0.000 0.000 0.000
#> GSM35505 5 0.1399 0.7014 0.020 0.000 0.028 0.000 0.952
#> GSM35507 1 0.2723 0.9136 0.864 0.000 0.012 0.124 0.000
#> GSM35510 2 0.0000 0.8786 0.000 1.000 0.000 0.000 0.000
#> GSM35514 1 0.0000 0.9446 1.000 0.000 0.000 0.000 0.000
#> GSM35517 2 0.2561 0.8709 0.000 0.856 0.000 0.144 0.000
#> GSM35520 5 0.2642 0.7014 0.004 0.024 0.084 0.000 0.888
#> GSM35523 1 0.2881 0.9112 0.860 0.004 0.012 0.124 0.000
#> GSM35529 2 0.0000 0.8786 0.000 1.000 0.000 0.000 0.000
#> GSM35531 2 0.2648 0.8696 0.000 0.848 0.000 0.152 0.000
#> GSM35534 2 0.2648 0.8696 0.000 0.848 0.000 0.152 0.000
#> GSM35536 1 0.0000 0.9446 1.000 0.000 0.000 0.000 0.000
#> GSM35538 1 0.2011 0.9312 0.908 0.000 0.004 0.088 0.000
#> GSM35539 1 0.2011 0.9312 0.908 0.000 0.004 0.088 0.000
#> GSM35540 2 0.0000 0.8786 0.000 1.000 0.000 0.000 0.000
#> GSM35541 2 0.2648 0.8696 0.000 0.848 0.000 0.152 0.000
#> GSM35442 1 0.0290 0.9413 0.992 0.000 0.008 0.000 0.000
#> GSM35447 5 0.1106 0.7089 0.012 0.000 0.024 0.000 0.964
#> GSM35450 1 0.2011 0.9312 0.908 0.000 0.004 0.088 0.000
#> GSM35453 1 0.0290 0.9413 0.992 0.000 0.008 0.000 0.000
#> GSM35456 1 0.2723 0.9136 0.864 0.000 0.012 0.124 0.000
#> GSM35464 1 0.2833 0.9136 0.864 0.004 0.012 0.120 0.000
#> GSM35467 1 0.0000 0.9446 1.000 0.000 0.000 0.000 0.000
#> GSM35470 1 0.2139 0.8894 0.916 0.000 0.052 0.000 0.032
#> GSM35479 3 0.4322 0.5663 0.088 0.000 0.768 0.000 0.144
#> GSM35484 1 0.1792 0.9335 0.916 0.000 0.000 0.084 0.000
#> GSM35488 1 0.0000 0.9446 1.000 0.000 0.000 0.000 0.000
#> GSM35491 1 0.0000 0.9446 1.000 0.000 0.000 0.000 0.000
#> GSM35494 3 0.4322 0.5663 0.088 0.000 0.768 0.000 0.144
#> GSM35498 1 0.2723 0.9136 0.864 0.000 0.012 0.124 0.000
#> GSM35501 1 0.0000 0.9446 1.000 0.000 0.000 0.000 0.000
#> GSM35509 3 0.4201 0.3190 0.000 0.000 0.592 0.000 0.408
#> GSM35513 1 0.0000 0.9446 1.000 0.000 0.000 0.000 0.000
#> GSM35516 2 0.3461 0.8039 0.004 0.772 0.000 0.224 0.000
#> GSM35522 1 0.2881 0.9112 0.860 0.004 0.012 0.124 0.000
#> GSM35525 1 0.0000 0.9446 1.000 0.000 0.000 0.000 0.000
#> GSM35528 1 0.2011 0.9312 0.908 0.000 0.004 0.088 0.000
#> GSM35533 1 0.1792 0.9335 0.916 0.000 0.000 0.084 0.000
#> GSM35537 1 0.2139 0.8894 0.916 0.000 0.052 0.000 0.032
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM35441 2 0.0000 0.879 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM35446 4 0.1334 0.738 0.000 0.000 0.032 0.948 0.020 0.000
#> GSM35449 2 0.0000 0.879 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM35455 2 0.0000 0.879 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM35458 5 0.0000 0.846 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM35460 4 0.1334 0.738 0.000 0.000 0.032 0.948 0.020 0.000
#> GSM35461 5 0.4256 0.194 0.016 0.000 0.464 0.000 0.520 0.000
#> GSM35463 2 0.2378 0.870 0.000 0.848 0.000 0.000 0.000 0.152
#> GSM35472 5 0.2053 0.872 0.000 0.000 0.108 0.004 0.888 0.000
#> GSM35475 5 0.0000 0.846 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM35483 2 0.5257 0.684 0.000 0.668 0.000 0.028 0.160 0.144
#> GSM35496 3 0.0260 0.746 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM35497 2 0.0000 0.879 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM35504 2 0.5766 0.211 0.000 0.620 0.000 0.172 0.044 0.164
#> GSM35508 6 0.4313 1.000 0.000 0.148 0.000 0.124 0.000 0.728
#> GSM35511 4 0.3893 0.693 0.000 0.000 0.000 0.768 0.092 0.140
#> GSM35512 5 0.2053 0.872 0.000 0.000 0.108 0.004 0.888 0.000
#> GSM35515 5 0.0000 0.846 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM35519 5 0.2053 0.872 0.000 0.000 0.108 0.004 0.888 0.000
#> GSM35527 6 0.4313 1.000 0.000 0.148 0.000 0.124 0.000 0.728
#> GSM35532 4 0.3893 0.693 0.000 0.000 0.000 0.768 0.092 0.140
#> GSM35439 2 0.2378 0.870 0.000 0.848 0.000 0.000 0.000 0.152
#> GSM35443 1 0.1643 0.926 0.924 0.000 0.068 0.008 0.000 0.000
#> GSM35445 1 0.1643 0.926 0.924 0.000 0.068 0.008 0.000 0.000
#> GSM35448 4 0.3670 0.509 0.000 0.000 0.012 0.704 0.284 0.000
#> GSM35451 1 0.1307 0.912 0.952 0.000 0.008 0.008 0.000 0.032
#> GSM35454 5 0.2784 0.855 0.008 0.000 0.132 0.012 0.848 0.000
#> GSM35457 2 0.0000 0.879 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM35465 2 0.0000 0.879 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM35468 1 0.1524 0.929 0.932 0.000 0.060 0.008 0.000 0.000
#> GSM35471 1 0.1453 0.909 0.944 0.000 0.008 0.008 0.000 0.040
#> GSM35473 1 0.1524 0.929 0.932 0.000 0.060 0.008 0.000 0.000
#> GSM35477 1 0.1307 0.912 0.952 0.000 0.008 0.008 0.000 0.032
#> GSM35480 1 0.1267 0.929 0.940 0.000 0.060 0.000 0.000 0.000
#> GSM35482 3 0.0260 0.746 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM35485 2 0.2378 0.870 0.000 0.848 0.000 0.000 0.000 0.152
#> GSM35489 2 0.2378 0.870 0.000 0.848 0.000 0.000 0.000 0.152
#> GSM35492 1 0.1524 0.929 0.932 0.000 0.060 0.008 0.000 0.000
#> GSM35495 3 0.6095 0.170 0.000 0.000 0.360 0.360 0.280 0.000
#> GSM35499 2 0.0000 0.879 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM35502 1 0.1524 0.929 0.932 0.000 0.060 0.008 0.000 0.000
#> GSM35505 5 0.2784 0.855 0.008 0.000 0.132 0.012 0.848 0.000
#> GSM35507 1 0.2656 0.862 0.860 0.000 0.008 0.012 0.000 0.120
#> GSM35510 2 0.0000 0.879 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM35514 1 0.1524 0.929 0.932 0.000 0.060 0.008 0.000 0.000
#> GSM35517 2 0.2300 0.871 0.000 0.856 0.000 0.000 0.000 0.144
#> GSM35520 5 0.0000 0.846 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM35523 1 0.2798 0.859 0.856 0.004 0.008 0.012 0.000 0.120
#> GSM35529 2 0.0000 0.879 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM35531 2 0.2378 0.870 0.000 0.848 0.000 0.000 0.000 0.152
#> GSM35534 2 0.2378 0.870 0.000 0.848 0.000 0.000 0.000 0.152
#> GSM35536 1 0.1524 0.929 0.932 0.000 0.060 0.008 0.000 0.000
#> GSM35538 1 0.1149 0.914 0.960 0.000 0.008 0.008 0.000 0.024
#> GSM35539 1 0.1149 0.914 0.960 0.000 0.008 0.008 0.000 0.024
#> GSM35540 2 0.0000 0.879 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM35541 2 0.2378 0.870 0.000 0.848 0.000 0.000 0.000 0.152
#> GSM35442 1 0.1643 0.926 0.924 0.000 0.068 0.008 0.000 0.000
#> GSM35447 5 0.2489 0.862 0.000 0.000 0.128 0.012 0.860 0.000
#> GSM35450 1 0.1149 0.914 0.960 0.000 0.008 0.008 0.000 0.024
#> GSM35453 1 0.1643 0.926 0.924 0.000 0.068 0.008 0.000 0.000
#> GSM35456 1 0.2656 0.862 0.860 0.000 0.008 0.012 0.000 0.120
#> GSM35464 1 0.2687 0.862 0.860 0.004 0.004 0.012 0.000 0.120
#> GSM35467 1 0.1524 0.929 0.932 0.000 0.060 0.008 0.000 0.000
#> GSM35470 1 0.2558 0.877 0.840 0.000 0.156 0.004 0.000 0.000
#> GSM35479 3 0.0260 0.746 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM35484 1 0.0993 0.917 0.964 0.000 0.000 0.012 0.000 0.024
#> GSM35488 1 0.1267 0.929 0.940 0.000 0.060 0.000 0.000 0.000
#> GSM35491 1 0.1524 0.929 0.932 0.000 0.060 0.008 0.000 0.000
#> GSM35494 3 0.0260 0.746 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM35498 1 0.2656 0.862 0.860 0.000 0.008 0.012 0.000 0.120
#> GSM35501 1 0.1524 0.929 0.932 0.000 0.060 0.008 0.000 0.000
#> GSM35509 3 0.5705 0.378 0.000 0.000 0.516 0.204 0.280 0.000
#> GSM35513 1 0.1524 0.929 0.932 0.000 0.060 0.008 0.000 0.000
#> GSM35516 2 0.3812 0.804 0.056 0.772 0.000 0.004 0.000 0.168
#> GSM35522 1 0.2798 0.859 0.856 0.004 0.008 0.012 0.000 0.120
#> GSM35525 1 0.1267 0.929 0.940 0.000 0.060 0.000 0.000 0.000
#> GSM35528 1 0.1149 0.914 0.960 0.000 0.008 0.008 0.000 0.024
#> GSM35533 1 0.0993 0.917 0.964 0.000 0.000 0.012 0.000 0.024
#> GSM35537 1 0.2558 0.877 0.840 0.000 0.156 0.004 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n time(p) k
#> ATC:hclust 70 1.24e-07 2
#> ATC:hclust 79 2.39e-06 3
#> ATC:hclust 69 5.91e-06 4
#> ATC:hclust 70 1.74e-05 5
#> ATC:hclust 75 6.20e-06 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "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 7758 rows and 79 columns.
#> Top rows (776, 1552, 2328, 3103, 3879) 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 0.955 0.973 0.5031 0.494 0.494
#> 3 3 0.833 0.936 0.949 0.3139 0.774 0.572
#> 4 4 0.746 0.681 0.835 0.1117 0.931 0.797
#> 5 5 0.757 0.762 0.822 0.0675 0.882 0.602
#> 6 6 0.820 0.728 0.804 0.0438 0.975 0.879
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
#> GSM35441 2 0.2948 0.955633 0.052 0.948
#> GSM35446 2 0.0672 0.951900 0.008 0.992
#> GSM35449 2 0.2948 0.955633 0.052 0.948
#> GSM35455 2 0.2948 0.955633 0.052 0.948
#> GSM35458 2 0.0672 0.951900 0.008 0.992
#> GSM35460 2 0.0672 0.951900 0.008 0.992
#> GSM35461 1 0.2948 0.950536 0.948 0.052
#> GSM35463 2 0.2948 0.955633 0.052 0.948
#> GSM35472 2 0.0672 0.951900 0.008 0.992
#> GSM35475 2 0.0672 0.951900 0.008 0.992
#> GSM35483 2 0.0000 0.951210 0.000 1.000
#> GSM35496 1 0.2948 0.950536 0.948 0.052
#> GSM35497 2 0.2948 0.955633 0.052 0.948
#> GSM35504 2 0.0000 0.951210 0.000 1.000
#> GSM35508 2 0.0000 0.951210 0.000 1.000
#> GSM35511 2 0.0672 0.951900 0.008 0.992
#> GSM35512 2 0.0672 0.951900 0.008 0.992
#> GSM35515 2 0.0672 0.951900 0.008 0.992
#> GSM35519 2 0.0672 0.951900 0.008 0.992
#> GSM35527 2 0.0000 0.951210 0.000 1.000
#> GSM35532 2 0.0672 0.951900 0.008 0.992
#> GSM35439 2 0.2948 0.955633 0.052 0.948
#> GSM35443 1 0.0000 0.990406 1.000 0.000
#> GSM35445 1 0.0000 0.990406 1.000 0.000
#> GSM35448 2 0.0672 0.951900 0.008 0.992
#> GSM35451 1 0.0672 0.984115 0.992 0.008
#> GSM35454 1 0.0672 0.985164 0.992 0.008
#> GSM35457 2 0.2948 0.955633 0.052 0.948
#> GSM35465 2 0.2948 0.955633 0.052 0.948
#> GSM35468 1 0.0000 0.990406 1.000 0.000
#> GSM35471 1 0.0000 0.990406 1.000 0.000
#> GSM35473 1 0.0000 0.990406 1.000 0.000
#> GSM35477 1 0.0000 0.990406 1.000 0.000
#> GSM35480 1 0.0000 0.990406 1.000 0.000
#> GSM35482 1 0.2948 0.950536 0.948 0.052
#> GSM35485 2 0.2948 0.955633 0.052 0.948
#> GSM35489 2 0.2948 0.955633 0.052 0.948
#> GSM35492 1 0.0000 0.990406 1.000 0.000
#> GSM35495 2 0.3431 0.916883 0.064 0.936
#> GSM35499 2 0.2948 0.955633 0.052 0.948
#> GSM35502 1 0.0000 0.990406 1.000 0.000
#> GSM35505 1 0.2948 0.950536 0.948 0.052
#> GSM35507 1 0.0672 0.984115 0.992 0.008
#> GSM35510 2 0.2948 0.955633 0.052 0.948
#> GSM35514 1 0.0000 0.990406 1.000 0.000
#> GSM35517 2 0.2948 0.955633 0.052 0.948
#> GSM35520 2 0.0000 0.951210 0.000 1.000
#> GSM35523 1 0.0000 0.990406 1.000 0.000
#> GSM35529 2 0.2948 0.955633 0.052 0.948
#> GSM35531 2 0.2948 0.955633 0.052 0.948
#> GSM35534 2 0.2948 0.955633 0.052 0.948
#> GSM35536 1 0.0000 0.990406 1.000 0.000
#> GSM35538 1 0.0000 0.990406 1.000 0.000
#> GSM35539 1 0.0000 0.990406 1.000 0.000
#> GSM35540 2 0.0000 0.951210 0.000 1.000
#> GSM35541 2 0.2948 0.955633 0.052 0.948
#> GSM35442 1 0.0376 0.987920 0.996 0.004
#> GSM35447 2 0.9998 0.000135 0.492 0.508
#> GSM35450 1 0.0000 0.990406 1.000 0.000
#> GSM35453 1 0.0000 0.990406 1.000 0.000
#> GSM35456 1 0.0000 0.990406 1.000 0.000
#> GSM35464 2 0.2948 0.955633 0.052 0.948
#> GSM35467 1 0.0000 0.990406 1.000 0.000
#> GSM35470 1 0.0000 0.990406 1.000 0.000
#> GSM35479 1 0.2948 0.950536 0.948 0.052
#> GSM35484 1 0.0000 0.990406 1.000 0.000
#> GSM35488 1 0.0000 0.990406 1.000 0.000
#> GSM35491 1 0.0000 0.990406 1.000 0.000
#> GSM35494 1 0.2948 0.950536 0.948 0.052
#> GSM35498 1 0.0000 0.990406 1.000 0.000
#> GSM35501 1 0.0000 0.990406 1.000 0.000
#> GSM35509 2 0.6048 0.824308 0.148 0.852
#> GSM35513 1 0.0000 0.990406 1.000 0.000
#> GSM35516 2 0.2948 0.955633 0.052 0.948
#> GSM35522 1 0.0672 0.984115 0.992 0.008
#> GSM35525 1 0.0000 0.990406 1.000 0.000
#> GSM35528 1 0.0000 0.990406 1.000 0.000
#> GSM35533 1 0.0000 0.990406 1.000 0.000
#> GSM35537 1 0.0000 0.990406 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM35441 2 0.0000 0.980 0.000 1.000 0.000
#> GSM35446 3 0.3192 0.918 0.000 0.112 0.888
#> GSM35449 2 0.0000 0.980 0.000 1.000 0.000
#> GSM35455 2 0.0000 0.980 0.000 1.000 0.000
#> GSM35458 3 0.3192 0.918 0.000 0.112 0.888
#> GSM35460 3 0.3192 0.918 0.000 0.112 0.888
#> GSM35461 3 0.4178 0.805 0.172 0.000 0.828
#> GSM35463 2 0.0000 0.980 0.000 1.000 0.000
#> GSM35472 3 0.3116 0.918 0.000 0.108 0.892
#> GSM35475 3 0.3192 0.918 0.000 0.112 0.888
#> GSM35483 2 0.0000 0.980 0.000 1.000 0.000
#> GSM35496 3 0.2066 0.896 0.060 0.000 0.940
#> GSM35497 2 0.0000 0.980 0.000 1.000 0.000
#> GSM35504 2 0.0000 0.980 0.000 1.000 0.000
#> GSM35508 2 0.5058 0.629 0.000 0.756 0.244
#> GSM35511 3 0.3192 0.918 0.000 0.112 0.888
#> GSM35512 3 0.1753 0.914 0.000 0.048 0.952
#> GSM35515 3 0.3192 0.918 0.000 0.112 0.888
#> GSM35519 3 0.3192 0.918 0.000 0.112 0.888
#> GSM35527 2 0.0000 0.980 0.000 1.000 0.000
#> GSM35532 3 0.3192 0.918 0.000 0.112 0.888
#> GSM35439 2 0.0000 0.980 0.000 1.000 0.000
#> GSM35443 1 0.0747 0.964 0.984 0.000 0.016
#> GSM35445 1 0.0747 0.964 0.984 0.000 0.016
#> GSM35448 3 0.3192 0.918 0.000 0.112 0.888
#> GSM35451 1 0.1753 0.946 0.952 0.000 0.048
#> GSM35454 3 0.4235 0.800 0.176 0.000 0.824
#> GSM35457 2 0.0000 0.980 0.000 1.000 0.000
#> GSM35465 2 0.0000 0.980 0.000 1.000 0.000
#> GSM35468 1 0.0747 0.964 0.984 0.000 0.016
#> GSM35471 1 0.2878 0.928 0.904 0.000 0.096
#> GSM35473 1 0.0747 0.964 0.984 0.000 0.016
#> GSM35477 1 0.1753 0.946 0.952 0.000 0.048
#> GSM35480 1 0.0747 0.964 0.984 0.000 0.016
#> GSM35482 3 0.2261 0.893 0.068 0.000 0.932
#> GSM35485 2 0.0000 0.980 0.000 1.000 0.000
#> GSM35489 2 0.0000 0.980 0.000 1.000 0.000
#> GSM35492 1 0.0747 0.964 0.984 0.000 0.016
#> GSM35495 3 0.1753 0.914 0.000 0.048 0.952
#> GSM35499 2 0.0000 0.980 0.000 1.000 0.000
#> GSM35502 1 0.0747 0.964 0.984 0.000 0.016
#> GSM35505 3 0.2066 0.896 0.060 0.000 0.940
#> GSM35507 1 0.7133 0.708 0.712 0.192 0.096
#> GSM35510 2 0.0000 0.980 0.000 1.000 0.000
#> GSM35514 1 0.0747 0.964 0.984 0.000 0.016
#> GSM35517 2 0.0000 0.980 0.000 1.000 0.000
#> GSM35520 3 0.3192 0.918 0.000 0.112 0.888
#> GSM35523 1 0.2878 0.928 0.904 0.000 0.096
#> GSM35529 2 0.0000 0.980 0.000 1.000 0.000
#> GSM35531 2 0.0000 0.980 0.000 1.000 0.000
#> GSM35534 2 0.0000 0.980 0.000 1.000 0.000
#> GSM35536 1 0.0747 0.964 0.984 0.000 0.016
#> GSM35538 1 0.1753 0.946 0.952 0.000 0.048
#> GSM35539 1 0.1753 0.946 0.952 0.000 0.048
#> GSM35540 2 0.0000 0.980 0.000 1.000 0.000
#> GSM35541 2 0.0000 0.980 0.000 1.000 0.000
#> GSM35442 1 0.0747 0.964 0.984 0.000 0.016
#> GSM35447 3 0.1753 0.899 0.048 0.000 0.952
#> GSM35450 1 0.1753 0.946 0.952 0.000 0.048
#> GSM35453 1 0.0747 0.964 0.984 0.000 0.016
#> GSM35456 1 0.2878 0.928 0.904 0.000 0.096
#> GSM35464 2 0.3610 0.869 0.016 0.888 0.096
#> GSM35467 1 0.0747 0.964 0.984 0.000 0.016
#> GSM35470 1 0.1163 0.959 0.972 0.000 0.028
#> GSM35479 3 0.2261 0.893 0.068 0.000 0.932
#> GSM35484 1 0.0424 0.963 0.992 0.000 0.008
#> GSM35488 1 0.0000 0.961 1.000 0.000 0.000
#> GSM35491 1 0.0747 0.964 0.984 0.000 0.016
#> GSM35494 3 0.4346 0.790 0.184 0.000 0.816
#> GSM35498 1 0.2878 0.928 0.904 0.000 0.096
#> GSM35501 1 0.0747 0.964 0.984 0.000 0.016
#> GSM35509 3 0.1753 0.914 0.000 0.048 0.952
#> GSM35513 1 0.0747 0.964 0.984 0.000 0.016
#> GSM35516 2 0.2492 0.917 0.016 0.936 0.048
#> GSM35522 1 0.2878 0.928 0.904 0.000 0.096
#> GSM35525 1 0.0592 0.963 0.988 0.000 0.012
#> GSM35528 1 0.1753 0.946 0.952 0.000 0.048
#> GSM35533 1 0.0892 0.961 0.980 0.000 0.020
#> GSM35537 1 0.2165 0.939 0.936 0.000 0.064
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM35441 2 0.0336 0.905 0.000 0.992 0.000 0.008
#> GSM35446 3 0.1211 0.829 0.000 0.000 0.960 0.040
#> GSM35449 2 0.0000 0.904 0.000 1.000 0.000 0.000
#> GSM35455 2 0.0000 0.904 0.000 1.000 0.000 0.000
#> GSM35458 3 0.1716 0.821 0.000 0.000 0.936 0.064
#> GSM35460 3 0.2408 0.838 0.000 0.000 0.896 0.104
#> GSM35461 3 0.6041 0.735 0.060 0.000 0.608 0.332
#> GSM35463 2 0.3074 0.889 0.000 0.848 0.000 0.152
#> GSM35472 3 0.1637 0.841 0.000 0.000 0.940 0.060
#> GSM35475 3 0.1716 0.821 0.000 0.000 0.936 0.064
#> GSM35483 2 0.6243 0.743 0.000 0.668 0.172 0.160
#> GSM35496 3 0.5349 0.765 0.024 0.000 0.640 0.336
#> GSM35497 2 0.0000 0.904 0.000 1.000 0.000 0.000
#> GSM35504 2 0.1970 0.872 0.000 0.932 0.008 0.060
#> GSM35508 2 0.6532 0.325 0.000 0.548 0.368 0.084
#> GSM35511 3 0.1637 0.823 0.000 0.000 0.940 0.060
#> GSM35512 3 0.2216 0.840 0.000 0.000 0.908 0.092
#> GSM35515 3 0.1716 0.821 0.000 0.000 0.936 0.064
#> GSM35519 3 0.0592 0.834 0.000 0.000 0.984 0.016
#> GSM35527 2 0.2882 0.846 0.000 0.892 0.024 0.084
#> GSM35532 3 0.1474 0.826 0.000 0.000 0.948 0.052
#> GSM35439 2 0.3074 0.889 0.000 0.848 0.000 0.152
#> GSM35443 1 0.0000 0.779 1.000 0.000 0.000 0.000
#> GSM35445 1 0.0000 0.779 1.000 0.000 0.000 0.000
#> GSM35448 3 0.1118 0.831 0.000 0.000 0.964 0.036
#> GSM35451 1 0.4985 -0.434 0.532 0.000 0.000 0.468
#> GSM35454 3 0.6200 0.705 0.064 0.000 0.580 0.356
#> GSM35457 2 0.0000 0.904 0.000 1.000 0.000 0.000
#> GSM35465 2 0.0000 0.904 0.000 1.000 0.000 0.000
#> GSM35468 1 0.0000 0.779 1.000 0.000 0.000 0.000
#> GSM35471 4 0.4961 0.633 0.448 0.000 0.000 0.552
#> GSM35473 1 0.0000 0.779 1.000 0.000 0.000 0.000
#> GSM35477 1 0.4985 -0.434 0.532 0.000 0.000 0.468
#> GSM35480 1 0.0000 0.779 1.000 0.000 0.000 0.000
#> GSM35482 3 0.5565 0.754 0.032 0.000 0.624 0.344
#> GSM35485 2 0.3074 0.889 0.000 0.848 0.000 0.152
#> GSM35489 2 0.3074 0.889 0.000 0.848 0.000 0.152
#> GSM35492 1 0.0000 0.779 1.000 0.000 0.000 0.000
#> GSM35495 3 0.4277 0.801 0.000 0.000 0.720 0.280
#> GSM35499 2 0.2216 0.898 0.000 0.908 0.000 0.092
#> GSM35502 1 0.0000 0.779 1.000 0.000 0.000 0.000
#> GSM35505 3 0.4222 0.804 0.000 0.000 0.728 0.272
#> GSM35507 4 0.6933 0.584 0.300 0.140 0.000 0.560
#> GSM35510 2 0.0000 0.904 0.000 1.000 0.000 0.000
#> GSM35514 1 0.0000 0.779 1.000 0.000 0.000 0.000
#> GSM35517 2 0.1557 0.903 0.000 0.944 0.000 0.056
#> GSM35520 3 0.2413 0.810 0.000 0.020 0.916 0.064
#> GSM35523 4 0.4877 0.674 0.408 0.000 0.000 0.592
#> GSM35529 2 0.0188 0.903 0.000 0.996 0.000 0.004
#> GSM35531 2 0.3074 0.889 0.000 0.848 0.000 0.152
#> GSM35534 2 0.3074 0.889 0.000 0.848 0.000 0.152
#> GSM35536 1 0.0000 0.779 1.000 0.000 0.000 0.000
#> GSM35538 1 0.4888 -0.238 0.588 0.000 0.000 0.412
#> GSM35539 1 0.4888 -0.238 0.588 0.000 0.000 0.412
#> GSM35540 2 0.0000 0.904 0.000 1.000 0.000 0.000
#> GSM35541 2 0.2868 0.893 0.000 0.864 0.000 0.136
#> GSM35442 1 0.2737 0.622 0.888 0.000 0.008 0.104
#> GSM35447 3 0.2216 0.841 0.000 0.000 0.908 0.092
#> GSM35450 1 0.4888 -0.238 0.588 0.000 0.000 0.412
#> GSM35453 1 0.1211 0.727 0.960 0.000 0.000 0.040
#> GSM35456 4 0.4961 0.633 0.448 0.000 0.000 0.552
#> GSM35464 4 0.4941 -0.142 0.000 0.436 0.000 0.564
#> GSM35467 1 0.0000 0.779 1.000 0.000 0.000 0.000
#> GSM35470 1 0.5000 -0.481 0.500 0.000 0.000 0.500
#> GSM35479 3 0.5442 0.763 0.028 0.000 0.636 0.336
#> GSM35484 1 0.0000 0.779 1.000 0.000 0.000 0.000
#> GSM35488 1 0.0000 0.779 1.000 0.000 0.000 0.000
#> GSM35491 1 0.0000 0.779 1.000 0.000 0.000 0.000
#> GSM35494 3 0.6561 0.692 0.092 0.000 0.564 0.344
#> GSM35498 4 0.4898 0.672 0.416 0.000 0.000 0.584
#> GSM35501 1 0.0000 0.779 1.000 0.000 0.000 0.000
#> GSM35509 3 0.4605 0.776 0.000 0.000 0.664 0.336
#> GSM35513 1 0.0000 0.779 1.000 0.000 0.000 0.000
#> GSM35516 2 0.3400 0.873 0.000 0.820 0.000 0.180
#> GSM35522 4 0.5638 0.676 0.388 0.028 0.000 0.584
#> GSM35525 1 0.0000 0.779 1.000 0.000 0.000 0.000
#> GSM35528 1 0.4888 -0.238 0.588 0.000 0.000 0.412
#> GSM35533 1 0.0188 0.774 0.996 0.000 0.000 0.004
#> GSM35537 4 0.4999 0.411 0.492 0.000 0.000 0.508
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM35441 2 0.0290 0.836 0.000 0.992 0.000 0.008 0.000
#> GSM35446 5 0.4762 0.757 0.000 0.000 0.236 0.064 0.700
#> GSM35449 2 0.0000 0.835 0.000 1.000 0.000 0.000 0.000
#> GSM35455 2 0.0000 0.835 0.000 1.000 0.000 0.000 0.000
#> GSM35458 5 0.3632 0.763 0.000 0.004 0.176 0.020 0.800
#> GSM35460 5 0.5245 0.684 0.000 0.000 0.328 0.064 0.608
#> GSM35461 3 0.1408 0.694 0.008 0.000 0.948 0.000 0.044
#> GSM35463 2 0.5317 0.798 0.000 0.688 0.008 0.196 0.108
#> GSM35472 5 0.4425 0.542 0.000 0.000 0.452 0.004 0.544
#> GSM35475 5 0.3456 0.763 0.000 0.000 0.184 0.016 0.800
#> GSM35483 2 0.6597 0.558 0.000 0.484 0.008 0.176 0.332
#> GSM35496 3 0.0981 0.711 0.008 0.000 0.972 0.008 0.012
#> GSM35497 2 0.0000 0.835 0.000 1.000 0.000 0.000 0.000
#> GSM35504 2 0.2992 0.750 0.000 0.868 0.000 0.068 0.064
#> GSM35508 5 0.6156 0.261 0.000 0.376 0.008 0.108 0.508
#> GSM35511 5 0.4373 0.741 0.000 0.000 0.160 0.080 0.760
#> GSM35512 5 0.4425 0.528 0.000 0.000 0.452 0.004 0.544
#> GSM35515 5 0.3632 0.763 0.000 0.004 0.176 0.020 0.800
#> GSM35519 5 0.3728 0.762 0.000 0.000 0.244 0.008 0.748
#> GSM35527 2 0.4406 0.648 0.000 0.764 0.000 0.108 0.128
#> GSM35532 5 0.4201 0.768 0.000 0.000 0.204 0.044 0.752
#> GSM35439 2 0.5481 0.792 0.000 0.672 0.008 0.200 0.120
#> GSM35443 1 0.0162 0.988 0.996 0.000 0.004 0.000 0.000
#> GSM35445 1 0.0162 0.988 0.996 0.000 0.004 0.000 0.000
#> GSM35448 5 0.4398 0.763 0.000 0.000 0.240 0.040 0.720
#> GSM35451 4 0.4227 0.836 0.292 0.000 0.000 0.692 0.016
#> GSM35454 3 0.1280 0.699 0.024 0.000 0.960 0.008 0.008
#> GSM35457 2 0.0000 0.835 0.000 1.000 0.000 0.000 0.000
#> GSM35465 2 0.0324 0.834 0.000 0.992 0.000 0.004 0.004
#> GSM35468 1 0.0000 0.990 1.000 0.000 0.000 0.000 0.000
#> GSM35471 4 0.4799 0.843 0.228 0.000 0.060 0.708 0.004
#> GSM35473 1 0.0000 0.990 1.000 0.000 0.000 0.000 0.000
#> GSM35477 4 0.4227 0.836 0.292 0.000 0.000 0.692 0.016
#> GSM35480 1 0.0290 0.985 0.992 0.000 0.008 0.000 0.000
#> GSM35482 3 0.0981 0.711 0.008 0.000 0.972 0.008 0.012
#> GSM35485 2 0.5481 0.792 0.000 0.672 0.008 0.200 0.120
#> GSM35489 2 0.5317 0.798 0.000 0.688 0.008 0.196 0.108
#> GSM35492 1 0.0000 0.990 1.000 0.000 0.000 0.000 0.000
#> GSM35495 3 0.2179 0.614 0.000 0.000 0.896 0.004 0.100
#> GSM35499 2 0.3341 0.830 0.000 0.840 0.008 0.128 0.024
#> GSM35502 1 0.0000 0.990 1.000 0.000 0.000 0.000 0.000
#> GSM35505 3 0.2877 0.554 0.004 0.000 0.848 0.004 0.144
#> GSM35507 4 0.5567 0.766 0.128 0.084 0.060 0.724 0.004
#> GSM35510 2 0.0000 0.835 0.000 1.000 0.000 0.000 0.000
#> GSM35514 1 0.0000 0.990 1.000 0.000 0.000 0.000 0.000
#> GSM35517 2 0.2597 0.835 0.000 0.884 0.000 0.092 0.024
#> GSM35520 5 0.3943 0.750 0.000 0.028 0.156 0.016 0.800
#> GSM35523 4 0.5391 0.789 0.164 0.000 0.140 0.688 0.008
#> GSM35529 2 0.0404 0.831 0.000 0.988 0.000 0.012 0.000
#> GSM35531 2 0.5568 0.786 0.000 0.660 0.008 0.212 0.120
#> GSM35534 2 0.5481 0.792 0.000 0.672 0.008 0.200 0.120
#> GSM35536 1 0.0000 0.990 1.000 0.000 0.000 0.000 0.000
#> GSM35538 4 0.4822 0.801 0.344 0.000 0.008 0.628 0.020
#> GSM35539 4 0.4920 0.795 0.348 0.000 0.008 0.620 0.024
#> GSM35540 2 0.0566 0.831 0.000 0.984 0.000 0.012 0.004
#> GSM35541 2 0.5008 0.807 0.000 0.724 0.008 0.160 0.108
#> GSM35442 1 0.1341 0.921 0.944 0.000 0.056 0.000 0.000
#> GSM35447 3 0.4562 -0.491 0.000 0.000 0.496 0.008 0.496
#> GSM35450 4 0.4822 0.801 0.344 0.000 0.008 0.628 0.020
#> GSM35453 1 0.0703 0.962 0.976 0.000 0.024 0.000 0.000
#> GSM35456 4 0.4799 0.842 0.228 0.000 0.060 0.708 0.004
#> GSM35464 4 0.3010 0.543 0.000 0.172 0.000 0.824 0.004
#> GSM35467 1 0.0000 0.990 1.000 0.000 0.000 0.000 0.000
#> GSM35470 3 0.7012 -0.297 0.288 0.000 0.388 0.316 0.008
#> GSM35479 3 0.0981 0.711 0.008 0.000 0.972 0.008 0.012
#> GSM35484 1 0.0162 0.988 0.996 0.000 0.004 0.000 0.000
#> GSM35488 1 0.0162 0.987 0.996 0.000 0.000 0.000 0.004
#> GSM35491 1 0.0000 0.990 1.000 0.000 0.000 0.000 0.000
#> GSM35494 3 0.0740 0.709 0.008 0.000 0.980 0.008 0.004
#> GSM35498 4 0.5063 0.801 0.164 0.000 0.120 0.712 0.004
#> GSM35501 1 0.0000 0.990 1.000 0.000 0.000 0.000 0.000
#> GSM35509 3 0.0898 0.706 0.000 0.000 0.972 0.008 0.020
#> GSM35513 1 0.0000 0.990 1.000 0.000 0.000 0.000 0.000
#> GSM35516 2 0.5666 0.772 0.000 0.640 0.008 0.240 0.112
#> GSM35522 4 0.5644 0.785 0.140 0.028 0.116 0.708 0.008
#> GSM35525 1 0.0740 0.974 0.980 0.000 0.008 0.004 0.008
#> GSM35528 4 0.4905 0.800 0.344 0.000 0.008 0.624 0.024
#> GSM35533 1 0.0566 0.980 0.984 0.000 0.012 0.000 0.004
#> GSM35537 3 0.6955 -0.341 0.248 0.000 0.388 0.356 0.008
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM35441 2 0.3961 0.389 0.000 0.556 0.000 0.004 0.000 0.440
#> GSM35446 5 0.3831 0.796 0.000 0.000 0.044 0.028 0.796 0.132
#> GSM35449 2 0.3975 0.374 0.000 0.544 0.000 0.004 0.000 0.452
#> GSM35455 2 0.3971 0.382 0.000 0.548 0.000 0.004 0.000 0.448
#> GSM35458 5 0.3111 0.809 0.000 0.016 0.040 0.020 0.868 0.056
#> GSM35460 5 0.5385 0.725 0.000 0.000 0.168 0.036 0.660 0.136
#> GSM35461 3 0.2563 0.773 0.000 0.000 0.880 0.004 0.076 0.040
#> GSM35463 2 0.0725 0.547 0.000 0.976 0.000 0.012 0.000 0.012
#> GSM35472 5 0.3714 0.681 0.000 0.000 0.264 0.008 0.720 0.008
#> GSM35475 5 0.1988 0.822 0.000 0.016 0.040 0.004 0.924 0.016
#> GSM35483 2 0.3613 0.254 0.000 0.772 0.000 0.008 0.196 0.024
#> GSM35496 3 0.0748 0.818 0.000 0.000 0.976 0.004 0.016 0.004
#> GSM35497 2 0.3971 0.382 0.000 0.548 0.000 0.004 0.000 0.448
#> GSM35504 6 0.4170 0.357 0.000 0.328 0.000 0.020 0.004 0.648
#> GSM35508 6 0.4929 0.443 0.000 0.040 0.004 0.032 0.260 0.664
#> GSM35511 5 0.3129 0.775 0.000 0.000 0.004 0.024 0.820 0.152
#> GSM35512 5 0.3644 0.694 0.000 0.000 0.252 0.008 0.732 0.008
#> GSM35515 5 0.3111 0.809 0.000 0.016 0.040 0.020 0.868 0.056
#> GSM35519 5 0.1644 0.825 0.000 0.012 0.052 0.000 0.932 0.004
#> GSM35527 6 0.4519 0.560 0.000 0.248 0.004 0.028 0.024 0.696
#> GSM35532 5 0.3399 0.794 0.000 0.000 0.024 0.024 0.820 0.132
#> GSM35439 2 0.0622 0.543 0.000 0.980 0.000 0.008 0.012 0.000
#> GSM35443 1 0.1788 0.940 0.916 0.000 0.004 0.004 0.000 0.076
#> GSM35445 1 0.1588 0.943 0.924 0.000 0.004 0.000 0.000 0.072
#> GSM35448 5 0.3784 0.805 0.000 0.000 0.048 0.036 0.808 0.108
#> GSM35451 4 0.3092 0.927 0.104 0.000 0.000 0.836 0.000 0.060
#> GSM35454 3 0.2118 0.800 0.004 0.000 0.916 0.012 0.020 0.048
#> GSM35457 2 0.3971 0.382 0.000 0.548 0.000 0.004 0.000 0.448
#> GSM35465 2 0.3975 0.378 0.000 0.544 0.000 0.004 0.000 0.452
#> GSM35468 1 0.0000 0.961 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35471 4 0.2020 0.928 0.096 0.000 0.008 0.896 0.000 0.000
#> GSM35473 1 0.0363 0.961 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM35477 4 0.3092 0.927 0.104 0.000 0.000 0.836 0.000 0.060
#> GSM35480 1 0.1049 0.957 0.960 0.000 0.008 0.000 0.000 0.032
#> GSM35482 3 0.0622 0.819 0.000 0.000 0.980 0.008 0.012 0.000
#> GSM35485 2 0.0622 0.543 0.000 0.980 0.000 0.008 0.012 0.000
#> GSM35489 2 0.0260 0.547 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM35492 1 0.1285 0.951 0.944 0.000 0.004 0.000 0.000 0.052
#> GSM35495 3 0.2170 0.786 0.000 0.000 0.908 0.016 0.060 0.016
#> GSM35499 2 0.3690 0.462 0.000 0.684 0.000 0.008 0.000 0.308
#> GSM35502 1 0.0363 0.961 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM35505 3 0.4590 0.467 0.000 0.000 0.668 0.012 0.272 0.048
#> GSM35507 4 0.2844 0.905 0.060 0.028 0.008 0.880 0.000 0.024
#> GSM35510 2 0.3971 0.382 0.000 0.548 0.000 0.004 0.000 0.448
#> GSM35514 1 0.0363 0.961 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM35517 2 0.3288 0.478 0.000 0.724 0.000 0.000 0.000 0.276
#> GSM35520 5 0.1921 0.819 0.000 0.032 0.024 0.004 0.928 0.012
#> GSM35523 4 0.3682 0.894 0.080 0.000 0.028 0.824 0.004 0.064
#> GSM35529 2 0.3982 0.355 0.000 0.536 0.000 0.004 0.000 0.460
#> GSM35531 2 0.1078 0.531 0.000 0.964 0.000 0.016 0.008 0.012
#> GSM35534 2 0.0622 0.543 0.000 0.980 0.000 0.008 0.012 0.000
#> GSM35536 1 0.0146 0.961 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM35538 4 0.3469 0.918 0.120 0.000 0.004 0.812 0.000 0.064
#> GSM35539 4 0.3883 0.912 0.120 0.000 0.008 0.792 0.004 0.076
#> GSM35540 2 0.4120 0.327 0.000 0.524 0.000 0.004 0.004 0.468
#> GSM35541 2 0.0632 0.548 0.000 0.976 0.000 0.000 0.000 0.024
#> GSM35442 1 0.2685 0.906 0.872 0.000 0.044 0.004 0.000 0.080
#> GSM35447 5 0.4022 0.614 0.000 0.000 0.288 0.008 0.688 0.016
#> GSM35450 4 0.3469 0.918 0.120 0.000 0.004 0.812 0.000 0.064
#> GSM35453 1 0.1148 0.953 0.960 0.000 0.016 0.004 0.000 0.020
#> GSM35456 4 0.2555 0.925 0.096 0.000 0.008 0.876 0.000 0.020
#> GSM35464 4 0.2436 0.826 0.000 0.088 0.000 0.880 0.000 0.032
#> GSM35467 1 0.0363 0.961 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM35470 3 0.6858 0.327 0.168 0.000 0.512 0.212 0.004 0.104
#> GSM35479 3 0.0964 0.817 0.000 0.000 0.968 0.016 0.012 0.004
#> GSM35484 1 0.1949 0.934 0.904 0.000 0.004 0.004 0.000 0.088
#> GSM35488 1 0.0777 0.956 0.972 0.000 0.004 0.000 0.000 0.024
#> GSM35491 1 0.1285 0.951 0.944 0.000 0.004 0.000 0.000 0.052
#> GSM35494 3 0.0622 0.819 0.000 0.000 0.980 0.008 0.012 0.000
#> GSM35498 4 0.2595 0.922 0.084 0.000 0.016 0.880 0.000 0.020
#> GSM35501 1 0.0363 0.961 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM35509 3 0.1167 0.817 0.000 0.000 0.960 0.020 0.012 0.008
#> GSM35513 1 0.0363 0.961 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM35516 2 0.2199 0.451 0.000 0.892 0.000 0.088 0.000 0.020
#> GSM35522 4 0.3615 0.894 0.072 0.004 0.020 0.832 0.004 0.068
#> GSM35525 1 0.1554 0.941 0.940 0.000 0.008 0.004 0.004 0.044
#> GSM35528 4 0.3731 0.917 0.116 0.000 0.004 0.800 0.004 0.076
#> GSM35533 1 0.2261 0.923 0.884 0.000 0.004 0.008 0.000 0.104
#> GSM35537 3 0.6730 0.277 0.128 0.000 0.508 0.264 0.004 0.096
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 time(p) k
#> ATC:kmeans 78 2.73e-06 2
#> ATC:kmeans 79 9.57e-06 3
#> ATC:kmeans 69 2.16e-04 4
#> ATC:kmeans 75 2.03e-06 5
#> ATC:kmeans 61 1.20e-05 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "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 7758 rows and 79 columns.
#> Top rows (776, 1552, 2328, 3103, 3879) 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 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 0.990 0.996 0.5066 0.494 0.494
#> 3 3 0.982 0.960 0.983 0.3098 0.756 0.544
#> 4 4 0.947 0.955 0.970 0.1257 0.903 0.715
#> 5 5 0.965 0.920 0.961 0.0625 0.932 0.741
#> 6 6 0.911 0.902 0.919 0.0408 0.954 0.776
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
#> GSM35441 2 0.000 0.991 0.000 1.000
#> GSM35446 2 0.000 0.991 0.000 1.000
#> GSM35449 2 0.000 0.991 0.000 1.000
#> GSM35455 2 0.000 0.991 0.000 1.000
#> GSM35458 2 0.000 0.991 0.000 1.000
#> GSM35460 2 0.000 0.991 0.000 1.000
#> GSM35461 1 0.000 1.000 1.000 0.000
#> GSM35463 2 0.000 0.991 0.000 1.000
#> GSM35472 2 0.000 0.991 0.000 1.000
#> GSM35475 2 0.000 0.991 0.000 1.000
#> GSM35483 2 0.000 0.991 0.000 1.000
#> GSM35496 1 0.000 1.000 1.000 0.000
#> GSM35497 2 0.000 0.991 0.000 1.000
#> GSM35504 2 0.000 0.991 0.000 1.000
#> GSM35508 2 0.000 0.991 0.000 1.000
#> GSM35511 2 0.000 0.991 0.000 1.000
#> GSM35512 2 0.000 0.991 0.000 1.000
#> GSM35515 2 0.000 0.991 0.000 1.000
#> GSM35519 2 0.000 0.991 0.000 1.000
#> GSM35527 2 0.000 0.991 0.000 1.000
#> GSM35532 2 0.000 0.991 0.000 1.000
#> GSM35439 2 0.000 0.991 0.000 1.000
#> GSM35443 1 0.000 1.000 1.000 0.000
#> GSM35445 1 0.000 1.000 1.000 0.000
#> GSM35448 2 0.000 0.991 0.000 1.000
#> GSM35451 1 0.000 1.000 1.000 0.000
#> GSM35454 1 0.000 1.000 1.000 0.000
#> GSM35457 2 0.000 0.991 0.000 1.000
#> GSM35465 2 0.000 0.991 0.000 1.000
#> GSM35468 1 0.000 1.000 1.000 0.000
#> GSM35471 1 0.000 1.000 1.000 0.000
#> GSM35473 1 0.000 1.000 1.000 0.000
#> GSM35477 1 0.000 1.000 1.000 0.000
#> GSM35480 1 0.000 1.000 1.000 0.000
#> GSM35482 1 0.000 1.000 1.000 0.000
#> GSM35485 2 0.000 0.991 0.000 1.000
#> GSM35489 2 0.000 0.991 0.000 1.000
#> GSM35492 1 0.000 1.000 1.000 0.000
#> GSM35495 2 0.000 0.991 0.000 1.000
#> GSM35499 2 0.000 0.991 0.000 1.000
#> GSM35502 1 0.000 1.000 1.000 0.000
#> GSM35505 1 0.000 1.000 1.000 0.000
#> GSM35507 1 0.000 1.000 1.000 0.000
#> GSM35510 2 0.000 0.991 0.000 1.000
#> GSM35514 1 0.000 1.000 1.000 0.000
#> GSM35517 2 0.000 0.991 0.000 1.000
#> GSM35520 2 0.000 0.991 0.000 1.000
#> GSM35523 1 0.000 1.000 1.000 0.000
#> GSM35529 2 0.000 0.991 0.000 1.000
#> GSM35531 2 0.000 0.991 0.000 1.000
#> GSM35534 2 0.000 0.991 0.000 1.000
#> GSM35536 1 0.000 1.000 1.000 0.000
#> GSM35538 1 0.000 1.000 1.000 0.000
#> GSM35539 1 0.000 1.000 1.000 0.000
#> GSM35540 2 0.000 0.991 0.000 1.000
#> GSM35541 2 0.000 0.991 0.000 1.000
#> GSM35442 1 0.000 1.000 1.000 0.000
#> GSM35447 2 0.827 0.651 0.260 0.740
#> GSM35450 1 0.000 1.000 1.000 0.000
#> GSM35453 1 0.000 1.000 1.000 0.000
#> GSM35456 1 0.000 1.000 1.000 0.000
#> GSM35464 2 0.000 0.991 0.000 1.000
#> GSM35467 1 0.000 1.000 1.000 0.000
#> GSM35470 1 0.000 1.000 1.000 0.000
#> GSM35479 1 0.000 1.000 1.000 0.000
#> GSM35484 1 0.000 1.000 1.000 0.000
#> GSM35488 1 0.000 1.000 1.000 0.000
#> GSM35491 1 0.000 1.000 1.000 0.000
#> GSM35494 1 0.000 1.000 1.000 0.000
#> GSM35498 1 0.000 1.000 1.000 0.000
#> GSM35501 1 0.000 1.000 1.000 0.000
#> GSM35509 2 0.430 0.900 0.088 0.912
#> GSM35513 1 0.000 1.000 1.000 0.000
#> GSM35516 2 0.000 0.991 0.000 1.000
#> GSM35522 1 0.000 1.000 1.000 0.000
#> GSM35525 1 0.000 1.000 1.000 0.000
#> GSM35528 1 0.000 1.000 1.000 0.000
#> GSM35533 1 0.000 1.000 1.000 0.000
#> GSM35537 1 0.000 1.000 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM35441 2 0.0000 0.969 0.000 1.000 0.000
#> GSM35446 3 0.0000 0.967 0.000 0.000 1.000
#> GSM35449 2 0.0000 0.969 0.000 1.000 0.000
#> GSM35455 2 0.0000 0.969 0.000 1.000 0.000
#> GSM35458 3 0.0000 0.967 0.000 0.000 1.000
#> GSM35460 3 0.0000 0.967 0.000 0.000 1.000
#> GSM35461 3 0.4399 0.788 0.188 0.000 0.812
#> GSM35463 2 0.0000 0.969 0.000 1.000 0.000
#> GSM35472 3 0.0000 0.967 0.000 0.000 1.000
#> GSM35475 3 0.0000 0.967 0.000 0.000 1.000
#> GSM35483 2 0.0000 0.969 0.000 1.000 0.000
#> GSM35496 3 0.0000 0.967 0.000 0.000 1.000
#> GSM35497 2 0.0000 0.969 0.000 1.000 0.000
#> GSM35504 2 0.0000 0.969 0.000 1.000 0.000
#> GSM35508 2 0.5465 0.574 0.000 0.712 0.288
#> GSM35511 3 0.0000 0.967 0.000 0.000 1.000
#> GSM35512 3 0.0000 0.967 0.000 0.000 1.000
#> GSM35515 3 0.0000 0.967 0.000 0.000 1.000
#> GSM35519 3 0.0000 0.967 0.000 0.000 1.000
#> GSM35527 2 0.0000 0.969 0.000 1.000 0.000
#> GSM35532 3 0.0000 0.967 0.000 0.000 1.000
#> GSM35439 2 0.0000 0.969 0.000 1.000 0.000
#> GSM35443 1 0.0000 0.998 1.000 0.000 0.000
#> GSM35445 1 0.0000 0.998 1.000 0.000 0.000
#> GSM35448 3 0.0000 0.967 0.000 0.000 1.000
#> GSM35451 1 0.0000 0.998 1.000 0.000 0.000
#> GSM35454 3 0.4555 0.773 0.200 0.000 0.800
#> GSM35457 2 0.0000 0.969 0.000 1.000 0.000
#> GSM35465 2 0.0000 0.969 0.000 1.000 0.000
#> GSM35468 1 0.0000 0.998 1.000 0.000 0.000
#> GSM35471 1 0.0000 0.998 1.000 0.000 0.000
#> GSM35473 1 0.0000 0.998 1.000 0.000 0.000
#> GSM35477 1 0.0000 0.998 1.000 0.000 0.000
#> GSM35480 1 0.0000 0.998 1.000 0.000 0.000
#> GSM35482 3 0.0592 0.958 0.012 0.000 0.988
#> GSM35485 2 0.0000 0.969 0.000 1.000 0.000
#> GSM35489 2 0.0000 0.969 0.000 1.000 0.000
#> GSM35492 1 0.0000 0.998 1.000 0.000 0.000
#> GSM35495 3 0.0000 0.967 0.000 0.000 1.000
#> GSM35499 2 0.0000 0.969 0.000 1.000 0.000
#> GSM35502 1 0.0000 0.998 1.000 0.000 0.000
#> GSM35505 3 0.0000 0.967 0.000 0.000 1.000
#> GSM35507 2 0.6079 0.357 0.388 0.612 0.000
#> GSM35510 2 0.0000 0.969 0.000 1.000 0.000
#> GSM35514 1 0.0000 0.998 1.000 0.000 0.000
#> GSM35517 2 0.0000 0.969 0.000 1.000 0.000
#> GSM35520 3 0.0592 0.958 0.000 0.012 0.988
#> GSM35523 1 0.0000 0.998 1.000 0.000 0.000
#> GSM35529 2 0.0000 0.969 0.000 1.000 0.000
#> GSM35531 2 0.0000 0.969 0.000 1.000 0.000
#> GSM35534 2 0.0000 0.969 0.000 1.000 0.000
#> GSM35536 1 0.0000 0.998 1.000 0.000 0.000
#> GSM35538 1 0.0000 0.998 1.000 0.000 0.000
#> GSM35539 1 0.0000 0.998 1.000 0.000 0.000
#> GSM35540 2 0.0000 0.969 0.000 1.000 0.000
#> GSM35541 2 0.0000 0.969 0.000 1.000 0.000
#> GSM35442 1 0.0000 0.998 1.000 0.000 0.000
#> GSM35447 3 0.0000 0.967 0.000 0.000 1.000
#> GSM35450 1 0.0000 0.998 1.000 0.000 0.000
#> GSM35453 1 0.0000 0.998 1.000 0.000 0.000
#> GSM35456 1 0.0000 0.998 1.000 0.000 0.000
#> GSM35464 2 0.0000 0.969 0.000 1.000 0.000
#> GSM35467 1 0.0000 0.998 1.000 0.000 0.000
#> GSM35470 1 0.0000 0.998 1.000 0.000 0.000
#> GSM35479 3 0.0000 0.967 0.000 0.000 1.000
#> GSM35484 1 0.0000 0.998 1.000 0.000 0.000
#> GSM35488 1 0.0000 0.998 1.000 0.000 0.000
#> GSM35491 1 0.0000 0.998 1.000 0.000 0.000
#> GSM35494 3 0.4555 0.773 0.200 0.000 0.800
#> GSM35498 1 0.0000 0.998 1.000 0.000 0.000
#> GSM35501 1 0.0000 0.998 1.000 0.000 0.000
#> GSM35509 3 0.0000 0.967 0.000 0.000 1.000
#> GSM35513 1 0.0000 0.998 1.000 0.000 0.000
#> GSM35516 2 0.0000 0.969 0.000 1.000 0.000
#> GSM35522 1 0.1643 0.952 0.956 0.044 0.000
#> GSM35525 1 0.0000 0.998 1.000 0.000 0.000
#> GSM35528 1 0.0000 0.998 1.000 0.000 0.000
#> GSM35533 1 0.0000 0.998 1.000 0.000 0.000
#> GSM35537 1 0.0000 0.998 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM35441 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM35446 3 0.0000 0.922 0.000 0.000 1.000 0.000
#> GSM35449 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM35455 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM35458 3 0.0000 0.922 0.000 0.000 1.000 0.000
#> GSM35460 3 0.0000 0.922 0.000 0.000 1.000 0.000
#> GSM35461 3 0.4540 0.804 0.196 0.000 0.772 0.032
#> GSM35463 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM35472 3 0.0000 0.922 0.000 0.000 1.000 0.000
#> GSM35475 3 0.0000 0.922 0.000 0.000 1.000 0.000
#> GSM35483 2 0.0336 0.981 0.000 0.992 0.008 0.000
#> GSM35496 3 0.4375 0.820 0.180 0.000 0.788 0.032
#> GSM35497 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM35504 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM35508 2 0.3907 0.701 0.000 0.768 0.232 0.000
#> GSM35511 3 0.0000 0.922 0.000 0.000 1.000 0.000
#> GSM35512 3 0.0000 0.922 0.000 0.000 1.000 0.000
#> GSM35515 3 0.0000 0.922 0.000 0.000 1.000 0.000
#> GSM35519 3 0.0000 0.922 0.000 0.000 1.000 0.000
#> GSM35527 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM35532 3 0.0000 0.922 0.000 0.000 1.000 0.000
#> GSM35439 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM35443 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM35445 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM35448 3 0.0000 0.922 0.000 0.000 1.000 0.000
#> GSM35451 4 0.1022 0.995 0.032 0.000 0.000 0.968
#> GSM35454 3 0.4540 0.804 0.196 0.000 0.772 0.032
#> GSM35457 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM35465 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM35468 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM35471 4 0.1022 0.995 0.032 0.000 0.000 0.968
#> GSM35473 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM35477 4 0.1022 0.995 0.032 0.000 0.000 0.968
#> GSM35480 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM35482 3 0.4375 0.820 0.180 0.000 0.788 0.032
#> GSM35485 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM35489 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM35492 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM35495 3 0.1022 0.915 0.000 0.000 0.968 0.032
#> GSM35499 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM35502 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM35505 3 0.2699 0.890 0.068 0.000 0.904 0.028
#> GSM35507 4 0.1109 0.992 0.028 0.004 0.000 0.968
#> GSM35510 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM35514 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM35517 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM35520 3 0.2011 0.857 0.000 0.080 0.920 0.000
#> GSM35523 4 0.0921 0.993 0.028 0.000 0.000 0.972
#> GSM35529 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM35531 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM35534 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM35536 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM35538 4 0.1022 0.995 0.032 0.000 0.000 0.968
#> GSM35539 4 0.1022 0.995 0.032 0.000 0.000 0.968
#> GSM35540 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM35541 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM35442 1 0.0336 0.985 0.992 0.000 0.000 0.008
#> GSM35447 3 0.0336 0.921 0.000 0.000 0.992 0.008
#> GSM35450 4 0.1022 0.995 0.032 0.000 0.000 0.968
#> GSM35453 1 0.0188 0.988 0.996 0.000 0.000 0.004
#> GSM35456 4 0.1022 0.995 0.032 0.000 0.000 0.968
#> GSM35464 4 0.1022 0.959 0.000 0.032 0.000 0.968
#> GSM35467 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM35470 1 0.0592 0.981 0.984 0.000 0.000 0.016
#> GSM35479 3 0.4375 0.820 0.180 0.000 0.788 0.032
#> GSM35484 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM35488 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM35491 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM35494 3 0.4579 0.799 0.200 0.000 0.768 0.032
#> GSM35498 4 0.0921 0.993 0.028 0.000 0.000 0.972
#> GSM35501 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM35509 3 0.1022 0.915 0.000 0.000 0.968 0.032
#> GSM35513 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM35516 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM35522 4 0.0921 0.993 0.028 0.000 0.000 0.972
#> GSM35525 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM35528 4 0.1022 0.995 0.032 0.000 0.000 0.968
#> GSM35533 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM35537 1 0.2973 0.836 0.856 0.000 0.000 0.144
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM35441 2 0.0000 0.970 0.000 1.000 0.000 0.000 0.000
#> GSM35446 5 0.0609 0.941 0.000 0.000 0.020 0.000 0.980
#> GSM35449 2 0.0000 0.970 0.000 1.000 0.000 0.000 0.000
#> GSM35455 2 0.0000 0.970 0.000 1.000 0.000 0.000 0.000
#> GSM35458 5 0.0162 0.940 0.000 0.000 0.004 0.000 0.996
#> GSM35460 5 0.2424 0.879 0.000 0.000 0.132 0.000 0.868
#> GSM35461 3 0.0807 0.854 0.012 0.000 0.976 0.000 0.012
#> GSM35463 2 0.0960 0.964 0.000 0.972 0.016 0.008 0.004
#> GSM35472 5 0.2471 0.875 0.000 0.000 0.136 0.000 0.864
#> GSM35475 5 0.0162 0.942 0.000 0.000 0.004 0.000 0.996
#> GSM35483 2 0.4884 0.353 0.000 0.584 0.016 0.008 0.392
#> GSM35496 3 0.0579 0.854 0.008 0.000 0.984 0.000 0.008
#> GSM35497 2 0.0000 0.970 0.000 1.000 0.000 0.000 0.000
#> GSM35504 2 0.0000 0.970 0.000 1.000 0.000 0.000 0.000
#> GSM35508 5 0.2020 0.852 0.000 0.100 0.000 0.000 0.900
#> GSM35511 5 0.0290 0.943 0.000 0.000 0.008 0.000 0.992
#> GSM35512 5 0.2516 0.872 0.000 0.000 0.140 0.000 0.860
#> GSM35515 5 0.0162 0.940 0.000 0.000 0.004 0.000 0.996
#> GSM35519 5 0.0290 0.943 0.000 0.000 0.008 0.000 0.992
#> GSM35527 2 0.0162 0.968 0.000 0.996 0.000 0.000 0.004
#> GSM35532 5 0.0290 0.943 0.000 0.000 0.008 0.000 0.992
#> GSM35439 2 0.1087 0.963 0.000 0.968 0.016 0.008 0.008
#> GSM35443 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM35445 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM35448 5 0.0510 0.942 0.000 0.000 0.016 0.000 0.984
#> GSM35451 4 0.0290 0.969 0.008 0.000 0.000 0.992 0.000
#> GSM35454 3 0.0693 0.854 0.012 0.000 0.980 0.000 0.008
#> GSM35457 2 0.0000 0.970 0.000 1.000 0.000 0.000 0.000
#> GSM35465 2 0.0000 0.970 0.000 1.000 0.000 0.000 0.000
#> GSM35468 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM35471 4 0.0290 0.969 0.008 0.000 0.000 0.992 0.000
#> GSM35473 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM35477 4 0.0290 0.969 0.008 0.000 0.000 0.992 0.000
#> GSM35480 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM35482 3 0.0579 0.854 0.008 0.000 0.984 0.000 0.008
#> GSM35485 2 0.1087 0.963 0.000 0.968 0.016 0.008 0.008
#> GSM35489 2 0.0960 0.964 0.000 0.972 0.016 0.008 0.004
#> GSM35492 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM35495 3 0.0703 0.846 0.000 0.000 0.976 0.000 0.024
#> GSM35499 2 0.0000 0.970 0.000 1.000 0.000 0.000 0.000
#> GSM35502 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM35505 3 0.3519 0.605 0.008 0.000 0.776 0.000 0.216
#> GSM35507 4 0.0290 0.965 0.000 0.008 0.000 0.992 0.000
#> GSM35510 2 0.0000 0.970 0.000 1.000 0.000 0.000 0.000
#> GSM35514 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM35517 2 0.0000 0.970 0.000 1.000 0.000 0.000 0.000
#> GSM35520 5 0.0000 0.940 0.000 0.000 0.000 0.000 1.000
#> GSM35523 4 0.0290 0.964 0.000 0.000 0.008 0.992 0.000
#> GSM35529 2 0.0000 0.970 0.000 1.000 0.000 0.000 0.000
#> GSM35531 2 0.1087 0.963 0.000 0.968 0.016 0.008 0.008
#> GSM35534 2 0.1087 0.963 0.000 0.968 0.016 0.008 0.008
#> GSM35536 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM35538 4 0.1608 0.932 0.072 0.000 0.000 0.928 0.000
#> GSM35539 4 0.1908 0.909 0.092 0.000 0.000 0.908 0.000
#> GSM35540 2 0.0000 0.970 0.000 1.000 0.000 0.000 0.000
#> GSM35541 2 0.0960 0.964 0.000 0.972 0.016 0.008 0.004
#> GSM35442 1 0.0162 0.995 0.996 0.000 0.004 0.000 0.000
#> GSM35447 5 0.2690 0.854 0.000 0.000 0.156 0.000 0.844
#> GSM35450 4 0.1478 0.939 0.064 0.000 0.000 0.936 0.000
#> GSM35453 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM35456 4 0.0290 0.969 0.008 0.000 0.000 0.992 0.000
#> GSM35464 4 0.0290 0.965 0.000 0.008 0.000 0.992 0.000
#> GSM35467 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM35470 3 0.4743 0.170 0.472 0.000 0.512 0.016 0.000
#> GSM35479 3 0.0579 0.854 0.008 0.000 0.984 0.000 0.008
#> GSM35484 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM35488 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM35491 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM35494 3 0.0693 0.854 0.012 0.000 0.980 0.000 0.008
#> GSM35498 4 0.0324 0.967 0.004 0.000 0.004 0.992 0.000
#> GSM35501 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM35509 3 0.0609 0.848 0.000 0.000 0.980 0.000 0.020
#> GSM35513 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM35516 2 0.0960 0.964 0.000 0.972 0.016 0.008 0.004
#> GSM35522 4 0.0290 0.965 0.000 0.008 0.000 0.992 0.000
#> GSM35525 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM35528 4 0.1478 0.939 0.064 0.000 0.000 0.936 0.000
#> GSM35533 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM35537 3 0.5280 0.233 0.440 0.000 0.512 0.048 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM35441 2 0.0363 0.951 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM35446 5 0.1225 0.922 0.000 0.000 0.036 0.000 0.952 0.012
#> GSM35449 2 0.0000 0.958 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM35455 2 0.0000 0.958 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM35458 5 0.1152 0.917 0.000 0.004 0.000 0.000 0.952 0.044
#> GSM35460 5 0.2968 0.827 0.000 0.000 0.168 0.000 0.816 0.016
#> GSM35461 3 0.1176 0.815 0.000 0.000 0.956 0.000 0.020 0.024
#> GSM35463 6 0.3221 0.965 0.000 0.264 0.000 0.000 0.000 0.736
#> GSM35472 5 0.3176 0.829 0.000 0.000 0.156 0.000 0.812 0.032
#> GSM35475 5 0.0363 0.930 0.000 0.000 0.000 0.000 0.988 0.012
#> GSM35483 6 0.4377 0.814 0.000 0.160 0.000 0.000 0.120 0.720
#> GSM35496 3 0.0000 0.829 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM35497 2 0.0000 0.958 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM35504 2 0.0405 0.953 0.000 0.988 0.000 0.000 0.004 0.008
#> GSM35508 2 0.3404 0.639 0.000 0.760 0.000 0.000 0.224 0.016
#> GSM35511 5 0.0146 0.930 0.000 0.000 0.000 0.000 0.996 0.004
#> GSM35512 5 0.3027 0.838 0.000 0.000 0.148 0.000 0.824 0.028
#> GSM35515 5 0.1152 0.917 0.000 0.004 0.000 0.000 0.952 0.044
#> GSM35519 5 0.0146 0.930 0.000 0.000 0.000 0.000 0.996 0.004
#> GSM35527 2 0.0820 0.938 0.000 0.972 0.000 0.000 0.016 0.012
#> GSM35532 5 0.0146 0.930 0.000 0.000 0.000 0.000 0.996 0.004
#> GSM35439 6 0.3198 0.964 0.000 0.260 0.000 0.000 0.000 0.740
#> GSM35443 1 0.0000 0.994 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35445 1 0.0000 0.994 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35448 5 0.0914 0.928 0.000 0.000 0.016 0.000 0.968 0.016
#> GSM35451 4 0.1204 0.931 0.000 0.000 0.000 0.944 0.000 0.056
#> GSM35454 3 0.0935 0.820 0.000 0.000 0.964 0.000 0.004 0.032
#> GSM35457 2 0.0146 0.956 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM35465 2 0.0260 0.955 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM35468 1 0.0000 0.994 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35471 4 0.0146 0.934 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM35473 1 0.0000 0.994 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35477 4 0.1204 0.931 0.000 0.000 0.000 0.944 0.000 0.056
#> GSM35480 1 0.0146 0.991 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM35482 3 0.0000 0.829 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM35485 6 0.3221 0.965 0.000 0.264 0.000 0.000 0.000 0.736
#> GSM35489 6 0.3221 0.965 0.000 0.264 0.000 0.000 0.000 0.736
#> GSM35492 1 0.0000 0.994 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35495 3 0.1334 0.813 0.000 0.000 0.948 0.000 0.020 0.032
#> GSM35499 2 0.0363 0.955 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM35502 1 0.0000 0.994 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35505 3 0.4453 0.185 0.000 0.000 0.592 0.000 0.372 0.036
#> GSM35507 4 0.1075 0.930 0.000 0.000 0.000 0.952 0.000 0.048
#> GSM35510 2 0.0146 0.956 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM35514 1 0.0000 0.994 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35517 2 0.1007 0.913 0.000 0.956 0.000 0.000 0.000 0.044
#> GSM35520 5 0.0260 0.929 0.000 0.000 0.000 0.000 0.992 0.008
#> GSM35523 4 0.2006 0.900 0.000 0.000 0.004 0.892 0.000 0.104
#> GSM35529 2 0.0000 0.958 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM35531 6 0.3221 0.965 0.000 0.264 0.000 0.000 0.000 0.736
#> GSM35534 6 0.3175 0.961 0.000 0.256 0.000 0.000 0.000 0.744
#> GSM35536 1 0.0000 0.994 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35538 4 0.2258 0.907 0.060 0.000 0.000 0.896 0.000 0.044
#> GSM35539 4 0.2837 0.875 0.088 0.000 0.000 0.856 0.000 0.056
#> GSM35540 2 0.0458 0.952 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM35541 6 0.3221 0.965 0.000 0.264 0.000 0.000 0.000 0.736
#> GSM35442 1 0.0146 0.991 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM35447 5 0.2442 0.896 0.000 0.000 0.068 0.000 0.884 0.048
#> GSM35450 4 0.2134 0.912 0.052 0.000 0.000 0.904 0.000 0.044
#> GSM35453 1 0.0000 0.994 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35456 4 0.1007 0.931 0.000 0.000 0.000 0.956 0.000 0.044
#> GSM35464 4 0.1075 0.930 0.000 0.000 0.000 0.952 0.000 0.048
#> GSM35467 1 0.0000 0.994 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35470 3 0.5749 0.270 0.392 0.000 0.492 0.028 0.000 0.088
#> GSM35479 3 0.0000 0.829 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM35484 1 0.0547 0.978 0.980 0.000 0.000 0.000 0.000 0.020
#> GSM35488 1 0.0000 0.994 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35491 1 0.0000 0.994 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35494 3 0.0000 0.829 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM35498 4 0.1075 0.930 0.000 0.000 0.000 0.952 0.000 0.048
#> GSM35501 1 0.0000 0.994 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35509 3 0.0000 0.829 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM35513 1 0.0000 0.994 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35516 6 0.3348 0.923 0.000 0.216 0.000 0.016 0.000 0.768
#> GSM35522 4 0.1863 0.903 0.000 0.000 0.000 0.896 0.000 0.104
#> GSM35525 1 0.1088 0.957 0.960 0.000 0.000 0.024 0.000 0.016
#> GSM35528 4 0.2265 0.911 0.052 0.000 0.000 0.896 0.000 0.052
#> GSM35533 1 0.1074 0.959 0.960 0.000 0.000 0.012 0.000 0.028
#> GSM35537 3 0.6136 0.322 0.360 0.000 0.492 0.060 0.000 0.088
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 time(p) k
#> ATC:skmeans 79 6.81e-06 2
#> ATC:skmeans 78 9.67e-06 3
#> ATC:skmeans 79 1.58e-05 4
#> ATC:skmeans 76 3.32e-06 5
#> ATC:skmeans 76 1.94e-05 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "pam"]
# you can also extract it by
# res = res_list["ATC:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 7758 rows and 79 columns.
#> Top rows (776, 1552, 2328, 3103, 3879) 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 0.846 0.908 0.962 0.5051 0.494 0.494
#> 3 3 0.686 0.838 0.926 0.2845 0.741 0.527
#> 4 4 0.928 0.932 0.967 0.1654 0.793 0.477
#> 5 5 0.905 0.848 0.933 0.0494 0.950 0.800
#> 6 6 0.937 0.859 0.941 0.0447 0.943 0.735
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] 4 5
There is also optional best \(k\) = 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
#> GSM35441 2 0.0000 0.951 0.000 1.000
#> GSM35446 2 0.0376 0.950 0.004 0.996
#> GSM35449 2 0.0000 0.951 0.000 1.000
#> GSM35455 2 0.0000 0.951 0.000 1.000
#> GSM35458 1 0.9427 0.441 0.640 0.360
#> GSM35460 2 0.0376 0.950 0.004 0.996
#> GSM35461 1 0.0000 0.965 1.000 0.000
#> GSM35463 2 0.0000 0.951 0.000 1.000
#> GSM35472 2 0.0376 0.950 0.004 0.996
#> GSM35475 2 0.9580 0.364 0.380 0.620
#> GSM35483 2 0.0000 0.951 0.000 1.000
#> GSM35496 1 0.0000 0.965 1.000 0.000
#> GSM35497 2 0.0000 0.951 0.000 1.000
#> GSM35504 2 0.0000 0.951 0.000 1.000
#> GSM35508 2 0.0000 0.951 0.000 1.000
#> GSM35511 2 0.0376 0.950 0.004 0.996
#> GSM35512 1 0.8608 0.590 0.716 0.284
#> GSM35515 1 0.9427 0.441 0.640 0.360
#> GSM35519 2 0.0376 0.950 0.004 0.996
#> GSM35527 2 0.0000 0.951 0.000 1.000
#> GSM35532 2 0.0376 0.950 0.004 0.996
#> GSM35439 2 0.0000 0.951 0.000 1.000
#> GSM35443 1 0.0000 0.965 1.000 0.000
#> GSM35445 1 0.0000 0.965 1.000 0.000
#> GSM35448 2 0.0376 0.950 0.004 0.996
#> GSM35451 1 0.0000 0.965 1.000 0.000
#> GSM35454 1 0.0000 0.965 1.000 0.000
#> GSM35457 2 0.0000 0.951 0.000 1.000
#> GSM35465 2 0.0000 0.951 0.000 1.000
#> GSM35468 1 0.0000 0.965 1.000 0.000
#> GSM35471 1 0.8861 0.525 0.696 0.304
#> GSM35473 1 0.0000 0.965 1.000 0.000
#> GSM35477 1 0.0000 0.965 1.000 0.000
#> GSM35480 1 0.0000 0.965 1.000 0.000
#> GSM35482 1 0.0000 0.965 1.000 0.000
#> GSM35485 2 0.0000 0.951 0.000 1.000
#> GSM35489 2 0.0000 0.951 0.000 1.000
#> GSM35492 1 0.0000 0.965 1.000 0.000
#> GSM35495 2 0.6623 0.786 0.172 0.828
#> GSM35499 2 0.0000 0.951 0.000 1.000
#> GSM35502 1 0.0000 0.965 1.000 0.000
#> GSM35505 1 0.0000 0.965 1.000 0.000
#> GSM35507 2 0.7602 0.722 0.220 0.780
#> GSM35510 2 0.0000 0.951 0.000 1.000
#> GSM35514 1 0.0000 0.965 1.000 0.000
#> GSM35517 2 0.0000 0.951 0.000 1.000
#> GSM35520 2 0.0376 0.950 0.004 0.996
#> GSM35523 1 0.0000 0.965 1.000 0.000
#> GSM35529 2 0.0000 0.951 0.000 1.000
#> GSM35531 2 0.0376 0.950 0.004 0.996
#> GSM35534 2 0.0000 0.951 0.000 1.000
#> GSM35536 1 0.0000 0.965 1.000 0.000
#> GSM35538 1 0.0000 0.965 1.000 0.000
#> GSM35539 1 0.0000 0.965 1.000 0.000
#> GSM35540 2 0.0000 0.951 0.000 1.000
#> GSM35541 2 0.0000 0.951 0.000 1.000
#> GSM35442 1 0.0000 0.965 1.000 0.000
#> GSM35447 1 0.0000 0.965 1.000 0.000
#> GSM35450 1 0.0000 0.965 1.000 0.000
#> GSM35453 1 0.0000 0.965 1.000 0.000
#> GSM35456 1 0.0000 0.965 1.000 0.000
#> GSM35464 2 0.0000 0.951 0.000 1.000
#> GSM35467 1 0.0000 0.965 1.000 0.000
#> GSM35470 1 0.0000 0.965 1.000 0.000
#> GSM35479 1 0.0000 0.965 1.000 0.000
#> GSM35484 1 0.0000 0.965 1.000 0.000
#> GSM35488 1 0.0000 0.965 1.000 0.000
#> GSM35491 1 0.0000 0.965 1.000 0.000
#> GSM35494 1 0.0000 0.965 1.000 0.000
#> GSM35498 2 0.9552 0.430 0.376 0.624
#> GSM35501 1 0.0000 0.965 1.000 0.000
#> GSM35509 2 0.6712 0.781 0.176 0.824
#> GSM35513 1 0.0000 0.965 1.000 0.000
#> GSM35516 2 0.0000 0.951 0.000 1.000
#> GSM35522 2 0.9170 0.522 0.332 0.668
#> GSM35525 1 0.0000 0.965 1.000 0.000
#> GSM35528 1 0.0000 0.965 1.000 0.000
#> GSM35533 1 0.0000 0.965 1.000 0.000
#> GSM35537 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
#> GSM35441 2 0.0000 0.926 0.000 1.000 0.000
#> GSM35446 3 0.3551 0.742 0.000 0.132 0.868
#> GSM35449 2 0.0000 0.926 0.000 1.000 0.000
#> GSM35455 2 0.0000 0.926 0.000 1.000 0.000
#> GSM35458 3 0.6339 0.426 0.360 0.008 0.632
#> GSM35460 3 0.0424 0.808 0.000 0.008 0.992
#> GSM35461 3 0.3879 0.750 0.152 0.000 0.848
#> GSM35463 2 0.0000 0.926 0.000 1.000 0.000
#> GSM35472 3 0.0237 0.809 0.000 0.004 0.996
#> GSM35475 3 0.0424 0.808 0.000 0.008 0.992
#> GSM35483 2 0.5835 0.465 0.000 0.660 0.340
#> GSM35496 3 0.5560 0.562 0.300 0.000 0.700
#> GSM35497 2 0.0000 0.926 0.000 1.000 0.000
#> GSM35504 2 0.0000 0.926 0.000 1.000 0.000
#> GSM35508 2 0.0237 0.923 0.000 0.996 0.004
#> GSM35511 3 0.3551 0.742 0.000 0.132 0.868
#> GSM35512 3 0.0000 0.808 0.000 0.000 1.000
#> GSM35515 3 0.6155 0.496 0.328 0.008 0.664
#> GSM35519 3 0.0424 0.808 0.000 0.008 0.992
#> GSM35527 2 0.0000 0.926 0.000 1.000 0.000
#> GSM35532 3 0.3551 0.742 0.000 0.132 0.868
#> GSM35439 2 0.0000 0.926 0.000 1.000 0.000
#> GSM35443 1 0.0000 0.949 1.000 0.000 0.000
#> GSM35445 1 0.0000 0.949 1.000 0.000 0.000
#> GSM35448 3 0.3412 0.748 0.000 0.124 0.876
#> GSM35451 1 0.3482 0.859 0.872 0.000 0.128
#> GSM35454 1 0.5138 0.680 0.748 0.000 0.252
#> GSM35457 2 0.0000 0.926 0.000 1.000 0.000
#> GSM35465 2 0.0000 0.926 0.000 1.000 0.000
#> GSM35468 1 0.0000 0.949 1.000 0.000 0.000
#> GSM35471 1 0.3551 0.855 0.868 0.000 0.132
#> GSM35473 1 0.0000 0.949 1.000 0.000 0.000
#> GSM35477 1 0.3192 0.872 0.888 0.000 0.112
#> GSM35480 1 0.0000 0.949 1.000 0.000 0.000
#> GSM35482 3 0.6140 0.337 0.404 0.000 0.596
#> GSM35485 2 0.0000 0.926 0.000 1.000 0.000
#> GSM35489 2 0.0000 0.926 0.000 1.000 0.000
#> GSM35492 1 0.0000 0.949 1.000 0.000 0.000
#> GSM35495 3 0.0000 0.808 0.000 0.000 1.000
#> GSM35499 2 0.0000 0.926 0.000 1.000 0.000
#> GSM35502 1 0.0000 0.949 1.000 0.000 0.000
#> GSM35505 3 0.4291 0.729 0.180 0.000 0.820
#> GSM35507 1 0.3551 0.855 0.868 0.000 0.132
#> GSM35510 2 0.0000 0.926 0.000 1.000 0.000
#> GSM35514 1 0.0000 0.949 1.000 0.000 0.000
#> GSM35517 2 0.0000 0.926 0.000 1.000 0.000
#> GSM35520 3 0.3551 0.742 0.000 0.132 0.868
#> GSM35523 1 0.3551 0.855 0.868 0.000 0.132
#> GSM35529 2 0.0000 0.926 0.000 1.000 0.000
#> GSM35531 2 0.9173 0.267 0.304 0.520 0.176
#> GSM35534 2 0.3192 0.825 0.000 0.888 0.112
#> GSM35536 1 0.0000 0.949 1.000 0.000 0.000
#> GSM35538 1 0.0000 0.949 1.000 0.000 0.000
#> GSM35539 1 0.0000 0.949 1.000 0.000 0.000
#> GSM35540 2 0.0000 0.926 0.000 1.000 0.000
#> GSM35541 2 0.0000 0.926 0.000 1.000 0.000
#> GSM35442 1 0.0000 0.949 1.000 0.000 0.000
#> GSM35447 3 0.2448 0.793 0.076 0.000 0.924
#> GSM35450 1 0.0000 0.949 1.000 0.000 0.000
#> GSM35453 1 0.0000 0.949 1.000 0.000 0.000
#> GSM35456 1 0.3551 0.855 0.868 0.000 0.132
#> GSM35464 2 0.3551 0.799 0.000 0.868 0.132
#> GSM35467 1 0.0000 0.949 1.000 0.000 0.000
#> GSM35470 1 0.0424 0.945 0.992 0.000 0.008
#> GSM35479 3 0.6062 0.386 0.384 0.000 0.616
#> GSM35484 1 0.0000 0.949 1.000 0.000 0.000
#> GSM35488 1 0.0000 0.949 1.000 0.000 0.000
#> GSM35491 1 0.0000 0.949 1.000 0.000 0.000
#> GSM35494 1 0.4974 0.709 0.764 0.000 0.236
#> GSM35498 1 0.3551 0.855 0.868 0.000 0.132
#> GSM35501 1 0.0000 0.949 1.000 0.000 0.000
#> GSM35509 3 0.0000 0.808 0.000 0.000 1.000
#> GSM35513 1 0.0000 0.949 1.000 0.000 0.000
#> GSM35516 2 0.3412 0.808 0.000 0.876 0.124
#> GSM35522 2 0.8101 0.491 0.228 0.640 0.132
#> GSM35525 1 0.0000 0.949 1.000 0.000 0.000
#> GSM35528 1 0.0424 0.945 0.992 0.000 0.008
#> GSM35533 1 0.0000 0.949 1.000 0.000 0.000
#> GSM35537 1 0.0424 0.945 0.992 0.000 0.008
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM35441 2 0.0000 0.987 0.000 1.000 0.000 0.000
#> GSM35446 3 0.0000 0.988 0.000 0.000 1.000 0.000
#> GSM35449 2 0.0000 0.987 0.000 1.000 0.000 0.000
#> GSM35455 2 0.0000 0.987 0.000 1.000 0.000 0.000
#> GSM35458 3 0.0469 0.978 0.012 0.000 0.988 0.000
#> GSM35460 3 0.0000 0.988 0.000 0.000 1.000 0.000
#> GSM35461 1 0.2814 0.845 0.868 0.000 0.132 0.000
#> GSM35463 2 0.0000 0.987 0.000 1.000 0.000 0.000
#> GSM35472 3 0.0000 0.988 0.000 0.000 1.000 0.000
#> GSM35475 3 0.0000 0.988 0.000 0.000 1.000 0.000
#> GSM35483 3 0.3024 0.819 0.000 0.148 0.852 0.000
#> GSM35496 1 0.2814 0.845 0.868 0.000 0.132 0.000
#> GSM35497 2 0.0000 0.987 0.000 1.000 0.000 0.000
#> GSM35504 2 0.0000 0.987 0.000 1.000 0.000 0.000
#> GSM35508 2 0.0000 0.987 0.000 1.000 0.000 0.000
#> GSM35511 3 0.0000 0.988 0.000 0.000 1.000 0.000
#> GSM35512 3 0.0000 0.988 0.000 0.000 1.000 0.000
#> GSM35515 3 0.0336 0.982 0.008 0.000 0.992 0.000
#> GSM35519 3 0.0000 0.988 0.000 0.000 1.000 0.000
#> GSM35527 2 0.0000 0.987 0.000 1.000 0.000 0.000
#> GSM35532 3 0.0000 0.988 0.000 0.000 1.000 0.000
#> GSM35439 2 0.0000 0.987 0.000 1.000 0.000 0.000
#> GSM35443 1 0.0000 0.948 1.000 0.000 0.000 0.000
#> GSM35445 1 0.0000 0.948 1.000 0.000 0.000 0.000
#> GSM35448 3 0.0000 0.988 0.000 0.000 1.000 0.000
#> GSM35451 4 0.0000 0.946 0.000 0.000 0.000 1.000
#> GSM35454 4 0.0707 0.938 0.020 0.000 0.000 0.980
#> GSM35457 2 0.0000 0.987 0.000 1.000 0.000 0.000
#> GSM35465 2 0.0000 0.987 0.000 1.000 0.000 0.000
#> GSM35468 1 0.0000 0.948 1.000 0.000 0.000 0.000
#> GSM35471 4 0.0000 0.946 0.000 0.000 0.000 1.000
#> GSM35473 1 0.0000 0.948 1.000 0.000 0.000 0.000
#> GSM35477 4 0.0000 0.946 0.000 0.000 0.000 1.000
#> GSM35480 1 0.0707 0.936 0.980 0.000 0.000 0.020
#> GSM35482 1 0.5990 0.665 0.688 0.000 0.124 0.188
#> GSM35485 2 0.0000 0.987 0.000 1.000 0.000 0.000
#> GSM35489 2 0.0000 0.987 0.000 1.000 0.000 0.000
#> GSM35492 1 0.0000 0.948 1.000 0.000 0.000 0.000
#> GSM35495 3 0.0000 0.988 0.000 0.000 1.000 0.000
#> GSM35499 2 0.0000 0.987 0.000 1.000 0.000 0.000
#> GSM35502 1 0.0000 0.948 1.000 0.000 0.000 0.000
#> GSM35505 3 0.0188 0.985 0.004 0.000 0.996 0.000
#> GSM35507 4 0.0000 0.946 0.000 0.000 0.000 1.000
#> GSM35510 2 0.0000 0.987 0.000 1.000 0.000 0.000
#> GSM35514 1 0.0000 0.948 1.000 0.000 0.000 0.000
#> GSM35517 2 0.0000 0.987 0.000 1.000 0.000 0.000
#> GSM35520 3 0.0000 0.988 0.000 0.000 1.000 0.000
#> GSM35523 4 0.0000 0.946 0.000 0.000 0.000 1.000
#> GSM35529 2 0.0000 0.987 0.000 1.000 0.000 0.000
#> GSM35531 4 0.2542 0.883 0.000 0.084 0.012 0.904
#> GSM35534 2 0.4040 0.663 0.000 0.752 0.248 0.000
#> GSM35536 1 0.0000 0.948 1.000 0.000 0.000 0.000
#> GSM35538 4 0.1118 0.929 0.036 0.000 0.000 0.964
#> GSM35539 4 0.0000 0.946 0.000 0.000 0.000 1.000
#> GSM35540 2 0.0000 0.987 0.000 1.000 0.000 0.000
#> GSM35541 2 0.0000 0.987 0.000 1.000 0.000 0.000
#> GSM35442 1 0.0000 0.948 1.000 0.000 0.000 0.000
#> GSM35447 3 0.0000 0.988 0.000 0.000 1.000 0.000
#> GSM35450 4 0.0000 0.946 0.000 0.000 0.000 1.000
#> GSM35453 1 0.0000 0.948 1.000 0.000 0.000 0.000
#> GSM35456 4 0.0000 0.946 0.000 0.000 0.000 1.000
#> GSM35464 4 0.0707 0.937 0.000 0.020 0.000 0.980
#> GSM35467 1 0.0000 0.948 1.000 0.000 0.000 0.000
#> GSM35470 4 0.2081 0.892 0.084 0.000 0.000 0.916
#> GSM35479 1 0.3398 0.863 0.872 0.000 0.060 0.068
#> GSM35484 1 0.0000 0.948 1.000 0.000 0.000 0.000
#> GSM35488 1 0.0000 0.948 1.000 0.000 0.000 0.000
#> GSM35491 1 0.0000 0.948 1.000 0.000 0.000 0.000
#> GSM35494 1 0.5408 0.291 0.576 0.000 0.016 0.408
#> GSM35498 4 0.0000 0.946 0.000 0.000 0.000 1.000
#> GSM35501 1 0.0000 0.948 1.000 0.000 0.000 0.000
#> GSM35509 4 0.3873 0.719 0.000 0.000 0.228 0.772
#> GSM35513 1 0.0000 0.948 1.000 0.000 0.000 0.000
#> GSM35516 4 0.1302 0.922 0.000 0.044 0.000 0.956
#> GSM35522 4 0.0000 0.946 0.000 0.000 0.000 1.000
#> GSM35525 1 0.0707 0.936 0.980 0.000 0.000 0.020
#> GSM35528 4 0.0000 0.946 0.000 0.000 0.000 1.000
#> GSM35533 4 0.3123 0.815 0.156 0.000 0.000 0.844
#> GSM35537 4 0.4382 0.568 0.296 0.000 0.000 0.704
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM35441 2 0.0000 0.9734 0.000 1.000 0.000 0.000 0.000
#> GSM35446 5 0.0000 0.9464 0.000 0.000 0.000 0.000 1.000
#> GSM35449 2 0.0000 0.9734 0.000 1.000 0.000 0.000 0.000
#> GSM35455 2 0.0000 0.9734 0.000 1.000 0.000 0.000 0.000
#> GSM35458 5 0.1357 0.9150 0.004 0.000 0.048 0.000 0.948
#> GSM35460 3 0.4273 0.3268 0.000 0.000 0.552 0.000 0.448
#> GSM35461 3 0.6739 0.2809 0.348 0.000 0.392 0.000 0.260
#> GSM35463 2 0.0703 0.9611 0.000 0.976 0.024 0.000 0.000
#> GSM35472 5 0.1121 0.9095 0.000 0.000 0.044 0.000 0.956
#> GSM35475 5 0.0000 0.9464 0.000 0.000 0.000 0.000 1.000
#> GSM35483 5 0.3146 0.7992 0.000 0.092 0.052 0.000 0.856
#> GSM35496 3 0.1341 0.8004 0.000 0.000 0.944 0.000 0.056
#> GSM35497 2 0.0000 0.9734 0.000 1.000 0.000 0.000 0.000
#> GSM35504 2 0.0000 0.9734 0.000 1.000 0.000 0.000 0.000
#> GSM35508 2 0.0000 0.9734 0.000 1.000 0.000 0.000 0.000
#> GSM35511 5 0.0000 0.9464 0.000 0.000 0.000 0.000 1.000
#> GSM35512 5 0.0000 0.9464 0.000 0.000 0.000 0.000 1.000
#> GSM35515 5 0.1041 0.9273 0.004 0.000 0.032 0.000 0.964
#> GSM35519 5 0.0000 0.9464 0.000 0.000 0.000 0.000 1.000
#> GSM35527 2 0.0000 0.9734 0.000 1.000 0.000 0.000 0.000
#> GSM35532 5 0.0000 0.9464 0.000 0.000 0.000 0.000 1.000
#> GSM35439 2 0.1661 0.9324 0.000 0.940 0.024 0.000 0.036
#> GSM35443 1 0.0000 0.9424 1.000 0.000 0.000 0.000 0.000
#> GSM35445 1 0.0000 0.9424 1.000 0.000 0.000 0.000 0.000
#> GSM35448 5 0.1410 0.8949 0.000 0.000 0.060 0.000 0.940
#> GSM35451 4 0.0000 0.8742 0.000 0.000 0.000 1.000 0.000
#> GSM35454 4 0.4452 0.0417 0.004 0.000 0.496 0.500 0.000
#> GSM35457 2 0.0000 0.9734 0.000 1.000 0.000 0.000 0.000
#> GSM35465 2 0.0000 0.9734 0.000 1.000 0.000 0.000 0.000
#> GSM35468 1 0.0000 0.9424 1.000 0.000 0.000 0.000 0.000
#> GSM35471 4 0.0000 0.8742 0.000 0.000 0.000 1.000 0.000
#> GSM35473 1 0.0000 0.9424 1.000 0.000 0.000 0.000 0.000
#> GSM35477 4 0.0000 0.8742 0.000 0.000 0.000 1.000 0.000
#> GSM35480 1 0.4126 0.4054 0.620 0.000 0.000 0.380 0.000
#> GSM35482 3 0.1341 0.8004 0.000 0.000 0.944 0.000 0.056
#> GSM35485 2 0.1818 0.9245 0.000 0.932 0.024 0.000 0.044
#> GSM35489 2 0.0703 0.9611 0.000 0.976 0.024 0.000 0.000
#> GSM35492 1 0.0000 0.9424 1.000 0.000 0.000 0.000 0.000
#> GSM35495 3 0.3932 0.5642 0.000 0.000 0.672 0.000 0.328
#> GSM35499 2 0.0404 0.9678 0.000 0.988 0.012 0.000 0.000
#> GSM35502 1 0.0000 0.9424 1.000 0.000 0.000 0.000 0.000
#> GSM35505 5 0.3003 0.7190 0.000 0.000 0.188 0.000 0.812
#> GSM35507 4 0.0000 0.8742 0.000 0.000 0.000 1.000 0.000
#> GSM35510 2 0.0000 0.9734 0.000 1.000 0.000 0.000 0.000
#> GSM35514 1 0.0000 0.9424 1.000 0.000 0.000 0.000 0.000
#> GSM35517 2 0.0000 0.9734 0.000 1.000 0.000 0.000 0.000
#> GSM35520 5 0.0404 0.9409 0.000 0.000 0.012 0.000 0.988
#> GSM35523 4 0.0000 0.8742 0.000 0.000 0.000 1.000 0.000
#> GSM35529 2 0.0000 0.9734 0.000 1.000 0.000 0.000 0.000
#> GSM35531 4 0.3782 0.7481 0.000 0.084 0.024 0.836 0.056
#> GSM35534 2 0.4292 0.6098 0.000 0.704 0.024 0.000 0.272
#> GSM35536 1 0.0000 0.9424 1.000 0.000 0.000 0.000 0.000
#> GSM35538 4 0.0510 0.8645 0.016 0.000 0.000 0.984 0.000
#> GSM35539 4 0.0000 0.8742 0.000 0.000 0.000 1.000 0.000
#> GSM35540 2 0.0000 0.9734 0.000 1.000 0.000 0.000 0.000
#> GSM35541 2 0.0000 0.9734 0.000 1.000 0.000 0.000 0.000
#> GSM35442 1 0.0000 0.9424 1.000 0.000 0.000 0.000 0.000
#> GSM35447 5 0.0000 0.9464 0.000 0.000 0.000 0.000 1.000
#> GSM35450 4 0.0000 0.8742 0.000 0.000 0.000 1.000 0.000
#> GSM35453 1 0.0000 0.9424 1.000 0.000 0.000 0.000 0.000
#> GSM35456 4 0.0000 0.8742 0.000 0.000 0.000 1.000 0.000
#> GSM35464 4 0.4264 0.4042 0.000 0.376 0.004 0.620 0.000
#> GSM35467 1 0.0000 0.9424 1.000 0.000 0.000 0.000 0.000
#> GSM35470 4 0.0992 0.8584 0.008 0.000 0.024 0.968 0.000
#> GSM35479 3 0.1341 0.8004 0.000 0.000 0.944 0.000 0.056
#> GSM35484 1 0.0000 0.9424 1.000 0.000 0.000 0.000 0.000
#> GSM35488 1 0.0162 0.9387 0.996 0.000 0.000 0.004 0.000
#> GSM35491 1 0.0000 0.9424 1.000 0.000 0.000 0.000 0.000
#> GSM35494 3 0.1605 0.7721 0.004 0.000 0.944 0.040 0.012
#> GSM35498 4 0.0000 0.8742 0.000 0.000 0.000 1.000 0.000
#> GSM35501 1 0.0000 0.9424 1.000 0.000 0.000 0.000 0.000
#> GSM35509 3 0.1430 0.7991 0.000 0.000 0.944 0.004 0.052
#> GSM35513 1 0.0000 0.9424 1.000 0.000 0.000 0.000 0.000
#> GSM35516 4 0.4779 0.3510 0.000 0.388 0.024 0.588 0.000
#> GSM35522 4 0.0000 0.8742 0.000 0.000 0.000 1.000 0.000
#> GSM35525 1 0.4126 0.4054 0.620 0.000 0.000 0.380 0.000
#> GSM35528 4 0.0000 0.8742 0.000 0.000 0.000 1.000 0.000
#> GSM35533 4 0.3452 0.6082 0.244 0.000 0.000 0.756 0.000
#> GSM35537 4 0.2329 0.7783 0.000 0.000 0.124 0.876 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM35441 2 0.0000 0.9990 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM35446 5 0.0000 0.9608 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM35449 2 0.0000 0.9990 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM35455 2 0.0000 0.9990 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM35458 5 0.1152 0.9325 0.000 0.000 0.044 0.000 0.952 0.004
#> GSM35460 3 0.3833 0.2791 0.000 0.000 0.556 0.000 0.444 0.000
#> GSM35461 3 0.6034 0.2451 0.348 0.000 0.400 0.000 0.252 0.000
#> GSM35463 6 0.0146 0.9256 0.000 0.004 0.000 0.000 0.000 0.996
#> GSM35472 5 0.0000 0.9608 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM35475 5 0.0000 0.9608 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM35483 6 0.0260 0.9197 0.000 0.000 0.000 0.000 0.008 0.992
#> GSM35496 3 0.1007 0.7483 0.000 0.000 0.956 0.000 0.044 0.000
#> GSM35497 2 0.0000 0.9990 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM35504 2 0.0000 0.9990 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM35508 2 0.0000 0.9990 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM35511 5 0.0000 0.9608 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM35512 5 0.0000 0.9608 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM35515 5 0.1152 0.9325 0.000 0.000 0.044 0.000 0.952 0.004
#> GSM35519 5 0.0000 0.9608 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM35527 2 0.0000 0.9990 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM35532 5 0.0000 0.9608 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM35439 6 0.0260 0.9253 0.000 0.008 0.000 0.000 0.000 0.992
#> GSM35443 1 0.0000 0.9344 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35445 1 0.0000 0.9344 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35448 5 0.1267 0.9041 0.000 0.000 0.060 0.000 0.940 0.000
#> GSM35451 4 0.0000 0.9316 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM35454 3 0.3857 0.0937 0.000 0.000 0.532 0.468 0.000 0.000
#> GSM35457 2 0.0000 0.9990 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM35465 2 0.0146 0.9953 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM35468 1 0.0000 0.9344 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35471 4 0.0000 0.9316 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM35473 1 0.0000 0.9344 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35477 4 0.0146 0.9307 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM35480 1 0.3828 0.2331 0.560 0.000 0.000 0.440 0.000 0.000
#> GSM35482 3 0.1007 0.7483 0.000 0.000 0.956 0.000 0.044 0.000
#> GSM35485 6 0.0260 0.9253 0.000 0.008 0.000 0.000 0.000 0.992
#> GSM35489 6 0.0146 0.9256 0.000 0.004 0.000 0.000 0.000 0.996
#> GSM35492 1 0.0000 0.9344 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35495 3 0.3499 0.5206 0.000 0.000 0.680 0.000 0.320 0.000
#> GSM35499 6 0.3833 0.1990 0.000 0.444 0.000 0.000 0.000 0.556
#> GSM35502 1 0.0000 0.9344 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35505 5 0.2697 0.7226 0.000 0.000 0.188 0.000 0.812 0.000
#> GSM35507 4 0.0146 0.9307 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM35510 2 0.0000 0.9990 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM35514 1 0.0000 0.9344 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35517 2 0.0000 0.9990 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM35520 5 0.0865 0.9330 0.000 0.000 0.000 0.000 0.964 0.036
#> GSM35523 4 0.0000 0.9316 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM35529 2 0.0000 0.9990 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM35531 6 0.0146 0.9218 0.000 0.000 0.000 0.004 0.000 0.996
#> GSM35534 6 0.0260 0.9253 0.000 0.008 0.000 0.000 0.000 0.992
#> GSM35536 1 0.0000 0.9344 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35538 4 0.0458 0.9202 0.016 0.000 0.000 0.984 0.000 0.000
#> GSM35539 4 0.0000 0.9316 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM35540 2 0.0260 0.9923 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM35541 2 0.0000 0.9990 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM35442 1 0.0000 0.9344 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35447 5 0.0000 0.9608 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM35450 4 0.0000 0.9316 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM35453 1 0.0000 0.9344 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35456 4 0.0146 0.9307 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM35464 4 0.5116 0.3143 0.000 0.344 0.000 0.560 0.000 0.096
#> GSM35467 1 0.0000 0.9344 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35470 4 0.0891 0.9127 0.008 0.000 0.024 0.968 0.000 0.000
#> GSM35479 3 0.1007 0.7483 0.000 0.000 0.956 0.000 0.044 0.000
#> GSM35484 1 0.0000 0.9344 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35488 1 0.0146 0.9307 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM35491 1 0.0000 0.9344 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35494 3 0.1124 0.7248 0.000 0.000 0.956 0.036 0.008 0.000
#> GSM35498 4 0.0146 0.9307 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM35501 1 0.0000 0.9344 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35509 3 0.1007 0.7483 0.000 0.000 0.956 0.000 0.044 0.000
#> GSM35513 1 0.0000 0.9344 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35516 6 0.0146 0.9256 0.000 0.004 0.000 0.000 0.000 0.996
#> GSM35522 4 0.0000 0.9316 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM35525 1 0.3828 0.2331 0.560 0.000 0.000 0.440 0.000 0.000
#> GSM35528 4 0.0000 0.9316 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM35533 4 0.2823 0.6814 0.204 0.000 0.000 0.796 0.000 0.000
#> GSM35537 4 0.2135 0.8097 0.000 0.000 0.128 0.872 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 time(p) k
#> ATC:pam 75 2.20e-04 2
#> ATC:pam 72 4.32e-06 3
#> ATC:pam 78 1.19e-06 4
#> ATC:pam 72 6.62e-06 5
#> ATC:pam 72 8.78e-05 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "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 7758 rows and 79 columns.
#> Top rows (776, 1552, 2328, 3103, 3879) are extracted by 'ATC' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.970 0.969 0.4893 0.496 0.496
#> 3 3 0.885 0.958 0.963 0.3309 0.771 0.569
#> 4 4 0.732 0.731 0.883 0.1304 0.774 0.443
#> 5 5 0.690 0.752 0.818 0.0609 0.957 0.830
#> 6 6 0.868 0.826 0.924 0.0615 0.918 0.643
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
#> GSM35441 2 0.0000 0.997 0.000 1.000
#> GSM35446 2 0.0000 0.997 0.000 1.000
#> GSM35449 2 0.0000 0.997 0.000 1.000
#> GSM35455 2 0.0000 0.997 0.000 1.000
#> GSM35458 2 0.0000 0.997 0.000 1.000
#> GSM35460 2 0.0000 0.997 0.000 1.000
#> GSM35461 1 0.3879 0.966 0.924 0.076
#> GSM35463 2 0.0000 0.997 0.000 1.000
#> GSM35472 2 0.0000 0.997 0.000 1.000
#> GSM35475 2 0.0000 0.997 0.000 1.000
#> GSM35483 2 0.0000 0.997 0.000 1.000
#> GSM35496 1 0.3879 0.966 0.924 0.076
#> GSM35497 2 0.0000 0.997 0.000 1.000
#> GSM35504 2 0.0000 0.997 0.000 1.000
#> GSM35508 2 0.0000 0.997 0.000 1.000
#> GSM35511 2 0.0000 0.997 0.000 1.000
#> GSM35512 2 0.0000 0.997 0.000 1.000
#> GSM35515 2 0.0000 0.997 0.000 1.000
#> GSM35519 2 0.0000 0.997 0.000 1.000
#> GSM35527 2 0.0000 0.997 0.000 1.000
#> GSM35532 2 0.0000 0.997 0.000 1.000
#> GSM35439 2 0.0000 0.997 0.000 1.000
#> GSM35443 1 0.0938 0.946 0.988 0.012
#> GSM35445 1 0.0000 0.941 1.000 0.000
#> GSM35448 2 0.0000 0.997 0.000 1.000
#> GSM35451 1 0.3879 0.966 0.924 0.076
#> GSM35454 1 0.3879 0.966 0.924 0.076
#> GSM35457 2 0.0000 0.997 0.000 1.000
#> GSM35465 2 0.0000 0.997 0.000 1.000
#> GSM35468 1 0.0000 0.941 1.000 0.000
#> GSM35471 1 0.3879 0.966 0.924 0.076
#> GSM35473 1 0.0000 0.941 1.000 0.000
#> GSM35477 1 0.3879 0.966 0.924 0.076
#> GSM35480 1 0.3879 0.966 0.924 0.076
#> GSM35482 1 0.3879 0.966 0.924 0.076
#> GSM35485 2 0.0000 0.997 0.000 1.000
#> GSM35489 2 0.0000 0.997 0.000 1.000
#> GSM35492 1 0.0000 0.941 1.000 0.000
#> GSM35495 1 0.9000 0.631 0.684 0.316
#> GSM35499 2 0.0000 0.997 0.000 1.000
#> GSM35502 1 0.0000 0.941 1.000 0.000
#> GSM35505 2 0.4690 0.879 0.100 0.900
#> GSM35507 1 0.3879 0.966 0.924 0.076
#> GSM35510 2 0.0000 0.997 0.000 1.000
#> GSM35514 1 0.0000 0.941 1.000 0.000
#> GSM35517 2 0.0000 0.997 0.000 1.000
#> GSM35520 2 0.0000 0.997 0.000 1.000
#> GSM35523 1 0.3879 0.966 0.924 0.076
#> GSM35529 2 0.0000 0.997 0.000 1.000
#> GSM35531 2 0.0000 0.997 0.000 1.000
#> GSM35534 2 0.0000 0.997 0.000 1.000
#> GSM35536 1 0.0000 0.941 1.000 0.000
#> GSM35538 1 0.3879 0.966 0.924 0.076
#> GSM35539 1 0.3879 0.966 0.924 0.076
#> GSM35540 2 0.0000 0.997 0.000 1.000
#> GSM35541 2 0.0000 0.997 0.000 1.000
#> GSM35442 1 0.3879 0.966 0.924 0.076
#> GSM35447 2 0.0000 0.997 0.000 1.000
#> GSM35450 1 0.3879 0.966 0.924 0.076
#> GSM35453 1 0.3879 0.966 0.924 0.076
#> GSM35456 1 0.3879 0.966 0.924 0.076
#> GSM35464 1 0.3879 0.966 0.924 0.076
#> GSM35467 1 0.0000 0.941 1.000 0.000
#> GSM35470 1 0.3879 0.966 0.924 0.076
#> GSM35479 1 0.3879 0.966 0.924 0.076
#> GSM35484 1 0.1414 0.949 0.980 0.020
#> GSM35488 1 0.1633 0.951 0.976 0.024
#> GSM35491 1 0.0000 0.941 1.000 0.000
#> GSM35494 1 0.3879 0.966 0.924 0.076
#> GSM35498 1 0.3879 0.966 0.924 0.076
#> GSM35501 1 0.0000 0.941 1.000 0.000
#> GSM35509 1 0.3879 0.966 0.924 0.076
#> GSM35513 1 0.0000 0.941 1.000 0.000
#> GSM35516 2 0.0000 0.997 0.000 1.000
#> GSM35522 1 0.3879 0.966 0.924 0.076
#> GSM35525 1 0.3879 0.966 0.924 0.076
#> GSM35528 1 0.3879 0.966 0.924 0.076
#> GSM35533 1 0.1414 0.949 0.980 0.020
#> GSM35537 1 0.3879 0.966 0.924 0.076
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM35441 2 0.0424 0.995 0.000 0.992 0.008
#> GSM35446 3 0.2448 0.909 0.000 0.076 0.924
#> GSM35449 2 0.0000 0.991 0.000 1.000 0.000
#> GSM35455 2 0.0000 0.991 0.000 1.000 0.000
#> GSM35458 3 0.2711 0.892 0.000 0.088 0.912
#> GSM35460 3 0.2448 0.909 0.000 0.076 0.924
#> GSM35461 3 0.3851 0.878 0.136 0.004 0.860
#> GSM35463 2 0.0424 0.995 0.000 0.992 0.008
#> GSM35472 3 0.1163 0.919 0.000 0.028 0.972
#> GSM35475 3 0.1289 0.917 0.000 0.032 0.968
#> GSM35483 2 0.0592 0.993 0.000 0.988 0.012
#> GSM35496 3 0.3851 0.878 0.136 0.004 0.860
#> GSM35497 2 0.0000 0.991 0.000 1.000 0.000
#> GSM35504 2 0.0424 0.995 0.000 0.992 0.008
#> GSM35508 2 0.0892 0.983 0.000 0.980 0.020
#> GSM35511 3 0.2448 0.909 0.000 0.076 0.924
#> GSM35512 3 0.1163 0.919 0.000 0.028 0.972
#> GSM35515 3 0.1031 0.917 0.000 0.024 0.976
#> GSM35519 3 0.1753 0.915 0.000 0.048 0.952
#> GSM35527 2 0.0892 0.983 0.000 0.980 0.020
#> GSM35532 3 0.2448 0.909 0.000 0.076 0.924
#> GSM35439 2 0.0424 0.995 0.000 0.992 0.008
#> GSM35443 1 0.0237 0.979 0.996 0.000 0.004
#> GSM35445 1 0.1031 0.972 0.976 0.000 0.024
#> GSM35448 3 0.2448 0.909 0.000 0.076 0.924
#> GSM35451 1 0.1170 0.981 0.976 0.016 0.008
#> GSM35454 3 0.3851 0.878 0.136 0.004 0.860
#> GSM35457 2 0.0000 0.991 0.000 1.000 0.000
#> GSM35465 2 0.0000 0.991 0.000 1.000 0.000
#> GSM35468 1 0.1031 0.972 0.976 0.000 0.024
#> GSM35471 1 0.1170 0.981 0.976 0.016 0.008
#> GSM35473 1 0.1031 0.972 0.976 0.000 0.024
#> GSM35477 1 0.1170 0.981 0.976 0.016 0.008
#> GSM35480 1 0.0661 0.981 0.988 0.004 0.008
#> GSM35482 3 0.3851 0.878 0.136 0.004 0.860
#> GSM35485 2 0.0424 0.995 0.000 0.992 0.008
#> GSM35489 2 0.0424 0.995 0.000 0.992 0.008
#> GSM35492 1 0.1031 0.972 0.976 0.000 0.024
#> GSM35495 3 0.1267 0.912 0.024 0.004 0.972
#> GSM35499 2 0.0424 0.995 0.000 0.992 0.008
#> GSM35502 1 0.1031 0.972 0.976 0.000 0.024
#> GSM35505 3 0.1399 0.919 0.004 0.028 0.968
#> GSM35507 1 0.1170 0.981 0.976 0.016 0.008
#> GSM35510 2 0.0000 0.991 0.000 1.000 0.000
#> GSM35514 1 0.1031 0.972 0.976 0.000 0.024
#> GSM35517 2 0.0424 0.995 0.000 0.992 0.008
#> GSM35520 3 0.4842 0.740 0.000 0.224 0.776
#> GSM35523 1 0.1170 0.981 0.976 0.016 0.008
#> GSM35529 2 0.0000 0.991 0.000 1.000 0.000
#> GSM35531 2 0.0424 0.995 0.000 0.992 0.008
#> GSM35534 2 0.0424 0.995 0.000 0.992 0.008
#> GSM35536 1 0.0892 0.973 0.980 0.000 0.020
#> GSM35538 1 0.1170 0.981 0.976 0.016 0.008
#> GSM35539 1 0.1170 0.981 0.976 0.016 0.008
#> GSM35540 2 0.0424 0.995 0.000 0.992 0.008
#> GSM35541 2 0.0424 0.995 0.000 0.992 0.008
#> GSM35442 1 0.1129 0.977 0.976 0.004 0.020
#> GSM35447 3 0.1163 0.919 0.000 0.028 0.972
#> GSM35450 1 0.1170 0.981 0.976 0.016 0.008
#> GSM35453 1 0.1399 0.978 0.968 0.004 0.028
#> GSM35456 1 0.1170 0.981 0.976 0.016 0.008
#> GSM35464 1 0.1585 0.973 0.964 0.028 0.008
#> GSM35467 1 0.1031 0.972 0.976 0.000 0.024
#> GSM35470 1 0.1129 0.977 0.976 0.004 0.020
#> GSM35479 3 0.3851 0.878 0.136 0.004 0.860
#> GSM35484 1 0.0424 0.980 0.992 0.000 0.008
#> GSM35488 1 0.1015 0.981 0.980 0.012 0.008
#> GSM35491 1 0.1031 0.972 0.976 0.000 0.024
#> GSM35494 3 0.3851 0.878 0.136 0.004 0.860
#> GSM35498 1 0.1170 0.981 0.976 0.016 0.008
#> GSM35501 1 0.1031 0.972 0.976 0.000 0.024
#> GSM35509 3 0.3851 0.878 0.136 0.004 0.860
#> GSM35513 1 0.1031 0.972 0.976 0.000 0.024
#> GSM35516 2 0.0424 0.995 0.000 0.992 0.008
#> GSM35522 1 0.1170 0.981 0.976 0.016 0.008
#> GSM35525 1 0.1170 0.981 0.976 0.016 0.008
#> GSM35528 1 0.1170 0.981 0.976 0.016 0.008
#> GSM35533 1 0.0848 0.981 0.984 0.008 0.008
#> GSM35537 1 0.1129 0.977 0.976 0.004 0.020
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM35441 2 0.1118 0.809 0.000 0.964 0.036 0.000
#> GSM35446 3 0.0000 0.841 0.000 0.000 1.000 0.000
#> GSM35449 2 0.0000 0.833 0.000 1.000 0.000 0.000
#> GSM35455 2 0.0000 0.833 0.000 1.000 0.000 0.000
#> GSM35458 3 0.0000 0.841 0.000 0.000 1.000 0.000
#> GSM35460 3 0.0000 0.841 0.000 0.000 1.000 0.000
#> GSM35461 4 0.4222 0.745 0.272 0.000 0.000 0.728
#> GSM35463 2 0.4925 0.254 0.000 0.572 0.428 0.000
#> GSM35472 3 0.0000 0.841 0.000 0.000 1.000 0.000
#> GSM35475 3 0.0000 0.841 0.000 0.000 1.000 0.000
#> GSM35483 3 0.4382 0.498 0.000 0.296 0.704 0.000
#> GSM35496 4 0.4222 0.745 0.272 0.000 0.000 0.728
#> GSM35497 2 0.0000 0.833 0.000 1.000 0.000 0.000
#> GSM35504 2 0.0000 0.833 0.000 1.000 0.000 0.000
#> GSM35508 2 0.0000 0.833 0.000 1.000 0.000 0.000
#> GSM35511 3 0.0000 0.841 0.000 0.000 1.000 0.000
#> GSM35512 3 0.0000 0.841 0.000 0.000 1.000 0.000
#> GSM35515 3 0.0000 0.841 0.000 0.000 1.000 0.000
#> GSM35519 3 0.0000 0.841 0.000 0.000 1.000 0.000
#> GSM35527 2 0.0000 0.833 0.000 1.000 0.000 0.000
#> GSM35532 3 0.0000 0.841 0.000 0.000 1.000 0.000
#> GSM35439 3 0.4955 0.160 0.000 0.444 0.556 0.000
#> GSM35443 1 0.3219 0.783 0.836 0.000 0.000 0.164
#> GSM35445 1 0.0592 0.873 0.984 0.000 0.000 0.016
#> GSM35448 3 0.0000 0.841 0.000 0.000 1.000 0.000
#> GSM35451 4 0.0000 0.825 0.000 0.000 0.000 1.000
#> GSM35454 4 0.4222 0.745 0.272 0.000 0.000 0.728
#> GSM35457 2 0.0000 0.833 0.000 1.000 0.000 0.000
#> GSM35465 2 0.0000 0.833 0.000 1.000 0.000 0.000
#> GSM35468 1 0.0000 0.877 1.000 0.000 0.000 0.000
#> GSM35471 4 0.0000 0.825 0.000 0.000 0.000 1.000
#> GSM35473 1 0.0000 0.877 1.000 0.000 0.000 0.000
#> GSM35477 4 0.0000 0.825 0.000 0.000 0.000 1.000
#> GSM35480 4 0.4222 0.745 0.272 0.000 0.000 0.728
#> GSM35482 4 0.4222 0.745 0.272 0.000 0.000 0.728
#> GSM35485 3 0.4955 0.160 0.000 0.444 0.556 0.000
#> GSM35489 2 0.4925 0.254 0.000 0.572 0.428 0.000
#> GSM35492 1 0.0000 0.877 1.000 0.000 0.000 0.000
#> GSM35495 4 0.5292 0.687 0.064 0.000 0.208 0.728
#> GSM35499 2 0.0188 0.831 0.000 0.996 0.004 0.000
#> GSM35502 1 0.0000 0.877 1.000 0.000 0.000 0.000
#> GSM35505 3 0.2999 0.703 0.004 0.000 0.864 0.132
#> GSM35507 4 0.0000 0.825 0.000 0.000 0.000 1.000
#> GSM35510 2 0.0000 0.833 0.000 1.000 0.000 0.000
#> GSM35514 1 0.0000 0.877 1.000 0.000 0.000 0.000
#> GSM35517 2 0.4925 0.254 0.000 0.572 0.428 0.000
#> GSM35520 3 0.0000 0.841 0.000 0.000 1.000 0.000
#> GSM35523 4 0.0000 0.825 0.000 0.000 0.000 1.000
#> GSM35529 2 0.0000 0.833 0.000 1.000 0.000 0.000
#> GSM35531 3 0.4948 0.173 0.000 0.440 0.560 0.000
#> GSM35534 3 0.4948 0.173 0.000 0.440 0.560 0.000
#> GSM35536 1 0.1557 0.857 0.944 0.000 0.000 0.056
#> GSM35538 4 0.0000 0.825 0.000 0.000 0.000 1.000
#> GSM35539 4 0.0000 0.825 0.000 0.000 0.000 1.000
#> GSM35540 2 0.0000 0.833 0.000 1.000 0.000 0.000
#> GSM35541 2 0.4925 0.254 0.000 0.572 0.428 0.000
#> GSM35442 1 0.3266 0.779 0.832 0.000 0.000 0.168
#> GSM35447 3 0.0000 0.841 0.000 0.000 1.000 0.000
#> GSM35450 4 0.0000 0.825 0.000 0.000 0.000 1.000
#> GSM35453 1 0.3219 0.783 0.836 0.000 0.000 0.164
#> GSM35456 4 0.0000 0.825 0.000 0.000 0.000 1.000
#> GSM35464 4 0.0000 0.825 0.000 0.000 0.000 1.000
#> GSM35467 1 0.0000 0.877 1.000 0.000 0.000 0.000
#> GSM35470 4 0.4222 0.745 0.272 0.000 0.000 0.728
#> GSM35479 4 0.4222 0.745 0.272 0.000 0.000 0.728
#> GSM35484 1 0.4193 0.630 0.732 0.000 0.000 0.268
#> GSM35488 1 0.4925 0.152 0.572 0.000 0.000 0.428
#> GSM35491 1 0.0000 0.877 1.000 0.000 0.000 0.000
#> GSM35494 4 0.4222 0.745 0.272 0.000 0.000 0.728
#> GSM35498 4 0.0000 0.825 0.000 0.000 0.000 1.000
#> GSM35501 1 0.0000 0.877 1.000 0.000 0.000 0.000
#> GSM35509 4 0.4222 0.745 0.272 0.000 0.000 0.728
#> GSM35513 1 0.0000 0.877 1.000 0.000 0.000 0.000
#> GSM35516 2 0.4967 0.174 0.000 0.548 0.452 0.000
#> GSM35522 4 0.0000 0.825 0.000 0.000 0.000 1.000
#> GSM35525 4 0.4222 0.745 0.272 0.000 0.000 0.728
#> GSM35528 4 0.0000 0.825 0.000 0.000 0.000 1.000
#> GSM35533 1 0.4222 0.622 0.728 0.000 0.000 0.272
#> GSM35537 4 0.4222 0.745 0.272 0.000 0.000 0.728
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM35441 2 0.0510 0.758 0.000 0.984 0.000 0.000 0.016
#> GSM35446 5 0.0000 0.960 0.000 0.000 0.000 0.000 1.000
#> GSM35449 2 0.0000 0.774 0.000 1.000 0.000 0.000 0.000
#> GSM35455 2 0.0000 0.774 0.000 1.000 0.000 0.000 0.000
#> GSM35458 5 0.0162 0.959 0.000 0.000 0.004 0.000 0.996
#> GSM35460 5 0.0609 0.940 0.000 0.000 0.000 0.020 0.980
#> GSM35461 4 0.5720 0.516 0.000 0.000 0.124 0.600 0.276
#> GSM35463 3 0.5935 1.000 0.000 0.268 0.580 0.000 0.152
#> GSM35472 5 0.0290 0.953 0.000 0.000 0.000 0.008 0.992
#> GSM35475 5 0.0162 0.959 0.000 0.000 0.004 0.000 0.996
#> GSM35483 5 0.3333 0.607 0.000 0.208 0.004 0.000 0.788
#> GSM35496 4 0.5720 0.516 0.000 0.000 0.124 0.600 0.276
#> GSM35497 2 0.0000 0.774 0.000 1.000 0.000 0.000 0.000
#> GSM35504 2 0.3661 0.559 0.000 0.724 0.000 0.000 0.276
#> GSM35508 2 0.3661 0.559 0.000 0.724 0.000 0.000 0.276
#> GSM35511 5 0.0000 0.960 0.000 0.000 0.000 0.000 1.000
#> GSM35512 5 0.0000 0.960 0.000 0.000 0.000 0.000 1.000
#> GSM35515 5 0.0162 0.959 0.000 0.000 0.004 0.000 0.996
#> GSM35519 5 0.0162 0.959 0.000 0.000 0.004 0.000 0.996
#> GSM35527 2 0.3661 0.559 0.000 0.724 0.000 0.000 0.276
#> GSM35532 5 0.0000 0.960 0.000 0.000 0.000 0.000 1.000
#> GSM35439 3 0.5935 1.000 0.000 0.268 0.580 0.000 0.152
#> GSM35443 1 0.2561 0.822 0.856 0.000 0.000 0.144 0.000
#> GSM35445 1 0.0162 0.895 0.996 0.000 0.000 0.004 0.000
#> GSM35448 5 0.0000 0.960 0.000 0.000 0.000 0.000 1.000
#> GSM35451 4 0.3661 0.676 0.000 0.000 0.276 0.724 0.000
#> GSM35454 4 0.6235 0.507 0.076 0.000 0.048 0.600 0.276
#> GSM35457 2 0.0000 0.774 0.000 1.000 0.000 0.000 0.000
#> GSM35465 2 0.0000 0.774 0.000 1.000 0.000 0.000 0.000
#> GSM35468 1 0.0000 0.896 1.000 0.000 0.000 0.000 0.000
#> GSM35471 4 0.2516 0.707 0.000 0.000 0.140 0.860 0.000
#> GSM35473 1 0.0000 0.896 1.000 0.000 0.000 0.000 0.000
#> GSM35477 4 0.3707 0.673 0.000 0.000 0.284 0.716 0.000
#> GSM35480 4 0.6172 0.379 0.288 0.000 0.152 0.556 0.004
#> GSM35482 4 0.5720 0.516 0.000 0.000 0.124 0.600 0.276
#> GSM35485 3 0.5935 1.000 0.000 0.268 0.580 0.000 0.152
#> GSM35489 3 0.5935 1.000 0.000 0.268 0.580 0.000 0.152
#> GSM35492 1 0.0000 0.896 1.000 0.000 0.000 0.000 0.000
#> GSM35495 4 0.5368 0.468 0.000 0.000 0.072 0.596 0.332
#> GSM35499 2 0.0000 0.774 0.000 1.000 0.000 0.000 0.000
#> GSM35502 1 0.0000 0.896 1.000 0.000 0.000 0.000 0.000
#> GSM35505 5 0.2471 0.796 0.000 0.000 0.000 0.136 0.864
#> GSM35507 4 0.2674 0.708 0.000 0.000 0.140 0.856 0.004
#> GSM35510 2 0.0000 0.774 0.000 1.000 0.000 0.000 0.000
#> GSM35514 1 0.0000 0.896 1.000 0.000 0.000 0.000 0.000
#> GSM35517 2 0.6298 -0.728 0.000 0.436 0.412 0.000 0.152
#> GSM35520 5 0.0162 0.959 0.000 0.000 0.004 0.000 0.996
#> GSM35523 4 0.0609 0.712 0.000 0.000 0.000 0.980 0.020
#> GSM35529 2 0.0000 0.774 0.000 1.000 0.000 0.000 0.000
#> GSM35531 3 0.5935 1.000 0.000 0.268 0.580 0.000 0.152
#> GSM35534 3 0.5935 1.000 0.000 0.268 0.580 0.000 0.152
#> GSM35536 1 0.0000 0.896 1.000 0.000 0.000 0.000 0.000
#> GSM35538 4 0.3730 0.672 0.000 0.000 0.288 0.712 0.000
#> GSM35539 4 0.3661 0.677 0.000 0.000 0.276 0.724 0.000
#> GSM35540 2 0.3661 0.559 0.000 0.724 0.000 0.000 0.276
#> GSM35541 3 0.5935 1.000 0.000 0.268 0.580 0.000 0.152
#> GSM35442 1 0.5905 0.428 0.580 0.000 0.000 0.144 0.276
#> GSM35447 5 0.0000 0.960 0.000 0.000 0.000 0.000 1.000
#> GSM35450 4 0.3730 0.672 0.000 0.000 0.288 0.712 0.000
#> GSM35453 1 0.3011 0.814 0.844 0.000 0.000 0.140 0.016
#> GSM35456 4 0.2516 0.707 0.000 0.000 0.140 0.860 0.000
#> GSM35464 4 0.2653 0.674 0.000 0.096 0.024 0.880 0.000
#> GSM35467 1 0.0000 0.896 1.000 0.000 0.000 0.000 0.000
#> GSM35470 4 0.2873 0.651 0.120 0.000 0.000 0.860 0.020
#> GSM35479 4 0.5720 0.516 0.000 0.000 0.124 0.600 0.276
#> GSM35484 1 0.2890 0.807 0.836 0.000 0.000 0.160 0.004
#> GSM35488 1 0.5576 0.243 0.536 0.000 0.076 0.388 0.000
#> GSM35491 1 0.0000 0.896 1.000 0.000 0.000 0.000 0.000
#> GSM35494 4 0.5720 0.516 0.000 0.000 0.124 0.600 0.276
#> GSM35498 4 0.2674 0.708 0.000 0.000 0.140 0.856 0.004
#> GSM35501 1 0.0000 0.896 1.000 0.000 0.000 0.000 0.000
#> GSM35509 4 0.5720 0.516 0.000 0.000 0.124 0.600 0.276
#> GSM35513 1 0.0000 0.896 1.000 0.000 0.000 0.000 0.000
#> GSM35516 3 0.5935 1.000 0.000 0.268 0.580 0.000 0.152
#> GSM35522 4 0.0609 0.712 0.000 0.000 0.000 0.980 0.020
#> GSM35525 4 0.4840 0.613 0.124 0.000 0.152 0.724 0.000
#> GSM35528 4 0.3684 0.675 0.000 0.000 0.280 0.720 0.000
#> GSM35533 1 0.2930 0.805 0.832 0.000 0.000 0.164 0.004
#> GSM35537 4 0.2561 0.669 0.096 0.000 0.000 0.884 0.020
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM35441 2 0.0547 0.872 0.000 0.980 0.000 0.000 0.000 0.020
#> GSM35446 5 0.0937 0.922 0.000 0.000 0.040 0.000 0.960 0.000
#> GSM35449 2 0.0000 0.884 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM35455 2 0.0000 0.884 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM35458 5 0.0000 0.918 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM35460 5 0.3309 0.630 0.000 0.000 0.280 0.000 0.720 0.000
#> GSM35461 3 0.4893 0.469 0.340 0.000 0.584 0.000 0.076 0.000
#> GSM35463 6 0.0000 0.891 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM35472 5 0.3288 0.638 0.000 0.000 0.276 0.000 0.724 0.000
#> GSM35475 5 0.0000 0.918 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM35483 6 0.4167 0.348 0.000 0.000 0.020 0.000 0.368 0.612
#> GSM35496 3 0.0000 0.836 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM35497 2 0.0000 0.884 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM35504 2 0.3748 0.744 0.000 0.784 0.108 0.000 0.108 0.000
#> GSM35508 2 0.4972 0.513 0.000 0.620 0.272 0.000 0.108 0.000
#> GSM35511 5 0.2135 0.846 0.000 0.000 0.128 0.000 0.872 0.000
#> GSM35512 5 0.0937 0.922 0.000 0.000 0.040 0.000 0.960 0.000
#> GSM35515 5 0.0000 0.918 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM35519 5 0.0000 0.918 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM35527 2 0.4972 0.513 0.000 0.620 0.272 0.000 0.108 0.000
#> GSM35532 5 0.0937 0.922 0.000 0.000 0.040 0.000 0.960 0.000
#> GSM35439 6 0.0000 0.891 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM35443 1 0.0000 0.940 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35445 1 0.0000 0.940 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35448 5 0.0790 0.923 0.000 0.000 0.032 0.000 0.968 0.000
#> GSM35451 4 0.0000 0.920 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM35454 3 0.4859 0.536 0.304 0.000 0.612 0.000 0.084 0.000
#> GSM35457 2 0.0000 0.884 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM35465 2 0.0000 0.884 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM35468 1 0.0000 0.940 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35471 4 0.0547 0.919 0.000 0.000 0.020 0.980 0.000 0.000
#> GSM35473 1 0.0000 0.940 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35477 4 0.0000 0.920 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM35480 1 0.3725 0.574 0.676 0.000 0.008 0.316 0.000 0.000
#> GSM35482 3 0.0000 0.836 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM35485 6 0.0000 0.891 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM35489 6 0.0000 0.891 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM35492 1 0.0000 0.940 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35495 3 0.2178 0.740 0.000 0.000 0.868 0.000 0.132 0.000
#> GSM35499 2 0.0146 0.881 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM35502 1 0.0000 0.940 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35505 5 0.1075 0.916 0.000 0.000 0.048 0.000 0.952 0.000
#> GSM35507 4 0.0713 0.916 0.000 0.000 0.028 0.972 0.000 0.000
#> GSM35510 2 0.0000 0.884 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM35514 1 0.0000 0.940 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35517 6 0.3867 0.062 0.000 0.488 0.000 0.000 0.000 0.512
#> GSM35520 5 0.0000 0.918 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM35523 4 0.3531 0.476 0.000 0.000 0.328 0.672 0.000 0.000
#> GSM35529 2 0.0000 0.884 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM35531 6 0.0000 0.891 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM35534 6 0.0000 0.891 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM35536 1 0.0000 0.940 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35538 4 0.0000 0.920 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM35539 4 0.0000 0.920 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM35540 2 0.3748 0.744 0.000 0.784 0.108 0.000 0.108 0.000
#> GSM35541 6 0.0000 0.891 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM35442 1 0.1958 0.837 0.896 0.000 0.100 0.000 0.004 0.000
#> GSM35447 5 0.0713 0.923 0.000 0.000 0.028 0.000 0.972 0.000
#> GSM35450 4 0.0000 0.920 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM35453 1 0.0937 0.903 0.960 0.000 0.040 0.000 0.000 0.000
#> GSM35456 4 0.0547 0.919 0.000 0.000 0.020 0.980 0.000 0.000
#> GSM35464 4 0.0865 0.911 0.000 0.000 0.036 0.964 0.000 0.000
#> GSM35467 1 0.0000 0.940 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35470 3 0.2772 0.704 0.004 0.000 0.816 0.180 0.000 0.000
#> GSM35479 3 0.0000 0.836 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM35484 1 0.0146 0.938 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM35488 1 0.0713 0.922 0.972 0.000 0.000 0.028 0.000 0.000
#> GSM35491 1 0.0000 0.940 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35494 3 0.0000 0.836 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM35498 4 0.0790 0.914 0.000 0.000 0.032 0.968 0.000 0.000
#> GSM35501 1 0.0000 0.940 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35509 3 0.0000 0.836 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM35513 1 0.0000 0.940 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM35516 6 0.0000 0.891 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM35522 4 0.3531 0.476 0.000 0.000 0.328 0.672 0.000 0.000
#> GSM35525 1 0.3838 0.286 0.552 0.000 0.000 0.448 0.000 0.000
#> GSM35528 4 0.0000 0.920 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM35533 1 0.0146 0.938 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM35537 3 0.2562 0.714 0.000 0.000 0.828 0.172 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 time(p) k
#> ATC:mclust 79 3.90e-07 2
#> ATC:mclust 79 2.39e-06 3
#> ATC:mclust 68 9.53e-06 4
#> ATC:mclust 74 4.48e-06 5
#> ATC:mclust 73 1.32e-05 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "NMF"]
# you can also extract it by
# res = res_list["ATC:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 7758 rows and 79 columns.
#> Top rows (776, 1552, 2328, 3103, 3879) are extracted by 'ATC' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.922 0.926 0.972 0.5015 0.498 0.498
#> 3 3 0.871 0.876 0.948 0.3084 0.736 0.518
#> 4 4 0.602 0.655 0.824 0.1040 0.821 0.548
#> 5 5 0.634 0.541 0.720 0.0584 0.870 0.608
#> 6 6 0.637 0.498 0.736 0.0480 0.868 0.561
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
#> GSM35441 2 0.0000 0.97093 0.000 1.000
#> GSM35446 2 0.0000 0.97093 0.000 1.000
#> GSM35449 2 0.0000 0.97093 0.000 1.000
#> GSM35455 2 0.0000 0.97093 0.000 1.000
#> GSM35458 2 0.6438 0.79871 0.164 0.836
#> GSM35460 2 0.0000 0.97093 0.000 1.000
#> GSM35461 1 0.0000 0.96913 1.000 0.000
#> GSM35463 2 0.0000 0.97093 0.000 1.000
#> GSM35472 2 0.0000 0.97093 0.000 1.000
#> GSM35475 2 0.0376 0.96808 0.004 0.996
#> GSM35483 2 0.0000 0.97093 0.000 1.000
#> GSM35496 1 0.0000 0.96913 1.000 0.000
#> GSM35497 2 0.0000 0.97093 0.000 1.000
#> GSM35504 2 0.0000 0.97093 0.000 1.000
#> GSM35508 2 0.0000 0.97093 0.000 1.000
#> GSM35511 2 0.0000 0.97093 0.000 1.000
#> GSM35512 1 0.9427 0.42765 0.640 0.360
#> GSM35515 2 0.6247 0.80954 0.156 0.844
#> GSM35519 2 0.0000 0.97093 0.000 1.000
#> GSM35527 2 0.0000 0.97093 0.000 1.000
#> GSM35532 2 0.0000 0.97093 0.000 1.000
#> GSM35439 2 0.0000 0.97093 0.000 1.000
#> GSM35443 1 0.0000 0.96913 1.000 0.000
#> GSM35445 1 0.0000 0.96913 1.000 0.000
#> GSM35448 2 0.0000 0.97093 0.000 1.000
#> GSM35451 1 0.0000 0.96913 1.000 0.000
#> GSM35454 1 0.0000 0.96913 1.000 0.000
#> GSM35457 2 0.0000 0.97093 0.000 1.000
#> GSM35465 2 0.0000 0.97093 0.000 1.000
#> GSM35468 1 0.0000 0.96913 1.000 0.000
#> GSM35471 1 0.0000 0.96913 1.000 0.000
#> GSM35473 1 0.0000 0.96913 1.000 0.000
#> GSM35477 1 0.0000 0.96913 1.000 0.000
#> GSM35480 1 0.0000 0.96913 1.000 0.000
#> GSM35482 1 0.0000 0.96913 1.000 0.000
#> GSM35485 2 0.0000 0.97093 0.000 1.000
#> GSM35489 2 0.0000 0.97093 0.000 1.000
#> GSM35492 1 0.0000 0.96913 1.000 0.000
#> GSM35495 1 1.0000 -0.00581 0.504 0.496
#> GSM35499 2 0.0000 0.97093 0.000 1.000
#> GSM35502 1 0.0000 0.96913 1.000 0.000
#> GSM35505 1 0.0000 0.96913 1.000 0.000
#> GSM35507 1 0.8861 0.55275 0.696 0.304
#> GSM35510 2 0.0000 0.97093 0.000 1.000
#> GSM35514 1 0.0000 0.96913 1.000 0.000
#> GSM35517 2 0.0000 0.97093 0.000 1.000
#> GSM35520 2 0.0000 0.97093 0.000 1.000
#> GSM35523 1 0.0000 0.96913 1.000 0.000
#> GSM35529 2 0.0000 0.97093 0.000 1.000
#> GSM35531 2 0.1633 0.95232 0.024 0.976
#> GSM35534 2 0.0000 0.97093 0.000 1.000
#> GSM35536 1 0.0000 0.96913 1.000 0.000
#> GSM35538 1 0.0000 0.96913 1.000 0.000
#> GSM35539 1 0.0000 0.96913 1.000 0.000
#> GSM35540 2 0.0000 0.97093 0.000 1.000
#> GSM35541 2 0.0000 0.97093 0.000 1.000
#> GSM35442 1 0.0000 0.96913 1.000 0.000
#> GSM35447 1 0.0376 0.96563 0.996 0.004
#> GSM35450 1 0.0000 0.96913 1.000 0.000
#> GSM35453 1 0.0000 0.96913 1.000 0.000
#> GSM35456 1 0.0000 0.96913 1.000 0.000
#> GSM35464 2 0.5178 0.85892 0.116 0.884
#> GSM35467 1 0.0000 0.96913 1.000 0.000
#> GSM35470 1 0.0000 0.96913 1.000 0.000
#> GSM35479 1 0.0000 0.96913 1.000 0.000
#> GSM35484 1 0.0000 0.96913 1.000 0.000
#> GSM35488 1 0.0000 0.96913 1.000 0.000
#> GSM35491 1 0.0000 0.96913 1.000 0.000
#> GSM35494 1 0.0000 0.96913 1.000 0.000
#> GSM35498 1 0.0000 0.96913 1.000 0.000
#> GSM35501 1 0.0000 0.96913 1.000 0.000
#> GSM35509 2 0.9998 0.00433 0.492 0.508
#> GSM35513 1 0.0000 0.96913 1.000 0.000
#> GSM35516 2 0.0938 0.96190 0.012 0.988
#> GSM35522 1 0.3584 0.90237 0.932 0.068
#> GSM35525 1 0.0000 0.96913 1.000 0.000
#> GSM35528 1 0.0000 0.96913 1.000 0.000
#> GSM35533 1 0.0000 0.96913 1.000 0.000
#> GSM35537 1 0.0000 0.96913 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM35441 2 0.0000 0.9301 0.000 1.000 0.000
#> GSM35446 3 0.0000 0.8761 0.000 0.000 1.000
#> GSM35449 2 0.0000 0.9301 0.000 1.000 0.000
#> GSM35455 2 0.0000 0.9301 0.000 1.000 0.000
#> GSM35458 3 0.6955 0.4241 0.032 0.332 0.636
#> GSM35460 3 0.0000 0.8761 0.000 0.000 1.000
#> GSM35461 3 0.6154 0.4050 0.408 0.000 0.592
#> GSM35463 2 0.0000 0.9301 0.000 1.000 0.000
#> GSM35472 3 0.0000 0.8761 0.000 0.000 1.000
#> GSM35475 3 0.0000 0.8761 0.000 0.000 1.000
#> GSM35483 2 0.0424 0.9248 0.000 0.992 0.008
#> GSM35496 3 0.3267 0.8265 0.116 0.000 0.884
#> GSM35497 2 0.0000 0.9301 0.000 1.000 0.000
#> GSM35504 2 0.1411 0.9038 0.000 0.964 0.036
#> GSM35508 2 0.6168 0.2843 0.000 0.588 0.412
#> GSM35511 3 0.0000 0.8761 0.000 0.000 1.000
#> GSM35512 3 0.0000 0.8761 0.000 0.000 1.000
#> GSM35515 3 0.0000 0.8761 0.000 0.000 1.000
#> GSM35519 3 0.0000 0.8761 0.000 0.000 1.000
#> GSM35527 2 0.2537 0.8651 0.000 0.920 0.080
#> GSM35532 3 0.0000 0.8761 0.000 0.000 1.000
#> GSM35439 2 0.0000 0.9301 0.000 1.000 0.000
#> GSM35443 1 0.0000 0.9849 1.000 0.000 0.000
#> GSM35445 1 0.0000 0.9849 1.000 0.000 0.000
#> GSM35448 3 0.0000 0.8761 0.000 0.000 1.000
#> GSM35451 1 0.3551 0.8446 0.868 0.132 0.000
#> GSM35454 1 0.2356 0.9110 0.928 0.000 0.072
#> GSM35457 2 0.0000 0.9301 0.000 1.000 0.000
#> GSM35465 2 0.0000 0.9301 0.000 1.000 0.000
#> GSM35468 1 0.0000 0.9849 1.000 0.000 0.000
#> GSM35471 1 0.1643 0.9494 0.956 0.044 0.000
#> GSM35473 1 0.0000 0.9849 1.000 0.000 0.000
#> GSM35477 1 0.1643 0.9492 0.956 0.044 0.000
#> GSM35480 1 0.0000 0.9849 1.000 0.000 0.000
#> GSM35482 3 0.3267 0.8261 0.116 0.000 0.884
#> GSM35485 2 0.0000 0.9301 0.000 1.000 0.000
#> GSM35489 2 0.0000 0.9301 0.000 1.000 0.000
#> GSM35492 1 0.0000 0.9849 1.000 0.000 0.000
#> GSM35495 3 0.0000 0.8761 0.000 0.000 1.000
#> GSM35499 2 0.0000 0.9301 0.000 1.000 0.000
#> GSM35502 1 0.0000 0.9849 1.000 0.000 0.000
#> GSM35505 3 0.5497 0.6288 0.292 0.000 0.708
#> GSM35507 2 0.6126 0.3250 0.400 0.600 0.000
#> GSM35510 2 0.0000 0.9301 0.000 1.000 0.000
#> GSM35514 1 0.0000 0.9849 1.000 0.000 0.000
#> GSM35517 2 0.0000 0.9301 0.000 1.000 0.000
#> GSM35520 3 0.5621 0.4980 0.000 0.308 0.692
#> GSM35523 1 0.0237 0.9828 0.996 0.004 0.000
#> GSM35529 2 0.0000 0.9301 0.000 1.000 0.000
#> GSM35531 2 0.0237 0.9273 0.004 0.996 0.000
#> GSM35534 2 0.0000 0.9301 0.000 1.000 0.000
#> GSM35536 1 0.0000 0.9849 1.000 0.000 0.000
#> GSM35538 1 0.0237 0.9828 0.996 0.004 0.000
#> GSM35539 1 0.0000 0.9849 1.000 0.000 0.000
#> GSM35540 2 0.2165 0.8813 0.000 0.936 0.064
#> GSM35541 2 0.0000 0.9301 0.000 1.000 0.000
#> GSM35442 1 0.0747 0.9722 0.984 0.000 0.016
#> GSM35447 3 0.1031 0.8692 0.024 0.000 0.976
#> GSM35450 1 0.0592 0.9773 0.988 0.012 0.000
#> GSM35453 1 0.0000 0.9849 1.000 0.000 0.000
#> GSM35456 1 0.2066 0.9331 0.940 0.060 0.000
#> GSM35464 2 0.0237 0.9272 0.004 0.996 0.000
#> GSM35467 1 0.0000 0.9849 1.000 0.000 0.000
#> GSM35470 1 0.0000 0.9849 1.000 0.000 0.000
#> GSM35479 3 0.3686 0.8104 0.140 0.000 0.860
#> GSM35484 1 0.0000 0.9849 1.000 0.000 0.000
#> GSM35488 1 0.0000 0.9849 1.000 0.000 0.000
#> GSM35491 1 0.0000 0.9849 1.000 0.000 0.000
#> GSM35494 3 0.6225 0.3420 0.432 0.000 0.568
#> GSM35498 1 0.0747 0.9742 0.984 0.016 0.000
#> GSM35501 1 0.0000 0.9849 1.000 0.000 0.000
#> GSM35509 3 0.0592 0.8733 0.012 0.000 0.988
#> GSM35513 1 0.0000 0.9849 1.000 0.000 0.000
#> GSM35516 2 0.0000 0.9301 0.000 1.000 0.000
#> GSM35522 2 0.6305 0.0564 0.484 0.516 0.000
#> GSM35525 1 0.0000 0.9849 1.000 0.000 0.000
#> GSM35528 1 0.0237 0.9828 0.996 0.004 0.000
#> GSM35533 1 0.0000 0.9849 1.000 0.000 0.000
#> GSM35537 1 0.0000 0.9849 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM35441 2 0.3942 0.6531 0.000 0.764 0.000 0.236
#> GSM35446 3 0.3486 0.6925 0.000 0.000 0.812 0.188
#> GSM35449 2 0.1716 0.7113 0.000 0.936 0.000 0.064
#> GSM35455 2 0.2704 0.7059 0.000 0.876 0.000 0.124
#> GSM35458 4 0.2611 0.7073 0.096 0.000 0.008 0.896
#> GSM35460 3 0.1716 0.7541 0.000 0.000 0.936 0.064
#> GSM35461 1 0.5660 0.3163 0.576 0.000 0.396 0.028
#> GSM35463 2 0.4008 0.6398 0.000 0.756 0.000 0.244
#> GSM35472 3 0.2149 0.7501 0.000 0.000 0.912 0.088
#> GSM35475 4 0.2297 0.7298 0.024 0.004 0.044 0.928
#> GSM35483 4 0.2469 0.7237 0.000 0.108 0.000 0.892
#> GSM35496 3 0.2861 0.7397 0.096 0.000 0.888 0.016
#> GSM35497 2 0.3975 0.6480 0.000 0.760 0.000 0.240
#> GSM35504 2 0.4248 0.6411 0.000 0.768 0.012 0.220
#> GSM35508 3 0.6251 0.4500 0.000 0.140 0.664 0.196
#> GSM35511 3 0.3024 0.7130 0.000 0.000 0.852 0.148
#> GSM35512 3 0.5108 0.5204 0.020 0.000 0.672 0.308
#> GSM35515 4 0.3247 0.7047 0.060 0.000 0.060 0.880
#> GSM35519 4 0.3208 0.6645 0.004 0.000 0.148 0.848
#> GSM35527 2 0.5327 0.5960 0.000 0.720 0.060 0.220
#> GSM35532 4 0.4996 -0.0585 0.000 0.000 0.484 0.516
#> GSM35439 4 0.4632 0.4250 0.004 0.308 0.000 0.688
#> GSM35443 1 0.1557 0.8600 0.944 0.000 0.000 0.056
#> GSM35445 1 0.0376 0.8740 0.992 0.000 0.004 0.004
#> GSM35448 4 0.4453 0.5650 0.000 0.012 0.244 0.744
#> GSM35451 2 0.5682 0.3496 0.352 0.612 0.000 0.036
#> GSM35454 1 0.3808 0.7595 0.812 0.000 0.176 0.012
#> GSM35457 2 0.1716 0.7114 0.000 0.936 0.000 0.064
#> GSM35465 2 0.0657 0.6958 0.000 0.984 0.004 0.012
#> GSM35468 1 0.0469 0.8745 0.988 0.000 0.000 0.012
#> GSM35471 2 0.6579 0.2992 0.336 0.592 0.024 0.048
#> GSM35473 1 0.0921 0.8723 0.972 0.000 0.000 0.028
#> GSM35477 1 0.4425 0.7609 0.800 0.160 0.004 0.036
#> GSM35480 1 0.2463 0.8539 0.924 0.008 0.032 0.036
#> GSM35482 3 0.3266 0.6823 0.168 0.000 0.832 0.000
#> GSM35485 4 0.3649 0.6265 0.000 0.204 0.000 0.796
#> GSM35489 2 0.4907 0.3706 0.000 0.580 0.000 0.420
#> GSM35492 1 0.0921 0.8723 0.972 0.000 0.000 0.028
#> GSM35495 3 0.0921 0.7565 0.000 0.000 0.972 0.028
#> GSM35499 2 0.2149 0.7115 0.000 0.912 0.000 0.088
#> GSM35502 1 0.0469 0.8743 0.988 0.000 0.000 0.012
#> GSM35505 1 0.6988 0.0799 0.500 0.000 0.120 0.380
#> GSM35507 2 0.4371 0.6036 0.124 0.820 0.008 0.048
#> GSM35510 2 0.1716 0.7114 0.000 0.936 0.000 0.064
#> GSM35514 1 0.0817 0.8737 0.976 0.000 0.000 0.024
#> GSM35517 2 0.4746 0.4847 0.000 0.632 0.000 0.368
#> GSM35520 4 0.2048 0.7430 0.000 0.064 0.008 0.928
#> GSM35523 2 0.7643 0.1742 0.344 0.524 0.084 0.048
#> GSM35529 2 0.2814 0.7036 0.000 0.868 0.000 0.132
#> GSM35531 4 0.4775 0.6751 0.076 0.140 0.000 0.784
#> GSM35534 4 0.2760 0.7107 0.000 0.128 0.000 0.872
#> GSM35536 1 0.0469 0.8747 0.988 0.000 0.000 0.012
#> GSM35538 1 0.2825 0.8442 0.908 0.048 0.008 0.036
#> GSM35539 1 0.3583 0.8267 0.876 0.060 0.016 0.048
#> GSM35540 2 0.3032 0.7013 0.000 0.868 0.008 0.124
#> GSM35541 2 0.4888 0.3742 0.000 0.588 0.000 0.412
#> GSM35442 1 0.1302 0.8678 0.956 0.000 0.000 0.044
#> GSM35447 4 0.7382 0.1870 0.276 0.000 0.208 0.516
#> GSM35450 1 0.2124 0.8546 0.932 0.040 0.000 0.028
#> GSM35453 1 0.1059 0.8746 0.972 0.000 0.012 0.016
#> GSM35456 2 0.6821 0.0253 0.432 0.496 0.024 0.048
#> GSM35464 2 0.2040 0.6685 0.012 0.936 0.004 0.048
#> GSM35467 1 0.1302 0.8666 0.956 0.000 0.000 0.044
#> GSM35470 1 0.5232 0.7635 0.788 0.044 0.120 0.048
#> GSM35479 3 0.3400 0.7111 0.128 0.004 0.856 0.012
#> GSM35484 1 0.1867 0.8490 0.928 0.000 0.000 0.072
#> GSM35488 1 0.0817 0.8683 0.976 0.000 0.000 0.024
#> GSM35491 1 0.0707 0.8739 0.980 0.000 0.000 0.020
#> GSM35494 3 0.6354 0.1646 0.396 0.008 0.548 0.048
#> GSM35498 1 0.7401 0.1069 0.464 0.432 0.056 0.048
#> GSM35501 1 0.0469 0.8745 0.988 0.000 0.000 0.012
#> GSM35509 3 0.1229 0.7475 0.004 0.020 0.968 0.008
#> GSM35513 1 0.1389 0.8648 0.952 0.000 0.000 0.048
#> GSM35516 2 0.3801 0.6600 0.000 0.780 0.000 0.220
#> GSM35522 2 0.5178 0.5835 0.116 0.792 0.044 0.048
#> GSM35525 1 0.2335 0.8548 0.928 0.008 0.020 0.044
#> GSM35528 1 0.4983 0.7582 0.788 0.144 0.020 0.048
#> GSM35533 1 0.1389 0.8648 0.952 0.000 0.000 0.048
#> GSM35537 1 0.6266 0.7035 0.724 0.088 0.140 0.048
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM35441 2 0.2674 0.5825 0.000 0.868 0.000 0.012 0.120
#> GSM35446 3 0.3234 0.7101 0.000 0.000 0.852 0.084 0.064
#> GSM35449 5 0.6804 -0.0278 0.000 0.304 0.000 0.324 0.372
#> GSM35455 2 0.6210 0.2955 0.000 0.492 0.000 0.148 0.360
#> GSM35458 5 0.1741 0.4705 0.024 0.000 0.000 0.040 0.936
#> GSM35460 3 0.1942 0.7052 0.000 0.000 0.920 0.068 0.012
#> GSM35461 1 0.5201 0.6727 0.744 0.000 0.124 0.060 0.072
#> GSM35463 2 0.3055 0.5755 0.000 0.864 0.000 0.064 0.072
#> GSM35472 3 0.2136 0.7273 0.000 0.000 0.904 0.088 0.008
#> GSM35475 5 0.5691 0.2842 0.012 0.004 0.088 0.248 0.648
#> GSM35483 5 0.6878 0.2356 0.000 0.280 0.004 0.308 0.408
#> GSM35496 3 0.2946 0.6952 0.088 0.000 0.868 0.044 0.000
#> GSM35497 5 0.5572 0.3491 0.000 0.164 0.000 0.192 0.644
#> GSM35504 2 0.6009 0.2766 0.000 0.516 0.008 0.092 0.384
#> GSM35508 5 0.5633 0.3932 0.000 0.004 0.080 0.336 0.580
#> GSM35511 5 0.5659 0.2553 0.000 0.000 0.320 0.100 0.580
#> GSM35512 3 0.3995 0.6870 0.000 0.000 0.776 0.180 0.044
#> GSM35515 5 0.1372 0.4692 0.024 0.000 0.016 0.004 0.956
#> GSM35519 4 0.6901 -0.4354 0.000 0.004 0.268 0.368 0.360
#> GSM35527 5 0.5787 0.3762 0.000 0.092 0.004 0.340 0.564
#> GSM35532 5 0.6131 0.1771 0.000 0.000 0.284 0.168 0.548
#> GSM35439 5 0.6698 0.2055 0.008 0.308 0.000 0.204 0.480
#> GSM35443 1 0.3087 0.8231 0.868 0.000 0.004 0.064 0.064
#> GSM35445 1 0.1082 0.8704 0.964 0.000 0.008 0.028 0.000
#> GSM35448 3 0.6363 0.4683 0.000 0.016 0.584 0.200 0.200
#> GSM35451 2 0.4457 0.3783 0.208 0.740 0.004 0.048 0.000
#> GSM35454 3 0.4854 0.6796 0.072 0.016 0.740 0.172 0.000
#> GSM35457 2 0.3800 0.5901 0.000 0.812 0.000 0.108 0.080
#> GSM35465 2 0.3656 0.5526 0.000 0.784 0.000 0.196 0.020
#> GSM35468 1 0.0703 0.8715 0.976 0.000 0.000 0.000 0.024
#> GSM35471 2 0.6121 0.1338 0.256 0.576 0.004 0.164 0.000
#> GSM35473 1 0.0693 0.8731 0.980 0.000 0.000 0.008 0.012
#> GSM35477 1 0.4068 0.7233 0.792 0.144 0.004 0.060 0.000
#> GSM35480 1 0.1205 0.8622 0.956 0.000 0.004 0.040 0.000
#> GSM35482 3 0.5173 0.5324 0.184 0.000 0.704 0.104 0.008
#> GSM35485 2 0.6749 -0.1078 0.000 0.400 0.000 0.272 0.328
#> GSM35489 2 0.2685 0.5795 0.000 0.880 0.000 0.092 0.028
#> GSM35492 1 0.1243 0.8702 0.960 0.000 0.004 0.008 0.028
#> GSM35495 3 0.2753 0.7299 0.012 0.008 0.876 0.104 0.000
#> GSM35499 2 0.0404 0.6030 0.000 0.988 0.000 0.012 0.000
#> GSM35502 1 0.0798 0.8732 0.976 0.000 0.000 0.008 0.016
#> GSM35505 3 0.5268 0.6218 0.040 0.000 0.660 0.276 0.024
#> GSM35507 2 0.5811 0.3023 0.140 0.596 0.000 0.264 0.000
#> GSM35510 2 0.1549 0.6069 0.000 0.944 0.000 0.016 0.040
#> GSM35514 1 0.1670 0.8611 0.936 0.000 0.000 0.012 0.052
#> GSM35517 2 0.4800 0.3266 0.000 0.604 0.000 0.028 0.368
#> GSM35520 5 0.5531 0.3439 0.004 0.048 0.020 0.288 0.640
#> GSM35523 4 0.7445 -0.2187 0.332 0.272 0.032 0.364 0.000
#> GSM35529 2 0.6498 0.2558 0.000 0.452 0.000 0.196 0.352
#> GSM35531 2 0.6353 0.1370 0.004 0.516 0.048 0.384 0.048
#> GSM35534 2 0.6808 -0.1849 0.000 0.360 0.000 0.300 0.340
#> GSM35536 1 0.0703 0.8715 0.976 0.000 0.000 0.000 0.024
#> GSM35538 1 0.0963 0.8646 0.964 0.000 0.000 0.036 0.000
#> GSM35539 1 0.1798 0.8494 0.928 0.004 0.004 0.064 0.000
#> GSM35540 2 0.2889 0.5989 0.000 0.880 0.016 0.084 0.020
#> GSM35541 2 0.4822 0.4451 0.000 0.704 0.000 0.076 0.220
#> GSM35442 1 0.1934 0.8616 0.932 0.000 0.008 0.020 0.040
#> GSM35447 3 0.6529 0.3682 0.012 0.000 0.504 0.332 0.152
#> GSM35450 1 0.2300 0.8445 0.908 0.052 0.000 0.040 0.000
#> GSM35453 1 0.0162 0.8721 0.996 0.000 0.004 0.000 0.000
#> GSM35456 1 0.5704 0.5089 0.660 0.124 0.004 0.204 0.008
#> GSM35464 2 0.3812 0.5360 0.020 0.780 0.000 0.196 0.004
#> GSM35467 1 0.1430 0.8609 0.944 0.000 0.000 0.004 0.052
#> GSM35470 1 0.3969 0.7456 0.808 0.004 0.092 0.096 0.000
#> GSM35479 3 0.3427 0.6727 0.108 0.000 0.836 0.056 0.000
#> GSM35484 1 0.3737 0.7948 0.836 0.008 0.012 0.108 0.036
#> GSM35488 1 0.0404 0.8706 0.988 0.000 0.000 0.012 0.000
#> GSM35491 1 0.0912 0.8726 0.972 0.000 0.000 0.012 0.016
#> GSM35494 3 0.4830 0.4671 0.256 0.000 0.684 0.060 0.000
#> GSM35498 1 0.6980 -0.2249 0.384 0.380 0.012 0.224 0.000
#> GSM35501 1 0.0510 0.8722 0.984 0.000 0.000 0.000 0.016
#> GSM35509 3 0.2293 0.7059 0.016 0.000 0.900 0.084 0.000
#> GSM35513 1 0.1571 0.8568 0.936 0.000 0.000 0.004 0.060
#> GSM35516 2 0.1731 0.5955 0.000 0.932 0.004 0.060 0.004
#> GSM35522 2 0.5691 0.2582 0.084 0.516 0.000 0.400 0.000
#> GSM35525 1 0.1282 0.8608 0.952 0.000 0.004 0.044 0.000
#> GSM35528 1 0.1908 0.8362 0.908 0.000 0.000 0.092 0.000
#> GSM35533 1 0.3100 0.8057 0.852 0.008 0.008 0.128 0.004
#> GSM35537 1 0.4729 0.6065 0.708 0.004 0.052 0.236 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM35441 4 0.4652 0.3312 0.000 0.352 0.000 0.600 0.004 0.044
#> GSM35446 3 0.3738 0.6451 0.000 0.044 0.808 0.000 0.116 0.032
#> GSM35449 6 0.4622 0.4470 0.000 0.036 0.000 0.348 0.008 0.608
#> GSM35455 4 0.5959 0.2467 0.000 0.280 0.000 0.516 0.012 0.192
#> GSM35458 2 0.5327 0.2569 0.024 0.612 0.000 0.000 0.084 0.280
#> GSM35460 3 0.0665 0.7220 0.000 0.008 0.980 0.000 0.008 0.004
#> GSM35461 5 0.5620 0.0808 0.348 0.000 0.020 0.004 0.544 0.084
#> GSM35463 2 0.4459 0.0478 0.000 0.548 0.000 0.428 0.012 0.012
#> GSM35472 3 0.3230 0.6249 0.000 0.000 0.776 0.000 0.212 0.012
#> GSM35475 5 0.6109 0.1795 0.004 0.164 0.012 0.000 0.468 0.352
#> GSM35483 2 0.1672 0.5343 0.000 0.940 0.012 0.028 0.004 0.016
#> GSM35496 3 0.2709 0.7160 0.044 0.000 0.884 0.000 0.032 0.040
#> GSM35497 6 0.5703 0.5115 0.000 0.220 0.000 0.228 0.004 0.548
#> GSM35504 2 0.6686 0.0719 0.000 0.480 0.024 0.324 0.036 0.136
#> GSM35508 6 0.3182 0.6357 0.000 0.044 0.004 0.084 0.016 0.852
#> GSM35511 6 0.5157 0.1914 0.000 0.072 0.148 0.000 0.080 0.700
#> GSM35512 3 0.5306 0.3043 0.000 0.040 0.576 0.000 0.340 0.044
#> GSM35515 2 0.5609 0.0940 0.016 0.500 0.000 0.000 0.096 0.388
#> GSM35519 5 0.7007 0.4003 0.000 0.228 0.140 0.000 0.476 0.156
#> GSM35527 6 0.3295 0.6671 0.000 0.056 0.000 0.128 0.000 0.816
#> GSM35532 2 0.7403 -0.2086 0.000 0.376 0.228 0.000 0.136 0.260
#> GSM35439 2 0.2656 0.5229 0.004 0.884 0.000 0.060 0.008 0.044
#> GSM35443 1 0.4211 0.3258 0.532 0.000 0.000 0.008 0.456 0.004
#> GSM35445 1 0.2009 0.8057 0.904 0.000 0.004 0.008 0.084 0.000
#> GSM35448 2 0.4463 -0.0509 0.000 0.508 0.468 0.000 0.020 0.004
#> GSM35451 4 0.3960 0.5589 0.076 0.012 0.000 0.796 0.108 0.008
#> GSM35454 3 0.4814 0.4424 0.040 0.000 0.628 0.020 0.312 0.000
#> GSM35457 4 0.3703 0.5439 0.000 0.132 0.000 0.792 0.004 0.072
#> GSM35465 4 0.1908 0.5474 0.000 0.004 0.000 0.900 0.000 0.096
#> GSM35468 1 0.0777 0.8283 0.972 0.000 0.000 0.000 0.024 0.004
#> GSM35471 4 0.3492 0.5438 0.120 0.004 0.000 0.824 0.024 0.028
#> GSM35473 1 0.0520 0.8287 0.984 0.008 0.000 0.000 0.008 0.000
#> GSM35477 4 0.6104 0.0266 0.288 0.000 0.000 0.364 0.348 0.000
#> GSM35480 1 0.1949 0.8108 0.904 0.004 0.000 0.000 0.088 0.004
#> GSM35482 3 0.5838 0.4099 0.216 0.004 0.628 0.004 0.052 0.096
#> GSM35485 2 0.2699 0.5308 0.000 0.856 0.000 0.124 0.012 0.008
#> GSM35489 4 0.3927 0.4602 0.000 0.260 0.000 0.712 0.024 0.004
#> GSM35492 1 0.2668 0.7599 0.828 0.000 0.000 0.004 0.168 0.000
#> GSM35495 3 0.1124 0.7211 0.000 0.008 0.956 0.000 0.036 0.000
#> GSM35499 4 0.2985 0.5831 0.000 0.100 0.000 0.844 0.056 0.000
#> GSM35502 1 0.1802 0.8134 0.916 0.012 0.000 0.000 0.072 0.000
#> GSM35505 5 0.5293 0.0567 0.056 0.024 0.372 0.000 0.548 0.000
#> GSM35507 4 0.3573 0.5332 0.048 0.004 0.000 0.836 0.052 0.060
#> GSM35510 4 0.3894 0.5116 0.000 0.220 0.000 0.740 0.004 0.036
#> GSM35514 1 0.1010 0.8277 0.960 0.000 0.000 0.000 0.036 0.004
#> GSM35517 4 0.5715 0.2167 0.000 0.364 0.000 0.484 0.004 0.148
#> GSM35520 2 0.5193 0.2731 0.000 0.644 0.008 0.000 0.176 0.172
#> GSM35523 1 0.7659 0.1997 0.448 0.004 0.028 0.236 0.168 0.116
#> GSM35529 4 0.5929 0.1929 0.000 0.200 0.000 0.528 0.012 0.260
#> GSM35531 2 0.5241 0.1647 0.000 0.552 0.024 0.372 0.052 0.000
#> GSM35534 2 0.1398 0.5408 0.000 0.940 0.008 0.052 0.000 0.000
#> GSM35536 1 0.0937 0.8256 0.960 0.000 0.000 0.000 0.040 0.000
#> GSM35538 1 0.0914 0.8289 0.968 0.000 0.000 0.016 0.016 0.000
#> GSM35539 1 0.1956 0.8130 0.908 0.000 0.000 0.008 0.080 0.004
#> GSM35540 4 0.3682 0.5134 0.000 0.028 0.004 0.796 0.016 0.156
#> GSM35541 2 0.3215 0.4401 0.000 0.756 0.000 0.240 0.004 0.000
#> GSM35442 1 0.3005 0.7838 0.856 0.008 0.036 0.000 0.096 0.004
#> GSM35447 5 0.6782 0.1199 0.000 0.184 0.364 0.000 0.392 0.060
#> GSM35450 1 0.3932 0.6763 0.760 0.000 0.000 0.184 0.048 0.008
#> GSM35453 1 0.1124 0.8253 0.956 0.008 0.000 0.000 0.036 0.000
#> GSM35456 4 0.6207 0.0201 0.416 0.000 0.000 0.436 0.072 0.076
#> GSM35464 4 0.1080 0.5772 0.004 0.000 0.000 0.960 0.032 0.004
#> GSM35467 1 0.1074 0.8285 0.960 0.012 0.000 0.000 0.028 0.000
#> GSM35470 1 0.4256 0.6771 0.744 0.000 0.112 0.000 0.140 0.004
#> GSM35479 3 0.2941 0.6692 0.064 0.000 0.856 0.000 0.076 0.004
#> GSM35484 1 0.4764 0.2396 0.492 0.008 0.004 0.024 0.472 0.000
#> GSM35488 1 0.0508 0.8287 0.984 0.000 0.000 0.004 0.012 0.000
#> GSM35491 1 0.3073 0.7265 0.788 0.000 0.000 0.008 0.204 0.000
#> GSM35494 3 0.3632 0.6034 0.148 0.004 0.800 0.000 0.040 0.008
#> GSM35498 4 0.5558 0.4291 0.148 0.004 0.008 0.676 0.124 0.040
#> GSM35501 1 0.2039 0.8099 0.908 0.016 0.000 0.000 0.072 0.004
#> GSM35509 3 0.0725 0.7188 0.000 0.000 0.976 0.000 0.012 0.012
#> GSM35513 1 0.1155 0.8277 0.956 0.004 0.000 0.000 0.036 0.004
#> GSM35516 4 0.4095 0.5462 0.000 0.100 0.000 0.748 0.152 0.000
#> GSM35522 4 0.6831 0.1656 0.128 0.004 0.004 0.544 0.148 0.172
#> GSM35525 1 0.2333 0.7927 0.872 0.004 0.000 0.000 0.120 0.004
#> GSM35528 1 0.1405 0.8278 0.948 0.000 0.000 0.024 0.024 0.004
#> GSM35533 1 0.4649 0.5307 0.632 0.024 0.004 0.016 0.324 0.000
#> GSM35537 1 0.4710 0.6720 0.736 0.004 0.048 0.004 0.168 0.040
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n time(p) k
#> ATC:NMF 76 9.68e-07 2
#> ATC:NMF 72 1.22e-05 3
#> ATC:NMF 64 5.08e-04 4
#> ATC:NMF 49 1.13e-02 5
#> ATC:NMF 48 1.92e-05 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
sessionInfo()
#> R version 3.6.0 (2019-04-26)
#> Platform: x86_64-pc-linux-gnu (64-bit)
#> Running under: CentOS Linux 7 (Core)
#>
#> Matrix products: default
#> BLAS: /usr/lib64/libblas.so.3.4.2
#> LAPACK: /usr/lib64/liblapack.so.3.4.2
#>
#> locale:
#> [1] LC_CTYPE=en_GB.UTF-8 LC_NUMERIC=C LC_TIME=en_GB.UTF-8
#> [4] LC_COLLATE=en_GB.UTF-8 LC_MONETARY=en_GB.UTF-8 LC_MESSAGES=en_GB.UTF-8
#> [7] LC_PAPER=en_GB.UTF-8 LC_NAME=C LC_ADDRESS=C
#> [10] LC_TELEPHONE=C LC_MEASUREMENT=en_GB.UTF-8 LC_IDENTIFICATION=C
#>
#> attached base packages:
#> [1] grid stats graphics grDevices utils datasets methods base
#>
#> other attached packages:
#> [1] genefilter_1.66.0 ComplexHeatmap_2.3.1 markdown_1.1 knitr_1.26
#> [5] GetoptLong_0.1.7 cola_1.3.2
#>
#> loaded via a namespace (and not attached):
#> [1] circlize_0.4.8 shape_1.4.4 xfun_0.11 slam_0.1-46
#> [5] lattice_0.20-38 splines_3.6.0 colorspace_1.4-1 vctrs_0.2.0
#> [9] stats4_3.6.0 blob_1.2.0 XML_3.98-1.20 survival_2.44-1.1
#> [13] rlang_0.4.2 pillar_1.4.2 DBI_1.0.0 BiocGenerics_0.30.0
#> [17] bit64_0.9-7 RColorBrewer_1.1-2 matrixStats_0.55.0 stringr_1.4.0
#> [21] GlobalOptions_0.1.1 evaluate_0.14 memoise_1.1.0 Biobase_2.44.0
#> [25] IRanges_2.18.3 parallel_3.6.0 AnnotationDbi_1.46.1 highr_0.8
#> [29] Rcpp_1.0.3 xtable_1.8-4 backports_1.1.5 S4Vectors_0.22.1
#> [33] annotate_1.62.0 skmeans_0.2-11 bit_1.1-14 microbenchmark_1.4-7
#> [37] brew_1.0-6 impute_1.58.0 rjson_0.2.20 png_0.1-7
#> [41] digest_0.6.23 stringi_1.4.3 polyclip_1.10-0 clue_0.3-57
#> [45] tools_3.6.0 bitops_1.0-6 magrittr_1.5 eulerr_6.0.0
#> [49] RCurl_1.95-4.12 RSQLite_2.1.4 tibble_2.1.3 cluster_2.1.0
#> [53] crayon_1.3.4 pkgconfig_2.0.3 zeallot_0.1.0 Matrix_1.2-17
#> [57] xml2_1.2.2 httr_1.4.1 R6_2.4.1 mclust_5.4.5
#> [61] compiler_3.6.0