Date: 2019-12-25 20:43:12 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 18172 rows and 71 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] 18172 71
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 | ||
|---|---|---|---|---|---|---|
| MAD:kmeans | 2 | 1.000 | 0.965 | 0.986 | ** | |
| MAD:skmeans | 2 | 1.000 | 0.989 | 0.995 | ** | |
| ATC:kmeans | 3 | 1.000 | 0.974 | 0.988 | ** | 2 |
| CV:skmeans | 2 | 0.970 | 0.927 | 0.970 | ** | |
| ATC:pam | 3 | 0.952 | 0.937 | 0.975 | ** | |
| MAD:NMF | 2 | 0.940 | 0.944 | 0.975 | * | |
| SD:skmeans | 2 | 0.938 | 0.907 | 0.965 | * | |
| ATC:skmeans | 5 | 0.912 | 0.862 | 0.919 | * | 2 |
| ATC:NMF | 2 | 0.910 | 0.911 | 0.964 | * | |
| ATC:mclust | 2 | 0.910 | 0.895 | 0.960 | * | |
| MAD:pam | 2 | 0.865 | 0.892 | 0.955 | ||
| CV:kmeans | 2 | 0.858 | 0.915 | 0.954 | ||
| SD:pam | 2 | 0.853 | 0.888 | 0.953 | ||
| SD:NMF | 2 | 0.779 | 0.889 | 0.953 | ||
| SD:kmeans | 2 | 0.777 | 0.857 | 0.936 | ||
| CV:pam | 6 | 0.754 | 0.634 | 0.833 | ||
| CV:NMF | 2 | 0.681 | 0.822 | 0.918 | ||
| MAD:mclust | 3 | 0.629 | 0.647 | 0.855 | ||
| CV:mclust | 5 | 0.618 | 0.690 | 0.782 | ||
| ATC:hclust | 3 | 0.524 | 0.774 | 0.878 | ||
| SD:mclust | 3 | 0.502 | 0.794 | 0.855 | ||
| SD:hclust | 5 | 0.476 | 0.611 | 0.723 | ||
| MAD:hclust | 2 | 0.403 | 0.854 | 0.886 | ||
| CV:hclust | 3 | 0.370 | 0.593 | 0.745 |
**: 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 0.779 0.889 0.953 0.501 0.501 0.501
#> CV:NMF 2 0.681 0.822 0.918 0.460 0.505 0.505
#> MAD:NMF 2 0.940 0.944 0.975 0.506 0.493 0.493
#> ATC:NMF 2 0.910 0.911 0.964 0.502 0.494 0.494
#> SD:skmeans 2 0.938 0.907 0.965 0.507 0.494 0.494
#> CV:skmeans 2 0.970 0.927 0.970 0.504 0.501 0.501
#> MAD:skmeans 2 1.000 0.989 0.995 0.507 0.493 0.493
#> ATC:skmeans 2 1.000 0.965 0.986 0.507 0.493 0.493
#> SD:mclust 2 0.427 0.792 0.888 0.404 0.590 0.590
#> CV:mclust 2 0.664 0.866 0.931 0.397 0.577 0.577
#> MAD:mclust 2 0.368 0.846 0.896 0.388 0.566 0.566
#> ATC:mclust 2 0.910 0.895 0.960 0.422 0.577 0.577
#> SD:kmeans 2 0.777 0.857 0.936 0.494 0.515 0.515
#> CV:kmeans 2 0.858 0.915 0.954 0.476 0.501 0.501
#> MAD:kmeans 2 1.000 0.965 0.986 0.506 0.494 0.494
#> ATC:kmeans 2 1.000 0.958 0.982 0.502 0.498 0.498
#> SD:pam 2 0.853 0.888 0.953 0.497 0.505 0.505
#> CV:pam 2 0.472 0.758 0.815 0.428 0.529 0.529
#> MAD:pam 2 0.865 0.892 0.955 0.498 0.498 0.498
#> ATC:pam 2 0.670 0.806 0.917 0.485 0.493 0.493
#> SD:hclust 2 0.303 0.676 0.783 0.386 0.556 0.556
#> CV:hclust 2 0.591 0.732 0.884 0.405 0.631 0.631
#> MAD:hclust 2 0.403 0.854 0.886 0.457 0.494 0.494
#> ATC:hclust 2 0.358 0.718 0.834 0.429 0.505 0.505
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 0.756 0.863 0.934 0.319 0.752 0.544
#> CV:NMF 3 0.326 0.408 0.709 0.369 0.803 0.634
#> MAD:NMF 3 0.602 0.730 0.873 0.313 0.697 0.465
#> ATC:NMF 3 0.599 0.790 0.851 0.308 0.726 0.497
#> SD:skmeans 3 0.722 0.818 0.918 0.309 0.804 0.622
#> CV:skmeans 3 0.660 0.731 0.808 0.287 0.788 0.597
#> MAD:skmeans 3 0.860 0.846 0.938 0.309 0.758 0.546
#> ATC:skmeans 3 0.723 0.628 0.858 0.235 0.931 0.861
#> SD:mclust 3 0.502 0.794 0.855 0.570 0.642 0.438
#> CV:mclust 3 0.364 0.557 0.802 0.533 0.651 0.451
#> MAD:mclust 3 0.629 0.647 0.855 0.642 0.705 0.505
#> ATC:mclust 3 0.498 0.755 0.836 0.435 0.771 0.614
#> SD:kmeans 3 0.790 0.852 0.919 0.312 0.657 0.434
#> CV:kmeans 3 0.528 0.626 0.838 0.317 0.631 0.402
#> MAD:kmeans 3 0.755 0.862 0.923 0.304 0.703 0.472
#> ATC:kmeans 3 1.000 0.974 0.988 0.250 0.687 0.470
#> SD:pam 3 0.590 0.752 0.874 0.260 0.668 0.455
#> CV:pam 3 0.394 0.564 0.762 0.382 0.594 0.399
#> MAD:pam 3 0.556 0.636 0.808 0.288 0.709 0.490
#> ATC:pam 3 0.952 0.937 0.975 0.224 0.602 0.387
#> SD:hclust 3 0.303 0.490 0.683 0.493 0.650 0.449
#> CV:hclust 3 0.370 0.593 0.745 0.529 0.657 0.483
#> MAD:hclust 3 0.498 0.759 0.863 0.333 0.874 0.751
#> ATC:hclust 3 0.524 0.774 0.878 0.375 0.784 0.610
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.728 0.769 0.886 0.1240 0.779 0.457
#> CV:NMF 4 0.532 0.675 0.824 0.1377 0.703 0.370
#> MAD:NMF 4 0.812 0.831 0.916 0.1149 0.776 0.456
#> ATC:NMF 4 0.596 0.711 0.839 0.0864 0.917 0.762
#> SD:skmeans 4 0.685 0.732 0.868 0.1143 0.905 0.734
#> CV:skmeans 4 0.762 0.724 0.880 0.1239 0.822 0.554
#> MAD:skmeans 4 0.711 0.731 0.860 0.1181 0.874 0.655
#> ATC:skmeans 4 0.829 0.751 0.851 0.1335 0.801 0.564
#> SD:mclust 4 0.557 0.505 0.776 0.1086 0.885 0.699
#> CV:mclust 4 0.457 0.484 0.681 0.1309 0.843 0.593
#> MAD:mclust 4 0.536 0.594 0.782 0.0956 0.882 0.677
#> ATC:mclust 4 0.509 0.592 0.745 0.1105 0.720 0.412
#> SD:kmeans 4 0.610 0.614 0.817 0.1298 0.872 0.657
#> CV:kmeans 4 0.597 0.697 0.800 0.1675 0.839 0.587
#> MAD:kmeans 4 0.606 0.590 0.733 0.1178 0.850 0.598
#> ATC:kmeans 4 0.672 0.727 0.836 0.1544 0.769 0.470
#> SD:pam 4 0.533 0.470 0.703 0.1241 0.847 0.659
#> CV:pam 4 0.609 0.628 0.821 0.1921 0.760 0.489
#> MAD:pam 4 0.440 0.420 0.686 0.1343 0.736 0.407
#> ATC:pam 4 0.839 0.810 0.928 0.2043 0.751 0.470
#> SD:hclust 4 0.392 0.428 0.712 0.1868 0.849 0.635
#> CV:hclust 4 0.428 0.441 0.693 0.1420 0.813 0.524
#> MAD:hclust 4 0.519 0.628 0.747 0.1330 0.891 0.720
#> ATC:hclust 4 0.558 0.611 0.789 0.1648 0.885 0.730
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.731 0.688 0.848 0.0434 0.922 0.723
#> CV:NMF 5 0.506 0.511 0.696 0.0658 0.891 0.657
#> MAD:NMF 5 0.717 0.762 0.857 0.0432 0.918 0.721
#> ATC:NMF 5 0.562 0.512 0.786 0.0404 0.981 0.935
#> SD:skmeans 5 0.630 0.599 0.777 0.0635 0.910 0.691
#> CV:skmeans 5 0.682 0.598 0.784 0.0635 0.906 0.697
#> MAD:skmeans 5 0.660 0.647 0.792 0.0579 0.950 0.822
#> ATC:skmeans 5 0.912 0.862 0.919 0.0634 0.944 0.808
#> SD:mclust 5 0.539 0.580 0.760 0.0691 0.855 0.583
#> CV:mclust 5 0.618 0.690 0.782 0.1078 0.885 0.630
#> MAD:mclust 5 0.611 0.538 0.670 0.0666 0.878 0.619
#> ATC:mclust 5 0.643 0.763 0.873 0.0885 0.938 0.799
#> SD:kmeans 5 0.615 0.500 0.736 0.0690 0.829 0.472
#> CV:kmeans 5 0.685 0.626 0.759 0.0683 0.908 0.663
#> MAD:kmeans 5 0.631 0.604 0.774 0.0654 0.888 0.617
#> ATC:kmeans 5 0.791 0.834 0.901 0.0771 0.932 0.755
#> SD:pam 5 0.556 0.407 0.667 0.0886 0.744 0.380
#> CV:pam 5 0.698 0.623 0.822 0.0997 0.896 0.657
#> MAD:pam 5 0.522 0.417 0.655 0.0671 0.893 0.648
#> ATC:pam 5 0.835 0.791 0.914 0.1171 0.864 0.557
#> SD:hclust 5 0.476 0.611 0.723 0.0826 0.868 0.621
#> CV:hclust 5 0.480 0.479 0.693 0.0571 0.838 0.514
#> MAD:hclust 5 0.573 0.596 0.732 0.0933 0.930 0.774
#> ATC:hclust 5 0.611 0.499 0.739 0.0959 0.856 0.606
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.673 0.521 0.743 0.0477 0.923 0.715
#> CV:NMF 6 0.484 0.434 0.680 0.0435 0.893 0.626
#> MAD:NMF 6 0.653 0.564 0.752 0.0547 0.939 0.756
#> ATC:NMF 6 0.630 0.635 0.791 0.0445 0.902 0.658
#> SD:skmeans 6 0.646 0.499 0.718 0.0405 0.962 0.832
#> CV:skmeans 6 0.674 0.576 0.749 0.0404 0.950 0.798
#> MAD:skmeans 6 0.658 0.536 0.753 0.0376 0.961 0.842
#> ATC:skmeans 6 0.808 0.707 0.853 0.0392 0.994 0.977
#> SD:mclust 6 0.609 0.632 0.777 0.0556 0.861 0.501
#> CV:mclust 6 0.716 0.619 0.774 0.0623 0.895 0.608
#> MAD:mclust 6 0.660 0.587 0.750 0.0717 0.800 0.363
#> ATC:mclust 6 0.668 0.516 0.722 0.0773 0.877 0.579
#> SD:kmeans 6 0.660 0.472 0.636 0.0477 0.880 0.518
#> CV:kmeans 6 0.768 0.762 0.804 0.0458 0.895 0.556
#> MAD:kmeans 6 0.689 0.568 0.665 0.0433 0.901 0.584
#> ATC:kmeans 6 0.769 0.711 0.825 0.0508 0.905 0.606
#> SD:pam 6 0.581 0.290 0.634 0.0582 0.808 0.356
#> CV:pam 6 0.754 0.634 0.833 0.0395 0.900 0.607
#> MAD:pam 6 0.587 0.318 0.651 0.0487 0.832 0.405
#> ATC:pam 6 0.850 0.735 0.880 0.0335 0.941 0.723
#> SD:hclust 6 0.558 0.520 0.733 0.0496 0.969 0.883
#> CV:hclust 6 0.567 0.478 0.671 0.0402 0.918 0.698
#> MAD:hclust 6 0.601 0.549 0.701 0.0473 0.936 0.775
#> ATC:hclust 6 0.725 0.631 0.801 0.0710 0.906 0.630
Following heatmap plots the partition for each combination of methods and the lightness correspond to the silhouette scores for samples in each method. On top the consensus subgroup is inferred from all methods by taking the mean silhouette scores as weight.
collect_stats(res_list, k = 2)
collect_stats(res_list, k = 3)
collect_stats(res_list, k = 4)
collect_stats(res_list, k = 5)
collect_stats(res_list, k = 6)
Collect partitions from all methods:
collect_classes(res_list, k = 2)
collect_classes(res_list, k = 3)
collect_classes(res_list, k = 4)
collect_classes(res_list, k = 5)
collect_classes(res_list, k = 6)
Overlap of top rows from different top-row methods:
top_rows_overlap(res_list, top_n = 1000, method = "euler")
top_rows_overlap(res_list, top_n = 2000, method = "euler")
top_rows_overlap(res_list, top_n = 3000, method = "euler")
top_rows_overlap(res_list, top_n = 4000, method = "euler")
top_rows_overlap(res_list, top_n = 5000, method = "euler")
Also visualize the correspondance of rankings between different top-row methods:
top_rows_overlap(res_list, top_n = 1000, method = "correspondance")
top_rows_overlap(res_list, top_n = 2000, method = "correspondance")
top_rows_overlap(res_list, top_n = 3000, method = "correspondance")
top_rows_overlap(res_list, top_n = 4000, method = "correspondance")
top_rows_overlap(res_list, top_n = 5000, method = "correspondance")
Heatmaps of the top rows:
top_rows_heatmap(res_list, top_n = 1000)
top_rows_heatmap(res_list, top_n = 2000)
top_rows_heatmap(res_list, top_n = 3000)
top_rows_heatmap(res_list, top_n = 4000)
top_rows_heatmap(res_list, top_n = 5000)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res_list, k = 2)
#> n stress(p) development.stage(p) k
#> SD:NMF 66 0.620 1.18e-03 2
#> CV:NMF 64 0.897 2.53e-01 2
#> MAD:NMF 70 1.000 1.86e-05 2
#> ATC:NMF 68 0.466 2.64e-02 2
#> SD:skmeans 66 0.805 2.98e-04 2
#> CV:skmeans 67 0.522 1.05e-01 2
#> MAD:skmeans 71 0.907 1.36e-05 2
#> ATC:skmeans 70 0.342 5.29e-02 2
#> SD:mclust 69 0.732 3.22e-04 2
#> CV:mclust 69 0.941 5.47e-04 2
#> MAD:mclust 70 0.602 2.32e-04 2
#> ATC:mclust 66 0.876 4.79e-04 2
#> SD:kmeans 65 0.887 2.21e-04 2
#> CV:kmeans 71 0.394 1.32e-01 2
#> MAD:kmeans 70 0.632 3.64e-05 2
#> ATC:kmeans 70 0.347 2.21e-02 2
#> SD:pam 66 0.301 5.99e-03 2
#> CV:pam 68 0.577 3.81e-01 2
#> MAD:pam 67 0.892 4.35e-04 2
#> ATC:pam 62 0.435 2.01e-02 2
#> SD:hclust 64 0.677 2.35e-02 2
#> CV:hclust 59 0.600 1.00e+00 2
#> MAD:hclust 70 0.821 3.64e-05 2
#> ATC:hclust 63 0.382 3.19e-03 2
test_to_known_factors(res_list, k = 3)
#> n stress(p) development.stage(p) k
#> SD:NMF 69 0.172 6.31e-07 3
#> CV:NMF 34 0.463 4.51e-02 3
#> MAD:NMF 61 0.234 6.34e-10 3
#> ATC:NMF 67 0.900 1.41e-06 3
#> SD:skmeans 66 0.857 4.98e-06 3
#> CV:skmeans 60 0.341 8.90e-03 3
#> MAD:skmeans 64 0.722 7.11e-08 3
#> ATC:skmeans 53 0.454 1.16e-02 3
#> SD:mclust 69 0.478 6.94e-14 3
#> CV:mclust 52 0.904 1.80e-05 3
#> MAD:mclust 51 0.388 1.12e-07 3
#> ATC:mclust 67 0.825 5.46e-06 3
#> SD:kmeans 65 0.912 5.11e-07 3
#> CV:kmeans 52 0.679 5.78e-03 3
#> MAD:kmeans 68 0.991 1.77e-08 3
#> ATC:kmeans 71 0.935 3.74e-03 3
#> SD:pam 64 0.582 8.09e-05 3
#> CV:pam 36 0.895 1.70e-03 3
#> MAD:pam 51 0.889 3.97e-06 3
#> ATC:pam 69 0.994 3.63e-03 3
#> SD:hclust 43 0.467 7.66e-04 3
#> CV:hclust 54 0.612 6.12e-02 3
#> MAD:hclust 64 0.932 1.53e-05 3
#> ATC:hclust 64 0.835 3.75e-03 3
test_to_known_factors(res_list, k = 4)
#> n stress(p) development.stage(p) k
#> SD:NMF 66 0.3596 1.16e-08 4
#> CV:NMF 62 0.6242 2.01e-07 4
#> MAD:NMF 67 0.5996 4.45e-09 4
#> ATC:NMF 63 0.9580 6.40e-09 4
#> SD:skmeans 62 0.7669 1.17e-05 4
#> CV:skmeans 60 0.6752 6.71e-04 4
#> MAD:skmeans 62 0.7577 7.90e-11 4
#> ATC:skmeans 62 0.3546 1.75e-04 4
#> SD:mclust 48 0.8344 3.14e-10 4
#> CV:mclust 44 0.9833 1.62e-05 4
#> MAD:mclust 49 0.0924 6.36e-09 4
#> ATC:mclust 49 0.7541 1.38e-05 4
#> SD:kmeans 51 0.7076 1.52e-06 4
#> CV:kmeans 60 0.8069 1.07e-03 4
#> MAD:kmeans 50 0.4731 1.79e-08 4
#> ATC:kmeans 57 0.4114 8.45e-05 4
#> SD:pam 29 1.0000 1.00e+00 4
#> CV:pam 43 0.6739 3.94e-02 4
#> MAD:pam 32 0.2091 3.24e-06 4
#> ATC:pam 62 0.5657 1.41e-03 4
#> SD:hclust 45 0.9257 8.00e-07 4
#> CV:hclust 35 0.7532 2.59e-02 4
#> MAD:hclust 57 0.6872 5.23e-07 4
#> ATC:hclust 58 0.6964 9.97e-04 4
test_to_known_factors(res_list, k = 5)
#> n stress(p) development.stage(p) k
#> SD:NMF 57 0.4161 6.46e-09 5
#> CV:NMF 48 0.8772 3.20e-08 5
#> MAD:NMF 66 0.7657 9.43e-10 5
#> ATC:NMF 40 0.9511 4.54e-05 5
#> SD:skmeans 49 0.8661 3.40e-06 5
#> CV:skmeans 55 0.9074 1.01e-04 5
#> MAD:skmeans 59 0.9135 3.80e-11 5
#> ATC:skmeans 68 0.8483 5.67e-04 5
#> SD:mclust 48 0.0798 1.07e-08 5
#> CV:mclust 62 0.3796 5.56e-09 5
#> MAD:mclust 50 0.1177 1.17e-08 5
#> ATC:mclust 68 0.9854 3.64e-06 5
#> SD:kmeans 46 0.5715 3.47e-07 5
#> CV:kmeans 52 0.6881 8.65e-04 5
#> MAD:kmeans 57 0.9297 1.24e-11 5
#> ATC:kmeans 69 0.7650 1.29e-05 5
#> SD:pam 26 0.1699 9.54e-06 5
#> CV:pam 55 0.8930 2.04e-02 5
#> MAD:pam 30 0.2290 1.81e-06 5
#> ATC:pam 58 0.7538 1.72e-03 5
#> SD:hclust 60 0.7481 3.48e-07 5
#> CV:hclust 42 0.6251 2.44e-03 5
#> MAD:hclust 56 0.2360 8.32e-06 5
#> ATC:hclust 36 0.6414 7.28e-04 5
test_to_known_factors(res_list, k = 6)
#> n stress(p) development.stage(p) k
#> SD:NMF 47 0.64646 5.32e-07 6
#> CV:NMF 44 0.85038 1.06e-06 6
#> MAD:NMF 45 0.89132 1.04e-06 6
#> ATC:NMF 59 0.95761 4.20e-07 6
#> SD:skmeans 45 0.94292 1.59e-07 6
#> CV:skmeans 47 0.99642 6.38e-04 6
#> MAD:skmeans 45 0.77696 9.25e-10 6
#> ATC:skmeans 59 0.78915 2.50e-03 6
#> SD:mclust 53 0.25523 4.92e-08 6
#> CV:mclust 51 0.48777 1.16e-06 6
#> MAD:mclust 45 0.06525 2.15e-06 6
#> ATC:mclust 40 0.98977 4.70e-04 6
#> SD:kmeans 43 0.57403 2.14e-07 6
#> CV:kmeans 63 0.91810 1.20e-05 6
#> MAD:kmeans 49 0.38642 2.22e-09 6
#> ATC:kmeans 61 0.85998 9.81e-06 6
#> SD:pam 15 0.29958 5.53e-04 6
#> CV:pam 52 0.77357 1.03e-02 6
#> MAD:pam 14 0.00702 9.12e-04 6
#> ATC:pam 54 0.70942 1.24e-03 6
#> SD:hclust 40 0.48343 5.18e-06 6
#> CV:hclust 42 0.29842 5.03e-03 6
#> MAD:hclust 51 0.10987 3.68e-08 6
#> ATC:hclust 53 0.44747 3.18e-04 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 18172 rows and 71 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.303 0.676 0.783 0.3859 0.556 0.556
#> 3 3 0.303 0.490 0.683 0.4929 0.650 0.449
#> 4 4 0.392 0.428 0.712 0.1868 0.849 0.635
#> 5 5 0.476 0.611 0.723 0.0826 0.868 0.621
#> 6 6 0.558 0.520 0.733 0.0496 0.969 0.883
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
#> GSM182755 1 0.6247 0.732 0.844 0.156
#> GSM182756 1 0.8608 0.602 0.716 0.284
#> GSM182757 2 0.9710 0.521 0.400 0.600
#> GSM182758 1 0.8608 0.599 0.716 0.284
#> GSM182759 2 0.9323 0.592 0.348 0.652
#> GSM182760 1 0.8713 0.586 0.708 0.292
#> GSM182761 2 0.9795 0.487 0.416 0.584
#> GSM182762 1 0.8386 0.601 0.732 0.268
#> GSM182763 2 0.9881 0.434 0.436 0.564
#> GSM182764 2 0.9635 0.542 0.388 0.612
#> GSM182765 2 0.9552 0.561 0.376 0.624
#> GSM182766 2 0.6623 0.674 0.172 0.828
#> GSM182767 1 0.8661 0.593 0.712 0.288
#> GSM182768 1 0.6801 0.734 0.820 0.180
#> GSM182769 1 0.3114 0.819 0.944 0.056
#> GSM182770 2 0.0000 0.663 0.000 1.000
#> GSM182771 2 0.8955 0.621 0.312 0.688
#> GSM182772 2 0.0000 0.663 0.000 1.000
#> GSM182773 1 0.3114 0.819 0.944 0.056
#> GSM182774 1 0.4161 0.816 0.916 0.084
#> GSM182775 1 0.2948 0.819 0.948 0.052
#> GSM182776 1 0.3114 0.819 0.944 0.056
#> GSM182777 1 0.3114 0.820 0.944 0.056
#> GSM182802 2 0.2948 0.670 0.052 0.948
#> GSM182803 1 0.0938 0.813 0.988 0.012
#> GSM182804 1 0.8813 0.536 0.700 0.300
#> GSM182805 2 0.2948 0.670 0.052 0.948
#> GSM182806 1 0.0000 0.810 1.000 0.000
#> GSM182807 1 0.0000 0.810 1.000 0.000
#> GSM182808 1 0.0000 0.810 1.000 0.000
#> GSM182809 1 0.4161 0.816 0.916 0.084
#> GSM182810 1 0.3879 0.818 0.924 0.076
#> GSM182811 1 0.3879 0.818 0.924 0.076
#> GSM182812 1 0.0000 0.810 1.000 0.000
#> GSM182813 1 0.0000 0.810 1.000 0.000
#> GSM182778 2 0.0000 0.663 0.000 1.000
#> GSM182779 2 0.9795 0.487 0.416 0.584
#> GSM182780 2 0.9933 0.365 0.452 0.548
#> GSM182781 1 0.8608 0.601 0.716 0.284
#> GSM182782 2 0.0000 0.663 0.000 1.000
#> GSM182783 2 0.9954 0.336 0.460 0.540
#> GSM182784 1 0.8763 0.576 0.704 0.296
#> GSM182785 1 0.8861 0.559 0.696 0.304
#> GSM182786 2 0.0000 0.663 0.000 1.000
#> GSM182787 2 0.9795 0.482 0.416 0.584
#> GSM182788 2 0.0000 0.663 0.000 1.000
#> GSM182789 1 0.9988 -0.142 0.520 0.480
#> GSM182790 1 0.8608 0.599 0.716 0.284
#> GSM182791 1 0.4939 0.807 0.892 0.108
#> GSM182792 1 0.4431 0.813 0.908 0.092
#> GSM182793 2 0.6712 0.639 0.176 0.824
#> GSM182794 1 0.8661 0.593 0.712 0.288
#> GSM182795 1 0.8909 0.549 0.692 0.308
#> GSM182796 2 0.7883 0.660 0.236 0.764
#> GSM182797 1 0.0000 0.810 1.000 0.000
#> GSM182798 2 0.9044 0.618 0.320 0.680
#> GSM182799 1 0.7602 0.683 0.780 0.220
#> GSM182800 1 0.1633 0.814 0.976 0.024
#> GSM182801 1 0.2948 0.819 0.948 0.052
#> GSM182814 1 0.0000 0.810 1.000 0.000
#> GSM182815 1 0.8713 0.560 0.708 0.292
#> GSM182816 1 0.0000 0.810 1.000 0.000
#> GSM182817 1 0.6148 0.772 0.848 0.152
#> GSM182818 1 0.4939 0.805 0.892 0.108
#> GSM182819 1 0.0000 0.810 1.000 0.000
#> GSM182820 1 0.0000 0.810 1.000 0.000
#> GSM182821 1 0.7056 0.738 0.808 0.192
#> GSM182822 1 0.3879 0.818 0.924 0.076
#> GSM182823 1 0.0000 0.810 1.000 0.000
#> GSM182824 1 0.0000 0.810 1.000 0.000
#> GSM182825 1 0.0000 0.810 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM182755 1 0.6111 0.1306 0.604 0.000 0.396
#> GSM182756 3 0.6282 0.5443 0.324 0.012 0.664
#> GSM182757 3 0.6730 0.4111 0.036 0.284 0.680
#> GSM182758 3 0.6129 0.5433 0.324 0.008 0.668
#> GSM182759 3 0.6773 0.2778 0.024 0.340 0.636
#> GSM182760 3 0.6255 0.5436 0.320 0.012 0.668
#> GSM182761 3 0.6066 0.4568 0.024 0.248 0.728
#> GSM182762 3 0.6994 0.4856 0.360 0.028 0.612
#> GSM182763 3 0.6685 0.4813 0.048 0.244 0.708
#> GSM182764 3 0.6570 0.3853 0.028 0.292 0.680
#> GSM182765 3 0.7491 0.3199 0.056 0.324 0.620
#> GSM182766 2 0.7169 0.2609 0.024 0.520 0.456
#> GSM182767 3 0.6102 0.5494 0.320 0.008 0.672
#> GSM182768 3 0.7601 -0.1653 0.416 0.044 0.540
#> GSM182769 1 0.6062 0.5331 0.616 0.000 0.384
#> GSM182770 2 0.3482 0.7818 0.000 0.872 0.128
#> GSM182771 3 0.7396 -0.2273 0.032 0.480 0.488
#> GSM182772 2 0.3482 0.7818 0.000 0.872 0.128
#> GSM182773 1 0.6045 0.5341 0.620 0.000 0.380
#> GSM182774 1 0.6225 0.4448 0.568 0.000 0.432
#> GSM182775 1 0.5968 0.5498 0.636 0.000 0.364
#> GSM182776 1 0.6045 0.5378 0.620 0.000 0.380
#> GSM182777 1 0.5968 0.5464 0.636 0.000 0.364
#> GSM182802 2 0.4504 0.7621 0.000 0.804 0.196
#> GSM182803 1 0.1411 0.6756 0.964 0.000 0.036
#> GSM182804 3 0.8007 0.1102 0.244 0.116 0.640
#> GSM182805 2 0.4504 0.7621 0.000 0.804 0.196
#> GSM182806 1 0.0000 0.6854 1.000 0.000 0.000
#> GSM182807 1 0.0000 0.6854 1.000 0.000 0.000
#> GSM182808 1 0.0000 0.6854 1.000 0.000 0.000
#> GSM182809 1 0.6252 0.4133 0.556 0.000 0.444
#> GSM182810 1 0.6180 0.4585 0.584 0.000 0.416
#> GSM182811 1 0.6180 0.4585 0.584 0.000 0.416
#> GSM182812 1 0.3272 0.6698 0.892 0.004 0.104
#> GSM182813 1 0.0000 0.6854 1.000 0.000 0.000
#> GSM182778 2 0.2356 0.7755 0.000 0.928 0.072
#> GSM182779 3 0.6066 0.4568 0.024 0.248 0.728
#> GSM182780 3 0.7001 0.5199 0.084 0.200 0.716
#> GSM182781 3 0.5733 0.5459 0.324 0.000 0.676
#> GSM182782 2 0.2356 0.7755 0.000 0.928 0.072
#> GSM182783 3 0.7107 0.5286 0.092 0.196 0.712
#> GSM182784 3 0.6200 0.5573 0.312 0.012 0.676
#> GSM182785 3 0.6387 0.5661 0.300 0.020 0.680
#> GSM182786 2 0.2356 0.7755 0.000 0.928 0.072
#> GSM182787 3 0.6624 0.4650 0.044 0.248 0.708
#> GSM182788 2 0.2356 0.7755 0.000 0.928 0.072
#> GSM182789 3 0.7451 0.5851 0.144 0.156 0.700
#> GSM182790 3 0.6102 0.5479 0.320 0.008 0.672
#> GSM182791 1 0.7575 0.3807 0.504 0.040 0.456
#> GSM182792 1 0.6260 0.4263 0.552 0.000 0.448
#> GSM182793 2 0.6627 0.5773 0.020 0.644 0.336
#> GSM182794 3 0.6102 0.5494 0.320 0.008 0.672
#> GSM182795 3 0.6630 0.5685 0.300 0.028 0.672
#> GSM182796 2 0.6252 0.3585 0.000 0.556 0.444
#> GSM182797 1 0.0237 0.6856 0.996 0.000 0.004
#> GSM182798 2 0.7004 0.3480 0.020 0.552 0.428
#> GSM182799 3 0.8390 -0.0624 0.340 0.100 0.560
#> GSM182800 1 0.5956 0.6168 0.768 0.044 0.188
#> GSM182801 1 0.5988 0.5485 0.632 0.000 0.368
#> GSM182814 1 0.0237 0.6844 0.996 0.004 0.000
#> GSM182815 3 0.7507 0.0986 0.288 0.068 0.644
#> GSM182816 1 0.0237 0.6844 0.996 0.004 0.000
#> GSM182817 1 0.6683 0.1976 0.500 0.008 0.492
#> GSM182818 3 0.6299 -0.3228 0.476 0.000 0.524
#> GSM182819 1 0.0237 0.6844 0.996 0.004 0.000
#> GSM182820 1 0.0000 0.6854 1.000 0.000 0.000
#> GSM182821 3 0.6912 -0.0603 0.444 0.016 0.540
#> GSM182822 1 0.6180 0.4585 0.584 0.000 0.416
#> GSM182823 1 0.0237 0.6844 0.996 0.004 0.000
#> GSM182824 1 0.0237 0.6844 0.996 0.004 0.000
#> GSM182825 1 0.4035 0.6483 0.880 0.040 0.080
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM182755 3 0.5150 0.2590 0.396 0.000 0.596 0.008
#> GSM182756 3 0.3172 0.6658 0.112 0.004 0.872 0.012
#> GSM182757 3 0.4122 0.5968 0.000 0.236 0.760 0.004
#> GSM182758 3 0.2799 0.6680 0.108 0.000 0.884 0.008
#> GSM182759 3 0.4560 0.5305 0.000 0.296 0.700 0.004
#> GSM182760 3 0.2805 0.6698 0.100 0.000 0.888 0.012
#> GSM182761 3 0.3831 0.6254 0.000 0.204 0.792 0.004
#> GSM182762 3 0.3351 0.6224 0.148 0.000 0.844 0.008
#> GSM182763 3 0.4114 0.6369 0.008 0.200 0.788 0.004
#> GSM182764 3 0.4431 0.5831 0.004 0.252 0.740 0.004
#> GSM182765 3 0.5198 0.5453 0.016 0.288 0.688 0.008
#> GSM182766 3 0.5691 0.1256 0.000 0.468 0.508 0.024
#> GSM182767 3 0.2928 0.6702 0.108 0.000 0.880 0.012
#> GSM182768 4 0.7054 0.4267 0.236 0.004 0.172 0.588
#> GSM182769 1 0.7640 0.0383 0.432 0.000 0.212 0.356
#> GSM182770 2 0.3439 0.8373 0.000 0.868 0.048 0.084
#> GSM182771 3 0.5807 0.0311 0.016 0.484 0.492 0.008
#> GSM182772 2 0.3439 0.8373 0.000 0.868 0.048 0.084
#> GSM182773 1 0.7668 0.0411 0.432 0.000 0.220 0.348
#> GSM182774 1 0.7923 -0.1499 0.344 0.000 0.332 0.324
#> GSM182775 1 0.7584 0.0590 0.448 0.000 0.204 0.348
#> GSM182776 1 0.7634 0.0447 0.436 0.000 0.212 0.352
#> GSM182777 1 0.7617 0.0603 0.452 0.000 0.216 0.332
#> GSM182802 2 0.4465 0.8019 0.000 0.800 0.056 0.144
#> GSM182803 1 0.2032 0.5512 0.936 0.000 0.036 0.028
#> GSM182804 4 0.4439 0.5032 0.112 0.008 0.060 0.820
#> GSM182805 2 0.4614 0.7999 0.000 0.792 0.064 0.144
#> GSM182806 1 0.0188 0.5664 0.996 0.000 0.004 0.000
#> GSM182807 1 0.0188 0.5664 0.996 0.000 0.004 0.000
#> GSM182808 1 0.0000 0.5646 1.000 0.000 0.000 0.000
#> GSM182809 4 0.7910 0.0941 0.316 0.000 0.320 0.364
#> GSM182810 1 0.7916 -0.1611 0.356 0.000 0.316 0.328
#> GSM182811 1 0.7921 -0.1713 0.348 0.000 0.320 0.332
#> GSM182812 1 0.3486 0.4728 0.812 0.000 0.000 0.188
#> GSM182813 1 0.0000 0.5646 1.000 0.000 0.000 0.000
#> GSM182778 2 0.0469 0.8467 0.000 0.988 0.012 0.000
#> GSM182779 3 0.3831 0.6254 0.000 0.204 0.792 0.004
#> GSM182780 3 0.6086 0.6138 0.008 0.148 0.704 0.140
#> GSM182781 3 0.2714 0.6695 0.112 0.000 0.884 0.004
#> GSM182782 2 0.0469 0.8467 0.000 0.988 0.012 0.000
#> GSM182783 3 0.6164 0.6191 0.012 0.144 0.704 0.140
#> GSM182784 3 0.2715 0.6756 0.100 0.004 0.892 0.004
#> GSM182785 3 0.2401 0.6780 0.092 0.004 0.904 0.000
#> GSM182786 2 0.0469 0.8467 0.000 0.988 0.012 0.000
#> GSM182787 3 0.5356 0.6095 0.000 0.200 0.728 0.072
#> GSM182788 2 0.0469 0.8467 0.000 0.988 0.012 0.000
#> GSM182789 3 0.4843 0.6676 0.016 0.108 0.804 0.072
#> GSM182790 3 0.2654 0.6702 0.108 0.000 0.888 0.004
#> GSM182791 4 0.7676 0.2163 0.308 0.000 0.240 0.452
#> GSM182792 1 0.7916 -0.1491 0.352 0.000 0.312 0.336
#> GSM182793 4 0.6376 -0.4035 0.000 0.432 0.064 0.504
#> GSM182794 3 0.2928 0.6702 0.108 0.000 0.880 0.012
#> GSM182795 3 0.3383 0.6777 0.100 0.016 0.872 0.012
#> GSM182796 2 0.5126 0.0675 0.000 0.552 0.444 0.004
#> GSM182797 1 0.0336 0.5663 0.992 0.000 0.008 0.000
#> GSM182798 3 0.7591 -0.0056 0.000 0.368 0.432 0.200
#> GSM182799 4 0.5438 0.5185 0.176 0.008 0.072 0.744
#> GSM182800 1 0.4936 0.3361 0.672 0.000 0.012 0.316
#> GSM182801 1 0.7515 0.0438 0.448 0.000 0.188 0.364
#> GSM182814 1 0.1118 0.5653 0.964 0.000 0.000 0.036
#> GSM182815 4 0.5734 0.5349 0.148 0.008 0.112 0.732
#> GSM182816 1 0.0707 0.5669 0.980 0.000 0.000 0.020
#> GSM182817 3 0.7777 -0.3221 0.268 0.000 0.428 0.304
#> GSM182818 4 0.5697 0.3949 0.292 0.000 0.052 0.656
#> GSM182819 1 0.0707 0.5669 0.980 0.000 0.000 0.020
#> GSM182820 1 0.0188 0.5664 0.996 0.000 0.004 0.000
#> GSM182821 3 0.7606 -0.2538 0.228 0.000 0.468 0.304
#> GSM182822 1 0.7916 -0.1611 0.356 0.000 0.316 0.328
#> GSM182823 1 0.1118 0.5653 0.964 0.000 0.000 0.036
#> GSM182824 1 0.1118 0.5653 0.964 0.000 0.000 0.036
#> GSM182825 1 0.3688 0.4595 0.792 0.000 0.000 0.208
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM182755 5 0.771 0.0907 0.212 0.000 0.212 0.100 0.476
#> GSM182756 5 0.392 0.6274 0.032 0.000 0.156 0.012 0.800
#> GSM182757 5 0.406 0.6589 0.000 0.172 0.000 0.052 0.776
#> GSM182758 5 0.338 0.6825 0.032 0.000 0.108 0.012 0.848
#> GSM182759 5 0.465 0.6041 0.000 0.220 0.000 0.064 0.716
#> GSM182760 5 0.311 0.6840 0.028 0.000 0.112 0.004 0.856
#> GSM182761 5 0.382 0.6827 0.000 0.148 0.000 0.052 0.800
#> GSM182762 5 0.524 0.5354 0.044 0.000 0.172 0.060 0.724
#> GSM182763 5 0.383 0.6893 0.000 0.128 0.004 0.056 0.812
#> GSM182764 5 0.439 0.6489 0.000 0.180 0.000 0.068 0.752
#> GSM182765 5 0.506 0.6100 0.000 0.188 0.008 0.092 0.712
#> GSM182766 5 0.584 0.2621 0.000 0.384 0.000 0.100 0.516
#> GSM182767 5 0.332 0.6850 0.032 0.000 0.104 0.012 0.852
#> GSM182768 3 0.690 0.5023 0.140 0.000 0.592 0.176 0.092
#> GSM182769 3 0.567 0.6474 0.296 0.000 0.604 0.004 0.096
#> GSM182770 2 0.317 0.6992 0.000 0.816 0.000 0.176 0.008
#> GSM182771 5 0.601 0.2023 0.000 0.384 0.008 0.092 0.516
#> GSM182772 2 0.317 0.6992 0.000 0.816 0.000 0.176 0.008
#> GSM182773 3 0.581 0.6502 0.292 0.000 0.600 0.008 0.100
#> GSM182774 3 0.630 0.6867 0.216 0.000 0.572 0.008 0.204
#> GSM182775 3 0.574 0.6377 0.308 0.000 0.596 0.008 0.088
#> GSM182776 3 0.568 0.6465 0.300 0.000 0.600 0.004 0.096
#> GSM182777 3 0.589 0.6351 0.312 0.000 0.580 0.008 0.100
#> GSM182802 2 0.416 0.6491 0.000 0.748 0.020 0.224 0.008
#> GSM182803 1 0.246 0.8367 0.888 0.000 0.096 0.000 0.016
#> GSM182804 4 0.465 0.3015 0.020 0.000 0.372 0.608 0.000
#> GSM182805 2 0.436 0.6467 0.000 0.740 0.020 0.224 0.016
#> GSM182806 1 0.131 0.8833 0.956 0.000 0.020 0.024 0.000
#> GSM182807 1 0.131 0.8833 0.956 0.000 0.020 0.024 0.000
#> GSM182808 1 0.121 0.8833 0.960 0.000 0.016 0.024 0.000
#> GSM182809 3 0.635 0.6645 0.168 0.000 0.600 0.024 0.208
#> GSM182810 3 0.627 0.6565 0.188 0.000 0.588 0.012 0.212
#> GSM182811 3 0.615 0.6505 0.172 0.000 0.604 0.012 0.212
#> GSM182812 1 0.407 0.7561 0.792 0.000 0.112 0.096 0.000
#> GSM182813 1 0.121 0.8833 0.960 0.000 0.016 0.024 0.000
#> GSM182778 2 0.000 0.7329 0.000 1.000 0.000 0.000 0.000
#> GSM182779 5 0.382 0.6827 0.000 0.148 0.000 0.052 0.800
#> GSM182780 5 0.570 0.6567 0.000 0.096 0.072 0.124 0.708
#> GSM182781 5 0.319 0.6925 0.024 0.000 0.092 0.020 0.864
#> GSM182782 2 0.000 0.7329 0.000 1.000 0.000 0.000 0.000
#> GSM182783 5 0.566 0.6623 0.000 0.088 0.076 0.124 0.712
#> GSM182784 5 0.298 0.6917 0.032 0.000 0.096 0.004 0.868
#> GSM182785 5 0.300 0.6959 0.028 0.004 0.092 0.004 0.872
#> GSM182786 2 0.000 0.7329 0.000 1.000 0.000 0.000 0.000
#> GSM182787 5 0.525 0.6683 0.000 0.144 0.040 0.084 0.732
#> GSM182788 2 0.000 0.7329 0.000 1.000 0.000 0.000 0.000
#> GSM182789 5 0.459 0.7066 0.000 0.064 0.068 0.076 0.792
#> GSM182790 5 0.332 0.6845 0.032 0.000 0.104 0.012 0.852
#> GSM182791 3 0.672 0.5535 0.124 0.000 0.612 0.092 0.172
#> GSM182792 3 0.621 0.6865 0.220 0.000 0.584 0.008 0.188
#> GSM182793 4 0.480 -0.0119 0.000 0.372 0.020 0.604 0.004
#> GSM182794 5 0.332 0.6850 0.032 0.000 0.104 0.012 0.852
#> GSM182795 5 0.366 0.6941 0.032 0.012 0.100 0.012 0.844
#> GSM182796 2 0.560 -0.1539 0.000 0.468 0.000 0.072 0.460
#> GSM182797 1 0.149 0.8800 0.948 0.000 0.024 0.028 0.000
#> GSM182798 5 0.664 0.1965 0.000 0.256 0.000 0.296 0.448
#> GSM182799 3 0.575 0.0491 0.036 0.000 0.616 0.300 0.048
#> GSM182800 1 0.614 0.3428 0.520 0.000 0.352 0.124 0.004
#> GSM182801 3 0.554 0.6282 0.312 0.000 0.604 0.004 0.080
#> GSM182814 1 0.158 0.8720 0.944 0.000 0.032 0.024 0.000
#> GSM182815 3 0.549 -0.2773 0.052 0.000 0.484 0.460 0.004
#> GSM182816 1 0.088 0.8822 0.968 0.000 0.032 0.000 0.000
#> GSM182817 3 0.643 0.5923 0.156 0.000 0.516 0.008 0.320
#> GSM182818 3 0.565 0.2292 0.156 0.000 0.648 0.192 0.004
#> GSM182819 1 0.088 0.8822 0.968 0.000 0.032 0.000 0.000
#> GSM182820 1 0.131 0.8833 0.956 0.000 0.020 0.024 0.000
#> GSM182821 3 0.634 0.5169 0.120 0.000 0.504 0.012 0.364
#> GSM182822 3 0.627 0.6565 0.188 0.000 0.588 0.012 0.212
#> GSM182823 1 0.158 0.8720 0.944 0.000 0.032 0.024 0.000
#> GSM182824 1 0.166 0.8708 0.940 0.000 0.036 0.024 0.000
#> GSM182825 1 0.507 0.6262 0.676 0.000 0.240 0.084 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM182755 5 0.6949 0.0000 0.080 0.000 0.200 0.000 0.432 0.288
#> GSM182756 3 0.5492 0.2020 0.000 0.000 0.552 0.000 0.168 0.280
#> GSM182757 3 0.1599 0.5719 0.000 0.024 0.940 0.008 0.028 0.000
#> GSM182758 3 0.5134 0.3979 0.000 0.000 0.620 0.000 0.152 0.228
#> GSM182759 3 0.2777 0.5391 0.000 0.032 0.880 0.044 0.044 0.000
#> GSM182760 3 0.4954 0.4046 0.000 0.000 0.640 0.000 0.128 0.232
#> GSM182761 3 0.0777 0.5780 0.000 0.024 0.972 0.000 0.000 0.004
#> GSM182762 3 0.5870 -0.2352 0.000 0.000 0.480 0.000 0.276 0.244
#> GSM182763 3 0.1785 0.5798 0.000 0.008 0.936 0.012 0.016 0.028
#> GSM182764 3 0.1930 0.5640 0.000 0.028 0.924 0.012 0.036 0.000
#> GSM182765 3 0.4018 0.5260 0.000 0.036 0.816 0.064 0.060 0.024
#> GSM182766 3 0.5074 0.3628 0.000 0.188 0.684 0.096 0.032 0.000
#> GSM182767 3 0.5134 0.3973 0.000 0.000 0.620 0.000 0.152 0.228
#> GSM182768 6 0.5961 0.4540 0.124 0.000 0.020 0.168 0.048 0.640
#> GSM182769 6 0.4236 0.5782 0.240 0.000 0.008 0.008 0.028 0.716
#> GSM182770 2 0.4102 0.7272 0.000 0.720 0.044 0.232 0.004 0.000
#> GSM182771 3 0.6019 0.3130 0.000 0.232 0.616 0.068 0.060 0.024
#> GSM182772 2 0.4102 0.7272 0.000 0.720 0.044 0.232 0.004 0.000
#> GSM182773 6 0.4378 0.5754 0.236 0.000 0.012 0.008 0.032 0.712
#> GSM182774 6 0.5348 0.5217 0.164 0.000 0.084 0.048 0.012 0.692
#> GSM182775 6 0.4400 0.5684 0.256 0.000 0.008 0.008 0.032 0.696
#> GSM182776 6 0.4296 0.5786 0.240 0.000 0.012 0.004 0.032 0.712
#> GSM182777 6 0.4709 0.5613 0.252 0.000 0.020 0.008 0.036 0.684
#> GSM182802 2 0.4581 0.6823 0.000 0.652 0.044 0.296 0.004 0.004
#> GSM182803 1 0.2709 0.7922 0.848 0.000 0.000 0.000 0.020 0.132
#> GSM182804 4 0.5250 0.5311 0.004 0.008 0.000 0.624 0.260 0.104
#> GSM182805 2 0.4697 0.6749 0.000 0.644 0.052 0.296 0.004 0.004
#> GSM182806 1 0.2294 0.8540 0.892 0.000 0.000 0.000 0.072 0.036
#> GSM182807 1 0.2294 0.8540 0.892 0.000 0.000 0.000 0.072 0.036
#> GSM182808 1 0.2088 0.8549 0.904 0.000 0.000 0.000 0.068 0.028
#> GSM182809 6 0.5845 0.4886 0.104 0.000 0.068 0.064 0.076 0.688
#> GSM182810 6 0.5736 0.4529 0.100 0.000 0.072 0.052 0.080 0.696
#> GSM182811 6 0.5456 0.4346 0.076 0.000 0.072 0.052 0.080 0.720
#> GSM182812 1 0.4120 0.7523 0.784 0.000 0.000 0.116 0.060 0.040
#> GSM182813 1 0.2088 0.8549 0.904 0.000 0.000 0.000 0.068 0.028
#> GSM182778 2 0.0790 0.7613 0.000 0.968 0.032 0.000 0.000 0.000
#> GSM182779 3 0.0922 0.5778 0.000 0.024 0.968 0.000 0.004 0.004
#> GSM182780 3 0.3908 0.4977 0.000 0.008 0.784 0.104 0.000 0.104
#> GSM182781 3 0.5008 0.4189 0.000 0.000 0.644 0.000 0.168 0.188
#> GSM182782 2 0.0790 0.7613 0.000 0.968 0.032 0.000 0.000 0.000
#> GSM182783 3 0.4473 0.4875 0.000 0.008 0.756 0.104 0.016 0.116
#> GSM182784 3 0.4845 0.4334 0.000 0.000 0.660 0.000 0.132 0.208
#> GSM182785 3 0.4729 0.4444 0.000 0.000 0.676 0.000 0.128 0.196
#> GSM182786 2 0.0790 0.7613 0.000 0.968 0.032 0.000 0.000 0.000
#> GSM182787 3 0.2818 0.5517 0.000 0.024 0.876 0.048 0.000 0.052
#> GSM182788 2 0.0790 0.7613 0.000 0.968 0.032 0.000 0.000 0.000
#> GSM182789 3 0.3693 0.5325 0.000 0.000 0.800 0.048 0.016 0.136
#> GSM182790 3 0.5134 0.3953 0.000 0.000 0.620 0.000 0.152 0.228
#> GSM182791 6 0.6113 0.4132 0.064 0.000 0.076 0.044 0.172 0.644
#> GSM182792 6 0.4592 0.5445 0.164 0.000 0.076 0.016 0.008 0.736
#> GSM182793 4 0.4576 -0.1500 0.000 0.344 0.004 0.616 0.032 0.004
#> GSM182794 3 0.5134 0.3973 0.000 0.000 0.620 0.000 0.152 0.228
#> GSM182795 3 0.4906 0.4339 0.000 0.000 0.652 0.000 0.136 0.212
#> GSM182796 3 0.5447 0.2713 0.000 0.276 0.612 0.068 0.044 0.000
#> GSM182797 1 0.2433 0.8489 0.884 0.000 0.000 0.000 0.072 0.044
#> GSM182798 3 0.5734 0.2606 0.000 0.080 0.584 0.284 0.052 0.000
#> GSM182799 6 0.6446 -0.0033 0.016 0.004 0.012 0.228 0.224 0.516
#> GSM182800 1 0.6287 0.3226 0.500 0.000 0.000 0.028 0.256 0.216
#> GSM182801 6 0.4056 0.5667 0.264 0.000 0.000 0.008 0.024 0.704
#> GSM182814 1 0.1297 0.8472 0.948 0.000 0.000 0.000 0.040 0.012
#> GSM182815 4 0.5455 0.4137 0.000 0.008 0.000 0.552 0.112 0.328
#> GSM182816 1 0.0632 0.8579 0.976 0.000 0.000 0.000 0.000 0.024
#> GSM182817 6 0.5938 0.2939 0.060 0.000 0.152 0.040 0.084 0.664
#> GSM182818 6 0.6812 -0.1333 0.052 0.004 0.000 0.224 0.264 0.456
#> GSM182819 1 0.0713 0.8580 0.972 0.000 0.000 0.000 0.000 0.028
#> GSM182820 1 0.2294 0.8540 0.892 0.000 0.000 0.000 0.072 0.036
#> GSM182821 6 0.5385 0.1984 0.020 0.000 0.180 0.032 0.084 0.684
#> GSM182822 6 0.5736 0.4529 0.100 0.000 0.072 0.052 0.080 0.696
#> GSM182823 1 0.1297 0.8472 0.948 0.000 0.000 0.000 0.040 0.012
#> GSM182824 1 0.1367 0.8461 0.944 0.000 0.000 0.000 0.044 0.012
#> GSM182825 1 0.4704 0.5947 0.664 0.000 0.000 0.000 0.236 0.100
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 stress(p) development.stage(p) k
#> SD:hclust 64 0.677 2.35e-02 2
#> SD:hclust 43 0.467 7.66e-04 3
#> SD:hclust 45 0.926 8.00e-07 4
#> SD:hclust 60 0.748 3.48e-07 5
#> SD:hclust 40 0.483 5.18e-06 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "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 18172 rows and 71 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.777 0.857 0.936 0.4939 0.515 0.515
#> 3 3 0.790 0.852 0.919 0.3122 0.657 0.434
#> 4 4 0.610 0.614 0.817 0.1298 0.872 0.657
#> 5 5 0.615 0.500 0.736 0.0690 0.829 0.472
#> 6 6 0.660 0.472 0.636 0.0477 0.880 0.518
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
#> GSM182755 1 0.0672 0.889 0.992 0.008
#> GSM182756 1 0.9970 0.288 0.532 0.468
#> GSM182757 2 0.0000 0.988 0.000 1.000
#> GSM182758 2 0.0000 0.988 0.000 1.000
#> GSM182759 2 0.0000 0.988 0.000 1.000
#> GSM182760 1 0.9000 0.595 0.684 0.316
#> GSM182761 2 0.0000 0.988 0.000 1.000
#> GSM182762 1 0.9970 0.288 0.532 0.468
#> GSM182763 2 0.0000 0.988 0.000 1.000
#> GSM182764 2 0.0000 0.988 0.000 1.000
#> GSM182765 2 0.0000 0.988 0.000 1.000
#> GSM182766 2 0.0000 0.988 0.000 1.000
#> GSM182767 1 0.9795 0.415 0.584 0.416
#> GSM182768 1 0.0672 0.889 0.992 0.008
#> GSM182769 1 0.0000 0.892 1.000 0.000
#> GSM182770 2 0.0000 0.988 0.000 1.000
#> GSM182771 2 0.0000 0.988 0.000 1.000
#> GSM182772 2 0.0000 0.988 0.000 1.000
#> GSM182773 1 0.0000 0.892 1.000 0.000
#> GSM182774 1 0.0000 0.892 1.000 0.000
#> GSM182775 1 0.0000 0.892 1.000 0.000
#> GSM182776 1 0.0000 0.892 1.000 0.000
#> GSM182777 1 0.0000 0.892 1.000 0.000
#> GSM182802 2 0.0000 0.988 0.000 1.000
#> GSM182803 1 0.0000 0.892 1.000 0.000
#> GSM182804 1 0.1843 0.879 0.972 0.028
#> GSM182805 2 0.0000 0.988 0.000 1.000
#> GSM182806 1 0.0000 0.892 1.000 0.000
#> GSM182807 1 0.0000 0.892 1.000 0.000
#> GSM182808 1 0.0000 0.892 1.000 0.000
#> GSM182809 1 0.2423 0.872 0.960 0.040
#> GSM182810 1 0.0000 0.892 1.000 0.000
#> GSM182811 1 0.0000 0.892 1.000 0.000
#> GSM182812 1 0.0000 0.892 1.000 0.000
#> GSM182813 1 0.0000 0.892 1.000 0.000
#> GSM182778 2 0.0000 0.988 0.000 1.000
#> GSM182779 2 0.0000 0.988 0.000 1.000
#> GSM182780 2 0.0000 0.988 0.000 1.000
#> GSM182781 1 0.9087 0.568 0.676 0.324
#> GSM182782 2 0.0000 0.988 0.000 1.000
#> GSM182783 2 0.0000 0.988 0.000 1.000
#> GSM182784 2 0.6343 0.776 0.160 0.840
#> GSM182785 2 0.0000 0.988 0.000 1.000
#> GSM182786 2 0.0000 0.988 0.000 1.000
#> GSM182787 2 0.0000 0.988 0.000 1.000
#> GSM182788 2 0.0000 0.988 0.000 1.000
#> GSM182789 2 0.0000 0.988 0.000 1.000
#> GSM182790 1 0.9209 0.552 0.664 0.336
#> GSM182791 1 0.4298 0.838 0.912 0.088
#> GSM182792 1 0.0672 0.889 0.992 0.008
#> GSM182793 2 0.0000 0.988 0.000 1.000
#> GSM182794 1 0.9775 0.423 0.588 0.412
#> GSM182795 2 0.5294 0.839 0.120 0.880
#> GSM182796 2 0.0000 0.988 0.000 1.000
#> GSM182797 1 0.0000 0.892 1.000 0.000
#> GSM182798 2 0.0000 0.988 0.000 1.000
#> GSM182799 1 0.4298 0.838 0.912 0.088
#> GSM182800 1 0.0000 0.892 1.000 0.000
#> GSM182801 1 0.0000 0.892 1.000 0.000
#> GSM182814 1 0.0000 0.892 1.000 0.000
#> GSM182815 1 0.8713 0.606 0.708 0.292
#> GSM182816 1 0.0000 0.892 1.000 0.000
#> GSM182817 1 0.9983 0.264 0.524 0.476
#> GSM182818 1 0.0000 0.892 1.000 0.000
#> GSM182819 1 0.0000 0.892 1.000 0.000
#> GSM182820 1 0.0000 0.892 1.000 0.000
#> GSM182821 1 0.9993 0.241 0.516 0.484
#> GSM182822 1 0.0000 0.892 1.000 0.000
#> GSM182823 1 0.0000 0.892 1.000 0.000
#> GSM182824 1 0.0000 0.892 1.000 0.000
#> GSM182825 1 0.0000 0.892 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM182755 3 0.6045 0.371 0.380 0.000 0.620
#> GSM182756 3 0.0424 0.888 0.008 0.000 0.992
#> GSM182757 3 0.1753 0.875 0.000 0.048 0.952
#> GSM182758 3 0.0983 0.887 0.004 0.016 0.980
#> GSM182759 2 0.2959 0.936 0.000 0.900 0.100
#> GSM182760 3 0.0747 0.886 0.016 0.000 0.984
#> GSM182761 3 0.2537 0.854 0.000 0.080 0.920
#> GSM182762 3 0.0424 0.888 0.008 0.000 0.992
#> GSM182763 3 0.1964 0.869 0.000 0.056 0.944
#> GSM182764 3 0.3192 0.830 0.000 0.112 0.888
#> GSM182765 3 0.1031 0.885 0.000 0.024 0.976
#> GSM182766 2 0.1964 0.971 0.000 0.944 0.056
#> GSM182767 3 0.0424 0.888 0.008 0.000 0.992
#> GSM182768 3 0.6416 0.564 0.304 0.020 0.676
#> GSM182769 1 0.1964 0.913 0.944 0.000 0.056
#> GSM182770 2 0.1643 0.969 0.000 0.956 0.044
#> GSM182771 3 0.6180 0.308 0.000 0.416 0.584
#> GSM182772 2 0.1643 0.969 0.000 0.956 0.044
#> GSM182773 3 0.2486 0.859 0.060 0.008 0.932
#> GSM182774 1 0.2486 0.899 0.932 0.008 0.060
#> GSM182775 1 0.6154 0.303 0.592 0.000 0.408
#> GSM182776 1 0.1860 0.915 0.948 0.000 0.052
#> GSM182777 3 0.2261 0.858 0.068 0.000 0.932
#> GSM182802 2 0.1411 0.965 0.000 0.964 0.036
#> GSM182803 1 0.0747 0.928 0.984 0.000 0.016
#> GSM182804 1 0.2947 0.892 0.920 0.060 0.020
#> GSM182805 2 0.1529 0.967 0.000 0.960 0.040
#> GSM182806 1 0.0747 0.928 0.984 0.000 0.016
#> GSM182807 1 0.0747 0.928 0.984 0.000 0.016
#> GSM182808 1 0.0747 0.928 0.984 0.000 0.016
#> GSM182809 1 0.7181 0.230 0.564 0.028 0.408
#> GSM182810 1 0.0424 0.923 0.992 0.008 0.000
#> GSM182811 1 0.1031 0.918 0.976 0.024 0.000
#> GSM182812 1 0.0592 0.922 0.988 0.012 0.000
#> GSM182813 1 0.0747 0.928 0.984 0.000 0.016
#> GSM182778 2 0.1964 0.971 0.000 0.944 0.056
#> GSM182779 3 0.3340 0.822 0.000 0.120 0.880
#> GSM182780 3 0.1643 0.876 0.000 0.044 0.956
#> GSM182781 3 0.0592 0.888 0.012 0.000 0.988
#> GSM182782 2 0.1964 0.971 0.000 0.944 0.056
#> GSM182783 3 0.1878 0.877 0.004 0.044 0.952
#> GSM182784 3 0.1015 0.888 0.008 0.012 0.980
#> GSM182785 3 0.0983 0.887 0.004 0.016 0.980
#> GSM182786 2 0.1964 0.971 0.000 0.944 0.056
#> GSM182787 2 0.4178 0.850 0.000 0.828 0.172
#> GSM182788 2 0.1964 0.971 0.000 0.944 0.056
#> GSM182789 3 0.0983 0.887 0.004 0.016 0.980
#> GSM182790 3 0.0592 0.888 0.012 0.000 0.988
#> GSM182791 3 0.5343 0.783 0.132 0.052 0.816
#> GSM182792 3 0.4861 0.768 0.180 0.012 0.808
#> GSM182793 2 0.0592 0.940 0.000 0.988 0.012
#> GSM182794 3 0.0592 0.888 0.012 0.000 0.988
#> GSM182795 3 0.0983 0.887 0.004 0.016 0.980
#> GSM182796 2 0.1860 0.971 0.000 0.948 0.052
#> GSM182797 1 0.1753 0.917 0.952 0.000 0.048
#> GSM182798 2 0.2711 0.926 0.000 0.912 0.088
#> GSM182799 3 0.7640 0.340 0.372 0.052 0.576
#> GSM182800 1 0.3472 0.890 0.904 0.040 0.056
#> GSM182801 1 0.1860 0.915 0.948 0.000 0.052
#> GSM182814 1 0.0747 0.928 0.984 0.000 0.016
#> GSM182815 1 0.5882 0.494 0.652 0.348 0.000
#> GSM182816 1 0.0747 0.928 0.984 0.000 0.016
#> GSM182817 3 0.5507 0.785 0.136 0.056 0.808
#> GSM182818 1 0.1163 0.916 0.972 0.028 0.000
#> GSM182819 1 0.0747 0.928 0.984 0.000 0.016
#> GSM182820 1 0.0747 0.928 0.984 0.000 0.016
#> GSM182821 3 0.1482 0.884 0.020 0.012 0.968
#> GSM182822 1 0.0424 0.923 0.992 0.008 0.000
#> GSM182823 1 0.0747 0.928 0.984 0.000 0.016
#> GSM182824 1 0.0747 0.928 0.984 0.000 0.016
#> GSM182825 1 0.1647 0.910 0.960 0.036 0.004
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM182755 1 0.6698 0.15956 0.556 0.000 0.340 0.104
#> GSM182756 3 0.2216 0.83675 0.000 0.000 0.908 0.092
#> GSM182757 3 0.1109 0.82072 0.000 0.028 0.968 0.004
#> GSM182758 3 0.2149 0.83777 0.000 0.000 0.912 0.088
#> GSM182759 2 0.4792 0.60566 0.000 0.680 0.312 0.008
#> GSM182760 3 0.3172 0.79874 0.000 0.000 0.840 0.160
#> GSM182761 3 0.2401 0.77966 0.000 0.092 0.904 0.004
#> GSM182762 3 0.0592 0.83411 0.000 0.000 0.984 0.016
#> GSM182763 3 0.1042 0.82249 0.000 0.020 0.972 0.008
#> GSM182764 3 0.2944 0.74795 0.000 0.128 0.868 0.004
#> GSM182765 3 0.0188 0.83132 0.000 0.000 0.996 0.004
#> GSM182766 2 0.0672 0.85488 0.000 0.984 0.008 0.008
#> GSM182767 3 0.3172 0.79874 0.000 0.000 0.840 0.160
#> GSM182768 4 0.6004 0.50408 0.076 0.000 0.276 0.648
#> GSM182769 1 0.5560 0.26122 0.584 0.000 0.024 0.392
#> GSM182770 2 0.1661 0.84918 0.000 0.944 0.004 0.052
#> GSM182771 3 0.6316 0.22156 0.000 0.324 0.596 0.080
#> GSM182772 2 0.1661 0.84918 0.000 0.944 0.004 0.052
#> GSM182773 3 0.5657 0.50260 0.044 0.000 0.644 0.312
#> GSM182774 4 0.6023 0.37270 0.328 0.000 0.060 0.612
#> GSM182775 1 0.7231 -0.05274 0.464 0.000 0.144 0.392
#> GSM182776 1 0.5233 0.37897 0.648 0.000 0.020 0.332
#> GSM182777 3 0.6664 0.47721 0.152 0.000 0.616 0.232
#> GSM182802 2 0.3539 0.79678 0.000 0.820 0.004 0.176
#> GSM182803 1 0.0188 0.70956 0.996 0.004 0.000 0.000
#> GSM182804 4 0.3335 0.52500 0.128 0.000 0.016 0.856
#> GSM182805 2 0.3681 0.79660 0.000 0.816 0.008 0.176
#> GSM182806 1 0.0469 0.71156 0.988 0.000 0.000 0.012
#> GSM182807 1 0.0469 0.71156 0.988 0.000 0.000 0.012
#> GSM182808 1 0.0469 0.71156 0.988 0.000 0.000 0.012
#> GSM182809 4 0.4388 0.58182 0.136 0.004 0.048 0.812
#> GSM182810 1 0.4907 0.09072 0.580 0.000 0.000 0.420
#> GSM182811 4 0.5132 0.18369 0.448 0.004 0.000 0.548
#> GSM182812 1 0.4817 0.20367 0.612 0.000 0.000 0.388
#> GSM182813 1 0.0469 0.71156 0.988 0.000 0.000 0.012
#> GSM182778 2 0.0188 0.85446 0.000 0.996 0.004 0.000
#> GSM182779 3 0.2944 0.74795 0.000 0.128 0.868 0.004
#> GSM182780 3 0.1488 0.83709 0.000 0.012 0.956 0.032
#> GSM182781 3 0.2530 0.82841 0.000 0.000 0.888 0.112
#> GSM182782 2 0.0188 0.85446 0.000 0.996 0.004 0.000
#> GSM182783 3 0.2255 0.84048 0.000 0.012 0.920 0.068
#> GSM182784 3 0.2149 0.83777 0.000 0.000 0.912 0.088
#> GSM182785 3 0.0336 0.83271 0.000 0.000 0.992 0.008
#> GSM182786 2 0.0188 0.85446 0.000 0.996 0.004 0.000
#> GSM182787 2 0.5236 0.31019 0.000 0.560 0.432 0.008
#> GSM182788 2 0.0188 0.85446 0.000 0.996 0.004 0.000
#> GSM182789 3 0.1302 0.84059 0.000 0.000 0.956 0.044
#> GSM182790 3 0.3172 0.79874 0.000 0.000 0.840 0.160
#> GSM182791 4 0.5306 0.31456 0.020 0.000 0.348 0.632
#> GSM182792 4 0.6521 0.19040 0.076 0.000 0.412 0.512
#> GSM182793 2 0.4509 0.70782 0.000 0.708 0.004 0.288
#> GSM182794 3 0.3172 0.79874 0.000 0.000 0.840 0.160
#> GSM182795 3 0.2081 0.83815 0.000 0.000 0.916 0.084
#> GSM182796 2 0.2714 0.81427 0.000 0.884 0.112 0.004
#> GSM182797 1 0.2408 0.64699 0.896 0.000 0.000 0.104
#> GSM182798 2 0.5496 0.74913 0.000 0.724 0.188 0.088
#> GSM182799 4 0.2399 0.58730 0.032 0.000 0.048 0.920
#> GSM182800 4 0.4609 0.49146 0.224 0.000 0.024 0.752
#> GSM182801 1 0.5355 0.33014 0.620 0.000 0.020 0.360
#> GSM182814 1 0.0592 0.70633 0.984 0.000 0.000 0.016
#> GSM182815 4 0.5911 0.48153 0.180 0.084 0.016 0.720
#> GSM182816 1 0.0592 0.70633 0.984 0.000 0.000 0.016
#> GSM182817 3 0.6499 0.26145 0.060 0.012 0.588 0.340
#> GSM182818 4 0.4920 0.33618 0.368 0.004 0.000 0.628
#> GSM182819 1 0.0000 0.71009 1.000 0.000 0.000 0.000
#> GSM182820 1 0.0469 0.71156 0.988 0.000 0.000 0.012
#> GSM182821 3 0.3765 0.77887 0.004 0.004 0.812 0.180
#> GSM182822 1 0.5165 -0.08251 0.512 0.004 0.000 0.484
#> GSM182823 1 0.0592 0.70633 0.984 0.000 0.000 0.016
#> GSM182824 1 0.0592 0.70633 0.984 0.000 0.000 0.016
#> GSM182825 1 0.4998 0.00849 0.512 0.000 0.000 0.488
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM182755 1 0.6569 0.12779 0.496 0.000 0.288 0.004 0.212
#> GSM182756 5 0.4171 0.35438 0.000 0.000 0.396 0.000 0.604
#> GSM182757 5 0.0912 0.67805 0.000 0.012 0.016 0.000 0.972
#> GSM182758 5 0.4161 0.36374 0.000 0.000 0.392 0.000 0.608
#> GSM182759 5 0.3870 0.39054 0.000 0.260 0.004 0.004 0.732
#> GSM182760 3 0.4219 0.16470 0.000 0.000 0.584 0.000 0.416
#> GSM182761 5 0.1484 0.67106 0.000 0.048 0.008 0.000 0.944
#> GSM182762 5 0.1341 0.67052 0.000 0.000 0.056 0.000 0.944
#> GSM182763 5 0.0451 0.67765 0.000 0.000 0.008 0.004 0.988
#> GSM182764 5 0.1430 0.66701 0.000 0.052 0.004 0.000 0.944
#> GSM182765 5 0.0609 0.67729 0.000 0.000 0.020 0.000 0.980
#> GSM182766 2 0.4393 0.72252 0.000 0.752 0.004 0.052 0.192
#> GSM182767 3 0.4227 0.15328 0.000 0.000 0.580 0.000 0.420
#> GSM182768 3 0.4386 0.56442 0.024 0.000 0.788 0.132 0.056
#> GSM182769 3 0.4121 0.51749 0.168 0.000 0.784 0.036 0.012
#> GSM182770 2 0.2286 0.78378 0.000 0.888 0.000 0.108 0.004
#> GSM182771 5 0.5847 0.32483 0.000 0.160 0.024 0.152 0.664
#> GSM182772 2 0.2286 0.78378 0.000 0.888 0.000 0.108 0.004
#> GSM182773 3 0.3197 0.57096 0.012 0.000 0.832 0.004 0.152
#> GSM182774 3 0.6653 -0.15733 0.136 0.000 0.476 0.368 0.020
#> GSM182775 3 0.3675 0.56672 0.124 0.000 0.828 0.016 0.032
#> GSM182776 3 0.4798 0.38036 0.268 0.000 0.684 0.044 0.004
#> GSM182777 3 0.3146 0.60289 0.052 0.000 0.856 0.000 0.092
#> GSM182802 2 0.5071 0.66856 0.000 0.616 0.004 0.340 0.040
#> GSM182803 1 0.1469 0.76567 0.948 0.000 0.016 0.036 0.000
#> GSM182804 4 0.2352 0.55861 0.004 0.008 0.092 0.896 0.000
#> GSM182805 2 0.5071 0.66856 0.000 0.616 0.004 0.340 0.040
#> GSM182806 1 0.1571 0.78474 0.936 0.000 0.060 0.004 0.000
#> GSM182807 1 0.1571 0.78474 0.936 0.000 0.060 0.004 0.000
#> GSM182808 1 0.1410 0.78458 0.940 0.000 0.060 0.000 0.000
#> GSM182809 4 0.5175 0.58346 0.072 0.000 0.240 0.680 0.008
#> GSM182810 1 0.5737 -0.47918 0.464 0.000 0.084 0.452 0.000
#> GSM182811 4 0.5701 0.60307 0.332 0.000 0.100 0.568 0.000
#> GSM182812 1 0.5283 -0.34224 0.508 0.000 0.048 0.444 0.000
#> GSM182813 1 0.1410 0.78458 0.940 0.000 0.060 0.000 0.000
#> GSM182778 2 0.1195 0.78666 0.000 0.960 0.028 0.000 0.012
#> GSM182779 5 0.1270 0.66718 0.000 0.052 0.000 0.000 0.948
#> GSM182780 5 0.1357 0.67665 0.000 0.000 0.048 0.004 0.948
#> GSM182781 5 0.4287 0.19890 0.000 0.000 0.460 0.000 0.540
#> GSM182782 2 0.1195 0.78666 0.000 0.960 0.028 0.000 0.012
#> GSM182783 5 0.3774 0.50430 0.000 0.000 0.296 0.000 0.704
#> GSM182784 5 0.4101 0.39325 0.000 0.000 0.372 0.000 0.628
#> GSM182785 5 0.1792 0.65998 0.000 0.000 0.084 0.000 0.916
#> GSM182786 2 0.1195 0.78666 0.000 0.960 0.028 0.000 0.012
#> GSM182787 5 0.2629 0.59282 0.000 0.136 0.000 0.004 0.860
#> GSM182788 2 0.1195 0.78666 0.000 0.960 0.028 0.000 0.012
#> GSM182789 5 0.3210 0.58250 0.000 0.000 0.212 0.000 0.788
#> GSM182790 3 0.4210 0.16707 0.000 0.000 0.588 0.000 0.412
#> GSM182791 3 0.4129 0.49586 0.000 0.000 0.756 0.204 0.040
#> GSM182792 3 0.4065 0.59312 0.020 0.000 0.816 0.080 0.084
#> GSM182793 2 0.6341 0.52115 0.000 0.488 0.064 0.408 0.040
#> GSM182794 3 0.4210 0.16707 0.000 0.000 0.588 0.000 0.412
#> GSM182795 5 0.4150 0.36925 0.000 0.000 0.388 0.000 0.612
#> GSM182796 2 0.4789 0.43611 0.000 0.608 0.004 0.020 0.368
#> GSM182797 1 0.2732 0.68430 0.840 0.000 0.160 0.000 0.000
#> GSM182798 5 0.7015 -0.30297 0.000 0.372 0.032 0.156 0.440
#> GSM182799 3 0.4434 0.00288 0.004 0.000 0.536 0.460 0.000
#> GSM182800 3 0.5671 0.14057 0.096 0.000 0.568 0.336 0.000
#> GSM182801 3 0.4823 0.30766 0.316 0.000 0.644 0.040 0.000
#> GSM182814 1 0.0880 0.77327 0.968 0.000 0.000 0.032 0.000
#> GSM182815 4 0.3073 0.63972 0.068 0.008 0.052 0.872 0.000
#> GSM182816 1 0.1168 0.77183 0.960 0.000 0.008 0.032 0.000
#> GSM182817 5 0.6187 -0.02717 0.032 0.000 0.060 0.444 0.464
#> GSM182818 4 0.5218 0.69520 0.180 0.000 0.136 0.684 0.000
#> GSM182819 1 0.0566 0.78033 0.984 0.000 0.004 0.012 0.000
#> GSM182820 1 0.1571 0.78474 0.936 0.000 0.060 0.004 0.000
#> GSM182821 5 0.5944 0.17665 0.000 0.000 0.404 0.108 0.488
#> GSM182822 4 0.6047 0.52543 0.376 0.000 0.124 0.500 0.000
#> GSM182823 1 0.1168 0.77154 0.960 0.000 0.008 0.032 0.000
#> GSM182824 1 0.1168 0.77154 0.960 0.000 0.008 0.032 0.000
#> GSM182825 4 0.5828 0.41762 0.380 0.000 0.100 0.520 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM182755 6 0.7251 0.0106 0.324 0.000 0.216 0.000 0.104 0.356
#> GSM182756 3 0.1492 0.5813 0.000 0.000 0.940 0.000 0.024 0.036
#> GSM182757 5 0.4184 0.4447 0.000 0.012 0.484 0.000 0.504 0.000
#> GSM182758 3 0.0891 0.5829 0.000 0.000 0.968 0.000 0.008 0.024
#> GSM182759 5 0.4946 0.5648 0.000 0.100 0.284 0.000 0.616 0.000
#> GSM182760 3 0.3390 0.3174 0.000 0.000 0.704 0.000 0.000 0.296
#> GSM182761 3 0.4593 -0.4895 0.000 0.036 0.492 0.000 0.472 0.000
#> GSM182762 3 0.4338 -0.4276 0.000 0.000 0.492 0.000 0.488 0.020
#> GSM182763 5 0.3975 0.4932 0.000 0.000 0.452 0.000 0.544 0.004
#> GSM182764 5 0.4509 0.5146 0.000 0.032 0.436 0.000 0.532 0.000
#> GSM182765 5 0.4039 0.5023 0.000 0.000 0.424 0.000 0.568 0.008
#> GSM182766 2 0.5624 0.3181 0.000 0.484 0.044 0.020 0.432 0.020
#> GSM182767 3 0.3050 0.4178 0.000 0.000 0.764 0.000 0.000 0.236
#> GSM182768 6 0.4024 0.7306 0.000 0.000 0.180 0.064 0.004 0.752
#> GSM182769 6 0.3159 0.7361 0.020 0.000 0.152 0.008 0.000 0.820
#> GSM182770 2 0.4796 0.7054 0.000 0.708 0.000 0.092 0.176 0.024
#> GSM182771 5 0.4577 0.5324 0.000 0.048 0.156 0.040 0.748 0.008
#> GSM182772 2 0.4826 0.7047 0.000 0.704 0.000 0.092 0.180 0.024
#> GSM182773 6 0.3619 0.6301 0.000 0.000 0.316 0.004 0.000 0.680
#> GSM182774 6 0.5284 0.5204 0.028 0.000 0.056 0.216 0.024 0.676
#> GSM182775 6 0.2882 0.7351 0.008 0.000 0.180 0.000 0.000 0.812
#> GSM182776 6 0.3610 0.7132 0.048 0.000 0.104 0.012 0.012 0.824
#> GSM182777 6 0.3309 0.6590 0.000 0.000 0.280 0.000 0.000 0.720
#> GSM182802 2 0.6635 0.5032 0.000 0.400 0.000 0.312 0.256 0.032
#> GSM182803 1 0.2340 0.7433 0.900 0.000 0.000 0.060 0.016 0.024
#> GSM182804 4 0.3892 0.4669 0.012 0.000 0.000 0.788 0.120 0.080
#> GSM182805 2 0.6625 0.4994 0.000 0.400 0.000 0.320 0.248 0.032
#> GSM182806 1 0.2798 0.7800 0.852 0.000 0.000 0.000 0.036 0.112
#> GSM182807 1 0.2798 0.7800 0.852 0.000 0.000 0.000 0.036 0.112
#> GSM182808 1 0.2706 0.7817 0.860 0.000 0.000 0.000 0.036 0.104
#> GSM182809 4 0.3759 0.4671 0.008 0.000 0.024 0.752 0.000 0.216
#> GSM182810 4 0.5715 0.2999 0.432 0.000 0.000 0.456 0.024 0.088
#> GSM182811 4 0.5324 0.5288 0.284 0.000 0.000 0.612 0.028 0.076
#> GSM182812 1 0.5183 -0.1465 0.540 0.000 0.000 0.392 0.028 0.040
#> GSM182813 1 0.2843 0.7796 0.848 0.000 0.000 0.000 0.036 0.116
#> GSM182778 2 0.0000 0.7267 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM182779 5 0.4504 0.5164 0.000 0.032 0.432 0.000 0.536 0.000
#> GSM182780 3 0.3684 -0.0369 0.000 0.000 0.664 0.000 0.332 0.004
#> GSM182781 3 0.3333 0.5060 0.000 0.000 0.784 0.000 0.024 0.192
#> GSM182782 2 0.0000 0.7267 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM182783 3 0.1918 0.5205 0.000 0.000 0.904 0.000 0.088 0.008
#> GSM182784 3 0.0508 0.5806 0.000 0.000 0.984 0.000 0.004 0.012
#> GSM182785 3 0.3221 0.1721 0.000 0.000 0.736 0.000 0.264 0.000
#> GSM182786 2 0.0000 0.7267 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM182787 3 0.5116 -0.4682 0.000 0.068 0.484 0.000 0.444 0.004
#> GSM182788 2 0.0000 0.7267 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM182789 3 0.2178 0.4396 0.000 0.000 0.868 0.000 0.132 0.000
#> GSM182790 3 0.3710 0.3209 0.000 0.000 0.696 0.000 0.012 0.292
#> GSM182791 6 0.6423 0.5646 0.000 0.000 0.204 0.164 0.080 0.552
#> GSM182792 6 0.3912 0.7265 0.000 0.000 0.204 0.044 0.004 0.748
#> GSM182793 4 0.7111 -0.3996 0.000 0.272 0.000 0.344 0.312 0.072
#> GSM182794 3 0.3371 0.3269 0.000 0.000 0.708 0.000 0.000 0.292
#> GSM182795 3 0.1418 0.5788 0.000 0.000 0.944 0.000 0.024 0.032
#> GSM182796 5 0.4876 0.1398 0.000 0.368 0.068 0.000 0.564 0.000
#> GSM182797 1 0.4534 0.4357 0.580 0.000 0.000 0.000 0.040 0.380
#> GSM182798 5 0.5305 0.3205 0.000 0.136 0.080 0.048 0.712 0.024
#> GSM182799 6 0.6318 0.2892 0.004 0.000 0.064 0.364 0.088 0.480
#> GSM182800 6 0.6402 0.5163 0.032 0.000 0.072 0.216 0.084 0.596
#> GSM182801 6 0.3561 0.7005 0.072 0.000 0.088 0.012 0.004 0.824
#> GSM182814 1 0.2112 0.7586 0.916 0.000 0.000 0.036 0.028 0.020
#> GSM182815 4 0.3177 0.5478 0.052 0.000 0.000 0.856 0.052 0.040
#> GSM182816 1 0.2262 0.7553 0.908 0.000 0.000 0.036 0.036 0.020
#> GSM182817 5 0.5868 0.0561 0.012 0.000 0.068 0.400 0.492 0.028
#> GSM182818 4 0.4348 0.5958 0.120 0.000 0.000 0.748 0.012 0.120
#> GSM182819 1 0.1232 0.7771 0.956 0.000 0.000 0.004 0.016 0.024
#> GSM182820 1 0.2798 0.7800 0.852 0.000 0.000 0.000 0.036 0.112
#> GSM182821 3 0.4934 0.3981 0.004 0.000 0.696 0.208 0.048 0.044
#> GSM182822 4 0.5630 0.4576 0.344 0.000 0.000 0.540 0.024 0.092
#> GSM182823 1 0.1932 0.7631 0.924 0.000 0.000 0.040 0.020 0.016
#> GSM182824 1 0.1932 0.7631 0.924 0.000 0.000 0.040 0.020 0.016
#> GSM182825 4 0.6120 0.2396 0.412 0.000 0.000 0.444 0.048 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 stress(p) development.stage(p) k
#> SD:kmeans 65 0.887 2.21e-04 2
#> SD:kmeans 65 0.912 5.11e-07 3
#> SD:kmeans 51 0.708 1.52e-06 4
#> SD:kmeans 46 0.572 3.47e-07 5
#> SD:kmeans 43 0.574 2.14e-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 18172 rows and 71 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.938 0.907 0.965 0.5067 0.494 0.494
#> 3 3 0.722 0.818 0.918 0.3091 0.804 0.622
#> 4 4 0.685 0.732 0.868 0.1143 0.905 0.734
#> 5 5 0.630 0.599 0.777 0.0635 0.910 0.691
#> 6 6 0.646 0.499 0.718 0.0405 0.962 0.832
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
#> GSM182755 1 0.000 0.9462 1.000 0.000
#> GSM182756 2 0.204 0.9503 0.032 0.968
#> GSM182757 2 0.000 0.9781 0.000 1.000
#> GSM182758 2 0.000 0.9781 0.000 1.000
#> GSM182759 2 0.000 0.9781 0.000 1.000
#> GSM182760 1 0.961 0.3744 0.616 0.384
#> GSM182761 2 0.000 0.9781 0.000 1.000
#> GSM182762 2 0.224 0.9465 0.036 0.964
#> GSM182763 2 0.000 0.9781 0.000 1.000
#> GSM182764 2 0.000 0.9781 0.000 1.000
#> GSM182765 2 0.000 0.9781 0.000 1.000
#> GSM182766 2 0.000 0.9781 0.000 1.000
#> GSM182767 2 0.689 0.7631 0.184 0.816
#> GSM182768 1 0.000 0.9462 1.000 0.000
#> GSM182769 1 0.000 0.9462 1.000 0.000
#> GSM182770 2 0.000 0.9781 0.000 1.000
#> GSM182771 2 0.000 0.9781 0.000 1.000
#> GSM182772 2 0.000 0.9781 0.000 1.000
#> GSM182773 1 0.000 0.9462 1.000 0.000
#> GSM182774 1 0.000 0.9462 1.000 0.000
#> GSM182775 1 0.000 0.9462 1.000 0.000
#> GSM182776 1 0.000 0.9462 1.000 0.000
#> GSM182777 1 0.000 0.9462 1.000 0.000
#> GSM182802 2 0.000 0.9781 0.000 1.000
#> GSM182803 1 0.000 0.9462 1.000 0.000
#> GSM182804 1 0.224 0.9181 0.964 0.036
#> GSM182805 2 0.000 0.9781 0.000 1.000
#> GSM182806 1 0.000 0.9462 1.000 0.000
#> GSM182807 1 0.000 0.9462 1.000 0.000
#> GSM182808 1 0.000 0.9462 1.000 0.000
#> GSM182809 1 0.224 0.9181 0.964 0.036
#> GSM182810 1 0.000 0.9462 1.000 0.000
#> GSM182811 1 0.000 0.9462 1.000 0.000
#> GSM182812 1 0.000 0.9462 1.000 0.000
#> GSM182813 1 0.000 0.9462 1.000 0.000
#> GSM182778 2 0.000 0.9781 0.000 1.000
#> GSM182779 2 0.000 0.9781 0.000 1.000
#> GSM182780 2 0.000 0.9781 0.000 1.000
#> GSM182781 1 1.000 0.0249 0.504 0.496
#> GSM182782 2 0.000 0.9781 0.000 1.000
#> GSM182783 2 0.000 0.9781 0.000 1.000
#> GSM182784 2 0.000 0.9781 0.000 1.000
#> GSM182785 2 0.000 0.9781 0.000 1.000
#> GSM182786 2 0.000 0.9781 0.000 1.000
#> GSM182787 2 0.000 0.9781 0.000 1.000
#> GSM182788 2 0.000 0.9781 0.000 1.000
#> GSM182789 2 0.000 0.9781 0.000 1.000
#> GSM182790 1 1.000 0.0249 0.504 0.496
#> GSM182791 1 0.000 0.9462 1.000 0.000
#> GSM182792 1 0.000 0.9462 1.000 0.000
#> GSM182793 2 0.000 0.9781 0.000 1.000
#> GSM182794 2 0.932 0.4401 0.348 0.652
#> GSM182795 2 0.000 0.9781 0.000 1.000
#> GSM182796 2 0.000 0.9781 0.000 1.000
#> GSM182797 1 0.000 0.9462 1.000 0.000
#> GSM182798 2 0.000 0.9781 0.000 1.000
#> GSM182799 1 0.224 0.9181 0.964 0.036
#> GSM182800 1 0.000 0.9462 1.000 0.000
#> GSM182801 1 0.000 0.9462 1.000 0.000
#> GSM182814 1 0.000 0.9462 1.000 0.000
#> GSM182815 1 0.932 0.4702 0.652 0.348
#> GSM182816 1 0.000 0.9462 1.000 0.000
#> GSM182817 2 0.358 0.9108 0.068 0.932
#> GSM182818 1 0.000 0.9462 1.000 0.000
#> GSM182819 1 0.000 0.9462 1.000 0.000
#> GSM182820 1 0.000 0.9462 1.000 0.000
#> GSM182821 2 0.000 0.9781 0.000 1.000
#> GSM182822 1 0.000 0.9462 1.000 0.000
#> GSM182823 1 0.000 0.9462 1.000 0.000
#> GSM182824 1 0.000 0.9462 1.000 0.000
#> GSM182825 1 0.000 0.9462 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM182755 3 0.5905 0.445 0.352 0.000 0.648
#> GSM182756 3 0.0000 0.903 0.000 0.000 1.000
#> GSM182757 3 0.6045 0.336 0.000 0.380 0.620
#> GSM182758 3 0.0000 0.903 0.000 0.000 1.000
#> GSM182759 2 0.0000 0.924 0.000 1.000 0.000
#> GSM182760 3 0.0000 0.903 0.000 0.000 1.000
#> GSM182761 2 0.4974 0.705 0.000 0.764 0.236
#> GSM182762 3 0.2400 0.867 0.004 0.064 0.932
#> GSM182763 2 0.1031 0.910 0.000 0.976 0.024
#> GSM182764 2 0.4555 0.745 0.000 0.800 0.200
#> GSM182765 2 0.5706 0.539 0.000 0.680 0.320
#> GSM182766 2 0.0000 0.924 0.000 1.000 0.000
#> GSM182767 3 0.0000 0.903 0.000 0.000 1.000
#> GSM182768 1 0.5733 0.578 0.676 0.000 0.324
#> GSM182769 1 0.3619 0.804 0.864 0.000 0.136
#> GSM182770 2 0.0000 0.924 0.000 1.000 0.000
#> GSM182771 2 0.0000 0.924 0.000 1.000 0.000
#> GSM182772 2 0.0000 0.924 0.000 1.000 0.000
#> GSM182773 3 0.2261 0.859 0.068 0.000 0.932
#> GSM182774 1 0.0000 0.894 1.000 0.000 0.000
#> GSM182775 1 0.5810 0.558 0.664 0.000 0.336
#> GSM182776 1 0.0000 0.894 1.000 0.000 0.000
#> GSM182777 3 0.2625 0.843 0.084 0.000 0.916
#> GSM182802 2 0.0000 0.924 0.000 1.000 0.000
#> GSM182803 1 0.0000 0.894 1.000 0.000 0.000
#> GSM182804 1 0.3686 0.786 0.860 0.140 0.000
#> GSM182805 2 0.0000 0.924 0.000 1.000 0.000
#> GSM182806 1 0.0000 0.894 1.000 0.000 0.000
#> GSM182807 1 0.0000 0.894 1.000 0.000 0.000
#> GSM182808 1 0.0000 0.894 1.000 0.000 0.000
#> GSM182809 1 0.3340 0.804 0.880 0.120 0.000
#> GSM182810 1 0.0000 0.894 1.000 0.000 0.000
#> GSM182811 1 0.0000 0.894 1.000 0.000 0.000
#> GSM182812 1 0.0000 0.894 1.000 0.000 0.000
#> GSM182813 1 0.0000 0.894 1.000 0.000 0.000
#> GSM182778 2 0.0000 0.924 0.000 1.000 0.000
#> GSM182779 2 0.2711 0.862 0.000 0.912 0.088
#> GSM182780 2 0.0424 0.920 0.000 0.992 0.008
#> GSM182781 3 0.0000 0.903 0.000 0.000 1.000
#> GSM182782 2 0.0000 0.924 0.000 1.000 0.000
#> GSM182783 2 0.5216 0.651 0.000 0.740 0.260
#> GSM182784 3 0.0000 0.903 0.000 0.000 1.000
#> GSM182785 3 0.3116 0.824 0.000 0.108 0.892
#> GSM182786 2 0.0000 0.924 0.000 1.000 0.000
#> GSM182787 2 0.0000 0.924 0.000 1.000 0.000
#> GSM182788 2 0.0000 0.924 0.000 1.000 0.000
#> GSM182789 3 0.4504 0.715 0.000 0.196 0.804
#> GSM182790 3 0.0000 0.903 0.000 0.000 1.000
#> GSM182791 1 0.7223 0.353 0.548 0.028 0.424
#> GSM182792 1 0.6244 0.343 0.560 0.000 0.440
#> GSM182793 2 0.0000 0.924 0.000 1.000 0.000
#> GSM182794 3 0.0000 0.903 0.000 0.000 1.000
#> GSM182795 3 0.0747 0.896 0.000 0.016 0.984
#> GSM182796 2 0.0000 0.924 0.000 1.000 0.000
#> GSM182797 1 0.2165 0.858 0.936 0.000 0.064
#> GSM182798 2 0.0000 0.924 0.000 1.000 0.000
#> GSM182799 1 0.8626 0.501 0.580 0.140 0.280
#> GSM182800 1 0.0592 0.888 0.988 0.000 0.012
#> GSM182801 1 0.2959 0.833 0.900 0.000 0.100
#> GSM182814 1 0.0000 0.894 1.000 0.000 0.000
#> GSM182815 1 0.6291 0.165 0.532 0.468 0.000
#> GSM182816 1 0.0000 0.894 1.000 0.000 0.000
#> GSM182817 2 0.4974 0.666 0.236 0.764 0.000
#> GSM182818 1 0.0000 0.894 1.000 0.000 0.000
#> GSM182819 1 0.0000 0.894 1.000 0.000 0.000
#> GSM182820 1 0.0000 0.894 1.000 0.000 0.000
#> GSM182821 2 0.4968 0.745 0.012 0.800 0.188
#> GSM182822 1 0.0000 0.894 1.000 0.000 0.000
#> GSM182823 1 0.0000 0.894 1.000 0.000 0.000
#> GSM182824 1 0.0000 0.894 1.000 0.000 0.000
#> GSM182825 1 0.0000 0.894 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM182755 1 0.4086 0.631 0.776 0.000 0.216 0.008
#> GSM182756 3 0.0188 0.852 0.000 0.000 0.996 0.004
#> GSM182757 3 0.4713 0.364 0.000 0.360 0.640 0.000
#> GSM182758 3 0.0672 0.853 0.000 0.008 0.984 0.008
#> GSM182759 2 0.0000 0.847 0.000 1.000 0.000 0.000
#> GSM182760 3 0.0817 0.849 0.000 0.000 0.976 0.024
#> GSM182761 2 0.4193 0.629 0.000 0.732 0.268 0.000
#> GSM182762 3 0.2654 0.787 0.004 0.108 0.888 0.000
#> GSM182763 2 0.0817 0.841 0.000 0.976 0.024 0.000
#> GSM182764 2 0.3942 0.669 0.000 0.764 0.236 0.000
#> GSM182765 2 0.4356 0.589 0.000 0.708 0.292 0.000
#> GSM182766 2 0.0188 0.847 0.000 0.996 0.000 0.004
#> GSM182767 3 0.0707 0.850 0.000 0.000 0.980 0.020
#> GSM182768 4 0.5650 0.692 0.180 0.000 0.104 0.716
#> GSM182769 1 0.4540 0.659 0.772 0.000 0.032 0.196
#> GSM182770 2 0.1118 0.838 0.000 0.964 0.000 0.036
#> GSM182771 2 0.0188 0.847 0.000 0.996 0.000 0.004
#> GSM182772 2 0.1022 0.840 0.000 0.968 0.000 0.032
#> GSM182773 3 0.5889 0.529 0.116 0.000 0.696 0.188
#> GSM182774 1 0.3219 0.775 0.836 0.000 0.000 0.164
#> GSM182775 1 0.6823 0.351 0.604 0.000 0.196 0.200
#> GSM182776 1 0.1557 0.835 0.944 0.000 0.000 0.056
#> GSM182777 3 0.7149 0.189 0.316 0.000 0.528 0.156
#> GSM182802 2 0.2589 0.792 0.000 0.884 0.000 0.116
#> GSM182803 1 0.0921 0.864 0.972 0.000 0.000 0.028
#> GSM182804 4 0.3674 0.734 0.104 0.044 0.000 0.852
#> GSM182805 2 0.2530 0.795 0.000 0.888 0.000 0.112
#> GSM182806 1 0.0000 0.863 1.000 0.000 0.000 0.000
#> GSM182807 1 0.0000 0.863 1.000 0.000 0.000 0.000
#> GSM182808 1 0.0000 0.863 1.000 0.000 0.000 0.000
#> GSM182809 4 0.4464 0.711 0.208 0.024 0.000 0.768
#> GSM182810 1 0.1792 0.846 0.932 0.000 0.000 0.068
#> GSM182811 1 0.3649 0.702 0.796 0.000 0.000 0.204
#> GSM182812 1 0.2647 0.804 0.880 0.000 0.000 0.120
#> GSM182813 1 0.0000 0.863 1.000 0.000 0.000 0.000
#> GSM182778 2 0.0188 0.847 0.000 0.996 0.000 0.004
#> GSM182779 2 0.2149 0.810 0.000 0.912 0.088 0.000
#> GSM182780 2 0.4727 0.734 0.000 0.792 0.100 0.108
#> GSM182781 3 0.0188 0.852 0.004 0.000 0.996 0.000
#> GSM182782 2 0.0188 0.847 0.000 0.996 0.000 0.004
#> GSM182783 2 0.6007 0.269 0.000 0.548 0.408 0.044
#> GSM182784 3 0.0188 0.852 0.000 0.004 0.996 0.000
#> GSM182785 3 0.1637 0.826 0.000 0.060 0.940 0.000
#> GSM182786 2 0.0188 0.847 0.000 0.996 0.000 0.004
#> GSM182787 2 0.0188 0.847 0.000 0.996 0.000 0.004
#> GSM182788 2 0.0188 0.847 0.000 0.996 0.000 0.004
#> GSM182789 3 0.3539 0.716 0.000 0.176 0.820 0.004
#> GSM182790 3 0.0592 0.851 0.000 0.000 0.984 0.016
#> GSM182791 4 0.3190 0.705 0.016 0.008 0.096 0.880
#> GSM182792 4 0.6469 0.608 0.164 0.000 0.192 0.644
#> GSM182793 2 0.4888 0.374 0.000 0.588 0.000 0.412
#> GSM182794 3 0.1118 0.842 0.000 0.000 0.964 0.036
#> GSM182795 3 0.1677 0.842 0.000 0.040 0.948 0.012
#> GSM182796 2 0.0000 0.847 0.000 1.000 0.000 0.000
#> GSM182797 1 0.2412 0.806 0.908 0.000 0.008 0.084
#> GSM182798 2 0.0817 0.842 0.000 0.976 0.000 0.024
#> GSM182799 4 0.0524 0.734 0.004 0.000 0.008 0.988
#> GSM182800 4 0.3945 0.656 0.216 0.000 0.004 0.780
#> GSM182801 1 0.4194 0.647 0.764 0.000 0.008 0.228
#> GSM182814 1 0.0921 0.864 0.972 0.000 0.000 0.028
#> GSM182815 4 0.4856 0.718 0.136 0.084 0.000 0.780
#> GSM182816 1 0.0921 0.864 0.972 0.000 0.000 0.028
#> GSM182817 2 0.6910 0.258 0.324 0.548 0.000 0.128
#> GSM182818 4 0.4941 0.321 0.436 0.000 0.000 0.564
#> GSM182819 1 0.0921 0.864 0.972 0.000 0.000 0.028
#> GSM182820 1 0.0000 0.863 1.000 0.000 0.000 0.000
#> GSM182821 2 0.8053 0.286 0.020 0.488 0.224 0.268
#> GSM182822 1 0.1867 0.842 0.928 0.000 0.000 0.072
#> GSM182823 1 0.0921 0.864 0.972 0.000 0.000 0.028
#> GSM182824 1 0.0921 0.864 0.972 0.000 0.000 0.028
#> GSM182825 1 0.4643 0.427 0.656 0.000 0.000 0.344
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM182755 1 0.5914 0.4292 0.644 0.000 0.176 0.016 0.164
#> GSM182756 5 0.1628 0.7447 0.000 0.000 0.056 0.008 0.936
#> GSM182757 5 0.6169 0.3062 0.000 0.312 0.108 0.016 0.564
#> GSM182758 5 0.2052 0.7429 0.000 0.004 0.080 0.004 0.912
#> GSM182759 2 0.1569 0.7792 0.000 0.944 0.044 0.008 0.004
#> GSM182760 5 0.3132 0.6837 0.000 0.000 0.172 0.008 0.820
#> GSM182761 2 0.5776 0.4021 0.000 0.592 0.064 0.020 0.324
#> GSM182762 5 0.5887 0.5828 0.000 0.136 0.164 0.032 0.668
#> GSM182763 2 0.3674 0.7400 0.000 0.840 0.068 0.016 0.076
#> GSM182764 2 0.6554 0.3931 0.000 0.540 0.136 0.024 0.300
#> GSM182765 2 0.6479 0.4311 0.000 0.568 0.132 0.028 0.272
#> GSM182766 2 0.0000 0.7828 0.000 1.000 0.000 0.000 0.000
#> GSM182767 5 0.2798 0.7091 0.000 0.000 0.140 0.008 0.852
#> GSM182768 3 0.5930 0.4621 0.060 0.000 0.664 0.204 0.072
#> GSM182769 3 0.5211 0.2708 0.432 0.000 0.524 0.000 0.044
#> GSM182770 2 0.2020 0.7466 0.000 0.900 0.000 0.100 0.000
#> GSM182771 2 0.3796 0.7431 0.000 0.820 0.076 0.100 0.004
#> GSM182772 2 0.1965 0.7485 0.000 0.904 0.000 0.096 0.000
#> GSM182773 3 0.4482 0.2389 0.012 0.000 0.612 0.000 0.376
#> GSM182774 1 0.4404 0.6965 0.760 0.000 0.152 0.088 0.000
#> GSM182775 3 0.6001 0.4990 0.280 0.000 0.580 0.004 0.136
#> GSM182776 1 0.3366 0.6221 0.768 0.000 0.232 0.000 0.000
#> GSM182777 3 0.6507 0.3117 0.156 0.000 0.484 0.008 0.352
#> GSM182802 2 0.3895 0.5030 0.000 0.680 0.000 0.320 0.000
#> GSM182803 1 0.1408 0.8174 0.948 0.000 0.008 0.044 0.000
#> GSM182804 4 0.3858 0.4113 0.016 0.024 0.156 0.804 0.000
#> GSM182805 2 0.4029 0.5003 0.000 0.680 0.004 0.316 0.000
#> GSM182806 1 0.0880 0.8355 0.968 0.000 0.032 0.000 0.000
#> GSM182807 1 0.0880 0.8355 0.968 0.000 0.032 0.000 0.000
#> GSM182808 1 0.0794 0.8349 0.972 0.000 0.028 0.000 0.000
#> GSM182809 4 0.4893 0.5184 0.164 0.016 0.080 0.740 0.000
#> GSM182810 1 0.2377 0.7675 0.872 0.000 0.000 0.128 0.000
#> GSM182811 1 0.4504 0.1614 0.564 0.000 0.008 0.428 0.000
#> GSM182812 1 0.2773 0.7351 0.836 0.000 0.000 0.164 0.000
#> GSM182813 1 0.0880 0.8334 0.968 0.000 0.032 0.000 0.000
#> GSM182778 2 0.0000 0.7828 0.000 1.000 0.000 0.000 0.000
#> GSM182779 2 0.4975 0.6663 0.000 0.736 0.068 0.024 0.172
#> GSM182780 2 0.6267 0.5620 0.000 0.656 0.076 0.116 0.152
#> GSM182781 5 0.2130 0.7412 0.000 0.000 0.080 0.012 0.908
#> GSM182782 2 0.0000 0.7828 0.000 1.000 0.000 0.000 0.000
#> GSM182783 5 0.6430 0.0454 0.000 0.432 0.052 0.056 0.460
#> GSM182784 5 0.1329 0.7456 0.000 0.004 0.032 0.008 0.956
#> GSM182785 5 0.3850 0.6900 0.000 0.044 0.128 0.012 0.816
#> GSM182786 2 0.0000 0.7828 0.000 1.000 0.000 0.000 0.000
#> GSM182787 2 0.1469 0.7751 0.000 0.948 0.016 0.000 0.036
#> GSM182788 2 0.0000 0.7828 0.000 1.000 0.000 0.000 0.000
#> GSM182789 5 0.4255 0.6780 0.000 0.140 0.060 0.012 0.788
#> GSM182790 5 0.3203 0.6855 0.000 0.000 0.168 0.012 0.820
#> GSM182791 3 0.5355 0.2210 0.008 0.000 0.552 0.400 0.040
#> GSM182792 3 0.5203 0.5108 0.068 0.000 0.748 0.080 0.104
#> GSM182793 2 0.6024 0.1950 0.000 0.512 0.124 0.364 0.000
#> GSM182794 5 0.3487 0.6477 0.000 0.000 0.212 0.008 0.780
#> GSM182795 5 0.3525 0.7157 0.000 0.032 0.120 0.012 0.836
#> GSM182796 2 0.1885 0.7769 0.000 0.932 0.044 0.020 0.004
#> GSM182797 1 0.3489 0.6467 0.784 0.000 0.208 0.004 0.004
#> GSM182798 2 0.3700 0.7526 0.000 0.832 0.084 0.076 0.008
#> GSM182799 3 0.4446 0.1171 0.000 0.000 0.520 0.476 0.004
#> GSM182800 3 0.6313 0.2921 0.188 0.000 0.516 0.296 0.000
#> GSM182801 3 0.4890 0.2161 0.452 0.000 0.524 0.024 0.000
#> GSM182814 1 0.0404 0.8373 0.988 0.000 0.000 0.012 0.000
#> GSM182815 4 0.3429 0.5669 0.100 0.040 0.012 0.848 0.000
#> GSM182816 1 0.0000 0.8386 1.000 0.000 0.000 0.000 0.000
#> GSM182817 4 0.7800 0.4273 0.256 0.204 0.080 0.456 0.004
#> GSM182818 4 0.4416 0.4071 0.356 0.000 0.012 0.632 0.000
#> GSM182819 1 0.0162 0.8383 0.996 0.000 0.004 0.000 0.000
#> GSM182820 1 0.0880 0.8355 0.968 0.000 0.032 0.000 0.000
#> GSM182821 4 0.8370 0.2766 0.032 0.308 0.100 0.416 0.144
#> GSM182822 1 0.3013 0.7242 0.832 0.000 0.008 0.160 0.000
#> GSM182823 1 0.0000 0.8386 1.000 0.000 0.000 0.000 0.000
#> GSM182824 1 0.0162 0.8384 0.996 0.000 0.000 0.004 0.000
#> GSM182825 1 0.5589 0.4501 0.628 0.000 0.128 0.244 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM182755 1 0.7040 0.091254 0.464 0.000 0.116 0.000 0.204 0.216
#> GSM182756 3 0.3624 0.656525 0.000 0.000 0.784 0.000 0.156 0.060
#> GSM182757 5 0.6195 0.326096 0.000 0.272 0.336 0.000 0.388 0.004
#> GSM182758 3 0.2077 0.681438 0.000 0.004 0.916 0.004 0.032 0.044
#> GSM182759 2 0.2389 0.636728 0.000 0.864 0.008 0.000 0.128 0.000
#> GSM182760 3 0.4771 0.607554 0.000 0.000 0.652 0.000 0.100 0.248
#> GSM182761 2 0.5711 -0.039346 0.000 0.540 0.192 0.004 0.264 0.000
#> GSM182762 5 0.5813 0.163154 0.000 0.116 0.288 0.000 0.564 0.032
#> GSM182763 2 0.4330 0.387081 0.000 0.680 0.044 0.000 0.272 0.004
#> GSM182764 5 0.5541 0.312160 0.000 0.392 0.136 0.000 0.472 0.000
#> GSM182765 5 0.6054 0.370608 0.000 0.348 0.144 0.004 0.488 0.016
#> GSM182766 2 0.0458 0.704275 0.000 0.984 0.000 0.000 0.016 0.000
#> GSM182767 3 0.3284 0.670347 0.000 0.000 0.800 0.000 0.032 0.168
#> GSM182768 6 0.4125 0.490686 0.016 0.000 0.036 0.192 0.004 0.752
#> GSM182769 6 0.4526 0.531650 0.280 0.000 0.032 0.008 0.008 0.672
#> GSM182770 2 0.2887 0.663569 0.000 0.844 0.000 0.036 0.120 0.000
#> GSM182771 2 0.4284 0.558859 0.000 0.676 0.008 0.016 0.292 0.008
#> GSM182772 2 0.2956 0.661920 0.000 0.840 0.000 0.040 0.120 0.000
#> GSM182773 6 0.3716 0.455559 0.012 0.000 0.248 0.000 0.008 0.732
#> GSM182774 1 0.5586 0.537127 0.648 0.000 0.004 0.140 0.036 0.172
#> GSM182775 6 0.4431 0.603326 0.152 0.000 0.080 0.004 0.016 0.748
#> GSM182776 1 0.4365 0.392397 0.640 0.000 0.008 0.008 0.012 0.332
#> GSM182777 6 0.5374 0.514482 0.128 0.000 0.176 0.000 0.036 0.660
#> GSM182802 2 0.4965 0.504177 0.000 0.660 0.000 0.136 0.200 0.004
#> GSM182803 1 0.1065 0.774719 0.964 0.000 0.000 0.020 0.008 0.008
#> GSM182804 4 0.2421 0.517004 0.000 0.004 0.004 0.896 0.044 0.052
#> GSM182805 2 0.4955 0.495007 0.000 0.660 0.000 0.132 0.204 0.004
#> GSM182806 1 0.1049 0.775845 0.960 0.000 0.000 0.000 0.008 0.032
#> GSM182807 1 0.1225 0.774535 0.952 0.000 0.000 0.000 0.012 0.036
#> GSM182808 1 0.1124 0.775231 0.956 0.000 0.000 0.000 0.008 0.036
#> GSM182809 4 0.4951 0.598771 0.148 0.012 0.000 0.728 0.068 0.044
#> GSM182810 1 0.3309 0.641385 0.788 0.000 0.000 0.192 0.016 0.004
#> GSM182811 1 0.5664 0.042406 0.492 0.000 0.000 0.384 0.112 0.012
#> GSM182812 1 0.3383 0.564282 0.728 0.000 0.000 0.268 0.000 0.004
#> GSM182813 1 0.1124 0.775231 0.956 0.000 0.000 0.000 0.008 0.036
#> GSM182778 2 0.0000 0.704101 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM182779 2 0.4874 0.202287 0.000 0.608 0.084 0.000 0.308 0.000
#> GSM182780 2 0.6417 0.313759 0.000 0.592 0.160 0.108 0.132 0.008
#> GSM182781 3 0.4573 0.584676 0.000 0.000 0.676 0.000 0.236 0.088
#> GSM182782 2 0.0000 0.704101 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM182783 3 0.5902 0.052471 0.000 0.368 0.512 0.028 0.084 0.008
#> GSM182784 3 0.3316 0.642860 0.000 0.004 0.804 0.000 0.164 0.028
#> GSM182785 3 0.4700 0.353368 0.000 0.036 0.592 0.004 0.364 0.004
#> GSM182786 2 0.0000 0.704101 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM182787 2 0.2128 0.662017 0.000 0.908 0.032 0.004 0.056 0.000
#> GSM182788 2 0.0000 0.704101 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM182789 3 0.4954 0.468728 0.000 0.116 0.692 0.008 0.176 0.008
#> GSM182790 3 0.3861 0.651336 0.000 0.000 0.756 0.000 0.060 0.184
#> GSM182791 6 0.5775 -0.075354 0.000 0.000 0.060 0.444 0.048 0.448
#> GSM182792 6 0.3502 0.560787 0.008 0.000 0.088 0.060 0.012 0.832
#> GSM182793 2 0.5952 0.287621 0.000 0.520 0.004 0.352 0.084 0.040
#> GSM182794 3 0.3780 0.609728 0.000 0.000 0.728 0.004 0.020 0.248
#> GSM182795 3 0.4102 0.622780 0.000 0.048 0.808 0.016 0.072 0.056
#> GSM182796 2 0.1957 0.687877 0.000 0.888 0.000 0.000 0.112 0.000
#> GSM182797 1 0.4515 0.314547 0.608 0.000 0.008 0.000 0.028 0.356
#> GSM182798 2 0.4341 0.607319 0.000 0.712 0.000 0.048 0.228 0.012
#> GSM182799 4 0.4810 -0.044804 0.000 0.000 0.008 0.552 0.040 0.400
#> GSM182800 6 0.6062 0.000714 0.108 0.000 0.000 0.416 0.036 0.440
#> GSM182801 6 0.4099 0.514324 0.276 0.000 0.004 0.016 0.008 0.696
#> GSM182814 1 0.0935 0.769166 0.964 0.000 0.000 0.032 0.000 0.004
#> GSM182815 4 0.4463 0.577763 0.076 0.020 0.000 0.748 0.152 0.004
#> GSM182816 1 0.0458 0.775834 0.984 0.000 0.000 0.016 0.000 0.000
#> GSM182817 5 0.7911 -0.252006 0.192 0.132 0.000 0.276 0.368 0.032
#> GSM182818 4 0.4998 0.399928 0.316 0.000 0.000 0.608 0.064 0.012
#> GSM182819 1 0.0405 0.776958 0.988 0.000 0.000 0.004 0.000 0.008
#> GSM182820 1 0.1225 0.774535 0.952 0.000 0.000 0.000 0.012 0.036
#> GSM182821 5 0.8652 0.079579 0.008 0.244 0.200 0.208 0.284 0.056
#> GSM182822 1 0.4071 0.588337 0.736 0.000 0.000 0.216 0.036 0.012
#> GSM182823 1 0.0547 0.774830 0.980 0.000 0.000 0.020 0.000 0.000
#> GSM182824 1 0.0458 0.775834 0.984 0.000 0.000 0.016 0.000 0.000
#> GSM182825 1 0.4435 0.351711 0.580 0.000 0.000 0.392 0.004 0.024
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 stress(p) development.stage(p) k
#> SD:skmeans 66 0.805 2.98e-04 2
#> SD:skmeans 66 0.857 4.98e-06 3
#> SD:skmeans 62 0.767 1.17e-05 4
#> SD:skmeans 49 0.866 3.40e-06 5
#> SD:skmeans 45 0.943 1.59e-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", "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 18172 rows and 71 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.853 0.888 0.953 0.4970 0.505 0.505
#> 3 3 0.590 0.752 0.874 0.2601 0.668 0.455
#> 4 4 0.533 0.470 0.703 0.1241 0.847 0.659
#> 5 5 0.556 0.407 0.667 0.0886 0.744 0.380
#> 6 6 0.581 0.290 0.634 0.0582 0.808 0.356
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
#> GSM182755 1 0.0376 0.941 0.996 0.004
#> GSM182756 1 0.9686 0.388 0.604 0.396
#> GSM182757 2 0.0000 0.959 0.000 1.000
#> GSM182758 2 0.0000 0.959 0.000 1.000
#> GSM182759 2 0.0000 0.959 0.000 1.000
#> GSM182760 1 0.4562 0.873 0.904 0.096
#> GSM182761 2 0.0000 0.959 0.000 1.000
#> GSM182762 1 0.6623 0.792 0.828 0.172
#> GSM182763 2 0.0000 0.959 0.000 1.000
#> GSM182764 2 0.0000 0.959 0.000 1.000
#> GSM182765 1 0.9909 0.247 0.556 0.444
#> GSM182766 2 0.0000 0.959 0.000 1.000
#> GSM182767 1 0.8555 0.642 0.720 0.280
#> GSM182768 1 0.0376 0.941 0.996 0.004
#> GSM182769 1 0.0000 0.942 1.000 0.000
#> GSM182770 2 0.0000 0.959 0.000 1.000
#> GSM182771 2 0.9248 0.446 0.340 0.660
#> GSM182772 2 0.0000 0.959 0.000 1.000
#> GSM182773 1 0.0376 0.941 0.996 0.004
#> GSM182774 1 0.0000 0.942 1.000 0.000
#> GSM182775 1 0.0376 0.941 0.996 0.004
#> GSM182776 1 0.0376 0.941 0.996 0.004
#> GSM182777 1 0.0376 0.941 0.996 0.004
#> GSM182802 2 0.0000 0.959 0.000 1.000
#> GSM182803 1 0.0000 0.942 1.000 0.000
#> GSM182804 1 0.0000 0.942 1.000 0.000
#> GSM182805 2 0.0000 0.959 0.000 1.000
#> GSM182806 1 0.0000 0.942 1.000 0.000
#> GSM182807 1 0.0000 0.942 1.000 0.000
#> GSM182808 1 0.0000 0.942 1.000 0.000
#> GSM182809 1 0.0672 0.937 0.992 0.008
#> GSM182810 1 0.0000 0.942 1.000 0.000
#> GSM182811 1 0.0000 0.942 1.000 0.000
#> GSM182812 1 0.0000 0.942 1.000 0.000
#> GSM182813 1 0.0000 0.942 1.000 0.000
#> GSM182778 2 0.0000 0.959 0.000 1.000
#> GSM182779 2 0.0000 0.959 0.000 1.000
#> GSM182780 2 0.0000 0.959 0.000 1.000
#> GSM182781 1 0.4562 0.873 0.904 0.096
#> GSM182782 2 0.0000 0.959 0.000 1.000
#> GSM182783 2 0.0000 0.959 0.000 1.000
#> GSM182784 2 0.0000 0.959 0.000 1.000
#> GSM182785 2 0.0000 0.959 0.000 1.000
#> GSM182786 2 0.0000 0.959 0.000 1.000
#> GSM182787 2 0.0000 0.959 0.000 1.000
#> GSM182788 2 0.0000 0.959 0.000 1.000
#> GSM182789 2 0.0000 0.959 0.000 1.000
#> GSM182790 1 0.4562 0.873 0.904 0.096
#> GSM182791 1 0.2603 0.914 0.956 0.044
#> GSM182792 1 0.0376 0.941 0.996 0.004
#> GSM182793 2 0.0672 0.952 0.008 0.992
#> GSM182794 1 0.7376 0.746 0.792 0.208
#> GSM182795 2 0.0376 0.956 0.004 0.996
#> GSM182796 2 0.0000 0.959 0.000 1.000
#> GSM182797 1 0.0000 0.942 1.000 0.000
#> GSM182798 2 0.0000 0.959 0.000 1.000
#> GSM182799 1 0.9209 0.487 0.664 0.336
#> GSM182800 1 0.0000 0.942 1.000 0.000
#> GSM182801 1 0.0000 0.942 1.000 0.000
#> GSM182814 1 0.0000 0.942 1.000 0.000
#> GSM182815 2 0.9881 0.216 0.436 0.564
#> GSM182816 1 0.0000 0.942 1.000 0.000
#> GSM182817 2 0.8955 0.520 0.312 0.688
#> GSM182818 1 0.0000 0.942 1.000 0.000
#> GSM182819 1 0.0000 0.942 1.000 0.000
#> GSM182820 1 0.0000 0.942 1.000 0.000
#> GSM182821 2 0.0000 0.959 0.000 1.000
#> GSM182822 1 0.0000 0.942 1.000 0.000
#> GSM182823 1 0.0000 0.942 1.000 0.000
#> GSM182824 1 0.0000 0.942 1.000 0.000
#> GSM182825 1 0.0000 0.942 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM182755 1 0.4842 0.7920 0.776 0.000 0.224
#> GSM182756 3 0.2810 0.7995 0.036 0.036 0.928
#> GSM182757 3 0.3412 0.8023 0.000 0.124 0.876
#> GSM182758 3 0.1529 0.8035 0.000 0.040 0.960
#> GSM182759 3 0.6252 0.3199 0.000 0.444 0.556
#> GSM182760 3 0.1860 0.7564 0.052 0.000 0.948
#> GSM182761 3 0.3941 0.7882 0.000 0.156 0.844
#> GSM182762 1 0.5244 0.7702 0.756 0.004 0.240
#> GSM182763 3 0.3412 0.8037 0.000 0.124 0.876
#> GSM182764 3 0.5431 0.6495 0.000 0.284 0.716
#> GSM182765 3 0.1031 0.7986 0.000 0.024 0.976
#> GSM182766 2 0.5327 0.5715 0.000 0.728 0.272
#> GSM182767 3 0.1289 0.8016 0.000 0.032 0.968
#> GSM182768 1 0.5098 0.7907 0.752 0.000 0.248
#> GSM182769 1 0.3192 0.8808 0.888 0.000 0.112
#> GSM182770 2 0.0000 0.8354 0.000 1.000 0.000
#> GSM182771 3 0.4861 0.7001 0.008 0.192 0.800
#> GSM182772 2 0.0000 0.8354 0.000 1.000 0.000
#> GSM182773 3 0.1411 0.7815 0.036 0.000 0.964
#> GSM182774 1 0.3879 0.8516 0.848 0.000 0.152
#> GSM182775 1 0.3267 0.8788 0.884 0.000 0.116
#> GSM182776 1 0.2878 0.8872 0.904 0.000 0.096
#> GSM182777 1 0.4796 0.7959 0.780 0.000 0.220
#> GSM182802 2 0.6140 0.2180 0.000 0.596 0.404
#> GSM182803 1 0.0892 0.9004 0.980 0.000 0.020
#> GSM182804 3 0.6215 0.2400 0.428 0.000 0.572
#> GSM182805 2 0.6045 0.2945 0.000 0.620 0.380
#> GSM182806 1 0.0000 0.9002 1.000 0.000 0.000
#> GSM182807 1 0.0237 0.9007 0.996 0.000 0.004
#> GSM182808 1 0.0000 0.9002 1.000 0.000 0.000
#> GSM182809 3 0.4605 0.6316 0.204 0.000 0.796
#> GSM182810 1 0.0892 0.9004 0.980 0.000 0.020
#> GSM182811 1 0.1289 0.8982 0.968 0.000 0.032
#> GSM182812 1 0.0000 0.9002 1.000 0.000 0.000
#> GSM182813 1 0.0424 0.9008 0.992 0.000 0.008
#> GSM182778 2 0.0000 0.8354 0.000 1.000 0.000
#> GSM182779 3 0.5465 0.6444 0.000 0.288 0.712
#> GSM182780 3 0.3879 0.7906 0.000 0.152 0.848
#> GSM182781 3 0.6305 -0.1831 0.484 0.000 0.516
#> GSM182782 2 0.0000 0.8354 0.000 1.000 0.000
#> GSM182783 3 0.3412 0.8029 0.000 0.124 0.876
#> GSM182784 3 0.3267 0.8034 0.000 0.116 0.884
#> GSM182785 3 0.3551 0.7997 0.000 0.132 0.868
#> GSM182786 2 0.0000 0.8354 0.000 1.000 0.000
#> GSM182787 3 0.3941 0.7882 0.000 0.156 0.844
#> GSM182788 2 0.0000 0.8354 0.000 1.000 0.000
#> GSM182789 3 0.3941 0.7882 0.000 0.156 0.844
#> GSM182790 3 0.2261 0.7699 0.068 0.000 0.932
#> GSM182791 3 0.0000 0.7890 0.000 0.000 1.000
#> GSM182792 1 0.6168 0.5164 0.588 0.000 0.412
#> GSM182793 3 0.5760 0.3814 0.000 0.328 0.672
#> GSM182794 3 0.0237 0.7914 0.000 0.004 0.996
#> GSM182795 3 0.2261 0.8052 0.000 0.068 0.932
#> GSM182796 2 0.2796 0.7690 0.000 0.908 0.092
#> GSM182797 1 0.2711 0.8817 0.912 0.000 0.088
#> GSM182798 3 0.4887 0.6786 0.000 0.228 0.772
#> GSM182799 3 0.0592 0.7897 0.012 0.000 0.988
#> GSM182800 1 0.3267 0.8705 0.884 0.000 0.116
#> GSM182801 1 0.3192 0.8751 0.888 0.000 0.112
#> GSM182814 1 0.0000 0.9002 1.000 0.000 0.000
#> GSM182815 1 0.9820 -0.0151 0.428 0.276 0.296
#> GSM182816 1 0.0000 0.9002 1.000 0.000 0.000
#> GSM182817 3 0.5267 0.7369 0.140 0.044 0.816
#> GSM182818 1 0.0424 0.9006 0.992 0.000 0.008
#> GSM182819 1 0.0000 0.9002 1.000 0.000 0.000
#> GSM182820 1 0.1031 0.8992 0.976 0.000 0.024
#> GSM182821 3 0.4345 0.7952 0.016 0.136 0.848
#> GSM182822 1 0.1411 0.8982 0.964 0.000 0.036
#> GSM182823 1 0.0000 0.9002 1.000 0.000 0.000
#> GSM182824 1 0.0000 0.9002 1.000 0.000 0.000
#> GSM182825 1 0.2261 0.8853 0.932 0.000 0.068
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM182755 1 0.0927 0.4859 0.976 0.000 0.008 0.016
#> GSM182756 3 0.4245 0.6088 0.196 0.000 0.784 0.020
#> GSM182757 3 0.3400 0.7013 0.044 0.004 0.876 0.076
#> GSM182758 3 0.4215 0.6533 0.104 0.000 0.824 0.072
#> GSM182759 3 0.7093 0.4631 0.000 0.220 0.568 0.212
#> GSM182760 3 0.6458 0.3343 0.408 0.000 0.520 0.072
#> GSM182761 3 0.3249 0.6825 0.000 0.008 0.852 0.140
#> GSM182762 1 0.4860 0.2777 0.768 0.004 0.044 0.184
#> GSM182763 3 0.4538 0.6964 0.048 0.004 0.800 0.148
#> GSM182764 3 0.5857 0.6131 0.000 0.108 0.696 0.196
#> GSM182765 3 0.6343 0.6378 0.096 0.004 0.644 0.256
#> GSM182766 3 0.7613 0.0814 0.000 0.204 0.428 0.368
#> GSM182767 3 0.6396 0.3761 0.380 0.000 0.548 0.072
#> GSM182768 1 0.2742 0.4177 0.900 0.000 0.024 0.076
#> GSM182769 1 0.0592 0.4904 0.984 0.000 0.000 0.016
#> GSM182770 2 0.4123 0.8194 0.000 0.772 0.008 0.220
#> GSM182771 3 0.6204 0.6147 0.004 0.124 0.680 0.192
#> GSM182772 2 0.4123 0.8194 0.000 0.772 0.008 0.220
#> GSM182773 1 0.6080 -0.3319 0.488 0.000 0.468 0.044
#> GSM182774 1 0.5346 0.4029 0.692 0.004 0.032 0.272
#> GSM182775 1 0.1059 0.4812 0.972 0.000 0.016 0.012
#> GSM182776 1 0.0921 0.4923 0.972 0.000 0.000 0.028
#> GSM182777 1 0.1022 0.4745 0.968 0.000 0.032 0.000
#> GSM182802 3 0.7608 0.1178 0.000 0.200 0.408 0.392
#> GSM182803 1 0.4933 0.3787 0.568 0.000 0.000 0.432
#> GSM182804 4 0.6980 0.4337 0.128 0.004 0.300 0.568
#> GSM182805 3 0.7706 0.0932 0.000 0.224 0.412 0.364
#> GSM182806 1 0.4313 0.4659 0.736 0.004 0.000 0.260
#> GSM182807 1 0.4877 0.3920 0.592 0.000 0.000 0.408
#> GSM182808 1 0.4283 0.4676 0.740 0.004 0.000 0.256
#> GSM182809 4 0.6419 0.3214 0.068 0.000 0.420 0.512
#> GSM182810 1 0.5126 0.3614 0.552 0.004 0.000 0.444
#> GSM182811 1 0.4948 0.3560 0.560 0.000 0.000 0.440
#> GSM182812 1 0.5112 0.3663 0.560 0.004 0.000 0.436
#> GSM182813 1 0.4103 0.4655 0.744 0.000 0.000 0.256
#> GSM182778 2 0.0336 0.8961 0.000 0.992 0.008 0.000
#> GSM182779 3 0.5369 0.6447 0.000 0.112 0.744 0.144
#> GSM182780 3 0.2384 0.6978 0.008 0.004 0.916 0.072
#> GSM182781 1 0.4122 0.2184 0.760 0.000 0.236 0.004
#> GSM182782 2 0.0336 0.8961 0.000 0.992 0.008 0.000
#> GSM182783 3 0.1575 0.6998 0.028 0.004 0.956 0.012
#> GSM182784 3 0.2081 0.6875 0.084 0.000 0.916 0.000
#> GSM182785 3 0.4468 0.6935 0.052 0.004 0.808 0.136
#> GSM182786 2 0.0336 0.8961 0.000 0.992 0.008 0.000
#> GSM182787 3 0.2329 0.6947 0.000 0.012 0.916 0.072
#> GSM182788 2 0.0336 0.8961 0.000 0.992 0.008 0.000
#> GSM182789 3 0.2010 0.6985 0.004 0.004 0.932 0.060
#> GSM182790 1 0.4994 -0.2943 0.520 0.000 0.480 0.000
#> GSM182791 3 0.5223 0.6268 0.136 0.004 0.764 0.096
#> GSM182792 1 0.7012 -0.1450 0.496 0.004 0.396 0.104
#> GSM182793 3 0.6794 0.3919 0.012 0.064 0.480 0.444
#> GSM182794 3 0.5119 0.6242 0.148 0.004 0.768 0.080
#> GSM182795 3 0.3198 0.6790 0.040 0.000 0.880 0.080
#> GSM182796 2 0.5288 0.7219 0.000 0.732 0.068 0.200
#> GSM182797 1 0.0592 0.4901 0.984 0.000 0.000 0.016
#> GSM182798 3 0.7084 0.5562 0.000 0.176 0.560 0.264
#> GSM182799 3 0.5530 0.6125 0.152 0.004 0.740 0.104
#> GSM182800 1 0.5047 0.3364 0.636 0.004 0.004 0.356
#> GSM182801 1 0.1706 0.4759 0.948 0.000 0.016 0.036
#> GSM182814 1 0.5119 0.3651 0.556 0.004 0.000 0.440
#> GSM182815 4 0.3337 0.2741 0.032 0.060 0.020 0.888
#> GSM182816 1 0.5070 0.3837 0.580 0.004 0.000 0.416
#> GSM182817 3 0.5346 0.5596 0.076 0.000 0.732 0.192
#> GSM182818 1 0.4955 0.3634 0.556 0.000 0.000 0.444
#> GSM182819 1 0.4955 0.3647 0.556 0.000 0.000 0.444
#> GSM182820 1 0.2011 0.4909 0.920 0.000 0.000 0.080
#> GSM182821 3 0.1191 0.6978 0.004 0.004 0.968 0.024
#> GSM182822 1 0.5236 0.3546 0.560 0.000 0.008 0.432
#> GSM182823 1 0.5119 0.3651 0.556 0.004 0.000 0.440
#> GSM182824 1 0.5119 0.3651 0.556 0.004 0.000 0.440
#> GSM182825 4 0.5168 -0.4347 0.496 0.004 0.000 0.500
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM182755 3 0.1364 0.53139 0.036 0.000 0.952 0.012 0.000
#> GSM182756 4 0.4276 0.32256 0.000 0.000 0.380 0.616 0.004
#> GSM182757 5 0.5052 0.36950 0.000 0.000 0.048 0.340 0.612
#> GSM182758 4 0.4240 0.42805 0.000 0.000 0.228 0.736 0.036
#> GSM182759 5 0.3002 0.51275 0.000 0.028 0.000 0.116 0.856
#> GSM182760 3 0.4804 -0.08696 0.008 0.000 0.524 0.460 0.008
#> GSM182761 5 0.3835 0.44406 0.000 0.008 0.000 0.260 0.732
#> GSM182762 5 0.5347 0.16178 0.004 0.000 0.424 0.044 0.528
#> GSM182763 5 0.5071 0.41635 0.004 0.000 0.048 0.308 0.640
#> GSM182764 5 0.3318 0.49865 0.000 0.012 0.000 0.180 0.808
#> GSM182765 5 0.5422 0.34933 0.004 0.000 0.076 0.296 0.624
#> GSM182766 5 0.5511 0.41403 0.256 0.052 0.000 0.032 0.660
#> GSM182767 3 0.4452 -0.13808 0.000 0.000 0.500 0.496 0.004
#> GSM182768 3 0.1412 0.54778 0.008 0.000 0.952 0.036 0.004
#> GSM182769 3 0.1877 0.50666 0.064 0.000 0.924 0.012 0.000
#> GSM182770 2 0.4640 0.73187 0.256 0.696 0.000 0.000 0.048
#> GSM182771 4 0.5798 0.08704 0.004 0.056 0.008 0.484 0.448
#> GSM182772 2 0.4706 0.72924 0.256 0.692 0.000 0.000 0.052
#> GSM182773 3 0.4390 0.01368 0.000 0.000 0.568 0.428 0.004
#> GSM182774 3 0.6594 -0.47252 0.324 0.000 0.500 0.164 0.012
#> GSM182775 3 0.1267 0.54108 0.024 0.000 0.960 0.012 0.004
#> GSM182776 3 0.2580 0.49013 0.064 0.000 0.892 0.044 0.000
#> GSM182777 3 0.0566 0.54808 0.000 0.000 0.984 0.012 0.004
#> GSM182802 5 0.5954 0.37593 0.264 0.060 0.000 0.048 0.628
#> GSM182803 1 0.5166 0.76963 0.528 0.000 0.436 0.032 0.004
#> GSM182804 4 0.6435 0.11148 0.308 0.000 0.092 0.560 0.040
#> GSM182805 5 0.6496 0.37238 0.260 0.068 0.000 0.080 0.592
#> GSM182806 3 0.4375 -0.11293 0.420 0.000 0.576 0.000 0.004
#> GSM182807 1 0.4331 0.74625 0.596 0.000 0.400 0.000 0.004
#> GSM182808 3 0.4321 -0.05138 0.396 0.000 0.600 0.000 0.004
#> GSM182809 4 0.4743 0.12394 0.472 0.000 0.016 0.512 0.000
#> GSM182810 1 0.4192 0.82165 0.596 0.000 0.404 0.000 0.000
#> GSM182811 1 0.4966 0.80799 0.564 0.000 0.404 0.032 0.000
#> GSM182812 1 0.4045 0.82411 0.644 0.000 0.356 0.000 0.000
#> GSM182813 3 0.4437 -0.32532 0.464 0.000 0.532 0.000 0.004
#> GSM182778 2 0.0000 0.87663 0.000 1.000 0.000 0.000 0.000
#> GSM182779 5 0.4806 0.12763 0.000 0.016 0.012 0.336 0.636
#> GSM182780 4 0.4310 0.29099 0.000 0.000 0.004 0.604 0.392
#> GSM182781 3 0.3909 0.45642 0.000 0.000 0.760 0.216 0.024
#> GSM182782 2 0.0000 0.87663 0.000 1.000 0.000 0.000 0.000
#> GSM182783 4 0.3928 0.38760 0.000 0.000 0.004 0.700 0.296
#> GSM182784 4 0.4930 0.40507 0.000 0.000 0.084 0.696 0.220
#> GSM182785 5 0.4780 0.42976 0.000 0.000 0.048 0.280 0.672
#> GSM182786 2 0.0000 0.87663 0.000 1.000 0.000 0.000 0.000
#> GSM182787 4 0.4403 0.20949 0.004 0.000 0.000 0.560 0.436
#> GSM182788 2 0.0000 0.87663 0.000 1.000 0.000 0.000 0.000
#> GSM182789 4 0.4211 0.32939 0.000 0.000 0.004 0.636 0.360
#> GSM182790 3 0.4397 -0.00166 0.000 0.000 0.564 0.432 0.004
#> GSM182791 4 0.0693 0.45276 0.008 0.000 0.012 0.980 0.000
#> GSM182792 4 0.4726 -0.01623 0.020 0.000 0.400 0.580 0.000
#> GSM182793 4 0.6778 -0.13903 0.264 0.000 0.004 0.448 0.284
#> GSM182794 4 0.3768 0.43104 0.008 0.000 0.228 0.760 0.004
#> GSM182795 4 0.1908 0.45504 0.000 0.000 0.000 0.908 0.092
#> GSM182796 5 0.4415 -0.10042 0.004 0.444 0.000 0.000 0.552
#> GSM182797 3 0.2471 0.49676 0.136 0.000 0.864 0.000 0.000
#> GSM182798 5 0.6065 0.29098 0.012 0.092 0.000 0.364 0.532
#> GSM182799 4 0.1095 0.44763 0.008 0.000 0.012 0.968 0.012
#> GSM182800 3 0.6741 -0.19561 0.176 0.000 0.492 0.316 0.016
#> GSM182801 3 0.0833 0.54937 0.004 0.000 0.976 0.016 0.004
#> GSM182814 1 0.3983 0.82221 0.660 0.000 0.340 0.000 0.000
#> GSM182815 1 0.4449 0.25576 0.776 0.000 0.008 0.104 0.112
#> GSM182816 1 0.4425 0.78435 0.544 0.000 0.452 0.000 0.004
#> GSM182817 4 0.6677 0.21121 0.152 0.000 0.016 0.472 0.360
#> GSM182818 1 0.4299 0.82049 0.608 0.000 0.388 0.004 0.000
#> GSM182819 1 0.4973 0.81897 0.592 0.000 0.376 0.028 0.004
#> GSM182820 3 0.2719 0.48658 0.144 0.000 0.852 0.000 0.004
#> GSM182821 4 0.3816 0.38007 0.000 0.000 0.000 0.696 0.304
#> GSM182822 1 0.4510 0.80284 0.560 0.000 0.432 0.008 0.000
#> GSM182823 1 0.3790 0.78063 0.724 0.000 0.272 0.000 0.004
#> GSM182824 1 0.3636 0.78215 0.728 0.000 0.272 0.000 0.000
#> GSM182825 1 0.5921 0.74639 0.560 0.000 0.344 0.084 0.012
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM182755 3 0.4435 0.3265 0.392 0.000 0.580 0.000 0.004 0.024
#> GSM182756 3 0.3763 0.3236 0.000 0.000 0.812 0.100 0.044 0.044
#> GSM182757 5 0.3738 0.3618 0.000 0.000 0.208 0.040 0.752 0.000
#> GSM182758 3 0.5374 0.1620 0.000 0.000 0.672 0.132 0.148 0.048
#> GSM182759 5 0.1349 0.3350 0.000 0.000 0.004 0.056 0.940 0.000
#> GSM182760 3 0.1872 0.4138 0.004 0.000 0.920 0.008 0.064 0.004
#> GSM182761 5 0.0748 0.3741 0.000 0.000 0.016 0.004 0.976 0.004
#> GSM182762 5 0.6158 0.0716 0.024 0.000 0.356 0.156 0.464 0.000
#> GSM182763 5 0.3488 0.3661 0.000 0.000 0.184 0.036 0.780 0.000
#> GSM182764 5 0.0777 0.3588 0.000 0.000 0.004 0.024 0.972 0.000
#> GSM182765 5 0.5561 -0.0428 0.000 0.000 0.136 0.428 0.436 0.000
#> GSM182766 5 0.4619 -0.0497 0.000 0.024 0.012 0.388 0.576 0.000
#> GSM182767 3 0.1226 0.4136 0.000 0.000 0.952 0.004 0.040 0.004
#> GSM182768 3 0.4266 0.3628 0.348 0.000 0.628 0.008 0.000 0.016
#> GSM182769 3 0.4184 0.3119 0.408 0.000 0.576 0.000 0.000 0.016
#> GSM182770 2 0.3810 0.5615 0.000 0.572 0.000 0.428 0.000 0.000
#> GSM182771 4 0.6594 0.1504 0.008 0.028 0.308 0.456 0.200 0.000
#> GSM182772 2 0.3833 0.5454 0.000 0.556 0.000 0.444 0.000 0.000
#> GSM182773 3 0.0405 0.4306 0.008 0.000 0.988 0.000 0.004 0.000
#> GSM182774 1 0.5431 0.3413 0.672 0.000 0.164 0.116 0.004 0.044
#> GSM182775 3 0.4141 0.3357 0.388 0.000 0.596 0.000 0.000 0.016
#> GSM182776 3 0.4199 0.3066 0.416 0.000 0.568 0.000 0.000 0.016
#> GSM182777 3 0.4052 0.3618 0.356 0.000 0.628 0.000 0.000 0.016
#> GSM182802 4 0.4485 0.2295 0.020 0.032 0.000 0.680 0.268 0.000
#> GSM182803 1 0.3810 -0.1811 0.572 0.000 0.000 0.000 0.000 0.428
#> GSM182804 1 0.7486 -0.1260 0.324 0.000 0.232 0.304 0.000 0.140
#> GSM182805 4 0.4964 0.0401 0.012 0.040 0.000 0.484 0.464 0.000
#> GSM182806 6 0.3053 0.7000 0.168 0.000 0.020 0.000 0.000 0.812
#> GSM182807 6 0.4018 0.6711 0.324 0.000 0.020 0.000 0.000 0.656
#> GSM182808 6 0.3688 0.7169 0.256 0.000 0.020 0.000 0.000 0.724
#> GSM182809 1 0.5587 0.0666 0.508 0.000 0.356 0.132 0.004 0.000
#> GSM182810 1 0.0260 0.5070 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM182811 1 0.0000 0.5075 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM182812 1 0.2219 0.4751 0.864 0.000 0.000 0.000 0.000 0.136
#> GSM182813 6 0.3657 0.6950 0.100 0.000 0.108 0.000 0.000 0.792
#> GSM182778 2 0.0000 0.8199 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM182779 5 0.5058 0.2458 0.000 0.000 0.292 0.108 0.600 0.000
#> GSM182780 5 0.5633 0.2673 0.000 0.000 0.340 0.060 0.552 0.048
#> GSM182781 3 0.4756 0.4402 0.204 0.000 0.712 0.016 0.052 0.016
#> GSM182782 2 0.0000 0.8199 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM182783 5 0.6210 0.2168 0.000 0.000 0.396 0.108 0.448 0.048
#> GSM182784 3 0.5958 -0.1364 0.000 0.000 0.548 0.100 0.304 0.048
#> GSM182785 5 0.2848 0.3780 0.000 0.000 0.176 0.000 0.816 0.008
#> GSM182786 2 0.0000 0.8199 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM182787 5 0.4493 0.2946 0.000 0.000 0.312 0.036 0.644 0.008
#> GSM182788 2 0.0000 0.8199 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM182789 5 0.5819 0.2639 0.000 0.000 0.340 0.076 0.536 0.048
#> GSM182790 3 0.0405 0.4295 0.008 0.000 0.988 0.000 0.004 0.000
#> GSM182791 3 0.7119 -0.0734 0.012 0.000 0.416 0.340 0.084 0.148
#> GSM182792 4 0.7824 -0.1892 0.228 0.000 0.320 0.320 0.028 0.104
#> GSM182793 4 0.4387 0.2741 0.000 0.000 0.008 0.736 0.104 0.152
#> GSM182794 3 0.5795 0.1153 0.000 0.000 0.588 0.268 0.052 0.092
#> GSM182795 3 0.6861 -0.0733 0.000 0.000 0.424 0.320 0.184 0.072
#> GSM182796 5 0.5799 -0.1461 0.000 0.392 0.000 0.180 0.428 0.000
#> GSM182797 3 0.5558 -0.2023 0.136 0.000 0.448 0.000 0.000 0.416
#> GSM182798 4 0.4649 0.1126 0.000 0.028 0.004 0.604 0.356 0.008
#> GSM182799 3 0.7054 -0.0999 0.012 0.000 0.428 0.324 0.068 0.168
#> GSM182800 1 0.7289 0.1976 0.432 0.000 0.136 0.260 0.004 0.168
#> GSM182801 3 0.4131 0.3577 0.356 0.000 0.624 0.000 0.000 0.020
#> GSM182814 1 0.2597 0.4471 0.824 0.000 0.000 0.000 0.000 0.176
#> GSM182815 1 0.3907 0.2147 0.588 0.000 0.000 0.408 0.004 0.000
#> GSM182816 1 0.3565 0.1687 0.692 0.000 0.004 0.000 0.000 0.304
#> GSM182817 4 0.7394 0.1676 0.168 0.000 0.320 0.384 0.120 0.008
#> GSM182818 1 0.2213 0.5038 0.904 0.000 0.020 0.004 0.004 0.068
#> GSM182819 1 0.3854 -0.2438 0.536 0.000 0.000 0.000 0.000 0.464
#> GSM182820 6 0.4877 0.5392 0.148 0.000 0.192 0.000 0.000 0.660
#> GSM182821 5 0.6263 0.2178 0.000 0.000 0.368 0.112 0.468 0.052
#> GSM182822 1 0.0909 0.5074 0.968 0.000 0.020 0.012 0.000 0.000
#> GSM182823 6 0.3737 0.3849 0.392 0.000 0.000 0.000 0.000 0.608
#> GSM182824 1 0.3847 -0.1667 0.544 0.000 0.000 0.000 0.000 0.456
#> GSM182825 1 0.3924 0.4636 0.740 0.000 0.000 0.052 0.000 0.208
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 stress(p) development.stage(p) k
#> SD:pam 66 0.301 5.99e-03 2
#> SD:pam 64 0.582 8.09e-05 3
#> SD:pam 29 1.000 1.00e+00 4
#> SD:pam 26 0.170 9.54e-06 5
#> SD:pam 15 0.300 5.53e-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 18172 rows and 71 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.427 0.792 0.888 0.4044 0.590 0.590
#> 3 3 0.502 0.794 0.855 0.5704 0.642 0.438
#> 4 4 0.557 0.505 0.776 0.1086 0.885 0.699
#> 5 5 0.539 0.580 0.760 0.0691 0.855 0.583
#> 6 6 0.609 0.632 0.777 0.0556 0.861 0.501
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
#> GSM182755 2 0.7299 0.76989 0.204 0.796
#> GSM182756 1 0.8909 0.50116 0.692 0.308
#> GSM182757 2 0.8144 0.73629 0.252 0.748
#> GSM182758 1 0.0376 0.82400 0.996 0.004
#> GSM182759 2 0.7528 0.77178 0.216 0.784
#> GSM182760 1 0.0376 0.82400 0.996 0.004
#> GSM182761 2 0.8016 0.74664 0.244 0.756
#> GSM182762 2 0.7950 0.75162 0.240 0.760
#> GSM182763 2 0.7528 0.77178 0.216 0.784
#> GSM182764 2 0.7883 0.75646 0.236 0.764
#> GSM182765 2 0.7528 0.77178 0.216 0.784
#> GSM182766 2 0.2236 0.86874 0.036 0.964
#> GSM182767 1 0.0376 0.82400 0.996 0.004
#> GSM182768 1 0.7139 0.79117 0.804 0.196
#> GSM182769 1 0.6712 0.80942 0.824 0.176
#> GSM182770 2 0.2043 0.86967 0.032 0.968
#> GSM182771 2 0.0000 0.87085 0.000 1.000
#> GSM182772 2 0.2043 0.86967 0.032 0.968
#> GSM182773 1 0.3114 0.83172 0.944 0.056
#> GSM182774 2 0.2423 0.86995 0.040 0.960
#> GSM182775 1 0.6438 0.81633 0.836 0.164
#> GSM182776 2 0.7674 0.76494 0.224 0.776
#> GSM182777 1 0.0938 0.82609 0.988 0.012
#> GSM182802 2 0.0000 0.87085 0.000 1.000
#> GSM182803 2 0.0000 0.87085 0.000 1.000
#> GSM182804 2 0.0376 0.87034 0.004 0.996
#> GSM182805 2 0.0000 0.87085 0.000 1.000
#> GSM182806 2 0.1843 0.86917 0.028 0.972
#> GSM182807 2 0.6887 0.78379 0.184 0.816
#> GSM182808 2 0.4431 0.84213 0.092 0.908
#> GSM182809 2 0.2236 0.86874 0.036 0.964
#> GSM182810 2 0.0000 0.87085 0.000 1.000
#> GSM182811 2 0.0000 0.87085 0.000 1.000
#> GSM182812 2 0.0000 0.87085 0.000 1.000
#> GSM182813 2 0.6887 0.78379 0.184 0.816
#> GSM182778 2 0.2236 0.86957 0.036 0.964
#> GSM182779 2 0.7528 0.77178 0.216 0.784
#> GSM182780 1 0.9732 0.52937 0.596 0.404
#> GSM182781 1 0.8813 0.50997 0.700 0.300
#> GSM182782 2 0.2236 0.86957 0.036 0.964
#> GSM182783 1 0.6887 0.80313 0.816 0.184
#> GSM182784 1 0.0376 0.82400 0.996 0.004
#> GSM182785 2 0.9170 0.61389 0.332 0.668
#> GSM182786 2 0.2236 0.86957 0.036 0.964
#> GSM182787 2 0.7528 0.77178 0.216 0.784
#> GSM182788 2 0.2236 0.86957 0.036 0.964
#> GSM182789 1 0.4022 0.83200 0.920 0.080
#> GSM182790 1 0.0376 0.82400 0.996 0.004
#> GSM182791 1 0.9732 0.52937 0.596 0.404
#> GSM182792 1 0.6623 0.81241 0.828 0.172
#> GSM182793 2 0.2236 0.86874 0.036 0.964
#> GSM182794 1 0.0376 0.82400 0.996 0.004
#> GSM182795 1 0.6438 0.81633 0.836 0.164
#> GSM182796 2 0.1843 0.87063 0.028 0.972
#> GSM182797 2 0.7528 0.76697 0.216 0.784
#> GSM182798 2 0.1414 0.87136 0.020 0.980
#> GSM182799 2 0.8813 0.42696 0.300 0.700
#> GSM182800 2 0.9795 -0.00308 0.416 0.584
#> GSM182801 1 0.7528 0.76772 0.784 0.216
#> GSM182814 2 0.0000 0.87085 0.000 1.000
#> GSM182815 2 0.0376 0.87034 0.004 0.996
#> GSM182816 2 0.0000 0.87085 0.000 1.000
#> GSM182817 2 0.0000 0.87085 0.000 1.000
#> GSM182818 2 0.0376 0.87034 0.004 0.996
#> GSM182819 2 0.0000 0.87085 0.000 1.000
#> GSM182820 2 0.6887 0.78379 0.184 0.816
#> GSM182821 2 0.7528 0.77178 0.216 0.784
#> GSM182822 2 0.0000 0.87085 0.000 1.000
#> GSM182823 2 0.0000 0.87085 0.000 1.000
#> GSM182824 2 0.0000 0.87085 0.000 1.000
#> GSM182825 2 0.0376 0.87034 0.004 0.996
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM182755 1 0.8122 0.471 0.648 0.184 0.168
#> GSM182756 3 0.1170 0.905 0.016 0.008 0.976
#> GSM182757 2 0.7640 0.619 0.056 0.592 0.352
#> GSM182758 3 0.0000 0.902 0.000 0.000 1.000
#> GSM182759 2 0.5932 0.806 0.056 0.780 0.164
#> GSM182760 3 0.0000 0.902 0.000 0.000 1.000
#> GSM182761 2 0.6098 0.803 0.056 0.768 0.176
#> GSM182762 2 0.8608 0.698 0.192 0.604 0.204
#> GSM182763 2 0.7308 0.707 0.056 0.648 0.296
#> GSM182764 2 0.5988 0.805 0.056 0.776 0.168
#> GSM182765 2 0.7537 0.653 0.056 0.612 0.332
#> GSM182766 2 0.6586 0.774 0.056 0.728 0.216
#> GSM182767 3 0.0000 0.902 0.000 0.000 1.000
#> GSM182768 3 0.2356 0.906 0.072 0.000 0.928
#> GSM182769 3 0.2537 0.903 0.080 0.000 0.920
#> GSM182770 2 0.4654 0.762 0.208 0.792 0.000
#> GSM182771 2 0.6669 0.297 0.468 0.524 0.008
#> GSM182772 2 0.4654 0.762 0.208 0.792 0.000
#> GSM182773 3 0.1753 0.912 0.048 0.000 0.952
#> GSM182774 1 0.6262 0.619 0.696 0.020 0.284
#> GSM182775 3 0.2537 0.903 0.080 0.000 0.920
#> GSM182776 3 0.3695 0.873 0.108 0.012 0.880
#> GSM182777 3 0.2261 0.908 0.068 0.000 0.932
#> GSM182802 1 0.4842 0.642 0.776 0.224 0.000
#> GSM182803 1 0.0000 0.852 1.000 0.000 0.000
#> GSM182804 1 0.7785 0.669 0.672 0.192 0.136
#> GSM182805 1 0.4842 0.642 0.776 0.224 0.000
#> GSM182806 1 0.0747 0.850 0.984 0.000 0.016
#> GSM182807 1 0.2537 0.817 0.920 0.000 0.080
#> GSM182808 1 0.1031 0.848 0.976 0.000 0.024
#> GSM182809 1 0.7163 0.533 0.628 0.040 0.332
#> GSM182810 1 0.0000 0.852 1.000 0.000 0.000
#> GSM182811 1 0.0424 0.851 0.992 0.008 0.000
#> GSM182812 1 0.0424 0.851 0.992 0.008 0.000
#> GSM182813 1 0.3412 0.775 0.876 0.000 0.124
#> GSM182778 2 0.3879 0.753 0.152 0.848 0.000
#> GSM182779 2 0.6148 0.807 0.076 0.776 0.148
#> GSM182780 3 0.1877 0.911 0.032 0.012 0.956
#> GSM182781 3 0.1267 0.903 0.024 0.004 0.972
#> GSM182782 2 0.4345 0.766 0.136 0.848 0.016
#> GSM182783 3 0.1289 0.911 0.032 0.000 0.968
#> GSM182784 3 0.0000 0.902 0.000 0.000 1.000
#> GSM182785 3 0.2773 0.887 0.048 0.024 0.928
#> GSM182786 2 0.4047 0.757 0.148 0.848 0.004
#> GSM182787 2 0.5988 0.805 0.056 0.776 0.168
#> GSM182788 2 0.4261 0.764 0.140 0.848 0.012
#> GSM182789 3 0.1031 0.911 0.024 0.000 0.976
#> GSM182790 3 0.0000 0.902 0.000 0.000 1.000
#> GSM182791 3 0.6239 0.792 0.072 0.160 0.768
#> GSM182792 3 0.2356 0.906 0.072 0.000 0.928
#> GSM182793 3 0.6836 0.729 0.056 0.240 0.704
#> GSM182794 3 0.0000 0.902 0.000 0.000 1.000
#> GSM182795 3 0.1289 0.911 0.032 0.000 0.968
#> GSM182796 2 0.4654 0.762 0.208 0.792 0.000
#> GSM182797 3 0.6018 0.620 0.308 0.008 0.684
#> GSM182798 2 0.4452 0.634 0.192 0.808 0.000
#> GSM182799 3 0.6935 0.771 0.096 0.176 0.728
#> GSM182800 3 0.6567 0.785 0.088 0.160 0.752
#> GSM182801 3 0.2537 0.903 0.080 0.000 0.920
#> GSM182814 1 0.0000 0.852 1.000 0.000 0.000
#> GSM182815 1 0.5094 0.761 0.824 0.040 0.136
#> GSM182816 1 0.0000 0.852 1.000 0.000 0.000
#> GSM182817 1 0.2280 0.827 0.940 0.052 0.008
#> GSM182818 1 0.4810 0.767 0.832 0.028 0.140
#> GSM182819 1 0.0000 0.852 1.000 0.000 0.000
#> GSM182820 1 0.2537 0.817 0.920 0.000 0.080
#> GSM182821 2 0.7980 0.763 0.168 0.660 0.172
#> GSM182822 1 0.0000 0.852 1.000 0.000 0.000
#> GSM182823 1 0.0000 0.852 1.000 0.000 0.000
#> GSM182824 1 0.0237 0.851 0.996 0.004 0.000
#> GSM182825 1 0.7595 0.679 0.688 0.176 0.136
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM182755 1 0.6729 0.5235 0.680 0.164 0.036 0.120
#> GSM182756 3 0.0524 0.6912 0.000 0.004 0.988 0.008
#> GSM182757 2 0.6965 0.1002 0.000 0.460 0.428 0.112
#> GSM182758 3 0.0592 0.6924 0.000 0.016 0.984 0.000
#> GSM182759 2 0.4953 0.5750 0.000 0.776 0.120 0.104
#> GSM182760 3 0.0000 0.6912 0.000 0.000 1.000 0.000
#> GSM182761 2 0.6499 0.4017 0.000 0.612 0.276 0.112
#> GSM182762 2 0.9190 0.2241 0.308 0.416 0.132 0.144
#> GSM182763 3 0.6881 -0.1415 0.000 0.428 0.468 0.104
#> GSM182764 2 0.5628 0.5687 0.000 0.724 0.132 0.144
#> GSM182765 3 0.7149 -0.1672 0.000 0.416 0.452 0.132
#> GSM182766 2 0.6118 0.4034 0.000 0.672 0.208 0.120
#> GSM182767 3 0.0000 0.6912 0.000 0.000 1.000 0.000
#> GSM182768 3 0.2847 0.6644 0.016 0.004 0.896 0.084
#> GSM182769 3 0.4477 0.5567 0.108 0.000 0.808 0.084
#> GSM182770 2 0.0817 0.6132 0.000 0.976 0.000 0.024
#> GSM182771 2 0.4755 0.5506 0.000 0.760 0.040 0.200
#> GSM182772 2 0.1716 0.6073 0.000 0.936 0.000 0.064
#> GSM182773 3 0.2053 0.6773 0.000 0.004 0.924 0.072
#> GSM182774 1 0.7980 0.0107 0.480 0.108 0.364 0.048
#> GSM182775 3 0.4288 0.5917 0.084 0.004 0.828 0.084
#> GSM182776 3 0.6420 0.3871 0.140 0.104 0.712 0.044
#> GSM182777 3 0.0895 0.6917 0.000 0.020 0.976 0.004
#> GSM182802 2 0.5432 0.3913 0.032 0.652 0.000 0.316
#> GSM182803 1 0.0188 0.8107 0.996 0.000 0.000 0.004
#> GSM182804 1 0.8090 0.0666 0.408 0.168 0.024 0.400
#> GSM182805 2 0.5432 0.3913 0.032 0.652 0.000 0.316
#> GSM182806 1 0.0188 0.8107 0.996 0.000 0.000 0.004
#> GSM182807 1 0.0188 0.8107 0.996 0.000 0.000 0.004
#> GSM182808 1 0.0376 0.8086 0.992 0.000 0.004 0.004
#> GSM182809 3 0.8830 -0.2391 0.376 0.176 0.380 0.068
#> GSM182810 1 0.0188 0.8095 0.996 0.000 0.000 0.004
#> GSM182811 1 0.2334 0.7602 0.908 0.088 0.000 0.004
#> GSM182812 1 0.1867 0.7703 0.928 0.072 0.000 0.000
#> GSM182813 1 0.0000 0.8103 1.000 0.000 0.000 0.000
#> GSM182778 2 0.2589 0.6122 0.000 0.884 0.000 0.116
#> GSM182779 2 0.5527 0.5448 0.000 0.728 0.168 0.104
#> GSM182780 3 0.2081 0.6462 0.000 0.084 0.916 0.000
#> GSM182781 3 0.0804 0.6920 0.000 0.012 0.980 0.008
#> GSM182782 2 0.2589 0.6122 0.000 0.884 0.000 0.116
#> GSM182783 3 0.2081 0.6462 0.000 0.084 0.916 0.000
#> GSM182784 3 0.0000 0.6912 0.000 0.000 1.000 0.000
#> GSM182785 3 0.4662 0.4807 0.000 0.092 0.796 0.112
#> GSM182786 2 0.2589 0.6122 0.000 0.884 0.000 0.116
#> GSM182787 2 0.5119 0.5717 0.000 0.764 0.124 0.112
#> GSM182788 2 0.2589 0.6122 0.000 0.884 0.000 0.116
#> GSM182789 3 0.1716 0.6670 0.000 0.064 0.936 0.000
#> GSM182790 3 0.0000 0.6912 0.000 0.000 1.000 0.000
#> GSM182791 3 0.5574 0.1329 0.000 0.048 0.668 0.284
#> GSM182792 3 0.2452 0.6705 0.004 0.004 0.908 0.084
#> GSM182793 4 0.7598 0.0000 0.000 0.216 0.324 0.460
#> GSM182794 3 0.0000 0.6912 0.000 0.000 1.000 0.000
#> GSM182795 3 0.1637 0.6697 0.000 0.060 0.940 0.000
#> GSM182796 2 0.3610 0.5359 0.000 0.800 0.000 0.200
#> GSM182797 1 0.6556 0.1604 0.592 0.052 0.336 0.020
#> GSM182798 2 0.5594 0.2088 0.000 0.520 0.020 0.460
#> GSM182799 3 0.7332 -0.6284 0.000 0.164 0.480 0.356
#> GSM182800 3 0.7024 -0.3449 0.104 0.004 0.488 0.404
#> GSM182801 3 0.4801 0.5566 0.108 0.008 0.800 0.084
#> GSM182814 1 0.0188 0.8107 0.996 0.000 0.000 0.004
#> GSM182815 1 0.7279 0.4952 0.612 0.168 0.024 0.196
#> GSM182816 1 0.0000 0.8103 1.000 0.000 0.000 0.000
#> GSM182817 1 0.8675 0.0609 0.392 0.292 0.036 0.280
#> GSM182818 1 0.5500 0.6714 0.768 0.112 0.024 0.096
#> GSM182819 1 0.0188 0.8107 0.996 0.000 0.000 0.004
#> GSM182820 1 0.0188 0.8107 0.996 0.000 0.000 0.004
#> GSM182821 2 0.9411 0.1869 0.204 0.420 0.236 0.140
#> GSM182822 1 0.1733 0.7929 0.948 0.024 0.000 0.028
#> GSM182823 1 0.0188 0.8107 0.996 0.000 0.000 0.004
#> GSM182824 1 0.0188 0.8095 0.996 0.000 0.000 0.004
#> GSM182825 1 0.6429 0.4202 0.588 0.088 0.000 0.324
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM182755 1 0.5078 0.6285 0.744 0.000 0.040 0.072 0.144
#> GSM182756 3 0.4847 0.6573 0.000 0.080 0.720 0.004 0.196
#> GSM182757 5 0.3196 0.5940 0.004 0.000 0.192 0.000 0.804
#> GSM182758 3 0.4433 0.7153 0.000 0.080 0.784 0.016 0.120
#> GSM182759 5 0.1822 0.6002 0.004 0.000 0.024 0.036 0.936
#> GSM182760 3 0.3520 0.7170 0.000 0.080 0.840 0.004 0.076
#> GSM182761 5 0.1041 0.6063 0.004 0.000 0.032 0.000 0.964
#> GSM182762 5 0.5070 0.5568 0.036 0.000 0.052 0.184 0.728
#> GSM182763 5 0.5293 0.5639 0.004 0.000 0.236 0.092 0.668
#> GSM182764 5 0.2520 0.5802 0.004 0.000 0.012 0.096 0.888
#> GSM182765 5 0.5482 0.5547 0.004 0.000 0.268 0.092 0.636
#> GSM182766 5 0.7734 0.4409 0.004 0.108 0.204 0.184 0.500
#> GSM182767 3 0.3520 0.7170 0.000 0.080 0.840 0.004 0.076
#> GSM182768 3 0.4256 0.6991 0.076 0.012 0.812 0.088 0.012
#> GSM182769 3 0.4210 0.6866 0.132 0.012 0.804 0.040 0.012
#> GSM182770 2 0.5589 0.3201 0.000 0.548 0.000 0.372 0.080
#> GSM182771 5 0.6542 0.1980 0.004 0.200 0.000 0.300 0.496
#> GSM182772 2 0.5726 0.3196 0.004 0.548 0.000 0.368 0.080
#> GSM182773 3 0.2626 0.7264 0.040 0.012 0.908 0.028 0.012
#> GSM182774 1 0.6501 -0.1765 0.444 0.000 0.440 0.076 0.040
#> GSM182775 3 0.4210 0.6866 0.132 0.012 0.804 0.040 0.012
#> GSM182776 3 0.6980 0.4153 0.280 0.000 0.536 0.068 0.116
#> GSM182777 3 0.5611 0.7313 0.080 0.080 0.744 0.024 0.072
#> GSM182802 4 0.6217 0.1211 0.008 0.296 0.000 0.556 0.140
#> GSM182803 1 0.0290 0.8845 0.992 0.000 0.000 0.000 0.008
#> GSM182804 4 0.1668 0.4533 0.028 0.000 0.000 0.940 0.032
#> GSM182805 4 0.6712 0.1911 0.008 0.216 0.000 0.484 0.292
#> GSM182806 1 0.0000 0.8864 1.000 0.000 0.000 0.000 0.000
#> GSM182807 1 0.0000 0.8864 1.000 0.000 0.000 0.000 0.000
#> GSM182808 1 0.0000 0.8864 1.000 0.000 0.000 0.000 0.000
#> GSM182809 3 0.6643 0.1186 0.084 0.000 0.444 0.428 0.044
#> GSM182810 1 0.0290 0.8845 0.992 0.000 0.000 0.000 0.008
#> GSM182811 1 0.2723 0.7585 0.864 0.000 0.000 0.124 0.012
#> GSM182812 1 0.2074 0.8179 0.896 0.000 0.000 0.104 0.000
#> GSM182813 1 0.0162 0.8861 0.996 0.000 0.000 0.000 0.004
#> GSM182778 2 0.2488 0.7742 0.000 0.872 0.000 0.004 0.124
#> GSM182779 5 0.1041 0.6063 0.004 0.000 0.032 0.000 0.964
#> GSM182780 3 0.5740 0.4437 0.000 0.000 0.612 0.144 0.244
#> GSM182781 3 0.3367 0.6973 0.004 0.008 0.828 0.008 0.152
#> GSM182782 2 0.2488 0.7742 0.000 0.872 0.000 0.004 0.124
#> GSM182783 3 0.4764 0.6657 0.000 0.000 0.732 0.140 0.128
#> GSM182784 3 0.4847 0.6472 0.000 0.080 0.720 0.004 0.196
#> GSM182785 5 0.4299 0.4563 0.004 0.000 0.316 0.008 0.672
#> GSM182786 2 0.2488 0.7742 0.000 0.872 0.000 0.004 0.124
#> GSM182787 5 0.3433 0.5984 0.004 0.000 0.032 0.132 0.832
#> GSM182788 2 0.2488 0.7742 0.000 0.872 0.000 0.004 0.124
#> GSM182789 3 0.4270 0.4808 0.000 0.000 0.668 0.012 0.320
#> GSM182790 3 0.3520 0.7170 0.000 0.080 0.840 0.004 0.076
#> GSM182791 3 0.5468 0.4483 0.028 0.012 0.600 0.348 0.012
#> GSM182792 3 0.3778 0.7135 0.068 0.012 0.844 0.064 0.012
#> GSM182793 4 0.1808 0.4393 0.000 0.020 0.004 0.936 0.040
#> GSM182794 3 0.3520 0.7170 0.000 0.080 0.840 0.004 0.076
#> GSM182795 3 0.2964 0.7208 0.000 0.000 0.856 0.024 0.120
#> GSM182796 5 0.6530 0.1948 0.004 0.200 0.000 0.296 0.500
#> GSM182797 1 0.4366 0.7140 0.804 0.000 0.044 0.064 0.088
#> GSM182798 4 0.5051 -0.2398 0.004 0.024 0.000 0.492 0.480
#> GSM182799 4 0.5224 0.1540 0.004 0.016 0.300 0.648 0.032
#> GSM182800 3 0.6572 0.4554 0.124 0.020 0.580 0.264 0.012
#> GSM182801 3 0.4429 0.6608 0.168 0.012 0.776 0.032 0.012
#> GSM182814 1 0.0290 0.8861 0.992 0.000 0.000 0.008 0.000
#> GSM182815 4 0.4537 0.4142 0.204 0.016 0.000 0.744 0.036
#> GSM182816 1 0.0290 0.8861 0.992 0.000 0.000 0.008 0.000
#> GSM182817 5 0.7397 -0.0263 0.316 0.028 0.000 0.288 0.368
#> GSM182818 4 0.4961 -0.0218 0.448 0.000 0.000 0.524 0.028
#> GSM182819 1 0.0000 0.8864 1.000 0.000 0.000 0.000 0.000
#> GSM182820 1 0.0162 0.8861 0.996 0.000 0.000 0.000 0.004
#> GSM182821 5 0.7226 0.4107 0.100 0.000 0.148 0.200 0.552
#> GSM182822 1 0.1117 0.8698 0.964 0.000 0.000 0.016 0.020
#> GSM182823 1 0.0290 0.8861 0.992 0.000 0.000 0.008 0.000
#> GSM182824 1 0.0510 0.8838 0.984 0.000 0.000 0.016 0.000
#> GSM182825 1 0.4235 0.5069 0.656 0.000 0.000 0.336 0.008
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM182755 1 0.7315 0.28900 0.496 0.000 0.076 0.220 0.164 0.044
#> GSM182756 3 0.4520 0.80343 0.000 0.000 0.704 0.000 0.128 0.168
#> GSM182757 5 0.1918 0.62799 0.000 0.000 0.008 0.000 0.904 0.088
#> GSM182758 3 0.5948 0.17860 0.000 0.000 0.428 0.000 0.348 0.224
#> GSM182759 5 0.0508 0.62772 0.000 0.004 0.000 0.012 0.984 0.000
#> GSM182760 3 0.3671 0.85313 0.000 0.000 0.756 0.000 0.036 0.208
#> GSM182761 5 0.0146 0.62704 0.000 0.004 0.000 0.000 0.996 0.000
#> GSM182762 5 0.5921 0.54168 0.040 0.000 0.072 0.200 0.644 0.044
#> GSM182763 5 0.3981 0.59660 0.000 0.000 0.076 0.008 0.772 0.144
#> GSM182764 5 0.2946 0.53332 0.004 0.004 0.000 0.184 0.808 0.000
#> GSM182765 5 0.5781 0.58033 0.000 0.000 0.076 0.140 0.640 0.144
#> GSM182766 5 0.6414 0.38445 0.004 0.068 0.008 0.252 0.564 0.104
#> GSM182767 3 0.3612 0.85523 0.000 0.000 0.764 0.000 0.036 0.200
#> GSM182768 6 0.2582 0.75679 0.028 0.000 0.060 0.008 0.012 0.892
#> GSM182769 6 0.1858 0.77898 0.092 0.000 0.000 0.000 0.004 0.904
#> GSM182770 4 0.2662 0.61574 0.004 0.152 0.000 0.840 0.004 0.000
#> GSM182771 4 0.4634 0.39164 0.004 0.056 0.000 0.640 0.300 0.000
#> GSM182772 4 0.2662 0.61574 0.004 0.152 0.000 0.840 0.004 0.000
#> GSM182773 6 0.2326 0.71406 0.008 0.000 0.092 0.000 0.012 0.888
#> GSM182774 1 0.5613 0.42915 0.596 0.000 0.004 0.124 0.016 0.260
#> GSM182775 6 0.1806 0.77996 0.088 0.000 0.000 0.000 0.004 0.908
#> GSM182776 6 0.5728 0.34230 0.336 0.000 0.008 0.104 0.012 0.540
#> GSM182777 6 0.3363 0.70355 0.036 0.000 0.108 0.000 0.024 0.832
#> GSM182802 4 0.2243 0.62775 0.004 0.112 0.000 0.880 0.004 0.000
#> GSM182803 1 0.0692 0.84242 0.976 0.000 0.000 0.000 0.004 0.020
#> GSM182804 4 0.5977 0.44309 0.220 0.000 0.076 0.600 0.000 0.104
#> GSM182805 4 0.2641 0.63762 0.004 0.072 0.000 0.876 0.048 0.000
#> GSM182806 1 0.1866 0.83732 0.908 0.000 0.084 0.000 0.008 0.000
#> GSM182807 1 0.1970 0.83503 0.900 0.000 0.092 0.000 0.008 0.000
#> GSM182808 1 0.1866 0.83726 0.908 0.000 0.084 0.000 0.008 0.000
#> GSM182809 4 0.5777 0.27586 0.320 0.000 0.004 0.520 0.004 0.152
#> GSM182810 1 0.0458 0.84276 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM182811 1 0.2950 0.73887 0.828 0.000 0.000 0.148 0.000 0.024
#> GSM182812 1 0.1994 0.82327 0.920 0.004 0.008 0.052 0.000 0.016
#> GSM182813 1 0.1918 0.83616 0.904 0.000 0.088 0.000 0.008 0.000
#> GSM182778 2 0.0260 1.00000 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM182779 5 0.0146 0.62704 0.000 0.004 0.000 0.000 0.996 0.000
#> GSM182780 5 0.7000 0.09353 0.000 0.004 0.252 0.052 0.380 0.312
#> GSM182781 3 0.4889 0.71853 0.000 0.000 0.604 0.000 0.084 0.312
#> GSM182782 2 0.0260 1.00000 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM182783 5 0.6925 0.00434 0.000 0.004 0.252 0.044 0.368 0.332
#> GSM182784 3 0.4218 0.81239 0.000 0.000 0.736 0.000 0.108 0.156
#> GSM182785 5 0.3958 0.57678 0.000 0.000 0.128 0.000 0.764 0.108
#> GSM182786 2 0.0260 1.00000 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM182787 5 0.0935 0.62754 0.000 0.004 0.000 0.032 0.964 0.000
#> GSM182788 2 0.0260 1.00000 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM182789 5 0.5826 0.18516 0.000 0.000 0.272 0.000 0.492 0.236
#> GSM182790 3 0.3612 0.85523 0.000 0.000 0.764 0.000 0.036 0.200
#> GSM182791 6 0.3317 0.65497 0.004 0.000 0.088 0.080 0.000 0.828
#> GSM182792 6 0.2689 0.76197 0.040 0.000 0.060 0.004 0.012 0.884
#> GSM182793 4 0.4086 0.58118 0.000 0.004 0.136 0.768 0.004 0.088
#> GSM182794 3 0.3612 0.85523 0.000 0.000 0.764 0.000 0.036 0.200
#> GSM182795 5 0.6071 -0.02123 0.000 0.000 0.272 0.000 0.392 0.336
#> GSM182796 4 0.5137 0.40130 0.004 0.104 0.000 0.604 0.288 0.000
#> GSM182797 1 0.6036 0.60490 0.644 0.000 0.088 0.104 0.016 0.148
#> GSM182798 4 0.5503 0.44009 0.004 0.028 0.076 0.624 0.264 0.004
#> GSM182799 4 0.5554 0.15932 0.000 0.000 0.136 0.456 0.000 0.408
#> GSM182800 6 0.3903 0.61493 0.016 0.000 0.084 0.108 0.000 0.792
#> GSM182801 6 0.1958 0.77416 0.100 0.000 0.000 0.000 0.004 0.896
#> GSM182814 1 0.0405 0.84315 0.988 0.004 0.008 0.000 0.000 0.000
#> GSM182815 4 0.3855 0.46702 0.272 0.000 0.000 0.704 0.000 0.024
#> GSM182816 1 0.0405 0.84315 0.988 0.004 0.008 0.000 0.000 0.000
#> GSM182817 4 0.4733 0.62730 0.124 0.008 0.008 0.752 0.084 0.024
#> GSM182818 1 0.4474 0.24678 0.560 0.000 0.004 0.412 0.000 0.024
#> GSM182819 1 0.0260 0.84535 0.992 0.000 0.008 0.000 0.000 0.000
#> GSM182820 1 0.1970 0.83503 0.900 0.000 0.092 0.000 0.008 0.000
#> GSM182821 5 0.6629 0.48312 0.040 0.000 0.092 0.228 0.572 0.068
#> GSM182822 1 0.1844 0.84096 0.932 0.000 0.028 0.012 0.004 0.024
#> GSM182823 1 0.0405 0.84315 0.988 0.004 0.008 0.000 0.000 0.000
#> GSM182824 1 0.0508 0.84357 0.984 0.004 0.012 0.000 0.000 0.000
#> GSM182825 1 0.5371 0.60795 0.684 0.000 0.076 0.136 0.000 0.104
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 stress(p) development.stage(p) k
#> SD:mclust 69 0.7321 3.22e-04 2
#> SD:mclust 69 0.4780 6.94e-14 3
#> SD:mclust 48 0.8344 3.14e-10 4
#> SD:mclust 48 0.0798 1.07e-08 5
#> SD:mclust 53 0.2552 4.92e-08 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "NMF"]
# you can also extract it by
# res = res_list["SD:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 18172 rows and 71 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.779 0.889 0.953 0.5014 0.501 0.501
#> 3 3 0.756 0.863 0.934 0.3191 0.752 0.544
#> 4 4 0.728 0.769 0.886 0.1240 0.779 0.457
#> 5 5 0.731 0.688 0.848 0.0434 0.922 0.723
#> 6 6 0.673 0.521 0.743 0.0477 0.923 0.715
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
#> GSM182755 1 0.4690 0.856 0.900 0.100
#> GSM182756 2 0.9129 0.449 0.328 0.672
#> GSM182757 2 0.0000 0.971 0.000 1.000
#> GSM182758 2 0.0000 0.971 0.000 1.000
#> GSM182759 2 0.0000 0.971 0.000 1.000
#> GSM182760 1 0.6712 0.782 0.824 0.176
#> GSM182761 2 0.0000 0.971 0.000 1.000
#> GSM182762 1 0.8861 0.605 0.696 0.304
#> GSM182763 2 0.0000 0.971 0.000 1.000
#> GSM182764 2 0.0000 0.971 0.000 1.000
#> GSM182765 2 0.0672 0.964 0.008 0.992
#> GSM182766 2 0.0000 0.971 0.000 1.000
#> GSM182767 1 0.9988 0.169 0.520 0.480
#> GSM182768 1 0.0000 0.930 1.000 0.000
#> GSM182769 1 0.0000 0.930 1.000 0.000
#> GSM182770 2 0.0000 0.971 0.000 1.000
#> GSM182771 2 0.0000 0.971 0.000 1.000
#> GSM182772 2 0.0000 0.971 0.000 1.000
#> GSM182773 1 0.0000 0.930 1.000 0.000
#> GSM182774 1 0.0000 0.930 1.000 0.000
#> GSM182775 1 0.0000 0.930 1.000 0.000
#> GSM182776 1 0.0000 0.930 1.000 0.000
#> GSM182777 1 0.0000 0.930 1.000 0.000
#> GSM182802 2 0.0000 0.971 0.000 1.000
#> GSM182803 1 0.0000 0.930 1.000 0.000
#> GSM182804 1 0.0672 0.925 0.992 0.008
#> GSM182805 2 0.0000 0.971 0.000 1.000
#> GSM182806 1 0.0000 0.930 1.000 0.000
#> GSM182807 1 0.0000 0.930 1.000 0.000
#> GSM182808 1 0.0000 0.930 1.000 0.000
#> GSM182809 1 0.2423 0.903 0.960 0.040
#> GSM182810 1 0.0000 0.930 1.000 0.000
#> GSM182811 1 0.0000 0.930 1.000 0.000
#> GSM182812 1 0.0000 0.930 1.000 0.000
#> GSM182813 1 0.0000 0.930 1.000 0.000
#> GSM182778 2 0.0000 0.971 0.000 1.000
#> GSM182779 2 0.0000 0.971 0.000 1.000
#> GSM182780 2 0.0000 0.971 0.000 1.000
#> GSM182781 1 0.7299 0.751 0.796 0.204
#> GSM182782 2 0.0000 0.971 0.000 1.000
#> GSM182783 2 0.0000 0.971 0.000 1.000
#> GSM182784 2 0.0938 0.961 0.012 0.988
#> GSM182785 2 0.0000 0.971 0.000 1.000
#> GSM182786 2 0.0000 0.971 0.000 1.000
#> GSM182787 2 0.0000 0.971 0.000 1.000
#> GSM182788 2 0.0000 0.971 0.000 1.000
#> GSM182789 2 0.0000 0.971 0.000 1.000
#> GSM182790 1 0.7453 0.741 0.788 0.212
#> GSM182791 1 0.0938 0.923 0.988 0.012
#> GSM182792 1 0.0000 0.930 1.000 0.000
#> GSM182793 2 0.0000 0.971 0.000 1.000
#> GSM182794 1 0.8327 0.671 0.736 0.264
#> GSM182795 2 0.0000 0.971 0.000 1.000
#> GSM182796 2 0.0000 0.971 0.000 1.000
#> GSM182797 1 0.0000 0.930 1.000 0.000
#> GSM182798 2 0.0000 0.971 0.000 1.000
#> GSM182799 1 0.9795 0.284 0.584 0.416
#> GSM182800 1 0.0000 0.930 1.000 0.000
#> GSM182801 1 0.0000 0.930 1.000 0.000
#> GSM182814 1 0.0000 0.930 1.000 0.000
#> GSM182815 2 0.9170 0.482 0.332 0.668
#> GSM182816 1 0.0000 0.930 1.000 0.000
#> GSM182817 1 0.9427 0.499 0.640 0.360
#> GSM182818 1 0.0000 0.930 1.000 0.000
#> GSM182819 1 0.0000 0.930 1.000 0.000
#> GSM182820 1 0.0000 0.930 1.000 0.000
#> GSM182821 2 0.4815 0.859 0.104 0.896
#> GSM182822 1 0.0000 0.930 1.000 0.000
#> GSM182823 1 0.0000 0.930 1.000 0.000
#> GSM182824 1 0.0000 0.930 1.000 0.000
#> GSM182825 1 0.0000 0.930 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM182755 3 0.0000 0.905 0.000 0.000 1.000
#> GSM182756 3 0.0892 0.894 0.000 0.020 0.980
#> GSM182757 2 0.2165 0.911 0.000 0.936 0.064
#> GSM182758 2 0.4452 0.803 0.000 0.808 0.192
#> GSM182759 2 0.0000 0.947 0.000 1.000 0.000
#> GSM182760 3 0.0000 0.905 0.000 0.000 1.000
#> GSM182761 2 0.0424 0.944 0.000 0.992 0.008
#> GSM182762 3 0.1031 0.892 0.000 0.024 0.976
#> GSM182763 2 0.0000 0.947 0.000 1.000 0.000
#> GSM182764 2 0.0000 0.947 0.000 1.000 0.000
#> GSM182765 2 0.0424 0.943 0.000 0.992 0.008
#> GSM182766 2 0.0000 0.947 0.000 1.000 0.000
#> GSM182767 3 0.0000 0.905 0.000 0.000 1.000
#> GSM182768 3 0.2066 0.878 0.060 0.000 0.940
#> GSM182769 3 0.0000 0.905 0.000 0.000 1.000
#> GSM182770 2 0.0000 0.947 0.000 1.000 0.000
#> GSM182771 2 0.0000 0.947 0.000 1.000 0.000
#> GSM182772 2 0.0000 0.947 0.000 1.000 0.000
#> GSM182773 3 0.0000 0.905 0.000 0.000 1.000
#> GSM182774 3 0.4887 0.742 0.228 0.000 0.772
#> GSM182775 3 0.0000 0.905 0.000 0.000 1.000
#> GSM182776 3 0.0000 0.905 0.000 0.000 1.000
#> GSM182777 3 0.0000 0.905 0.000 0.000 1.000
#> GSM182802 1 0.4974 0.654 0.764 0.236 0.000
#> GSM182803 3 0.6154 0.387 0.408 0.000 0.592
#> GSM182804 1 0.0000 0.910 1.000 0.000 0.000
#> GSM182805 2 0.0747 0.937 0.016 0.984 0.000
#> GSM182806 3 0.4452 0.783 0.192 0.000 0.808
#> GSM182807 3 0.3816 0.825 0.148 0.000 0.852
#> GSM182808 3 0.4121 0.807 0.168 0.000 0.832
#> GSM182809 1 0.0000 0.910 1.000 0.000 0.000
#> GSM182810 1 0.0000 0.910 1.000 0.000 0.000
#> GSM182811 1 0.0000 0.910 1.000 0.000 0.000
#> GSM182812 1 0.0000 0.910 1.000 0.000 0.000
#> GSM182813 3 0.3752 0.828 0.144 0.000 0.856
#> GSM182778 2 0.0000 0.947 0.000 1.000 0.000
#> GSM182779 2 0.0000 0.947 0.000 1.000 0.000
#> GSM182780 2 0.0000 0.947 0.000 1.000 0.000
#> GSM182781 3 0.0000 0.905 0.000 0.000 1.000
#> GSM182782 2 0.0000 0.947 0.000 1.000 0.000
#> GSM182783 2 0.3482 0.864 0.000 0.872 0.128
#> GSM182784 3 0.4842 0.652 0.000 0.224 0.776
#> GSM182785 2 0.4842 0.765 0.000 0.776 0.224
#> GSM182786 2 0.0000 0.947 0.000 1.000 0.000
#> GSM182787 2 0.0000 0.947 0.000 1.000 0.000
#> GSM182788 2 0.0000 0.947 0.000 1.000 0.000
#> GSM182789 2 0.3752 0.850 0.000 0.856 0.144
#> GSM182790 3 0.0000 0.905 0.000 0.000 1.000
#> GSM182791 1 0.9891 0.112 0.404 0.280 0.316
#> GSM182792 3 0.0000 0.905 0.000 0.000 1.000
#> GSM182793 2 0.5431 0.583 0.284 0.716 0.000
#> GSM182794 3 0.0424 0.901 0.000 0.008 0.992
#> GSM182795 2 0.3619 0.858 0.000 0.864 0.136
#> GSM182796 2 0.0000 0.947 0.000 1.000 0.000
#> GSM182797 3 0.0000 0.905 0.000 0.000 1.000
#> GSM182798 2 0.0000 0.947 0.000 1.000 0.000
#> GSM182799 1 0.0000 0.910 1.000 0.000 0.000
#> GSM182800 1 0.2625 0.853 0.916 0.000 0.084
#> GSM182801 3 0.1411 0.893 0.036 0.000 0.964
#> GSM182814 1 0.0000 0.910 1.000 0.000 0.000
#> GSM182815 1 0.0000 0.910 1.000 0.000 0.000
#> GSM182816 1 0.4887 0.662 0.772 0.000 0.228
#> GSM182817 2 0.3921 0.859 0.036 0.884 0.080
#> GSM182818 1 0.0000 0.910 1.000 0.000 0.000
#> GSM182819 3 0.4974 0.731 0.236 0.000 0.764
#> GSM182820 3 0.3686 0.831 0.140 0.000 0.860
#> GSM182821 2 0.0000 0.947 0.000 1.000 0.000
#> GSM182822 1 0.3752 0.787 0.856 0.000 0.144
#> GSM182823 1 0.1031 0.900 0.976 0.000 0.024
#> GSM182824 1 0.1031 0.900 0.976 0.000 0.024
#> GSM182825 1 0.0000 0.910 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM182755 1 0.0469 0.824 0.988 0.000 0.012 0.000
#> GSM182756 3 0.4431 0.640 0.304 0.000 0.696 0.000
#> GSM182757 2 0.4040 0.683 0.000 0.752 0.248 0.000
#> GSM182758 3 0.0592 0.877 0.000 0.016 0.984 0.000
#> GSM182759 2 0.0188 0.950 0.000 0.996 0.004 0.000
#> GSM182760 3 0.0469 0.879 0.012 0.000 0.988 0.000
#> GSM182761 2 0.2704 0.847 0.000 0.876 0.124 0.000
#> GSM182762 1 0.4655 0.598 0.760 0.208 0.032 0.000
#> GSM182763 2 0.0817 0.941 0.000 0.976 0.024 0.000
#> GSM182764 2 0.0000 0.950 0.000 1.000 0.000 0.000
#> GSM182765 2 0.3899 0.825 0.052 0.840 0.108 0.000
#> GSM182766 2 0.0707 0.943 0.000 0.980 0.020 0.000
#> GSM182767 3 0.0592 0.878 0.016 0.000 0.984 0.000
#> GSM182768 3 0.0707 0.872 0.000 0.000 0.980 0.020
#> GSM182769 3 0.2999 0.814 0.132 0.000 0.864 0.004
#> GSM182770 2 0.0188 0.949 0.000 0.996 0.004 0.000
#> GSM182771 2 0.0188 0.949 0.000 0.996 0.000 0.004
#> GSM182772 2 0.0000 0.950 0.000 1.000 0.000 0.000
#> GSM182773 3 0.0188 0.878 0.004 0.000 0.996 0.000
#> GSM182774 1 0.4741 0.624 0.744 0.000 0.028 0.228
#> GSM182775 3 0.2408 0.834 0.104 0.000 0.896 0.000
#> GSM182776 1 0.4543 0.362 0.676 0.000 0.324 0.000
#> GSM182777 3 0.4624 0.587 0.340 0.000 0.660 0.000
#> GSM182802 2 0.1716 0.903 0.000 0.936 0.000 0.064
#> GSM182803 1 0.2011 0.762 0.920 0.000 0.000 0.080
#> GSM182804 4 0.0000 0.694 0.000 0.000 0.000 1.000
#> GSM182805 2 0.0524 0.944 0.004 0.988 0.000 0.008
#> GSM182806 1 0.0336 0.827 0.992 0.000 0.000 0.008
#> GSM182807 1 0.0188 0.829 0.996 0.000 0.000 0.004
#> GSM182808 1 0.0188 0.829 0.996 0.000 0.000 0.004
#> GSM182809 4 0.1940 0.718 0.076 0.000 0.000 0.924
#> GSM182810 4 0.4250 0.692 0.276 0.000 0.000 0.724
#> GSM182811 4 0.4706 0.700 0.248 0.020 0.000 0.732
#> GSM182812 4 0.3074 0.727 0.152 0.000 0.000 0.848
#> GSM182813 1 0.0000 0.828 1.000 0.000 0.000 0.000
#> GSM182778 2 0.0188 0.950 0.000 0.996 0.004 0.000
#> GSM182779 2 0.0188 0.950 0.000 0.996 0.004 0.000
#> GSM182780 3 0.0895 0.874 0.000 0.020 0.976 0.004
#> GSM182781 3 0.4679 0.559 0.352 0.000 0.648 0.000
#> GSM182782 2 0.0000 0.950 0.000 1.000 0.000 0.000
#> GSM182783 3 0.0707 0.874 0.000 0.020 0.980 0.000
#> GSM182784 3 0.1151 0.877 0.024 0.008 0.968 0.000
#> GSM182785 3 0.5375 0.710 0.116 0.140 0.744 0.000
#> GSM182786 2 0.0188 0.950 0.000 0.996 0.004 0.000
#> GSM182787 2 0.0336 0.949 0.000 0.992 0.008 0.000
#> GSM182788 2 0.0188 0.950 0.000 0.996 0.004 0.000
#> GSM182789 3 0.0592 0.877 0.000 0.016 0.984 0.000
#> GSM182790 3 0.0921 0.877 0.028 0.000 0.972 0.000
#> GSM182791 3 0.2589 0.807 0.000 0.000 0.884 0.116
#> GSM182792 3 0.0188 0.877 0.000 0.000 0.996 0.004
#> GSM182793 4 0.7469 0.180 0.000 0.312 0.200 0.488
#> GSM182794 3 0.0469 0.879 0.012 0.000 0.988 0.000
#> GSM182795 3 0.0592 0.877 0.000 0.016 0.984 0.000
#> GSM182796 2 0.0000 0.950 0.000 1.000 0.000 0.000
#> GSM182797 1 0.0592 0.821 0.984 0.000 0.016 0.000
#> GSM182798 2 0.0000 0.950 0.000 1.000 0.000 0.000
#> GSM182799 3 0.4624 0.509 0.000 0.000 0.660 0.340
#> GSM182800 4 0.4713 0.223 0.000 0.000 0.360 0.640
#> GSM182801 3 0.4744 0.651 0.284 0.000 0.704 0.012
#> GSM182814 4 0.4454 0.662 0.308 0.000 0.000 0.692
#> GSM182815 4 0.0188 0.694 0.000 0.004 0.000 0.996
#> GSM182816 4 0.4331 0.683 0.288 0.000 0.000 0.712
#> GSM182817 2 0.4399 0.677 0.224 0.760 0.000 0.016
#> GSM182818 4 0.3528 0.721 0.192 0.000 0.000 0.808
#> GSM182819 1 0.1022 0.811 0.968 0.000 0.000 0.032
#> GSM182820 1 0.0188 0.829 0.996 0.000 0.000 0.004
#> GSM182821 2 0.1114 0.941 0.016 0.972 0.008 0.004
#> GSM182822 4 0.4994 0.334 0.480 0.000 0.000 0.520
#> GSM182823 1 0.4998 -0.336 0.512 0.000 0.000 0.488
#> GSM182824 4 0.4277 0.689 0.280 0.000 0.000 0.720
#> GSM182825 4 0.0000 0.694 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
#> GSM182755 2 0.0566 0.4845 0.012 0.984 0.000 0.000 0.004
#> GSM182756 3 0.4039 0.6866 0.000 0.268 0.720 0.004 0.008
#> GSM182757 5 0.4644 0.7539 0.000 0.092 0.116 0.020 0.772
#> GSM182758 3 0.0854 0.8388 0.000 0.012 0.976 0.008 0.004
#> GSM182759 5 0.0671 0.8875 0.000 0.004 0.000 0.016 0.980
#> GSM182760 3 0.2068 0.8259 0.000 0.092 0.904 0.004 0.000
#> GSM182761 5 0.4237 0.7061 0.000 0.008 0.212 0.028 0.752
#> GSM182762 2 0.2337 0.4499 0.004 0.904 0.008 0.004 0.080
#> GSM182763 5 0.1612 0.8856 0.000 0.024 0.016 0.012 0.948
#> GSM182764 5 0.1251 0.8869 0.000 0.036 0.000 0.008 0.956
#> GSM182765 5 0.4880 0.6642 0.000 0.256 0.012 0.040 0.692
#> GSM182766 5 0.1800 0.8769 0.000 0.000 0.048 0.020 0.932
#> GSM182767 3 0.0968 0.8351 0.000 0.012 0.972 0.012 0.004
#> GSM182768 3 0.0510 0.8370 0.000 0.000 0.984 0.016 0.000
#> GSM182769 3 0.3651 0.7624 0.028 0.160 0.808 0.004 0.000
#> GSM182770 5 0.0324 0.8891 0.000 0.000 0.004 0.004 0.992
#> GSM182771 5 0.2376 0.8647 0.000 0.052 0.000 0.044 0.904
#> GSM182772 5 0.0510 0.8877 0.000 0.000 0.000 0.016 0.984
#> GSM182773 3 0.0162 0.8370 0.000 0.000 0.996 0.004 0.000
#> GSM182774 2 0.5940 0.0606 0.036 0.564 0.048 0.352 0.000
#> GSM182775 3 0.4029 0.6257 0.000 0.316 0.680 0.004 0.000
#> GSM182776 2 0.5771 -0.1441 0.088 0.480 0.432 0.000 0.000
#> GSM182777 3 0.3730 0.6714 0.000 0.288 0.712 0.000 0.000
#> GSM182802 5 0.0798 0.8877 0.008 0.000 0.000 0.016 0.976
#> GSM182803 1 0.1851 0.8032 0.912 0.088 0.000 0.000 0.000
#> GSM182804 4 0.1892 0.8827 0.080 0.000 0.004 0.916 0.000
#> GSM182805 5 0.3601 0.7741 0.136 0.008 0.000 0.032 0.824
#> GSM182806 2 0.4397 0.0286 0.432 0.564 0.004 0.000 0.000
#> GSM182807 2 0.4452 -0.1609 0.496 0.500 0.004 0.000 0.000
#> GSM182808 1 0.3317 0.7112 0.804 0.188 0.004 0.004 0.000
#> GSM182809 1 0.1419 0.8128 0.956 0.016 0.012 0.016 0.000
#> GSM182810 1 0.0404 0.8255 0.988 0.000 0.000 0.012 0.000
#> GSM182811 1 0.0162 0.8259 0.996 0.000 0.000 0.004 0.000
#> GSM182812 1 0.4088 0.3514 0.632 0.000 0.000 0.368 0.000
#> GSM182813 2 0.4101 0.2680 0.332 0.664 0.004 0.000 0.000
#> GSM182778 5 0.0833 0.8876 0.000 0.004 0.004 0.016 0.976
#> GSM182779 5 0.1059 0.8897 0.000 0.020 0.004 0.008 0.968
#> GSM182780 3 0.1704 0.8191 0.000 0.004 0.928 0.068 0.000
#> GSM182781 2 0.4659 -0.3278 0.000 0.500 0.488 0.012 0.000
#> GSM182782 5 0.0867 0.8885 0.000 0.008 0.008 0.008 0.976
#> GSM182783 3 0.0613 0.8368 0.000 0.004 0.984 0.008 0.004
#> GSM182784 3 0.1560 0.8364 0.000 0.028 0.948 0.020 0.004
#> GSM182785 3 0.4272 0.7596 0.000 0.156 0.784 0.020 0.040
#> GSM182786 5 0.0727 0.8881 0.000 0.004 0.004 0.012 0.980
#> GSM182787 5 0.3502 0.8164 0.004 0.012 0.112 0.028 0.844
#> GSM182788 5 0.0727 0.8883 0.000 0.004 0.004 0.012 0.980
#> GSM182789 3 0.1710 0.8226 0.000 0.012 0.944 0.024 0.020
#> GSM182790 3 0.1965 0.8231 0.000 0.096 0.904 0.000 0.000
#> GSM182791 3 0.4171 0.3765 0.000 0.000 0.604 0.396 0.000
#> GSM182792 3 0.2149 0.8322 0.000 0.048 0.916 0.036 0.000
#> GSM182793 4 0.1547 0.8626 0.004 0.000 0.016 0.948 0.032
#> GSM182794 3 0.1444 0.8403 0.000 0.040 0.948 0.012 0.000
#> GSM182795 3 0.0867 0.8347 0.000 0.008 0.976 0.008 0.008
#> GSM182796 5 0.0566 0.8880 0.000 0.004 0.000 0.012 0.984
#> GSM182797 2 0.1357 0.4966 0.048 0.948 0.004 0.000 0.000
#> GSM182798 5 0.4761 0.4497 0.000 0.028 0.000 0.356 0.616
#> GSM182799 3 0.3968 0.6197 0.004 0.004 0.716 0.276 0.000
#> GSM182800 4 0.1808 0.8718 0.020 0.004 0.040 0.936 0.000
#> GSM182801 3 0.5877 0.3387 0.072 0.384 0.532 0.012 0.000
#> GSM182814 1 0.0451 0.8263 0.988 0.004 0.000 0.008 0.000
#> GSM182815 1 0.3838 0.5228 0.716 0.000 0.004 0.280 0.000
#> GSM182816 1 0.1153 0.8269 0.964 0.024 0.004 0.008 0.000
#> GSM182817 5 0.4202 0.6611 0.228 0.012 0.000 0.016 0.744
#> GSM182818 1 0.1314 0.8174 0.960 0.012 0.012 0.016 0.000
#> GSM182819 1 0.3160 0.7241 0.808 0.188 0.004 0.000 0.000
#> GSM182820 1 0.4199 0.5406 0.692 0.296 0.004 0.008 0.000
#> GSM182821 1 0.6585 0.3676 0.600 0.024 0.080 0.032 0.264
#> GSM182822 1 0.1631 0.8204 0.948 0.020 0.004 0.024 0.004
#> GSM182823 1 0.2233 0.7981 0.892 0.104 0.000 0.004 0.000
#> GSM182824 1 0.1059 0.8273 0.968 0.020 0.004 0.008 0.000
#> GSM182825 4 0.3003 0.7929 0.188 0.000 0.000 0.812 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM182755 5 0.0810 0.4413 0.004 0.008 0.008 0.000 0.976 0.004
#> GSM182756 3 0.5067 0.4997 0.004 0.008 0.672 0.000 0.136 0.180
#> GSM182757 3 0.7243 -0.2993 0.000 0.276 0.320 0.000 0.088 0.316
#> GSM182758 3 0.2300 0.6237 0.000 0.000 0.856 0.000 0.000 0.144
#> GSM182759 2 0.0653 0.8145 0.000 0.980 0.000 0.004 0.012 0.004
#> GSM182760 3 0.3017 0.6274 0.000 0.000 0.840 0.000 0.052 0.108
#> GSM182761 2 0.6418 -0.3255 0.000 0.336 0.336 0.000 0.012 0.316
#> GSM182762 5 0.5215 -0.1076 0.000 0.124 0.060 0.000 0.696 0.120
#> GSM182763 2 0.3475 0.7871 0.000 0.836 0.016 0.012 0.040 0.096
#> GSM182764 2 0.2344 0.8055 0.000 0.896 0.004 0.000 0.048 0.052
#> GSM182765 2 0.5754 0.3108 0.000 0.544 0.028 0.020 0.356 0.052
#> GSM182766 2 0.4046 0.6491 0.000 0.752 0.068 0.004 0.000 0.176
#> GSM182767 3 0.2805 0.5964 0.000 0.000 0.812 0.004 0.000 0.184
#> GSM182768 3 0.2253 0.6254 0.004 0.000 0.896 0.012 0.004 0.084
#> GSM182769 3 0.3286 0.6091 0.016 0.000 0.832 0.000 0.116 0.036
#> GSM182770 2 0.0790 0.8182 0.000 0.968 0.000 0.000 0.000 0.032
#> GSM182771 2 0.2925 0.7749 0.000 0.864 0.000 0.012 0.064 0.060
#> GSM182772 2 0.1010 0.8160 0.000 0.960 0.000 0.004 0.000 0.036
#> GSM182773 3 0.1888 0.6353 0.000 0.000 0.916 0.004 0.012 0.068
#> GSM182774 6 0.8042 0.0000 0.060 0.016 0.184 0.060 0.288 0.392
#> GSM182775 3 0.3784 0.5428 0.000 0.000 0.736 0.004 0.236 0.024
#> GSM182776 3 0.6685 -0.1851 0.064 0.000 0.460 0.000 0.304 0.172
#> GSM182777 3 0.3669 0.5887 0.008 0.000 0.784 0.004 0.176 0.028
#> GSM182802 2 0.2251 0.7981 0.036 0.904 0.000 0.008 0.000 0.052
#> GSM182803 1 0.2726 0.6584 0.856 0.000 0.000 0.000 0.112 0.032
#> GSM182804 4 0.1088 0.6307 0.016 0.000 0.000 0.960 0.000 0.024
#> GSM182805 2 0.4218 0.6888 0.112 0.748 0.000 0.000 0.004 0.136
#> GSM182806 5 0.4283 0.2955 0.384 0.000 0.000 0.000 0.592 0.024
#> GSM182807 1 0.3975 0.0407 0.544 0.000 0.000 0.000 0.452 0.004
#> GSM182808 1 0.3807 0.5261 0.740 0.000 0.004 0.000 0.228 0.028
#> GSM182809 1 0.3146 0.6786 0.844 0.000 0.012 0.028 0.004 0.112
#> GSM182810 1 0.3367 0.6644 0.804 0.000 0.000 0.012 0.020 0.164
#> GSM182811 1 0.2482 0.6784 0.848 0.000 0.000 0.000 0.004 0.148
#> GSM182812 1 0.5962 0.3248 0.488 0.000 0.000 0.260 0.004 0.248
#> GSM182813 5 0.3833 0.3902 0.344 0.000 0.000 0.000 0.648 0.008
#> GSM182778 2 0.0713 0.8172 0.000 0.972 0.000 0.000 0.000 0.028
#> GSM182779 2 0.2976 0.7747 0.000 0.860 0.028 0.000 0.024 0.088
#> GSM182780 3 0.4910 0.4188 0.000 0.008 0.620 0.068 0.000 0.304
#> GSM182781 3 0.5773 0.1898 0.000 0.012 0.532 0.000 0.148 0.308
#> GSM182782 2 0.1970 0.8080 0.000 0.900 0.008 0.000 0.000 0.092
#> GSM182783 3 0.3707 0.4525 0.000 0.008 0.680 0.000 0.000 0.312
#> GSM182784 3 0.2941 0.6099 0.000 0.000 0.780 0.000 0.000 0.220
#> GSM182785 3 0.5123 0.3819 0.000 0.004 0.588 0.000 0.092 0.316
#> GSM182786 2 0.1007 0.8141 0.000 0.956 0.000 0.000 0.000 0.044
#> GSM182787 2 0.4620 0.5810 0.000 0.640 0.068 0.000 0.000 0.292
#> GSM182788 2 0.1204 0.8141 0.000 0.944 0.000 0.000 0.000 0.056
#> GSM182789 3 0.3774 0.5362 0.000 0.008 0.664 0.000 0.000 0.328
#> GSM182790 3 0.3295 0.6048 0.000 0.000 0.816 0.000 0.056 0.128
#> GSM182791 4 0.4887 0.4555 0.000 0.000 0.280 0.624 0.000 0.096
#> GSM182792 3 0.3337 0.6173 0.000 0.000 0.840 0.044 0.028 0.088
#> GSM182793 4 0.1148 0.6408 0.000 0.016 0.004 0.960 0.000 0.020
#> GSM182794 3 0.4656 0.5029 0.004 0.004 0.680 0.016 0.032 0.264
#> GSM182795 3 0.2762 0.6088 0.000 0.000 0.804 0.000 0.000 0.196
#> GSM182796 2 0.0291 0.8145 0.000 0.992 0.000 0.004 0.000 0.004
#> GSM182797 5 0.2119 0.4784 0.044 0.000 0.036 0.000 0.912 0.008
#> GSM182798 4 0.4631 0.1188 0.000 0.440 0.000 0.528 0.012 0.020
#> GSM182799 4 0.5555 0.2913 0.000 0.000 0.380 0.480 0.000 0.140
#> GSM182800 4 0.0692 0.6445 0.000 0.000 0.020 0.976 0.000 0.004
#> GSM182801 3 0.6734 0.3153 0.092 0.000 0.572 0.052 0.216 0.068
#> GSM182814 1 0.3166 0.6618 0.800 0.000 0.000 0.008 0.008 0.184
#> GSM182815 1 0.5731 0.4328 0.552 0.000 0.000 0.184 0.008 0.256
#> GSM182816 1 0.2259 0.6884 0.904 0.000 0.000 0.008 0.044 0.044
#> GSM182817 2 0.4837 0.5606 0.232 0.680 0.000 0.000 0.024 0.064
#> GSM182818 1 0.3061 0.6745 0.816 0.000 0.004 0.004 0.008 0.168
#> GSM182819 1 0.3424 0.6012 0.772 0.000 0.000 0.000 0.204 0.024
#> GSM182820 1 0.4967 0.3877 0.644 0.000 0.004 0.000 0.244 0.108
#> GSM182821 1 0.7089 0.1203 0.444 0.128 0.112 0.000 0.008 0.308
#> GSM182822 1 0.1010 0.6895 0.960 0.000 0.000 0.000 0.004 0.036
#> GSM182823 1 0.3691 0.6175 0.768 0.000 0.000 0.004 0.192 0.036
#> GSM182824 1 0.1477 0.6836 0.940 0.000 0.000 0.008 0.048 0.004
#> GSM182825 4 0.2218 0.5891 0.104 0.000 0.000 0.884 0.000 0.012
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n stress(p) development.stage(p) k
#> SD:NMF 66 0.620 1.18e-03 2
#> SD:NMF 69 0.172 6.31e-07 3
#> SD:NMF 66 0.360 1.16e-08 4
#> SD:NMF 57 0.416 6.46e-09 5
#> SD:NMF 47 0.646 5.32e-07 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "hclust"]
# you can also extract it by
# res = res_list["CV:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 18172 rows and 71 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.591 0.732 0.884 0.4047 0.631 0.631
#> 3 3 0.370 0.593 0.745 0.5289 0.657 0.483
#> 4 4 0.428 0.441 0.693 0.1420 0.813 0.524
#> 5 5 0.480 0.479 0.693 0.0571 0.838 0.514
#> 6 6 0.567 0.478 0.671 0.0402 0.918 0.698
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
#> GSM182755 1 0.0000 0.8532 1.000 0.000
#> GSM182756 1 0.4562 0.8191 0.904 0.096
#> GSM182757 1 0.4161 0.8275 0.916 0.084
#> GSM182758 1 0.5178 0.8043 0.884 0.116
#> GSM182759 1 0.8207 0.6705 0.744 0.256
#> GSM182760 1 0.8713 0.6134 0.708 0.292
#> GSM182761 1 0.9993 0.2193 0.516 0.484
#> GSM182762 1 0.0000 0.8532 1.000 0.000
#> GSM182763 1 0.9248 0.5511 0.660 0.340
#> GSM182764 1 0.1633 0.8543 0.976 0.024
#> GSM182765 1 0.2236 0.8520 0.964 0.036
#> GSM182766 2 0.0000 0.8803 0.000 1.000
#> GSM182767 1 0.9491 0.4989 0.632 0.368
#> GSM182768 1 0.9954 0.2858 0.540 0.460
#> GSM182769 1 0.4022 0.8272 0.920 0.080
#> GSM182770 2 0.0000 0.8803 0.000 1.000
#> GSM182771 1 0.2043 0.8517 0.968 0.032
#> GSM182772 2 0.0000 0.8803 0.000 1.000
#> GSM182773 1 0.2423 0.8476 0.960 0.040
#> GSM182774 1 0.0938 0.8543 0.988 0.012
#> GSM182775 1 0.1414 0.8534 0.980 0.020
#> GSM182776 1 0.0938 0.8543 0.988 0.012
#> GSM182777 1 0.1414 0.8534 0.980 0.020
#> GSM182802 2 0.0000 0.8803 0.000 1.000
#> GSM182803 1 0.0000 0.8532 1.000 0.000
#> GSM182804 2 0.0000 0.8803 0.000 1.000
#> GSM182805 2 0.0000 0.8803 0.000 1.000
#> GSM182806 1 0.0000 0.8532 1.000 0.000
#> GSM182807 1 0.0000 0.8532 1.000 0.000
#> GSM182808 1 0.0000 0.8532 1.000 0.000
#> GSM182809 1 0.9983 0.2445 0.524 0.476
#> GSM182810 1 0.1184 0.8549 0.984 0.016
#> GSM182811 1 0.1414 0.8546 0.980 0.020
#> GSM182812 1 0.2423 0.8493 0.960 0.040
#> GSM182813 1 0.0000 0.8532 1.000 0.000
#> GSM182778 2 0.0000 0.8803 0.000 1.000
#> GSM182779 1 0.3114 0.8427 0.944 0.056
#> GSM182780 2 0.9922 -0.0126 0.448 0.552
#> GSM182781 1 0.0000 0.8532 1.000 0.000
#> GSM182782 2 0.0000 0.8803 0.000 1.000
#> GSM182783 2 0.9661 0.2417 0.392 0.608
#> GSM182784 1 0.9460 0.5061 0.636 0.364
#> GSM182785 1 0.9881 0.3596 0.564 0.436
#> GSM182786 2 0.0000 0.8803 0.000 1.000
#> GSM182787 2 0.9922 -0.0126 0.448 0.552
#> GSM182788 2 0.0000 0.8803 0.000 1.000
#> GSM182789 1 0.9977 0.2578 0.528 0.472
#> GSM182790 1 0.0938 0.8540 0.988 0.012
#> GSM182791 1 0.9833 0.3860 0.576 0.424
#> GSM182792 1 0.9661 0.4565 0.608 0.392
#> GSM182793 2 0.0000 0.8803 0.000 1.000
#> GSM182794 1 0.1414 0.8534 0.980 0.020
#> GSM182795 1 0.9323 0.5413 0.652 0.348
#> GSM182796 1 0.2043 0.8517 0.968 0.032
#> GSM182797 1 0.0000 0.8532 1.000 0.000
#> GSM182798 1 0.2043 0.8517 0.968 0.032
#> GSM182799 2 0.7528 0.6370 0.216 0.784
#> GSM182800 1 0.0376 0.8538 0.996 0.004
#> GSM182801 1 0.0000 0.8532 1.000 0.000
#> GSM182814 1 0.0000 0.8532 1.000 0.000
#> GSM182815 2 0.0000 0.8803 0.000 1.000
#> GSM182816 1 0.0000 0.8532 1.000 0.000
#> GSM182817 1 0.2603 0.8486 0.956 0.044
#> GSM182818 2 0.0000 0.8803 0.000 1.000
#> GSM182819 1 0.0000 0.8532 1.000 0.000
#> GSM182820 1 0.0000 0.8532 1.000 0.000
#> GSM182821 1 0.9933 0.3163 0.548 0.452
#> GSM182822 1 0.8608 0.6248 0.716 0.284
#> GSM182823 1 0.0000 0.8532 1.000 0.000
#> GSM182824 1 0.0000 0.8532 1.000 0.000
#> GSM182825 1 0.0938 0.8543 0.988 0.012
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM182755 1 0.0237 0.6188 0.996 0.000 0.004
#> GSM182756 3 0.2625 0.5266 0.084 0.000 0.916
#> GSM182757 3 0.5728 0.3945 0.196 0.032 0.772
#> GSM182758 3 0.1753 0.5485 0.048 0.000 0.952
#> GSM182759 3 0.5067 0.6154 0.052 0.116 0.832
#> GSM182760 3 0.7960 0.6357 0.120 0.232 0.648
#> GSM182761 3 0.5785 0.6037 0.000 0.332 0.668
#> GSM182762 1 0.5465 0.6453 0.712 0.000 0.288
#> GSM182763 3 0.5901 0.6451 0.040 0.192 0.768
#> GSM182764 1 0.6180 0.5801 0.584 0.000 0.416
#> GSM182765 1 0.6168 0.5983 0.588 0.000 0.412
#> GSM182766 2 0.0747 0.9571 0.000 0.984 0.016
#> GSM182767 3 0.6224 0.6710 0.032 0.240 0.728
#> GSM182768 3 0.6369 0.6327 0.016 0.316 0.668
#> GSM182769 3 0.3918 0.4911 0.140 0.004 0.856
#> GSM182770 2 0.0237 0.9628 0.000 0.996 0.004
#> GSM182771 1 0.6111 0.6098 0.604 0.000 0.396
#> GSM182772 2 0.0237 0.9628 0.000 0.996 0.004
#> GSM182773 3 0.4682 0.4334 0.192 0.004 0.804
#> GSM182774 1 0.6308 0.5298 0.508 0.000 0.492
#> GSM182775 3 0.4974 0.3629 0.236 0.000 0.764
#> GSM182776 1 0.6308 0.5298 0.508 0.000 0.492
#> GSM182777 3 0.4887 0.3782 0.228 0.000 0.772
#> GSM182802 2 0.0424 0.9618 0.000 0.992 0.008
#> GSM182803 1 0.5948 0.6315 0.640 0.000 0.360
#> GSM182804 2 0.1031 0.9530 0.000 0.976 0.024
#> GSM182805 2 0.1031 0.9530 0.000 0.976 0.024
#> GSM182806 1 0.0237 0.6188 0.996 0.000 0.004
#> GSM182807 1 0.0237 0.6188 0.996 0.000 0.004
#> GSM182808 1 0.2959 0.6189 0.900 0.000 0.100
#> GSM182809 3 0.5733 0.6133 0.000 0.324 0.676
#> GSM182810 1 0.6267 0.5768 0.548 0.000 0.452
#> GSM182811 1 0.6274 0.5725 0.544 0.000 0.456
#> GSM182812 1 0.6267 0.5812 0.548 0.000 0.452
#> GSM182813 1 0.0237 0.6188 0.996 0.000 0.004
#> GSM182778 2 0.0000 0.9622 0.000 1.000 0.000
#> GSM182779 3 0.5988 -0.1356 0.368 0.000 0.632
#> GSM182780 3 0.6111 0.4863 0.000 0.396 0.604
#> GSM182781 1 0.6309 0.2585 0.504 0.000 0.496
#> GSM182782 2 0.0000 0.9622 0.000 1.000 0.000
#> GSM182783 3 0.6521 0.1511 0.004 0.492 0.504
#> GSM182784 3 0.6335 0.6702 0.036 0.240 0.724
#> GSM182785 3 0.5864 0.6558 0.008 0.288 0.704
#> GSM182786 2 0.0000 0.9622 0.000 1.000 0.000
#> GSM182787 3 0.6140 0.4793 0.000 0.404 0.596
#> GSM182788 2 0.0000 0.9622 0.000 1.000 0.000
#> GSM182789 3 0.5956 0.6192 0.004 0.324 0.672
#> GSM182790 3 0.4842 0.3820 0.224 0.000 0.776
#> GSM182791 3 0.6096 0.6643 0.016 0.280 0.704
#> GSM182792 3 0.5977 0.6736 0.020 0.252 0.728
#> GSM182793 2 0.0237 0.9628 0.000 0.996 0.004
#> GSM182794 3 0.4887 0.3782 0.228 0.000 0.772
#> GSM182795 3 0.5803 0.6701 0.028 0.212 0.760
#> GSM182796 1 0.6062 0.6145 0.616 0.000 0.384
#> GSM182797 1 0.0237 0.6188 0.996 0.000 0.004
#> GSM182798 1 0.6045 0.6163 0.620 0.000 0.380
#> GSM182799 2 0.5929 0.4033 0.004 0.676 0.320
#> GSM182800 1 0.6204 0.5701 0.576 0.000 0.424
#> GSM182801 3 0.6079 0.1516 0.388 0.000 0.612
#> GSM182814 1 0.6111 0.6169 0.604 0.000 0.396
#> GSM182815 2 0.0424 0.9618 0.000 0.992 0.008
#> GSM182816 1 0.6308 -0.0201 0.508 0.000 0.492
#> GSM182817 3 0.5810 -0.1324 0.336 0.000 0.664
#> GSM182818 2 0.0000 0.9622 0.000 1.000 0.000
#> GSM182819 1 0.6308 -0.0201 0.508 0.000 0.492
#> GSM182820 1 0.0237 0.6188 0.996 0.000 0.004
#> GSM182821 3 0.5785 0.6424 0.004 0.300 0.696
#> GSM182822 3 0.7835 0.6265 0.112 0.232 0.656
#> GSM182823 1 0.0237 0.6188 0.996 0.000 0.004
#> GSM182824 1 0.2959 0.6189 0.900 0.000 0.100
#> GSM182825 1 0.6235 0.5914 0.564 0.000 0.436
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM182755 1 0.0000 0.54414 1.000 0.000 0.000 0.000
#> GSM182756 3 0.5856 0.05497 0.032 0.000 0.504 0.464
#> GSM182757 4 0.6741 0.20361 0.092 0.000 0.424 0.484
#> GSM182758 3 0.5244 0.21274 0.008 0.000 0.556 0.436
#> GSM182759 3 0.5560 0.40449 0.036 0.004 0.668 0.292
#> GSM182760 3 0.5427 0.58256 0.052 0.008 0.728 0.212
#> GSM182761 3 0.1118 0.73064 0.000 0.036 0.964 0.000
#> GSM182762 1 0.6054 0.12335 0.592 0.000 0.056 0.352
#> GSM182763 3 0.4640 0.64862 0.032 0.024 0.808 0.136
#> GSM182764 1 0.7006 -0.11584 0.456 0.000 0.116 0.428
#> GSM182765 1 0.6800 -0.07086 0.460 0.000 0.096 0.444
#> GSM182766 2 0.3052 0.89428 0.000 0.860 0.136 0.004
#> GSM182767 3 0.3484 0.69589 0.004 0.008 0.844 0.144
#> GSM182768 3 0.4094 0.71762 0.000 0.056 0.828 0.116
#> GSM182769 4 0.6705 0.06390 0.088 0.000 0.440 0.472
#> GSM182770 2 0.2089 0.89241 0.000 0.932 0.048 0.020
#> GSM182771 1 0.6915 -0.01190 0.476 0.000 0.108 0.416
#> GSM182772 2 0.2469 0.90093 0.000 0.892 0.108 0.000
#> GSM182773 4 0.7020 0.22186 0.124 0.000 0.376 0.500
#> GSM182774 4 0.6648 0.15679 0.372 0.000 0.092 0.536
#> GSM182775 4 0.7307 0.35756 0.168 0.004 0.288 0.540
#> GSM182776 4 0.6648 0.15679 0.372 0.000 0.092 0.536
#> GSM182777 4 0.7128 0.32742 0.152 0.000 0.320 0.528
#> GSM182802 2 0.2773 0.89893 0.000 0.880 0.116 0.004
#> GSM182803 1 0.6371 -0.00345 0.508 0.000 0.064 0.428
#> GSM182804 2 0.5902 0.80735 0.000 0.696 0.184 0.120
#> GSM182805 2 0.3208 0.88739 0.000 0.848 0.148 0.004
#> GSM182806 1 0.0000 0.54414 1.000 0.000 0.000 0.000
#> GSM182807 1 0.0000 0.54414 1.000 0.000 0.000 0.000
#> GSM182808 1 0.2408 0.49641 0.896 0.000 0.000 0.104
#> GSM182809 3 0.1452 0.73295 0.000 0.036 0.956 0.008
#> GSM182810 4 0.6906 0.09284 0.408 0.000 0.108 0.484
#> GSM182811 4 0.6944 0.09627 0.404 0.000 0.112 0.484
#> GSM182812 4 0.6965 0.01279 0.428 0.000 0.112 0.460
#> GSM182813 1 0.0000 0.54414 1.000 0.000 0.000 0.000
#> GSM182778 2 0.2385 0.88249 0.000 0.920 0.028 0.052
#> GSM182779 4 0.7612 0.25975 0.264 0.000 0.260 0.476
#> GSM182780 3 0.2546 0.70477 0.000 0.092 0.900 0.008
#> GSM182781 4 0.6949 0.12595 0.408 0.000 0.112 0.480
#> GSM182782 2 0.2385 0.88249 0.000 0.920 0.028 0.052
#> GSM182783 3 0.7198 0.31493 0.000 0.280 0.540 0.180
#> GSM182784 3 0.3534 0.69252 0.004 0.008 0.840 0.148
#> GSM182785 3 0.1635 0.73700 0.000 0.008 0.948 0.044
#> GSM182786 2 0.2385 0.88249 0.000 0.920 0.028 0.052
#> GSM182787 3 0.2737 0.70095 0.000 0.104 0.888 0.008
#> GSM182788 2 0.2385 0.88249 0.000 0.920 0.028 0.052
#> GSM182789 3 0.1356 0.73555 0.000 0.032 0.960 0.008
#> GSM182790 4 0.7142 0.31560 0.152 0.000 0.324 0.524
#> GSM182791 3 0.1824 0.73741 0.000 0.004 0.936 0.060
#> GSM182792 3 0.2831 0.72106 0.000 0.004 0.876 0.120
#> GSM182793 2 0.2469 0.90093 0.000 0.892 0.108 0.000
#> GSM182794 4 0.7128 0.32742 0.152 0.000 0.320 0.528
#> GSM182795 3 0.4941 0.66603 0.004 0.048 0.764 0.184
#> GSM182796 1 0.6901 0.00179 0.488 0.000 0.108 0.404
#> GSM182797 1 0.0000 0.54414 1.000 0.000 0.000 0.000
#> GSM182798 1 0.6822 -0.00110 0.488 0.000 0.100 0.412
#> GSM182799 3 0.7181 0.05800 0.000 0.336 0.512 0.152
#> GSM182800 1 0.6277 -0.12400 0.476 0.000 0.056 0.468
#> GSM182801 4 0.8427 0.22378 0.332 0.024 0.248 0.396
#> GSM182814 4 0.6395 -0.01184 0.464 0.000 0.064 0.472
#> GSM182815 2 0.5568 0.82968 0.000 0.728 0.152 0.120
#> GSM182816 1 0.7878 -0.00578 0.508 0.016 0.220 0.256
#> GSM182817 4 0.7297 0.33208 0.220 0.000 0.244 0.536
#> GSM182818 2 0.5664 0.83146 0.000 0.720 0.124 0.156
#> GSM182819 1 0.7878 -0.00578 0.508 0.016 0.220 0.256
#> GSM182820 1 0.0000 0.54414 1.000 0.000 0.000 0.000
#> GSM182821 3 0.0937 0.73779 0.000 0.012 0.976 0.012
#> GSM182822 3 0.5205 0.41671 0.008 0.012 0.672 0.308
#> GSM182823 1 0.0000 0.54414 1.000 0.000 0.000 0.000
#> GSM182824 1 0.2408 0.49641 0.896 0.000 0.000 0.104
#> GSM182825 4 0.6693 0.05681 0.424 0.000 0.088 0.488
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM182755 1 0.405 0.6495 0.644 0.000 0.000 0.000 0.356
#> GSM182756 3 0.763 0.5002 0.124 0.000 0.504 0.204 0.168
#> GSM182757 5 0.706 -0.1540 0.080 0.000 0.384 0.084 0.452
#> GSM182758 3 0.720 0.5438 0.100 0.000 0.556 0.196 0.148
#> GSM182759 3 0.655 0.5277 0.064 0.004 0.604 0.084 0.244
#> GSM182760 3 0.509 0.6485 0.056 0.000 0.748 0.060 0.136
#> GSM182761 3 0.178 0.6432 0.000 0.024 0.940 0.008 0.028
#> GSM182762 5 0.427 0.5731 0.180 0.000 0.024 0.024 0.772
#> GSM182763 3 0.518 0.6371 0.040 0.020 0.764 0.064 0.112
#> GSM182764 5 0.457 0.6524 0.092 0.000 0.084 0.036 0.788
#> GSM182765 5 0.447 0.6660 0.076 0.000 0.064 0.060 0.800
#> GSM182766 2 0.305 0.4143 0.000 0.852 0.120 0.028 0.000
#> GSM182767 3 0.312 0.6818 0.004 0.000 0.864 0.048 0.084
#> GSM182768 3 0.425 0.6518 0.012 0.036 0.824 0.068 0.060
#> GSM182769 3 0.810 0.4296 0.172 0.000 0.436 0.200 0.192
#> GSM182770 2 0.314 0.3826 0.000 0.832 0.016 0.152 0.000
#> GSM182771 5 0.376 0.6629 0.080 0.000 0.044 0.036 0.840
#> GSM182772 2 0.207 0.4288 0.000 0.896 0.104 0.000 0.000
#> GSM182773 3 0.839 0.3538 0.204 0.000 0.372 0.204 0.220
#> GSM182774 5 0.315 0.6758 0.072 0.000 0.020 0.036 0.872
#> GSM182775 1 0.844 -0.1293 0.372 0.004 0.180 0.180 0.264
#> GSM182776 5 0.315 0.6758 0.072 0.000 0.020 0.036 0.872
#> GSM182777 3 0.852 0.2685 0.228 0.000 0.316 0.200 0.256
#> GSM182802 2 0.311 0.3916 0.000 0.852 0.112 0.036 0.000
#> GSM182803 5 0.269 0.6154 0.128 0.000 0.004 0.004 0.864
#> GSM182804 2 0.567 -0.1197 0.000 0.632 0.176 0.192 0.000
#> GSM182805 2 0.355 0.3646 0.000 0.820 0.136 0.044 0.000
#> GSM182806 1 0.405 0.6495 0.644 0.000 0.000 0.000 0.356
#> GSM182807 1 0.405 0.6495 0.644 0.000 0.000 0.000 0.356
#> GSM182808 1 0.441 0.5642 0.556 0.000 0.000 0.004 0.440
#> GSM182809 3 0.208 0.6462 0.000 0.024 0.928 0.016 0.032
#> GSM182810 5 0.212 0.6946 0.032 0.000 0.036 0.008 0.924
#> GSM182811 5 0.220 0.6955 0.032 0.000 0.040 0.008 0.920
#> GSM182812 5 0.315 0.6720 0.052 0.000 0.044 0.028 0.876
#> GSM182813 1 0.405 0.6495 0.644 0.000 0.000 0.000 0.356
#> GSM182778 2 0.388 0.3529 0.000 0.708 0.004 0.288 0.000
#> GSM182779 5 0.783 0.3225 0.212 0.000 0.172 0.140 0.476
#> GSM182780 3 0.252 0.6162 0.000 0.060 0.900 0.036 0.004
#> GSM182781 5 0.708 0.0974 0.404 0.000 0.048 0.128 0.420
#> GSM182782 2 0.388 0.3529 0.000 0.708 0.004 0.288 0.000
#> GSM182783 3 0.823 -0.0139 0.176 0.260 0.444 0.100 0.020
#> GSM182784 3 0.318 0.6814 0.004 0.000 0.860 0.048 0.088
#> GSM182785 3 0.207 0.6755 0.000 0.000 0.912 0.012 0.076
#> GSM182786 2 0.388 0.3529 0.000 0.708 0.004 0.288 0.000
#> GSM182787 3 0.269 0.6095 0.000 0.076 0.888 0.032 0.004
#> GSM182788 2 0.388 0.3529 0.000 0.708 0.004 0.288 0.000
#> GSM182789 3 0.165 0.6504 0.000 0.020 0.944 0.004 0.032
#> GSM182790 3 0.851 0.2833 0.236 0.000 0.324 0.200 0.240
#> GSM182791 3 0.217 0.6754 0.012 0.000 0.912 0.004 0.072
#> GSM182792 3 0.305 0.6837 0.012 0.000 0.872 0.032 0.084
#> GSM182793 2 0.236 0.4244 0.000 0.888 0.104 0.008 0.000
#> GSM182794 3 0.852 0.2685 0.228 0.000 0.316 0.200 0.256
#> GSM182795 3 0.580 0.6650 0.084 0.040 0.732 0.044 0.100
#> GSM182796 5 0.356 0.6610 0.072 0.000 0.044 0.032 0.852
#> GSM182797 1 0.405 0.6495 0.644 0.000 0.000 0.000 0.356
#> GSM182798 5 0.356 0.6640 0.072 0.000 0.044 0.032 0.852
#> GSM182799 3 0.723 -0.1046 0.024 0.292 0.476 0.200 0.008
#> GSM182800 5 0.605 0.4342 0.172 0.000 0.064 0.096 0.668
#> GSM182801 1 0.731 0.2095 0.568 0.004 0.144 0.132 0.152
#> GSM182814 5 0.223 0.6603 0.092 0.000 0.004 0.004 0.900
#> GSM182815 2 0.540 -0.0979 0.000 0.664 0.152 0.184 0.000
#> GSM182816 1 0.463 0.4038 0.788 0.000 0.092 0.056 0.064
#> GSM182817 5 0.531 0.5499 0.060 0.000 0.172 0.048 0.720
#> GSM182818 4 0.553 0.0000 0.004 0.472 0.044 0.476 0.004
#> GSM182819 1 0.463 0.4038 0.788 0.000 0.092 0.056 0.064
#> GSM182820 1 0.405 0.6495 0.644 0.000 0.000 0.000 0.356
#> GSM182821 3 0.168 0.6619 0.000 0.004 0.940 0.012 0.044
#> GSM182822 3 0.454 0.4536 0.000 0.004 0.608 0.008 0.380
#> GSM182823 1 0.405 0.6495 0.644 0.000 0.000 0.000 0.356
#> GSM182824 1 0.441 0.5642 0.556 0.000 0.000 0.004 0.440
#> GSM182825 5 0.193 0.6842 0.052 0.000 0.016 0.004 0.928
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM182755 1 0.3647 0.72638 0.640 0.000 0.000 0.000 0.360 0.000
#> GSM182756 3 0.5644 -0.29509 0.016 0.000 0.464 0.000 0.096 0.424
#> GSM182757 3 0.6376 -0.21499 0.012 0.000 0.368 0.000 0.348 0.272
#> GSM182758 3 0.5112 -0.12224 0.000 0.000 0.516 0.000 0.084 0.400
#> GSM182759 3 0.5617 0.31856 0.008 0.004 0.612 0.004 0.164 0.208
#> GSM182760 3 0.4749 0.47108 0.040 0.000 0.720 0.000 0.068 0.172
#> GSM182761 3 0.1059 0.65815 0.000 0.016 0.964 0.004 0.016 0.000
#> GSM182762 5 0.5121 0.57284 0.172 0.000 0.016 0.000 0.668 0.144
#> GSM182763 3 0.4295 0.54565 0.008 0.016 0.776 0.004 0.068 0.128
#> GSM182764 5 0.5186 0.62925 0.080 0.000 0.064 0.000 0.692 0.164
#> GSM182765 5 0.5174 0.64913 0.076 0.000 0.044 0.000 0.672 0.208
#> GSM182766 2 0.3150 0.44609 0.000 0.828 0.120 0.052 0.000 0.000
#> GSM182767 3 0.3062 0.60418 0.000 0.000 0.836 0.000 0.052 0.112
#> GSM182768 3 0.4709 0.60591 0.032 0.036 0.784 0.024 0.036 0.088
#> GSM182769 6 0.6250 0.40712 0.044 0.000 0.396 0.000 0.120 0.440
#> GSM182770 2 0.3629 0.39240 0.000 0.712 0.012 0.276 0.000 0.000
#> GSM182771 5 0.4801 0.67039 0.084 0.000 0.048 0.000 0.728 0.140
#> GSM182772 2 0.2118 0.45814 0.000 0.888 0.104 0.008 0.000 0.000
#> GSM182773 6 0.6593 0.55187 0.076 0.000 0.332 0.000 0.128 0.464
#> GSM182774 5 0.2239 0.70278 0.020 0.000 0.008 0.000 0.900 0.072
#> GSM182775 6 0.7079 0.51296 0.312 0.000 0.092 0.004 0.168 0.424
#> GSM182776 5 0.2239 0.70278 0.020 0.000 0.008 0.000 0.900 0.072
#> GSM182777 6 0.6734 0.61628 0.084 0.000 0.280 0.000 0.156 0.480
#> GSM182802 2 0.3220 0.41220 0.000 0.832 0.108 0.056 0.000 0.004
#> GSM182803 5 0.2212 0.63668 0.112 0.000 0.000 0.000 0.880 0.008
#> GSM182804 2 0.5409 0.08866 0.000 0.612 0.176 0.204 0.000 0.008
#> GSM182805 2 0.3576 0.39715 0.000 0.800 0.136 0.060 0.000 0.004
#> GSM182806 1 0.3647 0.72638 0.640 0.000 0.000 0.000 0.360 0.000
#> GSM182807 1 0.3647 0.72638 0.640 0.000 0.000 0.000 0.360 0.000
#> GSM182808 1 0.4072 0.62953 0.544 0.000 0.000 0.000 0.448 0.008
#> GSM182809 3 0.1406 0.65908 0.000 0.016 0.952 0.004 0.020 0.008
#> GSM182810 5 0.1528 0.72460 0.016 0.000 0.028 0.000 0.944 0.012
#> GSM182811 5 0.1605 0.72548 0.016 0.000 0.032 0.000 0.940 0.012
#> GSM182812 5 0.3046 0.67648 0.032 0.000 0.032 0.000 0.860 0.076
#> GSM182813 1 0.3647 0.72638 0.640 0.000 0.000 0.000 0.360 0.000
#> GSM182778 2 0.3854 0.36050 0.000 0.536 0.000 0.464 0.000 0.000
#> GSM182779 6 0.6503 0.04922 0.064 0.000 0.144 0.000 0.300 0.492
#> GSM182780 3 0.1969 0.64369 0.000 0.052 0.920 0.020 0.004 0.004
#> GSM182781 6 0.6193 0.05281 0.232 0.000 0.012 0.000 0.296 0.460
#> GSM182782 2 0.3854 0.36050 0.000 0.536 0.000 0.464 0.000 0.000
#> GSM182783 3 0.7066 0.00627 0.020 0.260 0.424 0.028 0.004 0.264
#> GSM182784 3 0.3078 0.60370 0.000 0.000 0.836 0.000 0.056 0.108
#> GSM182785 3 0.1909 0.65985 0.000 0.000 0.920 0.004 0.052 0.024
#> GSM182786 2 0.3854 0.36050 0.000 0.536 0.000 0.464 0.000 0.000
#> GSM182787 3 0.2213 0.64094 0.000 0.068 0.904 0.020 0.004 0.004
#> GSM182788 2 0.3854 0.36050 0.000 0.536 0.000 0.464 0.000 0.000
#> GSM182789 3 0.0909 0.66160 0.000 0.012 0.968 0.000 0.020 0.000
#> GSM182790 6 0.6733 0.61167 0.088 0.000 0.284 0.000 0.148 0.480
#> GSM182791 3 0.2411 0.65854 0.024 0.000 0.900 0.000 0.044 0.032
#> GSM182792 3 0.3387 0.63308 0.024 0.000 0.836 0.000 0.052 0.088
#> GSM182793 2 0.1863 0.45534 0.000 0.896 0.104 0.000 0.000 0.000
#> GSM182794 6 0.6734 0.61628 0.084 0.000 0.280 0.000 0.156 0.480
#> GSM182795 3 0.4393 0.55718 0.000 0.036 0.748 0.000 0.052 0.164
#> GSM182796 5 0.4647 0.67275 0.084 0.000 0.048 0.000 0.744 0.124
#> GSM182797 1 0.3647 0.72638 0.640 0.000 0.000 0.000 0.360 0.000
#> GSM182798 5 0.4585 0.67570 0.084 0.000 0.044 0.000 0.748 0.124
#> GSM182799 3 0.7235 -0.04591 0.048 0.288 0.456 0.164 0.000 0.044
#> GSM182800 5 0.5457 0.32745 0.084 0.000 0.036 0.000 0.616 0.264
#> GSM182801 1 0.6316 -0.15633 0.540 0.000 0.060 0.016 0.080 0.304
#> GSM182814 5 0.1643 0.69180 0.068 0.000 0.000 0.000 0.924 0.008
#> GSM182815 2 0.5172 0.11258 0.000 0.644 0.148 0.200 0.000 0.008
#> GSM182816 1 0.3337 0.32131 0.824 0.000 0.004 0.000 0.064 0.108
#> GSM182817 5 0.5164 0.46325 0.008 0.000 0.172 0.000 0.648 0.172
#> GSM182818 4 0.5957 0.00000 0.008 0.264 0.016 0.560 0.000 0.152
#> GSM182819 1 0.3337 0.32131 0.824 0.000 0.004 0.000 0.064 0.108
#> GSM182820 1 0.3647 0.72638 0.640 0.000 0.000 0.000 0.360 0.000
#> GSM182821 3 0.0972 0.66300 0.000 0.000 0.964 0.000 0.028 0.008
#> GSM182822 3 0.3965 0.30351 0.000 0.000 0.604 0.000 0.388 0.008
#> GSM182823 1 0.3647 0.72638 0.640 0.000 0.000 0.000 0.360 0.000
#> GSM182824 1 0.4072 0.62953 0.544 0.000 0.000 0.000 0.448 0.008
#> GSM182825 5 0.1230 0.71539 0.028 0.000 0.008 0.000 0.956 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 stress(p) development.stage(p) k
#> CV:hclust 59 0.600 1.00000 2
#> CV:hclust 54 0.612 0.06124 3
#> CV:hclust 35 0.753 0.02587 4
#> CV:hclust 42 0.625 0.00244 5
#> CV:hclust 42 0.298 0.00503 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 18172 rows and 71 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.858 0.915 0.954 0.4764 0.501 0.501
#> 3 3 0.528 0.626 0.838 0.3173 0.631 0.402
#> 4 4 0.597 0.697 0.800 0.1675 0.839 0.587
#> 5 5 0.685 0.626 0.759 0.0683 0.908 0.663
#> 6 6 0.768 0.762 0.804 0.0458 0.895 0.556
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
#> GSM182755 1 0.000 0.999 1.000 0.000
#> GSM182756 1 0.118 0.982 0.984 0.016
#> GSM182757 1 0.000 0.999 1.000 0.000
#> GSM182758 2 0.886 0.673 0.304 0.696
#> GSM182759 2 0.278 0.869 0.048 0.952
#> GSM182760 1 0.118 0.982 0.984 0.016
#> GSM182761 2 0.000 0.889 0.000 1.000
#> GSM182762 1 0.000 0.999 1.000 0.000
#> GSM182763 2 0.430 0.848 0.088 0.912
#> GSM182764 1 0.000 0.999 1.000 0.000
#> GSM182765 1 0.000 0.999 1.000 0.000
#> GSM182766 2 0.000 0.889 0.000 1.000
#> GSM182767 2 0.971 0.507 0.400 0.600
#> GSM182768 2 0.886 0.673 0.304 0.696
#> GSM182769 1 0.000 0.999 1.000 0.000
#> GSM182770 2 0.000 0.889 0.000 1.000
#> GSM182771 1 0.000 0.999 1.000 0.000
#> GSM182772 2 0.000 0.889 0.000 1.000
#> GSM182773 1 0.118 0.982 0.984 0.016
#> GSM182774 1 0.000 0.999 1.000 0.000
#> GSM182775 1 0.000 0.999 1.000 0.000
#> GSM182776 1 0.000 0.999 1.000 0.000
#> GSM182777 1 0.000 0.999 1.000 0.000
#> GSM182802 2 0.000 0.889 0.000 1.000
#> GSM182803 1 0.000 0.999 1.000 0.000
#> GSM182804 2 0.000 0.889 0.000 1.000
#> GSM182805 2 0.000 0.889 0.000 1.000
#> GSM182806 1 0.000 0.999 1.000 0.000
#> GSM182807 1 0.000 0.999 1.000 0.000
#> GSM182808 1 0.000 0.999 1.000 0.000
#> GSM182809 2 0.000 0.889 0.000 1.000
#> GSM182810 1 0.000 0.999 1.000 0.000
#> GSM182811 1 0.000 0.999 1.000 0.000
#> GSM182812 1 0.000 0.999 1.000 0.000
#> GSM182813 1 0.000 0.999 1.000 0.000
#> GSM182778 2 0.000 0.889 0.000 1.000
#> GSM182779 1 0.000 0.999 1.000 0.000
#> GSM182780 2 0.000 0.889 0.000 1.000
#> GSM182781 1 0.000 0.999 1.000 0.000
#> GSM182782 2 0.000 0.889 0.000 1.000
#> GSM182783 2 0.000 0.889 0.000 1.000
#> GSM182784 2 0.971 0.507 0.400 0.600
#> GSM182785 2 0.909 0.644 0.324 0.676
#> GSM182786 2 0.000 0.889 0.000 1.000
#> GSM182787 2 0.000 0.889 0.000 1.000
#> GSM182788 2 0.000 0.889 0.000 1.000
#> GSM182789 2 0.204 0.877 0.032 0.968
#> GSM182790 1 0.000 0.999 1.000 0.000
#> GSM182791 2 0.886 0.673 0.304 0.696
#> GSM182792 2 0.961 0.540 0.384 0.616
#> GSM182793 2 0.000 0.889 0.000 1.000
#> GSM182794 1 0.000 0.999 1.000 0.000
#> GSM182795 2 0.886 0.673 0.304 0.696
#> GSM182796 1 0.000 0.999 1.000 0.000
#> GSM182797 1 0.000 0.999 1.000 0.000
#> GSM182798 1 0.000 0.999 1.000 0.000
#> GSM182799 2 0.000 0.889 0.000 1.000
#> GSM182800 1 0.000 0.999 1.000 0.000
#> GSM182801 1 0.000 0.999 1.000 0.000
#> GSM182814 1 0.000 0.999 1.000 0.000
#> GSM182815 2 0.000 0.889 0.000 1.000
#> GSM182816 1 0.000 0.999 1.000 0.000
#> GSM182817 1 0.000 0.999 1.000 0.000
#> GSM182818 2 0.000 0.889 0.000 1.000
#> GSM182819 1 0.000 0.999 1.000 0.000
#> GSM182820 1 0.000 0.999 1.000 0.000
#> GSM182821 2 0.886 0.673 0.304 0.696
#> GSM182822 1 0.000 0.999 1.000 0.000
#> GSM182823 1 0.000 0.999 1.000 0.000
#> GSM182824 1 0.000 0.999 1.000 0.000
#> GSM182825 1 0.000 0.999 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM182755 1 0.0237 0.7863 0.996 0.000 0.004
#> GSM182756 3 0.1711 0.7052 0.032 0.008 0.960
#> GSM182757 3 0.2356 0.6768 0.072 0.000 0.928
#> GSM182758 3 0.2537 0.7317 0.000 0.080 0.920
#> GSM182759 3 0.2625 0.7313 0.000 0.084 0.916
#> GSM182760 3 0.1711 0.7052 0.032 0.008 0.960
#> GSM182761 3 0.3482 0.7087 0.000 0.128 0.872
#> GSM182762 1 0.2448 0.7695 0.924 0.000 0.076
#> GSM182763 3 0.2711 0.7300 0.000 0.088 0.912
#> GSM182764 3 0.6026 0.2093 0.376 0.000 0.624
#> GSM182765 3 0.6305 -0.1389 0.484 0.000 0.516
#> GSM182766 2 0.1411 0.9963 0.000 0.964 0.036
#> GSM182767 3 0.2625 0.7317 0.000 0.084 0.916
#> GSM182768 3 0.2625 0.7317 0.000 0.084 0.916
#> GSM182769 3 0.1860 0.6925 0.052 0.000 0.948
#> GSM182770 2 0.1411 0.9963 0.000 0.964 0.036
#> GSM182771 1 0.6299 0.2045 0.524 0.000 0.476
#> GSM182772 2 0.1411 0.9963 0.000 0.964 0.036
#> GSM182773 3 0.1711 0.7052 0.032 0.008 0.960
#> GSM182774 3 0.6295 -0.1238 0.472 0.000 0.528
#> GSM182775 3 0.5988 0.2734 0.368 0.000 0.632
#> GSM182776 3 0.6274 -0.0729 0.456 0.000 0.544
#> GSM182777 1 0.5621 0.5639 0.692 0.000 0.308
#> GSM182802 2 0.1289 0.9947 0.000 0.968 0.032
#> GSM182803 1 0.1529 0.7842 0.960 0.000 0.040
#> GSM182804 2 0.1289 0.9947 0.000 0.968 0.032
#> GSM182805 2 0.1289 0.9947 0.000 0.968 0.032
#> GSM182806 1 0.0237 0.7863 0.996 0.000 0.004
#> GSM182807 1 0.0237 0.7863 0.996 0.000 0.004
#> GSM182808 1 0.1163 0.7848 0.972 0.000 0.028
#> GSM182809 3 0.4974 0.5917 0.000 0.236 0.764
#> GSM182810 3 0.6483 -0.0368 0.452 0.004 0.544
#> GSM182811 1 0.6520 0.1749 0.508 0.004 0.488
#> GSM182812 1 0.6235 0.2878 0.564 0.000 0.436
#> GSM182813 1 0.0237 0.7863 0.996 0.000 0.004
#> GSM182778 2 0.1411 0.9963 0.000 0.964 0.036
#> GSM182779 3 0.6274 -0.0449 0.456 0.000 0.544
#> GSM182780 3 0.5733 0.4258 0.000 0.324 0.676
#> GSM182781 1 0.2261 0.7718 0.932 0.000 0.068
#> GSM182782 2 0.1411 0.9963 0.000 0.964 0.036
#> GSM182783 3 0.5497 0.4867 0.000 0.292 0.708
#> GSM182784 3 0.2625 0.7317 0.000 0.084 0.916
#> GSM182785 3 0.2625 0.7317 0.000 0.084 0.916
#> GSM182786 2 0.1411 0.9963 0.000 0.964 0.036
#> GSM182787 2 0.1411 0.9963 0.000 0.964 0.036
#> GSM182788 2 0.1411 0.9963 0.000 0.964 0.036
#> GSM182789 3 0.2878 0.7264 0.000 0.096 0.904
#> GSM182790 3 0.5291 0.4689 0.268 0.000 0.732
#> GSM182791 3 0.2625 0.7317 0.000 0.084 0.916
#> GSM182792 3 0.1753 0.7261 0.000 0.048 0.952
#> GSM182793 2 0.1411 0.9963 0.000 0.964 0.036
#> GSM182794 3 0.4702 0.5481 0.212 0.000 0.788
#> GSM182795 3 0.2448 0.7314 0.000 0.076 0.924
#> GSM182796 1 0.6299 0.2045 0.524 0.000 0.476
#> GSM182797 1 0.0237 0.7863 0.996 0.000 0.004
#> GSM182798 1 0.6274 0.2503 0.544 0.000 0.456
#> GSM182799 3 0.6079 0.2710 0.000 0.388 0.612
#> GSM182800 3 0.6299 -0.1350 0.476 0.000 0.524
#> GSM182801 1 0.4842 0.6581 0.776 0.000 0.224
#> GSM182814 1 0.1411 0.7845 0.964 0.000 0.036
#> GSM182815 2 0.1289 0.9947 0.000 0.968 0.032
#> GSM182816 1 0.4099 0.7134 0.852 0.008 0.140
#> GSM182817 3 0.6483 -0.0945 0.452 0.004 0.544
#> GSM182818 2 0.0661 0.9707 0.004 0.988 0.008
#> GSM182819 1 0.2384 0.7784 0.936 0.008 0.056
#> GSM182820 1 0.0237 0.7863 0.996 0.000 0.004
#> GSM182821 3 0.2711 0.7316 0.000 0.088 0.912
#> GSM182822 3 0.1765 0.6999 0.040 0.004 0.956
#> GSM182823 1 0.0237 0.7863 0.996 0.000 0.004
#> GSM182824 1 0.1289 0.7840 0.968 0.000 0.032
#> GSM182825 1 0.6267 0.2429 0.548 0.000 0.452
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM182755 1 0.0188 0.7643 0.996 0.000 0.000 0.004
#> GSM182756 3 0.2334 0.7609 0.004 0.000 0.908 0.088
#> GSM182757 4 0.4687 0.5168 0.004 0.004 0.288 0.704
#> GSM182758 3 0.0524 0.7988 0.000 0.008 0.988 0.004
#> GSM182759 3 0.3810 0.7201 0.000 0.008 0.804 0.188
#> GSM182760 3 0.2944 0.7322 0.004 0.000 0.868 0.128
#> GSM182761 3 0.3279 0.7844 0.000 0.032 0.872 0.096
#> GSM182762 1 0.5212 0.1850 0.588 0.004 0.004 0.404
#> GSM182763 3 0.2611 0.7900 0.000 0.008 0.896 0.096
#> GSM182764 4 0.6103 0.7048 0.192 0.004 0.116 0.688
#> GSM182765 4 0.5961 0.7069 0.220 0.004 0.088 0.688
#> GSM182766 2 0.1059 0.9681 0.000 0.972 0.012 0.016
#> GSM182767 3 0.0927 0.7950 0.000 0.008 0.976 0.016
#> GSM182768 3 0.0804 0.7989 0.000 0.008 0.980 0.012
#> GSM182769 3 0.4720 0.4813 0.004 0.000 0.672 0.324
#> GSM182770 2 0.1059 0.9693 0.000 0.972 0.012 0.016
#> GSM182771 4 0.5604 0.6989 0.232 0.004 0.060 0.704
#> GSM182772 2 0.0937 0.9695 0.000 0.976 0.012 0.012
#> GSM182773 3 0.3306 0.7147 0.004 0.000 0.840 0.156
#> GSM182774 4 0.4893 0.7170 0.168 0.000 0.064 0.768
#> GSM182775 3 0.7078 -0.0816 0.124 0.000 0.456 0.420
#> GSM182776 4 0.6703 0.5635 0.156 0.000 0.232 0.612
#> GSM182777 4 0.7563 0.3642 0.236 0.000 0.280 0.484
#> GSM182802 2 0.1488 0.9668 0.000 0.956 0.012 0.032
#> GSM182803 1 0.4955 0.3596 0.648 0.000 0.008 0.344
#> GSM182804 2 0.1677 0.9646 0.000 0.948 0.012 0.040
#> GSM182805 2 0.1388 0.9675 0.000 0.960 0.012 0.028
#> GSM182806 1 0.0188 0.7643 0.996 0.000 0.000 0.004
#> GSM182807 1 0.0000 0.7656 1.000 0.000 0.000 0.000
#> GSM182808 1 0.1867 0.7391 0.928 0.000 0.000 0.072
#> GSM182809 3 0.4727 0.7414 0.000 0.100 0.792 0.108
#> GSM182810 4 0.6278 0.6474 0.228 0.000 0.120 0.652
#> GSM182811 4 0.5590 0.6734 0.244 0.000 0.064 0.692
#> GSM182812 4 0.6200 0.5539 0.356 0.000 0.064 0.580
#> GSM182813 1 0.0000 0.7656 1.000 0.000 0.000 0.000
#> GSM182778 2 0.1767 0.9636 0.000 0.944 0.012 0.044
#> GSM182779 4 0.6529 0.6885 0.208 0.004 0.140 0.648
#> GSM182780 3 0.3787 0.7504 0.000 0.124 0.840 0.036
#> GSM182781 1 0.4950 0.2663 0.620 0.000 0.004 0.376
#> GSM182782 2 0.1767 0.9636 0.000 0.944 0.012 0.044
#> GSM182783 3 0.3271 0.7523 0.000 0.132 0.856 0.012
#> GSM182784 3 0.0804 0.7964 0.000 0.008 0.980 0.012
#> GSM182785 3 0.2546 0.7921 0.000 0.008 0.900 0.092
#> GSM182786 2 0.1767 0.9636 0.000 0.944 0.012 0.044
#> GSM182787 2 0.2635 0.9182 0.000 0.904 0.076 0.020
#> GSM182788 2 0.1767 0.9636 0.000 0.944 0.012 0.044
#> GSM182789 3 0.2480 0.7938 0.000 0.008 0.904 0.088
#> GSM182790 3 0.6575 0.0877 0.080 0.000 0.508 0.412
#> GSM182791 3 0.2198 0.7966 0.000 0.008 0.920 0.072
#> GSM182792 3 0.1635 0.8033 0.000 0.008 0.948 0.044
#> GSM182793 2 0.1584 0.9675 0.000 0.952 0.012 0.036
#> GSM182794 3 0.6309 0.3342 0.076 0.000 0.588 0.336
#> GSM182795 3 0.1151 0.8029 0.000 0.008 0.968 0.024
#> GSM182796 4 0.5642 0.7011 0.228 0.004 0.064 0.704
#> GSM182797 1 0.0188 0.7643 0.996 0.000 0.000 0.004
#> GSM182798 4 0.5626 0.6898 0.244 0.004 0.056 0.696
#> GSM182799 3 0.4197 0.7165 0.000 0.156 0.808 0.036
#> GSM182800 4 0.6423 0.6115 0.196 0.000 0.156 0.648
#> GSM182801 1 0.7313 0.1593 0.508 0.000 0.176 0.316
#> GSM182814 1 0.5040 0.2951 0.628 0.000 0.008 0.364
#> GSM182815 2 0.1584 0.9659 0.000 0.952 0.012 0.036
#> GSM182816 1 0.5109 0.6264 0.736 0.000 0.052 0.212
#> GSM182817 4 0.4513 0.7242 0.120 0.000 0.076 0.804
#> GSM182818 2 0.1824 0.9518 0.000 0.936 0.004 0.060
#> GSM182819 1 0.4599 0.6495 0.760 0.000 0.028 0.212
#> GSM182820 1 0.0000 0.7656 1.000 0.000 0.000 0.000
#> GSM182821 3 0.2198 0.7981 0.000 0.008 0.920 0.072
#> GSM182822 3 0.4977 0.2536 0.000 0.000 0.540 0.460
#> GSM182823 1 0.0188 0.7644 0.996 0.000 0.000 0.004
#> GSM182824 1 0.2412 0.7322 0.908 0.000 0.008 0.084
#> GSM182825 4 0.5917 0.5746 0.320 0.000 0.056 0.624
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM182755 1 0.0290 0.7457 0.992 0.000 0.000 0.000 0.008
#> GSM182756 3 0.4157 0.4569 0.000 0.000 0.716 0.264 0.020
#> GSM182757 5 0.3612 0.5021 0.004 0.000 0.100 0.064 0.832
#> GSM182758 3 0.0000 0.8507 0.000 0.000 1.000 0.000 0.000
#> GSM182759 3 0.3160 0.7216 0.000 0.000 0.808 0.004 0.188
#> GSM182760 3 0.4527 0.4079 0.000 0.000 0.692 0.272 0.036
#> GSM182761 3 0.2629 0.8242 0.000 0.032 0.896 0.008 0.064
#> GSM182762 5 0.5754 0.2352 0.380 0.000 0.004 0.080 0.536
#> GSM182763 3 0.1638 0.8395 0.000 0.000 0.932 0.004 0.064
#> GSM182764 5 0.3704 0.5739 0.076 0.000 0.044 0.036 0.844
#> GSM182765 5 0.3765 0.5751 0.080 0.000 0.040 0.040 0.840
#> GSM182766 2 0.1124 0.8863 0.000 0.960 0.000 0.036 0.004
#> GSM182767 3 0.0963 0.8340 0.000 0.000 0.964 0.036 0.000
#> GSM182768 3 0.0703 0.8468 0.000 0.000 0.976 0.024 0.000
#> GSM182769 4 0.5099 0.6038 0.000 0.000 0.336 0.612 0.052
#> GSM182770 2 0.0566 0.8844 0.000 0.984 0.000 0.004 0.012
#> GSM182771 5 0.2575 0.5885 0.100 0.000 0.012 0.004 0.884
#> GSM182772 2 0.0404 0.8849 0.000 0.988 0.000 0.000 0.012
#> GSM182773 3 0.4958 -0.0114 0.000 0.000 0.568 0.400 0.032
#> GSM182774 5 0.5353 0.3164 0.036 0.000 0.012 0.384 0.568
#> GSM182775 4 0.5910 0.6446 0.032 0.000 0.192 0.660 0.116
#> GSM182776 4 0.5940 0.5480 0.032 0.000 0.108 0.652 0.208
#> GSM182777 4 0.6616 0.6027 0.052 0.000 0.148 0.600 0.200
#> GSM182802 2 0.3242 0.8750 0.000 0.844 0.000 0.116 0.040
#> GSM182803 1 0.6788 -0.0524 0.372 0.000 0.000 0.344 0.284
#> GSM182804 2 0.3880 0.8618 0.000 0.800 0.004 0.152 0.044
#> GSM182805 2 0.3339 0.8732 0.000 0.836 0.000 0.124 0.040
#> GSM182806 1 0.0290 0.7457 0.992 0.000 0.000 0.000 0.008
#> GSM182807 1 0.0162 0.7464 0.996 0.000 0.000 0.000 0.004
#> GSM182808 1 0.1872 0.7222 0.928 0.000 0.000 0.052 0.020
#> GSM182809 3 0.4271 0.7474 0.000 0.064 0.808 0.092 0.036
#> GSM182810 5 0.6675 0.1912 0.084 0.000 0.048 0.392 0.476
#> GSM182811 5 0.6130 0.3407 0.080 0.000 0.024 0.344 0.552
#> GSM182812 5 0.6450 0.3536 0.172 0.000 0.008 0.292 0.528
#> GSM182813 1 0.0162 0.7464 0.996 0.000 0.000 0.000 0.004
#> GSM182778 2 0.2351 0.8676 0.000 0.896 0.000 0.088 0.016
#> GSM182779 5 0.5874 0.4271 0.076 0.000 0.092 0.140 0.692
#> GSM182780 3 0.2409 0.8262 0.000 0.056 0.908 0.028 0.008
#> GSM182781 5 0.6431 0.1244 0.396 0.000 0.004 0.152 0.448
#> GSM182782 2 0.2351 0.8676 0.000 0.896 0.000 0.088 0.016
#> GSM182783 3 0.2576 0.8242 0.000 0.056 0.900 0.036 0.008
#> GSM182784 3 0.0510 0.8456 0.000 0.000 0.984 0.016 0.000
#> GSM182785 3 0.1478 0.8406 0.000 0.000 0.936 0.000 0.064
#> GSM182786 2 0.2351 0.8676 0.000 0.896 0.000 0.088 0.016
#> GSM182787 2 0.4479 0.6445 0.000 0.720 0.240 0.036 0.004
#> GSM182788 2 0.2351 0.8676 0.000 0.896 0.000 0.088 0.016
#> GSM182789 3 0.1331 0.8498 0.000 0.000 0.952 0.008 0.040
#> GSM182790 4 0.6932 0.5471 0.020 0.000 0.344 0.452 0.184
#> GSM182791 3 0.1041 0.8517 0.000 0.000 0.964 0.004 0.032
#> GSM182792 3 0.0510 0.8463 0.000 0.000 0.984 0.016 0.000
#> GSM182793 2 0.3012 0.8770 0.000 0.860 0.000 0.104 0.036
#> GSM182794 4 0.6988 0.4715 0.024 0.000 0.392 0.412 0.172
#> GSM182795 3 0.0000 0.8507 0.000 0.000 1.000 0.000 0.000
#> GSM182796 5 0.2735 0.5848 0.084 0.000 0.036 0.000 0.880
#> GSM182797 1 0.0290 0.7457 0.992 0.000 0.000 0.000 0.008
#> GSM182798 5 0.2411 0.5873 0.108 0.000 0.008 0.000 0.884
#> GSM182799 3 0.3410 0.7971 0.000 0.064 0.860 0.052 0.024
#> GSM182800 4 0.6338 0.4320 0.044 0.000 0.088 0.588 0.280
#> GSM182801 4 0.6342 0.5226 0.188 0.000 0.096 0.640 0.076
#> GSM182814 1 0.6825 -0.1620 0.340 0.000 0.000 0.328 0.332
#> GSM182815 2 0.3608 0.8663 0.000 0.812 0.000 0.148 0.040
#> GSM182816 1 0.5511 0.3667 0.544 0.000 0.024 0.404 0.028
#> GSM182817 5 0.5190 0.3763 0.020 0.000 0.024 0.344 0.612
#> GSM182818 2 0.4393 0.8423 0.000 0.756 0.000 0.168 0.076
#> GSM182819 1 0.5155 0.4006 0.560 0.000 0.008 0.404 0.028
#> GSM182820 1 0.0290 0.7457 0.992 0.000 0.000 0.000 0.008
#> GSM182821 3 0.0955 0.8521 0.000 0.000 0.968 0.004 0.028
#> GSM182822 4 0.6775 0.1961 0.000 0.000 0.284 0.388 0.328
#> GSM182823 1 0.0162 0.7464 0.996 0.000 0.000 0.000 0.004
#> GSM182824 1 0.4485 0.5466 0.680 0.000 0.000 0.292 0.028
#> GSM182825 5 0.6561 0.2186 0.104 0.000 0.028 0.392 0.476
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM182755 1 0.0000 0.981 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM182756 6 0.4410 0.215 0.000 0.000 0.472 0.008 0.012 0.508
#> GSM182757 5 0.1649 0.826 0.000 0.000 0.032 0.000 0.932 0.036
#> GSM182758 3 0.1219 0.891 0.000 0.000 0.948 0.000 0.004 0.048
#> GSM182759 3 0.2871 0.737 0.000 0.000 0.804 0.004 0.192 0.000
#> GSM182760 6 0.4524 0.252 0.000 0.000 0.452 0.004 0.024 0.520
#> GSM182761 3 0.1167 0.895 0.000 0.012 0.960 0.008 0.020 0.000
#> GSM182762 5 0.3909 0.691 0.244 0.000 0.000 0.000 0.720 0.036
#> GSM182763 3 0.0692 0.901 0.000 0.000 0.976 0.004 0.020 0.000
#> GSM182764 5 0.1726 0.858 0.044 0.000 0.012 0.000 0.932 0.012
#> GSM182765 5 0.1718 0.858 0.044 0.000 0.008 0.000 0.932 0.016
#> GSM182766 2 0.1837 0.896 0.000 0.932 0.020 0.032 0.004 0.012
#> GSM182767 3 0.1753 0.861 0.000 0.000 0.912 0.000 0.004 0.084
#> GSM182768 3 0.1749 0.895 0.000 0.000 0.932 0.024 0.008 0.036
#> GSM182769 6 0.4483 0.627 0.000 0.000 0.104 0.152 0.012 0.732
#> GSM182770 2 0.0862 0.894 0.000 0.972 0.000 0.008 0.004 0.016
#> GSM182771 5 0.1789 0.849 0.044 0.000 0.000 0.032 0.924 0.000
#> GSM182772 2 0.0862 0.894 0.000 0.972 0.000 0.008 0.004 0.016
#> GSM182773 6 0.3714 0.606 0.000 0.000 0.264 0.008 0.008 0.720
#> GSM182774 4 0.5133 0.755 0.000 0.000 0.000 0.592 0.292 0.116
#> GSM182775 6 0.4377 0.599 0.008 0.000 0.036 0.180 0.028 0.748
#> GSM182776 6 0.5048 0.422 0.000 0.000 0.024 0.308 0.052 0.616
#> GSM182777 6 0.4646 0.600 0.008 0.000 0.036 0.172 0.048 0.736
#> GSM182802 2 0.2806 0.885 0.000 0.884 0.012 0.048 0.016 0.040
#> GSM182803 4 0.5551 0.683 0.140 0.000 0.000 0.668 0.100 0.092
#> GSM182804 2 0.4159 0.853 0.000 0.804 0.028 0.084 0.028 0.056
#> GSM182805 2 0.2874 0.884 0.000 0.880 0.012 0.048 0.016 0.044
#> GSM182806 1 0.0000 0.981 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM182807 1 0.0000 0.981 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM182808 1 0.2586 0.861 0.868 0.000 0.000 0.100 0.000 0.032
#> GSM182809 3 0.3897 0.799 0.000 0.032 0.824 0.068 0.028 0.048
#> GSM182810 4 0.4755 0.811 0.016 0.000 0.000 0.680 0.236 0.068
#> GSM182811 4 0.3903 0.783 0.012 0.000 0.000 0.680 0.304 0.004
#> GSM182812 4 0.4271 0.790 0.028 0.000 0.000 0.672 0.292 0.008
#> GSM182813 1 0.0000 0.981 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM182778 2 0.3256 0.865 0.000 0.844 0.008 0.104 0.016 0.028
#> GSM182779 5 0.3212 0.820 0.044 0.000 0.028 0.004 0.856 0.068
#> GSM182780 3 0.1570 0.892 0.000 0.016 0.944 0.028 0.008 0.004
#> GSM182781 5 0.6123 0.502 0.256 0.000 0.000 0.044 0.552 0.148
#> GSM182782 2 0.3165 0.865 0.000 0.848 0.008 0.104 0.012 0.028
#> GSM182783 3 0.2232 0.891 0.000 0.016 0.916 0.028 0.012 0.028
#> GSM182784 3 0.1732 0.871 0.000 0.000 0.920 0.004 0.004 0.072
#> GSM182785 3 0.0632 0.902 0.000 0.000 0.976 0.000 0.024 0.000
#> GSM182786 2 0.3165 0.865 0.000 0.848 0.008 0.104 0.012 0.028
#> GSM182787 3 0.4903 0.228 0.000 0.396 0.556 0.032 0.012 0.004
#> GSM182788 2 0.3165 0.865 0.000 0.848 0.008 0.104 0.012 0.028
#> GSM182789 3 0.0653 0.903 0.000 0.000 0.980 0.004 0.012 0.004
#> GSM182790 6 0.4776 0.636 0.008 0.000 0.172 0.044 0.048 0.728
#> GSM182791 3 0.0717 0.903 0.000 0.000 0.976 0.000 0.008 0.016
#> GSM182792 3 0.0858 0.900 0.000 0.000 0.968 0.000 0.004 0.028
#> GSM182793 2 0.1983 0.893 0.000 0.924 0.008 0.012 0.012 0.044
#> GSM182794 6 0.4846 0.633 0.008 0.000 0.184 0.032 0.060 0.716
#> GSM182795 3 0.0713 0.901 0.000 0.000 0.972 0.000 0.000 0.028
#> GSM182796 5 0.1857 0.850 0.044 0.000 0.004 0.028 0.924 0.000
#> GSM182797 1 0.0000 0.981 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM182798 5 0.1789 0.849 0.044 0.000 0.000 0.032 0.924 0.000
#> GSM182799 3 0.2478 0.879 0.000 0.012 0.904 0.032 0.024 0.028
#> GSM182800 6 0.5860 0.227 0.004 0.000 0.016 0.328 0.124 0.528
#> GSM182801 6 0.4712 0.584 0.036 0.000 0.028 0.200 0.016 0.720
#> GSM182814 4 0.5361 0.763 0.120 0.000 0.000 0.672 0.160 0.048
#> GSM182815 2 0.3713 0.864 0.000 0.828 0.012 0.080 0.028 0.052
#> GSM182816 6 0.6406 0.125 0.336 0.000 0.004 0.236 0.012 0.412
#> GSM182817 4 0.3636 0.769 0.000 0.000 0.000 0.676 0.320 0.004
#> GSM182818 2 0.4809 0.823 0.000 0.740 0.012 0.108 0.028 0.112
#> GSM182819 6 0.6386 0.096 0.356 0.000 0.004 0.224 0.012 0.404
#> GSM182820 1 0.0000 0.981 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM182821 3 0.0881 0.904 0.000 0.000 0.972 0.008 0.008 0.012
#> GSM182822 4 0.5646 0.710 0.000 0.000 0.084 0.652 0.168 0.096
#> GSM182823 1 0.0000 0.981 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM182824 4 0.5037 0.282 0.380 0.000 0.000 0.540 0.000 0.080
#> GSM182825 4 0.4912 0.813 0.024 0.000 0.000 0.672 0.236 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 stress(p) development.stage(p) k
#> CV:kmeans 71 0.394 0.131845 2
#> CV:kmeans 52 0.679 0.005783 3
#> CV:kmeans 60 0.807 0.001074 4
#> CV:kmeans 52 0.688 0.000865 5
#> CV:kmeans 63 0.918 0.000012 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 18172 rows and 71 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.970 0.927 0.970 0.5039 0.501 0.501
#> 3 3 0.660 0.731 0.808 0.2873 0.788 0.597
#> 4 4 0.762 0.724 0.880 0.1239 0.822 0.554
#> 5 5 0.682 0.598 0.784 0.0635 0.906 0.697
#> 6 6 0.674 0.576 0.749 0.0404 0.950 0.798
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM182755 1 0.0000 0.947 1.000 0.000
#> GSM182756 1 0.9795 0.332 0.584 0.416
#> GSM182757 1 0.0000 0.947 1.000 0.000
#> GSM182758 2 0.0000 0.995 0.000 1.000
#> GSM182759 2 0.0000 0.995 0.000 1.000
#> GSM182760 1 0.9710 0.373 0.600 0.400
#> GSM182761 2 0.0000 0.995 0.000 1.000
#> GSM182762 1 0.0000 0.947 1.000 0.000
#> GSM182763 2 0.0000 0.995 0.000 1.000
#> GSM182764 1 0.0000 0.947 1.000 0.000
#> GSM182765 1 0.0000 0.947 1.000 0.000
#> GSM182766 2 0.0000 0.995 0.000 1.000
#> GSM182767 2 0.3733 0.919 0.072 0.928
#> GSM182768 2 0.0000 0.995 0.000 1.000
#> GSM182769 1 0.0000 0.947 1.000 0.000
#> GSM182770 2 0.0000 0.995 0.000 1.000
#> GSM182771 1 0.0376 0.944 0.996 0.004
#> GSM182772 2 0.0000 0.995 0.000 1.000
#> GSM182773 1 0.9866 0.287 0.568 0.432
#> GSM182774 1 0.0000 0.947 1.000 0.000
#> GSM182775 1 0.0000 0.947 1.000 0.000
#> GSM182776 1 0.0000 0.947 1.000 0.000
#> GSM182777 1 0.0000 0.947 1.000 0.000
#> GSM182802 2 0.0000 0.995 0.000 1.000
#> GSM182803 1 0.0000 0.947 1.000 0.000
#> GSM182804 2 0.0000 0.995 0.000 1.000
#> GSM182805 2 0.0000 0.995 0.000 1.000
#> GSM182806 1 0.0000 0.947 1.000 0.000
#> GSM182807 1 0.0000 0.947 1.000 0.000
#> GSM182808 1 0.0000 0.947 1.000 0.000
#> GSM182809 2 0.0000 0.995 0.000 1.000
#> GSM182810 1 0.0000 0.947 1.000 0.000
#> GSM182811 1 0.4161 0.879 0.916 0.084
#> GSM182812 1 0.3879 0.886 0.924 0.076
#> GSM182813 1 0.0000 0.947 1.000 0.000
#> GSM182778 2 0.0000 0.995 0.000 1.000
#> GSM182779 1 0.1843 0.927 0.972 0.028
#> GSM182780 2 0.0000 0.995 0.000 1.000
#> GSM182781 1 0.0000 0.947 1.000 0.000
#> GSM182782 2 0.0000 0.995 0.000 1.000
#> GSM182783 2 0.0000 0.995 0.000 1.000
#> GSM182784 2 0.3879 0.914 0.076 0.924
#> GSM182785 2 0.0000 0.995 0.000 1.000
#> GSM182786 2 0.0000 0.995 0.000 1.000
#> GSM182787 2 0.0000 0.995 0.000 1.000
#> GSM182788 2 0.0000 0.995 0.000 1.000
#> GSM182789 2 0.0000 0.995 0.000 1.000
#> GSM182790 1 0.0000 0.947 1.000 0.000
#> GSM182791 2 0.0000 0.995 0.000 1.000
#> GSM182792 2 0.0000 0.995 0.000 1.000
#> GSM182793 2 0.0000 0.995 0.000 1.000
#> GSM182794 1 0.0000 0.947 1.000 0.000
#> GSM182795 2 0.0000 0.995 0.000 1.000
#> GSM182796 1 0.6343 0.797 0.840 0.160
#> GSM182797 1 0.0000 0.947 1.000 0.000
#> GSM182798 1 0.0000 0.947 1.000 0.000
#> GSM182799 2 0.0000 0.995 0.000 1.000
#> GSM182800 1 0.0000 0.947 1.000 0.000
#> GSM182801 1 0.0000 0.947 1.000 0.000
#> GSM182814 1 0.0000 0.947 1.000 0.000
#> GSM182815 2 0.0000 0.995 0.000 1.000
#> GSM182816 1 0.0000 0.947 1.000 0.000
#> GSM182817 1 0.0000 0.947 1.000 0.000
#> GSM182818 2 0.0000 0.995 0.000 1.000
#> GSM182819 1 0.0000 0.947 1.000 0.000
#> GSM182820 1 0.0000 0.947 1.000 0.000
#> GSM182821 2 0.0000 0.995 0.000 1.000
#> GSM182822 1 0.9775 0.339 0.588 0.412
#> GSM182823 1 0.0000 0.947 1.000 0.000
#> GSM182824 1 0.0000 0.947 1.000 0.000
#> GSM182825 1 0.0000 0.947 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM182755 1 0.5465 0.782 0.712 0.000 0.288
#> GSM182756 3 0.0237 0.689 0.000 0.004 0.996
#> GSM182757 1 0.6026 0.249 0.624 0.000 0.376
#> GSM182758 3 0.5859 0.358 0.000 0.344 0.656
#> GSM182759 2 0.3030 0.868 0.092 0.904 0.004
#> GSM182760 3 0.0237 0.689 0.000 0.004 0.996
#> GSM182761 2 0.0000 0.956 0.000 1.000 0.000
#> GSM182762 1 0.5785 0.764 0.668 0.000 0.332
#> GSM182763 2 0.0000 0.956 0.000 1.000 0.000
#> GSM182764 1 0.2796 0.698 0.908 0.000 0.092
#> GSM182765 1 0.2796 0.698 0.908 0.000 0.092
#> GSM182766 2 0.0000 0.956 0.000 1.000 0.000
#> GSM182767 3 0.3816 0.662 0.000 0.148 0.852
#> GSM182768 3 0.5882 0.351 0.000 0.348 0.652
#> GSM182769 3 0.2165 0.679 0.064 0.000 0.936
#> GSM182770 2 0.0000 0.956 0.000 1.000 0.000
#> GSM182771 1 0.2066 0.683 0.940 0.000 0.060
#> GSM182772 2 0.0000 0.956 0.000 1.000 0.000
#> GSM182773 3 0.2280 0.685 0.052 0.008 0.940
#> GSM182774 1 0.3340 0.757 0.880 0.000 0.120
#> GSM182775 3 0.2959 0.654 0.100 0.000 0.900
#> GSM182776 3 0.6299 -0.300 0.476 0.000 0.524
#> GSM182777 3 0.5706 0.255 0.320 0.000 0.680
#> GSM182802 2 0.0000 0.956 0.000 1.000 0.000
#> GSM182803 1 0.5431 0.783 0.716 0.000 0.284
#> GSM182804 2 0.0000 0.956 0.000 1.000 0.000
#> GSM182805 2 0.0000 0.956 0.000 1.000 0.000
#> GSM182806 1 0.5431 0.783 0.716 0.000 0.284
#> GSM182807 1 0.5431 0.783 0.716 0.000 0.284
#> GSM182808 1 0.5431 0.783 0.716 0.000 0.284
#> GSM182809 2 0.0000 0.956 0.000 1.000 0.000
#> GSM182810 1 0.4702 0.778 0.788 0.000 0.212
#> GSM182811 1 0.0892 0.696 0.980 0.020 0.000
#> GSM182812 1 0.0000 0.708 1.000 0.000 0.000
#> GSM182813 1 0.5431 0.783 0.716 0.000 0.284
#> GSM182778 2 0.0000 0.956 0.000 1.000 0.000
#> GSM182779 1 0.3116 0.692 0.892 0.000 0.108
#> GSM182780 2 0.1031 0.944 0.000 0.976 0.024
#> GSM182781 1 0.5835 0.764 0.660 0.000 0.340
#> GSM182782 2 0.0000 0.956 0.000 1.000 0.000
#> GSM182783 2 0.2796 0.893 0.000 0.908 0.092
#> GSM182784 3 0.3686 0.666 0.000 0.140 0.860
#> GSM182785 2 0.3715 0.855 0.004 0.868 0.128
#> GSM182786 2 0.0000 0.956 0.000 1.000 0.000
#> GSM182787 2 0.0000 0.956 0.000 1.000 0.000
#> GSM182788 2 0.0000 0.956 0.000 1.000 0.000
#> GSM182789 2 0.1643 0.932 0.000 0.956 0.044
#> GSM182790 3 0.1163 0.680 0.028 0.000 0.972
#> GSM182791 2 0.2711 0.899 0.000 0.912 0.088
#> GSM182792 3 0.5905 0.343 0.000 0.352 0.648
#> GSM182793 2 0.0000 0.956 0.000 1.000 0.000
#> GSM182794 3 0.0424 0.686 0.008 0.000 0.992
#> GSM182795 2 0.6215 0.277 0.000 0.572 0.428
#> GSM182796 1 0.2486 0.677 0.932 0.008 0.060
#> GSM182797 1 0.5431 0.783 0.716 0.000 0.284
#> GSM182798 1 0.2066 0.683 0.940 0.000 0.060
#> GSM182799 2 0.2959 0.888 0.000 0.900 0.100
#> GSM182800 1 0.5465 0.780 0.712 0.000 0.288
#> GSM182801 3 0.5621 0.323 0.308 0.000 0.692
#> GSM182814 1 0.5098 0.781 0.752 0.000 0.248
#> GSM182815 2 0.0000 0.956 0.000 1.000 0.000
#> GSM182816 3 0.5650 0.318 0.312 0.000 0.688
#> GSM182817 1 0.0237 0.707 0.996 0.000 0.004
#> GSM182818 2 0.0000 0.956 0.000 1.000 0.000
#> GSM182819 1 0.6309 0.337 0.504 0.000 0.496
#> GSM182820 1 0.5431 0.783 0.716 0.000 0.284
#> GSM182821 2 0.0592 0.951 0.000 0.988 0.012
#> GSM182822 3 0.9122 0.352 0.280 0.184 0.536
#> GSM182823 1 0.5431 0.783 0.716 0.000 0.284
#> GSM182824 1 0.5431 0.783 0.716 0.000 0.284
#> GSM182825 1 0.4796 0.778 0.780 0.000 0.220
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM182755 1 0.1637 0.8252 0.940 0.000 0.000 0.060
#> GSM182756 3 0.0804 0.8258 0.008 0.000 0.980 0.012
#> GSM182757 4 0.2456 0.8334 0.068 0.008 0.008 0.916
#> GSM182758 3 0.0469 0.8277 0.000 0.012 0.988 0.000
#> GSM182759 2 0.1940 0.8324 0.000 0.924 0.000 0.076
#> GSM182760 3 0.1398 0.8186 0.040 0.000 0.956 0.004
#> GSM182761 2 0.0336 0.8859 0.000 0.992 0.008 0.000
#> GSM182762 4 0.4866 0.3889 0.404 0.000 0.000 0.596
#> GSM182763 2 0.0469 0.8841 0.000 0.988 0.012 0.000
#> GSM182764 4 0.1940 0.8391 0.076 0.000 0.000 0.924
#> GSM182765 4 0.2198 0.8394 0.072 0.000 0.008 0.920
#> GSM182766 2 0.0000 0.8887 0.000 1.000 0.000 0.000
#> GSM182767 3 0.0524 0.8290 0.008 0.004 0.988 0.000
#> GSM182768 3 0.1004 0.8264 0.000 0.024 0.972 0.004
#> GSM182769 3 0.4212 0.6435 0.216 0.000 0.772 0.012
#> GSM182770 2 0.0000 0.8887 0.000 1.000 0.000 0.000
#> GSM182771 4 0.0707 0.8233 0.020 0.000 0.000 0.980
#> GSM182772 2 0.0000 0.8887 0.000 1.000 0.000 0.000
#> GSM182773 3 0.2255 0.7965 0.068 0.000 0.920 0.012
#> GSM182774 1 0.2737 0.8049 0.888 0.000 0.008 0.104
#> GSM182775 1 0.5108 0.5345 0.672 0.000 0.308 0.020
#> GSM182776 1 0.0937 0.8401 0.976 0.000 0.012 0.012
#> GSM182777 1 0.5141 0.6646 0.756 0.000 0.160 0.084
#> GSM182802 2 0.0336 0.8881 0.000 0.992 0.000 0.008
#> GSM182803 1 0.0188 0.8430 0.996 0.000 0.004 0.000
#> GSM182804 2 0.0336 0.8881 0.000 0.992 0.000 0.008
#> GSM182805 2 0.0336 0.8881 0.000 0.992 0.000 0.008
#> GSM182806 1 0.1211 0.8360 0.960 0.000 0.000 0.040
#> GSM182807 1 0.0469 0.8440 0.988 0.000 0.000 0.012
#> GSM182808 1 0.0000 0.8433 1.000 0.000 0.000 0.000
#> GSM182809 2 0.0336 0.8881 0.000 0.992 0.000 0.008
#> GSM182810 1 0.2048 0.8122 0.928 0.000 0.008 0.064
#> GSM182811 1 0.5193 0.2864 0.580 0.000 0.008 0.412
#> GSM182812 1 0.5125 0.3434 0.604 0.000 0.008 0.388
#> GSM182813 1 0.0469 0.8440 0.988 0.000 0.000 0.012
#> GSM182778 2 0.0000 0.8887 0.000 1.000 0.000 0.000
#> GSM182779 4 0.2376 0.8382 0.068 0.000 0.016 0.916
#> GSM182780 2 0.3486 0.7291 0.000 0.812 0.188 0.000
#> GSM182781 4 0.4992 0.1927 0.476 0.000 0.000 0.524
#> GSM182782 2 0.0000 0.8887 0.000 1.000 0.000 0.000
#> GSM182783 2 0.4843 0.3853 0.000 0.604 0.396 0.000
#> GSM182784 3 0.0524 0.8290 0.008 0.004 0.988 0.000
#> GSM182785 3 0.5143 -0.0416 0.000 0.456 0.540 0.004
#> GSM182786 2 0.0000 0.8887 0.000 1.000 0.000 0.000
#> GSM182787 2 0.0000 0.8887 0.000 1.000 0.000 0.000
#> GSM182788 2 0.0000 0.8887 0.000 1.000 0.000 0.000
#> GSM182789 2 0.4624 0.5118 0.000 0.660 0.340 0.000
#> GSM182790 1 0.7838 -0.0940 0.404 0.000 0.280 0.316
#> GSM182791 2 0.5288 0.1874 0.000 0.520 0.472 0.008
#> GSM182792 3 0.1302 0.8191 0.000 0.044 0.956 0.000
#> GSM182793 2 0.0336 0.8881 0.000 0.992 0.000 0.008
#> GSM182794 3 0.7396 0.2235 0.268 0.000 0.516 0.216
#> GSM182795 3 0.3024 0.7262 0.000 0.148 0.852 0.000
#> GSM182796 4 0.0707 0.8233 0.020 0.000 0.000 0.980
#> GSM182797 1 0.1474 0.8300 0.948 0.000 0.000 0.052
#> GSM182798 4 0.0707 0.8233 0.020 0.000 0.000 0.980
#> GSM182799 2 0.5288 0.1725 0.000 0.520 0.472 0.008
#> GSM182800 1 0.1042 0.8439 0.972 0.000 0.008 0.020
#> GSM182801 1 0.3333 0.7900 0.872 0.000 0.088 0.040
#> GSM182814 1 0.0524 0.8418 0.988 0.000 0.004 0.008
#> GSM182815 2 0.0336 0.8881 0.000 0.992 0.000 0.008
#> GSM182816 1 0.1174 0.8380 0.968 0.000 0.020 0.012
#> GSM182817 1 0.5296 0.0376 0.500 0.000 0.008 0.492
#> GSM182818 2 0.0336 0.8881 0.000 0.992 0.000 0.008
#> GSM182819 1 0.0804 0.8403 0.980 0.000 0.008 0.012
#> GSM182820 1 0.1022 0.8390 0.968 0.000 0.000 0.032
#> GSM182821 2 0.4539 0.6285 0.000 0.720 0.272 0.008
#> GSM182822 1 0.4401 0.7602 0.832 0.016 0.068 0.084
#> GSM182823 1 0.0469 0.8440 0.988 0.000 0.000 0.012
#> GSM182824 1 0.0000 0.8433 1.000 0.000 0.000 0.000
#> GSM182825 1 0.1970 0.8142 0.932 0.000 0.008 0.060
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM182755 1 0.1041 0.6453 0.964 0.000 0.000 0.004 0.032
#> GSM182756 3 0.4520 0.6251 0.032 0.000 0.748 0.200 0.020
#> GSM182757 5 0.2072 0.8577 0.036 0.000 0.020 0.016 0.928
#> GSM182758 3 0.1717 0.6973 0.000 0.004 0.936 0.052 0.008
#> GSM182759 2 0.3674 0.7091 0.000 0.812 0.016 0.016 0.156
#> GSM182760 3 0.5770 0.5925 0.108 0.000 0.684 0.168 0.040
#> GSM182761 2 0.3321 0.7456 0.000 0.832 0.136 0.032 0.000
#> GSM182762 5 0.4390 0.1720 0.428 0.000 0.000 0.004 0.568
#> GSM182763 2 0.3477 0.7623 0.000 0.840 0.116 0.032 0.012
#> GSM182764 5 0.1121 0.8725 0.044 0.000 0.000 0.000 0.956
#> GSM182765 5 0.0955 0.8760 0.028 0.000 0.000 0.004 0.968
#> GSM182766 2 0.0404 0.8297 0.000 0.988 0.000 0.012 0.000
#> GSM182767 3 0.0932 0.6994 0.000 0.004 0.972 0.020 0.004
#> GSM182768 3 0.3416 0.6925 0.000 0.072 0.840 0.088 0.000
#> GSM182769 3 0.6816 0.2820 0.236 0.000 0.460 0.296 0.008
#> GSM182770 2 0.0703 0.8299 0.000 0.976 0.000 0.024 0.000
#> GSM182771 5 0.1168 0.8642 0.008 0.000 0.000 0.032 0.960
#> GSM182772 2 0.0794 0.8294 0.000 0.972 0.000 0.028 0.000
#> GSM182773 3 0.5671 0.5286 0.100 0.000 0.628 0.264 0.008
#> GSM182774 1 0.5398 -0.0823 0.648 0.000 0.000 0.240 0.112
#> GSM182775 1 0.6582 0.3489 0.500 0.000 0.184 0.308 0.008
#> GSM182776 1 0.3578 0.5908 0.784 0.000 0.004 0.204 0.008
#> GSM182777 1 0.5692 0.4826 0.640 0.000 0.072 0.264 0.024
#> GSM182802 2 0.1608 0.8234 0.000 0.928 0.000 0.072 0.000
#> GSM182803 1 0.1764 0.5928 0.928 0.000 0.000 0.064 0.008
#> GSM182804 2 0.2561 0.7981 0.000 0.856 0.000 0.144 0.000
#> GSM182805 2 0.1671 0.8223 0.000 0.924 0.000 0.076 0.000
#> GSM182806 1 0.0609 0.6469 0.980 0.000 0.000 0.000 0.020
#> GSM182807 1 0.0451 0.6443 0.988 0.000 0.000 0.004 0.008
#> GSM182808 1 0.0579 0.6431 0.984 0.000 0.000 0.008 0.008
#> GSM182809 2 0.2690 0.7913 0.000 0.844 0.000 0.156 0.000
#> GSM182810 4 0.4829 0.6849 0.484 0.000 0.000 0.496 0.020
#> GSM182811 4 0.6105 0.7863 0.392 0.008 0.000 0.500 0.100
#> GSM182812 4 0.6069 0.7668 0.432 0.000 0.000 0.448 0.120
#> GSM182813 1 0.0290 0.6449 0.992 0.000 0.000 0.000 0.008
#> GSM182778 2 0.0693 0.8264 0.000 0.980 0.008 0.012 0.000
#> GSM182779 5 0.1442 0.8725 0.032 0.000 0.004 0.012 0.952
#> GSM182780 2 0.4637 0.5179 0.000 0.672 0.292 0.036 0.000
#> GSM182781 1 0.4798 0.1162 0.540 0.000 0.000 0.020 0.440
#> GSM182782 2 0.0693 0.8264 0.000 0.980 0.008 0.012 0.000
#> GSM182783 2 0.5216 0.1257 0.000 0.520 0.436 0.044 0.000
#> GSM182784 3 0.1243 0.6989 0.000 0.004 0.960 0.028 0.008
#> GSM182785 3 0.5804 0.3613 0.000 0.312 0.604 0.044 0.040
#> GSM182786 2 0.0693 0.8264 0.000 0.980 0.008 0.012 0.000
#> GSM182787 2 0.1914 0.8077 0.000 0.924 0.060 0.016 0.000
#> GSM182788 2 0.0693 0.8264 0.000 0.980 0.008 0.012 0.000
#> GSM182789 2 0.5143 0.2024 0.000 0.532 0.428 0.040 0.000
#> GSM182790 1 0.7798 0.3070 0.448 0.000 0.176 0.272 0.104
#> GSM182791 3 0.5836 0.1434 0.000 0.384 0.516 0.100 0.000
#> GSM182792 3 0.2830 0.6963 0.000 0.044 0.876 0.080 0.000
#> GSM182793 2 0.1410 0.8271 0.000 0.940 0.000 0.060 0.000
#> GSM182794 1 0.8025 0.1953 0.404 0.000 0.244 0.248 0.104
#> GSM182795 3 0.3477 0.6824 0.000 0.112 0.832 0.056 0.000
#> GSM182796 5 0.0992 0.8667 0.008 0.000 0.000 0.024 0.968
#> GSM182797 1 0.0771 0.6477 0.976 0.000 0.000 0.004 0.020
#> GSM182798 5 0.1082 0.8652 0.008 0.000 0.000 0.028 0.964
#> GSM182799 3 0.6007 0.0549 0.000 0.396 0.488 0.116 0.000
#> GSM182800 1 0.2233 0.6368 0.904 0.000 0.000 0.080 0.016
#> GSM182801 1 0.4699 0.5428 0.716 0.000 0.032 0.236 0.016
#> GSM182814 1 0.3098 0.4039 0.836 0.000 0.000 0.148 0.016
#> GSM182815 2 0.2561 0.7981 0.000 0.856 0.000 0.144 0.000
#> GSM182816 1 0.3996 0.5741 0.752 0.000 0.012 0.228 0.008
#> GSM182817 4 0.6569 0.7073 0.336 0.000 0.000 0.448 0.216
#> GSM182818 2 0.2561 0.7977 0.000 0.856 0.000 0.144 0.000
#> GSM182819 1 0.3170 0.6084 0.828 0.000 0.008 0.160 0.004
#> GSM182820 1 0.0510 0.6468 0.984 0.000 0.000 0.000 0.016
#> GSM182821 2 0.6377 0.1582 0.000 0.452 0.380 0.168 0.000
#> GSM182822 4 0.5303 0.6354 0.256 0.016 0.032 0.680 0.016
#> GSM182823 1 0.0579 0.6414 0.984 0.000 0.000 0.008 0.008
#> GSM182824 1 0.1410 0.6062 0.940 0.000 0.000 0.060 0.000
#> GSM182825 1 0.4821 -0.6994 0.516 0.000 0.000 0.464 0.020
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM182755 1 0.0790 0.71889 0.968 0.000 0.000 0.000 0.032 0.000
#> GSM182756 3 0.4592 -0.03895 0.024 0.000 0.564 0.004 0.004 0.404
#> GSM182757 5 0.2299 0.85851 0.012 0.000 0.008 0.012 0.904 0.064
#> GSM182758 3 0.3420 0.36691 0.000 0.000 0.748 0.012 0.000 0.240
#> GSM182759 2 0.3972 0.70303 0.000 0.800 0.012 0.016 0.112 0.060
#> GSM182760 3 0.5385 -0.04932 0.076 0.000 0.556 0.004 0.012 0.352
#> GSM182761 2 0.4760 0.59915 0.000 0.696 0.208 0.020 0.000 0.076
#> GSM182762 5 0.4578 0.21430 0.396 0.000 0.000 0.004 0.568 0.032
#> GSM182763 2 0.4866 0.65548 0.000 0.732 0.152 0.024 0.020 0.072
#> GSM182764 5 0.1493 0.87215 0.004 0.000 0.000 0.004 0.936 0.056
#> GSM182765 5 0.0865 0.87947 0.000 0.000 0.000 0.000 0.964 0.036
#> GSM182766 2 0.0508 0.80141 0.000 0.984 0.000 0.004 0.000 0.012
#> GSM182767 3 0.2473 0.47869 0.000 0.000 0.856 0.008 0.000 0.136
#> GSM182768 3 0.4488 0.49430 0.000 0.036 0.724 0.040 0.000 0.200
#> GSM182769 6 0.6193 0.56516 0.184 0.000 0.276 0.028 0.000 0.512
#> GSM182770 2 0.0603 0.80183 0.000 0.980 0.000 0.004 0.000 0.016
#> GSM182771 5 0.0858 0.87815 0.000 0.000 0.000 0.028 0.968 0.004
#> GSM182772 2 0.0603 0.80140 0.000 0.980 0.000 0.004 0.000 0.016
#> GSM182773 6 0.5487 0.26094 0.080 0.000 0.416 0.016 0.000 0.488
#> GSM182774 1 0.5891 0.00108 0.524 0.000 0.000 0.336 0.108 0.032
#> GSM182775 1 0.5535 -0.41373 0.460 0.000 0.076 0.020 0.000 0.444
#> GSM182776 1 0.4319 0.58337 0.724 0.000 0.000 0.108 0.000 0.168
#> GSM182777 1 0.4532 0.14617 0.628 0.000 0.020 0.004 0.012 0.336
#> GSM182802 2 0.2129 0.78959 0.000 0.904 0.000 0.040 0.000 0.056
#> GSM182803 1 0.3198 0.58376 0.796 0.000 0.000 0.188 0.008 0.008
#> GSM182804 2 0.3466 0.75051 0.000 0.816 0.004 0.084 0.000 0.096
#> GSM182805 2 0.2070 0.79002 0.000 0.908 0.000 0.044 0.000 0.048
#> GSM182806 1 0.0653 0.72571 0.980 0.000 0.000 0.004 0.012 0.004
#> GSM182807 1 0.0767 0.72563 0.976 0.000 0.000 0.008 0.012 0.004
#> GSM182808 1 0.0692 0.72386 0.976 0.000 0.000 0.020 0.000 0.004
#> GSM182809 2 0.4001 0.73127 0.000 0.784 0.016 0.092 0.000 0.108
#> GSM182810 4 0.3357 0.82595 0.224 0.000 0.000 0.764 0.004 0.008
#> GSM182811 4 0.4074 0.82957 0.184 0.000 0.000 0.756 0.040 0.020
#> GSM182812 4 0.4731 0.81139 0.232 0.000 0.000 0.672 0.092 0.004
#> GSM182813 1 0.0622 0.72555 0.980 0.000 0.000 0.008 0.012 0.000
#> GSM182778 2 0.1078 0.79817 0.000 0.964 0.012 0.008 0.000 0.016
#> GSM182779 5 0.1194 0.87859 0.000 0.000 0.004 0.008 0.956 0.032
#> GSM182780 2 0.5137 0.43832 0.000 0.588 0.328 0.012 0.000 0.072
#> GSM182781 1 0.4943 0.24147 0.576 0.000 0.000 0.008 0.360 0.056
#> GSM182782 2 0.1251 0.79643 0.000 0.956 0.012 0.008 0.000 0.024
#> GSM182783 2 0.6057 -0.01690 0.000 0.456 0.368 0.016 0.000 0.160
#> GSM182784 3 0.1866 0.49289 0.000 0.000 0.908 0.008 0.000 0.084
#> GSM182785 3 0.6409 0.46004 0.000 0.196 0.588 0.028 0.044 0.144
#> GSM182786 2 0.1409 0.79469 0.000 0.948 0.012 0.008 0.000 0.032
#> GSM182787 2 0.3281 0.73280 0.000 0.828 0.124 0.012 0.000 0.036
#> GSM182788 2 0.1409 0.79469 0.000 0.948 0.012 0.008 0.000 0.032
#> GSM182789 2 0.5541 0.05185 0.000 0.452 0.448 0.016 0.000 0.084
#> GSM182790 6 0.6564 0.42277 0.408 0.000 0.092 0.016 0.056 0.428
#> GSM182791 3 0.6636 0.32586 0.000 0.288 0.456 0.048 0.000 0.208
#> GSM182792 3 0.4105 0.49587 0.000 0.020 0.752 0.040 0.000 0.188
#> GSM182793 2 0.1760 0.79627 0.000 0.928 0.004 0.020 0.000 0.048
#> GSM182794 6 0.6872 0.56687 0.352 0.000 0.160 0.012 0.052 0.424
#> GSM182795 3 0.5173 0.49061 0.000 0.104 0.668 0.028 0.000 0.200
#> GSM182796 5 0.0692 0.88082 0.000 0.000 0.000 0.020 0.976 0.004
#> GSM182797 1 0.0458 0.72437 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM182798 5 0.0692 0.88082 0.000 0.000 0.000 0.020 0.976 0.004
#> GSM182799 3 0.6895 0.22953 0.000 0.332 0.408 0.072 0.000 0.188
#> GSM182800 1 0.4395 0.62588 0.740 0.000 0.000 0.164 0.016 0.080
#> GSM182801 1 0.4190 0.47244 0.724 0.000 0.012 0.040 0.000 0.224
#> GSM182814 1 0.3940 0.22252 0.640 0.000 0.000 0.348 0.000 0.012
#> GSM182815 2 0.3516 0.74857 0.000 0.812 0.004 0.088 0.000 0.096
#> GSM182816 1 0.4513 0.54339 0.704 0.000 0.000 0.124 0.000 0.172
#> GSM182817 4 0.5240 0.76663 0.256 0.000 0.000 0.636 0.080 0.028
#> GSM182818 2 0.3227 0.75731 0.000 0.828 0.000 0.088 0.000 0.084
#> GSM182819 1 0.3914 0.60975 0.768 0.000 0.000 0.104 0.000 0.128
#> GSM182820 1 0.0508 0.72541 0.984 0.000 0.000 0.004 0.012 0.000
#> GSM182821 3 0.7149 0.15332 0.000 0.316 0.372 0.088 0.000 0.224
#> GSM182822 4 0.4565 0.66900 0.100 0.004 0.020 0.744 0.000 0.132
#> GSM182823 1 0.1500 0.71716 0.936 0.000 0.000 0.052 0.012 0.000
#> GSM182824 1 0.2473 0.67010 0.856 0.000 0.000 0.136 0.000 0.008
#> GSM182825 4 0.3371 0.77822 0.292 0.000 0.000 0.708 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 stress(p) development.stage(p) k
#> CV:skmeans 67 0.522 0.104950 2
#> CV:skmeans 60 0.341 0.008898 3
#> CV:skmeans 60 0.675 0.000671 4
#> CV:skmeans 55 0.907 0.000101 5
#> CV:skmeans 47 0.996 0.000638 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 18172 rows and 71 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.472 0.758 0.815 0.4284 0.529 0.529
#> 3 3 0.394 0.564 0.762 0.3823 0.594 0.399
#> 4 4 0.609 0.628 0.821 0.1921 0.760 0.489
#> 5 5 0.698 0.623 0.822 0.0997 0.896 0.657
#> 6 6 0.754 0.634 0.833 0.0395 0.900 0.607
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
#> GSM182755 1 0.9866 0.638 0.568 0.432
#> GSM182756 1 0.0000 0.689 1.000 0.000
#> GSM182757 1 0.0000 0.689 1.000 0.000
#> GSM182758 1 0.7299 0.139 0.796 0.204
#> GSM182759 2 0.9866 0.999 0.432 0.568
#> GSM182760 1 0.0000 0.689 1.000 0.000
#> GSM182761 2 0.9866 0.999 0.432 0.568
#> GSM182762 1 0.9833 0.639 0.576 0.424
#> GSM182763 2 0.9866 0.999 0.432 0.568
#> GSM182764 1 0.0938 0.692 0.988 0.012
#> GSM182765 1 0.0000 0.689 1.000 0.000
#> GSM182766 2 0.9866 0.999 0.432 0.568
#> GSM182767 2 0.9866 0.999 0.432 0.568
#> GSM182768 1 0.8763 -0.297 0.704 0.296
#> GSM182769 1 0.0000 0.689 1.000 0.000
#> GSM182770 2 0.9866 0.999 0.432 0.568
#> GSM182771 1 0.2043 0.696 0.968 0.032
#> GSM182772 2 0.9866 0.999 0.432 0.568
#> GSM182773 1 0.0000 0.689 1.000 0.000
#> GSM182774 1 0.0000 0.689 1.000 0.000
#> GSM182775 1 0.4161 0.689 0.916 0.084
#> GSM182776 1 0.0000 0.689 1.000 0.000
#> GSM182777 1 0.2236 0.696 0.964 0.036
#> GSM182802 2 0.9866 0.999 0.432 0.568
#> GSM182803 1 0.9866 0.638 0.568 0.432
#> GSM182804 2 0.9909 0.980 0.444 0.556
#> GSM182805 2 0.9866 0.999 0.432 0.568
#> GSM182806 1 0.9866 0.638 0.568 0.432
#> GSM182807 1 0.9866 0.638 0.568 0.432
#> GSM182808 1 0.9866 0.638 0.568 0.432
#> GSM182809 2 0.9866 0.999 0.432 0.568
#> GSM182810 1 0.0000 0.689 1.000 0.000
#> GSM182811 1 0.0000 0.689 1.000 0.000
#> GSM182812 1 0.0000 0.689 1.000 0.000
#> GSM182813 1 0.9866 0.638 0.568 0.432
#> GSM182778 2 0.9866 0.999 0.432 0.568
#> GSM182779 1 0.2043 0.696 0.968 0.032
#> GSM182780 2 0.9866 0.999 0.432 0.568
#> GSM182781 1 0.9866 0.638 0.568 0.432
#> GSM182782 2 0.9866 0.999 0.432 0.568
#> GSM182783 2 0.9866 0.999 0.432 0.568
#> GSM182784 2 0.9866 0.999 0.432 0.568
#> GSM182785 2 0.9866 0.999 0.432 0.568
#> GSM182786 2 0.9866 0.999 0.432 0.568
#> GSM182787 2 0.9866 0.999 0.432 0.568
#> GSM182788 2 0.9866 0.999 0.432 0.568
#> GSM182789 2 0.9866 0.999 0.432 0.568
#> GSM182790 1 0.8443 0.665 0.728 0.272
#> GSM182791 1 0.8386 -0.175 0.732 0.268
#> GSM182792 1 0.0000 0.689 1.000 0.000
#> GSM182793 2 0.9866 0.999 0.432 0.568
#> GSM182794 1 0.0376 0.690 0.996 0.004
#> GSM182795 1 0.0000 0.689 1.000 0.000
#> GSM182796 1 0.1633 0.695 0.976 0.024
#> GSM182797 1 0.9866 0.638 0.568 0.432
#> GSM182798 1 0.2043 0.696 0.968 0.032
#> GSM182799 2 0.9866 0.999 0.432 0.568
#> GSM182800 1 0.0000 0.689 1.000 0.000
#> GSM182801 1 0.8443 0.668 0.728 0.272
#> GSM182814 1 0.8207 0.669 0.744 0.256
#> GSM182815 2 0.9866 0.999 0.432 0.568
#> GSM182816 1 0.9866 0.638 0.568 0.432
#> GSM182817 1 0.0000 0.689 1.000 0.000
#> GSM182818 2 0.9866 0.999 0.432 0.568
#> GSM182819 1 0.9866 0.638 0.568 0.432
#> GSM182820 1 0.9866 0.638 0.568 0.432
#> GSM182821 2 0.9866 0.999 0.432 0.568
#> GSM182822 1 0.0000 0.689 1.000 0.000
#> GSM182823 1 0.9866 0.638 0.568 0.432
#> GSM182824 1 0.9866 0.638 0.568 0.432
#> GSM182825 1 0.0000 0.689 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM182755 1 0.0000 0.771 1.000 0.000 0.000
#> GSM182756 3 0.5785 0.473 0.332 0.000 0.668
#> GSM182757 3 0.3686 0.492 0.140 0.000 0.860
#> GSM182758 3 0.6807 0.558 0.172 0.092 0.736
#> GSM182759 3 0.5058 0.396 0.000 0.244 0.756
#> GSM182760 3 0.5016 0.531 0.240 0.000 0.760
#> GSM182761 3 0.6252 0.251 0.000 0.444 0.556
#> GSM182762 1 0.6225 0.571 0.568 0.000 0.432
#> GSM182763 3 0.5138 0.385 0.000 0.252 0.748
#> GSM182764 3 0.2537 0.520 0.080 0.000 0.920
#> GSM182765 3 0.0424 0.541 0.008 0.000 0.992
#> GSM182766 2 0.0000 0.940 0.000 1.000 0.000
#> GSM182767 3 0.6215 0.282 0.000 0.428 0.572
#> GSM182768 3 0.8016 0.545 0.188 0.156 0.656
#> GSM182769 3 0.5785 0.473 0.332 0.000 0.668
#> GSM182770 2 0.0000 0.940 0.000 1.000 0.000
#> GSM182771 3 0.4178 0.453 0.172 0.000 0.828
#> GSM182772 2 0.0000 0.940 0.000 1.000 0.000
#> GSM182773 3 0.5785 0.473 0.332 0.000 0.668
#> GSM182774 3 0.5785 0.473 0.332 0.000 0.668
#> GSM182775 3 0.6180 0.266 0.416 0.000 0.584
#> GSM182776 3 0.5785 0.473 0.332 0.000 0.668
#> GSM182777 3 0.5988 0.405 0.368 0.000 0.632
#> GSM182802 2 0.0000 0.940 0.000 1.000 0.000
#> GSM182803 1 0.5016 0.715 0.760 0.000 0.240
#> GSM182804 2 0.6584 0.275 0.012 0.608 0.380
#> GSM182805 2 0.0000 0.940 0.000 1.000 0.000
#> GSM182806 1 0.2448 0.709 0.924 0.000 0.076
#> GSM182807 1 0.0000 0.771 1.000 0.000 0.000
#> GSM182808 1 0.0237 0.771 0.996 0.000 0.004
#> GSM182809 3 0.6244 0.259 0.000 0.440 0.560
#> GSM182810 3 0.5785 0.473 0.332 0.000 0.668
#> GSM182811 3 0.5785 0.473 0.332 0.000 0.668
#> GSM182812 3 0.5785 0.473 0.332 0.000 0.668
#> GSM182813 1 0.0000 0.771 1.000 0.000 0.000
#> GSM182778 2 0.0000 0.940 0.000 1.000 0.000
#> GSM182779 3 0.4178 0.453 0.172 0.000 0.828
#> GSM182780 3 0.6252 0.251 0.000 0.444 0.556
#> GSM182781 1 0.5016 0.715 0.760 0.000 0.240
#> GSM182782 2 0.0000 0.940 0.000 1.000 0.000
#> GSM182783 3 0.6252 0.251 0.000 0.444 0.556
#> GSM182784 3 0.6215 0.282 0.000 0.428 0.572
#> GSM182785 3 0.6225 0.276 0.000 0.432 0.568
#> GSM182786 2 0.0000 0.940 0.000 1.000 0.000
#> GSM182787 3 0.6252 0.251 0.000 0.444 0.556
#> GSM182788 2 0.0000 0.940 0.000 1.000 0.000
#> GSM182789 3 0.6252 0.251 0.000 0.444 0.556
#> GSM182790 1 0.6111 0.432 0.604 0.000 0.396
#> GSM182791 3 0.7298 0.560 0.100 0.200 0.700
#> GSM182792 3 0.4452 0.547 0.192 0.000 0.808
#> GSM182793 2 0.0000 0.940 0.000 1.000 0.000
#> GSM182794 3 0.0237 0.539 0.004 0.000 0.996
#> GSM182795 3 0.4682 0.548 0.192 0.004 0.804
#> GSM182796 3 0.4062 0.465 0.164 0.000 0.836
#> GSM182797 1 0.0000 0.771 1.000 0.000 0.000
#> GSM182798 3 0.4605 0.434 0.204 0.000 0.796
#> GSM182799 3 0.6225 0.276 0.000 0.432 0.568
#> GSM182800 3 0.5529 0.500 0.296 0.000 0.704
#> GSM182801 1 0.6126 0.403 0.600 0.000 0.400
#> GSM182814 1 0.6180 0.353 0.584 0.000 0.416
#> GSM182815 2 0.0000 0.940 0.000 1.000 0.000
#> GSM182816 1 0.4974 0.719 0.764 0.000 0.236
#> GSM182817 3 0.5785 0.473 0.332 0.000 0.668
#> GSM182818 2 0.4062 0.704 0.000 0.836 0.164
#> GSM182819 1 0.4974 0.719 0.764 0.000 0.236
#> GSM182820 1 0.0000 0.771 1.000 0.000 0.000
#> GSM182821 3 0.6225 0.276 0.000 0.432 0.568
#> GSM182822 3 0.5706 0.484 0.320 0.000 0.680
#> GSM182823 1 0.0000 0.771 1.000 0.000 0.000
#> GSM182824 1 0.4291 0.743 0.820 0.000 0.180
#> GSM182825 3 0.5785 0.473 0.332 0.000 0.668
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM182755 4 0.0000 1.00000 0.000 0.000 0.000 1.000
#> GSM182756 1 0.4855 0.31124 0.600 0.000 0.400 0.000
#> GSM182757 3 0.3569 0.37293 0.196 0.000 0.804 0.000
#> GSM182758 3 0.6494 0.33981 0.340 0.088 0.572 0.000
#> GSM182759 3 0.0188 0.55905 0.000 0.004 0.996 0.000
#> GSM182760 1 0.4999 0.04571 0.508 0.000 0.492 0.000
#> GSM182761 3 0.4955 0.44148 0.000 0.444 0.556 0.000
#> GSM182762 1 0.6310 0.25423 0.512 0.000 0.428 0.060
#> GSM182763 3 0.0817 0.55819 0.000 0.024 0.976 0.000
#> GSM182764 3 0.2329 0.50751 0.072 0.000 0.916 0.012
#> GSM182765 3 0.0336 0.55475 0.008 0.000 0.992 0.000
#> GSM182766 2 0.0000 0.93147 0.000 1.000 0.000 0.000
#> GSM182767 3 0.4925 0.46103 0.000 0.428 0.572 0.000
#> GSM182768 3 0.6950 0.45743 0.272 0.156 0.572 0.000
#> GSM182769 1 0.0000 0.79562 1.000 0.000 0.000 0.000
#> GSM182770 2 0.0000 0.93147 0.000 1.000 0.000 0.000
#> GSM182771 3 0.4790 0.00791 0.380 0.000 0.620 0.000
#> GSM182772 2 0.0000 0.93147 0.000 1.000 0.000 0.000
#> GSM182773 1 0.0188 0.79442 0.996 0.000 0.004 0.000
#> GSM182774 1 0.0000 0.79562 1.000 0.000 0.000 0.000
#> GSM182775 1 0.0000 0.79562 1.000 0.000 0.000 0.000
#> GSM182776 1 0.0000 0.79562 1.000 0.000 0.000 0.000
#> GSM182777 1 0.0000 0.79562 1.000 0.000 0.000 0.000
#> GSM182802 2 0.0000 0.93147 0.000 1.000 0.000 0.000
#> GSM182803 1 0.0188 0.79482 0.996 0.000 0.000 0.004
#> GSM182804 2 0.5217 0.05506 0.012 0.608 0.380 0.000
#> GSM182805 2 0.0000 0.93147 0.000 1.000 0.000 0.000
#> GSM182806 4 0.0000 1.00000 0.000 0.000 0.000 1.000
#> GSM182807 4 0.0000 1.00000 0.000 0.000 0.000 1.000
#> GSM182808 4 0.0000 1.00000 0.000 0.000 0.000 1.000
#> GSM182809 3 0.4948 0.44723 0.000 0.440 0.560 0.000
#> GSM182810 1 0.1940 0.75823 0.924 0.000 0.076 0.000
#> GSM182811 1 0.4866 0.30261 0.596 0.000 0.404 0.000
#> GSM182812 1 0.4843 0.32032 0.604 0.000 0.396 0.000
#> GSM182813 4 0.0000 1.00000 0.000 0.000 0.000 1.000
#> GSM182778 2 0.0000 0.93147 0.000 1.000 0.000 0.000
#> GSM182779 3 0.4382 0.20256 0.296 0.000 0.704 0.000
#> GSM182780 3 0.4955 0.44148 0.000 0.444 0.556 0.000
#> GSM182781 1 0.0188 0.79451 0.996 0.000 0.000 0.004
#> GSM182782 2 0.0000 0.93147 0.000 1.000 0.000 0.000
#> GSM182783 3 0.4955 0.44148 0.000 0.444 0.556 0.000
#> GSM182784 3 0.4925 0.46103 0.000 0.428 0.572 0.000
#> GSM182785 3 0.4933 0.45674 0.000 0.432 0.568 0.000
#> GSM182786 2 0.0000 0.93147 0.000 1.000 0.000 0.000
#> GSM182787 3 0.4955 0.44148 0.000 0.444 0.556 0.000
#> GSM182788 2 0.0000 0.93147 0.000 1.000 0.000 0.000
#> GSM182789 3 0.4955 0.44148 0.000 0.444 0.556 0.000
#> GSM182790 1 0.0000 0.79562 1.000 0.000 0.000 0.000
#> GSM182791 3 0.7054 0.50872 0.232 0.196 0.572 0.000
#> GSM182792 3 0.4925 0.12783 0.428 0.000 0.572 0.000
#> GSM182793 2 0.0000 0.93147 0.000 1.000 0.000 0.000
#> GSM182794 3 0.1211 0.53956 0.040 0.000 0.960 0.000
#> GSM182795 3 0.4925 0.12783 0.428 0.000 0.572 0.000
#> GSM182796 3 0.3400 0.39596 0.180 0.000 0.820 0.000
#> GSM182797 4 0.0000 1.00000 0.000 0.000 0.000 1.000
#> GSM182798 3 0.3853 0.40842 0.160 0.000 0.820 0.020
#> GSM182799 3 0.4925 0.46103 0.000 0.428 0.572 0.000
#> GSM182800 1 0.2216 0.74505 0.908 0.000 0.092 0.000
#> GSM182801 1 0.0000 0.79562 1.000 0.000 0.000 0.000
#> GSM182814 1 0.0000 0.79562 1.000 0.000 0.000 0.000
#> GSM182815 2 0.0000 0.93147 0.000 1.000 0.000 0.000
#> GSM182816 1 0.4382 0.56746 0.704 0.000 0.000 0.296
#> GSM182817 1 0.4134 0.56430 0.740 0.000 0.260 0.000
#> GSM182818 2 0.3219 0.66140 0.000 0.836 0.164 0.000
#> GSM182819 1 0.4855 0.40392 0.600 0.000 0.000 0.400
#> GSM182820 4 0.0000 1.00000 0.000 0.000 0.000 1.000
#> GSM182821 3 0.4925 0.46103 0.000 0.428 0.572 0.000
#> GSM182822 1 0.4500 0.48450 0.684 0.000 0.316 0.000
#> GSM182823 4 0.0000 1.00000 0.000 0.000 0.000 1.000
#> GSM182824 1 0.2973 0.69217 0.856 0.000 0.000 0.144
#> GSM182825 1 0.0000 0.79562 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM182755 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000
#> GSM182756 1 0.5819 0.4282 0.600 0.000 0.148 0.000 0.252
#> GSM182757 5 0.3197 0.7169 0.024 0.000 0.140 0.000 0.836
#> GSM182758 3 0.3508 0.6449 0.000 0.000 0.748 0.000 0.252
#> GSM182759 5 0.3983 0.4262 0.000 0.000 0.340 0.000 0.660
#> GSM182760 1 0.6553 0.1623 0.472 0.000 0.292 0.000 0.236
#> GSM182761 3 0.4242 -0.1511 0.000 0.428 0.572 0.000 0.000
#> GSM182762 5 0.4990 0.3678 0.360 0.000 0.000 0.040 0.600
#> GSM182763 3 0.1792 0.6102 0.000 0.000 0.916 0.000 0.084
#> GSM182764 5 0.2605 0.6931 0.000 0.000 0.148 0.000 0.852
#> GSM182765 5 0.0510 0.7974 0.000 0.000 0.016 0.000 0.984
#> GSM182766 2 0.4152 0.6931 0.000 0.692 0.296 0.000 0.012
#> GSM182767 3 0.5191 0.6060 0.000 0.088 0.660 0.000 0.252
#> GSM182768 3 0.3508 0.6449 0.000 0.000 0.748 0.000 0.252
#> GSM182769 1 0.0000 0.7928 1.000 0.000 0.000 0.000 0.000
#> GSM182770 2 0.0000 0.7520 0.000 1.000 0.000 0.000 0.000
#> GSM182771 5 0.2130 0.7661 0.080 0.000 0.012 0.000 0.908
#> GSM182772 2 0.0162 0.7518 0.000 0.996 0.000 0.000 0.004
#> GSM182773 1 0.0162 0.7917 0.996 0.000 0.004 0.000 0.000
#> GSM182774 1 0.0000 0.7928 1.000 0.000 0.000 0.000 0.000
#> GSM182775 1 0.0000 0.7928 1.000 0.000 0.000 0.000 0.000
#> GSM182776 1 0.0000 0.7928 1.000 0.000 0.000 0.000 0.000
#> GSM182777 1 0.0000 0.7928 1.000 0.000 0.000 0.000 0.000
#> GSM182802 2 0.0290 0.7518 0.000 0.992 0.000 0.000 0.008
#> GSM182803 1 0.0162 0.7919 0.996 0.000 0.000 0.004 0.000
#> GSM182804 3 0.3051 0.4187 0.000 0.120 0.852 0.000 0.028
#> GSM182805 2 0.3890 0.7110 0.000 0.736 0.252 0.000 0.012
#> GSM182806 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000
#> GSM182807 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000
#> GSM182808 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000
#> GSM182809 3 0.3039 0.6486 0.000 0.000 0.808 0.000 0.192
#> GSM182810 1 0.1997 0.7592 0.924 0.000 0.040 0.000 0.036
#> GSM182811 1 0.5866 0.4230 0.596 0.000 0.156 0.000 0.248
#> GSM182812 1 0.4588 0.4458 0.604 0.000 0.016 0.000 0.380
#> GSM182813 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000
#> GSM182778 2 0.0162 0.7518 0.000 0.996 0.000 0.000 0.004
#> GSM182779 5 0.1522 0.7907 0.044 0.000 0.012 0.000 0.944
#> GSM182780 3 0.4242 -0.1511 0.000 0.428 0.572 0.000 0.000
#> GSM182781 1 0.0162 0.7916 0.996 0.000 0.000 0.004 0.000
#> GSM182782 2 0.3353 0.7357 0.000 0.796 0.196 0.000 0.008
#> GSM182783 3 0.1851 0.4936 0.000 0.088 0.912 0.000 0.000
#> GSM182784 2 0.6718 -0.3068 0.000 0.400 0.348 0.000 0.252
#> GSM182785 2 0.6588 -0.2677 0.000 0.400 0.392 0.000 0.208
#> GSM182786 2 0.2011 0.7540 0.000 0.908 0.088 0.000 0.004
#> GSM182787 3 0.4390 -0.1597 0.000 0.428 0.568 0.000 0.004
#> GSM182788 2 0.3550 0.7222 0.000 0.760 0.236 0.000 0.004
#> GSM182789 3 0.5810 -0.0198 0.000 0.428 0.480 0.000 0.092
#> GSM182790 1 0.0000 0.7928 1.000 0.000 0.000 0.000 0.000
#> GSM182791 3 0.3508 0.6449 0.000 0.000 0.748 0.000 0.252
#> GSM182792 3 0.3508 0.6449 0.000 0.000 0.748 0.000 0.252
#> GSM182793 2 0.3388 0.5496 0.000 0.792 0.200 0.000 0.008
#> GSM182794 3 0.4342 0.6125 0.040 0.000 0.728 0.000 0.232
#> GSM182795 3 0.3508 0.6449 0.000 0.000 0.748 0.000 0.252
#> GSM182796 5 0.0693 0.8012 0.008 0.000 0.012 0.000 0.980
#> GSM182797 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000
#> GSM182798 5 0.0693 0.8012 0.008 0.000 0.012 0.000 0.980
#> GSM182799 3 0.3003 0.6413 0.000 0.000 0.812 0.000 0.188
#> GSM182800 1 0.4747 0.0827 0.500 0.000 0.484 0.000 0.016
#> GSM182801 1 0.0000 0.7928 1.000 0.000 0.000 0.000 0.000
#> GSM182814 1 0.0000 0.7928 1.000 0.000 0.000 0.000 0.000
#> GSM182815 2 0.0798 0.7465 0.000 0.976 0.016 0.000 0.008
#> GSM182816 1 0.3774 0.5630 0.704 0.000 0.000 0.296 0.000
#> GSM182817 1 0.4558 0.6077 0.740 0.000 0.080 0.000 0.180
#> GSM182818 2 0.4016 0.7064 0.000 0.716 0.272 0.000 0.012
#> GSM182819 1 0.4182 0.3929 0.600 0.000 0.000 0.400 0.000
#> GSM182820 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000
#> GSM182821 3 0.3508 0.6449 0.000 0.000 0.748 0.000 0.252
#> GSM182822 1 0.5305 0.5445 0.676 0.000 0.172 0.000 0.152
#> GSM182823 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000
#> GSM182824 1 0.2561 0.6991 0.856 0.000 0.000 0.144 0.000
#> GSM182825 1 0.0000 0.7928 1.000 0.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM182755 1 0.0000 1.00000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM182756 6 0.3975 0.41101 0.000 0.000 0.392 0.000 0.008 0.600
#> GSM182757 5 0.4092 0.56917 0.000 0.000 0.344 0.000 0.636 0.020
#> GSM182758 3 0.0000 0.74210 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM182759 5 0.5031 0.25369 0.000 0.000 0.448 0.072 0.480 0.000
#> GSM182760 3 0.4083 -0.05744 0.000 0.000 0.532 0.000 0.008 0.460
#> GSM182761 4 0.3288 0.44055 0.000 0.000 0.276 0.724 0.000 0.000
#> GSM182762 5 0.4396 0.42312 0.036 0.000 0.000 0.000 0.612 0.352
#> GSM182763 3 0.2527 0.60601 0.000 0.000 0.832 0.168 0.000 0.000
#> GSM182764 5 0.3578 0.57807 0.000 0.000 0.340 0.000 0.660 0.000
#> GSM182765 5 0.1714 0.73569 0.000 0.000 0.092 0.000 0.908 0.000
#> GSM182766 4 0.1265 0.54927 0.000 0.008 0.044 0.948 0.000 0.000
#> GSM182767 3 0.1663 0.68876 0.000 0.000 0.912 0.088 0.000 0.000
#> GSM182768 3 0.0000 0.74210 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM182769 6 0.0000 0.83464 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM182770 4 0.4517 0.20293 0.000 0.444 0.000 0.524 0.032 0.000
#> GSM182771 5 0.1082 0.72560 0.000 0.000 0.040 0.000 0.956 0.004
#> GSM182772 2 0.1789 0.73228 0.000 0.924 0.000 0.044 0.032 0.000
#> GSM182773 6 0.0000 0.83464 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM182774 6 0.0000 0.83464 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM182775 6 0.0000 0.83464 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM182776 6 0.0000 0.83464 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM182777 6 0.0260 0.83320 0.000 0.000 0.000 0.000 0.008 0.992
#> GSM182802 4 0.4170 0.38179 0.000 0.308 0.000 0.660 0.032 0.000
#> GSM182803 6 0.0146 0.83421 0.004 0.000 0.000 0.000 0.000 0.996
#> GSM182804 4 0.3810 0.14119 0.000 0.000 0.428 0.572 0.000 0.000
#> GSM182805 4 0.0000 0.54543 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM182806 1 0.0000 1.00000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM182807 1 0.0000 1.00000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM182808 1 0.0000 1.00000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM182809 3 0.1327 0.71304 0.000 0.000 0.936 0.064 0.000 0.000
#> GSM182810 6 0.2433 0.79516 0.000 0.044 0.072 0.000 0.000 0.884
#> GSM182811 6 0.5256 0.40925 0.000 0.044 0.368 0.000 0.032 0.556
#> GSM182812 6 0.6062 0.47620 0.000 0.044 0.140 0.000 0.256 0.560
#> GSM182813 1 0.0000 1.00000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM182778 2 0.1007 0.74972 0.000 0.956 0.000 0.044 0.000 0.000
#> GSM182779 5 0.1556 0.73678 0.000 0.000 0.080 0.000 0.920 0.000
#> GSM182780 4 0.3288 0.44055 0.000 0.000 0.276 0.724 0.000 0.000
#> GSM182781 6 0.0146 0.83408 0.000 0.000 0.000 0.000 0.004 0.996
#> GSM182782 2 0.3409 0.71444 0.000 0.700 0.000 0.300 0.000 0.000
#> GSM182783 3 0.3717 0.23964 0.000 0.000 0.616 0.384 0.000 0.000
#> GSM182784 3 0.3993 0.17563 0.000 0.000 0.592 0.400 0.008 0.000
#> GSM182785 3 0.4067 0.08364 0.000 0.000 0.548 0.444 0.008 0.000
#> GSM182786 2 0.2491 0.78058 0.000 0.836 0.000 0.164 0.000 0.000
#> GSM182787 4 0.1168 0.54183 0.000 0.028 0.016 0.956 0.000 0.000
#> GSM182788 2 0.3499 0.68571 0.000 0.680 0.000 0.320 0.000 0.000
#> GSM182789 4 0.3817 0.12815 0.000 0.000 0.432 0.568 0.000 0.000
#> GSM182790 6 0.0000 0.83464 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM182791 3 0.0000 0.74210 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM182792 3 0.0146 0.74129 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM182793 4 0.6429 0.27148 0.000 0.308 0.200 0.460 0.032 0.000
#> GSM182794 3 0.1257 0.72627 0.000 0.000 0.952 0.000 0.020 0.028
#> GSM182795 3 0.0000 0.74210 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM182796 5 0.0937 0.72605 0.000 0.000 0.040 0.000 0.960 0.000
#> GSM182797 1 0.0000 1.00000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM182798 5 0.0937 0.72605 0.000 0.000 0.040 0.000 0.960 0.000
#> GSM182799 3 0.2092 0.64604 0.000 0.000 0.876 0.124 0.000 0.000
#> GSM182800 3 0.4097 0.00113 0.000 0.000 0.504 0.000 0.008 0.488
#> GSM182801 6 0.0260 0.83320 0.000 0.000 0.000 0.000 0.008 0.992
#> GSM182814 6 0.1007 0.82071 0.000 0.044 0.000 0.000 0.000 0.956
#> GSM182815 4 0.4590 0.38245 0.000 0.308 0.016 0.644 0.032 0.000
#> GSM182816 6 0.3371 0.60155 0.292 0.000 0.000 0.000 0.000 0.708
#> GSM182817 6 0.3175 0.64358 0.000 0.000 0.256 0.000 0.000 0.744
#> GSM182818 4 0.0547 0.55078 0.000 0.000 0.020 0.980 0.000 0.000
#> GSM182819 6 0.3756 0.41890 0.400 0.000 0.000 0.000 0.000 0.600
#> GSM182820 1 0.0000 1.00000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM182821 3 0.0000 0.74210 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM182822 6 0.4408 0.52129 0.000 0.044 0.320 0.000 0.000 0.636
#> GSM182823 1 0.0000 1.00000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM182824 6 0.3066 0.73889 0.124 0.044 0.000 0.000 0.000 0.832
#> GSM182825 6 0.1007 0.82071 0.000 0.044 0.000 0.000 0.000 0.956
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 stress(p) development.stage(p) k
#> CV:pam 68 0.577 0.3813 2
#> CV:pam 36 0.895 0.0017 3
#> CV:pam 43 0.674 0.0394 4
#> CV:pam 55 0.893 0.0204 5
#> CV:pam 52 0.774 0.0103 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 18172 rows and 71 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 5.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.664 0.866 0.931 0.3967 0.577 0.577
#> 3 3 0.364 0.557 0.802 0.5330 0.651 0.451
#> 4 4 0.457 0.484 0.681 0.1309 0.843 0.593
#> 5 5 0.618 0.690 0.782 0.1078 0.885 0.630
#> 6 6 0.716 0.619 0.774 0.0623 0.895 0.608
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
#> GSM182755 1 0.1633 0.950 0.976 0.024
#> GSM182756 2 0.0000 0.838 0.000 1.000
#> GSM182757 1 0.2423 0.940 0.960 0.040
#> GSM182758 2 0.0000 0.838 0.000 1.000
#> GSM182759 1 0.1633 0.950 0.976 0.024
#> GSM182760 2 0.7139 0.769 0.196 0.804
#> GSM182761 1 0.8081 0.647 0.752 0.248
#> GSM182762 1 0.1633 0.950 0.976 0.024
#> GSM182763 1 0.2043 0.946 0.968 0.032
#> GSM182764 1 0.1633 0.950 0.976 0.024
#> GSM182765 1 0.1633 0.950 0.976 0.024
#> GSM182766 1 0.1633 0.950 0.976 0.024
#> GSM182767 2 0.0000 0.838 0.000 1.000
#> GSM182768 2 0.0000 0.838 0.000 1.000
#> GSM182769 2 0.0672 0.837 0.008 0.992
#> GSM182770 1 0.0376 0.954 0.996 0.004
#> GSM182771 1 0.1414 0.951 0.980 0.020
#> GSM182772 1 0.0376 0.954 0.996 0.004
#> GSM182773 2 0.0000 0.838 0.000 1.000
#> GSM182774 1 0.0376 0.954 0.996 0.004
#> GSM182775 2 0.0000 0.838 0.000 1.000
#> GSM182776 1 0.7299 0.728 0.796 0.204
#> GSM182777 2 0.9460 0.556 0.364 0.636
#> GSM182802 1 0.0376 0.954 0.996 0.004
#> GSM182803 1 0.0376 0.954 0.996 0.004
#> GSM182804 1 0.0376 0.954 0.996 0.004
#> GSM182805 1 0.0376 0.954 0.996 0.004
#> GSM182806 1 0.0000 0.952 1.000 0.000
#> GSM182807 1 0.0376 0.954 0.996 0.004
#> GSM182808 1 0.0672 0.954 0.992 0.008
#> GSM182809 1 0.0376 0.954 0.996 0.004
#> GSM182810 1 0.0376 0.954 0.996 0.004
#> GSM182811 1 0.0376 0.954 0.996 0.004
#> GSM182812 1 0.0376 0.954 0.996 0.004
#> GSM182813 1 0.0376 0.954 0.996 0.004
#> GSM182778 1 0.1843 0.950 0.972 0.028
#> GSM182779 1 0.2603 0.937 0.956 0.044
#> GSM182780 2 0.7139 0.770 0.196 0.804
#> GSM182781 1 0.5059 0.863 0.888 0.112
#> GSM182782 1 0.1414 0.951 0.980 0.020
#> GSM182783 2 0.1414 0.835 0.020 0.980
#> GSM182784 2 0.0000 0.838 0.000 1.000
#> GSM182785 2 0.9635 0.507 0.388 0.612
#> GSM182786 1 0.1633 0.950 0.976 0.024
#> GSM182787 1 0.7602 0.710 0.780 0.220
#> GSM182788 1 0.1633 0.950 0.976 0.024
#> GSM182789 2 0.7745 0.744 0.228 0.772
#> GSM182790 2 0.0000 0.838 0.000 1.000
#> GSM182791 2 0.9754 0.450 0.408 0.592
#> GSM182792 2 0.7745 0.745 0.228 0.772
#> GSM182793 1 0.0376 0.954 0.996 0.004
#> GSM182794 2 0.8327 0.711 0.264 0.736
#> GSM182795 2 0.0000 0.838 0.000 1.000
#> GSM182796 1 0.1414 0.951 0.980 0.020
#> GSM182797 1 0.1633 0.950 0.976 0.024
#> GSM182798 1 0.1414 0.951 0.980 0.020
#> GSM182799 2 0.9922 0.216 0.448 0.552
#> GSM182800 1 0.0938 0.953 0.988 0.012
#> GSM182801 2 0.6438 0.753 0.164 0.836
#> GSM182814 1 0.0376 0.954 0.996 0.004
#> GSM182815 1 0.0376 0.954 0.996 0.004
#> GSM182816 1 0.7056 0.748 0.808 0.192
#> GSM182817 1 0.0376 0.954 0.996 0.004
#> GSM182818 1 0.0376 0.954 0.996 0.004
#> GSM182819 1 0.7056 0.748 0.808 0.192
#> GSM182820 1 0.1843 0.950 0.972 0.028
#> GSM182821 1 0.7950 0.662 0.760 0.240
#> GSM182822 1 0.0376 0.954 0.996 0.004
#> GSM182823 1 0.0376 0.954 0.996 0.004
#> GSM182824 1 0.0376 0.954 0.996 0.004
#> GSM182825 1 0.0376 0.954 0.996 0.004
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM182755 1 0.6990 0.5231 0.728 0.108 0.164
#> GSM182756 3 0.0000 0.6867 0.000 0.000 1.000
#> GSM182757 3 0.8737 -0.0430 0.428 0.108 0.464
#> GSM182758 3 0.0000 0.6867 0.000 0.000 1.000
#> GSM182759 3 0.8633 -0.0552 0.436 0.100 0.464
#> GSM182760 3 0.2959 0.6641 0.000 0.100 0.900
#> GSM182761 3 0.5397 0.5483 0.000 0.280 0.720
#> GSM182762 1 0.7610 0.4918 0.676 0.108 0.216
#> GSM182763 3 0.4335 0.6416 0.036 0.100 0.864
#> GSM182764 3 0.8737 -0.0430 0.428 0.108 0.464
#> GSM182765 1 0.8569 0.2510 0.508 0.100 0.392
#> GSM182766 2 0.1289 0.8646 0.032 0.968 0.000
#> GSM182767 3 0.0000 0.6867 0.000 0.000 1.000
#> GSM182768 3 0.0000 0.6867 0.000 0.000 1.000
#> GSM182769 3 0.6225 0.0514 0.432 0.000 0.568
#> GSM182770 2 0.3551 0.8843 0.132 0.868 0.000
#> GSM182771 1 0.8238 0.4709 0.596 0.104 0.300
#> GSM182772 2 0.3551 0.8843 0.132 0.868 0.000
#> GSM182773 3 0.0000 0.6867 0.000 0.000 1.000
#> GSM182774 1 0.5560 0.5399 0.700 0.000 0.300
#> GSM182775 3 0.6126 0.1313 0.400 0.000 0.600
#> GSM182776 1 0.6309 0.0931 0.504 0.000 0.496
#> GSM182777 3 0.8587 0.0385 0.400 0.100 0.500
#> GSM182802 2 0.3116 0.8871 0.108 0.892 0.000
#> GSM182803 1 0.0237 0.6541 0.996 0.004 0.000
#> GSM182804 2 0.3116 0.8871 0.108 0.892 0.000
#> GSM182805 2 0.3116 0.8871 0.108 0.892 0.000
#> GSM182806 1 0.0237 0.6541 0.996 0.004 0.000
#> GSM182807 1 0.0237 0.6541 0.996 0.004 0.000
#> GSM182808 1 0.0000 0.6536 1.000 0.000 0.000
#> GSM182809 2 0.8301 0.4032 0.108 0.592 0.300
#> GSM182810 1 0.6630 0.5372 0.672 0.028 0.300
#> GSM182811 1 0.6630 0.5372 0.672 0.028 0.300
#> GSM182812 1 0.6630 0.5372 0.672 0.028 0.300
#> GSM182813 1 0.0237 0.6541 0.996 0.004 0.000
#> GSM182778 2 0.1289 0.8646 0.032 0.968 0.000
#> GSM182779 3 0.8737 -0.0430 0.428 0.108 0.464
#> GSM182780 3 0.1411 0.6846 0.000 0.036 0.964
#> GSM182781 1 0.6990 0.5231 0.728 0.108 0.164
#> GSM182782 2 0.1289 0.8646 0.032 0.968 0.000
#> GSM182783 3 0.0237 0.6846 0.000 0.004 0.996
#> GSM182784 3 0.0000 0.6867 0.000 0.000 1.000
#> GSM182785 3 0.2959 0.6641 0.000 0.100 0.900
#> GSM182786 2 0.1289 0.8646 0.032 0.968 0.000
#> GSM182787 2 0.4605 0.6368 0.000 0.796 0.204
#> GSM182788 2 0.1289 0.8646 0.032 0.968 0.000
#> GSM182789 3 0.1289 0.6853 0.000 0.032 0.968
#> GSM182790 3 0.6126 0.1313 0.400 0.000 0.600
#> GSM182791 3 0.2959 0.6641 0.000 0.100 0.900
#> GSM182792 3 0.0000 0.6867 0.000 0.000 1.000
#> GSM182793 2 0.3116 0.8871 0.108 0.892 0.000
#> GSM182794 3 0.8587 0.0385 0.400 0.100 0.500
#> GSM182795 3 0.0000 0.6867 0.000 0.000 1.000
#> GSM182796 1 0.8238 0.4709 0.596 0.104 0.300
#> GSM182797 1 0.3116 0.6229 0.892 0.108 0.000
#> GSM182798 1 0.8238 0.4709 0.596 0.104 0.300
#> GSM182799 3 0.4346 0.5809 0.000 0.184 0.816
#> GSM182800 1 0.8040 0.4824 0.608 0.092 0.300
#> GSM182801 3 0.6140 0.1226 0.404 0.000 0.596
#> GSM182814 1 0.1163 0.6470 0.972 0.028 0.000
#> GSM182815 2 0.3116 0.8871 0.108 0.892 0.000
#> GSM182816 1 0.4555 0.5500 0.800 0.000 0.200
#> GSM182817 1 0.5785 0.5401 0.696 0.004 0.300
#> GSM182818 2 0.3116 0.8871 0.108 0.892 0.000
#> GSM182819 1 0.4555 0.5500 0.800 0.000 0.200
#> GSM182820 1 0.2959 0.6255 0.900 0.100 0.000
#> GSM182821 3 0.2796 0.6462 0.092 0.000 0.908
#> GSM182822 1 0.6476 0.2333 0.548 0.004 0.448
#> GSM182823 1 0.1163 0.6470 0.972 0.028 0.000
#> GSM182824 1 0.1163 0.6470 0.972 0.028 0.000
#> GSM182825 1 0.6630 0.5372 0.672 0.028 0.300
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM182755 4 0.4800 0.3649 0.044 0.000 0.196 0.760
#> GSM182756 3 0.0336 0.7809 0.000 0.000 0.992 0.008
#> GSM182757 4 0.5668 0.0310 0.024 0.000 0.444 0.532
#> GSM182758 3 0.0000 0.7801 0.000 0.000 1.000 0.000
#> GSM182759 3 0.5887 0.2528 0.028 0.004 0.548 0.420
#> GSM182760 3 0.2281 0.7505 0.000 0.000 0.904 0.096
#> GSM182761 3 0.4364 0.6357 0.016 0.000 0.764 0.220
#> GSM182762 4 0.4149 0.3938 0.028 0.000 0.168 0.804
#> GSM182763 3 0.3791 0.6626 0.004 0.000 0.796 0.200
#> GSM182764 4 0.6422 0.3768 0.120 0.000 0.248 0.632
#> GSM182765 4 0.5929 0.3709 0.108 0.000 0.204 0.688
#> GSM182766 2 0.6835 0.6789 0.088 0.580 0.012 0.320
#> GSM182767 3 0.0524 0.7808 0.004 0.000 0.988 0.008
#> GSM182768 3 0.0592 0.7736 0.016 0.000 0.984 0.000
#> GSM182769 3 0.4053 0.5524 0.004 0.000 0.768 0.228
#> GSM182770 2 0.4352 0.7649 0.080 0.816 0.000 0.104
#> GSM182771 4 0.5573 0.1393 0.368 0.000 0.028 0.604
#> GSM182772 2 0.3198 0.7741 0.080 0.880 0.000 0.040
#> GSM182773 3 0.0657 0.7808 0.004 0.000 0.984 0.012
#> GSM182774 1 0.5343 0.6860 0.656 0.000 0.028 0.316
#> GSM182775 3 0.4088 0.5475 0.004 0.000 0.764 0.232
#> GSM182776 3 0.7761 -0.3371 0.376 0.000 0.388 0.236
#> GSM182777 3 0.5526 0.2248 0.020 0.000 0.564 0.416
#> GSM182802 2 0.0000 0.7786 0.000 1.000 0.000 0.000
#> GSM182803 1 0.4877 0.6368 0.592 0.000 0.000 0.408
#> GSM182804 2 0.0188 0.7775 0.004 0.996 0.000 0.000
#> GSM182805 2 0.0000 0.7786 0.000 1.000 0.000 0.000
#> GSM182806 4 0.4985 -0.4412 0.468 0.000 0.000 0.532
#> GSM182807 4 0.5000 -0.5367 0.496 0.000 0.000 0.504
#> GSM182808 4 0.5695 -0.5240 0.476 0.000 0.024 0.500
#> GSM182809 2 0.7577 0.2369 0.160 0.484 0.348 0.008
#> GSM182810 1 0.5716 0.7050 0.680 0.000 0.068 0.252
#> GSM182811 1 0.5413 0.7161 0.712 0.004 0.048 0.236
#> GSM182812 1 0.4954 0.7271 0.736 0.004 0.028 0.232
#> GSM182813 4 0.4999 -0.5319 0.492 0.000 0.000 0.508
#> GSM182778 2 0.8217 0.6412 0.212 0.456 0.024 0.308
#> GSM182779 4 0.5138 0.1903 0.008 0.000 0.392 0.600
#> GSM182780 3 0.1629 0.7719 0.024 0.000 0.952 0.024
#> GSM182781 4 0.5343 0.3761 0.028 0.000 0.316 0.656
#> GSM182782 2 0.7617 0.6421 0.216 0.452 0.000 0.332
#> GSM182783 3 0.0817 0.7689 0.024 0.000 0.976 0.000
#> GSM182784 3 0.0524 0.7808 0.004 0.000 0.988 0.008
#> GSM182785 3 0.3266 0.6979 0.000 0.000 0.832 0.168
#> GSM182786 2 0.7617 0.6421 0.216 0.452 0.000 0.332
#> GSM182787 3 0.7708 0.4363 0.096 0.216 0.604 0.084
#> GSM182788 2 0.7617 0.6421 0.216 0.452 0.000 0.332
#> GSM182789 3 0.0927 0.7795 0.008 0.000 0.976 0.016
#> GSM182790 3 0.3942 0.5429 0.000 0.000 0.764 0.236
#> GSM182791 3 0.2125 0.7602 0.004 0.000 0.920 0.076
#> GSM182792 3 0.0336 0.7809 0.000 0.000 0.992 0.008
#> GSM182793 2 0.0469 0.7795 0.000 0.988 0.000 0.012
#> GSM182794 3 0.4679 0.4082 0.000 0.000 0.648 0.352
#> GSM182795 3 0.0000 0.7801 0.000 0.000 1.000 0.000
#> GSM182796 4 0.5543 0.1576 0.360 0.000 0.028 0.612
#> GSM182797 4 0.4499 0.2122 0.160 0.000 0.048 0.792
#> GSM182798 4 0.5543 0.1576 0.360 0.000 0.028 0.612
#> GSM182799 3 0.1151 0.7684 0.024 0.008 0.968 0.000
#> GSM182800 4 0.7862 0.0759 0.308 0.000 0.296 0.396
#> GSM182801 3 0.4898 0.4708 0.024 0.000 0.716 0.260
#> GSM182814 1 0.5024 0.6873 0.632 0.000 0.008 0.360
#> GSM182815 2 0.0000 0.7786 0.000 1.000 0.000 0.000
#> GSM182816 4 0.7803 0.1374 0.252 0.000 0.352 0.396
#> GSM182817 1 0.5506 0.7205 0.700 0.004 0.048 0.248
#> GSM182818 2 0.0817 0.7683 0.024 0.976 0.000 0.000
#> GSM182819 4 0.7828 0.1207 0.264 0.000 0.340 0.396
#> GSM182820 4 0.5254 -0.0751 0.300 0.000 0.028 0.672
#> GSM182821 3 0.0804 0.7794 0.012 0.000 0.980 0.008
#> GSM182822 1 0.7807 0.1121 0.420 0.000 0.288 0.292
#> GSM182823 1 0.4866 0.6292 0.596 0.000 0.000 0.404
#> GSM182824 1 0.4888 0.6306 0.588 0.000 0.000 0.412
#> GSM182825 1 0.4987 0.7293 0.732 0.004 0.028 0.236
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM182755 5 0.4419 0.5974 0.052 0.008 0.008 0.152 0.780
#> GSM182756 3 0.2583 0.8177 0.000 0.000 0.864 0.132 0.004
#> GSM182757 5 0.7439 0.6014 0.076 0.112 0.208 0.032 0.572
#> GSM182758 3 0.1043 0.8327 0.000 0.000 0.960 0.040 0.000
#> GSM182759 5 0.6704 0.4015 0.024 0.132 0.372 0.000 0.472
#> GSM182760 3 0.3106 0.8168 0.000 0.000 0.844 0.132 0.024
#> GSM182761 3 0.4953 0.5628 0.000 0.216 0.696 0.000 0.088
#> GSM182762 5 0.3612 0.6859 0.036 0.100 0.004 0.016 0.844
#> GSM182763 3 0.4803 0.5615 0.000 0.096 0.720 0.000 0.184
#> GSM182764 5 0.5379 0.6903 0.104 0.112 0.044 0.004 0.736
#> GSM182765 5 0.5529 0.6903 0.092 0.116 0.040 0.016 0.736
#> GSM182766 2 0.1806 0.9467 0.000 0.940 0.016 0.028 0.016
#> GSM182767 3 0.2233 0.8254 0.000 0.000 0.892 0.104 0.004
#> GSM182768 3 0.0162 0.8332 0.000 0.000 0.996 0.004 0.000
#> GSM182769 3 0.5078 0.7542 0.064 0.000 0.740 0.156 0.040
#> GSM182770 4 0.4310 0.7895 0.004 0.392 0.000 0.604 0.000
#> GSM182771 5 0.5396 0.6539 0.280 0.080 0.004 0.000 0.636
#> GSM182772 4 0.4151 0.8566 0.004 0.344 0.000 0.652 0.000
#> GSM182773 3 0.2787 0.8171 0.004 0.000 0.856 0.136 0.004
#> GSM182774 1 0.2450 0.6675 0.896 0.000 0.028 0.000 0.076
#> GSM182775 3 0.5707 0.7048 0.112 0.000 0.692 0.156 0.040
#> GSM182776 1 0.7277 -0.0569 0.412 0.000 0.396 0.128 0.064
#> GSM182777 3 0.7789 0.4780 0.136 0.008 0.512 0.144 0.200
#> GSM182802 4 0.3928 0.8994 0.004 0.296 0.000 0.700 0.000
#> GSM182803 1 0.1725 0.6889 0.936 0.000 0.000 0.020 0.044
#> GSM182804 4 0.3928 0.8994 0.004 0.296 0.000 0.700 0.000
#> GSM182805 4 0.3928 0.8994 0.004 0.296 0.000 0.700 0.000
#> GSM182806 1 0.5251 0.5656 0.680 0.000 0.000 0.136 0.184
#> GSM182807 1 0.5500 0.5658 0.648 0.000 0.000 0.140 0.212
#> GSM182808 1 0.4986 0.6408 0.736 0.004 0.024 0.052 0.184
#> GSM182809 4 0.5291 0.4367 0.040 0.020 0.268 0.668 0.004
#> GSM182810 1 0.0771 0.6813 0.976 0.004 0.000 0.000 0.020
#> GSM182811 1 0.1074 0.6811 0.968 0.004 0.000 0.012 0.016
#> GSM182812 1 0.1074 0.6811 0.968 0.004 0.000 0.012 0.016
#> GSM182813 1 0.5680 0.5402 0.620 0.000 0.000 0.140 0.240
#> GSM182778 2 0.0671 0.9785 0.000 0.980 0.004 0.000 0.016
#> GSM182779 5 0.6350 0.6640 0.044 0.088 0.120 0.056 0.692
#> GSM182780 3 0.0510 0.8310 0.000 0.000 0.984 0.000 0.016
#> GSM182781 5 0.5887 0.6247 0.048 0.012 0.100 0.136 0.704
#> GSM182782 2 0.0404 0.9837 0.000 0.988 0.000 0.000 0.012
#> GSM182783 3 0.0290 0.8323 0.000 0.000 0.992 0.000 0.008
#> GSM182784 3 0.2124 0.8270 0.000 0.000 0.900 0.096 0.004
#> GSM182785 3 0.4255 0.6570 0.000 0.096 0.776 0.000 0.128
#> GSM182786 2 0.0404 0.9837 0.000 0.988 0.000 0.000 0.012
#> GSM182787 3 0.3993 0.6657 0.000 0.216 0.756 0.000 0.028
#> GSM182788 2 0.0404 0.9837 0.000 0.988 0.000 0.000 0.012
#> GSM182789 3 0.0609 0.8305 0.000 0.000 0.980 0.000 0.020
#> GSM182790 3 0.5154 0.7335 0.108 0.000 0.732 0.136 0.024
#> GSM182791 3 0.0865 0.8294 0.000 0.000 0.972 0.004 0.024
#> GSM182792 3 0.0912 0.8340 0.000 0.000 0.972 0.012 0.016
#> GSM182793 4 0.3928 0.8994 0.004 0.296 0.000 0.700 0.000
#> GSM182794 3 0.6720 0.5993 0.060 0.004 0.608 0.136 0.192
#> GSM182795 3 0.0290 0.8323 0.000 0.000 0.992 0.000 0.008
#> GSM182796 5 0.5447 0.6648 0.248 0.112 0.000 0.000 0.640
#> GSM182797 5 0.4419 0.5974 0.052 0.008 0.008 0.152 0.780
#> GSM182798 5 0.5405 0.6638 0.256 0.104 0.000 0.000 0.640
#> GSM182799 3 0.0854 0.8316 0.000 0.012 0.976 0.004 0.008
#> GSM182800 1 0.7074 0.3301 0.512 0.000 0.308 0.084 0.096
#> GSM182801 3 0.5780 0.6974 0.112 0.000 0.684 0.164 0.040
#> GSM182814 1 0.1202 0.6897 0.960 0.004 0.000 0.004 0.032
#> GSM182815 4 0.3928 0.8994 0.004 0.296 0.000 0.700 0.000
#> GSM182816 1 0.7887 0.0687 0.376 0.004 0.376 0.108 0.136
#> GSM182817 1 0.1202 0.6808 0.960 0.004 0.000 0.004 0.032
#> GSM182818 4 0.3928 0.8994 0.004 0.296 0.000 0.700 0.000
#> GSM182819 1 0.7674 0.3413 0.460 0.000 0.288 0.108 0.144
#> GSM182820 5 0.6080 0.1159 0.332 0.000 0.000 0.140 0.528
#> GSM182821 3 0.0566 0.8314 0.000 0.000 0.984 0.004 0.012
#> GSM182822 1 0.5908 0.3938 0.564 0.000 0.340 0.012 0.084
#> GSM182823 1 0.4444 0.6156 0.760 0.000 0.000 0.136 0.104
#> GSM182824 1 0.3339 0.6740 0.840 0.000 0.000 0.048 0.112
#> GSM182825 1 0.0771 0.6813 0.976 0.004 0.000 0.000 0.020
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM182755 6 0.6296 0.09686 0.000 0.000 0.008 0.284 0.320 0.388
#> GSM182756 3 0.2805 0.73427 0.000 0.000 0.812 0.000 0.004 0.184
#> GSM182757 5 0.0935 0.85380 0.004 0.000 0.032 0.000 0.964 0.000
#> GSM182758 3 0.0000 0.80308 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM182759 3 0.4221 0.38519 0.000 0.008 0.588 0.000 0.396 0.008
#> GSM182760 3 0.3104 0.73399 0.000 0.000 0.800 0.000 0.016 0.184
#> GSM182761 3 0.3496 0.70437 0.000 0.052 0.804 0.000 0.140 0.004
#> GSM182762 5 0.1219 0.84065 0.000 0.000 0.000 0.048 0.948 0.004
#> GSM182763 3 0.2632 0.71724 0.000 0.000 0.832 0.000 0.164 0.004
#> GSM182764 5 0.0260 0.86434 0.008 0.000 0.000 0.000 0.992 0.000
#> GSM182765 5 0.0260 0.86434 0.008 0.000 0.000 0.000 0.992 0.000
#> GSM182766 2 0.2293 0.85542 0.000 0.896 0.016 0.080 0.004 0.004
#> GSM182767 3 0.2146 0.77344 0.000 0.000 0.880 0.000 0.004 0.116
#> GSM182768 3 0.1610 0.77147 0.000 0.000 0.916 0.000 0.000 0.084
#> GSM182769 6 0.5607 0.00890 0.148 0.000 0.316 0.000 0.004 0.532
#> GSM182770 4 0.3765 0.69438 0.000 0.404 0.000 0.596 0.000 0.000
#> GSM182771 5 0.2420 0.84594 0.032 0.068 0.000 0.000 0.892 0.008
#> GSM182772 4 0.3828 0.63355 0.000 0.440 0.000 0.560 0.000 0.000
#> GSM182773 3 0.3426 0.67463 0.000 0.000 0.720 0.000 0.004 0.276
#> GSM182774 1 0.0000 0.81218 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM182775 6 0.6035 0.09155 0.236 0.000 0.300 0.000 0.004 0.460
#> GSM182776 6 0.5382 -0.03317 0.352 0.000 0.108 0.000 0.004 0.536
#> GSM182777 3 0.7487 0.00605 0.236 0.000 0.332 0.000 0.140 0.292
#> GSM182802 4 0.3351 0.82520 0.000 0.288 0.000 0.712 0.000 0.000
#> GSM182803 1 0.1588 0.75584 0.924 0.000 0.000 0.072 0.000 0.004
#> GSM182804 4 0.3351 0.82520 0.000 0.288 0.000 0.712 0.000 0.000
#> GSM182805 4 0.3351 0.82520 0.000 0.288 0.000 0.712 0.000 0.000
#> GSM182806 6 0.6641 0.35441 0.236 0.000 0.000 0.288 0.040 0.436
#> GSM182807 6 0.6121 0.32350 0.272 0.000 0.000 0.288 0.004 0.436
#> GSM182808 1 0.5714 0.24962 0.540 0.000 0.012 0.140 0.000 0.308
#> GSM182809 4 0.4086 0.08603 0.008 0.000 0.464 0.528 0.000 0.000
#> GSM182810 1 0.0000 0.81218 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM182811 1 0.0260 0.81015 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM182812 1 0.0260 0.81015 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM182813 6 0.6074 0.33591 0.256 0.000 0.000 0.288 0.004 0.452
#> GSM182778 2 0.0146 0.96735 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM182779 5 0.1946 0.81728 0.004 0.000 0.072 0.000 0.912 0.012
#> GSM182780 3 0.0405 0.80336 0.000 0.000 0.988 0.000 0.008 0.004
#> GSM182781 5 0.6054 0.10457 0.000 0.000 0.008 0.272 0.484 0.236
#> GSM182782 2 0.0146 0.96735 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM182783 3 0.0405 0.80336 0.000 0.000 0.988 0.000 0.008 0.004
#> GSM182784 3 0.2100 0.77516 0.000 0.000 0.884 0.000 0.004 0.112
#> GSM182785 3 0.2100 0.75804 0.000 0.000 0.884 0.000 0.112 0.004
#> GSM182786 2 0.0146 0.96735 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM182787 3 0.3693 0.55623 0.000 0.280 0.708 0.000 0.008 0.004
#> GSM182788 2 0.0146 0.96735 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM182789 3 0.0405 0.80336 0.000 0.000 0.988 0.000 0.008 0.004
#> GSM182790 3 0.4756 0.53331 0.068 0.000 0.636 0.000 0.004 0.292
#> GSM182791 3 0.0260 0.80385 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM182792 3 0.0405 0.80376 0.000 0.000 0.988 0.000 0.008 0.004
#> GSM182793 4 0.3351 0.82520 0.000 0.288 0.000 0.712 0.000 0.000
#> GSM182794 3 0.6023 0.49626 0.036 0.000 0.540 0.000 0.132 0.292
#> GSM182795 3 0.0146 0.80369 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM182796 5 0.1957 0.85210 0.008 0.072 0.000 0.000 0.912 0.008
#> GSM182797 6 0.6296 0.09686 0.000 0.000 0.008 0.284 0.320 0.388
#> GSM182798 5 0.1957 0.85210 0.008 0.072 0.000 0.000 0.912 0.008
#> GSM182799 3 0.2883 0.66608 0.000 0.000 0.788 0.000 0.000 0.212
#> GSM182800 1 0.5956 0.15837 0.524 0.000 0.208 0.000 0.012 0.256
#> GSM182801 6 0.5899 0.12093 0.236 0.000 0.256 0.000 0.004 0.504
#> GSM182814 1 0.0000 0.81218 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM182815 4 0.3351 0.82520 0.000 0.288 0.000 0.712 0.000 0.000
#> GSM182816 6 0.6272 0.08607 0.300 0.004 0.016 0.176 0.004 0.500
#> GSM182817 1 0.0146 0.81156 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM182818 4 0.3351 0.82520 0.000 0.288 0.000 0.712 0.000 0.000
#> GSM182819 6 0.5920 0.15107 0.260 0.000 0.012 0.176 0.004 0.548
#> GSM182820 6 0.7331 0.36716 0.180 0.000 0.000 0.288 0.144 0.388
#> GSM182821 3 0.0260 0.80385 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM182822 1 0.3027 0.61399 0.824 0.000 0.148 0.000 0.000 0.028
#> GSM182823 6 0.6205 0.28222 0.316 0.000 0.000 0.288 0.004 0.392
#> GSM182824 1 0.4593 0.52639 0.704 0.004 0.000 0.112 0.000 0.180
#> GSM182825 1 0.0000 0.81218 1.000 0.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n stress(p) development.stage(p) k
#> CV:mclust 69 0.941 5.47e-04 2
#> CV:mclust 52 0.904 1.80e-05 3
#> CV:mclust 44 0.983 1.62e-05 4
#> CV:mclust 62 0.380 5.56e-09 5
#> CV:mclust 51 0.488 1.16e-06 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "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 18172 rows and 71 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.681 0.822 0.918 0.4604 0.505 0.505
#> 3 3 0.326 0.408 0.709 0.3692 0.803 0.634
#> 4 4 0.532 0.675 0.824 0.1377 0.703 0.370
#> 5 5 0.506 0.511 0.696 0.0658 0.891 0.657
#> 6 6 0.484 0.434 0.680 0.0435 0.893 0.626
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
#> GSM182755 1 0.0000 0.961 1.000 0.000
#> GSM182756 1 0.7299 0.683 0.796 0.204
#> GSM182757 1 0.5178 0.832 0.884 0.116
#> GSM182758 2 0.9710 0.512 0.400 0.600
#> GSM182759 2 0.7602 0.704 0.220 0.780
#> GSM182760 1 0.4431 0.865 0.908 0.092
#> GSM182761 2 0.5408 0.768 0.124 0.876
#> GSM182762 1 0.0000 0.961 1.000 0.000
#> GSM182763 2 0.9209 0.592 0.336 0.664
#> GSM182764 1 0.0000 0.961 1.000 0.000
#> GSM182765 1 0.0000 0.961 1.000 0.000
#> GSM182766 2 0.0000 0.824 0.000 1.000
#> GSM182767 2 0.9896 0.435 0.440 0.560
#> GSM182768 2 0.9710 0.512 0.400 0.600
#> GSM182769 1 0.0000 0.961 1.000 0.000
#> GSM182770 2 0.0000 0.824 0.000 1.000
#> GSM182771 1 0.0000 0.961 1.000 0.000
#> GSM182772 2 0.0000 0.824 0.000 1.000
#> GSM182773 1 0.6531 0.750 0.832 0.168
#> GSM182774 1 0.0000 0.961 1.000 0.000
#> GSM182775 1 0.0000 0.961 1.000 0.000
#> GSM182776 1 0.0000 0.961 1.000 0.000
#> GSM182777 1 0.0000 0.961 1.000 0.000
#> GSM182802 2 0.0000 0.824 0.000 1.000
#> GSM182803 1 0.0000 0.961 1.000 0.000
#> GSM182804 2 0.0000 0.824 0.000 1.000
#> GSM182805 2 0.0000 0.824 0.000 1.000
#> GSM182806 1 0.0000 0.961 1.000 0.000
#> GSM182807 1 0.0000 0.961 1.000 0.000
#> GSM182808 1 0.0000 0.961 1.000 0.000
#> GSM182809 2 0.2236 0.811 0.036 0.964
#> GSM182810 1 0.0000 0.961 1.000 0.000
#> GSM182811 1 0.0000 0.961 1.000 0.000
#> GSM182812 1 0.0672 0.954 0.992 0.008
#> GSM182813 1 0.0000 0.961 1.000 0.000
#> GSM182778 2 0.0000 0.824 0.000 1.000
#> GSM182779 1 0.2043 0.931 0.968 0.032
#> GSM182780 2 0.0000 0.824 0.000 1.000
#> GSM182781 1 0.0000 0.961 1.000 0.000
#> GSM182782 2 0.0000 0.824 0.000 1.000
#> GSM182783 2 0.0000 0.824 0.000 1.000
#> GSM182784 2 0.9954 0.384 0.460 0.540
#> GSM182785 2 0.9983 0.338 0.476 0.524
#> GSM182786 2 0.0000 0.824 0.000 1.000
#> GSM182787 2 0.0000 0.824 0.000 1.000
#> GSM182788 2 0.0000 0.824 0.000 1.000
#> GSM182789 2 0.9686 0.517 0.396 0.604
#> GSM182790 1 0.0000 0.961 1.000 0.000
#> GSM182791 2 0.9775 0.491 0.412 0.588
#> GSM182792 1 0.9944 -0.142 0.544 0.456
#> GSM182793 2 0.0000 0.824 0.000 1.000
#> GSM182794 1 0.0000 0.961 1.000 0.000
#> GSM182795 2 0.9896 0.435 0.440 0.560
#> GSM182796 1 0.3431 0.894 0.936 0.064
#> GSM182797 1 0.0000 0.961 1.000 0.000
#> GSM182798 1 0.0000 0.961 1.000 0.000
#> GSM182799 2 0.0000 0.824 0.000 1.000
#> GSM182800 1 0.0000 0.961 1.000 0.000
#> GSM182801 1 0.0000 0.961 1.000 0.000
#> GSM182814 1 0.0000 0.961 1.000 0.000
#> GSM182815 2 0.0000 0.824 0.000 1.000
#> GSM182816 1 0.0000 0.961 1.000 0.000
#> GSM182817 1 0.0000 0.961 1.000 0.000
#> GSM182818 2 0.0000 0.824 0.000 1.000
#> GSM182819 1 0.0000 0.961 1.000 0.000
#> GSM182820 1 0.0000 0.961 1.000 0.000
#> GSM182821 2 0.9866 0.452 0.432 0.568
#> GSM182822 1 0.4022 0.880 0.920 0.080
#> GSM182823 1 0.0000 0.961 1.000 0.000
#> GSM182824 1 0.0000 0.961 1.000 0.000
#> GSM182825 1 0.0000 0.961 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM182755 3 0.3412 0.67476 0.124 0.000 0.876
#> GSM182756 3 0.5891 0.45482 0.036 0.200 0.764
#> GSM182757 3 0.9050 0.30083 0.164 0.304 0.532
#> GSM182758 2 0.8737 0.28837 0.108 0.464 0.428
#> GSM182759 2 0.6282 0.37234 0.324 0.664 0.012
#> GSM182760 3 0.3832 0.59996 0.036 0.076 0.888
#> GSM182761 2 0.2414 0.59467 0.040 0.940 0.020
#> GSM182762 3 0.4702 0.64408 0.212 0.000 0.788
#> GSM182763 2 0.6518 0.49893 0.080 0.752 0.168
#> GSM182764 3 0.9752 0.23116 0.352 0.232 0.416
#> GSM182765 3 0.5812 0.61114 0.264 0.012 0.724
#> GSM182766 2 0.0237 0.59488 0.004 0.996 0.000
#> GSM182767 2 0.8892 0.27155 0.120 0.444 0.436
#> GSM182768 1 0.8834 0.20776 0.464 0.116 0.420
#> GSM182769 3 0.5968 0.17057 0.364 0.000 0.636
#> GSM182770 2 0.2711 0.56165 0.088 0.912 0.000
#> GSM182771 3 0.6204 0.43692 0.424 0.000 0.576
#> GSM182772 2 0.0592 0.59403 0.012 0.988 0.000
#> GSM182773 3 0.6986 0.29711 0.256 0.056 0.688
#> GSM182774 3 0.5363 0.57493 0.276 0.000 0.724
#> GSM182775 3 0.1411 0.64983 0.036 0.000 0.964
#> GSM182776 3 0.1860 0.67229 0.052 0.000 0.948
#> GSM182777 3 0.1411 0.64983 0.036 0.000 0.964
#> GSM182802 2 0.6302 -0.17163 0.480 0.520 0.000
#> GSM182803 3 0.4605 0.63317 0.204 0.000 0.796
#> GSM182804 1 0.5905 0.30242 0.648 0.352 0.000
#> GSM182805 1 0.5859 0.26863 0.656 0.344 0.000
#> GSM182806 3 0.5650 0.54831 0.312 0.000 0.688
#> GSM182807 3 0.3267 0.67414 0.116 0.000 0.884
#> GSM182808 3 0.1753 0.66605 0.048 0.000 0.952
#> GSM182809 1 0.6295 0.16281 0.528 0.472 0.000
#> GSM182810 1 0.6079 0.10798 0.612 0.000 0.388
#> GSM182811 1 0.5835 0.08070 0.660 0.000 0.340
#> GSM182812 1 0.4931 0.29009 0.768 0.000 0.232
#> GSM182813 3 0.3482 0.67143 0.128 0.000 0.872
#> GSM182778 2 0.0000 0.59429 0.000 1.000 0.000
#> GSM182779 3 0.7160 0.47169 0.148 0.132 0.720
#> GSM182780 2 0.5212 0.55607 0.108 0.828 0.064
#> GSM182781 3 0.0747 0.66856 0.016 0.000 0.984
#> GSM182782 2 0.2711 0.57046 0.088 0.912 0.000
#> GSM182783 2 0.6500 0.52539 0.140 0.760 0.100
#> GSM182784 2 0.8892 0.27155 0.120 0.444 0.436
#> GSM182785 2 0.8454 0.11041 0.088 0.480 0.432
#> GSM182786 2 0.2711 0.57046 0.088 0.912 0.000
#> GSM182787 2 0.1411 0.58548 0.036 0.964 0.000
#> GSM182788 2 0.3038 0.56132 0.104 0.896 0.000
#> GSM182789 2 0.8569 0.32479 0.100 0.508 0.392
#> GSM182790 3 0.1411 0.64983 0.036 0.000 0.964
#> GSM182791 1 0.9977 0.05116 0.352 0.300 0.348
#> GSM182792 3 0.9686 -0.15351 0.308 0.240 0.452
#> GSM182793 2 0.5098 0.35601 0.248 0.752 0.000
#> GSM182794 3 0.1647 0.64829 0.036 0.004 0.960
#> GSM182795 2 0.8792 0.27976 0.112 0.456 0.432
#> GSM182796 1 0.9587 -0.18827 0.440 0.204 0.356
#> GSM182797 3 0.3340 0.67491 0.120 0.000 0.880
#> GSM182798 3 0.6633 0.40590 0.444 0.008 0.548
#> GSM182799 1 0.8898 0.14175 0.500 0.372 0.128
#> GSM182800 3 0.2796 0.67733 0.092 0.000 0.908
#> GSM182801 3 0.1411 0.64983 0.036 0.000 0.964
#> GSM182814 3 0.6308 0.24786 0.492 0.000 0.508
#> GSM182815 1 0.6299 0.15673 0.524 0.476 0.000
#> GSM182816 3 0.6168 0.10879 0.412 0.000 0.588
#> GSM182817 3 0.5948 0.48359 0.360 0.000 0.640
#> GSM182818 1 0.5650 0.33122 0.688 0.312 0.000
#> GSM182819 3 0.3686 0.67101 0.140 0.000 0.860
#> GSM182820 3 0.3879 0.66402 0.152 0.000 0.848
#> GSM182821 3 0.9810 -0.25964 0.372 0.240 0.388
#> GSM182822 1 0.7159 0.00722 0.528 0.024 0.448
#> GSM182823 3 0.5497 0.56392 0.292 0.000 0.708
#> GSM182824 3 0.4750 0.54648 0.216 0.000 0.784
#> GSM182825 1 0.5397 0.28435 0.720 0.000 0.280
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM182755 1 0.3172 0.7540 0.840 0.000 0.160 0.000
#> GSM182756 3 0.1389 0.8566 0.048 0.000 0.952 0.000
#> GSM182757 2 0.7379 -0.1410 0.384 0.452 0.164 0.000
#> GSM182758 3 0.0188 0.8519 0.000 0.000 0.996 0.004
#> GSM182759 2 0.3257 0.6891 0.152 0.844 0.004 0.000
#> GSM182760 3 0.1474 0.8558 0.052 0.000 0.948 0.000
#> GSM182761 2 0.3484 0.7825 0.008 0.844 0.144 0.004
#> GSM182762 1 0.2799 0.7631 0.884 0.008 0.108 0.000
#> GSM182763 2 0.2899 0.7984 0.004 0.880 0.112 0.004
#> GSM182764 1 0.6024 0.2822 0.540 0.416 0.044 0.000
#> GSM182765 1 0.5727 0.6901 0.704 0.200 0.096 0.000
#> GSM182766 2 0.2983 0.8123 0.012 0.896 0.076 0.016
#> GSM182767 3 0.0000 0.8527 0.000 0.000 1.000 0.000
#> GSM182768 3 0.1109 0.8406 0.000 0.004 0.968 0.028
#> GSM182769 3 0.1940 0.8481 0.076 0.000 0.924 0.000
#> GSM182770 2 0.6356 0.5276 0.000 0.604 0.088 0.308
#> GSM182771 1 0.3074 0.6305 0.848 0.152 0.000 0.000
#> GSM182772 2 0.3931 0.7626 0.000 0.832 0.040 0.128
#> GSM182773 3 0.1389 0.8566 0.048 0.000 0.952 0.000
#> GSM182774 1 0.1792 0.7538 0.932 0.000 0.068 0.000
#> GSM182775 3 0.2760 0.8214 0.128 0.000 0.872 0.000
#> GSM182776 3 0.4454 0.5831 0.308 0.000 0.692 0.000
#> GSM182777 3 0.2973 0.8088 0.144 0.000 0.856 0.000
#> GSM182802 4 0.1356 0.7395 0.008 0.032 0.000 0.960
#> GSM182803 1 0.2796 0.7559 0.892 0.000 0.092 0.016
#> GSM182804 4 0.1211 0.7544 0.040 0.000 0.000 0.960
#> GSM182805 4 0.4605 0.6636 0.072 0.132 0.000 0.796
#> GSM182806 1 0.1474 0.7471 0.948 0.000 0.052 0.000
#> GSM182807 1 0.2973 0.7583 0.856 0.000 0.144 0.000
#> GSM182808 1 0.4830 0.4339 0.608 0.000 0.392 0.000
#> GSM182809 4 0.0524 0.7492 0.008 0.004 0.000 0.988
#> GSM182810 4 0.4535 0.6597 0.240 0.000 0.016 0.744
#> GSM182811 1 0.4817 0.0748 0.612 0.000 0.000 0.388
#> GSM182812 4 0.4679 0.5198 0.352 0.000 0.000 0.648
#> GSM182813 1 0.2760 0.7614 0.872 0.000 0.128 0.000
#> GSM182778 2 0.3547 0.7987 0.000 0.864 0.072 0.064
#> GSM182779 1 0.6944 0.3347 0.484 0.404 0.112 0.000
#> GSM182780 3 0.4589 0.6426 0.000 0.168 0.784 0.048
#> GSM182781 1 0.4998 0.1260 0.512 0.000 0.488 0.000
#> GSM182782 2 0.1917 0.8084 0.012 0.944 0.036 0.008
#> GSM182783 3 0.3899 0.7306 0.000 0.052 0.840 0.108
#> GSM182784 3 0.0000 0.8527 0.000 0.000 1.000 0.000
#> GSM182785 3 0.5007 0.6503 0.172 0.068 0.760 0.000
#> GSM182786 2 0.0992 0.7983 0.008 0.976 0.012 0.004
#> GSM182787 2 0.3958 0.7695 0.000 0.824 0.144 0.032
#> GSM182788 2 0.0524 0.7906 0.008 0.988 0.000 0.004
#> GSM182789 3 0.0895 0.8484 0.000 0.020 0.976 0.004
#> GSM182790 3 0.2647 0.8271 0.120 0.000 0.880 0.000
#> GSM182791 3 0.4219 0.7429 0.136 0.004 0.820 0.040
#> GSM182792 3 0.1305 0.8574 0.036 0.000 0.960 0.004
#> GSM182793 4 0.6793 0.1520 0.000 0.288 0.132 0.580
#> GSM182794 3 0.2589 0.8299 0.116 0.000 0.884 0.000
#> GSM182795 3 0.0707 0.8472 0.000 0.000 0.980 0.020
#> GSM182796 1 0.4843 0.3223 0.604 0.396 0.000 0.000
#> GSM182797 1 0.3172 0.7540 0.840 0.000 0.160 0.000
#> GSM182798 1 0.3172 0.6259 0.840 0.160 0.000 0.000
#> GSM182799 3 0.5464 0.5839 0.000 0.064 0.708 0.228
#> GSM182800 1 0.4103 0.6734 0.744 0.000 0.256 0.000
#> GSM182801 3 0.2973 0.8088 0.144 0.000 0.856 0.000
#> GSM182814 1 0.5170 0.5199 0.724 0.000 0.048 0.228
#> GSM182815 4 0.0000 0.7462 0.000 0.000 0.000 1.000
#> GSM182816 3 0.4375 0.7632 0.180 0.000 0.788 0.032
#> GSM182817 1 0.1936 0.6853 0.940 0.032 0.000 0.028
#> GSM182818 4 0.1211 0.7544 0.040 0.000 0.000 0.960
#> GSM182819 1 0.2814 0.7615 0.868 0.000 0.132 0.000
#> GSM182820 1 0.2868 0.7609 0.864 0.000 0.136 0.000
#> GSM182821 3 0.5539 0.6720 0.064 0.016 0.744 0.176
#> GSM182822 4 0.7081 0.1285 0.352 0.000 0.136 0.512
#> GSM182823 1 0.1637 0.7504 0.940 0.000 0.060 0.000
#> GSM182824 1 0.6113 0.6249 0.636 0.000 0.284 0.080
#> GSM182825 4 0.4103 0.6633 0.256 0.000 0.000 0.744
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM182755 1 0.2448 0.6010 0.892 0.000 0.088 0.000 0.020
#> GSM182756 3 0.5739 0.6808 0.196 0.024 0.668 0.000 0.112
#> GSM182757 1 0.7572 -0.1087 0.452 0.172 0.076 0.000 0.300
#> GSM182758 3 0.4606 0.7247 0.108 0.012 0.768 0.000 0.112
#> GSM182759 2 0.4129 0.6158 0.040 0.756 0.000 0.000 0.204
#> GSM182760 3 0.2482 0.7493 0.084 0.000 0.892 0.000 0.024
#> GSM182761 2 0.1915 0.7519 0.000 0.928 0.032 0.000 0.040
#> GSM182762 1 0.4046 0.4491 0.780 0.008 0.032 0.000 0.180
#> GSM182763 2 0.3736 0.6939 0.004 0.824 0.100 0.000 0.072
#> GSM182764 1 0.6341 -0.2849 0.524 0.220 0.000 0.000 0.256
#> GSM182765 1 0.6547 -0.5070 0.452 0.108 0.024 0.000 0.416
#> GSM182766 2 0.2116 0.7603 0.000 0.912 0.004 0.008 0.076
#> GSM182767 3 0.3613 0.7317 0.048 0.076 0.848 0.000 0.028
#> GSM182768 3 0.1616 0.7273 0.004 0.008 0.948 0.008 0.032
#> GSM182769 3 0.4679 0.7173 0.124 0.000 0.740 0.000 0.136
#> GSM182770 2 0.5122 0.3773 0.000 0.584 0.012 0.380 0.024
#> GSM182771 1 0.4961 -0.4423 0.520 0.020 0.000 0.004 0.456
#> GSM182772 2 0.3622 0.7298 0.000 0.820 0.000 0.124 0.056
#> GSM182773 3 0.1300 0.7427 0.028 0.000 0.956 0.000 0.016
#> GSM182774 1 0.3773 0.4736 0.800 0.000 0.032 0.004 0.164
#> GSM182775 3 0.1872 0.7425 0.052 0.000 0.928 0.000 0.020
#> GSM182776 3 0.5223 0.3124 0.444 0.000 0.512 0.000 0.044
#> GSM182777 3 0.2624 0.7363 0.116 0.000 0.872 0.000 0.012
#> GSM182802 4 0.1041 0.7185 0.000 0.032 0.000 0.964 0.004
#> GSM182803 1 0.2006 0.6079 0.932 0.000 0.024 0.020 0.024
#> GSM182804 4 0.0162 0.7272 0.000 0.000 0.000 0.996 0.004
#> GSM182805 2 0.7840 -0.0564 0.044 0.368 0.008 0.296 0.284
#> GSM182806 1 0.2248 0.5657 0.900 0.000 0.012 0.000 0.088
#> GSM182807 1 0.1270 0.6123 0.948 0.000 0.052 0.000 0.000
#> GSM182808 1 0.4441 0.4309 0.720 0.000 0.236 0.000 0.044
#> GSM182809 4 0.3432 0.7205 0.016 0.012 0.024 0.860 0.088
#> GSM182810 4 0.5368 0.2357 0.416 0.000 0.016 0.540 0.028
#> GSM182811 1 0.5691 0.0947 0.536 0.000 0.000 0.376 0.088
#> GSM182812 4 0.4453 0.5749 0.228 0.000 0.000 0.724 0.048
#> GSM182813 1 0.1043 0.6124 0.960 0.000 0.040 0.000 0.000
#> GSM182778 2 0.1924 0.7506 0.000 0.924 0.008 0.064 0.004
#> GSM182779 5 0.8287 0.4236 0.208 0.268 0.152 0.000 0.372
#> GSM182780 3 0.4257 0.6695 0.000 0.164 0.780 0.016 0.040
#> GSM182781 3 0.6669 0.1903 0.368 0.000 0.400 0.000 0.232
#> GSM182782 2 0.1608 0.7552 0.000 0.928 0.000 0.000 0.072
#> GSM182783 3 0.7154 0.5179 0.020 0.048 0.580 0.180 0.172
#> GSM182784 3 0.3288 0.7485 0.060 0.028 0.868 0.000 0.044
#> GSM182785 3 0.7577 0.4295 0.212 0.248 0.468 0.000 0.072
#> GSM182786 2 0.2280 0.7272 0.000 0.880 0.000 0.000 0.120
#> GSM182787 2 0.1560 0.7531 0.000 0.948 0.028 0.004 0.020
#> GSM182788 2 0.3305 0.6264 0.000 0.776 0.000 0.000 0.224
#> GSM182789 3 0.7364 0.3700 0.116 0.352 0.448 0.000 0.084
#> GSM182790 3 0.5283 0.6774 0.204 0.000 0.672 0.000 0.124
#> GSM182791 3 0.5969 0.6786 0.140 0.072 0.704 0.016 0.068
#> GSM182792 3 0.1808 0.7455 0.040 0.004 0.936 0.000 0.020
#> GSM182793 4 0.5573 0.3325 0.000 0.264 0.016 0.644 0.076
#> GSM182794 3 0.2727 0.7415 0.116 0.000 0.868 0.000 0.016
#> GSM182795 3 0.4726 0.7179 0.080 0.008 0.756 0.004 0.152
#> GSM182796 5 0.6525 0.5705 0.308 0.220 0.000 0.000 0.472
#> GSM182797 1 0.2740 0.5961 0.876 0.000 0.096 0.000 0.028
#> GSM182798 5 0.5293 0.3698 0.460 0.048 0.000 0.000 0.492
#> GSM182799 3 0.4229 0.6550 0.000 0.024 0.800 0.124 0.052
#> GSM182800 3 0.7398 0.0694 0.328 0.000 0.448 0.060 0.164
#> GSM182801 3 0.2054 0.7387 0.052 0.000 0.920 0.000 0.028
#> GSM182814 1 0.5069 0.3295 0.648 0.000 0.012 0.304 0.036
#> GSM182815 4 0.0771 0.7214 0.000 0.004 0.000 0.976 0.020
#> GSM182816 1 0.6186 -0.1111 0.496 0.000 0.412 0.040 0.052
#> GSM182817 1 0.2605 0.5539 0.896 0.004 0.000 0.044 0.056
#> GSM182818 4 0.4608 0.6445 0.008 0.016 0.004 0.688 0.284
#> GSM182819 1 0.1484 0.6123 0.944 0.000 0.048 0.000 0.008
#> GSM182820 1 0.1893 0.6052 0.928 0.000 0.048 0.000 0.024
#> GSM182821 3 0.8309 0.2322 0.180 0.280 0.388 0.004 0.148
#> GSM182822 1 0.6667 0.3887 0.640 0.024 0.044 0.160 0.132
#> GSM182823 1 0.2666 0.5747 0.892 0.000 0.020 0.012 0.076
#> GSM182824 1 0.5212 0.5080 0.740 0.000 0.136 0.064 0.060
#> GSM182825 4 0.4946 0.5319 0.260 0.000 0.004 0.680 0.056
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM182755 1 0.3652 0.5955 0.816 0.000 0.084 0.000 0.080 0.020
#> GSM182756 3 0.7766 0.0279 0.228 0.012 0.356 0.000 0.152 0.252
#> GSM182757 1 0.8546 -0.0657 0.340 0.112 0.132 0.000 0.224 0.192
#> GSM182758 3 0.7592 0.0968 0.156 0.016 0.404 0.000 0.148 0.276
#> GSM182759 2 0.3804 0.4491 0.008 0.656 0.000 0.000 0.336 0.000
#> GSM182760 3 0.2526 0.6146 0.096 0.000 0.876 0.000 0.004 0.024
#> GSM182761 2 0.3437 0.6149 0.000 0.832 0.092 0.000 0.052 0.024
#> GSM182762 1 0.5544 0.0554 0.588 0.016 0.056 0.000 0.316 0.024
#> GSM182763 2 0.6245 0.3243 0.016 0.520 0.232 0.000 0.224 0.008
#> GSM182764 5 0.6531 0.4291 0.356 0.180 0.020 0.000 0.432 0.012
#> GSM182765 5 0.5640 0.6291 0.296 0.048 0.036 0.000 0.600 0.020
#> GSM182766 2 0.3210 0.6413 0.000 0.836 0.004 0.016 0.124 0.020
#> GSM182767 3 0.4088 0.6015 0.076 0.064 0.808 0.000 0.020 0.032
#> GSM182768 3 0.3254 0.5838 0.028 0.004 0.868 0.024 0.040 0.036
#> GSM182769 3 0.7204 0.0506 0.140 0.000 0.400 0.000 0.152 0.308
#> GSM182770 2 0.4759 0.1911 0.000 0.540 0.000 0.420 0.016 0.024
#> GSM182771 5 0.4001 0.6849 0.268 0.020 0.000 0.000 0.704 0.008
#> GSM182772 2 0.3874 0.6009 0.000 0.760 0.000 0.172 0.068 0.000
#> GSM182773 3 0.3031 0.6017 0.048 0.000 0.860 0.000 0.020 0.072
#> GSM182774 1 0.4982 0.3538 0.684 0.000 0.020 0.020 0.232 0.044
#> GSM182775 3 0.3514 0.6061 0.096 0.000 0.828 0.000 0.040 0.036
#> GSM182776 1 0.5333 0.0489 0.516 0.000 0.408 0.000 0.036 0.040
#> GSM182777 3 0.3729 0.5993 0.136 0.000 0.800 0.000 0.040 0.024
#> GSM182802 4 0.1757 0.6962 0.000 0.076 0.000 0.916 0.008 0.000
#> GSM182803 1 0.2494 0.6487 0.900 0.000 0.004 0.036 0.032 0.028
#> GSM182804 4 0.0837 0.7103 0.004 0.004 0.020 0.972 0.000 0.000
#> GSM182805 6 0.6370 -0.1218 0.028 0.336 0.000 0.116 0.020 0.500
#> GSM182806 1 0.2488 0.5866 0.864 0.000 0.004 0.000 0.124 0.008
#> GSM182807 1 0.1138 0.6553 0.960 0.000 0.024 0.000 0.012 0.004
#> GSM182808 1 0.4206 0.5984 0.780 0.000 0.128 0.004 0.048 0.040
#> GSM182809 4 0.4451 0.6350 0.036 0.028 0.036 0.784 0.004 0.112
#> GSM182810 1 0.5649 0.3068 0.556 0.000 0.004 0.332 0.024 0.084
#> GSM182811 1 0.6457 0.3317 0.556 0.000 0.000 0.208 0.124 0.112
#> GSM182812 4 0.3867 0.6153 0.128 0.000 0.000 0.780 0.088 0.004
#> GSM182813 1 0.0806 0.6558 0.972 0.000 0.020 0.000 0.008 0.000
#> GSM182778 2 0.1562 0.6470 0.000 0.940 0.004 0.032 0.024 0.000
#> GSM182779 5 0.8376 0.2228 0.104 0.172 0.176 0.000 0.392 0.156
#> GSM182780 3 0.4292 0.4909 0.000 0.204 0.740 0.016 0.016 0.024
#> GSM182781 6 0.7654 -0.1284 0.228 0.000 0.264 0.000 0.196 0.312
#> GSM182782 2 0.1918 0.6487 0.000 0.904 0.000 0.000 0.088 0.008
#> GSM182783 6 0.8576 -0.0351 0.024 0.052 0.288 0.140 0.160 0.336
#> GSM182784 3 0.4221 0.5881 0.080 0.060 0.800 0.000 0.020 0.040
#> GSM182785 3 0.7590 0.3025 0.156 0.228 0.472 0.000 0.076 0.068
#> GSM182786 2 0.2100 0.6395 0.000 0.884 0.004 0.000 0.112 0.000
#> GSM182787 2 0.2288 0.6267 0.000 0.900 0.068 0.000 0.016 0.016
#> GSM182788 2 0.3626 0.5008 0.000 0.704 0.004 0.000 0.288 0.004
#> GSM182789 2 0.7290 0.0331 0.104 0.444 0.328 0.000 0.060 0.064
#> GSM182790 3 0.7454 0.0524 0.240 0.000 0.352 0.000 0.136 0.272
#> GSM182791 3 0.6534 0.5141 0.164 0.052 0.640 0.052 0.036 0.056
#> GSM182792 3 0.3762 0.6072 0.076 0.008 0.836 0.024 0.028 0.028
#> GSM182793 4 0.4854 0.5008 0.000 0.240 0.028 0.684 0.008 0.040
#> GSM182794 3 0.4330 0.5969 0.156 0.000 0.756 0.000 0.048 0.040
#> GSM182795 3 0.7444 0.0354 0.116 0.016 0.396 0.000 0.152 0.320
#> GSM182796 5 0.4425 0.6153 0.152 0.132 0.000 0.000 0.716 0.000
#> GSM182797 1 0.3490 0.5982 0.828 0.000 0.068 0.000 0.084 0.020
#> GSM182798 5 0.3831 0.6802 0.268 0.012 0.000 0.000 0.712 0.008
#> GSM182799 3 0.4927 0.5086 0.004 0.032 0.760 0.092 0.060 0.052
#> GSM182800 3 0.8036 0.0854 0.252 0.000 0.392 0.140 0.164 0.052
#> GSM182801 3 0.3823 0.5875 0.100 0.000 0.808 0.000 0.040 0.052
#> GSM182814 1 0.4745 0.5400 0.716 0.000 0.000 0.184 0.048 0.052
#> GSM182815 4 0.1096 0.7071 0.000 0.004 0.020 0.964 0.004 0.008
#> GSM182816 1 0.5699 0.4482 0.640 0.000 0.228 0.044 0.068 0.020
#> GSM182817 1 0.4413 0.5803 0.780 0.004 0.004 0.044 0.092 0.076
#> GSM182818 6 0.5180 -0.2408 0.016 0.048 0.004 0.328 0.004 0.600
#> GSM182819 1 0.1218 0.6590 0.956 0.000 0.028 0.000 0.012 0.004
#> GSM182820 1 0.2925 0.6298 0.864 0.000 0.060 0.000 0.064 0.012
#> GSM182821 2 0.7777 -0.1152 0.292 0.292 0.132 0.000 0.012 0.272
#> GSM182822 1 0.6254 0.5151 0.644 0.028 0.032 0.084 0.032 0.180
#> GSM182823 1 0.3353 0.6101 0.844 0.000 0.004 0.020 0.076 0.056
#> GSM182824 1 0.4411 0.6271 0.792 0.000 0.064 0.052 0.064 0.028
#> GSM182825 4 0.5297 0.2534 0.352 0.000 0.000 0.556 0.012 0.080
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n stress(p) development.stage(p) k
#> CV:NMF 64 0.897 2.53e-01 2
#> CV:NMF 34 0.463 4.51e-02 3
#> CV:NMF 62 0.624 2.01e-07 4
#> CV:NMF 48 0.877 3.20e-08 5
#> CV:NMF 44 0.850 1.06e-06 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "hclust"]
# you can also extract it by
# res = res_list["MAD:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 18172 rows and 71 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.403 0.854 0.886 0.4568 0.494 0.494
#> 3 3 0.498 0.759 0.863 0.3325 0.874 0.751
#> 4 4 0.519 0.628 0.747 0.1330 0.891 0.720
#> 5 5 0.573 0.596 0.732 0.0933 0.930 0.774
#> 6 6 0.601 0.549 0.701 0.0473 0.936 0.775
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM182755 1 0.9866 -0.0547 0.568 0.432
#> GSM182756 2 0.7299 0.8856 0.204 0.796
#> GSM182757 2 0.6531 0.9006 0.168 0.832
#> GSM182758 2 0.7299 0.8856 0.204 0.796
#> GSM182759 2 0.6148 0.8990 0.152 0.848
#> GSM182760 2 0.7299 0.8866 0.204 0.796
#> GSM182761 2 0.6623 0.9004 0.172 0.828
#> GSM182762 2 0.8144 0.8426 0.252 0.748
#> GSM182763 2 0.6712 0.8997 0.176 0.824
#> GSM182764 2 0.6247 0.8996 0.156 0.844
#> GSM182765 2 0.6148 0.8990 0.152 0.848
#> GSM182766 2 0.2603 0.8480 0.044 0.956
#> GSM182767 2 0.7299 0.8856 0.204 0.796
#> GSM182768 1 0.2423 0.9128 0.960 0.040
#> GSM182769 1 0.5178 0.8563 0.884 0.116
#> GSM182770 2 0.0000 0.8220 0.000 1.000
#> GSM182771 2 0.5946 0.8969 0.144 0.856
#> GSM182772 2 0.0000 0.8220 0.000 1.000
#> GSM182773 1 0.5294 0.8525 0.880 0.120
#> GSM182774 1 0.3114 0.9056 0.944 0.056
#> GSM182775 1 0.4690 0.8705 0.900 0.100
#> GSM182776 1 0.3733 0.8950 0.928 0.072
#> GSM182777 1 0.7139 0.7522 0.804 0.196
#> GSM182802 2 0.1184 0.8315 0.016 0.984
#> GSM182803 1 0.2236 0.9112 0.964 0.036
#> GSM182804 1 0.8386 0.6592 0.732 0.268
#> GSM182805 2 0.1184 0.8315 0.016 0.984
#> GSM182806 1 0.0000 0.9193 1.000 0.000
#> GSM182807 1 0.0000 0.9193 1.000 0.000
#> GSM182808 1 0.0000 0.9193 1.000 0.000
#> GSM182809 1 0.1843 0.9178 0.972 0.028
#> GSM182810 1 0.1843 0.9178 0.972 0.028
#> GSM182811 1 0.2603 0.9113 0.956 0.044
#> GSM182812 1 0.0000 0.9193 1.000 0.000
#> GSM182813 1 0.0000 0.9193 1.000 0.000
#> GSM182778 2 0.0000 0.8220 0.000 1.000
#> GSM182779 2 0.6623 0.9004 0.172 0.828
#> GSM182780 2 0.6531 0.9008 0.168 0.832
#> GSM182781 2 0.7299 0.8856 0.204 0.796
#> GSM182782 2 0.0000 0.8220 0.000 1.000
#> GSM182783 2 0.6712 0.8998 0.176 0.824
#> GSM182784 2 0.6887 0.8966 0.184 0.816
#> GSM182785 2 0.6801 0.8983 0.180 0.820
#> GSM182786 2 0.0000 0.8220 0.000 1.000
#> GSM182787 2 0.6712 0.8996 0.176 0.824
#> GSM182788 2 0.0000 0.8220 0.000 1.000
#> GSM182789 2 0.6801 0.8983 0.180 0.820
#> GSM182790 2 0.7299 0.8856 0.204 0.796
#> GSM182791 1 0.7950 0.6695 0.760 0.240
#> GSM182792 1 0.5408 0.8491 0.876 0.124
#> GSM182793 2 0.0938 0.8243 0.012 0.988
#> GSM182794 2 0.7376 0.8822 0.208 0.792
#> GSM182795 2 0.7602 0.8709 0.220 0.780
#> GSM182796 2 0.5629 0.8928 0.132 0.868
#> GSM182797 1 0.0000 0.9193 1.000 0.000
#> GSM182798 2 0.5629 0.8928 0.132 0.868
#> GSM182799 1 0.1843 0.9180 0.972 0.028
#> GSM182800 1 0.0672 0.9197 0.992 0.008
#> GSM182801 1 0.1633 0.9181 0.976 0.024
#> GSM182814 1 0.0000 0.9193 1.000 0.000
#> GSM182815 1 0.8386 0.6592 0.732 0.268
#> GSM182816 1 0.0000 0.9193 1.000 0.000
#> GSM182817 2 0.9815 0.5105 0.420 0.580
#> GSM182818 1 0.0672 0.9197 0.992 0.008
#> GSM182819 1 0.0000 0.9193 1.000 0.000
#> GSM182820 1 0.0000 0.9193 1.000 0.000
#> GSM182821 2 0.9710 0.5598 0.400 0.600
#> GSM182822 1 0.1843 0.9178 0.972 0.028
#> GSM182823 1 0.0000 0.9193 1.000 0.000
#> GSM182824 1 0.0000 0.9193 1.000 0.000
#> GSM182825 1 0.0000 0.9193 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM182755 3 0.7069 0.216 0.408 0.024 0.568
#> GSM182756 3 0.1163 0.793 0.028 0.000 0.972
#> GSM182757 3 0.3941 0.720 0.000 0.156 0.844
#> GSM182758 3 0.1163 0.793 0.028 0.000 0.972
#> GSM182759 3 0.4605 0.671 0.000 0.204 0.796
#> GSM182760 3 0.1525 0.794 0.032 0.004 0.964
#> GSM182761 3 0.2796 0.768 0.000 0.092 0.908
#> GSM182762 3 0.2998 0.765 0.068 0.016 0.916
#> GSM182763 3 0.2165 0.781 0.000 0.064 0.936
#> GSM182764 3 0.4555 0.676 0.000 0.200 0.800
#> GSM182765 3 0.5497 0.530 0.000 0.292 0.708
#> GSM182766 3 0.6079 0.257 0.000 0.388 0.612
#> GSM182767 3 0.1163 0.793 0.028 0.000 0.972
#> GSM182768 1 0.4413 0.868 0.852 0.024 0.124
#> GSM182769 1 0.5156 0.792 0.776 0.008 0.216
#> GSM182770 2 0.5327 0.801 0.000 0.728 0.272
#> GSM182771 3 0.6062 0.307 0.000 0.384 0.616
#> GSM182772 2 0.5327 0.801 0.000 0.728 0.272
#> GSM182773 1 0.5202 0.788 0.772 0.008 0.220
#> GSM182774 1 0.3918 0.873 0.868 0.012 0.120
#> GSM182775 1 0.4963 0.806 0.792 0.008 0.200
#> GSM182776 1 0.4164 0.860 0.848 0.008 0.144
#> GSM182777 1 0.5988 0.671 0.688 0.008 0.304
#> GSM182802 2 0.5465 0.786 0.000 0.712 0.288
#> GSM182803 1 0.2703 0.877 0.928 0.016 0.056
#> GSM182804 1 0.7599 0.622 0.656 0.084 0.260
#> GSM182805 2 0.5497 0.783 0.000 0.708 0.292
#> GSM182806 1 0.0747 0.882 0.984 0.016 0.000
#> GSM182807 1 0.0747 0.882 0.984 0.016 0.000
#> GSM182808 1 0.0747 0.882 0.984 0.016 0.000
#> GSM182809 1 0.4056 0.876 0.876 0.032 0.092
#> GSM182810 1 0.4056 0.876 0.876 0.032 0.092
#> GSM182811 1 0.4371 0.870 0.860 0.032 0.108
#> GSM182812 1 0.0237 0.883 0.996 0.004 0.000
#> GSM182813 1 0.0747 0.882 0.984 0.016 0.000
#> GSM182778 2 0.2165 0.806 0.000 0.936 0.064
#> GSM182779 3 0.3038 0.761 0.000 0.104 0.896
#> GSM182780 3 0.1163 0.789 0.000 0.028 0.972
#> GSM182781 3 0.1031 0.793 0.024 0.000 0.976
#> GSM182782 2 0.2165 0.806 0.000 0.936 0.064
#> GSM182783 3 0.1015 0.793 0.008 0.012 0.980
#> GSM182784 3 0.0829 0.793 0.004 0.012 0.984
#> GSM182785 3 0.0592 0.792 0.000 0.012 0.988
#> GSM182786 2 0.2165 0.806 0.000 0.936 0.064
#> GSM182787 3 0.2625 0.773 0.000 0.084 0.916
#> GSM182788 2 0.2165 0.806 0.000 0.936 0.064
#> GSM182789 3 0.0747 0.792 0.000 0.016 0.984
#> GSM182790 3 0.1163 0.793 0.028 0.000 0.972
#> GSM182791 1 0.6129 0.639 0.668 0.008 0.324
#> GSM182792 1 0.5012 0.808 0.788 0.008 0.204
#> GSM182793 2 0.5363 0.794 0.000 0.724 0.276
#> GSM182794 3 0.1289 0.792 0.032 0.000 0.968
#> GSM182795 3 0.1643 0.785 0.044 0.000 0.956
#> GSM182796 3 0.6168 0.236 0.000 0.412 0.588
#> GSM182797 1 0.1170 0.884 0.976 0.016 0.008
#> GSM182798 3 0.6126 0.258 0.000 0.400 0.600
#> GSM182799 1 0.4094 0.877 0.872 0.028 0.100
#> GSM182800 1 0.2414 0.887 0.940 0.020 0.040
#> GSM182801 1 0.3832 0.878 0.880 0.020 0.100
#> GSM182814 1 0.0237 0.883 0.996 0.004 0.000
#> GSM182815 1 0.7665 0.611 0.648 0.084 0.268
#> GSM182816 1 0.0237 0.883 0.996 0.004 0.000
#> GSM182817 3 0.6762 0.459 0.288 0.036 0.676
#> GSM182818 1 0.3213 0.884 0.912 0.028 0.060
#> GSM182819 1 0.0237 0.883 0.996 0.004 0.000
#> GSM182820 1 0.0747 0.882 0.984 0.016 0.000
#> GSM182821 3 0.6562 0.491 0.264 0.036 0.700
#> GSM182822 1 0.4056 0.876 0.876 0.032 0.092
#> GSM182823 1 0.0237 0.883 0.996 0.004 0.000
#> GSM182824 1 0.0237 0.883 0.996 0.004 0.000
#> GSM182825 1 0.0424 0.883 0.992 0.008 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM182755 3 0.5805 0.3124 0.388 0.000 0.576 0.036
#> GSM182756 3 0.0895 0.8129 0.004 0.000 0.976 0.020
#> GSM182757 3 0.4037 0.7559 0.000 0.112 0.832 0.056
#> GSM182758 3 0.0779 0.8131 0.004 0.000 0.980 0.016
#> GSM182759 3 0.4656 0.7159 0.000 0.160 0.784 0.056
#> GSM182760 3 0.1749 0.8140 0.012 0.012 0.952 0.024
#> GSM182761 3 0.2840 0.7970 0.000 0.044 0.900 0.056
#> GSM182762 3 0.2275 0.7900 0.048 0.004 0.928 0.020
#> GSM182763 3 0.1867 0.8052 0.000 0.072 0.928 0.000
#> GSM182764 3 0.4609 0.7198 0.000 0.156 0.788 0.056
#> GSM182765 3 0.4868 0.5809 0.000 0.304 0.684 0.012
#> GSM182766 3 0.5300 0.3561 0.000 0.408 0.580 0.012
#> GSM182767 3 0.0779 0.8131 0.004 0.000 0.980 0.016
#> GSM182768 4 0.6668 0.6528 0.380 0.000 0.092 0.528
#> GSM182769 4 0.7647 0.5373 0.388 0.000 0.208 0.404
#> GSM182770 2 0.2593 0.8205 0.000 0.892 0.104 0.004
#> GSM182771 3 0.4925 0.3671 0.000 0.428 0.572 0.000
#> GSM182772 2 0.2593 0.8205 0.000 0.892 0.104 0.004
#> GSM182773 4 0.7665 0.5355 0.384 0.000 0.212 0.404
#> GSM182774 4 0.6627 0.6300 0.412 0.000 0.084 0.504
#> GSM182775 1 0.7589 -0.5761 0.408 0.000 0.196 0.396
#> GSM182776 4 0.6944 0.6298 0.404 0.000 0.112 0.484
#> GSM182777 1 0.7877 -0.4554 0.388 0.000 0.300 0.312
#> GSM182802 2 0.3099 0.8175 0.000 0.876 0.104 0.020
#> GSM182803 1 0.5640 0.3849 0.656 0.024 0.012 0.308
#> GSM182804 4 0.8243 0.4681 0.168 0.160 0.100 0.572
#> GSM182805 2 0.3160 0.8162 0.000 0.872 0.108 0.020
#> GSM182806 1 0.0336 0.6962 0.992 0.000 0.000 0.008
#> GSM182807 1 0.0188 0.6973 0.996 0.000 0.000 0.004
#> GSM182808 1 0.0000 0.6967 1.000 0.000 0.000 0.000
#> GSM182809 4 0.5423 0.6324 0.332 0.000 0.028 0.640
#> GSM182810 4 0.5460 0.6267 0.340 0.000 0.028 0.632
#> GSM182811 4 0.5857 0.6041 0.340 0.008 0.032 0.620
#> GSM182812 1 0.2149 0.7009 0.912 0.000 0.000 0.088
#> GSM182813 1 0.0188 0.6973 0.996 0.000 0.000 0.004
#> GSM182778 2 0.5010 0.7995 0.000 0.700 0.024 0.276
#> GSM182779 3 0.3090 0.7916 0.000 0.056 0.888 0.056
#> GSM182780 3 0.1118 0.8144 0.000 0.036 0.964 0.000
#> GSM182781 3 0.0592 0.8131 0.000 0.000 0.984 0.016
#> GSM182782 2 0.5010 0.7995 0.000 0.700 0.024 0.276
#> GSM182783 3 0.1284 0.8169 0.000 0.024 0.964 0.012
#> GSM182784 3 0.0592 0.8156 0.000 0.016 0.984 0.000
#> GSM182785 3 0.0707 0.8152 0.000 0.020 0.980 0.000
#> GSM182786 2 0.5010 0.7995 0.000 0.700 0.024 0.276
#> GSM182787 3 0.2675 0.8005 0.000 0.044 0.908 0.048
#> GSM182788 2 0.5010 0.7995 0.000 0.700 0.024 0.276
#> GSM182789 3 0.0817 0.8152 0.000 0.024 0.976 0.000
#> GSM182790 3 0.0779 0.8131 0.004 0.000 0.980 0.016
#> GSM182791 4 0.7863 0.4664 0.300 0.000 0.304 0.396
#> GSM182792 4 0.7489 0.6018 0.364 0.000 0.184 0.452
#> GSM182793 2 0.3037 0.8172 0.000 0.880 0.100 0.020
#> GSM182794 3 0.0895 0.8127 0.004 0.000 0.976 0.020
#> GSM182795 3 0.1543 0.8080 0.008 0.004 0.956 0.032
#> GSM182796 3 0.6819 0.3703 0.000 0.312 0.564 0.124
#> GSM182797 1 0.0937 0.6885 0.976 0.000 0.012 0.012
#> GSM182798 3 0.4955 0.3298 0.000 0.444 0.556 0.000
#> GSM182799 4 0.6497 0.6534 0.376 0.004 0.068 0.552
#> GSM182800 1 0.5284 0.0682 0.616 0.000 0.016 0.368
#> GSM182801 4 0.6392 0.6333 0.404 0.000 0.068 0.528
#> GSM182814 1 0.2149 0.7009 0.912 0.000 0.000 0.088
#> GSM182815 4 0.8133 0.4625 0.156 0.160 0.100 0.584
#> GSM182816 1 0.3942 0.5422 0.764 0.000 0.000 0.236
#> GSM182817 3 0.6724 0.3873 0.052 0.028 0.588 0.332
#> GSM182818 4 0.4790 0.5885 0.380 0.000 0.000 0.620
#> GSM182819 1 0.3942 0.5422 0.764 0.000 0.000 0.236
#> GSM182820 1 0.0336 0.6962 0.992 0.000 0.000 0.008
#> GSM182821 3 0.6273 0.4529 0.048 0.016 0.624 0.312
#> GSM182822 4 0.5460 0.6267 0.340 0.000 0.028 0.632
#> GSM182823 1 0.2149 0.7009 0.912 0.000 0.000 0.088
#> GSM182824 1 0.2149 0.7009 0.912 0.000 0.000 0.088
#> GSM182825 1 0.3801 0.5707 0.780 0.000 0.000 0.220
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM182755 1 0.7842 -0.0727 0.352 0.000 0.068 0.248 0.332
#> GSM182756 5 0.2984 0.7588 0.000 0.000 0.032 0.108 0.860
#> GSM182757 5 0.3578 0.7262 0.000 0.048 0.000 0.132 0.820
#> GSM182758 5 0.2769 0.7598 0.000 0.000 0.032 0.092 0.876
#> GSM182759 5 0.4779 0.6756 0.000 0.096 0.004 0.164 0.736
#> GSM182760 5 0.2155 0.7786 0.008 0.008 0.028 0.028 0.928
#> GSM182761 5 0.2130 0.7624 0.000 0.012 0.000 0.080 0.908
#> GSM182762 5 0.5028 0.6561 0.040 0.000 0.036 0.204 0.720
#> GSM182763 5 0.1981 0.7704 0.000 0.048 0.000 0.028 0.924
#> GSM182764 5 0.4728 0.6789 0.000 0.092 0.004 0.164 0.740
#> GSM182765 5 0.6133 0.5027 0.004 0.276 0.008 0.124 0.588
#> GSM182766 5 0.5256 0.3483 0.000 0.420 0.000 0.048 0.532
#> GSM182767 5 0.2824 0.7587 0.000 0.000 0.032 0.096 0.872
#> GSM182768 3 0.4841 0.6504 0.200 0.000 0.732 0.028 0.040
#> GSM182769 3 0.6751 0.6055 0.212 0.000 0.596 0.104 0.088
#> GSM182770 2 0.0000 0.7695 0.000 1.000 0.000 0.000 0.000
#> GSM182771 5 0.6374 0.2911 0.004 0.400 0.008 0.112 0.476
#> GSM182772 2 0.0000 0.7695 0.000 1.000 0.000 0.000 0.000
#> GSM182773 3 0.6772 0.6043 0.208 0.000 0.596 0.104 0.092
#> GSM182774 3 0.4898 0.6402 0.200 0.000 0.728 0.048 0.024
#> GSM182775 3 0.6784 0.5987 0.232 0.000 0.584 0.096 0.088
#> GSM182776 3 0.5607 0.6421 0.220 0.000 0.676 0.064 0.040
#> GSM182777 3 0.7636 0.5085 0.220 0.000 0.492 0.104 0.184
#> GSM182802 2 0.0771 0.7656 0.000 0.976 0.020 0.004 0.000
#> GSM182803 3 0.5893 -0.2379 0.460 0.016 0.464 0.060 0.000
#> GSM182804 3 0.6480 0.4040 0.040 0.260 0.584 0.116 0.000
#> GSM182805 2 0.0932 0.7620 0.000 0.972 0.020 0.004 0.004
#> GSM182806 1 0.1041 0.7093 0.964 0.000 0.032 0.004 0.000
#> GSM182807 1 0.0955 0.7101 0.968 0.000 0.028 0.004 0.000
#> GSM182808 1 0.0703 0.7107 0.976 0.000 0.024 0.000 0.000
#> GSM182809 3 0.3635 0.5972 0.088 0.000 0.836 0.068 0.008
#> GSM182810 3 0.3798 0.5907 0.100 0.000 0.824 0.068 0.008
#> GSM182811 3 0.4168 0.5634 0.112 0.004 0.804 0.072 0.008
#> GSM182812 1 0.4031 0.6803 0.772 0.000 0.184 0.044 0.000
#> GSM182813 1 0.0955 0.7101 0.968 0.000 0.028 0.004 0.000
#> GSM182778 4 0.4748 1.0000 0.000 0.492 0.000 0.492 0.016
#> GSM182779 5 0.2408 0.7579 0.000 0.016 0.000 0.092 0.892
#> GSM182780 5 0.0794 0.7761 0.000 0.028 0.000 0.000 0.972
#> GSM182781 5 0.2351 0.7685 0.000 0.000 0.016 0.088 0.896
#> GSM182782 4 0.4748 1.0000 0.000 0.492 0.000 0.492 0.016
#> GSM182783 5 0.2547 0.7727 0.000 0.016 0.016 0.068 0.900
#> GSM182784 5 0.0290 0.7764 0.000 0.008 0.000 0.000 0.992
#> GSM182785 5 0.0404 0.7760 0.000 0.012 0.000 0.000 0.988
#> GSM182786 4 0.4748 1.0000 0.000 0.492 0.000 0.492 0.016
#> GSM182787 5 0.2046 0.7654 0.000 0.016 0.000 0.068 0.916
#> GSM182788 2 0.4748 -1.0000 0.000 0.492 0.000 0.492 0.016
#> GSM182789 5 0.0510 0.7761 0.000 0.016 0.000 0.000 0.984
#> GSM182790 5 0.2824 0.7591 0.000 0.000 0.032 0.096 0.872
#> GSM182791 3 0.6809 0.5503 0.124 0.000 0.588 0.076 0.212
#> GSM182792 3 0.6311 0.6345 0.184 0.000 0.644 0.076 0.096
#> GSM182793 2 0.0609 0.7570 0.000 0.980 0.000 0.020 0.000
#> GSM182794 5 0.3058 0.7546 0.000 0.000 0.044 0.096 0.860
#> GSM182795 5 0.3090 0.7534 0.000 0.000 0.052 0.088 0.860
#> GSM182796 5 0.6947 0.2542 0.004 0.236 0.008 0.292 0.460
#> GSM182797 1 0.1872 0.6876 0.928 0.000 0.052 0.020 0.000
#> GSM182798 5 0.6356 0.2420 0.004 0.424 0.008 0.108 0.456
#> GSM182799 3 0.4556 0.6562 0.160 0.004 0.772 0.024 0.040
#> GSM182800 3 0.5143 0.1523 0.420 0.000 0.544 0.032 0.004
#> GSM182801 3 0.4821 0.6457 0.208 0.000 0.728 0.024 0.040
#> GSM182814 1 0.4031 0.6803 0.772 0.000 0.184 0.044 0.000
#> GSM182815 3 0.6226 0.3907 0.028 0.260 0.600 0.112 0.000
#> GSM182816 1 0.5240 0.3998 0.584 0.000 0.360 0.056 0.000
#> GSM182817 5 0.7101 0.2313 0.008 0.028 0.360 0.144 0.460
#> GSM182818 3 0.4855 0.5822 0.168 0.000 0.720 0.112 0.000
#> GSM182819 1 0.5240 0.3998 0.584 0.000 0.360 0.056 0.000
#> GSM182820 1 0.1041 0.7093 0.964 0.000 0.032 0.004 0.000
#> GSM182821 5 0.6783 0.3026 0.004 0.020 0.344 0.140 0.492
#> GSM182822 3 0.3798 0.5907 0.100 0.000 0.824 0.068 0.008
#> GSM182823 1 0.4031 0.6803 0.772 0.000 0.184 0.044 0.000
#> GSM182824 1 0.4031 0.6803 0.772 0.000 0.184 0.044 0.000
#> GSM182825 1 0.5036 0.4918 0.628 0.000 0.320 0.052 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM182755 5 0.8081 0.18034 0.296 0.004 0.156 0.144 0.360 0.040
#> GSM182756 3 0.4133 0.64994 0.000 0.000 0.772 0.024 0.064 0.140
#> GSM182757 3 0.3295 0.66666 0.000 0.012 0.800 0.176 0.012 0.000
#> GSM182758 3 0.3222 0.67919 0.000 0.000 0.824 0.024 0.012 0.140
#> GSM182759 3 0.4756 0.59787 0.000 0.060 0.696 0.216 0.028 0.000
#> GSM182760 3 0.1932 0.72288 0.004 0.004 0.912 0.004 0.000 0.076
#> GSM182761 3 0.1700 0.71729 0.000 0.004 0.916 0.080 0.000 0.000
#> GSM182762 3 0.6040 0.20750 0.004 0.004 0.528 0.136 0.312 0.016
#> GSM182763 3 0.1864 0.72203 0.000 0.040 0.924 0.032 0.004 0.000
#> GSM182764 3 0.4701 0.60136 0.000 0.056 0.700 0.216 0.028 0.000
#> GSM182765 3 0.6425 0.34250 0.000 0.260 0.524 0.152 0.064 0.000
#> GSM182766 3 0.5265 0.28704 0.000 0.388 0.520 0.088 0.004 0.000
#> GSM182767 3 0.3300 0.67374 0.000 0.000 0.816 0.024 0.012 0.148
#> GSM182768 6 0.3738 0.57823 0.100 0.000 0.008 0.016 0.060 0.816
#> GSM182769 6 0.3650 0.54959 0.116 0.000 0.032 0.020 0.012 0.820
#> GSM182770 2 0.0291 0.72561 0.000 0.992 0.004 0.004 0.000 0.000
#> GSM182771 3 0.6608 0.00289 0.000 0.384 0.412 0.140 0.064 0.000
#> GSM182772 2 0.0291 0.72561 0.000 0.992 0.004 0.004 0.000 0.000
#> GSM182773 6 0.3721 0.54733 0.116 0.000 0.036 0.020 0.012 0.816
#> GSM182774 6 0.4933 0.52798 0.128 0.000 0.008 0.004 0.172 0.688
#> GSM182775 6 0.4150 0.55133 0.132 0.000 0.032 0.020 0.028 0.788
#> GSM182776 6 0.4580 0.56239 0.124 0.000 0.008 0.008 0.124 0.736
#> GSM182777 6 0.5260 0.44363 0.136 0.000 0.128 0.024 0.016 0.696
#> GSM182802 2 0.1080 0.71598 0.000 0.960 0.004 0.000 0.032 0.004
#> GSM182803 1 0.6678 0.36120 0.428 0.000 0.000 0.044 0.308 0.220
#> GSM182804 6 0.7817 0.08407 0.072 0.260 0.000 0.044 0.280 0.344
#> GSM182805 2 0.1155 0.71278 0.000 0.956 0.004 0.000 0.036 0.004
#> GSM182806 1 0.1788 0.69557 0.916 0.000 0.000 0.004 0.004 0.076
#> GSM182807 1 0.1732 0.69605 0.920 0.000 0.000 0.004 0.004 0.072
#> GSM182808 1 0.1444 0.69812 0.928 0.000 0.000 0.000 0.000 0.072
#> GSM182809 6 0.5224 0.22577 0.092 0.000 0.000 0.000 0.440 0.468
#> GSM182810 6 0.5262 0.21545 0.096 0.000 0.000 0.000 0.448 0.456
#> GSM182811 5 0.5508 -0.37638 0.112 0.000 0.000 0.004 0.472 0.412
#> GSM182812 1 0.4417 0.71401 0.748 0.000 0.000 0.056 0.160 0.036
#> GSM182813 1 0.1732 0.69605 0.920 0.000 0.000 0.004 0.004 0.072
#> GSM182778 4 0.3835 1.00000 0.000 0.320 0.012 0.668 0.000 0.000
#> GSM182779 3 0.2113 0.71146 0.000 0.008 0.896 0.092 0.004 0.000
#> GSM182780 3 0.0547 0.73023 0.000 0.020 0.980 0.000 0.000 0.000
#> GSM182781 3 0.2829 0.70292 0.000 0.000 0.864 0.024 0.016 0.096
#> GSM182782 4 0.3835 1.00000 0.000 0.320 0.012 0.668 0.000 0.000
#> GSM182783 3 0.2804 0.71086 0.000 0.012 0.876 0.020 0.012 0.080
#> GSM182784 3 0.0291 0.72955 0.000 0.004 0.992 0.000 0.000 0.004
#> GSM182785 3 0.0146 0.72927 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM182786 4 0.3835 1.00000 0.000 0.320 0.012 0.668 0.000 0.000
#> GSM182787 3 0.1643 0.72035 0.000 0.008 0.924 0.068 0.000 0.000
#> GSM182788 4 0.3835 1.00000 0.000 0.320 0.012 0.668 0.000 0.000
#> GSM182789 3 0.0260 0.72978 0.000 0.008 0.992 0.000 0.000 0.000
#> GSM182790 3 0.3261 0.67685 0.000 0.000 0.820 0.024 0.012 0.144
#> GSM182791 6 0.4244 0.41480 0.080 0.000 0.168 0.000 0.008 0.744
#> GSM182792 6 0.3533 0.56025 0.100 0.000 0.052 0.000 0.024 0.824
#> GSM182793 2 0.0912 0.71723 0.000 0.972 0.004 0.012 0.004 0.008
#> GSM182794 3 0.3411 0.66457 0.000 0.000 0.804 0.024 0.012 0.160
#> GSM182795 3 0.3375 0.66866 0.000 0.000 0.808 0.024 0.012 0.156
#> GSM182796 3 0.6790 0.15826 0.000 0.204 0.412 0.328 0.056 0.000
#> GSM182797 1 0.3015 0.64106 0.844 0.000 0.000 0.024 0.012 0.120
#> GSM182798 2 0.6546 -0.15675 0.000 0.404 0.400 0.136 0.060 0.000
#> GSM182799 6 0.4043 0.56507 0.084 0.004 0.008 0.020 0.080 0.804
#> GSM182800 6 0.6211 0.08827 0.356 0.000 0.000 0.040 0.128 0.476
#> GSM182801 6 0.4094 0.57632 0.112 0.000 0.008 0.016 0.076 0.788
#> GSM182814 1 0.4417 0.71401 0.748 0.000 0.000 0.056 0.160 0.036
#> GSM182815 6 0.7688 0.07799 0.056 0.260 0.000 0.044 0.304 0.336
#> GSM182816 1 0.6162 0.53619 0.560 0.000 0.000 0.048 0.228 0.164
#> GSM182817 5 0.6555 0.43727 0.004 0.012 0.304 0.016 0.472 0.192
#> GSM182818 6 0.6175 0.28992 0.072 0.000 0.000 0.076 0.376 0.476
#> GSM182819 1 0.6162 0.53619 0.560 0.000 0.000 0.048 0.228 0.164
#> GSM182820 1 0.1788 0.69557 0.916 0.000 0.000 0.004 0.004 0.076
#> GSM182821 5 0.6491 0.41447 0.000 0.012 0.336 0.016 0.444 0.192
#> GSM182822 6 0.5262 0.21545 0.096 0.000 0.000 0.000 0.448 0.456
#> GSM182823 1 0.4417 0.71401 0.748 0.000 0.000 0.056 0.160 0.036
#> GSM182824 1 0.4417 0.71401 0.748 0.000 0.000 0.056 0.160 0.036
#> GSM182825 1 0.5880 0.59153 0.604 0.000 0.000 0.056 0.220 0.120
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 stress(p) development.stage(p) k
#> MAD:hclust 70 0.821 3.64e-05 2
#> MAD:hclust 64 0.932 1.53e-05 3
#> MAD:hclust 57 0.687 5.23e-07 4
#> MAD:hclust 56 0.236 8.32e-06 5
#> MAD:hclust 51 0.110 3.68e-08 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "kmeans"]
# you can also extract it by
# res = res_list["MAD:kmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 18172 rows and 71 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.965 0.986 0.5059 0.494 0.494
#> 3 3 0.755 0.862 0.923 0.3037 0.703 0.472
#> 4 4 0.606 0.590 0.733 0.1178 0.850 0.598
#> 5 5 0.631 0.604 0.774 0.0654 0.888 0.617
#> 6 6 0.689 0.568 0.665 0.0433 0.901 0.584
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
#> GSM182755 1 0.6247 0.8039 0.844 0.156
#> GSM182756 2 0.0000 0.9909 0.000 1.000
#> GSM182757 2 0.0000 0.9909 0.000 1.000
#> GSM182758 2 0.0000 0.9909 0.000 1.000
#> GSM182759 2 0.0000 0.9909 0.000 1.000
#> GSM182760 2 0.0672 0.9854 0.008 0.992
#> GSM182761 2 0.0000 0.9909 0.000 1.000
#> GSM182762 2 0.0000 0.9909 0.000 1.000
#> GSM182763 2 0.0000 0.9909 0.000 1.000
#> GSM182764 2 0.0000 0.9909 0.000 1.000
#> GSM182765 2 0.0000 0.9909 0.000 1.000
#> GSM182766 2 0.0000 0.9909 0.000 1.000
#> GSM182767 2 0.0672 0.9854 0.008 0.992
#> GSM182768 1 0.0000 0.9801 1.000 0.000
#> GSM182769 1 0.0000 0.9801 1.000 0.000
#> GSM182770 2 0.0000 0.9909 0.000 1.000
#> GSM182771 2 0.0000 0.9909 0.000 1.000
#> GSM182772 2 0.0000 0.9909 0.000 1.000
#> GSM182773 1 0.0000 0.9801 1.000 0.000
#> GSM182774 1 0.0000 0.9801 1.000 0.000
#> GSM182775 1 0.0000 0.9801 1.000 0.000
#> GSM182776 1 0.0000 0.9801 1.000 0.000
#> GSM182777 1 0.0000 0.9801 1.000 0.000
#> GSM182802 2 0.0000 0.9909 0.000 1.000
#> GSM182803 1 0.0000 0.9801 1.000 0.000
#> GSM182804 1 0.0000 0.9801 1.000 0.000
#> GSM182805 2 0.0000 0.9909 0.000 1.000
#> GSM182806 1 0.0000 0.9801 1.000 0.000
#> GSM182807 1 0.0000 0.9801 1.000 0.000
#> GSM182808 1 0.0000 0.9801 1.000 0.000
#> GSM182809 1 0.0000 0.9801 1.000 0.000
#> GSM182810 1 0.0000 0.9801 1.000 0.000
#> GSM182811 1 0.0000 0.9801 1.000 0.000
#> GSM182812 1 0.0000 0.9801 1.000 0.000
#> GSM182813 1 0.0000 0.9801 1.000 0.000
#> GSM182778 2 0.0000 0.9909 0.000 1.000
#> GSM182779 2 0.0000 0.9909 0.000 1.000
#> GSM182780 2 0.0000 0.9909 0.000 1.000
#> GSM182781 2 0.1184 0.9784 0.016 0.984
#> GSM182782 2 0.0000 0.9909 0.000 1.000
#> GSM182783 2 0.0000 0.9909 0.000 1.000
#> GSM182784 2 0.0000 0.9909 0.000 1.000
#> GSM182785 2 0.0000 0.9909 0.000 1.000
#> GSM182786 2 0.0000 0.9909 0.000 1.000
#> GSM182787 2 0.0000 0.9909 0.000 1.000
#> GSM182788 2 0.0000 0.9909 0.000 1.000
#> GSM182789 2 0.0000 0.9909 0.000 1.000
#> GSM182790 2 0.1184 0.9784 0.016 0.984
#> GSM182791 1 0.9993 0.0428 0.516 0.484
#> GSM182792 1 0.0000 0.9801 1.000 0.000
#> GSM182793 2 0.0000 0.9909 0.000 1.000
#> GSM182794 2 0.0672 0.9854 0.008 0.992
#> GSM182795 2 0.0000 0.9909 0.000 1.000
#> GSM182796 2 0.0000 0.9909 0.000 1.000
#> GSM182797 1 0.0000 0.9801 1.000 0.000
#> GSM182798 2 0.0000 0.9909 0.000 1.000
#> GSM182799 1 0.0000 0.9801 1.000 0.000
#> GSM182800 1 0.0000 0.9801 1.000 0.000
#> GSM182801 1 0.0000 0.9801 1.000 0.000
#> GSM182814 1 0.0000 0.9801 1.000 0.000
#> GSM182815 1 0.0000 0.9801 1.000 0.000
#> GSM182816 1 0.0000 0.9801 1.000 0.000
#> GSM182817 2 0.8207 0.6495 0.256 0.744
#> GSM182818 1 0.0000 0.9801 1.000 0.000
#> GSM182819 1 0.0000 0.9801 1.000 0.000
#> GSM182820 1 0.0000 0.9801 1.000 0.000
#> GSM182821 2 0.0672 0.9854 0.008 0.992
#> GSM182822 1 0.0000 0.9801 1.000 0.000
#> GSM182823 1 0.0000 0.9801 1.000 0.000
#> GSM182824 1 0.0000 0.9801 1.000 0.000
#> GSM182825 1 0.0000 0.9801 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM182755 3 0.4235 0.777 0.176 0.000 0.824
#> GSM182756 3 0.0000 0.892 0.000 0.000 1.000
#> GSM182757 3 0.5905 0.288 0.000 0.352 0.648
#> GSM182758 3 0.0000 0.892 0.000 0.000 1.000
#> GSM182759 2 0.2356 0.897 0.000 0.928 0.072
#> GSM182760 3 0.0000 0.892 0.000 0.000 1.000
#> GSM182761 2 0.5733 0.647 0.000 0.676 0.324
#> GSM182762 3 0.0237 0.891 0.000 0.004 0.996
#> GSM182763 3 0.4974 0.588 0.000 0.236 0.764
#> GSM182764 2 0.6215 0.441 0.000 0.572 0.428
#> GSM182765 3 0.3038 0.801 0.000 0.104 0.896
#> GSM182766 2 0.2356 0.897 0.000 0.928 0.072
#> GSM182767 3 0.0000 0.892 0.000 0.000 1.000
#> GSM182768 3 0.5514 0.764 0.156 0.044 0.800
#> GSM182769 1 0.2796 0.913 0.908 0.000 0.092
#> GSM182770 2 0.1529 0.891 0.000 0.960 0.040
#> GSM182771 2 0.4235 0.799 0.000 0.824 0.176
#> GSM182772 2 0.1529 0.891 0.000 0.960 0.040
#> GSM182773 3 0.3276 0.854 0.068 0.024 0.908
#> GSM182774 1 0.3445 0.910 0.896 0.016 0.088
#> GSM182775 3 0.5859 0.501 0.344 0.000 0.656
#> GSM182776 1 0.2537 0.921 0.920 0.000 0.080
#> GSM182777 3 0.2711 0.851 0.088 0.000 0.912
#> GSM182802 2 0.0000 0.867 0.000 1.000 0.000
#> GSM182803 1 0.0237 0.958 0.996 0.004 0.000
#> GSM182804 1 0.3742 0.917 0.892 0.072 0.036
#> GSM182805 2 0.0237 0.870 0.000 0.996 0.004
#> GSM182806 1 0.0000 0.959 1.000 0.000 0.000
#> GSM182807 1 0.0000 0.959 1.000 0.000 0.000
#> GSM182808 1 0.0000 0.959 1.000 0.000 0.000
#> GSM182809 1 0.4370 0.901 0.868 0.056 0.076
#> GSM182810 1 0.0000 0.959 1.000 0.000 0.000
#> GSM182811 1 0.1529 0.944 0.960 0.040 0.000
#> GSM182812 1 0.0000 0.959 1.000 0.000 0.000
#> GSM182813 1 0.0000 0.959 1.000 0.000 0.000
#> GSM182778 2 0.2356 0.897 0.000 0.928 0.072
#> GSM182779 2 0.6215 0.443 0.000 0.572 0.428
#> GSM182780 3 0.1289 0.869 0.000 0.032 0.968
#> GSM182781 3 0.0000 0.892 0.000 0.000 1.000
#> GSM182782 2 0.2356 0.897 0.000 0.928 0.072
#> GSM182783 3 0.0237 0.891 0.000 0.004 0.996
#> GSM182784 3 0.0000 0.892 0.000 0.000 1.000
#> GSM182785 3 0.0000 0.892 0.000 0.000 1.000
#> GSM182786 2 0.2356 0.897 0.000 0.928 0.072
#> GSM182787 2 0.4555 0.804 0.000 0.800 0.200
#> GSM182788 2 0.2356 0.897 0.000 0.928 0.072
#> GSM182789 3 0.0237 0.891 0.000 0.004 0.996
#> GSM182790 3 0.0000 0.892 0.000 0.000 1.000
#> GSM182791 3 0.3148 0.860 0.036 0.048 0.916
#> GSM182792 3 0.4636 0.815 0.104 0.044 0.852
#> GSM182793 2 0.0424 0.870 0.000 0.992 0.008
#> GSM182794 3 0.0000 0.892 0.000 0.000 1.000
#> GSM182795 3 0.0000 0.892 0.000 0.000 1.000
#> GSM182796 2 0.2066 0.895 0.000 0.940 0.060
#> GSM182797 1 0.0747 0.954 0.984 0.000 0.016
#> GSM182798 2 0.1643 0.892 0.000 0.956 0.044
#> GSM182799 3 0.6107 0.728 0.184 0.052 0.764
#> GSM182800 1 0.3445 0.910 0.896 0.016 0.088
#> GSM182801 1 0.2711 0.916 0.912 0.000 0.088
#> GSM182814 1 0.0000 0.959 1.000 0.000 0.000
#> GSM182815 1 0.3742 0.917 0.892 0.072 0.036
#> GSM182816 1 0.0000 0.959 1.000 0.000 0.000
#> GSM182817 1 0.6452 0.777 0.760 0.088 0.152
#> GSM182818 1 0.1163 0.949 0.972 0.028 0.000
#> GSM182819 1 0.0000 0.959 1.000 0.000 0.000
#> GSM182820 1 0.0000 0.959 1.000 0.000 0.000
#> GSM182821 3 0.1753 0.873 0.000 0.048 0.952
#> GSM182822 1 0.0237 0.958 0.996 0.004 0.000
#> GSM182823 1 0.0000 0.959 1.000 0.000 0.000
#> GSM182824 1 0.0000 0.959 1.000 0.000 0.000
#> GSM182825 1 0.0000 0.959 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM182755 3 0.6892 0.3098 0.240 0.004 0.604 0.152
#> GSM182756 3 0.0336 0.7365 0.000 0.000 0.992 0.008
#> GSM182757 3 0.6078 0.4042 0.000 0.312 0.620 0.068
#> GSM182758 3 0.0000 0.7357 0.000 0.000 1.000 0.000
#> GSM182759 2 0.4203 0.7252 0.000 0.824 0.108 0.068
#> GSM182760 3 0.1118 0.7217 0.000 0.000 0.964 0.036
#> GSM182761 3 0.6371 0.1416 0.000 0.428 0.508 0.064
#> GSM182762 3 0.2965 0.7145 0.000 0.036 0.892 0.072
#> GSM182763 3 0.4534 0.6500 0.000 0.132 0.800 0.068
#> GSM182764 3 0.6337 0.2576 0.000 0.380 0.552 0.068
#> GSM182765 3 0.3056 0.7130 0.000 0.040 0.888 0.072
#> GSM182766 2 0.1733 0.7979 0.000 0.948 0.024 0.028
#> GSM182767 3 0.1389 0.7152 0.000 0.000 0.952 0.048
#> GSM182768 4 0.5781 0.1317 0.028 0.000 0.480 0.492
#> GSM182769 4 0.7748 0.5026 0.336 0.004 0.208 0.452
#> GSM182770 2 0.3751 0.7702 0.000 0.800 0.004 0.196
#> GSM182771 2 0.7121 0.6402 0.000 0.544 0.164 0.292
#> GSM182772 2 0.3791 0.7707 0.000 0.796 0.004 0.200
#> GSM182773 3 0.5039 0.1029 0.000 0.004 0.592 0.404
#> GSM182774 4 0.6770 0.5005 0.292 0.000 0.128 0.580
#> GSM182775 4 0.7558 0.4017 0.168 0.004 0.372 0.456
#> GSM182776 4 0.6932 0.3921 0.404 0.004 0.096 0.496
#> GSM182777 3 0.5706 0.0201 0.020 0.004 0.556 0.420
#> GSM182802 2 0.4776 0.6597 0.000 0.624 0.000 0.376
#> GSM182803 1 0.1302 0.8459 0.956 0.000 0.000 0.044
#> GSM182804 4 0.5378 0.1121 0.348 0.016 0.004 0.632
#> GSM182805 2 0.4713 0.6767 0.000 0.640 0.000 0.360
#> GSM182806 1 0.1489 0.8334 0.952 0.004 0.000 0.044
#> GSM182807 1 0.1489 0.8334 0.952 0.004 0.000 0.044
#> GSM182808 1 0.1489 0.8334 0.952 0.004 0.000 0.044
#> GSM182809 4 0.4746 0.4751 0.168 0.000 0.056 0.776
#> GSM182810 1 0.2647 0.8064 0.880 0.000 0.000 0.120
#> GSM182811 1 0.4624 0.5129 0.660 0.000 0.000 0.340
#> GSM182812 1 0.2281 0.8233 0.904 0.000 0.000 0.096
#> GSM182813 1 0.1489 0.8334 0.952 0.004 0.000 0.044
#> GSM182778 2 0.1151 0.7979 0.000 0.968 0.024 0.008
#> GSM182779 3 0.6326 0.2654 0.000 0.376 0.556 0.068
#> GSM182780 3 0.2282 0.7244 0.000 0.052 0.924 0.024
#> GSM182781 3 0.0592 0.7368 0.000 0.000 0.984 0.016
#> GSM182782 2 0.1151 0.7979 0.000 0.968 0.024 0.008
#> GSM182783 3 0.0188 0.7364 0.000 0.004 0.996 0.000
#> GSM182784 3 0.0000 0.7357 0.000 0.000 1.000 0.000
#> GSM182785 3 0.2739 0.7185 0.000 0.036 0.904 0.060
#> GSM182786 2 0.1151 0.7979 0.000 0.968 0.024 0.008
#> GSM182787 2 0.5535 0.1159 0.000 0.560 0.420 0.020
#> GSM182788 2 0.1151 0.7979 0.000 0.968 0.024 0.008
#> GSM182789 3 0.1109 0.7340 0.000 0.028 0.968 0.004
#> GSM182790 3 0.1557 0.7129 0.000 0.000 0.944 0.056
#> GSM182791 3 0.4933 0.0482 0.000 0.000 0.568 0.432
#> GSM182792 3 0.5285 -0.1034 0.008 0.000 0.524 0.468
#> GSM182793 2 0.4655 0.7260 0.000 0.684 0.004 0.312
#> GSM182794 3 0.1474 0.7124 0.000 0.000 0.948 0.052
#> GSM182795 3 0.0707 0.7284 0.000 0.000 0.980 0.020
#> GSM182796 2 0.1820 0.7929 0.000 0.944 0.020 0.036
#> GSM182797 1 0.4522 0.4052 0.728 0.004 0.004 0.264
#> GSM182798 2 0.5446 0.7471 0.000 0.680 0.044 0.276
#> GSM182799 4 0.5881 0.2588 0.036 0.000 0.420 0.544
#> GSM182800 4 0.6843 0.4691 0.356 0.000 0.112 0.532
#> GSM182801 4 0.7375 0.4445 0.404 0.004 0.140 0.452
#> GSM182814 1 0.1022 0.8479 0.968 0.000 0.000 0.032
#> GSM182815 4 0.5464 0.1180 0.344 0.020 0.004 0.632
#> GSM182816 1 0.1118 0.8479 0.964 0.000 0.000 0.036
#> GSM182817 4 0.7841 0.1484 0.244 0.028 0.184 0.544
#> GSM182818 1 0.4679 0.5004 0.648 0.000 0.000 0.352
#> GSM182819 1 0.1118 0.8479 0.964 0.000 0.000 0.036
#> GSM182820 1 0.1489 0.8334 0.952 0.004 0.000 0.044
#> GSM182821 3 0.3356 0.6333 0.000 0.000 0.824 0.176
#> GSM182822 1 0.4193 0.6307 0.732 0.000 0.000 0.268
#> GSM182823 1 0.0000 0.8455 1.000 0.000 0.000 0.000
#> GSM182824 1 0.0000 0.8455 1.000 0.000 0.000 0.000
#> GSM182825 1 0.2345 0.8209 0.900 0.000 0.000 0.100
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM182755 5 0.8037 -0.00345 0.316 0.000 0.256 0.088 0.340
#> GSM182756 5 0.3053 0.75975 0.000 0.000 0.164 0.008 0.828
#> GSM182757 5 0.3932 0.62456 0.000 0.140 0.000 0.064 0.796
#> GSM182758 5 0.2773 0.75868 0.000 0.000 0.164 0.000 0.836
#> GSM182759 2 0.5908 0.39405 0.000 0.512 0.000 0.108 0.380
#> GSM182760 5 0.3366 0.70767 0.000 0.000 0.232 0.000 0.768
#> GSM182761 5 0.3958 0.59829 0.000 0.184 0.000 0.040 0.776
#> GSM182762 5 0.2124 0.71739 0.000 0.000 0.004 0.096 0.900
#> GSM182763 5 0.2550 0.70759 0.000 0.020 0.004 0.084 0.892
#> GSM182764 5 0.4624 0.56728 0.000 0.164 0.000 0.096 0.740
#> GSM182765 5 0.2720 0.70885 0.000 0.004 0.020 0.096 0.880
#> GSM182766 2 0.4195 0.68840 0.000 0.796 0.008 0.092 0.104
#> GSM182767 5 0.3366 0.70767 0.000 0.000 0.232 0.000 0.768
#> GSM182768 3 0.2959 0.83775 0.008 0.000 0.864 0.016 0.112
#> GSM182769 3 0.2144 0.82614 0.068 0.000 0.912 0.000 0.020
#> GSM182770 2 0.4040 0.60308 0.000 0.724 0.016 0.260 0.000
#> GSM182771 4 0.7401 -0.41967 0.000 0.332 0.032 0.384 0.252
#> GSM182772 2 0.4194 0.60350 0.000 0.720 0.016 0.260 0.004
#> GSM182773 3 0.2732 0.81158 0.000 0.000 0.840 0.000 0.160
#> GSM182774 3 0.4821 0.67947 0.096 0.000 0.764 0.112 0.028
#> GSM182775 3 0.2388 0.84428 0.028 0.000 0.900 0.000 0.072
#> GSM182776 3 0.4021 0.71472 0.148 0.000 0.800 0.036 0.016
#> GSM182777 3 0.2563 0.83309 0.008 0.000 0.872 0.000 0.120
#> GSM182802 4 0.4585 -0.13272 0.000 0.396 0.008 0.592 0.004
#> GSM182803 1 0.3454 0.75472 0.816 0.000 0.028 0.156 0.000
#> GSM182804 4 0.4320 0.51467 0.096 0.004 0.120 0.780 0.000
#> GSM182805 4 0.4449 -0.11727 0.000 0.388 0.004 0.604 0.004
#> GSM182806 1 0.2171 0.77312 0.912 0.000 0.064 0.024 0.000
#> GSM182807 1 0.2171 0.77312 0.912 0.000 0.064 0.024 0.000
#> GSM182808 1 0.2079 0.77259 0.916 0.000 0.064 0.020 0.000
#> GSM182809 4 0.4928 0.05036 0.020 0.000 0.428 0.548 0.004
#> GSM182810 1 0.4615 0.63042 0.700 0.000 0.048 0.252 0.000
#> GSM182811 4 0.5736 -0.05697 0.400 0.000 0.088 0.512 0.000
#> GSM182812 1 0.3772 0.72743 0.792 0.000 0.036 0.172 0.000
#> GSM182813 1 0.2079 0.77259 0.916 0.000 0.064 0.020 0.000
#> GSM182778 2 0.0771 0.70905 0.000 0.976 0.004 0.000 0.020
#> GSM182779 5 0.4355 0.58426 0.000 0.164 0.000 0.076 0.760
#> GSM182780 5 0.2367 0.76531 0.000 0.004 0.072 0.020 0.904
#> GSM182781 5 0.3280 0.75650 0.000 0.000 0.176 0.012 0.812
#> GSM182782 2 0.0771 0.70905 0.000 0.976 0.004 0.000 0.020
#> GSM182783 5 0.2732 0.76021 0.000 0.000 0.160 0.000 0.840
#> GSM182784 5 0.2773 0.75868 0.000 0.000 0.164 0.000 0.836
#> GSM182785 5 0.0671 0.74811 0.000 0.000 0.004 0.016 0.980
#> GSM182786 2 0.0771 0.70905 0.000 0.976 0.004 0.000 0.020
#> GSM182787 5 0.4339 0.50652 0.000 0.296 0.000 0.020 0.684
#> GSM182788 2 0.0771 0.70905 0.000 0.976 0.004 0.000 0.020
#> GSM182789 5 0.2074 0.76768 0.000 0.000 0.104 0.000 0.896
#> GSM182790 5 0.3689 0.68371 0.000 0.000 0.256 0.004 0.740
#> GSM182791 3 0.3183 0.80951 0.000 0.000 0.828 0.016 0.156
#> GSM182792 3 0.2536 0.83075 0.000 0.000 0.868 0.004 0.128
#> GSM182793 2 0.5300 0.39236 0.000 0.528 0.028 0.432 0.012
#> GSM182794 5 0.3534 0.68317 0.000 0.000 0.256 0.000 0.744
#> GSM182795 5 0.2813 0.75682 0.000 0.000 0.168 0.000 0.832
#> GSM182796 2 0.4535 0.63306 0.000 0.748 0.000 0.092 0.160
#> GSM182797 1 0.4702 0.12937 0.552 0.000 0.432 0.016 0.000
#> GSM182798 2 0.7103 0.43162 0.000 0.432 0.024 0.340 0.204
#> GSM182799 3 0.3392 0.82529 0.008 0.000 0.852 0.060 0.080
#> GSM182800 3 0.3748 0.75915 0.100 0.000 0.832 0.052 0.016
#> GSM182801 3 0.3124 0.77508 0.136 0.000 0.844 0.004 0.016
#> GSM182814 1 0.2653 0.78322 0.880 0.000 0.024 0.096 0.000
#> GSM182815 4 0.4320 0.51467 0.096 0.004 0.120 0.780 0.000
#> GSM182816 1 0.2707 0.78206 0.876 0.000 0.024 0.100 0.000
#> GSM182817 4 0.3640 0.41628 0.040 0.000 0.028 0.844 0.088
#> GSM182818 4 0.6270 -0.09998 0.404 0.008 0.116 0.472 0.000
#> GSM182819 1 0.2653 0.78374 0.880 0.000 0.024 0.096 0.000
#> GSM182820 1 0.2171 0.77312 0.912 0.000 0.064 0.024 0.000
#> GSM182821 5 0.6234 0.44972 0.000 0.000 0.176 0.296 0.528
#> GSM182822 1 0.5708 0.25793 0.504 0.000 0.084 0.412 0.000
#> GSM182823 1 0.0404 0.78565 0.988 0.000 0.000 0.012 0.000
#> GSM182824 1 0.1216 0.78929 0.960 0.000 0.020 0.020 0.000
#> GSM182825 1 0.3885 0.72057 0.784 0.000 0.040 0.176 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM182755 1 0.7933 0.0247 0.372 0.000 0.136 0.032 0.200 0.260
#> GSM182756 3 0.5011 0.7994 0.000 0.000 0.508 0.000 0.420 0.072
#> GSM182757 5 0.1812 0.6727 0.000 0.008 0.080 0.000 0.912 0.000
#> GSM182758 3 0.5176 0.8069 0.000 0.000 0.508 0.004 0.412 0.076
#> GSM182759 5 0.3465 0.4530 0.000 0.132 0.048 0.008 0.812 0.000
#> GSM182760 3 0.5418 0.7963 0.000 0.000 0.508 0.000 0.368 0.124
#> GSM182761 5 0.2833 0.5928 0.000 0.012 0.148 0.000 0.836 0.004
#> GSM182762 5 0.2500 0.6330 0.000 0.000 0.116 0.012 0.868 0.004
#> GSM182763 5 0.2234 0.6371 0.000 0.000 0.124 0.004 0.872 0.000
#> GSM182764 5 0.1149 0.6483 0.000 0.008 0.024 0.008 0.960 0.000
#> GSM182765 5 0.2596 0.6375 0.000 0.004 0.104 0.016 0.872 0.004
#> GSM182766 2 0.4216 0.5746 0.000 0.676 0.032 0.004 0.288 0.000
#> GSM182767 3 0.5557 0.7888 0.000 0.000 0.512 0.004 0.356 0.128
#> GSM182768 6 0.2182 0.8618 0.000 0.000 0.068 0.020 0.008 0.904
#> GSM182769 6 0.0622 0.8653 0.012 0.000 0.008 0.000 0.000 0.980
#> GSM182770 2 0.0146 0.5868 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM182771 2 0.5159 0.3859 0.000 0.532 0.008 0.068 0.392 0.000
#> GSM182772 2 0.0363 0.5873 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM182773 6 0.2837 0.8203 0.004 0.000 0.144 0.004 0.008 0.840
#> GSM182774 6 0.3840 0.7365 0.020 0.000 0.028 0.152 0.008 0.792
#> GSM182775 6 0.0909 0.8662 0.012 0.000 0.020 0.000 0.000 0.968
#> GSM182776 6 0.2303 0.8088 0.024 0.000 0.020 0.052 0.000 0.904
#> GSM182777 6 0.2009 0.8463 0.008 0.000 0.084 0.004 0.000 0.904
#> GSM182802 2 0.3935 0.3434 0.000 0.692 0.012 0.288 0.008 0.000
#> GSM182803 1 0.5341 0.4347 0.580 0.000 0.108 0.304 0.000 0.008
#> GSM182804 4 0.5474 0.5948 0.052 0.140 0.040 0.704 0.000 0.064
#> GSM182805 2 0.3991 0.3278 0.000 0.680 0.012 0.300 0.008 0.000
#> GSM182806 1 0.1913 0.5568 0.908 0.000 0.000 0.012 0.000 0.080
#> GSM182807 1 0.1913 0.5568 0.908 0.000 0.000 0.012 0.000 0.080
#> GSM182808 1 0.1501 0.5614 0.924 0.000 0.000 0.000 0.000 0.076
#> GSM182809 4 0.4761 0.3919 0.016 0.016 0.016 0.632 0.000 0.320
#> GSM182810 1 0.6040 0.1094 0.420 0.000 0.140 0.420 0.000 0.020
#> GSM182811 4 0.4576 0.4496 0.264 0.000 0.044 0.676 0.000 0.016
#> GSM182812 1 0.5673 0.4777 0.572 0.000 0.164 0.252 0.000 0.012
#> GSM182813 1 0.1501 0.5614 0.924 0.000 0.000 0.000 0.000 0.076
#> GSM182778 2 0.6762 0.5607 0.000 0.516 0.240 0.140 0.100 0.004
#> GSM182779 5 0.0806 0.6680 0.000 0.008 0.020 0.000 0.972 0.000
#> GSM182780 5 0.4282 -0.4519 0.000 0.000 0.420 0.000 0.560 0.020
#> GSM182781 3 0.5224 0.7700 0.000 0.000 0.468 0.000 0.440 0.092
#> GSM182782 2 0.6762 0.5607 0.000 0.516 0.240 0.140 0.100 0.004
#> GSM182783 3 0.5061 0.7988 0.000 0.000 0.496 0.000 0.428 0.076
#> GSM182784 3 0.5015 0.8009 0.000 0.000 0.504 0.000 0.424 0.072
#> GSM182785 5 0.3830 -0.1633 0.000 0.000 0.376 0.000 0.620 0.004
#> GSM182786 2 0.6762 0.5607 0.000 0.516 0.240 0.140 0.100 0.004
#> GSM182787 5 0.4403 0.4485 0.000 0.100 0.172 0.000 0.724 0.004
#> GSM182788 2 0.6762 0.5607 0.000 0.516 0.240 0.140 0.100 0.004
#> GSM182789 3 0.4834 0.7050 0.000 0.000 0.484 0.004 0.468 0.044
#> GSM182790 3 0.5828 0.7344 0.000 0.000 0.480 0.004 0.344 0.172
#> GSM182791 6 0.3800 0.7901 0.000 0.000 0.168 0.048 0.008 0.776
#> GSM182792 6 0.2262 0.8590 0.000 0.000 0.080 0.016 0.008 0.896
#> GSM182793 2 0.4102 0.4978 0.000 0.776 0.036 0.152 0.032 0.004
#> GSM182794 3 0.5797 0.7415 0.000 0.000 0.488 0.004 0.340 0.168
#> GSM182795 3 0.5188 0.8018 0.000 0.000 0.496 0.004 0.424 0.076
#> GSM182796 2 0.6311 0.4715 0.000 0.448 0.076 0.084 0.392 0.000
#> GSM182797 1 0.4184 0.0379 0.556 0.000 0.008 0.004 0.000 0.432
#> GSM182798 2 0.4669 0.4467 0.000 0.592 0.008 0.036 0.364 0.000
#> GSM182799 6 0.3314 0.8323 0.000 0.000 0.092 0.076 0.004 0.828
#> GSM182800 6 0.3167 0.8152 0.028 0.000 0.040 0.080 0.000 0.852
#> GSM182801 6 0.0891 0.8537 0.024 0.000 0.000 0.008 0.000 0.968
#> GSM182814 1 0.5104 0.5606 0.656 0.000 0.164 0.172 0.000 0.008
#> GSM182815 4 0.5075 0.6057 0.056 0.144 0.016 0.724 0.000 0.060
#> GSM182816 1 0.5253 0.5549 0.644 0.000 0.160 0.184 0.000 0.012
#> GSM182817 4 0.5856 0.3677 0.028 0.160 0.008 0.612 0.192 0.000
#> GSM182818 4 0.5464 0.4652 0.312 0.004 0.044 0.592 0.000 0.048
#> GSM182819 1 0.5102 0.5583 0.656 0.000 0.160 0.176 0.000 0.008
#> GSM182820 1 0.1913 0.5568 0.908 0.000 0.000 0.012 0.000 0.080
#> GSM182821 3 0.6905 0.2319 0.000 0.000 0.376 0.372 0.176 0.076
#> GSM182822 4 0.5092 0.3031 0.356 0.000 0.044 0.576 0.000 0.024
#> GSM182823 1 0.3821 0.5836 0.772 0.000 0.148 0.080 0.000 0.000
#> GSM182824 1 0.4615 0.5802 0.712 0.000 0.164 0.116 0.000 0.008
#> GSM182825 1 0.5673 0.4768 0.572 0.000 0.164 0.252 0.000 0.012
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n stress(p) development.stage(p) k
#> MAD:kmeans 70 0.632 3.64e-05 2
#> MAD:kmeans 68 0.991 1.77e-08 3
#> MAD:kmeans 50 0.473 1.79e-08 4
#> MAD:kmeans 57 0.930 1.24e-11 5
#> MAD:kmeans 49 0.386 2.22e-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["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 18172 rows and 71 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.989 0.995 0.5072 0.493 0.493
#> 3 3 0.860 0.846 0.938 0.3091 0.758 0.546
#> 4 4 0.711 0.731 0.860 0.1181 0.874 0.655
#> 5 5 0.660 0.647 0.792 0.0579 0.950 0.822
#> 6 6 0.658 0.536 0.753 0.0376 0.961 0.842
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
#> GSM182755 1 0.0672 0.982 0.992 0.008
#> GSM182756 2 0.0000 1.000 0.000 1.000
#> GSM182757 2 0.0000 1.000 0.000 1.000
#> GSM182758 2 0.0000 1.000 0.000 1.000
#> GSM182759 2 0.0000 1.000 0.000 1.000
#> GSM182760 2 0.0000 1.000 0.000 1.000
#> GSM182761 2 0.0000 1.000 0.000 1.000
#> GSM182762 2 0.0000 1.000 0.000 1.000
#> GSM182763 2 0.0000 1.000 0.000 1.000
#> GSM182764 2 0.0000 1.000 0.000 1.000
#> GSM182765 2 0.0000 1.000 0.000 1.000
#> GSM182766 2 0.0000 1.000 0.000 1.000
#> GSM182767 2 0.0000 1.000 0.000 1.000
#> GSM182768 1 0.0000 0.989 1.000 0.000
#> GSM182769 1 0.0000 0.989 1.000 0.000
#> GSM182770 2 0.0000 1.000 0.000 1.000
#> GSM182771 2 0.0000 1.000 0.000 1.000
#> GSM182772 2 0.0000 1.000 0.000 1.000
#> GSM182773 1 0.0000 0.989 1.000 0.000
#> GSM182774 1 0.0000 0.989 1.000 0.000
#> GSM182775 1 0.0000 0.989 1.000 0.000
#> GSM182776 1 0.0000 0.989 1.000 0.000
#> GSM182777 1 0.0000 0.989 1.000 0.000
#> GSM182802 2 0.0000 1.000 0.000 1.000
#> GSM182803 1 0.0000 0.989 1.000 0.000
#> GSM182804 1 0.0000 0.989 1.000 0.000
#> GSM182805 2 0.0000 1.000 0.000 1.000
#> GSM182806 1 0.0000 0.989 1.000 0.000
#> GSM182807 1 0.0000 0.989 1.000 0.000
#> GSM182808 1 0.0000 0.989 1.000 0.000
#> GSM182809 1 0.0000 0.989 1.000 0.000
#> GSM182810 1 0.0000 0.989 1.000 0.000
#> GSM182811 1 0.0000 0.989 1.000 0.000
#> GSM182812 1 0.0000 0.989 1.000 0.000
#> GSM182813 1 0.0000 0.989 1.000 0.000
#> GSM182778 2 0.0000 1.000 0.000 1.000
#> GSM182779 2 0.0000 1.000 0.000 1.000
#> GSM182780 2 0.0000 1.000 0.000 1.000
#> GSM182781 2 0.0000 1.000 0.000 1.000
#> GSM182782 2 0.0000 1.000 0.000 1.000
#> GSM182783 2 0.0000 1.000 0.000 1.000
#> GSM182784 2 0.0000 1.000 0.000 1.000
#> GSM182785 2 0.0000 1.000 0.000 1.000
#> GSM182786 2 0.0000 1.000 0.000 1.000
#> GSM182787 2 0.0000 1.000 0.000 1.000
#> GSM182788 2 0.0000 1.000 0.000 1.000
#> GSM182789 2 0.0000 1.000 0.000 1.000
#> GSM182790 2 0.0000 1.000 0.000 1.000
#> GSM182791 1 0.4431 0.896 0.908 0.092
#> GSM182792 1 0.0000 0.989 1.000 0.000
#> GSM182793 2 0.0000 1.000 0.000 1.000
#> GSM182794 2 0.0000 1.000 0.000 1.000
#> GSM182795 2 0.0000 1.000 0.000 1.000
#> GSM182796 2 0.0000 1.000 0.000 1.000
#> GSM182797 1 0.0000 0.989 1.000 0.000
#> GSM182798 2 0.0000 1.000 0.000 1.000
#> GSM182799 1 0.0000 0.989 1.000 0.000
#> GSM182800 1 0.0000 0.989 1.000 0.000
#> GSM182801 1 0.0000 0.989 1.000 0.000
#> GSM182814 1 0.0000 0.989 1.000 0.000
#> GSM182815 1 0.0000 0.989 1.000 0.000
#> GSM182816 1 0.0000 0.989 1.000 0.000
#> GSM182817 1 0.8207 0.659 0.744 0.256
#> GSM182818 1 0.0000 0.989 1.000 0.000
#> GSM182819 1 0.0000 0.989 1.000 0.000
#> GSM182820 1 0.0000 0.989 1.000 0.000
#> GSM182821 2 0.0000 1.000 0.000 1.000
#> GSM182822 1 0.0000 0.989 1.000 0.000
#> GSM182823 1 0.0000 0.989 1.000 0.000
#> GSM182824 1 0.0000 0.989 1.000 0.000
#> GSM182825 1 0.0000 0.989 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM182755 1 0.5591 0.524 0.696 0.000 0.304
#> GSM182756 3 0.0000 0.850 0.000 0.000 1.000
#> GSM182757 2 0.1643 0.931 0.000 0.956 0.044
#> GSM182758 3 0.0000 0.850 0.000 0.000 1.000
#> GSM182759 2 0.0237 0.960 0.000 0.996 0.004
#> GSM182760 3 0.0000 0.850 0.000 0.000 1.000
#> GSM182761 2 0.1411 0.937 0.000 0.964 0.036
#> GSM182762 2 0.2165 0.912 0.000 0.936 0.064
#> GSM182763 2 0.0237 0.960 0.000 0.996 0.004
#> GSM182764 2 0.0237 0.960 0.000 0.996 0.004
#> GSM182765 2 0.0592 0.955 0.000 0.988 0.012
#> GSM182766 2 0.0237 0.960 0.000 0.996 0.004
#> GSM182767 3 0.0000 0.850 0.000 0.000 1.000
#> GSM182768 3 0.6111 0.335 0.396 0.000 0.604
#> GSM182769 1 0.5529 0.546 0.704 0.000 0.296
#> GSM182770 2 0.0000 0.959 0.000 1.000 0.000
#> GSM182771 2 0.0000 0.959 0.000 1.000 0.000
#> GSM182772 2 0.0000 0.959 0.000 1.000 0.000
#> GSM182773 3 0.0424 0.848 0.008 0.000 0.992
#> GSM182774 1 0.0000 0.952 1.000 0.000 0.000
#> GSM182775 1 0.6252 0.152 0.556 0.000 0.444
#> GSM182776 1 0.0000 0.952 1.000 0.000 0.000
#> GSM182777 3 0.1411 0.835 0.036 0.000 0.964
#> GSM182802 2 0.0000 0.959 0.000 1.000 0.000
#> GSM182803 1 0.0000 0.952 1.000 0.000 0.000
#> GSM182804 1 0.0237 0.950 0.996 0.004 0.000
#> GSM182805 2 0.0000 0.959 0.000 1.000 0.000
#> GSM182806 1 0.0000 0.952 1.000 0.000 0.000
#> GSM182807 1 0.0000 0.952 1.000 0.000 0.000
#> GSM182808 1 0.0000 0.952 1.000 0.000 0.000
#> GSM182809 1 0.0000 0.952 1.000 0.000 0.000
#> GSM182810 1 0.0000 0.952 1.000 0.000 0.000
#> GSM182811 1 0.0237 0.950 0.996 0.004 0.000
#> GSM182812 1 0.0000 0.952 1.000 0.000 0.000
#> GSM182813 1 0.0000 0.952 1.000 0.000 0.000
#> GSM182778 2 0.0237 0.960 0.000 0.996 0.004
#> GSM182779 2 0.0424 0.958 0.000 0.992 0.008
#> GSM182780 2 0.3816 0.805 0.000 0.852 0.148
#> GSM182781 3 0.0000 0.850 0.000 0.000 1.000
#> GSM182782 2 0.0237 0.960 0.000 0.996 0.004
#> GSM182783 3 0.3267 0.772 0.000 0.116 0.884
#> GSM182784 3 0.0000 0.850 0.000 0.000 1.000
#> GSM182785 3 0.6204 0.255 0.000 0.424 0.576
#> GSM182786 2 0.0237 0.960 0.000 0.996 0.004
#> GSM182787 2 0.0237 0.960 0.000 0.996 0.004
#> GSM182788 2 0.0237 0.960 0.000 0.996 0.004
#> GSM182789 3 0.5835 0.461 0.000 0.340 0.660
#> GSM182790 3 0.0000 0.850 0.000 0.000 1.000
#> GSM182791 3 0.2066 0.819 0.060 0.000 0.940
#> GSM182792 3 0.5363 0.574 0.276 0.000 0.724
#> GSM182793 2 0.0000 0.959 0.000 1.000 0.000
#> GSM182794 3 0.0000 0.850 0.000 0.000 1.000
#> GSM182795 3 0.0000 0.850 0.000 0.000 1.000
#> GSM182796 2 0.0000 0.959 0.000 1.000 0.000
#> GSM182797 1 0.0237 0.949 0.996 0.000 0.004
#> GSM182798 2 0.0000 0.959 0.000 1.000 0.000
#> GSM182799 3 0.6045 0.374 0.380 0.000 0.620
#> GSM182800 1 0.0424 0.946 0.992 0.000 0.008
#> GSM182801 1 0.2448 0.880 0.924 0.000 0.076
#> GSM182814 1 0.0000 0.952 1.000 0.000 0.000
#> GSM182815 1 0.0424 0.946 0.992 0.008 0.000
#> GSM182816 1 0.0000 0.952 1.000 0.000 0.000
#> GSM182817 2 0.6274 0.154 0.456 0.544 0.000
#> GSM182818 1 0.0000 0.952 1.000 0.000 0.000
#> GSM182819 1 0.0000 0.952 1.000 0.000 0.000
#> GSM182820 1 0.0000 0.952 1.000 0.000 0.000
#> GSM182821 3 0.6235 0.275 0.000 0.436 0.564
#> GSM182822 1 0.0000 0.952 1.000 0.000 0.000
#> GSM182823 1 0.0000 0.952 1.000 0.000 0.000
#> GSM182824 1 0.0000 0.952 1.000 0.000 0.000
#> GSM182825 1 0.0000 0.952 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM182755 1 0.7337 0.1519 0.524 0.000 0.272 0.204
#> GSM182756 3 0.0524 0.8802 0.000 0.004 0.988 0.008
#> GSM182757 2 0.4994 0.1865 0.000 0.520 0.480 0.000
#> GSM182758 3 0.0336 0.8802 0.000 0.000 0.992 0.008
#> GSM182759 2 0.1211 0.8591 0.000 0.960 0.040 0.000
#> GSM182760 3 0.2216 0.8312 0.000 0.000 0.908 0.092
#> GSM182761 2 0.4948 0.2998 0.000 0.560 0.440 0.000
#> GSM182762 3 0.4964 0.2420 0.004 0.380 0.616 0.000
#> GSM182763 2 0.2149 0.8442 0.000 0.912 0.088 0.000
#> GSM182764 2 0.2868 0.8153 0.000 0.864 0.136 0.000
#> GSM182765 2 0.2408 0.8375 0.000 0.896 0.104 0.000
#> GSM182766 2 0.1109 0.8607 0.000 0.968 0.028 0.004
#> GSM182767 3 0.1557 0.8572 0.000 0.000 0.944 0.056
#> GSM182768 4 0.3486 0.8129 0.044 0.000 0.092 0.864
#> GSM182769 4 0.4635 0.7668 0.216 0.000 0.028 0.756
#> GSM182770 2 0.1118 0.8465 0.000 0.964 0.000 0.036
#> GSM182771 2 0.1059 0.8537 0.000 0.972 0.012 0.016
#> GSM182772 2 0.1022 0.8478 0.000 0.968 0.000 0.032
#> GSM182773 4 0.4543 0.6267 0.000 0.000 0.324 0.676
#> GSM182774 1 0.2921 0.7366 0.860 0.000 0.000 0.140
#> GSM182775 4 0.4920 0.7894 0.192 0.000 0.052 0.756
#> GSM182776 1 0.4866 0.1950 0.596 0.000 0.000 0.404
#> GSM182777 4 0.6110 0.7265 0.100 0.000 0.240 0.660
#> GSM182802 2 0.2704 0.7973 0.000 0.876 0.000 0.124
#> GSM182803 1 0.0469 0.8359 0.988 0.000 0.000 0.012
#> GSM182804 1 0.5492 0.5487 0.640 0.032 0.000 0.328
#> GSM182805 2 0.2704 0.7973 0.000 0.876 0.000 0.124
#> GSM182806 1 0.1022 0.8296 0.968 0.000 0.000 0.032
#> GSM182807 1 0.1118 0.8281 0.964 0.000 0.000 0.036
#> GSM182808 1 0.1211 0.8262 0.960 0.000 0.000 0.040
#> GSM182809 1 0.5587 0.4826 0.600 0.028 0.000 0.372
#> GSM182810 1 0.0469 0.8342 0.988 0.000 0.000 0.012
#> GSM182811 1 0.1792 0.8083 0.932 0.000 0.000 0.068
#> GSM182812 1 0.0188 0.8358 0.996 0.000 0.000 0.004
#> GSM182813 1 0.1302 0.8241 0.956 0.000 0.000 0.044
#> GSM182778 2 0.1004 0.8605 0.000 0.972 0.024 0.004
#> GSM182779 2 0.2921 0.8085 0.000 0.860 0.140 0.000
#> GSM182780 2 0.5360 0.2656 0.000 0.552 0.436 0.012
#> GSM182781 3 0.0188 0.8797 0.000 0.000 0.996 0.004
#> GSM182782 2 0.0921 0.8608 0.000 0.972 0.028 0.000
#> GSM182783 3 0.2334 0.8389 0.000 0.088 0.908 0.004
#> GSM182784 3 0.0336 0.8802 0.000 0.000 0.992 0.008
#> GSM182785 3 0.2589 0.8039 0.000 0.116 0.884 0.000
#> GSM182786 2 0.0921 0.8608 0.000 0.972 0.028 0.000
#> GSM182787 2 0.1661 0.8571 0.000 0.944 0.052 0.004
#> GSM182788 2 0.0921 0.8608 0.000 0.972 0.028 0.000
#> GSM182789 3 0.2408 0.8251 0.000 0.104 0.896 0.000
#> GSM182790 3 0.2011 0.8409 0.000 0.000 0.920 0.080
#> GSM182791 4 0.3764 0.7313 0.000 0.000 0.216 0.784
#> GSM182792 4 0.3760 0.8039 0.028 0.000 0.136 0.836
#> GSM182793 2 0.2345 0.8159 0.000 0.900 0.000 0.100
#> GSM182794 3 0.2704 0.7914 0.000 0.000 0.876 0.124
#> GSM182795 3 0.0937 0.8793 0.000 0.012 0.976 0.012
#> GSM182796 2 0.1022 0.8602 0.000 0.968 0.032 0.000
#> GSM182797 1 0.5000 -0.1566 0.504 0.000 0.000 0.496
#> GSM182798 2 0.1059 0.8537 0.000 0.972 0.012 0.016
#> GSM182799 4 0.2660 0.7916 0.036 0.000 0.056 0.908
#> GSM182800 4 0.3873 0.7378 0.228 0.000 0.000 0.772
#> GSM182801 4 0.3870 0.7678 0.208 0.000 0.004 0.788
#> GSM182814 1 0.0000 0.8361 1.000 0.000 0.000 0.000
#> GSM182815 1 0.6106 0.5044 0.604 0.064 0.000 0.332
#> GSM182816 1 0.0188 0.8362 0.996 0.000 0.000 0.004
#> GSM182817 1 0.6011 0.6019 0.700 0.172 0.004 0.124
#> GSM182818 1 0.2760 0.7703 0.872 0.000 0.000 0.128
#> GSM182819 1 0.0188 0.8362 0.996 0.000 0.000 0.004
#> GSM182820 1 0.1118 0.8281 0.964 0.000 0.000 0.036
#> GSM182821 2 0.8337 0.0587 0.036 0.408 0.384 0.172
#> GSM182822 1 0.0592 0.8329 0.984 0.000 0.000 0.016
#> GSM182823 1 0.0188 0.8362 0.996 0.000 0.000 0.004
#> GSM182824 1 0.0188 0.8362 0.996 0.000 0.000 0.004
#> GSM182825 1 0.0336 0.8359 0.992 0.000 0.000 0.008
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM182755 1 0.7783 0.2441 0.516 0.020 0.096 0.236 0.132
#> GSM182756 3 0.2313 0.8555 0.000 0.012 0.916 0.032 0.040
#> GSM182757 2 0.6039 0.4894 0.000 0.580 0.288 0.124 0.008
#> GSM182758 3 0.2072 0.8580 0.000 0.036 0.928 0.020 0.016
#> GSM182759 2 0.1768 0.7446 0.000 0.924 0.004 0.072 0.000
#> GSM182760 3 0.3284 0.8082 0.000 0.000 0.828 0.024 0.148
#> GSM182761 2 0.5045 0.4780 0.000 0.636 0.308 0.056 0.000
#> GSM182762 2 0.7033 0.3529 0.000 0.440 0.304 0.240 0.016
#> GSM182763 2 0.2676 0.7423 0.000 0.884 0.036 0.080 0.000
#> GSM182764 2 0.4548 0.6844 0.000 0.752 0.076 0.168 0.004
#> GSM182765 2 0.5358 0.6528 0.000 0.680 0.088 0.220 0.012
#> GSM182766 2 0.1043 0.7448 0.000 0.960 0.000 0.040 0.000
#> GSM182767 3 0.2880 0.8311 0.000 0.004 0.868 0.020 0.108
#> GSM182768 5 0.1661 0.7860 0.000 0.000 0.036 0.024 0.940
#> GSM182769 5 0.3694 0.7616 0.140 0.000 0.020 0.020 0.820
#> GSM182770 2 0.3480 0.6450 0.000 0.752 0.000 0.248 0.000
#> GSM182771 2 0.4834 0.6519 0.000 0.656 0.028 0.308 0.008
#> GSM182772 2 0.3452 0.6476 0.000 0.756 0.000 0.244 0.000
#> GSM182773 5 0.3496 0.7112 0.000 0.000 0.200 0.012 0.788
#> GSM182774 1 0.4657 0.5814 0.752 0.000 0.004 0.128 0.116
#> GSM182775 5 0.4154 0.7821 0.092 0.000 0.048 0.044 0.816
#> GSM182776 1 0.5627 0.2699 0.548 0.000 0.000 0.084 0.368
#> GSM182777 5 0.5490 0.7360 0.064 0.000 0.140 0.076 0.720
#> GSM182802 2 0.4430 0.3707 0.000 0.540 0.000 0.456 0.004
#> GSM182803 1 0.0609 0.7638 0.980 0.000 0.000 0.020 0.000
#> GSM182804 4 0.6531 0.5017 0.360 0.012 0.000 0.484 0.144
#> GSM182805 2 0.4219 0.4280 0.000 0.584 0.000 0.416 0.000
#> GSM182806 1 0.2248 0.7436 0.900 0.000 0.000 0.088 0.012
#> GSM182807 1 0.2189 0.7446 0.904 0.000 0.000 0.084 0.012
#> GSM182808 1 0.2293 0.7431 0.900 0.000 0.000 0.084 0.016
#> GSM182809 1 0.6686 -0.4965 0.420 0.004 0.000 0.376 0.200
#> GSM182810 1 0.1430 0.7429 0.944 0.000 0.000 0.052 0.004
#> GSM182811 1 0.3602 0.5549 0.796 0.000 0.000 0.180 0.024
#> GSM182812 1 0.1282 0.7466 0.952 0.000 0.000 0.044 0.004
#> GSM182813 1 0.2540 0.7360 0.888 0.000 0.000 0.088 0.024
#> GSM182778 2 0.0324 0.7455 0.000 0.992 0.004 0.004 0.000
#> GSM182779 2 0.3439 0.7238 0.000 0.844 0.092 0.060 0.004
#> GSM182780 2 0.5033 0.2518 0.000 0.568 0.400 0.028 0.004
#> GSM182781 3 0.3336 0.8141 0.004 0.004 0.856 0.088 0.048
#> GSM182782 2 0.0162 0.7461 0.000 0.996 0.004 0.000 0.000
#> GSM182783 3 0.3706 0.7480 0.000 0.180 0.796 0.012 0.012
#> GSM182784 3 0.1808 0.8521 0.000 0.040 0.936 0.020 0.004
#> GSM182785 3 0.4094 0.7592 0.000 0.128 0.788 0.084 0.000
#> GSM182786 2 0.0162 0.7461 0.000 0.996 0.004 0.000 0.000
#> GSM182787 2 0.2136 0.7260 0.000 0.904 0.088 0.008 0.000
#> GSM182788 2 0.0162 0.7461 0.000 0.996 0.004 0.000 0.000
#> GSM182789 3 0.3565 0.7902 0.000 0.144 0.816 0.040 0.000
#> GSM182790 3 0.3752 0.7988 0.000 0.004 0.812 0.044 0.140
#> GSM182791 5 0.5043 0.6529 0.000 0.000 0.160 0.136 0.704
#> GSM182792 5 0.2722 0.7863 0.008 0.000 0.060 0.040 0.892
#> GSM182793 2 0.4794 0.5367 0.000 0.624 0.000 0.344 0.032
#> GSM182794 3 0.3847 0.7571 0.000 0.000 0.784 0.036 0.180
#> GSM182795 3 0.2899 0.8486 0.000 0.056 0.888 0.032 0.024
#> GSM182796 2 0.2844 0.7388 0.000 0.876 0.028 0.092 0.004
#> GSM182797 1 0.5834 0.2775 0.544 0.000 0.000 0.108 0.348
#> GSM182798 2 0.4522 0.6901 0.000 0.720 0.032 0.240 0.008
#> GSM182799 5 0.3080 0.7218 0.004 0.000 0.020 0.124 0.852
#> GSM182800 5 0.4974 0.6140 0.212 0.000 0.000 0.092 0.696
#> GSM182801 5 0.3099 0.7668 0.132 0.000 0.008 0.012 0.848
#> GSM182814 1 0.0404 0.7616 0.988 0.000 0.000 0.012 0.000
#> GSM182815 4 0.6591 0.5220 0.364 0.024 0.000 0.492 0.120
#> GSM182816 1 0.0162 0.7633 0.996 0.000 0.000 0.004 0.000
#> GSM182817 4 0.6156 0.3784 0.412 0.072 0.016 0.496 0.004
#> GSM182818 1 0.4252 0.5128 0.764 0.000 0.000 0.172 0.064
#> GSM182819 1 0.0510 0.7632 0.984 0.000 0.000 0.016 0.000
#> GSM182820 1 0.2293 0.7431 0.900 0.000 0.000 0.084 0.016
#> GSM182821 4 0.8638 0.0261 0.040 0.304 0.264 0.324 0.068
#> GSM182822 1 0.2172 0.7195 0.908 0.000 0.000 0.076 0.016
#> GSM182823 1 0.0404 0.7646 0.988 0.000 0.000 0.012 0.000
#> GSM182824 1 0.0290 0.7626 0.992 0.000 0.000 0.008 0.000
#> GSM182825 1 0.1809 0.7344 0.928 0.000 0.000 0.060 0.012
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM182755 1 0.7057 0.2351 0.420 0.368 0.040 0.024 0.008 0.140
#> GSM182756 3 0.3309 0.7255 0.000 0.172 0.800 0.004 0.000 0.024
#> GSM182757 5 0.5591 -0.2518 0.000 0.232 0.196 0.004 0.568 0.000
#> GSM182758 3 0.1067 0.7618 0.000 0.024 0.964 0.004 0.004 0.004
#> GSM182759 5 0.1728 0.5989 0.000 0.064 0.004 0.008 0.924 0.000
#> GSM182760 3 0.4632 0.6959 0.000 0.152 0.712 0.008 0.000 0.128
#> GSM182761 5 0.5209 0.0901 0.000 0.172 0.160 0.008 0.656 0.004
#> GSM182762 2 0.6101 0.0000 0.000 0.520 0.152 0.016 0.304 0.008
#> GSM182763 5 0.3637 0.4907 0.000 0.140 0.052 0.004 0.800 0.004
#> GSM182764 5 0.4544 0.1495 0.000 0.292 0.052 0.004 0.652 0.000
#> GSM182765 5 0.5210 -0.1057 0.000 0.380 0.044 0.020 0.552 0.004
#> GSM182766 5 0.0717 0.6224 0.000 0.016 0.000 0.008 0.976 0.000
#> GSM182767 3 0.2697 0.7543 0.000 0.068 0.876 0.008 0.000 0.048
#> GSM182768 6 0.1555 0.7642 0.000 0.008 0.012 0.040 0.000 0.940
#> GSM182769 6 0.3621 0.7147 0.140 0.044 0.008 0.004 0.000 0.804
#> GSM182770 5 0.3865 0.4776 0.000 0.032 0.000 0.248 0.720 0.000
#> GSM182771 5 0.5590 0.3200 0.000 0.232 0.000 0.220 0.548 0.000
#> GSM182772 5 0.3668 0.4946 0.000 0.028 0.000 0.228 0.744 0.000
#> GSM182773 6 0.3752 0.6875 0.000 0.052 0.168 0.004 0.000 0.776
#> GSM182774 1 0.5993 0.4940 0.624 0.116 0.000 0.120 0.000 0.140
#> GSM182775 6 0.3471 0.7553 0.040 0.076 0.040 0.004 0.000 0.840
#> GSM182776 1 0.5683 0.1636 0.496 0.096 0.000 0.020 0.000 0.388
#> GSM182777 6 0.5407 0.6604 0.040 0.164 0.120 0.004 0.000 0.672
#> GSM182802 4 0.4475 0.0959 0.000 0.032 0.000 0.556 0.412 0.000
#> GSM182803 1 0.1794 0.7804 0.924 0.036 0.000 0.040 0.000 0.000
#> GSM182804 4 0.5855 0.4474 0.208 0.100 0.000 0.628 0.008 0.056
#> GSM182805 4 0.4529 -0.0125 0.000 0.032 0.000 0.508 0.460 0.000
#> GSM182806 1 0.2468 0.7639 0.880 0.096 0.000 0.016 0.000 0.008
#> GSM182807 1 0.2418 0.7655 0.884 0.092 0.000 0.016 0.000 0.008
#> GSM182808 1 0.2367 0.7665 0.888 0.088 0.000 0.016 0.000 0.008
#> GSM182809 4 0.6023 0.3623 0.288 0.040 0.000 0.564 0.008 0.100
#> GSM182810 1 0.2501 0.7357 0.872 0.016 0.000 0.108 0.000 0.004
#> GSM182811 1 0.4047 0.5016 0.676 0.028 0.000 0.296 0.000 0.000
#> GSM182812 1 0.2113 0.7525 0.896 0.008 0.000 0.092 0.000 0.004
#> GSM182813 1 0.2878 0.7539 0.860 0.100 0.000 0.016 0.000 0.024
#> GSM182778 5 0.0000 0.6229 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM182779 5 0.4117 0.4074 0.000 0.144 0.096 0.004 0.756 0.000
#> GSM182780 5 0.5945 -0.0271 0.000 0.132 0.280 0.020 0.560 0.008
#> GSM182781 3 0.3680 0.6644 0.000 0.232 0.744 0.004 0.000 0.020
#> GSM182782 5 0.0000 0.6229 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM182783 3 0.4411 0.6488 0.000 0.088 0.760 0.016 0.128 0.008
#> GSM182784 3 0.2716 0.7343 0.000 0.132 0.852 0.004 0.008 0.004
#> GSM182785 3 0.5558 0.3859 0.000 0.264 0.588 0.008 0.136 0.004
#> GSM182786 5 0.0000 0.6229 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM182787 5 0.3669 0.4866 0.000 0.084 0.092 0.008 0.812 0.004
#> GSM182788 5 0.0000 0.6229 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM182789 3 0.4723 0.5917 0.000 0.132 0.720 0.012 0.132 0.004
#> GSM182790 3 0.3686 0.7192 0.000 0.124 0.788 0.000 0.000 0.088
#> GSM182791 6 0.6294 0.5665 0.000 0.148 0.148 0.116 0.000 0.588
#> GSM182792 6 0.2655 0.7614 0.000 0.060 0.020 0.036 0.000 0.884
#> GSM182793 5 0.5467 0.2536 0.000 0.116 0.000 0.320 0.556 0.008
#> GSM182794 3 0.4162 0.6779 0.000 0.100 0.752 0.004 0.000 0.144
#> GSM182795 3 0.3026 0.7491 0.000 0.068 0.868 0.008 0.020 0.036
#> GSM182796 5 0.2282 0.5927 0.000 0.088 0.000 0.024 0.888 0.000
#> GSM182797 1 0.5880 0.2892 0.512 0.144 0.000 0.016 0.000 0.328
#> GSM182798 5 0.5008 0.4191 0.000 0.212 0.000 0.148 0.640 0.000
#> GSM182799 6 0.4228 0.6800 0.000 0.088 0.012 0.144 0.000 0.756
#> GSM182800 6 0.6062 0.5878 0.164 0.124 0.000 0.100 0.000 0.612
#> GSM182801 6 0.2711 0.7578 0.080 0.024 0.000 0.020 0.000 0.876
#> GSM182814 1 0.0935 0.7777 0.964 0.004 0.000 0.032 0.000 0.000
#> GSM182815 4 0.4078 0.4949 0.224 0.008 0.000 0.736 0.012 0.020
#> GSM182816 1 0.0858 0.7781 0.968 0.004 0.000 0.028 0.000 0.000
#> GSM182817 4 0.5961 0.4174 0.232 0.128 0.000 0.588 0.052 0.000
#> GSM182818 1 0.4522 0.5180 0.684 0.028 0.000 0.260 0.000 0.028
#> GSM182819 1 0.0820 0.7825 0.972 0.016 0.000 0.012 0.000 0.000
#> GSM182820 1 0.2568 0.7622 0.876 0.096 0.000 0.016 0.000 0.012
#> GSM182821 4 0.8214 0.0351 0.016 0.152 0.240 0.372 0.196 0.024
#> GSM182822 1 0.3041 0.7248 0.832 0.040 0.000 0.128 0.000 0.000
#> GSM182823 1 0.1003 0.7827 0.964 0.020 0.000 0.016 0.000 0.000
#> GSM182824 1 0.0260 0.7825 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM182825 1 0.2002 0.7604 0.908 0.012 0.000 0.076 0.000 0.004
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n stress(p) development.stage(p) k
#> MAD:skmeans 71 0.907 1.36e-05 2
#> MAD:skmeans 64 0.722 7.11e-08 3
#> MAD:skmeans 62 0.758 7.90e-11 4
#> MAD:skmeans 59 0.913 3.80e-11 5
#> MAD:skmeans 45 0.777 9.25e-10 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "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 18172 rows and 71 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.865 0.892 0.955 0.4982 0.498 0.498
#> 3 3 0.556 0.636 0.808 0.2885 0.709 0.490
#> 4 4 0.440 0.420 0.686 0.1343 0.736 0.407
#> 5 5 0.522 0.417 0.655 0.0671 0.893 0.648
#> 6 6 0.587 0.318 0.651 0.0487 0.832 0.405
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
#> GSM182755 1 0.3879 0.9053 0.924 0.076
#> GSM182756 2 0.1843 0.9318 0.028 0.972
#> GSM182757 2 0.0000 0.9576 0.000 1.000
#> GSM182758 2 0.0000 0.9576 0.000 1.000
#> GSM182759 2 0.0000 0.9576 0.000 1.000
#> GSM182760 1 0.6438 0.8205 0.836 0.164
#> GSM182761 2 0.0000 0.9576 0.000 1.000
#> GSM182762 2 0.9983 0.0128 0.476 0.524
#> GSM182763 2 0.0000 0.9576 0.000 1.000
#> GSM182764 2 0.0000 0.9576 0.000 1.000
#> GSM182765 2 0.8661 0.5574 0.288 0.712
#> GSM182766 2 0.0000 0.9576 0.000 1.000
#> GSM182767 2 0.0672 0.9506 0.008 0.992
#> GSM182768 1 0.2778 0.9222 0.952 0.048
#> GSM182769 1 0.0376 0.9435 0.996 0.004
#> GSM182770 2 0.0000 0.9576 0.000 1.000
#> GSM182771 1 0.9996 0.0853 0.512 0.488
#> GSM182772 2 0.0000 0.9576 0.000 1.000
#> GSM182773 1 0.4022 0.9027 0.920 0.080
#> GSM182774 1 0.0376 0.9435 0.996 0.004
#> GSM182775 1 0.0938 0.9405 0.988 0.012
#> GSM182776 1 0.1184 0.9388 0.984 0.016
#> GSM182777 1 0.4022 0.9025 0.920 0.080
#> GSM182802 2 0.0000 0.9576 0.000 1.000
#> GSM182803 1 0.0000 0.9444 1.000 0.000
#> GSM182804 1 0.0000 0.9444 1.000 0.000
#> GSM182805 2 0.0000 0.9576 0.000 1.000
#> GSM182806 1 0.0000 0.9444 1.000 0.000
#> GSM182807 1 0.0000 0.9444 1.000 0.000
#> GSM182808 1 0.0000 0.9444 1.000 0.000
#> GSM182809 1 0.0376 0.9434 0.996 0.004
#> GSM182810 1 0.0000 0.9444 1.000 0.000
#> GSM182811 1 0.0000 0.9444 1.000 0.000
#> GSM182812 1 0.0000 0.9444 1.000 0.000
#> GSM182813 1 0.0000 0.9444 1.000 0.000
#> GSM182778 2 0.0000 0.9576 0.000 1.000
#> GSM182779 2 0.0000 0.9576 0.000 1.000
#> GSM182780 2 0.0000 0.9576 0.000 1.000
#> GSM182781 1 0.6438 0.8205 0.836 0.164
#> GSM182782 2 0.0000 0.9576 0.000 1.000
#> GSM182783 2 0.0000 0.9576 0.000 1.000
#> GSM182784 2 0.0000 0.9576 0.000 1.000
#> GSM182785 2 0.0000 0.9576 0.000 1.000
#> GSM182786 2 0.0000 0.9576 0.000 1.000
#> GSM182787 2 0.0000 0.9576 0.000 1.000
#> GSM182788 2 0.0000 0.9576 0.000 1.000
#> GSM182789 2 0.0000 0.9576 0.000 1.000
#> GSM182790 1 0.6438 0.8205 0.836 0.164
#> GSM182791 1 0.6148 0.8340 0.848 0.152
#> GSM182792 1 0.3879 0.9053 0.924 0.076
#> GSM182793 2 0.0000 0.9576 0.000 1.000
#> GSM182794 2 0.9635 0.3141 0.388 0.612
#> GSM182795 2 0.0000 0.9576 0.000 1.000
#> GSM182796 2 0.0000 0.9576 0.000 1.000
#> GSM182797 1 0.0000 0.9444 1.000 0.000
#> GSM182798 2 0.0000 0.9576 0.000 1.000
#> GSM182799 1 0.4022 0.9027 0.920 0.080
#> GSM182800 1 0.0000 0.9444 1.000 0.000
#> GSM182801 1 0.0376 0.9435 0.996 0.004
#> GSM182814 1 0.0000 0.9444 1.000 0.000
#> GSM182815 1 0.0000 0.9444 1.000 0.000
#> GSM182816 1 0.0000 0.9444 1.000 0.000
#> GSM182817 1 0.9552 0.3866 0.624 0.376
#> GSM182818 1 0.0000 0.9444 1.000 0.000
#> GSM182819 1 0.0000 0.9444 1.000 0.000
#> GSM182820 1 0.0000 0.9444 1.000 0.000
#> GSM182821 2 0.0000 0.9576 0.000 1.000
#> GSM182822 1 0.0000 0.9444 1.000 0.000
#> GSM182823 1 0.0000 0.9444 1.000 0.000
#> GSM182824 1 0.0000 0.9444 1.000 0.000
#> GSM182825 1 0.0000 0.9444 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM182755 1 0.5678 0.5837 0.684 0.000 0.316
#> GSM182756 3 0.2356 0.6568 0.000 0.072 0.928
#> GSM182757 3 0.5882 0.3697 0.000 0.348 0.652
#> GSM182758 3 0.0000 0.6708 0.000 0.000 1.000
#> GSM182759 2 0.3752 0.6736 0.000 0.856 0.144
#> GSM182760 3 0.0000 0.6708 0.000 0.000 1.000
#> GSM182761 2 0.4887 0.5646 0.000 0.772 0.228
#> GSM182762 3 0.7533 0.2473 0.392 0.044 0.564
#> GSM182763 3 0.4605 0.5737 0.000 0.204 0.796
#> GSM182764 2 0.6111 0.3405 0.000 0.604 0.396
#> GSM182765 3 0.1964 0.6613 0.000 0.056 0.944
#> GSM182766 2 0.5948 0.3921 0.000 0.640 0.360
#> GSM182767 3 0.0000 0.6708 0.000 0.000 1.000
#> GSM182768 1 0.6260 0.4314 0.552 0.000 0.448
#> GSM182769 1 0.3116 0.8578 0.892 0.000 0.108
#> GSM182770 2 0.0000 0.7393 0.000 1.000 0.000
#> GSM182771 3 0.5553 0.4305 0.004 0.272 0.724
#> GSM182772 2 0.0000 0.7393 0.000 1.000 0.000
#> GSM182773 3 0.0000 0.6708 0.000 0.000 1.000
#> GSM182774 1 0.0892 0.8888 0.980 0.000 0.020
#> GSM182775 1 0.3619 0.8384 0.864 0.000 0.136
#> GSM182776 1 0.3551 0.8414 0.868 0.000 0.132
#> GSM182777 1 0.5810 0.5490 0.664 0.000 0.336
#> GSM182802 2 0.6168 0.2921 0.000 0.588 0.412
#> GSM182803 1 0.0000 0.8917 1.000 0.000 0.000
#> GSM182804 1 0.5254 0.6525 0.736 0.000 0.264
#> GSM182805 2 0.6154 0.3025 0.000 0.592 0.408
#> GSM182806 1 0.2165 0.8783 0.936 0.000 0.064
#> GSM182807 1 0.0000 0.8917 1.000 0.000 0.000
#> GSM182808 1 0.2066 0.8796 0.940 0.000 0.060
#> GSM182809 3 0.5810 0.4014 0.336 0.000 0.664
#> GSM182810 1 0.0000 0.8917 1.000 0.000 0.000
#> GSM182811 1 0.0000 0.8917 1.000 0.000 0.000
#> GSM182812 1 0.0000 0.8917 1.000 0.000 0.000
#> GSM182813 1 0.1163 0.8880 0.972 0.000 0.028
#> GSM182778 2 0.0000 0.7393 0.000 1.000 0.000
#> GSM182779 2 0.6274 0.1676 0.000 0.544 0.456
#> GSM182780 3 0.6095 0.2808 0.000 0.392 0.608
#> GSM182781 3 0.5397 0.4875 0.280 0.000 0.720
#> GSM182782 2 0.0000 0.7393 0.000 1.000 0.000
#> GSM182783 3 0.2796 0.6515 0.000 0.092 0.908
#> GSM182784 3 0.5785 0.3954 0.000 0.332 0.668
#> GSM182785 3 0.6026 0.3129 0.000 0.376 0.624
#> GSM182786 2 0.0000 0.7393 0.000 1.000 0.000
#> GSM182787 3 0.6126 0.2605 0.000 0.400 0.600
#> GSM182788 2 0.0000 0.7393 0.000 1.000 0.000
#> GSM182789 3 0.6126 0.2605 0.000 0.400 0.600
#> GSM182790 3 0.4974 0.5268 0.236 0.000 0.764
#> GSM182791 3 0.0000 0.6708 0.000 0.000 1.000
#> GSM182792 3 0.6026 0.0558 0.376 0.000 0.624
#> GSM182793 3 0.3038 0.6395 0.000 0.104 0.896
#> GSM182794 3 0.0000 0.6708 0.000 0.000 1.000
#> GSM182795 3 0.2625 0.6494 0.000 0.084 0.916
#> GSM182796 2 0.0000 0.7393 0.000 1.000 0.000
#> GSM182797 1 0.2959 0.8621 0.900 0.000 0.100
#> GSM182798 3 0.6140 0.1588 0.000 0.404 0.596
#> GSM182799 3 0.0000 0.6708 0.000 0.000 1.000
#> GSM182800 1 0.5733 0.6253 0.676 0.000 0.324
#> GSM182801 1 0.4452 0.8073 0.808 0.000 0.192
#> GSM182814 1 0.0000 0.8917 1.000 0.000 0.000
#> GSM182815 1 0.5365 0.6653 0.744 0.004 0.252
#> GSM182816 1 0.0000 0.8917 1.000 0.000 0.000
#> GSM182817 3 0.6798 0.3959 0.400 0.016 0.584
#> GSM182818 1 0.0000 0.8917 1.000 0.000 0.000
#> GSM182819 1 0.0000 0.8917 1.000 0.000 0.000
#> GSM182820 1 0.2261 0.8769 0.932 0.000 0.068
#> GSM182821 3 0.5785 0.3995 0.000 0.332 0.668
#> GSM182822 1 0.0000 0.8917 1.000 0.000 0.000
#> GSM182823 1 0.0000 0.8917 1.000 0.000 0.000
#> GSM182824 1 0.0000 0.8917 1.000 0.000 0.000
#> GSM182825 1 0.0237 0.8906 0.996 0.000 0.004
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM182755 4 0.5599 0.5766 0.288 0.000 0.048 0.664
#> GSM182756 3 0.6158 0.2755 0.000 0.080 0.628 0.292
#> GSM182757 3 0.1118 0.4810 0.000 0.000 0.964 0.036
#> GSM182758 3 0.6698 0.4167 0.000 0.256 0.604 0.140
#> GSM182759 3 0.5947 -0.3648 0.000 0.384 0.572 0.044
#> GSM182760 4 0.6702 0.2965 0.000 0.100 0.356 0.544
#> GSM182761 3 0.4898 0.0115 0.000 0.260 0.716 0.024
#> GSM182762 4 0.8771 0.4448 0.140 0.116 0.244 0.500
#> GSM182763 3 0.4462 0.5197 0.000 0.164 0.792 0.044
#> GSM182764 3 0.4867 0.1060 0.000 0.232 0.736 0.032
#> GSM182765 3 0.6726 0.4367 0.000 0.364 0.536 0.100
#> GSM182766 3 0.5968 -0.0449 0.000 0.252 0.664 0.084
#> GSM182767 4 0.6843 0.0958 0.000 0.100 0.440 0.460
#> GSM182768 4 0.7044 0.6068 0.108 0.092 0.120 0.680
#> GSM182769 4 0.5047 0.5403 0.316 0.000 0.016 0.668
#> GSM182770 2 0.5941 0.6479 0.000 0.652 0.276 0.072
#> GSM182771 2 0.7149 -0.2101 0.000 0.552 0.264 0.184
#> GSM182772 2 0.6022 0.6436 0.000 0.656 0.260 0.084
#> GSM182773 4 0.6627 0.3000 0.000 0.096 0.348 0.556
#> GSM182774 1 0.6773 0.5369 0.660 0.160 0.020 0.160
#> GSM182775 4 0.5430 0.5653 0.300 0.000 0.036 0.664
#> GSM182776 4 0.5228 0.5495 0.312 0.000 0.024 0.664
#> GSM182777 4 0.6181 0.6162 0.204 0.000 0.128 0.668
#> GSM182802 3 0.7232 -0.1377 0.000 0.320 0.516 0.164
#> GSM182803 1 0.3486 0.6408 0.812 0.000 0.000 0.188
#> GSM182804 1 0.7646 0.4018 0.500 0.256 0.004 0.240
#> GSM182805 3 0.6514 -0.0166 0.000 0.212 0.636 0.152
#> GSM182806 1 0.4855 0.2399 0.600 0.000 0.000 0.400
#> GSM182807 1 0.3907 0.6740 0.768 0.000 0.000 0.232
#> GSM182808 1 0.4522 0.4517 0.680 0.000 0.000 0.320
#> GSM182809 1 0.9036 0.2397 0.472 0.212 0.204 0.112
#> GSM182810 1 0.2868 0.6750 0.864 0.000 0.000 0.136
#> GSM182811 1 0.3895 0.6694 0.832 0.036 0.000 0.132
#> GSM182812 1 0.0000 0.6915 1.000 0.000 0.000 0.000
#> GSM182813 1 0.3907 0.5699 0.768 0.000 0.000 0.232
#> GSM182778 2 0.4730 0.6681 0.000 0.636 0.364 0.000
#> GSM182779 3 0.3636 0.2682 0.000 0.172 0.820 0.008
#> GSM182780 3 0.3013 0.4693 0.000 0.032 0.888 0.080
#> GSM182781 3 0.6750 0.0569 0.128 0.000 0.584 0.288
#> GSM182782 2 0.4730 0.6681 0.000 0.636 0.364 0.000
#> GSM182783 3 0.6209 0.4979 0.000 0.232 0.656 0.112
#> GSM182784 3 0.0188 0.4912 0.000 0.000 0.996 0.004
#> GSM182785 3 0.1624 0.4690 0.000 0.020 0.952 0.028
#> GSM182786 2 0.4730 0.6681 0.000 0.636 0.364 0.000
#> GSM182787 3 0.2760 0.3854 0.000 0.128 0.872 0.000
#> GSM182788 2 0.4730 0.6681 0.000 0.636 0.364 0.000
#> GSM182789 3 0.0817 0.4734 0.000 0.024 0.976 0.000
#> GSM182790 3 0.6884 0.0634 0.108 0.008 0.584 0.300
#> GSM182791 3 0.7362 0.4225 0.000 0.256 0.524 0.220
#> GSM182792 4 0.9299 -0.0118 0.088 0.256 0.288 0.368
#> GSM182793 3 0.7569 0.3657 0.000 0.368 0.436 0.196
#> GSM182794 3 0.7362 0.4225 0.000 0.256 0.524 0.220
#> GSM182795 3 0.6474 0.4882 0.000 0.256 0.624 0.120
#> GSM182796 2 0.4546 0.6593 0.000 0.732 0.256 0.012
#> GSM182797 4 0.4327 0.5211 0.216 0.000 0.016 0.768
#> GSM182798 2 0.6656 -0.0502 0.000 0.620 0.160 0.220
#> GSM182799 3 0.7499 0.3997 0.000 0.256 0.500 0.244
#> GSM182800 1 0.8295 0.1884 0.380 0.256 0.016 0.348
#> GSM182801 4 0.6816 0.6211 0.180 0.040 0.108 0.672
#> GSM182814 1 0.0000 0.6915 1.000 0.000 0.000 0.000
#> GSM182815 1 0.6828 0.5142 0.588 0.148 0.000 0.264
#> GSM182816 1 0.2921 0.6744 0.860 0.000 0.000 0.140
#> GSM182817 1 0.9074 -0.0467 0.384 0.200 0.336 0.080
#> GSM182818 1 0.0921 0.6955 0.972 0.000 0.000 0.028
#> GSM182819 1 0.1867 0.6935 0.928 0.000 0.000 0.072
#> GSM182820 4 0.4008 0.4741 0.244 0.000 0.000 0.756
#> GSM182821 3 0.2706 0.4855 0.000 0.020 0.900 0.080
#> GSM182822 1 0.3444 0.6418 0.816 0.000 0.000 0.184
#> GSM182823 1 0.2408 0.6592 0.896 0.000 0.000 0.104
#> GSM182824 1 0.2408 0.6592 0.896 0.000 0.000 0.104
#> GSM182825 1 0.0188 0.6919 0.996 0.000 0.000 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM182755 4 0.4724 0.6605 0.168 0.000 0.080 0.744 0.008
#> GSM182756 3 0.4806 0.3598 0.000 0.000 0.688 0.252 0.060
#> GSM182757 3 0.3196 0.4200 0.000 0.004 0.804 0.000 0.192
#> GSM182758 3 0.5110 0.3539 0.000 0.000 0.680 0.096 0.224
#> GSM182759 3 0.6158 0.1517 0.000 0.184 0.552 0.000 0.264
#> GSM182760 4 0.5587 0.1922 0.000 0.000 0.428 0.500 0.072
#> GSM182761 3 0.6050 0.1398 0.000 0.312 0.544 0.000 0.144
#> GSM182762 5 0.7838 0.0138 0.072 0.012 0.232 0.208 0.476
#> GSM182763 3 0.4339 0.3752 0.000 0.020 0.684 0.000 0.296
#> GSM182764 3 0.5770 0.2300 0.000 0.140 0.604 0.000 0.256
#> GSM182765 5 0.4040 0.1743 0.000 0.012 0.276 0.000 0.712
#> GSM182766 5 0.7115 -0.1234 0.000 0.288 0.328 0.012 0.372
#> GSM182767 3 0.5524 -0.0350 0.000 0.000 0.516 0.416 0.068
#> GSM182768 4 0.5665 0.6247 0.056 0.000 0.208 0.680 0.056
#> GSM182769 4 0.4657 0.6135 0.172 0.000 0.024 0.756 0.048
#> GSM182770 2 0.5910 0.5531 0.000 0.596 0.100 0.012 0.292
#> GSM182771 5 0.4315 0.3723 0.000 0.068 0.156 0.004 0.772
#> GSM182772 2 0.5791 0.5449 0.000 0.588 0.080 0.012 0.320
#> GSM182773 4 0.5524 0.2182 0.000 0.000 0.416 0.516 0.068
#> GSM182774 1 0.6991 0.4227 0.492 0.000 0.024 0.244 0.240
#> GSM182775 4 0.4548 0.6727 0.156 0.000 0.096 0.748 0.000
#> GSM182776 4 0.4298 0.6434 0.184 0.000 0.060 0.756 0.000
#> GSM182777 4 0.5060 0.6600 0.104 0.000 0.204 0.692 0.000
#> GSM182802 5 0.5991 0.1183 0.000 0.068 0.452 0.016 0.464
#> GSM182803 1 0.3612 0.6218 0.732 0.000 0.000 0.268 0.000
#> GSM182804 1 0.6460 0.2614 0.440 0.000 0.004 0.156 0.400
#> GSM182805 3 0.5957 -0.0810 0.000 0.068 0.508 0.016 0.408
#> GSM182806 4 0.4446 -0.1808 0.476 0.000 0.000 0.520 0.004
#> GSM182807 1 0.4397 0.6023 0.564 0.000 0.000 0.432 0.004
#> GSM182808 1 0.4446 0.2778 0.520 0.000 0.000 0.476 0.004
#> GSM182809 1 0.6780 0.1051 0.496 0.000 0.192 0.016 0.296
#> GSM182810 1 0.3305 0.6526 0.776 0.000 0.000 0.224 0.000
#> GSM182811 1 0.4134 0.6450 0.744 0.000 0.000 0.224 0.032
#> GSM182812 1 0.0404 0.6731 0.988 0.000 0.000 0.012 0.000
#> GSM182813 1 0.4251 0.4277 0.624 0.000 0.000 0.372 0.004
#> GSM182778 2 0.0404 0.8420 0.000 0.988 0.012 0.000 0.000
#> GSM182779 3 0.2735 0.4570 0.000 0.036 0.880 0.000 0.084
#> GSM182780 3 0.3326 0.3999 0.000 0.024 0.824 0.000 0.152
#> GSM182781 3 0.6644 0.2546 0.064 0.000 0.596 0.224 0.116
#> GSM182782 2 0.1012 0.8299 0.000 0.968 0.012 0.000 0.020
#> GSM182783 3 0.4218 0.3139 0.000 0.000 0.660 0.008 0.332
#> GSM182784 3 0.0290 0.4819 0.000 0.000 0.992 0.000 0.008
#> GSM182785 3 0.2722 0.4498 0.000 0.020 0.872 0.000 0.108
#> GSM182786 2 0.0404 0.8420 0.000 0.988 0.012 0.000 0.000
#> GSM182787 3 0.3612 0.3231 0.000 0.228 0.764 0.000 0.008
#> GSM182788 2 0.0404 0.8420 0.000 0.988 0.012 0.000 0.000
#> GSM182789 3 0.0865 0.4797 0.000 0.024 0.972 0.000 0.004
#> GSM182790 3 0.5175 0.2737 0.052 0.000 0.664 0.272 0.012
#> GSM182791 3 0.5308 0.2245 0.000 0.000 0.532 0.052 0.416
#> GSM182792 5 0.7630 0.0491 0.052 0.000 0.296 0.252 0.400
#> GSM182793 5 0.3462 0.3173 0.000 0.000 0.196 0.012 0.792
#> GSM182794 3 0.5499 0.2319 0.000 0.000 0.532 0.068 0.400
#> GSM182795 3 0.4595 0.2523 0.000 0.004 0.588 0.008 0.400
#> GSM182796 2 0.1478 0.8132 0.000 0.936 0.000 0.000 0.064
#> GSM182797 4 0.0671 0.5667 0.016 0.000 0.000 0.980 0.004
#> GSM182798 5 0.1704 0.3944 0.000 0.068 0.004 0.000 0.928
#> GSM182799 3 0.5861 0.1999 0.000 0.000 0.500 0.100 0.400
#> GSM182800 5 0.7019 -0.1211 0.300 0.000 0.020 0.220 0.460
#> GSM182801 4 0.5266 0.6555 0.096 0.000 0.208 0.688 0.008
#> GSM182814 1 0.0510 0.6722 0.984 0.000 0.000 0.016 0.000
#> GSM182815 1 0.5920 0.5111 0.580 0.000 0.000 0.148 0.272
#> GSM182816 1 0.3336 0.6517 0.772 0.000 0.000 0.228 0.000
#> GSM182817 5 0.8095 0.2608 0.296 0.012 0.248 0.064 0.380
#> GSM182818 1 0.1043 0.6821 0.960 0.000 0.000 0.040 0.000
#> GSM182819 1 0.2561 0.6780 0.856 0.000 0.000 0.144 0.000
#> GSM182820 4 0.1124 0.5604 0.036 0.000 0.000 0.960 0.004
#> GSM182821 3 0.3477 0.3888 0.012 0.004 0.816 0.004 0.164
#> GSM182822 1 0.3561 0.6272 0.740 0.000 0.000 0.260 0.000
#> GSM182823 1 0.3491 0.5813 0.768 0.000 0.000 0.228 0.004
#> GSM182824 1 0.3461 0.5837 0.772 0.000 0.000 0.224 0.004
#> GSM182825 1 0.0404 0.6731 0.988 0.000 0.000 0.012 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM182755 6 0.2092 0.48838 0.000 0.000 0.124 0.000 0.000 0.876
#> GSM182756 3 0.2668 0.37083 0.000 0.000 0.828 0.004 0.000 0.168
#> GSM182757 3 0.4905 -0.35159 0.000 0.000 0.528 0.064 0.408 0.000
#> GSM182758 3 0.2308 0.37303 0.000 0.000 0.892 0.040 0.000 0.068
#> GSM182759 5 0.5107 0.58986 0.000 0.048 0.204 0.068 0.680 0.000
#> GSM182760 3 0.4176 0.25034 0.000 0.000 0.580 0.000 0.016 0.404
#> GSM182761 5 0.4655 0.58249 0.000 0.112 0.208 0.000 0.680 0.000
#> GSM182762 4 0.6099 -0.12542 0.000 0.000 0.372 0.420 0.200 0.008
#> GSM182763 5 0.5100 0.44185 0.000 0.000 0.392 0.084 0.524 0.000
#> GSM182764 5 0.5181 0.57666 0.000 0.016 0.212 0.120 0.652 0.000
#> GSM182765 4 0.5286 0.06643 0.000 0.000 0.296 0.572 0.132 0.000
#> GSM182766 5 0.4497 0.27774 0.000 0.064 0.008 0.232 0.696 0.000
#> GSM182767 3 0.3499 0.31354 0.000 0.000 0.680 0.000 0.000 0.320
#> GSM182768 6 0.3695 0.21028 0.000 0.000 0.376 0.000 0.000 0.624
#> GSM182769 6 0.1995 0.47166 0.000 0.000 0.052 0.036 0.000 0.912
#> GSM182770 4 0.5878 0.23759 0.000 0.204 0.000 0.440 0.356 0.000
#> GSM182771 4 0.3047 0.42391 0.000 0.008 0.060 0.852 0.080 0.000
#> GSM182772 4 0.5724 0.25715 0.000 0.184 0.000 0.492 0.324 0.000
#> GSM182773 3 0.4348 0.24748 0.000 0.000 0.560 0.024 0.000 0.416
#> GSM182774 6 0.7276 0.02114 0.200 0.000 0.168 0.104 0.028 0.500
#> GSM182775 6 0.2219 0.48821 0.000 0.000 0.136 0.000 0.000 0.864
#> GSM182776 6 0.1556 0.48286 0.000 0.000 0.080 0.000 0.000 0.920
#> GSM182777 6 0.3659 0.23045 0.000 0.000 0.364 0.000 0.000 0.636
#> GSM182802 4 0.4325 0.25452 0.000 0.008 0.008 0.504 0.480 0.000
#> GSM182803 6 0.4234 -0.07601 0.408 0.000 0.000 0.004 0.012 0.576
#> GSM182804 4 0.8250 -0.01591 0.240 0.000 0.172 0.380 0.080 0.128
#> GSM182805 5 0.3023 0.21794 0.000 0.004 0.008 0.180 0.808 0.000
#> GSM182806 1 0.3276 0.36351 0.764 0.000 0.000 0.004 0.004 0.228
#> GSM182807 1 0.3804 0.24265 0.656 0.000 0.000 0.000 0.008 0.336
#> GSM182808 1 0.3314 0.36851 0.740 0.000 0.000 0.000 0.004 0.256
#> GSM182809 1 0.7063 0.05327 0.392 0.000 0.200 0.348 0.024 0.036
#> GSM182810 6 0.4630 -0.09315 0.404 0.000 0.000 0.008 0.028 0.560
#> GSM182811 6 0.4849 -0.08673 0.396 0.000 0.008 0.008 0.028 0.560
#> GSM182812 1 0.3651 0.56592 0.752 0.000 0.000 0.008 0.016 0.224
#> GSM182813 1 0.2320 0.49031 0.864 0.000 0.000 0.000 0.004 0.132
#> GSM182778 2 0.0000 0.97491 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM182779 5 0.4076 0.43619 0.000 0.000 0.452 0.008 0.540 0.000
#> GSM182780 5 0.5829 0.03462 0.000 0.000 0.380 0.188 0.432 0.000
#> GSM182781 3 0.4259 0.31634 0.000 0.000 0.740 0.096 0.004 0.160
#> GSM182782 2 0.0146 0.97197 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM182783 3 0.5117 0.33601 0.000 0.000 0.596 0.288 0.116 0.000
#> GSM182784 3 0.3050 0.07856 0.000 0.000 0.764 0.000 0.236 0.000
#> GSM182785 5 0.3860 0.41274 0.000 0.000 0.472 0.000 0.528 0.000
#> GSM182786 2 0.0000 0.97491 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM182787 5 0.5602 0.36135 0.000 0.188 0.276 0.000 0.536 0.000
#> GSM182788 2 0.0000 0.97491 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM182789 3 0.3789 -0.26364 0.000 0.000 0.584 0.000 0.416 0.000
#> GSM182790 3 0.2664 0.36789 0.000 0.000 0.816 0.000 0.000 0.184
#> GSM182791 3 0.3659 0.29891 0.000 0.000 0.636 0.364 0.000 0.000
#> GSM182792 3 0.5887 0.04757 0.000 0.000 0.432 0.364 0.000 0.204
#> GSM182793 4 0.4746 0.34828 0.000 0.000 0.236 0.660 0.104 0.000
#> GSM182794 3 0.3899 0.30518 0.000 0.000 0.628 0.364 0.000 0.008
#> GSM182795 3 0.4493 0.31538 0.000 0.000 0.596 0.364 0.040 0.000
#> GSM182796 2 0.1926 0.89991 0.000 0.912 0.000 0.068 0.020 0.000
#> GSM182797 6 0.3905 0.38159 0.212 0.000 0.040 0.000 0.004 0.744
#> GSM182798 4 0.2020 0.39881 0.000 0.008 0.000 0.896 0.096 0.000
#> GSM182799 3 0.4367 0.29095 0.000 0.000 0.604 0.364 0.000 0.032
#> GSM182800 4 0.7668 -0.00174 0.196 0.000 0.176 0.380 0.008 0.240
#> GSM182801 6 0.3620 0.24660 0.000 0.000 0.352 0.000 0.000 0.648
#> GSM182814 1 0.3651 0.56592 0.752 0.000 0.000 0.008 0.016 0.224
#> GSM182815 1 0.7646 0.22611 0.372 0.000 0.016 0.192 0.296 0.124
#> GSM182816 6 0.3823 -0.11025 0.436 0.000 0.000 0.000 0.000 0.564
#> GSM182817 4 0.7218 0.31543 0.044 0.000 0.176 0.504 0.064 0.212
#> GSM182818 1 0.4350 0.51916 0.676 0.000 0.000 0.008 0.036 0.280
#> GSM182819 1 0.4475 0.27966 0.528 0.000 0.000 0.008 0.016 0.448
#> GSM182820 6 0.3536 0.34071 0.252 0.000 0.008 0.000 0.004 0.736
#> GSM182821 3 0.5894 0.07263 0.000 0.000 0.452 0.216 0.332 0.000
#> GSM182822 6 0.4708 -0.07720 0.396 0.000 0.008 0.008 0.020 0.568
#> GSM182823 1 0.0146 0.57321 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM182824 1 0.0146 0.57321 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM182825 1 0.3651 0.56592 0.752 0.000 0.000 0.008 0.016 0.224
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n stress(p) development.stage(p) k
#> MAD:pam 67 0.89207 4.35e-04 2
#> MAD:pam 51 0.88938 3.97e-06 3
#> MAD:pam 32 0.20913 3.24e-06 4
#> MAD:pam 30 0.22905 1.81e-06 5
#> MAD:pam 14 0.00702 9.12e-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", "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 18172 rows and 71 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.368 0.846 0.896 0.3883 0.566 0.566
#> 3 3 0.629 0.647 0.855 0.6424 0.705 0.505
#> 4 4 0.536 0.594 0.782 0.0956 0.882 0.677
#> 5 5 0.611 0.538 0.670 0.0666 0.878 0.619
#> 6 6 0.660 0.587 0.750 0.0717 0.800 0.363
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
#> GSM182755 2 0.0376 0.890 0.004 0.996
#> GSM182756 1 0.5946 0.793 0.856 0.144
#> GSM182757 2 0.6973 0.838 0.188 0.812
#> GSM182758 1 0.0376 0.802 0.996 0.004
#> GSM182759 2 0.6048 0.880 0.148 0.852
#> GSM182760 1 0.0000 0.800 1.000 0.000
#> GSM182761 2 0.6048 0.880 0.148 0.852
#> GSM182762 2 0.6048 0.880 0.148 0.852
#> GSM182763 2 0.6048 0.880 0.148 0.852
#> GSM182764 2 0.6048 0.880 0.148 0.852
#> GSM182765 2 0.6048 0.880 0.148 0.852
#> GSM182766 2 0.6048 0.880 0.148 0.852
#> GSM182767 1 0.0000 0.800 1.000 0.000
#> GSM182768 1 0.8016 0.795 0.756 0.244
#> GSM182769 1 0.7674 0.811 0.776 0.224
#> GSM182770 2 0.5946 0.881 0.144 0.856
#> GSM182771 2 0.5629 0.884 0.132 0.868
#> GSM182772 2 0.5946 0.881 0.144 0.856
#> GSM182773 1 0.7056 0.824 0.808 0.192
#> GSM182774 2 0.5737 0.884 0.136 0.864
#> GSM182775 1 0.7376 0.821 0.792 0.208
#> GSM182776 2 0.6343 0.869 0.160 0.840
#> GSM182777 1 0.4298 0.826 0.912 0.088
#> GSM182802 2 0.0000 0.889 0.000 1.000
#> GSM182803 2 0.0000 0.889 0.000 1.000
#> GSM182804 2 0.5629 0.884 0.132 0.868
#> GSM182805 2 0.0000 0.889 0.000 1.000
#> GSM182806 2 0.0376 0.890 0.004 0.996
#> GSM182807 2 0.0376 0.890 0.004 0.996
#> GSM182808 2 0.0376 0.890 0.004 0.996
#> GSM182809 2 0.5946 0.882 0.144 0.856
#> GSM182810 2 0.0000 0.889 0.000 1.000
#> GSM182811 2 0.0000 0.889 0.000 1.000
#> GSM182812 2 0.0000 0.889 0.000 1.000
#> GSM182813 2 0.0376 0.890 0.004 0.996
#> GSM182778 2 0.5946 0.881 0.144 0.856
#> GSM182779 2 0.6048 0.880 0.148 0.852
#> GSM182780 1 0.8443 0.763 0.728 0.272
#> GSM182781 1 0.6801 0.745 0.820 0.180
#> GSM182782 2 0.6048 0.880 0.148 0.852
#> GSM182783 1 0.7376 0.821 0.792 0.208
#> GSM182784 1 0.0938 0.803 0.988 0.012
#> GSM182785 1 0.7745 0.718 0.772 0.228
#> GSM182786 2 0.5946 0.881 0.144 0.856
#> GSM182787 2 0.6048 0.880 0.148 0.852
#> GSM182788 2 0.6048 0.880 0.148 0.852
#> GSM182789 1 0.3431 0.822 0.936 0.064
#> GSM182790 1 0.0000 0.800 1.000 0.000
#> GSM182791 1 0.8386 0.769 0.732 0.268
#> GSM182792 1 0.8081 0.791 0.752 0.248
#> GSM182793 2 0.5946 0.881 0.144 0.856
#> GSM182794 1 0.0000 0.800 1.000 0.000
#> GSM182795 1 0.7376 0.821 0.792 0.208
#> GSM182796 2 0.5946 0.881 0.144 0.856
#> GSM182797 2 0.0938 0.886 0.012 0.988
#> GSM182798 2 0.5629 0.884 0.132 0.868
#> GSM182799 1 0.9881 0.391 0.564 0.436
#> GSM182800 2 0.8955 0.580 0.312 0.688
#> GSM182801 1 0.8327 0.773 0.736 0.264
#> GSM182814 2 0.0000 0.889 0.000 1.000
#> GSM182815 2 0.0000 0.889 0.000 1.000
#> GSM182816 2 0.0000 0.889 0.000 1.000
#> GSM182817 2 0.0000 0.889 0.000 1.000
#> GSM182818 2 0.0376 0.890 0.004 0.996
#> GSM182819 2 0.0000 0.889 0.000 1.000
#> GSM182820 2 0.0376 0.890 0.004 0.996
#> GSM182821 2 0.1184 0.889 0.016 0.984
#> GSM182822 2 0.0376 0.890 0.004 0.996
#> GSM182823 2 0.0000 0.889 0.000 1.000
#> GSM182824 2 0.0000 0.889 0.000 1.000
#> GSM182825 2 0.0000 0.889 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM182755 1 0.1964 0.7459 0.944 0.000 0.056
#> GSM182756 3 0.0000 0.7122 0.000 0.000 1.000
#> GSM182757 2 0.3755 0.8757 0.008 0.872 0.120
#> GSM182758 3 0.0000 0.7122 0.000 0.000 1.000
#> GSM182759 2 0.0892 0.9202 0.020 0.980 0.000
#> GSM182760 3 0.0000 0.7122 0.000 0.000 1.000
#> GSM182761 2 0.3120 0.9052 0.012 0.908 0.080
#> GSM182762 2 0.3583 0.9105 0.044 0.900 0.056
#> GSM182763 2 0.3502 0.9011 0.020 0.896 0.084
#> GSM182764 2 0.3009 0.9158 0.028 0.920 0.052
#> GSM182765 2 0.3910 0.8854 0.020 0.876 0.104
#> GSM182766 2 0.2636 0.9134 0.020 0.932 0.048
#> GSM182767 3 0.0000 0.7122 0.000 0.000 1.000
#> GSM182768 3 0.6260 0.2413 0.448 0.000 0.552
#> GSM182769 1 0.6309 -0.1085 0.504 0.000 0.496
#> GSM182770 2 0.0892 0.9202 0.020 0.980 0.000
#> GSM182771 2 0.2902 0.9120 0.064 0.920 0.016
#> GSM182772 2 0.1031 0.9204 0.024 0.976 0.000
#> GSM182773 3 0.6215 0.2782 0.428 0.000 0.572
#> GSM182774 1 0.1753 0.7597 0.952 0.000 0.048
#> GSM182775 3 0.6267 0.2251 0.452 0.000 0.548
#> GSM182776 1 0.6421 0.1379 0.572 0.004 0.424
#> GSM182777 3 0.6235 0.2655 0.436 0.000 0.564
#> GSM182802 2 0.3192 0.8801 0.112 0.888 0.000
#> GSM182803 1 0.0000 0.7945 1.000 0.000 0.000
#> GSM182804 1 0.8248 0.2128 0.560 0.088 0.352
#> GSM182805 2 0.3192 0.8801 0.112 0.888 0.000
#> GSM182806 1 0.0000 0.7945 1.000 0.000 0.000
#> GSM182807 1 0.0000 0.7945 1.000 0.000 0.000
#> GSM182808 1 0.0000 0.7945 1.000 0.000 0.000
#> GSM182809 1 0.8346 0.1849 0.548 0.092 0.360
#> GSM182810 1 0.0000 0.7945 1.000 0.000 0.000
#> GSM182811 1 0.0000 0.7945 1.000 0.000 0.000
#> GSM182812 1 0.0000 0.7945 1.000 0.000 0.000
#> GSM182813 1 0.0000 0.7945 1.000 0.000 0.000
#> GSM182778 2 0.0000 0.9139 0.000 1.000 0.000
#> GSM182779 2 0.2846 0.9133 0.020 0.924 0.056
#> GSM182780 3 0.6994 0.1739 0.020 0.424 0.556
#> GSM182781 3 0.0000 0.7122 0.000 0.000 1.000
#> GSM182782 2 0.0000 0.9139 0.000 1.000 0.000
#> GSM182783 3 0.5722 0.4519 0.004 0.292 0.704
#> GSM182784 3 0.0000 0.7122 0.000 0.000 1.000
#> GSM182785 3 0.0237 0.7115 0.000 0.004 0.996
#> GSM182786 2 0.0000 0.9139 0.000 1.000 0.000
#> GSM182787 2 0.3415 0.8774 0.020 0.900 0.080
#> GSM182788 2 0.0000 0.9139 0.000 1.000 0.000
#> GSM182789 3 0.0424 0.7105 0.000 0.008 0.992
#> GSM182790 3 0.0000 0.7122 0.000 0.000 1.000
#> GSM182791 3 0.6260 0.2413 0.448 0.000 0.552
#> GSM182792 3 0.6260 0.2413 0.448 0.000 0.552
#> GSM182793 2 0.6849 0.2638 0.020 0.600 0.380
#> GSM182794 3 0.0000 0.7122 0.000 0.000 1.000
#> GSM182795 3 0.0592 0.7091 0.000 0.012 0.988
#> GSM182796 2 0.1753 0.9164 0.048 0.952 0.000
#> GSM182797 1 0.1525 0.7715 0.964 0.004 0.032
#> GSM182798 2 0.1753 0.9164 0.048 0.952 0.000
#> GSM182799 3 0.6260 0.2413 0.448 0.000 0.552
#> GSM182800 1 0.6505 -0.0123 0.528 0.004 0.468
#> GSM182801 1 0.6309 -0.1085 0.504 0.000 0.496
#> GSM182814 1 0.0000 0.7945 1.000 0.000 0.000
#> GSM182815 1 0.8068 0.2965 0.596 0.088 0.316
#> GSM182816 1 0.0000 0.7945 1.000 0.000 0.000
#> GSM182817 1 0.6204 0.2674 0.576 0.424 0.000
#> GSM182818 1 0.5678 0.4039 0.684 0.000 0.316
#> GSM182819 1 0.0000 0.7945 1.000 0.000 0.000
#> GSM182820 1 0.0000 0.7945 1.000 0.000 0.000
#> GSM182821 3 0.9969 0.1936 0.308 0.320 0.372
#> GSM182822 1 0.0000 0.7945 1.000 0.000 0.000
#> GSM182823 1 0.0000 0.7945 1.000 0.000 0.000
#> GSM182824 1 0.0000 0.7945 1.000 0.000 0.000
#> GSM182825 1 0.0000 0.7945 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM182755 1 0.5955 0.621 0.732 0.060 0.168 0.040
#> GSM182756 3 0.0188 0.790 0.000 0.000 0.996 0.004
#> GSM182757 2 0.4624 0.520 0.000 0.660 0.340 0.000
#> GSM182758 3 0.0376 0.790 0.000 0.004 0.992 0.004
#> GSM182759 2 0.4621 0.515 0.000 0.708 0.284 0.008
#> GSM182760 3 0.0188 0.790 0.000 0.000 0.996 0.004
#> GSM182761 2 0.4543 0.530 0.000 0.676 0.324 0.000
#> GSM182762 2 0.5487 0.513 0.024 0.644 0.328 0.004
#> GSM182763 2 0.4564 0.528 0.000 0.672 0.328 0.000
#> GSM182764 2 0.5343 0.522 0.000 0.656 0.316 0.028
#> GSM182765 2 0.4624 0.520 0.000 0.660 0.340 0.000
#> GSM182766 2 0.4188 0.389 0.000 0.812 0.148 0.040
#> GSM182767 3 0.0188 0.790 0.000 0.000 0.996 0.004
#> GSM182768 3 0.5080 0.729 0.092 0.000 0.764 0.144
#> GSM182769 3 0.6855 0.539 0.276 0.000 0.580 0.144
#> GSM182770 2 0.5119 -0.162 0.000 0.556 0.004 0.440
#> GSM182771 4 0.7566 0.309 0.000 0.392 0.192 0.416
#> GSM182772 2 0.5132 -0.182 0.000 0.548 0.004 0.448
#> GSM182773 3 0.3991 0.759 0.048 0.000 0.832 0.120
#> GSM182774 1 0.4094 0.777 0.828 0.000 0.056 0.116
#> GSM182775 3 0.6034 0.664 0.164 0.000 0.688 0.148
#> GSM182776 3 0.6863 0.439 0.348 0.000 0.536 0.116
#> GSM182777 3 0.3780 0.733 0.148 0.004 0.832 0.016
#> GSM182802 4 0.4240 0.442 0.012 0.200 0.004 0.784
#> GSM182803 1 0.0000 0.878 1.000 0.000 0.000 0.000
#> GSM182804 1 0.6090 0.355 0.512 0.036 0.004 0.448
#> GSM182805 4 0.5134 0.452 0.012 0.320 0.004 0.664
#> GSM182806 1 0.1118 0.874 0.964 0.000 0.000 0.036
#> GSM182807 1 0.1305 0.874 0.960 0.000 0.004 0.036
#> GSM182808 1 0.1584 0.872 0.952 0.000 0.012 0.036
#> GSM182809 1 0.6858 0.190 0.532 0.004 0.368 0.096
#> GSM182810 1 0.0000 0.878 1.000 0.000 0.000 0.000
#> GSM182811 1 0.1109 0.870 0.968 0.000 0.004 0.028
#> GSM182812 1 0.0592 0.876 0.984 0.000 0.000 0.016
#> GSM182813 1 0.1706 0.870 0.948 0.000 0.016 0.036
#> GSM182778 2 0.2216 0.254 0.000 0.908 0.000 0.092
#> GSM182779 2 0.4543 0.530 0.000 0.676 0.324 0.000
#> GSM182780 3 0.2760 0.678 0.000 0.128 0.872 0.000
#> GSM182781 3 0.0000 0.790 0.000 0.000 1.000 0.000
#> GSM182782 2 0.2216 0.254 0.000 0.908 0.000 0.092
#> GSM182783 3 0.0817 0.780 0.000 0.024 0.976 0.000
#> GSM182784 3 0.0188 0.790 0.000 0.000 0.996 0.004
#> GSM182785 3 0.0817 0.779 0.000 0.024 0.976 0.000
#> GSM182786 2 0.2216 0.254 0.000 0.908 0.000 0.092
#> GSM182787 2 0.4898 0.396 0.000 0.584 0.416 0.000
#> GSM182788 2 0.2216 0.254 0.000 0.908 0.000 0.092
#> GSM182789 3 0.0336 0.788 0.000 0.008 0.992 0.000
#> GSM182790 3 0.0188 0.790 0.000 0.000 0.996 0.004
#> GSM182791 3 0.4153 0.755 0.048 0.000 0.820 0.132
#> GSM182792 3 0.5080 0.729 0.092 0.000 0.764 0.144
#> GSM182793 4 0.7922 0.293 0.012 0.304 0.212 0.472
#> GSM182794 3 0.0188 0.790 0.000 0.000 0.996 0.004
#> GSM182795 3 0.0376 0.790 0.000 0.004 0.992 0.004
#> GSM182796 2 0.5386 -0.328 0.000 0.612 0.020 0.368
#> GSM182797 1 0.3570 0.804 0.860 0.000 0.092 0.048
#> GSM182798 4 0.7451 0.319 0.000 0.412 0.172 0.416
#> GSM182799 3 0.5272 0.727 0.096 0.004 0.760 0.140
#> GSM182800 3 0.6337 0.448 0.360 0.000 0.568 0.072
#> GSM182801 3 0.6584 0.477 0.336 0.000 0.568 0.096
#> GSM182814 1 0.0592 0.876 0.984 0.000 0.000 0.016
#> GSM182815 1 0.6086 0.349 0.516 0.036 0.004 0.444
#> GSM182816 1 0.0592 0.876 0.984 0.000 0.000 0.016
#> GSM182817 4 0.9656 0.296 0.168 0.264 0.196 0.372
#> GSM182818 1 0.4284 0.728 0.780 0.000 0.020 0.200
#> GSM182819 1 0.0000 0.878 1.000 0.000 0.000 0.000
#> GSM182820 1 0.1305 0.874 0.960 0.000 0.004 0.036
#> GSM182821 3 0.6576 -0.191 0.068 0.412 0.516 0.004
#> GSM182822 1 0.0376 0.877 0.992 0.000 0.004 0.004
#> GSM182823 1 0.0592 0.876 0.984 0.000 0.000 0.016
#> GSM182824 1 0.0336 0.878 0.992 0.000 0.000 0.008
#> GSM182825 1 0.0707 0.876 0.980 0.000 0.000 0.020
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM182755 1 0.8283 0.4179 0.464 0.040 0.184 0.076 0.236
#> GSM182756 3 0.0404 0.6204 0.000 0.000 0.988 0.000 0.012
#> GSM182757 5 0.6796 0.5945 0.000 0.312 0.308 0.000 0.380
#> GSM182758 3 0.0404 0.6233 0.000 0.012 0.988 0.000 0.000
#> GSM182759 5 0.6790 0.5695 0.000 0.328 0.292 0.000 0.380
#> GSM182760 3 0.0324 0.6274 0.000 0.000 0.992 0.004 0.004
#> GSM182761 5 0.6796 0.5945 0.000 0.312 0.308 0.000 0.380
#> GSM182762 5 0.7035 0.4830 0.004 0.204 0.312 0.016 0.464
#> GSM182763 5 0.7135 0.5869 0.000 0.312 0.316 0.012 0.360
#> GSM182764 5 0.6928 0.5865 0.000 0.316 0.300 0.004 0.380
#> GSM182765 5 0.7143 0.5740 0.000 0.316 0.324 0.012 0.348
#> GSM182766 2 0.7528 -0.0471 0.000 0.468 0.184 0.072 0.276
#> GSM182767 3 0.0162 0.6271 0.000 0.000 0.996 0.004 0.000
#> GSM182768 3 0.5365 0.5734 0.032 0.000 0.572 0.016 0.380
#> GSM182769 3 0.5445 0.5681 0.036 0.000 0.564 0.016 0.384
#> GSM182770 4 0.3949 0.7040 0.000 0.332 0.000 0.668 0.000
#> GSM182771 2 0.7135 0.2927 0.000 0.400 0.028 0.384 0.188
#> GSM182772 4 0.3949 0.7040 0.000 0.332 0.000 0.668 0.000
#> GSM182773 3 0.5365 0.5734 0.032 0.000 0.572 0.016 0.380
#> GSM182774 1 0.6309 0.4835 0.600 0.020 0.084 0.016 0.280
#> GSM182775 3 0.5375 0.5708 0.032 0.000 0.568 0.016 0.384
#> GSM182776 1 0.7145 -0.1815 0.340 0.012 0.316 0.000 0.332
#> GSM182777 3 0.5318 0.5844 0.052 0.000 0.636 0.012 0.300
#> GSM182802 4 0.3586 0.6998 0.000 0.264 0.000 0.736 0.000
#> GSM182803 1 0.0324 0.8137 0.992 0.000 0.000 0.004 0.004
#> GSM182804 4 0.5368 0.5148 0.108 0.076 0.000 0.736 0.080
#> GSM182805 4 0.3707 0.6790 0.000 0.284 0.000 0.716 0.000
#> GSM182806 1 0.4930 0.7156 0.696 0.000 0.000 0.084 0.220
#> GSM182807 1 0.5110 0.7081 0.680 0.000 0.000 0.096 0.224
#> GSM182808 1 0.3866 0.7658 0.808 0.000 0.000 0.096 0.096
#> GSM182809 5 0.8314 -0.2539 0.248 0.024 0.268 0.068 0.392
#> GSM182810 1 0.0324 0.8139 0.992 0.000 0.004 0.000 0.004
#> GSM182811 1 0.1717 0.7855 0.936 0.008 0.000 0.052 0.004
#> GSM182812 1 0.0693 0.8107 0.980 0.000 0.000 0.012 0.008
#> GSM182813 1 0.5110 0.7081 0.680 0.000 0.000 0.096 0.224
#> GSM182778 2 0.0000 0.5000 0.000 1.000 0.000 0.000 0.000
#> GSM182779 5 0.6796 0.5945 0.000 0.312 0.308 0.000 0.380
#> GSM182780 3 0.3706 0.4487 0.000 0.180 0.796 0.012 0.012
#> GSM182781 3 0.0000 0.6264 0.000 0.000 1.000 0.000 0.000
#> GSM182782 2 0.0000 0.5000 0.000 1.000 0.000 0.000 0.000
#> GSM182783 3 0.3203 0.4845 0.000 0.168 0.820 0.012 0.000
#> GSM182784 3 0.0404 0.6204 0.000 0.000 0.988 0.000 0.012
#> GSM182785 3 0.4725 0.1831 0.000 0.080 0.720 0.000 0.200
#> GSM182786 2 0.0000 0.5000 0.000 1.000 0.000 0.000 0.000
#> GSM182787 3 0.6672 -0.6304 0.000 0.232 0.392 0.000 0.376
#> GSM182788 2 0.0000 0.5000 0.000 1.000 0.000 0.000 0.000
#> GSM182789 3 0.2423 0.5583 0.000 0.080 0.896 0.000 0.024
#> GSM182790 3 0.0324 0.6274 0.000 0.000 0.992 0.004 0.004
#> GSM182791 3 0.5365 0.5734 0.032 0.000 0.572 0.016 0.380
#> GSM182792 3 0.5365 0.5734 0.032 0.000 0.572 0.016 0.380
#> GSM182793 4 0.4147 0.6988 0.000 0.316 0.000 0.676 0.008
#> GSM182794 3 0.0324 0.6274 0.000 0.000 0.992 0.004 0.004
#> GSM182795 3 0.2563 0.5438 0.000 0.120 0.872 0.008 0.000
#> GSM182796 2 0.6560 0.4127 0.000 0.548 0.016 0.248 0.188
#> GSM182797 1 0.5903 0.6620 0.608 0.000 0.016 0.096 0.280
#> GSM182798 2 0.7135 0.2927 0.000 0.400 0.028 0.384 0.188
#> GSM182799 3 0.6307 0.5601 0.032 0.024 0.552 0.036 0.356
#> GSM182800 5 0.7643 -0.3100 0.288 0.004 0.304 0.036 0.368
#> GSM182801 3 0.6046 0.5059 0.108 0.000 0.512 0.004 0.376
#> GSM182814 1 0.0693 0.8107 0.980 0.000 0.000 0.012 0.008
#> GSM182815 4 0.5016 0.4970 0.184 0.076 0.000 0.724 0.016
#> GSM182816 1 0.0693 0.8107 0.980 0.000 0.000 0.012 0.008
#> GSM182817 2 0.9160 0.2321 0.212 0.308 0.036 0.256 0.188
#> GSM182818 1 0.1461 0.8031 0.952 0.000 0.004 0.016 0.028
#> GSM182819 1 0.0324 0.8137 0.992 0.000 0.000 0.004 0.004
#> GSM182820 1 0.5110 0.7081 0.680 0.000 0.000 0.096 0.224
#> GSM182821 3 0.6728 0.1160 0.032 0.172 0.616 0.020 0.160
#> GSM182822 1 0.0613 0.8132 0.984 0.000 0.004 0.004 0.008
#> GSM182823 1 0.0693 0.8107 0.980 0.000 0.000 0.012 0.008
#> GSM182824 1 0.0451 0.8128 0.988 0.000 0.000 0.008 0.004
#> GSM182825 1 0.0703 0.8118 0.976 0.000 0.000 0.024 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM182755 4 0.6457 0.5283 0.080 0.000 0.200 0.604 0.068 0.048
#> GSM182756 3 0.6442 0.4347 0.000 0.036 0.504 0.188 0.004 0.268
#> GSM182757 3 0.1307 0.5624 0.000 0.008 0.952 0.008 0.032 0.000
#> GSM182758 3 0.6376 0.4224 0.000 0.036 0.488 0.188 0.000 0.288
#> GSM182759 3 0.4775 0.3236 0.000 0.188 0.720 0.008 0.040 0.044
#> GSM182760 3 0.6603 0.4167 0.000 0.040 0.472 0.196 0.004 0.288
#> GSM182761 3 0.1483 0.5574 0.000 0.012 0.944 0.008 0.036 0.000
#> GSM182762 3 0.2240 0.5653 0.000 0.000 0.904 0.008 0.056 0.032
#> GSM182763 3 0.2593 0.5447 0.000 0.012 0.884 0.000 0.036 0.068
#> GSM182764 3 0.1882 0.5508 0.000 0.012 0.920 0.008 0.060 0.000
#> GSM182765 3 0.3025 0.5562 0.000 0.004 0.856 0.004 0.060 0.076
#> GSM182766 3 0.6247 -0.0990 0.000 0.240 0.520 0.000 0.208 0.032
#> GSM182767 3 0.6547 0.4182 0.000 0.036 0.476 0.196 0.004 0.288
#> GSM182768 6 0.0405 0.6929 0.008 0.004 0.000 0.000 0.000 0.988
#> GSM182769 6 0.1196 0.6917 0.008 0.000 0.040 0.000 0.000 0.952
#> GSM182770 5 0.2146 0.6065 0.000 0.044 0.044 0.000 0.908 0.004
#> GSM182771 5 0.5965 0.3288 0.004 0.240 0.236 0.000 0.516 0.004
#> GSM182772 5 0.1511 0.6084 0.000 0.044 0.012 0.000 0.940 0.004
#> GSM182773 6 0.1265 0.6902 0.008 0.000 0.044 0.000 0.000 0.948
#> GSM182774 6 0.4292 0.1327 0.416 0.000 0.008 0.004 0.004 0.568
#> GSM182775 6 0.1265 0.6902 0.008 0.000 0.044 0.000 0.000 0.948
#> GSM182776 6 0.3648 0.6320 0.128 0.000 0.040 0.024 0.000 0.808
#> GSM182777 6 0.4879 0.3530 0.008 0.028 0.280 0.016 0.008 0.660
#> GSM182802 5 0.1440 0.6097 0.000 0.032 0.012 0.004 0.948 0.004
#> GSM182803 1 0.2484 0.8952 0.896 0.004 0.000 0.056 0.012 0.032
#> GSM182804 5 0.5772 0.4046 0.216 0.036 0.004 0.052 0.652 0.040
#> GSM182805 5 0.1829 0.6021 0.000 0.064 0.012 0.000 0.920 0.004
#> GSM182806 4 0.3834 0.8530 0.268 0.000 0.000 0.708 0.000 0.024
#> GSM182807 4 0.3766 0.8642 0.256 0.000 0.000 0.720 0.000 0.024
#> GSM182808 4 0.3789 0.8563 0.260 0.000 0.000 0.716 0.000 0.024
#> GSM182809 6 0.5427 0.1741 0.396 0.004 0.008 0.004 0.068 0.520
#> GSM182810 1 0.1989 0.9017 0.916 0.004 0.000 0.052 0.000 0.028
#> GSM182811 1 0.3565 0.7917 0.828 0.004 0.004 0.020 0.108 0.036
#> GSM182812 1 0.0000 0.9057 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM182813 4 0.3619 0.8676 0.232 0.000 0.000 0.744 0.000 0.024
#> GSM182778 2 0.1757 0.9938 0.000 0.916 0.008 0.000 0.076 0.000
#> GSM182779 3 0.2476 0.5415 0.000 0.012 0.900 0.008 0.036 0.044
#> GSM182780 6 0.6103 0.0809 0.000 0.004 0.308 0.100 0.048 0.540
#> GSM182781 3 0.6193 0.3670 0.000 0.036 0.500 0.120 0.004 0.340
#> GSM182782 2 0.1701 0.9979 0.000 0.920 0.008 0.000 0.072 0.000
#> GSM182783 6 0.5955 0.1751 0.000 0.004 0.268 0.100 0.048 0.580
#> GSM182784 3 0.6456 0.4378 0.000 0.036 0.504 0.196 0.004 0.260
#> GSM182785 3 0.3243 0.5667 0.000 0.016 0.844 0.076 0.000 0.064
#> GSM182786 2 0.1701 0.9979 0.000 0.920 0.008 0.000 0.072 0.000
#> GSM182787 3 0.4938 0.3625 0.000 0.180 0.712 0.008 0.036 0.064
#> GSM182788 2 0.1701 0.9979 0.000 0.920 0.008 0.000 0.072 0.000
#> GSM182789 3 0.5378 0.4255 0.000 0.008 0.576 0.112 0.000 0.304
#> GSM182790 3 0.6603 0.4167 0.000 0.040 0.472 0.196 0.004 0.288
#> GSM182791 6 0.0551 0.6925 0.008 0.004 0.004 0.000 0.000 0.984
#> GSM182792 6 0.0405 0.6929 0.008 0.004 0.000 0.000 0.000 0.988
#> GSM182793 5 0.2179 0.5930 0.000 0.004 0.064 0.016 0.908 0.008
#> GSM182794 3 0.6603 0.4167 0.000 0.040 0.472 0.196 0.004 0.288
#> GSM182795 6 0.5423 0.1360 0.000 0.004 0.308 0.112 0.004 0.572
#> GSM182796 5 0.6114 0.1602 0.000 0.348 0.236 0.000 0.412 0.004
#> GSM182797 4 0.4446 0.7891 0.152 0.000 0.004 0.724 0.000 0.120
#> GSM182798 5 0.5884 0.3161 0.000 0.252 0.236 0.000 0.508 0.004
#> GSM182799 6 0.1652 0.6815 0.004 0.004 0.004 0.004 0.048 0.936
#> GSM182800 6 0.5101 0.4657 0.208 0.008 0.000 0.048 0.048 0.688
#> GSM182801 6 0.1196 0.6917 0.008 0.000 0.040 0.000 0.000 0.952
#> GSM182814 1 0.0000 0.9057 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM182815 5 0.5644 0.4072 0.236 0.032 0.004 0.044 0.648 0.036
#> GSM182816 1 0.0000 0.9057 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM182817 5 0.7387 0.3477 0.244 0.004 0.232 0.044 0.440 0.036
#> GSM182818 1 0.2393 0.8938 0.892 0.000 0.000 0.064 0.004 0.040
#> GSM182819 1 0.2145 0.8920 0.900 0.000 0.000 0.072 0.000 0.028
#> GSM182820 4 0.3670 0.8698 0.240 0.000 0.000 0.736 0.000 0.024
#> GSM182821 6 0.6086 -0.0236 0.016 0.000 0.416 0.028 0.080 0.460
#> GSM182822 1 0.2972 0.8274 0.836 0.000 0.000 0.128 0.000 0.036
#> GSM182823 1 0.0146 0.9048 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM182824 1 0.0260 0.9084 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM182825 1 0.2544 0.8785 0.896 0.004 0.000 0.024 0.048 0.028
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n stress(p) development.stage(p) k
#> MAD:mclust 70 0.6019 2.32e-04 2
#> MAD:mclust 51 0.3884 1.12e-07 3
#> MAD:mclust 49 0.0924 6.36e-09 4
#> MAD:mclust 50 0.1177 1.17e-08 5
#> MAD:mclust 45 0.0652 2.15e-06 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "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 18172 rows and 71 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.940 0.944 0.975 0.5058 0.493 0.493
#> 3 3 0.602 0.730 0.873 0.3130 0.697 0.465
#> 4 4 0.812 0.831 0.916 0.1149 0.776 0.456
#> 5 5 0.717 0.762 0.857 0.0432 0.918 0.721
#> 6 6 0.653 0.564 0.752 0.0547 0.939 0.756
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
#> GSM182755 1 0.7219 0.744 0.800 0.200
#> GSM182756 2 0.0000 0.968 0.000 1.000
#> GSM182757 2 0.0000 0.968 0.000 1.000
#> GSM182758 2 0.0000 0.968 0.000 1.000
#> GSM182759 2 0.0000 0.968 0.000 1.000
#> GSM182760 2 0.6973 0.770 0.188 0.812
#> GSM182761 2 0.0000 0.968 0.000 1.000
#> GSM182762 2 0.5059 0.864 0.112 0.888
#> GSM182763 2 0.0000 0.968 0.000 1.000
#> GSM182764 2 0.0000 0.968 0.000 1.000
#> GSM182765 2 0.0000 0.968 0.000 1.000
#> GSM182766 2 0.0000 0.968 0.000 1.000
#> GSM182767 2 0.0376 0.965 0.004 0.996
#> GSM182768 1 0.0000 0.980 1.000 0.000
#> GSM182769 1 0.0000 0.980 1.000 0.000
#> GSM182770 2 0.0000 0.968 0.000 1.000
#> GSM182771 2 0.0000 0.968 0.000 1.000
#> GSM182772 2 0.0000 0.968 0.000 1.000
#> GSM182773 1 0.0376 0.977 0.996 0.004
#> GSM182774 1 0.0000 0.980 1.000 0.000
#> GSM182775 1 0.0000 0.980 1.000 0.000
#> GSM182776 1 0.0000 0.980 1.000 0.000
#> GSM182777 1 0.0000 0.980 1.000 0.000
#> GSM182802 2 0.0000 0.968 0.000 1.000
#> GSM182803 1 0.0000 0.980 1.000 0.000
#> GSM182804 1 0.0000 0.980 1.000 0.000
#> GSM182805 2 0.0000 0.968 0.000 1.000
#> GSM182806 1 0.0000 0.980 1.000 0.000
#> GSM182807 1 0.0000 0.980 1.000 0.000
#> GSM182808 1 0.0000 0.980 1.000 0.000
#> GSM182809 1 0.0000 0.980 1.000 0.000
#> GSM182810 1 0.0000 0.980 1.000 0.000
#> GSM182811 1 0.0000 0.980 1.000 0.000
#> GSM182812 1 0.0000 0.980 1.000 0.000
#> GSM182813 1 0.0000 0.980 1.000 0.000
#> GSM182778 2 0.0000 0.968 0.000 1.000
#> GSM182779 2 0.0000 0.968 0.000 1.000
#> GSM182780 2 0.0000 0.968 0.000 1.000
#> GSM182781 2 0.9686 0.368 0.396 0.604
#> GSM182782 2 0.0000 0.968 0.000 1.000
#> GSM182783 2 0.0000 0.968 0.000 1.000
#> GSM182784 2 0.0000 0.968 0.000 1.000
#> GSM182785 2 0.0000 0.968 0.000 1.000
#> GSM182786 2 0.0000 0.968 0.000 1.000
#> GSM182787 2 0.0000 0.968 0.000 1.000
#> GSM182788 2 0.0000 0.968 0.000 1.000
#> GSM182789 2 0.0000 0.968 0.000 1.000
#> GSM182790 2 0.9000 0.555 0.316 0.684
#> GSM182791 1 0.4161 0.902 0.916 0.084
#> GSM182792 1 0.0000 0.980 1.000 0.000
#> GSM182793 2 0.0000 0.968 0.000 1.000
#> GSM182794 2 0.3879 0.901 0.076 0.924
#> GSM182795 2 0.0000 0.968 0.000 1.000
#> GSM182796 2 0.0000 0.968 0.000 1.000
#> GSM182797 1 0.0000 0.980 1.000 0.000
#> GSM182798 2 0.0000 0.968 0.000 1.000
#> GSM182799 1 0.3733 0.914 0.928 0.072
#> GSM182800 1 0.0000 0.980 1.000 0.000
#> GSM182801 1 0.0000 0.980 1.000 0.000
#> GSM182814 1 0.0000 0.980 1.000 0.000
#> GSM182815 1 0.1633 0.961 0.976 0.024
#> GSM182816 1 0.0000 0.980 1.000 0.000
#> GSM182817 1 0.8207 0.651 0.744 0.256
#> GSM182818 1 0.0000 0.980 1.000 0.000
#> GSM182819 1 0.0000 0.980 1.000 0.000
#> GSM182820 1 0.0000 0.980 1.000 0.000
#> GSM182821 2 0.0672 0.962 0.008 0.992
#> GSM182822 1 0.0000 0.980 1.000 0.000
#> GSM182823 1 0.0000 0.980 1.000 0.000
#> GSM182824 1 0.0000 0.980 1.000 0.000
#> GSM182825 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
#> GSM182755 3 0.4324 0.736 0.028 0.112 0.860
#> GSM182756 3 0.4796 0.518 0.000 0.220 0.780
#> GSM182757 2 0.4842 0.748 0.000 0.776 0.224
#> GSM182758 2 0.6008 0.603 0.000 0.628 0.372
#> GSM182759 2 0.0237 0.862 0.000 0.996 0.004
#> GSM182760 3 0.0237 0.785 0.000 0.004 0.996
#> GSM182761 2 0.4346 0.776 0.000 0.816 0.184
#> GSM182762 3 0.5327 0.572 0.000 0.272 0.728
#> GSM182763 2 0.0237 0.862 0.000 0.996 0.004
#> GSM182764 2 0.0592 0.860 0.000 0.988 0.012
#> GSM182765 2 0.0424 0.861 0.000 0.992 0.008
#> GSM182766 2 0.0237 0.862 0.000 0.996 0.004
#> GSM182767 3 0.1643 0.766 0.000 0.044 0.956
#> GSM182768 3 0.5506 0.591 0.220 0.016 0.764
#> GSM182769 3 0.0237 0.786 0.004 0.000 0.996
#> GSM182770 2 0.0000 0.862 0.000 1.000 0.000
#> GSM182771 2 0.0000 0.862 0.000 1.000 0.000
#> GSM182772 2 0.0000 0.862 0.000 1.000 0.000
#> GSM182773 3 0.0000 0.786 0.000 0.000 1.000
#> GSM182774 1 0.6295 -0.126 0.528 0.000 0.472
#> GSM182775 3 0.0237 0.786 0.004 0.000 0.996
#> GSM182776 3 0.2959 0.761 0.100 0.000 0.900
#> GSM182777 3 0.0000 0.786 0.000 0.000 1.000
#> GSM182802 1 0.6045 0.368 0.620 0.380 0.000
#> GSM182803 1 0.3412 0.783 0.876 0.000 0.124
#> GSM182804 1 0.0000 0.882 1.000 0.000 0.000
#> GSM182805 2 0.1411 0.842 0.036 0.964 0.000
#> GSM182806 3 0.6079 0.444 0.388 0.000 0.612
#> GSM182807 3 0.6026 0.469 0.376 0.000 0.624
#> GSM182808 3 0.6026 0.469 0.376 0.000 0.624
#> GSM182809 1 0.0000 0.882 1.000 0.000 0.000
#> GSM182810 1 0.0000 0.882 1.000 0.000 0.000
#> GSM182811 1 0.0000 0.882 1.000 0.000 0.000
#> GSM182812 1 0.0000 0.882 1.000 0.000 0.000
#> GSM182813 3 0.5968 0.487 0.364 0.000 0.636
#> GSM182778 2 0.0000 0.862 0.000 1.000 0.000
#> GSM182779 2 0.0000 0.862 0.000 1.000 0.000
#> GSM182780 2 0.4750 0.753 0.000 0.784 0.216
#> GSM182781 3 0.0000 0.786 0.000 0.000 1.000
#> GSM182782 2 0.0000 0.862 0.000 1.000 0.000
#> GSM182783 2 0.5785 0.651 0.000 0.668 0.332
#> GSM182784 2 0.6225 0.502 0.000 0.568 0.432
#> GSM182785 2 0.5988 0.608 0.000 0.632 0.368
#> GSM182786 2 0.0000 0.862 0.000 1.000 0.000
#> GSM182787 2 0.0424 0.861 0.000 0.992 0.008
#> GSM182788 2 0.0000 0.862 0.000 1.000 0.000
#> GSM182789 2 0.5905 0.628 0.000 0.648 0.352
#> GSM182790 3 0.0000 0.786 0.000 0.000 1.000
#> GSM182791 2 0.6244 0.482 0.000 0.560 0.440
#> GSM182792 3 0.0000 0.786 0.000 0.000 1.000
#> GSM182793 2 0.2261 0.819 0.068 0.932 0.000
#> GSM182794 3 0.1643 0.767 0.000 0.044 0.956
#> GSM182795 2 0.5835 0.643 0.000 0.660 0.340
#> GSM182796 2 0.0000 0.862 0.000 1.000 0.000
#> GSM182797 3 0.3340 0.749 0.120 0.000 0.880
#> GSM182798 2 0.0000 0.862 0.000 1.000 0.000
#> GSM182799 1 0.4842 0.597 0.776 0.000 0.224
#> GSM182800 1 0.3941 0.739 0.844 0.000 0.156
#> GSM182801 3 0.4399 0.699 0.188 0.000 0.812
#> GSM182814 1 0.0000 0.882 1.000 0.000 0.000
#> GSM182815 1 0.0000 0.882 1.000 0.000 0.000
#> GSM182816 1 0.1163 0.869 0.972 0.000 0.028
#> GSM182817 2 0.6473 0.445 0.332 0.652 0.016
#> GSM182818 1 0.0237 0.881 0.996 0.000 0.004
#> GSM182819 3 0.6305 0.192 0.484 0.000 0.516
#> GSM182820 3 0.5968 0.487 0.364 0.000 0.636
#> GSM182821 2 0.0000 0.862 0.000 1.000 0.000
#> GSM182822 1 0.0592 0.878 0.988 0.000 0.012
#> GSM182823 1 0.3192 0.796 0.888 0.000 0.112
#> GSM182824 1 0.0592 0.878 0.988 0.000 0.012
#> GSM182825 1 0.0000 0.882 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM182755 1 0.0000 0.8369 1.000 0.000 0.000 0.000
#> GSM182756 3 0.1297 0.9196 0.016 0.020 0.964 0.000
#> GSM182757 2 0.2281 0.8690 0.000 0.904 0.096 0.000
#> GSM182758 3 0.0188 0.9332 0.000 0.004 0.996 0.000
#> GSM182759 2 0.0336 0.9363 0.000 0.992 0.008 0.000
#> GSM182760 3 0.0376 0.9329 0.004 0.004 0.992 0.000
#> GSM182761 2 0.3400 0.7769 0.000 0.820 0.180 0.000
#> GSM182762 1 0.5511 0.0159 0.500 0.484 0.016 0.000
#> GSM182763 2 0.0921 0.9289 0.000 0.972 0.028 0.000
#> GSM182764 2 0.0000 0.9374 0.000 1.000 0.000 0.000
#> GSM182765 2 0.0921 0.9261 0.000 0.972 0.028 0.000
#> GSM182766 2 0.0000 0.9374 0.000 1.000 0.000 0.000
#> GSM182767 3 0.0188 0.9332 0.000 0.004 0.996 0.000
#> GSM182768 3 0.0469 0.9298 0.000 0.000 0.988 0.012
#> GSM182769 3 0.0657 0.9290 0.012 0.000 0.984 0.004
#> GSM182770 2 0.0188 0.9377 0.000 0.996 0.004 0.000
#> GSM182771 2 0.0188 0.9357 0.000 0.996 0.000 0.004
#> GSM182772 2 0.0000 0.9374 0.000 1.000 0.000 0.000
#> GSM182773 3 0.0000 0.9325 0.000 0.000 1.000 0.000
#> GSM182774 1 0.5137 0.2703 0.544 0.004 0.000 0.452
#> GSM182775 3 0.0469 0.9297 0.012 0.000 0.988 0.000
#> GSM182776 3 0.5161 0.1894 0.476 0.000 0.520 0.004
#> GSM182777 3 0.3486 0.7815 0.188 0.000 0.812 0.000
#> GSM182802 2 0.3569 0.7528 0.000 0.804 0.000 0.196
#> GSM182803 1 0.4072 0.5581 0.748 0.000 0.000 0.252
#> GSM182804 4 0.0000 0.8301 0.000 0.000 0.000 1.000
#> GSM182805 2 0.0188 0.9377 0.000 0.996 0.004 0.000
#> GSM182806 1 0.0188 0.8387 0.996 0.000 0.000 0.004
#> GSM182807 1 0.0188 0.8387 0.996 0.000 0.000 0.004
#> GSM182808 1 0.0524 0.8356 0.988 0.000 0.008 0.004
#> GSM182809 4 0.1109 0.8432 0.028 0.000 0.004 0.968
#> GSM182810 4 0.3528 0.8264 0.192 0.000 0.000 0.808
#> GSM182811 4 0.2610 0.8471 0.088 0.012 0.000 0.900
#> GSM182812 4 0.1474 0.8479 0.052 0.000 0.000 0.948
#> GSM182813 1 0.0188 0.8387 0.996 0.000 0.000 0.004
#> GSM182778 2 0.0188 0.9377 0.000 0.996 0.004 0.000
#> GSM182779 2 0.0188 0.9377 0.000 0.996 0.004 0.000
#> GSM182780 3 0.0657 0.9309 0.004 0.012 0.984 0.000
#> GSM182781 3 0.3726 0.7436 0.212 0.000 0.788 0.000
#> GSM182782 2 0.0188 0.9377 0.000 0.996 0.004 0.000
#> GSM182783 3 0.0336 0.9319 0.000 0.008 0.992 0.000
#> GSM182784 3 0.0188 0.9332 0.000 0.004 0.996 0.000
#> GSM182785 3 0.1661 0.8990 0.004 0.052 0.944 0.000
#> GSM182786 2 0.0188 0.9377 0.000 0.996 0.004 0.000
#> GSM182787 2 0.1118 0.9237 0.000 0.964 0.036 0.000
#> GSM182788 2 0.0188 0.9377 0.000 0.996 0.004 0.000
#> GSM182789 3 0.0188 0.9332 0.000 0.004 0.996 0.000
#> GSM182790 3 0.0376 0.9329 0.004 0.004 0.992 0.000
#> GSM182791 3 0.0469 0.9298 0.000 0.000 0.988 0.012
#> GSM182792 3 0.0188 0.9320 0.004 0.000 0.996 0.000
#> GSM182793 2 0.5636 0.3402 0.000 0.552 0.024 0.424
#> GSM182794 3 0.0188 0.9332 0.000 0.004 0.996 0.000
#> GSM182795 3 0.0188 0.9332 0.000 0.004 0.996 0.000
#> GSM182796 2 0.0000 0.9374 0.000 1.000 0.000 0.000
#> GSM182797 1 0.0000 0.8369 1.000 0.000 0.000 0.000
#> GSM182798 2 0.0000 0.9374 0.000 1.000 0.000 0.000
#> GSM182799 3 0.3649 0.7613 0.000 0.000 0.796 0.204
#> GSM182800 4 0.2281 0.7507 0.000 0.000 0.096 0.904
#> GSM182801 3 0.4458 0.7762 0.116 0.000 0.808 0.076
#> GSM182814 4 0.3688 0.8175 0.208 0.000 0.000 0.792
#> GSM182815 4 0.0188 0.8325 0.004 0.000 0.000 0.996
#> GSM182816 4 0.3791 0.8203 0.200 0.000 0.004 0.796
#> GSM182817 2 0.2918 0.8373 0.116 0.876 0.000 0.008
#> GSM182818 4 0.3908 0.8105 0.212 0.000 0.004 0.784
#> GSM182819 1 0.1557 0.8091 0.944 0.000 0.000 0.056
#> GSM182820 1 0.0188 0.8387 0.996 0.000 0.000 0.004
#> GSM182821 2 0.3013 0.8658 0.080 0.888 0.032 0.000
#> GSM182822 4 0.4837 0.6162 0.348 0.000 0.004 0.648
#> GSM182823 1 0.3024 0.7197 0.852 0.000 0.000 0.148
#> GSM182824 4 0.4155 0.7867 0.240 0.000 0.004 0.756
#> GSM182825 4 0.0000 0.8301 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
#> GSM182755 2 0.1202 0.6730 0.032 0.960 0.004 0.000 0.004
#> GSM182756 3 0.3902 0.8271 0.000 0.152 0.804 0.028 0.016
#> GSM182757 5 0.4044 0.7878 0.000 0.148 0.024 0.028 0.800
#> GSM182758 3 0.0807 0.8936 0.000 0.012 0.976 0.012 0.000
#> GSM182759 5 0.1568 0.8647 0.000 0.036 0.000 0.020 0.944
#> GSM182760 3 0.1952 0.8819 0.000 0.084 0.912 0.004 0.000
#> GSM182761 5 0.4998 0.7238 0.000 0.044 0.160 0.052 0.744
#> GSM182762 2 0.3827 0.5256 0.000 0.812 0.020 0.024 0.144
#> GSM182763 5 0.2420 0.8633 0.000 0.036 0.036 0.016 0.912
#> GSM182764 5 0.1798 0.8627 0.000 0.064 0.004 0.004 0.928
#> GSM182765 5 0.5287 0.6120 0.000 0.260 0.004 0.080 0.656
#> GSM182766 5 0.1518 0.8663 0.000 0.004 0.004 0.048 0.944
#> GSM182767 3 0.1074 0.8884 0.000 0.012 0.968 0.016 0.004
#> GSM182768 3 0.0963 0.8912 0.000 0.000 0.964 0.036 0.000
#> GSM182769 3 0.2313 0.8907 0.012 0.032 0.916 0.040 0.000
#> GSM182770 5 0.0854 0.8706 0.000 0.008 0.004 0.012 0.976
#> GSM182771 5 0.4351 0.7605 0.000 0.100 0.000 0.132 0.768
#> GSM182772 5 0.0794 0.8685 0.000 0.000 0.000 0.028 0.972
#> GSM182773 3 0.0404 0.8924 0.000 0.000 0.988 0.012 0.000
#> GSM182774 4 0.5222 0.4453 0.020 0.244 0.012 0.692 0.032
#> GSM182775 3 0.3059 0.8679 0.004 0.108 0.860 0.028 0.000
#> GSM182776 3 0.4524 0.6131 0.020 0.336 0.644 0.000 0.000
#> GSM182777 3 0.3477 0.8426 0.024 0.140 0.828 0.008 0.000
#> GSM182802 5 0.3019 0.8211 0.088 0.000 0.000 0.048 0.864
#> GSM182803 1 0.1124 0.8209 0.960 0.036 0.000 0.004 0.000
#> GSM182804 4 0.3074 0.7260 0.196 0.000 0.000 0.804 0.000
#> GSM182805 5 0.4063 0.7775 0.112 0.020 0.000 0.056 0.812
#> GSM182806 1 0.4262 0.2608 0.560 0.440 0.000 0.000 0.000
#> GSM182807 1 0.3752 0.6052 0.708 0.292 0.000 0.000 0.000
#> GSM182808 1 0.3006 0.7589 0.836 0.156 0.004 0.004 0.000
#> GSM182809 1 0.2574 0.7360 0.876 0.012 0.000 0.112 0.000
#> GSM182810 1 0.1357 0.8126 0.948 0.004 0.000 0.048 0.000
#> GSM182811 1 0.0963 0.8158 0.964 0.000 0.000 0.036 0.000
#> GSM182812 4 0.3707 0.7087 0.284 0.000 0.000 0.716 0.000
#> GSM182813 2 0.4182 0.0917 0.400 0.600 0.000 0.000 0.000
#> GSM182778 5 0.1883 0.8602 0.000 0.012 0.008 0.048 0.932
#> GSM182779 5 0.1630 0.8711 0.000 0.036 0.004 0.016 0.944
#> GSM182780 3 0.1731 0.8912 0.000 0.012 0.940 0.040 0.008
#> GSM182781 3 0.5184 0.3479 0.000 0.456 0.508 0.032 0.004
#> GSM182782 5 0.1285 0.8664 0.000 0.004 0.004 0.036 0.956
#> GSM182783 3 0.1300 0.8936 0.000 0.016 0.956 0.028 0.000
#> GSM182784 3 0.1393 0.8830 0.000 0.012 0.956 0.024 0.008
#> GSM182785 3 0.3592 0.8401 0.000 0.124 0.832 0.016 0.028
#> GSM182786 5 0.1770 0.8615 0.000 0.008 0.008 0.048 0.936
#> GSM182787 5 0.4565 0.7757 0.012 0.020 0.116 0.060 0.792
#> GSM182788 5 0.1644 0.8628 0.000 0.004 0.008 0.048 0.940
#> GSM182789 3 0.2228 0.8621 0.000 0.016 0.920 0.044 0.020
#> GSM182790 3 0.2006 0.8846 0.000 0.072 0.916 0.012 0.000
#> GSM182791 3 0.1608 0.8858 0.000 0.000 0.928 0.072 0.000
#> GSM182792 3 0.2535 0.8838 0.000 0.032 0.892 0.076 0.000
#> GSM182793 4 0.2112 0.6289 0.004 0.000 0.004 0.908 0.084
#> GSM182794 3 0.0798 0.8944 0.000 0.016 0.976 0.008 0.000
#> GSM182795 3 0.1130 0.8881 0.004 0.012 0.968 0.012 0.004
#> GSM182796 5 0.0671 0.8687 0.000 0.004 0.000 0.016 0.980
#> GSM182797 2 0.1892 0.6752 0.080 0.916 0.004 0.000 0.000
#> GSM182798 5 0.3420 0.8187 0.000 0.084 0.000 0.076 0.840
#> GSM182799 3 0.2069 0.8794 0.000 0.012 0.912 0.076 0.000
#> GSM182800 4 0.3278 0.6589 0.056 0.024 0.052 0.868 0.000
#> GSM182801 3 0.5582 0.6852 0.152 0.052 0.708 0.088 0.000
#> GSM182814 1 0.1894 0.7956 0.920 0.008 0.000 0.072 0.000
#> GSM182815 4 0.4114 0.6129 0.376 0.000 0.000 0.624 0.000
#> GSM182816 1 0.1282 0.8145 0.952 0.004 0.000 0.044 0.000
#> GSM182817 5 0.4996 0.5506 0.280 0.004 0.000 0.052 0.664
#> GSM182818 1 0.1211 0.8142 0.960 0.016 0.000 0.024 0.000
#> GSM182819 1 0.1965 0.8050 0.904 0.096 0.000 0.000 0.000
#> GSM182820 1 0.3243 0.7271 0.812 0.180 0.004 0.004 0.000
#> GSM182821 1 0.6382 0.4789 0.668 0.024 0.072 0.064 0.172
#> GSM182822 1 0.1197 0.8120 0.952 0.000 0.000 0.048 0.000
#> GSM182823 1 0.3934 0.6719 0.740 0.244 0.000 0.016 0.000
#> GSM182824 1 0.0703 0.8189 0.976 0.000 0.000 0.024 0.000
#> GSM182825 4 0.4138 0.5908 0.384 0.000 0.000 0.616 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM182755 5 0.1471 0.6471 0.000 0.000 0.004 0.000 0.932 0.064
#> GSM182756 6 0.5014 0.4113 0.000 0.008 0.368 0.000 0.060 0.564
#> GSM182757 6 0.5989 0.3601 0.000 0.288 0.088 0.000 0.064 0.560
#> GSM182758 3 0.3634 0.3971 0.000 0.000 0.696 0.000 0.008 0.296
#> GSM182759 2 0.0993 0.8153 0.000 0.964 0.000 0.000 0.024 0.012
#> GSM182760 3 0.3979 0.4360 0.000 0.000 0.708 0.000 0.036 0.256
#> GSM182761 6 0.5618 0.2991 0.000 0.312 0.100 0.008 0.012 0.568
#> GSM182762 5 0.4173 0.5243 0.000 0.056 0.016 0.000 0.752 0.176
#> GSM182763 2 0.4459 0.7439 0.000 0.772 0.068 0.008 0.044 0.108
#> GSM182764 2 0.2750 0.8045 0.000 0.868 0.000 0.004 0.080 0.048
#> GSM182765 2 0.6551 0.4711 0.000 0.544 0.020 0.048 0.252 0.136
#> GSM182766 2 0.4041 0.6697 0.000 0.736 0.040 0.008 0.000 0.216
#> GSM182767 3 0.2191 0.6056 0.004 0.000 0.876 0.000 0.000 0.120
#> GSM182768 3 0.1633 0.6266 0.000 0.000 0.932 0.024 0.000 0.044
#> GSM182769 3 0.3819 0.5747 0.032 0.000 0.788 0.000 0.028 0.152
#> GSM182770 2 0.1333 0.8171 0.000 0.944 0.000 0.008 0.000 0.048
#> GSM182771 2 0.3441 0.7783 0.000 0.832 0.000 0.076 0.072 0.020
#> GSM182772 2 0.1218 0.8197 0.000 0.956 0.000 0.012 0.004 0.028
#> GSM182773 3 0.1663 0.6185 0.000 0.000 0.912 0.000 0.000 0.088
#> GSM182774 4 0.6591 0.2392 0.008 0.004 0.028 0.460 0.164 0.336
#> GSM182775 3 0.3324 0.6018 0.000 0.000 0.824 0.004 0.060 0.112
#> GSM182776 6 0.7366 0.2387 0.068 0.000 0.280 0.012 0.296 0.344
#> GSM182777 3 0.4449 0.5527 0.040 0.000 0.760 0.000 0.108 0.092
#> GSM182802 2 0.2885 0.7834 0.044 0.868 0.000 0.076 0.004 0.008
#> GSM182803 1 0.1500 0.7802 0.936 0.000 0.000 0.000 0.052 0.012
#> GSM182804 4 0.1663 0.6564 0.088 0.000 0.000 0.912 0.000 0.000
#> GSM182805 2 0.4142 0.6964 0.168 0.752 0.000 0.008 0.000 0.072
#> GSM182806 1 0.4602 0.0471 0.492 0.000 0.000 0.004 0.476 0.028
#> GSM182807 1 0.3349 0.6616 0.748 0.000 0.000 0.000 0.244 0.008
#> GSM182808 1 0.2944 0.7342 0.832 0.000 0.008 0.000 0.148 0.012
#> GSM182809 1 0.2311 0.7490 0.880 0.000 0.000 0.104 0.000 0.016
#> GSM182810 1 0.3229 0.7169 0.828 0.000 0.000 0.120 0.004 0.048
#> GSM182811 1 0.2451 0.7634 0.888 0.000 0.000 0.068 0.004 0.040
#> GSM182812 4 0.3876 0.6334 0.156 0.000 0.000 0.772 0.004 0.068
#> GSM182813 5 0.3993 0.0364 0.400 0.000 0.000 0.000 0.592 0.008
#> GSM182778 2 0.2257 0.7951 0.000 0.876 0.000 0.008 0.000 0.116
#> GSM182779 2 0.3820 0.7100 0.000 0.756 0.008 0.000 0.032 0.204
#> GSM182780 6 0.4456 0.2959 0.000 0.004 0.456 0.020 0.000 0.520
#> GSM182781 6 0.5434 0.4658 0.000 0.000 0.268 0.004 0.148 0.580
#> GSM182782 2 0.1049 0.8182 0.000 0.960 0.000 0.008 0.000 0.032
#> GSM182783 6 0.3997 0.2145 0.000 0.000 0.488 0.004 0.000 0.508
#> GSM182784 3 0.3945 0.2082 0.000 0.000 0.612 0.008 0.000 0.380
#> GSM182785 6 0.5314 0.4388 0.000 0.024 0.348 0.004 0.052 0.572
#> GSM182786 2 0.1196 0.8162 0.000 0.952 0.000 0.008 0.000 0.040
#> GSM182787 2 0.5014 0.4181 0.000 0.564 0.060 0.008 0.000 0.368
#> GSM182788 2 0.0858 0.8171 0.000 0.968 0.000 0.004 0.000 0.028
#> GSM182789 3 0.4325 -0.1386 0.000 0.008 0.504 0.008 0.000 0.480
#> GSM182790 3 0.4246 0.1316 0.000 0.000 0.580 0.000 0.020 0.400
#> GSM182791 3 0.5034 0.4696 0.000 0.000 0.672 0.172 0.012 0.144
#> GSM182792 3 0.3566 0.6061 0.000 0.000 0.812 0.076 0.008 0.104
#> GSM182793 4 0.3337 0.5927 0.000 0.060 0.020 0.852 0.012 0.056
#> GSM182794 3 0.3073 0.5907 0.000 0.000 0.816 0.004 0.016 0.164
#> GSM182795 3 0.3791 0.3951 0.004 0.008 0.688 0.000 0.000 0.300
#> GSM182796 2 0.0520 0.8152 0.000 0.984 0.000 0.000 0.008 0.008
#> GSM182797 5 0.1973 0.6480 0.064 0.000 0.012 0.004 0.916 0.004
#> GSM182798 2 0.4901 0.6563 0.000 0.712 0.000 0.168 0.068 0.052
#> GSM182799 3 0.4026 0.5257 0.000 0.000 0.752 0.160 0.000 0.088
#> GSM182800 4 0.3310 0.5909 0.000 0.000 0.048 0.848 0.052 0.052
#> GSM182801 3 0.5784 0.4917 0.080 0.000 0.688 0.120 0.052 0.060
#> GSM182814 1 0.3142 0.7329 0.840 0.000 0.000 0.108 0.008 0.044
#> GSM182815 4 0.4750 0.4647 0.340 0.000 0.000 0.596 0.000 0.064
#> GSM182816 1 0.2170 0.7820 0.908 0.000 0.000 0.060 0.016 0.016
#> GSM182817 2 0.5656 0.3892 0.324 0.556 0.000 0.008 0.012 0.100
#> GSM182818 1 0.1901 0.7785 0.924 0.000 0.008 0.028 0.000 0.040
#> GSM182819 1 0.2540 0.7670 0.872 0.000 0.000 0.004 0.104 0.020
#> GSM182820 1 0.3293 0.7220 0.824 0.000 0.008 0.000 0.128 0.040
#> GSM182821 1 0.6628 0.3788 0.592 0.164 0.100 0.012 0.008 0.124
#> GSM182822 1 0.0837 0.7863 0.972 0.000 0.000 0.004 0.004 0.020
#> GSM182823 1 0.4192 0.3498 0.572 0.000 0.000 0.016 0.412 0.000
#> GSM182824 1 0.1633 0.7881 0.932 0.000 0.000 0.044 0.024 0.000
#> GSM182825 4 0.4022 0.3914 0.360 0.000 0.000 0.628 0.004 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 stress(p) development.stage(p) k
#> MAD:NMF 70 1.000 1.86e-05 2
#> MAD:NMF 61 0.234 6.34e-10 3
#> MAD:NMF 67 0.600 4.45e-09 4
#> MAD:NMF 66 0.766 9.43e-10 5
#> MAD:NMF 45 0.891 1.04e-06 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "hclust"]
# you can also extract it by
# res = res_list["ATC:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 18172 rows and 71 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.358 0.718 0.834 0.4293 0.505 0.505
#> 3 3 0.524 0.774 0.878 0.3753 0.784 0.610
#> 4 4 0.558 0.611 0.789 0.1648 0.885 0.730
#> 5 5 0.611 0.499 0.739 0.0959 0.856 0.606
#> 6 6 0.725 0.631 0.801 0.0710 0.906 0.630
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
#> GSM182755 1 0.0000 0.8737 1.000 0.000
#> GSM182756 2 0.9998 0.3998 0.492 0.508
#> GSM182757 2 0.7883 0.8024 0.236 0.764
#> GSM182758 2 0.8763 0.7601 0.296 0.704
#> GSM182759 2 0.7139 0.8024 0.196 0.804
#> GSM182760 2 0.9988 0.4368 0.480 0.520
#> GSM182761 2 0.6887 0.7994 0.184 0.816
#> GSM182762 1 0.9970 -0.2950 0.532 0.468
#> GSM182763 2 0.7056 0.8017 0.192 0.808
#> GSM182764 2 0.7883 0.8024 0.236 0.764
#> GSM182765 2 0.8016 0.7999 0.244 0.756
#> GSM182766 2 0.0000 0.7109 0.000 1.000
#> GSM182767 2 0.9993 0.4253 0.484 0.516
#> GSM182768 2 0.9754 0.6051 0.408 0.592
#> GSM182769 1 0.0672 0.8716 0.992 0.008
#> GSM182770 2 0.0000 0.7109 0.000 1.000
#> GSM182771 2 0.7883 0.8024 0.236 0.764
#> GSM182772 2 0.0000 0.7109 0.000 1.000
#> GSM182773 1 0.1184 0.8682 0.984 0.016
#> GSM182774 1 0.3431 0.8336 0.936 0.064
#> GSM182775 1 0.0672 0.8716 0.992 0.008
#> GSM182776 1 0.3114 0.8409 0.944 0.056
#> GSM182777 1 0.6438 0.6992 0.836 0.164
#> GSM182802 2 0.0000 0.7109 0.000 1.000
#> GSM182803 1 0.0000 0.8737 1.000 0.000
#> GSM182804 2 0.8144 0.7964 0.252 0.748
#> GSM182805 2 0.0000 0.7109 0.000 1.000
#> GSM182806 1 0.0000 0.8737 1.000 0.000
#> GSM182807 1 0.0000 0.8737 1.000 0.000
#> GSM182808 1 0.0000 0.8737 1.000 0.000
#> GSM182809 2 0.8443 0.7829 0.272 0.728
#> GSM182810 1 0.2603 0.8500 0.956 0.044
#> GSM182811 1 0.7674 0.6027 0.776 0.224
#> GSM182812 1 0.0938 0.8688 0.988 0.012
#> GSM182813 1 0.0000 0.8737 1.000 0.000
#> GSM182778 2 0.0000 0.7109 0.000 1.000
#> GSM182779 2 0.7139 0.8024 0.196 0.804
#> GSM182780 2 0.7056 0.8017 0.192 0.808
#> GSM182781 1 0.9661 0.0498 0.608 0.392
#> GSM182782 2 0.0000 0.7109 0.000 1.000
#> GSM182783 2 0.2948 0.7368 0.052 0.948
#> GSM182784 2 0.9988 0.4368 0.480 0.520
#> GSM182785 2 0.8016 0.8005 0.244 0.756
#> GSM182786 2 0.0000 0.7109 0.000 1.000
#> GSM182787 2 0.6887 0.7994 0.184 0.816
#> GSM182788 2 0.0000 0.7109 0.000 1.000
#> GSM182789 2 0.8016 0.8005 0.244 0.756
#> GSM182790 1 0.9686 0.0336 0.604 0.396
#> GSM182791 2 0.9754 0.6051 0.408 0.592
#> GSM182792 2 0.9754 0.6051 0.408 0.592
#> GSM182793 2 0.0000 0.7109 0.000 1.000
#> GSM182794 1 0.9686 0.0336 0.604 0.396
#> GSM182795 2 0.8813 0.7559 0.300 0.700
#> GSM182796 2 0.7219 0.8028 0.200 0.800
#> GSM182797 1 0.0000 0.8737 1.000 0.000
#> GSM182798 2 0.7883 0.8024 0.236 0.764
#> GSM182799 2 0.8144 0.7964 0.252 0.748
#> GSM182800 1 0.3114 0.8409 0.944 0.056
#> GSM182801 1 0.0000 0.8737 1.000 0.000
#> GSM182814 1 0.0000 0.8737 1.000 0.000
#> GSM182815 2 0.8144 0.7964 0.252 0.748
#> GSM182816 1 0.0000 0.8737 1.000 0.000
#> GSM182817 2 0.9732 0.6117 0.404 0.596
#> GSM182818 2 0.8327 0.7885 0.264 0.736
#> GSM182819 1 0.0000 0.8737 1.000 0.000
#> GSM182820 1 0.0000 0.8737 1.000 0.000
#> GSM182821 2 0.9754 0.6051 0.408 0.592
#> GSM182822 1 0.7674 0.6027 0.776 0.224
#> GSM182823 1 0.0000 0.8737 1.000 0.000
#> GSM182824 1 0.0000 0.8737 1.000 0.000
#> GSM182825 1 0.0000 0.8737 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM182755 1 0.0000 0.821 1.000 0.000 0.000
#> GSM182756 3 0.4750 0.702 0.216 0.000 0.784
#> GSM182757 3 0.1529 0.846 0.000 0.040 0.960
#> GSM182758 3 0.1585 0.846 0.028 0.008 0.964
#> GSM182759 3 0.2537 0.827 0.000 0.080 0.920
#> GSM182760 3 0.4605 0.718 0.204 0.000 0.796
#> GSM182761 3 0.2796 0.818 0.000 0.092 0.908
#> GSM182762 3 0.5254 0.624 0.264 0.000 0.736
#> GSM182763 3 0.2625 0.824 0.000 0.084 0.916
#> GSM182764 3 0.1529 0.846 0.000 0.040 0.960
#> GSM182765 3 0.1289 0.848 0.000 0.032 0.968
#> GSM182766 2 0.4235 0.847 0.000 0.824 0.176
#> GSM182767 3 0.4654 0.713 0.208 0.000 0.792
#> GSM182768 3 0.3551 0.789 0.132 0.000 0.868
#> GSM182769 1 0.4654 0.769 0.792 0.000 0.208
#> GSM182770 2 0.0000 0.927 0.000 1.000 0.000
#> GSM182771 3 0.1529 0.846 0.000 0.040 0.960
#> GSM182772 2 0.0000 0.927 0.000 1.000 0.000
#> GSM182773 1 0.5178 0.733 0.744 0.000 0.256
#> GSM182774 1 0.5529 0.677 0.704 0.000 0.296
#> GSM182775 1 0.4452 0.778 0.808 0.000 0.192
#> GSM182776 1 0.5178 0.727 0.744 0.000 0.256
#> GSM182777 1 0.6079 0.479 0.612 0.000 0.388
#> GSM182802 2 0.4399 0.836 0.000 0.812 0.188
#> GSM182803 1 0.0000 0.821 1.000 0.000 0.000
#> GSM182804 3 0.1031 0.850 0.000 0.024 0.976
#> GSM182805 2 0.4399 0.836 0.000 0.812 0.188
#> GSM182806 1 0.0000 0.821 1.000 0.000 0.000
#> GSM182807 1 0.0000 0.821 1.000 0.000 0.000
#> GSM182808 1 0.0000 0.821 1.000 0.000 0.000
#> GSM182809 3 0.1337 0.851 0.012 0.016 0.972
#> GSM182810 1 0.5098 0.737 0.752 0.000 0.248
#> GSM182811 1 0.6286 0.297 0.536 0.000 0.464
#> GSM182812 1 0.4974 0.753 0.764 0.000 0.236
#> GSM182813 1 0.0000 0.821 1.000 0.000 0.000
#> GSM182778 2 0.0000 0.927 0.000 1.000 0.000
#> GSM182779 3 0.2537 0.827 0.000 0.080 0.920
#> GSM182780 3 0.2625 0.824 0.000 0.084 0.916
#> GSM182781 3 0.5926 0.417 0.356 0.000 0.644
#> GSM182782 2 0.0000 0.927 0.000 1.000 0.000
#> GSM182783 3 0.5810 0.430 0.000 0.336 0.664
#> GSM182784 3 0.4605 0.718 0.204 0.000 0.796
#> GSM182785 3 0.1289 0.849 0.000 0.032 0.968
#> GSM182786 2 0.0000 0.927 0.000 1.000 0.000
#> GSM182787 3 0.2796 0.818 0.000 0.092 0.908
#> GSM182788 2 0.0000 0.927 0.000 1.000 0.000
#> GSM182789 3 0.1289 0.849 0.000 0.032 0.968
#> GSM182790 3 0.5905 0.427 0.352 0.000 0.648
#> GSM182791 3 0.3551 0.789 0.132 0.000 0.868
#> GSM182792 3 0.3551 0.789 0.132 0.000 0.868
#> GSM182793 2 0.2261 0.904 0.000 0.932 0.068
#> GSM182794 3 0.5905 0.427 0.352 0.000 0.648
#> GSM182795 3 0.1399 0.845 0.028 0.004 0.968
#> GSM182796 3 0.2448 0.829 0.000 0.076 0.924
#> GSM182797 1 0.0000 0.821 1.000 0.000 0.000
#> GSM182798 3 0.1529 0.846 0.000 0.040 0.960
#> GSM182799 3 0.1031 0.850 0.000 0.024 0.976
#> GSM182800 1 0.5178 0.727 0.744 0.000 0.256
#> GSM182801 1 0.1643 0.818 0.956 0.000 0.044
#> GSM182814 1 0.0000 0.821 1.000 0.000 0.000
#> GSM182815 3 0.1031 0.850 0.000 0.024 0.976
#> GSM182816 1 0.0000 0.821 1.000 0.000 0.000
#> GSM182817 3 0.3482 0.791 0.128 0.000 0.872
#> GSM182818 3 0.0592 0.850 0.000 0.012 0.988
#> GSM182819 1 0.0000 0.821 1.000 0.000 0.000
#> GSM182820 1 0.0000 0.821 1.000 0.000 0.000
#> GSM182821 3 0.3551 0.789 0.132 0.000 0.868
#> GSM182822 1 0.6286 0.297 0.536 0.000 0.464
#> GSM182823 1 0.0000 0.821 1.000 0.000 0.000
#> GSM182824 1 0.0000 0.821 1.000 0.000 0.000
#> GSM182825 1 0.4796 0.763 0.780 0.000 0.220
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM182755 1 0.0000 0.781 1.000 0.000 0.000 0.000
#> GSM182756 3 0.1297 0.581 0.016 0.000 0.964 0.020
#> GSM182757 3 0.5131 0.554 0.000 0.028 0.692 0.280
#> GSM182758 3 0.4360 0.589 0.000 0.008 0.744 0.248
#> GSM182759 3 0.6277 0.452 0.000 0.068 0.572 0.360
#> GSM182760 3 0.0895 0.586 0.004 0.000 0.976 0.020
#> GSM182761 3 0.6549 0.341 0.000 0.076 0.488 0.436
#> GSM182762 3 0.1716 0.545 0.064 0.000 0.936 0.000
#> GSM182763 3 0.6425 0.377 0.000 0.068 0.508 0.424
#> GSM182764 3 0.5131 0.554 0.000 0.028 0.692 0.280
#> GSM182765 3 0.4936 0.557 0.000 0.020 0.700 0.280
#> GSM182766 2 0.3768 0.778 0.000 0.808 0.008 0.184
#> GSM182767 3 0.1042 0.585 0.008 0.000 0.972 0.020
#> GSM182768 3 0.3208 0.602 0.004 0.000 0.848 0.148
#> GSM182769 1 0.5268 0.610 0.592 0.000 0.396 0.012
#> GSM182770 2 0.0000 0.905 0.000 1.000 0.000 0.000
#> GSM182771 3 0.5131 0.554 0.000 0.028 0.692 0.280
#> GSM182772 2 0.0000 0.905 0.000 1.000 0.000 0.000
#> GSM182773 1 0.4972 0.530 0.544 0.000 0.456 0.000
#> GSM182774 1 0.6319 0.523 0.504 0.000 0.436 0.060
#> GSM182775 1 0.4830 0.617 0.608 0.000 0.392 0.000
#> GSM182776 1 0.6079 0.576 0.544 0.000 0.408 0.048
#> GSM182777 3 0.4888 -0.229 0.412 0.000 0.588 0.000
#> GSM182802 2 0.4121 0.762 0.000 0.796 0.020 0.184
#> GSM182803 1 0.0336 0.780 0.992 0.000 0.008 0.000
#> GSM182804 4 0.2124 0.957 0.000 0.008 0.068 0.924
#> GSM182805 2 0.4121 0.762 0.000 0.796 0.020 0.184
#> GSM182806 1 0.0000 0.781 1.000 0.000 0.000 0.000
#> GSM182807 1 0.0000 0.781 1.000 0.000 0.000 0.000
#> GSM182808 1 0.0000 0.781 1.000 0.000 0.000 0.000
#> GSM182809 3 0.5321 0.369 0.004 0.004 0.528 0.464
#> GSM182810 1 0.6477 0.607 0.552 0.000 0.368 0.080
#> GSM182811 3 0.7143 -0.217 0.380 0.000 0.484 0.136
#> GSM182812 1 0.6992 0.631 0.564 0.000 0.280 0.156
#> GSM182813 1 0.0000 0.781 1.000 0.000 0.000 0.000
#> GSM182778 2 0.0000 0.905 0.000 1.000 0.000 0.000
#> GSM182779 3 0.5901 0.523 0.000 0.068 0.652 0.280
#> GSM182780 3 0.6425 0.377 0.000 0.068 0.508 0.424
#> GSM182781 3 0.3123 0.466 0.156 0.000 0.844 0.000
#> GSM182782 2 0.0000 0.905 0.000 1.000 0.000 0.000
#> GSM182783 3 0.7900 -0.110 0.000 0.320 0.372 0.308
#> GSM182784 3 0.1004 0.586 0.004 0.000 0.972 0.024
#> GSM182785 3 0.5543 0.509 0.000 0.028 0.612 0.360
#> GSM182786 2 0.0000 0.905 0.000 1.000 0.000 0.000
#> GSM182787 3 0.6549 0.341 0.000 0.076 0.488 0.436
#> GSM182788 2 0.0000 0.905 0.000 1.000 0.000 0.000
#> GSM182789 3 0.5543 0.509 0.000 0.028 0.612 0.360
#> GSM182790 3 0.3074 0.470 0.152 0.000 0.848 0.000
#> GSM182791 3 0.3052 0.604 0.004 0.000 0.860 0.136
#> GSM182792 3 0.3052 0.604 0.004 0.000 0.860 0.136
#> GSM182793 2 0.1978 0.877 0.000 0.928 0.004 0.068
#> GSM182794 3 0.3074 0.470 0.152 0.000 0.848 0.000
#> GSM182795 3 0.4053 0.595 0.000 0.004 0.768 0.228
#> GSM182796 3 0.5835 0.527 0.000 0.064 0.656 0.280
#> GSM182797 1 0.0000 0.781 1.000 0.000 0.000 0.000
#> GSM182798 3 0.5131 0.554 0.000 0.028 0.692 0.280
#> GSM182799 4 0.2124 0.957 0.000 0.008 0.068 0.924
#> GSM182800 1 0.6253 0.584 0.544 0.000 0.396 0.060
#> GSM182801 1 0.3764 0.726 0.784 0.000 0.216 0.000
#> GSM182814 1 0.0000 0.781 1.000 0.000 0.000 0.000
#> GSM182815 4 0.2124 0.957 0.000 0.008 0.068 0.924
#> GSM182816 1 0.0000 0.781 1.000 0.000 0.000 0.000
#> GSM182817 3 0.1867 0.607 0.000 0.000 0.928 0.072
#> GSM182818 4 0.0188 0.877 0.000 0.000 0.004 0.996
#> GSM182819 1 0.0000 0.781 1.000 0.000 0.000 0.000
#> GSM182820 1 0.0000 0.781 1.000 0.000 0.000 0.000
#> GSM182821 3 0.3052 0.604 0.004 0.000 0.860 0.136
#> GSM182822 3 0.7143 -0.217 0.380 0.000 0.484 0.136
#> GSM182823 1 0.0000 0.781 1.000 0.000 0.000 0.000
#> GSM182824 1 0.0000 0.781 1.000 0.000 0.000 0.000
#> GSM182825 1 0.6693 0.646 0.580 0.000 0.304 0.116
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM182755 1 0.0000 0.76530 1.000 0.000 0.000 0.000 0.000
#> GSM182756 3 0.1732 0.44013 0.000 0.000 0.920 0.000 0.080
#> GSM182757 5 0.2732 0.68614 0.000 0.000 0.160 0.000 0.840
#> GSM182758 3 0.3816 -0.00244 0.000 0.000 0.696 0.000 0.304
#> GSM182759 5 0.3452 0.63856 0.000 0.032 0.148 0.000 0.820
#> GSM182760 3 0.1851 0.43704 0.000 0.000 0.912 0.000 0.088
#> GSM182761 5 0.5026 0.43320 0.000 0.040 0.372 0.000 0.588
#> GSM182762 3 0.4444 0.23954 0.012 0.000 0.624 0.000 0.364
#> GSM182763 5 0.4920 0.43724 0.000 0.032 0.384 0.000 0.584
#> GSM182764 5 0.2732 0.68614 0.000 0.000 0.160 0.000 0.840
#> GSM182765 5 0.2813 0.67824 0.000 0.000 0.168 0.000 0.832
#> GSM182766 2 0.3527 0.78529 0.000 0.792 0.000 0.016 0.192
#> GSM182767 3 0.1792 0.43859 0.000 0.000 0.916 0.000 0.084
#> GSM182768 3 0.3362 0.39492 0.000 0.000 0.844 0.080 0.076
#> GSM182769 1 0.5521 0.34634 0.496 0.000 0.452 0.012 0.040
#> GSM182770 2 0.0000 0.90048 0.000 1.000 0.000 0.000 0.000
#> GSM182771 5 0.2732 0.68614 0.000 0.000 0.160 0.000 0.840
#> GSM182772 2 0.0000 0.90048 0.000 1.000 0.000 0.000 0.000
#> GSM182773 3 0.4449 -0.31717 0.484 0.000 0.512 0.000 0.004
#> GSM182774 3 0.6371 -0.29360 0.436 0.000 0.460 0.060 0.044
#> GSM182775 1 0.5165 0.36170 0.512 0.000 0.448 0.000 0.040
#> GSM182776 1 0.6571 0.29061 0.448 0.000 0.432 0.048 0.072
#> GSM182777 3 0.6254 -0.03117 0.340 0.000 0.500 0.000 0.160
#> GSM182802 2 0.3630 0.77201 0.000 0.780 0.000 0.016 0.204
#> GSM182803 1 0.0290 0.76258 0.992 0.000 0.008 0.000 0.000
#> GSM182804 4 0.4317 0.91400 0.000 0.000 0.076 0.764 0.160
#> GSM182805 2 0.3630 0.77201 0.000 0.780 0.000 0.016 0.204
#> GSM182806 1 0.0000 0.76530 1.000 0.000 0.000 0.000 0.000
#> GSM182807 1 0.0000 0.76530 1.000 0.000 0.000 0.000 0.000
#> GSM182808 1 0.0000 0.76530 1.000 0.000 0.000 0.000 0.000
#> GSM182809 3 0.5584 -0.08366 0.000 0.000 0.532 0.392 0.076
#> GSM182810 1 0.6887 0.33852 0.464 0.000 0.388 0.080 0.068
#> GSM182811 3 0.6922 0.09280 0.320 0.000 0.512 0.112 0.056
#> GSM182812 1 0.7055 0.41650 0.488 0.000 0.312 0.160 0.040
#> GSM182813 1 0.0000 0.76530 1.000 0.000 0.000 0.000 0.000
#> GSM182778 2 0.0000 0.90048 0.000 1.000 0.000 0.000 0.000
#> GSM182779 5 0.3276 0.68180 0.000 0.032 0.132 0.000 0.836
#> GSM182780 5 0.4920 0.43724 0.000 0.032 0.384 0.000 0.584
#> GSM182781 3 0.5467 0.33334 0.100 0.000 0.624 0.000 0.276
#> GSM182782 2 0.0000 0.90048 0.000 1.000 0.000 0.000 0.000
#> GSM182783 3 0.7935 -0.22257 0.000 0.296 0.332 0.072 0.300
#> GSM182784 3 0.1908 0.43738 0.000 0.000 0.908 0.000 0.092
#> GSM182785 3 0.4306 -0.37082 0.000 0.000 0.508 0.000 0.492
#> GSM182786 2 0.0000 0.90048 0.000 1.000 0.000 0.000 0.000
#> GSM182787 5 0.5026 0.43320 0.000 0.040 0.372 0.000 0.588
#> GSM182788 2 0.0000 0.90048 0.000 1.000 0.000 0.000 0.000
#> GSM182789 3 0.4306 -0.37082 0.000 0.000 0.508 0.000 0.492
#> GSM182790 3 0.5421 0.33413 0.096 0.000 0.628 0.000 0.276
#> GSM182791 3 0.3090 0.40131 0.000 0.000 0.860 0.052 0.088
#> GSM182792 3 0.3090 0.40131 0.000 0.000 0.860 0.052 0.088
#> GSM182793 2 0.1845 0.87096 0.000 0.928 0.000 0.016 0.056
#> GSM182794 3 0.5421 0.33413 0.096 0.000 0.628 0.000 0.276
#> GSM182795 3 0.3586 0.10646 0.000 0.000 0.736 0.000 0.264
#> GSM182796 5 0.3182 0.68021 0.000 0.032 0.124 0.000 0.844
#> GSM182797 1 0.0000 0.76530 1.000 0.000 0.000 0.000 0.000
#> GSM182798 5 0.2732 0.68614 0.000 0.000 0.160 0.000 0.840
#> GSM182799 4 0.4317 0.91400 0.000 0.000 0.076 0.764 0.160
#> GSM182800 1 0.6725 0.29950 0.448 0.000 0.420 0.060 0.072
#> GSM182801 1 0.4477 0.58897 0.708 0.000 0.252 0.000 0.040
#> GSM182814 1 0.0000 0.76530 1.000 0.000 0.000 0.000 0.000
#> GSM182815 4 0.4317 0.91400 0.000 0.000 0.076 0.764 0.160
#> GSM182816 1 0.0000 0.76530 1.000 0.000 0.000 0.000 0.000
#> GSM182817 5 0.4300 -0.04195 0.000 0.000 0.476 0.000 0.524
#> GSM182818 4 0.0404 0.74708 0.000 0.000 0.000 0.988 0.012
#> GSM182819 1 0.0000 0.76530 1.000 0.000 0.000 0.000 0.000
#> GSM182820 1 0.0000 0.76530 1.000 0.000 0.000 0.000 0.000
#> GSM182821 3 0.3090 0.40131 0.000 0.000 0.860 0.052 0.088
#> GSM182822 3 0.6922 0.09280 0.320 0.000 0.512 0.112 0.056
#> GSM182823 1 0.0000 0.76530 1.000 0.000 0.000 0.000 0.000
#> GSM182824 1 0.0000 0.76530 1.000 0.000 0.000 0.000 0.000
#> GSM182825 1 0.6796 0.41055 0.496 0.000 0.348 0.116 0.040
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM182755 1 0.0000 0.9973 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM182756 3 0.2948 0.5543 0.000 0.000 0.804 0.000 0.188 0.008
#> GSM182757 5 0.0865 0.6373 0.000 0.000 0.036 0.000 0.964 0.000
#> GSM182758 3 0.3774 0.2554 0.000 0.000 0.592 0.000 0.408 0.000
#> GSM182759 5 0.2402 0.5729 0.000 0.000 0.140 0.000 0.856 0.004
#> GSM182760 3 0.2902 0.5578 0.000 0.000 0.800 0.000 0.196 0.004
#> GSM182761 5 0.4763 0.2672 0.000 0.008 0.468 0.024 0.496 0.004
#> GSM182762 3 0.4704 0.2058 0.000 0.000 0.488 0.000 0.468 0.044
#> GSM182763 5 0.4527 0.2725 0.000 0.000 0.456 0.024 0.516 0.004
#> GSM182764 5 0.0865 0.6373 0.000 0.000 0.036 0.000 0.964 0.000
#> GSM182765 5 0.1007 0.6285 0.000 0.000 0.044 0.000 0.956 0.000
#> GSM182766 2 0.4882 0.7396 0.000 0.728 0.060 0.020 0.164 0.028
#> GSM182767 3 0.2871 0.5576 0.000 0.000 0.804 0.000 0.192 0.004
#> GSM182768 3 0.4233 0.5442 0.000 0.000 0.736 0.080 0.180 0.004
#> GSM182769 6 0.2473 0.7396 0.008 0.000 0.136 0.000 0.000 0.856
#> GSM182770 2 0.0000 0.8799 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM182771 5 0.0865 0.6373 0.000 0.000 0.036 0.000 0.964 0.000
#> GSM182772 2 0.0000 0.8799 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM182773 6 0.3841 0.5909 0.004 0.000 0.380 0.000 0.000 0.616
#> GSM182774 6 0.4391 0.6923 0.012 0.000 0.236 0.000 0.048 0.704
#> GSM182775 6 0.3236 0.7248 0.024 0.000 0.180 0.000 0.000 0.796
#> GSM182776 6 0.3053 0.7512 0.016 0.000 0.080 0.000 0.048 0.856
#> GSM182777 6 0.5724 0.5184 0.008 0.000 0.312 0.000 0.152 0.528
#> GSM182802 2 0.5105 0.7324 0.000 0.716 0.060 0.032 0.164 0.028
#> GSM182803 1 0.0363 0.9862 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM182804 4 0.2946 0.9223 0.000 0.000 0.176 0.812 0.012 0.000
#> GSM182805 2 0.5105 0.7324 0.000 0.716 0.060 0.032 0.164 0.028
#> GSM182806 1 0.0000 0.9973 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM182807 1 0.0000 0.9973 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM182808 1 0.0000 0.9973 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM182809 3 0.5889 0.1428 0.000 0.000 0.424 0.400 0.172 0.004
#> GSM182810 6 0.2849 0.7395 0.020 0.000 0.056 0.008 0.036 0.880
#> GSM182811 6 0.6556 0.4652 0.012 0.000 0.264 0.052 0.144 0.528
#> GSM182812 6 0.2146 0.6586 0.024 0.000 0.008 0.060 0.000 0.908
#> GSM182813 1 0.0000 0.9973 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM182778 2 0.0000 0.8799 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM182779 5 0.0603 0.6321 0.000 0.000 0.016 0.000 0.980 0.004
#> GSM182780 5 0.4527 0.2725 0.000 0.000 0.456 0.024 0.516 0.004
#> GSM182781 3 0.5555 0.2511 0.000 0.000 0.480 0.000 0.380 0.140
#> GSM182782 2 0.0000 0.8799 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM182783 3 0.7628 -0.0713 0.000 0.232 0.444 0.120 0.172 0.032
#> GSM182784 3 0.2871 0.5583 0.000 0.000 0.804 0.000 0.192 0.004
#> GSM182785 3 0.4532 -0.1614 0.000 0.000 0.508 0.024 0.464 0.004
#> GSM182786 2 0.0000 0.8799 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM182787 5 0.4763 0.2672 0.000 0.008 0.468 0.024 0.496 0.004
#> GSM182788 2 0.0000 0.8799 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM182789 3 0.4532 -0.1614 0.000 0.000 0.508 0.024 0.464 0.004
#> GSM182790 3 0.5492 0.2629 0.000 0.000 0.492 0.000 0.376 0.132
#> GSM182791 3 0.3946 0.5511 0.000 0.000 0.752 0.052 0.192 0.004
#> GSM182792 3 0.3946 0.5511 0.000 0.000 0.752 0.052 0.192 0.004
#> GSM182793 2 0.2562 0.8390 0.000 0.892 0.060 0.016 0.004 0.028
#> GSM182794 3 0.5492 0.2629 0.000 0.000 0.492 0.000 0.376 0.132
#> GSM182795 3 0.3672 0.3381 0.000 0.000 0.632 0.000 0.368 0.000
#> GSM182796 5 0.0000 0.6317 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM182797 1 0.0000 0.9973 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM182798 5 0.0865 0.6373 0.000 0.000 0.036 0.000 0.964 0.000
#> GSM182799 4 0.2946 0.9223 0.000 0.000 0.176 0.812 0.012 0.000
#> GSM182800 6 0.2889 0.7480 0.016 0.000 0.068 0.000 0.048 0.868
#> GSM182801 6 0.3390 0.4793 0.296 0.000 0.000 0.000 0.000 0.704
#> GSM182814 1 0.0363 0.9873 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM182815 4 0.2946 0.9223 0.000 0.000 0.176 0.812 0.012 0.000
#> GSM182816 1 0.0000 0.9973 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM182817 5 0.3647 -0.0966 0.000 0.000 0.360 0.000 0.640 0.000
#> GSM182818 4 0.1572 0.7582 0.000 0.000 0.028 0.936 0.000 0.036
#> GSM182819 1 0.0000 0.9973 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM182820 1 0.0000 0.9973 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM182821 3 0.3946 0.5511 0.000 0.000 0.752 0.052 0.192 0.004
#> GSM182822 6 0.6556 0.4652 0.012 0.000 0.264 0.052 0.144 0.528
#> GSM182823 1 0.0146 0.9939 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM182824 1 0.0000 0.9973 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM182825 6 0.2198 0.6982 0.032 0.000 0.032 0.024 0.000 0.912
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 stress(p) development.stage(p) k
#> ATC:hclust 63 0.382 0.003193 2
#> ATC:hclust 64 0.835 0.003748 3
#> ATC:hclust 58 0.696 0.000997 4
#> ATC:hclust 36 0.641 0.000728 5
#> ATC:hclust 53 0.447 0.000318 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 18172 rows and 71 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.958 0.982 0.5024 0.498 0.498
#> 3 3 1.000 0.974 0.988 0.2501 0.687 0.470
#> 4 4 0.672 0.727 0.836 0.1544 0.769 0.470
#> 5 5 0.791 0.834 0.901 0.0771 0.932 0.755
#> 6 6 0.769 0.711 0.825 0.0508 0.905 0.606
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
#> GSM182755 1 0.0000 0.986 1.000 0.000
#> GSM182756 1 0.7376 0.734 0.792 0.208
#> GSM182757 2 0.0376 0.977 0.004 0.996
#> GSM182758 2 0.0376 0.977 0.004 0.996
#> GSM182759 2 0.0000 0.977 0.000 1.000
#> GSM182760 1 0.7376 0.734 0.792 0.208
#> GSM182761 2 0.0000 0.977 0.000 1.000
#> GSM182762 1 0.0000 0.986 1.000 0.000
#> GSM182763 2 0.0000 0.977 0.000 1.000
#> GSM182764 2 0.0376 0.977 0.004 0.996
#> GSM182765 2 0.0376 0.977 0.004 0.996
#> GSM182766 2 0.0000 0.977 0.000 1.000
#> GSM182767 2 0.9833 0.265 0.424 0.576
#> GSM182768 2 0.2603 0.939 0.044 0.956
#> GSM182769 1 0.0000 0.986 1.000 0.000
#> GSM182770 2 0.0000 0.977 0.000 1.000
#> GSM182771 2 0.0376 0.977 0.004 0.996
#> GSM182772 2 0.0000 0.977 0.000 1.000
#> GSM182773 1 0.0000 0.986 1.000 0.000
#> GSM182774 1 0.0000 0.986 1.000 0.000
#> GSM182775 1 0.0000 0.986 1.000 0.000
#> GSM182776 1 0.0000 0.986 1.000 0.000
#> GSM182777 1 0.0000 0.986 1.000 0.000
#> GSM182802 2 0.0000 0.977 0.000 1.000
#> GSM182803 1 0.0000 0.986 1.000 0.000
#> GSM182804 2 0.0376 0.977 0.004 0.996
#> GSM182805 2 0.0000 0.977 0.000 1.000
#> GSM182806 1 0.0000 0.986 1.000 0.000
#> GSM182807 1 0.0000 0.986 1.000 0.000
#> GSM182808 1 0.0000 0.986 1.000 0.000
#> GSM182809 2 0.0376 0.977 0.004 0.996
#> GSM182810 1 0.0000 0.986 1.000 0.000
#> GSM182811 1 0.0000 0.986 1.000 0.000
#> GSM182812 1 0.0000 0.986 1.000 0.000
#> GSM182813 1 0.0000 0.986 1.000 0.000
#> GSM182778 2 0.0000 0.977 0.000 1.000
#> GSM182779 2 0.0000 0.977 0.000 1.000
#> GSM182780 2 0.0000 0.977 0.000 1.000
#> GSM182781 1 0.0000 0.986 1.000 0.000
#> GSM182782 2 0.0000 0.977 0.000 1.000
#> GSM182783 2 0.0000 0.977 0.000 1.000
#> GSM182784 2 0.0376 0.977 0.004 0.996
#> GSM182785 2 0.0376 0.977 0.004 0.996
#> GSM182786 2 0.0000 0.977 0.000 1.000
#> GSM182787 2 0.0000 0.977 0.000 1.000
#> GSM182788 2 0.0000 0.977 0.000 1.000
#> GSM182789 2 0.0000 0.977 0.000 1.000
#> GSM182790 1 0.0000 0.986 1.000 0.000
#> GSM182791 2 0.0376 0.977 0.004 0.996
#> GSM182792 2 0.8909 0.554 0.308 0.692
#> GSM182793 2 0.0000 0.977 0.000 1.000
#> GSM182794 1 0.0000 0.986 1.000 0.000
#> GSM182795 2 0.0376 0.977 0.004 0.996
#> GSM182796 2 0.0000 0.977 0.000 1.000
#> GSM182797 1 0.0000 0.986 1.000 0.000
#> GSM182798 2 0.0376 0.977 0.004 0.996
#> GSM182799 2 0.0376 0.977 0.004 0.996
#> GSM182800 1 0.0000 0.986 1.000 0.000
#> GSM182801 1 0.0000 0.986 1.000 0.000
#> GSM182814 1 0.0000 0.986 1.000 0.000
#> GSM182815 2 0.0000 0.977 0.000 1.000
#> GSM182816 1 0.0000 0.986 1.000 0.000
#> GSM182817 2 0.0376 0.977 0.004 0.996
#> GSM182818 2 0.0376 0.977 0.004 0.996
#> GSM182819 1 0.0000 0.986 1.000 0.000
#> GSM182820 1 0.0000 0.986 1.000 0.000
#> GSM182821 2 0.0376 0.977 0.004 0.996
#> GSM182822 1 0.0000 0.986 1.000 0.000
#> GSM182823 1 0.0000 0.986 1.000 0.000
#> GSM182824 1 0.0000 0.986 1.000 0.000
#> GSM182825 1 0.0000 0.986 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM182755 1 0.0000 0.984 1.00 0.000 0.000
#> GSM182756 3 0.0000 0.987 0.00 0.000 1.000
#> GSM182757 3 0.0000 0.987 0.00 0.000 1.000
#> GSM182758 3 0.0000 0.987 0.00 0.000 1.000
#> GSM182759 3 0.3038 0.889 0.00 0.104 0.896
#> GSM182760 3 0.0000 0.987 0.00 0.000 1.000
#> GSM182761 2 0.3340 0.858 0.00 0.880 0.120
#> GSM182762 3 0.0000 0.987 0.00 0.000 1.000
#> GSM182763 3 0.0000 0.987 0.00 0.000 1.000
#> GSM182764 3 0.0000 0.987 0.00 0.000 1.000
#> GSM182765 3 0.0000 0.987 0.00 0.000 1.000
#> GSM182766 2 0.0000 0.985 0.00 1.000 0.000
#> GSM182767 3 0.0000 0.987 0.00 0.000 1.000
#> GSM182768 3 0.0000 0.987 0.00 0.000 1.000
#> GSM182769 1 0.0892 0.974 0.98 0.000 0.020
#> GSM182770 2 0.0000 0.985 0.00 1.000 0.000
#> GSM182771 3 0.0000 0.987 0.00 0.000 1.000
#> GSM182772 2 0.0000 0.985 0.00 1.000 0.000
#> GSM182773 3 0.0000 0.987 0.00 0.000 1.000
#> GSM182774 3 0.0000 0.987 0.00 0.000 1.000
#> GSM182775 1 0.0000 0.984 1.00 0.000 0.000
#> GSM182776 1 0.0892 0.974 0.98 0.000 0.020
#> GSM182777 1 0.0892 0.974 0.98 0.000 0.020
#> GSM182802 2 0.0000 0.985 0.00 1.000 0.000
#> GSM182803 1 0.0000 0.984 1.00 0.000 0.000
#> GSM182804 3 0.0000 0.987 0.00 0.000 1.000
#> GSM182805 2 0.0000 0.985 0.00 1.000 0.000
#> GSM182806 1 0.0000 0.984 1.00 0.000 0.000
#> GSM182807 1 0.0000 0.984 1.00 0.000 0.000
#> GSM182808 1 0.0000 0.984 1.00 0.000 0.000
#> GSM182809 3 0.0000 0.987 0.00 0.000 1.000
#> GSM182810 1 0.0892 0.974 0.98 0.000 0.020
#> GSM182811 3 0.0000 0.987 0.00 0.000 1.000
#> GSM182812 1 0.0892 0.974 0.98 0.000 0.020
#> GSM182813 1 0.0000 0.984 1.00 0.000 0.000
#> GSM182778 2 0.0000 0.985 0.00 1.000 0.000
#> GSM182779 3 0.0000 0.987 0.00 0.000 1.000
#> GSM182780 3 0.1964 0.937 0.00 0.056 0.944
#> GSM182781 1 0.4002 0.791 0.84 0.000 0.160
#> GSM182782 2 0.0000 0.985 0.00 1.000 0.000
#> GSM182783 3 0.4235 0.797 0.00 0.176 0.824
#> GSM182784 3 0.0000 0.987 0.00 0.000 1.000
#> GSM182785 3 0.0000 0.987 0.00 0.000 1.000
#> GSM182786 2 0.0000 0.985 0.00 1.000 0.000
#> GSM182787 2 0.0000 0.985 0.00 1.000 0.000
#> GSM182788 2 0.0000 0.985 0.00 1.000 0.000
#> GSM182789 3 0.0000 0.987 0.00 0.000 1.000
#> GSM182790 3 0.0000 0.987 0.00 0.000 1.000
#> GSM182791 3 0.0000 0.987 0.00 0.000 1.000
#> GSM182792 3 0.0000 0.987 0.00 0.000 1.000
#> GSM182793 2 0.0000 0.985 0.00 1.000 0.000
#> GSM182794 3 0.0000 0.987 0.00 0.000 1.000
#> GSM182795 3 0.0000 0.987 0.00 0.000 1.000
#> GSM182796 3 0.2878 0.897 0.00 0.096 0.904
#> GSM182797 1 0.0000 0.984 1.00 0.000 0.000
#> GSM182798 3 0.0000 0.987 0.00 0.000 1.000
#> GSM182799 3 0.0000 0.987 0.00 0.000 1.000
#> GSM182800 1 0.0892 0.974 0.98 0.000 0.020
#> GSM182801 1 0.0000 0.984 1.00 0.000 0.000
#> GSM182814 1 0.0000 0.984 1.00 0.000 0.000
#> GSM182815 2 0.1289 0.956 0.00 0.968 0.032
#> GSM182816 1 0.0000 0.984 1.00 0.000 0.000
#> GSM182817 3 0.0000 0.987 0.00 0.000 1.000
#> GSM182818 3 0.0000 0.987 0.00 0.000 1.000
#> GSM182819 1 0.0000 0.984 1.00 0.000 0.000
#> GSM182820 1 0.0000 0.984 1.00 0.000 0.000
#> GSM182821 3 0.0000 0.987 0.00 0.000 1.000
#> GSM182822 3 0.0000 0.987 0.00 0.000 1.000
#> GSM182823 1 0.0000 0.984 1.00 0.000 0.000
#> GSM182824 1 0.0000 0.984 1.00 0.000 0.000
#> GSM182825 1 0.0000 0.984 1.00 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM182755 1 0.0000 0.9919 1.000 0.000 0.000 0.000
#> GSM182756 4 0.4916 0.3580 0.000 0.000 0.424 0.576
#> GSM182757 3 0.1867 0.7977 0.000 0.000 0.928 0.072
#> GSM182758 3 0.2216 0.7953 0.000 0.000 0.908 0.092
#> GSM182759 3 0.1174 0.7920 0.000 0.020 0.968 0.012
#> GSM182760 4 0.4933 0.3381 0.000 0.000 0.432 0.568
#> GSM182761 3 0.2737 0.7358 0.000 0.104 0.888 0.008
#> GSM182762 4 0.4877 0.4263 0.000 0.000 0.408 0.592
#> GSM182763 3 0.0336 0.7992 0.000 0.000 0.992 0.008
#> GSM182764 3 0.1867 0.7977 0.000 0.000 0.928 0.072
#> GSM182765 3 0.1867 0.7977 0.000 0.000 0.928 0.072
#> GSM182766 2 0.0336 0.9720 0.000 0.992 0.008 0.000
#> GSM182767 3 0.4948 0.0464 0.000 0.000 0.560 0.440
#> GSM182768 4 0.4761 0.2526 0.000 0.000 0.372 0.628
#> GSM182769 4 0.4973 0.5494 0.348 0.000 0.008 0.644
#> GSM182770 2 0.0000 0.9748 0.000 1.000 0.000 0.000
#> GSM182771 3 0.1637 0.8012 0.000 0.000 0.940 0.060
#> GSM182772 2 0.0000 0.9748 0.000 1.000 0.000 0.000
#> GSM182773 4 0.3688 0.6279 0.000 0.000 0.208 0.792
#> GSM182774 4 0.3688 0.6285 0.000 0.000 0.208 0.792
#> GSM182775 4 0.4990 0.5459 0.352 0.000 0.008 0.640
#> GSM182776 4 0.4973 0.5494 0.348 0.000 0.008 0.644
#> GSM182777 4 0.4957 0.5812 0.320 0.000 0.012 0.668
#> GSM182802 2 0.0469 0.9701 0.000 0.988 0.012 0.000
#> GSM182803 1 0.1792 0.9048 0.932 0.000 0.000 0.068
#> GSM182804 3 0.4948 0.4682 0.000 0.000 0.560 0.440
#> GSM182805 2 0.3300 0.8398 0.000 0.848 0.144 0.008
#> GSM182806 1 0.0000 0.9919 1.000 0.000 0.000 0.000
#> GSM182807 1 0.0000 0.9919 1.000 0.000 0.000 0.000
#> GSM182808 1 0.0000 0.9919 1.000 0.000 0.000 0.000
#> GSM182809 3 0.4948 0.4682 0.000 0.000 0.560 0.440
#> GSM182810 4 0.4222 0.5887 0.272 0.000 0.000 0.728
#> GSM182811 4 0.2011 0.6338 0.000 0.000 0.080 0.920
#> GSM182812 4 0.3400 0.5935 0.180 0.000 0.000 0.820
#> GSM182813 1 0.0000 0.9919 1.000 0.000 0.000 0.000
#> GSM182778 2 0.0000 0.9748 0.000 1.000 0.000 0.000
#> GSM182779 3 0.0592 0.8017 0.000 0.000 0.984 0.016
#> GSM182780 3 0.2142 0.7794 0.000 0.016 0.928 0.056
#> GSM182781 4 0.5719 0.6778 0.152 0.000 0.132 0.716
#> GSM182782 2 0.0000 0.9748 0.000 1.000 0.000 0.000
#> GSM182783 3 0.3280 0.7424 0.000 0.016 0.860 0.124
#> GSM182784 3 0.2216 0.7953 0.000 0.000 0.908 0.092
#> GSM182785 3 0.1716 0.7996 0.000 0.000 0.936 0.064
#> GSM182786 2 0.0000 0.9748 0.000 1.000 0.000 0.000
#> GSM182787 2 0.2198 0.9217 0.000 0.920 0.072 0.008
#> GSM182788 2 0.0000 0.9748 0.000 1.000 0.000 0.000
#> GSM182789 3 0.0592 0.7998 0.000 0.000 0.984 0.016
#> GSM182790 4 0.4134 0.6005 0.000 0.000 0.260 0.740
#> GSM182791 3 0.4040 0.6593 0.000 0.000 0.752 0.248
#> GSM182792 4 0.4955 0.1953 0.000 0.000 0.444 0.556
#> GSM182793 2 0.0000 0.9748 0.000 1.000 0.000 0.000
#> GSM182794 4 0.4679 0.4937 0.000 0.000 0.352 0.648
#> GSM182795 3 0.2081 0.7989 0.000 0.000 0.916 0.084
#> GSM182796 3 0.1042 0.7954 0.000 0.020 0.972 0.008
#> GSM182797 1 0.0000 0.9919 1.000 0.000 0.000 0.000
#> GSM182798 3 0.1389 0.8029 0.000 0.000 0.952 0.048
#> GSM182799 3 0.4948 0.4682 0.000 0.000 0.560 0.440
#> GSM182800 4 0.4722 0.5857 0.300 0.000 0.008 0.692
#> GSM182801 4 0.4955 0.3635 0.444 0.000 0.000 0.556
#> GSM182814 1 0.0000 0.9919 1.000 0.000 0.000 0.000
#> GSM182815 3 0.7792 0.0928 0.000 0.332 0.412 0.256
#> GSM182816 1 0.0188 0.9890 0.996 0.000 0.000 0.004
#> GSM182817 3 0.2647 0.7793 0.000 0.000 0.880 0.120
#> GSM182818 3 0.4994 0.3947 0.000 0.000 0.520 0.480
#> GSM182819 1 0.0188 0.9890 0.996 0.000 0.000 0.004
#> GSM182820 1 0.0000 0.9919 1.000 0.000 0.000 0.000
#> GSM182821 3 0.2647 0.7815 0.000 0.000 0.880 0.120
#> GSM182822 4 0.3024 0.6387 0.000 0.000 0.148 0.852
#> GSM182823 1 0.0000 0.9919 1.000 0.000 0.000 0.000
#> GSM182824 1 0.0000 0.9919 1.000 0.000 0.000 0.000
#> GSM182825 4 0.4790 0.4992 0.380 0.000 0.000 0.620
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM182755 1 0.0703 0.977 0.976 0.000 0.000 0.024 0.000
#> GSM182756 3 0.4850 0.634 0.000 0.000 0.696 0.072 0.232
#> GSM182757 5 0.0671 0.880 0.000 0.000 0.016 0.004 0.980
#> GSM182758 5 0.2850 0.861 0.000 0.000 0.036 0.092 0.872
#> GSM182759 5 0.1732 0.861 0.000 0.000 0.000 0.080 0.920
#> GSM182760 3 0.5167 0.601 0.000 0.000 0.664 0.088 0.248
#> GSM182761 5 0.2513 0.868 0.000 0.000 0.008 0.116 0.876
#> GSM182762 3 0.4084 0.609 0.000 0.000 0.668 0.004 0.328
#> GSM182763 5 0.2358 0.873 0.000 0.000 0.008 0.104 0.888
#> GSM182764 5 0.0671 0.880 0.000 0.000 0.016 0.004 0.980
#> GSM182765 5 0.0865 0.877 0.000 0.000 0.024 0.004 0.972
#> GSM182766 2 0.1251 0.939 0.000 0.956 0.000 0.036 0.008
#> GSM182767 3 0.5584 0.479 0.000 0.000 0.584 0.092 0.324
#> GSM182768 3 0.5413 0.583 0.000 0.000 0.664 0.172 0.164
#> GSM182769 3 0.1300 0.787 0.028 0.000 0.956 0.016 0.000
#> GSM182770 2 0.0000 0.956 0.000 1.000 0.000 0.000 0.000
#> GSM182771 5 0.1018 0.882 0.000 0.000 0.016 0.016 0.968
#> GSM182772 2 0.0000 0.956 0.000 1.000 0.000 0.000 0.000
#> GSM182773 3 0.0404 0.793 0.000 0.000 0.988 0.000 0.012
#> GSM182774 3 0.0613 0.793 0.004 0.000 0.984 0.004 0.008
#> GSM182775 3 0.1364 0.787 0.036 0.000 0.952 0.012 0.000
#> GSM182776 3 0.1300 0.787 0.028 0.000 0.956 0.016 0.000
#> GSM182777 3 0.0798 0.794 0.016 0.000 0.976 0.000 0.008
#> GSM182802 2 0.1408 0.935 0.000 0.948 0.000 0.044 0.008
#> GSM182803 1 0.2300 0.901 0.904 0.000 0.072 0.024 0.000
#> GSM182804 4 0.2260 0.879 0.000 0.000 0.028 0.908 0.064
#> GSM182805 2 0.3362 0.837 0.000 0.844 0.000 0.076 0.080
#> GSM182806 1 0.0162 0.983 0.996 0.000 0.000 0.004 0.000
#> GSM182807 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000
#> GSM182808 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000
#> GSM182809 4 0.2260 0.879 0.000 0.000 0.028 0.908 0.064
#> GSM182810 3 0.1310 0.787 0.024 0.000 0.956 0.020 0.000
#> GSM182811 3 0.2068 0.745 0.004 0.000 0.904 0.092 0.000
#> GSM182812 4 0.4510 0.260 0.008 0.000 0.432 0.560 0.000
#> GSM182813 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000
#> GSM182778 2 0.0000 0.956 0.000 1.000 0.000 0.000 0.000
#> GSM182779 5 0.1704 0.866 0.000 0.000 0.004 0.068 0.928
#> GSM182780 5 0.3093 0.850 0.000 0.000 0.008 0.168 0.824
#> GSM182781 3 0.1173 0.793 0.012 0.000 0.964 0.004 0.020
#> GSM182782 2 0.0000 0.956 0.000 1.000 0.000 0.000 0.000
#> GSM182783 5 0.4341 0.566 0.000 0.000 0.008 0.364 0.628
#> GSM182784 5 0.3003 0.857 0.000 0.000 0.044 0.092 0.864
#> GSM182785 5 0.1469 0.885 0.000 0.000 0.016 0.036 0.948
#> GSM182786 2 0.0000 0.956 0.000 1.000 0.000 0.000 0.000
#> GSM182787 2 0.3242 0.850 0.000 0.852 0.000 0.076 0.072
#> GSM182788 2 0.0000 0.956 0.000 1.000 0.000 0.000 0.000
#> GSM182789 5 0.3013 0.854 0.000 0.000 0.008 0.160 0.832
#> GSM182790 3 0.1478 0.779 0.000 0.000 0.936 0.000 0.064
#> GSM182791 5 0.4123 0.800 0.000 0.000 0.108 0.104 0.788
#> GSM182792 3 0.5141 0.599 0.000 0.000 0.672 0.092 0.236
#> GSM182793 2 0.0162 0.955 0.000 0.996 0.000 0.004 0.000
#> GSM182794 3 0.3274 0.694 0.000 0.000 0.780 0.000 0.220
#> GSM182795 5 0.2761 0.866 0.000 0.000 0.024 0.104 0.872
#> GSM182796 5 0.1831 0.862 0.000 0.000 0.004 0.076 0.920
#> GSM182797 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000
#> GSM182798 5 0.1018 0.882 0.000 0.000 0.016 0.016 0.968
#> GSM182799 4 0.2260 0.879 0.000 0.000 0.028 0.908 0.064
#> GSM182800 3 0.1211 0.789 0.024 0.000 0.960 0.016 0.000
#> GSM182801 3 0.4054 0.604 0.204 0.000 0.760 0.036 0.000
#> GSM182814 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000
#> GSM182815 4 0.1522 0.845 0.000 0.012 0.000 0.944 0.044
#> GSM182816 1 0.0963 0.973 0.964 0.000 0.000 0.036 0.000
#> GSM182817 5 0.2416 0.827 0.000 0.000 0.100 0.012 0.888
#> GSM182818 4 0.1997 0.867 0.000 0.000 0.036 0.924 0.040
#> GSM182819 1 0.0963 0.973 0.964 0.000 0.000 0.036 0.000
#> GSM182820 1 0.0703 0.977 0.976 0.000 0.000 0.024 0.000
#> GSM182821 5 0.3918 0.808 0.000 0.000 0.100 0.096 0.804
#> GSM182822 3 0.0955 0.787 0.004 0.000 0.968 0.028 0.000
#> GSM182823 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000
#> GSM182824 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000
#> GSM182825 3 0.3906 0.569 0.240 0.000 0.744 0.016 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM182755 1 0.1787 0.9223 0.920 0.000 0.068 0.008 0.000 0.004
#> GSM182756 3 0.3766 0.6149 0.000 0.000 0.720 0.000 0.024 0.256
#> GSM182757 5 0.2219 0.7137 0.000 0.000 0.136 0.000 0.864 0.000
#> GSM182758 3 0.3830 0.2193 0.000 0.000 0.620 0.000 0.376 0.004
#> GSM182759 5 0.0603 0.7184 0.000 0.000 0.016 0.004 0.980 0.000
#> GSM182760 3 0.3720 0.6338 0.000 0.000 0.736 0.000 0.028 0.236
#> GSM182761 5 0.2624 0.6993 0.000 0.004 0.148 0.004 0.844 0.000
#> GSM182762 3 0.5446 0.5014 0.000 0.000 0.568 0.000 0.176 0.256
#> GSM182763 5 0.2178 0.7069 0.000 0.000 0.132 0.000 0.868 0.000
#> GSM182764 5 0.2178 0.7158 0.000 0.000 0.132 0.000 0.868 0.000
#> GSM182765 5 0.3244 0.5381 0.000 0.000 0.268 0.000 0.732 0.000
#> GSM182766 2 0.3038 0.8379 0.000 0.856 0.072 0.012 0.060 0.000
#> GSM182767 3 0.3679 0.6517 0.000 0.000 0.760 0.000 0.040 0.200
#> GSM182768 3 0.4028 0.6302 0.000 0.000 0.756 0.048 0.012 0.184
#> GSM182769 6 0.1152 0.8260 0.004 0.000 0.044 0.000 0.000 0.952
#> GSM182770 2 0.0000 0.8792 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM182771 5 0.2300 0.7090 0.000 0.000 0.144 0.000 0.856 0.000
#> GSM182772 2 0.0000 0.8792 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM182773 6 0.3607 0.4846 0.000 0.000 0.348 0.000 0.000 0.652
#> GSM182774 6 0.2994 0.7190 0.000 0.000 0.208 0.000 0.004 0.788
#> GSM182775 6 0.1082 0.8262 0.004 0.000 0.040 0.000 0.000 0.956
#> GSM182776 6 0.1152 0.8260 0.004 0.000 0.044 0.000 0.000 0.952
#> GSM182777 6 0.2902 0.7361 0.004 0.000 0.196 0.000 0.000 0.800
#> GSM182802 2 0.2756 0.8491 0.000 0.876 0.072 0.020 0.032 0.000
#> GSM182803 1 0.4366 0.6948 0.720 0.000 0.068 0.008 0.000 0.204
#> GSM182804 4 0.1686 0.9611 0.000 0.000 0.064 0.924 0.012 0.000
#> GSM182805 2 0.4976 0.6629 0.000 0.656 0.072 0.020 0.252 0.000
#> GSM182806 1 0.0000 0.9483 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM182807 1 0.0000 0.9483 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM182808 1 0.0000 0.9483 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM182809 4 0.1802 0.9603 0.000 0.000 0.072 0.916 0.012 0.000
#> GSM182810 6 0.1674 0.8045 0.004 0.000 0.004 0.068 0.000 0.924
#> GSM182811 6 0.2679 0.7940 0.000 0.000 0.032 0.096 0.004 0.868
#> GSM182812 6 0.4048 0.4711 0.012 0.000 0.012 0.292 0.000 0.684
#> GSM182813 1 0.0000 0.9483 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM182778 2 0.1237 0.8763 0.000 0.956 0.020 0.020 0.000 0.004
#> GSM182779 5 0.0000 0.7216 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM182780 5 0.3559 0.6273 0.000 0.004 0.240 0.012 0.744 0.000
#> GSM182781 6 0.3636 0.5472 0.000 0.000 0.320 0.000 0.004 0.676
#> GSM182782 2 0.1237 0.8763 0.000 0.956 0.020 0.020 0.000 0.004
#> GSM182783 5 0.6289 0.0765 0.000 0.008 0.280 0.320 0.392 0.000
#> GSM182784 3 0.3684 0.3234 0.000 0.000 0.664 0.000 0.332 0.004
#> GSM182785 5 0.3515 0.5813 0.000 0.000 0.324 0.000 0.676 0.000
#> GSM182786 2 0.1237 0.8763 0.000 0.956 0.020 0.020 0.000 0.004
#> GSM182787 2 0.5115 0.6239 0.000 0.624 0.088 0.012 0.276 0.000
#> GSM182788 2 0.1237 0.8763 0.000 0.956 0.020 0.020 0.000 0.004
#> GSM182789 5 0.2969 0.6383 0.000 0.000 0.224 0.000 0.776 0.000
#> GSM182790 3 0.3986 0.0840 0.000 0.000 0.532 0.000 0.004 0.464
#> GSM182791 3 0.4436 0.3047 0.000 0.000 0.636 0.036 0.324 0.004
#> GSM182792 3 0.3678 0.6398 0.000 0.000 0.752 0.004 0.024 0.220
#> GSM182793 2 0.1462 0.8668 0.000 0.936 0.056 0.008 0.000 0.000
#> GSM182794 3 0.4065 0.5490 0.000 0.000 0.672 0.000 0.028 0.300
#> GSM182795 3 0.3804 0.0473 0.000 0.000 0.576 0.000 0.424 0.000
#> GSM182796 5 0.0405 0.7186 0.000 0.000 0.008 0.004 0.988 0.000
#> GSM182797 1 0.0000 0.9483 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM182798 5 0.2219 0.7143 0.000 0.000 0.136 0.000 0.864 0.000
#> GSM182799 4 0.2019 0.9504 0.000 0.000 0.088 0.900 0.012 0.000
#> GSM182800 6 0.0436 0.8236 0.004 0.000 0.004 0.004 0.000 0.988
#> GSM182801 6 0.2277 0.7865 0.032 0.000 0.076 0.000 0.000 0.892
#> GSM182814 1 0.0000 0.9483 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM182815 4 0.2402 0.9171 0.000 0.020 0.084 0.888 0.008 0.000
#> GSM182816 1 0.2622 0.8979 0.868 0.000 0.104 0.024 0.000 0.004
#> GSM182817 5 0.3774 0.1755 0.000 0.000 0.408 0.000 0.592 0.000
#> GSM182818 4 0.1668 0.9411 0.000 0.000 0.060 0.928 0.008 0.004
#> GSM182819 1 0.2622 0.8979 0.868 0.000 0.104 0.024 0.000 0.004
#> GSM182820 1 0.1493 0.9282 0.936 0.000 0.056 0.004 0.000 0.004
#> GSM182821 3 0.3807 0.2427 0.000 0.000 0.628 0.000 0.368 0.004
#> GSM182822 6 0.2011 0.8203 0.000 0.000 0.064 0.020 0.004 0.912
#> GSM182823 1 0.0000 0.9483 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM182824 1 0.0000 0.9483 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM182825 6 0.2442 0.7742 0.048 0.000 0.000 0.068 0.000 0.884
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 stress(p) development.stage(p) k
#> ATC:kmeans 70 0.347 2.21e-02 2
#> ATC:kmeans 71 0.935 3.74e-03 3
#> ATC:kmeans 57 0.411 8.45e-05 4
#> ATC:kmeans 69 0.765 1.29e-05 5
#> ATC:kmeans 61 0.860 9.81e-06 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "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 18172 rows and 71 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 5.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.965 0.986 0.5071 0.493 0.493
#> 3 3 0.723 0.628 0.858 0.2349 0.931 0.861
#> 4 4 0.829 0.751 0.851 0.1335 0.801 0.564
#> 5 5 0.912 0.862 0.919 0.0634 0.944 0.808
#> 6 6 0.808 0.707 0.853 0.0392 0.994 0.977
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
#> attr(,"optional")
#> [1] 2
There is also optional best \(k\) = 2 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM182755 1 0.000 0.978 1.000 0.000
#> GSM182756 1 0.000 0.978 1.000 0.000
#> GSM182757 2 0.000 0.993 0.000 1.000
#> GSM182758 2 0.000 0.993 0.000 1.000
#> GSM182759 2 0.000 0.993 0.000 1.000
#> GSM182760 1 0.000 0.978 1.000 0.000
#> GSM182761 2 0.000 0.993 0.000 1.000
#> GSM182762 1 0.000 0.978 1.000 0.000
#> GSM182763 2 0.000 0.993 0.000 1.000
#> GSM182764 2 0.000 0.993 0.000 1.000
#> GSM182765 2 0.000 0.993 0.000 1.000
#> GSM182766 2 0.000 0.993 0.000 1.000
#> GSM182767 1 0.909 0.527 0.676 0.324
#> GSM182768 1 0.978 0.316 0.588 0.412
#> GSM182769 1 0.000 0.978 1.000 0.000
#> GSM182770 2 0.000 0.993 0.000 1.000
#> GSM182771 2 0.000 0.993 0.000 1.000
#> GSM182772 2 0.000 0.993 0.000 1.000
#> GSM182773 1 0.000 0.978 1.000 0.000
#> GSM182774 1 0.000 0.978 1.000 0.000
#> GSM182775 1 0.000 0.978 1.000 0.000
#> GSM182776 1 0.000 0.978 1.000 0.000
#> GSM182777 1 0.000 0.978 1.000 0.000
#> GSM182802 2 0.000 0.993 0.000 1.000
#> GSM182803 1 0.000 0.978 1.000 0.000
#> GSM182804 2 0.000 0.993 0.000 1.000
#> GSM182805 2 0.000 0.993 0.000 1.000
#> GSM182806 1 0.000 0.978 1.000 0.000
#> GSM182807 1 0.000 0.978 1.000 0.000
#> GSM182808 1 0.000 0.978 1.000 0.000
#> GSM182809 2 0.000 0.993 0.000 1.000
#> GSM182810 1 0.000 0.978 1.000 0.000
#> GSM182811 1 0.000 0.978 1.000 0.000
#> GSM182812 1 0.000 0.978 1.000 0.000
#> GSM182813 1 0.000 0.978 1.000 0.000
#> GSM182778 2 0.000 0.993 0.000 1.000
#> GSM182779 2 0.000 0.993 0.000 1.000
#> GSM182780 2 0.000 0.993 0.000 1.000
#> GSM182781 1 0.000 0.978 1.000 0.000
#> GSM182782 2 0.000 0.993 0.000 1.000
#> GSM182783 2 0.000 0.993 0.000 1.000
#> GSM182784 2 0.000 0.993 0.000 1.000
#> GSM182785 2 0.000 0.993 0.000 1.000
#> GSM182786 2 0.000 0.993 0.000 1.000
#> GSM182787 2 0.000 0.993 0.000 1.000
#> GSM182788 2 0.000 0.993 0.000 1.000
#> GSM182789 2 0.000 0.993 0.000 1.000
#> GSM182790 1 0.000 0.978 1.000 0.000
#> GSM182791 2 0.000 0.993 0.000 1.000
#> GSM182792 1 0.000 0.978 1.000 0.000
#> GSM182793 2 0.000 0.993 0.000 1.000
#> GSM182794 1 0.000 0.978 1.000 0.000
#> GSM182795 2 0.000 0.993 0.000 1.000
#> GSM182796 2 0.000 0.993 0.000 1.000
#> GSM182797 1 0.000 0.978 1.000 0.000
#> GSM182798 2 0.000 0.993 0.000 1.000
#> GSM182799 2 0.000 0.993 0.000 1.000
#> GSM182800 1 0.000 0.978 1.000 0.000
#> GSM182801 1 0.000 0.978 1.000 0.000
#> GSM182814 1 0.000 0.978 1.000 0.000
#> GSM182815 2 0.000 0.993 0.000 1.000
#> GSM182816 1 0.000 0.978 1.000 0.000
#> GSM182817 2 0.814 0.653 0.252 0.748
#> GSM182818 2 0.000 0.993 0.000 1.000
#> GSM182819 1 0.000 0.978 1.000 0.000
#> GSM182820 1 0.000 0.978 1.000 0.000
#> GSM182821 2 0.000 0.993 0.000 1.000
#> GSM182822 1 0.000 0.978 1.000 0.000
#> GSM182823 1 0.000 0.978 1.000 0.000
#> GSM182824 1 0.000 0.978 1.000 0.000
#> GSM182825 1 0.000 0.978 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM182755 1 0.0000 0.8962 1.000 0.000 0.000
#> GSM182756 1 0.5948 0.5235 0.640 0.000 0.360
#> GSM182757 3 0.6308 0.3849 0.000 0.492 0.508
#> GSM182758 2 0.5988 -0.1746 0.000 0.632 0.368
#> GSM182759 2 0.0747 0.7195 0.000 0.984 0.016
#> GSM182760 1 0.5948 0.5235 0.640 0.000 0.360
#> GSM182761 2 0.0424 0.7241 0.000 0.992 0.008
#> GSM182762 1 0.6309 0.2644 0.500 0.000 0.500
#> GSM182763 2 0.0424 0.7241 0.000 0.992 0.008
#> GSM182764 3 0.6308 0.3849 0.000 0.492 0.508
#> GSM182765 3 0.6308 0.3849 0.000 0.492 0.508
#> GSM182766 2 0.0000 0.7281 0.000 1.000 0.000
#> GSM182767 1 0.9191 0.0122 0.432 0.148 0.420
#> GSM182768 3 0.5581 0.3058 0.036 0.176 0.788
#> GSM182769 1 0.0000 0.8962 1.000 0.000 0.000
#> GSM182770 2 0.0000 0.7281 0.000 1.000 0.000
#> GSM182771 2 0.4062 0.5597 0.000 0.836 0.164
#> GSM182772 2 0.0000 0.7281 0.000 1.000 0.000
#> GSM182773 1 0.0424 0.8908 0.992 0.000 0.008
#> GSM182774 1 0.0000 0.8962 1.000 0.000 0.000
#> GSM182775 1 0.0000 0.8962 1.000 0.000 0.000
#> GSM182776 1 0.0000 0.8962 1.000 0.000 0.000
#> GSM182777 1 0.0000 0.8962 1.000 0.000 0.000
#> GSM182802 2 0.0000 0.7281 0.000 1.000 0.000
#> GSM182803 1 0.0000 0.8962 1.000 0.000 0.000
#> GSM182804 2 0.6305 0.1757 0.000 0.516 0.484
#> GSM182805 2 0.0000 0.7281 0.000 1.000 0.000
#> GSM182806 1 0.0000 0.8962 1.000 0.000 0.000
#> GSM182807 1 0.0000 0.8962 1.000 0.000 0.000
#> GSM182808 1 0.0000 0.8962 1.000 0.000 0.000
#> GSM182809 2 0.6305 0.1757 0.000 0.516 0.484
#> GSM182810 1 0.0000 0.8962 1.000 0.000 0.000
#> GSM182811 1 0.4452 0.7105 0.808 0.000 0.192
#> GSM182812 1 0.6225 0.3350 0.568 0.000 0.432
#> GSM182813 1 0.0000 0.8962 1.000 0.000 0.000
#> GSM182778 2 0.0000 0.7281 0.000 1.000 0.000
#> GSM182779 2 0.4062 0.5597 0.000 0.836 0.164
#> GSM182780 2 0.0000 0.7281 0.000 1.000 0.000
#> GSM182781 1 0.0000 0.8962 1.000 0.000 0.000
#> GSM182782 2 0.0000 0.7281 0.000 1.000 0.000
#> GSM182783 2 0.0000 0.7281 0.000 1.000 0.000
#> GSM182784 2 0.5988 -0.1746 0.000 0.632 0.368
#> GSM182785 2 0.5948 -0.1585 0.000 0.640 0.360
#> GSM182786 2 0.0000 0.7281 0.000 1.000 0.000
#> GSM182787 2 0.0000 0.7281 0.000 1.000 0.000
#> GSM182788 2 0.0000 0.7281 0.000 1.000 0.000
#> GSM182789 2 0.0424 0.7241 0.000 0.992 0.008
#> GSM182790 1 0.5621 0.5943 0.692 0.000 0.308
#> GSM182791 2 0.6308 0.1637 0.000 0.508 0.492
#> GSM182792 3 0.5637 0.3187 0.172 0.040 0.788
#> GSM182793 2 0.0000 0.7281 0.000 1.000 0.000
#> GSM182794 1 0.5948 0.5235 0.640 0.000 0.360
#> GSM182795 2 0.0592 0.7221 0.000 0.988 0.012
#> GSM182796 2 0.4062 0.5597 0.000 0.836 0.164
#> GSM182797 1 0.0000 0.8962 1.000 0.000 0.000
#> GSM182798 2 0.4062 0.5597 0.000 0.836 0.164
#> GSM182799 2 0.6308 0.1637 0.000 0.508 0.492
#> GSM182800 1 0.0000 0.8962 1.000 0.000 0.000
#> GSM182801 1 0.0000 0.8962 1.000 0.000 0.000
#> GSM182814 1 0.0000 0.8962 1.000 0.000 0.000
#> GSM182815 2 0.6305 0.1757 0.000 0.516 0.484
#> GSM182816 1 0.0000 0.8962 1.000 0.000 0.000
#> GSM182817 2 0.6527 0.4015 0.068 0.744 0.188
#> GSM182818 2 0.6305 0.1757 0.000 0.516 0.484
#> GSM182819 1 0.0000 0.8962 1.000 0.000 0.000
#> GSM182820 1 0.0000 0.8962 1.000 0.000 0.000
#> GSM182821 2 0.2261 0.6854 0.000 0.932 0.068
#> GSM182822 1 0.0000 0.8962 1.000 0.000 0.000
#> GSM182823 1 0.0000 0.8962 1.000 0.000 0.000
#> GSM182824 1 0.0000 0.8962 1.000 0.000 0.000
#> GSM182825 1 0.0000 0.8962 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM182755 1 0.0000 0.9803 1.000 0.000 0.000 0.000
#> GSM182756 3 0.6929 0.5510 0.108 0.000 0.452 0.440
#> GSM182757 3 0.1940 0.5719 0.000 0.076 0.924 0.000
#> GSM182758 3 0.5731 0.6516 0.000 0.028 0.544 0.428
#> GSM182759 2 0.1389 0.8182 0.000 0.952 0.048 0.000
#> GSM182760 3 0.5576 0.6427 0.020 0.000 0.536 0.444
#> GSM182761 2 0.0592 0.8442 0.000 0.984 0.016 0.000
#> GSM182762 3 0.3166 0.6264 0.016 0.000 0.868 0.116
#> GSM182763 2 0.0707 0.8417 0.000 0.980 0.020 0.000
#> GSM182764 3 0.1940 0.5719 0.000 0.076 0.924 0.000
#> GSM182765 3 0.1716 0.5780 0.000 0.064 0.936 0.000
#> GSM182766 2 0.0000 0.8508 0.000 1.000 0.000 0.000
#> GSM182767 3 0.5297 0.6496 0.004 0.004 0.548 0.444
#> GSM182768 4 0.0188 0.1593 0.000 0.000 0.004 0.996
#> GSM182769 1 0.0000 0.9803 1.000 0.000 0.000 0.000
#> GSM182770 2 0.0000 0.8508 0.000 1.000 0.000 0.000
#> GSM182771 2 0.4967 0.3544 0.000 0.548 0.452 0.000
#> GSM182772 2 0.0000 0.8508 0.000 1.000 0.000 0.000
#> GSM182773 1 0.5108 0.5210 0.672 0.000 0.020 0.308
#> GSM182774 1 0.0000 0.9803 1.000 0.000 0.000 0.000
#> GSM182775 1 0.0000 0.9803 1.000 0.000 0.000 0.000
#> GSM182776 1 0.0000 0.9803 1.000 0.000 0.000 0.000
#> GSM182777 1 0.0000 0.9803 1.000 0.000 0.000 0.000
#> GSM182802 2 0.0000 0.8508 0.000 1.000 0.000 0.000
#> GSM182803 1 0.0000 0.9803 1.000 0.000 0.000 0.000
#> GSM182804 4 0.4948 0.6282 0.000 0.440 0.000 0.560
#> GSM182805 2 0.0000 0.8508 0.000 1.000 0.000 0.000
#> GSM182806 1 0.0000 0.9803 1.000 0.000 0.000 0.000
#> GSM182807 1 0.0000 0.9803 1.000 0.000 0.000 0.000
#> GSM182808 1 0.0000 0.9803 1.000 0.000 0.000 0.000
#> GSM182809 4 0.4948 0.6282 0.000 0.440 0.000 0.560
#> GSM182810 1 0.0000 0.9803 1.000 0.000 0.000 0.000
#> GSM182811 1 0.0000 0.9803 1.000 0.000 0.000 0.000
#> GSM182812 1 0.3024 0.8179 0.852 0.000 0.000 0.148
#> GSM182813 1 0.0000 0.9803 1.000 0.000 0.000 0.000
#> GSM182778 2 0.0000 0.8508 0.000 1.000 0.000 0.000
#> GSM182779 2 0.4967 0.3544 0.000 0.548 0.452 0.000
#> GSM182780 2 0.0000 0.8508 0.000 1.000 0.000 0.000
#> GSM182781 1 0.0469 0.9699 0.988 0.000 0.012 0.000
#> GSM182782 2 0.0000 0.8508 0.000 1.000 0.000 0.000
#> GSM182783 2 0.0000 0.8508 0.000 1.000 0.000 0.000
#> GSM182784 3 0.5366 0.6495 0.000 0.012 0.548 0.440
#> GSM182785 3 0.6140 0.6266 0.000 0.096 0.652 0.252
#> GSM182786 2 0.0000 0.8508 0.000 1.000 0.000 0.000
#> GSM182787 2 0.0000 0.8508 0.000 1.000 0.000 0.000
#> GSM182788 2 0.0000 0.8508 0.000 1.000 0.000 0.000
#> GSM182789 2 0.0657 0.8446 0.000 0.984 0.012 0.004
#> GSM182790 4 0.7700 -0.4853 0.228 0.000 0.344 0.428
#> GSM182791 4 0.4933 0.6278 0.000 0.432 0.000 0.568
#> GSM182792 4 0.0921 0.1281 0.000 0.000 0.028 0.972
#> GSM182793 2 0.0000 0.8508 0.000 1.000 0.000 0.000
#> GSM182794 3 0.5250 0.6512 0.008 0.000 0.552 0.440
#> GSM182795 2 0.0672 0.8439 0.000 0.984 0.008 0.008
#> GSM182796 2 0.4967 0.3544 0.000 0.548 0.452 0.000
#> GSM182797 1 0.0000 0.9803 1.000 0.000 0.000 0.000
#> GSM182798 2 0.4967 0.3544 0.000 0.548 0.452 0.000
#> GSM182799 4 0.4948 0.6282 0.000 0.440 0.000 0.560
#> GSM182800 1 0.0000 0.9803 1.000 0.000 0.000 0.000
#> GSM182801 1 0.0000 0.9803 1.000 0.000 0.000 0.000
#> GSM182814 1 0.0000 0.9803 1.000 0.000 0.000 0.000
#> GSM182815 4 0.4948 0.6282 0.000 0.440 0.000 0.560
#> GSM182816 1 0.0000 0.9803 1.000 0.000 0.000 0.000
#> GSM182817 3 0.5428 0.0198 0.016 0.360 0.620 0.004
#> GSM182818 4 0.4948 0.6282 0.000 0.440 0.000 0.560
#> GSM182819 1 0.0000 0.9803 1.000 0.000 0.000 0.000
#> GSM182820 1 0.0000 0.9803 1.000 0.000 0.000 0.000
#> GSM182821 2 0.4728 0.4877 0.000 0.752 0.216 0.032
#> GSM182822 1 0.0000 0.9803 1.000 0.000 0.000 0.000
#> GSM182823 1 0.0000 0.9803 1.000 0.000 0.000 0.000
#> GSM182824 1 0.0000 0.9803 1.000 0.000 0.000 0.000
#> GSM182825 1 0.0000 0.9803 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM182755 1 0.0794 0.942 0.972 0.000 0.028 0.000 0.000
#> GSM182756 3 0.0609 0.773 0.020 0.000 0.980 0.000 0.000
#> GSM182757 5 0.1124 0.739 0.000 0.004 0.036 0.000 0.960
#> GSM182758 3 0.5727 0.621 0.000 0.044 0.640 0.048 0.268
#> GSM182759 2 0.1082 0.943 0.000 0.964 0.000 0.008 0.028
#> GSM182760 3 0.0992 0.781 0.008 0.000 0.968 0.024 0.000
#> GSM182761 2 0.0290 0.951 0.000 0.992 0.000 0.008 0.000
#> GSM182762 3 0.3861 0.535 0.008 0.000 0.728 0.000 0.264
#> GSM182763 2 0.0162 0.954 0.000 0.996 0.000 0.004 0.000
#> GSM182764 5 0.1124 0.739 0.000 0.004 0.036 0.000 0.960
#> GSM182765 5 0.1124 0.739 0.000 0.004 0.036 0.000 0.960
#> GSM182766 2 0.0609 0.961 0.000 0.980 0.000 0.020 0.000
#> GSM182767 3 0.2654 0.770 0.000 0.000 0.888 0.048 0.064
#> GSM182768 4 0.1732 0.846 0.000 0.000 0.080 0.920 0.000
#> GSM182769 1 0.0609 0.946 0.980 0.000 0.020 0.000 0.000
#> GSM182770 2 0.0609 0.961 0.000 0.980 0.000 0.020 0.000
#> GSM182771 5 0.3305 0.790 0.000 0.224 0.000 0.000 0.776
#> GSM182772 2 0.0609 0.961 0.000 0.980 0.000 0.020 0.000
#> GSM182773 1 0.4310 0.411 0.604 0.000 0.392 0.004 0.000
#> GSM182774 1 0.0290 0.950 0.992 0.000 0.008 0.000 0.000
#> GSM182775 1 0.0794 0.942 0.972 0.000 0.028 0.000 0.000
#> GSM182776 1 0.0000 0.950 1.000 0.000 0.000 0.000 0.000
#> GSM182777 1 0.1851 0.898 0.912 0.000 0.088 0.000 0.000
#> GSM182802 2 0.0609 0.961 0.000 0.980 0.000 0.020 0.000
#> GSM182803 1 0.0162 0.950 0.996 0.000 0.004 0.000 0.000
#> GSM182804 4 0.1544 0.925 0.000 0.068 0.000 0.932 0.000
#> GSM182805 2 0.0609 0.961 0.000 0.980 0.000 0.020 0.000
#> GSM182806 1 0.0162 0.950 0.996 0.000 0.004 0.000 0.000
#> GSM182807 1 0.0162 0.950 0.996 0.000 0.004 0.000 0.000
#> GSM182808 1 0.0162 0.950 0.996 0.000 0.004 0.000 0.000
#> GSM182809 4 0.1544 0.925 0.000 0.068 0.000 0.932 0.000
#> GSM182810 1 0.1710 0.924 0.940 0.000 0.004 0.016 0.040
#> GSM182811 1 0.1808 0.921 0.936 0.000 0.004 0.020 0.040
#> GSM182812 1 0.2728 0.882 0.888 0.000 0.004 0.068 0.040
#> GSM182813 1 0.0162 0.950 0.996 0.000 0.004 0.000 0.000
#> GSM182778 2 0.0609 0.961 0.000 0.980 0.000 0.020 0.000
#> GSM182779 5 0.3876 0.686 0.000 0.316 0.000 0.000 0.684
#> GSM182780 2 0.0162 0.954 0.000 0.996 0.000 0.004 0.000
#> GSM182781 1 0.3857 0.596 0.688 0.000 0.312 0.000 0.000
#> GSM182782 2 0.0609 0.961 0.000 0.980 0.000 0.020 0.000
#> GSM182783 2 0.0451 0.957 0.000 0.988 0.004 0.008 0.000
#> GSM182784 3 0.4641 0.712 0.000 0.020 0.752 0.048 0.180
#> GSM182785 3 0.7615 0.231 0.000 0.308 0.364 0.044 0.284
#> GSM182786 2 0.0609 0.961 0.000 0.980 0.000 0.020 0.000
#> GSM182787 2 0.0000 0.955 0.000 1.000 0.000 0.000 0.000
#> GSM182788 2 0.0609 0.961 0.000 0.980 0.000 0.020 0.000
#> GSM182789 2 0.1471 0.920 0.000 0.952 0.004 0.020 0.024
#> GSM182790 3 0.1638 0.741 0.064 0.000 0.932 0.004 0.000
#> GSM182791 4 0.1502 0.914 0.000 0.056 0.004 0.940 0.000
#> GSM182792 4 0.3519 0.681 0.008 0.000 0.216 0.776 0.000
#> GSM182793 2 0.0609 0.961 0.000 0.980 0.000 0.020 0.000
#> GSM182794 3 0.0324 0.778 0.000 0.000 0.992 0.004 0.004
#> GSM182795 2 0.1799 0.910 0.000 0.940 0.012 0.028 0.020
#> GSM182796 5 0.3336 0.789 0.000 0.228 0.000 0.000 0.772
#> GSM182797 1 0.0162 0.950 0.996 0.000 0.004 0.000 0.000
#> GSM182798 5 0.3336 0.789 0.000 0.228 0.000 0.000 0.772
#> GSM182799 4 0.1410 0.926 0.000 0.060 0.000 0.940 0.000
#> GSM182800 1 0.0451 0.947 0.988 0.000 0.004 0.000 0.008
#> GSM182801 1 0.0000 0.950 1.000 0.000 0.000 0.000 0.000
#> GSM182814 1 0.0162 0.949 0.996 0.000 0.004 0.000 0.000
#> GSM182815 4 0.1608 0.923 0.000 0.072 0.000 0.928 0.000
#> GSM182816 1 0.0703 0.944 0.976 0.000 0.024 0.000 0.000
#> GSM182817 5 0.2304 0.772 0.000 0.068 0.020 0.004 0.908
#> GSM182818 4 0.1270 0.920 0.000 0.052 0.000 0.948 0.000
#> GSM182819 1 0.0794 0.942 0.972 0.000 0.028 0.000 0.000
#> GSM182820 1 0.0162 0.950 0.996 0.000 0.004 0.000 0.000
#> GSM182821 2 0.5790 0.483 0.000 0.652 0.032 0.080 0.236
#> GSM182822 1 0.1728 0.924 0.940 0.000 0.004 0.020 0.036
#> GSM182823 1 0.0162 0.949 0.996 0.000 0.004 0.000 0.000
#> GSM182824 1 0.0000 0.950 1.000 0.000 0.000 0.000 0.000
#> GSM182825 1 0.1710 0.924 0.940 0.000 0.004 0.016 0.040
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM182755 1 0.0937 0.8381 0.960 0.000 0.000 0.000 0.000 0.040
#> GSM182756 3 0.4200 -0.3120 0.012 0.000 0.592 0.000 0.004 0.392
#> GSM182757 5 0.2039 0.7476 0.000 0.000 0.076 0.000 0.904 0.020
#> GSM182758 3 0.3800 0.3935 0.000 0.036 0.764 0.000 0.192 0.008
#> GSM182759 2 0.0146 0.9430 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM182760 3 0.3606 0.0570 0.004 0.000 0.724 0.008 0.000 0.264
#> GSM182761 2 0.0603 0.9369 0.000 0.980 0.016 0.000 0.004 0.000
#> GSM182762 6 0.7081 0.5020 0.096 0.000 0.348 0.000 0.180 0.376
#> GSM182763 2 0.0405 0.9405 0.000 0.988 0.008 0.000 0.004 0.000
#> GSM182764 5 0.1320 0.7736 0.000 0.000 0.036 0.000 0.948 0.016
#> GSM182765 5 0.1257 0.7753 0.000 0.000 0.028 0.000 0.952 0.020
#> GSM182766 2 0.0000 0.9440 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM182767 3 0.2699 0.3014 0.000 0.000 0.856 0.012 0.008 0.124
#> GSM182768 4 0.4023 0.7294 0.000 0.000 0.144 0.756 0.000 0.100
#> GSM182769 1 0.2260 0.8148 0.860 0.000 0.000 0.000 0.000 0.140
#> GSM182770 2 0.0146 0.9434 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM182771 5 0.2362 0.8018 0.000 0.136 0.000 0.000 0.860 0.004
#> GSM182772 2 0.0146 0.9434 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM182773 1 0.5630 -0.0343 0.508 0.000 0.140 0.004 0.000 0.348
#> GSM182774 1 0.0790 0.8465 0.968 0.000 0.000 0.000 0.000 0.032
#> GSM182775 1 0.1204 0.8304 0.944 0.000 0.000 0.000 0.000 0.056
#> GSM182776 1 0.0146 0.8520 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM182777 1 0.2527 0.7221 0.832 0.000 0.000 0.000 0.000 0.168
#> GSM182802 2 0.0291 0.9418 0.000 0.992 0.000 0.004 0.000 0.004
#> GSM182803 1 0.0000 0.8522 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM182804 4 0.0603 0.8719 0.000 0.016 0.000 0.980 0.000 0.004
#> GSM182805 2 0.0291 0.9418 0.000 0.992 0.000 0.004 0.000 0.004
#> GSM182806 1 0.0000 0.8522 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM182807 1 0.0000 0.8522 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM182808 1 0.0000 0.8522 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM182809 4 0.0458 0.8727 0.000 0.016 0.000 0.984 0.000 0.000
#> GSM182810 1 0.3601 0.6718 0.684 0.000 0.000 0.004 0.000 0.312
#> GSM182811 1 0.4118 0.6484 0.660 0.000 0.000 0.028 0.000 0.312
#> GSM182812 1 0.4703 0.5989 0.620 0.000 0.000 0.068 0.000 0.312
#> GSM182813 1 0.0000 0.8522 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM182778 2 0.0000 0.9440 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM182779 5 0.3774 0.5714 0.000 0.328 0.008 0.000 0.664 0.000
#> GSM182780 2 0.0458 0.9385 0.000 0.984 0.016 0.000 0.000 0.000
#> GSM182781 1 0.5296 -0.2800 0.456 0.000 0.100 0.000 0.000 0.444
#> GSM182782 2 0.0000 0.9440 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM182783 2 0.0713 0.9316 0.000 0.972 0.028 0.000 0.000 0.000
#> GSM182784 3 0.2320 0.4051 0.000 0.000 0.864 0.000 0.132 0.004
#> GSM182785 3 0.5885 0.2781 0.000 0.208 0.564 0.000 0.208 0.020
#> GSM182786 2 0.0000 0.9440 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM182787 2 0.0000 0.9440 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM182788 2 0.0000 0.9440 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM182789 2 0.2572 0.8249 0.000 0.852 0.136 0.000 0.012 0.000
#> GSM182790 6 0.5368 0.4840 0.112 0.000 0.400 0.000 0.000 0.488
#> GSM182791 4 0.2271 0.8511 0.000 0.024 0.036 0.908 0.000 0.032
#> GSM182792 4 0.6084 0.2239 0.000 0.000 0.344 0.424 0.004 0.228
#> GSM182793 2 0.0146 0.9434 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM182794 3 0.4822 -0.5601 0.036 0.000 0.480 0.008 0.000 0.476
#> GSM182795 2 0.3804 0.7003 0.000 0.748 0.220 0.000 0.020 0.012
#> GSM182796 5 0.2219 0.8023 0.000 0.136 0.000 0.000 0.864 0.000
#> GSM182797 1 0.0000 0.8522 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM182798 5 0.2320 0.8038 0.000 0.132 0.000 0.000 0.864 0.004
#> GSM182799 4 0.1036 0.8664 0.000 0.004 0.008 0.964 0.000 0.024
#> GSM182800 1 0.2260 0.8040 0.860 0.000 0.000 0.000 0.000 0.140
#> GSM182801 1 0.0146 0.8520 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM182814 1 0.1663 0.8302 0.912 0.000 0.000 0.000 0.000 0.088
#> GSM182815 4 0.0777 0.8690 0.000 0.024 0.000 0.972 0.000 0.004
#> GSM182816 1 0.0937 0.8381 0.960 0.000 0.000 0.000 0.000 0.040
#> GSM182817 5 0.3242 0.7316 0.000 0.012 0.016 0.012 0.836 0.124
#> GSM182818 4 0.0520 0.8710 0.000 0.008 0.000 0.984 0.000 0.008
#> GSM182819 1 0.0937 0.8381 0.960 0.000 0.000 0.000 0.000 0.040
#> GSM182820 1 0.0000 0.8522 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM182821 2 0.7217 0.2401 0.000 0.516 0.216 0.044 0.140 0.084
#> GSM182822 1 0.3575 0.6936 0.708 0.000 0.000 0.008 0.000 0.284
#> GSM182823 1 0.1387 0.8363 0.932 0.000 0.000 0.000 0.000 0.068
#> GSM182824 1 0.1267 0.8390 0.940 0.000 0.000 0.000 0.000 0.060
#> GSM182825 1 0.3584 0.6758 0.688 0.000 0.000 0.004 0.000 0.308
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 stress(p) development.stage(p) k
#> ATC:skmeans 70 0.342 0.052856 2
#> ATC:skmeans 53 0.454 0.011634 3
#> ATC:skmeans 62 0.355 0.000175 4
#> ATC:skmeans 68 0.848 0.000567 5
#> ATC:skmeans 59 0.789 0.002499 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 18172 rows and 71 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.670 0.806 0.917 0.4847 0.493 0.493
#> 3 3 0.952 0.937 0.975 0.2237 0.602 0.387
#> 4 4 0.839 0.810 0.928 0.2043 0.751 0.470
#> 5 5 0.835 0.791 0.914 0.1171 0.864 0.557
#> 6 6 0.850 0.735 0.880 0.0335 0.941 0.723
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
#> GSM182755 1 0.0000 0.901 1.000 0.000
#> GSM182756 1 0.4690 0.880 0.900 0.100
#> GSM182757 2 0.0000 0.898 0.000 1.000
#> GSM182758 2 0.0000 0.898 0.000 1.000
#> GSM182759 2 0.0000 0.898 0.000 1.000
#> GSM182760 1 0.9170 0.538 0.668 0.332
#> GSM182761 2 0.0000 0.898 0.000 1.000
#> GSM182762 1 0.3584 0.906 0.932 0.068
#> GSM182763 2 0.0000 0.898 0.000 1.000
#> GSM182764 2 0.0000 0.898 0.000 1.000
#> GSM182765 2 0.9881 0.211 0.436 0.564
#> GSM182766 2 0.0000 0.898 0.000 1.000
#> GSM182767 1 0.9580 0.423 0.620 0.380
#> GSM182768 1 0.9922 0.210 0.552 0.448
#> GSM182769 1 0.3584 0.906 0.932 0.068
#> GSM182770 2 0.0000 0.898 0.000 1.000
#> GSM182771 2 0.9881 0.211 0.436 0.564
#> GSM182772 2 0.0000 0.898 0.000 1.000
#> GSM182773 1 0.3584 0.906 0.932 0.068
#> GSM182774 1 0.3584 0.906 0.932 0.068
#> GSM182775 1 0.3431 0.906 0.936 0.064
#> GSM182776 1 0.3584 0.906 0.932 0.068
#> GSM182777 1 0.3584 0.906 0.932 0.068
#> GSM182802 2 0.0000 0.898 0.000 1.000
#> GSM182803 1 0.0000 0.901 1.000 0.000
#> GSM182804 2 0.5946 0.764 0.144 0.856
#> GSM182805 2 0.0000 0.898 0.000 1.000
#> GSM182806 1 0.0000 0.901 1.000 0.000
#> GSM182807 1 0.0000 0.901 1.000 0.000
#> GSM182808 1 0.0000 0.901 1.000 0.000
#> GSM182809 2 0.9866 0.223 0.432 0.568
#> GSM182810 1 0.3584 0.906 0.932 0.068
#> GSM182811 1 0.3584 0.906 0.932 0.068
#> GSM182812 1 0.3584 0.906 0.932 0.068
#> GSM182813 1 0.0000 0.901 1.000 0.000
#> GSM182778 2 0.0000 0.898 0.000 1.000
#> GSM182779 2 0.0000 0.898 0.000 1.000
#> GSM182780 2 0.0000 0.898 0.000 1.000
#> GSM182781 1 0.3584 0.906 0.932 0.068
#> GSM182782 2 0.0000 0.898 0.000 1.000
#> GSM182783 2 0.0000 0.898 0.000 1.000
#> GSM182784 2 0.2603 0.865 0.044 0.956
#> GSM182785 2 0.0000 0.898 0.000 1.000
#> GSM182786 2 0.0000 0.898 0.000 1.000
#> GSM182787 2 0.0000 0.898 0.000 1.000
#> GSM182788 2 0.0000 0.898 0.000 1.000
#> GSM182789 2 0.0000 0.898 0.000 1.000
#> GSM182790 1 0.3584 0.906 0.932 0.068
#> GSM182791 2 0.9881 0.211 0.436 0.564
#> GSM182792 1 0.9209 0.530 0.664 0.336
#> GSM182793 2 0.0000 0.898 0.000 1.000
#> GSM182794 1 0.4298 0.891 0.912 0.088
#> GSM182795 2 0.0000 0.898 0.000 1.000
#> GSM182796 2 0.0000 0.898 0.000 1.000
#> GSM182797 1 0.0000 0.901 1.000 0.000
#> GSM182798 2 0.9815 0.256 0.420 0.580
#> GSM182799 2 0.0376 0.895 0.004 0.996
#> GSM182800 1 0.3584 0.906 0.932 0.068
#> GSM182801 1 0.0000 0.901 1.000 0.000
#> GSM182814 1 0.0000 0.901 1.000 0.000
#> GSM182815 2 0.0000 0.898 0.000 1.000
#> GSM182816 1 0.0000 0.901 1.000 0.000
#> GSM182817 1 0.9393 0.484 0.644 0.356
#> GSM182818 2 0.9881 0.211 0.436 0.564
#> GSM182819 1 0.0000 0.901 1.000 0.000
#> GSM182820 1 0.0000 0.901 1.000 0.000
#> GSM182821 2 0.5408 0.789 0.124 0.876
#> GSM182822 1 0.3584 0.906 0.932 0.068
#> GSM182823 1 0.0000 0.901 1.000 0.000
#> GSM182824 1 0.0000 0.901 1.000 0.000
#> GSM182825 1 0.0000 0.901 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM182755 1 0.0000 0.945 1.000 0.000 0.000
#> GSM182756 3 0.0000 0.973 0.000 0.000 1.000
#> GSM182757 3 0.0000 0.973 0.000 0.000 1.000
#> GSM182758 3 0.0000 0.973 0.000 0.000 1.000
#> GSM182759 3 0.0000 0.973 0.000 0.000 1.000
#> GSM182760 3 0.0000 0.973 0.000 0.000 1.000
#> GSM182761 2 0.0747 0.979 0.000 0.984 0.016
#> GSM182762 3 0.0000 0.973 0.000 0.000 1.000
#> GSM182763 3 0.0000 0.973 0.000 0.000 1.000
#> GSM182764 3 0.0000 0.973 0.000 0.000 1.000
#> GSM182765 3 0.0000 0.973 0.000 0.000 1.000
#> GSM182766 2 0.0000 0.998 0.000 1.000 0.000
#> GSM182767 3 0.0000 0.973 0.000 0.000 1.000
#> GSM182768 3 0.0000 0.973 0.000 0.000 1.000
#> GSM182769 1 0.6180 0.301 0.584 0.000 0.416
#> GSM182770 2 0.0000 0.998 0.000 1.000 0.000
#> GSM182771 3 0.0000 0.973 0.000 0.000 1.000
#> GSM182772 2 0.0000 0.998 0.000 1.000 0.000
#> GSM182773 3 0.0000 0.973 0.000 0.000 1.000
#> GSM182774 3 0.0000 0.973 0.000 0.000 1.000
#> GSM182775 1 0.2165 0.888 0.936 0.000 0.064
#> GSM182776 1 0.4235 0.753 0.824 0.000 0.176
#> GSM182777 1 0.2261 0.884 0.932 0.000 0.068
#> GSM182802 2 0.0000 0.998 0.000 1.000 0.000
#> GSM182803 1 0.0000 0.945 1.000 0.000 0.000
#> GSM182804 3 0.0000 0.973 0.000 0.000 1.000
#> GSM182805 2 0.0000 0.998 0.000 1.000 0.000
#> GSM182806 1 0.0000 0.945 1.000 0.000 0.000
#> GSM182807 1 0.0000 0.945 1.000 0.000 0.000
#> GSM182808 1 0.0000 0.945 1.000 0.000 0.000
#> GSM182809 3 0.0000 0.973 0.000 0.000 1.000
#> GSM182810 3 0.5138 0.652 0.252 0.000 0.748
#> GSM182811 3 0.0000 0.973 0.000 0.000 1.000
#> GSM182812 3 0.4062 0.794 0.164 0.000 0.836
#> GSM182813 1 0.0000 0.945 1.000 0.000 0.000
#> GSM182778 2 0.0000 0.998 0.000 1.000 0.000
#> GSM182779 3 0.0000 0.973 0.000 0.000 1.000
#> GSM182780 3 0.0000 0.973 0.000 0.000 1.000
#> GSM182781 3 0.5882 0.437 0.348 0.000 0.652
#> GSM182782 2 0.0000 0.998 0.000 1.000 0.000
#> GSM182783 3 0.0000 0.973 0.000 0.000 1.000
#> GSM182784 3 0.0000 0.973 0.000 0.000 1.000
#> GSM182785 3 0.0000 0.973 0.000 0.000 1.000
#> GSM182786 2 0.0000 0.998 0.000 1.000 0.000
#> GSM182787 2 0.0000 0.998 0.000 1.000 0.000
#> GSM182788 2 0.0000 0.998 0.000 1.000 0.000
#> GSM182789 3 0.0000 0.973 0.000 0.000 1.000
#> GSM182790 3 0.0000 0.973 0.000 0.000 1.000
#> GSM182791 3 0.0000 0.973 0.000 0.000 1.000
#> GSM182792 3 0.0000 0.973 0.000 0.000 1.000
#> GSM182793 2 0.0000 0.998 0.000 1.000 0.000
#> GSM182794 3 0.0000 0.973 0.000 0.000 1.000
#> GSM182795 3 0.0000 0.973 0.000 0.000 1.000
#> GSM182796 3 0.0424 0.966 0.000 0.008 0.992
#> GSM182797 1 0.0000 0.945 1.000 0.000 0.000
#> GSM182798 3 0.0000 0.973 0.000 0.000 1.000
#> GSM182799 3 0.0000 0.973 0.000 0.000 1.000
#> GSM182800 3 0.0592 0.962 0.012 0.000 0.988
#> GSM182801 1 0.0000 0.945 1.000 0.000 0.000
#> GSM182814 1 0.0000 0.945 1.000 0.000 0.000
#> GSM182815 3 0.4842 0.708 0.000 0.224 0.776
#> GSM182816 1 0.0000 0.945 1.000 0.000 0.000
#> GSM182817 3 0.0000 0.973 0.000 0.000 1.000
#> GSM182818 3 0.0000 0.973 0.000 0.000 1.000
#> GSM182819 1 0.0000 0.945 1.000 0.000 0.000
#> GSM182820 1 0.0000 0.945 1.000 0.000 0.000
#> GSM182821 3 0.0000 0.973 0.000 0.000 1.000
#> GSM182822 3 0.0000 0.973 0.000 0.000 1.000
#> GSM182823 1 0.0000 0.945 1.000 0.000 0.000
#> GSM182824 1 0.0000 0.945 1.000 0.000 0.000
#> GSM182825 1 0.0000 0.945 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM182755 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM182756 4 0.4866 0.388 0.000 0.000 0.404 0.596
#> GSM182757 3 0.0000 0.923 0.000 0.000 1.000 0.000
#> GSM182758 3 0.0336 0.922 0.000 0.000 0.992 0.008
#> GSM182759 3 0.0000 0.923 0.000 0.000 1.000 0.000
#> GSM182760 4 0.4996 0.199 0.000 0.000 0.484 0.516
#> GSM182761 3 0.4996 -0.100 0.000 0.484 0.516 0.000
#> GSM182762 4 0.0000 0.853 0.000 0.000 0.000 1.000
#> GSM182763 3 0.0000 0.923 0.000 0.000 1.000 0.000
#> GSM182764 3 0.0000 0.923 0.000 0.000 1.000 0.000
#> GSM182765 3 0.0188 0.923 0.000 0.000 0.996 0.004
#> GSM182766 2 0.1557 0.873 0.000 0.944 0.056 0.000
#> GSM182767 3 0.2281 0.853 0.000 0.000 0.904 0.096
#> GSM182768 3 0.2589 0.827 0.000 0.000 0.884 0.116
#> GSM182769 4 0.0469 0.852 0.012 0.000 0.000 0.988
#> GSM182770 2 0.0000 0.908 0.000 1.000 0.000 0.000
#> GSM182771 3 0.0188 0.923 0.000 0.000 0.996 0.004
#> GSM182772 2 0.0000 0.908 0.000 1.000 0.000 0.000
#> GSM182773 4 0.0000 0.853 0.000 0.000 0.000 1.000
#> GSM182774 4 0.0000 0.853 0.000 0.000 0.000 1.000
#> GSM182775 4 0.0469 0.852 0.012 0.000 0.000 0.988
#> GSM182776 4 0.0469 0.852 0.012 0.000 0.000 0.988
#> GSM182777 4 0.0469 0.852 0.012 0.000 0.000 0.988
#> GSM182802 2 0.3444 0.760 0.000 0.816 0.184 0.000
#> GSM182803 4 0.0469 0.852 0.012 0.000 0.000 0.988
#> GSM182804 3 0.0817 0.915 0.000 0.000 0.976 0.024
#> GSM182805 2 0.4866 0.350 0.000 0.596 0.404 0.000
#> GSM182806 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM182807 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM182808 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM182809 3 0.0469 0.921 0.000 0.000 0.988 0.012
#> GSM182810 4 0.0336 0.853 0.008 0.000 0.000 0.992
#> GSM182811 4 0.4277 0.601 0.000 0.000 0.280 0.720
#> GSM182812 4 0.0000 0.853 0.000 0.000 0.000 1.000
#> GSM182813 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM182778 2 0.0000 0.908 0.000 1.000 0.000 0.000
#> GSM182779 3 0.0000 0.923 0.000 0.000 1.000 0.000
#> GSM182780 3 0.0000 0.923 0.000 0.000 1.000 0.000
#> GSM182781 4 0.0469 0.852 0.012 0.000 0.000 0.988
#> GSM182782 2 0.0000 0.908 0.000 1.000 0.000 0.000
#> GSM182783 3 0.0000 0.923 0.000 0.000 1.000 0.000
#> GSM182784 3 0.0336 0.922 0.000 0.000 0.992 0.008
#> GSM182785 3 0.0000 0.923 0.000 0.000 1.000 0.000
#> GSM182786 2 0.0000 0.908 0.000 1.000 0.000 0.000
#> GSM182787 3 0.4996 -0.100 0.000 0.484 0.516 0.000
#> GSM182788 2 0.0000 0.908 0.000 1.000 0.000 0.000
#> GSM182789 3 0.0000 0.923 0.000 0.000 1.000 0.000
#> GSM182790 4 0.0000 0.853 0.000 0.000 0.000 1.000
#> GSM182791 3 0.1792 0.881 0.000 0.000 0.932 0.068
#> GSM182792 4 0.4996 0.199 0.000 0.000 0.484 0.516
#> GSM182793 2 0.0000 0.908 0.000 1.000 0.000 0.000
#> GSM182794 4 0.4996 0.199 0.000 0.000 0.484 0.516
#> GSM182795 3 0.0469 0.921 0.000 0.000 0.988 0.012
#> GSM182796 3 0.0000 0.923 0.000 0.000 1.000 0.000
#> GSM182797 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM182798 3 0.0188 0.923 0.000 0.000 0.996 0.004
#> GSM182799 3 0.0469 0.921 0.000 0.000 0.988 0.012
#> GSM182800 4 0.0000 0.853 0.000 0.000 0.000 1.000
#> GSM182801 4 0.0469 0.852 0.012 0.000 0.000 0.988
#> GSM182814 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM182815 3 0.4978 0.459 0.000 0.324 0.664 0.012
#> GSM182816 1 0.4855 0.384 0.600 0.000 0.000 0.400
#> GSM182817 3 0.1792 0.881 0.000 0.000 0.932 0.068
#> GSM182818 3 0.1389 0.898 0.000 0.000 0.952 0.048
#> GSM182819 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM182820 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM182821 3 0.0469 0.921 0.000 0.000 0.988 0.012
#> GSM182822 4 0.0000 0.853 0.000 0.000 0.000 1.000
#> GSM182823 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM182824 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM182825 4 0.0469 0.852 0.012 0.000 0.000 0.988
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM182755 1 0.000 0.958 1.0 0.000 0.000 0.000 0.000
#> GSM182756 3 0.424 0.201 0.0 0.000 0.572 0.428 0.000
#> GSM182757 5 0.000 0.717 0.0 0.000 0.000 0.000 1.000
#> GSM182758 4 0.403 0.325 0.0 0.000 0.000 0.648 0.352
#> GSM182759 5 0.000 0.717 0.0 0.000 0.000 0.000 1.000
#> GSM182760 4 0.000 0.881 0.0 0.000 0.000 1.000 0.000
#> GSM182761 5 0.000 0.717 0.0 0.000 0.000 0.000 1.000
#> GSM182762 3 0.406 0.480 0.0 0.000 0.640 0.000 0.360
#> GSM182763 5 0.351 0.613 0.0 0.000 0.000 0.252 0.748
#> GSM182764 5 0.000 0.717 0.0 0.000 0.000 0.000 1.000
#> GSM182765 5 0.403 0.418 0.0 0.000 0.000 0.352 0.648
#> GSM182766 2 0.141 0.910 0.0 0.940 0.000 0.000 0.060
#> GSM182767 4 0.000 0.881 0.0 0.000 0.000 1.000 0.000
#> GSM182768 4 0.000 0.881 0.0 0.000 0.000 1.000 0.000
#> GSM182769 3 0.000 0.945 0.0 0.000 1.000 0.000 0.000
#> GSM182770 2 0.000 0.961 0.0 1.000 0.000 0.000 0.000
#> GSM182771 5 0.405 0.411 0.0 0.000 0.000 0.356 0.644
#> GSM182772 2 0.000 0.961 0.0 1.000 0.000 0.000 0.000
#> GSM182773 3 0.000 0.945 0.0 0.000 1.000 0.000 0.000
#> GSM182774 3 0.000 0.945 0.0 0.000 1.000 0.000 0.000
#> GSM182775 3 0.000 0.945 0.0 0.000 1.000 0.000 0.000
#> GSM182776 3 0.000 0.945 0.0 0.000 1.000 0.000 0.000
#> GSM182777 3 0.000 0.945 0.0 0.000 1.000 0.000 0.000
#> GSM182802 2 0.307 0.716 0.0 0.804 0.000 0.000 0.196
#> GSM182803 3 0.000 0.945 0.0 0.000 1.000 0.000 0.000
#> GSM182804 4 0.000 0.881 0.0 0.000 0.000 1.000 0.000
#> GSM182805 5 0.415 0.318 0.0 0.388 0.000 0.000 0.612
#> GSM182806 1 0.000 0.958 1.0 0.000 0.000 0.000 0.000
#> GSM182807 1 0.000 0.958 1.0 0.000 0.000 0.000 0.000
#> GSM182808 1 0.000 0.958 1.0 0.000 0.000 0.000 0.000
#> GSM182809 4 0.000 0.881 0.0 0.000 0.000 1.000 0.000
#> GSM182810 3 0.000 0.945 0.0 0.000 1.000 0.000 0.000
#> GSM182811 4 0.318 0.641 0.0 0.000 0.208 0.792 0.000
#> GSM182812 3 0.000 0.945 0.0 0.000 1.000 0.000 0.000
#> GSM182813 1 0.000 0.958 1.0 0.000 0.000 0.000 0.000
#> GSM182778 2 0.000 0.961 0.0 1.000 0.000 0.000 0.000
#> GSM182779 5 0.000 0.717 0.0 0.000 0.000 0.000 1.000
#> GSM182780 5 0.406 0.477 0.0 0.000 0.000 0.360 0.640
#> GSM182781 3 0.000 0.945 0.0 0.000 1.000 0.000 0.000
#> GSM182782 2 0.000 0.961 0.0 1.000 0.000 0.000 0.000
#> GSM182783 5 0.410 0.455 0.0 0.000 0.000 0.372 0.628
#> GSM182784 4 0.407 0.295 0.0 0.000 0.000 0.636 0.364
#> GSM182785 5 0.293 0.670 0.0 0.000 0.000 0.180 0.820
#> GSM182786 2 0.000 0.961 0.0 1.000 0.000 0.000 0.000
#> GSM182787 5 0.406 0.372 0.0 0.360 0.000 0.000 0.640
#> GSM182788 2 0.000 0.961 0.0 1.000 0.000 0.000 0.000
#> GSM182789 5 0.406 0.477 0.0 0.000 0.000 0.360 0.640
#> GSM182790 3 0.000 0.945 0.0 0.000 1.000 0.000 0.000
#> GSM182791 4 0.000 0.881 0.0 0.000 0.000 1.000 0.000
#> GSM182792 4 0.000 0.881 0.0 0.000 0.000 1.000 0.000
#> GSM182793 2 0.000 0.961 0.0 1.000 0.000 0.000 0.000
#> GSM182794 4 0.228 0.767 0.0 0.000 0.120 0.880 0.000
#> GSM182795 4 0.191 0.795 0.0 0.000 0.000 0.908 0.092
#> GSM182796 5 0.000 0.717 0.0 0.000 0.000 0.000 1.000
#> GSM182797 1 0.000 0.958 1.0 0.000 0.000 0.000 0.000
#> GSM182798 5 0.403 0.418 0.0 0.000 0.000 0.352 0.648
#> GSM182799 4 0.000 0.881 0.0 0.000 0.000 1.000 0.000
#> GSM182800 3 0.000 0.945 0.0 0.000 1.000 0.000 0.000
#> GSM182801 3 0.000 0.945 0.0 0.000 1.000 0.000 0.000
#> GSM182814 1 0.000 0.958 1.0 0.000 0.000 0.000 0.000
#> GSM182815 4 0.318 0.645 0.0 0.208 0.000 0.792 0.000
#> GSM182816 1 0.418 0.348 0.6 0.000 0.400 0.000 0.000
#> GSM182817 4 0.000 0.881 0.0 0.000 0.000 1.000 0.000
#> GSM182818 4 0.000 0.881 0.0 0.000 0.000 1.000 0.000
#> GSM182819 1 0.000 0.958 1.0 0.000 0.000 0.000 0.000
#> GSM182820 1 0.000 0.958 1.0 0.000 0.000 0.000 0.000
#> GSM182821 4 0.000 0.881 0.0 0.000 0.000 1.000 0.000
#> GSM182822 3 0.000 0.945 0.0 0.000 1.000 0.000 0.000
#> GSM182823 1 0.000 0.958 1.0 0.000 0.000 0.000 0.000
#> GSM182824 1 0.000 0.958 1.0 0.000 0.000 0.000 0.000
#> GSM182825 3 0.000 0.945 0.0 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM182755 1 0.000 0.9548 1.0 0.000 0.000 0.000 0.000 0.000
#> GSM182756 6 0.412 0.2378 0.0 0.000 0.416 0.012 0.000 0.572
#> GSM182757 5 0.000 0.6714 0.0 0.000 0.000 0.000 1.000 0.000
#> GSM182758 3 0.549 0.3413 0.0 0.000 0.568 0.212 0.220 0.000
#> GSM182759 5 0.161 0.6000 0.0 0.000 0.000 0.084 0.916 0.000
#> GSM182760 3 0.000 0.8952 0.0 0.000 1.000 0.000 0.000 0.000
#> GSM182761 4 0.387 0.1715 0.0 0.000 0.000 0.516 0.484 0.000
#> GSM182762 5 0.387 -0.0407 0.0 0.000 0.000 0.000 0.516 0.484
#> GSM182763 5 0.487 0.2677 0.0 0.000 0.108 0.252 0.640 0.000
#> GSM182764 5 0.000 0.6714 0.0 0.000 0.000 0.000 1.000 0.000
#> GSM182765 5 0.294 0.5859 0.0 0.000 0.220 0.000 0.780 0.000
#> GSM182766 4 0.315 0.3086 0.0 0.252 0.000 0.748 0.000 0.000
#> GSM182767 3 0.000 0.8952 0.0 0.000 1.000 0.000 0.000 0.000
#> GSM182768 3 0.000 0.8952 0.0 0.000 1.000 0.000 0.000 0.000
#> GSM182769 6 0.000 0.9664 0.0 0.000 0.000 0.000 0.000 1.000
#> GSM182770 2 0.000 1.0000 0.0 1.000 0.000 0.000 0.000 0.000
#> GSM182771 5 0.294 0.5859 0.0 0.000 0.220 0.000 0.780 0.000
#> GSM182772 2 0.000 1.0000 0.0 1.000 0.000 0.000 0.000 0.000
#> GSM182773 6 0.000 0.9664 0.0 0.000 0.000 0.000 0.000 1.000
#> GSM182774 6 0.000 0.9664 0.0 0.000 0.000 0.000 0.000 1.000
#> GSM182775 6 0.000 0.9664 0.0 0.000 0.000 0.000 0.000 1.000
#> GSM182776 6 0.000 0.9664 0.0 0.000 0.000 0.000 0.000 1.000
#> GSM182777 6 0.000 0.9664 0.0 0.000 0.000 0.000 0.000 1.000
#> GSM182802 4 0.315 0.3086 0.0 0.252 0.000 0.748 0.000 0.000
#> GSM182803 6 0.000 0.9664 0.0 0.000 0.000 0.000 0.000 1.000
#> GSM182804 3 0.000 0.8952 0.0 0.000 1.000 0.000 0.000 0.000
#> GSM182805 4 0.315 0.3086 0.0 0.252 0.000 0.748 0.000 0.000
#> GSM182806 1 0.000 0.9548 1.0 0.000 0.000 0.000 0.000 0.000
#> GSM182807 1 0.000 0.9548 1.0 0.000 0.000 0.000 0.000 0.000
#> GSM182808 1 0.000 0.9548 1.0 0.000 0.000 0.000 0.000 0.000
#> GSM182809 3 0.000 0.8952 0.0 0.000 1.000 0.000 0.000 0.000
#> GSM182810 6 0.000 0.9664 0.0 0.000 0.000 0.000 0.000 1.000
#> GSM182811 3 0.285 0.6757 0.0 0.000 0.792 0.000 0.000 0.208
#> GSM182812 6 0.000 0.9664 0.0 0.000 0.000 0.000 0.000 1.000
#> GSM182813 1 0.000 0.9548 1.0 0.000 0.000 0.000 0.000 0.000
#> GSM182778 2 0.000 1.0000 0.0 1.000 0.000 0.000 0.000 0.000
#> GSM182779 5 0.026 0.6677 0.0 0.000 0.000 0.008 0.992 0.000
#> GSM182780 4 0.387 0.1715 0.0 0.000 0.000 0.516 0.484 0.000
#> GSM182781 6 0.000 0.9664 0.0 0.000 0.000 0.000 0.000 1.000
#> GSM182782 2 0.000 1.0000 0.0 1.000 0.000 0.000 0.000 0.000
#> GSM182783 4 0.368 0.2963 0.0 0.000 0.004 0.664 0.332 0.000
#> GSM182784 3 0.570 0.2567 0.0 0.000 0.524 0.252 0.224 0.000
#> GSM182785 5 0.408 0.3473 0.0 0.000 0.044 0.252 0.704 0.000
#> GSM182786 2 0.000 1.0000 0.0 1.000 0.000 0.000 0.000 0.000
#> GSM182787 4 0.387 0.1715 0.0 0.000 0.000 0.516 0.484 0.000
#> GSM182788 2 0.000 1.0000 0.0 1.000 0.000 0.000 0.000 0.000
#> GSM182789 4 0.387 0.1715 0.0 0.000 0.000 0.516 0.484 0.000
#> GSM182790 6 0.000 0.9664 0.0 0.000 0.000 0.000 0.000 1.000
#> GSM182791 3 0.000 0.8952 0.0 0.000 1.000 0.000 0.000 0.000
#> GSM182792 3 0.000 0.8952 0.0 0.000 1.000 0.000 0.000 0.000
#> GSM182793 4 0.322 0.2908 0.0 0.264 0.000 0.736 0.000 0.000
#> GSM182794 3 0.270 0.7680 0.0 0.000 0.856 0.000 0.028 0.116
#> GSM182795 3 0.172 0.8358 0.0 0.000 0.924 0.016 0.060 0.000
#> GSM182796 5 0.000 0.6714 0.0 0.000 0.000 0.000 1.000 0.000
#> GSM182797 1 0.000 0.9548 1.0 0.000 0.000 0.000 0.000 0.000
#> GSM182798 5 0.294 0.5859 0.0 0.000 0.220 0.000 0.780 0.000
#> GSM182799 3 0.000 0.8952 0.0 0.000 1.000 0.000 0.000 0.000
#> GSM182800 6 0.000 0.9664 0.0 0.000 0.000 0.000 0.000 1.000
#> GSM182801 6 0.000 0.9664 0.0 0.000 0.000 0.000 0.000 1.000
#> GSM182814 1 0.000 0.9548 1.0 0.000 0.000 0.000 0.000 0.000
#> GSM182815 4 0.567 0.0851 0.0 0.164 0.352 0.484 0.000 0.000
#> GSM182816 1 0.376 0.3465 0.6 0.000 0.000 0.000 0.000 0.400
#> GSM182817 3 0.000 0.8952 0.0 0.000 1.000 0.000 0.000 0.000
#> GSM182818 3 0.000 0.8952 0.0 0.000 1.000 0.000 0.000 0.000
#> GSM182819 1 0.000 0.9548 1.0 0.000 0.000 0.000 0.000 0.000
#> GSM182820 1 0.000 0.9548 1.0 0.000 0.000 0.000 0.000 0.000
#> GSM182821 3 0.000 0.8952 0.0 0.000 1.000 0.000 0.000 0.000
#> GSM182822 6 0.000 0.9664 0.0 0.000 0.000 0.000 0.000 1.000
#> GSM182823 1 0.000 0.9548 1.0 0.000 0.000 0.000 0.000 0.000
#> GSM182824 1 0.000 0.9548 1.0 0.000 0.000 0.000 0.000 0.000
#> GSM182825 6 0.000 0.9664 0.0 0.000 0.000 0.000 0.000 1.000
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 stress(p) development.stage(p) k
#> ATC:pam 62 0.435 0.02009 2
#> ATC:pam 69 0.994 0.00363 3
#> ATC:pam 62 0.566 0.00141 4
#> ATC:pam 58 0.754 0.00172 5
#> ATC:pam 54 0.709 0.00124 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 18172 rows and 71 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.910 0.895 0.960 0.4221 0.577 0.577
#> 3 3 0.498 0.755 0.836 0.4352 0.771 0.614
#> 4 4 0.509 0.592 0.745 0.1105 0.720 0.412
#> 5 5 0.643 0.763 0.873 0.0885 0.938 0.799
#> 6 6 0.668 0.516 0.722 0.0773 0.877 0.579
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
#> GSM182755 1 0.0000 0.9669 1.000 0.000
#> GSM182756 2 0.2948 0.9087 0.052 0.948
#> GSM182757 1 0.0938 0.9572 0.988 0.012
#> GSM182758 2 0.0000 0.9271 0.000 1.000
#> GSM182759 1 0.0000 0.9669 1.000 0.000
#> GSM182760 2 0.0000 0.9271 0.000 1.000
#> GSM182761 1 0.2043 0.9390 0.968 0.032
#> GSM182762 1 0.0000 0.9669 1.000 0.000
#> GSM182763 1 0.0938 0.9572 0.988 0.012
#> GSM182764 1 0.0000 0.9669 1.000 0.000
#> GSM182765 1 0.0000 0.9669 1.000 0.000
#> GSM182766 1 0.0000 0.9669 1.000 0.000
#> GSM182767 2 0.0000 0.9271 0.000 1.000
#> GSM182768 2 0.0000 0.9271 0.000 1.000
#> GSM182769 2 0.0376 0.9263 0.004 0.996
#> GSM182770 1 0.0000 0.9669 1.000 0.000
#> GSM182771 1 0.0000 0.9669 1.000 0.000
#> GSM182772 1 0.0000 0.9669 1.000 0.000
#> GSM182773 2 0.0000 0.9271 0.000 1.000
#> GSM182774 1 0.0000 0.9669 1.000 0.000
#> GSM182775 2 0.0000 0.9271 0.000 1.000
#> GSM182776 1 0.9954 0.0708 0.540 0.460
#> GSM182777 2 0.2778 0.9111 0.048 0.952
#> GSM182802 1 0.0000 0.9669 1.000 0.000
#> GSM182803 1 0.0000 0.9669 1.000 0.000
#> GSM182804 1 0.0000 0.9669 1.000 0.000
#> GSM182805 1 0.0000 0.9669 1.000 0.000
#> GSM182806 1 0.0000 0.9669 1.000 0.000
#> GSM182807 1 0.0000 0.9669 1.000 0.000
#> GSM182808 1 0.0000 0.9669 1.000 0.000
#> GSM182809 1 0.0000 0.9669 1.000 0.000
#> GSM182810 1 0.0000 0.9669 1.000 0.000
#> GSM182811 1 0.0000 0.9669 1.000 0.000
#> GSM182812 1 0.0000 0.9669 1.000 0.000
#> GSM182813 1 0.0000 0.9669 1.000 0.000
#> GSM182778 1 0.0000 0.9669 1.000 0.000
#> GSM182779 1 0.1633 0.9468 0.976 0.024
#> GSM182780 2 0.0000 0.9271 0.000 1.000
#> GSM182781 2 0.9996 0.0594 0.488 0.512
#> GSM182782 1 0.0000 0.9669 1.000 0.000
#> GSM182783 2 0.5737 0.8336 0.136 0.864
#> GSM182784 2 0.0000 0.9271 0.000 1.000
#> GSM182785 2 0.4022 0.8896 0.080 0.920
#> GSM182786 1 0.0000 0.9669 1.000 0.000
#> GSM182787 1 0.9710 0.2799 0.600 0.400
#> GSM182788 1 0.0000 0.9669 1.000 0.000
#> GSM182789 2 0.2603 0.9131 0.044 0.956
#> GSM182790 2 0.0000 0.9271 0.000 1.000
#> GSM182791 2 0.9795 0.3214 0.416 0.584
#> GSM182792 2 0.1633 0.9209 0.024 0.976
#> GSM182793 1 0.0000 0.9669 1.000 0.000
#> GSM182794 2 0.0000 0.9271 0.000 1.000
#> GSM182795 2 0.0000 0.9271 0.000 1.000
#> GSM182796 1 0.0000 0.9669 1.000 0.000
#> GSM182797 1 0.0000 0.9669 1.000 0.000
#> GSM182798 1 0.0000 0.9669 1.000 0.000
#> GSM182799 1 0.4298 0.8774 0.912 0.088
#> GSM182800 1 0.0000 0.9669 1.000 0.000
#> GSM182801 2 0.4690 0.8682 0.100 0.900
#> GSM182814 1 0.0000 0.9669 1.000 0.000
#> GSM182815 1 0.0000 0.9669 1.000 0.000
#> GSM182816 1 0.9850 0.1808 0.572 0.428
#> GSM182817 1 0.0000 0.9669 1.000 0.000
#> GSM182818 1 0.0000 0.9669 1.000 0.000
#> GSM182819 1 0.0000 0.9669 1.000 0.000
#> GSM182820 1 0.0000 0.9669 1.000 0.000
#> GSM182821 1 0.1633 0.9458 0.976 0.024
#> GSM182822 1 0.0000 0.9669 1.000 0.000
#> GSM182823 1 0.0000 0.9669 1.000 0.000
#> GSM182824 1 0.0000 0.9669 1.000 0.000
#> GSM182825 1 0.0000 0.9669 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM182755 1 0.4654 0.842 0.792 0.208 0.000
#> GSM182756 3 0.1163 0.897 0.000 0.028 0.972
#> GSM182757 2 0.5285 0.735 0.244 0.752 0.004
#> GSM182758 3 0.0000 0.901 0.000 0.000 1.000
#> GSM182759 2 0.4654 0.749 0.208 0.792 0.000
#> GSM182760 3 0.0000 0.901 0.000 0.000 1.000
#> GSM182761 2 0.6693 0.714 0.148 0.748 0.104
#> GSM182762 2 0.5098 0.733 0.248 0.752 0.000
#> GSM182763 2 0.5681 0.734 0.236 0.748 0.016
#> GSM182764 2 0.5058 0.734 0.244 0.756 0.000
#> GSM182765 2 0.5058 0.734 0.244 0.756 0.000
#> GSM182766 2 0.5178 0.735 0.256 0.744 0.000
#> GSM182767 3 0.0000 0.901 0.000 0.000 1.000
#> GSM182768 3 0.0000 0.901 0.000 0.000 1.000
#> GSM182769 3 0.1031 0.896 0.000 0.024 0.976
#> GSM182770 2 0.2356 0.715 0.072 0.928 0.000
#> GSM182771 2 0.4605 0.750 0.204 0.796 0.000
#> GSM182772 2 0.2959 0.727 0.100 0.900 0.000
#> GSM182773 3 0.0000 0.901 0.000 0.000 1.000
#> GSM182774 2 0.5098 0.729 0.248 0.752 0.000
#> GSM182775 3 0.0000 0.901 0.000 0.000 1.000
#> GSM182776 3 0.5635 0.707 0.036 0.180 0.784
#> GSM182777 3 0.1031 0.898 0.000 0.024 0.976
#> GSM182802 2 0.0592 0.744 0.012 0.988 0.000
#> GSM182803 1 0.5016 0.817 0.760 0.240 0.000
#> GSM182804 2 0.0237 0.740 0.000 0.996 0.004
#> GSM182805 2 0.2537 0.763 0.080 0.920 0.000
#> GSM182806 1 0.4842 0.844 0.776 0.224 0.000
#> GSM182807 1 0.5058 0.852 0.756 0.244 0.000
#> GSM182808 1 0.6154 0.770 0.592 0.408 0.000
#> GSM182809 2 0.0424 0.740 0.000 0.992 0.008
#> GSM182810 2 0.2878 0.672 0.096 0.904 0.000
#> GSM182811 2 0.2448 0.761 0.076 0.924 0.000
#> GSM182812 2 0.0237 0.739 0.004 0.996 0.000
#> GSM182813 1 0.5706 0.828 0.680 0.320 0.000
#> GSM182778 2 0.4178 0.728 0.172 0.828 0.000
#> GSM182779 2 0.5899 0.728 0.244 0.736 0.020
#> GSM182780 3 0.2165 0.871 0.000 0.064 0.936
#> GSM182781 3 0.6208 0.667 0.088 0.136 0.776
#> GSM182782 2 0.6126 0.604 0.400 0.600 0.000
#> GSM182783 3 0.6330 0.283 0.004 0.396 0.600
#> GSM182784 3 0.0000 0.901 0.000 0.000 1.000
#> GSM182785 3 0.2537 0.864 0.000 0.080 0.920
#> GSM182786 2 0.6126 0.604 0.400 0.600 0.000
#> GSM182787 2 0.6033 0.482 0.004 0.660 0.336
#> GSM182788 2 0.6126 0.604 0.400 0.600 0.000
#> GSM182789 3 0.1163 0.897 0.000 0.028 0.972
#> GSM182790 3 0.0000 0.901 0.000 0.000 1.000
#> GSM182791 3 0.4821 0.799 0.040 0.120 0.840
#> GSM182792 3 0.0892 0.899 0.000 0.020 0.980
#> GSM182793 2 0.0661 0.739 0.008 0.988 0.004
#> GSM182794 3 0.0000 0.901 0.000 0.000 1.000
#> GSM182795 3 0.0000 0.901 0.000 0.000 1.000
#> GSM182796 2 0.4605 0.750 0.204 0.796 0.000
#> GSM182797 1 0.4750 0.850 0.784 0.216 0.000
#> GSM182798 2 0.4605 0.750 0.204 0.796 0.000
#> GSM182799 2 0.4326 0.620 0.012 0.844 0.144
#> GSM182800 2 0.5178 0.527 0.164 0.808 0.028
#> GSM182801 3 0.3038 0.836 0.000 0.104 0.896
#> GSM182814 1 0.6244 0.751 0.560 0.440 0.000
#> GSM182815 2 0.0661 0.739 0.008 0.988 0.004
#> GSM182816 3 0.9150 0.292 0.232 0.224 0.544
#> GSM182817 2 0.4605 0.750 0.204 0.796 0.000
#> GSM182818 2 0.0661 0.739 0.008 0.988 0.004
#> GSM182819 1 0.4750 0.850 0.784 0.216 0.000
#> GSM182820 1 0.4750 0.850 0.784 0.216 0.000
#> GSM182821 2 0.8333 0.411 0.100 0.572 0.328
#> GSM182822 2 0.3042 0.711 0.040 0.920 0.040
#> GSM182823 1 0.6244 0.751 0.560 0.440 0.000
#> GSM182824 1 0.6168 0.766 0.588 0.412 0.000
#> GSM182825 2 0.3340 0.599 0.120 0.880 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM182755 1 0.6746 0.6281 0.568 0.000 0.116 0.316
#> GSM182756 3 0.0188 0.8360 0.000 0.000 0.996 0.004
#> GSM182757 3 0.5441 0.2790 0.004 0.012 0.588 0.396
#> GSM182758 3 0.0000 0.8358 0.000 0.000 1.000 0.000
#> GSM182759 4 0.4679 0.4917 0.000 0.352 0.000 0.648
#> GSM182760 3 0.0000 0.8358 0.000 0.000 1.000 0.000
#> GSM182761 3 0.4980 0.5529 0.008 0.012 0.708 0.272
#> GSM182762 4 0.7715 0.2727 0.160 0.044 0.208 0.588
#> GSM182763 3 0.5391 0.3208 0.004 0.012 0.604 0.380
#> GSM182764 4 0.6756 0.5062 0.000 0.188 0.200 0.612
#> GSM182765 4 0.6483 0.4089 0.000 0.092 0.324 0.584
#> GSM182766 2 0.4897 0.2115 0.004 0.668 0.004 0.324
#> GSM182767 3 0.0000 0.8358 0.000 0.000 1.000 0.000
#> GSM182768 3 0.0000 0.8358 0.000 0.000 1.000 0.000
#> GSM182769 3 0.0188 0.8355 0.000 0.004 0.996 0.000
#> GSM182770 2 0.2197 0.6298 0.004 0.916 0.000 0.080
#> GSM182771 4 0.4624 0.5024 0.000 0.340 0.000 0.660
#> GSM182772 2 0.2530 0.6208 0.004 0.896 0.000 0.100
#> GSM182773 3 0.0000 0.8358 0.000 0.000 1.000 0.000
#> GSM182774 1 0.7808 0.4935 0.480 0.044 0.096 0.380
#> GSM182775 3 0.0000 0.8358 0.000 0.000 1.000 0.000
#> GSM182776 3 0.1892 0.8215 0.004 0.016 0.944 0.036
#> GSM182777 3 0.0188 0.8360 0.000 0.000 0.996 0.004
#> GSM182802 2 0.3355 0.5897 0.004 0.836 0.000 0.160
#> GSM182803 1 0.4500 0.7904 0.684 0.000 0.000 0.316
#> GSM182804 2 0.7050 0.4104 0.004 0.460 0.104 0.432
#> GSM182805 2 0.4088 0.4817 0.004 0.764 0.000 0.232
#> GSM182806 1 0.4500 0.7904 0.684 0.000 0.000 0.316
#> GSM182807 1 0.4655 0.7919 0.684 0.004 0.000 0.312
#> GSM182808 1 0.5471 0.7834 0.684 0.048 0.000 0.268
#> GSM182809 3 0.9483 -0.0751 0.144 0.304 0.376 0.176
#> GSM182810 1 0.7254 0.4685 0.524 0.176 0.000 0.300
#> GSM182811 4 0.6798 -0.4550 0.396 0.100 0.000 0.504
#> GSM182812 4 0.7301 -0.0427 0.232 0.232 0.000 0.536
#> GSM182813 1 0.4957 0.7932 0.684 0.016 0.000 0.300
#> GSM182778 2 0.0927 0.6182 0.016 0.976 0.000 0.008
#> GSM182779 4 0.6935 0.4099 0.004 0.112 0.332 0.552
#> GSM182780 3 0.1743 0.8176 0.000 0.004 0.940 0.056
#> GSM182781 3 0.3764 0.6125 0.000 0.000 0.784 0.216
#> GSM182782 2 0.4673 0.5019 0.292 0.700 0.000 0.008
#> GSM182783 3 0.3409 0.7889 0.008 0.024 0.872 0.096
#> GSM182784 3 0.0000 0.8358 0.000 0.000 1.000 0.000
#> GSM182785 3 0.2053 0.8135 0.004 0.000 0.924 0.072
#> GSM182786 2 0.4673 0.5019 0.292 0.700 0.000 0.008
#> GSM182787 3 0.2927 0.7953 0.008 0.024 0.900 0.068
#> GSM182788 2 0.4673 0.5019 0.292 0.700 0.000 0.008
#> GSM182789 3 0.1792 0.8157 0.000 0.000 0.932 0.068
#> GSM182790 3 0.0000 0.8358 0.000 0.000 1.000 0.000
#> GSM182791 3 0.1822 0.8235 0.004 0.008 0.944 0.044
#> GSM182792 3 0.0000 0.8358 0.000 0.000 1.000 0.000
#> GSM182793 2 0.4718 0.5900 0.008 0.716 0.004 0.272
#> GSM182794 3 0.0188 0.8360 0.000 0.000 0.996 0.004
#> GSM182795 3 0.0000 0.8358 0.000 0.000 1.000 0.000
#> GSM182796 4 0.4936 0.4960 0.008 0.340 0.000 0.652
#> GSM182797 1 0.4500 0.7904 0.684 0.000 0.000 0.316
#> GSM182798 4 0.4936 0.4960 0.008 0.340 0.000 0.652
#> GSM182799 3 0.6850 0.4487 0.012 0.300 0.592 0.096
#> GSM182800 1 0.9357 0.1965 0.368 0.108 0.204 0.320
#> GSM182801 3 0.0657 0.8339 0.000 0.012 0.984 0.004
#> GSM182814 1 0.5519 0.7803 0.684 0.052 0.000 0.264
#> GSM182815 2 0.5509 0.5064 0.012 0.560 0.004 0.424
#> GSM182816 3 0.6163 0.2852 0.364 0.000 0.576 0.060
#> GSM182817 4 0.4917 0.5033 0.008 0.336 0.000 0.656
#> GSM182818 2 0.7365 0.4036 0.012 0.452 0.112 0.424
#> GSM182819 1 0.6878 0.6026 0.556 0.000 0.128 0.316
#> GSM182820 1 0.4500 0.7904 0.684 0.000 0.000 0.316
#> GSM182821 3 0.4406 0.7036 0.004 0.044 0.808 0.144
#> GSM182822 3 0.9195 -0.1515 0.148 0.128 0.412 0.312
#> GSM182823 1 0.5308 0.7893 0.684 0.036 0.000 0.280
#> GSM182824 1 0.5790 0.7521 0.684 0.080 0.000 0.236
#> GSM182825 1 0.7346 0.4268 0.520 0.200 0.000 0.280
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM182755 1 0.0000 0.854 1.000 0.000 0.000 0.000 0.000
#> GSM182756 3 0.0162 0.866 0.000 0.000 0.996 0.000 0.004
#> GSM182757 5 0.5882 0.354 0.008 0.000 0.280 0.112 0.600
#> GSM182758 3 0.0290 0.866 0.000 0.000 0.992 0.000 0.008
#> GSM182759 5 0.2935 0.790 0.016 0.004 0.000 0.120 0.860
#> GSM182760 3 0.0162 0.866 0.000 0.000 0.996 0.000 0.004
#> GSM182761 3 0.5665 0.598 0.004 0.000 0.624 0.112 0.260
#> GSM182762 5 0.2784 0.790 0.016 0.000 0.004 0.108 0.872
#> GSM182763 3 0.5779 0.602 0.008 0.000 0.624 0.116 0.252
#> GSM182764 5 0.2625 0.791 0.016 0.000 0.000 0.108 0.876
#> GSM182765 5 0.2784 0.791 0.016 0.000 0.004 0.108 0.872
#> GSM182766 2 0.6005 0.583 0.016 0.620 0.000 0.128 0.236
#> GSM182767 3 0.0162 0.866 0.000 0.000 0.996 0.000 0.004
#> GSM182768 3 0.0404 0.866 0.000 0.000 0.988 0.000 0.012
#> GSM182769 3 0.0324 0.865 0.000 0.000 0.992 0.004 0.004
#> GSM182770 2 0.4333 0.769 0.012 0.788 0.000 0.120 0.080
#> GSM182771 5 0.4889 0.750 0.016 0.108 0.000 0.128 0.748
#> GSM182772 2 0.4386 0.769 0.016 0.788 0.000 0.116 0.080
#> GSM182773 3 0.0162 0.865 0.000 0.000 0.996 0.000 0.004
#> GSM182774 1 0.5183 0.623 0.748 0.000 0.064 0.112 0.076
#> GSM182775 3 0.0324 0.865 0.000 0.000 0.992 0.004 0.004
#> GSM182776 3 0.1808 0.853 0.008 0.000 0.936 0.044 0.012
#> GSM182777 3 0.0000 0.865 0.000 0.000 1.000 0.000 0.000
#> GSM182802 2 0.4635 0.757 0.016 0.768 0.000 0.128 0.088
#> GSM182803 1 0.0162 0.851 0.996 0.000 0.004 0.000 0.000
#> GSM182804 4 0.1251 0.966 0.008 0.000 0.000 0.956 0.036
#> GSM182805 2 0.4635 0.757 0.016 0.768 0.000 0.128 0.088
#> GSM182806 1 0.0000 0.854 1.000 0.000 0.000 0.000 0.000
#> GSM182807 1 0.0000 0.854 1.000 0.000 0.000 0.000 0.000
#> GSM182808 1 0.0000 0.854 1.000 0.000 0.000 0.000 0.000
#> GSM182809 3 0.6503 0.621 0.116 0.000 0.628 0.180 0.076
#> GSM182810 1 0.3722 0.686 0.796 0.000 0.004 0.176 0.024
#> GSM182811 1 0.5778 0.272 0.556 0.000 0.004 0.352 0.088
#> GSM182812 4 0.1560 0.955 0.028 0.000 0.004 0.948 0.020
#> GSM182813 1 0.0000 0.854 1.000 0.000 0.000 0.000 0.000
#> GSM182778 2 0.0162 0.744 0.004 0.996 0.000 0.000 0.000
#> GSM182779 5 0.2746 0.770 0.008 0.000 0.008 0.112 0.872
#> GSM182780 3 0.3280 0.795 0.000 0.000 0.812 0.176 0.012
#> GSM182781 3 0.0000 0.865 0.000 0.000 1.000 0.000 0.000
#> GSM182782 2 0.0000 0.743 0.000 1.000 0.000 0.000 0.000
#> GSM182783 3 0.3527 0.786 0.000 0.000 0.792 0.192 0.016
#> GSM182784 3 0.0162 0.866 0.000 0.000 0.996 0.000 0.004
#> GSM182785 3 0.3682 0.806 0.000 0.000 0.820 0.108 0.072
#> GSM182786 2 0.0000 0.743 0.000 1.000 0.000 0.000 0.000
#> GSM182787 3 0.5850 0.596 0.004 0.004 0.624 0.124 0.244
#> GSM182788 2 0.0000 0.743 0.000 1.000 0.000 0.000 0.000
#> GSM182789 3 0.3141 0.821 0.000 0.000 0.852 0.108 0.040
#> GSM182790 3 0.0000 0.865 0.000 0.000 1.000 0.000 0.000
#> GSM182791 3 0.3059 0.825 0.004 0.000 0.860 0.108 0.028
#> GSM182792 3 0.0404 0.866 0.000 0.000 0.988 0.000 0.012
#> GSM182793 2 0.4837 0.538 0.008 0.624 0.000 0.348 0.020
#> GSM182794 3 0.0000 0.865 0.000 0.000 1.000 0.000 0.000
#> GSM182795 3 0.0290 0.866 0.000 0.000 0.992 0.000 0.008
#> GSM182796 5 0.3860 0.654 0.016 0.148 0.000 0.028 0.808
#> GSM182797 1 0.0000 0.854 1.000 0.000 0.000 0.000 0.000
#> GSM182798 5 0.3860 0.654 0.016 0.148 0.000 0.028 0.808
#> GSM182799 3 0.3462 0.785 0.000 0.000 0.792 0.196 0.012
#> GSM182800 1 0.4532 0.655 0.764 0.000 0.048 0.168 0.020
#> GSM182801 3 0.1205 0.860 0.000 0.000 0.956 0.040 0.004
#> GSM182814 1 0.0000 0.854 1.000 0.000 0.000 0.000 0.000
#> GSM182815 4 0.1251 0.968 0.008 0.000 0.000 0.956 0.036
#> GSM182816 1 0.5124 -0.121 0.488 0.000 0.480 0.028 0.004
#> GSM182817 5 0.5199 0.725 0.016 0.140 0.000 0.124 0.720
#> GSM182818 4 0.0579 0.958 0.008 0.000 0.000 0.984 0.008
#> GSM182819 1 0.0000 0.854 1.000 0.000 0.000 0.000 0.000
#> GSM182820 1 0.0000 0.854 1.000 0.000 0.000 0.000 0.000
#> GSM182821 3 0.5891 0.587 0.016 0.000 0.624 0.108 0.252
#> GSM182822 3 0.6404 0.595 0.180 0.000 0.632 0.128 0.060
#> GSM182823 1 0.0000 0.854 1.000 0.000 0.000 0.000 0.000
#> GSM182824 1 0.0000 0.854 1.000 0.000 0.000 0.000 0.000
#> GSM182825 1 0.4037 0.646 0.752 0.000 0.004 0.224 0.020
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM182755 1 0.0291 0.8992 0.992 0.000 0.004 0.000 0.000 0.004
#> GSM182756 3 0.3952 0.1760 0.000 0.000 0.672 0.020 0.000 0.308
#> GSM182757 5 0.4738 0.5567 0.000 0.000 0.064 0.000 0.600 0.336
#> GSM182758 3 0.4325 -0.2024 0.000 0.000 0.524 0.020 0.000 0.456
#> GSM182759 5 0.2624 0.7898 0.000 0.004 0.000 0.004 0.844 0.148
#> GSM182760 3 0.4018 0.1507 0.000 0.000 0.656 0.020 0.000 0.324
#> GSM182761 6 0.5335 0.6730 0.000 0.000 0.276 0.000 0.148 0.576
#> GSM182762 5 0.2980 0.7930 0.000 0.000 0.000 0.012 0.808 0.180
#> GSM182763 6 0.5177 0.5390 0.000 0.000 0.152 0.000 0.236 0.612
#> GSM182764 5 0.2772 0.7956 0.000 0.000 0.000 0.004 0.816 0.180
#> GSM182765 5 0.3386 0.7837 0.000 0.000 0.016 0.008 0.788 0.188
#> GSM182766 2 0.4441 0.7398 0.000 0.720 0.000 0.016 0.204 0.060
#> GSM182767 3 0.4310 -0.1411 0.000 0.000 0.540 0.020 0.000 0.440
#> GSM182768 3 0.3737 -0.1485 0.000 0.000 0.608 0.000 0.000 0.392
#> GSM182769 3 0.1341 0.4607 0.000 0.000 0.948 0.024 0.000 0.028
#> GSM182770 2 0.2867 0.8583 0.000 0.848 0.000 0.040 0.112 0.000
#> GSM182771 5 0.0972 0.7503 0.000 0.028 0.000 0.008 0.964 0.000
#> GSM182772 2 0.2709 0.8578 0.000 0.848 0.000 0.020 0.132 0.000
#> GSM182773 3 0.0000 0.4699 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM182774 3 0.6813 0.0433 0.316 0.000 0.476 0.020 0.136 0.052
#> GSM182775 3 0.0777 0.4671 0.000 0.000 0.972 0.024 0.000 0.004
#> GSM182776 3 0.1629 0.4444 0.004 0.000 0.940 0.004 0.024 0.028
#> GSM182777 3 0.0520 0.4703 0.000 0.000 0.984 0.008 0.000 0.008
#> GSM182802 2 0.3014 0.8509 0.000 0.832 0.000 0.036 0.132 0.000
#> GSM182803 1 0.0777 0.8988 0.972 0.000 0.004 0.000 0.000 0.024
#> GSM182804 4 0.1958 0.7281 0.000 0.000 0.004 0.896 0.100 0.000
#> GSM182805 2 0.2814 0.8392 0.000 0.820 0.000 0.008 0.172 0.000
#> GSM182806 1 0.0777 0.8988 0.972 0.000 0.004 0.000 0.000 0.024
#> GSM182807 1 0.0000 0.8996 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM182808 1 0.0146 0.8994 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM182809 4 0.7518 -0.2170 0.020 0.000 0.320 0.380 0.096 0.184
#> GSM182810 1 0.7767 0.0400 0.384 0.000 0.340 0.104 0.088 0.084
#> GSM182811 4 0.6598 0.4718 0.256 0.000 0.004 0.512 0.168 0.060
#> GSM182812 4 0.3679 0.7114 0.036 0.000 0.000 0.820 0.084 0.060
#> GSM182813 1 0.0146 0.8994 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM182778 2 0.0000 0.8425 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM182779 5 0.3670 0.7527 0.000 0.000 0.024 0.000 0.736 0.240
#> GSM182780 3 0.5238 -0.4342 0.000 0.000 0.492 0.016 0.056 0.436
#> GSM182781 3 0.2407 0.4612 0.016 0.000 0.904 0.024 0.008 0.048
#> GSM182782 2 0.0000 0.8425 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM182783 6 0.5531 0.4327 0.000 0.000 0.424 0.064 0.028 0.484
#> GSM182784 3 0.4314 -0.1597 0.000 0.000 0.536 0.020 0.000 0.444
#> GSM182785 6 0.5105 0.4875 0.000 0.000 0.432 0.000 0.080 0.488
#> GSM182786 2 0.0000 0.8425 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM182787 6 0.5395 0.6714 0.000 0.000 0.300 0.000 0.144 0.556
#> GSM182788 2 0.0000 0.8425 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM182789 3 0.4807 -0.4373 0.000 0.000 0.484 0.000 0.052 0.464
#> GSM182790 3 0.1950 0.4578 0.000 0.000 0.912 0.024 0.000 0.064
#> GSM182791 3 0.4751 -0.4096 0.000 0.000 0.512 0.008 0.032 0.448
#> GSM182792 3 0.3409 0.1108 0.000 0.000 0.700 0.000 0.000 0.300
#> GSM182793 2 0.4681 0.7651 0.000 0.732 0.000 0.140 0.096 0.032
#> GSM182794 3 0.2176 0.4539 0.000 0.000 0.896 0.024 0.000 0.080
#> GSM182795 3 0.4366 -0.2811 0.000 0.000 0.548 0.000 0.024 0.428
#> GSM182796 5 0.3601 0.6488 0.000 0.040 0.000 0.008 0.792 0.160
#> GSM182797 1 0.0000 0.8996 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM182798 5 0.3601 0.6488 0.000 0.040 0.000 0.008 0.792 0.160
#> GSM182799 6 0.5561 0.4359 0.000 0.000 0.408 0.068 0.028 0.496
#> GSM182800 3 0.6036 0.1031 0.328 0.000 0.548 0.028 0.064 0.032
#> GSM182801 3 0.1341 0.4608 0.000 0.000 0.948 0.028 0.000 0.024
#> GSM182814 1 0.1493 0.8774 0.936 0.000 0.000 0.004 0.004 0.056
#> GSM182815 4 0.1843 0.7311 0.000 0.000 0.004 0.912 0.080 0.004
#> GSM182816 3 0.4158 0.1123 0.416 0.000 0.572 0.004 0.000 0.008
#> GSM182817 5 0.1536 0.7359 0.000 0.040 0.000 0.004 0.940 0.016
#> GSM182818 4 0.1686 0.7263 0.000 0.000 0.000 0.924 0.064 0.012
#> GSM182819 1 0.0291 0.8992 0.992 0.000 0.004 0.000 0.000 0.004
#> GSM182820 1 0.0692 0.8987 0.976 0.000 0.004 0.000 0.000 0.020
#> GSM182821 6 0.5886 0.6456 0.000 0.000 0.252 0.016 0.184 0.548
#> GSM182822 3 0.5422 0.2502 0.108 0.000 0.700 0.024 0.128 0.040
#> GSM182823 1 0.0922 0.8966 0.968 0.000 0.000 0.004 0.004 0.024
#> GSM182824 1 0.0692 0.8983 0.976 0.000 0.000 0.000 0.004 0.020
#> GSM182825 1 0.5773 0.3919 0.604 0.000 0.000 0.248 0.064 0.084
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n stress(p) development.stage(p) k
#> ATC:mclust 66 0.876 4.79e-04 2
#> ATC:mclust 67 0.825 5.46e-06 3
#> ATC:mclust 49 0.754 1.38e-05 4
#> ATC:mclust 68 0.985 3.64e-06 5
#> ATC:mclust 40 0.990 4.70e-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["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 18172 rows and 71 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.910 0.911 0.964 0.5021 0.494 0.494
#> 3 3 0.599 0.790 0.851 0.3076 0.726 0.497
#> 4 4 0.596 0.711 0.839 0.0864 0.917 0.762
#> 5 5 0.562 0.512 0.786 0.0404 0.981 0.935
#> 6 6 0.630 0.635 0.791 0.0445 0.902 0.658
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
#> GSM182755 1 0.0000 0.9798 1.000 0.000
#> GSM182756 1 0.0000 0.9798 1.000 0.000
#> GSM182757 2 0.0000 0.9417 0.000 1.000
#> GSM182758 2 0.4161 0.8787 0.084 0.916
#> GSM182759 2 0.0000 0.9417 0.000 1.000
#> GSM182760 1 0.0000 0.9798 1.000 0.000
#> GSM182761 2 0.0000 0.9417 0.000 1.000
#> GSM182762 1 0.0000 0.9798 1.000 0.000
#> GSM182763 2 0.0000 0.9417 0.000 1.000
#> GSM182764 2 0.0000 0.9417 0.000 1.000
#> GSM182765 2 0.9998 0.0953 0.492 0.508
#> GSM182766 2 0.0000 0.9417 0.000 1.000
#> GSM182767 1 0.5294 0.8438 0.880 0.120
#> GSM182768 1 0.2236 0.9455 0.964 0.036
#> GSM182769 1 0.0000 0.9798 1.000 0.000
#> GSM182770 2 0.0000 0.9417 0.000 1.000
#> GSM182771 2 0.4298 0.8762 0.088 0.912
#> GSM182772 2 0.0000 0.9417 0.000 1.000
#> GSM182773 1 0.0000 0.9798 1.000 0.000
#> GSM182774 1 0.0000 0.9798 1.000 0.000
#> GSM182775 1 0.0000 0.9798 1.000 0.000
#> GSM182776 1 0.0000 0.9798 1.000 0.000
#> GSM182777 1 0.0000 0.9798 1.000 0.000
#> GSM182802 2 0.0000 0.9417 0.000 1.000
#> GSM182803 1 0.0000 0.9798 1.000 0.000
#> GSM182804 2 0.0000 0.9417 0.000 1.000
#> GSM182805 2 0.0000 0.9417 0.000 1.000
#> GSM182806 1 0.0000 0.9798 1.000 0.000
#> GSM182807 1 0.0000 0.9798 1.000 0.000
#> GSM182808 1 0.0000 0.9798 1.000 0.000
#> GSM182809 2 0.2236 0.9185 0.036 0.964
#> GSM182810 1 0.0000 0.9798 1.000 0.000
#> GSM182811 1 0.0000 0.9798 1.000 0.000
#> GSM182812 1 0.0000 0.9798 1.000 0.000
#> GSM182813 1 0.0000 0.9798 1.000 0.000
#> GSM182778 2 0.0000 0.9417 0.000 1.000
#> GSM182779 2 0.0000 0.9417 0.000 1.000
#> GSM182780 2 0.0000 0.9417 0.000 1.000
#> GSM182781 1 0.0000 0.9798 1.000 0.000
#> GSM182782 2 0.0000 0.9417 0.000 1.000
#> GSM182783 2 0.0000 0.9417 0.000 1.000
#> GSM182784 2 0.9323 0.5011 0.348 0.652
#> GSM182785 2 0.0000 0.9417 0.000 1.000
#> GSM182786 2 0.0000 0.9417 0.000 1.000
#> GSM182787 2 0.0000 0.9417 0.000 1.000
#> GSM182788 2 0.0000 0.9417 0.000 1.000
#> GSM182789 2 0.0000 0.9417 0.000 1.000
#> GSM182790 1 0.0000 0.9798 1.000 0.000
#> GSM182791 1 0.9983 -0.0154 0.524 0.476
#> GSM182792 1 0.0000 0.9798 1.000 0.000
#> GSM182793 2 0.0000 0.9417 0.000 1.000
#> GSM182794 1 0.0000 0.9798 1.000 0.000
#> GSM182795 2 0.0938 0.9346 0.012 0.988
#> GSM182796 2 0.0000 0.9417 0.000 1.000
#> GSM182797 1 0.0000 0.9798 1.000 0.000
#> GSM182798 2 0.5294 0.8446 0.120 0.880
#> GSM182799 2 0.0000 0.9417 0.000 1.000
#> GSM182800 1 0.0000 0.9798 1.000 0.000
#> GSM182801 1 0.0000 0.9798 1.000 0.000
#> GSM182814 1 0.0000 0.9798 1.000 0.000
#> GSM182815 2 0.0000 0.9417 0.000 1.000
#> GSM182816 1 0.0000 0.9798 1.000 0.000
#> GSM182817 1 0.2236 0.9458 0.964 0.036
#> GSM182818 2 0.8909 0.5865 0.308 0.692
#> GSM182819 1 0.0000 0.9798 1.000 0.000
#> GSM182820 1 0.0000 0.9798 1.000 0.000
#> GSM182821 2 0.9522 0.4498 0.372 0.628
#> GSM182822 1 0.0000 0.9798 1.000 0.000
#> GSM182823 1 0.0000 0.9798 1.000 0.000
#> GSM182824 1 0.0000 0.9798 1.000 0.000
#> GSM182825 1 0.0000 0.9798 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM182755 1 0.0000 0.913 1.000 0.000 0.000
#> GSM182756 3 0.5216 0.797 0.260 0.000 0.740
#> GSM182757 3 0.5619 0.757 0.012 0.244 0.744
#> GSM182758 3 0.5061 0.775 0.008 0.208 0.784
#> GSM182759 2 0.0747 0.865 0.000 0.984 0.016
#> GSM182760 3 0.5098 0.805 0.248 0.000 0.752
#> GSM182761 3 0.6079 0.493 0.000 0.388 0.612
#> GSM182762 1 0.1643 0.874 0.956 0.000 0.044
#> GSM182763 2 0.3267 0.795 0.000 0.884 0.116
#> GSM182764 2 0.2486 0.843 0.008 0.932 0.060
#> GSM182765 2 0.9410 0.184 0.220 0.504 0.276
#> GSM182766 2 0.1031 0.864 0.000 0.976 0.024
#> GSM182767 3 0.5921 0.816 0.212 0.032 0.756
#> GSM182768 3 0.6107 0.821 0.184 0.052 0.764
#> GSM182769 3 0.5138 0.803 0.252 0.000 0.748
#> GSM182770 2 0.1411 0.863 0.000 0.964 0.036
#> GSM182771 2 0.2339 0.847 0.048 0.940 0.012
#> GSM182772 2 0.0747 0.866 0.000 0.984 0.016
#> GSM182773 3 0.5098 0.805 0.248 0.000 0.752
#> GSM182774 1 0.0000 0.913 1.000 0.000 0.000
#> GSM182775 3 0.5465 0.764 0.288 0.000 0.712
#> GSM182776 1 0.4504 0.658 0.804 0.000 0.196
#> GSM182777 3 0.5327 0.784 0.272 0.000 0.728
#> GSM182802 2 0.1163 0.863 0.000 0.972 0.028
#> GSM182803 1 0.0000 0.913 1.000 0.000 0.000
#> GSM182804 2 0.5503 0.751 0.020 0.772 0.208
#> GSM182805 2 0.1031 0.864 0.000 0.976 0.024
#> GSM182806 1 0.0000 0.913 1.000 0.000 0.000
#> GSM182807 1 0.0000 0.913 1.000 0.000 0.000
#> GSM182808 1 0.0000 0.913 1.000 0.000 0.000
#> GSM182809 2 0.5331 0.774 0.024 0.792 0.184
#> GSM182810 1 0.2959 0.859 0.900 0.000 0.100
#> GSM182811 1 0.5061 0.777 0.784 0.008 0.208
#> GSM182812 1 0.4931 0.777 0.784 0.004 0.212
#> GSM182813 1 0.0000 0.913 1.000 0.000 0.000
#> GSM182778 2 0.1031 0.864 0.000 0.976 0.024
#> GSM182779 2 0.6302 -0.110 0.000 0.520 0.480
#> GSM182780 3 0.4796 0.767 0.000 0.220 0.780
#> GSM182781 3 0.5178 0.800 0.256 0.000 0.744
#> GSM182782 2 0.0892 0.865 0.000 0.980 0.020
#> GSM182783 3 0.4702 0.770 0.000 0.212 0.788
#> GSM182784 3 0.5932 0.800 0.056 0.164 0.780
#> GSM182785 3 0.5115 0.764 0.004 0.228 0.768
#> GSM182786 2 0.0592 0.866 0.000 0.988 0.012
#> GSM182787 2 0.1289 0.863 0.000 0.968 0.032
#> GSM182788 2 0.0592 0.865 0.000 0.988 0.012
#> GSM182789 3 0.4842 0.764 0.000 0.224 0.776
#> GSM182790 3 0.5138 0.803 0.252 0.000 0.748
#> GSM182791 3 0.6424 0.800 0.068 0.180 0.752
#> GSM182792 3 0.5244 0.808 0.240 0.004 0.756
#> GSM182793 2 0.1289 0.864 0.000 0.968 0.032
#> GSM182794 3 0.5138 0.803 0.252 0.000 0.748
#> GSM182795 3 0.4702 0.770 0.000 0.212 0.788
#> GSM182796 2 0.0592 0.863 0.000 0.988 0.012
#> GSM182797 1 0.0000 0.913 1.000 0.000 0.000
#> GSM182798 2 0.4540 0.787 0.124 0.848 0.028
#> GSM182799 3 0.4504 0.772 0.000 0.196 0.804
#> GSM182800 1 0.0000 0.913 1.000 0.000 0.000
#> GSM182801 1 0.6026 0.170 0.624 0.000 0.376
#> GSM182814 1 0.4555 0.790 0.800 0.000 0.200
#> GSM182815 2 0.4931 0.755 0.000 0.768 0.232
#> GSM182816 1 0.0000 0.913 1.000 0.000 0.000
#> GSM182817 1 0.4915 0.783 0.832 0.132 0.036
#> GSM182818 2 0.8876 0.519 0.220 0.576 0.204
#> GSM182819 1 0.0000 0.913 1.000 0.000 0.000
#> GSM182820 1 0.0000 0.913 1.000 0.000 0.000
#> GSM182821 2 0.5541 0.655 0.252 0.740 0.008
#> GSM182822 1 0.0424 0.910 0.992 0.000 0.008
#> GSM182823 1 0.0000 0.913 1.000 0.000 0.000
#> GSM182824 1 0.0000 0.913 1.000 0.000 0.000
#> GSM182825 1 0.4291 0.805 0.820 0.000 0.180
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM182755 1 0.2821 0.7964 0.900 0.004 0.020 0.076
#> GSM182756 3 0.3392 0.8274 0.124 0.000 0.856 0.020
#> GSM182757 2 0.6953 0.3212 0.012 0.480 0.432 0.076
#> GSM182758 3 0.0712 0.8395 0.004 0.008 0.984 0.004
#> GSM182759 2 0.2413 0.7307 0.000 0.916 0.020 0.064
#> GSM182760 3 0.2778 0.8418 0.080 0.004 0.900 0.016
#> GSM182761 2 0.4814 0.5304 0.000 0.676 0.316 0.008
#> GSM182762 1 0.6370 0.4965 0.668 0.004 0.180 0.148
#> GSM182763 2 0.4671 0.6447 0.000 0.752 0.220 0.028
#> GSM182764 2 0.4711 0.6577 0.000 0.784 0.064 0.152
#> GSM182765 2 0.9290 0.1834 0.220 0.448 0.180 0.152
#> GSM182766 2 0.2048 0.7487 0.000 0.928 0.064 0.008
#> GSM182767 3 0.1488 0.8482 0.032 0.000 0.956 0.012
#> GSM182768 3 0.2670 0.8355 0.024 0.000 0.904 0.072
#> GSM182769 3 0.5410 0.7314 0.192 0.000 0.728 0.080
#> GSM182770 2 0.2125 0.7441 0.000 0.920 0.076 0.004
#> GSM182771 2 0.4901 0.6320 0.048 0.784 0.012 0.156
#> GSM182772 2 0.1557 0.7512 0.000 0.944 0.056 0.000
#> GSM182773 3 0.3439 0.8437 0.084 0.000 0.868 0.048
#> GSM182774 1 0.1796 0.8315 0.948 0.004 0.016 0.032
#> GSM182775 3 0.3278 0.8356 0.116 0.000 0.864 0.020
#> GSM182776 1 0.5040 0.3287 0.628 0.000 0.364 0.008
#> GSM182777 3 0.3718 0.7986 0.168 0.000 0.820 0.012
#> GSM182802 2 0.0927 0.7422 0.000 0.976 0.016 0.008
#> GSM182803 1 0.0000 0.8482 1.000 0.000 0.000 0.000
#> GSM182804 4 0.7319 0.7147 0.156 0.384 0.000 0.460
#> GSM182805 2 0.0779 0.7434 0.000 0.980 0.016 0.004
#> GSM182806 1 0.0188 0.8487 0.996 0.000 0.000 0.004
#> GSM182807 1 0.0188 0.8487 0.996 0.000 0.000 0.004
#> GSM182808 1 0.0336 0.8478 0.992 0.000 0.000 0.008
#> GSM182809 4 0.6987 0.7881 0.136 0.260 0.008 0.596
#> GSM182810 1 0.2704 0.7742 0.876 0.000 0.000 0.124
#> GSM182811 1 0.2611 0.7826 0.896 0.008 0.000 0.096
#> GSM182812 1 0.4994 0.0271 0.520 0.000 0.000 0.480
#> GSM182813 1 0.0336 0.8478 0.992 0.000 0.000 0.008
#> GSM182778 2 0.1716 0.7496 0.000 0.936 0.064 0.000
#> GSM182779 2 0.6472 0.5243 0.000 0.640 0.212 0.148
#> GSM182780 3 0.1489 0.8249 0.000 0.044 0.952 0.004
#> GSM182781 3 0.6174 0.1998 0.460 0.004 0.496 0.040
#> GSM182782 2 0.1557 0.7512 0.000 0.944 0.056 0.000
#> GSM182783 3 0.3718 0.7546 0.000 0.012 0.820 0.168
#> GSM182784 3 0.0992 0.8418 0.008 0.004 0.976 0.012
#> GSM182785 3 0.4107 0.7268 0.012 0.128 0.832 0.028
#> GSM182786 2 0.1118 0.7493 0.000 0.964 0.036 0.000
#> GSM182787 2 0.2124 0.7481 0.000 0.924 0.068 0.008
#> GSM182788 2 0.0707 0.7449 0.000 0.980 0.020 0.000
#> GSM182789 3 0.1211 0.8285 0.000 0.040 0.960 0.000
#> GSM182790 3 0.2861 0.8411 0.096 0.000 0.888 0.016
#> GSM182791 3 0.3095 0.8209 0.012 0.020 0.892 0.076
#> GSM182792 3 0.2722 0.8488 0.064 0.000 0.904 0.032
#> GSM182793 2 0.2342 0.7407 0.000 0.912 0.080 0.008
#> GSM182794 3 0.2988 0.8357 0.112 0.000 0.876 0.012
#> GSM182795 3 0.0804 0.8362 0.000 0.008 0.980 0.012
#> GSM182796 2 0.3196 0.6847 0.000 0.856 0.008 0.136
#> GSM182797 1 0.1059 0.8408 0.972 0.000 0.012 0.016
#> GSM182798 2 0.5384 0.5791 0.088 0.748 0.004 0.160
#> GSM182799 3 0.4767 0.6590 0.000 0.020 0.724 0.256
#> GSM182800 1 0.0672 0.8451 0.984 0.000 0.008 0.008
#> GSM182801 3 0.5839 0.4890 0.352 0.000 0.604 0.044
#> GSM182814 1 0.2408 0.7824 0.896 0.000 0.000 0.104
#> GSM182815 4 0.4857 0.6754 0.000 0.324 0.008 0.668
#> GSM182816 1 0.4464 0.6045 0.768 0.000 0.208 0.024
#> GSM182817 1 0.4355 0.5938 0.772 0.212 0.004 0.012
#> GSM182818 4 0.7704 0.6958 0.236 0.196 0.020 0.548
#> GSM182819 1 0.0000 0.8482 1.000 0.000 0.000 0.000
#> GSM182820 1 0.0188 0.8487 0.996 0.000 0.000 0.004
#> GSM182821 2 0.6660 0.2264 0.252 0.628 0.112 0.008
#> GSM182822 1 0.2742 0.8036 0.900 0.000 0.024 0.076
#> GSM182823 1 0.0188 0.8477 0.996 0.000 0.000 0.004
#> GSM182824 1 0.0336 0.8467 0.992 0.000 0.000 0.008
#> GSM182825 1 0.4134 0.6033 0.740 0.000 0.000 0.260
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM182755 1 0.1200 0.8591 0.964 0.000 0.012 0.008 0.016
#> GSM182756 3 0.6268 -0.2534 0.140 0.000 0.508 0.004 0.348
#> GSM182757 2 0.7142 -0.1580 0.016 0.396 0.376 0.004 0.208
#> GSM182758 3 0.4961 -0.3150 0.024 0.008 0.608 0.000 0.360
#> GSM182759 2 0.1701 0.7224 0.000 0.936 0.000 0.016 0.048
#> GSM182760 3 0.2390 0.4939 0.084 0.000 0.896 0.000 0.020
#> GSM182761 2 0.4777 0.3988 0.000 0.620 0.356 0.008 0.016
#> GSM182762 1 0.6396 0.3346 0.568 0.000 0.220 0.012 0.200
#> GSM182763 2 0.4723 0.5377 0.000 0.688 0.272 0.008 0.032
#> GSM182764 2 0.5579 0.5799 0.004 0.660 0.064 0.020 0.252
#> GSM182765 2 0.8638 0.1815 0.180 0.376 0.144 0.020 0.280
#> GSM182766 2 0.0771 0.7379 0.000 0.976 0.020 0.000 0.004
#> GSM182767 3 0.2823 0.4874 0.064 0.004 0.888 0.004 0.040
#> GSM182768 3 0.2665 0.4315 0.020 0.000 0.900 0.032 0.048
#> GSM182769 3 0.7030 -0.2804 0.248 0.000 0.404 0.012 0.336
#> GSM182770 2 0.0671 0.7386 0.000 0.980 0.016 0.000 0.004
#> GSM182771 2 0.6113 0.4990 0.084 0.608 0.008 0.020 0.280
#> GSM182772 2 0.0290 0.7404 0.000 0.992 0.008 0.000 0.000
#> GSM182773 3 0.5040 -0.0315 0.040 0.000 0.664 0.012 0.284
#> GSM182774 1 0.3774 0.7229 0.804 0.000 0.028 0.008 0.160
#> GSM182775 3 0.3022 0.4829 0.136 0.000 0.848 0.004 0.012
#> GSM182776 1 0.4178 0.4751 0.696 0.000 0.292 0.004 0.008
#> GSM182777 3 0.3934 0.4068 0.244 0.000 0.740 0.000 0.016
#> GSM182802 2 0.0162 0.7398 0.000 0.996 0.000 0.000 0.004
#> GSM182803 1 0.0162 0.8713 0.996 0.000 0.000 0.004 0.000
#> GSM182804 4 0.5661 0.6151 0.120 0.272 0.000 0.608 0.000
#> GSM182805 2 0.0000 0.7400 0.000 1.000 0.000 0.000 0.000
#> GSM182806 1 0.0162 0.8713 0.996 0.000 0.000 0.004 0.000
#> GSM182807 1 0.0000 0.8714 1.000 0.000 0.000 0.000 0.000
#> GSM182808 1 0.0000 0.8714 1.000 0.000 0.000 0.000 0.000
#> GSM182809 4 0.5977 0.6492 0.104 0.228 0.012 0.644 0.012
#> GSM182810 1 0.1851 0.8242 0.912 0.000 0.000 0.088 0.000
#> GSM182811 1 0.2852 0.7299 0.828 0.000 0.000 0.172 0.000
#> GSM182812 4 0.4885 0.3077 0.400 0.000 0.000 0.572 0.028
#> GSM182813 1 0.0162 0.8707 0.996 0.000 0.000 0.004 0.000
#> GSM182778 2 0.0771 0.7378 0.000 0.976 0.020 0.000 0.004
#> GSM182779 2 0.6920 0.3921 0.000 0.476 0.196 0.020 0.308
#> GSM182780 3 0.3477 0.3715 0.000 0.112 0.832 0.000 0.056
#> GSM182781 3 0.6741 -0.2749 0.212 0.000 0.400 0.004 0.384
#> GSM182782 2 0.0162 0.7403 0.000 0.996 0.000 0.000 0.004
#> GSM182783 5 0.6524 0.0000 0.000 0.036 0.432 0.084 0.448
#> GSM182784 3 0.2355 0.4567 0.024 0.024 0.916 0.000 0.036
#> GSM182785 3 0.4117 0.3478 0.004 0.160 0.788 0.004 0.044
#> GSM182786 2 0.0162 0.7405 0.000 0.996 0.004 0.000 0.000
#> GSM182787 2 0.1469 0.7284 0.000 0.948 0.036 0.000 0.016
#> GSM182788 2 0.0290 0.7385 0.000 0.992 0.000 0.000 0.008
#> GSM182789 3 0.5268 0.1713 0.000 0.148 0.680 0.000 0.172
#> GSM182790 3 0.5927 0.0288 0.132 0.000 0.592 0.004 0.272
#> GSM182791 3 0.5138 0.3963 0.036 0.060 0.780 0.064 0.060
#> GSM182792 3 0.2976 0.4802 0.064 0.000 0.880 0.012 0.044
#> GSM182793 2 0.1471 0.7314 0.000 0.952 0.024 0.004 0.020
#> GSM182794 3 0.4489 0.4232 0.156 0.000 0.760 0.004 0.080
#> GSM182795 3 0.4748 -0.4734 0.000 0.016 0.596 0.004 0.384
#> GSM182796 2 0.3821 0.6327 0.000 0.764 0.000 0.020 0.216
#> GSM182797 1 0.0162 0.8707 0.996 0.000 0.000 0.004 0.000
#> GSM182798 2 0.5501 0.5256 0.052 0.628 0.000 0.020 0.300
#> GSM182799 3 0.4941 0.1596 0.000 0.024 0.744 0.156 0.076
#> GSM182800 1 0.3768 0.7280 0.812 0.000 0.144 0.008 0.036
#> GSM182801 3 0.4560 0.3561 0.268 0.000 0.700 0.012 0.020
#> GSM182814 1 0.2179 0.8107 0.896 0.000 0.000 0.100 0.004
#> GSM182815 4 0.3308 0.6053 0.000 0.144 0.004 0.832 0.020
#> GSM182816 1 0.1741 0.8402 0.936 0.000 0.040 0.024 0.000
#> GSM182817 1 0.3772 0.6401 0.792 0.172 0.000 0.000 0.036
#> GSM182818 4 0.6975 0.5984 0.124 0.056 0.012 0.584 0.224
#> GSM182819 1 0.0000 0.8714 1.000 0.000 0.000 0.000 0.000
#> GSM182820 1 0.0000 0.8714 1.000 0.000 0.000 0.000 0.000
#> GSM182821 2 0.6380 0.0820 0.324 0.548 0.108 0.008 0.012
#> GSM182822 1 0.1618 0.8505 0.944 0.000 0.008 0.040 0.008
#> GSM182823 1 0.0162 0.8711 0.996 0.000 0.000 0.004 0.000
#> GSM182824 1 0.0290 0.8703 0.992 0.000 0.000 0.008 0.000
#> GSM182825 1 0.3039 0.7092 0.808 0.000 0.000 0.192 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM182755 1 0.0964 0.863249 0.968 0.000 0.016 0.000 0.012 0.004
#> GSM182756 6 0.3988 0.729926 0.072 0.000 0.140 0.000 0.012 0.776
#> GSM182757 6 0.6340 0.399331 0.008 0.240 0.164 0.000 0.040 0.548
#> GSM182758 6 0.3649 0.710332 0.008 0.016 0.204 0.000 0.004 0.768
#> GSM182759 2 0.2558 0.552590 0.000 0.840 0.004 0.000 0.156 0.000
#> GSM182760 3 0.2999 0.695394 0.068 0.000 0.856 0.000 0.008 0.068
#> GSM182761 2 0.4214 -0.022730 0.000 0.528 0.460 0.000 0.008 0.004
#> GSM182762 1 0.6612 -0.000196 0.408 0.000 0.156 0.000 0.380 0.056
#> GSM182763 3 0.4758 0.058883 0.000 0.460 0.500 0.000 0.032 0.008
#> GSM182764 5 0.4935 0.609309 0.004 0.460 0.052 0.000 0.484 0.000
#> GSM182765 5 0.7299 0.606268 0.088 0.220 0.076 0.000 0.520 0.096
#> GSM182766 2 0.0665 0.784773 0.000 0.980 0.008 0.004 0.008 0.000
#> GSM182767 3 0.2014 0.710626 0.032 0.004 0.924 0.000 0.016 0.024
#> GSM182768 3 0.1337 0.698432 0.016 0.008 0.956 0.012 0.000 0.008
#> GSM182769 6 0.4969 0.523060 0.260 0.000 0.100 0.000 0.004 0.636
#> GSM182770 2 0.0912 0.780397 0.000 0.972 0.004 0.012 0.008 0.004
#> GSM182771 5 0.5247 0.710321 0.012 0.384 0.004 0.004 0.548 0.048
#> GSM182772 2 0.0405 0.786075 0.000 0.988 0.004 0.000 0.008 0.000
#> GSM182773 6 0.5666 0.176668 0.084 0.000 0.432 0.016 0.004 0.464
#> GSM182774 1 0.5106 0.349400 0.556 0.000 0.048 0.004 0.380 0.012
#> GSM182775 3 0.2196 0.687809 0.108 0.000 0.884 0.004 0.000 0.004
#> GSM182776 1 0.3622 0.620746 0.760 0.000 0.212 0.000 0.004 0.024
#> GSM182777 3 0.4883 0.512236 0.240 0.000 0.660 0.000 0.008 0.092
#> GSM182802 2 0.0665 0.783853 0.000 0.980 0.000 0.008 0.008 0.004
#> GSM182803 1 0.0405 0.870080 0.988 0.000 0.004 0.000 0.008 0.000
#> GSM182804 4 0.4197 0.575702 0.064 0.176 0.000 0.748 0.012 0.000
#> GSM182805 2 0.0551 0.783288 0.000 0.984 0.000 0.004 0.008 0.004
#> GSM182806 1 0.0436 0.869302 0.988 0.000 0.004 0.000 0.004 0.004
#> GSM182807 1 0.0291 0.869206 0.992 0.000 0.004 0.000 0.000 0.004
#> GSM182808 1 0.0551 0.869415 0.984 0.000 0.004 0.000 0.008 0.004
#> GSM182809 4 0.6144 0.406792 0.104 0.344 0.016 0.512 0.024 0.000
#> GSM182810 1 0.1285 0.847104 0.944 0.000 0.000 0.052 0.004 0.000
#> GSM182811 1 0.2706 0.757519 0.832 0.000 0.000 0.160 0.008 0.000
#> GSM182812 4 0.4901 0.504175 0.260 0.000 0.000 0.648 0.084 0.008
#> GSM182813 1 0.0146 0.869408 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM182778 2 0.0603 0.784029 0.000 0.980 0.016 0.000 0.004 0.000
#> GSM182779 5 0.7048 0.598469 0.000 0.264 0.096 0.000 0.436 0.204
#> GSM182780 3 0.3961 0.635497 0.000 0.112 0.764 0.000 0.000 0.124
#> GSM182781 6 0.3504 0.728380 0.052 0.000 0.112 0.000 0.016 0.820
#> GSM182782 2 0.0291 0.784823 0.000 0.992 0.000 0.000 0.004 0.004
#> GSM182783 6 0.3239 0.675099 0.000 0.016 0.100 0.044 0.000 0.840
#> GSM182784 3 0.3395 0.692500 0.032 0.032 0.840 0.000 0.004 0.092
#> GSM182785 3 0.4614 0.638096 0.004 0.124 0.756 0.004 0.032 0.080
#> GSM182786 2 0.0405 0.784602 0.000 0.988 0.004 0.000 0.008 0.000
#> GSM182787 2 0.1088 0.776117 0.000 0.960 0.024 0.000 0.016 0.000
#> GSM182788 2 0.0405 0.784602 0.000 0.988 0.004 0.000 0.008 0.000
#> GSM182789 3 0.6231 0.205145 0.000 0.192 0.488 0.004 0.016 0.300
#> GSM182790 6 0.5389 0.569152 0.140 0.000 0.272 0.000 0.004 0.584
#> GSM182791 3 0.5628 0.654894 0.036 0.076 0.724 0.084 0.024 0.056
#> GSM182792 3 0.2663 0.708306 0.060 0.004 0.892 0.020 0.012 0.012
#> GSM182793 2 0.1635 0.760553 0.000 0.944 0.012 0.016 0.016 0.012
#> GSM182794 3 0.5560 0.388285 0.172 0.000 0.584 0.000 0.008 0.236
#> GSM182795 6 0.3103 0.708761 0.000 0.008 0.208 0.000 0.000 0.784
#> GSM182796 2 0.4086 -0.554347 0.000 0.528 0.000 0.000 0.464 0.008
#> GSM182797 1 0.0436 0.868725 0.988 0.000 0.004 0.000 0.004 0.004
#> GSM182798 5 0.4338 0.674523 0.016 0.420 0.000 0.000 0.560 0.004
#> GSM182799 3 0.2754 0.631793 0.004 0.008 0.860 0.116 0.000 0.012
#> GSM182800 1 0.3288 0.763711 0.836 0.000 0.056 0.000 0.096 0.012
#> GSM182801 3 0.2700 0.638018 0.156 0.000 0.836 0.004 0.000 0.004
#> GSM182814 1 0.2726 0.787423 0.856 0.000 0.000 0.112 0.032 0.000
#> GSM182815 4 0.1398 0.601357 0.000 0.052 0.000 0.940 0.000 0.008
#> GSM182816 1 0.0982 0.864134 0.968 0.000 0.004 0.020 0.004 0.004
#> GSM182817 1 0.3727 0.634014 0.768 0.188 0.000 0.000 0.040 0.004
#> GSM182818 4 0.6904 0.489252 0.024 0.032 0.016 0.420 0.400 0.108
#> GSM182819 1 0.0291 0.868729 0.992 0.000 0.000 0.004 0.004 0.000
#> GSM182820 1 0.0436 0.868725 0.988 0.000 0.004 0.000 0.004 0.004
#> GSM182821 2 0.4875 0.145763 0.344 0.604 0.032 0.012 0.008 0.000
#> GSM182822 1 0.0820 0.865763 0.972 0.000 0.000 0.016 0.012 0.000
#> GSM182823 1 0.0508 0.867730 0.984 0.000 0.000 0.012 0.004 0.000
#> GSM182824 1 0.0622 0.866797 0.980 0.000 0.000 0.012 0.008 0.000
#> GSM182825 1 0.2092 0.795880 0.876 0.000 0.000 0.124 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 stress(p) development.stage(p) k
#> ATC:NMF 68 0.466 2.64e-02 2
#> ATC:NMF 67 0.900 1.41e-06 3
#> ATC:NMF 63 0.958 6.40e-09 4
#> ATC:NMF 40 0.951 4.54e-05 5
#> ATC:NMF 59 0.958 4.20e-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.
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