Date: 2019-12-25 21:14:01 CET, cola version: 1.3.2
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All available functions which can be applied to this res_list object:
res_list
#> A 'ConsensusPartitionList' object with 24 methods.
#> On a matrix with 51941 rows and 80 columns.
#> Top rows are extracted by 'SD, CV, MAD, ATC' methods.
#> Subgroups are detected by 'hclust, kmeans, skmeans, pam, mclust, NMF' method.
#> Number of partitions are tried for k = 2, 3, 4, 5, 6.
#> Performed in total 30000 partitions by row resampling.
#>
#> Following methods can be applied to this 'ConsensusPartitionList' object:
#> [1] "cola_report" "collect_classes" "collect_plots" "collect_stats"
#> [5] "colnames" "functional_enrichment" "get_anno_col" "get_anno"
#> [9] "get_classes" "get_matrix" "get_membership" "get_stats"
#> [13] "is_best_k" "is_stable_k" "ncol" "nrow"
#> [17] "rownames" "show" "suggest_best_k" "test_to_known_factors"
#> [21] "top_rows_heatmap" "top_rows_overlap"
#>
#> You can get result for a single method by, e.g. object["SD", "hclust"] or object["SD:hclust"]
#> or a subset of methods by object[c("SD", "CV")], c("hclust", "kmeans")]
The call of run_all_consensus_partition_methods() was:
#> run_all_consensus_partition_methods(data = mat, mc.cores = 4, anno = anno)
Dimension of the input matrix:
mat = get_matrix(res_list)
dim(mat)
#> [1] 51941 80
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 | ||
|---|---|---|---|---|---|---|
| ATC:kmeans | 3 | 1.000 | 0.964 | 0.981 | ** | |
| ATC:mclust | 4 | 0.941 | 0.929 | 0.975 | * | |
| CV:skmeans | 4 | 0.941 | 0.924 | 0.967 | * | |
| ATC:skmeans | 3 | 0.930 | 0.941 | 0.976 | * | 2 |
| MAD:mclust | 4 | 0.928 | 0.917 | 0.962 | * | |
| SD:pam | 2 | 0.925 | 0.925 | 0.944 | * | |
| CV:pam | 4 | 0.915 | 0.892 | 0.951 | * | |
| MAD:skmeans | 3 | 0.911 | 0.900 | 0.953 | * | |
| ATC:pam | 3 | 0.907 | 0.909 | 0.965 | * | |
| ATC:NMF | 3 | 0.903 | 0.892 | 0.955 | * | 2 |
| SD:skmeans | 4 | 0.891 | 0.903 | 0.958 | ||
| CV:NMF | 2 | 0.873 | 0.935 | 0.970 | ||
| SD:NMF | 2 | 0.851 | 0.923 | 0.967 | ||
| SD:kmeans | 2 | 0.809 | 0.925 | 0.962 | ||
| MAD:NMF | 2 | 0.802 | 0.925 | 0.968 | ||
| CV:mclust | 4 | 0.801 | 0.904 | 0.946 | ||
| CV:kmeans | 2 | 0.760 | 0.910 | 0.960 | ||
| SD:mclust | 4 | 0.729 | 0.848 | 0.919 | ||
| ATC:hclust | 3 | 0.729 | 0.782 | 0.896 | ||
| MAD:kmeans | 2 | 0.703 | 0.922 | 0.962 | ||
| MAD:pam | 2 | 0.500 | 0.882 | 0.928 | ||
| MAD:hclust | 2 | 0.487 | 0.728 | 0.875 | ||
| CV:hclust | 2 | 0.407 | 0.781 | 0.893 | ||
| SD:hclust | 2 | 0.402 | 0.762 | 0.885 |
**: 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 0.851 0.923 0.967 0.502 0.495 0.495
#> CV:NMF 2 0.873 0.935 0.970 0.505 0.494 0.494
#> MAD:NMF 2 0.802 0.925 0.968 0.504 0.495 0.495
#> ATC:NMF 2 0.949 0.954 0.979 0.494 0.502 0.502
#> SD:skmeans 2 0.685 0.902 0.955 0.505 0.495 0.495
#> CV:skmeans 2 0.828 0.896 0.956 0.506 0.494 0.494
#> MAD:skmeans 2 0.740 0.859 0.943 0.506 0.497 0.497
#> ATC:skmeans 2 1.000 0.970 0.988 0.506 0.494 0.494
#> SD:mclust 2 0.302 0.828 0.873 0.452 0.495 0.495
#> CV:mclust 2 0.419 0.768 0.861 0.348 0.708 0.708
#> MAD:mclust 2 0.463 0.827 0.894 0.303 0.742 0.742
#> ATC:mclust 2 0.369 0.858 0.878 0.331 0.647 0.647
#> SD:kmeans 2 0.809 0.925 0.962 0.501 0.499 0.499
#> CV:kmeans 2 0.760 0.910 0.960 0.501 0.499 0.499
#> MAD:kmeans 2 0.703 0.922 0.962 0.503 0.499 0.499
#> ATC:kmeans 2 0.711 0.862 0.935 0.480 0.497 0.497
#> SD:pam 2 0.925 0.925 0.944 0.470 0.525 0.525
#> CV:pam 2 0.640 0.828 0.905 0.475 0.519 0.519
#> MAD:pam 2 0.500 0.882 0.927 0.476 0.519 0.519
#> ATC:pam 2 0.713 0.915 0.951 0.488 0.494 0.494
#> SD:hclust 2 0.402 0.762 0.885 0.485 0.502 0.502
#> CV:hclust 2 0.407 0.781 0.893 0.470 0.525 0.525
#> MAD:hclust 2 0.487 0.728 0.875 0.486 0.505 0.505
#> ATC:hclust 2 0.873 0.893 0.960 0.348 0.661 0.661
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 0.521 0.672 0.809 0.327 0.745 0.529
#> CV:NMF 3 0.521 0.498 0.739 0.309 0.722 0.497
#> MAD:NMF 3 0.547 0.627 0.830 0.323 0.757 0.547
#> ATC:NMF 3 0.903 0.892 0.955 0.326 0.766 0.564
#> SD:skmeans 3 0.879 0.374 0.744 0.327 0.580 0.328
#> CV:skmeans 3 0.629 0.827 0.848 0.322 0.710 0.481
#> MAD:skmeans 3 0.911 0.900 0.953 0.323 0.721 0.495
#> ATC:skmeans 3 0.930 0.941 0.976 0.265 0.822 0.652
#> SD:mclust 3 0.341 0.707 0.772 0.337 0.732 0.517
#> CV:mclust 3 0.352 0.543 0.669 0.573 0.676 0.584
#> MAD:mclust 3 0.403 0.695 0.820 0.509 0.723 0.655
#> ATC:mclust 3 0.768 0.901 0.926 0.924 0.690 0.530
#> SD:kmeans 3 0.599 0.684 0.752 0.304 0.761 0.557
#> CV:kmeans 3 0.540 0.339 0.630 0.297 0.706 0.477
#> MAD:kmeans 3 0.554 0.683 0.777 0.309 0.795 0.609
#> ATC:kmeans 3 1.000 0.964 0.981 0.368 0.661 0.424
#> SD:pam 3 0.448 0.621 0.806 0.340 0.798 0.621
#> CV:pam 3 0.659 0.757 0.877 0.370 0.811 0.636
#> MAD:pam 3 0.529 0.657 0.818 0.371 0.820 0.653
#> ATC:pam 3 0.907 0.909 0.965 0.351 0.694 0.463
#> SD:hclust 3 0.311 0.566 0.736 0.330 0.841 0.682
#> CV:hclust 3 0.337 0.402 0.662 0.346 0.748 0.545
#> MAD:hclust 3 0.342 0.542 0.724 0.323 0.781 0.587
#> ATC:hclust 3 0.729 0.782 0.896 0.806 0.704 0.552
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.873 0.892 0.953 0.1346 0.803 0.491
#> CV:NMF 4 0.850 0.869 0.946 0.1423 0.811 0.508
#> MAD:NMF 4 0.897 0.914 0.962 0.1336 0.833 0.551
#> ATC:NMF 4 0.694 0.718 0.858 0.0587 0.835 0.608
#> SD:skmeans 4 0.891 0.903 0.958 0.1299 0.740 0.378
#> CV:skmeans 4 0.941 0.924 0.967 0.1333 0.816 0.515
#> MAD:skmeans 4 0.864 0.850 0.941 0.1298 0.832 0.547
#> ATC:skmeans 4 0.856 0.843 0.932 0.1175 0.922 0.784
#> SD:mclust 4 0.729 0.848 0.919 0.2189 0.824 0.545
#> CV:mclust 4 0.801 0.904 0.946 0.3522 0.633 0.359
#> MAD:mclust 4 0.928 0.917 0.962 0.6378 0.572 0.324
#> ATC:mclust 4 0.941 0.929 0.975 0.0557 0.915 0.779
#> SD:kmeans 4 0.860 0.884 0.929 0.1542 0.828 0.544
#> CV:kmeans 4 0.831 0.872 0.925 0.1568 0.777 0.440
#> MAD:kmeans 4 0.870 0.891 0.942 0.1465 0.829 0.550
#> ATC:kmeans 4 0.750 0.704 0.827 0.1107 0.936 0.815
#> SD:pam 4 0.552 0.669 0.843 0.1477 0.787 0.477
#> CV:pam 4 0.915 0.892 0.951 0.1148 0.760 0.428
#> MAD:pam 4 0.525 0.476 0.707 0.1264 0.806 0.504
#> ATC:pam 4 0.773 0.832 0.888 0.0838 0.934 0.815
#> SD:hclust 4 0.508 0.613 0.791 0.1418 0.808 0.509
#> CV:hclust 4 0.437 0.475 0.711 0.1501 0.741 0.387
#> MAD:hclust 4 0.492 0.547 0.751 0.1418 0.819 0.526
#> ATC:hclust 4 0.721 0.726 0.829 0.1281 0.918 0.780
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.732 0.719 0.858 0.0542 0.915 0.682
#> CV:NMF 5 0.856 0.835 0.918 0.0576 0.912 0.670
#> MAD:NMF 5 0.729 0.697 0.840 0.0558 0.915 0.680
#> ATC:NMF 5 0.532 0.457 0.705 0.0747 0.929 0.805
#> SD:skmeans 5 0.828 0.807 0.896 0.0564 0.933 0.735
#> CV:skmeans 5 0.799 0.745 0.845 0.0543 0.950 0.799
#> MAD:skmeans 5 0.839 0.841 0.910 0.0618 0.921 0.694
#> ATC:skmeans 5 0.839 0.776 0.894 0.0338 0.979 0.928
#> SD:mclust 5 0.683 0.715 0.813 0.0432 0.960 0.853
#> CV:mclust 5 0.695 0.679 0.841 0.0384 0.964 0.859
#> MAD:mclust 5 0.847 0.864 0.927 0.0668 0.925 0.712
#> ATC:mclust 5 0.794 0.718 0.840 0.1062 0.897 0.693
#> SD:kmeans 5 0.733 0.667 0.808 0.0607 0.944 0.778
#> CV:kmeans 5 0.749 0.623 0.783 0.0615 0.905 0.646
#> MAD:kmeans 5 0.739 0.721 0.833 0.0599 0.928 0.722
#> ATC:kmeans 5 0.715 0.674 0.786 0.0520 0.972 0.903
#> SD:pam 5 0.855 0.852 0.929 0.0972 0.792 0.388
#> CV:pam 5 0.695 0.539 0.759 0.0886 0.877 0.590
#> MAD:pam 5 0.700 0.511 0.758 0.0805 0.832 0.459
#> ATC:pam 5 0.831 0.877 0.925 0.0977 0.867 0.588
#> SD:hclust 5 0.624 0.637 0.785 0.0677 0.931 0.737
#> CV:hclust 5 0.556 0.564 0.761 0.0749 0.899 0.639
#> MAD:hclust 5 0.621 0.577 0.771 0.0761 0.900 0.631
#> ATC:hclust 5 0.737 0.694 0.821 0.0539 0.934 0.779
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.700 0.562 0.764 0.0388 0.941 0.747
#> CV:NMF 6 0.747 0.618 0.795 0.0390 0.972 0.867
#> MAD:NMF 6 0.678 0.545 0.739 0.0392 0.881 0.517
#> ATC:NMF 6 0.551 0.381 0.618 0.0514 0.886 0.666
#> SD:skmeans 6 0.777 0.708 0.850 0.0377 0.947 0.751
#> CV:skmeans 6 0.762 0.691 0.845 0.0395 0.936 0.707
#> MAD:skmeans 6 0.791 0.650 0.817 0.0366 0.960 0.806
#> ATC:skmeans 6 0.862 0.794 0.882 0.0317 0.941 0.787
#> SD:mclust 6 0.724 0.666 0.767 0.0619 0.916 0.682
#> CV:mclust 6 0.790 0.799 0.839 0.0742 0.918 0.654
#> MAD:mclust 6 0.860 0.880 0.918 0.0345 0.941 0.726
#> ATC:mclust 6 0.704 0.553 0.790 0.0628 0.959 0.839
#> SD:kmeans 6 0.727 0.608 0.786 0.0413 0.932 0.694
#> CV:kmeans 6 0.750 0.667 0.807 0.0427 0.919 0.636
#> MAD:kmeans 6 0.718 0.577 0.760 0.0410 0.947 0.753
#> ATC:kmeans 6 0.720 0.638 0.798 0.0442 0.927 0.731
#> SD:pam 6 0.775 0.753 0.849 0.0473 0.921 0.648
#> CV:pam 6 0.756 0.547 0.779 0.0591 0.863 0.463
#> MAD:pam 6 0.697 0.492 0.731 0.0525 0.883 0.518
#> ATC:pam 6 0.866 0.852 0.897 0.0510 0.932 0.697
#> SD:hclust 6 0.654 0.609 0.725 0.0364 0.963 0.831
#> CV:hclust 6 0.710 0.590 0.783 0.0576 0.949 0.756
#> MAD:hclust 6 0.659 0.533 0.722 0.0413 0.969 0.843
#> ATC:hclust 6 0.765 0.678 0.811 0.0321 0.957 0.831
Following heatmap plots the partition for each combination of methods and the lightness correspond to the silhouette scores for samples in each method. On top the consensus subgroup is inferred from all methods by taking the mean silhouette scores as weight.
collect_stats(res_list, k = 2)
collect_stats(res_list, k = 3)
collect_stats(res_list, k = 4)
collect_stats(res_list, k = 5)
collect_stats(res_list, k = 6)
Collect partitions from all methods:
collect_classes(res_list, k = 2)
collect_classes(res_list, k = 3)
collect_classes(res_list, k = 4)
collect_classes(res_list, k = 5)
collect_classes(res_list, k = 6)
Overlap of top rows from different top-row methods:
top_rows_overlap(res_list, top_n = 1000, method = "euler")
top_rows_overlap(res_list, top_n = 2000, method = "euler")
top_rows_overlap(res_list, top_n = 3000, method = "euler")
top_rows_overlap(res_list, top_n = 4000, method = "euler")
top_rows_overlap(res_list, top_n = 5000, method = "euler")
Also visualize the correspondance of rankings between different top-row methods:
top_rows_overlap(res_list, top_n = 1000, method = "correspondance")
top_rows_overlap(res_list, top_n = 2000, method = "correspondance")
top_rows_overlap(res_list, top_n = 3000, method = "correspondance")
top_rows_overlap(res_list, top_n = 4000, method = "correspondance")
top_rows_overlap(res_list, top_n = 5000, method = "correspondance")
Heatmaps of the top rows:
top_rows_heatmap(res_list, top_n = 1000)
top_rows_heatmap(res_list, top_n = 2000)
top_rows_heatmap(res_list, top_n = 3000)
top_rows_heatmap(res_list, top_n = 4000)
top_rows_heatmap(res_list, top_n = 5000)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res_list, k = 2)
#> n disease.state(p) k
#> SD:NMF 78 1.000 2
#> CV:NMF 79 1.000 2
#> MAD:NMF 78 1.000 2
#> ATC:NMF 79 1.000 2
#> SD:skmeans 79 1.000 2
#> CV:skmeans 74 1.000 2
#> MAD:skmeans 74 1.000 2
#> ATC:skmeans 78 0.692 2
#> SD:mclust 77 1.000 2
#> CV:mclust 80 0.847 2
#> MAD:mclust 79 0.911 2
#> ATC:mclust 80 0.220 2
#> SD:kmeans 80 1.000 2
#> CV:kmeans 79 1.000 2
#> MAD:kmeans 80 1.000 2
#> ATC:kmeans 79 0.718 2
#> SD:pam 79 0.391 2
#> CV:pam 79 0.485 2
#> MAD:pam 79 0.485 2
#> ATC:pam 78 0.925 2
#> SD:hclust 70 0.733 2
#> CV:hclust 74 1.000 2
#> MAD:hclust 66 0.631 2
#> ATC:hclust 75 0.486 2
test_to_known_factors(res_list, k = 3)
#> n disease.state(p) k
#> SD:NMF 69 0.952 3
#> CV:NMF 43 1.000 3
#> MAD:NMF 63 1.000 3
#> ATC:NMF 76 0.257 3
#> SD:skmeans 40 0.945 3
#> CV:skmeans 76 0.837 3
#> MAD:skmeans 76 0.894 3
#> ATC:skmeans 77 0.520 3
#> SD:mclust 69 0.530 3
#> CV:mclust 53 1.000 3
#> MAD:mclust 73 0.164 3
#> ATC:mclust 77 0.130 3
#> SD:kmeans 70 0.925 3
#> CV:kmeans 33 0.447 3
#> MAD:kmeans 71 0.960 3
#> ATC:kmeans 78 0.281 3
#> SD:pam 69 0.443 3
#> CV:pam 70 0.475 3
#> MAD:pam 67 0.447 3
#> ATC:pam 76 0.369 3
#> SD:hclust 63 0.936 3
#> CV:hclust 29 1.000 3
#> MAD:hclust 42 0.562 3
#> ATC:hclust 69 0.213 3
test_to_known_factors(res_list, k = 4)
#> n disease.state(p) k
#> SD:NMF 78 0.570 4
#> CV:NMF 74 0.471 4
#> MAD:NMF 79 0.441 4
#> ATC:NMF 70 0.670 4
#> SD:skmeans 77 0.284 4
#> CV:skmeans 77 0.210 4
#> MAD:skmeans 73 0.553 4
#> ATC:skmeans 75 0.654 4
#> SD:mclust 78 0.598 4
#> CV:mclust 79 0.700 4
#> MAD:mclust 78 0.478 4
#> ATC:mclust 78 0.168 4
#> SD:kmeans 77 0.343 4
#> CV:kmeans 76 0.345 4
#> MAD:kmeans 78 0.350 4
#> ATC:kmeans 62 0.734 4
#> SD:pam 66 0.487 4
#> CV:pam 76 0.537 4
#> MAD:pam 39 0.560 4
#> ATC:pam 76 0.502 4
#> SD:hclust 63 0.911 4
#> CV:hclust 48 0.922 4
#> MAD:hclust 53 0.676 4
#> ATC:hclust 72 0.301 4
test_to_known_factors(res_list, k = 5)
#> n disease.state(p) k
#> SD:NMF 69 0.238 5
#> CV:NMF 76 0.373 5
#> MAD:NMF 63 0.737 5
#> ATC:NMF 45 0.894 5
#> SD:skmeans 73 0.480 5
#> CV:skmeans 71 0.364 5
#> MAD:skmeans 78 0.744 5
#> ATC:skmeans 66 0.876 5
#> SD:mclust 74 0.631 5
#> CV:mclust 66 0.655 5
#> MAD:mclust 78 0.882 5
#> ATC:mclust 67 0.248 5
#> SD:kmeans 64 0.540 5
#> CV:kmeans 58 0.642 5
#> MAD:kmeans 70 0.625 5
#> ATC:kmeans 70 0.230 5
#> SD:pam 75 0.899 5
#> CV:pam 50 0.471 5
#> MAD:pam 44 0.604 5
#> ATC:pam 79 0.660 5
#> SD:hclust 70 0.490 5
#> CV:hclust 57 0.892 5
#> MAD:hclust 52 0.783 5
#> ATC:hclust 64 0.556 5
test_to_known_factors(res_list, k = 6)
#> n disease.state(p) k
#> SD:NMF 57 0.262 6
#> CV:NMF 63 0.220 6
#> MAD:NMF 53 0.221 6
#> ATC:NMF 34 0.742 6
#> SD:skmeans 67 0.216 6
#> CV:skmeans 68 0.171 6
#> MAD:skmeans 62 0.719 6
#> ATC:skmeans 66 0.847 6
#> SD:mclust 73 0.560 6
#> CV:mclust 78 0.676 6
#> MAD:mclust 79 0.840 6
#> ATC:mclust 56 0.439 6
#> SD:kmeans 60 0.234 6
#> CV:kmeans 64 0.531 6
#> MAD:kmeans 60 0.887 6
#> ATC:kmeans 66 0.388 6
#> SD:pam 73 0.398 6
#> CV:pam 59 0.391 6
#> MAD:pam 44 0.430 6
#> ATC:pam 77 0.835 6
#> SD:hclust 64 0.772 6
#> CV:hclust 60 0.523 6
#> MAD:hclust 52 0.692 6
#> ATC:hclust 63 0.586 6
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "hclust"]
# you can also extract it by
# res = res_list["SD:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 80 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 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 0.402 0.762 0.885 0.4848 0.502 0.502
#> 3 3 0.311 0.566 0.736 0.3300 0.841 0.682
#> 4 4 0.508 0.613 0.791 0.1418 0.808 0.509
#> 5 5 0.624 0.637 0.785 0.0677 0.931 0.737
#> 6 6 0.654 0.609 0.725 0.0364 0.963 0.831
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
#> GSM531602 2 0.0000 0.8735 0.000 1.000
#> GSM531604 2 0.7528 0.7205 0.216 0.784
#> GSM531606 2 0.6343 0.7906 0.160 0.840
#> GSM531607 2 0.0000 0.8735 0.000 1.000
#> GSM531608 1 0.7528 0.7302 0.784 0.216
#> GSM531610 2 0.0000 0.8735 0.000 1.000
#> GSM531612 2 0.0000 0.8735 0.000 1.000
#> GSM531613 2 0.0000 0.8735 0.000 1.000
#> GSM531614 2 0.0000 0.8735 0.000 1.000
#> GSM531616 1 0.0000 0.8538 1.000 0.000
#> GSM531618 2 0.7056 0.7620 0.192 0.808
#> GSM531619 1 0.1633 0.8548 0.976 0.024
#> GSM531620 1 0.2423 0.8563 0.960 0.040
#> GSM531623 1 0.0376 0.8546 0.996 0.004
#> GSM531625 1 0.0000 0.8538 1.000 0.000
#> GSM531626 1 0.0000 0.8538 1.000 0.000
#> GSM531632 1 0.0000 0.8538 1.000 0.000
#> GSM531638 1 0.0000 0.8538 1.000 0.000
#> GSM531639 1 0.3431 0.8498 0.936 0.064
#> GSM531641 2 0.0000 0.8735 0.000 1.000
#> GSM531642 2 0.9988 0.0509 0.480 0.520
#> GSM531643 1 0.4431 0.8333 0.908 0.092
#> GSM531644 2 0.9988 0.0509 0.480 0.520
#> GSM531645 2 0.0000 0.8735 0.000 1.000
#> GSM531646 1 0.0000 0.8538 1.000 0.000
#> GSM531647 1 0.0000 0.8538 1.000 0.000
#> GSM531648 2 0.5178 0.8286 0.116 0.884
#> GSM531650 1 0.3114 0.8511 0.944 0.056
#> GSM531651 1 0.0376 0.8546 0.996 0.004
#> GSM531652 2 0.8443 0.6411 0.272 0.728
#> GSM531656 1 0.3274 0.8497 0.940 0.060
#> GSM531659 2 0.8661 0.5993 0.288 0.712
#> GSM531661 1 0.7056 0.7520 0.808 0.192
#> GSM531662 1 0.8386 0.6673 0.732 0.268
#> GSM531663 2 0.5059 0.8237 0.112 0.888
#> GSM531664 1 0.3114 0.8511 0.944 0.056
#> GSM531666 1 0.9850 0.2624 0.572 0.428
#> GSM531667 1 0.8608 0.6544 0.716 0.284
#> GSM531668 2 0.2778 0.8620 0.048 0.952
#> GSM531669 1 0.2423 0.8548 0.960 0.040
#> GSM531671 1 0.8386 0.6673 0.732 0.268
#> GSM531672 2 0.0938 0.8705 0.012 0.988
#> GSM531673 1 0.8386 0.6673 0.732 0.268
#> GSM531676 1 0.9686 0.4327 0.604 0.396
#> GSM531679 2 0.6801 0.7678 0.180 0.820
#> GSM531681 2 0.0000 0.8735 0.000 1.000
#> GSM531682 2 0.6801 0.7678 0.180 0.820
#> GSM531683 2 0.0000 0.8735 0.000 1.000
#> GSM531684 2 0.6438 0.7868 0.164 0.836
#> GSM531685 1 0.5519 0.8156 0.872 0.128
#> GSM531686 2 0.0000 0.8735 0.000 1.000
#> GSM531687 1 0.9686 0.4327 0.604 0.396
#> GSM531688 1 0.5059 0.8255 0.888 0.112
#> GSM531690 2 0.0000 0.8735 0.000 1.000
#> GSM531693 1 0.5059 0.8255 0.888 0.112
#> GSM531695 1 0.9850 0.3450 0.572 0.428
#> GSM531603 2 0.0000 0.8735 0.000 1.000
#> GSM531609 2 0.0000 0.8735 0.000 1.000
#> GSM531611 2 0.0000 0.8735 0.000 1.000
#> GSM531621 1 0.0376 0.8546 0.996 0.004
#> GSM531622 1 0.1633 0.8548 0.976 0.024
#> GSM531628 1 0.3114 0.8511 0.944 0.056
#> GSM531630 1 0.1633 0.8548 0.976 0.024
#> GSM531633 1 0.0376 0.8546 0.996 0.004
#> GSM531635 1 0.0000 0.8538 1.000 0.000
#> GSM531640 1 0.1633 0.8548 0.976 0.024
#> GSM531649 1 0.0000 0.8538 1.000 0.000
#> GSM531653 1 0.0000 0.8538 1.000 0.000
#> GSM531657 2 0.6148 0.7972 0.152 0.848
#> GSM531665 2 0.9460 0.4280 0.364 0.636
#> GSM531670 1 0.3274 0.8497 0.940 0.060
#> GSM531674 1 0.2423 0.8548 0.960 0.040
#> GSM531675 2 0.0000 0.8735 0.000 1.000
#> GSM531677 2 0.3274 0.8530 0.060 0.940
#> GSM531678 2 0.6531 0.7829 0.168 0.832
#> GSM531680 1 0.9710 0.4233 0.600 0.400
#> GSM531689 1 0.9686 0.4327 0.604 0.396
#> GSM531691 1 0.9686 0.4327 0.604 0.396
#> GSM531692 1 0.7745 0.7210 0.772 0.228
#> GSM531694 2 0.0000 0.8735 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM531602 2 0.5919 0.74267 0.276 0.712 0.012
#> GSM531604 2 0.9335 0.58167 0.324 0.492 0.184
#> GSM531606 2 0.8894 0.64416 0.300 0.548 0.152
#> GSM531607 2 0.5919 0.74267 0.276 0.712 0.012
#> GSM531608 3 0.5831 0.62477 0.076 0.128 0.796
#> GSM531610 2 0.0892 0.75334 0.020 0.980 0.000
#> GSM531612 2 0.0892 0.75334 0.020 0.980 0.000
#> GSM531613 2 0.0892 0.75334 0.020 0.980 0.000
#> GSM531614 2 0.0892 0.75334 0.020 0.980 0.000
#> GSM531616 3 0.6244 -0.13067 0.440 0.000 0.560
#> GSM531618 2 0.6332 0.66494 0.088 0.768 0.144
#> GSM531619 3 0.0424 0.72630 0.008 0.000 0.992
#> GSM531620 3 0.3722 0.67438 0.088 0.024 0.888
#> GSM531623 3 0.0592 0.72593 0.012 0.000 0.988
#> GSM531625 3 0.1411 0.71482 0.036 0.000 0.964
#> GSM531626 3 0.1643 0.70972 0.044 0.000 0.956
#> GSM531632 1 0.5706 0.58510 0.680 0.000 0.320
#> GSM531638 3 0.6244 -0.13067 0.440 0.000 0.560
#> GSM531639 3 0.7517 0.08125 0.364 0.048 0.588
#> GSM531641 2 0.0892 0.75334 0.020 0.980 0.000
#> GSM531642 2 0.8869 -0.00308 0.380 0.496 0.124
#> GSM531643 1 0.7447 0.57350 0.652 0.068 0.280
#> GSM531644 2 0.8869 -0.00308 0.380 0.496 0.124
#> GSM531645 2 0.0892 0.75334 0.020 0.980 0.000
#> GSM531646 1 0.5968 0.54503 0.636 0.000 0.364
#> GSM531647 1 0.5706 0.58510 0.680 0.000 0.320
#> GSM531648 2 0.4914 0.70827 0.068 0.844 0.088
#> GSM531650 1 0.6562 0.60354 0.700 0.036 0.264
#> GSM531651 3 0.0592 0.72593 0.012 0.000 0.988
#> GSM531652 2 0.7276 0.53687 0.192 0.704 0.104
#> GSM531656 1 0.7555 0.33039 0.520 0.040 0.440
#> GSM531659 2 0.8808 0.53014 0.164 0.572 0.264
#> GSM531661 3 0.5407 0.63965 0.076 0.104 0.820
#> GSM531662 3 0.7562 0.55552 0.148 0.160 0.692
#> GSM531663 2 0.6111 0.72953 0.112 0.784 0.104
#> GSM531664 1 0.6562 0.60354 0.700 0.036 0.264
#> GSM531666 1 0.9259 0.21574 0.440 0.404 0.156
#> GSM531667 3 0.6935 0.56057 0.088 0.188 0.724
#> GSM531668 2 0.3263 0.75117 0.048 0.912 0.040
#> GSM531669 1 0.5363 0.60861 0.724 0.000 0.276
#> GSM531671 3 0.7617 0.55285 0.152 0.160 0.688
#> GSM531672 2 0.3045 0.76082 0.064 0.916 0.020
#> GSM531673 3 0.7562 0.55552 0.148 0.160 0.692
#> GSM531676 1 0.8427 0.29910 0.612 0.148 0.240
#> GSM531679 2 0.8158 0.63326 0.364 0.556 0.080
#> GSM531681 2 0.4291 0.76372 0.180 0.820 0.000
#> GSM531682 2 0.8158 0.63326 0.364 0.556 0.080
#> GSM531683 2 0.5737 0.74694 0.256 0.732 0.012
#> GSM531684 2 0.8941 0.64036 0.300 0.544 0.156
#> GSM531685 1 0.4702 0.58732 0.788 0.000 0.212
#> GSM531686 2 0.4291 0.76372 0.180 0.820 0.000
#> GSM531687 1 0.8427 0.29910 0.612 0.148 0.240
#> GSM531688 1 0.4399 0.60564 0.812 0.000 0.188
#> GSM531690 2 0.4291 0.76372 0.180 0.820 0.000
#> GSM531693 1 0.4702 0.60071 0.788 0.000 0.212
#> GSM531695 1 0.6625 0.38425 0.736 0.196 0.068
#> GSM531603 2 0.5919 0.74267 0.276 0.712 0.012
#> GSM531609 2 0.0892 0.75334 0.020 0.980 0.000
#> GSM531611 2 0.0892 0.75334 0.020 0.980 0.000
#> GSM531621 3 0.0592 0.72593 0.012 0.000 0.988
#> GSM531622 3 0.0424 0.72630 0.008 0.000 0.992
#> GSM531628 1 0.6562 0.60354 0.700 0.036 0.264
#> GSM531630 3 0.0424 0.72630 0.008 0.000 0.992
#> GSM531633 3 0.0592 0.72593 0.012 0.000 0.988
#> GSM531635 3 0.6274 -0.17795 0.456 0.000 0.544
#> GSM531640 3 0.0424 0.72630 0.008 0.000 0.992
#> GSM531649 1 0.5785 0.57712 0.668 0.000 0.332
#> GSM531653 1 0.5785 0.57712 0.668 0.000 0.332
#> GSM531657 2 0.6181 0.70823 0.072 0.772 0.156
#> GSM531665 2 0.9120 0.37439 0.156 0.504 0.340
#> GSM531670 1 0.7555 0.33039 0.520 0.040 0.440
#> GSM531674 1 0.5363 0.60861 0.724 0.000 0.276
#> GSM531675 2 0.4346 0.76340 0.184 0.816 0.000
#> GSM531677 2 0.5977 0.74332 0.252 0.728 0.020
#> GSM531678 2 0.8964 0.63873 0.296 0.544 0.160
#> GSM531680 1 0.6572 0.43276 0.748 0.172 0.080
#> GSM531689 1 0.8427 0.29910 0.612 0.148 0.240
#> GSM531691 1 0.8427 0.29910 0.612 0.148 0.240
#> GSM531692 1 0.6215 0.04763 0.572 0.000 0.428
#> GSM531694 2 0.5919 0.74267 0.276 0.712 0.012
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM531602 2 0.2775 0.6708 0.000 0.896 0.020 0.084
#> GSM531604 2 0.3552 0.6468 0.024 0.848 0.128 0.000
#> GSM531606 2 0.2345 0.6677 0.000 0.900 0.100 0.000
#> GSM531607 2 0.2843 0.6704 0.000 0.892 0.020 0.088
#> GSM531608 3 0.5309 0.7577 0.020 0.124 0.776 0.080
#> GSM531610 4 0.0000 0.7841 0.000 0.000 0.000 1.000
#> GSM531612 4 0.0000 0.7841 0.000 0.000 0.000 1.000
#> GSM531613 4 0.0000 0.7841 0.000 0.000 0.000 1.000
#> GSM531614 4 0.0000 0.7841 0.000 0.000 0.000 1.000
#> GSM531616 1 0.4564 0.5136 0.672 0.000 0.328 0.000
#> GSM531618 4 0.6653 0.6658 0.104 0.080 0.108 0.708
#> GSM531619 3 0.0000 0.8512 0.000 0.000 1.000 0.000
#> GSM531620 3 0.3877 0.7747 0.124 0.004 0.840 0.032
#> GSM531623 3 0.0707 0.8535 0.020 0.000 0.980 0.000
#> GSM531625 3 0.2469 0.8110 0.108 0.000 0.892 0.000
#> GSM531626 3 0.2589 0.8047 0.116 0.000 0.884 0.000
#> GSM531632 1 0.0188 0.7658 0.996 0.000 0.004 0.000
#> GSM531638 1 0.4564 0.5136 0.672 0.000 0.328 0.000
#> GSM531639 1 0.6414 0.3197 0.544 0.004 0.392 0.060
#> GSM531641 4 0.0000 0.7841 0.000 0.000 0.000 1.000
#> GSM531642 4 0.6093 0.1687 0.456 0.012 0.024 0.508
#> GSM531643 1 0.3027 0.7270 0.888 0.004 0.020 0.088
#> GSM531644 4 0.6093 0.1687 0.456 0.012 0.024 0.508
#> GSM531645 4 0.0000 0.7841 0.000 0.000 0.000 1.000
#> GSM531646 1 0.1389 0.7640 0.952 0.000 0.048 0.000
#> GSM531647 1 0.0188 0.7658 0.996 0.000 0.004 0.000
#> GSM531648 4 0.5034 0.7295 0.096 0.060 0.040 0.804
#> GSM531650 1 0.1557 0.7529 0.944 0.000 0.000 0.056
#> GSM531651 3 0.0707 0.8535 0.020 0.000 0.980 0.000
#> GSM531652 4 0.5468 0.6197 0.248 0.020 0.024 0.708
#> GSM531656 1 0.5109 0.6596 0.744 0.000 0.196 0.060
#> GSM531659 2 0.8860 0.0764 0.052 0.388 0.240 0.320
#> GSM531661 3 0.4714 0.7780 0.016 0.104 0.812 0.068
#> GSM531662 3 0.7588 0.6558 0.084 0.188 0.624 0.104
#> GSM531663 4 0.6543 0.4685 0.016 0.240 0.092 0.652
#> GSM531664 1 0.1557 0.7529 0.944 0.000 0.000 0.056
#> GSM531666 1 0.5837 0.0579 0.552 0.008 0.020 0.420
#> GSM531667 3 0.6380 0.6947 0.028 0.120 0.704 0.148
#> GSM531668 4 0.3661 0.7454 0.040 0.088 0.008 0.864
#> GSM531669 1 0.1356 0.7612 0.960 0.032 0.000 0.008
#> GSM531671 3 0.7645 0.6522 0.088 0.188 0.620 0.104
#> GSM531672 4 0.5626 0.4436 0.012 0.324 0.020 0.644
#> GSM531673 3 0.7588 0.6558 0.084 0.188 0.624 0.104
#> GSM531676 2 0.8162 0.1493 0.376 0.440 0.148 0.036
#> GSM531679 2 0.3477 0.6592 0.088 0.872 0.008 0.032
#> GSM531681 2 0.4697 0.4843 0.000 0.644 0.000 0.356
#> GSM531682 2 0.3477 0.6592 0.088 0.872 0.008 0.032
#> GSM531683 2 0.3160 0.6651 0.000 0.872 0.020 0.108
#> GSM531684 2 0.2345 0.6671 0.000 0.900 0.100 0.000
#> GSM531685 1 0.4627 0.6909 0.808 0.136 0.036 0.020
#> GSM531686 2 0.4697 0.4843 0.000 0.644 0.000 0.356
#> GSM531687 2 0.8162 0.1493 0.376 0.440 0.148 0.036
#> GSM531688 1 0.3160 0.7188 0.872 0.108 0.000 0.020
#> GSM531690 2 0.4406 0.5373 0.000 0.700 0.000 0.300
#> GSM531693 1 0.3853 0.7132 0.848 0.116 0.016 0.020
#> GSM531695 1 0.6206 0.1646 0.540 0.404 0.000 0.056
#> GSM531603 2 0.2843 0.6704 0.000 0.892 0.020 0.088
#> GSM531609 4 0.0000 0.7841 0.000 0.000 0.000 1.000
#> GSM531611 4 0.1211 0.7707 0.000 0.040 0.000 0.960
#> GSM531621 3 0.0707 0.8535 0.020 0.000 0.980 0.000
#> GSM531622 3 0.0000 0.8512 0.000 0.000 1.000 0.000
#> GSM531628 1 0.1557 0.7529 0.944 0.000 0.000 0.056
#> GSM531630 3 0.0000 0.8512 0.000 0.000 1.000 0.000
#> GSM531633 3 0.0707 0.8535 0.020 0.000 0.980 0.000
#> GSM531635 1 0.4431 0.5498 0.696 0.000 0.304 0.000
#> GSM531640 3 0.0000 0.8512 0.000 0.000 1.000 0.000
#> GSM531649 1 0.0592 0.7667 0.984 0.000 0.016 0.000
#> GSM531653 1 0.0592 0.7667 0.984 0.000 0.016 0.000
#> GSM531657 4 0.7084 0.5022 0.016 0.216 0.152 0.616
#> GSM531665 2 0.8944 0.1235 0.056 0.380 0.312 0.252
#> GSM531670 1 0.5109 0.6596 0.744 0.000 0.196 0.060
#> GSM531674 1 0.1356 0.7612 0.960 0.032 0.000 0.008
#> GSM531675 2 0.4382 0.5411 0.000 0.704 0.000 0.296
#> GSM531677 2 0.4801 0.6205 0.048 0.764 0.000 0.188
#> GSM531678 2 0.2654 0.6672 0.000 0.888 0.108 0.004
#> GSM531680 1 0.6645 0.1971 0.548 0.384 0.020 0.048
#> GSM531689 2 0.8162 0.1493 0.376 0.440 0.148 0.036
#> GSM531691 2 0.8162 0.1493 0.376 0.440 0.148 0.036
#> GSM531692 1 0.7912 -0.0274 0.360 0.312 0.328 0.000
#> GSM531694 2 0.2775 0.6708 0.000 0.896 0.020 0.084
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM531602 2 0.0000 0.6925 0.000 1.000 0.000 0.000 0.000
#> GSM531604 2 0.4073 0.5369 0.000 0.752 0.032 0.000 0.216
#> GSM531606 2 0.3359 0.6089 0.000 0.816 0.020 0.000 0.164
#> GSM531607 2 0.0162 0.6930 0.000 0.996 0.000 0.004 0.000
#> GSM531608 3 0.5692 0.7056 0.004 0.124 0.696 0.028 0.148
#> GSM531610 4 0.0404 0.7982 0.000 0.012 0.000 0.988 0.000
#> GSM531612 4 0.0404 0.7982 0.000 0.012 0.000 0.988 0.000
#> GSM531613 4 0.0404 0.7982 0.000 0.012 0.000 0.988 0.000
#> GSM531614 4 0.0404 0.7982 0.000 0.012 0.000 0.988 0.000
#> GSM531616 1 0.4437 0.5229 0.664 0.000 0.316 0.000 0.020
#> GSM531618 4 0.7871 0.6143 0.092 0.108 0.100 0.576 0.124
#> GSM531619 3 0.0290 0.8221 0.000 0.008 0.992 0.000 0.000
#> GSM531620 3 0.3534 0.7566 0.108 0.004 0.844 0.012 0.032
#> GSM531623 3 0.0404 0.8228 0.012 0.000 0.988 0.000 0.000
#> GSM531625 3 0.2616 0.7753 0.100 0.000 0.880 0.000 0.020
#> GSM531626 3 0.2722 0.7697 0.108 0.000 0.872 0.000 0.020
#> GSM531632 1 0.0162 0.7258 0.996 0.000 0.000 0.000 0.004
#> GSM531638 1 0.4437 0.5229 0.664 0.000 0.316 0.000 0.020
#> GSM531639 1 0.6006 0.3070 0.524 0.004 0.400 0.036 0.036
#> GSM531641 4 0.0404 0.7982 0.000 0.012 0.000 0.988 0.000
#> GSM531642 1 0.6621 0.0136 0.440 0.004 0.024 0.432 0.100
#> GSM531643 1 0.3042 0.7166 0.880 0.000 0.020 0.056 0.044
#> GSM531644 1 0.6621 0.0136 0.440 0.004 0.024 0.432 0.100
#> GSM531645 4 0.0404 0.7982 0.000 0.012 0.000 0.988 0.000
#> GSM531646 1 0.1399 0.7263 0.952 0.000 0.028 0.000 0.020
#> GSM531647 1 0.0162 0.7258 0.996 0.000 0.000 0.000 0.004
#> GSM531648 4 0.6350 0.6891 0.080 0.072 0.032 0.688 0.128
#> GSM531650 1 0.1753 0.7262 0.936 0.000 0.000 0.032 0.032
#> GSM531651 3 0.0404 0.8228 0.012 0.000 0.988 0.000 0.000
#> GSM531652 4 0.6594 0.5081 0.232 0.012 0.024 0.596 0.136
#> GSM531656 1 0.4879 0.6595 0.728 0.000 0.204 0.036 0.032
#> GSM531659 2 0.8282 0.1474 0.000 0.392 0.168 0.216 0.224
#> GSM531661 3 0.4944 0.7400 0.004 0.112 0.760 0.024 0.100
#> GSM531662 3 0.7274 0.5706 0.020 0.140 0.520 0.036 0.284
#> GSM531663 4 0.6527 0.4357 0.000 0.260 0.048 0.584 0.108
#> GSM531664 1 0.1753 0.7262 0.936 0.000 0.000 0.032 0.032
#> GSM531666 1 0.6155 0.2739 0.544 0.000 0.020 0.348 0.088
#> GSM531667 3 0.6659 0.6528 0.004 0.140 0.628 0.076 0.152
#> GSM531668 4 0.5233 0.7063 0.012 0.108 0.008 0.728 0.144
#> GSM531669 1 0.2583 0.6777 0.864 0.000 0.000 0.004 0.132
#> GSM531671 3 0.7337 0.5692 0.024 0.140 0.520 0.036 0.280
#> GSM531672 4 0.5751 0.3294 0.000 0.400 0.012 0.528 0.060
#> GSM531673 3 0.7274 0.5706 0.020 0.140 0.520 0.036 0.284
#> GSM531676 5 0.4520 0.8049 0.020 0.200 0.032 0.000 0.748
#> GSM531679 2 0.4016 0.5530 0.000 0.716 0.000 0.012 0.272
#> GSM531681 2 0.4754 0.5810 0.000 0.684 0.000 0.264 0.052
#> GSM531682 2 0.4016 0.5530 0.000 0.716 0.000 0.012 0.272
#> GSM531683 2 0.1408 0.6839 0.000 0.948 0.000 0.008 0.044
#> GSM531684 2 0.3438 0.6034 0.000 0.808 0.020 0.000 0.172
#> GSM531685 1 0.4849 0.2552 0.548 0.016 0.000 0.004 0.432
#> GSM531686 2 0.4754 0.5810 0.000 0.684 0.000 0.264 0.052
#> GSM531687 5 0.4520 0.8049 0.020 0.200 0.032 0.000 0.748
#> GSM531688 1 0.3875 0.5892 0.756 0.012 0.000 0.004 0.228
#> GSM531690 2 0.4433 0.6209 0.000 0.740 0.000 0.200 0.060
#> GSM531693 1 0.4044 0.5718 0.732 0.012 0.000 0.004 0.252
#> GSM531695 5 0.6456 0.6034 0.236 0.232 0.000 0.004 0.528
#> GSM531603 2 0.0162 0.6930 0.000 0.996 0.000 0.004 0.000
#> GSM531609 4 0.0404 0.7982 0.000 0.012 0.000 0.988 0.000
#> GSM531611 4 0.1430 0.7833 0.000 0.052 0.000 0.944 0.004
#> GSM531621 3 0.0404 0.8228 0.012 0.000 0.988 0.000 0.000
#> GSM531622 3 0.0290 0.8221 0.000 0.008 0.992 0.000 0.000
#> GSM531628 1 0.1753 0.7262 0.936 0.000 0.000 0.032 0.032
#> GSM531630 3 0.0290 0.8221 0.000 0.008 0.992 0.000 0.000
#> GSM531633 3 0.0404 0.8228 0.012 0.000 0.988 0.000 0.000
#> GSM531635 1 0.4297 0.5615 0.692 0.000 0.288 0.000 0.020
#> GSM531640 3 0.0290 0.8221 0.000 0.008 0.992 0.000 0.000
#> GSM531649 1 0.0510 0.7246 0.984 0.000 0.000 0.000 0.016
#> GSM531653 1 0.0510 0.7246 0.984 0.000 0.000 0.000 0.016
#> GSM531657 4 0.7494 0.4714 0.004 0.244 0.116 0.520 0.116
#> GSM531665 2 0.8309 0.1570 0.000 0.376 0.228 0.156 0.240
#> GSM531670 1 0.4879 0.6595 0.728 0.000 0.204 0.036 0.032
#> GSM531674 1 0.2583 0.6777 0.864 0.000 0.000 0.004 0.132
#> GSM531675 2 0.4400 0.6238 0.000 0.744 0.000 0.196 0.060
#> GSM531677 2 0.4322 0.6342 0.000 0.768 0.000 0.088 0.144
#> GSM531678 2 0.3632 0.6012 0.000 0.800 0.020 0.004 0.176
#> GSM531680 5 0.6103 0.6709 0.192 0.216 0.000 0.004 0.588
#> GSM531689 5 0.4520 0.8049 0.020 0.200 0.032 0.000 0.748
#> GSM531691 5 0.4520 0.8049 0.020 0.200 0.032 0.000 0.748
#> GSM531692 5 0.4673 0.6044 0.028 0.096 0.100 0.000 0.776
#> GSM531694 2 0.0000 0.6925 0.000 1.000 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
#> GSM531602 2 0.0260 0.6964 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM531604 2 0.3564 0.5474 0.000 0.724 0.000 0.000 0.264 0.012
#> GSM531606 2 0.2814 0.6223 0.000 0.820 0.000 0.000 0.172 0.008
#> GSM531607 2 0.0603 0.6949 0.000 0.980 0.000 0.004 0.000 0.016
#> GSM531608 3 0.5431 0.5907 0.000 0.064 0.632 0.000 0.056 0.248
#> GSM531610 4 0.0000 0.9113 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531612 4 0.0000 0.9113 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531613 4 0.0000 0.9113 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531614 4 0.0000 0.9113 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531616 1 0.4670 0.5202 0.640 0.000 0.308 0.000 0.020 0.032
#> GSM531618 6 0.6845 0.5535 0.076 0.052 0.084 0.236 0.000 0.552
#> GSM531619 3 0.0547 0.7840 0.000 0.000 0.980 0.000 0.000 0.020
#> GSM531620 3 0.3150 0.7077 0.088 0.000 0.844 0.000 0.008 0.060
#> GSM531623 3 0.0146 0.7849 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM531625 3 0.2629 0.7298 0.080 0.000 0.880 0.000 0.020 0.020
#> GSM531626 3 0.2734 0.7240 0.088 0.000 0.872 0.000 0.020 0.020
#> GSM531632 1 0.0405 0.7159 0.988 0.000 0.000 0.000 0.008 0.004
#> GSM531638 1 0.4670 0.5202 0.640 0.000 0.308 0.000 0.020 0.032
#> GSM531639 1 0.5363 0.2622 0.496 0.000 0.404 0.000 0.004 0.096
#> GSM531641 4 0.0000 0.9113 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531642 1 0.6172 -0.0236 0.428 0.000 0.016 0.180 0.000 0.376
#> GSM531643 1 0.2404 0.6892 0.872 0.000 0.016 0.000 0.000 0.112
#> GSM531644 1 0.6172 -0.0236 0.428 0.000 0.016 0.180 0.000 0.376
#> GSM531645 4 0.0000 0.9113 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531646 1 0.1802 0.7141 0.932 0.000 0.020 0.000 0.024 0.024
#> GSM531647 1 0.0405 0.7159 0.988 0.000 0.000 0.000 0.008 0.004
#> GSM531648 6 0.5596 0.4963 0.072 0.016 0.020 0.296 0.000 0.596
#> GSM531650 1 0.1267 0.7077 0.940 0.000 0.000 0.000 0.000 0.060
#> GSM531651 3 0.0146 0.7849 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM531652 6 0.5976 0.4326 0.224 0.000 0.016 0.224 0.000 0.536
#> GSM531656 1 0.4411 0.6204 0.712 0.000 0.204 0.000 0.004 0.080
#> GSM531659 6 0.8149 0.2828 0.000 0.292 0.120 0.092 0.124 0.372
#> GSM531661 3 0.4738 0.6519 0.000 0.056 0.712 0.000 0.040 0.192
#> GSM531662 3 0.6774 0.4151 0.004 0.068 0.464 0.000 0.156 0.308
#> GSM531663 4 0.6376 0.0178 0.000 0.236 0.008 0.524 0.028 0.204
#> GSM531664 1 0.1267 0.7077 0.940 0.000 0.000 0.000 0.000 0.060
#> GSM531666 1 0.5717 0.2274 0.536 0.000 0.016 0.124 0.000 0.324
#> GSM531667 3 0.6076 0.5009 0.000 0.080 0.568 0.012 0.052 0.288
#> GSM531668 6 0.4101 0.4583 0.000 0.028 0.000 0.308 0.000 0.664
#> GSM531669 1 0.2821 0.6596 0.832 0.000 0.000 0.000 0.152 0.016
#> GSM531671 3 0.6847 0.4133 0.008 0.068 0.464 0.000 0.152 0.308
#> GSM531672 2 0.6819 -0.3787 0.008 0.336 0.004 0.312 0.016 0.324
#> GSM531673 3 0.6774 0.4151 0.004 0.068 0.464 0.000 0.156 0.308
#> GSM531676 5 0.2581 0.8126 0.000 0.128 0.000 0.000 0.856 0.016
#> GSM531679 2 0.4869 0.5471 0.000 0.628 0.000 0.000 0.276 0.096
#> GSM531681 2 0.5779 0.5763 0.000 0.596 0.000 0.260 0.084 0.060
#> GSM531682 2 0.4869 0.5471 0.000 0.628 0.000 0.000 0.276 0.096
#> GSM531683 2 0.2226 0.6924 0.000 0.904 0.000 0.008 0.060 0.028
#> GSM531684 2 0.2882 0.6176 0.000 0.812 0.000 0.000 0.180 0.008
#> GSM531685 1 0.4651 0.1824 0.484 0.000 0.000 0.000 0.476 0.040
#> GSM531686 2 0.5779 0.5763 0.000 0.596 0.000 0.260 0.084 0.060
#> GSM531687 5 0.2581 0.8126 0.000 0.128 0.000 0.000 0.856 0.016
#> GSM531688 1 0.3841 0.5593 0.716 0.000 0.000 0.000 0.256 0.028
#> GSM531690 2 0.5612 0.6185 0.000 0.648 0.000 0.188 0.084 0.080
#> GSM531693 1 0.4151 0.5404 0.684 0.000 0.000 0.000 0.276 0.040
#> GSM531695 5 0.6275 0.6116 0.196 0.144 0.000 0.000 0.576 0.084
#> GSM531603 2 0.0603 0.6949 0.000 0.980 0.000 0.004 0.000 0.016
#> GSM531609 4 0.0000 0.9113 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531611 4 0.1257 0.8695 0.000 0.020 0.000 0.952 0.000 0.028
#> GSM531621 3 0.0146 0.7849 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM531622 3 0.0547 0.7840 0.000 0.000 0.980 0.000 0.000 0.020
#> GSM531628 1 0.1267 0.7077 0.940 0.000 0.000 0.000 0.000 0.060
#> GSM531630 3 0.0547 0.7840 0.000 0.000 0.980 0.000 0.000 0.020
#> GSM531633 3 0.0146 0.7849 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM531635 1 0.4414 0.5591 0.672 0.000 0.284 0.000 0.016 0.028
#> GSM531640 3 0.0547 0.7840 0.000 0.000 0.980 0.000 0.000 0.020
#> GSM531649 1 0.0909 0.7146 0.968 0.000 0.000 0.000 0.020 0.012
#> GSM531653 1 0.0909 0.7146 0.968 0.000 0.000 0.000 0.020 0.012
#> GSM531657 6 0.7265 0.4945 0.000 0.172 0.092 0.248 0.020 0.468
#> GSM531665 6 0.8177 0.2747 0.000 0.272 0.172 0.056 0.144 0.356
#> GSM531670 1 0.4411 0.6204 0.712 0.000 0.204 0.000 0.004 0.080
#> GSM531674 1 0.2821 0.6596 0.832 0.000 0.000 0.000 0.152 0.016
#> GSM531675 2 0.5584 0.6213 0.000 0.652 0.000 0.184 0.084 0.080
#> GSM531677 2 0.5500 0.6115 0.000 0.668 0.000 0.076 0.156 0.100
#> GSM531678 2 0.3329 0.6198 0.000 0.792 0.000 0.004 0.184 0.020
#> GSM531680 5 0.5316 0.6877 0.136 0.144 0.000 0.000 0.676 0.044
#> GSM531689 5 0.2581 0.8126 0.000 0.128 0.000 0.000 0.856 0.016
#> GSM531691 5 0.2664 0.8076 0.000 0.136 0.000 0.000 0.848 0.016
#> GSM531692 5 0.3198 0.6038 0.004 0.008 0.012 0.000 0.816 0.160
#> GSM531694 2 0.0260 0.6964 0.000 0.992 0.000 0.000 0.000 0.008
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> SD:hclust 70 0.733 2
#> SD:hclust 63 0.936 3
#> SD:hclust 63 0.911 4
#> SD:hclust 70 0.490 5
#> SD:hclust 64 0.772 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "kmeans"]
# you can also extract it by
# res = res_list["SD:kmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 80 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 0.809 0.925 0.962 0.5006 0.499 0.499
#> 3 3 0.599 0.684 0.752 0.3038 0.761 0.557
#> 4 4 0.860 0.884 0.929 0.1542 0.828 0.544
#> 5 5 0.733 0.667 0.808 0.0607 0.944 0.778
#> 6 6 0.727 0.608 0.786 0.0413 0.932 0.694
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
#> GSM531602 2 0.0376 0.951 0.004 0.996
#> GSM531604 2 0.6623 0.813 0.172 0.828
#> GSM531606 2 0.0376 0.951 0.004 0.996
#> GSM531607 2 0.0376 0.951 0.004 0.996
#> GSM531608 1 0.8443 0.658 0.728 0.272
#> GSM531610 2 0.0000 0.951 0.000 1.000
#> GSM531612 2 0.0000 0.951 0.000 1.000
#> GSM531613 2 0.0000 0.951 0.000 1.000
#> GSM531614 2 0.0000 0.951 0.000 1.000
#> GSM531616 1 0.0000 0.966 1.000 0.000
#> GSM531618 1 0.8016 0.703 0.756 0.244
#> GSM531619 1 0.6712 0.795 0.824 0.176
#> GSM531620 1 0.0000 0.966 1.000 0.000
#> GSM531623 1 0.0000 0.966 1.000 0.000
#> GSM531625 1 0.0000 0.966 1.000 0.000
#> GSM531626 1 0.0000 0.966 1.000 0.000
#> GSM531632 1 0.0376 0.966 0.996 0.004
#> GSM531638 1 0.0000 0.966 1.000 0.000
#> GSM531639 1 0.0000 0.966 1.000 0.000
#> GSM531641 2 0.0376 0.951 0.004 0.996
#> GSM531642 1 0.0376 0.966 0.996 0.004
#> GSM531643 1 0.0376 0.966 0.996 0.004
#> GSM531644 1 0.0376 0.966 0.996 0.004
#> GSM531645 2 0.0000 0.951 0.000 1.000
#> GSM531646 1 0.0376 0.966 0.996 0.004
#> GSM531647 1 0.0376 0.966 0.996 0.004
#> GSM531648 2 0.2423 0.921 0.040 0.960
#> GSM531650 1 0.0376 0.966 0.996 0.004
#> GSM531651 1 0.0000 0.966 1.000 0.000
#> GSM531652 1 0.0376 0.966 0.996 0.004
#> GSM531656 1 0.0000 0.966 1.000 0.000
#> GSM531659 2 0.0000 0.951 0.000 1.000
#> GSM531661 1 0.1414 0.954 0.980 0.020
#> GSM531662 1 0.0376 0.965 0.996 0.004
#> GSM531663 2 0.0376 0.951 0.004 0.996
#> GSM531664 1 0.0376 0.966 0.996 0.004
#> GSM531666 1 0.0376 0.966 0.996 0.004
#> GSM531667 1 0.7219 0.764 0.800 0.200
#> GSM531668 2 0.0376 0.951 0.004 0.996
#> GSM531669 1 0.0376 0.966 0.996 0.004
#> GSM531671 1 0.0376 0.966 0.996 0.004
#> GSM531672 2 0.0376 0.951 0.004 0.996
#> GSM531673 1 0.0376 0.965 0.996 0.004
#> GSM531676 2 0.9209 0.557 0.336 0.664
#> GSM531679 2 0.0000 0.951 0.000 1.000
#> GSM531681 2 0.0000 0.951 0.000 1.000
#> GSM531682 2 0.0000 0.951 0.000 1.000
#> GSM531683 2 0.0376 0.951 0.004 0.996
#> GSM531684 2 0.0376 0.951 0.004 0.996
#> GSM531685 1 0.2603 0.936 0.956 0.044
#> GSM531686 2 0.0000 0.951 0.000 1.000
#> GSM531687 2 0.7883 0.731 0.236 0.764
#> GSM531688 1 0.2603 0.936 0.956 0.044
#> GSM531690 2 0.0000 0.951 0.000 1.000
#> GSM531693 1 0.0376 0.966 0.996 0.004
#> GSM531695 2 0.7453 0.764 0.212 0.788
#> GSM531603 2 0.0376 0.951 0.004 0.996
#> GSM531609 2 0.0000 0.951 0.000 1.000
#> GSM531611 2 0.0000 0.951 0.000 1.000
#> GSM531621 1 0.0000 0.966 1.000 0.000
#> GSM531622 1 0.2236 0.941 0.964 0.036
#> GSM531628 1 0.0376 0.966 0.996 0.004
#> GSM531630 1 0.0000 0.966 1.000 0.000
#> GSM531633 1 0.0000 0.966 1.000 0.000
#> GSM531635 1 0.0376 0.966 0.996 0.004
#> GSM531640 1 0.7219 0.764 0.800 0.200
#> GSM531649 1 0.0376 0.966 0.996 0.004
#> GSM531653 1 0.0376 0.966 0.996 0.004
#> GSM531657 2 0.0376 0.951 0.004 0.996
#> GSM531665 1 0.0672 0.965 0.992 0.008
#> GSM531670 1 0.0000 0.966 1.000 0.000
#> GSM531674 1 0.0376 0.966 0.996 0.004
#> GSM531675 2 0.0000 0.951 0.000 1.000
#> GSM531677 2 0.0000 0.951 0.000 1.000
#> GSM531678 2 0.0376 0.951 0.004 0.996
#> GSM531680 2 0.7219 0.778 0.200 0.800
#> GSM531689 2 0.6531 0.813 0.168 0.832
#> GSM531691 2 0.7299 0.778 0.204 0.796
#> GSM531692 1 0.2603 0.934 0.956 0.044
#> GSM531694 2 0.0376 0.951 0.004 0.996
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM531602 2 0.2066 0.7158 0.000 0.940 0.060
#> GSM531604 2 0.4974 0.5366 0.000 0.764 0.236
#> GSM531606 2 0.2261 0.7121 0.000 0.932 0.068
#> GSM531607 2 0.2066 0.7158 0.000 0.940 0.060
#> GSM531608 3 0.6473 0.8859 0.332 0.016 0.652
#> GSM531610 2 0.6154 0.7442 0.000 0.592 0.408
#> GSM531612 2 0.6950 0.7368 0.020 0.572 0.408
#> GSM531613 2 0.6062 0.7506 0.000 0.616 0.384
#> GSM531614 2 0.6950 0.7368 0.020 0.572 0.408
#> GSM531616 3 0.6274 0.7931 0.456 0.000 0.544
#> GSM531618 2 0.9171 0.3156 0.312 0.516 0.172
#> GSM531619 3 0.6470 0.9031 0.356 0.012 0.632
#> GSM531620 3 0.6008 0.8979 0.372 0.000 0.628
#> GSM531623 3 0.6470 0.9031 0.356 0.012 0.632
#> GSM531625 3 0.6267 0.7996 0.452 0.000 0.548
#> GSM531626 3 0.6260 0.8044 0.448 0.000 0.552
#> GSM531632 1 0.0000 0.7391 1.000 0.000 0.000
#> GSM531638 3 0.6267 0.7996 0.452 0.000 0.548
#> GSM531639 1 0.5905 -0.2668 0.648 0.000 0.352
#> GSM531641 2 0.6950 0.7368 0.020 0.572 0.408
#> GSM531642 1 0.4605 0.5300 0.796 0.000 0.204
#> GSM531643 1 0.0892 0.7396 0.980 0.000 0.020
#> GSM531644 1 0.1643 0.7279 0.956 0.000 0.044
#> GSM531645 2 0.6950 0.7368 0.020 0.572 0.408
#> GSM531646 1 0.0000 0.7391 1.000 0.000 0.000
#> GSM531647 1 0.0000 0.7391 1.000 0.000 0.000
#> GSM531648 2 0.6910 0.7393 0.020 0.584 0.396
#> GSM531650 1 0.0892 0.7396 0.980 0.000 0.020
#> GSM531651 3 0.5988 0.8997 0.368 0.000 0.632
#> GSM531652 1 0.2356 0.7107 0.928 0.000 0.072
#> GSM531656 1 0.3267 0.5869 0.884 0.000 0.116
#> GSM531659 2 0.6095 0.7473 0.000 0.608 0.392
#> GSM531661 3 0.6543 0.8968 0.344 0.016 0.640
#> GSM531662 3 0.6543 0.8968 0.344 0.016 0.640
#> GSM531663 2 0.6154 0.7442 0.000 0.592 0.408
#> GSM531664 1 0.0892 0.7396 0.980 0.000 0.020
#> GSM531666 1 0.1860 0.7228 0.948 0.000 0.052
#> GSM531667 3 0.6470 0.9031 0.356 0.012 0.632
#> GSM531668 2 0.6235 0.7401 0.000 0.564 0.436
#> GSM531669 1 0.0000 0.7391 1.000 0.000 0.000
#> GSM531671 1 0.6154 -0.4619 0.592 0.000 0.408
#> GSM531672 2 0.6008 0.7527 0.000 0.628 0.372
#> GSM531673 3 0.7306 0.8674 0.340 0.044 0.616
#> GSM531676 1 0.6688 0.4358 0.580 0.408 0.012
#> GSM531679 2 0.2261 0.7121 0.000 0.932 0.068
#> GSM531681 2 0.5497 0.7580 0.000 0.708 0.292
#> GSM531682 2 0.2261 0.7121 0.000 0.932 0.068
#> GSM531683 2 0.1964 0.7166 0.000 0.944 0.056
#> GSM531684 2 0.6267 0.0576 0.000 0.548 0.452
#> GSM531685 1 0.6467 0.4674 0.604 0.388 0.008
#> GSM531686 2 0.5465 0.7580 0.000 0.712 0.288
#> GSM531687 1 0.6688 0.4358 0.580 0.408 0.012
#> GSM531688 1 0.6155 0.5170 0.664 0.328 0.008
#> GSM531690 2 0.5363 0.7586 0.000 0.724 0.276
#> GSM531693 1 0.0424 0.7376 0.992 0.000 0.008
#> GSM531695 1 0.6359 0.4890 0.628 0.364 0.008
#> GSM531603 2 0.2066 0.7158 0.000 0.940 0.060
#> GSM531609 2 0.6950 0.7368 0.020 0.572 0.408
#> GSM531611 2 0.6896 0.7435 0.020 0.588 0.392
#> GSM531621 3 0.6008 0.8979 0.372 0.000 0.628
#> GSM531622 3 0.6470 0.9031 0.356 0.012 0.632
#> GSM531628 1 0.0892 0.7396 0.980 0.000 0.020
#> GSM531630 3 0.6470 0.9031 0.356 0.012 0.632
#> GSM531633 3 0.6008 0.8979 0.372 0.000 0.628
#> GSM531635 1 0.0000 0.7391 1.000 0.000 0.000
#> GSM531640 3 0.6404 0.8940 0.344 0.012 0.644
#> GSM531649 1 0.0000 0.7391 1.000 0.000 0.000
#> GSM531653 1 0.0000 0.7391 1.000 0.000 0.000
#> GSM531657 2 0.6111 0.7461 0.000 0.604 0.396
#> GSM531665 1 0.4802 0.5261 0.824 0.020 0.156
#> GSM531670 1 0.3267 0.5869 0.884 0.000 0.116
#> GSM531674 1 0.0000 0.7391 1.000 0.000 0.000
#> GSM531675 2 0.0592 0.7243 0.000 0.988 0.012
#> GSM531677 2 0.0000 0.7214 0.000 1.000 0.000
#> GSM531678 2 0.2261 0.7121 0.000 0.932 0.068
#> GSM531680 1 0.6527 0.4453 0.588 0.404 0.008
#> GSM531689 2 0.4473 0.6218 0.008 0.828 0.164
#> GSM531691 2 0.4555 0.5862 0.000 0.800 0.200
#> GSM531692 3 0.6973 0.2239 0.020 0.416 0.564
#> GSM531694 2 0.2066 0.7158 0.000 0.940 0.060
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM531602 2 0.1489 0.925 0.000 0.952 0.004 0.044
#> GSM531604 2 0.1305 0.919 0.004 0.960 0.036 0.000
#> GSM531606 2 0.1674 0.928 0.004 0.952 0.012 0.032
#> GSM531607 2 0.1489 0.925 0.000 0.952 0.004 0.044
#> GSM531608 3 0.0000 0.942 0.000 0.000 1.000 0.000
#> GSM531610 4 0.0336 0.930 0.000 0.008 0.000 0.992
#> GSM531612 4 0.0000 0.926 0.000 0.000 0.000 1.000
#> GSM531613 4 0.0336 0.930 0.000 0.008 0.000 0.992
#> GSM531614 4 0.0336 0.930 0.000 0.008 0.000 0.992
#> GSM531616 3 0.1297 0.938 0.020 0.016 0.964 0.000
#> GSM531618 4 0.5992 0.478 0.032 0.020 0.300 0.648
#> GSM531619 3 0.0000 0.942 0.000 0.000 1.000 0.000
#> GSM531620 3 0.0592 0.947 0.016 0.000 0.984 0.000
#> GSM531623 3 0.0469 0.947 0.012 0.000 0.988 0.000
#> GSM531625 3 0.0779 0.946 0.016 0.004 0.980 0.000
#> GSM531626 3 0.0779 0.946 0.016 0.004 0.980 0.000
#> GSM531632 1 0.1059 0.932 0.972 0.012 0.016 0.000
#> GSM531638 3 0.1297 0.938 0.020 0.016 0.964 0.000
#> GSM531639 3 0.5646 0.282 0.384 0.016 0.592 0.008
#> GSM531641 4 0.0336 0.930 0.000 0.008 0.000 0.992
#> GSM531642 1 0.5295 0.610 0.688 0.016 0.284 0.012
#> GSM531643 1 0.1404 0.928 0.964 0.012 0.012 0.012
#> GSM531644 1 0.1404 0.928 0.964 0.012 0.012 0.012
#> GSM531645 4 0.0000 0.926 0.000 0.000 0.000 1.000
#> GSM531646 1 0.0927 0.932 0.976 0.008 0.016 0.000
#> GSM531647 1 0.1059 0.932 0.972 0.012 0.016 0.000
#> GSM531648 4 0.1059 0.918 0.012 0.016 0.000 0.972
#> GSM531650 1 0.0937 0.931 0.976 0.000 0.012 0.012
#> GSM531651 3 0.0469 0.947 0.012 0.000 0.988 0.000
#> GSM531652 1 0.2074 0.918 0.940 0.012 0.032 0.016
#> GSM531656 1 0.4862 0.715 0.744 0.020 0.228 0.008
#> GSM531659 4 0.1489 0.919 0.004 0.044 0.000 0.952
#> GSM531661 3 0.0000 0.942 0.000 0.000 1.000 0.000
#> GSM531662 3 0.0000 0.942 0.000 0.000 1.000 0.000
#> GSM531663 4 0.0336 0.930 0.000 0.008 0.000 0.992
#> GSM531664 1 0.1271 0.931 0.968 0.008 0.012 0.012
#> GSM531666 1 0.2196 0.920 0.936 0.016 0.032 0.016
#> GSM531667 3 0.0657 0.947 0.012 0.004 0.984 0.000
#> GSM531668 4 0.3072 0.858 0.004 0.124 0.004 0.868
#> GSM531669 1 0.1182 0.931 0.968 0.016 0.016 0.000
#> GSM531671 3 0.5110 0.471 0.328 0.016 0.656 0.000
#> GSM531672 4 0.1305 0.922 0.004 0.036 0.000 0.960
#> GSM531673 3 0.1661 0.900 0.004 0.052 0.944 0.000
#> GSM531676 2 0.2976 0.858 0.120 0.872 0.008 0.000
#> GSM531679 2 0.1356 0.928 0.008 0.960 0.000 0.032
#> GSM531681 4 0.3448 0.805 0.004 0.168 0.000 0.828
#> GSM531682 2 0.1488 0.928 0.012 0.956 0.000 0.032
#> GSM531683 2 0.1675 0.924 0.004 0.948 0.004 0.044
#> GSM531684 2 0.1743 0.911 0.004 0.940 0.056 0.000
#> GSM531685 2 0.4511 0.681 0.268 0.724 0.008 0.000
#> GSM531686 4 0.3448 0.805 0.004 0.168 0.000 0.828
#> GSM531687 2 0.3272 0.844 0.128 0.860 0.004 0.008
#> GSM531688 1 0.1004 0.919 0.972 0.024 0.004 0.000
#> GSM531690 4 0.3791 0.777 0.004 0.200 0.000 0.796
#> GSM531693 1 0.1042 0.922 0.972 0.020 0.008 0.000
#> GSM531695 1 0.2342 0.880 0.912 0.080 0.000 0.008
#> GSM531603 2 0.1489 0.925 0.000 0.952 0.004 0.044
#> GSM531609 4 0.0336 0.930 0.000 0.008 0.000 0.992
#> GSM531611 4 0.0336 0.930 0.000 0.008 0.000 0.992
#> GSM531621 3 0.0592 0.947 0.016 0.000 0.984 0.000
#> GSM531622 3 0.0592 0.947 0.016 0.000 0.984 0.000
#> GSM531628 1 0.1271 0.931 0.968 0.008 0.012 0.012
#> GSM531630 3 0.0592 0.947 0.016 0.000 0.984 0.000
#> GSM531633 3 0.0592 0.947 0.016 0.000 0.984 0.000
#> GSM531635 1 0.1406 0.931 0.960 0.024 0.016 0.000
#> GSM531640 3 0.0779 0.946 0.016 0.004 0.980 0.000
#> GSM531649 1 0.1059 0.932 0.972 0.012 0.016 0.000
#> GSM531653 1 0.1059 0.932 0.972 0.012 0.016 0.000
#> GSM531657 4 0.1305 0.922 0.004 0.036 0.000 0.960
#> GSM531665 1 0.5676 0.748 0.720 0.136 0.144 0.000
#> GSM531670 1 0.4862 0.715 0.744 0.020 0.228 0.008
#> GSM531674 1 0.1182 0.931 0.968 0.016 0.016 0.000
#> GSM531675 2 0.2473 0.899 0.012 0.908 0.000 0.080
#> GSM531677 2 0.1677 0.926 0.012 0.948 0.000 0.040
#> GSM531678 2 0.1674 0.928 0.012 0.952 0.004 0.032
#> GSM531680 2 0.4422 0.685 0.256 0.736 0.000 0.008
#> GSM531689 2 0.1124 0.925 0.012 0.972 0.004 0.012
#> GSM531691 2 0.1617 0.921 0.012 0.956 0.024 0.008
#> GSM531692 2 0.1929 0.911 0.024 0.940 0.036 0.000
#> GSM531694 2 0.1489 0.925 0.000 0.952 0.004 0.044
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM531602 2 0.0162 0.6115 0.000 0.996 0.000 0.004 0.000
#> GSM531604 2 0.4088 0.0150 0.000 0.632 0.000 0.000 0.368
#> GSM531606 2 0.1638 0.5749 0.000 0.932 0.000 0.004 0.064
#> GSM531607 2 0.0162 0.6115 0.000 0.996 0.000 0.004 0.000
#> GSM531608 3 0.1270 0.8898 0.000 0.000 0.948 0.000 0.052
#> GSM531610 4 0.0162 0.8204 0.000 0.000 0.000 0.996 0.004
#> GSM531612 4 0.0000 0.8215 0.000 0.000 0.000 1.000 0.000
#> GSM531613 4 0.0162 0.8204 0.000 0.000 0.000 0.996 0.004
#> GSM531614 4 0.0000 0.8215 0.000 0.000 0.000 1.000 0.000
#> GSM531616 3 0.1952 0.8703 0.004 0.000 0.912 0.000 0.084
#> GSM531618 4 0.8029 0.3181 0.008 0.064 0.248 0.364 0.316
#> GSM531619 3 0.0404 0.8999 0.000 0.000 0.988 0.000 0.012
#> GSM531620 3 0.0703 0.8978 0.000 0.000 0.976 0.000 0.024
#> GSM531623 3 0.0404 0.8999 0.000 0.000 0.988 0.000 0.012
#> GSM531625 3 0.0880 0.8950 0.000 0.000 0.968 0.000 0.032
#> GSM531626 3 0.1341 0.8871 0.000 0.000 0.944 0.000 0.056
#> GSM531632 1 0.0609 0.8280 0.980 0.000 0.000 0.000 0.020
#> GSM531638 3 0.1768 0.8757 0.004 0.000 0.924 0.000 0.072
#> GSM531639 3 0.6357 0.2257 0.288 0.000 0.512 0.000 0.200
#> GSM531641 4 0.0000 0.8215 0.000 0.000 0.000 1.000 0.000
#> GSM531642 1 0.6598 0.4812 0.484 0.000 0.208 0.004 0.304
#> GSM531643 1 0.2074 0.8122 0.896 0.000 0.000 0.000 0.104
#> GSM531644 1 0.3741 0.7272 0.732 0.000 0.000 0.004 0.264
#> GSM531645 4 0.0000 0.8215 0.000 0.000 0.000 1.000 0.000
#> GSM531646 1 0.0510 0.8293 0.984 0.000 0.000 0.000 0.016
#> GSM531647 1 0.0162 0.8315 0.996 0.000 0.000 0.000 0.004
#> GSM531648 4 0.5105 0.6579 0.000 0.076 0.000 0.660 0.264
#> GSM531650 1 0.0703 0.8317 0.976 0.000 0.000 0.000 0.024
#> GSM531651 3 0.0404 0.8999 0.000 0.000 0.988 0.000 0.012
#> GSM531652 1 0.3910 0.7192 0.720 0.000 0.000 0.008 0.272
#> GSM531656 1 0.5354 0.6548 0.668 0.000 0.192 0.000 0.140
#> GSM531659 4 0.5851 0.5925 0.000 0.132 0.000 0.580 0.288
#> GSM531661 3 0.1121 0.8927 0.000 0.000 0.956 0.000 0.044
#> GSM531662 3 0.2690 0.8135 0.000 0.000 0.844 0.000 0.156
#> GSM531663 4 0.0162 0.8204 0.000 0.000 0.000 0.996 0.004
#> GSM531664 1 0.0794 0.8318 0.972 0.000 0.000 0.000 0.028
#> GSM531666 1 0.3814 0.7205 0.720 0.000 0.000 0.004 0.276
#> GSM531667 3 0.1270 0.8887 0.000 0.000 0.948 0.000 0.052
#> GSM531668 2 0.6417 0.0446 0.000 0.508 0.000 0.228 0.264
#> GSM531669 1 0.0162 0.8315 0.996 0.000 0.000 0.000 0.004
#> GSM531671 3 0.6443 0.3982 0.248 0.000 0.504 0.000 0.248
#> GSM531672 4 0.5233 0.6679 0.000 0.128 0.000 0.680 0.192
#> GSM531673 3 0.4547 0.4726 0.000 0.012 0.588 0.000 0.400
#> GSM531676 5 0.5016 0.7225 0.044 0.348 0.000 0.000 0.608
#> GSM531679 2 0.3707 0.2936 0.000 0.716 0.000 0.000 0.284
#> GSM531681 4 0.4575 0.5643 0.000 0.236 0.000 0.712 0.052
#> GSM531682 2 0.3966 0.2528 0.000 0.664 0.000 0.000 0.336
#> GSM531683 2 0.0865 0.6026 0.000 0.972 0.000 0.004 0.024
#> GSM531684 2 0.4173 0.2047 0.000 0.688 0.012 0.000 0.300
#> GSM531685 5 0.5562 0.6341 0.156 0.200 0.000 0.000 0.644
#> GSM531686 4 0.4575 0.5643 0.000 0.236 0.000 0.712 0.052
#> GSM531687 5 0.5048 0.7016 0.040 0.380 0.000 0.000 0.580
#> GSM531688 1 0.3366 0.6301 0.768 0.000 0.000 0.000 0.232
#> GSM531690 2 0.5843 0.0457 0.000 0.512 0.000 0.388 0.100
#> GSM531693 1 0.3305 0.6514 0.776 0.000 0.000 0.000 0.224
#> GSM531695 1 0.5896 0.2530 0.564 0.128 0.000 0.000 0.308
#> GSM531603 2 0.0162 0.6115 0.000 0.996 0.000 0.004 0.000
#> GSM531609 4 0.0000 0.8215 0.000 0.000 0.000 1.000 0.000
#> GSM531611 4 0.0000 0.8215 0.000 0.000 0.000 1.000 0.000
#> GSM531621 3 0.0000 0.9011 0.000 0.000 1.000 0.000 0.000
#> GSM531622 3 0.0000 0.9011 0.000 0.000 1.000 0.000 0.000
#> GSM531628 1 0.0794 0.8318 0.972 0.000 0.000 0.000 0.028
#> GSM531630 3 0.0000 0.9011 0.000 0.000 1.000 0.000 0.000
#> GSM531633 3 0.0000 0.9011 0.000 0.000 1.000 0.000 0.000
#> GSM531635 1 0.2248 0.8147 0.900 0.000 0.012 0.000 0.088
#> GSM531640 3 0.0000 0.9011 0.000 0.000 1.000 0.000 0.000
#> GSM531649 1 0.1282 0.8227 0.952 0.000 0.004 0.000 0.044
#> GSM531653 1 0.0162 0.8315 0.996 0.000 0.000 0.000 0.004
#> GSM531657 4 0.5607 0.6335 0.000 0.140 0.000 0.632 0.228
#> GSM531665 5 0.2623 0.4278 0.096 0.016 0.004 0.000 0.884
#> GSM531670 1 0.5354 0.6548 0.668 0.000 0.192 0.000 0.140
#> GSM531674 1 0.0162 0.8315 0.996 0.000 0.000 0.000 0.004
#> GSM531675 2 0.4818 0.4611 0.000 0.720 0.000 0.100 0.180
#> GSM531677 2 0.3534 0.4310 0.000 0.744 0.000 0.000 0.256
#> GSM531678 2 0.4182 -0.1463 0.000 0.600 0.000 0.000 0.400
#> GSM531680 5 0.5850 0.6596 0.120 0.316 0.000 0.000 0.564
#> GSM531689 5 0.4268 0.6152 0.000 0.444 0.000 0.000 0.556
#> GSM531691 5 0.4192 0.6615 0.000 0.404 0.000 0.000 0.596
#> GSM531692 5 0.4045 0.6848 0.000 0.356 0.000 0.000 0.644
#> GSM531694 2 0.0162 0.6115 0.000 0.996 0.000 0.004 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM531602 2 0.1444 0.6280 0.000 0.928 0.000 0.000 0.072 0.000
#> GSM531604 5 0.5112 0.2578 0.000 0.376 0.000 0.000 0.536 0.088
#> GSM531606 2 0.2358 0.5926 0.000 0.876 0.000 0.000 0.108 0.016
#> GSM531607 2 0.1588 0.6283 0.000 0.924 0.000 0.000 0.072 0.004
#> GSM531608 3 0.3295 0.7773 0.000 0.000 0.816 0.000 0.056 0.128
#> GSM531610 4 0.0000 0.8979 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531612 4 0.0146 0.8989 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM531613 4 0.0146 0.8972 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM531614 4 0.0146 0.8989 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM531616 3 0.3434 0.7786 0.004 0.000 0.808 0.000 0.048 0.140
#> GSM531618 6 0.4881 0.6103 0.024 0.024 0.088 0.124 0.000 0.740
#> GSM531619 3 0.1408 0.8380 0.000 0.000 0.944 0.000 0.020 0.036
#> GSM531620 3 0.2527 0.8108 0.000 0.000 0.868 0.000 0.024 0.108
#> GSM531623 3 0.0935 0.8398 0.000 0.000 0.964 0.000 0.004 0.032
#> GSM531625 3 0.2255 0.8210 0.000 0.000 0.892 0.000 0.028 0.080
#> GSM531626 3 0.3249 0.7883 0.004 0.000 0.824 0.000 0.044 0.128
#> GSM531632 1 0.1408 0.7536 0.944 0.000 0.000 0.000 0.020 0.036
#> GSM531638 3 0.3356 0.7810 0.000 0.000 0.808 0.000 0.052 0.140
#> GSM531639 3 0.6122 0.0871 0.124 0.000 0.432 0.000 0.032 0.412
#> GSM531641 4 0.0146 0.8989 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM531642 6 0.4543 0.5282 0.252 0.000 0.052 0.000 0.012 0.684
#> GSM531643 1 0.3694 0.5223 0.740 0.000 0.000 0.000 0.028 0.232
#> GSM531644 6 0.4246 0.3914 0.400 0.000 0.000 0.000 0.020 0.580
#> GSM531645 4 0.0146 0.8989 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM531646 1 0.1845 0.7445 0.920 0.000 0.000 0.000 0.028 0.052
#> GSM531647 1 0.0000 0.7647 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM531648 6 0.4668 0.5589 0.008 0.044 0.000 0.292 0.004 0.652
#> GSM531650 1 0.0820 0.7602 0.972 0.000 0.000 0.000 0.012 0.016
#> GSM531651 3 0.1049 0.8388 0.000 0.000 0.960 0.000 0.008 0.032
#> GSM531652 6 0.4105 0.5112 0.332 0.000 0.004 0.000 0.016 0.648
#> GSM531656 1 0.6519 0.1590 0.476 0.000 0.180 0.000 0.048 0.296
#> GSM531659 6 0.5205 0.5658 0.000 0.096 0.000 0.188 0.040 0.676
#> GSM531661 3 0.3295 0.7753 0.000 0.000 0.816 0.000 0.056 0.128
#> GSM531662 3 0.4563 0.6645 0.000 0.000 0.700 0.000 0.136 0.164
#> GSM531663 4 0.0146 0.8972 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM531664 1 0.0820 0.7602 0.972 0.000 0.000 0.000 0.012 0.016
#> GSM531666 6 0.4199 0.5022 0.336 0.000 0.004 0.000 0.020 0.640
#> GSM531667 3 0.2651 0.8095 0.000 0.000 0.860 0.000 0.028 0.112
#> GSM531668 2 0.5305 -0.0678 0.000 0.516 0.000 0.072 0.012 0.400
#> GSM531669 1 0.0405 0.7643 0.988 0.000 0.000 0.000 0.008 0.004
#> GSM531671 3 0.7515 0.2132 0.152 0.000 0.344 0.000 0.232 0.272
#> GSM531672 6 0.5541 0.4262 0.000 0.136 0.000 0.324 0.004 0.536
#> GSM531673 5 0.6315 -0.0765 0.000 0.016 0.368 0.000 0.400 0.216
#> GSM531676 5 0.2669 0.6873 0.024 0.108 0.000 0.000 0.864 0.004
#> GSM531679 2 0.4712 0.2459 0.000 0.564 0.000 0.000 0.384 0.052
#> GSM531681 4 0.5257 0.4448 0.000 0.296 0.000 0.612 0.036 0.056
#> GSM531682 2 0.5403 0.2748 0.000 0.516 0.000 0.000 0.360 0.124
#> GSM531683 2 0.0790 0.6160 0.000 0.968 0.000 0.000 0.000 0.032
#> GSM531684 2 0.6104 0.0195 0.000 0.496 0.040 0.000 0.348 0.116
#> GSM531685 5 0.3236 0.6654 0.060 0.048 0.000 0.000 0.852 0.040
#> GSM531686 4 0.5545 0.4083 0.000 0.296 0.000 0.592 0.056 0.056
#> GSM531687 5 0.3048 0.6749 0.028 0.116 0.000 0.000 0.844 0.012
#> GSM531688 1 0.3489 0.5569 0.708 0.000 0.000 0.000 0.288 0.004
#> GSM531690 2 0.6462 0.3447 0.000 0.524 0.000 0.184 0.060 0.232
#> GSM531693 1 0.3575 0.5651 0.708 0.000 0.000 0.000 0.284 0.008
#> GSM531695 1 0.5520 0.0873 0.464 0.068 0.000 0.000 0.444 0.024
#> GSM531603 2 0.1588 0.6283 0.000 0.924 0.000 0.000 0.072 0.004
#> GSM531609 4 0.0146 0.8989 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM531611 4 0.0260 0.8981 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM531621 3 0.0146 0.8426 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM531622 3 0.0508 0.8416 0.000 0.000 0.984 0.000 0.012 0.004
#> GSM531628 1 0.0820 0.7602 0.972 0.000 0.000 0.000 0.012 0.016
#> GSM531630 3 0.0508 0.8416 0.000 0.000 0.984 0.000 0.012 0.004
#> GSM531633 3 0.0291 0.8427 0.000 0.000 0.992 0.000 0.004 0.004
#> GSM531635 1 0.4801 0.6062 0.724 0.000 0.068 0.000 0.052 0.156
#> GSM531640 3 0.1088 0.8392 0.000 0.000 0.960 0.000 0.016 0.024
#> GSM531649 1 0.2579 0.7194 0.872 0.000 0.000 0.000 0.040 0.088
#> GSM531653 1 0.0000 0.7647 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM531657 6 0.5783 0.4936 0.000 0.136 0.000 0.272 0.024 0.568
#> GSM531665 5 0.4224 0.5075 0.036 0.004 0.000 0.000 0.684 0.276
#> GSM531670 1 0.6519 0.1590 0.476 0.000 0.180 0.000 0.048 0.296
#> GSM531674 1 0.0260 0.7647 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM531675 2 0.6027 0.4471 0.000 0.568 0.000 0.036 0.176 0.220
#> GSM531677 2 0.5432 0.4196 0.000 0.588 0.000 0.004 0.248 0.160
#> GSM531678 5 0.4488 0.1318 0.000 0.420 0.000 0.000 0.548 0.032
#> GSM531680 5 0.3529 0.6471 0.048 0.120 0.000 0.000 0.816 0.016
#> GSM531689 5 0.2482 0.6641 0.000 0.148 0.000 0.000 0.848 0.004
#> GSM531691 5 0.2942 0.6777 0.000 0.132 0.000 0.000 0.836 0.032
#> GSM531692 5 0.3513 0.6580 0.004 0.084 0.000 0.000 0.812 0.100
#> GSM531694 2 0.1444 0.6280 0.000 0.928 0.000 0.000 0.072 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> SD:kmeans 80 1.000 2
#> SD:kmeans 70 0.925 3
#> SD:kmeans 77 0.343 4
#> SD:kmeans 64 0.540 5
#> SD:kmeans 60 0.234 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "skmeans"]
# you can also extract it by
# res = res_list["SD:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 80 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.685 0.902 0.955 0.5051 0.495 0.495
#> 3 3 0.879 0.374 0.744 0.3273 0.580 0.328
#> 4 4 0.891 0.903 0.958 0.1299 0.740 0.378
#> 5 5 0.828 0.807 0.896 0.0564 0.933 0.735
#> 6 6 0.777 0.708 0.850 0.0377 0.947 0.751
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM531602 2 0.0000 0.944 0.000 1.000
#> GSM531604 2 0.0376 0.941 0.004 0.996
#> GSM531606 2 0.0000 0.944 0.000 1.000
#> GSM531607 2 0.0000 0.944 0.000 1.000
#> GSM531608 2 0.9044 0.529 0.320 0.680
#> GSM531610 2 0.0000 0.944 0.000 1.000
#> GSM531612 2 0.0000 0.944 0.000 1.000
#> GSM531613 2 0.0000 0.944 0.000 1.000
#> GSM531614 2 0.0000 0.944 0.000 1.000
#> GSM531616 1 0.0000 0.954 1.000 0.000
#> GSM531618 2 0.9552 0.394 0.376 0.624
#> GSM531619 1 0.7219 0.758 0.800 0.200
#> GSM531620 1 0.0000 0.954 1.000 0.000
#> GSM531623 1 0.0000 0.954 1.000 0.000
#> GSM531625 1 0.0000 0.954 1.000 0.000
#> GSM531626 1 0.0000 0.954 1.000 0.000
#> GSM531632 1 0.0000 0.954 1.000 0.000
#> GSM531638 1 0.0000 0.954 1.000 0.000
#> GSM531639 1 0.0000 0.954 1.000 0.000
#> GSM531641 2 0.0000 0.944 0.000 1.000
#> GSM531642 1 0.0000 0.954 1.000 0.000
#> GSM531643 1 0.0000 0.954 1.000 0.000
#> GSM531644 1 0.0000 0.954 1.000 0.000
#> GSM531645 2 0.0000 0.944 0.000 1.000
#> GSM531646 1 0.0000 0.954 1.000 0.000
#> GSM531647 1 0.0000 0.954 1.000 0.000
#> GSM531648 2 0.7056 0.744 0.192 0.808
#> GSM531650 1 0.0000 0.954 1.000 0.000
#> GSM531651 1 0.0000 0.954 1.000 0.000
#> GSM531652 1 0.0376 0.951 0.996 0.004
#> GSM531656 1 0.0000 0.954 1.000 0.000
#> GSM531659 2 0.0000 0.944 0.000 1.000
#> GSM531661 1 0.6973 0.773 0.812 0.188
#> GSM531662 1 0.0000 0.954 1.000 0.000
#> GSM531663 2 0.0000 0.944 0.000 1.000
#> GSM531664 1 0.0000 0.954 1.000 0.000
#> GSM531666 1 0.0376 0.951 0.996 0.004
#> GSM531667 1 0.7219 0.758 0.800 0.200
#> GSM531668 2 0.0000 0.944 0.000 1.000
#> GSM531669 1 0.0000 0.954 1.000 0.000
#> GSM531671 1 0.0000 0.954 1.000 0.000
#> GSM531672 2 0.0000 0.944 0.000 1.000
#> GSM531673 1 0.5178 0.850 0.884 0.116
#> GSM531676 2 0.7219 0.758 0.200 0.800
#> GSM531679 2 0.0000 0.944 0.000 1.000
#> GSM531681 2 0.0000 0.944 0.000 1.000
#> GSM531682 2 0.0000 0.944 0.000 1.000
#> GSM531683 2 0.0000 0.944 0.000 1.000
#> GSM531684 2 0.0000 0.944 0.000 1.000
#> GSM531685 1 0.7056 0.755 0.808 0.192
#> GSM531686 2 0.0000 0.944 0.000 1.000
#> GSM531687 2 0.7219 0.758 0.200 0.800
#> GSM531688 1 0.7056 0.755 0.808 0.192
#> GSM531690 2 0.0000 0.944 0.000 1.000
#> GSM531693 1 0.0000 0.954 1.000 0.000
#> GSM531695 2 0.7219 0.758 0.200 0.800
#> GSM531603 2 0.0000 0.944 0.000 1.000
#> GSM531609 2 0.0000 0.944 0.000 1.000
#> GSM531611 2 0.0000 0.944 0.000 1.000
#> GSM531621 1 0.0000 0.954 1.000 0.000
#> GSM531622 1 0.7139 0.763 0.804 0.196
#> GSM531628 1 0.0000 0.954 1.000 0.000
#> GSM531630 1 0.0000 0.954 1.000 0.000
#> GSM531633 1 0.0000 0.954 1.000 0.000
#> GSM531635 1 0.0000 0.954 1.000 0.000
#> GSM531640 1 0.7219 0.758 0.800 0.200
#> GSM531649 1 0.0000 0.954 1.000 0.000
#> GSM531653 1 0.0000 0.954 1.000 0.000
#> GSM531657 2 0.0000 0.944 0.000 1.000
#> GSM531665 1 0.0000 0.954 1.000 0.000
#> GSM531670 1 0.0000 0.954 1.000 0.000
#> GSM531674 1 0.0000 0.954 1.000 0.000
#> GSM531675 2 0.0000 0.944 0.000 1.000
#> GSM531677 2 0.0000 0.944 0.000 1.000
#> GSM531678 2 0.0000 0.944 0.000 1.000
#> GSM531680 2 0.7219 0.758 0.200 0.800
#> GSM531689 2 0.0376 0.941 0.004 0.996
#> GSM531691 2 0.7219 0.758 0.200 0.800
#> GSM531692 1 0.7056 0.755 0.808 0.192
#> GSM531694 2 0.0000 0.944 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM531602 2 0.6309 0.588 0.496 0.504 0.000
#> GSM531604 3 0.6832 0.395 0.020 0.376 0.604
#> GSM531606 2 0.6309 0.588 0.496 0.504 0.000
#> GSM531607 2 0.6309 0.588 0.496 0.504 0.000
#> GSM531608 3 0.0237 0.945 0.004 0.000 0.996
#> GSM531610 2 0.6309 0.586 0.500 0.500 0.000
#> GSM531612 1 0.6309 -0.615 0.500 0.500 0.000
#> GSM531613 1 0.6309 -0.615 0.500 0.500 0.000
#> GSM531614 2 0.6309 0.586 0.500 0.500 0.000
#> GSM531616 3 0.2356 0.892 0.000 0.072 0.928
#> GSM531618 1 0.9014 -0.265 0.484 0.136 0.380
#> GSM531619 3 0.0000 0.948 0.000 0.000 1.000
#> GSM531620 3 0.0000 0.948 0.000 0.000 1.000
#> GSM531623 3 0.0000 0.948 0.000 0.000 1.000
#> GSM531625 3 0.0000 0.948 0.000 0.000 1.000
#> GSM531626 3 0.0000 0.948 0.000 0.000 1.000
#> GSM531632 1 0.6521 0.466 0.500 0.496 0.004
#> GSM531638 3 0.0000 0.948 0.000 0.000 1.000
#> GSM531639 3 0.5529 0.613 0.000 0.296 0.704
#> GSM531641 1 0.6309 -0.615 0.500 0.500 0.000
#> GSM531642 2 0.8190 -0.461 0.432 0.496 0.072
#> GSM531643 1 0.6521 0.466 0.500 0.496 0.004
#> GSM531644 1 0.6521 0.466 0.500 0.496 0.004
#> GSM531645 2 0.6309 0.586 0.500 0.500 0.000
#> GSM531646 1 0.6521 0.466 0.500 0.496 0.004
#> GSM531647 1 0.6521 0.466 0.500 0.496 0.004
#> GSM531648 2 0.6309 0.586 0.500 0.500 0.000
#> GSM531650 1 0.6521 0.466 0.500 0.496 0.004
#> GSM531651 3 0.0000 0.948 0.000 0.000 1.000
#> GSM531652 1 0.6521 0.466 0.500 0.496 0.004
#> GSM531656 2 0.8947 -0.423 0.372 0.496 0.132
#> GSM531659 2 0.6309 0.586 0.500 0.500 0.000
#> GSM531661 3 0.0000 0.948 0.000 0.000 1.000
#> GSM531662 3 0.0000 0.948 0.000 0.000 1.000
#> GSM531663 1 0.6309 -0.615 0.500 0.500 0.000
#> GSM531664 1 0.6521 0.466 0.500 0.496 0.004
#> GSM531666 1 0.6521 0.466 0.500 0.496 0.004
#> GSM531667 3 0.0000 0.948 0.000 0.000 1.000
#> GSM531668 1 0.6309 -0.615 0.500 0.500 0.000
#> GSM531669 1 0.6521 0.466 0.500 0.496 0.004
#> GSM531671 3 0.5875 0.751 0.136 0.072 0.792
#> GSM531672 2 0.6309 0.586 0.500 0.500 0.000
#> GSM531673 3 0.0237 0.945 0.000 0.004 0.996
#> GSM531676 1 0.6309 0.464 0.500 0.500 0.000
#> GSM531679 2 0.6309 0.588 0.496 0.504 0.000
#> GSM531681 1 0.6309 -0.615 0.500 0.500 0.000
#> GSM531682 2 0.6309 0.588 0.496 0.504 0.000
#> GSM531683 2 0.6309 0.588 0.496 0.504 0.000
#> GSM531684 3 0.2031 0.911 0.016 0.032 0.952
#> GSM531685 1 0.6309 0.464 0.500 0.500 0.000
#> GSM531686 1 0.6309 -0.615 0.500 0.500 0.000
#> GSM531687 2 0.6309 -0.502 0.500 0.500 0.000
#> GSM531688 2 0.6309 -0.502 0.500 0.500 0.000
#> GSM531690 1 0.6309 -0.615 0.500 0.500 0.000
#> GSM531693 1 0.6309 0.464 0.500 0.500 0.000
#> GSM531695 2 0.6309 -0.502 0.500 0.500 0.000
#> GSM531603 2 0.6309 0.588 0.496 0.504 0.000
#> GSM531609 1 0.6309 -0.615 0.500 0.500 0.000
#> GSM531611 1 0.6309 -0.615 0.500 0.500 0.000
#> GSM531621 3 0.0000 0.948 0.000 0.000 1.000
#> GSM531622 3 0.0000 0.948 0.000 0.000 1.000
#> GSM531628 1 0.6521 0.466 0.500 0.496 0.004
#> GSM531630 3 0.0000 0.948 0.000 0.000 1.000
#> GSM531633 3 0.0000 0.948 0.000 0.000 1.000
#> GSM531635 1 0.6521 0.466 0.500 0.496 0.004
#> GSM531640 3 0.0000 0.948 0.000 0.000 1.000
#> GSM531649 1 0.6521 0.466 0.500 0.496 0.004
#> GSM531653 1 0.6521 0.466 0.500 0.496 0.004
#> GSM531657 2 0.6309 0.586 0.500 0.500 0.000
#> GSM531665 1 0.9423 0.136 0.492 0.204 0.304
#> GSM531670 2 0.8947 -0.423 0.372 0.496 0.132
#> GSM531674 1 0.6521 0.466 0.500 0.496 0.004
#> GSM531675 2 0.6309 0.588 0.496 0.504 0.000
#> GSM531677 2 0.6309 0.588 0.496 0.504 0.000
#> GSM531678 2 0.6309 0.588 0.496 0.504 0.000
#> GSM531680 1 0.6309 0.464 0.500 0.500 0.000
#> GSM531689 1 0.6309 -0.593 0.504 0.496 0.000
#> GSM531691 1 0.9713 -0.405 0.404 0.376 0.220
#> GSM531692 3 0.1989 0.914 0.048 0.004 0.948
#> GSM531694 2 0.6309 0.588 0.496 0.504 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM531602 2 0.0000 0.937 0.000 1.000 0.000 0.000
#> GSM531604 2 0.0000 0.937 0.000 1.000 0.000 0.000
#> GSM531606 2 0.0000 0.937 0.000 1.000 0.000 0.000
#> GSM531607 2 0.0000 0.937 0.000 1.000 0.000 0.000
#> GSM531608 3 0.0000 0.966 0.000 0.000 1.000 0.000
#> GSM531610 4 0.0000 0.975 0.000 0.000 0.000 1.000
#> GSM531612 4 0.0000 0.975 0.000 0.000 0.000 1.000
#> GSM531613 4 0.0000 0.975 0.000 0.000 0.000 1.000
#> GSM531614 4 0.0000 0.975 0.000 0.000 0.000 1.000
#> GSM531616 3 0.0000 0.966 0.000 0.000 1.000 0.000
#> GSM531618 4 0.0000 0.975 0.000 0.000 0.000 1.000
#> GSM531619 3 0.0000 0.966 0.000 0.000 1.000 0.000
#> GSM531620 3 0.0000 0.966 0.000 0.000 1.000 0.000
#> GSM531623 3 0.0000 0.966 0.000 0.000 1.000 0.000
#> GSM531625 3 0.0000 0.966 0.000 0.000 1.000 0.000
#> GSM531626 3 0.0000 0.966 0.000 0.000 1.000 0.000
#> GSM531632 1 0.0000 0.939 1.000 0.000 0.000 0.000
#> GSM531638 3 0.0000 0.966 0.000 0.000 1.000 0.000
#> GSM531639 3 0.4679 0.405 0.352 0.000 0.648 0.000
#> GSM531641 4 0.0000 0.975 0.000 0.000 0.000 1.000
#> GSM531642 1 0.3801 0.716 0.780 0.000 0.220 0.000
#> GSM531643 1 0.0000 0.939 1.000 0.000 0.000 0.000
#> GSM531644 1 0.0000 0.939 1.000 0.000 0.000 0.000
#> GSM531645 4 0.0000 0.975 0.000 0.000 0.000 1.000
#> GSM531646 1 0.0000 0.939 1.000 0.000 0.000 0.000
#> GSM531647 1 0.0000 0.939 1.000 0.000 0.000 0.000
#> GSM531648 4 0.0000 0.975 0.000 0.000 0.000 1.000
#> GSM531650 1 0.0000 0.939 1.000 0.000 0.000 0.000
#> GSM531651 3 0.0000 0.966 0.000 0.000 1.000 0.000
#> GSM531652 1 0.1118 0.912 0.964 0.000 0.000 0.036
#> GSM531656 1 0.3610 0.744 0.800 0.000 0.200 0.000
#> GSM531659 4 0.0000 0.975 0.000 0.000 0.000 1.000
#> GSM531661 3 0.0000 0.966 0.000 0.000 1.000 0.000
#> GSM531662 3 0.0000 0.966 0.000 0.000 1.000 0.000
#> GSM531663 4 0.0000 0.975 0.000 0.000 0.000 1.000
#> GSM531664 1 0.0000 0.939 1.000 0.000 0.000 0.000
#> GSM531666 1 0.0188 0.936 0.996 0.000 0.000 0.004
#> GSM531667 3 0.0000 0.966 0.000 0.000 1.000 0.000
#> GSM531668 4 0.0000 0.975 0.000 0.000 0.000 1.000
#> GSM531669 1 0.0000 0.939 1.000 0.000 0.000 0.000
#> GSM531671 3 0.3801 0.688 0.220 0.000 0.780 0.000
#> GSM531672 4 0.0000 0.975 0.000 0.000 0.000 1.000
#> GSM531673 3 0.0000 0.966 0.000 0.000 1.000 0.000
#> GSM531676 2 0.1211 0.915 0.040 0.960 0.000 0.000
#> GSM531679 2 0.0000 0.937 0.000 1.000 0.000 0.000
#> GSM531681 4 0.2814 0.859 0.000 0.132 0.000 0.868
#> GSM531682 2 0.0000 0.937 0.000 1.000 0.000 0.000
#> GSM531683 2 0.0000 0.937 0.000 1.000 0.000 0.000
#> GSM531684 2 0.0000 0.937 0.000 1.000 0.000 0.000
#> GSM531685 2 0.3688 0.752 0.208 0.792 0.000 0.000
#> GSM531686 4 0.2814 0.859 0.000 0.132 0.000 0.868
#> GSM531687 2 0.1302 0.912 0.044 0.956 0.000 0.000
#> GSM531688 1 0.0000 0.939 1.000 0.000 0.000 0.000
#> GSM531690 4 0.2814 0.859 0.000 0.132 0.000 0.868
#> GSM531693 1 0.0000 0.939 1.000 0.000 0.000 0.000
#> GSM531695 2 0.5000 0.117 0.496 0.504 0.000 0.000
#> GSM531603 2 0.0000 0.937 0.000 1.000 0.000 0.000
#> GSM531609 4 0.0000 0.975 0.000 0.000 0.000 1.000
#> GSM531611 4 0.0000 0.975 0.000 0.000 0.000 1.000
#> GSM531621 3 0.0000 0.966 0.000 0.000 1.000 0.000
#> GSM531622 3 0.0000 0.966 0.000 0.000 1.000 0.000
#> GSM531628 1 0.0000 0.939 1.000 0.000 0.000 0.000
#> GSM531630 3 0.0000 0.966 0.000 0.000 1.000 0.000
#> GSM531633 3 0.0000 0.966 0.000 0.000 1.000 0.000
#> GSM531635 1 0.0000 0.939 1.000 0.000 0.000 0.000
#> GSM531640 3 0.0000 0.966 0.000 0.000 1.000 0.000
#> GSM531649 1 0.0000 0.939 1.000 0.000 0.000 0.000
#> GSM531653 1 0.0000 0.939 1.000 0.000 0.000 0.000
#> GSM531657 4 0.0000 0.975 0.000 0.000 0.000 1.000
#> GSM531665 1 0.7270 0.247 0.504 0.164 0.332 0.000
#> GSM531670 1 0.3610 0.744 0.800 0.000 0.200 0.000
#> GSM531674 1 0.0000 0.939 1.000 0.000 0.000 0.000
#> GSM531675 2 0.3873 0.688 0.000 0.772 0.000 0.228
#> GSM531677 2 0.0000 0.937 0.000 1.000 0.000 0.000
#> GSM531678 2 0.0000 0.937 0.000 1.000 0.000 0.000
#> GSM531680 2 0.3569 0.767 0.196 0.804 0.000 0.000
#> GSM531689 2 0.0000 0.937 0.000 1.000 0.000 0.000
#> GSM531691 2 0.0000 0.937 0.000 1.000 0.000 0.000
#> GSM531692 2 0.0000 0.937 0.000 1.000 0.000 0.000
#> GSM531694 2 0.0000 0.937 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM531602 2 0.0000 0.90298 0.000 1.000 0.000 0.000 0.000
#> GSM531604 2 0.2929 0.77885 0.000 0.820 0.000 0.000 0.180
#> GSM531606 2 0.0162 0.90176 0.000 0.996 0.000 0.000 0.004
#> GSM531607 2 0.0000 0.90298 0.000 1.000 0.000 0.000 0.000
#> GSM531608 3 0.0000 0.94413 0.000 0.000 1.000 0.000 0.000
#> GSM531610 4 0.0000 0.87163 0.000 0.000 0.000 1.000 0.000
#> GSM531612 4 0.0000 0.87163 0.000 0.000 0.000 1.000 0.000
#> GSM531613 4 0.0000 0.87163 0.000 0.000 0.000 1.000 0.000
#> GSM531614 4 0.0000 0.87163 0.000 0.000 0.000 1.000 0.000
#> GSM531616 3 0.0162 0.94202 0.000 0.000 0.996 0.000 0.004
#> GSM531618 4 0.3551 0.77296 0.004 0.020 0.004 0.820 0.152
#> GSM531619 3 0.0000 0.94413 0.000 0.000 1.000 0.000 0.000
#> GSM531620 3 0.0000 0.94413 0.000 0.000 1.000 0.000 0.000
#> GSM531623 3 0.0000 0.94413 0.000 0.000 1.000 0.000 0.000
#> GSM531625 3 0.0000 0.94413 0.000 0.000 1.000 0.000 0.000
#> GSM531626 3 0.0000 0.94413 0.000 0.000 1.000 0.000 0.000
#> GSM531632 1 0.1121 0.88448 0.956 0.000 0.000 0.000 0.044
#> GSM531638 3 0.0162 0.94202 0.000 0.000 0.996 0.000 0.004
#> GSM531639 3 0.5014 0.29184 0.368 0.000 0.592 0.000 0.040
#> GSM531641 4 0.0000 0.87163 0.000 0.000 0.000 1.000 0.000
#> GSM531642 1 0.5307 0.66551 0.676 0.000 0.168 0.000 0.156
#> GSM531643 1 0.1608 0.87484 0.928 0.000 0.000 0.000 0.072
#> GSM531644 1 0.2690 0.82775 0.844 0.000 0.000 0.000 0.156
#> GSM531645 4 0.0000 0.87163 0.000 0.000 0.000 1.000 0.000
#> GSM531646 1 0.0510 0.89933 0.984 0.000 0.000 0.000 0.016
#> GSM531647 1 0.0510 0.89933 0.984 0.000 0.000 0.000 0.016
#> GSM531648 4 0.2763 0.78880 0.004 0.000 0.000 0.848 0.148
#> GSM531650 1 0.0000 0.89984 1.000 0.000 0.000 0.000 0.000
#> GSM531651 3 0.0000 0.94413 0.000 0.000 1.000 0.000 0.000
#> GSM531652 1 0.2690 0.82775 0.844 0.000 0.000 0.000 0.156
#> GSM531656 1 0.3844 0.73302 0.792 0.000 0.164 0.000 0.044
#> GSM531659 4 0.1043 0.85944 0.000 0.000 0.000 0.960 0.040
#> GSM531661 3 0.0000 0.94413 0.000 0.000 1.000 0.000 0.000
#> GSM531662 3 0.1809 0.89165 0.000 0.012 0.928 0.000 0.060
#> GSM531663 4 0.0000 0.87163 0.000 0.000 0.000 1.000 0.000
#> GSM531664 1 0.0000 0.89984 1.000 0.000 0.000 0.000 0.000
#> GSM531666 1 0.2690 0.82775 0.844 0.000 0.000 0.000 0.156
#> GSM531667 3 0.0162 0.94174 0.000 0.000 0.996 0.000 0.004
#> GSM531668 4 0.5498 0.20262 0.000 0.440 0.000 0.496 0.064
#> GSM531669 1 0.1121 0.88448 0.956 0.000 0.000 0.000 0.044
#> GSM531671 3 0.5361 0.54764 0.244 0.008 0.664 0.000 0.084
#> GSM531672 4 0.0963 0.86087 0.000 0.000 0.000 0.964 0.036
#> GSM531673 3 0.3039 0.79699 0.000 0.012 0.836 0.000 0.152
#> GSM531676 5 0.3304 0.77746 0.016 0.168 0.000 0.000 0.816
#> GSM531679 2 0.1270 0.89070 0.000 0.948 0.000 0.000 0.052
#> GSM531681 4 0.4306 -0.00543 0.000 0.492 0.000 0.508 0.000
#> GSM531682 2 0.1197 0.89199 0.000 0.952 0.000 0.000 0.048
#> GSM531683 2 0.0000 0.90298 0.000 1.000 0.000 0.000 0.000
#> GSM531684 2 0.2516 0.81350 0.000 0.860 0.000 0.000 0.140
#> GSM531685 5 0.3359 0.77961 0.072 0.084 0.000 0.000 0.844
#> GSM531686 4 0.4306 -0.00543 0.000 0.492 0.000 0.508 0.000
#> GSM531687 5 0.3696 0.75938 0.016 0.212 0.000 0.000 0.772
#> GSM531688 5 0.4171 0.49844 0.396 0.000 0.000 0.000 0.604
#> GSM531690 2 0.4045 0.36920 0.000 0.644 0.000 0.356 0.000
#> GSM531693 5 0.4182 0.49034 0.400 0.000 0.000 0.000 0.600
#> GSM531695 5 0.5771 0.62975 0.316 0.112 0.000 0.000 0.572
#> GSM531603 2 0.0000 0.90298 0.000 1.000 0.000 0.000 0.000
#> GSM531609 4 0.0000 0.87163 0.000 0.000 0.000 1.000 0.000
#> GSM531611 4 0.0000 0.87163 0.000 0.000 0.000 1.000 0.000
#> GSM531621 3 0.0000 0.94413 0.000 0.000 1.000 0.000 0.000
#> GSM531622 3 0.0000 0.94413 0.000 0.000 1.000 0.000 0.000
#> GSM531628 1 0.0162 0.89998 0.996 0.000 0.000 0.000 0.004
#> GSM531630 3 0.0000 0.94413 0.000 0.000 1.000 0.000 0.000
#> GSM531633 3 0.0000 0.94413 0.000 0.000 1.000 0.000 0.000
#> GSM531635 1 0.0609 0.90024 0.980 0.000 0.000 0.000 0.020
#> GSM531640 3 0.0000 0.94413 0.000 0.000 1.000 0.000 0.000
#> GSM531649 1 0.0510 0.89933 0.984 0.000 0.000 0.000 0.016
#> GSM531653 1 0.0510 0.89933 0.984 0.000 0.000 0.000 0.016
#> GSM531657 4 0.1364 0.85784 0.000 0.012 0.000 0.952 0.036
#> GSM531665 5 0.3351 0.74855 0.148 0.004 0.020 0.000 0.828
#> GSM531670 1 0.3844 0.73302 0.792 0.000 0.164 0.000 0.044
#> GSM531674 1 0.0880 0.89161 0.968 0.000 0.000 0.000 0.032
#> GSM531675 2 0.1410 0.86923 0.000 0.940 0.000 0.060 0.000
#> GSM531677 2 0.1282 0.89302 0.000 0.952 0.000 0.004 0.044
#> GSM531678 2 0.2773 0.79518 0.000 0.836 0.000 0.000 0.164
#> GSM531680 5 0.4066 0.77397 0.044 0.188 0.000 0.000 0.768
#> GSM531689 5 0.3508 0.71345 0.000 0.252 0.000 0.000 0.748
#> GSM531691 5 0.3242 0.73567 0.000 0.216 0.000 0.000 0.784
#> GSM531692 5 0.3013 0.77218 0.008 0.160 0.000 0.000 0.832
#> GSM531694 2 0.0000 0.90298 0.000 1.000 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
#> GSM531602 2 0.0146 0.8106 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM531604 2 0.5400 0.2079 0.000 0.484 0.000 0.000 0.400 0.116
#> GSM531606 2 0.1036 0.8030 0.000 0.964 0.000 0.004 0.024 0.008
#> GSM531607 2 0.0291 0.8102 0.000 0.992 0.000 0.004 0.004 0.000
#> GSM531608 3 0.2163 0.8289 0.000 0.000 0.892 0.000 0.016 0.092
#> GSM531610 4 0.0000 0.8412 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531612 4 0.0000 0.8412 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531613 4 0.0000 0.8412 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531614 4 0.0000 0.8412 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531616 3 0.3053 0.7921 0.024 0.004 0.828 0.000 0.000 0.144
#> GSM531618 6 0.4103 0.4152 0.000 0.012 0.012 0.304 0.000 0.672
#> GSM531619 3 0.0146 0.8671 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM531620 3 0.0458 0.8667 0.000 0.000 0.984 0.000 0.000 0.016
#> GSM531623 3 0.0146 0.8671 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM531625 3 0.2001 0.8348 0.004 0.004 0.900 0.000 0.000 0.092
#> GSM531626 3 0.2001 0.8348 0.004 0.004 0.900 0.000 0.000 0.092
#> GSM531632 1 0.0603 0.8148 0.980 0.000 0.000 0.000 0.016 0.004
#> GSM531638 3 0.2695 0.8028 0.008 0.004 0.844 0.000 0.000 0.144
#> GSM531639 3 0.5587 0.3743 0.156 0.004 0.548 0.000 0.000 0.292
#> GSM531641 4 0.0000 0.8412 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531642 6 0.3156 0.6480 0.180 0.000 0.020 0.000 0.000 0.800
#> GSM531643 1 0.2003 0.7372 0.884 0.000 0.000 0.000 0.000 0.116
#> GSM531644 6 0.3756 0.5263 0.400 0.000 0.000 0.000 0.000 0.600
#> GSM531645 4 0.0000 0.8412 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531646 1 0.0632 0.8121 0.976 0.000 0.000 0.000 0.000 0.024
#> GSM531647 1 0.0291 0.8175 0.992 0.000 0.000 0.000 0.004 0.004
#> GSM531648 6 0.3620 0.3319 0.000 0.000 0.000 0.352 0.000 0.648
#> GSM531650 1 0.0547 0.8136 0.980 0.000 0.000 0.000 0.000 0.020
#> GSM531651 3 0.0146 0.8671 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM531652 6 0.3446 0.6700 0.308 0.000 0.000 0.000 0.000 0.692
#> GSM531656 1 0.4697 0.5649 0.708 0.004 0.096 0.000 0.008 0.184
#> GSM531659 4 0.3636 0.5265 0.000 0.004 0.000 0.676 0.000 0.320
#> GSM531661 3 0.2398 0.8202 0.000 0.000 0.876 0.000 0.020 0.104
#> GSM531662 3 0.4154 0.7166 0.000 0.000 0.744 0.000 0.112 0.144
#> GSM531663 4 0.0000 0.8412 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531664 1 0.0692 0.8146 0.976 0.000 0.000 0.000 0.004 0.020
#> GSM531666 6 0.3428 0.6710 0.304 0.000 0.000 0.000 0.000 0.696
#> GSM531667 3 0.1501 0.8449 0.000 0.000 0.924 0.000 0.000 0.076
#> GSM531668 2 0.4220 0.5851 0.000 0.732 0.000 0.172 0.000 0.096
#> GSM531669 1 0.0508 0.8162 0.984 0.000 0.000 0.000 0.012 0.004
#> GSM531671 3 0.7022 0.1881 0.340 0.000 0.404 0.000 0.116 0.140
#> GSM531672 4 0.4110 0.5554 0.000 0.040 0.000 0.692 0.000 0.268
#> GSM531673 3 0.5244 0.6033 0.000 0.012 0.644 0.000 0.192 0.152
#> GSM531676 5 0.1663 0.8322 0.000 0.088 0.000 0.000 0.912 0.000
#> GSM531679 2 0.2491 0.7785 0.000 0.868 0.000 0.000 0.112 0.020
#> GSM531681 4 0.4293 0.4965 0.000 0.292 0.000 0.672 0.012 0.024
#> GSM531682 2 0.2726 0.7780 0.000 0.856 0.000 0.000 0.112 0.032
#> GSM531683 2 0.0508 0.8102 0.000 0.984 0.000 0.004 0.000 0.012
#> GSM531684 2 0.6012 0.4702 0.000 0.604 0.084 0.000 0.204 0.108
#> GSM531685 5 0.0881 0.8096 0.012 0.008 0.000 0.000 0.972 0.008
#> GSM531686 4 0.4360 0.4985 0.000 0.288 0.000 0.672 0.016 0.024
#> GSM531687 5 0.1863 0.8260 0.000 0.104 0.000 0.000 0.896 0.000
#> GSM531688 1 0.3991 0.0547 0.524 0.000 0.000 0.000 0.472 0.004
#> GSM531690 2 0.4269 0.6427 0.000 0.736 0.000 0.196 0.016 0.052
#> GSM531693 1 0.3950 0.1826 0.564 0.000 0.000 0.000 0.432 0.004
#> GSM531695 5 0.5664 0.2845 0.364 0.116 0.000 0.000 0.508 0.012
#> GSM531603 2 0.0146 0.8106 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM531609 4 0.0000 0.8412 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531611 4 0.0000 0.8412 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531621 3 0.0260 0.8675 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM531622 3 0.0000 0.8671 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531628 1 0.0692 0.8146 0.976 0.000 0.000 0.000 0.004 0.020
#> GSM531630 3 0.0146 0.8676 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM531633 3 0.0363 0.8672 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM531635 1 0.2714 0.7307 0.848 0.004 0.012 0.000 0.000 0.136
#> GSM531640 3 0.0713 0.8629 0.000 0.000 0.972 0.000 0.000 0.028
#> GSM531649 1 0.1908 0.7630 0.900 0.004 0.000 0.000 0.000 0.096
#> GSM531653 1 0.0146 0.8180 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM531657 4 0.4453 0.4562 0.000 0.044 0.000 0.624 0.000 0.332
#> GSM531665 5 0.3532 0.7076 0.064 0.000 0.000 0.000 0.796 0.140
#> GSM531670 1 0.4741 0.5582 0.704 0.004 0.100 0.000 0.008 0.184
#> GSM531674 1 0.0363 0.8173 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM531675 2 0.3366 0.7718 0.000 0.844 0.000 0.060 0.044 0.052
#> GSM531677 2 0.2911 0.7790 0.000 0.856 0.000 0.008 0.100 0.036
#> GSM531678 2 0.3965 0.3889 0.000 0.604 0.000 0.000 0.388 0.008
#> GSM531680 5 0.2135 0.8101 0.000 0.128 0.000 0.000 0.872 0.000
#> GSM531689 5 0.2146 0.8185 0.000 0.116 0.000 0.000 0.880 0.004
#> GSM531691 5 0.1913 0.8285 0.000 0.080 0.000 0.000 0.908 0.012
#> GSM531692 5 0.2446 0.7449 0.000 0.012 0.000 0.000 0.864 0.124
#> GSM531694 2 0.0146 0.8106 0.000 0.996 0.000 0.004 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> SD:skmeans 79 1.000 2
#> SD:skmeans 40 0.945 3
#> SD:skmeans 77 0.284 4
#> SD:skmeans 73 0.480 5
#> SD:skmeans 67 0.216 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "pam"]
# you can also extract it by
# res = res_list["SD:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 80 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 0.925 0.925 0.944 0.4700 0.525 0.525
#> 3 3 0.448 0.621 0.806 0.3399 0.798 0.621
#> 4 4 0.552 0.669 0.843 0.1477 0.787 0.477
#> 5 5 0.855 0.852 0.929 0.0972 0.792 0.388
#> 6 6 0.775 0.753 0.849 0.0473 0.921 0.648
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
#> GSM531602 2 0.0376 0.935 0.004 0.996
#> GSM531604 2 0.0376 0.935 0.004 0.996
#> GSM531606 2 0.0376 0.935 0.004 0.996
#> GSM531607 2 0.0000 0.934 0.000 1.000
#> GSM531608 1 0.4161 0.953 0.916 0.084
#> GSM531610 1 0.4161 0.953 0.916 0.084
#> GSM531612 1 0.4161 0.953 0.916 0.084
#> GSM531613 1 0.7139 0.835 0.804 0.196
#> GSM531614 1 0.4161 0.953 0.916 0.084
#> GSM531616 1 0.0000 0.942 1.000 0.000
#> GSM531618 1 0.4161 0.953 0.916 0.084
#> GSM531619 1 0.4161 0.953 0.916 0.084
#> GSM531620 1 0.0000 0.942 1.000 0.000
#> GSM531623 1 0.4161 0.953 0.916 0.084
#> GSM531625 1 0.0000 0.942 1.000 0.000
#> GSM531626 1 0.0000 0.942 1.000 0.000
#> GSM531632 1 0.0376 0.940 0.996 0.004
#> GSM531638 1 0.0000 0.942 1.000 0.000
#> GSM531639 1 0.0000 0.942 1.000 0.000
#> GSM531641 1 0.4161 0.953 0.916 0.084
#> GSM531642 1 0.4161 0.953 0.916 0.084
#> GSM531643 1 0.0000 0.942 1.000 0.000
#> GSM531644 1 0.0000 0.942 1.000 0.000
#> GSM531645 1 0.4161 0.953 0.916 0.084
#> GSM531646 1 0.0376 0.940 0.996 0.004
#> GSM531647 1 0.0376 0.940 0.996 0.004
#> GSM531648 1 0.4161 0.953 0.916 0.084
#> GSM531650 1 0.0376 0.940 0.996 0.004
#> GSM531651 1 0.0000 0.942 1.000 0.000
#> GSM531652 1 0.4161 0.953 0.916 0.084
#> GSM531656 1 0.0000 0.942 1.000 0.000
#> GSM531659 1 0.4161 0.953 0.916 0.084
#> GSM531661 1 0.4161 0.953 0.916 0.084
#> GSM531662 1 0.4161 0.953 0.916 0.084
#> GSM531663 1 0.4161 0.953 0.916 0.084
#> GSM531664 2 0.9248 0.630 0.340 0.660
#> GSM531666 1 0.4161 0.953 0.916 0.084
#> GSM531667 1 0.4161 0.953 0.916 0.084
#> GSM531668 1 0.4161 0.953 0.916 0.084
#> GSM531669 2 0.9833 0.443 0.424 0.576
#> GSM531671 1 0.1414 0.932 0.980 0.020
#> GSM531672 1 0.4161 0.953 0.916 0.084
#> GSM531673 1 0.4161 0.953 0.916 0.084
#> GSM531676 2 0.4161 0.904 0.084 0.916
#> GSM531679 2 0.0000 0.934 0.000 1.000
#> GSM531681 2 0.0376 0.935 0.004 0.996
#> GSM531682 2 0.0376 0.935 0.004 0.996
#> GSM531683 2 0.0376 0.935 0.004 0.996
#> GSM531684 2 0.0376 0.935 0.004 0.996
#> GSM531685 2 0.4161 0.904 0.084 0.916
#> GSM531686 2 0.0000 0.934 0.000 1.000
#> GSM531687 2 0.7219 0.833 0.200 0.800
#> GSM531688 2 0.4161 0.904 0.084 0.916
#> GSM531690 2 0.0376 0.935 0.004 0.996
#> GSM531693 2 0.4298 0.903 0.088 0.912
#> GSM531695 2 0.4161 0.904 0.084 0.916
#> GSM531603 2 0.0376 0.935 0.004 0.996
#> GSM531609 1 0.4161 0.953 0.916 0.084
#> GSM531611 1 0.4161 0.953 0.916 0.084
#> GSM531621 1 0.0000 0.942 1.000 0.000
#> GSM531622 1 0.4161 0.953 0.916 0.084
#> GSM531628 1 0.0376 0.940 0.996 0.004
#> GSM531630 1 0.4161 0.953 0.916 0.084
#> GSM531633 1 0.0000 0.942 1.000 0.000
#> GSM531635 1 0.0000 0.942 1.000 0.000
#> GSM531640 1 0.4161 0.953 0.916 0.084
#> GSM531649 1 0.0000 0.942 1.000 0.000
#> GSM531653 1 0.0376 0.940 0.996 0.004
#> GSM531657 1 0.4161 0.953 0.916 0.084
#> GSM531665 2 0.5294 0.850 0.120 0.880
#> GSM531670 1 0.0000 0.942 1.000 0.000
#> GSM531674 2 0.7139 0.834 0.196 0.804
#> GSM531675 2 0.0376 0.935 0.004 0.996
#> GSM531677 2 0.0000 0.934 0.000 1.000
#> GSM531678 2 0.0376 0.935 0.004 0.996
#> GSM531680 2 0.4431 0.902 0.092 0.908
#> GSM531689 2 0.0000 0.934 0.000 1.000
#> GSM531691 2 0.2948 0.907 0.052 0.948
#> GSM531692 2 0.4161 0.904 0.084 0.916
#> GSM531694 2 0.0376 0.935 0.004 0.996
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM531602 2 0.3826 0.8844 0.124 0.868 0.008
#> GSM531604 2 0.3644 0.8407 0.004 0.872 0.124
#> GSM531606 2 0.3826 0.8844 0.124 0.868 0.008
#> GSM531607 2 0.3412 0.8838 0.124 0.876 0.000
#> GSM531608 3 0.2796 0.5972 0.092 0.000 0.908
#> GSM531610 1 0.0000 0.6047 1.000 0.000 0.000
#> GSM531612 1 0.0000 0.6047 1.000 0.000 0.000
#> GSM531613 1 0.0237 0.6010 0.996 0.004 0.000
#> GSM531614 1 0.0000 0.6047 1.000 0.000 0.000
#> GSM531616 3 0.6286 -0.3021 0.464 0.000 0.536
#> GSM531618 1 0.5363 0.6982 0.724 0.000 0.276
#> GSM531619 3 0.0000 0.6882 0.000 0.000 1.000
#> GSM531620 3 0.0000 0.6882 0.000 0.000 1.000
#> GSM531623 3 0.0000 0.6882 0.000 0.000 1.000
#> GSM531625 3 0.0000 0.6882 0.000 0.000 1.000
#> GSM531626 3 0.6267 -0.2726 0.452 0.000 0.548
#> GSM531632 1 0.9009 0.4199 0.464 0.132 0.404
#> GSM531638 3 0.6286 -0.3021 0.464 0.000 0.536
#> GSM531639 1 0.6126 0.5725 0.600 0.000 0.400
#> GSM531641 1 0.0000 0.6047 1.000 0.000 0.000
#> GSM531642 1 0.5968 0.6265 0.636 0.000 0.364
#> GSM531643 1 0.8318 0.6368 0.600 0.116 0.284
#> GSM531644 1 0.8318 0.6364 0.600 0.116 0.284
#> GSM531645 1 0.0000 0.6047 1.000 0.000 0.000
#> GSM531646 1 0.8968 0.4174 0.464 0.128 0.408
#> GSM531647 1 0.9009 0.4199 0.464 0.132 0.404
#> GSM531648 1 0.5363 0.6982 0.724 0.000 0.276
#> GSM531650 1 0.8435 0.6335 0.600 0.132 0.268
#> GSM531651 3 0.0000 0.6882 0.000 0.000 1.000
#> GSM531652 1 0.5363 0.6982 0.724 0.000 0.276
#> GSM531656 1 0.7141 0.5995 0.600 0.032 0.368
#> GSM531659 1 0.5363 0.6982 0.724 0.000 0.276
#> GSM531661 3 0.0000 0.6882 0.000 0.000 1.000
#> GSM531662 3 0.0237 0.6856 0.004 0.000 0.996
#> GSM531663 1 0.2066 0.6298 0.940 0.000 0.060
#> GSM531664 2 0.6091 0.6467 0.092 0.784 0.124
#> GSM531666 1 0.5988 0.6227 0.632 0.000 0.368
#> GSM531667 1 0.5835 0.6381 0.660 0.000 0.340
#> GSM531668 1 0.4654 0.6844 0.792 0.000 0.208
#> GSM531669 2 0.7065 0.5116 0.228 0.700 0.072
#> GSM531671 3 0.8981 -0.3691 0.424 0.128 0.448
#> GSM531672 1 0.5363 0.6982 0.724 0.000 0.276
#> GSM531673 3 0.3686 0.5566 0.140 0.000 0.860
#> GSM531676 2 0.0000 0.8614 0.000 1.000 0.000
#> GSM531679 2 0.3267 0.8842 0.116 0.884 0.000
#> GSM531681 2 0.6126 0.6706 0.400 0.600 0.000
#> GSM531682 2 0.3826 0.8844 0.124 0.868 0.008
#> GSM531683 2 0.3826 0.8844 0.124 0.868 0.008
#> GSM531684 3 0.6359 -0.0651 0.004 0.404 0.592
#> GSM531685 2 0.0000 0.8614 0.000 1.000 0.000
#> GSM531686 2 0.5621 0.7544 0.308 0.692 0.000
#> GSM531687 2 0.4002 0.8025 0.000 0.840 0.160
#> GSM531688 2 0.0000 0.8614 0.000 1.000 0.000
#> GSM531690 2 0.3715 0.8834 0.128 0.868 0.004
#> GSM531693 2 0.0000 0.8614 0.000 1.000 0.000
#> GSM531695 2 0.0000 0.8614 0.000 1.000 0.000
#> GSM531603 2 0.3826 0.8844 0.124 0.868 0.008
#> GSM531609 1 0.0000 0.6047 1.000 0.000 0.000
#> GSM531611 1 0.0592 0.6107 0.988 0.000 0.012
#> GSM531621 3 0.0000 0.6882 0.000 0.000 1.000
#> GSM531622 3 0.0000 0.6882 0.000 0.000 1.000
#> GSM531628 1 0.8435 0.6335 0.600 0.132 0.268
#> GSM531630 3 0.3619 0.5595 0.136 0.000 0.864
#> GSM531633 3 0.0000 0.6882 0.000 0.000 1.000
#> GSM531635 3 0.7389 -0.3485 0.464 0.032 0.504
#> GSM531640 1 0.5497 0.6920 0.708 0.000 0.292
#> GSM531649 3 0.7389 -0.3485 0.464 0.032 0.504
#> GSM531653 1 0.9009 0.4199 0.464 0.132 0.404
#> GSM531657 1 0.5363 0.6982 0.724 0.000 0.276
#> GSM531665 2 0.3120 0.8288 0.012 0.908 0.080
#> GSM531670 1 0.7141 0.5995 0.600 0.032 0.368
#> GSM531674 2 0.2356 0.8229 0.000 0.928 0.072
#> GSM531675 2 0.3826 0.8844 0.124 0.868 0.008
#> GSM531677 2 0.3412 0.8838 0.124 0.876 0.000
#> GSM531678 2 0.3826 0.8844 0.124 0.868 0.008
#> GSM531680 2 0.2625 0.8552 0.000 0.916 0.084
#> GSM531689 2 0.3207 0.8587 0.012 0.904 0.084
#> GSM531691 2 0.3482 0.8389 0.000 0.872 0.128
#> GSM531692 2 0.1753 0.8649 0.000 0.952 0.048
#> GSM531694 2 0.3826 0.8844 0.124 0.868 0.008
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM531602 2 0.0188 0.8224 0.000 0.996 0.000 0.004
#> GSM531604 2 0.1792 0.8013 0.000 0.932 0.068 0.000
#> GSM531606 2 0.0188 0.8224 0.000 0.996 0.000 0.004
#> GSM531607 2 0.0188 0.8224 0.000 0.996 0.000 0.004
#> GSM531608 3 0.1302 0.7909 0.000 0.044 0.956 0.000
#> GSM531610 4 0.0000 0.9073 0.000 0.000 0.000 1.000
#> GSM531612 4 0.0000 0.9073 0.000 0.000 0.000 1.000
#> GSM531613 4 0.0000 0.9073 0.000 0.000 0.000 1.000
#> GSM531614 4 0.0000 0.9073 0.000 0.000 0.000 1.000
#> GSM531616 3 0.3726 0.6359 0.212 0.000 0.788 0.000
#> GSM531618 1 0.7202 0.3247 0.504 0.364 0.128 0.004
#> GSM531619 3 0.0000 0.8157 0.000 0.000 1.000 0.000
#> GSM531620 3 0.0000 0.8157 0.000 0.000 1.000 0.000
#> GSM531623 3 0.0000 0.8157 0.000 0.000 1.000 0.000
#> GSM531625 3 0.0000 0.8157 0.000 0.000 1.000 0.000
#> GSM531626 3 0.3649 0.6443 0.204 0.000 0.796 0.000
#> GSM531632 1 0.2868 0.6404 0.864 0.000 0.136 0.000
#> GSM531638 3 0.3726 0.6359 0.212 0.000 0.788 0.000
#> GSM531639 1 0.7216 0.2953 0.508 0.156 0.336 0.000
#> GSM531641 4 0.0000 0.9073 0.000 0.000 0.000 1.000
#> GSM531642 1 0.6324 0.5651 0.660 0.168 0.172 0.000
#> GSM531643 1 0.2760 0.6458 0.872 0.000 0.128 0.000
#> GSM531644 1 0.2760 0.6458 0.872 0.000 0.128 0.000
#> GSM531645 4 0.0000 0.9073 0.000 0.000 0.000 1.000
#> GSM531646 1 0.2868 0.6404 0.864 0.000 0.136 0.000
#> GSM531647 1 0.2868 0.6404 0.864 0.000 0.136 0.000
#> GSM531648 1 0.7335 0.5340 0.648 0.068 0.128 0.156
#> GSM531650 1 0.0000 0.6693 1.000 0.000 0.000 0.000
#> GSM531651 3 0.0000 0.8157 0.000 0.000 1.000 0.000
#> GSM531652 1 0.4664 0.6169 0.800 0.068 0.128 0.004
#> GSM531656 1 0.6826 0.5146 0.600 0.228 0.172 0.000
#> GSM531659 2 0.7136 0.1346 0.340 0.528 0.128 0.004
#> GSM531661 3 0.1389 0.7839 0.000 0.048 0.952 0.000
#> GSM531662 3 0.1389 0.7839 0.000 0.048 0.952 0.000
#> GSM531663 4 0.6913 0.5476 0.172 0.068 0.084 0.676
#> GSM531664 1 0.4277 0.4276 0.720 0.280 0.000 0.000
#> GSM531666 1 0.7050 0.4897 0.564 0.264 0.172 0.000
#> GSM531667 3 0.6376 0.4049 0.340 0.068 0.588 0.004
#> GSM531668 4 0.7711 0.1834 0.340 0.132 0.024 0.504
#> GSM531669 1 0.3649 0.5370 0.796 0.204 0.000 0.000
#> GSM531671 3 0.7110 0.0687 0.412 0.128 0.460 0.000
#> GSM531672 2 0.7136 0.1346 0.340 0.528 0.128 0.004
#> GSM531673 3 0.4307 0.7124 0.144 0.048 0.808 0.000
#> GSM531676 2 0.2530 0.7894 0.112 0.888 0.000 0.000
#> GSM531679 2 0.0000 0.8221 0.000 1.000 0.000 0.000
#> GSM531681 4 0.0188 0.9044 0.000 0.004 0.000 0.996
#> GSM531682 2 0.1576 0.8086 0.000 0.948 0.048 0.004
#> GSM531683 2 0.0188 0.8224 0.000 0.996 0.000 0.004
#> GSM531684 3 0.4164 0.5619 0.000 0.264 0.736 0.000
#> GSM531685 2 0.3024 0.7677 0.148 0.852 0.000 0.000
#> GSM531686 2 0.4624 0.4671 0.000 0.660 0.000 0.340
#> GSM531687 2 0.4095 0.7271 0.024 0.804 0.172 0.000
#> GSM531688 2 0.3610 0.7331 0.200 0.800 0.000 0.000
#> GSM531690 2 0.1724 0.8132 0.000 0.948 0.020 0.032
#> GSM531693 2 0.3649 0.7293 0.204 0.796 0.000 0.000
#> GSM531695 2 0.3528 0.7389 0.192 0.808 0.000 0.000
#> GSM531603 2 0.0188 0.8224 0.000 0.996 0.000 0.004
#> GSM531609 4 0.0000 0.9073 0.000 0.000 0.000 1.000
#> GSM531611 4 0.0707 0.8903 0.000 0.000 0.020 0.980
#> GSM531621 3 0.0000 0.8157 0.000 0.000 1.000 0.000
#> GSM531622 3 0.0000 0.8157 0.000 0.000 1.000 0.000
#> GSM531628 1 0.0000 0.6693 1.000 0.000 0.000 0.000
#> GSM531630 3 0.2868 0.7207 0.136 0.000 0.864 0.000
#> GSM531633 3 0.0000 0.8157 0.000 0.000 1.000 0.000
#> GSM531635 1 0.4454 0.5450 0.692 0.000 0.308 0.000
#> GSM531640 3 0.6180 0.4258 0.340 0.056 0.600 0.004
#> GSM531649 1 0.3400 0.6206 0.820 0.000 0.180 0.000
#> GSM531653 1 0.2868 0.6404 0.864 0.000 0.136 0.000
#> GSM531657 2 0.7136 0.1346 0.340 0.528 0.128 0.004
#> GSM531665 2 0.4410 0.7436 0.064 0.808 0.128 0.000
#> GSM531670 2 0.7408 0.0654 0.364 0.464 0.172 0.000
#> GSM531674 1 0.4624 0.2961 0.660 0.340 0.000 0.000
#> GSM531675 2 0.1576 0.8086 0.000 0.948 0.048 0.004
#> GSM531677 2 0.0188 0.8224 0.000 0.996 0.000 0.004
#> GSM531678 2 0.0000 0.8221 0.000 1.000 0.000 0.000
#> GSM531680 2 0.4274 0.7549 0.148 0.808 0.044 0.000
#> GSM531689 2 0.1888 0.8091 0.016 0.940 0.044 0.000
#> GSM531691 2 0.2730 0.7944 0.016 0.896 0.088 0.000
#> GSM531692 2 0.2131 0.8094 0.032 0.932 0.036 0.000
#> GSM531694 2 0.0188 0.8224 0.000 0.996 0.000 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM531602 2 0.0162 0.9241 0.000 0.996 0.000 0.000 0.004
#> GSM531604 2 0.0290 0.9204 0.000 0.992 0.008 0.000 0.000
#> GSM531606 2 0.1430 0.8752 0.000 0.944 0.052 0.000 0.004
#> GSM531607 2 0.0000 0.9240 0.000 1.000 0.000 0.000 0.000
#> GSM531608 3 0.0000 0.9692 0.000 0.000 1.000 0.000 0.000
#> GSM531610 4 0.0000 0.8810 0.000 0.000 0.000 1.000 0.000
#> GSM531612 4 0.0000 0.8810 0.000 0.000 0.000 1.000 0.000
#> GSM531613 4 0.0000 0.8810 0.000 0.000 0.000 1.000 0.000
#> GSM531614 4 0.0000 0.8810 0.000 0.000 0.000 1.000 0.000
#> GSM531616 5 0.2179 0.8441 0.112 0.000 0.000 0.000 0.888
#> GSM531618 5 0.1205 0.8942 0.040 0.004 0.000 0.000 0.956
#> GSM531619 3 0.0000 0.9692 0.000 0.000 1.000 0.000 0.000
#> GSM531620 3 0.1357 0.9626 0.004 0.000 0.948 0.000 0.048
#> GSM531623 3 0.0000 0.9692 0.000 0.000 1.000 0.000 0.000
#> GSM531625 3 0.1357 0.9626 0.004 0.000 0.948 0.000 0.048
#> GSM531626 5 0.2464 0.8457 0.096 0.000 0.016 0.000 0.888
#> GSM531632 1 0.1197 0.8996 0.952 0.000 0.000 0.000 0.048
#> GSM531638 5 0.2074 0.8486 0.104 0.000 0.000 0.000 0.896
#> GSM531639 5 0.0162 0.8856 0.004 0.000 0.000 0.000 0.996
#> GSM531641 4 0.0000 0.8810 0.000 0.000 0.000 1.000 0.000
#> GSM531642 5 0.1357 0.8933 0.048 0.004 0.000 0.000 0.948
#> GSM531643 5 0.1478 0.8900 0.064 0.000 0.000 0.000 0.936
#> GSM531644 5 0.1270 0.8927 0.052 0.000 0.000 0.000 0.948
#> GSM531645 4 0.0000 0.8810 0.000 0.000 0.000 1.000 0.000
#> GSM531646 1 0.1197 0.8996 0.952 0.000 0.000 0.000 0.048
#> GSM531647 1 0.0000 0.9185 1.000 0.000 0.000 0.000 0.000
#> GSM531648 5 0.1197 0.8929 0.048 0.000 0.000 0.000 0.952
#> GSM531650 1 0.1851 0.8608 0.912 0.000 0.000 0.000 0.088
#> GSM531651 3 0.0000 0.9692 0.000 0.000 1.000 0.000 0.000
#> GSM531652 5 0.1197 0.8929 0.048 0.000 0.000 0.000 0.952
#> GSM531656 5 0.1270 0.8927 0.052 0.000 0.000 0.000 0.948
#> GSM531659 5 0.1197 0.8862 0.000 0.048 0.000 0.000 0.952
#> GSM531661 3 0.0000 0.9692 0.000 0.000 1.000 0.000 0.000
#> GSM531662 3 0.0000 0.9692 0.000 0.000 1.000 0.000 0.000
#> GSM531663 4 0.4273 0.1656 0.000 0.000 0.000 0.552 0.448
#> GSM531664 1 0.2179 0.8727 0.896 0.100 0.000 0.000 0.004
#> GSM531666 5 0.1357 0.8933 0.048 0.004 0.000 0.000 0.948
#> GSM531667 5 0.3039 0.7773 0.000 0.000 0.192 0.000 0.808
#> GSM531668 5 0.4147 0.7180 0.000 0.004 0.048 0.172 0.776
#> GSM531669 1 0.0162 0.9180 0.996 0.000 0.000 0.000 0.004
#> GSM531671 1 0.1557 0.8973 0.940 0.000 0.052 0.000 0.008
#> GSM531672 5 0.1197 0.8862 0.000 0.048 0.000 0.000 0.952
#> GSM531673 3 0.1121 0.9335 0.000 0.000 0.956 0.000 0.044
#> GSM531676 2 0.0609 0.9124 0.020 0.980 0.000 0.000 0.000
#> GSM531679 2 0.0000 0.9240 0.000 1.000 0.000 0.000 0.000
#> GSM531681 4 0.4304 0.0345 0.000 0.484 0.000 0.516 0.000
#> GSM531682 2 0.0290 0.9228 0.000 0.992 0.000 0.000 0.008
#> GSM531683 2 0.0000 0.9240 0.000 1.000 0.000 0.000 0.000
#> GSM531684 3 0.0000 0.9692 0.000 0.000 1.000 0.000 0.000
#> GSM531685 1 0.2813 0.8255 0.832 0.168 0.000 0.000 0.000
#> GSM531686 2 0.0404 0.9191 0.000 0.988 0.000 0.012 0.000
#> GSM531687 5 0.2813 0.7981 0.000 0.168 0.000 0.000 0.832
#> GSM531688 1 0.2813 0.8255 0.832 0.168 0.000 0.000 0.000
#> GSM531690 2 0.0162 0.9241 0.000 0.996 0.000 0.000 0.004
#> GSM531693 1 0.1410 0.9009 0.940 0.060 0.000 0.000 0.000
#> GSM531695 1 0.3003 0.8028 0.812 0.188 0.000 0.000 0.000
#> GSM531603 5 0.4304 0.1883 0.000 0.484 0.000 0.000 0.516
#> GSM531609 4 0.0000 0.8810 0.000 0.000 0.000 1.000 0.000
#> GSM531611 4 0.0794 0.8610 0.000 0.000 0.000 0.972 0.028
#> GSM531621 3 0.1357 0.9626 0.004 0.000 0.948 0.000 0.048
#> GSM531622 3 0.1357 0.9626 0.004 0.000 0.948 0.000 0.048
#> GSM531628 1 0.0162 0.9180 0.996 0.000 0.000 0.000 0.004
#> GSM531630 3 0.1270 0.9620 0.000 0.000 0.948 0.000 0.052
#> GSM531633 3 0.1357 0.9626 0.004 0.000 0.948 0.000 0.048
#> GSM531635 5 0.2329 0.8360 0.124 0.000 0.000 0.000 0.876
#> GSM531640 5 0.0162 0.8847 0.000 0.000 0.004 0.000 0.996
#> GSM531649 1 0.0000 0.9185 1.000 0.000 0.000 0.000 0.000
#> GSM531653 1 0.0000 0.9185 1.000 0.000 0.000 0.000 0.000
#> GSM531657 5 0.1197 0.8862 0.000 0.048 0.000 0.000 0.952
#> GSM531665 5 0.3810 0.7760 0.040 0.168 0.000 0.000 0.792
#> GSM531670 5 0.1270 0.8857 0.000 0.052 0.000 0.000 0.948
#> GSM531674 1 0.0162 0.9188 0.996 0.004 0.000 0.000 0.000
#> GSM531675 2 0.0162 0.9241 0.000 0.996 0.000 0.000 0.004
#> GSM531677 2 0.0162 0.9241 0.000 0.996 0.000 0.000 0.004
#> GSM531678 2 0.0162 0.9227 0.000 0.996 0.000 0.000 0.004
#> GSM531680 2 0.4135 0.4234 0.340 0.656 0.000 0.000 0.004
#> GSM531689 2 0.0000 0.9240 0.000 1.000 0.000 0.000 0.000
#> GSM531691 2 0.2329 0.7883 0.000 0.876 0.000 0.000 0.124
#> GSM531692 2 0.5668 0.0511 0.416 0.504 0.080 0.000 0.000
#> GSM531694 2 0.0162 0.9241 0.000 0.996 0.000 0.000 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM531602 2 0.4093 0.667 0.404 0.584 0.000 0.000 0.012 0.000
#> GSM531604 2 0.3548 0.494 0.068 0.812 0.008 0.000 0.112 0.000
#> GSM531606 2 0.5862 0.567 0.404 0.448 0.136 0.000 0.012 0.000
#> GSM531607 2 0.4093 0.667 0.404 0.584 0.000 0.000 0.012 0.000
#> GSM531608 3 0.0000 0.923 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531610 4 0.0000 0.936 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531612 4 0.0000 0.936 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531613 4 0.0000 0.936 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531614 4 0.0000 0.936 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531616 6 0.2066 0.834 0.052 0.000 0.000 0.000 0.040 0.908
#> GSM531618 6 0.2255 0.882 0.088 0.016 0.000 0.000 0.004 0.892
#> GSM531619 3 0.0000 0.923 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531620 3 0.2573 0.902 0.000 0.000 0.864 0.000 0.024 0.112
#> GSM531623 3 0.0000 0.923 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531625 3 0.2573 0.902 0.000 0.000 0.864 0.000 0.024 0.112
#> GSM531626 6 0.1890 0.842 0.044 0.000 0.008 0.000 0.024 0.924
#> GSM531632 1 0.5389 0.823 0.460 0.000 0.000 0.000 0.428 0.112
#> GSM531638 6 0.1856 0.840 0.048 0.000 0.000 0.000 0.032 0.920
#> GSM531639 6 0.0000 0.864 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM531641 4 0.0000 0.936 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531642 6 0.1957 0.879 0.112 0.000 0.000 0.000 0.000 0.888
#> GSM531643 6 0.2750 0.862 0.136 0.000 0.000 0.000 0.020 0.844
#> GSM531644 6 0.2100 0.879 0.112 0.000 0.000 0.000 0.004 0.884
#> GSM531645 4 0.0000 0.936 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531646 1 0.5389 0.823 0.460 0.000 0.000 0.000 0.428 0.112
#> GSM531647 1 0.3765 0.931 0.596 0.000 0.000 0.000 0.404 0.000
#> GSM531648 6 0.2404 0.877 0.112 0.016 0.000 0.000 0.000 0.872
#> GSM531650 1 0.4584 0.895 0.556 0.000 0.000 0.000 0.404 0.040
#> GSM531651 3 0.0000 0.923 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531652 6 0.2100 0.879 0.112 0.004 0.000 0.000 0.000 0.884
#> GSM531656 6 0.1957 0.879 0.112 0.000 0.000 0.000 0.000 0.888
#> GSM531659 6 0.2135 0.835 0.000 0.128 0.000 0.000 0.000 0.872
#> GSM531661 3 0.0000 0.923 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531662 3 0.0260 0.920 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM531663 4 0.4012 0.419 0.000 0.016 0.000 0.640 0.000 0.344
#> GSM531664 1 0.3975 0.887 0.544 0.000 0.000 0.000 0.452 0.004
#> GSM531666 6 0.1957 0.879 0.112 0.000 0.000 0.000 0.000 0.888
#> GSM531667 6 0.2793 0.783 0.000 0.000 0.200 0.000 0.000 0.800
#> GSM531668 6 0.5686 0.297 0.404 0.012 0.112 0.000 0.000 0.472
#> GSM531669 1 0.3765 0.931 0.596 0.000 0.000 0.000 0.404 0.000
#> GSM531671 1 0.5858 0.808 0.452 0.000 0.124 0.000 0.408 0.016
#> GSM531672 6 0.2404 0.837 0.000 0.016 0.000 0.000 0.112 0.872
#> GSM531673 3 0.1367 0.891 0.000 0.000 0.944 0.000 0.012 0.044
#> GSM531676 5 0.3996 0.682 0.008 0.352 0.000 0.000 0.636 0.004
#> GSM531679 2 0.0363 0.632 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM531681 2 0.3823 0.303 0.000 0.564 0.000 0.436 0.000 0.000
#> GSM531682 2 0.0363 0.637 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM531683 2 0.4093 0.667 0.404 0.584 0.000 0.000 0.012 0.000
#> GSM531684 3 0.0363 0.918 0.000 0.000 0.988 0.000 0.012 0.000
#> GSM531685 5 0.3578 0.683 0.000 0.340 0.000 0.000 0.660 0.000
#> GSM531686 2 0.3371 0.529 0.000 0.708 0.000 0.292 0.000 0.000
#> GSM531687 5 0.5221 0.652 0.000 0.328 0.000 0.000 0.560 0.112
#> GSM531688 5 0.4576 -0.696 0.400 0.040 0.000 0.000 0.560 0.000
#> GSM531690 2 0.0603 0.642 0.000 0.980 0.000 0.016 0.000 0.004
#> GSM531693 5 0.4028 -0.546 0.308 0.024 0.000 0.000 0.668 0.000
#> GSM531695 5 0.3650 0.644 0.012 0.280 0.000 0.000 0.708 0.000
#> GSM531603 5 0.4326 0.296 0.404 0.024 0.000 0.000 0.572 0.000
#> GSM531609 4 0.0000 0.936 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531611 4 0.0632 0.914 0.000 0.000 0.000 0.976 0.000 0.024
#> GSM531621 3 0.2573 0.902 0.000 0.000 0.864 0.000 0.024 0.112
#> GSM531622 3 0.2573 0.902 0.000 0.000 0.864 0.000 0.024 0.112
#> GSM531628 1 0.3765 0.931 0.596 0.000 0.000 0.000 0.404 0.000
#> GSM531630 3 0.2219 0.898 0.000 0.000 0.864 0.000 0.000 0.136
#> GSM531633 3 0.2573 0.902 0.000 0.000 0.864 0.000 0.024 0.112
#> GSM531635 6 0.2066 0.834 0.052 0.000 0.000 0.000 0.040 0.908
#> GSM531640 6 0.0000 0.864 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM531649 1 0.3890 0.929 0.596 0.000 0.000 0.000 0.400 0.004
#> GSM531653 1 0.3765 0.931 0.596 0.000 0.000 0.000 0.404 0.000
#> GSM531657 6 0.2135 0.835 0.000 0.128 0.000 0.000 0.000 0.872
#> GSM531665 5 0.5520 0.578 0.000 0.240 0.000 0.000 0.560 0.200
#> GSM531670 6 0.1957 0.837 0.000 0.000 0.000 0.000 0.112 0.888
#> GSM531674 1 0.3765 0.931 0.596 0.000 0.000 0.000 0.404 0.000
#> GSM531675 2 0.0146 0.637 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM531677 2 0.0000 0.636 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531678 5 0.4856 0.665 0.000 0.360 0.000 0.000 0.572 0.068
#> GSM531680 5 0.4048 0.683 0.012 0.340 0.000 0.000 0.644 0.004
#> GSM531689 5 0.3937 0.636 0.000 0.424 0.000 0.000 0.572 0.004
#> GSM531691 5 0.4961 0.664 0.000 0.348 0.000 0.000 0.572 0.080
#> GSM531692 5 0.5629 0.575 0.000 0.324 0.148 0.000 0.524 0.004
#> GSM531694 2 0.3765 0.666 0.404 0.596 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)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> SD:pam 79 0.391 2
#> SD:pam 69 0.443 3
#> SD:pam 66 0.487 4
#> SD:pam 75 0.899 5
#> SD:pam 73 0.398 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "mclust"]
# you can also extract it by
# res = res_list["SD:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 80 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.302 0.828 0.873 0.4519 0.495 0.495
#> 3 3 0.341 0.707 0.772 0.3375 0.732 0.517
#> 4 4 0.729 0.848 0.919 0.2189 0.824 0.545
#> 5 5 0.683 0.715 0.813 0.0432 0.960 0.853
#> 6 6 0.724 0.666 0.767 0.0619 0.916 0.682
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM531602 2 0.1184 0.890 0.016 0.984
#> GSM531604 2 0.1184 0.890 0.016 0.984
#> GSM531606 2 0.1184 0.890 0.016 0.984
#> GSM531607 2 0.1184 0.890 0.016 0.984
#> GSM531608 1 0.6623 0.883 0.828 0.172
#> GSM531610 2 0.5178 0.864 0.116 0.884
#> GSM531612 2 0.5178 0.864 0.116 0.884
#> GSM531613 2 0.5178 0.864 0.116 0.884
#> GSM531614 2 0.5178 0.864 0.116 0.884
#> GSM531616 1 0.2948 0.844 0.948 0.052
#> GSM531618 2 0.7299 0.777 0.204 0.796
#> GSM531619 1 0.0672 0.822 0.992 0.008
#> GSM531620 1 0.0672 0.822 0.992 0.008
#> GSM531623 1 0.0672 0.822 0.992 0.008
#> GSM531625 1 0.0672 0.822 0.992 0.008
#> GSM531626 1 0.0672 0.822 0.992 0.008
#> GSM531632 1 0.6438 0.885 0.836 0.164
#> GSM531638 1 0.0672 0.822 0.992 0.008
#> GSM531639 1 0.6531 0.884 0.832 0.168
#> GSM531641 2 0.5178 0.864 0.116 0.884
#> GSM531642 1 0.6531 0.884 0.832 0.168
#> GSM531643 1 0.6531 0.884 0.832 0.168
#> GSM531644 1 0.6623 0.883 0.828 0.172
#> GSM531645 2 0.5178 0.864 0.116 0.884
#> GSM531646 1 0.6343 0.885 0.840 0.160
#> GSM531647 1 0.6343 0.885 0.840 0.160
#> GSM531648 2 0.5178 0.864 0.116 0.884
#> GSM531650 1 0.6343 0.885 0.840 0.160
#> GSM531651 1 0.0672 0.822 0.992 0.008
#> GSM531652 1 0.9460 0.577 0.636 0.364
#> GSM531656 1 0.6531 0.884 0.832 0.168
#> GSM531659 2 0.5629 0.863 0.132 0.868
#> GSM531661 1 0.6712 0.882 0.824 0.176
#> GSM531662 1 0.8207 0.816 0.744 0.256
#> GSM531663 2 0.5629 0.863 0.132 0.868
#> GSM531664 1 0.6438 0.885 0.836 0.164
#> GSM531666 1 0.6887 0.874 0.816 0.184
#> GSM531667 1 0.3733 0.853 0.928 0.072
#> GSM531668 2 0.5629 0.863 0.132 0.868
#> GSM531669 1 0.6712 0.880 0.824 0.176
#> GSM531671 1 0.7056 0.873 0.808 0.192
#> GSM531672 2 0.5629 0.863 0.132 0.868
#> GSM531673 1 0.8909 0.758 0.692 0.308
#> GSM531676 2 0.7602 0.647 0.220 0.780
#> GSM531679 2 0.1184 0.890 0.016 0.984
#> GSM531681 2 0.1184 0.890 0.016 0.984
#> GSM531682 2 0.1184 0.890 0.016 0.984
#> GSM531683 2 0.1184 0.890 0.016 0.984
#> GSM531684 2 0.1184 0.890 0.016 0.984
#> GSM531685 2 0.9427 0.271 0.360 0.640
#> GSM531686 2 0.1184 0.890 0.016 0.984
#> GSM531687 2 0.8267 0.562 0.260 0.740
#> GSM531688 1 0.9209 0.716 0.664 0.336
#> GSM531690 2 0.1184 0.890 0.016 0.984
#> GSM531693 1 0.8608 0.779 0.716 0.284
#> GSM531695 1 0.9970 0.421 0.532 0.468
#> GSM531603 2 0.1184 0.890 0.016 0.984
#> GSM531609 2 0.5178 0.864 0.116 0.884
#> GSM531611 2 0.5629 0.863 0.132 0.868
#> GSM531621 1 0.0672 0.822 0.992 0.008
#> GSM531622 1 0.0938 0.823 0.988 0.012
#> GSM531628 1 0.6343 0.885 0.840 0.160
#> GSM531630 1 0.0672 0.822 0.992 0.008
#> GSM531633 1 0.0672 0.822 0.992 0.008
#> GSM531635 1 0.6531 0.884 0.832 0.168
#> GSM531640 1 0.6623 0.883 0.828 0.172
#> GSM531649 1 0.6438 0.885 0.836 0.164
#> GSM531653 1 0.6343 0.885 0.840 0.160
#> GSM531657 2 0.5629 0.863 0.132 0.868
#> GSM531665 1 0.9580 0.597 0.620 0.380
#> GSM531670 1 0.6623 0.883 0.828 0.172
#> GSM531674 1 0.6438 0.885 0.836 0.164
#> GSM531675 2 0.1184 0.890 0.016 0.984
#> GSM531677 2 0.1184 0.890 0.016 0.984
#> GSM531678 2 0.1184 0.890 0.016 0.984
#> GSM531680 2 0.9522 0.215 0.372 0.628
#> GSM531689 2 0.1184 0.890 0.016 0.984
#> GSM531691 2 0.1184 0.890 0.016 0.984
#> GSM531692 2 0.4161 0.851 0.084 0.916
#> GSM531694 2 0.1184 0.890 0.016 0.984
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM531602 2 0.0424 0.8169 0.008 0.992 0.000
#> GSM531604 2 0.0000 0.8177 0.000 1.000 0.000
#> GSM531606 2 0.0000 0.8177 0.000 1.000 0.000
#> GSM531607 2 0.0424 0.8169 0.008 0.992 0.000
#> GSM531608 3 0.7692 0.5786 0.136 0.184 0.680
#> GSM531610 1 0.4796 0.7912 0.780 0.220 0.000
#> GSM531612 1 0.4702 0.7896 0.788 0.212 0.000
#> GSM531613 1 0.5244 0.7919 0.756 0.240 0.004
#> GSM531614 1 0.4702 0.7896 0.788 0.212 0.000
#> GSM531616 3 0.7816 0.7815 0.200 0.132 0.668
#> GSM531618 1 0.7622 0.7228 0.608 0.332 0.060
#> GSM531619 3 0.5109 0.7492 0.212 0.008 0.780
#> GSM531620 3 0.5536 0.7539 0.200 0.024 0.776
#> GSM531623 3 0.5109 0.7492 0.212 0.008 0.780
#> GSM531625 3 0.7657 0.7810 0.208 0.116 0.676
#> GSM531626 3 0.7843 0.7829 0.208 0.128 0.664
#> GSM531632 3 0.4676 0.8015 0.040 0.112 0.848
#> GSM531638 3 0.7816 0.7815 0.200 0.132 0.668
#> GSM531639 3 0.6685 0.7022 0.048 0.244 0.708
#> GSM531641 1 0.4702 0.7896 0.788 0.212 0.000
#> GSM531642 3 0.7012 0.6056 0.040 0.308 0.652
#> GSM531643 3 0.5094 0.7997 0.040 0.136 0.824
#> GSM531644 3 0.5875 0.7750 0.056 0.160 0.784
#> GSM531645 1 0.4702 0.7896 0.788 0.212 0.000
#> GSM531646 3 0.4891 0.8006 0.040 0.124 0.836
#> GSM531647 3 0.4676 0.8015 0.040 0.112 0.848
#> GSM531648 1 0.4931 0.7912 0.784 0.212 0.004
#> GSM531650 3 0.4676 0.8015 0.040 0.112 0.848
#> GSM531651 3 0.5109 0.7492 0.212 0.008 0.780
#> GSM531652 1 0.9663 0.4768 0.456 0.308 0.236
#> GSM531656 3 0.5094 0.7997 0.040 0.136 0.824
#> GSM531659 1 0.7163 0.7420 0.628 0.332 0.040
#> GSM531661 1 0.9355 0.0704 0.492 0.320 0.188
#> GSM531662 2 0.6521 0.2469 0.340 0.644 0.016
#> GSM531663 1 0.7163 0.7420 0.628 0.332 0.040
#> GSM531664 3 0.4676 0.8015 0.040 0.112 0.848
#> GSM531666 3 0.8582 0.4606 0.124 0.308 0.568
#> GSM531667 3 0.5541 0.7574 0.252 0.008 0.740
#> GSM531668 1 0.7163 0.7420 0.628 0.332 0.040
#> GSM531669 3 0.5637 0.7588 0.040 0.172 0.788
#> GSM531671 2 0.6255 0.3748 0.300 0.684 0.016
#> GSM531672 1 0.6482 0.7887 0.716 0.244 0.040
#> GSM531673 2 0.6057 0.2809 0.340 0.656 0.004
#> GSM531676 2 0.0424 0.8151 0.000 0.992 0.008
#> GSM531679 2 0.0237 0.8178 0.004 0.996 0.000
#> GSM531681 2 0.5650 0.2992 0.312 0.688 0.000
#> GSM531682 2 0.0237 0.8178 0.004 0.996 0.000
#> GSM531683 2 0.0424 0.8169 0.008 0.992 0.000
#> GSM531684 2 0.4931 0.5298 0.232 0.768 0.000
#> GSM531685 2 0.1031 0.8041 0.000 0.976 0.024
#> GSM531686 2 0.5650 0.2992 0.312 0.688 0.000
#> GSM531687 2 0.0237 0.8166 0.000 0.996 0.004
#> GSM531688 2 0.1411 0.7961 0.000 0.964 0.036
#> GSM531690 2 0.5650 0.2992 0.312 0.688 0.000
#> GSM531693 2 0.4291 0.6207 0.000 0.820 0.180
#> GSM531695 2 0.1411 0.7961 0.000 0.964 0.036
#> GSM531603 2 0.3816 0.6776 0.148 0.852 0.000
#> GSM531609 1 0.4702 0.7896 0.788 0.212 0.000
#> GSM531611 1 0.7163 0.7420 0.628 0.332 0.040
#> GSM531621 3 0.5109 0.7492 0.212 0.008 0.780
#> GSM531622 3 0.5109 0.7492 0.212 0.008 0.780
#> GSM531628 3 0.4676 0.8015 0.040 0.112 0.848
#> GSM531630 3 0.5109 0.7492 0.212 0.008 0.780
#> GSM531633 3 0.5109 0.7492 0.212 0.008 0.780
#> GSM531635 3 0.5028 0.8010 0.040 0.132 0.828
#> GSM531640 3 0.5109 0.7492 0.212 0.008 0.780
#> GSM531649 3 0.5028 0.8010 0.040 0.132 0.828
#> GSM531653 3 0.4676 0.8015 0.040 0.112 0.848
#> GSM531657 1 0.7163 0.7420 0.628 0.332 0.040
#> GSM531665 2 0.7353 0.1651 0.316 0.632 0.052
#> GSM531670 3 0.5094 0.7997 0.040 0.136 0.824
#> GSM531674 3 0.4891 0.7967 0.040 0.124 0.836
#> GSM531675 2 0.5650 0.2992 0.312 0.688 0.000
#> GSM531677 2 0.0237 0.8178 0.004 0.996 0.000
#> GSM531678 2 0.0424 0.8169 0.008 0.992 0.000
#> GSM531680 2 0.0747 0.8109 0.000 0.984 0.016
#> GSM531689 2 0.0000 0.8177 0.000 1.000 0.000
#> GSM531691 2 0.0000 0.8177 0.000 1.000 0.000
#> GSM531692 2 0.1129 0.8038 0.020 0.976 0.004
#> GSM531694 2 0.0424 0.8169 0.008 0.992 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM531602 2 0.0000 0.939 0.000 1.000 0.000 0.000
#> GSM531604 2 0.0000 0.939 0.000 1.000 0.000 0.000
#> GSM531606 2 0.0000 0.939 0.000 1.000 0.000 0.000
#> GSM531607 2 0.0000 0.939 0.000 1.000 0.000 0.000
#> GSM531608 3 0.0000 0.921 0.000 0.000 1.000 0.000
#> GSM531610 4 0.0000 0.873 0.000 0.000 0.000 1.000
#> GSM531612 4 0.0000 0.873 0.000 0.000 0.000 1.000
#> GSM531613 4 0.0000 0.873 0.000 0.000 0.000 1.000
#> GSM531614 4 0.0000 0.873 0.000 0.000 0.000 1.000
#> GSM531616 3 0.0000 0.921 0.000 0.000 1.000 0.000
#> GSM531618 4 0.3837 0.805 0.000 0.000 0.224 0.776
#> GSM531619 3 0.0000 0.921 0.000 0.000 1.000 0.000
#> GSM531620 3 0.0000 0.921 0.000 0.000 1.000 0.000
#> GSM531623 3 0.0000 0.921 0.000 0.000 1.000 0.000
#> GSM531625 3 0.0000 0.921 0.000 0.000 1.000 0.000
#> GSM531626 3 0.0000 0.921 0.000 0.000 1.000 0.000
#> GSM531632 1 0.0000 0.862 1.000 0.000 0.000 0.000
#> GSM531638 3 0.0000 0.921 0.000 0.000 1.000 0.000
#> GSM531639 3 0.4877 0.121 0.408 0.000 0.592 0.000
#> GSM531641 4 0.0000 0.873 0.000 0.000 0.000 1.000
#> GSM531642 1 0.4072 0.758 0.748 0.000 0.252 0.000
#> GSM531643 1 0.3266 0.836 0.832 0.000 0.168 0.000
#> GSM531644 1 0.3668 0.826 0.808 0.000 0.188 0.004
#> GSM531645 4 0.0000 0.873 0.000 0.000 0.000 1.000
#> GSM531646 1 0.0469 0.864 0.988 0.000 0.012 0.000
#> GSM531647 1 0.0336 0.864 0.992 0.000 0.008 0.000
#> GSM531648 4 0.1716 0.870 0.000 0.000 0.064 0.936
#> GSM531650 1 0.0000 0.862 1.000 0.000 0.000 0.000
#> GSM531651 3 0.0000 0.921 0.000 0.000 1.000 0.000
#> GSM531652 1 0.4095 0.818 0.792 0.000 0.192 0.016
#> GSM531656 1 0.3610 0.819 0.800 0.000 0.200 0.000
#> GSM531659 4 0.5653 0.767 0.000 0.096 0.192 0.712
#> GSM531661 3 0.0707 0.898 0.000 0.020 0.980 0.000
#> GSM531662 3 0.3356 0.688 0.000 0.176 0.824 0.000
#> GSM531663 4 0.3528 0.835 0.000 0.000 0.192 0.808
#> GSM531664 1 0.0000 0.862 1.000 0.000 0.000 0.000
#> GSM531666 1 0.3610 0.819 0.800 0.000 0.200 0.000
#> GSM531667 3 0.0000 0.921 0.000 0.000 1.000 0.000
#> GSM531668 4 0.5212 0.798 0.000 0.068 0.192 0.740
#> GSM531669 1 0.0000 0.862 1.000 0.000 0.000 0.000
#> GSM531671 3 0.7526 0.126 0.332 0.200 0.468 0.000
#> GSM531672 4 0.3528 0.835 0.000 0.000 0.192 0.808
#> GSM531673 2 0.4103 0.660 0.000 0.744 0.256 0.000
#> GSM531676 2 0.0000 0.939 0.000 1.000 0.000 0.000
#> GSM531679 2 0.0000 0.939 0.000 1.000 0.000 0.000
#> GSM531681 2 0.3837 0.723 0.000 0.776 0.000 0.224
#> GSM531682 2 0.0000 0.939 0.000 1.000 0.000 0.000
#> GSM531683 2 0.0000 0.939 0.000 1.000 0.000 0.000
#> GSM531684 2 0.0000 0.939 0.000 1.000 0.000 0.000
#> GSM531685 2 0.3726 0.725 0.212 0.788 0.000 0.000
#> GSM531686 2 0.1118 0.915 0.000 0.964 0.000 0.036
#> GSM531687 2 0.0000 0.939 0.000 1.000 0.000 0.000
#> GSM531688 1 0.3528 0.762 0.808 0.192 0.000 0.000
#> GSM531690 2 0.3610 0.752 0.000 0.800 0.000 0.200
#> GSM531693 1 0.3569 0.758 0.804 0.196 0.000 0.000
#> GSM531695 1 0.3610 0.754 0.800 0.200 0.000 0.000
#> GSM531603 2 0.0000 0.939 0.000 1.000 0.000 0.000
#> GSM531609 4 0.0000 0.873 0.000 0.000 0.000 1.000
#> GSM531611 4 0.3528 0.835 0.000 0.000 0.192 0.808
#> GSM531621 3 0.0000 0.921 0.000 0.000 1.000 0.000
#> GSM531622 3 0.0000 0.921 0.000 0.000 1.000 0.000
#> GSM531628 1 0.0000 0.862 1.000 0.000 0.000 0.000
#> GSM531630 3 0.0000 0.921 0.000 0.000 1.000 0.000
#> GSM531633 3 0.0000 0.921 0.000 0.000 1.000 0.000
#> GSM531635 1 0.3610 0.819 0.800 0.000 0.200 0.000
#> GSM531640 3 0.0000 0.921 0.000 0.000 1.000 0.000
#> GSM531649 1 0.2704 0.851 0.876 0.000 0.124 0.000
#> GSM531653 1 0.0336 0.864 0.992 0.000 0.008 0.000
#> GSM531657 4 0.3528 0.835 0.000 0.000 0.192 0.808
#> GSM531665 2 0.6163 0.576 0.160 0.676 0.164 0.000
#> GSM531670 1 0.3610 0.819 0.800 0.000 0.200 0.000
#> GSM531674 1 0.0000 0.862 1.000 0.000 0.000 0.000
#> GSM531675 2 0.0000 0.939 0.000 1.000 0.000 0.000
#> GSM531677 2 0.0000 0.939 0.000 1.000 0.000 0.000
#> GSM531678 2 0.0000 0.939 0.000 1.000 0.000 0.000
#> GSM531680 2 0.2647 0.840 0.120 0.880 0.000 0.000
#> GSM531689 2 0.0000 0.939 0.000 1.000 0.000 0.000
#> GSM531691 2 0.0000 0.939 0.000 1.000 0.000 0.000
#> GSM531692 2 0.0000 0.939 0.000 1.000 0.000 0.000
#> GSM531694 2 0.0000 0.939 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM531602 2 0.0703 0.7990 0.000 0.976 0.000 0.000 NA
#> GSM531604 2 0.2648 0.7800 0.000 0.848 0.000 0.000 NA
#> GSM531606 2 0.0404 0.8059 0.000 0.988 0.000 0.000 NA
#> GSM531607 2 0.0000 0.8058 0.000 1.000 0.000 0.000 NA
#> GSM531608 3 0.1341 0.8617 0.000 0.056 0.944 0.000 NA
#> GSM531610 4 0.1908 0.7867 0.000 0.000 0.000 0.908 NA
#> GSM531612 4 0.1908 0.7867 0.000 0.000 0.000 0.908 NA
#> GSM531613 4 0.0963 0.7932 0.000 0.036 0.000 0.964 NA
#> GSM531614 4 0.1908 0.7867 0.000 0.000 0.000 0.908 NA
#> GSM531616 3 0.4088 0.6342 0.000 0.000 0.632 0.000 NA
#> GSM531618 4 0.7075 0.5054 0.000 0.260 0.068 0.536 NA
#> GSM531619 3 0.0000 0.9038 0.000 0.000 1.000 0.000 NA
#> GSM531620 3 0.1043 0.8893 0.000 0.000 0.960 0.000 NA
#> GSM531623 3 0.0000 0.9038 0.000 0.000 1.000 0.000 NA
#> GSM531625 3 0.0000 0.9038 0.000 0.000 1.000 0.000 NA
#> GSM531626 3 0.3707 0.7343 0.000 0.000 0.716 0.000 NA
#> GSM531632 1 0.0000 0.7434 1.000 0.000 0.000 0.000 NA
#> GSM531638 3 0.3274 0.7898 0.000 0.000 0.780 0.000 NA
#> GSM531639 1 0.6638 0.4891 0.452 0.000 0.276 0.000 NA
#> GSM531641 4 0.1908 0.7867 0.000 0.000 0.000 0.908 NA
#> GSM531642 1 0.8413 0.5843 0.448 0.060 0.156 0.068 NA
#> GSM531643 1 0.7056 0.6453 0.548 0.012 0.064 0.092 NA
#> GSM531644 1 0.7370 0.6336 0.528 0.024 0.064 0.096 NA
#> GSM531645 4 0.1908 0.7867 0.000 0.000 0.000 0.908 NA
#> GSM531646 1 0.0703 0.7423 0.976 0.000 0.000 0.000 NA
#> GSM531647 1 0.0000 0.7434 1.000 0.000 0.000 0.000 NA
#> GSM531648 4 0.1195 0.7829 0.000 0.012 0.000 0.960 NA
#> GSM531650 1 0.0000 0.7434 1.000 0.000 0.000 0.000 NA
#> GSM531651 3 0.0000 0.9038 0.000 0.000 1.000 0.000 NA
#> GSM531652 1 0.8164 0.5549 0.448 0.036 0.068 0.160 NA
#> GSM531656 1 0.6285 0.5948 0.536 0.000 0.220 0.000 NA
#> GSM531659 4 0.5340 0.5919 0.000 0.288 0.036 0.648 NA
#> GSM531661 3 0.2127 0.8014 0.000 0.108 0.892 0.000 NA
#> GSM531662 3 0.4238 0.2880 0.000 0.368 0.628 0.000 NA
#> GSM531663 4 0.4573 0.6527 0.000 0.260 0.008 0.704 NA
#> GSM531664 1 0.0000 0.7434 1.000 0.000 0.000 0.000 NA
#> GSM531666 1 0.7985 0.6006 0.488 0.060 0.068 0.096 NA
#> GSM531667 3 0.0162 0.9016 0.000 0.004 0.996 0.000 NA
#> GSM531668 4 0.4796 0.6006 0.000 0.300 0.008 0.664 NA
#> GSM531669 1 0.0000 0.7434 1.000 0.000 0.000 0.000 NA
#> GSM531671 2 0.7705 0.2007 0.060 0.392 0.312 0.000 NA
#> GSM531672 4 0.3183 0.7810 0.000 0.108 0.008 0.856 NA
#> GSM531673 2 0.5255 0.5288 0.000 0.624 0.304 0.000 NA
#> GSM531676 2 0.4060 0.6747 0.000 0.640 0.000 0.000 NA
#> GSM531679 2 0.0000 0.8058 0.000 1.000 0.000 0.000 NA
#> GSM531681 2 0.3016 0.6980 0.000 0.848 0.000 0.132 NA
#> GSM531682 2 0.0000 0.8058 0.000 1.000 0.000 0.000 NA
#> GSM531683 2 0.0000 0.8058 0.000 1.000 0.000 0.000 NA
#> GSM531684 2 0.0880 0.8040 0.000 0.968 0.000 0.000 NA
#> GSM531685 2 0.6296 0.5443 0.160 0.480 0.000 0.000 NA
#> GSM531686 2 0.1943 0.7707 0.000 0.924 0.000 0.056 NA
#> GSM531687 2 0.4151 0.6803 0.004 0.652 0.000 0.000 NA
#> GSM531688 1 0.6622 0.0837 0.440 0.232 0.000 0.000 NA
#> GSM531690 2 0.3151 0.6814 0.000 0.836 0.000 0.144 NA
#> GSM531693 1 0.5987 0.3524 0.544 0.132 0.000 0.000 NA
#> GSM531695 2 0.6767 0.3676 0.280 0.392 0.000 0.000 NA
#> GSM531603 2 0.0000 0.8058 0.000 1.000 0.000 0.000 NA
#> GSM531609 4 0.1908 0.7867 0.000 0.000 0.000 0.908 NA
#> GSM531611 4 0.3077 0.7828 0.000 0.100 0.008 0.864 NA
#> GSM531621 3 0.0000 0.9038 0.000 0.000 1.000 0.000 NA
#> GSM531622 3 0.0000 0.9038 0.000 0.000 1.000 0.000 NA
#> GSM531628 1 0.0000 0.7434 1.000 0.000 0.000 0.000 NA
#> GSM531630 3 0.0000 0.9038 0.000 0.000 1.000 0.000 NA
#> GSM531633 3 0.0000 0.9038 0.000 0.000 1.000 0.000 NA
#> GSM531635 1 0.5668 0.6637 0.624 0.000 0.144 0.000 NA
#> GSM531640 3 0.0000 0.9038 0.000 0.000 1.000 0.000 NA
#> GSM531649 1 0.2659 0.7360 0.888 0.000 0.060 0.000 NA
#> GSM531653 1 0.0000 0.7434 1.000 0.000 0.000 0.000 NA
#> GSM531657 4 0.4573 0.6527 0.000 0.260 0.008 0.704 NA
#> GSM531665 2 0.5887 0.6268 0.024 0.580 0.064 0.000 NA
#> GSM531670 1 0.6285 0.5948 0.536 0.000 0.220 0.000 NA
#> GSM531674 1 0.0000 0.7434 1.000 0.000 0.000 0.000 NA
#> GSM531675 2 0.0609 0.8028 0.000 0.980 0.000 0.000 NA
#> GSM531677 2 0.0609 0.8028 0.000 0.980 0.000 0.000 NA
#> GSM531678 2 0.0000 0.8058 0.000 1.000 0.000 0.000 NA
#> GSM531680 2 0.5644 0.6242 0.096 0.576 0.000 0.000 NA
#> GSM531689 2 0.2471 0.7836 0.000 0.864 0.000 0.000 NA
#> GSM531691 2 0.2690 0.7785 0.000 0.844 0.000 0.000 NA
#> GSM531692 2 0.4045 0.6776 0.000 0.644 0.000 0.000 NA
#> GSM531694 2 0.0703 0.7990 0.000 0.976 0.000 0.000 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM531602 2 0.0692 0.729 0.000 0.976 0.000 0.000 0.020 0.004
#> GSM531604 2 0.6044 -0.709 0.000 0.376 0.000 0.000 0.252 0.372
#> GSM531606 2 0.4453 -0.100 0.000 0.592 0.000 0.000 0.036 0.372
#> GSM531607 2 0.0937 0.735 0.000 0.960 0.000 0.000 0.040 0.000
#> GSM531608 3 0.2320 0.774 0.000 0.004 0.864 0.000 0.000 0.132
#> GSM531610 4 0.0000 0.838 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531612 4 0.0000 0.838 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531613 4 0.0458 0.838 0.000 0.000 0.000 0.984 0.000 0.016
#> GSM531614 4 0.0000 0.838 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531616 3 0.4120 0.654 0.008 0.000 0.692 0.000 0.024 0.276
#> GSM531618 4 0.6402 0.551 0.020 0.096 0.040 0.496 0.000 0.348
#> GSM531619 3 0.0632 0.852 0.000 0.000 0.976 0.000 0.000 0.024
#> GSM531620 3 0.1082 0.847 0.000 0.000 0.956 0.000 0.004 0.040
#> GSM531623 3 0.0000 0.860 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531625 3 0.0146 0.859 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM531626 3 0.3619 0.710 0.000 0.000 0.744 0.000 0.024 0.232
#> GSM531632 1 0.0000 0.718 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM531638 3 0.3168 0.762 0.000 0.000 0.804 0.000 0.024 0.172
#> GSM531639 1 0.6384 0.600 0.460 0.000 0.236 0.000 0.024 0.280
#> GSM531641 4 0.0000 0.838 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531642 1 0.5779 0.669 0.512 0.004 0.180 0.000 0.000 0.304
#> GSM531643 1 0.5578 0.687 0.544 0.004 0.124 0.004 0.000 0.324
#> GSM531644 1 0.5711 0.680 0.528 0.004 0.124 0.008 0.000 0.336
#> GSM531645 4 0.0000 0.838 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531646 1 0.0790 0.722 0.968 0.000 0.000 0.000 0.000 0.032
#> GSM531647 1 0.0000 0.718 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM531648 4 0.2400 0.832 0.000 0.004 0.008 0.872 0.000 0.116
#> GSM531650 1 0.0000 0.718 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM531651 3 0.0000 0.860 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531652 1 0.6254 0.662 0.504 0.004 0.124 0.040 0.000 0.328
#> GSM531656 1 0.6067 0.675 0.532 0.000 0.184 0.000 0.024 0.260
#> GSM531659 4 0.6053 0.681 0.000 0.140 0.024 0.596 0.020 0.220
#> GSM531661 3 0.0405 0.855 0.000 0.008 0.988 0.000 0.004 0.000
#> GSM531662 3 0.6155 0.239 0.000 0.196 0.588 0.000 0.076 0.140
#> GSM531663 4 0.4508 0.797 0.000 0.048 0.008 0.716 0.012 0.216
#> GSM531664 1 0.0000 0.718 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM531666 1 0.5656 0.671 0.512 0.004 0.124 0.004 0.000 0.356
#> GSM531667 3 0.1714 0.812 0.000 0.000 0.908 0.000 0.000 0.092
#> GSM531668 4 0.5925 0.671 0.000 0.152 0.008 0.580 0.020 0.240
#> GSM531669 1 0.0260 0.712 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM531671 3 0.7894 -0.268 0.040 0.140 0.364 0.000 0.312 0.144
#> GSM531672 4 0.4266 0.804 0.000 0.028 0.008 0.732 0.016 0.216
#> GSM531673 6 0.7344 0.658 0.000 0.272 0.128 0.000 0.216 0.384
#> GSM531676 5 0.3287 0.522 0.012 0.220 0.000 0.000 0.768 0.000
#> GSM531679 2 0.1387 0.730 0.000 0.932 0.000 0.000 0.068 0.000
#> GSM531681 2 0.3404 0.665 0.000 0.760 0.000 0.000 0.224 0.016
#> GSM531682 2 0.1863 0.710 0.000 0.896 0.000 0.000 0.104 0.000
#> GSM531683 2 0.0260 0.734 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM531684 2 0.4514 -0.114 0.000 0.588 0.000 0.000 0.040 0.372
#> GSM531685 5 0.3946 0.635 0.076 0.168 0.000 0.000 0.756 0.000
#> GSM531686 2 0.3404 0.665 0.000 0.760 0.000 0.000 0.224 0.016
#> GSM531687 5 0.3023 0.519 0.004 0.212 0.000 0.000 0.784 0.000
#> GSM531688 5 0.4247 0.582 0.296 0.040 0.000 0.000 0.664 0.000
#> GSM531690 2 0.3404 0.665 0.000 0.760 0.000 0.000 0.224 0.016
#> GSM531693 5 0.4105 0.529 0.348 0.020 0.000 0.000 0.632 0.000
#> GSM531695 5 0.4506 0.667 0.176 0.120 0.000 0.000 0.704 0.000
#> GSM531603 2 0.0146 0.730 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM531609 4 0.0000 0.838 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531611 4 0.3783 0.816 0.000 0.028 0.028 0.788 0.000 0.156
#> GSM531621 3 0.0000 0.860 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531622 3 0.0000 0.860 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531628 1 0.0000 0.718 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM531630 3 0.0000 0.860 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531633 3 0.0000 0.860 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531635 1 0.5582 0.702 0.608 0.000 0.132 0.000 0.024 0.236
#> GSM531640 3 0.1863 0.804 0.000 0.000 0.896 0.000 0.000 0.104
#> GSM531649 1 0.2383 0.722 0.880 0.000 0.024 0.000 0.000 0.096
#> GSM531653 1 0.0000 0.718 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM531657 4 0.4929 0.780 0.000 0.064 0.008 0.688 0.020 0.220
#> GSM531665 6 0.7584 0.466 0.024 0.164 0.120 0.000 0.272 0.420
#> GSM531670 1 0.6050 0.676 0.536 0.000 0.184 0.000 0.024 0.256
#> GSM531674 1 0.0146 0.716 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM531675 2 0.3404 0.665 0.000 0.760 0.000 0.000 0.224 0.016
#> GSM531677 2 0.1814 0.727 0.000 0.900 0.000 0.000 0.100 0.000
#> GSM531678 2 0.0000 0.731 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531680 5 0.4261 0.669 0.112 0.156 0.000 0.000 0.732 0.000
#> GSM531689 2 0.3653 0.327 0.000 0.692 0.000 0.000 0.300 0.008
#> GSM531691 6 0.6104 0.684 0.000 0.292 0.000 0.000 0.336 0.372
#> GSM531692 6 0.6087 0.678 0.000 0.276 0.000 0.000 0.352 0.372
#> GSM531694 2 0.0692 0.729 0.000 0.976 0.000 0.000 0.020 0.004
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> SD:mclust 77 1.000 2
#> SD:mclust 69 0.530 3
#> SD:mclust 78 0.598 4
#> SD:mclust 74 0.631 5
#> SD:mclust 73 0.560 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "NMF"]
# you can also extract it by
# res = res_list["SD:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 80 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 0.851 0.923 0.967 0.5018 0.495 0.495
#> 3 3 0.521 0.672 0.809 0.3265 0.745 0.529
#> 4 4 0.873 0.892 0.953 0.1346 0.803 0.491
#> 5 5 0.732 0.719 0.858 0.0542 0.915 0.682
#> 6 6 0.700 0.562 0.764 0.0388 0.941 0.747
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
#> GSM531602 2 0.0000 0.941 0.000 1.000
#> GSM531604 2 0.2236 0.915 0.036 0.964
#> GSM531606 2 0.0000 0.941 0.000 1.000
#> GSM531607 2 0.0000 0.941 0.000 1.000
#> GSM531608 2 0.9896 0.220 0.440 0.560
#> GSM531610 2 0.0000 0.941 0.000 1.000
#> GSM531612 2 0.0000 0.941 0.000 1.000
#> GSM531613 2 0.0000 0.941 0.000 1.000
#> GSM531614 2 0.0000 0.941 0.000 1.000
#> GSM531616 1 0.0000 0.984 1.000 0.000
#> GSM531618 2 0.9909 0.209 0.444 0.556
#> GSM531619 1 0.0376 0.981 0.996 0.004
#> GSM531620 1 0.0000 0.984 1.000 0.000
#> GSM531623 1 0.0000 0.984 1.000 0.000
#> GSM531625 1 0.0000 0.984 1.000 0.000
#> GSM531626 1 0.0000 0.984 1.000 0.000
#> GSM531632 1 0.0000 0.984 1.000 0.000
#> GSM531638 1 0.0000 0.984 1.000 0.000
#> GSM531639 1 0.0000 0.984 1.000 0.000
#> GSM531641 2 0.0000 0.941 0.000 1.000
#> GSM531642 1 0.0000 0.984 1.000 0.000
#> GSM531643 1 0.0000 0.984 1.000 0.000
#> GSM531644 1 0.0000 0.984 1.000 0.000
#> GSM531645 2 0.0000 0.941 0.000 1.000
#> GSM531646 1 0.0000 0.984 1.000 0.000
#> GSM531647 1 0.0000 0.984 1.000 0.000
#> GSM531648 2 0.0000 0.941 0.000 1.000
#> GSM531650 1 0.0000 0.984 1.000 0.000
#> GSM531651 1 0.0000 0.984 1.000 0.000
#> GSM531652 1 0.0000 0.984 1.000 0.000
#> GSM531656 1 0.0000 0.984 1.000 0.000
#> GSM531659 2 0.0000 0.941 0.000 1.000
#> GSM531661 1 0.0376 0.981 0.996 0.004
#> GSM531662 1 0.0000 0.984 1.000 0.000
#> GSM531663 2 0.0000 0.941 0.000 1.000
#> GSM531664 1 0.0000 0.984 1.000 0.000
#> GSM531666 1 0.2778 0.942 0.952 0.048
#> GSM531667 1 0.6247 0.808 0.844 0.156
#> GSM531668 2 0.0000 0.941 0.000 1.000
#> GSM531669 1 0.0000 0.984 1.000 0.000
#> GSM531671 1 0.0000 0.984 1.000 0.000
#> GSM531672 2 0.0000 0.941 0.000 1.000
#> GSM531673 1 0.3879 0.912 0.924 0.076
#> GSM531676 2 0.9286 0.526 0.344 0.656
#> GSM531679 2 0.0000 0.941 0.000 1.000
#> GSM531681 2 0.0000 0.941 0.000 1.000
#> GSM531682 2 0.0000 0.941 0.000 1.000
#> GSM531683 2 0.0000 0.941 0.000 1.000
#> GSM531684 2 0.0000 0.941 0.000 1.000
#> GSM531685 1 0.0000 0.984 1.000 0.000
#> GSM531686 2 0.0000 0.941 0.000 1.000
#> GSM531687 2 0.7376 0.750 0.208 0.792
#> GSM531688 1 0.1184 0.971 0.984 0.016
#> GSM531690 2 0.0000 0.941 0.000 1.000
#> GSM531693 1 0.0000 0.984 1.000 0.000
#> GSM531695 2 0.7219 0.760 0.200 0.800
#> GSM531603 2 0.0000 0.941 0.000 1.000
#> GSM531609 2 0.0000 0.941 0.000 1.000
#> GSM531611 2 0.0000 0.941 0.000 1.000
#> GSM531621 1 0.0000 0.984 1.000 0.000
#> GSM531622 1 0.0000 0.984 1.000 0.000
#> GSM531628 1 0.0000 0.984 1.000 0.000
#> GSM531630 1 0.0000 0.984 1.000 0.000
#> GSM531633 1 0.0000 0.984 1.000 0.000
#> GSM531635 1 0.0000 0.984 1.000 0.000
#> GSM531640 1 0.5059 0.867 0.888 0.112
#> GSM531649 1 0.0000 0.984 1.000 0.000
#> GSM531653 1 0.0000 0.984 1.000 0.000
#> GSM531657 2 0.0000 0.941 0.000 1.000
#> GSM531665 1 0.6343 0.801 0.840 0.160
#> GSM531670 1 0.0000 0.984 1.000 0.000
#> GSM531674 1 0.0000 0.984 1.000 0.000
#> GSM531675 2 0.0000 0.941 0.000 1.000
#> GSM531677 2 0.0000 0.941 0.000 1.000
#> GSM531678 2 0.0000 0.941 0.000 1.000
#> GSM531680 2 0.7219 0.760 0.200 0.800
#> GSM531689 2 0.0000 0.941 0.000 1.000
#> GSM531691 2 0.7219 0.760 0.200 0.800
#> GSM531692 1 0.1843 0.961 0.972 0.028
#> GSM531694 2 0.0000 0.941 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM531602 2 0.5650 0.8006 0.000 0.688 0.312
#> GSM531604 3 0.3340 0.4333 0.000 0.120 0.880
#> GSM531606 2 0.5785 0.7864 0.000 0.668 0.332
#> GSM531607 2 0.5650 0.8006 0.000 0.688 0.312
#> GSM531608 3 0.1411 0.6427 0.036 0.000 0.964
#> GSM531610 2 0.0000 0.7644 0.000 1.000 0.000
#> GSM531612 2 0.0592 0.7549 0.012 0.988 0.000
#> GSM531613 2 0.0000 0.7644 0.000 1.000 0.000
#> GSM531614 2 0.0000 0.7644 0.000 1.000 0.000
#> GSM531616 1 0.5098 0.3542 0.752 0.000 0.248
#> GSM531618 2 0.7447 0.4028 0.160 0.700 0.140
#> GSM531619 3 0.5650 0.7701 0.312 0.000 0.688
#> GSM531620 3 0.5650 0.7701 0.312 0.000 0.688
#> GSM531623 3 0.5650 0.7701 0.312 0.000 0.688
#> GSM531625 3 0.5650 0.7701 0.312 0.000 0.688
#> GSM531626 3 0.5650 0.7701 0.312 0.000 0.688
#> GSM531632 1 0.0000 0.7509 1.000 0.000 0.000
#> GSM531638 3 0.5650 0.7701 0.312 0.000 0.688
#> GSM531639 3 0.6305 0.4938 0.484 0.000 0.516
#> GSM531641 2 0.0000 0.7644 0.000 1.000 0.000
#> GSM531642 1 0.5115 0.7215 0.796 0.188 0.016
#> GSM531643 1 0.4121 0.7312 0.832 0.168 0.000
#> GSM531644 1 0.5650 0.6440 0.688 0.312 0.000
#> GSM531645 2 0.2959 0.6601 0.100 0.900 0.000
#> GSM531646 1 0.0000 0.7509 1.000 0.000 0.000
#> GSM531647 1 0.0000 0.7509 1.000 0.000 0.000
#> GSM531648 2 0.4702 0.4790 0.212 0.788 0.000
#> GSM531650 1 0.3192 0.7454 0.888 0.112 0.000
#> GSM531651 3 0.5650 0.7701 0.312 0.000 0.688
#> GSM531652 1 0.5621 0.6474 0.692 0.308 0.000
#> GSM531656 1 0.1289 0.7248 0.968 0.000 0.032
#> GSM531659 2 0.1753 0.7806 0.000 0.952 0.048
#> GSM531661 3 0.3038 0.6800 0.104 0.000 0.896
#> GSM531662 3 0.1753 0.6509 0.048 0.000 0.952
#> GSM531663 2 0.3816 0.7995 0.000 0.852 0.148
#> GSM531664 1 0.4399 0.7228 0.812 0.188 0.000
#> GSM531666 1 0.5560 0.6536 0.700 0.300 0.000
#> GSM531667 3 0.5650 0.7701 0.312 0.000 0.688
#> GSM531668 2 0.5650 0.8006 0.000 0.688 0.312
#> GSM531669 1 0.0000 0.7509 1.000 0.000 0.000
#> GSM531671 1 0.5882 0.0238 0.652 0.000 0.348
#> GSM531672 2 0.0000 0.7644 0.000 1.000 0.000
#> GSM531673 3 0.0000 0.6170 0.000 0.000 1.000
#> GSM531676 1 0.9882 -0.0964 0.408 0.280 0.312
#> GSM531679 2 0.5650 0.8006 0.000 0.688 0.312
#> GSM531681 2 0.4931 0.8029 0.000 0.768 0.232
#> GSM531682 2 0.5650 0.8006 0.000 0.688 0.312
#> GSM531683 2 0.5650 0.8006 0.000 0.688 0.312
#> GSM531684 3 0.0592 0.6046 0.000 0.012 0.988
#> GSM531685 1 0.7138 0.5077 0.644 0.044 0.312
#> GSM531686 2 0.4002 0.8009 0.000 0.840 0.160
#> GSM531687 2 0.9989 0.2710 0.336 0.352 0.312
#> GSM531688 1 0.0747 0.7491 0.984 0.000 0.016
#> GSM531690 2 0.5497 0.8031 0.000 0.708 0.292
#> GSM531693 1 0.0000 0.7509 1.000 0.000 0.000
#> GSM531695 1 0.7595 0.6476 0.688 0.176 0.136
#> GSM531603 2 0.5835 0.7795 0.000 0.660 0.340
#> GSM531609 2 0.0000 0.7644 0.000 1.000 0.000
#> GSM531611 2 0.0000 0.7644 0.000 1.000 0.000
#> GSM531621 3 0.5650 0.7701 0.312 0.000 0.688
#> GSM531622 3 0.5650 0.7701 0.312 0.000 0.688
#> GSM531628 1 0.3686 0.7397 0.860 0.140 0.000
#> GSM531630 3 0.5650 0.7701 0.312 0.000 0.688
#> GSM531633 3 0.5650 0.7701 0.312 0.000 0.688
#> GSM531635 1 0.0000 0.7509 1.000 0.000 0.000
#> GSM531640 3 0.5650 0.7701 0.312 0.000 0.688
#> GSM531649 1 0.0000 0.7509 1.000 0.000 0.000
#> GSM531653 1 0.0000 0.7509 1.000 0.000 0.000
#> GSM531657 2 0.0592 0.7691 0.000 0.988 0.012
#> GSM531665 1 0.9106 0.2307 0.536 0.284 0.180
#> GSM531670 1 0.1964 0.6989 0.944 0.000 0.056
#> GSM531674 1 0.0000 0.7509 1.000 0.000 0.000
#> GSM531675 2 0.5650 0.8006 0.000 0.688 0.312
#> GSM531677 2 0.5650 0.8006 0.000 0.688 0.312
#> GSM531678 2 0.5650 0.8006 0.000 0.688 0.312
#> GSM531680 1 0.8683 0.5151 0.592 0.236 0.172
#> GSM531689 2 0.5650 0.8006 0.000 0.688 0.312
#> GSM531691 3 0.6308 -0.5755 0.000 0.492 0.508
#> GSM531692 3 0.4555 0.3962 0.200 0.000 0.800
#> GSM531694 2 0.5650 0.8006 0.000 0.688 0.312
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM531602 2 0.0000 0.930 0.000 1.000 0.000 0.000
#> GSM531604 2 0.0000 0.930 0.000 1.000 0.000 0.000
#> GSM531606 2 0.0000 0.930 0.000 1.000 0.000 0.000
#> GSM531607 2 0.0000 0.930 0.000 1.000 0.000 0.000
#> GSM531608 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> GSM531610 4 0.0000 0.983 0.000 0.000 0.000 1.000
#> GSM531612 4 0.0000 0.983 0.000 0.000 0.000 1.000
#> GSM531613 4 0.0000 0.983 0.000 0.000 0.000 1.000
#> GSM531614 4 0.0000 0.983 0.000 0.000 0.000 1.000
#> GSM531616 3 0.3219 0.781 0.164 0.000 0.836 0.000
#> GSM531618 4 0.0188 0.980 0.000 0.000 0.004 0.996
#> GSM531619 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> GSM531620 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> GSM531623 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> GSM531625 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> GSM531626 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> GSM531632 1 0.0000 0.931 1.000 0.000 0.000 0.000
#> GSM531638 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> GSM531639 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> GSM531641 4 0.0000 0.983 0.000 0.000 0.000 1.000
#> GSM531642 4 0.3208 0.819 0.004 0.000 0.148 0.848
#> GSM531643 1 0.0000 0.931 1.000 0.000 0.000 0.000
#> GSM531644 1 0.0469 0.924 0.988 0.000 0.000 0.012
#> GSM531645 4 0.0000 0.983 0.000 0.000 0.000 1.000
#> GSM531646 1 0.0000 0.931 1.000 0.000 0.000 0.000
#> GSM531647 1 0.0000 0.931 1.000 0.000 0.000 0.000
#> GSM531648 4 0.0000 0.983 0.000 0.000 0.000 1.000
#> GSM531650 1 0.0000 0.931 1.000 0.000 0.000 0.000
#> GSM531651 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> GSM531652 4 0.1211 0.947 0.040 0.000 0.000 0.960
#> GSM531656 1 0.3219 0.770 0.836 0.000 0.164 0.000
#> GSM531659 4 0.1389 0.937 0.000 0.048 0.000 0.952
#> GSM531661 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> GSM531662 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> GSM531663 4 0.0000 0.983 0.000 0.000 0.000 1.000
#> GSM531664 1 0.0000 0.931 1.000 0.000 0.000 0.000
#> GSM531666 1 0.4040 0.657 0.752 0.000 0.000 0.248
#> GSM531667 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> GSM531668 2 0.4072 0.665 0.000 0.748 0.000 0.252
#> GSM531669 1 0.0000 0.931 1.000 0.000 0.000 0.000
#> GSM531671 3 0.5942 0.223 0.412 0.040 0.548 0.000
#> GSM531672 4 0.0000 0.983 0.000 0.000 0.000 1.000
#> GSM531673 3 0.3400 0.754 0.000 0.180 0.820 0.000
#> GSM531676 2 0.2647 0.837 0.120 0.880 0.000 0.000
#> GSM531679 2 0.0000 0.930 0.000 1.000 0.000 0.000
#> GSM531681 2 0.4431 0.610 0.000 0.696 0.000 0.304
#> GSM531682 2 0.0000 0.930 0.000 1.000 0.000 0.000
#> GSM531683 2 0.0000 0.930 0.000 1.000 0.000 0.000
#> GSM531684 2 0.2281 0.861 0.000 0.904 0.096 0.000
#> GSM531685 1 0.4072 0.643 0.748 0.252 0.000 0.000
#> GSM531686 2 0.4134 0.678 0.000 0.740 0.000 0.260
#> GSM531687 2 0.2081 0.873 0.084 0.916 0.000 0.000
#> GSM531688 1 0.0000 0.931 1.000 0.000 0.000 0.000
#> GSM531690 2 0.1211 0.906 0.000 0.960 0.000 0.040
#> GSM531693 1 0.0000 0.931 1.000 0.000 0.000 0.000
#> GSM531695 1 0.0336 0.926 0.992 0.008 0.000 0.000
#> GSM531603 2 0.0000 0.930 0.000 1.000 0.000 0.000
#> GSM531609 4 0.0000 0.983 0.000 0.000 0.000 1.000
#> GSM531611 4 0.0000 0.983 0.000 0.000 0.000 1.000
#> GSM531621 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> GSM531622 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> GSM531628 1 0.0000 0.931 1.000 0.000 0.000 0.000
#> GSM531630 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> GSM531633 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> GSM531635 1 0.0000 0.931 1.000 0.000 0.000 0.000
#> GSM531640 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> GSM531649 1 0.0000 0.931 1.000 0.000 0.000 0.000
#> GSM531653 1 0.0000 0.931 1.000 0.000 0.000 0.000
#> GSM531657 4 0.0000 0.983 0.000 0.000 0.000 1.000
#> GSM531665 2 0.4500 0.532 0.316 0.684 0.000 0.000
#> GSM531670 1 0.3400 0.749 0.820 0.000 0.180 0.000
#> GSM531674 1 0.0000 0.931 1.000 0.000 0.000 0.000
#> GSM531675 2 0.0000 0.930 0.000 1.000 0.000 0.000
#> GSM531677 2 0.0000 0.930 0.000 1.000 0.000 0.000
#> GSM531678 2 0.0000 0.930 0.000 1.000 0.000 0.000
#> GSM531680 1 0.4866 0.291 0.596 0.404 0.000 0.000
#> GSM531689 2 0.0000 0.930 0.000 1.000 0.000 0.000
#> GSM531691 2 0.0000 0.930 0.000 1.000 0.000 0.000
#> GSM531692 2 0.0469 0.924 0.012 0.988 0.000 0.000
#> GSM531694 2 0.0000 0.930 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM531602 2 0.3395 0.67038 0.000 0.764 0.000 0.000 0.236
#> GSM531604 2 0.0000 0.76625 0.000 1.000 0.000 0.000 0.000
#> GSM531606 2 0.1965 0.75493 0.000 0.904 0.000 0.000 0.096
#> GSM531607 2 0.3305 0.68137 0.000 0.776 0.000 0.000 0.224
#> GSM531608 3 0.0324 0.91951 0.000 0.000 0.992 0.004 0.004
#> GSM531610 4 0.0000 0.87470 0.000 0.000 0.000 1.000 0.000
#> GSM531612 4 0.0000 0.87470 0.000 0.000 0.000 1.000 0.000
#> GSM531613 4 0.0000 0.87470 0.000 0.000 0.000 1.000 0.000
#> GSM531614 4 0.0000 0.87470 0.000 0.000 0.000 1.000 0.000
#> GSM531616 3 0.4356 0.45718 0.340 0.000 0.648 0.000 0.012
#> GSM531618 5 0.2482 0.72698 0.000 0.000 0.024 0.084 0.892
#> GSM531619 3 0.1121 0.91532 0.000 0.000 0.956 0.000 0.044
#> GSM531620 3 0.3039 0.81674 0.012 0.000 0.836 0.000 0.152
#> GSM531623 3 0.0510 0.91971 0.000 0.000 0.984 0.000 0.016
#> GSM531625 3 0.1408 0.91267 0.008 0.000 0.948 0.000 0.044
#> GSM531626 3 0.1597 0.90732 0.012 0.000 0.940 0.000 0.048
#> GSM531632 1 0.0693 0.82168 0.980 0.000 0.012 0.000 0.008
#> GSM531638 3 0.0703 0.91824 0.000 0.000 0.976 0.000 0.024
#> GSM531639 3 0.1522 0.91080 0.012 0.000 0.944 0.000 0.044
#> GSM531641 4 0.0000 0.87470 0.000 0.000 0.000 1.000 0.000
#> GSM531642 5 0.6128 0.61815 0.184 0.000 0.032 0.144 0.640
#> GSM531643 1 0.2966 0.73541 0.816 0.000 0.000 0.000 0.184
#> GSM531644 1 0.4291 0.21208 0.536 0.000 0.000 0.000 0.464
#> GSM531645 4 0.0000 0.87470 0.000 0.000 0.000 1.000 0.000
#> GSM531646 1 0.0579 0.82298 0.984 0.000 0.008 0.000 0.008
#> GSM531647 1 0.0162 0.82411 0.996 0.000 0.000 0.000 0.004
#> GSM531648 5 0.3550 0.62268 0.000 0.000 0.004 0.236 0.760
#> GSM531650 1 0.2230 0.78454 0.884 0.000 0.000 0.000 0.116
#> GSM531651 3 0.0290 0.91933 0.000 0.000 0.992 0.000 0.008
#> GSM531652 5 0.4803 0.65419 0.184 0.000 0.012 0.068 0.736
#> GSM531656 1 0.5670 0.56551 0.632 0.000 0.192 0.000 0.176
#> GSM531659 4 0.6605 0.00138 0.000 0.288 0.000 0.460 0.252
#> GSM531661 3 0.0794 0.91809 0.000 0.000 0.972 0.000 0.028
#> GSM531662 3 0.1124 0.91323 0.000 0.004 0.960 0.000 0.036
#> GSM531663 4 0.0000 0.87470 0.000 0.000 0.000 1.000 0.000
#> GSM531664 1 0.2648 0.76258 0.848 0.000 0.000 0.000 0.152
#> GSM531666 5 0.2286 0.72014 0.108 0.000 0.000 0.004 0.888
#> GSM531667 3 0.2690 0.82666 0.000 0.000 0.844 0.000 0.156
#> GSM531668 5 0.3639 0.63331 0.000 0.164 0.020 0.008 0.808
#> GSM531669 1 0.0290 0.82412 0.992 0.000 0.000 0.000 0.008
#> GSM531671 1 0.5140 0.49047 0.668 0.016 0.272 0.000 0.044
#> GSM531672 5 0.3950 0.69570 0.000 0.048 0.004 0.152 0.796
#> GSM531673 3 0.4442 0.53699 0.000 0.284 0.688 0.000 0.028
#> GSM531676 2 0.3160 0.66380 0.188 0.808 0.000 0.000 0.004
#> GSM531679 2 0.0162 0.76659 0.000 0.996 0.000 0.000 0.004
#> GSM531681 4 0.2648 0.74353 0.000 0.152 0.000 0.848 0.000
#> GSM531682 2 0.1341 0.76245 0.000 0.944 0.000 0.000 0.056
#> GSM531683 2 0.2329 0.74381 0.000 0.876 0.000 0.000 0.124
#> GSM531684 2 0.4747 0.45622 0.000 0.620 0.352 0.000 0.028
#> GSM531685 1 0.5062 0.34890 0.608 0.356 0.016 0.000 0.020
#> GSM531686 4 0.2605 0.74956 0.000 0.148 0.000 0.852 0.000
#> GSM531687 2 0.4269 0.61871 0.232 0.732 0.000 0.000 0.036
#> GSM531688 1 0.1082 0.81688 0.964 0.028 0.000 0.000 0.008
#> GSM531690 2 0.4182 0.33405 0.000 0.600 0.000 0.000 0.400
#> GSM531693 1 0.0992 0.81858 0.968 0.024 0.000 0.000 0.008
#> GSM531695 1 0.5104 0.50277 0.632 0.060 0.000 0.000 0.308
#> GSM531603 5 0.4227 0.06854 0.000 0.420 0.000 0.000 0.580
#> GSM531609 4 0.0000 0.87470 0.000 0.000 0.000 1.000 0.000
#> GSM531611 4 0.0000 0.87470 0.000 0.000 0.000 1.000 0.000
#> GSM531621 3 0.0963 0.91560 0.000 0.000 0.964 0.000 0.036
#> GSM531622 3 0.1043 0.91611 0.000 0.000 0.960 0.000 0.040
#> GSM531628 1 0.1544 0.80766 0.932 0.000 0.000 0.000 0.068
#> GSM531630 3 0.0880 0.91694 0.000 0.000 0.968 0.000 0.032
#> GSM531633 3 0.1043 0.91045 0.000 0.000 0.960 0.000 0.040
#> GSM531635 1 0.0566 0.82509 0.984 0.000 0.004 0.000 0.012
#> GSM531640 3 0.0963 0.91681 0.000 0.000 0.964 0.000 0.036
#> GSM531649 1 0.1082 0.81822 0.964 0.000 0.008 0.000 0.028
#> GSM531653 1 0.0451 0.82454 0.988 0.000 0.004 0.000 0.008
#> GSM531657 4 0.4846 0.24160 0.000 0.020 0.004 0.588 0.388
#> GSM531665 2 0.4947 0.31308 0.396 0.576 0.024 0.000 0.004
#> GSM531670 1 0.5396 0.57826 0.656 0.000 0.220 0.000 0.124
#> GSM531674 1 0.0290 0.82328 0.992 0.000 0.000 0.000 0.008
#> GSM531675 2 0.2813 0.71697 0.000 0.832 0.000 0.000 0.168
#> GSM531677 2 0.0162 0.76655 0.000 0.996 0.000 0.000 0.004
#> GSM531678 2 0.2017 0.73433 0.000 0.912 0.008 0.080 0.000
#> GSM531680 2 0.6024 0.14453 0.412 0.472 0.000 0.000 0.116
#> GSM531689 2 0.0290 0.76665 0.000 0.992 0.000 0.000 0.008
#> GSM531691 2 0.2482 0.72629 0.000 0.892 0.084 0.000 0.024
#> GSM531692 2 0.3416 0.70447 0.124 0.840 0.016 0.000 0.020
#> GSM531694 2 0.3177 0.69446 0.000 0.792 0.000 0.000 0.208
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM531602 2 0.5775 0.4799 0.000 0.496 0.000 0.000 0.296 0.208
#> GSM531604 2 0.1531 0.7100 0.000 0.928 0.004 0.000 0.068 0.000
#> GSM531606 2 0.4330 0.6560 0.000 0.696 0.000 0.000 0.236 0.068
#> GSM531607 2 0.5661 0.5156 0.000 0.528 0.000 0.000 0.268 0.204
#> GSM531608 3 0.3821 0.5276 0.000 0.000 0.772 0.148 0.080 0.000
#> GSM531610 4 0.0000 0.9858 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531612 4 0.0000 0.9858 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531613 4 0.0000 0.9858 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531614 4 0.0000 0.9858 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531616 3 0.6109 -0.5831 0.364 0.000 0.424 0.000 0.204 0.008
#> GSM531618 6 0.3985 0.6189 0.000 0.000 0.024 0.032 0.180 0.764
#> GSM531619 3 0.3515 0.5621 0.000 0.000 0.676 0.000 0.324 0.000
#> GSM531620 3 0.5190 -0.0630 0.028 0.000 0.536 0.000 0.396 0.040
#> GSM531623 3 0.0865 0.6160 0.000 0.000 0.964 0.000 0.036 0.000
#> GSM531625 3 0.3163 0.4648 0.004 0.000 0.764 0.000 0.232 0.000
#> GSM531626 3 0.4992 -0.0279 0.112 0.000 0.620 0.000 0.268 0.000
#> GSM531632 1 0.4495 0.2818 0.708 0.000 0.092 0.000 0.196 0.004
#> GSM531638 3 0.3743 0.5838 0.024 0.000 0.724 0.000 0.252 0.000
#> GSM531639 3 0.3613 0.5668 0.052 0.000 0.828 0.000 0.056 0.064
#> GSM531641 4 0.0000 0.9858 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531642 6 0.4691 0.5728 0.160 0.000 0.016 0.072 0.016 0.736
#> GSM531643 1 0.2651 0.6831 0.860 0.000 0.000 0.000 0.028 0.112
#> GSM531644 6 0.3993 0.2091 0.400 0.000 0.000 0.000 0.008 0.592
#> GSM531645 4 0.0000 0.9858 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531646 1 0.2946 0.5479 0.812 0.000 0.012 0.000 0.176 0.000
#> GSM531647 1 0.2048 0.6373 0.880 0.000 0.000 0.000 0.120 0.000
#> GSM531648 6 0.2848 0.6357 0.000 0.000 0.004 0.104 0.036 0.856
#> GSM531650 1 0.2066 0.6971 0.904 0.000 0.000 0.000 0.024 0.072
#> GSM531651 3 0.1327 0.6022 0.000 0.000 0.936 0.000 0.064 0.000
#> GSM531652 6 0.3234 0.6134 0.120 0.000 0.004 0.028 0.012 0.836
#> GSM531656 1 0.4977 0.5174 0.696 0.000 0.148 0.000 0.024 0.132
#> GSM531659 6 0.6388 0.4268 0.000 0.216 0.000 0.236 0.040 0.508
#> GSM531661 3 0.2178 0.6163 0.000 0.000 0.868 0.000 0.132 0.000
#> GSM531662 3 0.4230 0.3939 0.000 0.056 0.716 0.000 0.224 0.004
#> GSM531663 4 0.0000 0.9858 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531664 1 0.2473 0.6690 0.856 0.000 0.000 0.000 0.008 0.136
#> GSM531666 6 0.3641 0.5350 0.248 0.000 0.000 0.000 0.020 0.732
#> GSM531667 3 0.4757 0.4977 0.000 0.000 0.676 0.000 0.144 0.180
#> GSM531668 6 0.5014 0.4460 0.000 0.036 0.024 0.000 0.372 0.568
#> GSM531669 1 0.2442 0.6127 0.852 0.000 0.000 0.000 0.144 0.004
#> GSM531671 5 0.7118 0.0000 0.308 0.048 0.308 0.000 0.328 0.008
#> GSM531672 6 0.2883 0.6448 0.000 0.020 0.000 0.036 0.076 0.868
#> GSM531673 3 0.6273 -0.1214 0.020 0.184 0.488 0.000 0.304 0.004
#> GSM531676 2 0.4333 0.1166 0.376 0.596 0.000 0.000 0.028 0.000
#> GSM531679 2 0.2094 0.7073 0.000 0.900 0.000 0.000 0.080 0.020
#> GSM531681 4 0.1007 0.9457 0.000 0.044 0.000 0.956 0.000 0.000
#> GSM531682 2 0.3123 0.7019 0.000 0.832 0.000 0.000 0.112 0.056
#> GSM531683 2 0.4756 0.6342 0.000 0.672 0.000 0.000 0.200 0.128
#> GSM531684 2 0.6258 0.1997 0.000 0.408 0.316 0.000 0.268 0.008
#> GSM531685 1 0.5464 0.1414 0.464 0.452 0.052 0.000 0.032 0.000
#> GSM531686 4 0.1444 0.9155 0.000 0.072 0.000 0.928 0.000 0.000
#> GSM531687 1 0.5625 0.3608 0.540 0.356 0.000 0.000 0.052 0.052
#> GSM531688 1 0.1480 0.7008 0.940 0.040 0.000 0.000 0.020 0.000
#> GSM531690 6 0.4880 0.2243 0.000 0.344 0.000 0.012 0.048 0.596
#> GSM531693 1 0.2190 0.6897 0.900 0.040 0.000 0.000 0.060 0.000
#> GSM531695 1 0.4006 0.6431 0.792 0.044 0.000 0.000 0.048 0.116
#> GSM531603 6 0.5590 0.3264 0.000 0.144 0.004 0.000 0.320 0.532
#> GSM531609 4 0.0000 0.9858 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531611 4 0.0000 0.9858 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531621 3 0.1765 0.5828 0.000 0.000 0.904 0.000 0.096 0.000
#> GSM531622 3 0.3151 0.5942 0.000 0.000 0.748 0.000 0.252 0.000
#> GSM531628 1 0.1700 0.6942 0.916 0.000 0.000 0.000 0.004 0.080
#> GSM531630 3 0.3464 0.5714 0.000 0.000 0.688 0.000 0.312 0.000
#> GSM531633 3 0.2595 0.5301 0.000 0.000 0.836 0.000 0.160 0.004
#> GSM531635 1 0.0713 0.6933 0.972 0.000 0.000 0.000 0.028 0.000
#> GSM531640 3 0.4195 0.5522 0.000 0.000 0.648 0.008 0.328 0.016
#> GSM531649 1 0.3960 0.4508 0.752 0.000 0.072 0.000 0.176 0.000
#> GSM531653 1 0.2595 0.6404 0.872 0.000 0.044 0.000 0.084 0.000
#> GSM531657 6 0.4993 0.5765 0.000 0.004 0.008 0.228 0.096 0.664
#> GSM531665 2 0.4191 0.6027 0.140 0.780 0.012 0.000 0.028 0.040
#> GSM531670 1 0.5500 0.4022 0.636 0.004 0.224 0.000 0.028 0.108
#> GSM531674 1 0.0291 0.7011 0.992 0.000 0.000 0.000 0.004 0.004
#> GSM531675 2 0.4378 0.4616 0.000 0.632 0.000 0.000 0.040 0.328
#> GSM531677 2 0.1719 0.6956 0.000 0.924 0.000 0.000 0.016 0.060
#> GSM531678 2 0.3374 0.6558 0.000 0.836 0.032 0.096 0.036 0.000
#> GSM531680 1 0.5693 0.4380 0.596 0.288 0.008 0.000 0.060 0.048
#> GSM531689 2 0.1151 0.6917 0.012 0.956 0.000 0.000 0.032 0.000
#> GSM531691 2 0.2781 0.6715 0.008 0.868 0.084 0.000 0.040 0.000
#> GSM531692 2 0.3514 0.6492 0.092 0.828 0.052 0.000 0.028 0.000
#> GSM531694 2 0.5336 0.5726 0.000 0.584 0.000 0.000 0.256 0.160
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> SD:NMF 78 1.000 2
#> SD:NMF 69 0.952 3
#> SD:NMF 78 0.570 4
#> SD:NMF 69 0.238 5
#> SD:NMF 57 0.262 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "hclust"]
# you can also extract it by
# res = res_list["CV:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 80 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.407 0.781 0.893 0.4698 0.525 0.525
#> 3 3 0.337 0.402 0.662 0.3456 0.748 0.545
#> 4 4 0.437 0.475 0.711 0.1501 0.741 0.387
#> 5 5 0.556 0.564 0.761 0.0749 0.899 0.639
#> 6 6 0.710 0.590 0.783 0.0576 0.949 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
#> GSM531602 2 0.0000 0.8764 0.000 1.000
#> GSM531604 1 0.8763 0.6391 0.704 0.296
#> GSM531606 2 0.8081 0.6597 0.248 0.752
#> GSM531607 2 0.6887 0.7450 0.184 0.816
#> GSM531608 1 0.2603 0.8737 0.956 0.044
#> GSM531610 2 0.0000 0.8764 0.000 1.000
#> GSM531612 2 0.0000 0.8764 0.000 1.000
#> GSM531613 2 0.0000 0.8764 0.000 1.000
#> GSM531614 2 0.0000 0.8764 0.000 1.000
#> GSM531616 1 0.0000 0.8721 1.000 0.000
#> GSM531618 1 0.9833 0.2661 0.576 0.424
#> GSM531619 1 0.2236 0.8738 0.964 0.036
#> GSM531620 1 0.3584 0.8692 0.932 0.068
#> GSM531623 1 0.0376 0.8729 0.996 0.004
#> GSM531625 1 0.0000 0.8721 1.000 0.000
#> GSM531626 1 0.0000 0.8721 1.000 0.000
#> GSM531632 1 0.0000 0.8721 1.000 0.000
#> GSM531638 1 0.0000 0.8721 1.000 0.000
#> GSM531639 1 0.3733 0.8697 0.928 0.072
#> GSM531641 2 0.0000 0.8764 0.000 1.000
#> GSM531642 1 0.9933 0.2102 0.548 0.452
#> GSM531643 1 0.5629 0.8377 0.868 0.132
#> GSM531644 1 0.9933 0.2102 0.548 0.452
#> GSM531645 2 0.0000 0.8764 0.000 1.000
#> GSM531646 1 0.0000 0.8721 1.000 0.000
#> GSM531647 1 0.0000 0.8721 1.000 0.000
#> GSM531648 2 1.0000 -0.0892 0.500 0.500
#> GSM531650 1 0.2778 0.8740 0.952 0.048
#> GSM531651 1 0.0376 0.8729 0.996 0.004
#> GSM531652 1 0.9988 0.1156 0.520 0.480
#> GSM531656 1 0.4562 0.8597 0.904 0.096
#> GSM531659 2 0.7950 0.6897 0.240 0.760
#> GSM531661 1 0.2778 0.8731 0.952 0.048
#> GSM531662 1 0.7376 0.7553 0.792 0.208
#> GSM531663 2 0.5294 0.8160 0.120 0.880
#> GSM531664 1 0.4815 0.8557 0.896 0.104
#> GSM531666 1 0.9170 0.5414 0.668 0.332
#> GSM531667 1 0.2778 0.8731 0.952 0.048
#> GSM531668 2 0.9933 0.1048 0.452 0.548
#> GSM531669 1 0.3584 0.8726 0.932 0.068
#> GSM531671 1 0.6148 0.8093 0.848 0.152
#> GSM531672 2 0.2236 0.8626 0.036 0.964
#> GSM531673 1 0.7376 0.7553 0.792 0.208
#> GSM531676 1 0.6343 0.8172 0.840 0.160
#> GSM531679 2 0.0672 0.8745 0.008 0.992
#> GSM531681 2 0.0000 0.8764 0.000 1.000
#> GSM531682 2 0.1414 0.8704 0.020 0.980
#> GSM531683 2 0.0000 0.8764 0.000 1.000
#> GSM531684 2 0.8081 0.6597 0.248 0.752
#> GSM531685 1 0.6048 0.8313 0.852 0.148
#> GSM531686 2 0.0000 0.8764 0.000 1.000
#> GSM531687 1 0.6343 0.8172 0.840 0.160
#> GSM531688 1 0.3584 0.8717 0.932 0.068
#> GSM531690 2 0.0000 0.8764 0.000 1.000
#> GSM531693 1 0.3584 0.8717 0.932 0.068
#> GSM531695 1 0.6712 0.8115 0.824 0.176
#> GSM531603 2 0.6887 0.7450 0.184 0.816
#> GSM531609 2 0.0000 0.8764 0.000 1.000
#> GSM531611 2 0.0000 0.8764 0.000 1.000
#> GSM531621 1 0.0376 0.8729 0.996 0.004
#> GSM531622 1 0.2236 0.8738 0.964 0.036
#> GSM531628 1 0.2603 0.8742 0.956 0.044
#> GSM531630 1 0.2236 0.8738 0.964 0.036
#> GSM531633 1 0.0376 0.8729 0.996 0.004
#> GSM531635 1 0.0000 0.8721 1.000 0.000
#> GSM531640 1 0.2236 0.8738 0.964 0.036
#> GSM531649 1 0.0000 0.8721 1.000 0.000
#> GSM531653 1 0.0000 0.8721 1.000 0.000
#> GSM531657 2 0.7883 0.6936 0.236 0.764
#> GSM531665 2 0.8386 0.6439 0.268 0.732
#> GSM531670 1 0.4562 0.8597 0.904 0.096
#> GSM531674 1 0.3274 0.8739 0.940 0.060
#> GSM531675 2 0.0000 0.8764 0.000 1.000
#> GSM531677 2 0.0672 0.8745 0.008 0.992
#> GSM531678 2 0.8081 0.6597 0.248 0.752
#> GSM531680 1 0.6801 0.8076 0.820 0.180
#> GSM531689 1 0.6712 0.8042 0.824 0.176
#> GSM531691 1 0.6712 0.8042 0.824 0.176
#> GSM531692 1 0.5737 0.8341 0.864 0.136
#> GSM531694 2 0.0000 0.8764 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM531602 2 0.5397 0.7731 0.000 0.720 0.280
#> GSM531604 3 0.4662 0.2933 0.124 0.032 0.844
#> GSM531606 3 0.6672 -0.4528 0.008 0.472 0.520
#> GSM531607 2 0.8886 0.6487 0.188 0.572 0.240
#> GSM531608 3 0.6244 0.3152 0.440 0.000 0.560
#> GSM531610 2 0.0000 0.8164 0.000 1.000 0.000
#> GSM531612 2 0.0000 0.8164 0.000 1.000 0.000
#> GSM531613 2 0.0000 0.8164 0.000 1.000 0.000
#> GSM531614 2 0.0000 0.8164 0.000 1.000 0.000
#> GSM531616 1 0.5926 0.0462 0.644 0.000 0.356
#> GSM531618 1 0.9129 0.2429 0.480 0.372 0.148
#> GSM531619 3 0.6252 0.3189 0.444 0.000 0.556
#> GSM531620 1 0.7705 0.1075 0.604 0.064 0.332
#> GSM531623 3 0.6302 0.2820 0.480 0.000 0.520
#> GSM531625 1 0.6305 -0.2860 0.516 0.000 0.484
#> GSM531626 1 0.6305 -0.2860 0.516 0.000 0.484
#> GSM531632 1 0.3619 0.4136 0.864 0.000 0.136
#> GSM531638 1 0.5926 0.0462 0.644 0.000 0.356
#> GSM531639 1 0.7128 0.2750 0.684 0.064 0.252
#> GSM531641 2 0.0237 0.8172 0.000 0.996 0.004
#> GSM531642 1 0.7883 0.2462 0.516 0.428 0.056
#> GSM531643 1 0.4662 0.5104 0.844 0.124 0.032
#> GSM531644 1 0.7883 0.2462 0.516 0.428 0.056
#> GSM531645 2 0.0000 0.8164 0.000 1.000 0.000
#> GSM531646 1 0.3816 0.4036 0.852 0.000 0.148
#> GSM531647 1 0.1163 0.4968 0.972 0.000 0.028
#> GSM531648 1 0.8523 0.1133 0.464 0.444 0.092
#> GSM531650 1 0.1878 0.5196 0.952 0.044 0.004
#> GSM531651 3 0.6302 0.2820 0.480 0.000 0.520
#> GSM531652 1 0.8331 0.1713 0.484 0.436 0.080
#> GSM531656 1 0.5582 0.4872 0.812 0.088 0.100
#> GSM531659 2 0.8392 0.6225 0.176 0.624 0.200
#> GSM531661 3 0.6451 0.3141 0.436 0.004 0.560
#> GSM531662 3 0.8827 0.1258 0.384 0.120 0.496
#> GSM531663 2 0.6622 0.7657 0.088 0.748 0.164
#> GSM531664 1 0.3295 0.5195 0.896 0.096 0.008
#> GSM531666 1 0.7012 0.3887 0.652 0.308 0.040
#> GSM531667 3 0.6451 0.3141 0.436 0.004 0.560
#> GSM531668 2 0.8925 -0.0135 0.412 0.464 0.124
#> GSM531669 1 0.4335 0.4767 0.864 0.036 0.100
#> GSM531671 1 0.8507 -0.0720 0.484 0.092 0.424
#> GSM531672 2 0.5047 0.8148 0.036 0.824 0.140
#> GSM531673 3 0.8827 0.1258 0.384 0.120 0.496
#> GSM531676 3 0.6445 0.2876 0.308 0.020 0.672
#> GSM531679 2 0.4931 0.8025 0.000 0.768 0.232
#> GSM531681 2 0.1289 0.8197 0.000 0.968 0.032
#> GSM531682 2 0.5335 0.8022 0.008 0.760 0.232
#> GSM531683 2 0.5178 0.7891 0.000 0.744 0.256
#> GSM531684 3 0.6672 -0.4528 0.008 0.472 0.520
#> GSM531685 3 0.7067 0.0244 0.468 0.020 0.512
#> GSM531686 2 0.1289 0.8197 0.000 0.968 0.032
#> GSM531687 3 0.6445 0.2876 0.308 0.020 0.672
#> GSM531688 1 0.4921 0.4183 0.816 0.020 0.164
#> GSM531690 2 0.4452 0.8111 0.000 0.808 0.192
#> GSM531693 1 0.4921 0.4183 0.816 0.020 0.164
#> GSM531695 1 0.7564 0.2451 0.636 0.068 0.296
#> GSM531603 2 0.8886 0.6487 0.188 0.572 0.240
#> GSM531609 2 0.0000 0.8164 0.000 1.000 0.000
#> GSM531611 2 0.0000 0.8164 0.000 1.000 0.000
#> GSM531621 3 0.6302 0.2820 0.480 0.000 0.520
#> GSM531622 3 0.6252 0.3189 0.444 0.000 0.556
#> GSM531628 1 0.1765 0.5187 0.956 0.040 0.004
#> GSM531630 3 0.6252 0.3189 0.444 0.000 0.556
#> GSM531633 3 0.6302 0.2820 0.480 0.000 0.520
#> GSM531635 1 0.5859 0.0615 0.656 0.000 0.344
#> GSM531640 3 0.6252 0.3189 0.444 0.000 0.556
#> GSM531649 1 0.1163 0.4968 0.972 0.000 0.028
#> GSM531653 1 0.1163 0.4968 0.972 0.000 0.028
#> GSM531657 2 0.8307 0.6202 0.192 0.632 0.176
#> GSM531665 2 0.8675 0.5787 0.184 0.596 0.220
#> GSM531670 1 0.5582 0.4872 0.812 0.088 0.100
#> GSM531674 1 0.3742 0.4963 0.892 0.036 0.072
#> GSM531675 2 0.4842 0.8032 0.000 0.776 0.224
#> GSM531677 2 0.4931 0.8025 0.000 0.768 0.232
#> GSM531678 3 0.6672 -0.4528 0.008 0.472 0.520
#> GSM531680 1 0.7536 0.2363 0.632 0.064 0.304
#> GSM531689 3 0.6326 0.2929 0.292 0.020 0.688
#> GSM531691 3 0.6326 0.2929 0.292 0.020 0.688
#> GSM531692 3 0.5216 0.3152 0.260 0.000 0.740
#> GSM531694 2 0.5397 0.7731 0.000 0.720 0.280
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM531602 2 0.0000 0.684668 0.000 1.000 0.000 0.000
#> GSM531604 3 0.9586 0.168804 0.144 0.276 0.372 0.208
#> GSM531606 2 0.5811 0.557105 0.028 0.740 0.160 0.072
#> GSM531607 2 0.5873 0.500038 0.188 0.712 0.008 0.092
#> GSM531608 3 0.1151 0.714074 0.024 0.008 0.968 0.000
#> GSM531610 4 0.3873 0.689164 0.000 0.228 0.000 0.772
#> GSM531612 4 0.3873 0.689164 0.000 0.228 0.000 0.772
#> GSM531613 4 0.4040 0.667784 0.000 0.248 0.000 0.752
#> GSM531614 4 0.3873 0.689164 0.000 0.228 0.000 0.772
#> GSM531616 3 0.4804 0.394994 0.384 0.000 0.616 0.000
#> GSM531618 1 0.8975 0.000932 0.384 0.064 0.224 0.328
#> GSM531619 3 0.0000 0.712648 0.000 0.000 1.000 0.000
#> GSM531620 3 0.6100 0.404683 0.304 0.000 0.624 0.072
#> GSM531623 3 0.1118 0.716516 0.036 0.000 0.964 0.000
#> GSM531625 3 0.2704 0.689437 0.124 0.000 0.876 0.000
#> GSM531626 3 0.2704 0.689437 0.124 0.000 0.876 0.000
#> GSM531632 1 0.4072 0.440644 0.748 0.000 0.252 0.000
#> GSM531638 3 0.4804 0.394994 0.384 0.000 0.616 0.000
#> GSM531639 3 0.6559 0.055958 0.452 0.004 0.480 0.064
#> GSM531641 4 0.4267 0.683658 0.008 0.216 0.004 0.772
#> GSM531642 1 0.7477 -0.000351 0.448 0.012 0.124 0.416
#> GSM531643 1 0.4801 0.571064 0.800 0.008 0.084 0.108
#> GSM531644 1 0.7477 -0.000351 0.448 0.012 0.124 0.416
#> GSM531645 4 0.4086 0.685040 0.008 0.216 0.000 0.776
#> GSM531646 1 0.4331 0.386114 0.712 0.000 0.288 0.000
#> GSM531647 1 0.2704 0.579480 0.876 0.000 0.124 0.000
#> GSM531648 4 0.7918 0.018101 0.400 0.024 0.144 0.432
#> GSM531650 1 0.2816 0.603989 0.900 0.000 0.064 0.036
#> GSM531651 3 0.1118 0.716516 0.036 0.000 0.964 0.000
#> GSM531652 4 0.7774 -0.031701 0.420 0.020 0.136 0.424
#> GSM531656 1 0.5479 0.529215 0.740 0.008 0.180 0.072
#> GSM531659 2 0.8476 0.388889 0.120 0.552 0.156 0.172
#> GSM531661 3 0.1339 0.713382 0.024 0.008 0.964 0.004
#> GSM531662 3 0.9067 0.284695 0.272 0.108 0.448 0.172
#> GSM531663 2 0.6939 0.514011 0.056 0.660 0.080 0.204
#> GSM531664 1 0.3526 0.599639 0.872 0.008 0.040 0.080
#> GSM531666 1 0.6841 0.308613 0.600 0.012 0.100 0.288
#> GSM531667 3 0.1339 0.713382 0.024 0.008 0.964 0.004
#> GSM531668 4 0.8681 0.077603 0.368 0.084 0.128 0.420
#> GSM531669 1 0.3819 0.605837 0.860 0.016 0.036 0.088
#> GSM531671 3 0.8410 0.284372 0.320 0.060 0.476 0.144
#> GSM531672 2 0.5927 0.471075 0.036 0.680 0.024 0.260
#> GSM531673 3 0.9067 0.284695 0.272 0.108 0.448 0.172
#> GSM531676 1 0.9415 -0.026933 0.348 0.112 0.332 0.208
#> GSM531679 2 0.2053 0.688248 0.004 0.924 0.000 0.072
#> GSM531681 4 0.4977 0.327882 0.000 0.460 0.000 0.540
#> GSM531682 2 0.2384 0.690316 0.004 0.916 0.008 0.072
#> GSM531683 2 0.0817 0.689357 0.000 0.976 0.000 0.024
#> GSM531684 2 0.5811 0.557105 0.028 0.740 0.160 0.072
#> GSM531685 1 0.8685 0.251809 0.508 0.088 0.208 0.196
#> GSM531686 4 0.4977 0.327882 0.000 0.460 0.000 0.540
#> GSM531687 1 0.9415 -0.026933 0.348 0.112 0.332 0.208
#> GSM531688 1 0.4739 0.578981 0.804 0.028 0.032 0.136
#> GSM531690 2 0.2469 0.650812 0.000 0.892 0.000 0.108
#> GSM531693 1 0.4739 0.578981 0.804 0.028 0.032 0.136
#> GSM531695 1 0.5842 0.498205 0.688 0.092 0.000 0.220
#> GSM531603 2 0.5873 0.500038 0.188 0.712 0.008 0.092
#> GSM531609 4 0.3873 0.689164 0.000 0.228 0.000 0.772
#> GSM531611 4 0.3873 0.689164 0.000 0.228 0.000 0.772
#> GSM531621 3 0.1118 0.716516 0.036 0.000 0.964 0.000
#> GSM531622 3 0.0000 0.712648 0.000 0.000 1.000 0.000
#> GSM531628 1 0.2722 0.603942 0.904 0.000 0.064 0.032
#> GSM531630 3 0.0000 0.712648 0.000 0.000 1.000 0.000
#> GSM531633 3 0.1118 0.716516 0.036 0.000 0.964 0.000
#> GSM531635 3 0.4898 0.341203 0.416 0.000 0.584 0.000
#> GSM531640 3 0.0000 0.712648 0.000 0.000 1.000 0.000
#> GSM531649 1 0.2704 0.579480 0.876 0.000 0.124 0.000
#> GSM531653 1 0.2704 0.579480 0.876 0.000 0.124 0.000
#> GSM531657 2 0.8907 0.169235 0.156 0.460 0.100 0.284
#> GSM531665 2 0.8730 0.359735 0.128 0.524 0.176 0.172
#> GSM531670 1 0.5479 0.529215 0.740 0.008 0.180 0.072
#> GSM531674 1 0.3221 0.609990 0.888 0.008 0.036 0.068
#> GSM531675 2 0.1716 0.684119 0.000 0.936 0.000 0.064
#> GSM531677 2 0.2053 0.688248 0.004 0.924 0.000 0.072
#> GSM531678 2 0.5903 0.553943 0.032 0.736 0.160 0.072
#> GSM531680 1 0.5923 0.494377 0.684 0.100 0.000 0.216
#> GSM531689 1 0.9535 -0.039561 0.332 0.128 0.332 0.208
#> GSM531691 1 0.9535 -0.039561 0.332 0.128 0.332 0.208
#> GSM531692 3 0.9189 0.100470 0.300 0.092 0.400 0.208
#> GSM531694 2 0.0000 0.684668 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM531602 2 0.0609 0.7286 0.000 0.980 0.000 0.000 0.020
#> GSM531604 5 0.6406 0.4655 0.008 0.240 0.200 0.000 0.552
#> GSM531606 2 0.4763 0.5201 0.000 0.712 0.076 0.000 0.212
#> GSM531607 2 0.5837 0.5636 0.172 0.684 0.000 0.084 0.060
#> GSM531608 3 0.1026 0.7697 0.024 0.004 0.968 0.000 0.004
#> GSM531610 4 0.0963 0.8295 0.000 0.036 0.000 0.964 0.000
#> GSM531612 4 0.0963 0.8295 0.000 0.036 0.000 0.964 0.000
#> GSM531613 4 0.1732 0.7988 0.000 0.080 0.000 0.920 0.000
#> GSM531614 4 0.0963 0.8295 0.000 0.036 0.000 0.964 0.000
#> GSM531616 3 0.5941 0.3898 0.376 0.000 0.544 0.036 0.044
#> GSM531618 1 0.9295 0.2365 0.340 0.060 0.192 0.236 0.172
#> GSM531619 3 0.0000 0.7710 0.000 0.000 1.000 0.000 0.000
#> GSM531620 3 0.6419 0.4243 0.284 0.000 0.580 0.048 0.088
#> GSM531623 3 0.1117 0.7723 0.016 0.000 0.964 0.000 0.020
#> GSM531625 3 0.4128 0.7080 0.096 0.000 0.816 0.036 0.052
#> GSM531626 3 0.4128 0.7080 0.096 0.000 0.816 0.036 0.052
#> GSM531632 1 0.4371 0.5393 0.780 0.000 0.156 0.036 0.028
#> GSM531638 3 0.5941 0.3898 0.376 0.000 0.544 0.036 0.044
#> GSM531639 3 0.6562 0.0485 0.432 0.004 0.456 0.044 0.064
#> GSM531641 4 0.1356 0.8223 0.012 0.028 0.004 0.956 0.000
#> GSM531642 1 0.7984 0.2710 0.408 0.004 0.100 0.316 0.172
#> GSM531643 1 0.3839 0.6239 0.844 0.004 0.052 0.056 0.044
#> GSM531644 1 0.7984 0.2710 0.408 0.004 0.100 0.316 0.172
#> GSM531645 4 0.1195 0.8237 0.012 0.028 0.000 0.960 0.000
#> GSM531646 1 0.4858 0.5117 0.736 0.000 0.192 0.036 0.036
#> GSM531647 1 0.2532 0.6190 0.908 0.000 0.028 0.036 0.028
#> GSM531648 1 0.8433 0.1875 0.360 0.016 0.120 0.332 0.172
#> GSM531650 1 0.0693 0.6358 0.980 0.000 0.012 0.008 0.000
#> GSM531651 3 0.1117 0.7723 0.016 0.000 0.964 0.000 0.020
#> GSM531652 1 0.8288 0.2236 0.380 0.012 0.112 0.324 0.172
#> GSM531656 1 0.4526 0.5658 0.780 0.004 0.148 0.036 0.032
#> GSM531659 2 0.8058 0.5099 0.092 0.556 0.140 0.104 0.108
#> GSM531661 3 0.1187 0.7679 0.024 0.004 0.964 0.004 0.004
#> GSM531662 5 0.8046 0.2859 0.148 0.064 0.292 0.036 0.460
#> GSM531663 2 0.6652 0.5766 0.048 0.644 0.076 0.192 0.040
#> GSM531664 1 0.2074 0.6334 0.928 0.004 0.004 0.032 0.032
#> GSM531666 1 0.6142 0.5142 0.652 0.004 0.068 0.212 0.064
#> GSM531667 3 0.1187 0.7679 0.024 0.004 0.964 0.004 0.004
#> GSM531668 4 0.9000 -0.2274 0.320 0.060 0.108 0.332 0.180
#> GSM531669 1 0.2488 0.5574 0.872 0.000 0.000 0.004 0.124
#> GSM531671 5 0.8218 0.1229 0.240 0.032 0.320 0.044 0.364
#> GSM531672 2 0.5927 0.5529 0.044 0.660 0.024 0.240 0.032
#> GSM531673 5 0.8046 0.2859 0.148 0.064 0.292 0.036 0.460
#> GSM531676 5 0.4318 0.6655 0.040 0.032 0.136 0.000 0.792
#> GSM531679 2 0.1725 0.7356 0.000 0.936 0.000 0.044 0.020
#> GSM531681 4 0.4114 0.4082 0.000 0.376 0.000 0.624 0.000
#> GSM531682 2 0.2073 0.7363 0.008 0.928 0.004 0.044 0.016
#> GSM531683 2 0.0807 0.7340 0.000 0.976 0.000 0.012 0.012
#> GSM531684 2 0.4793 0.5160 0.000 0.708 0.076 0.000 0.216
#> GSM531685 5 0.5343 0.5585 0.212 0.008 0.100 0.000 0.680
#> GSM531686 4 0.4114 0.4082 0.000 0.376 0.000 0.624 0.000
#> GSM531687 5 0.4318 0.6655 0.040 0.032 0.136 0.000 0.792
#> GSM531688 1 0.3741 0.3883 0.732 0.004 0.000 0.000 0.264
#> GSM531690 2 0.2068 0.7108 0.000 0.904 0.000 0.092 0.004
#> GSM531693 1 0.3766 0.3824 0.728 0.004 0.000 0.000 0.268
#> GSM531695 5 0.5399 0.0823 0.476 0.032 0.000 0.012 0.480
#> GSM531603 2 0.5837 0.5636 0.172 0.684 0.000 0.084 0.060
#> GSM531609 4 0.0963 0.8295 0.000 0.036 0.000 0.964 0.000
#> GSM531611 4 0.0963 0.8295 0.000 0.036 0.000 0.964 0.000
#> GSM531621 3 0.1117 0.7723 0.016 0.000 0.964 0.000 0.020
#> GSM531622 3 0.0000 0.7710 0.000 0.000 1.000 0.000 0.000
#> GSM531628 1 0.0854 0.6359 0.976 0.000 0.012 0.008 0.004
#> GSM531630 3 0.0000 0.7710 0.000 0.000 1.000 0.000 0.000
#> GSM531633 3 0.1117 0.7723 0.016 0.000 0.964 0.000 0.020
#> GSM531635 3 0.5884 0.3098 0.416 0.000 0.512 0.036 0.036
#> GSM531640 3 0.0000 0.7710 0.000 0.000 1.000 0.000 0.000
#> GSM531649 1 0.2777 0.6175 0.896 0.000 0.028 0.036 0.040
#> GSM531653 1 0.2777 0.6175 0.896 0.000 0.028 0.036 0.040
#> GSM531657 2 0.8695 0.3495 0.128 0.468 0.088 0.208 0.108
#> GSM531665 2 0.8316 0.4846 0.096 0.528 0.152 0.104 0.120
#> GSM531670 1 0.4526 0.5658 0.780 0.004 0.148 0.036 0.032
#> GSM531674 1 0.2068 0.5884 0.904 0.000 0.000 0.004 0.092
#> GSM531675 2 0.1357 0.7331 0.000 0.948 0.000 0.048 0.004
#> GSM531677 2 0.1725 0.7356 0.000 0.936 0.000 0.044 0.020
#> GSM531678 2 0.4850 0.5060 0.000 0.700 0.076 0.000 0.224
#> GSM531680 5 0.5311 0.2463 0.396 0.032 0.000 0.012 0.560
#> GSM531689 5 0.4380 0.6634 0.028 0.048 0.136 0.000 0.788
#> GSM531691 5 0.4380 0.6634 0.028 0.048 0.136 0.000 0.788
#> GSM531692 5 0.4460 0.6259 0.032 0.016 0.204 0.000 0.748
#> GSM531694 2 0.0609 0.7286 0.000 0.980 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
#> GSM531602 2 0.0725 0.74765 0.000 0.976 0.000 0.000 0.012 0.012
#> GSM531604 5 0.4587 0.46224 0.008 0.224 0.016 0.000 0.708 0.044
#> GSM531606 2 0.3595 0.53999 0.000 0.704 0.000 0.000 0.288 0.008
#> GSM531607 2 0.4590 0.50131 0.000 0.668 0.000 0.048 0.012 0.272
#> GSM531608 3 0.1531 0.79877 0.000 0.000 0.928 0.000 0.004 0.068
#> GSM531610 4 0.0000 0.88567 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531612 4 0.0000 0.88567 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531613 4 0.1141 0.85700 0.000 0.052 0.000 0.948 0.000 0.000
#> GSM531614 4 0.0000 0.88567 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531616 3 0.5075 0.14859 0.452 0.000 0.480 0.000 0.004 0.064
#> GSM531618 6 0.4480 0.70399 0.052 0.036 0.104 0.028 0.000 0.780
#> GSM531619 3 0.0790 0.80711 0.000 0.000 0.968 0.000 0.000 0.032
#> GSM531620 3 0.5848 0.31167 0.108 0.000 0.544 0.024 0.004 0.320
#> GSM531623 3 0.0146 0.80497 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM531625 3 0.3840 0.69145 0.152 0.000 0.776 0.000 0.004 0.068
#> GSM531626 3 0.3840 0.69145 0.152 0.000 0.776 0.000 0.004 0.068
#> GSM531632 1 0.2794 0.64979 0.860 0.000 0.080 0.000 0.000 0.060
#> GSM531638 3 0.5075 0.14859 0.452 0.000 0.480 0.000 0.004 0.064
#> GSM531639 3 0.6210 -0.02697 0.140 0.000 0.456 0.024 0.004 0.376
#> GSM531641 4 0.0632 0.87477 0.000 0.000 0.000 0.976 0.000 0.024
#> GSM531642 6 0.3850 0.76484 0.080 0.000 0.036 0.076 0.000 0.808
#> GSM531643 1 0.4675 0.37753 0.584 0.000 0.024 0.016 0.000 0.376
#> GSM531644 6 0.3850 0.76484 0.080 0.000 0.036 0.076 0.000 0.808
#> GSM531645 4 0.0458 0.87918 0.000 0.000 0.000 0.984 0.000 0.016
#> GSM531646 1 0.3396 0.62427 0.812 0.000 0.116 0.000 0.000 0.072
#> GSM531647 1 0.0937 0.71234 0.960 0.000 0.000 0.000 0.000 0.040
#> GSM531648 6 0.3188 0.76942 0.032 0.000 0.040 0.076 0.000 0.852
#> GSM531650 1 0.2135 0.69843 0.872 0.000 0.000 0.000 0.000 0.128
#> GSM531651 3 0.0146 0.80497 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM531652 6 0.3524 0.77415 0.052 0.000 0.040 0.076 0.000 0.832
#> GSM531656 1 0.5611 0.43415 0.536 0.000 0.152 0.000 0.004 0.308
#> GSM531659 2 0.5377 0.31374 0.000 0.540 0.080 0.004 0.008 0.368
#> GSM531661 3 0.1588 0.79670 0.000 0.000 0.924 0.000 0.004 0.072
#> GSM531662 5 0.6680 0.12974 0.000 0.036 0.240 0.000 0.380 0.344
#> GSM531663 2 0.5643 0.55115 0.000 0.644 0.048 0.108 0.004 0.196
#> GSM531664 1 0.3482 0.53604 0.684 0.000 0.000 0.000 0.000 0.316
#> GSM531666 6 0.5001 0.09340 0.396 0.000 0.032 0.024 0.000 0.548
#> GSM531667 3 0.1588 0.79670 0.000 0.000 0.924 0.000 0.004 0.072
#> GSM531668 6 0.2882 0.72692 0.000 0.024 0.024 0.076 0.004 0.872
#> GSM531669 1 0.3458 0.66502 0.808 0.000 0.000 0.000 0.112 0.080
#> GSM531671 5 0.8010 0.11241 0.196 0.016 0.228 0.000 0.288 0.272
#> GSM531672 2 0.4810 0.56304 0.000 0.660 0.000 0.120 0.000 0.220
#> GSM531673 5 0.6680 0.12974 0.000 0.036 0.240 0.000 0.380 0.344
#> GSM531676 5 0.0547 0.66472 0.000 0.020 0.000 0.000 0.980 0.000
#> GSM531679 2 0.1434 0.75418 0.000 0.940 0.000 0.000 0.012 0.048
#> GSM531681 4 0.3717 0.44888 0.000 0.384 0.000 0.616 0.000 0.000
#> GSM531682 2 0.1524 0.75224 0.000 0.932 0.000 0.000 0.008 0.060
#> GSM531683 2 0.0777 0.75250 0.000 0.972 0.000 0.000 0.004 0.024
#> GSM531684 2 0.3615 0.53581 0.000 0.700 0.000 0.000 0.292 0.008
#> GSM531685 5 0.2838 0.54456 0.188 0.000 0.000 0.000 0.808 0.004
#> GSM531686 4 0.3717 0.44888 0.000 0.384 0.000 0.616 0.000 0.000
#> GSM531687 5 0.0547 0.66472 0.000 0.020 0.000 0.000 0.980 0.000
#> GSM531688 1 0.3405 0.51546 0.724 0.000 0.000 0.000 0.272 0.004
#> GSM531690 2 0.2070 0.74083 0.000 0.908 0.000 0.044 0.000 0.048
#> GSM531693 1 0.3426 0.50932 0.720 0.000 0.000 0.000 0.276 0.004
#> GSM531695 5 0.5491 0.00854 0.432 0.028 0.000 0.000 0.480 0.060
#> GSM531603 2 0.4590 0.50131 0.000 0.668 0.000 0.048 0.012 0.272
#> GSM531609 4 0.0000 0.88567 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531611 4 0.0146 0.88433 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM531621 3 0.0146 0.80497 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM531622 3 0.0790 0.80711 0.000 0.000 0.968 0.000 0.000 0.032
#> GSM531628 1 0.2092 0.69931 0.876 0.000 0.000 0.000 0.000 0.124
#> GSM531630 3 0.0790 0.80711 0.000 0.000 0.968 0.000 0.000 0.032
#> GSM531633 3 0.0146 0.80497 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM531635 1 0.4984 -0.13467 0.492 0.000 0.440 0.000 0.000 0.068
#> GSM531640 3 0.0790 0.80711 0.000 0.000 0.968 0.000 0.000 0.032
#> GSM531649 1 0.1285 0.71149 0.944 0.000 0.004 0.000 0.000 0.052
#> GSM531653 1 0.1285 0.71149 0.944 0.000 0.004 0.000 0.000 0.052
#> GSM531657 6 0.5523 -0.22159 0.000 0.456 0.052 0.036 0.000 0.456
#> GSM531665 2 0.5832 0.26904 0.000 0.512 0.080 0.004 0.032 0.372
#> GSM531670 1 0.5611 0.43415 0.536 0.000 0.152 0.000 0.004 0.308
#> GSM531674 1 0.3175 0.68742 0.832 0.000 0.000 0.000 0.088 0.080
#> GSM531675 2 0.1152 0.75319 0.000 0.952 0.000 0.004 0.000 0.044
#> GSM531677 2 0.1434 0.75418 0.000 0.940 0.000 0.000 0.012 0.048
#> GSM531678 2 0.3547 0.52553 0.000 0.696 0.000 0.000 0.300 0.004
#> GSM531680 5 0.5292 0.23261 0.344 0.028 0.000 0.000 0.572 0.056
#> GSM531689 5 0.0865 0.66149 0.000 0.036 0.000 0.000 0.964 0.000
#> GSM531691 5 0.0865 0.66149 0.000 0.036 0.000 0.000 0.964 0.000
#> GSM531692 5 0.1793 0.65321 0.008 0.004 0.016 0.000 0.932 0.040
#> GSM531694 2 0.0725 0.74765 0.000 0.976 0.000 0.000 0.012 0.012
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> CV:hclust 74 1.000 2
#> CV:hclust 29 1.000 3
#> CV:hclust 48 0.922 4
#> CV:hclust 57 0.892 5
#> CV:hclust 60 0.523 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "kmeans"]
# you can also extract it by
# res = res_list["CV:kmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 80 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 0.760 0.910 0.960 0.5007 0.499 0.499
#> 3 3 0.540 0.339 0.630 0.2974 0.706 0.477
#> 4 4 0.831 0.872 0.925 0.1568 0.777 0.440
#> 5 5 0.749 0.623 0.783 0.0615 0.905 0.646
#> 6 6 0.750 0.667 0.807 0.0427 0.919 0.636
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
#> GSM531602 2 0.0000 0.955 0.000 1.000
#> GSM531604 2 0.0376 0.952 0.004 0.996
#> GSM531606 2 0.0000 0.955 0.000 1.000
#> GSM531607 2 0.0000 0.955 0.000 1.000
#> GSM531608 1 0.7219 0.743 0.800 0.200
#> GSM531610 2 0.0000 0.955 0.000 1.000
#> GSM531612 2 0.0000 0.955 0.000 1.000
#> GSM531613 2 0.0000 0.955 0.000 1.000
#> GSM531614 2 0.0000 0.955 0.000 1.000
#> GSM531616 1 0.0000 0.955 1.000 0.000
#> GSM531618 1 0.7219 0.743 0.800 0.200
#> GSM531619 1 0.0000 0.955 1.000 0.000
#> GSM531620 1 0.0000 0.955 1.000 0.000
#> GSM531623 1 0.0000 0.955 1.000 0.000
#> GSM531625 1 0.0000 0.955 1.000 0.000
#> GSM531626 1 0.0000 0.955 1.000 0.000
#> GSM531632 1 0.0000 0.955 1.000 0.000
#> GSM531638 1 0.0000 0.955 1.000 0.000
#> GSM531639 1 0.0000 0.955 1.000 0.000
#> GSM531641 2 0.0000 0.955 0.000 1.000
#> GSM531642 1 0.0000 0.955 1.000 0.000
#> GSM531643 1 0.0000 0.955 1.000 0.000
#> GSM531644 1 0.0000 0.955 1.000 0.000
#> GSM531645 2 0.0000 0.955 0.000 1.000
#> GSM531646 1 0.0000 0.955 1.000 0.000
#> GSM531647 1 0.0000 0.955 1.000 0.000
#> GSM531648 2 0.9944 0.128 0.456 0.544
#> GSM531650 1 0.0000 0.955 1.000 0.000
#> GSM531651 1 0.0000 0.955 1.000 0.000
#> GSM531652 1 0.0000 0.955 1.000 0.000
#> GSM531656 1 0.0000 0.955 1.000 0.000
#> GSM531659 2 0.0000 0.955 0.000 1.000
#> GSM531661 1 0.0000 0.955 1.000 0.000
#> GSM531662 1 0.0000 0.955 1.000 0.000
#> GSM531663 2 0.0000 0.955 0.000 1.000
#> GSM531664 1 0.0000 0.955 1.000 0.000
#> GSM531666 1 0.7219 0.738 0.800 0.200
#> GSM531667 1 0.0000 0.955 1.000 0.000
#> GSM531668 2 0.0000 0.955 0.000 1.000
#> GSM531669 1 0.0000 0.955 1.000 0.000
#> GSM531671 1 0.0000 0.955 1.000 0.000
#> GSM531672 2 0.0000 0.955 0.000 1.000
#> GSM531673 1 0.7883 0.700 0.764 0.236
#> GSM531676 2 0.7219 0.755 0.200 0.800
#> GSM531679 2 0.0000 0.955 0.000 1.000
#> GSM531681 2 0.0000 0.955 0.000 1.000
#> GSM531682 2 0.0000 0.955 0.000 1.000
#> GSM531683 2 0.0000 0.955 0.000 1.000
#> GSM531684 2 0.0000 0.955 0.000 1.000
#> GSM531685 1 0.7883 0.700 0.764 0.236
#> GSM531686 2 0.0000 0.955 0.000 1.000
#> GSM531687 2 0.7219 0.755 0.200 0.800
#> GSM531688 1 0.8081 0.681 0.752 0.248
#> GSM531690 2 0.0000 0.955 0.000 1.000
#> GSM531693 1 0.0000 0.955 1.000 0.000
#> GSM531695 2 0.7219 0.755 0.200 0.800
#> GSM531603 2 0.0000 0.955 0.000 1.000
#> GSM531609 2 0.0000 0.955 0.000 1.000
#> GSM531611 2 0.0000 0.955 0.000 1.000
#> GSM531621 1 0.0000 0.955 1.000 0.000
#> GSM531622 1 0.0000 0.955 1.000 0.000
#> GSM531628 1 0.0000 0.955 1.000 0.000
#> GSM531630 1 0.0000 0.955 1.000 0.000
#> GSM531633 1 0.0000 0.955 1.000 0.000
#> GSM531635 1 0.0000 0.955 1.000 0.000
#> GSM531640 1 0.0000 0.955 1.000 0.000
#> GSM531649 1 0.0000 0.955 1.000 0.000
#> GSM531653 1 0.0000 0.955 1.000 0.000
#> GSM531657 2 0.0000 0.955 0.000 1.000
#> GSM531665 1 0.7056 0.762 0.808 0.192
#> GSM531670 1 0.0000 0.955 1.000 0.000
#> GSM531674 1 0.0000 0.955 1.000 0.000
#> GSM531675 2 0.0000 0.955 0.000 1.000
#> GSM531677 2 0.0000 0.955 0.000 1.000
#> GSM531678 2 0.0000 0.955 0.000 1.000
#> GSM531680 2 0.7139 0.760 0.196 0.804
#> GSM531689 2 0.0000 0.955 0.000 1.000
#> GSM531691 2 0.6712 0.785 0.176 0.824
#> GSM531692 1 0.7745 0.712 0.772 0.228
#> GSM531694 2 0.0000 0.955 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM531602 2 0.1129 0.6965 0.004 0.976 0.020
#> GSM531604 2 0.2680 0.6731 0.008 0.924 0.068
#> GSM531606 2 0.1129 0.6965 0.004 0.976 0.020
#> GSM531607 2 0.1129 0.6965 0.004 0.976 0.020
#> GSM531608 3 0.2492 0.6892 0.048 0.016 0.936
#> GSM531610 1 0.7583 -0.2868 0.492 0.468 0.040
#> GSM531612 1 0.7438 -0.1501 0.568 0.392 0.040
#> GSM531613 2 0.6955 0.2644 0.492 0.492 0.016
#> GSM531614 1 0.7438 -0.1501 0.568 0.392 0.040
#> GSM531616 3 0.1860 0.7239 0.052 0.000 0.948
#> GSM531618 3 0.9775 0.0038 0.288 0.272 0.440
#> GSM531619 3 0.0747 0.7406 0.000 0.016 0.984
#> GSM531620 3 0.0592 0.7413 0.000 0.012 0.988
#> GSM531623 3 0.0747 0.7406 0.000 0.016 0.984
#> GSM531625 3 0.1860 0.7239 0.052 0.000 0.948
#> GSM531626 3 0.1529 0.7280 0.040 0.000 0.960
#> GSM531632 3 0.6309 0.1550 0.496 0.000 0.504
#> GSM531638 3 0.1860 0.7239 0.052 0.000 0.948
#> GSM531639 3 0.5678 0.4596 0.316 0.000 0.684
#> GSM531641 1 0.7438 -0.1501 0.568 0.392 0.040
#> GSM531642 3 0.6516 0.2145 0.480 0.004 0.516
#> GSM531643 1 0.6308 -0.1947 0.508 0.000 0.492
#> GSM531644 1 0.6180 -0.1126 0.584 0.000 0.416
#> GSM531645 1 0.7438 -0.1501 0.568 0.392 0.040
#> GSM531646 3 0.6308 0.1650 0.492 0.000 0.508
#> GSM531647 1 0.6309 -0.2027 0.504 0.000 0.496
#> GSM531648 1 0.7551 -0.1308 0.580 0.372 0.048
#> GSM531650 1 0.6308 -0.1947 0.508 0.000 0.492
#> GSM531651 3 0.0592 0.7413 0.000 0.012 0.988
#> GSM531652 1 0.6432 -0.1306 0.568 0.004 0.428
#> GSM531656 3 0.6252 0.2705 0.444 0.000 0.556
#> GSM531659 2 0.7546 0.3526 0.396 0.560 0.044
#> GSM531661 3 0.0747 0.7406 0.000 0.016 0.984
#> GSM531662 3 0.0747 0.7406 0.000 0.016 0.984
#> GSM531663 1 0.7583 -0.2868 0.492 0.468 0.040
#> GSM531664 1 0.6421 -0.1215 0.572 0.004 0.424
#> GSM531666 1 0.6373 -0.1123 0.588 0.004 0.408
#> GSM531667 3 0.0747 0.7406 0.000 0.016 0.984
#> GSM531668 2 0.7956 0.3261 0.424 0.516 0.060
#> GSM531669 1 0.6516 -0.1819 0.516 0.004 0.480
#> GSM531671 3 0.3845 0.6887 0.116 0.012 0.872
#> GSM531672 2 0.7069 0.2790 0.472 0.508 0.020
#> GSM531673 2 0.6577 0.3090 0.008 0.572 0.420
#> GSM531676 2 0.6566 0.3767 0.348 0.636 0.016
#> GSM531679 2 0.1015 0.6953 0.008 0.980 0.012
#> GSM531681 2 0.6095 0.4159 0.392 0.608 0.000
#> GSM531682 2 0.0829 0.6959 0.004 0.984 0.012
#> GSM531683 2 0.0829 0.6954 0.004 0.984 0.012
#> GSM531684 2 0.2878 0.6573 0.000 0.904 0.096
#> GSM531685 2 0.6869 0.2672 0.424 0.560 0.016
#> GSM531686 2 0.6095 0.4159 0.392 0.608 0.000
#> GSM531687 2 0.6566 0.3767 0.348 0.636 0.016
#> GSM531688 1 0.6950 -0.1965 0.508 0.476 0.016
#> GSM531690 2 0.6140 0.3955 0.404 0.596 0.000
#> GSM531693 1 0.6822 -0.1875 0.508 0.012 0.480
#> GSM531695 2 0.6952 0.1773 0.480 0.504 0.016
#> GSM531603 2 0.1129 0.6965 0.004 0.976 0.020
#> GSM531609 1 0.7438 -0.1501 0.568 0.392 0.040
#> GSM531611 1 0.7276 -0.1700 0.564 0.404 0.032
#> GSM531621 3 0.0592 0.7413 0.000 0.012 0.988
#> GSM531622 3 0.0747 0.7406 0.000 0.016 0.984
#> GSM531628 1 0.6308 -0.1947 0.508 0.000 0.492
#> GSM531630 3 0.0747 0.7406 0.000 0.016 0.984
#> GSM531633 3 0.0592 0.7413 0.000 0.012 0.988
#> GSM531635 3 0.5810 0.4555 0.336 0.000 0.664
#> GSM531640 3 0.0747 0.7406 0.000 0.016 0.984
#> GSM531649 3 0.6215 0.3040 0.428 0.000 0.572
#> GSM531653 1 0.6309 -0.2027 0.504 0.000 0.496
#> GSM531657 2 0.7583 0.2551 0.468 0.492 0.040
#> GSM531665 3 0.9716 0.1647 0.344 0.228 0.428
#> GSM531670 3 0.6244 0.2772 0.440 0.000 0.560
#> GSM531674 1 0.6516 -0.1819 0.516 0.004 0.480
#> GSM531675 2 0.0237 0.6912 0.004 0.996 0.000
#> GSM531677 2 0.0237 0.6928 0.004 0.996 0.000
#> GSM531678 2 0.0592 0.6960 0.000 0.988 0.012
#> GSM531680 2 0.6566 0.3767 0.348 0.636 0.016
#> GSM531689 2 0.1315 0.6943 0.008 0.972 0.020
#> GSM531691 2 0.2680 0.6731 0.008 0.924 0.068
#> GSM531692 2 0.8650 0.3671 0.144 0.580 0.276
#> GSM531694 2 0.1129 0.6965 0.004 0.976 0.020
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM531602 2 0.1151 0.915 0.008 0.968 0.000 0.024
#> GSM531604 2 0.1247 0.914 0.012 0.968 0.016 0.004
#> GSM531606 2 0.1377 0.916 0.008 0.964 0.008 0.020
#> GSM531607 2 0.1151 0.915 0.008 0.968 0.000 0.024
#> GSM531608 3 0.0188 0.983 0.004 0.000 0.996 0.000
#> GSM531610 4 0.0376 0.881 0.000 0.004 0.004 0.992
#> GSM531612 4 0.0712 0.882 0.008 0.004 0.004 0.984
#> GSM531613 4 0.0188 0.880 0.000 0.004 0.000 0.996
#> GSM531614 4 0.0712 0.882 0.008 0.004 0.004 0.984
#> GSM531616 3 0.0804 0.980 0.012 0.008 0.980 0.000
#> GSM531618 4 0.6589 0.473 0.100 0.004 0.288 0.608
#> GSM531619 3 0.0188 0.983 0.004 0.000 0.996 0.000
#> GSM531620 3 0.0336 0.983 0.008 0.000 0.992 0.000
#> GSM531623 3 0.0188 0.983 0.004 0.000 0.996 0.000
#> GSM531625 3 0.0657 0.981 0.012 0.004 0.984 0.000
#> GSM531626 3 0.0657 0.981 0.012 0.004 0.984 0.000
#> GSM531632 1 0.1004 0.926 0.972 0.004 0.024 0.000
#> GSM531638 3 0.0804 0.980 0.012 0.008 0.980 0.000
#> GSM531639 1 0.5126 0.307 0.552 0.004 0.444 0.000
#> GSM531641 4 0.0712 0.882 0.008 0.004 0.004 0.984
#> GSM531642 1 0.4444 0.753 0.764 0.008 0.220 0.008
#> GSM531643 1 0.0895 0.926 0.976 0.004 0.020 0.000
#> GSM531644 1 0.1114 0.924 0.972 0.004 0.016 0.008
#> GSM531645 4 0.0712 0.882 0.008 0.004 0.004 0.984
#> GSM531646 1 0.1109 0.926 0.968 0.004 0.028 0.000
#> GSM531647 1 0.0707 0.926 0.980 0.000 0.020 0.000
#> GSM531648 4 0.2742 0.834 0.008 0.008 0.084 0.900
#> GSM531650 1 0.0707 0.926 0.980 0.000 0.020 0.000
#> GSM531651 3 0.0188 0.983 0.004 0.000 0.996 0.000
#> GSM531652 1 0.2778 0.887 0.900 0.004 0.080 0.016
#> GSM531656 1 0.4049 0.769 0.780 0.008 0.212 0.000
#> GSM531659 4 0.5467 0.425 0.008 0.400 0.008 0.584
#> GSM531661 3 0.0336 0.974 0.000 0.008 0.992 0.000
#> GSM531662 3 0.0804 0.964 0.008 0.012 0.980 0.000
#> GSM531663 4 0.0376 0.881 0.000 0.004 0.004 0.992
#> GSM531664 1 0.0657 0.922 0.984 0.004 0.012 0.000
#> GSM531666 1 0.1994 0.906 0.936 0.004 0.052 0.008
#> GSM531667 3 0.0564 0.980 0.004 0.004 0.988 0.004
#> GSM531668 4 0.4303 0.738 0.008 0.220 0.004 0.768
#> GSM531669 1 0.0937 0.921 0.976 0.012 0.012 0.000
#> GSM531671 3 0.3300 0.811 0.144 0.008 0.848 0.000
#> GSM531672 4 0.2216 0.853 0.000 0.092 0.000 0.908
#> GSM531673 2 0.4086 0.717 0.008 0.776 0.216 0.000
#> GSM531676 2 0.2125 0.888 0.076 0.920 0.004 0.000
#> GSM531679 2 0.1042 0.916 0.008 0.972 0.000 0.020
#> GSM531681 4 0.3400 0.777 0.000 0.180 0.000 0.820
#> GSM531682 2 0.1151 0.916 0.008 0.968 0.000 0.024
#> GSM531683 2 0.1151 0.915 0.008 0.968 0.000 0.024
#> GSM531684 2 0.1509 0.913 0.012 0.960 0.020 0.008
#> GSM531685 2 0.2773 0.854 0.116 0.880 0.004 0.000
#> GSM531686 4 0.3400 0.777 0.000 0.180 0.000 0.820
#> GSM531687 2 0.1824 0.896 0.060 0.936 0.004 0.000
#> GSM531688 1 0.0895 0.909 0.976 0.020 0.004 0.000
#> GSM531690 4 0.4250 0.691 0.000 0.276 0.000 0.724
#> GSM531693 1 0.0927 0.912 0.976 0.016 0.008 0.000
#> GSM531695 2 0.5000 0.120 0.496 0.504 0.000 0.000
#> GSM531603 2 0.1151 0.915 0.008 0.968 0.000 0.024
#> GSM531609 4 0.0712 0.882 0.008 0.004 0.004 0.984
#> GSM531611 4 0.0712 0.882 0.008 0.004 0.004 0.984
#> GSM531621 3 0.0336 0.983 0.008 0.000 0.992 0.000
#> GSM531622 3 0.0336 0.983 0.008 0.000 0.992 0.000
#> GSM531628 1 0.0707 0.926 0.980 0.000 0.020 0.000
#> GSM531630 3 0.0336 0.983 0.008 0.000 0.992 0.000
#> GSM531633 3 0.0336 0.983 0.008 0.000 0.992 0.000
#> GSM531635 1 0.1722 0.917 0.944 0.008 0.048 0.000
#> GSM531640 3 0.0524 0.982 0.008 0.004 0.988 0.000
#> GSM531649 1 0.1109 0.926 0.968 0.004 0.028 0.000
#> GSM531653 1 0.0707 0.926 0.980 0.000 0.020 0.000
#> GSM531657 4 0.2345 0.849 0.000 0.100 0.000 0.900
#> GSM531665 2 0.5608 0.716 0.120 0.736 0.140 0.004
#> GSM531670 1 0.4049 0.769 0.780 0.008 0.212 0.000
#> GSM531674 1 0.0937 0.921 0.976 0.012 0.012 0.000
#> GSM531675 2 0.1151 0.916 0.008 0.968 0.000 0.024
#> GSM531677 2 0.1151 0.916 0.008 0.968 0.000 0.024
#> GSM531678 2 0.1082 0.917 0.004 0.972 0.004 0.020
#> GSM531680 2 0.2149 0.881 0.088 0.912 0.000 0.000
#> GSM531689 2 0.0992 0.915 0.012 0.976 0.004 0.008
#> GSM531691 2 0.1124 0.914 0.012 0.972 0.012 0.004
#> GSM531692 2 0.2271 0.890 0.076 0.916 0.008 0.000
#> GSM531694 2 0.1151 0.915 0.008 0.968 0.000 0.024
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM531602 2 0.0000 0.63281 0.000 1.000 0.000 0.000 0.000
#> GSM531604 2 0.4201 -0.11590 0.000 0.592 0.000 0.000 0.408
#> GSM531606 2 0.2605 0.52022 0.000 0.852 0.000 0.000 0.148
#> GSM531607 2 0.0000 0.63281 0.000 1.000 0.000 0.000 0.000
#> GSM531608 3 0.0880 0.91384 0.000 0.000 0.968 0.000 0.032
#> GSM531610 4 0.0162 0.82279 0.000 0.004 0.000 0.996 0.000
#> GSM531612 4 0.0162 0.82279 0.000 0.004 0.000 0.996 0.000
#> GSM531613 4 0.0162 0.82279 0.000 0.004 0.000 0.996 0.000
#> GSM531614 4 0.0162 0.82279 0.000 0.004 0.000 0.996 0.000
#> GSM531616 3 0.1124 0.91577 0.000 0.000 0.960 0.004 0.036
#> GSM531618 5 0.9235 -0.21049 0.168 0.052 0.216 0.224 0.340
#> GSM531619 3 0.0000 0.92535 0.000 0.000 1.000 0.000 0.000
#> GSM531620 3 0.0671 0.92200 0.000 0.000 0.980 0.004 0.016
#> GSM531623 3 0.0000 0.92535 0.000 0.000 1.000 0.000 0.000
#> GSM531625 3 0.0865 0.91960 0.000 0.000 0.972 0.004 0.024
#> GSM531626 3 0.1124 0.91577 0.000 0.000 0.960 0.004 0.036
#> GSM531632 1 0.1043 0.81224 0.960 0.000 0.000 0.000 0.040
#> GSM531638 3 0.1124 0.91577 0.000 0.000 0.960 0.004 0.036
#> GSM531639 3 0.6330 -0.12721 0.416 0.000 0.444 0.004 0.136
#> GSM531641 4 0.0162 0.82279 0.000 0.004 0.000 0.996 0.000
#> GSM531642 1 0.6135 0.56124 0.532 0.000 0.128 0.004 0.336
#> GSM531643 1 0.2230 0.79434 0.884 0.000 0.000 0.000 0.116
#> GSM531644 1 0.3837 0.69047 0.692 0.000 0.000 0.000 0.308
#> GSM531645 4 0.0162 0.82279 0.000 0.004 0.000 0.996 0.000
#> GSM531646 1 0.0794 0.81711 0.972 0.000 0.000 0.000 0.028
#> GSM531647 1 0.0290 0.81870 0.992 0.000 0.000 0.000 0.008
#> GSM531648 4 0.7395 0.41834 0.060 0.116 0.012 0.480 0.332
#> GSM531650 1 0.0609 0.81943 0.980 0.000 0.000 0.000 0.020
#> GSM531651 3 0.0000 0.92535 0.000 0.000 1.000 0.000 0.000
#> GSM531652 1 0.4333 0.67654 0.672 0.004 0.004 0.004 0.316
#> GSM531656 1 0.5159 0.67113 0.688 0.000 0.188 0.000 0.124
#> GSM531659 5 0.6551 -0.15372 0.000 0.304 0.000 0.228 0.468
#> GSM531661 3 0.0880 0.91384 0.000 0.000 0.968 0.000 0.032
#> GSM531662 3 0.2536 0.83717 0.000 0.004 0.868 0.000 0.128
#> GSM531663 4 0.0162 0.82279 0.000 0.004 0.000 0.996 0.000
#> GSM531664 1 0.0609 0.81943 0.980 0.000 0.000 0.000 0.020
#> GSM531666 1 0.4500 0.66952 0.664 0.016 0.004 0.000 0.316
#> GSM531667 3 0.1792 0.87567 0.000 0.000 0.916 0.000 0.084
#> GSM531668 2 0.6477 -0.00151 0.000 0.464 0.000 0.196 0.340
#> GSM531669 1 0.0510 0.81747 0.984 0.000 0.000 0.000 0.016
#> GSM531671 3 0.5658 0.61854 0.120 0.004 0.652 0.004 0.220
#> GSM531672 4 0.6690 0.31200 0.000 0.300 0.000 0.432 0.268
#> GSM531673 5 0.6310 0.29956 0.000 0.328 0.152 0.004 0.516
#> GSM531676 5 0.4494 0.46223 0.012 0.380 0.000 0.000 0.608
#> GSM531679 2 0.3074 0.51371 0.000 0.804 0.000 0.000 0.196
#> GSM531681 4 0.4455 0.56640 0.000 0.260 0.000 0.704 0.036
#> GSM531682 2 0.3395 0.47745 0.000 0.764 0.000 0.000 0.236
#> GSM531683 2 0.0404 0.62962 0.000 0.988 0.000 0.000 0.012
#> GSM531684 2 0.4009 0.20675 0.000 0.684 0.004 0.000 0.312
#> GSM531685 5 0.5405 0.44911 0.072 0.304 0.000 0.004 0.620
#> GSM531686 4 0.4455 0.56640 0.000 0.260 0.000 0.704 0.036
#> GSM531687 5 0.4533 0.39200 0.008 0.448 0.000 0.000 0.544
#> GSM531688 1 0.3561 0.59528 0.740 0.000 0.000 0.000 0.260
#> GSM531690 2 0.5964 0.26981 0.000 0.588 0.000 0.232 0.180
#> GSM531693 1 0.3242 0.67404 0.784 0.000 0.000 0.000 0.216
#> GSM531695 1 0.6740 -0.15470 0.412 0.284 0.000 0.000 0.304
#> GSM531603 2 0.1121 0.60156 0.000 0.956 0.000 0.000 0.044
#> GSM531609 4 0.0162 0.82279 0.000 0.004 0.000 0.996 0.000
#> GSM531611 4 0.0162 0.82279 0.000 0.004 0.000 0.996 0.000
#> GSM531621 3 0.0000 0.92535 0.000 0.000 1.000 0.000 0.000
#> GSM531622 3 0.0000 0.92535 0.000 0.000 1.000 0.000 0.000
#> GSM531628 1 0.0609 0.81943 0.980 0.000 0.000 0.000 0.020
#> GSM531630 3 0.0000 0.92535 0.000 0.000 1.000 0.000 0.000
#> GSM531633 3 0.0000 0.92535 0.000 0.000 1.000 0.000 0.000
#> GSM531635 1 0.3425 0.76584 0.840 0.000 0.112 0.004 0.044
#> GSM531640 3 0.0000 0.92535 0.000 0.000 1.000 0.000 0.000
#> GSM531649 1 0.1205 0.81483 0.956 0.000 0.000 0.004 0.040
#> GSM531653 1 0.0510 0.81911 0.984 0.000 0.000 0.000 0.016
#> GSM531657 4 0.6742 0.29517 0.000 0.288 0.000 0.412 0.300
#> GSM531665 5 0.4711 0.36653 0.020 0.188 0.048 0.000 0.744
#> GSM531670 1 0.5159 0.67113 0.688 0.000 0.188 0.000 0.124
#> GSM531674 1 0.0162 0.81885 0.996 0.000 0.000 0.000 0.004
#> GSM531675 2 0.2424 0.58361 0.000 0.868 0.000 0.000 0.132
#> GSM531677 2 0.2516 0.57634 0.000 0.860 0.000 0.000 0.140
#> GSM531678 2 0.4074 0.12019 0.000 0.636 0.000 0.000 0.364
#> GSM531680 5 0.4658 0.31896 0.012 0.484 0.000 0.000 0.504
#> GSM531689 5 0.4273 0.39634 0.000 0.448 0.000 0.000 0.552
#> GSM531691 5 0.4227 0.42290 0.000 0.420 0.000 0.000 0.580
#> GSM531692 5 0.4517 0.46344 0.008 0.372 0.000 0.004 0.616
#> GSM531694 2 0.0000 0.63281 0.000 1.000 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
#> GSM531602 2 0.1007 0.7356 0.000 0.956 0.000 0.000 0.044 0.000
#> GSM531604 5 0.4473 0.5945 0.000 0.252 0.000 0.000 0.676 0.072
#> GSM531606 2 0.4044 0.3804 0.000 0.704 0.000 0.000 0.256 0.040
#> GSM531607 2 0.1152 0.7341 0.000 0.952 0.000 0.000 0.044 0.004
#> GSM531608 3 0.1625 0.8787 0.000 0.000 0.928 0.000 0.012 0.060
#> GSM531610 4 0.0146 0.8856 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM531612 4 0.0000 0.8865 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531613 4 0.0436 0.8830 0.000 0.004 0.000 0.988 0.004 0.004
#> GSM531614 4 0.0000 0.8865 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531616 3 0.2164 0.8742 0.000 0.012 0.908 0.000 0.020 0.060
#> GSM531618 6 0.5701 0.6264 0.116 0.032 0.060 0.104 0.000 0.688
#> GSM531619 3 0.0837 0.8982 0.000 0.004 0.972 0.000 0.004 0.020
#> GSM531620 3 0.1718 0.8858 0.000 0.008 0.932 0.000 0.016 0.044
#> GSM531623 3 0.0547 0.8994 0.000 0.000 0.980 0.000 0.000 0.020
#> GSM531625 3 0.1838 0.8842 0.000 0.012 0.928 0.000 0.020 0.040
#> GSM531626 3 0.1974 0.8803 0.000 0.012 0.920 0.000 0.020 0.048
#> GSM531632 1 0.1088 0.7693 0.960 0.000 0.000 0.000 0.016 0.024
#> GSM531638 3 0.2164 0.8742 0.000 0.012 0.908 0.000 0.020 0.060
#> GSM531639 6 0.6603 0.1912 0.240 0.008 0.364 0.000 0.016 0.372
#> GSM531641 4 0.0000 0.8865 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531642 6 0.3997 0.5366 0.288 0.000 0.004 0.020 0.000 0.688
#> GSM531643 1 0.3437 0.5536 0.752 0.004 0.000 0.000 0.008 0.236
#> GSM531644 6 0.3717 0.4325 0.384 0.000 0.000 0.000 0.000 0.616
#> GSM531645 4 0.0000 0.8865 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531646 1 0.1230 0.7672 0.956 0.008 0.000 0.000 0.008 0.028
#> GSM531647 1 0.0000 0.7740 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM531648 6 0.4822 0.5776 0.056 0.032 0.000 0.224 0.000 0.688
#> GSM531650 1 0.1010 0.7665 0.960 0.000 0.000 0.000 0.004 0.036
#> GSM531651 3 0.0547 0.8994 0.000 0.000 0.980 0.000 0.000 0.020
#> GSM531652 6 0.4092 0.4999 0.344 0.000 0.000 0.020 0.000 0.636
#> GSM531656 1 0.6118 0.3060 0.552 0.008 0.156 0.000 0.024 0.260
#> GSM531659 6 0.4220 0.5014 0.000 0.104 0.000 0.072 0.044 0.780
#> GSM531661 3 0.2581 0.8337 0.000 0.000 0.856 0.000 0.016 0.128
#> GSM531662 3 0.4709 0.6310 0.000 0.000 0.680 0.000 0.188 0.132
#> GSM531663 4 0.0405 0.8830 0.000 0.000 0.000 0.988 0.004 0.008
#> GSM531664 1 0.1367 0.7675 0.944 0.000 0.000 0.000 0.012 0.044
#> GSM531666 6 0.3986 0.4906 0.340 0.004 0.000 0.004 0.004 0.648
#> GSM531667 3 0.2631 0.8066 0.000 0.000 0.840 0.000 0.008 0.152
#> GSM531668 6 0.5412 0.2714 0.000 0.416 0.000 0.060 0.024 0.500
#> GSM531669 1 0.1341 0.7688 0.948 0.000 0.000 0.000 0.024 0.028
#> GSM531671 3 0.7332 0.3248 0.120 0.008 0.440 0.000 0.240 0.192
#> GSM531672 6 0.5746 0.2687 0.000 0.276 0.000 0.160 0.012 0.552
#> GSM531673 5 0.4976 0.6125 0.000 0.048 0.096 0.000 0.712 0.144
#> GSM531676 5 0.2563 0.7269 0.008 0.068 0.000 0.000 0.884 0.040
#> GSM531679 2 0.4954 0.6040 0.000 0.640 0.000 0.000 0.232 0.128
#> GSM531681 4 0.5931 0.2420 0.000 0.324 0.000 0.524 0.028 0.124
#> GSM531682 2 0.5466 0.5258 0.000 0.556 0.000 0.000 0.280 0.164
#> GSM531683 2 0.2221 0.7418 0.000 0.896 0.000 0.000 0.032 0.072
#> GSM531684 5 0.5087 0.4256 0.000 0.348 0.000 0.000 0.560 0.092
#> GSM531685 5 0.2001 0.7147 0.044 0.016 0.000 0.000 0.920 0.020
#> GSM531686 4 0.5931 0.2420 0.000 0.324 0.000 0.524 0.028 0.124
#> GSM531687 5 0.3675 0.6734 0.004 0.124 0.000 0.000 0.796 0.076
#> GSM531688 1 0.4022 0.5778 0.708 0.000 0.000 0.000 0.252 0.040
#> GSM531690 2 0.4677 0.6157 0.000 0.652 0.000 0.032 0.024 0.292
#> GSM531693 1 0.3301 0.6401 0.788 0.000 0.000 0.000 0.188 0.024
#> GSM531695 1 0.7035 -0.0981 0.364 0.192 0.000 0.000 0.360 0.084
#> GSM531603 2 0.1572 0.7241 0.000 0.936 0.000 0.000 0.036 0.028
#> GSM531609 4 0.0000 0.8865 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531611 4 0.0146 0.8858 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM531621 3 0.0000 0.9012 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531622 3 0.0146 0.9012 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM531628 1 0.0692 0.7720 0.976 0.000 0.000 0.000 0.004 0.020
#> GSM531630 3 0.0146 0.9012 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM531633 3 0.0000 0.9012 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531635 1 0.4857 0.5538 0.712 0.012 0.188 0.000 0.020 0.068
#> GSM531640 3 0.0551 0.9001 0.000 0.004 0.984 0.000 0.004 0.008
#> GSM531649 1 0.2512 0.7380 0.900 0.012 0.020 0.000 0.020 0.048
#> GSM531653 1 0.0000 0.7740 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM531657 6 0.5171 0.4159 0.000 0.196 0.000 0.140 0.012 0.652
#> GSM531665 5 0.4009 0.5718 0.012 0.008 0.000 0.000 0.676 0.304
#> GSM531670 1 0.6118 0.3060 0.552 0.008 0.156 0.000 0.024 0.260
#> GSM531674 1 0.1003 0.7733 0.964 0.000 0.000 0.000 0.016 0.020
#> GSM531675 2 0.4549 0.6769 0.000 0.680 0.000 0.000 0.088 0.232
#> GSM531677 2 0.4792 0.6686 0.000 0.672 0.000 0.000 0.148 0.180
#> GSM531678 5 0.4808 0.3024 0.000 0.360 0.000 0.000 0.576 0.064
#> GSM531680 5 0.4516 0.5837 0.012 0.184 0.000 0.000 0.720 0.084
#> GSM531689 5 0.2858 0.7043 0.000 0.124 0.000 0.000 0.844 0.032
#> GSM531691 5 0.1838 0.7346 0.000 0.068 0.000 0.000 0.916 0.016
#> GSM531692 5 0.2375 0.7197 0.008 0.036 0.000 0.000 0.896 0.060
#> GSM531694 2 0.1007 0.7356 0.000 0.956 0.000 0.000 0.044 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)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> CV:kmeans 79 1.000 2
#> CV:kmeans 33 0.447 3
#> CV:kmeans 76 0.345 4
#> CV:kmeans 58 0.642 5
#> CV:kmeans 64 0.531 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "skmeans"]
# you can also extract it by
# res = res_list["CV:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 80 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.828 0.896 0.956 0.5059 0.494 0.494
#> 3 3 0.629 0.827 0.848 0.3217 0.710 0.481
#> 4 4 0.941 0.924 0.967 0.1333 0.816 0.515
#> 5 5 0.799 0.745 0.845 0.0543 0.950 0.799
#> 6 6 0.762 0.691 0.845 0.0395 0.936 0.707
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM531602 2 0.0000 0.938 0.000 1.000
#> GSM531604 2 0.0000 0.938 0.000 1.000
#> GSM531606 2 0.0000 0.938 0.000 1.000
#> GSM531607 2 0.0000 0.938 0.000 1.000
#> GSM531608 1 0.7139 0.747 0.804 0.196
#> GSM531610 2 0.0000 0.938 0.000 1.000
#> GSM531612 2 0.0000 0.938 0.000 1.000
#> GSM531613 2 0.0000 0.938 0.000 1.000
#> GSM531614 2 0.0000 0.938 0.000 1.000
#> GSM531616 1 0.0000 0.966 1.000 0.000
#> GSM531618 1 0.9522 0.423 0.628 0.372
#> GSM531619 1 0.0672 0.960 0.992 0.008
#> GSM531620 1 0.0000 0.966 1.000 0.000
#> GSM531623 1 0.0000 0.966 1.000 0.000
#> GSM531625 1 0.0000 0.966 1.000 0.000
#> GSM531626 1 0.0000 0.966 1.000 0.000
#> GSM531632 1 0.0000 0.966 1.000 0.000
#> GSM531638 1 0.0000 0.966 1.000 0.000
#> GSM531639 1 0.0000 0.966 1.000 0.000
#> GSM531641 2 0.0000 0.938 0.000 1.000
#> GSM531642 1 0.0000 0.966 1.000 0.000
#> GSM531643 1 0.0000 0.966 1.000 0.000
#> GSM531644 1 0.0000 0.966 1.000 0.000
#> GSM531645 2 0.0000 0.938 0.000 1.000
#> GSM531646 1 0.0000 0.966 1.000 0.000
#> GSM531647 1 0.0000 0.966 1.000 0.000
#> GSM531648 1 0.9686 0.365 0.604 0.396
#> GSM531650 1 0.0000 0.966 1.000 0.000
#> GSM531651 1 0.0000 0.966 1.000 0.000
#> GSM531652 1 0.0000 0.966 1.000 0.000
#> GSM531656 1 0.0000 0.966 1.000 0.000
#> GSM531659 2 0.0000 0.938 0.000 1.000
#> GSM531661 1 0.0672 0.960 0.992 0.008
#> GSM531662 1 0.0000 0.966 1.000 0.000
#> GSM531663 2 0.0000 0.938 0.000 1.000
#> GSM531664 1 0.0000 0.966 1.000 0.000
#> GSM531666 1 0.5946 0.811 0.856 0.144
#> GSM531667 1 0.2778 0.925 0.952 0.048
#> GSM531668 2 0.0000 0.938 0.000 1.000
#> GSM531669 1 0.0000 0.966 1.000 0.000
#> GSM531671 1 0.0000 0.966 1.000 0.000
#> GSM531672 2 0.0000 0.938 0.000 1.000
#> GSM531673 2 0.9393 0.507 0.356 0.644
#> GSM531676 2 0.7139 0.750 0.196 0.804
#> GSM531679 2 0.0000 0.938 0.000 1.000
#> GSM531681 2 0.0000 0.938 0.000 1.000
#> GSM531682 2 0.0000 0.938 0.000 1.000
#> GSM531683 2 0.0000 0.938 0.000 1.000
#> GSM531684 2 0.0000 0.938 0.000 1.000
#> GSM531685 2 0.9686 0.426 0.396 0.604
#> GSM531686 2 0.0000 0.938 0.000 1.000
#> GSM531687 2 0.2778 0.904 0.048 0.952
#> GSM531688 2 0.9686 0.426 0.396 0.604
#> GSM531690 2 0.0000 0.938 0.000 1.000
#> GSM531693 1 0.0000 0.966 1.000 0.000
#> GSM531695 2 0.2778 0.904 0.048 0.952
#> GSM531603 2 0.0000 0.938 0.000 1.000
#> GSM531609 2 0.0000 0.938 0.000 1.000
#> GSM531611 2 0.0000 0.938 0.000 1.000
#> GSM531621 1 0.0000 0.966 1.000 0.000
#> GSM531622 1 0.0000 0.966 1.000 0.000
#> GSM531628 1 0.0000 0.966 1.000 0.000
#> GSM531630 1 0.0000 0.966 1.000 0.000
#> GSM531633 1 0.0000 0.966 1.000 0.000
#> GSM531635 1 0.0000 0.966 1.000 0.000
#> GSM531640 1 0.2778 0.925 0.952 0.048
#> GSM531649 1 0.0000 0.966 1.000 0.000
#> GSM531653 1 0.0000 0.966 1.000 0.000
#> GSM531657 2 0.0000 0.938 0.000 1.000
#> GSM531665 2 0.9795 0.377 0.416 0.584
#> GSM531670 1 0.0000 0.966 1.000 0.000
#> GSM531674 1 0.0000 0.966 1.000 0.000
#> GSM531675 2 0.0000 0.938 0.000 1.000
#> GSM531677 2 0.0000 0.938 0.000 1.000
#> GSM531678 2 0.0000 0.938 0.000 1.000
#> GSM531680 2 0.2778 0.904 0.048 0.952
#> GSM531689 2 0.0000 0.938 0.000 1.000
#> GSM531691 2 0.0376 0.935 0.004 0.996
#> GSM531692 2 0.9686 0.426 0.396 0.604
#> GSM531694 2 0.0000 0.938 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM531602 2 0.000 0.8966 0.000 1.000 0.000
#> GSM531604 2 0.429 0.7204 0.000 0.820 0.180
#> GSM531606 2 0.000 0.8966 0.000 1.000 0.000
#> GSM531607 2 0.000 0.8966 0.000 1.000 0.000
#> GSM531608 3 0.394 0.9203 0.156 0.000 0.844
#> GSM531610 2 0.394 0.8850 0.000 0.844 0.156
#> GSM531612 2 0.394 0.8850 0.000 0.844 0.156
#> GSM531613 2 0.394 0.8850 0.000 0.844 0.156
#> GSM531614 2 0.394 0.8850 0.000 0.844 0.156
#> GSM531616 3 0.406 0.9134 0.164 0.000 0.836
#> GSM531618 3 0.497 0.4137 0.000 0.236 0.764
#> GSM531619 3 0.394 0.9203 0.156 0.000 0.844
#> GSM531620 3 0.394 0.9203 0.156 0.000 0.844
#> GSM531623 3 0.394 0.9203 0.156 0.000 0.844
#> GSM531625 3 0.394 0.9203 0.156 0.000 0.844
#> GSM531626 3 0.394 0.9203 0.156 0.000 0.844
#> GSM531632 1 0.000 0.8531 1.000 0.000 0.000
#> GSM531638 3 0.394 0.9203 0.156 0.000 0.844
#> GSM531639 3 0.568 0.7197 0.316 0.000 0.684
#> GSM531641 2 0.394 0.8850 0.000 0.844 0.156
#> GSM531642 1 0.629 0.4473 0.536 0.000 0.464
#> GSM531643 1 0.000 0.8531 1.000 0.000 0.000
#> GSM531644 1 0.394 0.7930 0.844 0.000 0.156
#> GSM531645 2 0.394 0.8850 0.000 0.844 0.156
#> GSM531646 1 0.000 0.8531 1.000 0.000 0.000
#> GSM531647 1 0.000 0.8531 1.000 0.000 0.000
#> GSM531648 2 0.533 0.8065 0.004 0.748 0.248
#> GSM531650 1 0.000 0.8531 1.000 0.000 0.000
#> GSM531651 3 0.394 0.9203 0.156 0.000 0.844
#> GSM531652 1 0.510 0.7489 0.752 0.000 0.248
#> GSM531656 1 0.429 0.6580 0.820 0.000 0.180
#> GSM531659 2 0.394 0.8850 0.000 0.844 0.156
#> GSM531661 3 0.394 0.9203 0.156 0.000 0.844
#> GSM531662 3 0.394 0.9203 0.156 0.000 0.844
#> GSM531663 2 0.394 0.8850 0.000 0.844 0.156
#> GSM531664 1 0.394 0.7930 0.844 0.000 0.156
#> GSM531666 1 0.394 0.7930 0.844 0.000 0.156
#> GSM531667 3 0.394 0.9203 0.156 0.000 0.844
#> GSM531668 2 0.394 0.8850 0.000 0.844 0.156
#> GSM531669 1 0.000 0.8531 1.000 0.000 0.000
#> GSM531671 3 0.590 0.6702 0.352 0.000 0.648
#> GSM531672 2 0.394 0.8850 0.000 0.844 0.156
#> GSM531673 3 0.394 0.7436 0.000 0.156 0.844
#> GSM531676 1 0.400 0.8032 0.840 0.160 0.000
#> GSM531679 2 0.000 0.8966 0.000 1.000 0.000
#> GSM531681 2 0.000 0.8966 0.000 1.000 0.000
#> GSM531682 2 0.000 0.8966 0.000 1.000 0.000
#> GSM531683 2 0.000 0.8966 0.000 1.000 0.000
#> GSM531684 2 0.631 -0.0476 0.000 0.512 0.488
#> GSM531685 1 0.394 0.8050 0.844 0.156 0.000
#> GSM531686 2 0.000 0.8966 0.000 1.000 0.000
#> GSM531687 1 0.400 0.8032 0.840 0.160 0.000
#> GSM531688 1 0.394 0.8050 0.844 0.156 0.000
#> GSM531690 2 0.129 0.8963 0.000 0.968 0.032
#> GSM531693 1 0.000 0.8531 1.000 0.000 0.000
#> GSM531695 1 0.394 0.8050 0.844 0.156 0.000
#> GSM531603 2 0.000 0.8966 0.000 1.000 0.000
#> GSM531609 2 0.394 0.8850 0.000 0.844 0.156
#> GSM531611 2 0.394 0.8850 0.000 0.844 0.156
#> GSM531621 3 0.394 0.9203 0.156 0.000 0.844
#> GSM531622 3 0.394 0.9203 0.156 0.000 0.844
#> GSM531628 1 0.000 0.8531 1.000 0.000 0.000
#> GSM531630 3 0.394 0.9203 0.156 0.000 0.844
#> GSM531633 3 0.394 0.9203 0.156 0.000 0.844
#> GSM531635 1 0.382 0.6995 0.852 0.000 0.148
#> GSM531640 3 0.394 0.9203 0.156 0.000 0.844
#> GSM531649 1 0.000 0.8531 1.000 0.000 0.000
#> GSM531653 1 0.000 0.8531 1.000 0.000 0.000
#> GSM531657 2 0.394 0.8850 0.000 0.844 0.156
#> GSM531665 1 0.797 0.6532 0.660 0.156 0.184
#> GSM531670 1 0.429 0.6580 0.820 0.000 0.180
#> GSM531674 1 0.000 0.8531 1.000 0.000 0.000
#> GSM531675 2 0.000 0.8966 0.000 1.000 0.000
#> GSM531677 2 0.000 0.8966 0.000 1.000 0.000
#> GSM531678 2 0.000 0.8966 0.000 1.000 0.000
#> GSM531680 1 0.406 0.8009 0.836 0.164 0.000
#> GSM531689 2 0.000 0.8966 0.000 1.000 0.000
#> GSM531691 2 0.254 0.8398 0.000 0.920 0.080
#> GSM531692 3 0.906 0.2274 0.324 0.156 0.520
#> GSM531694 2 0.000 0.8966 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM531602 2 0.0000 0.949 0.000 1.000 0.000 0.000
#> GSM531604 2 0.0000 0.949 0.000 1.000 0.000 0.000
#> GSM531606 2 0.0000 0.949 0.000 1.000 0.000 0.000
#> GSM531607 2 0.0000 0.949 0.000 1.000 0.000 0.000
#> GSM531608 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM531610 4 0.0000 0.990 0.000 0.000 0.000 1.000
#> GSM531612 4 0.0000 0.990 0.000 0.000 0.000 1.000
#> GSM531613 4 0.0000 0.990 0.000 0.000 0.000 1.000
#> GSM531614 4 0.0000 0.990 0.000 0.000 0.000 1.000
#> GSM531616 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM531618 4 0.0000 0.990 0.000 0.000 0.000 1.000
#> GSM531619 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM531620 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM531623 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM531625 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM531626 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM531632 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM531638 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM531639 3 0.4624 0.448 0.340 0.000 0.660 0.000
#> GSM531641 4 0.0000 0.990 0.000 0.000 0.000 1.000
#> GSM531642 1 0.4307 0.757 0.784 0.000 0.192 0.024
#> GSM531643 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM531644 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM531645 4 0.0000 0.990 0.000 0.000 0.000 1.000
#> GSM531646 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM531647 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM531648 4 0.0000 0.990 0.000 0.000 0.000 1.000
#> GSM531650 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM531651 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM531652 1 0.0921 0.934 0.972 0.000 0.000 0.028
#> GSM531656 1 0.3569 0.765 0.804 0.000 0.196 0.000
#> GSM531659 4 0.0000 0.990 0.000 0.000 0.000 1.000
#> GSM531661 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM531662 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM531663 4 0.0000 0.990 0.000 0.000 0.000 1.000
#> GSM531664 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM531666 1 0.0188 0.950 0.996 0.000 0.000 0.004
#> GSM531667 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM531668 4 0.0000 0.990 0.000 0.000 0.000 1.000
#> GSM531669 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM531671 3 0.3569 0.730 0.196 0.000 0.804 0.000
#> GSM531672 4 0.0000 0.990 0.000 0.000 0.000 1.000
#> GSM531673 2 0.4713 0.441 0.000 0.640 0.360 0.000
#> GSM531676 2 0.0000 0.949 0.000 1.000 0.000 0.000
#> GSM531679 2 0.0000 0.949 0.000 1.000 0.000 0.000
#> GSM531681 4 0.1474 0.950 0.000 0.052 0.000 0.948
#> GSM531682 2 0.0000 0.949 0.000 1.000 0.000 0.000
#> GSM531683 2 0.0000 0.949 0.000 1.000 0.000 0.000
#> GSM531684 2 0.0000 0.949 0.000 1.000 0.000 0.000
#> GSM531685 2 0.0188 0.946 0.004 0.996 0.000 0.000
#> GSM531686 4 0.1557 0.946 0.000 0.056 0.000 0.944
#> GSM531687 2 0.0000 0.949 0.000 1.000 0.000 0.000
#> GSM531688 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM531690 4 0.1389 0.954 0.000 0.048 0.000 0.952
#> GSM531693 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM531695 2 0.4916 0.306 0.424 0.576 0.000 0.000
#> GSM531603 2 0.0000 0.949 0.000 1.000 0.000 0.000
#> GSM531609 4 0.0000 0.990 0.000 0.000 0.000 1.000
#> GSM531611 4 0.0000 0.990 0.000 0.000 0.000 1.000
#> GSM531621 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM531622 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM531628 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM531630 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM531633 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM531635 1 0.3444 0.767 0.816 0.000 0.184 0.000
#> GSM531640 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM531649 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM531653 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM531657 4 0.0000 0.990 0.000 0.000 0.000 1.000
#> GSM531665 2 0.5742 0.571 0.276 0.664 0.060 0.000
#> GSM531670 1 0.3610 0.760 0.800 0.000 0.200 0.000
#> GSM531674 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM531675 2 0.0000 0.949 0.000 1.000 0.000 0.000
#> GSM531677 2 0.0000 0.949 0.000 1.000 0.000 0.000
#> GSM531678 2 0.0000 0.949 0.000 1.000 0.000 0.000
#> GSM531680 2 0.0188 0.946 0.004 0.996 0.000 0.000
#> GSM531689 2 0.0000 0.949 0.000 1.000 0.000 0.000
#> GSM531691 2 0.0000 0.949 0.000 1.000 0.000 0.000
#> GSM531692 2 0.0000 0.949 0.000 1.000 0.000 0.000
#> GSM531694 2 0.0000 0.949 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM531602 2 0.0000 0.8080 0.000 1.000 0.000 0.000 0.000
#> GSM531604 2 0.3074 0.5647 0.000 0.804 0.000 0.000 0.196
#> GSM531606 2 0.0880 0.7854 0.000 0.968 0.000 0.000 0.032
#> GSM531607 2 0.0000 0.8080 0.000 1.000 0.000 0.000 0.000
#> GSM531608 3 0.0000 0.9496 0.000 0.000 1.000 0.000 0.000
#> GSM531610 4 0.0000 0.8373 0.000 0.000 0.000 1.000 0.000
#> GSM531612 4 0.0000 0.8373 0.000 0.000 0.000 1.000 0.000
#> GSM531613 4 0.0000 0.8373 0.000 0.000 0.000 1.000 0.000
#> GSM531614 4 0.0000 0.8373 0.000 0.000 0.000 1.000 0.000
#> GSM531616 3 0.0162 0.9470 0.004 0.000 0.996 0.000 0.000
#> GSM531618 4 0.4150 0.6565 0.000 0.000 0.000 0.612 0.388
#> GSM531619 3 0.0000 0.9496 0.000 0.000 1.000 0.000 0.000
#> GSM531620 3 0.0000 0.9496 0.000 0.000 1.000 0.000 0.000
#> GSM531623 3 0.0000 0.9496 0.000 0.000 1.000 0.000 0.000
#> GSM531625 3 0.0000 0.9496 0.000 0.000 1.000 0.000 0.000
#> GSM531626 3 0.0000 0.9496 0.000 0.000 1.000 0.000 0.000
#> GSM531632 1 0.0290 0.8176 0.992 0.000 0.000 0.000 0.008
#> GSM531638 3 0.0000 0.9496 0.000 0.000 1.000 0.000 0.000
#> GSM531639 3 0.5974 0.2909 0.292 0.000 0.564 0.000 0.144
#> GSM531641 4 0.0000 0.8373 0.000 0.000 0.000 1.000 0.000
#> GSM531642 1 0.6437 0.5046 0.492 0.000 0.092 0.028 0.388
#> GSM531643 1 0.1608 0.8005 0.928 0.000 0.000 0.000 0.072
#> GSM531644 1 0.3932 0.6578 0.672 0.000 0.000 0.000 0.328
#> GSM531645 4 0.0000 0.8373 0.000 0.000 0.000 1.000 0.000
#> GSM531646 1 0.0000 0.8198 1.000 0.000 0.000 0.000 0.000
#> GSM531647 1 0.0000 0.8198 1.000 0.000 0.000 0.000 0.000
#> GSM531648 4 0.4150 0.6565 0.000 0.000 0.000 0.612 0.388
#> GSM531650 1 0.0000 0.8198 1.000 0.000 0.000 0.000 0.000
#> GSM531651 3 0.0000 0.9496 0.000 0.000 1.000 0.000 0.000
#> GSM531652 1 0.4930 0.5764 0.580 0.000 0.000 0.032 0.388
#> GSM531656 1 0.3621 0.6939 0.788 0.000 0.192 0.000 0.020
#> GSM531659 4 0.4163 0.7568 0.000 0.032 0.000 0.740 0.228
#> GSM531661 3 0.0693 0.9374 0.000 0.008 0.980 0.000 0.012
#> GSM531662 3 0.1894 0.8906 0.000 0.008 0.920 0.000 0.072
#> GSM531663 4 0.0000 0.8373 0.000 0.000 0.000 1.000 0.000
#> GSM531664 1 0.0000 0.8198 1.000 0.000 0.000 0.000 0.000
#> GSM531666 1 0.4150 0.6144 0.612 0.000 0.000 0.000 0.388
#> GSM531667 3 0.1270 0.9098 0.000 0.000 0.948 0.000 0.052
#> GSM531668 4 0.6433 0.4997 0.000 0.268 0.000 0.504 0.228
#> GSM531669 1 0.0703 0.8107 0.976 0.000 0.000 0.000 0.024
#> GSM531671 3 0.5141 0.6213 0.212 0.012 0.700 0.000 0.076
#> GSM531672 4 0.3343 0.7845 0.000 0.016 0.000 0.812 0.172
#> GSM531673 2 0.6410 0.0386 0.000 0.488 0.320 0.000 0.192
#> GSM531676 5 0.4425 0.7689 0.004 0.452 0.000 0.000 0.544
#> GSM531679 2 0.0510 0.8030 0.000 0.984 0.000 0.000 0.016
#> GSM531681 4 0.4161 0.3484 0.000 0.392 0.000 0.608 0.000
#> GSM531682 2 0.0510 0.8030 0.000 0.984 0.000 0.000 0.016
#> GSM531683 2 0.0000 0.8080 0.000 1.000 0.000 0.000 0.000
#> GSM531684 2 0.2813 0.6228 0.000 0.832 0.000 0.000 0.168
#> GSM531685 5 0.5306 0.7346 0.072 0.316 0.000 0.000 0.612
#> GSM531686 4 0.4161 0.3484 0.000 0.392 0.000 0.608 0.000
#> GSM531687 5 0.4437 0.7595 0.004 0.464 0.000 0.000 0.532
#> GSM531688 1 0.4219 0.2333 0.584 0.000 0.000 0.000 0.416
#> GSM531690 2 0.5111 0.0261 0.000 0.552 0.000 0.408 0.040
#> GSM531693 1 0.4210 0.2433 0.588 0.000 0.000 0.000 0.412
#> GSM531695 5 0.6722 0.4849 0.316 0.268 0.000 0.000 0.416
#> GSM531603 2 0.0000 0.8080 0.000 1.000 0.000 0.000 0.000
#> GSM531609 4 0.0000 0.8373 0.000 0.000 0.000 1.000 0.000
#> GSM531611 4 0.0000 0.8373 0.000 0.000 0.000 1.000 0.000
#> GSM531621 3 0.0000 0.9496 0.000 0.000 1.000 0.000 0.000
#> GSM531622 3 0.0000 0.9496 0.000 0.000 1.000 0.000 0.000
#> GSM531628 1 0.0000 0.8198 1.000 0.000 0.000 0.000 0.000
#> GSM531630 3 0.0000 0.9496 0.000 0.000 1.000 0.000 0.000
#> GSM531633 3 0.0000 0.9496 0.000 0.000 1.000 0.000 0.000
#> GSM531635 1 0.2471 0.7482 0.864 0.000 0.136 0.000 0.000
#> GSM531640 3 0.0000 0.9496 0.000 0.000 1.000 0.000 0.000
#> GSM531649 1 0.0000 0.8198 1.000 0.000 0.000 0.000 0.000
#> GSM531653 1 0.0000 0.8198 1.000 0.000 0.000 0.000 0.000
#> GSM531657 4 0.3789 0.7675 0.000 0.020 0.000 0.768 0.212
#> GSM531665 5 0.6232 0.6172 0.160 0.200 0.024 0.000 0.616
#> GSM531670 1 0.3621 0.6939 0.788 0.000 0.192 0.000 0.020
#> GSM531674 1 0.0609 0.8125 0.980 0.000 0.000 0.000 0.020
#> GSM531675 2 0.0510 0.8037 0.000 0.984 0.000 0.000 0.016
#> GSM531677 2 0.0510 0.8030 0.000 0.984 0.000 0.000 0.016
#> GSM531678 2 0.2230 0.6848 0.000 0.884 0.000 0.000 0.116
#> GSM531680 5 0.4811 0.7657 0.020 0.452 0.000 0.000 0.528
#> GSM531689 5 0.4304 0.7264 0.000 0.484 0.000 0.000 0.516
#> GSM531691 5 0.4268 0.7456 0.000 0.444 0.000 0.000 0.556
#> GSM531692 5 0.4288 0.7553 0.004 0.384 0.000 0.000 0.612
#> GSM531694 2 0.0000 0.8080 0.000 1.000 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
#> GSM531602 2 0.0632 7.58e-01 0.000 0.976 0.000 0.000 0.024 0.000
#> GSM531604 5 0.4978 1.33e-01 0.000 0.396 0.000 0.000 0.532 0.072
#> GSM531606 2 0.3025 6.38e-01 0.000 0.820 0.000 0.000 0.156 0.024
#> GSM531607 2 0.0632 7.58e-01 0.000 0.976 0.000 0.000 0.024 0.000
#> GSM531608 3 0.0891 8.96e-01 0.000 0.000 0.968 0.000 0.008 0.024
#> GSM531610 4 0.0000 8.64e-01 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531612 4 0.0000 8.64e-01 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531613 4 0.0000 8.64e-01 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531614 4 0.0000 8.64e-01 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531616 3 0.1155 8.91e-01 0.004 0.000 0.956 0.000 0.004 0.036
#> GSM531618 6 0.2668 6.84e-01 0.000 0.000 0.004 0.168 0.000 0.828
#> GSM531619 3 0.0291 9.04e-01 0.000 0.000 0.992 0.000 0.004 0.004
#> GSM531620 3 0.0146 9.05e-01 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM531623 3 0.0291 9.04e-01 0.000 0.000 0.992 0.000 0.004 0.004
#> GSM531625 3 0.0790 8.97e-01 0.000 0.000 0.968 0.000 0.000 0.032
#> GSM531626 3 0.0790 8.97e-01 0.000 0.000 0.968 0.000 0.000 0.032
#> GSM531632 1 0.0000 8.65e-01 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM531638 3 0.1010 8.93e-01 0.000 0.000 0.960 0.000 0.004 0.036
#> GSM531639 3 0.5387 3.53e-01 0.120 0.000 0.560 0.000 0.004 0.316
#> GSM531641 4 0.0000 8.64e-01 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531642 6 0.2613 7.24e-01 0.140 0.000 0.012 0.000 0.000 0.848
#> GSM531643 1 0.2442 7.59e-01 0.852 0.000 0.000 0.000 0.004 0.144
#> GSM531644 6 0.3288 5.89e-01 0.276 0.000 0.000 0.000 0.000 0.724
#> GSM531645 4 0.0000 8.64e-01 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531646 1 0.0508 8.63e-01 0.984 0.000 0.000 0.000 0.004 0.012
#> GSM531647 1 0.0000 8.65e-01 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM531648 6 0.2631 6.77e-01 0.000 0.000 0.000 0.180 0.000 0.820
#> GSM531650 1 0.0363 8.62e-01 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM531651 3 0.0291 9.04e-01 0.000 0.000 0.992 0.000 0.004 0.004
#> GSM531652 6 0.2527 7.24e-01 0.168 0.000 0.000 0.000 0.000 0.832
#> GSM531656 1 0.4627 6.37e-01 0.716 0.000 0.164 0.000 0.012 0.108
#> GSM531659 6 0.6092 3.13e-01 0.000 0.160 0.000 0.312 0.024 0.504
#> GSM531661 3 0.2277 8.46e-01 0.000 0.000 0.892 0.000 0.032 0.076
#> GSM531662 3 0.4794 5.93e-01 0.000 0.004 0.668 0.000 0.228 0.100
#> GSM531663 4 0.0000 8.64e-01 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531664 1 0.0603 8.63e-01 0.980 0.000 0.000 0.000 0.004 0.016
#> GSM531666 6 0.2491 7.24e-01 0.164 0.000 0.000 0.000 0.000 0.836
#> GSM531667 3 0.1970 8.43e-01 0.000 0.000 0.900 0.000 0.008 0.092
#> GSM531668 2 0.5471 2.97e-01 0.000 0.608 0.004 0.188 0.004 0.196
#> GSM531669 1 0.0508 8.62e-01 0.984 0.000 0.000 0.000 0.012 0.004
#> GSM531671 3 0.7189 2.57e-01 0.212 0.004 0.448 0.000 0.228 0.108
#> GSM531672 4 0.5865 -1.65e-01 0.000 0.200 0.000 0.440 0.000 0.360
#> GSM531673 5 0.6819 2.60e-01 0.000 0.224 0.168 0.000 0.500 0.108
#> GSM531676 5 0.2912 6.39e-01 0.000 0.216 0.000 0.000 0.784 0.000
#> GSM531679 2 0.2950 7.02e-01 0.000 0.828 0.000 0.000 0.148 0.024
#> GSM531681 4 0.3917 5.55e-01 0.000 0.284 0.000 0.692 0.000 0.024
#> GSM531682 2 0.3065 6.94e-01 0.000 0.820 0.000 0.000 0.152 0.028
#> GSM531683 2 0.0508 7.53e-01 0.000 0.984 0.000 0.000 0.004 0.012
#> GSM531684 2 0.5102 8.33e-06 0.000 0.492 0.000 0.000 0.428 0.080
#> GSM531685 5 0.0692 6.42e-01 0.004 0.020 0.000 0.000 0.976 0.000
#> GSM531686 4 0.3876 5.67e-01 0.000 0.276 0.000 0.700 0.000 0.024
#> GSM531687 5 0.3271 6.25e-01 0.000 0.232 0.000 0.000 0.760 0.008
#> GSM531688 1 0.3819 4.74e-01 0.652 0.000 0.000 0.000 0.340 0.008
#> GSM531690 2 0.4228 5.32e-01 0.000 0.716 0.000 0.212 0.000 0.072
#> GSM531693 1 0.3215 6.46e-01 0.756 0.000 0.000 0.000 0.240 0.004
#> GSM531695 5 0.6262 2.97e-01 0.288 0.292 0.000 0.000 0.412 0.008
#> GSM531603 2 0.0632 7.58e-01 0.000 0.976 0.000 0.000 0.024 0.000
#> GSM531609 4 0.0000 8.64e-01 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531611 4 0.0000 8.64e-01 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531621 3 0.0146 9.05e-01 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM531622 3 0.0000 9.05e-01 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531628 1 0.0000 8.65e-01 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM531630 3 0.0000 9.05e-01 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531633 3 0.0146 9.05e-01 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM531635 1 0.3839 6.56e-01 0.748 0.000 0.212 0.000 0.004 0.036
#> GSM531640 3 0.0146 9.05e-01 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM531649 1 0.1194 8.50e-01 0.956 0.000 0.008 0.000 0.004 0.032
#> GSM531653 1 0.0146 8.65e-01 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM531657 6 0.5656 1.45e-01 0.000 0.152 0.000 0.408 0.000 0.440
#> GSM531665 5 0.4236 5.62e-01 0.088 0.028 0.000 0.000 0.772 0.112
#> GSM531670 1 0.4692 6.26e-01 0.708 0.000 0.172 0.000 0.012 0.108
#> GSM531674 1 0.0508 8.62e-01 0.984 0.000 0.000 0.000 0.012 0.004
#> GSM531675 2 0.2451 7.25e-01 0.000 0.884 0.000 0.000 0.056 0.060
#> GSM531677 2 0.2383 7.21e-01 0.000 0.880 0.000 0.000 0.096 0.024
#> GSM531678 2 0.4199 2.79e-01 0.000 0.600 0.000 0.000 0.380 0.020
#> GSM531680 5 0.3831 5.85e-01 0.012 0.268 0.000 0.000 0.712 0.008
#> GSM531689 5 0.3076 6.24e-01 0.000 0.240 0.000 0.000 0.760 0.000
#> GSM531691 5 0.2664 6.50e-01 0.000 0.184 0.000 0.000 0.816 0.000
#> GSM531692 5 0.2088 6.18e-01 0.000 0.028 0.000 0.000 0.904 0.068
#> GSM531694 2 0.0632 7.58e-01 0.000 0.976 0.000 0.000 0.024 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> CV:skmeans 74 1.000 2
#> CV:skmeans 76 0.837 3
#> CV:skmeans 77 0.210 4
#> CV:skmeans 71 0.364 5
#> CV:skmeans 68 0.171 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "pam"]
# you can also extract it by
# res = res_list["CV:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 80 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 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.640 0.828 0.905 0.4751 0.519 0.519
#> 3 3 0.659 0.757 0.877 0.3697 0.811 0.636
#> 4 4 0.915 0.892 0.951 0.1148 0.760 0.428
#> 5 5 0.695 0.539 0.759 0.0886 0.877 0.590
#> 6 6 0.756 0.547 0.779 0.0591 0.863 0.463
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM531602 2 0.0000 0.976 0.000 1.000
#> GSM531604 2 0.0000 0.976 0.000 1.000
#> GSM531606 2 0.0000 0.976 0.000 1.000
#> GSM531607 2 0.0000 0.976 0.000 1.000
#> GSM531608 1 0.0000 0.831 1.000 0.000
#> GSM531610 1 0.9460 0.633 0.636 0.364
#> GSM531612 1 0.9460 0.633 0.636 0.364
#> GSM531613 2 0.8955 0.383 0.312 0.688
#> GSM531614 1 0.9460 0.633 0.636 0.364
#> GSM531616 1 0.0000 0.831 1.000 0.000
#> GSM531618 1 0.1414 0.825 0.980 0.020
#> GSM531619 1 0.0000 0.831 1.000 0.000
#> GSM531620 1 0.0000 0.831 1.000 0.000
#> GSM531623 1 0.0000 0.831 1.000 0.000
#> GSM531625 1 0.0000 0.831 1.000 0.000
#> GSM531626 1 0.0000 0.831 1.000 0.000
#> GSM531632 1 0.0000 0.831 1.000 0.000
#> GSM531638 1 0.0000 0.831 1.000 0.000
#> GSM531639 1 0.0000 0.831 1.000 0.000
#> GSM531641 1 0.9460 0.633 0.636 0.364
#> GSM531642 1 0.9323 0.646 0.652 0.348
#> GSM531643 1 0.0000 0.831 1.000 0.000
#> GSM531644 1 0.9460 0.633 0.636 0.364
#> GSM531645 1 0.9460 0.633 0.636 0.364
#> GSM531646 1 0.0000 0.831 1.000 0.000
#> GSM531647 1 0.0000 0.831 1.000 0.000
#> GSM531648 1 0.9129 0.661 0.672 0.328
#> GSM531650 1 0.4562 0.795 0.904 0.096
#> GSM531651 1 0.0000 0.831 1.000 0.000
#> GSM531652 1 0.0000 0.831 1.000 0.000
#> GSM531656 1 0.9286 0.649 0.656 0.344
#> GSM531659 1 0.9460 0.633 0.636 0.364
#> GSM531661 1 0.0000 0.831 1.000 0.000
#> GSM531662 1 0.0000 0.831 1.000 0.000
#> GSM531663 1 0.9491 0.626 0.632 0.368
#> GSM531664 2 0.1633 0.952 0.024 0.976
#> GSM531666 1 0.9522 0.620 0.628 0.372
#> GSM531667 1 0.0000 0.831 1.000 0.000
#> GSM531668 1 0.9460 0.633 0.636 0.364
#> GSM531669 2 0.0672 0.970 0.008 0.992
#> GSM531671 1 0.0000 0.831 1.000 0.000
#> GSM531672 1 0.9460 0.633 0.636 0.364
#> GSM531673 1 0.9460 0.633 0.636 0.364
#> GSM531676 2 0.0000 0.976 0.000 1.000
#> GSM531679 2 0.0000 0.976 0.000 1.000
#> GSM531681 2 0.0000 0.976 0.000 1.000
#> GSM531682 2 0.0000 0.976 0.000 1.000
#> GSM531683 2 0.0000 0.976 0.000 1.000
#> GSM531684 2 0.0000 0.976 0.000 1.000
#> GSM531685 2 0.0000 0.976 0.000 1.000
#> GSM531686 2 0.0000 0.976 0.000 1.000
#> GSM531687 2 0.0672 0.970 0.008 0.992
#> GSM531688 2 0.0000 0.976 0.000 1.000
#> GSM531690 2 0.0000 0.976 0.000 1.000
#> GSM531693 2 0.0376 0.973 0.004 0.996
#> GSM531695 2 0.0000 0.976 0.000 1.000
#> GSM531603 2 0.0376 0.973 0.004 0.996
#> GSM531609 1 0.9460 0.633 0.636 0.364
#> GSM531611 1 0.9460 0.633 0.636 0.364
#> GSM531621 1 0.0000 0.831 1.000 0.000
#> GSM531622 1 0.0000 0.831 1.000 0.000
#> GSM531628 1 0.1633 0.824 0.976 0.024
#> GSM531630 1 0.0000 0.831 1.000 0.000
#> GSM531633 1 0.0000 0.831 1.000 0.000
#> GSM531635 1 0.0000 0.831 1.000 0.000
#> GSM531640 1 0.0000 0.831 1.000 0.000
#> GSM531649 1 0.0000 0.831 1.000 0.000
#> GSM531653 1 0.0000 0.831 1.000 0.000
#> GSM531657 1 0.9460 0.633 0.636 0.364
#> GSM531665 2 0.7219 0.672 0.200 0.800
#> GSM531670 1 0.9460 0.627 0.636 0.364
#> GSM531674 2 0.0672 0.970 0.008 0.992
#> GSM531675 2 0.0000 0.976 0.000 1.000
#> GSM531677 2 0.0000 0.976 0.000 1.000
#> GSM531678 2 0.0000 0.976 0.000 1.000
#> GSM531680 2 0.0000 0.976 0.000 1.000
#> GSM531689 2 0.0000 0.976 0.000 1.000
#> GSM531691 2 0.0000 0.976 0.000 1.000
#> GSM531692 2 0.0000 0.976 0.000 1.000
#> GSM531694 2 0.0000 0.976 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM531602 2 0.1411 0.937 0.036 0.964 0.000
#> GSM531604 2 0.1525 0.927 0.004 0.964 0.032
#> GSM531606 2 0.1411 0.937 0.036 0.964 0.000
#> GSM531607 2 0.1411 0.937 0.036 0.964 0.000
#> GSM531608 3 0.0000 0.798 0.000 0.000 1.000
#> GSM531610 1 0.0000 0.767 1.000 0.000 0.000
#> GSM531612 1 0.0000 0.767 1.000 0.000 0.000
#> GSM531613 2 0.6308 0.282 0.492 0.508 0.000
#> GSM531614 1 0.0000 0.767 1.000 0.000 0.000
#> GSM531616 3 0.4235 0.680 0.176 0.000 0.824
#> GSM531618 1 0.4702 0.741 0.788 0.000 0.212
#> GSM531619 3 0.0000 0.798 0.000 0.000 1.000
#> GSM531620 3 0.0000 0.798 0.000 0.000 1.000
#> GSM531623 3 0.0000 0.798 0.000 0.000 1.000
#> GSM531625 3 0.0000 0.798 0.000 0.000 1.000
#> GSM531626 3 0.0000 0.798 0.000 0.000 1.000
#> GSM531632 3 0.7339 0.295 0.392 0.036 0.572
#> GSM531638 3 0.2796 0.750 0.092 0.000 0.908
#> GSM531639 1 0.5291 0.689 0.732 0.000 0.268
#> GSM531641 1 0.0000 0.767 1.000 0.000 0.000
#> GSM531642 1 0.5633 0.721 0.768 0.208 0.024
#> GSM531643 1 0.6253 0.710 0.732 0.036 0.232
#> GSM531644 1 0.6882 0.745 0.732 0.096 0.172
#> GSM531645 1 0.0000 0.767 1.000 0.000 0.000
#> GSM531646 3 0.7339 0.295 0.392 0.036 0.572
#> GSM531647 3 0.7339 0.295 0.392 0.036 0.572
#> GSM531648 1 0.3941 0.764 0.844 0.000 0.156
#> GSM531650 1 0.6319 0.715 0.732 0.040 0.228
#> GSM531651 3 0.0000 0.798 0.000 0.000 1.000
#> GSM531652 1 0.4702 0.741 0.788 0.000 0.212
#> GSM531656 1 0.6437 0.727 0.732 0.048 0.220
#> GSM531659 1 0.5115 0.708 0.768 0.228 0.004
#> GSM531661 3 0.0000 0.798 0.000 0.000 1.000
#> GSM531662 3 0.0424 0.794 0.008 0.000 0.992
#> GSM531663 1 0.0592 0.766 0.988 0.012 0.000
#> GSM531664 2 0.0000 0.937 0.000 1.000 0.000
#> GSM531666 1 0.5115 0.708 0.768 0.228 0.004
#> GSM531667 3 0.6180 0.228 0.416 0.000 0.584
#> GSM531668 1 0.4233 0.743 0.836 0.160 0.004
#> GSM531669 2 0.0424 0.932 0.000 0.992 0.008
#> GSM531671 3 0.5503 0.638 0.208 0.020 0.772
#> GSM531672 1 0.5115 0.708 0.768 0.228 0.004
#> GSM531673 3 0.8261 0.171 0.340 0.092 0.568
#> GSM531676 2 0.0000 0.937 0.000 1.000 0.000
#> GSM531679 2 0.1411 0.937 0.036 0.964 0.000
#> GSM531681 2 0.5098 0.745 0.248 0.752 0.000
#> GSM531682 2 0.1411 0.937 0.036 0.964 0.000
#> GSM531683 2 0.1411 0.937 0.036 0.964 0.000
#> GSM531684 2 0.6215 0.346 0.000 0.572 0.428
#> GSM531685 2 0.0000 0.937 0.000 1.000 0.000
#> GSM531686 2 0.4654 0.790 0.208 0.792 0.000
#> GSM531687 2 0.0000 0.937 0.000 1.000 0.000
#> GSM531688 2 0.0000 0.937 0.000 1.000 0.000
#> GSM531690 2 0.1411 0.937 0.036 0.964 0.000
#> GSM531693 2 0.0237 0.935 0.000 0.996 0.004
#> GSM531695 2 0.0000 0.937 0.000 1.000 0.000
#> GSM531603 2 0.1411 0.937 0.036 0.964 0.000
#> GSM531609 1 0.0000 0.767 1.000 0.000 0.000
#> GSM531611 1 0.0000 0.767 1.000 0.000 0.000
#> GSM531621 3 0.0000 0.798 0.000 0.000 1.000
#> GSM531622 3 0.0000 0.798 0.000 0.000 1.000
#> GSM531628 1 0.6319 0.715 0.732 0.040 0.228
#> GSM531630 3 0.0000 0.798 0.000 0.000 1.000
#> GSM531633 3 0.0000 0.798 0.000 0.000 1.000
#> GSM531635 3 0.7339 0.295 0.392 0.036 0.572
#> GSM531640 1 0.5291 0.689 0.732 0.000 0.268
#> GSM531649 3 0.7339 0.295 0.392 0.036 0.572
#> GSM531653 1 0.7295 0.396 0.584 0.036 0.380
#> GSM531657 1 0.5115 0.708 0.768 0.228 0.004
#> GSM531665 2 0.0237 0.935 0.000 0.996 0.004
#> GSM531670 1 0.7079 0.740 0.720 0.104 0.176
#> GSM531674 2 0.0000 0.937 0.000 1.000 0.000
#> GSM531675 2 0.1411 0.937 0.036 0.964 0.000
#> GSM531677 2 0.1411 0.937 0.036 0.964 0.000
#> GSM531678 2 0.1411 0.937 0.036 0.964 0.000
#> GSM531680 2 0.0000 0.937 0.000 1.000 0.000
#> GSM531689 2 0.0747 0.938 0.016 0.984 0.000
#> GSM531691 2 0.0475 0.937 0.004 0.992 0.004
#> GSM531692 2 0.0000 0.937 0.000 1.000 0.000
#> GSM531694 2 0.1411 0.937 0.036 0.964 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM531602 2 0.0336 0.9590 0.000 0.992 0.000 0.008
#> GSM531604 2 0.0469 0.9561 0.000 0.988 0.012 0.000
#> GSM531606 2 0.0188 0.9597 0.000 0.996 0.000 0.004
#> GSM531607 2 0.0188 0.9597 0.000 0.996 0.000 0.004
#> GSM531608 3 0.0000 0.9751 0.000 0.000 1.000 0.000
#> GSM531610 4 0.0000 0.8910 0.000 0.000 0.000 1.000
#> GSM531612 4 0.0000 0.8910 0.000 0.000 0.000 1.000
#> GSM531613 4 0.0000 0.8910 0.000 0.000 0.000 1.000
#> GSM531614 4 0.0000 0.8910 0.000 0.000 0.000 1.000
#> GSM531616 3 0.0707 0.9622 0.020 0.000 0.980 0.000
#> GSM531618 1 0.4885 0.6999 0.760 0.204 0.016 0.020
#> GSM531619 3 0.0000 0.9751 0.000 0.000 1.000 0.000
#> GSM531620 3 0.0000 0.9751 0.000 0.000 1.000 0.000
#> GSM531623 3 0.0000 0.9751 0.000 0.000 1.000 0.000
#> GSM531625 3 0.0000 0.9751 0.000 0.000 1.000 0.000
#> GSM531626 3 0.0000 0.9751 0.000 0.000 1.000 0.000
#> GSM531632 1 0.0817 0.9039 0.976 0.000 0.024 0.000
#> GSM531638 3 0.0469 0.9684 0.012 0.000 0.988 0.000
#> GSM531639 1 0.4999 0.0626 0.508 0.000 0.492 0.000
#> GSM531641 4 0.0000 0.8910 0.000 0.000 0.000 1.000
#> GSM531642 1 0.3852 0.7402 0.800 0.192 0.008 0.000
#> GSM531643 1 0.0336 0.9026 0.992 0.000 0.008 0.000
#> GSM531644 1 0.0336 0.9026 0.992 0.000 0.008 0.000
#> GSM531645 4 0.0000 0.8910 0.000 0.000 0.000 1.000
#> GSM531646 1 0.0817 0.9039 0.976 0.000 0.024 0.000
#> GSM531647 1 0.0817 0.9039 0.976 0.000 0.024 0.000
#> GSM531648 1 0.2353 0.8714 0.928 0.024 0.008 0.040
#> GSM531650 1 0.0000 0.9029 1.000 0.000 0.000 0.000
#> GSM531651 3 0.0000 0.9751 0.000 0.000 1.000 0.000
#> GSM531652 1 0.1139 0.8945 0.972 0.012 0.008 0.008
#> GSM531656 1 0.3969 0.7422 0.804 0.180 0.016 0.000
#> GSM531659 2 0.1486 0.9424 0.024 0.960 0.008 0.008
#> GSM531661 3 0.0336 0.9696 0.000 0.008 0.992 0.000
#> GSM531662 3 0.0927 0.9654 0.016 0.008 0.976 0.000
#> GSM531663 4 0.2334 0.8230 0.004 0.088 0.000 0.908
#> GSM531664 1 0.0817 0.9001 0.976 0.024 0.000 0.000
#> GSM531666 2 0.4482 0.6115 0.264 0.728 0.008 0.000
#> GSM531667 3 0.1191 0.9564 0.024 0.004 0.968 0.004
#> GSM531668 4 0.7672 0.4304 0.024 0.316 0.136 0.524
#> GSM531669 1 0.0817 0.9001 0.976 0.024 0.000 0.000
#> GSM531671 3 0.5427 0.6818 0.100 0.148 0.748 0.004
#> GSM531672 2 0.1617 0.9400 0.024 0.956 0.008 0.012
#> GSM531673 3 0.1151 0.9600 0.024 0.008 0.968 0.000
#> GSM531676 2 0.0707 0.9559 0.020 0.980 0.000 0.000
#> GSM531679 2 0.0000 0.9596 0.000 1.000 0.000 0.000
#> GSM531681 4 0.4855 0.3440 0.000 0.400 0.000 0.600
#> GSM531682 2 0.0672 0.9574 0.000 0.984 0.008 0.008
#> GSM531683 2 0.0000 0.9596 0.000 1.000 0.000 0.000
#> GSM531684 3 0.1022 0.9505 0.000 0.032 0.968 0.000
#> GSM531685 2 0.0469 0.9577 0.012 0.988 0.000 0.000
#> GSM531686 2 0.4661 0.4127 0.000 0.652 0.000 0.348
#> GSM531687 2 0.0804 0.9572 0.012 0.980 0.008 0.000
#> GSM531688 2 0.0707 0.9559 0.020 0.980 0.000 0.000
#> GSM531690 2 0.0657 0.9579 0.000 0.984 0.004 0.012
#> GSM531693 2 0.1211 0.9427 0.040 0.960 0.000 0.000
#> GSM531695 2 0.0707 0.9559 0.020 0.980 0.000 0.000
#> GSM531603 2 0.0336 0.9590 0.000 0.992 0.000 0.008
#> GSM531609 4 0.0000 0.8910 0.000 0.000 0.000 1.000
#> GSM531611 4 0.0000 0.8910 0.000 0.000 0.000 1.000
#> GSM531621 3 0.0000 0.9751 0.000 0.000 1.000 0.000
#> GSM531622 3 0.0000 0.9751 0.000 0.000 1.000 0.000
#> GSM531628 1 0.0188 0.9041 0.996 0.000 0.004 0.000
#> GSM531630 3 0.0000 0.9751 0.000 0.000 1.000 0.000
#> GSM531633 3 0.0000 0.9751 0.000 0.000 1.000 0.000
#> GSM531635 1 0.1022 0.9024 0.968 0.000 0.032 0.000
#> GSM531640 3 0.0817 0.9606 0.024 0.000 0.976 0.000
#> GSM531649 1 0.0817 0.9039 0.976 0.000 0.024 0.000
#> GSM531653 1 0.0707 0.9047 0.980 0.000 0.020 0.000
#> GSM531657 2 0.1617 0.9400 0.024 0.956 0.008 0.012
#> GSM531665 2 0.0804 0.9572 0.012 0.980 0.008 0.000
#> GSM531670 2 0.1488 0.9439 0.032 0.956 0.012 0.000
#> GSM531674 1 0.0817 0.9001 0.976 0.024 0.000 0.000
#> GSM531675 2 0.0524 0.9587 0.000 0.988 0.004 0.008
#> GSM531677 2 0.0336 0.9590 0.000 0.992 0.000 0.008
#> GSM531678 2 0.0000 0.9596 0.000 1.000 0.000 0.000
#> GSM531680 2 0.0707 0.9559 0.020 0.980 0.000 0.000
#> GSM531689 2 0.0000 0.9596 0.000 1.000 0.000 0.000
#> GSM531691 2 0.0336 0.9580 0.000 0.992 0.008 0.000
#> GSM531692 2 0.0469 0.9577 0.012 0.988 0.000 0.000
#> GSM531694 2 0.0336 0.9590 0.000 0.992 0.000 0.008
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM531602 2 0.2389 0.7896 0.000 0.880 0.004 0.000 0.116
#> GSM531604 2 0.4182 0.3676 0.000 0.600 0.400 0.000 0.000
#> GSM531606 2 0.5454 0.3437 0.000 0.532 0.404 0.000 0.064
#> GSM531607 2 0.0963 0.8075 0.000 0.964 0.000 0.000 0.036
#> GSM531608 3 0.0000 0.7284 0.000 0.000 1.000 0.000 0.000
#> GSM531610 4 0.0000 0.9086 0.000 0.000 0.000 1.000 0.000
#> GSM531612 4 0.0000 0.9086 0.000 0.000 0.000 1.000 0.000
#> GSM531613 4 0.0000 0.9086 0.000 0.000 0.000 1.000 0.000
#> GSM531614 4 0.0000 0.9086 0.000 0.000 0.000 1.000 0.000
#> GSM531616 5 0.5435 -0.2196 0.428 0.000 0.060 0.000 0.512
#> GSM531618 5 0.4060 0.3305 0.360 0.000 0.000 0.000 0.640
#> GSM531619 3 0.0000 0.7284 0.000 0.000 1.000 0.000 0.000
#> GSM531620 3 0.4192 0.6471 0.000 0.000 0.596 0.000 0.404
#> GSM531623 3 0.0000 0.7284 0.000 0.000 1.000 0.000 0.000
#> GSM531625 3 0.4192 0.6471 0.000 0.000 0.596 0.000 0.404
#> GSM531626 3 0.4893 0.6197 0.028 0.000 0.568 0.000 0.404
#> GSM531632 1 0.4088 0.3627 0.632 0.000 0.000 0.000 0.368
#> GSM531638 5 0.6271 -0.2191 0.412 0.000 0.148 0.000 0.440
#> GSM531639 5 0.2230 0.2284 0.000 0.000 0.116 0.000 0.884
#> GSM531641 4 0.0000 0.9086 0.000 0.000 0.000 1.000 0.000
#> GSM531642 5 0.5876 0.2789 0.412 0.100 0.000 0.000 0.488
#> GSM531643 1 0.2929 0.3819 0.820 0.000 0.000 0.000 0.180
#> GSM531644 1 0.4302 -0.2606 0.520 0.000 0.000 0.000 0.480
#> GSM531645 4 0.0000 0.9086 0.000 0.000 0.000 1.000 0.000
#> GSM531646 1 0.4192 0.3332 0.596 0.000 0.000 0.000 0.404
#> GSM531647 1 0.0000 0.5907 1.000 0.000 0.000 0.000 0.000
#> GSM531648 5 0.4192 0.3111 0.404 0.000 0.000 0.000 0.596
#> GSM531650 1 0.1478 0.5377 0.936 0.000 0.000 0.000 0.064
#> GSM531651 3 0.0000 0.7284 0.000 0.000 1.000 0.000 0.000
#> GSM531652 5 0.4210 0.3055 0.412 0.000 0.000 0.000 0.588
#> GSM531656 5 0.5454 0.2411 0.452 0.060 0.000 0.000 0.488
#> GSM531659 5 0.4192 0.1079 0.000 0.404 0.000 0.000 0.596
#> GSM531661 3 0.0000 0.7284 0.000 0.000 1.000 0.000 0.000
#> GSM531662 3 0.0000 0.7284 0.000 0.000 1.000 0.000 0.000
#> GSM531663 4 0.3461 0.6510 0.000 0.000 0.004 0.772 0.224
#> GSM531664 1 0.4138 0.1561 0.616 0.384 0.000 0.000 0.000
#> GSM531666 5 0.6523 0.3399 0.232 0.288 0.000 0.000 0.480
#> GSM531667 3 0.3857 0.2902 0.000 0.000 0.688 0.000 0.312
#> GSM531668 5 0.4736 0.1938 0.000 0.020 0.404 0.000 0.576
#> GSM531669 1 0.0000 0.5907 1.000 0.000 0.000 0.000 0.000
#> GSM531671 1 0.4649 0.2765 0.580 0.000 0.404 0.000 0.016
#> GSM531672 5 0.4192 0.1079 0.000 0.404 0.000 0.000 0.596
#> GSM531673 3 0.0000 0.7284 0.000 0.000 1.000 0.000 0.000
#> GSM531676 2 0.1270 0.7975 0.052 0.948 0.000 0.000 0.000
#> GSM531679 2 0.0000 0.8053 0.000 1.000 0.000 0.000 0.000
#> GSM531681 4 0.4649 0.1759 0.000 0.404 0.000 0.580 0.016
#> GSM531682 2 0.2516 0.7857 0.000 0.860 0.000 0.000 0.140
#> GSM531683 2 0.0000 0.8053 0.000 1.000 0.000 0.000 0.000
#> GSM531684 3 0.0162 0.7254 0.000 0.004 0.996 0.000 0.000
#> GSM531685 2 0.1965 0.7807 0.096 0.904 0.000 0.000 0.000
#> GSM531686 2 0.4045 0.4522 0.000 0.644 0.000 0.356 0.000
#> GSM531687 2 0.1792 0.7741 0.000 0.916 0.000 0.000 0.084
#> GSM531688 2 0.2690 0.7430 0.156 0.844 0.000 0.000 0.000
#> GSM531690 2 0.2280 0.7900 0.000 0.880 0.000 0.000 0.120
#> GSM531693 1 0.4210 0.1353 0.588 0.412 0.000 0.000 0.000
#> GSM531695 2 0.2648 0.7465 0.152 0.848 0.000 0.000 0.000
#> GSM531603 2 0.2583 0.7855 0.000 0.864 0.004 0.000 0.132
#> GSM531609 4 0.0000 0.9086 0.000 0.000 0.000 1.000 0.000
#> GSM531611 4 0.0000 0.9086 0.000 0.000 0.000 1.000 0.000
#> GSM531621 3 0.4192 0.6471 0.000 0.000 0.596 0.000 0.404
#> GSM531622 3 0.4192 0.6471 0.000 0.000 0.596 0.000 0.404
#> GSM531628 1 0.0000 0.5907 1.000 0.000 0.000 0.000 0.000
#> GSM531630 3 0.4192 0.6471 0.000 0.000 0.596 0.000 0.404
#> GSM531633 3 0.4192 0.6471 0.000 0.000 0.596 0.000 0.404
#> GSM531635 5 0.4305 -0.2933 0.488 0.000 0.000 0.000 0.512
#> GSM531640 5 0.2230 0.2284 0.000 0.000 0.116 0.000 0.884
#> GSM531649 1 0.4182 0.3372 0.600 0.000 0.000 0.000 0.400
#> GSM531653 1 0.0000 0.5907 1.000 0.000 0.000 0.000 0.000
#> GSM531657 5 0.4331 0.1127 0.000 0.400 0.004 0.000 0.596
#> GSM531665 2 0.2074 0.7573 0.000 0.896 0.000 0.000 0.104
#> GSM531670 2 0.4304 -0.0871 0.000 0.516 0.000 0.000 0.484
#> GSM531674 1 0.0000 0.5907 1.000 0.000 0.000 0.000 0.000
#> GSM531675 2 0.2280 0.7900 0.000 0.880 0.000 0.000 0.120
#> GSM531677 2 0.2230 0.7905 0.000 0.884 0.000 0.000 0.116
#> GSM531678 2 0.0609 0.8038 0.000 0.980 0.000 0.000 0.020
#> GSM531680 2 0.1732 0.7858 0.080 0.920 0.000 0.000 0.000
#> GSM531689 2 0.0000 0.8053 0.000 1.000 0.000 0.000 0.000
#> GSM531691 2 0.0609 0.8038 0.000 0.980 0.000 0.000 0.020
#> GSM531692 2 0.4547 0.3628 0.012 0.588 0.400 0.000 0.000
#> GSM531694 2 0.2230 0.7905 0.000 0.884 0.000 0.000 0.116
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM531602 2 0.0000 0.78418 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531604 5 0.4301 0.31801 0.000 0.016 0.400 0.000 0.580 0.004
#> GSM531606 3 0.5978 -0.22230 0.000 0.228 0.404 0.000 0.368 0.000
#> GSM531607 2 0.4252 0.29491 0.000 0.652 0.000 0.000 0.036 0.312
#> GSM531608 3 0.0000 0.67902 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531610 4 0.0000 0.96447 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531612 4 0.0000 0.96447 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531613 4 0.0000 0.96447 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531614 4 0.0000 0.96447 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531616 1 0.2871 0.43300 0.804 0.000 0.004 0.000 0.000 0.192
#> GSM531618 6 0.4064 0.56151 0.016 0.000 0.000 0.000 0.360 0.624
#> GSM531619 3 0.0000 0.67902 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531620 3 0.3765 0.55746 0.404 0.000 0.596 0.000 0.000 0.000
#> GSM531623 3 0.0000 0.67902 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531625 3 0.3765 0.55746 0.404 0.000 0.596 0.000 0.000 0.000
#> GSM531626 3 0.3817 0.52462 0.432 0.000 0.568 0.000 0.000 0.000
#> GSM531632 1 0.0865 0.58541 0.964 0.000 0.000 0.000 0.036 0.000
#> GSM531638 1 0.3586 0.37816 0.796 0.000 0.124 0.000 0.000 0.080
#> GSM531639 6 0.3934 0.33384 0.376 0.000 0.008 0.000 0.000 0.616
#> GSM531641 4 0.0000 0.96447 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531642 6 0.3717 0.56148 0.000 0.000 0.000 0.000 0.384 0.616
#> GSM531643 5 0.6102 -0.48115 0.332 0.000 0.000 0.000 0.376 0.292
#> GSM531644 6 0.3934 0.55601 0.008 0.000 0.000 0.000 0.376 0.616
#> GSM531645 4 0.0000 0.96447 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531646 1 0.0000 0.56825 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM531647 1 0.3765 0.59671 0.596 0.000 0.000 0.000 0.404 0.000
#> GSM531648 6 0.3695 0.56113 0.000 0.000 0.000 0.000 0.376 0.624
#> GSM531650 1 0.4978 0.51680 0.532 0.000 0.000 0.000 0.396 0.072
#> GSM531651 3 0.0000 0.67902 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531652 6 0.3695 0.56113 0.000 0.000 0.000 0.000 0.376 0.624
#> GSM531656 6 0.3945 0.55816 0.008 0.000 0.000 0.000 0.380 0.612
#> GSM531659 6 0.0865 0.45094 0.000 0.036 0.000 0.000 0.000 0.964
#> GSM531661 3 0.0000 0.67902 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531662 3 0.0000 0.67902 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531663 4 0.3136 0.67184 0.000 0.000 0.004 0.768 0.000 0.228
#> GSM531664 5 0.2823 0.00499 0.204 0.000 0.000 0.000 0.796 0.000
#> GSM531666 6 0.3101 0.57105 0.000 0.000 0.000 0.000 0.244 0.756
#> GSM531667 3 0.3737 0.15205 0.000 0.000 0.608 0.000 0.000 0.392
#> GSM531668 3 0.5943 -0.09691 0.000 0.216 0.404 0.000 0.000 0.380
#> GSM531669 1 0.3765 0.59671 0.596 0.000 0.000 0.000 0.404 0.000
#> GSM531671 1 0.3899 0.30605 0.592 0.000 0.404 0.000 0.000 0.004
#> GSM531672 6 0.0000 0.42950 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM531673 3 0.0000 0.67902 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531676 5 0.3934 0.68366 0.000 0.008 0.000 0.000 0.616 0.376
#> GSM531679 2 0.2941 0.80667 0.000 0.780 0.000 0.000 0.220 0.000
#> GSM531681 2 0.2941 0.69769 0.000 0.780 0.000 0.220 0.000 0.000
#> GSM531682 2 0.3133 0.81153 0.000 0.780 0.000 0.000 0.212 0.008
#> GSM531683 2 0.0146 0.78581 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM531684 3 0.0000 0.67902 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531685 5 0.4110 0.67785 0.016 0.000 0.000 0.000 0.608 0.376
#> GSM531686 2 0.3052 0.70242 0.000 0.780 0.000 0.216 0.004 0.000
#> GSM531687 5 0.3747 0.67335 0.000 0.000 0.000 0.000 0.604 0.396
#> GSM531688 5 0.5845 0.56842 0.192 0.000 0.000 0.000 0.432 0.376
#> GSM531690 2 0.3103 0.81220 0.000 0.784 0.000 0.000 0.208 0.008
#> GSM531693 1 0.4333 0.20459 0.596 0.000 0.000 0.000 0.028 0.376
#> GSM531695 5 0.5826 0.57159 0.188 0.000 0.000 0.000 0.436 0.376
#> GSM531603 6 0.6081 -0.55986 0.000 0.220 0.004 0.000 0.376 0.400
#> GSM531609 4 0.0000 0.96447 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531611 4 0.0000 0.96447 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531621 3 0.3765 0.55746 0.404 0.000 0.596 0.000 0.000 0.000
#> GSM531622 3 0.3765 0.55746 0.404 0.000 0.596 0.000 0.000 0.000
#> GSM531628 1 0.3765 0.59671 0.596 0.000 0.000 0.000 0.404 0.000
#> GSM531630 3 0.3765 0.55746 0.404 0.000 0.596 0.000 0.000 0.000
#> GSM531633 3 0.3765 0.55746 0.404 0.000 0.596 0.000 0.000 0.000
#> GSM531635 1 0.2730 0.43625 0.808 0.000 0.000 0.000 0.000 0.192
#> GSM531640 6 0.3934 0.33384 0.376 0.000 0.008 0.000 0.000 0.616
#> GSM531649 1 0.0146 0.57154 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM531653 1 0.3765 0.59671 0.596 0.000 0.000 0.000 0.404 0.000
#> GSM531657 6 0.3695 0.26954 0.000 0.376 0.000 0.000 0.000 0.624
#> GSM531665 6 0.3804 -0.47811 0.000 0.000 0.000 0.000 0.424 0.576
#> GSM531670 6 0.0891 0.40745 0.008 0.000 0.000 0.000 0.024 0.968
#> GSM531674 1 0.3765 0.59671 0.596 0.000 0.000 0.000 0.404 0.000
#> GSM531675 2 0.3133 0.81153 0.000 0.780 0.000 0.000 0.212 0.008
#> GSM531677 2 0.3133 0.81153 0.000 0.780 0.000 0.000 0.212 0.008
#> GSM531678 5 0.4333 0.67799 0.000 0.028 0.000 0.000 0.596 0.376
#> GSM531680 5 0.3934 0.68366 0.000 0.008 0.000 0.000 0.616 0.376
#> GSM531689 5 0.4333 0.67799 0.000 0.028 0.000 0.000 0.596 0.376
#> GSM531691 5 0.4189 0.68134 0.000 0.020 0.000 0.000 0.604 0.376
#> GSM531692 5 0.3756 0.32748 0.000 0.000 0.400 0.000 0.600 0.000
#> GSM531694 2 0.0000 0.78418 0.000 1.000 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)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> CV:pam 79 0.485 2
#> CV:pam 70 0.475 3
#> CV:pam 76 0.537 4
#> CV:pam 50 0.471 5
#> CV:pam 59 0.391 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "mclust"]
# you can also extract it by
# res = res_list["CV:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 80 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 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.419 0.768 0.861 0.3481 0.708 0.708
#> 3 3 0.352 0.543 0.669 0.5725 0.676 0.584
#> 4 4 0.801 0.904 0.946 0.3522 0.633 0.359
#> 5 5 0.695 0.679 0.841 0.0384 0.964 0.859
#> 6 6 0.790 0.799 0.839 0.0742 0.918 0.654
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM531602 2 0.0000 0.821 0.000 1.000
#> GSM531604 2 0.0000 0.821 0.000 1.000
#> GSM531606 2 0.0000 0.821 0.000 1.000
#> GSM531607 2 0.0000 0.821 0.000 1.000
#> GSM531608 2 0.9635 0.573 0.388 0.612
#> GSM531610 2 0.1843 0.816 0.028 0.972
#> GSM531612 2 0.3274 0.807 0.060 0.940
#> GSM531613 2 0.0672 0.822 0.008 0.992
#> GSM531614 2 0.3274 0.807 0.060 0.940
#> GSM531616 1 0.7674 0.724 0.776 0.224
#> GSM531618 2 0.2948 0.811 0.052 0.948
#> GSM531619 1 0.0938 0.887 0.988 0.012
#> GSM531620 1 0.5629 0.861 0.868 0.132
#> GSM531623 1 0.0938 0.887 0.988 0.012
#> GSM531625 1 0.5842 0.854 0.860 0.140
#> GSM531626 1 0.6148 0.841 0.848 0.152
#> GSM531632 2 0.9170 0.646 0.332 0.668
#> GSM531638 1 0.5629 0.861 0.868 0.132
#> GSM531639 2 0.9460 0.614 0.364 0.636
#> GSM531641 2 0.3274 0.807 0.060 0.940
#> GSM531642 2 0.9129 0.658 0.328 0.672
#> GSM531643 2 0.9427 0.620 0.360 0.640
#> GSM531644 2 0.9209 0.651 0.336 0.664
#> GSM531645 2 0.3274 0.807 0.060 0.940
#> GSM531646 2 0.9460 0.614 0.364 0.636
#> GSM531647 2 0.9460 0.614 0.364 0.636
#> GSM531648 2 0.3274 0.807 0.060 0.940
#> GSM531650 2 0.9460 0.614 0.364 0.636
#> GSM531651 1 0.0938 0.887 0.988 0.012
#> GSM531652 2 0.7453 0.746 0.212 0.788
#> GSM531656 2 0.9427 0.618 0.360 0.640
#> GSM531659 2 0.0672 0.822 0.008 0.992
#> GSM531661 2 0.9129 0.650 0.328 0.672
#> GSM531662 2 0.8763 0.681 0.296 0.704
#> GSM531663 2 0.0672 0.822 0.008 0.992
#> GSM531664 2 0.9044 0.657 0.320 0.680
#> GSM531666 2 0.7602 0.739 0.220 0.780
#> GSM531667 1 0.8443 0.610 0.728 0.272
#> GSM531668 2 0.0672 0.822 0.008 0.992
#> GSM531669 2 0.9044 0.657 0.320 0.680
#> GSM531671 2 0.8763 0.681 0.296 0.704
#> GSM531672 2 0.0672 0.822 0.008 0.992
#> GSM531673 2 0.3733 0.810 0.072 0.928
#> GSM531676 2 0.2043 0.820 0.032 0.968
#> GSM531679 2 0.0000 0.821 0.000 1.000
#> GSM531681 2 0.0000 0.821 0.000 1.000
#> GSM531682 2 0.0000 0.821 0.000 1.000
#> GSM531683 2 0.0000 0.821 0.000 1.000
#> GSM531684 2 0.0000 0.821 0.000 1.000
#> GSM531685 2 0.2603 0.817 0.044 0.956
#> GSM531686 2 0.0000 0.821 0.000 1.000
#> GSM531687 2 0.2603 0.817 0.044 0.956
#> GSM531688 2 0.8386 0.701 0.268 0.732
#> GSM531690 2 0.0000 0.821 0.000 1.000
#> GSM531693 2 0.8661 0.684 0.288 0.712
#> GSM531695 2 0.7602 0.735 0.220 0.780
#> GSM531603 2 0.0000 0.821 0.000 1.000
#> GSM531609 2 0.3274 0.807 0.060 0.940
#> GSM531611 2 0.0672 0.822 0.008 0.992
#> GSM531621 1 0.0938 0.887 0.988 0.012
#> GSM531622 1 0.0938 0.887 0.988 0.012
#> GSM531628 2 0.9460 0.614 0.364 0.636
#> GSM531630 1 0.0938 0.887 0.988 0.012
#> GSM531633 1 0.0938 0.887 0.988 0.012
#> GSM531635 2 0.9460 0.614 0.364 0.636
#> GSM531640 1 0.4939 0.871 0.892 0.108
#> GSM531649 2 0.9460 0.614 0.364 0.636
#> GSM531653 2 0.9460 0.614 0.364 0.636
#> GSM531657 2 0.0672 0.822 0.008 0.992
#> GSM531665 2 0.5059 0.797 0.112 0.888
#> GSM531670 2 0.9044 0.657 0.320 0.680
#> GSM531674 2 0.9044 0.657 0.320 0.680
#> GSM531675 2 0.0000 0.821 0.000 1.000
#> GSM531677 2 0.0000 0.821 0.000 1.000
#> GSM531678 2 0.0000 0.821 0.000 1.000
#> GSM531680 2 0.4562 0.802 0.096 0.904
#> GSM531689 2 0.0000 0.821 0.000 1.000
#> GSM531691 2 0.0000 0.821 0.000 1.000
#> GSM531692 2 0.0672 0.822 0.008 0.992
#> GSM531694 2 0.0000 0.821 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM531602 2 0.6095 0.678 NA 0.608 0.000
#> GSM531604 2 0.6154 0.675 NA 0.592 0.000
#> GSM531606 2 0.6126 0.677 NA 0.600 0.000
#> GSM531607 2 0.6095 0.678 NA 0.608 0.000
#> GSM531608 3 0.7770 0.542 NA 0.088 0.640
#> GSM531610 2 0.5431 0.404 NA 0.716 0.000
#> GSM531612 2 0.5431 0.404 NA 0.716 0.000
#> GSM531613 2 0.3192 0.540 NA 0.888 0.000
#> GSM531614 2 0.5431 0.404 NA 0.716 0.000
#> GSM531616 3 0.9885 0.504 NA 0.284 0.408
#> GSM531618 2 0.0747 0.594 NA 0.984 0.016
#> GSM531619 3 0.5621 0.551 NA 0.000 0.692
#> GSM531620 3 0.7644 0.553 NA 0.068 0.624
#> GSM531623 3 0.5621 0.551 NA 0.000 0.692
#> GSM531625 3 0.9857 0.505 NA 0.276 0.416
#> GSM531626 3 0.9857 0.505 NA 0.276 0.416
#> GSM531632 3 0.6235 0.500 NA 0.436 0.564
#> GSM531638 3 0.9857 0.505 NA 0.276 0.416
#> GSM531639 2 0.6509 -0.360 NA 0.524 0.472
#> GSM531641 2 0.5431 0.404 NA 0.716 0.000
#> GSM531642 2 0.4974 0.335 NA 0.764 0.236
#> GSM531643 3 0.6235 0.500 NA 0.436 0.564
#> GSM531644 3 0.6308 0.400 NA 0.492 0.508
#> GSM531645 2 0.5431 0.404 NA 0.716 0.000
#> GSM531646 3 0.6235 0.500 NA 0.436 0.564
#> GSM531647 3 0.6235 0.500 NA 0.436 0.564
#> GSM531648 2 0.5397 0.407 NA 0.720 0.000
#> GSM531650 3 0.6235 0.500 NA 0.436 0.564
#> GSM531651 3 0.5621 0.551 NA 0.000 0.692
#> GSM531652 2 0.2537 0.553 NA 0.920 0.080
#> GSM531656 3 0.6235 0.500 NA 0.436 0.564
#> GSM531659 2 0.0000 0.603 NA 1.000 0.000
#> GSM531661 2 0.6559 0.160 NA 0.708 0.040
#> GSM531662 2 0.2200 0.611 NA 0.940 0.004
#> GSM531663 2 0.0000 0.603 NA 1.000 0.000
#> GSM531664 3 0.6235 0.500 NA 0.436 0.564
#> GSM531666 2 0.3816 0.476 NA 0.852 0.148
#> GSM531667 3 0.8275 0.548 NA 0.108 0.596
#> GSM531668 2 0.0000 0.603 NA 1.000 0.000
#> GSM531669 3 0.7641 0.436 NA 0.436 0.520
#> GSM531671 2 0.2486 0.610 NA 0.932 0.008
#> GSM531672 2 0.0892 0.596 NA 0.980 0.000
#> GSM531673 2 0.2200 0.611 NA 0.940 0.004
#> GSM531676 2 0.6154 0.675 NA 0.592 0.000
#> GSM531679 2 0.6095 0.678 NA 0.608 0.000
#> GSM531681 2 0.5835 0.676 NA 0.660 0.000
#> GSM531682 2 0.6095 0.678 NA 0.608 0.000
#> GSM531683 2 0.6095 0.678 NA 0.608 0.000
#> GSM531684 2 0.4796 0.660 NA 0.780 0.000
#> GSM531685 2 0.6154 0.675 NA 0.592 0.000
#> GSM531686 2 0.5859 0.676 NA 0.656 0.000
#> GSM531687 2 0.6154 0.675 NA 0.592 0.000
#> GSM531688 2 0.6154 0.675 NA 0.592 0.000
#> GSM531690 2 0.5835 0.676 NA 0.660 0.000
#> GSM531693 2 0.9963 0.116 NA 0.376 0.308
#> GSM531695 2 0.6154 0.675 NA 0.592 0.000
#> GSM531603 2 0.0592 0.609 NA 0.988 0.000
#> GSM531609 2 0.5431 0.404 NA 0.716 0.000
#> GSM531611 2 0.0237 0.602 NA 0.996 0.000
#> GSM531621 3 0.5621 0.551 NA 0.000 0.692
#> GSM531622 3 0.5621 0.551 NA 0.000 0.692
#> GSM531628 3 0.6235 0.500 NA 0.436 0.564
#> GSM531630 3 0.5621 0.551 NA 0.000 0.692
#> GSM531633 3 0.5621 0.551 NA 0.000 0.692
#> GSM531635 3 0.6235 0.500 NA 0.436 0.564
#> GSM531640 3 0.5621 0.551 NA 0.000 0.692
#> GSM531649 3 0.6235 0.500 NA 0.436 0.564
#> GSM531653 3 0.6235 0.500 NA 0.436 0.564
#> GSM531657 2 0.0000 0.603 NA 1.000 0.000
#> GSM531665 2 0.2550 0.607 NA 0.932 0.012
#> GSM531670 3 0.6274 0.470 NA 0.456 0.544
#> GSM531674 3 0.7138 0.469 NA 0.436 0.540
#> GSM531675 2 0.5882 0.676 NA 0.652 0.000
#> GSM531677 2 0.6095 0.678 NA 0.608 0.000
#> GSM531678 2 0.6095 0.678 NA 0.608 0.000
#> GSM531680 2 0.6154 0.675 NA 0.592 0.000
#> GSM531689 2 0.6154 0.675 NA 0.592 0.000
#> GSM531691 2 0.6154 0.675 NA 0.592 0.000
#> GSM531692 2 0.6154 0.675 NA 0.592 0.000
#> GSM531694 2 0.6095 0.678 NA 0.608 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM531602 2 0.0000 0.957 0.000 1.000 0.000 0.000
#> GSM531604 2 0.0000 0.957 0.000 1.000 0.000 0.000
#> GSM531606 2 0.0000 0.957 0.000 1.000 0.000 0.000
#> GSM531607 2 0.0000 0.957 0.000 1.000 0.000 0.000
#> GSM531608 3 0.1209 0.942 0.000 0.004 0.964 0.032
#> GSM531610 4 0.0000 0.919 0.000 0.000 0.000 1.000
#> GSM531612 4 0.0000 0.919 0.000 0.000 0.000 1.000
#> GSM531613 4 0.2805 0.920 0.012 0.100 0.000 0.888
#> GSM531614 4 0.0000 0.919 0.000 0.000 0.000 1.000
#> GSM531616 3 0.0469 0.959 0.012 0.000 0.988 0.000
#> GSM531618 4 0.4524 0.873 0.012 0.104 0.064 0.820
#> GSM531619 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM531620 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM531623 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM531625 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM531626 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM531632 1 0.0000 0.911 1.000 0.000 0.000 0.000
#> GSM531638 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM531639 1 0.5859 0.133 0.496 0.000 0.472 0.032
#> GSM531641 4 0.0000 0.919 0.000 0.000 0.000 1.000
#> GSM531642 1 0.4380 0.784 0.800 0.004 0.164 0.032
#> GSM531643 1 0.1209 0.913 0.964 0.004 0.032 0.000
#> GSM531644 1 0.1209 0.913 0.964 0.004 0.032 0.000
#> GSM531645 4 0.0000 0.919 0.000 0.000 0.000 1.000
#> GSM531646 1 0.1022 0.914 0.968 0.000 0.032 0.000
#> GSM531647 1 0.1022 0.914 0.968 0.000 0.032 0.000
#> GSM531648 4 0.1022 0.924 0.000 0.032 0.000 0.968
#> GSM531650 1 0.0000 0.911 1.000 0.000 0.000 0.000
#> GSM531651 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM531652 1 0.2441 0.897 0.920 0.004 0.056 0.020
#> GSM531656 1 0.4105 0.796 0.812 0.000 0.156 0.032
#> GSM531659 2 0.3718 0.797 0.012 0.820 0.000 0.168
#> GSM531661 3 0.1821 0.933 0.012 0.008 0.948 0.032
#> GSM531662 3 0.3860 0.820 0.012 0.104 0.852 0.032
#> GSM531663 4 0.2867 0.918 0.012 0.104 0.000 0.884
#> GSM531664 1 0.0000 0.911 1.000 0.000 0.000 0.000
#> GSM531666 1 0.3489 0.845 0.880 0.068 0.020 0.032
#> GSM531667 3 0.1356 0.940 0.008 0.000 0.960 0.032
#> GSM531668 4 0.3625 0.865 0.012 0.160 0.000 0.828
#> GSM531669 1 0.0000 0.911 1.000 0.000 0.000 0.000
#> GSM531671 3 0.5694 0.739 0.100 0.108 0.760 0.032
#> GSM531672 4 0.2867 0.918 0.012 0.104 0.000 0.884
#> GSM531673 2 0.4360 0.784 0.012 0.816 0.140 0.032
#> GSM531676 2 0.0000 0.957 0.000 1.000 0.000 0.000
#> GSM531679 2 0.0000 0.957 0.000 1.000 0.000 0.000
#> GSM531681 2 0.3074 0.831 0.000 0.848 0.000 0.152
#> GSM531682 2 0.0000 0.957 0.000 1.000 0.000 0.000
#> GSM531683 2 0.0000 0.957 0.000 1.000 0.000 0.000
#> GSM531684 2 0.0000 0.957 0.000 1.000 0.000 0.000
#> GSM531685 2 0.3311 0.794 0.172 0.828 0.000 0.000
#> GSM531686 2 0.1716 0.915 0.000 0.936 0.000 0.064
#> GSM531687 2 0.0000 0.957 0.000 1.000 0.000 0.000
#> GSM531688 1 0.0921 0.900 0.972 0.028 0.000 0.000
#> GSM531690 2 0.2589 0.869 0.000 0.884 0.000 0.116
#> GSM531693 1 0.0469 0.906 0.988 0.012 0.000 0.000
#> GSM531695 1 0.3975 0.671 0.760 0.240 0.000 0.000
#> GSM531603 2 0.0000 0.957 0.000 1.000 0.000 0.000
#> GSM531609 4 0.0000 0.919 0.000 0.000 0.000 1.000
#> GSM531611 4 0.2867 0.918 0.012 0.104 0.000 0.884
#> GSM531621 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM531622 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM531628 1 0.0000 0.911 1.000 0.000 0.000 0.000
#> GSM531630 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM531633 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM531635 1 0.1211 0.912 0.960 0.000 0.040 0.000
#> GSM531640 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM531649 1 0.1022 0.914 0.968 0.000 0.032 0.000
#> GSM531653 1 0.1022 0.914 0.968 0.000 0.032 0.000
#> GSM531657 4 0.2867 0.918 0.012 0.104 0.000 0.884
#> GSM531665 2 0.3414 0.868 0.020 0.884 0.064 0.032
#> GSM531670 1 0.4105 0.796 0.812 0.000 0.156 0.032
#> GSM531674 1 0.0000 0.911 1.000 0.000 0.000 0.000
#> GSM531675 2 0.0000 0.957 0.000 1.000 0.000 0.000
#> GSM531677 2 0.0000 0.957 0.000 1.000 0.000 0.000
#> GSM531678 2 0.0000 0.957 0.000 1.000 0.000 0.000
#> GSM531680 2 0.0469 0.950 0.012 0.988 0.000 0.000
#> GSM531689 2 0.0000 0.957 0.000 1.000 0.000 0.000
#> GSM531691 2 0.0000 0.957 0.000 1.000 0.000 0.000
#> GSM531692 2 0.0000 0.957 0.000 1.000 0.000 0.000
#> GSM531694 2 0.0000 0.957 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM531602 2 0.0404 0.744 0.000 0.988 0.000 0.000 0.012
#> GSM531604 2 0.3561 0.420 0.000 0.740 0.000 0.000 0.260
#> GSM531606 2 0.3305 0.491 0.000 0.776 0.000 0.000 0.224
#> GSM531607 2 0.0000 0.753 0.000 1.000 0.000 0.000 0.000
#> GSM531608 3 0.1243 0.879 0.008 0.028 0.960 0.000 0.004
#> GSM531610 4 0.0000 0.781 0.000 0.000 0.000 1.000 0.000
#> GSM531612 4 0.0000 0.781 0.000 0.000 0.000 1.000 0.000
#> GSM531613 4 0.4571 0.741 0.000 0.188 0.000 0.736 0.076
#> GSM531614 4 0.0000 0.781 0.000 0.000 0.000 1.000 0.000
#> GSM531616 3 0.3563 0.815 0.012 0.000 0.780 0.000 0.208
#> GSM531618 4 0.6337 0.646 0.072 0.216 0.024 0.648 0.040
#> GSM531619 3 0.0000 0.890 0.000 0.000 1.000 0.000 0.000
#> GSM531620 3 0.1430 0.882 0.000 0.004 0.944 0.000 0.052
#> GSM531623 3 0.0000 0.890 0.000 0.000 1.000 0.000 0.000
#> GSM531625 3 0.2172 0.873 0.000 0.016 0.908 0.000 0.076
#> GSM531626 3 0.3388 0.822 0.008 0.000 0.792 0.000 0.200
#> GSM531632 1 0.0404 0.834 0.988 0.000 0.000 0.000 0.012
#> GSM531638 3 0.3388 0.822 0.008 0.000 0.792 0.000 0.200
#> GSM531639 1 0.6026 0.654 0.652 0.036 0.192 0.000 0.120
#> GSM531641 4 0.0000 0.781 0.000 0.000 0.000 1.000 0.000
#> GSM531642 1 0.5613 0.711 0.716 0.088 0.120 0.000 0.076
#> GSM531643 1 0.2962 0.816 0.868 0.048 0.000 0.000 0.084
#> GSM531644 1 0.2962 0.816 0.868 0.048 0.000 0.000 0.084
#> GSM531645 4 0.0000 0.781 0.000 0.000 0.000 1.000 0.000
#> GSM531646 1 0.0162 0.836 0.996 0.000 0.000 0.000 0.004
#> GSM531647 1 0.0404 0.834 0.988 0.000 0.000 0.000 0.012
#> GSM531648 4 0.1608 0.778 0.000 0.072 0.000 0.928 0.000
#> GSM531650 1 0.0404 0.834 0.988 0.000 0.000 0.000 0.012
#> GSM531651 3 0.0000 0.890 0.000 0.000 1.000 0.000 0.000
#> GSM531652 1 0.4800 0.762 0.776 0.052 0.000 0.088 0.084
#> GSM531656 1 0.4458 0.776 0.784 0.016 0.100 0.000 0.100
#> GSM531659 2 0.5171 0.203 0.000 0.648 0.000 0.276 0.076
#> GSM531661 3 0.3476 0.773 0.000 0.088 0.836 0.000 0.076
#> GSM531662 3 0.5787 0.417 0.000 0.204 0.616 0.000 0.180
#> GSM531663 4 0.4793 0.726 0.000 0.216 0.000 0.708 0.076
#> GSM531664 1 0.1792 0.814 0.916 0.000 0.000 0.000 0.084
#> GSM531666 1 0.5097 0.718 0.728 0.108 0.016 0.000 0.148
#> GSM531667 3 0.1653 0.874 0.028 0.024 0.944 0.000 0.004
#> GSM531668 4 0.4959 0.692 0.000 0.240 0.000 0.684 0.076
#> GSM531669 1 0.1792 0.814 0.916 0.000 0.000 0.000 0.084
#> GSM531671 3 0.7363 0.141 0.048 0.216 0.468 0.000 0.268
#> GSM531672 4 0.4793 0.726 0.000 0.216 0.000 0.708 0.076
#> GSM531673 2 0.5475 0.107 0.000 0.604 0.088 0.000 0.308
#> GSM531676 5 0.4074 0.623 0.000 0.364 0.000 0.000 0.636
#> GSM531679 2 0.0000 0.753 0.000 1.000 0.000 0.000 0.000
#> GSM531681 2 0.1043 0.719 0.000 0.960 0.000 0.040 0.000
#> GSM531682 2 0.0404 0.748 0.000 0.988 0.000 0.000 0.012
#> GSM531683 2 0.0000 0.753 0.000 1.000 0.000 0.000 0.000
#> GSM531684 2 0.3491 0.479 0.000 0.768 0.004 0.000 0.228
#> GSM531685 5 0.5002 0.631 0.052 0.312 0.000 0.000 0.636
#> GSM531686 2 0.0162 0.752 0.000 0.996 0.000 0.004 0.000
#> GSM531687 2 0.4305 -0.475 0.000 0.512 0.000 0.000 0.488
#> GSM531688 1 0.6709 -0.339 0.400 0.248 0.000 0.000 0.352
#> GSM531690 2 0.0162 0.752 0.000 0.996 0.000 0.004 0.000
#> GSM531693 1 0.4066 0.573 0.672 0.004 0.000 0.000 0.324
#> GSM531695 5 0.6745 0.437 0.280 0.312 0.000 0.000 0.408
#> GSM531603 2 0.1197 0.716 0.000 0.952 0.000 0.000 0.048
#> GSM531609 4 0.0000 0.781 0.000 0.000 0.000 1.000 0.000
#> GSM531611 4 0.4763 0.729 0.000 0.212 0.000 0.712 0.076
#> GSM531621 3 0.0000 0.890 0.000 0.000 1.000 0.000 0.000
#> GSM531622 3 0.0000 0.890 0.000 0.000 1.000 0.000 0.000
#> GSM531628 1 0.0404 0.834 0.988 0.000 0.000 0.000 0.012
#> GSM531630 3 0.0000 0.890 0.000 0.000 1.000 0.000 0.000
#> GSM531633 3 0.0000 0.890 0.000 0.000 1.000 0.000 0.000
#> GSM531635 1 0.2967 0.820 0.868 0.016 0.012 0.000 0.104
#> GSM531640 3 0.0404 0.888 0.000 0.012 0.988 0.000 0.000
#> GSM531649 1 0.1717 0.835 0.936 0.008 0.004 0.000 0.052
#> GSM531653 1 0.0404 0.834 0.988 0.000 0.000 0.000 0.012
#> GSM531657 4 0.4793 0.726 0.000 0.216 0.000 0.708 0.076
#> GSM531665 5 0.5343 0.322 0.016 0.468 0.024 0.000 0.492
#> GSM531670 1 0.4834 0.773 0.752 0.016 0.100 0.000 0.132
#> GSM531674 1 0.1792 0.814 0.916 0.000 0.000 0.000 0.084
#> GSM531675 2 0.0000 0.753 0.000 1.000 0.000 0.000 0.000
#> GSM531677 2 0.0000 0.753 0.000 1.000 0.000 0.000 0.000
#> GSM531678 2 0.0000 0.753 0.000 1.000 0.000 0.000 0.000
#> GSM531680 2 0.4210 -0.317 0.000 0.588 0.000 0.000 0.412
#> GSM531689 2 0.2074 0.667 0.000 0.896 0.000 0.000 0.104
#> GSM531691 2 0.3684 0.372 0.000 0.720 0.000 0.000 0.280
#> GSM531692 5 0.4300 0.471 0.000 0.476 0.000 0.000 0.524
#> GSM531694 2 0.0404 0.744 0.000 0.988 0.000 0.000 0.012
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM531602 2 0.0458 0.862 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM531604 5 0.5630 0.658 0.000 0.232 0.000 0.000 0.540 0.228
#> GSM531606 5 0.4709 0.563 0.000 0.412 0.000 0.000 0.540 0.048
#> GSM531607 2 0.0146 0.867 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM531608 3 0.0260 0.939 0.000 0.008 0.992 0.000 0.000 0.000
#> GSM531610 4 0.0000 0.885 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531612 4 0.0000 0.885 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531613 4 0.0972 0.883 0.000 0.008 0.000 0.964 0.028 0.000
#> GSM531614 4 0.0000 0.885 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531616 3 0.2838 0.804 0.000 0.000 0.808 0.000 0.188 0.004
#> GSM531618 4 0.5034 0.693 0.028 0.016 0.020 0.652 0.280 0.004
#> GSM531619 3 0.0000 0.941 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531620 3 0.1814 0.883 0.000 0.000 0.900 0.000 0.100 0.000
#> GSM531623 3 0.0000 0.941 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531625 3 0.1075 0.923 0.000 0.000 0.952 0.000 0.048 0.000
#> GSM531626 3 0.2595 0.834 0.000 0.000 0.836 0.000 0.160 0.004
#> GSM531632 1 0.0291 0.805 0.992 0.000 0.000 0.000 0.004 0.004
#> GSM531638 3 0.2558 0.839 0.000 0.000 0.840 0.000 0.156 0.004
#> GSM531639 1 0.5437 0.672 0.568 0.000 0.136 0.000 0.292 0.004
#> GSM531641 4 0.0000 0.885 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531642 1 0.4980 0.716 0.588 0.012 0.044 0.000 0.352 0.004
#> GSM531643 1 0.3519 0.787 0.752 0.008 0.000 0.000 0.232 0.008
#> GSM531644 1 0.3736 0.774 0.716 0.008 0.000 0.000 0.268 0.008
#> GSM531645 4 0.0000 0.885 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531646 1 0.0547 0.810 0.980 0.000 0.000 0.000 0.020 0.000
#> GSM531647 1 0.0000 0.807 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM531648 4 0.0909 0.884 0.000 0.012 0.000 0.968 0.020 0.000
#> GSM531650 1 0.0000 0.807 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM531651 3 0.0000 0.941 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531652 1 0.5514 0.707 0.596 0.012 0.000 0.100 0.284 0.008
#> GSM531656 1 0.4751 0.733 0.624 0.000 0.076 0.000 0.300 0.000
#> GSM531659 4 0.5567 0.619 0.000 0.176 0.000 0.584 0.232 0.008
#> GSM531661 3 0.1391 0.908 0.000 0.016 0.944 0.000 0.040 0.000
#> GSM531662 5 0.4485 0.433 0.000 0.024 0.340 0.000 0.624 0.012
#> GSM531663 4 0.3088 0.844 0.000 0.020 0.000 0.808 0.172 0.000
#> GSM531664 1 0.0692 0.799 0.976 0.000 0.000 0.000 0.004 0.020
#> GSM531666 1 0.4447 0.723 0.600 0.020 0.004 0.000 0.372 0.004
#> GSM531667 3 0.0551 0.937 0.004 0.008 0.984 0.000 0.004 0.000
#> GSM531668 4 0.3837 0.811 0.000 0.052 0.000 0.752 0.196 0.000
#> GSM531669 1 0.0692 0.799 0.976 0.000 0.000 0.000 0.004 0.020
#> GSM531671 5 0.6193 0.461 0.004 0.044 0.200 0.000 0.572 0.180
#> GSM531672 4 0.3248 0.842 0.000 0.032 0.000 0.804 0.164 0.000
#> GSM531673 5 0.5540 0.676 0.000 0.136 0.044 0.000 0.648 0.172
#> GSM531676 6 0.1588 0.772 0.000 0.072 0.000 0.000 0.004 0.924
#> GSM531679 2 0.2562 0.834 0.000 0.828 0.000 0.000 0.000 0.172
#> GSM531681 2 0.2740 0.871 0.000 0.852 0.000 0.000 0.028 0.120
#> GSM531682 2 0.2234 0.875 0.000 0.872 0.000 0.000 0.004 0.124
#> GSM531683 2 0.0000 0.866 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531684 5 0.4941 0.611 0.000 0.376 0.000 0.000 0.552 0.072
#> GSM531685 6 0.2362 0.691 0.000 0.136 0.000 0.000 0.004 0.860
#> GSM531686 2 0.2740 0.871 0.000 0.852 0.000 0.000 0.028 0.120
#> GSM531687 6 0.1387 0.777 0.000 0.068 0.000 0.000 0.000 0.932
#> GSM531688 6 0.3512 0.717 0.196 0.032 0.000 0.000 0.000 0.772
#> GSM531690 2 0.2740 0.871 0.000 0.852 0.000 0.000 0.028 0.120
#> GSM531693 6 0.3699 0.558 0.336 0.000 0.000 0.000 0.004 0.660
#> GSM531695 6 0.2747 0.779 0.096 0.044 0.000 0.000 0.000 0.860
#> GSM531603 2 0.1524 0.825 0.000 0.932 0.000 0.000 0.060 0.008
#> GSM531609 4 0.0000 0.885 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531611 4 0.2133 0.875 0.020 0.016 0.000 0.912 0.052 0.000
#> GSM531621 3 0.0000 0.941 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531622 3 0.0000 0.941 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531628 1 0.0000 0.807 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM531630 3 0.0000 0.941 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531633 3 0.0000 0.941 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531635 1 0.3314 0.788 0.764 0.000 0.012 0.000 0.224 0.000
#> GSM531640 3 0.0260 0.939 0.000 0.008 0.992 0.000 0.000 0.000
#> GSM531649 1 0.2653 0.798 0.844 0.000 0.012 0.000 0.144 0.000
#> GSM531653 1 0.0000 0.807 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM531657 4 0.3122 0.843 0.000 0.020 0.000 0.804 0.176 0.000
#> GSM531665 5 0.4075 0.594 0.008 0.032 0.012 0.000 0.756 0.192
#> GSM531670 1 0.4703 0.732 0.620 0.000 0.068 0.000 0.312 0.000
#> GSM531674 1 0.0692 0.799 0.976 0.000 0.000 0.000 0.004 0.020
#> GSM531675 2 0.2558 0.876 0.000 0.868 0.000 0.000 0.028 0.104
#> GSM531677 2 0.2826 0.866 0.000 0.844 0.000 0.000 0.028 0.128
#> GSM531678 2 0.0000 0.866 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531680 6 0.1957 0.766 0.000 0.112 0.000 0.000 0.000 0.888
#> GSM531689 2 0.3490 0.545 0.000 0.724 0.000 0.000 0.008 0.268
#> GSM531691 5 0.5578 0.640 0.000 0.184 0.000 0.000 0.540 0.276
#> GSM531692 5 0.5509 0.623 0.000 0.160 0.000 0.000 0.540 0.300
#> GSM531694 2 0.0458 0.862 0.000 0.984 0.000 0.000 0.000 0.016
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> CV:mclust 80 0.847 2
#> CV:mclust 53 1.000 3
#> CV:mclust 79 0.700 4
#> CV:mclust 66 0.655 5
#> CV:mclust 78 0.676 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "NMF"]
# you can also extract it by
# res = res_list["CV:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 80 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 0.873 0.935 0.970 0.5046 0.494 0.494
#> 3 3 0.521 0.498 0.739 0.3091 0.722 0.497
#> 4 4 0.850 0.869 0.946 0.1423 0.811 0.508
#> 5 5 0.856 0.835 0.918 0.0576 0.912 0.670
#> 6 6 0.747 0.618 0.795 0.0390 0.972 0.867
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
#> GSM531602 2 0.0000 0.949 0.000 1.000
#> GSM531604 2 0.0000 0.949 0.000 1.000
#> GSM531606 2 0.0000 0.949 0.000 1.000
#> GSM531607 2 0.0000 0.949 0.000 1.000
#> GSM531608 1 0.8327 0.630 0.736 0.264
#> GSM531610 2 0.0000 0.949 0.000 1.000
#> GSM531612 2 0.0000 0.949 0.000 1.000
#> GSM531613 2 0.0000 0.949 0.000 1.000
#> GSM531614 2 0.0000 0.949 0.000 1.000
#> GSM531616 1 0.0000 0.989 1.000 0.000
#> GSM531618 2 0.9286 0.494 0.344 0.656
#> GSM531619 1 0.0000 0.989 1.000 0.000
#> GSM531620 1 0.0000 0.989 1.000 0.000
#> GSM531623 1 0.0000 0.989 1.000 0.000
#> GSM531625 1 0.0000 0.989 1.000 0.000
#> GSM531626 1 0.0000 0.989 1.000 0.000
#> GSM531632 1 0.0000 0.989 1.000 0.000
#> GSM531638 1 0.0000 0.989 1.000 0.000
#> GSM531639 1 0.0000 0.989 1.000 0.000
#> GSM531641 2 0.0000 0.949 0.000 1.000
#> GSM531642 1 0.0000 0.989 1.000 0.000
#> GSM531643 1 0.0000 0.989 1.000 0.000
#> GSM531644 1 0.0000 0.989 1.000 0.000
#> GSM531645 2 0.0000 0.949 0.000 1.000
#> GSM531646 1 0.0000 0.989 1.000 0.000
#> GSM531647 1 0.0000 0.989 1.000 0.000
#> GSM531648 2 0.0000 0.949 0.000 1.000
#> GSM531650 1 0.0000 0.989 1.000 0.000
#> GSM531651 1 0.0000 0.989 1.000 0.000
#> GSM531652 1 0.0000 0.989 1.000 0.000
#> GSM531656 1 0.0000 0.989 1.000 0.000
#> GSM531659 2 0.0000 0.949 0.000 1.000
#> GSM531661 1 0.0000 0.989 1.000 0.000
#> GSM531662 1 0.0000 0.989 1.000 0.000
#> GSM531663 2 0.0000 0.949 0.000 1.000
#> GSM531664 1 0.0000 0.989 1.000 0.000
#> GSM531666 2 0.9248 0.545 0.340 0.660
#> GSM531667 1 0.0376 0.985 0.996 0.004
#> GSM531668 2 0.0000 0.949 0.000 1.000
#> GSM531669 1 0.0000 0.989 1.000 0.000
#> GSM531671 1 0.0000 0.989 1.000 0.000
#> GSM531672 2 0.0000 0.949 0.000 1.000
#> GSM531673 2 0.9358 0.520 0.352 0.648
#> GSM531676 2 0.8081 0.699 0.248 0.752
#> GSM531679 2 0.0000 0.949 0.000 1.000
#> GSM531681 2 0.0000 0.949 0.000 1.000
#> GSM531682 2 0.0000 0.949 0.000 1.000
#> GSM531683 2 0.0000 0.949 0.000 1.000
#> GSM531684 2 0.0000 0.949 0.000 1.000
#> GSM531685 1 0.0376 0.985 0.996 0.004
#> GSM531686 2 0.0000 0.949 0.000 1.000
#> GSM531687 2 0.5946 0.828 0.144 0.856
#> GSM531688 1 0.5629 0.833 0.868 0.132
#> GSM531690 2 0.0000 0.949 0.000 1.000
#> GSM531693 1 0.0000 0.989 1.000 0.000
#> GSM531695 2 0.5519 0.844 0.128 0.872
#> GSM531603 2 0.0000 0.949 0.000 1.000
#> GSM531609 2 0.0000 0.949 0.000 1.000
#> GSM531611 2 0.0000 0.949 0.000 1.000
#> GSM531621 1 0.0000 0.989 1.000 0.000
#> GSM531622 1 0.0000 0.989 1.000 0.000
#> GSM531628 1 0.0000 0.989 1.000 0.000
#> GSM531630 1 0.0000 0.989 1.000 0.000
#> GSM531633 1 0.0000 0.989 1.000 0.000
#> GSM531635 1 0.0000 0.989 1.000 0.000
#> GSM531640 1 0.0000 0.989 1.000 0.000
#> GSM531649 1 0.0000 0.989 1.000 0.000
#> GSM531653 1 0.0000 0.989 1.000 0.000
#> GSM531657 2 0.0000 0.949 0.000 1.000
#> GSM531665 2 0.9000 0.590 0.316 0.684
#> GSM531670 1 0.0000 0.989 1.000 0.000
#> GSM531674 1 0.0000 0.989 1.000 0.000
#> GSM531675 2 0.0000 0.949 0.000 1.000
#> GSM531677 2 0.0000 0.949 0.000 1.000
#> GSM531678 2 0.0000 0.949 0.000 1.000
#> GSM531680 2 0.2948 0.912 0.052 0.948
#> GSM531689 2 0.0000 0.949 0.000 1.000
#> GSM531691 2 0.2043 0.927 0.032 0.968
#> GSM531692 1 0.0672 0.981 0.992 0.008
#> GSM531694 2 0.0000 0.949 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM531602 2 0.0000 0.7839 0.000 1.000 0.000
#> GSM531604 2 0.3619 0.6772 0.000 0.864 0.136
#> GSM531606 2 0.0000 0.7839 0.000 1.000 0.000
#> GSM531607 2 0.0000 0.7839 0.000 1.000 0.000
#> GSM531608 3 0.3325 0.6383 0.076 0.020 0.904
#> GSM531610 1 0.6305 0.2722 0.516 0.484 0.000
#> GSM531612 1 0.6267 0.3242 0.548 0.452 0.000
#> GSM531613 1 0.6308 0.2541 0.508 0.492 0.000
#> GSM531614 1 0.6291 0.3035 0.532 0.468 0.000
#> GSM531616 3 0.4796 0.6415 0.220 0.000 0.780
#> GSM531618 1 0.7170 0.3829 0.612 0.352 0.036
#> GSM531619 3 0.0000 0.7074 0.000 0.000 1.000
#> GSM531620 3 0.0000 0.7074 0.000 0.000 1.000
#> GSM531623 3 0.0000 0.7074 0.000 0.000 1.000
#> GSM531625 3 0.0000 0.7074 0.000 0.000 1.000
#> GSM531626 3 0.0000 0.7074 0.000 0.000 1.000
#> GSM531632 3 0.6295 0.5010 0.472 0.000 0.528
#> GSM531638 3 0.0000 0.7074 0.000 0.000 1.000
#> GSM531639 3 0.3038 0.6782 0.104 0.000 0.896
#> GSM531641 1 0.6295 0.2969 0.528 0.472 0.000
#> GSM531642 1 0.4555 0.2494 0.800 0.000 0.200
#> GSM531643 1 0.4842 0.1464 0.776 0.000 0.224
#> GSM531644 1 0.2448 0.3688 0.924 0.000 0.076
#> GSM531645 1 0.6192 0.3525 0.580 0.420 0.000
#> GSM531646 3 0.6299 0.4973 0.476 0.000 0.524
#> GSM531647 3 0.6307 0.4835 0.488 0.000 0.512
#> GSM531648 1 0.5859 0.3992 0.656 0.344 0.000
#> GSM531650 1 0.5327 0.0249 0.728 0.000 0.272
#> GSM531651 3 0.0000 0.7074 0.000 0.000 1.000
#> GSM531652 1 0.0000 0.4208 1.000 0.000 0.000
#> GSM531656 3 0.6299 0.4856 0.476 0.000 0.524
#> GSM531659 2 0.2625 0.7224 0.084 0.916 0.000
#> GSM531661 3 0.5497 0.3769 0.000 0.292 0.708
#> GSM531662 3 0.5988 0.2059 0.000 0.368 0.632
#> GSM531663 2 0.5397 0.3941 0.280 0.720 0.000
#> GSM531664 1 0.4555 0.1959 0.800 0.000 0.200
#> GSM531666 1 0.2711 0.3571 0.912 0.000 0.088
#> GSM531667 3 0.0592 0.7003 0.012 0.000 0.988
#> GSM531668 2 0.1411 0.7612 0.036 0.964 0.000
#> GSM531669 3 0.6307 0.4835 0.488 0.000 0.512
#> GSM531671 3 0.5122 0.6463 0.200 0.012 0.788
#> GSM531672 1 0.6308 0.2541 0.508 0.492 0.000
#> GSM531673 3 0.6291 -0.0856 0.000 0.468 0.532
#> GSM531676 2 0.5178 0.5083 0.256 0.744 0.000
#> GSM531679 2 0.0000 0.7839 0.000 1.000 0.000
#> GSM531681 2 0.2261 0.7349 0.068 0.932 0.000
#> GSM531682 2 0.0000 0.7839 0.000 1.000 0.000
#> GSM531683 2 0.0000 0.7839 0.000 1.000 0.000
#> GSM531684 2 0.6252 0.2450 0.000 0.556 0.444
#> GSM531685 2 0.9409 0.0597 0.360 0.460 0.180
#> GSM531686 2 0.5363 0.3887 0.276 0.724 0.000
#> GSM531687 2 0.4002 0.6429 0.160 0.840 0.000
#> GSM531688 1 0.9441 -0.2372 0.484 0.200 0.316
#> GSM531690 2 0.2066 0.7409 0.060 0.940 0.000
#> GSM531693 3 0.6299 0.4973 0.476 0.000 0.524
#> GSM531695 1 0.5968 0.1347 0.636 0.364 0.000
#> GSM531603 2 0.0000 0.7839 0.000 1.000 0.000
#> GSM531609 1 0.6280 0.3146 0.540 0.460 0.000
#> GSM531611 1 0.6295 0.2969 0.528 0.472 0.000
#> GSM531621 3 0.0000 0.7074 0.000 0.000 1.000
#> GSM531622 3 0.0237 0.7052 0.004 0.000 0.996
#> GSM531628 1 0.5760 -0.1333 0.672 0.000 0.328
#> GSM531630 3 0.0000 0.7074 0.000 0.000 1.000
#> GSM531633 3 0.0000 0.7074 0.000 0.000 1.000
#> GSM531635 3 0.6295 0.5010 0.472 0.000 0.528
#> GSM531640 3 0.2356 0.6516 0.072 0.000 0.928
#> GSM531649 3 0.6291 0.5039 0.468 0.000 0.532
#> GSM531653 3 0.6307 0.4835 0.488 0.000 0.512
#> GSM531657 2 0.6299 -0.2290 0.476 0.524 0.000
#> GSM531665 2 0.5787 0.6037 0.136 0.796 0.068
#> GSM531670 3 0.5988 0.5561 0.368 0.000 0.632
#> GSM531674 3 0.6307 0.4835 0.488 0.000 0.512
#> GSM531675 2 0.0000 0.7839 0.000 1.000 0.000
#> GSM531677 2 0.0000 0.7839 0.000 1.000 0.000
#> GSM531678 2 0.0000 0.7839 0.000 1.000 0.000
#> GSM531680 2 0.5098 0.5436 0.248 0.752 0.000
#> GSM531689 2 0.0000 0.7839 0.000 1.000 0.000
#> GSM531691 2 0.1411 0.7643 0.000 0.964 0.036
#> GSM531692 2 0.9029 0.2031 0.144 0.504 0.352
#> GSM531694 2 0.0000 0.7839 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM531602 2 0.0000 0.904 0.000 1.000 0.000 0.000
#> GSM531604 2 0.0000 0.904 0.000 1.000 0.000 0.000
#> GSM531606 2 0.0000 0.904 0.000 1.000 0.000 0.000
#> GSM531607 2 0.0000 0.904 0.000 1.000 0.000 0.000
#> GSM531608 3 0.0000 0.970 0.000 0.000 1.000 0.000
#> GSM531610 4 0.0000 0.947 0.000 0.000 0.000 1.000
#> GSM531612 4 0.0000 0.947 0.000 0.000 0.000 1.000
#> GSM531613 4 0.0000 0.947 0.000 0.000 0.000 1.000
#> GSM531614 4 0.0000 0.947 0.000 0.000 0.000 1.000
#> GSM531616 3 0.2408 0.862 0.104 0.000 0.896 0.000
#> GSM531618 4 0.0000 0.947 0.000 0.000 0.000 1.000
#> GSM531619 3 0.0000 0.970 0.000 0.000 1.000 0.000
#> GSM531620 3 0.0000 0.970 0.000 0.000 1.000 0.000
#> GSM531623 3 0.0000 0.970 0.000 0.000 1.000 0.000
#> GSM531625 3 0.0000 0.970 0.000 0.000 1.000 0.000
#> GSM531626 3 0.0000 0.970 0.000 0.000 1.000 0.000
#> GSM531632 1 0.0000 0.947 1.000 0.000 0.000 0.000
#> GSM531638 3 0.0000 0.970 0.000 0.000 1.000 0.000
#> GSM531639 3 0.0000 0.970 0.000 0.000 1.000 0.000
#> GSM531641 4 0.0000 0.947 0.000 0.000 0.000 1.000
#> GSM531642 4 0.1824 0.891 0.004 0.000 0.060 0.936
#> GSM531643 1 0.0000 0.947 1.000 0.000 0.000 0.000
#> GSM531644 1 0.0707 0.931 0.980 0.000 0.000 0.020
#> GSM531645 4 0.0000 0.947 0.000 0.000 0.000 1.000
#> GSM531646 1 0.0000 0.947 1.000 0.000 0.000 0.000
#> GSM531647 1 0.0000 0.947 1.000 0.000 0.000 0.000
#> GSM531648 4 0.0000 0.947 0.000 0.000 0.000 1.000
#> GSM531650 1 0.0000 0.947 1.000 0.000 0.000 0.000
#> GSM531651 3 0.0000 0.970 0.000 0.000 1.000 0.000
#> GSM531652 4 0.0000 0.947 0.000 0.000 0.000 1.000
#> GSM531656 1 0.2973 0.815 0.856 0.000 0.144 0.000
#> GSM531659 2 0.4522 0.560 0.000 0.680 0.000 0.320
#> GSM531661 3 0.0000 0.970 0.000 0.000 1.000 0.000
#> GSM531662 3 0.0000 0.970 0.000 0.000 1.000 0.000
#> GSM531663 4 0.0000 0.947 0.000 0.000 0.000 1.000
#> GSM531664 1 0.0000 0.947 1.000 0.000 0.000 0.000
#> GSM531666 4 0.4866 0.318 0.404 0.000 0.000 0.596
#> GSM531667 3 0.0000 0.970 0.000 0.000 1.000 0.000
#> GSM531668 2 0.4948 0.220 0.000 0.560 0.000 0.440
#> GSM531669 1 0.0000 0.947 1.000 0.000 0.000 0.000
#> GSM531671 3 0.6042 0.316 0.052 0.368 0.580 0.000
#> GSM531672 4 0.0000 0.947 0.000 0.000 0.000 1.000
#> GSM531673 2 0.4989 0.134 0.000 0.528 0.472 0.000
#> GSM531676 2 0.0592 0.896 0.016 0.984 0.000 0.000
#> GSM531679 2 0.0000 0.904 0.000 1.000 0.000 0.000
#> GSM531681 2 0.4585 0.525 0.000 0.668 0.000 0.332
#> GSM531682 2 0.0000 0.904 0.000 1.000 0.000 0.000
#> GSM531683 2 0.0000 0.904 0.000 1.000 0.000 0.000
#> GSM531684 2 0.2704 0.811 0.000 0.876 0.124 0.000
#> GSM531685 1 0.4776 0.358 0.624 0.376 0.000 0.000
#> GSM531686 4 0.4500 0.461 0.000 0.316 0.000 0.684
#> GSM531687 2 0.0188 0.902 0.004 0.996 0.000 0.000
#> GSM531688 1 0.0000 0.947 1.000 0.000 0.000 0.000
#> GSM531690 2 0.3400 0.746 0.000 0.820 0.000 0.180
#> GSM531693 1 0.0000 0.947 1.000 0.000 0.000 0.000
#> GSM531695 1 0.2469 0.852 0.892 0.108 0.000 0.000
#> GSM531603 2 0.0000 0.904 0.000 1.000 0.000 0.000
#> GSM531609 4 0.0000 0.947 0.000 0.000 0.000 1.000
#> GSM531611 4 0.0000 0.947 0.000 0.000 0.000 1.000
#> GSM531621 3 0.0000 0.970 0.000 0.000 1.000 0.000
#> GSM531622 3 0.0000 0.970 0.000 0.000 1.000 0.000
#> GSM531628 1 0.0000 0.947 1.000 0.000 0.000 0.000
#> GSM531630 3 0.0000 0.970 0.000 0.000 1.000 0.000
#> GSM531633 3 0.0000 0.970 0.000 0.000 1.000 0.000
#> GSM531635 1 0.0000 0.947 1.000 0.000 0.000 0.000
#> GSM531640 3 0.0000 0.970 0.000 0.000 1.000 0.000
#> GSM531649 1 0.0000 0.947 1.000 0.000 0.000 0.000
#> GSM531653 1 0.0000 0.947 1.000 0.000 0.000 0.000
#> GSM531657 4 0.0000 0.947 0.000 0.000 0.000 1.000
#> GSM531665 2 0.2704 0.813 0.124 0.876 0.000 0.000
#> GSM531670 1 0.3610 0.742 0.800 0.000 0.200 0.000
#> GSM531674 1 0.0000 0.947 1.000 0.000 0.000 0.000
#> GSM531675 2 0.0000 0.904 0.000 1.000 0.000 0.000
#> GSM531677 2 0.0000 0.904 0.000 1.000 0.000 0.000
#> GSM531678 2 0.0000 0.904 0.000 1.000 0.000 0.000
#> GSM531680 2 0.3123 0.775 0.156 0.844 0.000 0.000
#> GSM531689 2 0.0000 0.904 0.000 1.000 0.000 0.000
#> GSM531691 2 0.0000 0.904 0.000 1.000 0.000 0.000
#> GSM531692 2 0.0000 0.904 0.000 1.000 0.000 0.000
#> GSM531694 2 0.0000 0.904 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM531602 2 0.1732 0.8767 0.000 0.920 0.000 0.000 0.080
#> GSM531604 2 0.0000 0.9013 0.000 1.000 0.000 0.000 0.000
#> GSM531606 2 0.0290 0.9022 0.000 0.992 0.000 0.000 0.008
#> GSM531607 2 0.2127 0.8537 0.000 0.892 0.000 0.000 0.108
#> GSM531608 3 0.0510 0.9070 0.000 0.000 0.984 0.000 0.016
#> GSM531610 4 0.0000 0.9924 0.000 0.000 0.000 1.000 0.000
#> GSM531612 4 0.0000 0.9924 0.000 0.000 0.000 1.000 0.000
#> GSM531613 4 0.0000 0.9924 0.000 0.000 0.000 1.000 0.000
#> GSM531614 4 0.0000 0.9924 0.000 0.000 0.000 1.000 0.000
#> GSM531616 3 0.4040 0.6036 0.276 0.000 0.712 0.000 0.012
#> GSM531618 5 0.1117 0.8288 0.000 0.000 0.016 0.020 0.964
#> GSM531619 3 0.0162 0.9080 0.000 0.000 0.996 0.000 0.004
#> GSM531620 3 0.0671 0.9062 0.004 0.000 0.980 0.000 0.016
#> GSM531623 3 0.0162 0.9080 0.000 0.000 0.996 0.000 0.004
#> GSM531625 3 0.0955 0.9008 0.004 0.000 0.968 0.000 0.028
#> GSM531626 3 0.1082 0.8991 0.008 0.000 0.964 0.000 0.028
#> GSM531632 1 0.0404 0.9139 0.988 0.000 0.000 0.000 0.012
#> GSM531638 3 0.0290 0.9079 0.000 0.000 0.992 0.000 0.008
#> GSM531639 3 0.0609 0.9030 0.000 0.000 0.980 0.000 0.020
#> GSM531641 4 0.0000 0.9924 0.000 0.000 0.000 1.000 0.000
#> GSM531642 5 0.2387 0.8190 0.040 0.000 0.004 0.048 0.908
#> GSM531643 1 0.1121 0.9020 0.956 0.000 0.000 0.000 0.044
#> GSM531644 5 0.3707 0.5548 0.284 0.000 0.000 0.000 0.716
#> GSM531645 4 0.0000 0.9924 0.000 0.000 0.000 1.000 0.000
#> GSM531646 1 0.0404 0.9139 0.988 0.000 0.000 0.000 0.012
#> GSM531647 1 0.0000 0.9155 1.000 0.000 0.000 0.000 0.000
#> GSM531648 5 0.1571 0.8206 0.000 0.000 0.004 0.060 0.936
#> GSM531650 1 0.0963 0.9056 0.964 0.000 0.000 0.000 0.036
#> GSM531651 3 0.0162 0.9080 0.000 0.000 0.996 0.000 0.004
#> GSM531652 5 0.2036 0.8196 0.056 0.000 0.000 0.024 0.920
#> GSM531656 1 0.3255 0.8208 0.848 0.000 0.100 0.000 0.052
#> GSM531659 5 0.4886 0.1168 0.000 0.448 0.000 0.024 0.528
#> GSM531661 3 0.0162 0.9080 0.000 0.000 0.996 0.000 0.004
#> GSM531662 3 0.0955 0.9007 0.000 0.004 0.968 0.000 0.028
#> GSM531663 4 0.0000 0.9924 0.000 0.000 0.000 1.000 0.000
#> GSM531664 1 0.1478 0.8881 0.936 0.000 0.000 0.000 0.064
#> GSM531666 5 0.0794 0.8296 0.028 0.000 0.000 0.000 0.972
#> GSM531667 3 0.2690 0.7662 0.000 0.000 0.844 0.000 0.156
#> GSM531668 5 0.2833 0.7993 0.000 0.120 0.004 0.012 0.864
#> GSM531669 1 0.0162 0.9155 0.996 0.000 0.000 0.000 0.004
#> GSM531671 3 0.6813 0.2799 0.212 0.300 0.476 0.000 0.012
#> GSM531672 5 0.1369 0.8303 0.000 0.008 0.008 0.028 0.956
#> GSM531673 3 0.4905 -0.0237 0.000 0.476 0.500 0.000 0.024
#> GSM531676 2 0.1341 0.8801 0.056 0.944 0.000 0.000 0.000
#> GSM531679 2 0.0000 0.9013 0.000 1.000 0.000 0.000 0.000
#> GSM531681 4 0.1121 0.9465 0.000 0.044 0.000 0.956 0.000
#> GSM531682 2 0.0703 0.9005 0.000 0.976 0.000 0.000 0.024
#> GSM531683 2 0.0404 0.9024 0.000 0.988 0.000 0.000 0.012
#> GSM531684 2 0.3837 0.5526 0.000 0.692 0.308 0.000 0.000
#> GSM531685 1 0.4169 0.6334 0.724 0.256 0.004 0.000 0.016
#> GSM531686 4 0.0510 0.9775 0.000 0.016 0.000 0.984 0.000
#> GSM531687 2 0.1211 0.8983 0.024 0.960 0.000 0.000 0.016
#> GSM531688 1 0.0162 0.9154 0.996 0.000 0.000 0.000 0.004
#> GSM531690 5 0.3266 0.7361 0.000 0.200 0.000 0.004 0.796
#> GSM531693 1 0.0162 0.9158 0.996 0.000 0.000 0.000 0.004
#> GSM531695 1 0.5048 0.3128 0.580 0.040 0.000 0.000 0.380
#> GSM531603 5 0.3274 0.7119 0.000 0.220 0.000 0.000 0.780
#> GSM531609 4 0.0000 0.9924 0.000 0.000 0.000 1.000 0.000
#> GSM531611 4 0.0000 0.9924 0.000 0.000 0.000 1.000 0.000
#> GSM531621 3 0.0609 0.9046 0.000 0.000 0.980 0.000 0.020
#> GSM531622 3 0.0162 0.9080 0.000 0.000 0.996 0.000 0.004
#> GSM531628 1 0.0609 0.9119 0.980 0.000 0.000 0.000 0.020
#> GSM531630 3 0.0162 0.9080 0.000 0.000 0.996 0.000 0.004
#> GSM531633 3 0.0404 0.9076 0.000 0.000 0.988 0.000 0.012
#> GSM531635 1 0.0609 0.9116 0.980 0.000 0.000 0.000 0.020
#> GSM531640 3 0.0162 0.9080 0.000 0.000 0.996 0.000 0.004
#> GSM531649 1 0.0865 0.9084 0.972 0.000 0.004 0.000 0.024
#> GSM531653 1 0.0404 0.9152 0.988 0.000 0.000 0.000 0.012
#> GSM531657 5 0.3430 0.6792 0.000 0.000 0.004 0.220 0.776
#> GSM531665 2 0.1877 0.8747 0.064 0.924 0.000 0.000 0.012
#> GSM531670 1 0.3877 0.6971 0.764 0.000 0.212 0.000 0.024
#> GSM531674 1 0.0162 0.9154 0.996 0.000 0.000 0.000 0.004
#> GSM531675 2 0.3336 0.7066 0.000 0.772 0.000 0.000 0.228
#> GSM531677 2 0.0794 0.8998 0.000 0.972 0.000 0.000 0.028
#> GSM531678 2 0.1410 0.8748 0.000 0.940 0.000 0.060 0.000
#> GSM531680 2 0.4668 0.5974 0.272 0.684 0.000 0.000 0.044
#> GSM531689 2 0.0000 0.9013 0.000 1.000 0.000 0.000 0.000
#> GSM531691 2 0.0798 0.8976 0.000 0.976 0.008 0.000 0.016
#> GSM531692 2 0.2568 0.8376 0.092 0.888 0.004 0.000 0.016
#> GSM531694 2 0.1544 0.8834 0.000 0.932 0.000 0.000 0.068
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM531602 2 0.5002 0.4999 0.000 0.556 0.000 0.000 0.364 0.080
#> GSM531604 2 0.0865 0.6683 0.000 0.964 0.000 0.000 0.036 0.000
#> GSM531606 2 0.3575 0.6042 0.000 0.708 0.000 0.000 0.284 0.008
#> GSM531607 2 0.4974 0.5236 0.000 0.588 0.000 0.000 0.324 0.088
#> GSM531608 3 0.2728 0.6023 0.000 0.000 0.860 0.100 0.040 0.000
#> GSM531610 4 0.0000 0.9990 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531612 4 0.0000 0.9990 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531613 4 0.0000 0.9990 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531614 4 0.0000 0.9990 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531616 3 0.5634 -0.2308 0.316 0.000 0.512 0.000 0.172 0.000
#> GSM531618 6 0.3000 0.7110 0.000 0.000 0.032 0.004 0.124 0.840
#> GSM531619 3 0.3351 0.6125 0.000 0.000 0.712 0.000 0.288 0.000
#> GSM531620 3 0.3360 0.3632 0.004 0.000 0.732 0.000 0.264 0.000
#> GSM531623 3 0.0713 0.6666 0.000 0.000 0.972 0.000 0.028 0.000
#> GSM531625 3 0.3023 0.5761 0.000 0.000 0.768 0.000 0.232 0.000
#> GSM531626 3 0.3770 0.3278 0.028 0.000 0.728 0.000 0.244 0.000
#> GSM531632 1 0.3422 0.6811 0.788 0.000 0.036 0.000 0.176 0.000
#> GSM531638 3 0.3287 0.6457 0.012 0.000 0.768 0.000 0.220 0.000
#> GSM531639 3 0.3867 0.6436 0.008 0.000 0.760 0.000 0.192 0.040
#> GSM531641 4 0.0000 0.9990 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531642 6 0.2834 0.7002 0.128 0.000 0.016 0.008 0.000 0.848
#> GSM531643 1 0.1219 0.7818 0.948 0.000 0.000 0.000 0.004 0.048
#> GSM531644 6 0.3409 0.5204 0.300 0.000 0.000 0.000 0.000 0.700
#> GSM531645 4 0.0000 0.9990 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531646 1 0.2778 0.7266 0.824 0.000 0.008 0.000 0.168 0.000
#> GSM531647 1 0.2092 0.7653 0.876 0.000 0.000 0.000 0.124 0.000
#> GSM531648 6 0.0622 0.7450 0.000 0.000 0.000 0.008 0.012 0.980
#> GSM531650 1 0.1934 0.7907 0.916 0.000 0.000 0.000 0.044 0.040
#> GSM531651 3 0.0458 0.6603 0.000 0.000 0.984 0.000 0.016 0.000
#> GSM531652 6 0.1411 0.7375 0.060 0.000 0.000 0.000 0.004 0.936
#> GSM531656 1 0.4116 0.6593 0.780 0.000 0.088 0.000 0.024 0.108
#> GSM531659 6 0.5200 0.4554 0.004 0.284 0.008 0.008 0.068 0.628
#> GSM531661 3 0.1714 0.6667 0.000 0.000 0.908 0.000 0.092 0.000
#> GSM531662 3 0.3053 0.4941 0.000 0.020 0.812 0.000 0.168 0.000
#> GSM531663 4 0.0000 0.9990 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531664 1 0.1958 0.7519 0.896 0.000 0.000 0.000 0.004 0.100
#> GSM531666 6 0.2704 0.7064 0.140 0.000 0.000 0.000 0.016 0.844
#> GSM531667 3 0.3612 0.5311 0.000 0.000 0.780 0.000 0.052 0.168
#> GSM531668 6 0.5138 0.4288 0.000 0.036 0.028 0.000 0.400 0.536
#> GSM531669 1 0.2416 0.7445 0.844 0.000 0.000 0.000 0.156 0.000
#> GSM531671 5 0.6634 0.0000 0.144 0.056 0.344 0.000 0.452 0.004
#> GSM531672 6 0.1453 0.7501 0.000 0.008 0.000 0.008 0.040 0.944
#> GSM531673 3 0.6209 -0.4310 0.000 0.252 0.428 0.000 0.312 0.008
#> GSM531676 2 0.4025 0.3713 0.312 0.668 0.000 0.000 0.016 0.004
#> GSM531679 2 0.2003 0.6592 0.000 0.884 0.000 0.000 0.116 0.000
#> GSM531681 4 0.0260 0.9900 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM531682 2 0.3278 0.6446 0.000 0.808 0.000 0.000 0.152 0.040
#> GSM531683 2 0.3782 0.6245 0.000 0.740 0.000 0.000 0.224 0.036
#> GSM531684 2 0.6125 -0.0120 0.000 0.356 0.320 0.000 0.324 0.000
#> GSM531685 2 0.5215 -0.1079 0.460 0.468 0.012 0.000 0.060 0.000
#> GSM531686 4 0.0000 0.9990 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531687 2 0.5538 0.0448 0.436 0.472 0.000 0.000 0.064 0.028
#> GSM531688 1 0.1367 0.7831 0.944 0.044 0.000 0.000 0.012 0.000
#> GSM531690 6 0.3013 0.7148 0.000 0.088 0.000 0.000 0.068 0.844
#> GSM531693 1 0.2680 0.7777 0.860 0.032 0.000 0.000 0.108 0.000
#> GSM531695 1 0.4360 0.6503 0.768 0.040 0.000 0.000 0.092 0.100
#> GSM531603 6 0.5488 0.4294 0.000 0.112 0.008 0.000 0.340 0.540
#> GSM531609 4 0.0000 0.9990 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531611 4 0.0000 0.9990 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531621 3 0.1610 0.6630 0.000 0.000 0.916 0.000 0.084 0.000
#> GSM531622 3 0.2762 0.6585 0.000 0.000 0.804 0.000 0.196 0.000
#> GSM531628 1 0.0547 0.7886 0.980 0.000 0.000 0.000 0.000 0.020
#> GSM531630 3 0.3351 0.6141 0.000 0.000 0.712 0.000 0.288 0.000
#> GSM531633 3 0.1387 0.6366 0.000 0.000 0.932 0.000 0.068 0.000
#> GSM531635 1 0.1398 0.7902 0.940 0.000 0.008 0.000 0.052 0.000
#> GSM531640 3 0.3446 0.6018 0.000 0.000 0.692 0.000 0.308 0.000
#> GSM531649 1 0.3652 0.6734 0.768 0.000 0.044 0.000 0.188 0.000
#> GSM531653 1 0.2558 0.7626 0.868 0.000 0.028 0.000 0.104 0.000
#> GSM531657 6 0.2812 0.7205 0.000 0.008 0.000 0.028 0.104 0.860
#> GSM531665 2 0.3816 0.6301 0.068 0.820 0.008 0.000 0.072 0.032
#> GSM531670 1 0.5849 0.2228 0.576 0.012 0.304 0.000 0.056 0.052
#> GSM531674 1 0.0520 0.7912 0.984 0.000 0.000 0.000 0.008 0.008
#> GSM531675 2 0.4828 0.2923 0.000 0.568 0.000 0.000 0.064 0.368
#> GSM531677 2 0.2512 0.6548 0.000 0.880 0.000 0.000 0.060 0.060
#> GSM531678 2 0.2527 0.6340 0.000 0.876 0.000 0.084 0.040 0.000
#> GSM531680 1 0.5439 0.1869 0.524 0.380 0.000 0.000 0.080 0.016
#> GSM531689 2 0.0790 0.6633 0.000 0.968 0.000 0.000 0.032 0.000
#> GSM531691 2 0.2147 0.6474 0.000 0.896 0.020 0.000 0.084 0.000
#> GSM531692 2 0.2571 0.6333 0.064 0.876 0.000 0.000 0.060 0.000
#> GSM531694 2 0.4578 0.5573 0.000 0.624 0.000 0.000 0.320 0.056
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)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> CV:NMF 79 1.000 2
#> CV:NMF 43 1.000 3
#> CV:NMF 74 0.471 4
#> CV:NMF 76 0.373 5
#> CV:NMF 63 0.220 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "hclust"]
# you can also extract it by
# res = res_list["MAD:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 80 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 0.487 0.728 0.875 0.4865 0.505 0.505
#> 3 3 0.342 0.542 0.724 0.3232 0.781 0.587
#> 4 4 0.492 0.547 0.751 0.1418 0.819 0.526
#> 5 5 0.621 0.577 0.771 0.0761 0.900 0.631
#> 6 6 0.659 0.533 0.722 0.0413 0.969 0.843
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
#> GSM531602 2 0.0000 0.8952 0.000 1.000
#> GSM531604 2 0.9209 0.3983 0.336 0.664
#> GSM531606 2 0.2778 0.8739 0.048 0.952
#> GSM531607 2 0.0376 0.8948 0.004 0.996
#> GSM531608 1 0.8443 0.6430 0.728 0.272
#> GSM531610 2 0.0000 0.8952 0.000 1.000
#> GSM531612 2 0.0376 0.8953 0.004 0.996
#> GSM531613 2 0.0000 0.8952 0.000 1.000
#> GSM531614 2 0.0000 0.8952 0.000 1.000
#> GSM531616 1 0.0000 0.8177 1.000 0.000
#> GSM531618 2 0.6438 0.7677 0.164 0.836
#> GSM531619 1 0.0672 0.8180 0.992 0.008
#> GSM531620 1 0.0000 0.8177 1.000 0.000
#> GSM531623 1 0.0000 0.8177 1.000 0.000
#> GSM531625 1 0.0000 0.8177 1.000 0.000
#> GSM531626 1 0.0000 0.8177 1.000 0.000
#> GSM531632 1 0.0000 0.8177 1.000 0.000
#> GSM531638 1 0.0000 0.8177 1.000 0.000
#> GSM531639 1 0.2603 0.8125 0.956 0.044
#> GSM531641 2 0.0376 0.8953 0.004 0.996
#> GSM531642 1 0.9944 0.2656 0.544 0.456
#> GSM531643 1 0.4022 0.8031 0.920 0.080
#> GSM531644 1 0.9996 0.1608 0.512 0.488
#> GSM531645 2 0.0376 0.8953 0.004 0.996
#> GSM531646 1 0.0000 0.8177 1.000 0.000
#> GSM531647 1 0.0000 0.8177 1.000 0.000
#> GSM531648 2 0.8713 0.5582 0.292 0.708
#> GSM531650 1 0.4022 0.8016 0.920 0.080
#> GSM531651 1 0.0000 0.8177 1.000 0.000
#> GSM531652 2 0.8713 0.5582 0.292 0.708
#> GSM531656 1 0.2778 0.8122 0.952 0.048
#> GSM531659 2 0.8207 0.6046 0.256 0.744
#> GSM531661 1 0.7219 0.7147 0.800 0.200
#> GSM531662 1 0.9922 0.3426 0.552 0.448
#> GSM531663 2 0.5629 0.7894 0.132 0.868
#> GSM531664 1 0.4022 0.8016 0.920 0.080
#> GSM531666 2 0.9909 0.0964 0.444 0.556
#> GSM531667 1 0.8608 0.6307 0.716 0.284
#> GSM531668 2 0.2236 0.8823 0.036 0.964
#> GSM531669 1 0.2236 0.8140 0.964 0.036
#> GSM531671 1 0.9909 0.3528 0.556 0.444
#> GSM531672 2 0.0376 0.8953 0.004 0.996
#> GSM531673 1 0.9922 0.3426 0.552 0.448
#> GSM531676 1 0.9833 0.4244 0.576 0.424
#> GSM531679 2 0.2236 0.8818 0.036 0.964
#> GSM531681 2 0.0000 0.8952 0.000 1.000
#> GSM531682 2 0.1414 0.8911 0.020 0.980
#> GSM531683 2 0.0000 0.8952 0.000 1.000
#> GSM531684 2 0.3879 0.8501 0.076 0.924
#> GSM531685 1 0.8608 0.6478 0.716 0.284
#> GSM531686 2 0.0000 0.8952 0.000 1.000
#> GSM531687 1 0.9833 0.4244 0.576 0.424
#> GSM531688 1 0.8267 0.6743 0.740 0.260
#> GSM531690 2 0.0000 0.8952 0.000 1.000
#> GSM531693 1 0.8267 0.6743 0.740 0.260
#> GSM531695 1 0.9686 0.4777 0.604 0.396
#> GSM531603 2 0.0376 0.8948 0.004 0.996
#> GSM531609 2 0.0000 0.8952 0.000 1.000
#> GSM531611 2 0.0672 0.8946 0.008 0.992
#> GSM531621 1 0.0000 0.8177 1.000 0.000
#> GSM531622 1 0.0672 0.8180 0.992 0.008
#> GSM531628 1 0.4022 0.8016 0.920 0.080
#> GSM531630 1 0.0672 0.8180 0.992 0.008
#> GSM531633 1 0.0000 0.8177 1.000 0.000
#> GSM531635 1 0.0000 0.8177 1.000 0.000
#> GSM531640 1 0.0672 0.8180 0.992 0.008
#> GSM531649 1 0.0000 0.8177 1.000 0.000
#> GSM531653 1 0.0000 0.8177 1.000 0.000
#> GSM531657 2 0.3733 0.8607 0.072 0.928
#> GSM531665 2 0.9970 -0.0823 0.468 0.532
#> GSM531670 1 0.2778 0.8122 0.952 0.048
#> GSM531674 1 0.2236 0.8140 0.964 0.036
#> GSM531675 2 0.0000 0.8952 0.000 1.000
#> GSM531677 2 0.2236 0.8818 0.036 0.964
#> GSM531678 2 0.2948 0.8708 0.052 0.948
#> GSM531680 1 0.9710 0.4711 0.600 0.400
#> GSM531689 1 0.9833 0.4244 0.576 0.424
#> GSM531691 1 0.9866 0.4049 0.568 0.432
#> GSM531692 1 0.9087 0.5964 0.676 0.324
#> GSM531694 2 0.0000 0.8952 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM531602 2 0.5760 0.7015 0.000 0.672 0.328
#> GSM531604 3 0.7948 -0.0637 0.080 0.320 0.600
#> GSM531606 2 0.6095 0.6420 0.000 0.608 0.392
#> GSM531607 2 0.4351 0.7806 0.004 0.828 0.168
#> GSM531608 3 0.7772 0.4832 0.196 0.132 0.672
#> GSM531610 2 0.0000 0.7888 0.000 1.000 0.000
#> GSM531612 2 0.0747 0.7859 0.016 0.984 0.000
#> GSM531613 2 0.0000 0.7888 0.000 1.000 0.000
#> GSM531614 2 0.0000 0.7888 0.000 1.000 0.000
#> GSM531616 1 0.5560 0.3564 0.700 0.000 0.300
#> GSM531618 2 0.5473 0.7028 0.140 0.808 0.052
#> GSM531619 3 0.5859 0.4833 0.344 0.000 0.656
#> GSM531620 3 0.5988 0.4662 0.368 0.000 0.632
#> GSM531623 3 0.5926 0.4763 0.356 0.000 0.644
#> GSM531625 3 0.6008 0.4607 0.372 0.000 0.628
#> GSM531626 3 0.6008 0.4607 0.372 0.000 0.628
#> GSM531632 1 0.0592 0.6663 0.988 0.000 0.012
#> GSM531638 1 0.5560 0.3564 0.700 0.000 0.300
#> GSM531639 1 0.6699 0.4670 0.700 0.044 0.256
#> GSM531641 2 0.0747 0.7859 0.016 0.984 0.000
#> GSM531642 2 0.9383 -0.1001 0.384 0.444 0.172
#> GSM531643 1 0.3120 0.6557 0.908 0.080 0.012
#> GSM531644 1 0.6299 0.0138 0.524 0.476 0.000
#> GSM531645 2 0.0747 0.7859 0.016 0.984 0.000
#> GSM531646 1 0.1411 0.6580 0.964 0.000 0.036
#> GSM531647 1 0.0592 0.6663 0.988 0.000 0.012
#> GSM531648 2 0.6082 0.5188 0.296 0.692 0.012
#> GSM531650 1 0.2261 0.6564 0.932 0.068 0.000
#> GSM531651 3 0.5926 0.4763 0.356 0.000 0.644
#> GSM531652 2 0.6082 0.5188 0.296 0.692 0.012
#> GSM531656 1 0.6646 0.4878 0.712 0.048 0.240
#> GSM531659 2 0.7580 0.4961 0.056 0.604 0.340
#> GSM531661 3 0.7413 0.4897 0.224 0.092 0.684
#> GSM531662 3 0.7082 0.4314 0.120 0.156 0.724
#> GSM531663 2 0.4915 0.7021 0.012 0.804 0.184
#> GSM531664 1 0.2261 0.6564 0.932 0.068 0.000
#> GSM531666 2 0.6641 0.1552 0.448 0.544 0.008
#> GSM531667 3 0.8042 0.4763 0.200 0.148 0.652
#> GSM531668 2 0.2903 0.7887 0.028 0.924 0.048
#> GSM531669 1 0.3769 0.6197 0.880 0.016 0.104
#> GSM531671 3 0.7273 0.4274 0.132 0.156 0.712
#> GSM531672 2 0.1636 0.7917 0.016 0.964 0.020
#> GSM531673 3 0.7082 0.4314 0.120 0.156 0.724
#> GSM531676 3 0.9048 0.1967 0.288 0.172 0.540
#> GSM531679 2 0.6226 0.7386 0.028 0.720 0.252
#> GSM531681 2 0.1964 0.7934 0.000 0.944 0.056
#> GSM531682 2 0.5681 0.7527 0.016 0.748 0.236
#> GSM531683 2 0.5733 0.7043 0.000 0.676 0.324
#> GSM531684 2 0.6192 0.6028 0.000 0.580 0.420
#> GSM531685 1 0.8691 0.2515 0.528 0.116 0.356
#> GSM531686 2 0.1964 0.7934 0.000 0.944 0.056
#> GSM531687 3 0.9048 0.1967 0.288 0.172 0.540
#> GSM531688 1 0.7872 0.4174 0.652 0.112 0.236
#> GSM531690 2 0.3482 0.7845 0.000 0.872 0.128
#> GSM531693 1 0.8311 0.3591 0.596 0.112 0.292
#> GSM531695 1 0.9267 0.2665 0.528 0.224 0.248
#> GSM531603 2 0.4351 0.7806 0.004 0.828 0.168
#> GSM531609 2 0.0000 0.7888 0.000 1.000 0.000
#> GSM531611 2 0.0829 0.7889 0.012 0.984 0.004
#> GSM531621 3 0.5948 0.4728 0.360 0.000 0.640
#> GSM531622 3 0.5859 0.4833 0.344 0.000 0.656
#> GSM531628 1 0.2261 0.6564 0.932 0.068 0.000
#> GSM531630 3 0.5859 0.4833 0.344 0.000 0.656
#> GSM531633 3 0.5948 0.4728 0.360 0.000 0.640
#> GSM531635 1 0.3941 0.5675 0.844 0.000 0.156
#> GSM531640 3 0.5859 0.4833 0.344 0.000 0.656
#> GSM531649 1 0.0592 0.6663 0.988 0.000 0.012
#> GSM531653 1 0.0592 0.6663 0.988 0.000 0.012
#> GSM531657 2 0.4370 0.7773 0.056 0.868 0.076
#> GSM531665 3 0.8350 0.2616 0.120 0.280 0.600
#> GSM531670 1 0.6646 0.4878 0.712 0.048 0.240
#> GSM531674 1 0.3769 0.6197 0.880 0.016 0.104
#> GSM531675 2 0.4452 0.7718 0.000 0.808 0.192
#> GSM531677 2 0.6226 0.7386 0.028 0.720 0.252
#> GSM531678 2 0.6111 0.6368 0.000 0.604 0.396
#> GSM531680 1 0.9295 0.2616 0.524 0.224 0.252
#> GSM531689 3 0.9048 0.1967 0.288 0.172 0.540
#> GSM531691 3 0.8933 0.2130 0.276 0.168 0.556
#> GSM531692 3 0.5325 0.3293 0.248 0.004 0.748
#> GSM531694 2 0.5760 0.7015 0.000 0.672 0.328
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM531602 2 0.2921 0.560 0.000 0.860 0.000 0.140
#> GSM531604 2 0.4850 0.522 0.052 0.776 0.168 0.004
#> GSM531606 2 0.3991 0.578 0.000 0.832 0.048 0.120
#> GSM531607 2 0.5088 0.172 0.004 0.572 0.000 0.424
#> GSM531608 3 0.6084 0.558 0.016 0.220 0.692 0.072
#> GSM531610 4 0.0707 0.718 0.000 0.020 0.000 0.980
#> GSM531612 4 0.0000 0.718 0.000 0.000 0.000 1.000
#> GSM531613 4 0.0707 0.718 0.000 0.020 0.000 0.980
#> GSM531614 4 0.0707 0.718 0.000 0.020 0.000 0.980
#> GSM531616 1 0.4866 0.349 0.596 0.000 0.404 0.000
#> GSM531618 4 0.5573 0.653 0.132 0.072 0.032 0.764
#> GSM531619 3 0.0000 0.893 0.000 0.000 1.000 0.000
#> GSM531620 3 0.1474 0.883 0.052 0.000 0.948 0.000
#> GSM531623 3 0.0469 0.894 0.012 0.000 0.988 0.000
#> GSM531625 3 0.2081 0.861 0.084 0.000 0.916 0.000
#> GSM531626 3 0.2149 0.858 0.088 0.000 0.912 0.000
#> GSM531632 1 0.0000 0.731 1.000 0.000 0.000 0.000
#> GSM531638 1 0.4866 0.349 0.596 0.000 0.404 0.000
#> GSM531639 1 0.5569 0.536 0.660 0.000 0.296 0.044
#> GSM531641 4 0.0000 0.718 0.000 0.000 0.000 1.000
#> GSM531642 4 0.7544 0.176 0.340 0.000 0.200 0.460
#> GSM531643 1 0.2593 0.703 0.904 0.000 0.016 0.080
#> GSM531644 4 0.5512 0.135 0.492 0.000 0.016 0.492
#> GSM531645 4 0.0000 0.718 0.000 0.000 0.000 1.000
#> GSM531646 1 0.1022 0.730 0.968 0.000 0.032 0.000
#> GSM531647 1 0.0000 0.731 1.000 0.000 0.000 0.000
#> GSM531648 4 0.5022 0.555 0.264 0.000 0.028 0.708
#> GSM531650 1 0.2081 0.704 0.916 0.000 0.000 0.084
#> GSM531651 3 0.0469 0.894 0.012 0.000 0.988 0.000
#> GSM531652 4 0.5022 0.555 0.264 0.000 0.028 0.708
#> GSM531656 1 0.5498 0.563 0.680 0.000 0.272 0.048
#> GSM531659 4 0.8584 -0.052 0.056 0.360 0.164 0.420
#> GSM531661 3 0.5104 0.682 0.008 0.152 0.772 0.068
#> GSM531662 2 0.8343 0.137 0.100 0.420 0.404 0.076
#> GSM531663 4 0.5998 0.505 0.004 0.192 0.108 0.696
#> GSM531664 1 0.2081 0.704 0.916 0.000 0.000 0.084
#> GSM531666 4 0.5620 0.305 0.416 0.000 0.024 0.560
#> GSM531667 3 0.6404 0.541 0.020 0.216 0.676 0.088
#> GSM531668 4 0.3824 0.668 0.036 0.104 0.008 0.852
#> GSM531669 1 0.3217 0.685 0.860 0.128 0.000 0.012
#> GSM531671 2 0.8460 0.147 0.112 0.416 0.396 0.076
#> GSM531672 4 0.2921 0.658 0.000 0.140 0.000 0.860
#> GSM531673 2 0.8343 0.137 0.100 0.420 0.404 0.076
#> GSM531676 2 0.8203 0.246 0.268 0.508 0.184 0.040
#> GSM531679 2 0.3791 0.519 0.004 0.796 0.000 0.200
#> GSM531681 4 0.4431 0.452 0.000 0.304 0.000 0.696
#> GSM531682 2 0.4234 0.496 0.004 0.764 0.004 0.228
#> GSM531683 2 0.3074 0.556 0.000 0.848 0.000 0.152
#> GSM531684 2 0.4130 0.580 0.000 0.828 0.064 0.108
#> GSM531685 1 0.7565 0.316 0.508 0.368 0.084 0.040
#> GSM531686 4 0.4477 0.439 0.000 0.312 0.000 0.688
#> GSM531687 2 0.8203 0.246 0.268 0.508 0.184 0.040
#> GSM531688 1 0.5658 0.460 0.632 0.328 0.000 0.040
#> GSM531690 2 0.4761 0.304 0.000 0.628 0.000 0.372
#> GSM531693 1 0.6858 0.413 0.576 0.340 0.044 0.040
#> GSM531695 1 0.6952 0.255 0.480 0.420 0.004 0.096
#> GSM531603 2 0.5088 0.172 0.004 0.572 0.000 0.424
#> GSM531609 4 0.0707 0.718 0.000 0.020 0.000 0.980
#> GSM531611 4 0.1824 0.705 0.000 0.060 0.004 0.936
#> GSM531621 3 0.0921 0.892 0.028 0.000 0.972 0.000
#> GSM531622 3 0.0000 0.893 0.000 0.000 1.000 0.000
#> GSM531628 1 0.2081 0.704 0.916 0.000 0.000 0.084
#> GSM531630 3 0.0000 0.893 0.000 0.000 1.000 0.000
#> GSM531633 3 0.0921 0.892 0.028 0.000 0.972 0.000
#> GSM531635 1 0.3975 0.607 0.760 0.000 0.240 0.000
#> GSM531640 3 0.0000 0.893 0.000 0.000 1.000 0.000
#> GSM531649 1 0.0000 0.731 1.000 0.000 0.000 0.000
#> GSM531653 1 0.0000 0.731 1.000 0.000 0.000 0.000
#> GSM531657 4 0.6096 0.513 0.048 0.264 0.020 0.668
#> GSM531665 2 0.8720 0.324 0.100 0.464 0.312 0.124
#> GSM531670 1 0.5498 0.563 0.680 0.000 0.272 0.048
#> GSM531674 1 0.3217 0.685 0.860 0.128 0.000 0.012
#> GSM531675 2 0.4406 0.415 0.000 0.700 0.000 0.300
#> GSM531677 2 0.3791 0.519 0.004 0.796 0.000 0.200
#> GSM531678 2 0.4072 0.578 0.000 0.828 0.052 0.120
#> GSM531680 1 0.6955 0.248 0.476 0.424 0.004 0.096
#> GSM531689 2 0.8203 0.246 0.268 0.508 0.184 0.040
#> GSM531691 2 0.8128 0.268 0.256 0.516 0.192 0.036
#> GSM531692 2 0.7647 0.190 0.220 0.444 0.336 0.000
#> GSM531694 2 0.2921 0.560 0.000 0.860 0.000 0.140
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM531602 2 0.0794 0.7042 0.000 0.972 0.000 0.000 0.028
#> GSM531604 2 0.5246 0.2398 0.000 0.596 0.060 0.000 0.344
#> GSM531606 2 0.2305 0.6810 0.000 0.896 0.012 0.000 0.092
#> GSM531607 2 0.4650 0.4822 0.004 0.684 0.000 0.280 0.032
#> GSM531608 3 0.6184 0.4560 0.000 0.208 0.620 0.024 0.148
#> GSM531610 4 0.2153 0.7019 0.000 0.044 0.000 0.916 0.040
#> GSM531612 4 0.0162 0.7129 0.000 0.000 0.000 0.996 0.004
#> GSM531613 4 0.2153 0.7019 0.000 0.044 0.000 0.916 0.040
#> GSM531614 4 0.2074 0.7036 0.000 0.044 0.000 0.920 0.036
#> GSM531616 1 0.4557 0.4042 0.584 0.000 0.404 0.000 0.012
#> GSM531618 4 0.6435 0.6172 0.116 0.088 0.032 0.684 0.080
#> GSM531619 3 0.0000 0.8736 0.000 0.000 1.000 0.000 0.000
#> GSM531620 3 0.1408 0.8617 0.044 0.000 0.948 0.000 0.008
#> GSM531623 3 0.0451 0.8745 0.008 0.000 0.988 0.000 0.004
#> GSM531625 3 0.1956 0.8377 0.076 0.000 0.916 0.000 0.008
#> GSM531626 3 0.2017 0.8348 0.080 0.000 0.912 0.000 0.008
#> GSM531632 1 0.0609 0.7362 0.980 0.000 0.000 0.000 0.020
#> GSM531638 1 0.4557 0.4042 0.584 0.000 0.404 0.000 0.012
#> GSM531639 1 0.5053 0.5936 0.656 0.000 0.296 0.032 0.016
#> GSM531641 4 0.0162 0.7129 0.000 0.000 0.000 0.996 0.004
#> GSM531642 4 0.7643 0.0342 0.332 0.000 0.200 0.404 0.064
#> GSM531643 1 0.2482 0.7279 0.904 0.000 0.016 0.064 0.016
#> GSM531644 1 0.5932 -0.0684 0.488 0.000 0.016 0.432 0.064
#> GSM531645 4 0.0162 0.7129 0.000 0.000 0.000 0.996 0.004
#> GSM531646 1 0.1386 0.7380 0.952 0.000 0.032 0.000 0.016
#> GSM531647 1 0.0404 0.7373 0.988 0.000 0.000 0.000 0.012
#> GSM531648 4 0.5750 0.4861 0.260 0.000 0.028 0.640 0.072
#> GSM531650 1 0.2104 0.7254 0.916 0.000 0.000 0.060 0.024
#> GSM531651 3 0.0451 0.8745 0.008 0.000 0.988 0.000 0.004
#> GSM531652 4 0.5750 0.4861 0.260 0.000 0.028 0.640 0.072
#> GSM531656 1 0.4903 0.6229 0.680 0.000 0.272 0.036 0.012
#> GSM531659 2 0.8324 0.1416 0.016 0.360 0.084 0.320 0.220
#> GSM531661 3 0.5504 0.5765 0.000 0.140 0.700 0.024 0.136
#> GSM531662 5 0.7429 0.2211 0.000 0.308 0.276 0.032 0.384
#> GSM531663 4 0.6469 0.4412 0.000 0.208 0.068 0.620 0.104
#> GSM531664 1 0.2104 0.7254 0.916 0.000 0.000 0.060 0.024
#> GSM531666 4 0.6123 0.1677 0.412 0.000 0.024 0.496 0.068
#> GSM531667 3 0.6601 0.4404 0.004 0.204 0.604 0.040 0.148
#> GSM531668 4 0.5115 0.6266 0.012 0.152 0.008 0.736 0.092
#> GSM531669 1 0.3561 0.4707 0.740 0.000 0.000 0.000 0.260
#> GSM531671 5 0.7649 0.2271 0.008 0.304 0.268 0.032 0.388
#> GSM531672 4 0.3961 0.6255 0.004 0.184 0.000 0.780 0.032
#> GSM531673 5 0.7429 0.2211 0.000 0.308 0.276 0.032 0.384
#> GSM531676 5 0.4378 0.5619 0.012 0.156 0.048 0.004 0.780
#> GSM531679 2 0.3442 0.6925 0.000 0.836 0.000 0.060 0.104
#> GSM531681 4 0.4946 0.3374 0.000 0.368 0.000 0.596 0.036
#> GSM531682 2 0.3151 0.7029 0.000 0.864 0.004 0.068 0.064
#> GSM531683 2 0.1281 0.7083 0.000 0.956 0.000 0.012 0.032
#> GSM531684 2 0.2727 0.6615 0.000 0.868 0.016 0.000 0.116
#> GSM531685 5 0.4458 0.5524 0.192 0.056 0.004 0.000 0.748
#> GSM531686 4 0.4969 0.3193 0.000 0.376 0.000 0.588 0.036
#> GSM531687 5 0.4378 0.5619 0.012 0.156 0.048 0.004 0.780
#> GSM531688 5 0.5371 0.2735 0.420 0.056 0.000 0.000 0.524
#> GSM531690 2 0.3642 0.5743 0.000 0.760 0.000 0.232 0.008
#> GSM531693 5 0.5351 0.3904 0.348 0.056 0.004 0.000 0.592
#> GSM531695 5 0.6480 0.4713 0.260 0.116 0.000 0.040 0.584
#> GSM531603 2 0.4650 0.4822 0.004 0.684 0.000 0.280 0.032
#> GSM531609 4 0.2074 0.7036 0.000 0.044 0.000 0.920 0.036
#> GSM531611 4 0.1571 0.7038 0.000 0.060 0.004 0.936 0.000
#> GSM531621 3 0.0898 0.8723 0.020 0.000 0.972 0.000 0.008
#> GSM531622 3 0.0000 0.8736 0.000 0.000 1.000 0.000 0.000
#> GSM531628 1 0.2104 0.7254 0.916 0.000 0.000 0.060 0.024
#> GSM531630 3 0.0000 0.8736 0.000 0.000 1.000 0.000 0.000
#> GSM531633 3 0.0898 0.8723 0.020 0.000 0.972 0.000 0.008
#> GSM531635 1 0.3807 0.6450 0.748 0.000 0.240 0.000 0.012
#> GSM531640 3 0.0000 0.8736 0.000 0.000 1.000 0.000 0.000
#> GSM531649 1 0.0404 0.7373 0.988 0.000 0.000 0.000 0.012
#> GSM531653 1 0.0404 0.7373 0.988 0.000 0.000 0.000 0.012
#> GSM531657 4 0.6697 0.3736 0.032 0.308 0.020 0.560 0.080
#> GSM531665 2 0.7818 -0.1172 0.008 0.392 0.204 0.056 0.340
#> GSM531670 1 0.4903 0.6229 0.680 0.000 0.272 0.036 0.012
#> GSM531674 1 0.3561 0.4707 0.740 0.000 0.000 0.000 0.260
#> GSM531675 2 0.3013 0.6654 0.000 0.832 0.000 0.160 0.008
#> GSM531677 2 0.3442 0.6925 0.000 0.836 0.000 0.060 0.104
#> GSM531678 2 0.2361 0.6788 0.000 0.892 0.012 0.000 0.096
#> GSM531680 5 0.6460 0.4757 0.256 0.116 0.000 0.040 0.588
#> GSM531689 5 0.4378 0.5619 0.012 0.156 0.048 0.004 0.780
#> GSM531691 5 0.4628 0.5516 0.012 0.168 0.056 0.004 0.760
#> GSM531692 5 0.5820 0.4699 0.012 0.172 0.168 0.000 0.648
#> GSM531694 2 0.0794 0.7042 0.000 0.972 0.000 0.000 0.028
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM531602 2 0.0363 0.754 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM531604 2 0.4395 0.308 0.000 0.580 0.008 0.000 0.396 0.016
#> GSM531606 2 0.2009 0.733 0.000 0.904 0.004 0.000 0.084 0.008
#> GSM531607 2 0.4787 0.496 0.000 0.672 0.000 0.220 0.004 0.104
#> GSM531608 3 0.6648 0.375 0.000 0.108 0.532 0.000 0.200 0.160
#> GSM531610 4 0.3171 0.589 0.000 0.012 0.000 0.784 0.000 0.204
#> GSM531612 4 0.0146 0.510 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM531613 4 0.3230 0.589 0.000 0.012 0.000 0.776 0.000 0.212
#> GSM531614 4 0.3141 0.589 0.000 0.012 0.000 0.788 0.000 0.200
#> GSM531616 1 0.4435 0.393 0.580 0.000 0.392 0.000 0.004 0.024
#> GSM531618 6 0.6297 0.543 0.068 0.052 0.008 0.364 0.008 0.500
#> GSM531619 3 0.0632 0.854 0.000 0.000 0.976 0.000 0.000 0.024
#> GSM531620 3 0.1152 0.846 0.044 0.000 0.952 0.000 0.004 0.000
#> GSM531623 3 0.0436 0.857 0.004 0.000 0.988 0.000 0.004 0.004
#> GSM531625 3 0.1788 0.822 0.076 0.000 0.916 0.000 0.004 0.004
#> GSM531626 3 0.1843 0.819 0.080 0.000 0.912 0.000 0.004 0.004
#> GSM531632 1 0.0405 0.684 0.988 0.000 0.000 0.000 0.008 0.004
#> GSM531638 1 0.4435 0.393 0.580 0.000 0.392 0.000 0.004 0.024
#> GSM531639 1 0.5534 0.520 0.608 0.000 0.284 0.032 0.008 0.068
#> GSM531641 4 0.0146 0.510 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM531642 4 0.7762 -0.553 0.272 0.000 0.176 0.288 0.004 0.260
#> GSM531643 1 0.3029 0.624 0.840 0.000 0.000 0.036 0.004 0.120
#> GSM531644 1 0.6049 -0.473 0.416 0.000 0.000 0.292 0.000 0.292
#> GSM531645 4 0.0146 0.510 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM531646 1 0.1194 0.684 0.956 0.000 0.032 0.000 0.004 0.008
#> GSM531647 1 0.0146 0.686 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM531648 6 0.5736 0.694 0.188 0.000 0.000 0.320 0.000 0.492
#> GSM531650 1 0.2882 0.634 0.860 0.000 0.000 0.060 0.004 0.076
#> GSM531651 3 0.0291 0.857 0.004 0.000 0.992 0.000 0.004 0.000
#> GSM531652 6 0.5736 0.694 0.188 0.000 0.000 0.320 0.000 0.492
#> GSM531656 1 0.5443 0.539 0.628 0.000 0.256 0.032 0.004 0.080
#> GSM531659 2 0.8382 0.020 0.004 0.268 0.032 0.236 0.236 0.224
#> GSM531661 3 0.5930 0.494 0.000 0.080 0.616 0.000 0.192 0.112
#> GSM531662 5 0.7384 0.353 0.004 0.188 0.160 0.000 0.432 0.216
#> GSM531663 4 0.6987 0.415 0.000 0.156 0.012 0.524 0.124 0.184
#> GSM531664 1 0.2882 0.634 0.860 0.000 0.000 0.060 0.004 0.076
#> GSM531666 6 0.6219 0.489 0.340 0.000 0.000 0.284 0.004 0.372
#> GSM531667 3 0.7126 0.362 0.004 0.108 0.520 0.016 0.200 0.152
#> GSM531668 6 0.5437 0.120 0.000 0.092 0.000 0.416 0.008 0.484
#> GSM531669 1 0.4094 0.482 0.744 0.000 0.000 0.000 0.168 0.088
#> GSM531671 5 0.7591 0.359 0.016 0.184 0.160 0.000 0.432 0.208
#> GSM531672 4 0.4402 0.259 0.000 0.184 0.000 0.712 0.000 0.104
#> GSM531673 5 0.7384 0.353 0.004 0.188 0.160 0.000 0.432 0.216
#> GSM531676 5 0.1267 0.579 0.000 0.060 0.000 0.000 0.940 0.000
#> GSM531679 2 0.3727 0.729 0.000 0.784 0.000 0.000 0.128 0.088
#> GSM531681 4 0.5940 0.302 0.000 0.336 0.000 0.464 0.004 0.196
#> GSM531682 2 0.3528 0.740 0.000 0.816 0.000 0.008 0.084 0.092
#> GSM531683 2 0.0964 0.757 0.000 0.968 0.000 0.004 0.016 0.012
#> GSM531684 2 0.2473 0.716 0.000 0.876 0.008 0.000 0.104 0.012
#> GSM531685 5 0.4141 0.511 0.168 0.000 0.000 0.000 0.740 0.092
#> GSM531686 4 0.5953 0.284 0.000 0.344 0.000 0.456 0.004 0.196
#> GSM531687 5 0.1267 0.579 0.000 0.060 0.000 0.000 0.940 0.000
#> GSM531688 5 0.5146 0.228 0.396 0.000 0.000 0.000 0.516 0.088
#> GSM531690 2 0.4374 0.598 0.000 0.732 0.000 0.172 0.008 0.088
#> GSM531693 5 0.5016 0.344 0.324 0.000 0.000 0.000 0.584 0.092
#> GSM531695 5 0.6597 0.415 0.244 0.056 0.000 0.028 0.556 0.116
#> GSM531603 2 0.4787 0.496 0.000 0.672 0.000 0.220 0.004 0.104
#> GSM531609 4 0.3141 0.589 0.000 0.012 0.000 0.788 0.000 0.200
#> GSM531611 4 0.1524 0.513 0.000 0.060 0.000 0.932 0.000 0.008
#> GSM531621 3 0.0692 0.855 0.020 0.000 0.976 0.000 0.004 0.000
#> GSM531622 3 0.0547 0.856 0.000 0.000 0.980 0.000 0.000 0.020
#> GSM531628 1 0.2882 0.634 0.860 0.000 0.000 0.060 0.004 0.076
#> GSM531630 3 0.0547 0.856 0.000 0.000 0.980 0.000 0.000 0.020
#> GSM531633 3 0.0692 0.855 0.020 0.000 0.976 0.000 0.004 0.000
#> GSM531635 1 0.3622 0.583 0.744 0.000 0.236 0.000 0.004 0.016
#> GSM531640 3 0.0547 0.856 0.000 0.000 0.980 0.000 0.000 0.020
#> GSM531649 1 0.0146 0.686 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM531653 1 0.0146 0.686 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM531657 4 0.6716 -0.170 0.004 0.260 0.008 0.440 0.020 0.268
#> GSM531665 5 0.7917 0.182 0.012 0.276 0.112 0.024 0.396 0.180
#> GSM531670 1 0.5443 0.539 0.628 0.000 0.256 0.032 0.004 0.080
#> GSM531674 1 0.4094 0.482 0.744 0.000 0.000 0.000 0.168 0.088
#> GSM531675 2 0.3673 0.684 0.000 0.804 0.000 0.100 0.008 0.088
#> GSM531677 2 0.3727 0.729 0.000 0.784 0.000 0.000 0.128 0.088
#> GSM531678 2 0.2062 0.731 0.000 0.900 0.004 0.000 0.088 0.008
#> GSM531680 5 0.6578 0.420 0.240 0.056 0.000 0.028 0.560 0.116
#> GSM531689 5 0.1267 0.579 0.000 0.060 0.000 0.000 0.940 0.000
#> GSM531691 5 0.1845 0.571 0.000 0.072 0.004 0.000 0.916 0.008
#> GSM531692 5 0.4906 0.506 0.004 0.096 0.052 0.000 0.732 0.116
#> GSM531694 2 0.0363 0.754 0.000 0.988 0.000 0.000 0.012 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> MAD:hclust 66 0.631 2
#> MAD:hclust 42 0.562 3
#> MAD:hclust 53 0.676 4
#> MAD:hclust 52 0.783 5
#> MAD:hclust 52 0.692 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "kmeans"]
# you can also extract it by
# res = res_list["MAD:kmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 80 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 0.703 0.922 0.962 0.5028 0.499 0.499
#> 3 3 0.554 0.683 0.777 0.3089 0.795 0.609
#> 4 4 0.870 0.891 0.942 0.1465 0.829 0.550
#> 5 5 0.739 0.721 0.833 0.0599 0.928 0.722
#> 6 6 0.718 0.577 0.760 0.0410 0.947 0.753
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
#> GSM531602 2 0.0000 0.965 0.000 1.000
#> GSM531604 2 0.0376 0.963 0.004 0.996
#> GSM531606 2 0.0000 0.965 0.000 1.000
#> GSM531607 2 0.0000 0.965 0.000 1.000
#> GSM531608 1 0.9460 0.507 0.636 0.364
#> GSM531610 2 0.0000 0.965 0.000 1.000
#> GSM531612 2 0.0000 0.965 0.000 1.000
#> GSM531613 2 0.0000 0.965 0.000 1.000
#> GSM531614 2 0.0000 0.965 0.000 1.000
#> GSM531616 1 0.0000 0.952 1.000 0.000
#> GSM531618 1 0.7528 0.748 0.784 0.216
#> GSM531619 1 0.6531 0.808 0.832 0.168
#> GSM531620 1 0.0000 0.952 1.000 0.000
#> GSM531623 1 0.0000 0.952 1.000 0.000
#> GSM531625 1 0.0000 0.952 1.000 0.000
#> GSM531626 1 0.0000 0.952 1.000 0.000
#> GSM531632 1 0.0000 0.952 1.000 0.000
#> GSM531638 1 0.0000 0.952 1.000 0.000
#> GSM531639 1 0.0000 0.952 1.000 0.000
#> GSM531641 2 0.0000 0.965 0.000 1.000
#> GSM531642 1 0.0000 0.952 1.000 0.000
#> GSM531643 1 0.0000 0.952 1.000 0.000
#> GSM531644 1 0.0000 0.952 1.000 0.000
#> GSM531645 2 0.0000 0.965 0.000 1.000
#> GSM531646 1 0.0000 0.952 1.000 0.000
#> GSM531647 1 0.0000 0.952 1.000 0.000
#> GSM531648 2 0.6438 0.791 0.164 0.836
#> GSM531650 1 0.0000 0.952 1.000 0.000
#> GSM531651 1 0.0000 0.952 1.000 0.000
#> GSM531652 1 0.0000 0.952 1.000 0.000
#> GSM531656 1 0.0000 0.952 1.000 0.000
#> GSM531659 2 0.0000 0.965 0.000 1.000
#> GSM531661 1 0.5842 0.838 0.860 0.140
#> GSM531662 1 0.0000 0.952 1.000 0.000
#> GSM531663 2 0.0000 0.965 0.000 1.000
#> GSM531664 1 0.0000 0.952 1.000 0.000
#> GSM531666 1 0.0000 0.952 1.000 0.000
#> GSM531667 1 0.6973 0.784 0.812 0.188
#> GSM531668 2 0.0000 0.965 0.000 1.000
#> GSM531669 1 0.0000 0.952 1.000 0.000
#> GSM531671 1 0.0000 0.952 1.000 0.000
#> GSM531672 2 0.0000 0.965 0.000 1.000
#> GSM531673 1 0.5178 0.860 0.884 0.116
#> GSM531676 2 0.7376 0.755 0.208 0.792
#> GSM531679 2 0.0000 0.965 0.000 1.000
#> GSM531681 2 0.0000 0.965 0.000 1.000
#> GSM531682 2 0.0000 0.965 0.000 1.000
#> GSM531683 2 0.0000 0.965 0.000 1.000
#> GSM531684 2 0.0000 0.965 0.000 1.000
#> GSM531685 1 0.6438 0.808 0.836 0.164
#> GSM531686 2 0.0000 0.965 0.000 1.000
#> GSM531687 2 0.7219 0.766 0.200 0.800
#> GSM531688 1 0.6343 0.813 0.840 0.160
#> GSM531690 2 0.0000 0.965 0.000 1.000
#> GSM531693 1 0.0000 0.952 1.000 0.000
#> GSM531695 2 0.7219 0.766 0.200 0.800
#> GSM531603 2 0.0000 0.965 0.000 1.000
#> GSM531609 2 0.0000 0.965 0.000 1.000
#> GSM531611 2 0.0000 0.965 0.000 1.000
#> GSM531621 1 0.0000 0.952 1.000 0.000
#> GSM531622 1 0.0000 0.952 1.000 0.000
#> GSM531628 1 0.0000 0.952 1.000 0.000
#> GSM531630 1 0.0000 0.952 1.000 0.000
#> GSM531633 1 0.0000 0.952 1.000 0.000
#> GSM531635 1 0.0000 0.952 1.000 0.000
#> GSM531640 1 0.6531 0.808 0.832 0.168
#> GSM531649 1 0.0000 0.952 1.000 0.000
#> GSM531653 1 0.0000 0.952 1.000 0.000
#> GSM531657 2 0.0000 0.965 0.000 1.000
#> GSM531665 1 0.3879 0.897 0.924 0.076
#> GSM531670 1 0.0000 0.952 1.000 0.000
#> GSM531674 1 0.0000 0.952 1.000 0.000
#> GSM531675 2 0.0000 0.965 0.000 1.000
#> GSM531677 2 0.0000 0.965 0.000 1.000
#> GSM531678 2 0.0000 0.965 0.000 1.000
#> GSM531680 2 0.7219 0.766 0.200 0.800
#> GSM531689 2 0.0376 0.963 0.004 0.996
#> GSM531691 2 0.5737 0.842 0.136 0.864
#> GSM531692 1 0.6438 0.808 0.836 0.164
#> GSM531694 2 0.0000 0.965 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM531602 2 0.0237 0.745 0.000 0.996 0.004
#> GSM531604 2 0.2878 0.686 0.000 0.904 0.096
#> GSM531606 2 0.0892 0.738 0.000 0.980 0.020
#> GSM531607 2 0.0237 0.745 0.000 0.996 0.004
#> GSM531608 3 0.8005 0.747 0.224 0.128 0.648
#> GSM531610 2 0.6282 0.745 0.004 0.612 0.384
#> GSM531612 2 0.7099 0.735 0.028 0.588 0.384
#> GSM531613 2 0.6228 0.748 0.004 0.624 0.372
#> GSM531614 2 0.7099 0.735 0.028 0.588 0.384
#> GSM531616 3 0.6126 0.848 0.400 0.000 0.600
#> GSM531618 2 0.9419 0.496 0.192 0.480 0.328
#> GSM531619 3 0.7084 0.842 0.336 0.036 0.628
#> GSM531620 3 0.6095 0.853 0.392 0.000 0.608
#> GSM531623 3 0.6079 0.856 0.388 0.000 0.612
#> GSM531625 3 0.6126 0.848 0.400 0.000 0.600
#> GSM531626 3 0.6126 0.848 0.400 0.000 0.600
#> GSM531632 1 0.1163 0.742 0.972 0.000 0.028
#> GSM531638 3 0.6126 0.848 0.400 0.000 0.600
#> GSM531639 1 0.4399 0.451 0.812 0.000 0.188
#> GSM531641 2 0.7099 0.735 0.028 0.588 0.384
#> GSM531642 1 0.5254 0.571 0.736 0.000 0.264
#> GSM531643 1 0.1411 0.758 0.964 0.000 0.036
#> GSM531644 1 0.3752 0.690 0.856 0.000 0.144
#> GSM531645 2 0.7207 0.732 0.032 0.584 0.384
#> GSM531646 1 0.1163 0.742 0.972 0.000 0.028
#> GSM531647 1 0.0237 0.756 0.996 0.000 0.004
#> GSM531648 2 0.7311 0.730 0.036 0.580 0.384
#> GSM531650 1 0.1411 0.758 0.964 0.000 0.036
#> GSM531651 3 0.6079 0.856 0.388 0.000 0.612
#> GSM531652 1 0.4291 0.671 0.820 0.000 0.180
#> GSM531656 1 0.1529 0.729 0.960 0.000 0.040
#> GSM531659 2 0.6282 0.745 0.004 0.612 0.384
#> GSM531661 3 0.8266 0.750 0.240 0.136 0.624
#> GSM531662 3 0.8331 0.713 0.208 0.164 0.628
#> GSM531663 2 0.6282 0.745 0.004 0.612 0.384
#> GSM531664 1 0.1529 0.757 0.960 0.000 0.040
#> GSM531666 1 0.3879 0.683 0.848 0.000 0.152
#> GSM531667 3 0.7084 0.842 0.336 0.036 0.628
#> GSM531668 2 0.6282 0.745 0.004 0.612 0.384
#> GSM531669 1 0.0237 0.758 0.996 0.000 0.004
#> GSM531671 1 0.6483 -0.529 0.544 0.004 0.452
#> GSM531672 2 0.6228 0.748 0.004 0.624 0.372
#> GSM531673 3 0.8578 0.638 0.172 0.224 0.604
#> GSM531676 2 0.7063 -0.206 0.464 0.516 0.020
#> GSM531679 2 0.1031 0.737 0.000 0.976 0.024
#> GSM531681 2 0.4399 0.763 0.000 0.812 0.188
#> GSM531682 2 0.1031 0.737 0.000 0.976 0.024
#> GSM531683 2 0.0000 0.746 0.000 1.000 0.000
#> GSM531684 2 0.4504 0.568 0.000 0.804 0.196
#> GSM531685 1 0.6899 0.478 0.612 0.364 0.024
#> GSM531686 2 0.4399 0.763 0.000 0.812 0.188
#> GSM531687 2 0.7063 -0.206 0.464 0.516 0.020
#> GSM531688 1 0.6553 0.518 0.656 0.324 0.020
#> GSM531690 2 0.4399 0.763 0.000 0.812 0.188
#> GSM531693 1 0.1315 0.754 0.972 0.008 0.020
#> GSM531695 1 0.6543 0.503 0.640 0.344 0.016
#> GSM531603 2 0.0237 0.745 0.000 0.996 0.004
#> GSM531609 2 0.7099 0.735 0.028 0.588 0.384
#> GSM531611 2 0.7067 0.738 0.028 0.596 0.376
#> GSM531621 3 0.6079 0.856 0.388 0.000 0.612
#> GSM531622 3 0.6008 0.854 0.372 0.000 0.628
#> GSM531628 1 0.1411 0.758 0.964 0.000 0.036
#> GSM531630 3 0.6026 0.855 0.376 0.000 0.624
#> GSM531633 3 0.6079 0.856 0.388 0.000 0.612
#> GSM531635 1 0.1163 0.742 0.972 0.000 0.028
#> GSM531640 3 0.6057 0.832 0.340 0.004 0.656
#> GSM531649 1 0.1163 0.742 0.972 0.000 0.028
#> GSM531653 1 0.0237 0.756 0.996 0.000 0.004
#> GSM531657 2 0.6282 0.745 0.004 0.612 0.384
#> GSM531665 1 0.7394 0.447 0.652 0.284 0.064
#> GSM531670 1 0.1643 0.727 0.956 0.000 0.044
#> GSM531674 1 0.0237 0.758 0.996 0.000 0.004
#> GSM531675 2 0.3686 0.761 0.000 0.860 0.140
#> GSM531677 2 0.0237 0.745 0.000 0.996 0.004
#> GSM531678 2 0.1031 0.737 0.000 0.976 0.024
#> GSM531680 1 0.6931 0.289 0.528 0.456 0.016
#> GSM531689 2 0.2313 0.715 0.032 0.944 0.024
#> GSM531691 2 0.3742 0.678 0.036 0.892 0.072
#> GSM531692 3 0.8482 0.289 0.092 0.408 0.500
#> GSM531694 2 0.0237 0.745 0.000 0.996 0.004
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM531602 2 0.1209 0.917 0.000 0.964 0.004 0.032
#> GSM531604 2 0.0927 0.922 0.000 0.976 0.016 0.008
#> GSM531606 2 0.1059 0.923 0.000 0.972 0.016 0.012
#> GSM531607 2 0.1209 0.917 0.000 0.964 0.004 0.032
#> GSM531608 3 0.0000 0.949 0.000 0.000 1.000 0.000
#> GSM531610 4 0.0000 0.928 0.000 0.000 0.000 1.000
#> GSM531612 4 0.0000 0.928 0.000 0.000 0.000 1.000
#> GSM531613 4 0.0000 0.928 0.000 0.000 0.000 1.000
#> GSM531614 4 0.0000 0.928 0.000 0.000 0.000 1.000
#> GSM531616 3 0.0927 0.957 0.016 0.008 0.976 0.000
#> GSM531618 4 0.3997 0.732 0.012 0.008 0.164 0.816
#> GSM531619 3 0.0336 0.954 0.008 0.000 0.992 0.000
#> GSM531620 3 0.0927 0.957 0.016 0.008 0.976 0.000
#> GSM531623 3 0.0592 0.958 0.016 0.000 0.984 0.000
#> GSM531625 3 0.0927 0.957 0.016 0.008 0.976 0.000
#> GSM531626 3 0.0927 0.957 0.016 0.008 0.976 0.000
#> GSM531632 1 0.0188 0.955 0.996 0.000 0.004 0.000
#> GSM531638 3 0.0927 0.957 0.016 0.008 0.976 0.000
#> GSM531639 1 0.4158 0.736 0.768 0.008 0.224 0.000
#> GSM531641 4 0.0000 0.928 0.000 0.000 0.000 1.000
#> GSM531642 1 0.4175 0.774 0.792 0.008 0.192 0.008
#> GSM531643 1 0.0188 0.955 0.996 0.000 0.004 0.000
#> GSM531644 1 0.0188 0.953 0.996 0.000 0.000 0.004
#> GSM531645 4 0.0000 0.928 0.000 0.000 0.000 1.000
#> GSM531646 1 0.0188 0.955 0.996 0.000 0.004 0.000
#> GSM531647 1 0.0188 0.955 0.996 0.000 0.004 0.000
#> GSM531648 4 0.0000 0.928 0.000 0.000 0.000 1.000
#> GSM531650 1 0.0188 0.955 0.996 0.000 0.004 0.000
#> GSM531651 3 0.0592 0.958 0.016 0.000 0.984 0.000
#> GSM531652 1 0.1878 0.924 0.944 0.008 0.008 0.040
#> GSM531656 1 0.3545 0.815 0.828 0.008 0.164 0.000
#> GSM531659 4 0.0469 0.924 0.000 0.012 0.000 0.988
#> GSM531661 3 0.0000 0.949 0.000 0.000 1.000 0.000
#> GSM531662 3 0.3726 0.699 0.000 0.212 0.788 0.000
#> GSM531663 4 0.0000 0.928 0.000 0.000 0.000 1.000
#> GSM531664 1 0.0188 0.955 0.996 0.000 0.004 0.000
#> GSM531666 1 0.0524 0.952 0.988 0.008 0.000 0.004
#> GSM531667 3 0.0469 0.957 0.012 0.000 0.988 0.000
#> GSM531668 4 0.0524 0.924 0.000 0.008 0.004 0.988
#> GSM531669 1 0.0188 0.955 0.996 0.000 0.004 0.000
#> GSM531671 3 0.6242 0.473 0.308 0.080 0.612 0.000
#> GSM531672 4 0.0188 0.927 0.000 0.004 0.000 0.996
#> GSM531673 2 0.4040 0.658 0.000 0.752 0.248 0.000
#> GSM531676 2 0.1767 0.907 0.044 0.944 0.012 0.000
#> GSM531679 2 0.0524 0.922 0.004 0.988 0.000 0.008
#> GSM531681 4 0.4560 0.603 0.004 0.296 0.000 0.700
#> GSM531682 2 0.0859 0.923 0.004 0.980 0.008 0.008
#> GSM531683 2 0.1209 0.917 0.000 0.964 0.004 0.032
#> GSM531684 2 0.0817 0.920 0.000 0.976 0.024 0.000
#> GSM531685 2 0.3808 0.800 0.176 0.812 0.012 0.000
#> GSM531686 4 0.4608 0.592 0.004 0.304 0.000 0.692
#> GSM531687 2 0.2329 0.889 0.072 0.916 0.012 0.000
#> GSM531688 1 0.0524 0.945 0.988 0.004 0.008 0.000
#> GSM531690 4 0.4608 0.592 0.004 0.304 0.000 0.692
#> GSM531693 1 0.0524 0.945 0.988 0.004 0.008 0.000
#> GSM531695 1 0.0592 0.942 0.984 0.016 0.000 0.000
#> GSM531603 2 0.1209 0.917 0.000 0.964 0.004 0.032
#> GSM531609 4 0.0000 0.928 0.000 0.000 0.000 1.000
#> GSM531611 4 0.0000 0.928 0.000 0.000 0.000 1.000
#> GSM531621 3 0.0592 0.958 0.016 0.000 0.984 0.000
#> GSM531622 3 0.0592 0.958 0.016 0.000 0.984 0.000
#> GSM531628 1 0.0188 0.955 0.996 0.000 0.004 0.000
#> GSM531630 3 0.0592 0.958 0.016 0.000 0.984 0.000
#> GSM531633 3 0.0592 0.958 0.016 0.000 0.984 0.000
#> GSM531635 1 0.0524 0.952 0.988 0.008 0.004 0.000
#> GSM531640 3 0.0592 0.958 0.016 0.000 0.984 0.000
#> GSM531649 1 0.0524 0.952 0.988 0.008 0.004 0.000
#> GSM531653 1 0.0188 0.955 0.996 0.000 0.004 0.000
#> GSM531657 4 0.0469 0.924 0.000 0.012 0.000 0.988
#> GSM531665 2 0.3323 0.861 0.064 0.876 0.060 0.000
#> GSM531670 1 0.3498 0.820 0.832 0.008 0.160 0.000
#> GSM531674 1 0.0188 0.955 0.996 0.000 0.004 0.000
#> GSM531675 2 0.4800 0.453 0.004 0.656 0.000 0.340
#> GSM531677 2 0.1209 0.916 0.004 0.964 0.000 0.032
#> GSM531678 2 0.0804 0.923 0.000 0.980 0.012 0.008
#> GSM531680 2 0.3975 0.725 0.240 0.760 0.000 0.000
#> GSM531689 2 0.0992 0.923 0.004 0.976 0.012 0.008
#> GSM531691 2 0.0992 0.923 0.004 0.976 0.012 0.008
#> GSM531692 2 0.0657 0.920 0.004 0.984 0.012 0.000
#> GSM531694 2 0.1209 0.917 0.000 0.964 0.004 0.032
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM531602 2 0.0992 0.6788 0.000 0.968 0.000 0.008 0.024
#> GSM531604 2 0.4300 -0.2610 0.000 0.524 0.000 0.000 0.476
#> GSM531606 2 0.2929 0.5471 0.000 0.820 0.000 0.000 0.180
#> GSM531607 2 0.1082 0.6786 0.000 0.964 0.000 0.008 0.028
#> GSM531608 3 0.1671 0.9004 0.000 0.000 0.924 0.000 0.076
#> GSM531610 4 0.0404 0.8973 0.000 0.012 0.000 0.988 0.000
#> GSM531612 4 0.0162 0.8993 0.000 0.000 0.000 0.996 0.004
#> GSM531613 4 0.0404 0.8973 0.000 0.012 0.000 0.988 0.000
#> GSM531614 4 0.0000 0.8998 0.000 0.000 0.000 1.000 0.000
#> GSM531616 3 0.1597 0.9249 0.012 0.000 0.940 0.000 0.048
#> GSM531618 4 0.6332 0.6289 0.044 0.000 0.128 0.624 0.204
#> GSM531619 3 0.0566 0.9460 0.004 0.000 0.984 0.000 0.012
#> GSM531620 3 0.0865 0.9428 0.004 0.000 0.972 0.000 0.024
#> GSM531623 3 0.0162 0.9473 0.004 0.000 0.996 0.000 0.000
#> GSM531625 3 0.0865 0.9425 0.004 0.000 0.972 0.000 0.024
#> GSM531626 3 0.1124 0.9375 0.004 0.000 0.960 0.000 0.036
#> GSM531632 1 0.1851 0.8131 0.912 0.000 0.000 0.000 0.088
#> GSM531638 3 0.1357 0.9306 0.004 0.000 0.948 0.000 0.048
#> GSM531639 1 0.5725 0.6379 0.624 0.000 0.204 0.000 0.172
#> GSM531641 4 0.0162 0.8993 0.000 0.000 0.000 0.996 0.004
#> GSM531642 1 0.6012 0.6642 0.644 0.004 0.144 0.016 0.192
#> GSM531643 1 0.2389 0.8015 0.880 0.004 0.000 0.000 0.116
#> GSM531644 1 0.3511 0.7717 0.800 0.004 0.000 0.012 0.184
#> GSM531645 4 0.0162 0.8993 0.000 0.000 0.000 0.996 0.004
#> GSM531646 1 0.1544 0.8194 0.932 0.000 0.000 0.000 0.068
#> GSM531647 1 0.1270 0.8215 0.948 0.000 0.000 0.000 0.052
#> GSM531648 4 0.2929 0.8294 0.008 0.000 0.000 0.840 0.152
#> GSM531650 1 0.0324 0.8238 0.992 0.004 0.000 0.000 0.004
#> GSM531651 3 0.0162 0.9473 0.004 0.000 0.996 0.000 0.000
#> GSM531652 1 0.4056 0.7584 0.772 0.004 0.004 0.024 0.196
#> GSM531656 1 0.4840 0.7178 0.724 0.000 0.152 0.000 0.124
#> GSM531659 4 0.4610 0.7972 0.000 0.128 0.004 0.756 0.112
#> GSM531661 3 0.1671 0.9004 0.000 0.000 0.924 0.000 0.076
#> GSM531662 3 0.5168 0.2797 0.000 0.052 0.592 0.000 0.356
#> GSM531663 4 0.0510 0.8961 0.000 0.016 0.000 0.984 0.000
#> GSM531664 1 0.0324 0.8238 0.992 0.004 0.000 0.000 0.004
#> GSM531666 1 0.3808 0.7635 0.780 0.004 0.004 0.012 0.200
#> GSM531667 3 0.0451 0.9458 0.004 0.000 0.988 0.000 0.008
#> GSM531668 4 0.5159 0.7459 0.000 0.180 0.004 0.700 0.116
#> GSM531669 1 0.1478 0.8183 0.936 0.000 0.000 0.000 0.064
#> GSM531671 5 0.6167 0.1684 0.100 0.012 0.372 0.000 0.516
#> GSM531672 4 0.3876 0.8222 0.000 0.116 0.004 0.812 0.068
#> GSM531673 5 0.6156 0.5116 0.000 0.224 0.216 0.000 0.560
#> GSM531676 5 0.4638 0.6701 0.028 0.324 0.000 0.000 0.648
#> GSM531679 2 0.2020 0.6425 0.000 0.900 0.000 0.000 0.100
#> GSM531681 2 0.4859 0.3792 0.000 0.608 0.004 0.364 0.024
#> GSM531682 2 0.3109 0.5427 0.000 0.800 0.000 0.000 0.200
#> GSM531683 2 0.0290 0.6781 0.000 0.992 0.000 0.008 0.000
#> GSM531684 2 0.4264 0.0929 0.000 0.620 0.004 0.000 0.376
#> GSM531685 5 0.4548 0.6473 0.096 0.156 0.000 0.000 0.748
#> GSM531686 2 0.4832 0.3957 0.000 0.616 0.004 0.356 0.024
#> GSM531687 5 0.4733 0.6458 0.028 0.348 0.000 0.000 0.624
#> GSM531688 1 0.3999 0.5138 0.656 0.000 0.000 0.000 0.344
#> GSM531690 2 0.4944 0.4062 0.000 0.620 0.004 0.344 0.032
#> GSM531693 1 0.4015 0.5257 0.652 0.000 0.000 0.000 0.348
#> GSM531695 1 0.5929 0.3054 0.572 0.116 0.004 0.000 0.308
#> GSM531603 2 0.1251 0.6776 0.000 0.956 0.000 0.008 0.036
#> GSM531609 4 0.0000 0.8998 0.000 0.000 0.000 1.000 0.000
#> GSM531611 4 0.0000 0.8998 0.000 0.000 0.000 1.000 0.000
#> GSM531621 3 0.0162 0.9473 0.004 0.000 0.996 0.000 0.000
#> GSM531622 3 0.0566 0.9460 0.004 0.000 0.984 0.000 0.012
#> GSM531628 1 0.0324 0.8238 0.992 0.004 0.000 0.000 0.004
#> GSM531630 3 0.0566 0.9460 0.004 0.000 0.984 0.000 0.012
#> GSM531633 3 0.0162 0.9473 0.004 0.000 0.996 0.000 0.000
#> GSM531635 1 0.2660 0.8195 0.864 0.000 0.008 0.000 0.128
#> GSM531640 3 0.0566 0.9460 0.004 0.000 0.984 0.000 0.012
#> GSM531649 1 0.1671 0.8198 0.924 0.000 0.000 0.000 0.076
#> GSM531653 1 0.1270 0.8215 0.948 0.000 0.000 0.000 0.052
#> GSM531657 4 0.4078 0.8150 0.000 0.128 0.004 0.796 0.072
#> GSM531665 5 0.4443 0.6795 0.028 0.212 0.016 0.000 0.744
#> GSM531670 1 0.4848 0.7213 0.724 0.000 0.144 0.000 0.132
#> GSM531674 1 0.1410 0.8195 0.940 0.000 0.000 0.000 0.060
#> GSM531675 2 0.3602 0.6093 0.000 0.820 0.004 0.140 0.036
#> GSM531677 2 0.2407 0.6485 0.000 0.896 0.004 0.012 0.088
#> GSM531678 2 0.3684 0.3601 0.000 0.720 0.000 0.000 0.280
#> GSM531680 5 0.6465 0.4840 0.204 0.272 0.004 0.000 0.520
#> GSM531689 5 0.4171 0.5732 0.000 0.396 0.000 0.000 0.604
#> GSM531691 5 0.3966 0.6392 0.000 0.336 0.000 0.000 0.664
#> GSM531692 5 0.3730 0.6668 0.000 0.288 0.000 0.000 0.712
#> GSM531694 2 0.0992 0.6788 0.000 0.968 0.000 0.008 0.024
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM531602 2 0.2854 0.7013 0.000 0.860 0.000 0.004 0.048 0.088
#> GSM531604 5 0.5350 0.5336 0.000 0.212 0.000 0.000 0.592 0.196
#> GSM531606 2 0.4432 0.5442 0.000 0.708 0.000 0.000 0.188 0.104
#> GSM531607 2 0.2854 0.7013 0.000 0.860 0.000 0.004 0.048 0.088
#> GSM531608 3 0.4407 0.6294 0.000 0.000 0.692 0.000 0.076 0.232
#> GSM531610 4 0.0632 0.8257 0.000 0.024 0.000 0.976 0.000 0.000
#> GSM531612 4 0.0146 0.8293 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM531613 4 0.0632 0.8257 0.000 0.024 0.000 0.976 0.000 0.000
#> GSM531614 4 0.0000 0.8294 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531616 3 0.3722 0.7688 0.008 0.004 0.772 0.000 0.024 0.192
#> GSM531618 6 0.5465 -0.1558 0.012 0.012 0.056 0.424 0.000 0.496
#> GSM531619 3 0.1462 0.8615 0.000 0.000 0.936 0.000 0.008 0.056
#> GSM531620 3 0.3013 0.8155 0.000 0.004 0.832 0.000 0.024 0.140
#> GSM531623 3 0.0692 0.8718 0.000 0.000 0.976 0.000 0.004 0.020
#> GSM531625 3 0.2848 0.8238 0.000 0.004 0.848 0.000 0.024 0.124
#> GSM531626 3 0.3380 0.7968 0.004 0.004 0.804 0.000 0.024 0.164
#> GSM531632 1 0.2221 0.5769 0.896 0.000 0.000 0.000 0.032 0.072
#> GSM531638 3 0.3613 0.7727 0.004 0.004 0.776 0.000 0.024 0.192
#> GSM531639 6 0.6153 0.3136 0.368 0.004 0.168 0.000 0.012 0.448
#> GSM531641 4 0.0146 0.8293 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM531642 6 0.5507 0.4941 0.364 0.000 0.064 0.032 0.000 0.540
#> GSM531643 1 0.3934 -0.0994 0.616 0.000 0.000 0.000 0.008 0.376
#> GSM531644 1 0.4652 -0.4434 0.508 0.000 0.000 0.016 0.016 0.460
#> GSM531645 4 0.0146 0.8293 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM531646 1 0.2615 0.5571 0.876 0.000 0.008 0.000 0.028 0.088
#> GSM531647 1 0.0000 0.5971 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM531648 4 0.3954 0.4726 0.000 0.012 0.000 0.636 0.000 0.352
#> GSM531650 1 0.2060 0.5529 0.900 0.000 0.000 0.000 0.016 0.084
#> GSM531651 3 0.0777 0.8711 0.000 0.000 0.972 0.000 0.004 0.024
#> GSM531652 6 0.5295 0.4406 0.448 0.012 0.000 0.036 0.016 0.488
#> GSM531656 1 0.5784 -0.3386 0.488 0.004 0.084 0.000 0.024 0.400
#> GSM531659 4 0.6012 0.5544 0.000 0.224 0.000 0.540 0.020 0.216
#> GSM531661 3 0.4455 0.6232 0.000 0.000 0.688 0.000 0.080 0.232
#> GSM531662 5 0.6120 0.3398 0.000 0.008 0.308 0.000 0.456 0.228
#> GSM531663 4 0.0935 0.8228 0.000 0.032 0.000 0.964 0.000 0.004
#> GSM531664 1 0.2112 0.5577 0.896 0.000 0.000 0.000 0.016 0.088
#> GSM531666 6 0.5111 0.4208 0.456 0.012 0.000 0.024 0.016 0.492
#> GSM531667 3 0.2145 0.8404 0.000 0.000 0.900 0.000 0.028 0.072
#> GSM531668 4 0.6308 0.3300 0.000 0.340 0.000 0.404 0.012 0.244
#> GSM531669 1 0.1092 0.5978 0.960 0.000 0.000 0.000 0.020 0.020
#> GSM531671 5 0.6417 0.4835 0.052 0.000 0.176 0.000 0.516 0.256
#> GSM531672 4 0.4707 0.6580 0.000 0.204 0.000 0.676 0.000 0.120
#> GSM531673 5 0.5529 0.6127 0.000 0.036 0.124 0.000 0.636 0.204
#> GSM531676 5 0.2656 0.6474 0.008 0.120 0.000 0.000 0.860 0.012
#> GSM531679 2 0.3052 0.6459 0.000 0.780 0.000 0.000 0.216 0.004
#> GSM531681 2 0.4414 0.5421 0.000 0.672 0.000 0.280 0.040 0.008
#> GSM531682 2 0.3615 0.5463 0.000 0.700 0.000 0.000 0.292 0.008
#> GSM531683 2 0.0767 0.7121 0.000 0.976 0.000 0.004 0.012 0.008
#> GSM531684 5 0.6317 0.2752 0.000 0.328 0.012 0.000 0.408 0.252
#> GSM531685 5 0.2875 0.6599 0.064 0.036 0.000 0.000 0.872 0.028
#> GSM531686 2 0.4554 0.5522 0.000 0.668 0.000 0.272 0.052 0.008
#> GSM531687 5 0.3565 0.6077 0.008 0.156 0.000 0.000 0.796 0.040
#> GSM531688 1 0.4238 0.3755 0.628 0.000 0.000 0.000 0.344 0.028
#> GSM531690 2 0.4731 0.5732 0.000 0.692 0.000 0.228 0.048 0.032
#> GSM531693 1 0.4467 0.3898 0.632 0.000 0.000 0.000 0.320 0.048
#> GSM531695 1 0.6500 0.2383 0.464 0.076 0.000 0.000 0.348 0.112
#> GSM531603 2 0.2721 0.7008 0.000 0.868 0.000 0.004 0.040 0.088
#> GSM531609 4 0.0146 0.8293 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM531611 4 0.0146 0.8298 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM531621 3 0.0146 0.8735 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM531622 3 0.0405 0.8736 0.000 0.000 0.988 0.000 0.004 0.008
#> GSM531628 1 0.2006 0.5564 0.904 0.000 0.000 0.000 0.016 0.080
#> GSM531630 3 0.0405 0.8736 0.000 0.000 0.988 0.000 0.004 0.008
#> GSM531633 3 0.0603 0.8719 0.000 0.000 0.980 0.000 0.004 0.016
#> GSM531635 1 0.5034 0.2904 0.660 0.004 0.060 0.000 0.024 0.252
#> GSM531640 3 0.1219 0.8656 0.000 0.000 0.948 0.000 0.004 0.048
#> GSM531649 1 0.3225 0.5132 0.828 0.004 0.008 0.000 0.024 0.136
#> GSM531653 1 0.0000 0.5971 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM531657 4 0.4858 0.6363 0.000 0.228 0.000 0.652 0.000 0.120
#> GSM531665 5 0.3875 0.6743 0.020 0.036 0.000 0.000 0.776 0.168
#> GSM531670 1 0.5831 -0.3360 0.488 0.004 0.076 0.000 0.032 0.400
#> GSM531674 1 0.0909 0.5990 0.968 0.000 0.000 0.000 0.012 0.020
#> GSM531675 2 0.4029 0.6722 0.000 0.784 0.000 0.132 0.052 0.032
#> GSM531677 2 0.3288 0.6625 0.000 0.800 0.000 0.008 0.176 0.016
#> GSM531678 2 0.4929 0.1790 0.000 0.508 0.000 0.000 0.428 0.064
#> GSM531680 5 0.5377 0.4929 0.080 0.136 0.000 0.000 0.684 0.100
#> GSM531689 5 0.2841 0.6148 0.000 0.164 0.000 0.000 0.824 0.012
#> GSM531691 5 0.2312 0.6555 0.000 0.112 0.000 0.000 0.876 0.012
#> GSM531692 5 0.3516 0.6740 0.000 0.048 0.000 0.000 0.788 0.164
#> GSM531694 2 0.2854 0.7013 0.000 0.860 0.000 0.004 0.048 0.088
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> MAD:kmeans 80 1.000 2
#> MAD:kmeans 71 0.960 3
#> MAD:kmeans 78 0.350 4
#> MAD:kmeans 70 0.625 5
#> MAD:kmeans 60 0.887 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "skmeans"]
# you can also extract it by
# res = res_list["MAD:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 80 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.740 0.859 0.943 0.5059 0.497 0.497
#> 3 3 0.911 0.900 0.953 0.3225 0.721 0.495
#> 4 4 0.864 0.850 0.941 0.1298 0.832 0.547
#> 5 5 0.839 0.841 0.910 0.0618 0.921 0.694
#> 6 6 0.791 0.650 0.817 0.0366 0.960 0.806
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
#> GSM531602 2 0.0000 0.9601 0.000 1.000
#> GSM531604 2 0.0000 0.9601 0.000 1.000
#> GSM531606 2 0.0000 0.9601 0.000 1.000
#> GSM531607 2 0.0000 0.9601 0.000 1.000
#> GSM531608 2 0.1184 0.9469 0.016 0.984
#> GSM531610 2 0.0000 0.9601 0.000 1.000
#> GSM531612 2 0.0000 0.9601 0.000 1.000
#> GSM531613 2 0.0000 0.9601 0.000 1.000
#> GSM531614 2 0.0000 0.9601 0.000 1.000
#> GSM531616 1 0.0000 0.9129 1.000 0.000
#> GSM531618 1 0.9970 0.1825 0.532 0.468
#> GSM531619 1 0.7219 0.7323 0.800 0.200
#> GSM531620 1 0.0000 0.9129 1.000 0.000
#> GSM531623 1 0.0000 0.9129 1.000 0.000
#> GSM531625 1 0.0000 0.9129 1.000 0.000
#> GSM531626 1 0.0000 0.9129 1.000 0.000
#> GSM531632 1 0.0000 0.9129 1.000 0.000
#> GSM531638 1 0.0000 0.9129 1.000 0.000
#> GSM531639 1 0.0000 0.9129 1.000 0.000
#> GSM531641 2 0.0000 0.9601 0.000 1.000
#> GSM531642 1 0.0000 0.9129 1.000 0.000
#> GSM531643 1 0.0000 0.9129 1.000 0.000
#> GSM531644 1 0.0000 0.9129 1.000 0.000
#> GSM531645 2 0.0000 0.9601 0.000 1.000
#> GSM531646 1 0.0000 0.9129 1.000 0.000
#> GSM531647 1 0.0000 0.9129 1.000 0.000
#> GSM531648 2 0.9661 0.2650 0.392 0.608
#> GSM531650 1 0.0000 0.9129 1.000 0.000
#> GSM531651 1 0.0000 0.9129 1.000 0.000
#> GSM531652 1 0.0000 0.9129 1.000 0.000
#> GSM531656 1 0.0000 0.9129 1.000 0.000
#> GSM531659 2 0.0000 0.9601 0.000 1.000
#> GSM531661 1 0.7219 0.7323 0.800 0.200
#> GSM531662 1 0.2778 0.8794 0.952 0.048
#> GSM531663 2 0.0000 0.9601 0.000 1.000
#> GSM531664 1 0.0000 0.9129 1.000 0.000
#> GSM531666 1 0.0672 0.9076 0.992 0.008
#> GSM531667 1 0.7219 0.7323 0.800 0.200
#> GSM531668 2 0.0000 0.9601 0.000 1.000
#> GSM531669 1 0.0000 0.9129 1.000 0.000
#> GSM531671 1 0.0000 0.9129 1.000 0.000
#> GSM531672 2 0.0000 0.9601 0.000 1.000
#> GSM531673 1 0.9866 0.2566 0.568 0.432
#> GSM531676 2 0.7219 0.7373 0.200 0.800
#> GSM531679 2 0.0000 0.9601 0.000 1.000
#> GSM531681 2 0.0000 0.9601 0.000 1.000
#> GSM531682 2 0.0000 0.9601 0.000 1.000
#> GSM531683 2 0.0000 0.9601 0.000 1.000
#> GSM531684 2 0.0000 0.9601 0.000 1.000
#> GSM531685 1 0.9661 0.3651 0.608 0.392
#> GSM531686 2 0.0000 0.9601 0.000 1.000
#> GSM531687 2 0.7219 0.7373 0.200 0.800
#> GSM531688 1 0.9580 0.3940 0.620 0.380
#> GSM531690 2 0.0000 0.9601 0.000 1.000
#> GSM531693 1 0.0000 0.9129 1.000 0.000
#> GSM531695 2 0.7219 0.7373 0.200 0.800
#> GSM531603 2 0.0000 0.9601 0.000 1.000
#> GSM531609 2 0.0000 0.9601 0.000 1.000
#> GSM531611 2 0.0000 0.9601 0.000 1.000
#> GSM531621 1 0.0000 0.9129 1.000 0.000
#> GSM531622 1 0.0000 0.9129 1.000 0.000
#> GSM531628 1 0.0000 0.9129 1.000 0.000
#> GSM531630 1 0.0000 0.9129 1.000 0.000
#> GSM531633 1 0.0000 0.9129 1.000 0.000
#> GSM531635 1 0.0000 0.9129 1.000 0.000
#> GSM531640 1 0.7219 0.7323 0.800 0.200
#> GSM531649 1 0.0000 0.9129 1.000 0.000
#> GSM531653 1 0.0000 0.9129 1.000 0.000
#> GSM531657 2 0.0000 0.9601 0.000 1.000
#> GSM531665 1 0.8861 0.5537 0.696 0.304
#> GSM531670 1 0.0000 0.9129 1.000 0.000
#> GSM531674 1 0.0000 0.9129 1.000 0.000
#> GSM531675 2 0.0000 0.9601 0.000 1.000
#> GSM531677 2 0.0000 0.9601 0.000 1.000
#> GSM531678 2 0.0000 0.9601 0.000 1.000
#> GSM531680 2 0.7219 0.7373 0.200 0.800
#> GSM531689 2 0.0000 0.9601 0.000 1.000
#> GSM531691 2 0.1843 0.9360 0.028 0.972
#> GSM531692 1 0.9998 0.0535 0.508 0.492
#> GSM531694 2 0.0000 0.9601 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM531602 2 0.0892 0.969 0.020 0.980 0.000
#> GSM531604 3 0.7074 0.057 0.020 0.480 0.500
#> GSM531606 2 0.0892 0.969 0.020 0.980 0.000
#> GSM531607 2 0.0892 0.969 0.020 0.980 0.000
#> GSM531608 3 0.0237 0.917 0.000 0.004 0.996
#> GSM531610 2 0.0000 0.969 0.000 1.000 0.000
#> GSM531612 2 0.0000 0.969 0.000 1.000 0.000
#> GSM531613 2 0.0000 0.969 0.000 1.000 0.000
#> GSM531614 2 0.0000 0.969 0.000 1.000 0.000
#> GSM531616 3 0.0592 0.911 0.012 0.000 0.988
#> GSM531618 2 0.6881 0.305 0.020 0.592 0.388
#> GSM531619 3 0.0000 0.919 0.000 0.000 1.000
#> GSM531620 3 0.0000 0.919 0.000 0.000 1.000
#> GSM531623 3 0.0000 0.919 0.000 0.000 1.000
#> GSM531625 3 0.0000 0.919 0.000 0.000 1.000
#> GSM531626 3 0.0000 0.919 0.000 0.000 1.000
#> GSM531632 1 0.0892 0.958 0.980 0.000 0.020
#> GSM531638 3 0.0000 0.919 0.000 0.000 1.000
#> GSM531639 1 0.6204 0.321 0.576 0.000 0.424
#> GSM531641 2 0.0000 0.969 0.000 1.000 0.000
#> GSM531642 1 0.4953 0.779 0.808 0.016 0.176
#> GSM531643 1 0.0892 0.958 0.980 0.000 0.020
#> GSM531644 1 0.0983 0.952 0.980 0.016 0.004
#> GSM531645 2 0.0000 0.969 0.000 1.000 0.000
#> GSM531646 1 0.0892 0.958 0.980 0.000 0.020
#> GSM531647 1 0.0892 0.958 0.980 0.000 0.020
#> GSM531648 2 0.0892 0.954 0.020 0.980 0.000
#> GSM531650 1 0.0892 0.958 0.980 0.000 0.020
#> GSM531651 3 0.0000 0.919 0.000 0.000 1.000
#> GSM531652 1 0.4136 0.848 0.864 0.020 0.116
#> GSM531656 1 0.1411 0.949 0.964 0.000 0.036
#> GSM531659 2 0.0000 0.969 0.000 1.000 0.000
#> GSM531661 3 0.0000 0.919 0.000 0.000 1.000
#> GSM531662 3 0.0237 0.917 0.004 0.000 0.996
#> GSM531663 2 0.0000 0.969 0.000 1.000 0.000
#> GSM531664 1 0.1015 0.954 0.980 0.012 0.008
#> GSM531666 1 0.0892 0.949 0.980 0.020 0.000
#> GSM531667 3 0.0000 0.919 0.000 0.000 1.000
#> GSM531668 2 0.0000 0.969 0.000 1.000 0.000
#> GSM531669 1 0.0892 0.958 0.980 0.000 0.020
#> GSM531671 3 0.4555 0.723 0.200 0.000 0.800
#> GSM531672 2 0.0000 0.969 0.000 1.000 0.000
#> GSM531673 3 0.0892 0.905 0.020 0.000 0.980
#> GSM531676 1 0.0892 0.937 0.980 0.020 0.000
#> GSM531679 2 0.0892 0.969 0.020 0.980 0.000
#> GSM531681 2 0.0892 0.969 0.020 0.980 0.000
#> GSM531682 2 0.0892 0.969 0.020 0.980 0.000
#> GSM531683 2 0.0892 0.969 0.020 0.980 0.000
#> GSM531684 3 0.6161 0.583 0.020 0.272 0.708
#> GSM531685 1 0.0000 0.950 1.000 0.000 0.000
#> GSM531686 2 0.0892 0.969 0.020 0.980 0.000
#> GSM531687 1 0.0892 0.937 0.980 0.020 0.000
#> GSM531688 1 0.0000 0.950 1.000 0.000 0.000
#> GSM531690 2 0.0892 0.969 0.020 0.980 0.000
#> GSM531693 1 0.0892 0.958 0.980 0.000 0.020
#> GSM531695 1 0.0000 0.950 1.000 0.000 0.000
#> GSM531603 2 0.0892 0.969 0.020 0.980 0.000
#> GSM531609 2 0.0000 0.969 0.000 1.000 0.000
#> GSM531611 2 0.0000 0.969 0.000 1.000 0.000
#> GSM531621 3 0.0000 0.919 0.000 0.000 1.000
#> GSM531622 3 0.0000 0.919 0.000 0.000 1.000
#> GSM531628 1 0.0892 0.958 0.980 0.000 0.020
#> GSM531630 3 0.0000 0.919 0.000 0.000 1.000
#> GSM531633 3 0.0000 0.919 0.000 0.000 1.000
#> GSM531635 1 0.0892 0.958 0.980 0.000 0.020
#> GSM531640 3 0.0000 0.919 0.000 0.000 1.000
#> GSM531649 1 0.0892 0.958 0.980 0.000 0.020
#> GSM531653 1 0.0892 0.958 0.980 0.000 0.020
#> GSM531657 2 0.0000 0.969 0.000 1.000 0.000
#> GSM531665 3 0.6204 0.320 0.424 0.000 0.576
#> GSM531670 1 0.1289 0.952 0.968 0.000 0.032
#> GSM531674 1 0.0892 0.958 0.980 0.000 0.020
#> GSM531675 2 0.0892 0.969 0.020 0.980 0.000
#> GSM531677 2 0.0892 0.969 0.020 0.980 0.000
#> GSM531678 2 0.0892 0.969 0.020 0.980 0.000
#> GSM531680 1 0.0892 0.937 0.980 0.020 0.000
#> GSM531689 2 0.2537 0.917 0.080 0.920 0.000
#> GSM531691 2 0.4397 0.855 0.116 0.856 0.028
#> GSM531692 3 0.4452 0.753 0.192 0.000 0.808
#> GSM531694 2 0.0892 0.969 0.020 0.980 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM531602 2 0.0592 0.9035 0.000 0.984 0.000 0.016
#> GSM531604 2 0.0000 0.9047 0.000 1.000 0.000 0.000
#> GSM531606 2 0.0592 0.9035 0.000 0.984 0.000 0.016
#> GSM531607 2 0.0592 0.9035 0.000 0.984 0.000 0.016
#> GSM531608 3 0.0000 0.9566 0.000 0.000 1.000 0.000
#> GSM531610 4 0.0000 0.9282 0.000 0.000 0.000 1.000
#> GSM531612 4 0.0000 0.9282 0.000 0.000 0.000 1.000
#> GSM531613 4 0.0000 0.9282 0.000 0.000 0.000 1.000
#> GSM531614 4 0.0000 0.9282 0.000 0.000 0.000 1.000
#> GSM531616 3 0.0000 0.9566 0.000 0.000 1.000 0.000
#> GSM531618 4 0.1211 0.8906 0.000 0.000 0.040 0.960
#> GSM531619 3 0.0000 0.9566 0.000 0.000 1.000 0.000
#> GSM531620 3 0.0000 0.9566 0.000 0.000 1.000 0.000
#> GSM531623 3 0.0000 0.9566 0.000 0.000 1.000 0.000
#> GSM531625 3 0.0000 0.9566 0.000 0.000 1.000 0.000
#> GSM531626 3 0.0000 0.9566 0.000 0.000 1.000 0.000
#> GSM531632 1 0.0000 0.9389 1.000 0.000 0.000 0.000
#> GSM531638 3 0.0000 0.9566 0.000 0.000 1.000 0.000
#> GSM531639 1 0.4843 0.4204 0.604 0.000 0.396 0.000
#> GSM531641 4 0.0000 0.9282 0.000 0.000 0.000 1.000
#> GSM531642 1 0.4137 0.7478 0.780 0.000 0.208 0.012
#> GSM531643 1 0.0000 0.9389 1.000 0.000 0.000 0.000
#> GSM531644 1 0.0000 0.9389 1.000 0.000 0.000 0.000
#> GSM531645 4 0.0000 0.9282 0.000 0.000 0.000 1.000
#> GSM531646 1 0.0000 0.9389 1.000 0.000 0.000 0.000
#> GSM531647 1 0.0000 0.9389 1.000 0.000 0.000 0.000
#> GSM531648 4 0.0000 0.9282 0.000 0.000 0.000 1.000
#> GSM531650 1 0.0000 0.9389 1.000 0.000 0.000 0.000
#> GSM531651 3 0.0000 0.9566 0.000 0.000 1.000 0.000
#> GSM531652 1 0.1109 0.9174 0.968 0.000 0.004 0.028
#> GSM531656 1 0.3400 0.7879 0.820 0.000 0.180 0.000
#> GSM531659 4 0.0000 0.9282 0.000 0.000 0.000 1.000
#> GSM531661 3 0.0000 0.9566 0.000 0.000 1.000 0.000
#> GSM531662 3 0.3444 0.7699 0.000 0.184 0.816 0.000
#> GSM531663 4 0.0000 0.9282 0.000 0.000 0.000 1.000
#> GSM531664 1 0.0000 0.9389 1.000 0.000 0.000 0.000
#> GSM531666 1 0.0000 0.9389 1.000 0.000 0.000 0.000
#> GSM531667 3 0.0000 0.9566 0.000 0.000 1.000 0.000
#> GSM531668 4 0.0000 0.9282 0.000 0.000 0.000 1.000
#> GSM531669 1 0.0000 0.9389 1.000 0.000 0.000 0.000
#> GSM531671 3 0.4095 0.7338 0.192 0.016 0.792 0.000
#> GSM531672 4 0.0000 0.9282 0.000 0.000 0.000 1.000
#> GSM531673 3 0.4661 0.4953 0.000 0.348 0.652 0.000
#> GSM531676 2 0.0592 0.8977 0.016 0.984 0.000 0.000
#> GSM531679 2 0.0000 0.9047 0.000 1.000 0.000 0.000
#> GSM531681 4 0.5000 -0.0504 0.000 0.500 0.000 0.500
#> GSM531682 2 0.0188 0.9047 0.000 0.996 0.000 0.004
#> GSM531683 2 0.0592 0.9035 0.000 0.984 0.000 0.016
#> GSM531684 2 0.0000 0.9047 0.000 1.000 0.000 0.000
#> GSM531685 2 0.2921 0.7951 0.140 0.860 0.000 0.000
#> GSM531686 2 0.4999 -0.0225 0.000 0.508 0.000 0.492
#> GSM531687 2 0.0817 0.8934 0.024 0.976 0.000 0.000
#> GSM531688 1 0.0000 0.9389 1.000 0.000 0.000 0.000
#> GSM531690 4 0.4994 0.0245 0.000 0.480 0.000 0.520
#> GSM531693 1 0.0000 0.9389 1.000 0.000 0.000 0.000
#> GSM531695 1 0.3801 0.6719 0.780 0.220 0.000 0.000
#> GSM531603 2 0.0817 0.8984 0.000 0.976 0.000 0.024
#> GSM531609 4 0.0000 0.9282 0.000 0.000 0.000 1.000
#> GSM531611 4 0.0000 0.9282 0.000 0.000 0.000 1.000
#> GSM531621 3 0.0000 0.9566 0.000 0.000 1.000 0.000
#> GSM531622 3 0.0000 0.9566 0.000 0.000 1.000 0.000
#> GSM531628 1 0.0000 0.9389 1.000 0.000 0.000 0.000
#> GSM531630 3 0.0000 0.9566 0.000 0.000 1.000 0.000
#> GSM531633 3 0.0000 0.9566 0.000 0.000 1.000 0.000
#> GSM531635 1 0.0000 0.9389 1.000 0.000 0.000 0.000
#> GSM531640 3 0.0000 0.9566 0.000 0.000 1.000 0.000
#> GSM531649 1 0.0000 0.9389 1.000 0.000 0.000 0.000
#> GSM531653 1 0.0000 0.9389 1.000 0.000 0.000 0.000
#> GSM531657 4 0.0000 0.9282 0.000 0.000 0.000 1.000
#> GSM531665 2 0.5386 0.2943 0.020 0.612 0.368 0.000
#> GSM531670 1 0.3356 0.7923 0.824 0.000 0.176 0.000
#> GSM531674 1 0.0000 0.9389 1.000 0.000 0.000 0.000
#> GSM531675 2 0.4817 0.3224 0.000 0.612 0.000 0.388
#> GSM531677 2 0.0592 0.9035 0.000 0.984 0.000 0.016
#> GSM531678 2 0.0000 0.9047 0.000 1.000 0.000 0.000
#> GSM531680 2 0.3569 0.7393 0.196 0.804 0.000 0.000
#> GSM531689 2 0.0000 0.9047 0.000 1.000 0.000 0.000
#> GSM531691 2 0.0000 0.9047 0.000 1.000 0.000 0.000
#> GSM531692 2 0.0000 0.9047 0.000 1.000 0.000 0.000
#> GSM531694 2 0.0592 0.9035 0.000 0.984 0.000 0.016
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM531602 2 0.0000 0.918 0.000 1.000 0.000 0.000 0.000
#> GSM531604 2 0.3983 0.509 0.000 0.660 0.000 0.000 0.340
#> GSM531606 2 0.0404 0.915 0.000 0.988 0.000 0.000 0.012
#> GSM531607 2 0.0000 0.918 0.000 1.000 0.000 0.000 0.000
#> GSM531608 3 0.1668 0.891 0.000 0.028 0.940 0.000 0.032
#> GSM531610 4 0.0000 0.965 0.000 0.000 0.000 1.000 0.000
#> GSM531612 4 0.0000 0.965 0.000 0.000 0.000 1.000 0.000
#> GSM531613 4 0.0290 0.963 0.000 0.008 0.000 0.992 0.000
#> GSM531614 4 0.0000 0.965 0.000 0.000 0.000 1.000 0.000
#> GSM531616 3 0.0290 0.916 0.008 0.000 0.992 0.000 0.000
#> GSM531618 4 0.1187 0.946 0.004 0.004 0.004 0.964 0.024
#> GSM531619 3 0.0609 0.911 0.000 0.020 0.980 0.000 0.000
#> GSM531620 3 0.0000 0.921 0.000 0.000 1.000 0.000 0.000
#> GSM531623 3 0.0000 0.921 0.000 0.000 1.000 0.000 0.000
#> GSM531625 3 0.0000 0.921 0.000 0.000 1.000 0.000 0.000
#> GSM531626 3 0.0000 0.921 0.000 0.000 1.000 0.000 0.000
#> GSM531632 1 0.2852 0.776 0.828 0.000 0.000 0.000 0.172
#> GSM531638 3 0.0000 0.921 0.000 0.000 1.000 0.000 0.000
#> GSM531639 1 0.4329 0.595 0.672 0.000 0.312 0.000 0.016
#> GSM531641 4 0.0000 0.965 0.000 0.000 0.000 1.000 0.000
#> GSM531642 1 0.4230 0.729 0.764 0.000 0.196 0.016 0.024
#> GSM531643 1 0.0404 0.884 0.988 0.000 0.000 0.000 0.012
#> GSM531644 1 0.0992 0.879 0.968 0.000 0.000 0.008 0.024
#> GSM531645 4 0.0000 0.965 0.000 0.000 0.000 1.000 0.000
#> GSM531646 1 0.1197 0.881 0.952 0.000 0.000 0.000 0.048
#> GSM531647 1 0.1043 0.883 0.960 0.000 0.000 0.000 0.040
#> GSM531648 4 0.0703 0.952 0.000 0.000 0.000 0.976 0.024
#> GSM531650 1 0.0162 0.886 0.996 0.000 0.000 0.000 0.004
#> GSM531651 3 0.0000 0.921 0.000 0.000 1.000 0.000 0.000
#> GSM531652 1 0.2423 0.835 0.896 0.000 0.000 0.080 0.024
#> GSM531656 1 0.3048 0.768 0.820 0.000 0.176 0.000 0.004
#> GSM531659 4 0.1478 0.934 0.000 0.064 0.000 0.936 0.000
#> GSM531661 3 0.1750 0.889 0.000 0.028 0.936 0.000 0.036
#> GSM531662 3 0.4506 0.598 0.000 0.028 0.676 0.000 0.296
#> GSM531663 4 0.0510 0.961 0.000 0.016 0.000 0.984 0.000
#> GSM531664 1 0.0404 0.886 0.988 0.000 0.000 0.000 0.012
#> GSM531666 1 0.1310 0.875 0.956 0.000 0.000 0.020 0.024
#> GSM531667 3 0.0609 0.911 0.000 0.020 0.980 0.000 0.000
#> GSM531668 4 0.2377 0.882 0.000 0.128 0.000 0.872 0.000
#> GSM531669 1 0.2471 0.816 0.864 0.000 0.000 0.000 0.136
#> GSM531671 3 0.5579 0.292 0.072 0.000 0.508 0.000 0.420
#> GSM531672 4 0.1851 0.917 0.000 0.088 0.000 0.912 0.000
#> GSM531673 3 0.5003 0.361 0.000 0.032 0.544 0.000 0.424
#> GSM531676 5 0.2286 0.760 0.004 0.108 0.000 0.000 0.888
#> GSM531679 2 0.0703 0.914 0.000 0.976 0.000 0.000 0.024
#> GSM531681 2 0.1732 0.879 0.000 0.920 0.000 0.080 0.000
#> GSM531682 2 0.0794 0.913 0.000 0.972 0.000 0.000 0.028
#> GSM531683 2 0.0000 0.918 0.000 1.000 0.000 0.000 0.000
#> GSM531684 2 0.3424 0.666 0.000 0.760 0.000 0.000 0.240
#> GSM531685 5 0.0798 0.757 0.008 0.016 0.000 0.000 0.976
#> GSM531686 2 0.1732 0.879 0.000 0.920 0.000 0.080 0.000
#> GSM531687 5 0.3491 0.707 0.004 0.228 0.000 0.000 0.768
#> GSM531688 5 0.3876 0.541 0.316 0.000 0.000 0.000 0.684
#> GSM531690 2 0.1671 0.881 0.000 0.924 0.000 0.076 0.000
#> GSM531693 5 0.3876 0.541 0.316 0.000 0.000 0.000 0.684
#> GSM531695 5 0.6160 0.623 0.284 0.172 0.000 0.000 0.544
#> GSM531603 2 0.0000 0.918 0.000 1.000 0.000 0.000 0.000
#> GSM531609 4 0.0000 0.965 0.000 0.000 0.000 1.000 0.000
#> GSM531611 4 0.0000 0.965 0.000 0.000 0.000 1.000 0.000
#> GSM531621 3 0.0000 0.921 0.000 0.000 1.000 0.000 0.000
#> GSM531622 3 0.0000 0.921 0.000 0.000 1.000 0.000 0.000
#> GSM531628 1 0.0290 0.886 0.992 0.000 0.000 0.000 0.008
#> GSM531630 3 0.0000 0.921 0.000 0.000 1.000 0.000 0.000
#> GSM531633 3 0.0000 0.921 0.000 0.000 1.000 0.000 0.000
#> GSM531635 1 0.1753 0.883 0.936 0.000 0.032 0.000 0.032
#> GSM531640 3 0.0000 0.921 0.000 0.000 1.000 0.000 0.000
#> GSM531649 1 0.1648 0.884 0.940 0.000 0.020 0.000 0.040
#> GSM531653 1 0.1043 0.883 0.960 0.000 0.000 0.000 0.040
#> GSM531657 4 0.2020 0.907 0.000 0.100 0.000 0.900 0.000
#> GSM531665 5 0.0854 0.755 0.008 0.012 0.004 0.000 0.976
#> GSM531670 1 0.3132 0.770 0.820 0.000 0.172 0.000 0.008
#> GSM531674 1 0.1792 0.859 0.916 0.000 0.000 0.000 0.084
#> GSM531675 2 0.1270 0.898 0.000 0.948 0.000 0.052 0.000
#> GSM531677 2 0.0865 0.914 0.000 0.972 0.000 0.004 0.024
#> GSM531678 2 0.1608 0.877 0.000 0.928 0.000 0.000 0.072
#> GSM531680 5 0.5759 0.681 0.160 0.224 0.000 0.000 0.616
#> GSM531689 5 0.3636 0.655 0.000 0.272 0.000 0.000 0.728
#> GSM531691 5 0.3395 0.684 0.000 0.236 0.000 0.000 0.764
#> GSM531692 5 0.1608 0.754 0.000 0.072 0.000 0.000 0.928
#> GSM531694 2 0.0000 0.918 0.000 1.000 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
#> GSM531602 2 0.0865 0.89655 0.000 0.964 0.000 0.000 0.000 0.036
#> GSM531604 5 0.5999 0.15665 0.000 0.256 0.000 0.000 0.432 0.312
#> GSM531606 2 0.1995 0.86578 0.000 0.912 0.000 0.000 0.036 0.052
#> GSM531607 2 0.0865 0.89655 0.000 0.964 0.000 0.000 0.000 0.036
#> GSM531608 3 0.4408 0.41222 0.000 0.000 0.664 0.000 0.056 0.280
#> GSM531610 4 0.0260 0.87193 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM531612 4 0.0000 0.87278 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531613 4 0.0458 0.87018 0.000 0.016 0.000 0.984 0.000 0.000
#> GSM531614 4 0.0000 0.87278 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531616 3 0.2553 0.80698 0.008 0.000 0.848 0.000 0.000 0.144
#> GSM531618 4 0.4228 0.50677 0.000 0.000 0.020 0.588 0.000 0.392
#> GSM531619 3 0.0260 0.86588 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM531620 3 0.1714 0.84507 0.000 0.000 0.908 0.000 0.000 0.092
#> GSM531623 3 0.0146 0.86779 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM531625 3 0.2402 0.81470 0.004 0.000 0.856 0.000 0.000 0.140
#> GSM531626 3 0.2402 0.81470 0.004 0.000 0.856 0.000 0.000 0.140
#> GSM531632 1 0.1890 0.72017 0.916 0.000 0.000 0.000 0.024 0.060
#> GSM531638 3 0.2442 0.81110 0.004 0.000 0.852 0.000 0.000 0.144
#> GSM531639 6 0.6082 -0.09635 0.360 0.000 0.272 0.000 0.000 0.368
#> GSM531641 4 0.0000 0.87278 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531642 6 0.4800 -0.30221 0.372 0.000 0.032 0.016 0.000 0.580
#> GSM531643 1 0.2260 0.72100 0.860 0.000 0.000 0.000 0.000 0.140
#> GSM531644 1 0.4253 0.32397 0.524 0.000 0.000 0.016 0.000 0.460
#> GSM531645 4 0.0000 0.87278 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531646 1 0.1152 0.74815 0.952 0.000 0.000 0.000 0.004 0.044
#> GSM531647 1 0.0000 0.75919 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM531648 4 0.3578 0.59777 0.000 0.000 0.000 0.660 0.000 0.340
#> GSM531650 1 0.1141 0.75908 0.948 0.000 0.000 0.000 0.000 0.052
#> GSM531651 3 0.0146 0.86779 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM531652 1 0.4757 0.26562 0.484 0.000 0.000 0.048 0.000 0.468
#> GSM531656 1 0.4640 0.53063 0.676 0.000 0.080 0.000 0.004 0.240
#> GSM531659 4 0.2350 0.83105 0.000 0.100 0.000 0.880 0.000 0.020
#> GSM531661 3 0.4445 0.39486 0.000 0.000 0.656 0.000 0.056 0.288
#> GSM531662 6 0.6125 -0.00425 0.000 0.000 0.336 0.000 0.312 0.352
#> GSM531663 4 0.0713 0.86640 0.000 0.028 0.000 0.972 0.000 0.000
#> GSM531664 1 0.1141 0.75908 0.948 0.000 0.000 0.000 0.000 0.052
#> GSM531666 1 0.4401 0.30722 0.512 0.000 0.000 0.024 0.000 0.464
#> GSM531667 3 0.0547 0.85902 0.000 0.000 0.980 0.000 0.000 0.020
#> GSM531668 4 0.4583 0.39428 0.000 0.376 0.000 0.580 0.000 0.044
#> GSM531669 1 0.1082 0.74333 0.956 0.000 0.000 0.000 0.040 0.004
#> GSM531671 6 0.7452 -0.01907 0.164 0.000 0.184 0.000 0.292 0.360
#> GSM531672 4 0.2653 0.80137 0.000 0.144 0.000 0.844 0.000 0.012
#> GSM531673 5 0.6164 -0.09973 0.000 0.012 0.200 0.000 0.436 0.352
#> GSM531676 5 0.1714 0.59296 0.000 0.092 0.000 0.000 0.908 0.000
#> GSM531679 2 0.0291 0.89582 0.000 0.992 0.000 0.000 0.004 0.004
#> GSM531681 2 0.2101 0.83814 0.000 0.892 0.000 0.100 0.004 0.004
#> GSM531682 2 0.0291 0.89726 0.000 0.992 0.000 0.000 0.004 0.004
#> GSM531683 2 0.0458 0.89771 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM531684 2 0.7040 -0.01768 0.000 0.388 0.072 0.000 0.244 0.296
#> GSM531685 5 0.0837 0.56399 0.020 0.004 0.000 0.000 0.972 0.004
#> GSM531686 2 0.2149 0.83452 0.000 0.888 0.000 0.104 0.004 0.004
#> GSM531687 5 0.2362 0.58673 0.000 0.136 0.000 0.000 0.860 0.004
#> GSM531688 5 0.3975 0.24510 0.452 0.000 0.000 0.000 0.544 0.004
#> GSM531690 2 0.1668 0.86274 0.000 0.928 0.000 0.060 0.004 0.008
#> GSM531693 5 0.3975 0.24494 0.452 0.000 0.000 0.000 0.544 0.004
#> GSM531695 5 0.5579 0.36960 0.352 0.100 0.000 0.000 0.532 0.016
#> GSM531603 2 0.0865 0.89655 0.000 0.964 0.000 0.000 0.000 0.036
#> GSM531609 4 0.0000 0.87278 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531611 4 0.0000 0.87278 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531621 3 0.0713 0.86690 0.000 0.000 0.972 0.000 0.000 0.028
#> GSM531622 3 0.0146 0.86913 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM531628 1 0.1007 0.75999 0.956 0.000 0.000 0.000 0.000 0.044
#> GSM531630 3 0.0000 0.86893 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531633 3 0.1327 0.85684 0.000 0.000 0.936 0.000 0.000 0.064
#> GSM531635 1 0.3946 0.59462 0.756 0.000 0.076 0.000 0.000 0.168
#> GSM531640 3 0.0000 0.86893 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531649 1 0.2442 0.68023 0.852 0.000 0.004 0.000 0.000 0.144
#> GSM531653 1 0.0000 0.75919 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM531657 4 0.3133 0.74678 0.000 0.212 0.000 0.780 0.000 0.008
#> GSM531665 5 0.3584 0.36118 0.000 0.004 0.000 0.000 0.688 0.308
#> GSM531670 1 0.4698 0.53303 0.676 0.000 0.076 0.000 0.008 0.240
#> GSM531674 1 0.0937 0.74559 0.960 0.000 0.000 0.000 0.040 0.000
#> GSM531675 2 0.0665 0.89320 0.000 0.980 0.000 0.008 0.004 0.008
#> GSM531677 2 0.0291 0.89582 0.000 0.992 0.000 0.000 0.004 0.004
#> GSM531678 2 0.2909 0.76955 0.000 0.836 0.000 0.000 0.136 0.028
#> GSM531680 5 0.4695 0.53296 0.132 0.144 0.000 0.000 0.712 0.012
#> GSM531689 5 0.2877 0.57531 0.000 0.168 0.000 0.000 0.820 0.012
#> GSM531691 5 0.2163 0.58846 0.000 0.092 0.000 0.000 0.892 0.016
#> GSM531692 5 0.3758 0.34811 0.000 0.008 0.000 0.000 0.668 0.324
#> GSM531694 2 0.0865 0.89655 0.000 0.964 0.000 0.000 0.000 0.036
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> MAD:skmeans 74 1.000 2
#> MAD:skmeans 76 0.894 3
#> MAD:skmeans 73 0.553 4
#> MAD:skmeans 78 0.744 5
#> MAD:skmeans 62 0.719 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "pam"]
# you can also extract it by
# res = res_list["MAD:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 80 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 0.500 0.882 0.927 0.4758 0.519 0.519
#> 3 3 0.529 0.657 0.818 0.3714 0.820 0.653
#> 4 4 0.525 0.476 0.707 0.1264 0.806 0.504
#> 5 5 0.700 0.511 0.758 0.0805 0.832 0.459
#> 6 6 0.697 0.492 0.731 0.0525 0.883 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
#> GSM531602 2 0.0000 0.889 0.000 1.000
#> GSM531604 2 0.1843 0.886 0.028 0.972
#> GSM531606 2 0.0000 0.889 0.000 1.000
#> GSM531607 2 0.0000 0.889 0.000 1.000
#> GSM531608 1 0.6048 0.874 0.852 0.148
#> GSM531610 1 0.6148 0.871 0.848 0.152
#> GSM531612 1 0.6048 0.874 0.852 0.148
#> GSM531613 2 0.9686 0.224 0.396 0.604
#> GSM531614 1 0.6148 0.871 0.848 0.152
#> GSM531616 1 0.0000 0.937 1.000 0.000
#> GSM531618 1 0.6048 0.874 0.852 0.148
#> GSM531619 1 0.0000 0.937 1.000 0.000
#> GSM531620 1 0.0000 0.937 1.000 0.000
#> GSM531623 1 0.0000 0.937 1.000 0.000
#> GSM531625 1 0.0000 0.937 1.000 0.000
#> GSM531626 1 0.0000 0.937 1.000 0.000
#> GSM531632 1 0.0000 0.937 1.000 0.000
#> GSM531638 1 0.0000 0.937 1.000 0.000
#> GSM531639 1 0.0000 0.937 1.000 0.000
#> GSM531641 1 0.6048 0.874 0.852 0.148
#> GSM531642 1 0.0000 0.937 1.000 0.000
#> GSM531643 1 0.0000 0.937 1.000 0.000
#> GSM531644 1 0.0376 0.936 0.996 0.004
#> GSM531645 1 0.6048 0.874 0.852 0.148
#> GSM531646 1 0.0000 0.937 1.000 0.000
#> GSM531647 1 0.0000 0.937 1.000 0.000
#> GSM531648 1 0.6048 0.874 0.852 0.148
#> GSM531650 1 0.0000 0.937 1.000 0.000
#> GSM531651 1 0.0000 0.937 1.000 0.000
#> GSM531652 1 0.2603 0.922 0.956 0.044
#> GSM531656 1 0.0000 0.937 1.000 0.000
#> GSM531659 1 0.6048 0.874 0.852 0.148
#> GSM531661 1 0.0000 0.937 1.000 0.000
#> GSM531662 1 0.0376 0.936 0.996 0.004
#> GSM531663 1 0.7139 0.828 0.804 0.196
#> GSM531664 2 0.9552 0.603 0.376 0.624
#> GSM531666 1 0.0000 0.937 1.000 0.000
#> GSM531667 1 0.6048 0.874 0.852 0.148
#> GSM531668 1 0.6048 0.874 0.852 0.148
#> GSM531669 2 0.8909 0.719 0.308 0.692
#> GSM531671 1 0.2778 0.902 0.952 0.048
#> GSM531672 1 0.6048 0.874 0.852 0.148
#> GSM531673 1 0.1184 0.932 0.984 0.016
#> GSM531676 2 0.6048 0.859 0.148 0.852
#> GSM531679 2 0.0000 0.889 0.000 1.000
#> GSM531681 2 0.0000 0.889 0.000 1.000
#> GSM531682 2 0.0000 0.889 0.000 1.000
#> GSM531683 2 0.0000 0.889 0.000 1.000
#> GSM531684 2 0.0000 0.889 0.000 1.000
#> GSM531685 2 0.6048 0.859 0.148 0.852
#> GSM531686 2 0.0000 0.889 0.000 1.000
#> GSM531687 2 0.8207 0.783 0.256 0.744
#> GSM531688 2 0.6048 0.859 0.148 0.852
#> GSM531690 2 0.0000 0.889 0.000 1.000
#> GSM531693 2 0.8144 0.787 0.252 0.748
#> GSM531695 2 0.6048 0.859 0.148 0.852
#> GSM531603 2 0.3431 0.862 0.064 0.936
#> GSM531609 1 0.6148 0.871 0.848 0.152
#> GSM531611 1 0.6148 0.871 0.848 0.152
#> GSM531621 1 0.0000 0.937 1.000 0.000
#> GSM531622 1 0.2423 0.924 0.960 0.040
#> GSM531628 1 0.0000 0.937 1.000 0.000
#> GSM531630 1 0.0000 0.937 1.000 0.000
#> GSM531633 1 0.0000 0.937 1.000 0.000
#> GSM531635 1 0.0000 0.937 1.000 0.000
#> GSM531640 1 0.0000 0.937 1.000 0.000
#> GSM531649 1 0.0000 0.937 1.000 0.000
#> GSM531653 1 0.0000 0.937 1.000 0.000
#> GSM531657 1 0.6048 0.874 0.852 0.148
#> GSM531665 2 0.5178 0.860 0.116 0.884
#> GSM531670 1 0.0000 0.937 1.000 0.000
#> GSM531674 2 0.8207 0.783 0.256 0.744
#> GSM531675 2 0.0000 0.889 0.000 1.000
#> GSM531677 2 0.0000 0.889 0.000 1.000
#> GSM531678 2 0.0000 0.889 0.000 1.000
#> GSM531680 2 0.6048 0.859 0.148 0.852
#> GSM531689 2 0.5408 0.867 0.124 0.876
#> GSM531691 2 0.6048 0.859 0.148 0.852
#> GSM531692 2 0.6048 0.859 0.148 0.852
#> GSM531694 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
#> GSM531602 2 0.141 0.8228 0.036 0.964 0.000
#> GSM531604 2 0.000 0.8312 0.000 1.000 0.000
#> GSM531606 2 0.141 0.8228 0.036 0.964 0.000
#> GSM531607 2 0.000 0.8312 0.000 1.000 0.000
#> GSM531608 3 0.711 0.5051 0.092 0.196 0.712
#> GSM531610 1 0.455 0.7539 0.800 0.200 0.000
#> GSM531612 1 0.455 0.7539 0.800 0.200 0.000
#> GSM531613 2 0.623 -0.0304 0.436 0.564 0.000
#> GSM531614 1 0.455 0.7539 0.800 0.200 0.000
#> GSM531616 3 0.593 0.4959 0.356 0.000 0.644
#> GSM531618 1 0.478 0.7542 0.796 0.200 0.004
#> GSM531619 3 0.186 0.7665 0.052 0.000 0.948
#> GSM531620 3 0.186 0.7665 0.052 0.000 0.948
#> GSM531623 3 0.186 0.7665 0.052 0.000 0.948
#> GSM531625 3 0.186 0.7665 0.052 0.000 0.948
#> GSM531626 3 0.497 0.6467 0.236 0.000 0.764
#> GSM531632 1 0.630 -0.3316 0.516 0.000 0.484
#> GSM531638 3 0.599 0.4751 0.368 0.000 0.632
#> GSM531639 1 0.502 0.6088 0.760 0.000 0.240
#> GSM531641 1 0.455 0.7539 0.800 0.200 0.000
#> GSM531642 1 0.478 0.6481 0.796 0.004 0.200
#> GSM531643 1 0.493 0.6137 0.768 0.000 0.232
#> GSM531644 1 0.584 0.6347 0.768 0.036 0.196
#> GSM531645 1 0.455 0.7539 0.800 0.200 0.000
#> GSM531646 1 0.630 -0.3316 0.516 0.000 0.484
#> GSM531647 1 0.630 -0.3316 0.516 0.000 0.484
#> GSM531648 1 0.478 0.7542 0.796 0.200 0.004
#> GSM531650 1 0.271 0.5504 0.912 0.000 0.088
#> GSM531651 3 0.186 0.7665 0.052 0.000 0.948
#> GSM531652 1 0.478 0.6481 0.796 0.004 0.200
#> GSM531656 1 0.589 0.6333 0.764 0.036 0.200
#> GSM531659 1 0.478 0.7542 0.796 0.200 0.004
#> GSM531661 3 0.210 0.7645 0.052 0.004 0.944
#> GSM531662 3 0.344 0.7309 0.088 0.016 0.896
#> GSM531663 1 0.455 0.7539 0.800 0.200 0.000
#> GSM531664 2 0.735 0.7082 0.316 0.632 0.052
#> GSM531666 1 0.600 0.6362 0.760 0.040 0.200
#> GSM531667 1 0.554 0.7414 0.776 0.200 0.024
#> GSM531668 1 0.455 0.7539 0.800 0.200 0.000
#> GSM531669 2 0.689 0.7580 0.256 0.692 0.052
#> GSM531671 3 0.629 0.3688 0.464 0.000 0.536
#> GSM531672 1 0.478 0.7542 0.796 0.200 0.004
#> GSM531673 1 0.630 0.3438 0.608 0.004 0.388
#> GSM531676 2 0.478 0.7959 0.200 0.796 0.004
#> GSM531679 2 0.000 0.8312 0.000 1.000 0.000
#> GSM531681 2 0.153 0.8208 0.040 0.960 0.000
#> GSM531682 2 0.141 0.8228 0.036 0.964 0.000
#> GSM531683 2 0.141 0.8228 0.036 0.964 0.000
#> GSM531684 2 0.699 0.4483 0.036 0.644 0.320
#> GSM531685 2 0.631 0.7813 0.200 0.748 0.052
#> GSM531686 2 0.000 0.8312 0.000 1.000 0.000
#> GSM531687 2 0.537 0.7835 0.252 0.744 0.004
#> GSM531688 2 0.631 0.7813 0.200 0.748 0.052
#> GSM531690 2 0.141 0.8228 0.036 0.964 0.000
#> GSM531693 2 0.640 0.7792 0.200 0.744 0.056
#> GSM531695 2 0.631 0.7813 0.200 0.748 0.052
#> GSM531603 2 0.196 0.8072 0.056 0.944 0.000
#> GSM531609 1 0.455 0.7539 0.800 0.200 0.000
#> GSM531611 1 0.470 0.7497 0.788 0.212 0.000
#> GSM531621 3 0.186 0.7665 0.052 0.000 0.948
#> GSM531622 3 0.186 0.7665 0.052 0.000 0.948
#> GSM531628 1 0.336 0.5453 0.908 0.036 0.056
#> GSM531630 3 0.620 0.0944 0.424 0.000 0.576
#> GSM531633 3 0.186 0.7665 0.052 0.000 0.948
#> GSM531635 3 0.601 0.4717 0.372 0.000 0.628
#> GSM531640 1 0.520 0.6148 0.760 0.004 0.236
#> GSM531649 3 0.573 0.4789 0.324 0.000 0.676
#> GSM531653 3 0.622 0.3722 0.432 0.000 0.568
#> GSM531657 1 0.478 0.7542 0.796 0.200 0.004
#> GSM531665 2 0.484 0.8101 0.168 0.816 0.016
#> GSM531670 1 0.589 0.6333 0.764 0.036 0.200
#> GSM531674 2 0.635 0.7805 0.204 0.744 0.052
#> GSM531675 2 0.141 0.8228 0.036 0.964 0.000
#> GSM531677 2 0.141 0.8228 0.036 0.964 0.000
#> GSM531678 2 0.000 0.8312 0.000 1.000 0.000
#> GSM531680 2 0.631 0.7813 0.200 0.748 0.052
#> GSM531689 2 0.490 0.8018 0.172 0.812 0.016
#> GSM531691 2 0.473 0.6922 0.004 0.800 0.196
#> GSM531692 2 0.455 0.7967 0.200 0.800 0.000
#> GSM531694 2 0.141 0.8228 0.036 0.964 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM531602 2 0.4624 0.4408 0.000 0.660 0.000 0.340
#> GSM531604 2 0.0592 0.6684 0.000 0.984 0.000 0.016
#> GSM531606 2 0.4643 0.4355 0.000 0.656 0.000 0.344
#> GSM531607 2 0.1557 0.6604 0.000 0.944 0.000 0.056
#> GSM531608 3 0.3681 0.6396 0.024 0.124 0.848 0.004
#> GSM531610 4 0.1022 0.6926 0.000 0.032 0.000 0.968
#> GSM531612 4 0.0376 0.6889 0.004 0.004 0.000 0.992
#> GSM531613 4 0.1792 0.6648 0.000 0.068 0.000 0.932
#> GSM531614 4 0.1022 0.6926 0.000 0.032 0.000 0.968
#> GSM531616 3 0.3498 0.7052 0.044 0.016 0.880 0.060
#> GSM531618 1 0.7676 -0.3565 0.444 0.136 0.016 0.404
#> GSM531619 3 0.0000 0.7801 0.000 0.000 1.000 0.000
#> GSM531620 3 0.0000 0.7801 0.000 0.000 1.000 0.000
#> GSM531623 3 0.0000 0.7801 0.000 0.000 1.000 0.000
#> GSM531625 3 0.0000 0.7801 0.000 0.000 1.000 0.000
#> GSM531626 3 0.1854 0.7449 0.012 0.000 0.940 0.048
#> GSM531632 1 0.5038 0.2752 0.652 0.012 0.336 0.000
#> GSM531638 3 0.3649 0.6973 0.044 0.016 0.872 0.068
#> GSM531639 1 0.7393 0.4072 0.632 0.100 0.200 0.068
#> GSM531641 4 0.0000 0.6891 0.000 0.000 0.000 1.000
#> GSM531642 1 0.7909 -0.0565 0.476 0.028 0.140 0.356
#> GSM531643 1 0.4586 0.4703 0.796 0.000 0.136 0.068
#> GSM531644 1 0.4636 0.4675 0.792 0.000 0.140 0.068
#> GSM531645 4 0.0188 0.6906 0.000 0.004 0.000 0.996
#> GSM531646 1 0.5038 0.2752 0.652 0.012 0.336 0.000
#> GSM531647 1 0.5038 0.2752 0.652 0.012 0.336 0.000
#> GSM531648 4 0.7431 0.4613 0.336 0.124 0.016 0.524
#> GSM531650 1 0.0779 0.4933 0.980 0.004 0.000 0.016
#> GSM531651 3 0.0000 0.7801 0.000 0.000 1.000 0.000
#> GSM531652 1 0.5375 0.4410 0.744 0.000 0.140 0.116
#> GSM531656 1 0.8467 0.3306 0.480 0.312 0.140 0.068
#> GSM531659 4 0.8214 0.3864 0.336 0.236 0.016 0.412
#> GSM531661 3 0.0188 0.7781 0.000 0.004 0.996 0.000
#> GSM531662 3 0.0672 0.7738 0.008 0.008 0.984 0.000
#> GSM531663 4 0.3695 0.6451 0.016 0.156 0.000 0.828
#> GSM531664 1 0.4193 0.2692 0.732 0.268 0.000 0.000
#> GSM531666 1 0.8188 0.3838 0.544 0.248 0.140 0.068
#> GSM531667 1 0.9578 -0.2255 0.348 0.124 0.244 0.284
#> GSM531668 4 0.6911 0.4755 0.336 0.124 0.000 0.540
#> GSM531669 1 0.4543 0.1571 0.676 0.324 0.000 0.000
#> GSM531671 3 0.8073 0.0519 0.256 0.012 0.448 0.284
#> GSM531672 4 0.7431 0.4613 0.336 0.124 0.016 0.524
#> GSM531673 4 0.8577 0.0941 0.344 0.028 0.272 0.356
#> GSM531676 2 0.3356 0.6252 0.176 0.824 0.000 0.000
#> GSM531679 2 0.0921 0.6681 0.000 0.972 0.000 0.028
#> GSM531681 4 0.4103 0.4369 0.000 0.256 0.000 0.744
#> GSM531682 2 0.4643 0.4355 0.000 0.656 0.000 0.344
#> GSM531683 2 0.4643 0.4355 0.000 0.656 0.000 0.344
#> GSM531684 3 0.5780 -0.0492 0.000 0.476 0.496 0.028
#> GSM531685 2 0.3837 0.5998 0.224 0.776 0.000 0.000
#> GSM531686 2 0.2868 0.6207 0.000 0.864 0.000 0.136
#> GSM531687 2 0.4954 0.6066 0.144 0.788 0.016 0.052
#> GSM531688 2 0.3837 0.5998 0.224 0.776 0.000 0.000
#> GSM531690 2 0.4643 0.4355 0.000 0.656 0.000 0.344
#> GSM531693 2 0.4283 0.5752 0.256 0.740 0.004 0.000
#> GSM531695 2 0.3837 0.5998 0.224 0.776 0.000 0.000
#> GSM531603 2 0.5175 0.4595 0.004 0.656 0.012 0.328
#> GSM531609 4 0.1022 0.6926 0.000 0.032 0.000 0.968
#> GSM531611 4 0.2466 0.6436 0.004 0.096 0.000 0.900
#> GSM531621 3 0.0000 0.7801 0.000 0.000 1.000 0.000
#> GSM531622 3 0.0000 0.7801 0.000 0.000 1.000 0.000
#> GSM531628 1 0.0469 0.4941 0.988 0.012 0.000 0.000
#> GSM531630 3 0.4564 0.3418 0.328 0.000 0.672 0.000
#> GSM531633 3 0.0000 0.7801 0.000 0.000 1.000 0.000
#> GSM531635 3 0.6951 -0.1328 0.440 0.016 0.476 0.068
#> GSM531640 3 0.6863 0.1943 0.348 0.020 0.564 0.068
#> GSM531649 1 0.6013 0.0975 0.508 0.016 0.460 0.016
#> GSM531653 1 0.5268 0.2147 0.592 0.012 0.396 0.000
#> GSM531657 4 0.8214 0.3864 0.336 0.236 0.016 0.412
#> GSM531665 2 0.4117 0.6332 0.116 0.832 0.004 0.048
#> GSM531670 2 0.8554 -0.1954 0.348 0.444 0.140 0.068
#> GSM531674 1 0.4643 0.1106 0.656 0.344 0.000 0.000
#> GSM531675 2 0.4643 0.4355 0.000 0.656 0.000 0.344
#> GSM531677 2 0.4643 0.4355 0.000 0.656 0.000 0.344
#> GSM531678 2 0.0921 0.6681 0.000 0.972 0.000 0.028
#> GSM531680 2 0.3356 0.6318 0.176 0.824 0.000 0.000
#> GSM531689 2 0.2799 0.6488 0.108 0.884 0.008 0.000
#> GSM531691 2 0.2888 0.5839 0.004 0.872 0.124 0.000
#> GSM531692 2 0.3636 0.6245 0.172 0.820 0.008 0.000
#> GSM531694 2 0.4624 0.4408 0.000 0.660 0.000 0.340
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM531602 2 0.1608 0.7514 0.000 0.928 0.000 0.000 0.072
#> GSM531604 2 0.4210 0.3308 0.000 0.588 0.000 0.000 0.412
#> GSM531606 2 0.4300 0.3130 0.000 0.524 0.000 0.000 0.476
#> GSM531607 2 0.0794 0.7438 0.000 0.972 0.000 0.000 0.028
#> GSM531608 3 0.4192 0.6981 0.000 0.000 0.596 0.000 0.404
#> GSM531610 4 0.0000 0.9846 0.000 0.000 0.000 1.000 0.000
#> GSM531612 4 0.0000 0.9846 0.000 0.000 0.000 1.000 0.000
#> GSM531613 4 0.0000 0.9846 0.000 0.000 0.000 1.000 0.000
#> GSM531614 4 0.0000 0.9846 0.000 0.000 0.000 1.000 0.000
#> GSM531616 5 0.5293 0.4099 0.048 0.000 0.460 0.000 0.492
#> GSM531618 5 0.4973 0.4494 0.408 0.024 0.004 0.000 0.564
#> GSM531619 3 0.4192 0.6981 0.000 0.000 0.596 0.000 0.404
#> GSM531620 3 0.0000 0.6513 0.000 0.000 1.000 0.000 0.000
#> GSM531623 3 0.4192 0.6981 0.000 0.000 0.596 0.000 0.404
#> GSM531625 3 0.0000 0.6513 0.000 0.000 1.000 0.000 0.000
#> GSM531626 3 0.4451 -0.1192 0.016 0.000 0.644 0.000 0.340
#> GSM531632 1 0.4192 0.3663 0.596 0.000 0.404 0.000 0.000
#> GSM531638 5 0.5232 0.4177 0.044 0.000 0.456 0.000 0.500
#> GSM531639 5 0.6216 0.4926 0.096 0.016 0.372 0.000 0.516
#> GSM531641 4 0.0000 0.9846 0.000 0.000 0.000 1.000 0.000
#> GSM531642 5 0.4489 0.4422 0.420 0.008 0.000 0.000 0.572
#> GSM531643 1 0.4307 -0.4240 0.504 0.000 0.000 0.000 0.496
#> GSM531644 1 0.4307 -0.4240 0.504 0.000 0.000 0.000 0.496
#> GSM531645 4 0.0000 0.9846 0.000 0.000 0.000 1.000 0.000
#> GSM531646 1 0.4192 0.3663 0.596 0.000 0.404 0.000 0.000
#> GSM531647 1 0.1410 0.5741 0.940 0.000 0.060 0.000 0.000
#> GSM531648 5 0.5896 0.3920 0.060 0.024 0.000 0.352 0.564
#> GSM531650 1 0.1341 0.5134 0.944 0.000 0.000 0.000 0.056
#> GSM531651 3 0.4192 0.6981 0.000 0.000 0.596 0.000 0.404
#> GSM531652 5 0.4811 0.4184 0.452 0.020 0.000 0.000 0.528
#> GSM531656 5 0.5568 0.4239 0.412 0.072 0.000 0.000 0.516
#> GSM531659 5 0.5341 0.2769 0.060 0.376 0.000 0.000 0.564
#> GSM531661 3 0.4192 0.6981 0.000 0.000 0.596 0.000 0.404
#> GSM531662 3 0.4192 0.6981 0.000 0.000 0.596 0.000 0.404
#> GSM531663 4 0.2362 0.8680 0.000 0.024 0.000 0.900 0.076
#> GSM531664 1 0.1430 0.5747 0.944 0.052 0.000 0.000 0.004
#> GSM531666 5 0.5568 0.4239 0.412 0.072 0.000 0.000 0.516
#> GSM531667 5 0.1485 0.3277 0.000 0.020 0.032 0.000 0.948
#> GSM531668 5 0.5403 0.2174 0.060 0.024 0.000 0.244 0.672
#> GSM531669 1 0.1410 0.5843 0.940 0.060 0.000 0.000 0.000
#> GSM531671 1 0.4675 0.2334 0.544 0.004 0.008 0.000 0.444
#> GSM531672 5 0.5896 0.3920 0.060 0.024 0.000 0.352 0.564
#> GSM531673 5 0.3821 -0.1167 0.000 0.020 0.216 0.000 0.764
#> GSM531676 2 0.2848 0.6481 0.104 0.868 0.000 0.000 0.028
#> GSM531679 2 0.0000 0.7351 0.000 1.000 0.000 0.000 0.000
#> GSM531681 2 0.5188 0.2225 0.000 0.540 0.000 0.416 0.044
#> GSM531682 2 0.1608 0.7514 0.000 0.928 0.000 0.000 0.072
#> GSM531683 2 0.1608 0.7514 0.000 0.928 0.000 0.000 0.072
#> GSM531684 3 0.4674 0.6751 0.000 0.016 0.568 0.000 0.416
#> GSM531685 1 0.4562 0.1231 0.500 0.492 0.000 0.000 0.008
#> GSM531686 2 0.1410 0.7505 0.000 0.940 0.000 0.000 0.060
#> GSM531687 2 0.5176 -0.0995 0.040 0.492 0.000 0.000 0.468
#> GSM531688 1 0.4561 0.1324 0.504 0.488 0.000 0.000 0.008
#> GSM531690 2 0.1608 0.7514 0.000 0.928 0.000 0.000 0.072
#> GSM531693 1 0.4670 0.1988 0.548 0.440 0.004 0.000 0.008
#> GSM531695 1 0.4562 0.1136 0.496 0.496 0.000 0.000 0.008
#> GSM531603 2 0.4256 0.1897 0.000 0.564 0.000 0.000 0.436
#> GSM531609 4 0.0000 0.9846 0.000 0.000 0.000 1.000 0.000
#> GSM531611 4 0.0000 0.9846 0.000 0.000 0.000 1.000 0.000
#> GSM531621 3 0.0000 0.6513 0.000 0.000 1.000 0.000 0.000
#> GSM531622 3 0.0000 0.6513 0.000 0.000 1.000 0.000 0.000
#> GSM531628 1 0.0000 0.5578 1.000 0.000 0.000 0.000 0.000
#> GSM531630 3 0.1410 0.6201 0.060 0.000 0.940 0.000 0.000
#> GSM531633 3 0.0000 0.6513 0.000 0.000 1.000 0.000 0.000
#> GSM531635 5 0.5826 0.4516 0.096 0.000 0.404 0.000 0.500
#> GSM531640 5 0.5443 0.4417 0.060 0.000 0.436 0.000 0.504
#> GSM531649 1 0.3688 0.5231 0.816 0.000 0.124 0.000 0.060
#> GSM531653 1 0.1410 0.5741 0.940 0.000 0.060 0.000 0.000
#> GSM531657 5 0.5479 0.2828 0.060 0.372 0.000 0.004 0.564
#> GSM531665 2 0.6131 0.2421 0.208 0.564 0.000 0.000 0.228
#> GSM531670 5 0.5467 0.2741 0.064 0.412 0.000 0.000 0.524
#> GSM531674 1 0.1410 0.5843 0.940 0.060 0.000 0.000 0.000
#> GSM531675 2 0.1608 0.7514 0.000 0.928 0.000 0.000 0.072
#> GSM531677 2 0.1608 0.7514 0.000 0.928 0.000 0.000 0.072
#> GSM531678 2 0.0290 0.7329 0.000 0.992 0.000 0.000 0.008
#> GSM531680 2 0.4380 0.1544 0.376 0.616 0.000 0.000 0.008
#> GSM531689 2 0.0955 0.7222 0.004 0.968 0.000 0.000 0.028
#> GSM531691 2 0.0955 0.7222 0.004 0.968 0.000 0.000 0.028
#> GSM531692 2 0.5531 0.2617 0.056 0.508 0.004 0.000 0.432
#> GSM531694 2 0.1608 0.7514 0.000 0.928 0.000 0.000 0.072
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM531602 2 0.2491 0.86900 0.000 0.836 0.000 0.000 0.164 0.000
#> GSM531604 2 0.3266 0.78485 0.000 0.728 0.000 0.000 0.272 0.000
#> GSM531606 5 0.3737 -0.16922 0.000 0.392 0.000 0.000 0.608 0.000
#> GSM531607 2 0.2378 0.87748 0.000 0.848 0.000 0.000 0.152 0.000
#> GSM531608 3 0.3810 0.33679 0.000 0.000 0.572 0.000 0.428 0.000
#> GSM531610 4 0.0000 0.96543 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531612 4 0.0000 0.96543 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531613 4 0.0000 0.96543 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531614 4 0.0000 0.96543 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531616 3 0.5961 0.09185 0.232 0.000 0.432 0.000 0.000 0.336
#> GSM531618 6 0.3773 0.68774 0.204 0.044 0.000 0.000 0.000 0.752
#> GSM531619 3 0.3810 0.33679 0.000 0.000 0.572 0.000 0.428 0.000
#> GSM531620 3 0.0000 0.54297 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531623 3 0.3810 0.33679 0.000 0.000 0.572 0.000 0.428 0.000
#> GSM531625 3 0.0000 0.54297 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531626 3 0.5374 0.08139 0.116 0.000 0.504 0.000 0.000 0.380
#> GSM531632 1 0.3737 0.34366 0.608 0.000 0.392 0.000 0.000 0.000
#> GSM531638 3 0.5877 0.04824 0.200 0.000 0.428 0.000 0.000 0.372
#> GSM531639 6 0.2854 0.58235 0.000 0.000 0.208 0.000 0.000 0.792
#> GSM531641 4 0.0000 0.96543 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531642 6 0.2823 0.68898 0.204 0.000 0.000 0.000 0.000 0.796
#> GSM531643 6 0.3371 0.62408 0.292 0.000 0.000 0.000 0.000 0.708
#> GSM531644 6 0.2969 0.68123 0.224 0.000 0.000 0.000 0.000 0.776
#> GSM531645 4 0.0000 0.96543 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531646 1 0.3810 0.29251 0.572 0.000 0.428 0.000 0.000 0.000
#> GSM531647 1 0.0000 0.60822 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM531648 6 0.4587 0.61087 0.000 0.108 0.000 0.204 0.000 0.688
#> GSM531650 1 0.3515 0.19168 0.676 0.000 0.000 0.000 0.000 0.324
#> GSM531651 3 0.3810 0.33679 0.000 0.000 0.572 0.000 0.428 0.000
#> GSM531652 6 0.3261 0.69042 0.204 0.016 0.000 0.000 0.000 0.780
#> GSM531656 6 0.2964 0.68849 0.204 0.000 0.000 0.000 0.004 0.792
#> GSM531659 6 0.3464 0.58308 0.000 0.312 0.000 0.000 0.000 0.688
#> GSM531661 3 0.3810 0.33679 0.000 0.000 0.572 0.000 0.428 0.000
#> GSM531662 5 0.3860 -0.30685 0.000 0.000 0.472 0.000 0.528 0.000
#> GSM531663 4 0.2915 0.79719 0.000 0.184 0.000 0.808 0.000 0.008
#> GSM531664 1 0.3314 0.44936 0.764 0.000 0.000 0.000 0.224 0.012
#> GSM531666 6 0.2964 0.68849 0.204 0.000 0.000 0.000 0.004 0.792
#> GSM531667 6 0.4913 0.25141 0.000 0.028 0.020 0.000 0.428 0.524
#> GSM531668 6 0.6785 0.40201 0.000 0.108 0.000 0.124 0.300 0.468
#> GSM531669 1 0.0363 0.60747 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM531671 1 0.3823 0.22814 0.564 0.000 0.000 0.000 0.436 0.000
#> GSM531672 6 0.5310 0.59221 0.000 0.108 0.000 0.204 0.032 0.656
#> GSM531673 5 0.5633 -0.14976 0.000 0.000 0.196 0.000 0.532 0.272
#> GSM531676 5 0.6077 -0.02657 0.368 0.004 0.000 0.000 0.408 0.220
#> GSM531679 2 0.1957 0.85965 0.000 0.888 0.000 0.000 0.112 0.000
#> GSM531681 2 0.1957 0.83360 0.000 0.888 0.000 0.112 0.000 0.000
#> GSM531682 2 0.0146 0.89987 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM531683 2 0.1501 0.88104 0.000 0.924 0.000 0.000 0.076 0.000
#> GSM531684 5 0.4107 -0.28555 0.000 0.004 0.452 0.000 0.540 0.004
#> GSM531685 1 0.5900 -0.04431 0.412 0.000 0.000 0.000 0.384 0.204
#> GSM531686 2 0.0405 0.89824 0.000 0.988 0.000 0.000 0.008 0.004
#> GSM531687 5 0.5986 0.11039 0.232 0.000 0.000 0.000 0.408 0.360
#> GSM531688 1 0.5543 0.22201 0.556 0.000 0.000 0.000 0.240 0.204
#> GSM531690 2 0.0146 0.89987 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM531693 1 0.3171 0.48823 0.784 0.000 0.000 0.000 0.012 0.204
#> GSM531695 1 0.5883 0.00622 0.436 0.000 0.000 0.000 0.360 0.204
#> GSM531603 6 0.5391 -0.13007 0.000 0.112 0.000 0.000 0.432 0.456
#> GSM531609 4 0.0000 0.96543 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531611 4 0.1501 0.90673 0.000 0.076 0.000 0.924 0.000 0.000
#> GSM531621 3 0.0000 0.54297 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531622 3 0.0000 0.54297 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531628 1 0.2597 0.46600 0.824 0.000 0.000 0.000 0.000 0.176
#> GSM531630 3 0.2969 0.41499 0.000 0.000 0.776 0.000 0.000 0.224
#> GSM531633 3 0.0000 0.54297 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531635 3 0.5966 0.08407 0.232 0.000 0.428 0.000 0.000 0.340
#> GSM531640 6 0.2941 0.57684 0.000 0.000 0.220 0.000 0.000 0.780
#> GSM531649 1 0.3720 0.47326 0.736 0.000 0.236 0.000 0.000 0.028
#> GSM531653 1 0.0000 0.60822 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM531657 6 0.3464 0.58308 0.000 0.312 0.000 0.000 0.000 0.688
#> GSM531665 6 0.3945 0.01299 0.008 0.000 0.000 0.000 0.380 0.612
#> GSM531670 6 0.0363 0.61796 0.000 0.000 0.000 0.000 0.012 0.988
#> GSM531674 1 0.0363 0.60747 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM531675 2 0.0146 0.89987 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM531677 2 0.0146 0.89987 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM531678 5 0.5798 0.25723 0.000 0.312 0.000 0.000 0.484 0.204
#> GSM531680 5 0.6906 0.07064 0.320 0.068 0.000 0.000 0.408 0.204
#> GSM531689 5 0.5767 0.26305 0.000 0.300 0.000 0.000 0.496 0.204
#> GSM531691 5 0.6927 0.27584 0.152 0.148 0.000 0.000 0.496 0.204
#> GSM531692 5 0.1745 0.29862 0.056 0.020 0.000 0.000 0.924 0.000
#> GSM531694 2 0.2416 0.87380 0.000 0.844 0.000 0.000 0.156 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)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> MAD:pam 79 0.485 2
#> MAD:pam 67 0.447 3
#> MAD:pam 39 0.560 4
#> MAD:pam 44 0.604 5
#> MAD:pam 44 0.430 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "mclust"]
# you can also extract it by
# res = res_list["MAD:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 80 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.463 0.827 0.894 0.3035 0.742 0.742
#> 3 3 0.403 0.695 0.820 0.5087 0.723 0.655
#> 4 4 0.928 0.917 0.962 0.6378 0.572 0.324
#> 5 5 0.847 0.864 0.927 0.0668 0.925 0.712
#> 6 6 0.860 0.880 0.918 0.0345 0.941 0.726
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM531602 2 0.0000 0.868 0.000 1.000
#> GSM531604 2 0.0000 0.868 0.000 1.000
#> GSM531606 2 0.0000 0.868 0.000 1.000
#> GSM531607 2 0.0000 0.868 0.000 1.000
#> GSM531608 2 0.7453 0.785 0.212 0.788
#> GSM531610 2 0.0376 0.866 0.004 0.996
#> GSM531612 2 0.2603 0.841 0.044 0.956
#> GSM531613 2 0.0000 0.868 0.000 1.000
#> GSM531614 2 0.2236 0.842 0.036 0.964
#> GSM531616 1 0.6623 0.845 0.828 0.172
#> GSM531618 2 0.0000 0.868 0.000 1.000
#> GSM531619 1 0.9170 0.474 0.668 0.332
#> GSM531620 1 0.6247 0.865 0.844 0.156
#> GSM531623 1 0.2236 0.898 0.964 0.036
#> GSM531625 1 0.5294 0.884 0.880 0.120
#> GSM531626 1 0.6247 0.865 0.844 0.156
#> GSM531632 2 0.8016 0.766 0.244 0.756
#> GSM531638 1 0.5946 0.873 0.856 0.144
#> GSM531639 2 0.8016 0.766 0.244 0.756
#> GSM531641 2 0.2603 0.841 0.044 0.956
#> GSM531642 2 0.8144 0.759 0.252 0.748
#> GSM531643 2 0.8207 0.755 0.256 0.744
#> GSM531644 2 0.8016 0.767 0.244 0.756
#> GSM531645 2 0.2236 0.842 0.036 0.964
#> GSM531646 2 0.8207 0.755 0.256 0.744
#> GSM531647 2 0.8207 0.755 0.256 0.744
#> GSM531648 2 0.2603 0.841 0.044 0.956
#> GSM531650 2 0.8207 0.755 0.256 0.744
#> GSM531651 1 0.2236 0.898 0.964 0.036
#> GSM531652 2 0.3431 0.856 0.064 0.936
#> GSM531656 2 0.8016 0.766 0.244 0.756
#> GSM531659 2 0.0000 0.868 0.000 1.000
#> GSM531661 2 0.7883 0.771 0.236 0.764
#> GSM531662 2 0.5408 0.832 0.124 0.876
#> GSM531663 2 0.0000 0.868 0.000 1.000
#> GSM531664 2 0.8016 0.766 0.244 0.756
#> GSM531666 2 0.4161 0.850 0.084 0.916
#> GSM531667 2 0.8327 0.746 0.264 0.736
#> GSM531668 2 0.0000 0.868 0.000 1.000
#> GSM531669 2 0.8016 0.766 0.244 0.756
#> GSM531671 2 0.8016 0.766 0.244 0.756
#> GSM531672 2 0.0000 0.868 0.000 1.000
#> GSM531673 2 0.1633 0.866 0.024 0.976
#> GSM531676 2 0.1843 0.865 0.028 0.972
#> GSM531679 2 0.0000 0.868 0.000 1.000
#> GSM531681 2 0.0000 0.868 0.000 1.000
#> GSM531682 2 0.0000 0.868 0.000 1.000
#> GSM531683 2 0.0000 0.868 0.000 1.000
#> GSM531684 2 0.0000 0.868 0.000 1.000
#> GSM531685 2 0.3431 0.856 0.064 0.936
#> GSM531686 2 0.0000 0.868 0.000 1.000
#> GSM531687 2 0.1843 0.865 0.028 0.972
#> GSM531688 2 0.8016 0.766 0.244 0.756
#> GSM531690 2 0.0000 0.868 0.000 1.000
#> GSM531693 2 0.8016 0.766 0.244 0.756
#> GSM531695 2 0.7376 0.788 0.208 0.792
#> GSM531603 2 0.0000 0.868 0.000 1.000
#> GSM531609 2 0.2423 0.842 0.040 0.960
#> GSM531611 2 0.0000 0.868 0.000 1.000
#> GSM531621 1 0.2236 0.898 0.964 0.036
#> GSM531622 1 0.2236 0.898 0.964 0.036
#> GSM531628 2 0.8081 0.762 0.248 0.752
#> GSM531630 1 0.2236 0.898 0.964 0.036
#> GSM531633 1 0.2236 0.898 0.964 0.036
#> GSM531635 2 0.8207 0.755 0.256 0.744
#> GSM531640 2 0.9552 0.564 0.376 0.624
#> GSM531649 2 0.8207 0.755 0.256 0.744
#> GSM531653 2 0.8207 0.755 0.256 0.744
#> GSM531657 2 0.0000 0.868 0.000 1.000
#> GSM531665 2 0.1633 0.866 0.024 0.976
#> GSM531670 2 0.8016 0.766 0.244 0.756
#> GSM531674 2 0.8016 0.766 0.244 0.756
#> GSM531675 2 0.0000 0.868 0.000 1.000
#> GSM531677 2 0.0000 0.868 0.000 1.000
#> GSM531678 2 0.0000 0.868 0.000 1.000
#> GSM531680 2 0.3733 0.853 0.072 0.928
#> GSM531689 2 0.0000 0.868 0.000 1.000
#> GSM531691 2 0.0000 0.868 0.000 1.000
#> GSM531692 2 0.0376 0.868 0.004 0.996
#> GSM531694 2 0.0000 0.868 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM531602 2 0.0237 0.788 0.004 0.996 0.000
#> GSM531604 2 0.0000 0.789 0.000 1.000 0.000
#> GSM531606 2 0.0237 0.788 0.004 0.996 0.000
#> GSM531607 2 0.0237 0.788 0.004 0.996 0.000
#> GSM531608 3 0.6154 0.150 0.000 0.408 0.592
#> GSM531610 1 0.6291 0.696 0.532 0.468 0.000
#> GSM531612 1 0.5621 0.903 0.692 0.308 0.000
#> GSM531613 2 0.6307 -0.625 0.488 0.512 0.000
#> GSM531614 1 0.5621 0.903 0.692 0.308 0.000
#> GSM531616 2 0.6126 0.458 0.000 0.600 0.400
#> GSM531618 2 0.3644 0.699 0.124 0.872 0.004
#> GSM531619 3 0.4002 0.640 0.000 0.160 0.840
#> GSM531620 3 0.1289 0.752 0.000 0.032 0.968
#> GSM531623 3 0.0000 0.767 0.000 0.000 1.000
#> GSM531625 2 0.6192 0.416 0.000 0.580 0.420
#> GSM531626 3 0.6305 -0.174 0.000 0.484 0.516
#> GSM531632 2 0.7391 0.614 0.308 0.636 0.056
#> GSM531638 2 0.6192 0.414 0.000 0.580 0.420
#> GSM531639 2 0.5455 0.710 0.028 0.788 0.184
#> GSM531641 1 0.5621 0.903 0.692 0.308 0.000
#> GSM531642 2 0.5004 0.738 0.088 0.840 0.072
#> GSM531643 2 0.6662 0.694 0.192 0.736 0.072
#> GSM531644 2 0.4489 0.773 0.108 0.856 0.036
#> GSM531645 1 0.5621 0.903 0.692 0.308 0.000
#> GSM531646 2 0.7640 0.638 0.240 0.664 0.096
#> GSM531647 2 0.7841 0.614 0.272 0.636 0.092
#> GSM531648 1 0.5621 0.903 0.692 0.308 0.000
#> GSM531650 2 0.7424 0.618 0.300 0.640 0.060
#> GSM531651 3 0.0000 0.767 0.000 0.000 1.000
#> GSM531652 2 0.4293 0.709 0.164 0.832 0.004
#> GSM531656 2 0.5791 0.729 0.148 0.792 0.060
#> GSM531659 2 0.1964 0.772 0.056 0.944 0.000
#> GSM531661 2 0.3686 0.701 0.000 0.860 0.140
#> GSM531662 2 0.1289 0.787 0.000 0.968 0.032
#> GSM531663 2 0.3340 0.708 0.120 0.880 0.000
#> GSM531664 2 0.7301 0.615 0.308 0.640 0.052
#> GSM531666 2 0.2772 0.782 0.080 0.916 0.004
#> GSM531667 3 0.5138 0.489 0.000 0.252 0.748
#> GSM531668 2 0.2356 0.761 0.072 0.928 0.000
#> GSM531669 2 0.7301 0.615 0.308 0.640 0.052
#> GSM531671 2 0.1289 0.791 0.032 0.968 0.000
#> GSM531672 1 0.6305 0.658 0.516 0.484 0.000
#> GSM531673 2 0.0848 0.791 0.008 0.984 0.008
#> GSM531676 2 0.1289 0.791 0.032 0.968 0.000
#> GSM531679 2 0.0237 0.788 0.004 0.996 0.000
#> GSM531681 2 0.1964 0.772 0.056 0.944 0.000
#> GSM531682 2 0.0237 0.788 0.004 0.996 0.000
#> GSM531683 2 0.1289 0.782 0.032 0.968 0.000
#> GSM531684 2 0.0237 0.789 0.000 0.996 0.004
#> GSM531685 2 0.1529 0.790 0.040 0.960 0.000
#> GSM531686 2 0.1964 0.772 0.056 0.944 0.000
#> GSM531687 2 0.0892 0.791 0.020 0.980 0.000
#> GSM531688 2 0.4654 0.701 0.208 0.792 0.000
#> GSM531690 2 0.1964 0.772 0.056 0.944 0.000
#> GSM531693 2 0.5656 0.646 0.284 0.712 0.004
#> GSM531695 2 0.2959 0.769 0.100 0.900 0.000
#> GSM531603 2 0.1964 0.772 0.056 0.944 0.000
#> GSM531609 1 0.5621 0.903 0.692 0.308 0.000
#> GSM531611 2 0.2959 0.733 0.100 0.900 0.000
#> GSM531621 3 0.0000 0.767 0.000 0.000 1.000
#> GSM531622 3 0.0000 0.767 0.000 0.000 1.000
#> GSM531628 2 0.7391 0.614 0.308 0.636 0.056
#> GSM531630 3 0.0000 0.767 0.000 0.000 1.000
#> GSM531633 3 0.0000 0.767 0.000 0.000 1.000
#> GSM531635 2 0.7640 0.638 0.240 0.664 0.096
#> GSM531640 3 0.4452 0.595 0.000 0.192 0.808
#> GSM531649 2 0.7640 0.638 0.240 0.664 0.096
#> GSM531653 2 0.7677 0.632 0.252 0.656 0.092
#> GSM531657 2 0.3412 0.702 0.124 0.876 0.000
#> GSM531665 2 0.0892 0.791 0.020 0.980 0.000
#> GSM531670 2 0.5696 0.730 0.148 0.796 0.056
#> GSM531674 2 0.7301 0.615 0.308 0.640 0.052
#> GSM531675 2 0.1964 0.772 0.056 0.944 0.000
#> GSM531677 2 0.0237 0.788 0.004 0.996 0.000
#> GSM531678 2 0.0237 0.788 0.004 0.996 0.000
#> GSM531680 2 0.1753 0.787 0.048 0.952 0.000
#> GSM531689 2 0.0000 0.789 0.000 1.000 0.000
#> GSM531691 2 0.0000 0.789 0.000 1.000 0.000
#> GSM531692 2 0.0892 0.791 0.020 0.980 0.000
#> GSM531694 2 0.0237 0.788 0.004 0.996 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM531602 2 0.0000 0.963 0.000 1.000 0.000 0.000
#> GSM531604 2 0.0000 0.963 0.000 1.000 0.000 0.000
#> GSM531606 2 0.0000 0.963 0.000 1.000 0.000 0.000
#> GSM531607 2 0.0000 0.963 0.000 1.000 0.000 0.000
#> GSM531608 3 0.0469 0.957 0.000 0.012 0.988 0.000
#> GSM531610 4 0.0000 0.938 0.000 0.000 0.000 1.000
#> GSM531612 4 0.0000 0.938 0.000 0.000 0.000 1.000
#> GSM531613 4 0.0188 0.938 0.000 0.004 0.000 0.996
#> GSM531614 4 0.0000 0.938 0.000 0.000 0.000 1.000
#> GSM531616 3 0.0000 0.965 0.000 0.000 1.000 0.000
#> GSM531618 4 0.1398 0.914 0.000 0.004 0.040 0.956
#> GSM531619 3 0.0188 0.962 0.000 0.004 0.996 0.000
#> GSM531620 3 0.0000 0.965 0.000 0.000 1.000 0.000
#> GSM531623 3 0.0000 0.965 0.000 0.000 1.000 0.000
#> GSM531625 3 0.0000 0.965 0.000 0.000 1.000 0.000
#> GSM531626 3 0.0000 0.965 0.000 0.000 1.000 0.000
#> GSM531632 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM531638 3 0.0000 0.965 0.000 0.000 1.000 0.000
#> GSM531639 1 0.4655 0.569 0.684 0.004 0.312 0.000
#> GSM531641 4 0.0000 0.938 0.000 0.000 0.000 1.000
#> GSM531642 1 0.3791 0.763 0.796 0.000 0.200 0.004
#> GSM531643 1 0.0592 0.960 0.984 0.000 0.016 0.000
#> GSM531644 1 0.0592 0.960 0.984 0.000 0.016 0.000
#> GSM531645 4 0.0000 0.938 0.000 0.000 0.000 1.000
#> GSM531646 1 0.0592 0.960 0.984 0.000 0.016 0.000
#> GSM531647 1 0.0592 0.960 0.984 0.000 0.016 0.000
#> GSM531648 4 0.0188 0.938 0.000 0.004 0.000 0.996
#> GSM531650 1 0.0188 0.959 0.996 0.000 0.004 0.000
#> GSM531651 3 0.0000 0.965 0.000 0.000 1.000 0.000
#> GSM531652 4 0.5134 0.518 0.320 0.004 0.012 0.664
#> GSM531656 1 0.2530 0.885 0.896 0.004 0.100 0.000
#> GSM531659 4 0.3688 0.765 0.000 0.208 0.000 0.792
#> GSM531661 3 0.0592 0.953 0.000 0.016 0.984 0.000
#> GSM531662 3 0.2281 0.869 0.000 0.096 0.904 0.000
#> GSM531663 4 0.2973 0.842 0.000 0.144 0.000 0.856
#> GSM531664 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM531666 1 0.0992 0.956 0.976 0.004 0.012 0.008
#> GSM531667 3 0.0336 0.960 0.000 0.008 0.992 0.000
#> GSM531668 4 0.0592 0.934 0.000 0.016 0.000 0.984
#> GSM531669 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM531671 3 0.5352 0.335 0.388 0.016 0.596 0.000
#> GSM531672 4 0.0188 0.938 0.000 0.004 0.000 0.996
#> GSM531673 2 0.0000 0.963 0.000 1.000 0.000 0.000
#> GSM531676 2 0.1211 0.930 0.040 0.960 0.000 0.000
#> GSM531679 2 0.0000 0.963 0.000 1.000 0.000 0.000
#> GSM531681 2 0.1557 0.920 0.000 0.944 0.000 0.056
#> GSM531682 2 0.0000 0.963 0.000 1.000 0.000 0.000
#> GSM531683 2 0.0000 0.963 0.000 1.000 0.000 0.000
#> GSM531684 2 0.0000 0.963 0.000 1.000 0.000 0.000
#> GSM531685 2 0.4888 0.321 0.412 0.588 0.000 0.000
#> GSM531686 2 0.0188 0.961 0.000 0.996 0.000 0.004
#> GSM531687 2 0.0188 0.961 0.004 0.996 0.000 0.000
#> GSM531688 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM531690 2 0.1557 0.918 0.000 0.944 0.000 0.056
#> GSM531693 1 0.0592 0.953 0.984 0.016 0.000 0.000
#> GSM531695 1 0.0592 0.953 0.984 0.016 0.000 0.000
#> GSM531603 2 0.0000 0.963 0.000 1.000 0.000 0.000
#> GSM531609 4 0.0000 0.938 0.000 0.000 0.000 1.000
#> GSM531611 4 0.0188 0.938 0.000 0.004 0.000 0.996
#> GSM531621 3 0.0000 0.965 0.000 0.000 1.000 0.000
#> GSM531622 3 0.0000 0.965 0.000 0.000 1.000 0.000
#> GSM531628 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM531630 3 0.0000 0.965 0.000 0.000 1.000 0.000
#> GSM531633 3 0.0000 0.965 0.000 0.000 1.000 0.000
#> GSM531635 1 0.0592 0.960 0.984 0.000 0.016 0.000
#> GSM531640 3 0.0000 0.965 0.000 0.000 1.000 0.000
#> GSM531649 1 0.0592 0.960 0.984 0.000 0.016 0.000
#> GSM531653 1 0.0592 0.960 0.984 0.000 0.016 0.000
#> GSM531657 4 0.2647 0.864 0.000 0.120 0.000 0.880
#> GSM531665 2 0.0000 0.963 0.000 1.000 0.000 0.000
#> GSM531670 1 0.0927 0.953 0.976 0.016 0.008 0.000
#> GSM531674 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM531675 2 0.0592 0.952 0.000 0.984 0.000 0.016
#> GSM531677 2 0.0000 0.963 0.000 1.000 0.000 0.000
#> GSM531678 2 0.0000 0.963 0.000 1.000 0.000 0.000
#> GSM531680 2 0.3610 0.748 0.200 0.800 0.000 0.000
#> GSM531689 2 0.0000 0.963 0.000 1.000 0.000 0.000
#> GSM531691 2 0.0000 0.963 0.000 1.000 0.000 0.000
#> GSM531692 2 0.0000 0.963 0.000 1.000 0.000 0.000
#> GSM531694 2 0.0000 0.963 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM531602 2 0.0162 0.9766 0.000 0.996 0.000 0.000 0.004
#> GSM531604 5 0.2605 0.7874 0.000 0.148 0.000 0.000 0.852
#> GSM531606 2 0.3143 0.7066 0.000 0.796 0.000 0.000 0.204
#> GSM531607 2 0.0162 0.9766 0.000 0.996 0.000 0.000 0.004
#> GSM531608 3 0.0404 0.9856 0.000 0.012 0.988 0.000 0.000
#> GSM531610 4 0.0000 0.8998 0.000 0.000 0.000 1.000 0.000
#> GSM531612 4 0.0000 0.8998 0.000 0.000 0.000 1.000 0.000
#> GSM531613 4 0.0290 0.8982 0.000 0.008 0.000 0.992 0.000
#> GSM531614 4 0.0000 0.8998 0.000 0.000 0.000 1.000 0.000
#> GSM531616 3 0.0404 0.9895 0.000 0.000 0.988 0.000 0.012
#> GSM531618 4 0.1942 0.8613 0.000 0.012 0.068 0.920 0.000
#> GSM531619 3 0.0162 0.9920 0.000 0.004 0.996 0.000 0.000
#> GSM531620 3 0.0290 0.9906 0.000 0.000 0.992 0.000 0.008
#> GSM531623 3 0.0162 0.9922 0.000 0.000 0.996 0.000 0.004
#> GSM531625 3 0.0290 0.9906 0.000 0.000 0.992 0.000 0.008
#> GSM531626 3 0.0404 0.9895 0.000 0.000 0.988 0.000 0.012
#> GSM531632 1 0.0000 0.8851 1.000 0.000 0.000 0.000 0.000
#> GSM531638 3 0.0404 0.9895 0.000 0.000 0.988 0.000 0.012
#> GSM531639 1 0.4268 0.5116 0.648 0.000 0.344 0.000 0.008
#> GSM531641 4 0.0000 0.8998 0.000 0.000 0.000 1.000 0.000
#> GSM531642 1 0.5263 0.6787 0.704 0.008 0.188 0.096 0.004
#> GSM531643 1 0.0324 0.8845 0.992 0.004 0.004 0.000 0.000
#> GSM531644 1 0.0324 0.8845 0.992 0.004 0.004 0.000 0.000
#> GSM531645 4 0.0000 0.8998 0.000 0.000 0.000 1.000 0.000
#> GSM531646 1 0.0162 0.8856 0.996 0.000 0.004 0.000 0.000
#> GSM531647 1 0.0162 0.8856 0.996 0.000 0.004 0.000 0.000
#> GSM531648 4 0.0000 0.8998 0.000 0.000 0.000 1.000 0.000
#> GSM531650 1 0.0162 0.8856 0.996 0.000 0.004 0.000 0.000
#> GSM531651 3 0.0162 0.9922 0.000 0.000 0.996 0.000 0.004
#> GSM531652 4 0.3802 0.6904 0.228 0.004 0.004 0.760 0.004
#> GSM531656 1 0.3282 0.7505 0.804 0.000 0.188 0.000 0.008
#> GSM531659 4 0.3074 0.8164 0.000 0.196 0.000 0.804 0.000
#> GSM531661 3 0.0451 0.9860 0.000 0.008 0.988 0.000 0.004
#> GSM531662 5 0.3934 0.6689 0.000 0.016 0.244 0.000 0.740
#> GSM531663 4 0.3508 0.7483 0.000 0.252 0.000 0.748 0.000
#> GSM531664 1 0.0000 0.8851 1.000 0.000 0.000 0.000 0.000
#> GSM531666 1 0.1492 0.8625 0.948 0.008 0.004 0.040 0.000
#> GSM531667 3 0.0290 0.9893 0.000 0.008 0.992 0.000 0.000
#> GSM531668 4 0.2852 0.8342 0.000 0.172 0.000 0.828 0.000
#> GSM531669 1 0.0000 0.8851 1.000 0.000 0.000 0.000 0.000
#> GSM531671 5 0.3807 0.7215 0.008 0.012 0.204 0.000 0.776
#> GSM531672 4 0.3039 0.8197 0.000 0.192 0.000 0.808 0.000
#> GSM531673 5 0.1399 0.8418 0.000 0.020 0.028 0.000 0.952
#> GSM531676 5 0.0510 0.8447 0.000 0.016 0.000 0.000 0.984
#> GSM531679 2 0.0162 0.9766 0.000 0.996 0.000 0.000 0.004
#> GSM531681 2 0.0162 0.9729 0.000 0.996 0.000 0.004 0.000
#> GSM531682 2 0.0794 0.9547 0.000 0.972 0.000 0.000 0.028
#> GSM531683 2 0.0162 0.9766 0.000 0.996 0.000 0.000 0.004
#> GSM531684 5 0.3274 0.7199 0.000 0.220 0.000 0.000 0.780
#> GSM531685 5 0.0566 0.8430 0.004 0.012 0.000 0.000 0.984
#> GSM531686 2 0.0162 0.9729 0.000 0.996 0.000 0.004 0.000
#> GSM531687 5 0.3752 0.6046 0.000 0.292 0.000 0.000 0.708
#> GSM531688 1 0.3039 0.7497 0.808 0.000 0.000 0.000 0.192
#> GSM531690 2 0.0162 0.9729 0.000 0.996 0.000 0.004 0.000
#> GSM531693 1 0.2852 0.7711 0.828 0.000 0.000 0.000 0.172
#> GSM531695 1 0.3455 0.7269 0.784 0.008 0.000 0.000 0.208
#> GSM531603 2 0.0162 0.9766 0.000 0.996 0.000 0.000 0.004
#> GSM531609 4 0.0000 0.8998 0.000 0.000 0.000 1.000 0.000
#> GSM531611 4 0.0703 0.8964 0.000 0.024 0.000 0.976 0.000
#> GSM531621 3 0.0162 0.9922 0.000 0.000 0.996 0.000 0.004
#> GSM531622 3 0.0162 0.9920 0.000 0.004 0.996 0.000 0.000
#> GSM531628 1 0.0000 0.8851 1.000 0.000 0.000 0.000 0.000
#> GSM531630 3 0.0162 0.9922 0.000 0.000 0.996 0.000 0.004
#> GSM531633 3 0.0162 0.9922 0.000 0.000 0.996 0.000 0.004
#> GSM531635 1 0.0451 0.8840 0.988 0.000 0.008 0.000 0.004
#> GSM531640 3 0.0162 0.9920 0.000 0.004 0.996 0.000 0.000
#> GSM531649 1 0.0324 0.8849 0.992 0.000 0.004 0.000 0.004
#> GSM531653 1 0.0162 0.8856 0.996 0.000 0.004 0.000 0.000
#> GSM531657 4 0.3074 0.8164 0.000 0.196 0.000 0.804 0.000
#> GSM531665 5 0.0510 0.8447 0.000 0.016 0.000 0.000 0.984
#> GSM531670 1 0.3039 0.7809 0.836 0.000 0.152 0.000 0.012
#> GSM531674 1 0.0000 0.8851 1.000 0.000 0.000 0.000 0.000
#> GSM531675 2 0.0162 0.9729 0.000 0.996 0.000 0.004 0.000
#> GSM531677 2 0.0162 0.9766 0.000 0.996 0.000 0.000 0.004
#> GSM531678 2 0.0162 0.9766 0.000 0.996 0.000 0.000 0.004
#> GSM531680 1 0.6783 -0.0289 0.372 0.348 0.000 0.000 0.280
#> GSM531689 5 0.4278 0.3247 0.000 0.452 0.000 0.000 0.548
#> GSM531691 5 0.1043 0.8427 0.000 0.040 0.000 0.000 0.960
#> GSM531692 5 0.0510 0.8447 0.000 0.016 0.000 0.000 0.984
#> GSM531694 2 0.0162 0.9766 0.000 0.996 0.000 0.000 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM531602 2 0.0717 0.955 0.000 0.976 0.000 0.000 0.008 0.016
#> GSM531604 5 0.0260 0.913 0.000 0.008 0.000 0.000 0.992 0.000
#> GSM531606 5 0.3290 0.648 0.000 0.208 0.000 0.000 0.776 0.016
#> GSM531607 2 0.0260 0.961 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM531608 3 0.0436 0.960 0.000 0.004 0.988 0.000 0.004 0.004
#> GSM531610 4 0.0000 0.902 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531612 4 0.0146 0.902 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM531613 4 0.0603 0.902 0.000 0.016 0.000 0.980 0.004 0.000
#> GSM531614 4 0.0000 0.902 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531616 3 0.1908 0.926 0.004 0.000 0.900 0.000 0.000 0.096
#> GSM531618 4 0.2580 0.861 0.004 0.004 0.036 0.884 0.000 0.072
#> GSM531619 3 0.0146 0.964 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM531620 3 0.1556 0.938 0.000 0.000 0.920 0.000 0.000 0.080
#> GSM531623 3 0.0000 0.965 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531625 3 0.1501 0.940 0.000 0.000 0.924 0.000 0.000 0.076
#> GSM531626 3 0.1765 0.929 0.000 0.000 0.904 0.000 0.000 0.096
#> GSM531632 1 0.0146 0.876 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM531638 3 0.1765 0.929 0.000 0.000 0.904 0.000 0.000 0.096
#> GSM531639 1 0.3815 0.781 0.776 0.000 0.132 0.000 0.000 0.092
#> GSM531641 4 0.0000 0.902 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531642 1 0.4877 0.757 0.696 0.000 0.028 0.080 0.000 0.196
#> GSM531643 1 0.1957 0.856 0.888 0.000 0.000 0.000 0.000 0.112
#> GSM531644 1 0.2003 0.855 0.884 0.000 0.000 0.000 0.000 0.116
#> GSM531645 4 0.0146 0.902 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM531646 1 0.0622 0.879 0.980 0.000 0.008 0.000 0.000 0.012
#> GSM531647 1 0.0405 0.878 0.988 0.000 0.008 0.000 0.000 0.004
#> GSM531648 4 0.0146 0.902 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM531650 1 0.0146 0.876 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM531651 3 0.0000 0.965 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531652 1 0.5080 0.616 0.624 0.000 0.000 0.236 0.000 0.140
#> GSM531656 1 0.3650 0.796 0.792 0.000 0.116 0.000 0.000 0.092
#> GSM531659 4 0.3011 0.842 0.000 0.192 0.000 0.800 0.004 0.004
#> GSM531661 3 0.0665 0.954 0.000 0.008 0.980 0.000 0.008 0.004
#> GSM531662 5 0.0551 0.912 0.000 0.008 0.004 0.000 0.984 0.004
#> GSM531663 4 0.3043 0.838 0.000 0.196 0.000 0.796 0.004 0.004
#> GSM531664 1 0.0146 0.876 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM531666 1 0.3426 0.817 0.808 0.000 0.000 0.068 0.000 0.124
#> GSM531667 3 0.0436 0.960 0.000 0.004 0.988 0.000 0.004 0.004
#> GSM531668 4 0.2773 0.859 0.000 0.164 0.000 0.828 0.004 0.004
#> GSM531669 1 0.1501 0.824 0.924 0.000 0.000 0.000 0.000 0.076
#> GSM531671 5 0.3171 0.780 0.004 0.004 0.092 0.000 0.844 0.056
#> GSM531672 4 0.2979 0.845 0.000 0.188 0.000 0.804 0.004 0.004
#> GSM531673 5 0.0146 0.913 0.000 0.004 0.000 0.000 0.996 0.000
#> GSM531676 6 0.3163 0.770 0.000 0.004 0.000 0.000 0.232 0.764
#> GSM531679 2 0.0458 0.958 0.000 0.984 0.000 0.000 0.016 0.000
#> GSM531681 2 0.0000 0.959 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531682 2 0.0260 0.961 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM531683 2 0.0260 0.961 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM531684 5 0.0951 0.905 0.000 0.008 0.004 0.000 0.968 0.020
#> GSM531685 6 0.3163 0.770 0.000 0.004 0.000 0.000 0.232 0.764
#> GSM531686 2 0.0000 0.959 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531687 6 0.3163 0.770 0.000 0.004 0.000 0.000 0.232 0.764
#> GSM531688 6 0.3136 0.805 0.228 0.000 0.000 0.000 0.004 0.768
#> GSM531690 2 0.0000 0.959 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531693 6 0.3248 0.809 0.224 0.004 0.000 0.000 0.004 0.768
#> GSM531695 6 0.3248 0.809 0.224 0.004 0.000 0.000 0.004 0.768
#> GSM531603 2 0.0405 0.960 0.000 0.988 0.000 0.000 0.008 0.004
#> GSM531609 4 0.0146 0.902 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM531611 4 0.2196 0.882 0.004 0.108 0.000 0.884 0.004 0.000
#> GSM531621 3 0.0000 0.965 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531622 3 0.0000 0.965 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531628 1 0.0146 0.876 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM531630 3 0.0000 0.965 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531633 3 0.0790 0.957 0.000 0.000 0.968 0.000 0.000 0.032
#> GSM531635 1 0.1970 0.861 0.900 0.000 0.008 0.000 0.000 0.092
#> GSM531640 3 0.0000 0.965 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531649 1 0.1970 0.861 0.900 0.000 0.008 0.000 0.000 0.092
#> GSM531653 1 0.0405 0.878 0.988 0.000 0.008 0.000 0.000 0.004
#> GSM531657 4 0.2979 0.845 0.000 0.188 0.000 0.804 0.004 0.004
#> GSM531665 5 0.1588 0.861 0.000 0.004 0.000 0.000 0.924 0.072
#> GSM531670 1 0.3844 0.798 0.792 0.004 0.108 0.000 0.004 0.092
#> GSM531674 1 0.0632 0.867 0.976 0.000 0.000 0.000 0.000 0.024
#> GSM531675 2 0.0000 0.959 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531677 2 0.0260 0.961 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM531678 2 0.0914 0.951 0.000 0.968 0.000 0.000 0.016 0.016
#> GSM531680 6 0.4138 0.817 0.108 0.012 0.000 0.000 0.112 0.768
#> GSM531689 2 0.3684 0.390 0.000 0.628 0.000 0.000 0.372 0.000
#> GSM531691 5 0.0603 0.908 0.000 0.004 0.000 0.000 0.980 0.016
#> GSM531692 5 0.0146 0.913 0.000 0.004 0.000 0.000 0.996 0.000
#> GSM531694 2 0.0717 0.955 0.000 0.976 0.000 0.000 0.008 0.016
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> MAD:mclust 79 0.911 2
#> MAD:mclust 73 0.164 3
#> MAD:mclust 78 0.478 4
#> MAD:mclust 78 0.882 5
#> MAD:mclust 79 0.840 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "NMF"]
# you can also extract it by
# res = res_list["MAD:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 80 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 0.802 0.925 0.968 0.5039 0.495 0.495
#> 3 3 0.547 0.627 0.830 0.3225 0.757 0.547
#> 4 4 0.897 0.914 0.962 0.1336 0.833 0.551
#> 5 5 0.729 0.697 0.840 0.0558 0.915 0.680
#> 6 6 0.678 0.545 0.739 0.0392 0.881 0.517
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
#> GSM531602 2 0.0000 0.965 0.000 1.000
#> GSM531604 2 0.0000 0.965 0.000 1.000
#> GSM531606 2 0.0000 0.965 0.000 1.000
#> GSM531607 2 0.0000 0.965 0.000 1.000
#> GSM531608 2 0.6343 0.800 0.160 0.840
#> GSM531610 2 0.0000 0.965 0.000 1.000
#> GSM531612 2 0.0000 0.965 0.000 1.000
#> GSM531613 2 0.0000 0.965 0.000 1.000
#> GSM531614 2 0.0000 0.965 0.000 1.000
#> GSM531616 1 0.0000 0.965 1.000 0.000
#> GSM531618 1 0.9608 0.392 0.616 0.384
#> GSM531619 1 0.0000 0.965 1.000 0.000
#> GSM531620 1 0.0000 0.965 1.000 0.000
#> GSM531623 1 0.0000 0.965 1.000 0.000
#> GSM531625 1 0.0000 0.965 1.000 0.000
#> GSM531626 1 0.0000 0.965 1.000 0.000
#> GSM531632 1 0.0000 0.965 1.000 0.000
#> GSM531638 1 0.0000 0.965 1.000 0.000
#> GSM531639 1 0.0000 0.965 1.000 0.000
#> GSM531641 2 0.0000 0.965 0.000 1.000
#> GSM531642 1 0.0000 0.965 1.000 0.000
#> GSM531643 1 0.0000 0.965 1.000 0.000
#> GSM531644 1 0.0000 0.965 1.000 0.000
#> GSM531645 2 0.0000 0.965 0.000 1.000
#> GSM531646 1 0.0000 0.965 1.000 0.000
#> GSM531647 1 0.0000 0.965 1.000 0.000
#> GSM531648 2 0.0000 0.965 0.000 1.000
#> GSM531650 1 0.0000 0.965 1.000 0.000
#> GSM531651 1 0.0000 0.965 1.000 0.000
#> GSM531652 1 0.0000 0.965 1.000 0.000
#> GSM531656 1 0.0000 0.965 1.000 0.000
#> GSM531659 2 0.0000 0.965 0.000 1.000
#> GSM531661 1 0.0000 0.965 1.000 0.000
#> GSM531662 1 0.0000 0.965 1.000 0.000
#> GSM531663 2 0.0000 0.965 0.000 1.000
#> GSM531664 1 0.0000 0.965 1.000 0.000
#> GSM531666 1 0.5946 0.825 0.856 0.144
#> GSM531667 1 0.5519 0.842 0.872 0.128
#> GSM531668 2 0.0000 0.965 0.000 1.000
#> GSM531669 1 0.0000 0.965 1.000 0.000
#> GSM531671 1 0.0000 0.965 1.000 0.000
#> GSM531672 2 0.0000 0.965 0.000 1.000
#> GSM531673 1 0.8955 0.549 0.688 0.312
#> GSM531676 2 0.7376 0.743 0.208 0.792
#> GSM531679 2 0.0000 0.965 0.000 1.000
#> GSM531681 2 0.0000 0.965 0.000 1.000
#> GSM531682 2 0.0000 0.965 0.000 1.000
#> GSM531683 2 0.0000 0.965 0.000 1.000
#> GSM531684 2 0.0000 0.965 0.000 1.000
#> GSM531685 1 0.1414 0.949 0.980 0.020
#> GSM531686 2 0.0000 0.965 0.000 1.000
#> GSM531687 2 0.5737 0.839 0.136 0.864
#> GSM531688 1 0.5737 0.833 0.864 0.136
#> GSM531690 2 0.0000 0.965 0.000 1.000
#> GSM531693 1 0.0000 0.965 1.000 0.000
#> GSM531695 2 0.6048 0.825 0.148 0.852
#> GSM531603 2 0.0000 0.965 0.000 1.000
#> GSM531609 2 0.0000 0.965 0.000 1.000
#> GSM531611 2 0.0000 0.965 0.000 1.000
#> GSM531621 1 0.0000 0.965 1.000 0.000
#> GSM531622 1 0.0000 0.965 1.000 0.000
#> GSM531628 1 0.0000 0.965 1.000 0.000
#> GSM531630 1 0.0000 0.965 1.000 0.000
#> GSM531633 1 0.0000 0.965 1.000 0.000
#> GSM531635 1 0.0000 0.965 1.000 0.000
#> GSM531640 1 0.0000 0.965 1.000 0.000
#> GSM531649 1 0.0000 0.965 1.000 0.000
#> GSM531653 1 0.0000 0.965 1.000 0.000
#> GSM531657 2 0.0000 0.965 0.000 1.000
#> GSM531665 2 0.9922 0.185 0.448 0.552
#> GSM531670 1 0.0000 0.965 1.000 0.000
#> GSM531674 1 0.0000 0.965 1.000 0.000
#> GSM531675 2 0.0000 0.965 0.000 1.000
#> GSM531677 2 0.0000 0.965 0.000 1.000
#> GSM531678 2 0.0000 0.965 0.000 1.000
#> GSM531680 2 0.4939 0.870 0.108 0.892
#> GSM531689 2 0.0000 0.965 0.000 1.000
#> GSM531691 2 0.0938 0.956 0.012 0.988
#> GSM531692 1 0.7950 0.686 0.760 0.240
#> GSM531694 2 0.0000 0.965 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM531602 2 0.0000 0.8347 0.000 1.000 0.000
#> GSM531604 2 0.5650 0.4162 0.000 0.688 0.312
#> GSM531606 2 0.0000 0.8347 0.000 1.000 0.000
#> GSM531607 2 0.0000 0.8347 0.000 1.000 0.000
#> GSM531608 3 0.5926 0.4464 0.000 0.356 0.644
#> GSM531610 2 0.5497 0.6416 0.292 0.708 0.000
#> GSM531612 1 0.6260 -0.2027 0.552 0.448 0.000
#> GSM531613 2 0.5733 0.6074 0.324 0.676 0.000
#> GSM531614 2 0.6235 0.4452 0.436 0.564 0.000
#> GSM531616 3 0.5216 0.4411 0.260 0.000 0.740
#> GSM531618 1 0.8199 0.3508 0.640 0.160 0.200
#> GSM531619 3 0.0237 0.8234 0.000 0.004 0.996
#> GSM531620 3 0.0000 0.8253 0.000 0.000 1.000
#> GSM531623 3 0.0000 0.8253 0.000 0.000 1.000
#> GSM531625 3 0.0000 0.8253 0.000 0.000 1.000
#> GSM531626 3 0.0000 0.8253 0.000 0.000 1.000
#> GSM531632 1 0.6204 0.4509 0.576 0.000 0.424
#> GSM531638 3 0.0237 0.8221 0.004 0.000 0.996
#> GSM531639 3 0.6045 0.0296 0.380 0.000 0.620
#> GSM531641 2 0.6111 0.5134 0.396 0.604 0.000
#> GSM531642 1 0.1529 0.6610 0.960 0.000 0.040
#> GSM531643 1 0.0592 0.6641 0.988 0.000 0.012
#> GSM531644 1 0.0000 0.6615 1.000 0.000 0.000
#> GSM531645 1 0.6111 -0.0444 0.604 0.396 0.000
#> GSM531646 1 0.6095 0.5103 0.608 0.000 0.392
#> GSM531647 1 0.5905 0.5550 0.648 0.000 0.352
#> GSM531648 1 0.5785 0.1505 0.668 0.332 0.000
#> GSM531650 1 0.1163 0.6642 0.972 0.000 0.028
#> GSM531651 3 0.0000 0.8253 0.000 0.000 1.000
#> GSM531652 1 0.0237 0.6626 0.996 0.000 0.004
#> GSM531656 1 0.5591 0.5859 0.696 0.000 0.304
#> GSM531659 2 0.4555 0.7248 0.200 0.800 0.000
#> GSM531661 3 0.3267 0.7416 0.000 0.116 0.884
#> GSM531662 3 0.4452 0.6745 0.000 0.192 0.808
#> GSM531663 2 0.0237 0.8345 0.004 0.996 0.000
#> GSM531664 1 0.0237 0.6628 0.996 0.000 0.004
#> GSM531666 1 0.0000 0.6615 1.000 0.000 0.000
#> GSM531667 3 0.0237 0.8234 0.000 0.004 0.996
#> GSM531668 2 0.1411 0.8251 0.036 0.964 0.000
#> GSM531669 1 0.5905 0.5550 0.648 0.000 0.352
#> GSM531671 3 0.5291 0.4245 0.268 0.000 0.732
#> GSM531672 2 0.5905 0.5735 0.352 0.648 0.000
#> GSM531673 3 0.6008 0.4182 0.000 0.372 0.628
#> GSM531676 2 0.4931 0.6145 0.212 0.784 0.004
#> GSM531679 2 0.0000 0.8347 0.000 1.000 0.000
#> GSM531681 2 0.0237 0.8345 0.004 0.996 0.000
#> GSM531682 2 0.0000 0.8347 0.000 1.000 0.000
#> GSM531683 2 0.0000 0.8347 0.000 1.000 0.000
#> GSM531684 2 0.6260 0.0383 0.000 0.552 0.448
#> GSM531685 1 0.9602 0.0558 0.400 0.200 0.400
#> GSM531686 2 0.1529 0.8242 0.040 0.960 0.000
#> GSM531687 2 0.4409 0.6737 0.172 0.824 0.004
#> GSM531688 1 0.6420 0.5859 0.688 0.024 0.288
#> GSM531690 2 0.1031 0.8299 0.024 0.976 0.000
#> GSM531693 1 0.6079 0.5160 0.612 0.000 0.388
#> GSM531695 1 0.0000 0.6615 1.000 0.000 0.000
#> GSM531603 2 0.0000 0.8347 0.000 1.000 0.000
#> GSM531609 2 0.6274 0.4036 0.456 0.544 0.000
#> GSM531611 2 0.6225 0.4528 0.432 0.568 0.000
#> GSM531621 3 0.0000 0.8253 0.000 0.000 1.000
#> GSM531622 3 0.0000 0.8253 0.000 0.000 1.000
#> GSM531628 1 0.0747 0.6644 0.984 0.000 0.016
#> GSM531630 3 0.0000 0.8253 0.000 0.000 1.000
#> GSM531633 3 0.0000 0.8253 0.000 0.000 1.000
#> GSM531635 1 0.6079 0.5160 0.612 0.000 0.388
#> GSM531640 3 0.0000 0.8253 0.000 0.000 1.000
#> GSM531649 1 0.6111 0.5039 0.604 0.000 0.396
#> GSM531653 1 0.5988 0.5393 0.632 0.000 0.368
#> GSM531657 2 0.3192 0.7868 0.112 0.888 0.000
#> GSM531665 2 0.5263 0.7115 0.060 0.824 0.116
#> GSM531670 1 0.6111 0.5080 0.604 0.000 0.396
#> GSM531674 1 0.5810 0.5668 0.664 0.000 0.336
#> GSM531675 2 0.0237 0.8345 0.004 0.996 0.000
#> GSM531677 2 0.0237 0.8345 0.004 0.996 0.000
#> GSM531678 2 0.0000 0.8347 0.000 1.000 0.000
#> GSM531680 1 0.3784 0.5660 0.864 0.132 0.004
#> GSM531689 2 0.0000 0.8347 0.000 1.000 0.000
#> GSM531691 2 0.0000 0.8347 0.000 1.000 0.000
#> GSM531692 3 0.8264 0.4096 0.088 0.356 0.556
#> GSM531694 2 0.0000 0.8347 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM531602 2 0.0000 0.958 0.000 1.000 0.000 0.000
#> GSM531604 2 0.0000 0.958 0.000 1.000 0.000 0.000
#> GSM531606 2 0.0000 0.958 0.000 1.000 0.000 0.000
#> GSM531607 2 0.0000 0.958 0.000 1.000 0.000 0.000
#> GSM531608 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> GSM531610 4 0.0000 0.965 0.000 0.000 0.000 1.000
#> GSM531612 4 0.0000 0.965 0.000 0.000 0.000 1.000
#> GSM531613 4 0.0000 0.965 0.000 0.000 0.000 1.000
#> GSM531614 4 0.0000 0.965 0.000 0.000 0.000 1.000
#> GSM531616 3 0.4277 0.595 0.280 0.000 0.720 0.000
#> GSM531618 4 0.0000 0.965 0.000 0.000 0.000 1.000
#> GSM531619 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> GSM531620 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> GSM531623 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> GSM531625 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> GSM531626 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> GSM531632 1 0.0000 0.955 1.000 0.000 0.000 0.000
#> GSM531638 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> GSM531639 3 0.0592 0.943 0.016 0.000 0.984 0.000
#> GSM531641 4 0.0000 0.965 0.000 0.000 0.000 1.000
#> GSM531642 4 0.0188 0.962 0.000 0.000 0.004 0.996
#> GSM531643 1 0.0000 0.955 1.000 0.000 0.000 0.000
#> GSM531644 1 0.3764 0.712 0.784 0.000 0.000 0.216
#> GSM531645 4 0.0000 0.965 0.000 0.000 0.000 1.000
#> GSM531646 1 0.0000 0.955 1.000 0.000 0.000 0.000
#> GSM531647 1 0.0000 0.955 1.000 0.000 0.000 0.000
#> GSM531648 4 0.0000 0.965 0.000 0.000 0.000 1.000
#> GSM531650 1 0.0000 0.955 1.000 0.000 0.000 0.000
#> GSM531651 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> GSM531652 4 0.0000 0.965 0.000 0.000 0.000 1.000
#> GSM531656 1 0.0592 0.943 0.984 0.000 0.016 0.000
#> GSM531659 4 0.1867 0.905 0.000 0.072 0.000 0.928
#> GSM531661 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> GSM531662 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> GSM531663 4 0.0469 0.957 0.000 0.012 0.000 0.988
#> GSM531664 1 0.0000 0.955 1.000 0.000 0.000 0.000
#> GSM531666 4 0.3024 0.803 0.148 0.000 0.000 0.852
#> GSM531667 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> GSM531668 4 0.4564 0.532 0.000 0.328 0.000 0.672
#> GSM531669 1 0.0000 0.955 1.000 0.000 0.000 0.000
#> GSM531671 3 0.6477 0.156 0.420 0.072 0.508 0.000
#> GSM531672 4 0.0000 0.965 0.000 0.000 0.000 1.000
#> GSM531673 2 0.3649 0.759 0.000 0.796 0.204 0.000
#> GSM531676 2 0.2647 0.852 0.120 0.880 0.000 0.000
#> GSM531679 2 0.0000 0.958 0.000 1.000 0.000 0.000
#> GSM531681 2 0.0592 0.949 0.000 0.984 0.000 0.016
#> GSM531682 2 0.0000 0.958 0.000 1.000 0.000 0.000
#> GSM531683 2 0.0000 0.958 0.000 1.000 0.000 0.000
#> GSM531684 2 0.3649 0.761 0.000 0.796 0.204 0.000
#> GSM531685 1 0.4304 0.605 0.716 0.284 0.000 0.000
#> GSM531686 2 0.0707 0.947 0.000 0.980 0.000 0.020
#> GSM531687 2 0.3219 0.798 0.164 0.836 0.000 0.000
#> GSM531688 1 0.0000 0.955 1.000 0.000 0.000 0.000
#> GSM531690 2 0.2408 0.866 0.000 0.896 0.000 0.104
#> GSM531693 1 0.0000 0.955 1.000 0.000 0.000 0.000
#> GSM531695 1 0.0188 0.952 0.996 0.004 0.000 0.000
#> GSM531603 2 0.0000 0.958 0.000 1.000 0.000 0.000
#> GSM531609 4 0.0000 0.965 0.000 0.000 0.000 1.000
#> GSM531611 4 0.0000 0.965 0.000 0.000 0.000 1.000
#> GSM531621 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> GSM531622 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> GSM531628 1 0.0000 0.955 1.000 0.000 0.000 0.000
#> GSM531630 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> GSM531633 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> GSM531635 1 0.0000 0.955 1.000 0.000 0.000 0.000
#> GSM531640 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> GSM531649 1 0.0000 0.955 1.000 0.000 0.000 0.000
#> GSM531653 1 0.0000 0.955 1.000 0.000 0.000 0.000
#> GSM531657 4 0.0000 0.965 0.000 0.000 0.000 1.000
#> GSM531665 2 0.1118 0.934 0.036 0.964 0.000 0.000
#> GSM531670 1 0.0707 0.939 0.980 0.000 0.020 0.000
#> GSM531674 1 0.0000 0.955 1.000 0.000 0.000 0.000
#> GSM531675 2 0.0000 0.958 0.000 1.000 0.000 0.000
#> GSM531677 2 0.0000 0.958 0.000 1.000 0.000 0.000
#> GSM531678 2 0.0000 0.958 0.000 1.000 0.000 0.000
#> GSM531680 1 0.4008 0.674 0.756 0.244 0.000 0.000
#> GSM531689 2 0.0000 0.958 0.000 1.000 0.000 0.000
#> GSM531691 2 0.0000 0.958 0.000 1.000 0.000 0.000
#> GSM531692 2 0.0000 0.958 0.000 1.000 0.000 0.000
#> GSM531694 2 0.0000 0.958 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM531602 2 0.3636 0.6960 0.000 0.728 0.000 0.000 0.272
#> GSM531604 2 0.0000 0.7887 0.000 1.000 0.000 0.000 0.000
#> GSM531606 2 0.2605 0.7683 0.000 0.852 0.000 0.000 0.148
#> GSM531607 2 0.3661 0.6870 0.000 0.724 0.000 0.000 0.276
#> GSM531608 3 0.0324 0.9313 0.000 0.000 0.992 0.004 0.004
#> GSM531610 4 0.0000 0.9700 0.000 0.000 0.000 1.000 0.000
#> GSM531612 4 0.0290 0.9678 0.000 0.000 0.000 0.992 0.008
#> GSM531613 4 0.0000 0.9700 0.000 0.000 0.000 1.000 0.000
#> GSM531614 4 0.0000 0.9700 0.000 0.000 0.000 1.000 0.000
#> GSM531616 1 0.4734 0.2591 0.604 0.000 0.372 0.000 0.024
#> GSM531618 5 0.4551 0.3244 0.000 0.000 0.016 0.368 0.616
#> GSM531619 3 0.1341 0.9206 0.000 0.000 0.944 0.000 0.056
#> GSM531620 3 0.3924 0.8535 0.068 0.000 0.808 0.004 0.120
#> GSM531623 3 0.0000 0.9311 0.000 0.000 1.000 0.000 0.000
#> GSM531625 3 0.3192 0.8636 0.112 0.000 0.848 0.000 0.040
#> GSM531626 3 0.4163 0.7906 0.176 0.000 0.776 0.008 0.040
#> GSM531632 1 0.0865 0.7744 0.972 0.000 0.004 0.000 0.024
#> GSM531638 3 0.1012 0.9321 0.012 0.000 0.968 0.000 0.020
#> GSM531639 3 0.2729 0.8708 0.056 0.000 0.884 0.000 0.060
#> GSM531641 4 0.0290 0.9678 0.000 0.000 0.000 0.992 0.008
#> GSM531642 5 0.6271 0.3104 0.148 0.000 0.000 0.412 0.440
#> GSM531643 1 0.2891 0.7155 0.824 0.000 0.000 0.000 0.176
#> GSM531644 5 0.4546 0.0226 0.460 0.000 0.000 0.008 0.532
#> GSM531645 4 0.0404 0.9654 0.000 0.000 0.000 0.988 0.012
#> GSM531646 1 0.0609 0.7789 0.980 0.000 0.000 0.000 0.020
#> GSM531647 1 0.0703 0.7909 0.976 0.000 0.000 0.000 0.024
#> GSM531648 5 0.4305 0.1125 0.000 0.000 0.000 0.488 0.512
#> GSM531650 1 0.2813 0.7242 0.832 0.000 0.000 0.000 0.168
#> GSM531651 3 0.0000 0.9311 0.000 0.000 1.000 0.000 0.000
#> GSM531652 5 0.5373 0.4894 0.092 0.000 0.000 0.276 0.632
#> GSM531656 5 0.6180 -0.0149 0.404 0.000 0.136 0.000 0.460
#> GSM531659 4 0.1484 0.9143 0.000 0.048 0.000 0.944 0.008
#> GSM531661 3 0.0963 0.9272 0.000 0.000 0.964 0.000 0.036
#> GSM531662 3 0.3071 0.8652 0.012 0.080 0.872 0.000 0.036
#> GSM531663 4 0.0290 0.9639 0.000 0.008 0.000 0.992 0.000
#> GSM531664 1 0.3999 0.4506 0.656 0.000 0.000 0.000 0.344
#> GSM531666 5 0.2305 0.5471 0.092 0.000 0.000 0.012 0.896
#> GSM531667 3 0.1608 0.9103 0.000 0.000 0.928 0.000 0.072
#> GSM531668 5 0.4126 0.5266 0.000 0.104 0.004 0.096 0.796
#> GSM531669 1 0.0162 0.7855 0.996 0.000 0.000 0.000 0.004
#> GSM531671 1 0.5076 0.5560 0.744 0.132 0.092 0.000 0.032
#> GSM531672 5 0.3305 0.4903 0.000 0.000 0.000 0.224 0.776
#> GSM531673 2 0.5344 0.5130 0.032 0.636 0.304 0.000 0.028
#> GSM531676 2 0.2674 0.7198 0.120 0.868 0.000 0.000 0.012
#> GSM531679 2 0.0510 0.7912 0.000 0.984 0.000 0.000 0.016
#> GSM531681 2 0.4262 0.2461 0.000 0.560 0.000 0.440 0.000
#> GSM531682 2 0.0510 0.7909 0.000 0.984 0.000 0.000 0.016
#> GSM531683 2 0.2690 0.7613 0.000 0.844 0.000 0.000 0.156
#> GSM531684 2 0.5345 0.5664 0.000 0.632 0.280 0.000 0.088
#> GSM531685 1 0.5681 0.1018 0.504 0.436 0.040 0.000 0.020
#> GSM531686 2 0.4283 0.2066 0.000 0.544 0.000 0.456 0.000
#> GSM531687 2 0.6246 0.2975 0.272 0.536 0.000 0.000 0.192
#> GSM531688 1 0.1544 0.7833 0.932 0.000 0.000 0.000 0.068
#> GSM531690 2 0.3596 0.7251 0.000 0.776 0.000 0.012 0.212
#> GSM531693 1 0.0865 0.7902 0.972 0.004 0.000 0.000 0.024
#> GSM531695 5 0.4446 0.1576 0.400 0.008 0.000 0.000 0.592
#> GSM531603 5 0.3696 0.3468 0.000 0.212 0.016 0.000 0.772
#> GSM531609 4 0.0000 0.9700 0.000 0.000 0.000 1.000 0.000
#> GSM531611 4 0.0000 0.9700 0.000 0.000 0.000 1.000 0.000
#> GSM531621 3 0.1741 0.9175 0.024 0.000 0.936 0.000 0.040
#> GSM531622 3 0.0703 0.9299 0.000 0.000 0.976 0.000 0.024
#> GSM531628 1 0.2773 0.7276 0.836 0.000 0.000 0.000 0.164
#> GSM531630 3 0.0794 0.9292 0.000 0.000 0.972 0.000 0.028
#> GSM531633 3 0.1836 0.9162 0.032 0.000 0.932 0.000 0.036
#> GSM531635 1 0.1082 0.7915 0.964 0.000 0.008 0.000 0.028
#> GSM531640 3 0.0963 0.9277 0.000 0.000 0.964 0.000 0.036
#> GSM531649 1 0.1281 0.7663 0.956 0.000 0.012 0.000 0.032
#> GSM531653 1 0.1478 0.7868 0.936 0.000 0.000 0.000 0.064
#> GSM531657 4 0.2719 0.8027 0.000 0.004 0.000 0.852 0.144
#> GSM531665 2 0.3048 0.6694 0.176 0.820 0.004 0.000 0.000
#> GSM531670 1 0.5391 0.4522 0.616 0.000 0.084 0.000 0.300
#> GSM531674 1 0.1671 0.7803 0.924 0.000 0.000 0.000 0.076
#> GSM531675 2 0.2179 0.7777 0.000 0.888 0.000 0.000 0.112
#> GSM531677 2 0.0000 0.7887 0.000 1.000 0.000 0.000 0.000
#> GSM531678 2 0.0613 0.7904 0.000 0.984 0.004 0.004 0.008
#> GSM531680 5 0.6738 0.1985 0.280 0.308 0.000 0.000 0.412
#> GSM531689 2 0.0290 0.7899 0.000 0.992 0.000 0.000 0.008
#> GSM531691 2 0.1626 0.7813 0.000 0.940 0.044 0.000 0.016
#> GSM531692 2 0.2053 0.7708 0.024 0.924 0.048 0.000 0.004
#> GSM531694 2 0.3242 0.7338 0.000 0.784 0.000 0.000 0.216
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM531602 2 0.5468 0.5077 0.000 0.548 0.000 0.000 0.156 0.296
#> GSM531604 2 0.0935 0.7142 0.000 0.964 0.000 0.000 0.032 0.004
#> GSM531606 2 0.4626 0.6390 0.000 0.692 0.000 0.000 0.136 0.172
#> GSM531607 2 0.5480 0.5004 0.000 0.540 0.000 0.000 0.152 0.308
#> GSM531608 3 0.4340 0.7384 0.000 0.020 0.744 0.048 0.184 0.004
#> GSM531610 4 0.0000 0.8308 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531612 4 0.0000 0.8308 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531613 4 0.0000 0.8308 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531614 4 0.0000 0.8308 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531616 5 0.5393 0.4558 0.256 0.000 0.168 0.000 0.576 0.000
#> GSM531618 6 0.5615 0.5609 0.016 0.000 0.008 0.204 0.148 0.624
#> GSM531619 3 0.0363 0.7577 0.000 0.000 0.988 0.000 0.012 0.000
#> GSM531620 5 0.3231 0.4345 0.012 0.000 0.180 0.000 0.800 0.008
#> GSM531623 3 0.2697 0.7669 0.000 0.000 0.812 0.000 0.188 0.000
#> GSM531625 5 0.3923 0.1160 0.004 0.000 0.416 0.000 0.580 0.000
#> GSM531626 5 0.4258 0.4693 0.068 0.000 0.204 0.000 0.724 0.004
#> GSM531632 5 0.3864 -0.1444 0.480 0.000 0.000 0.000 0.520 0.000
#> GSM531638 3 0.1320 0.7770 0.016 0.000 0.948 0.000 0.036 0.000
#> GSM531639 3 0.6315 0.3785 0.216 0.000 0.560 0.000 0.152 0.072
#> GSM531641 4 0.0000 0.8308 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531642 6 0.5740 0.4505 0.180 0.000 0.000 0.264 0.008 0.548
#> GSM531643 1 0.2837 0.6943 0.856 0.000 0.000 0.000 0.056 0.088
#> GSM531644 1 0.4111 0.1255 0.536 0.000 0.000 0.004 0.004 0.456
#> GSM531645 4 0.0000 0.8308 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531646 1 0.3864 0.1184 0.520 0.000 0.000 0.000 0.480 0.000
#> GSM531647 1 0.3563 0.4446 0.664 0.000 0.000 0.000 0.336 0.000
#> GSM531648 6 0.4319 0.5041 0.012 0.000 0.000 0.256 0.036 0.696
#> GSM531650 1 0.3063 0.6909 0.840 0.000 0.000 0.000 0.068 0.092
#> GSM531651 3 0.2762 0.7631 0.000 0.000 0.804 0.000 0.196 0.000
#> GSM531652 6 0.4604 0.5707 0.092 0.000 0.000 0.172 0.016 0.720
#> GSM531656 1 0.4303 0.6007 0.752 0.000 0.108 0.000 0.012 0.128
#> GSM531659 4 0.6270 0.2524 0.004 0.232 0.000 0.544 0.036 0.184
#> GSM531661 3 0.3309 0.7520 0.000 0.004 0.788 0.000 0.192 0.016
#> GSM531662 5 0.6685 -0.0755 0.000 0.240 0.360 0.000 0.364 0.036
#> GSM531663 4 0.0260 0.8254 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM531664 1 0.2442 0.6646 0.852 0.000 0.000 0.000 0.004 0.144
#> GSM531666 6 0.4379 0.1525 0.396 0.000 0.000 0.000 0.028 0.576
#> GSM531667 3 0.3667 0.7395 0.000 0.000 0.788 0.000 0.132 0.080
#> GSM531668 6 0.4102 0.4987 0.000 0.044 0.000 0.004 0.232 0.720
#> GSM531669 1 0.3765 0.3217 0.596 0.000 0.000 0.000 0.404 0.000
#> GSM531671 5 0.4030 0.4852 0.196 0.032 0.020 0.000 0.752 0.000
#> GSM531672 6 0.3522 0.6201 0.024 0.000 0.000 0.072 0.076 0.828
#> GSM531673 5 0.6206 0.1124 0.004 0.348 0.100 0.000 0.500 0.048
#> GSM531676 2 0.3905 0.2995 0.356 0.636 0.000 0.000 0.004 0.004
#> GSM531679 2 0.3159 0.7046 0.000 0.832 0.000 0.000 0.068 0.100
#> GSM531681 4 0.3758 0.5243 0.000 0.324 0.000 0.668 0.008 0.000
#> GSM531682 2 0.3419 0.7007 0.000 0.812 0.000 0.000 0.084 0.104
#> GSM531683 2 0.4675 0.6327 0.000 0.672 0.000 0.000 0.104 0.224
#> GSM531684 2 0.5630 0.1996 0.000 0.464 0.440 0.000 0.052 0.044
#> GSM531685 2 0.5077 0.0940 0.404 0.516 0.000 0.000 0.080 0.000
#> GSM531686 4 0.3742 0.4997 0.004 0.348 0.000 0.648 0.000 0.000
#> GSM531687 1 0.4890 0.4667 0.640 0.288 0.000 0.000 0.020 0.052
#> GSM531688 1 0.1838 0.6845 0.916 0.068 0.000 0.000 0.016 0.000
#> GSM531690 6 0.4640 -0.2681 0.000 0.436 0.000 0.004 0.032 0.528
#> GSM531693 1 0.3341 0.6385 0.816 0.068 0.000 0.000 0.116 0.000
#> GSM531695 1 0.3778 0.6179 0.784 0.028 0.000 0.000 0.024 0.164
#> GSM531603 6 0.4778 0.4886 0.008 0.068 0.024 0.000 0.180 0.720
#> GSM531609 4 0.0000 0.8308 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531611 4 0.0000 0.8308 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531621 3 0.3634 0.5680 0.000 0.000 0.644 0.000 0.356 0.000
#> GSM531622 3 0.2118 0.7858 0.000 0.000 0.888 0.000 0.104 0.008
#> GSM531628 1 0.1500 0.6994 0.936 0.000 0.000 0.000 0.012 0.052
#> GSM531630 3 0.0363 0.7709 0.000 0.000 0.988 0.000 0.012 0.000
#> GSM531633 3 0.3989 0.3340 0.000 0.000 0.528 0.000 0.468 0.004
#> GSM531635 1 0.2003 0.6718 0.884 0.000 0.000 0.000 0.116 0.000
#> GSM531640 3 0.0725 0.7551 0.000 0.000 0.976 0.012 0.012 0.000
#> GSM531649 1 0.3843 0.2265 0.548 0.000 0.000 0.000 0.452 0.000
#> GSM531653 1 0.2664 0.6317 0.816 0.000 0.000 0.000 0.184 0.000
#> GSM531657 4 0.5005 0.0593 0.000 0.008 0.000 0.520 0.052 0.420
#> GSM531665 2 0.2377 0.6953 0.024 0.892 0.000 0.000 0.076 0.008
#> GSM531670 1 0.4128 0.6011 0.772 0.004 0.140 0.000 0.012 0.072
#> GSM531674 1 0.1007 0.6934 0.956 0.000 0.000 0.000 0.044 0.000
#> GSM531675 2 0.4183 0.5902 0.000 0.668 0.000 0.000 0.036 0.296
#> GSM531677 2 0.2081 0.7092 0.012 0.916 0.000 0.000 0.036 0.036
#> GSM531678 2 0.1995 0.6938 0.024 0.924 0.000 0.036 0.012 0.004
#> GSM531680 1 0.5025 0.5275 0.676 0.208 0.000 0.000 0.024 0.092
#> GSM531689 2 0.1511 0.6934 0.044 0.940 0.000 0.000 0.012 0.004
#> GSM531691 2 0.1937 0.6913 0.048 0.924 0.012 0.000 0.012 0.004
#> GSM531692 2 0.2008 0.7070 0.032 0.920 0.004 0.000 0.040 0.004
#> GSM531694 2 0.5065 0.5813 0.000 0.616 0.000 0.000 0.124 0.260
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> MAD:NMF 78 1.000 2
#> MAD:NMF 63 1.000 3
#> MAD:NMF 79 0.441 4
#> MAD:NMF 63 0.737 5
#> MAD:NMF 53 0.221 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "hclust"]
# you can also extract it by
# res = res_list["ATC:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 80 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 0.873 0.893 0.960 0.3480 0.661 0.661
#> 3 3 0.729 0.782 0.896 0.8056 0.704 0.552
#> 4 4 0.721 0.726 0.829 0.1281 0.918 0.780
#> 5 5 0.737 0.694 0.821 0.0539 0.934 0.779
#> 6 6 0.765 0.678 0.811 0.0321 0.957 0.831
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
#> GSM531602 2 0.000 0.9636 0.000 1.000
#> GSM531604 2 0.000 0.9636 0.000 1.000
#> GSM531606 2 0.000 0.9636 0.000 1.000
#> GSM531607 2 0.000 0.9636 0.000 1.000
#> GSM531608 1 0.000 0.9212 1.000 0.000
#> GSM531610 2 0.000 0.9636 0.000 1.000
#> GSM531612 2 0.000 0.9636 0.000 1.000
#> GSM531613 2 0.000 0.9636 0.000 1.000
#> GSM531614 2 0.000 0.9636 0.000 1.000
#> GSM531616 1 0.000 0.9212 1.000 0.000
#> GSM531618 2 0.000 0.9636 0.000 1.000
#> GSM531619 1 0.000 0.9212 1.000 0.000
#> GSM531620 1 0.850 0.6025 0.724 0.276
#> GSM531623 1 0.000 0.9212 1.000 0.000
#> GSM531625 1 0.000 0.9212 1.000 0.000
#> GSM531626 1 0.991 0.2160 0.556 0.444
#> GSM531632 2 0.714 0.7335 0.196 0.804
#> GSM531638 2 0.995 0.0896 0.460 0.540
#> GSM531639 2 0.000 0.9636 0.000 1.000
#> GSM531641 2 0.000 0.9636 0.000 1.000
#> GSM531642 2 0.000 0.9636 0.000 1.000
#> GSM531643 2 0.000 0.9636 0.000 1.000
#> GSM531644 2 0.000 0.9636 0.000 1.000
#> GSM531645 2 0.000 0.9636 0.000 1.000
#> GSM531646 2 0.996 0.0742 0.464 0.536
#> GSM531647 2 0.827 0.6251 0.260 0.740
#> GSM531648 2 0.000 0.9636 0.000 1.000
#> GSM531650 2 0.000 0.9636 0.000 1.000
#> GSM531651 1 0.000 0.9212 1.000 0.000
#> GSM531652 2 0.000 0.9636 0.000 1.000
#> GSM531656 2 0.000 0.9636 0.000 1.000
#> GSM531659 2 0.000 0.9636 0.000 1.000
#> GSM531661 1 0.000 0.9212 1.000 0.000
#> GSM531662 2 0.242 0.9262 0.040 0.960
#> GSM531663 2 0.000 0.9636 0.000 1.000
#> GSM531664 2 0.000 0.9636 0.000 1.000
#> GSM531666 2 0.000 0.9636 0.000 1.000
#> GSM531667 1 0.000 0.9212 1.000 0.000
#> GSM531668 2 0.000 0.9636 0.000 1.000
#> GSM531669 2 0.000 0.9636 0.000 1.000
#> GSM531671 2 0.278 0.9183 0.048 0.952
#> GSM531672 2 0.000 0.9636 0.000 1.000
#> GSM531673 2 0.000 0.9636 0.000 1.000
#> GSM531676 2 0.000 0.9636 0.000 1.000
#> GSM531679 2 0.000 0.9636 0.000 1.000
#> GSM531681 2 0.000 0.9636 0.000 1.000
#> GSM531682 2 0.000 0.9636 0.000 1.000
#> GSM531683 2 0.000 0.9636 0.000 1.000
#> GSM531684 2 0.000 0.9636 0.000 1.000
#> GSM531685 2 0.000 0.9636 0.000 1.000
#> GSM531686 2 0.000 0.9636 0.000 1.000
#> GSM531687 2 0.000 0.9636 0.000 1.000
#> GSM531688 2 0.000 0.9636 0.000 1.000
#> GSM531690 2 0.000 0.9636 0.000 1.000
#> GSM531693 2 0.000 0.9636 0.000 1.000
#> GSM531695 2 0.000 0.9636 0.000 1.000
#> GSM531603 2 0.000 0.9636 0.000 1.000
#> GSM531609 2 0.000 0.9636 0.000 1.000
#> GSM531611 2 0.000 0.9636 0.000 1.000
#> GSM531621 1 0.000 0.9212 1.000 0.000
#> GSM531622 1 0.000 0.9212 1.000 0.000
#> GSM531628 2 0.952 0.3742 0.372 0.628
#> GSM531630 1 0.000 0.9212 1.000 0.000
#> GSM531633 1 0.000 0.9212 1.000 0.000
#> GSM531635 1 0.000 0.9212 1.000 0.000
#> GSM531640 1 0.000 0.9212 1.000 0.000
#> GSM531649 1 0.991 0.2160 0.556 0.444
#> GSM531653 2 0.722 0.7271 0.200 0.800
#> GSM531657 2 0.000 0.9636 0.000 1.000
#> GSM531665 2 0.000 0.9636 0.000 1.000
#> GSM531670 2 0.000 0.9636 0.000 1.000
#> GSM531674 2 0.000 0.9636 0.000 1.000
#> GSM531675 2 0.000 0.9636 0.000 1.000
#> GSM531677 2 0.000 0.9636 0.000 1.000
#> GSM531678 2 0.000 0.9636 0.000 1.000
#> GSM531680 2 0.000 0.9636 0.000 1.000
#> GSM531689 2 0.000 0.9636 0.000 1.000
#> GSM531691 2 0.000 0.9636 0.000 1.000
#> GSM531692 2 0.000 0.9636 0.000 1.000
#> GSM531694 2 0.000 0.9636 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM531602 2 0.141 0.9566 0.036 0.964 0.000
#> GSM531604 1 0.327 0.8108 0.884 0.116 0.000
#> GSM531606 1 0.327 0.8108 0.884 0.116 0.000
#> GSM531607 2 0.614 0.2607 0.404 0.596 0.000
#> GSM531608 3 0.000 0.9049 0.000 0.000 1.000
#> GSM531610 1 0.116 0.8525 0.972 0.028 0.000
#> GSM531612 2 0.141 0.9566 0.036 0.964 0.000
#> GSM531613 2 0.141 0.9566 0.036 0.964 0.000
#> GSM531614 1 0.000 0.8395 1.000 0.000 0.000
#> GSM531616 3 0.000 0.9049 0.000 0.000 1.000
#> GSM531618 1 0.116 0.8556 0.972 0.028 0.000
#> GSM531619 3 0.141 0.8964 0.000 0.036 0.964
#> GSM531620 3 0.536 0.5598 0.276 0.000 0.724
#> GSM531623 3 0.000 0.9049 0.000 0.000 1.000
#> GSM531625 3 0.141 0.8964 0.000 0.036 0.964
#> GSM531626 3 0.625 0.1346 0.444 0.000 0.556
#> GSM531632 1 0.450 0.6682 0.804 0.000 0.196
#> GSM531638 1 0.628 0.0988 0.540 0.000 0.460
#> GSM531639 1 0.116 0.8556 0.972 0.028 0.000
#> GSM531641 1 0.595 0.4700 0.640 0.360 0.000
#> GSM531642 1 0.116 0.8556 0.972 0.028 0.000
#> GSM531643 1 0.116 0.8556 0.972 0.028 0.000
#> GSM531644 1 0.116 0.8556 0.972 0.028 0.000
#> GSM531645 1 0.116 0.8556 0.972 0.028 0.000
#> GSM531646 1 0.629 0.0837 0.536 0.000 0.464
#> GSM531647 1 0.522 0.5814 0.740 0.000 0.260
#> GSM531648 1 0.116 0.8556 0.972 0.028 0.000
#> GSM531650 1 0.116 0.8556 0.972 0.028 0.000
#> GSM531651 3 0.141 0.8964 0.000 0.036 0.964
#> GSM531652 1 0.116 0.8556 0.972 0.028 0.000
#> GSM531656 1 0.116 0.8556 0.972 0.028 0.000
#> GSM531659 1 0.116 0.8556 0.972 0.028 0.000
#> GSM531661 3 0.000 0.9049 0.000 0.000 1.000
#> GSM531662 1 0.176 0.8125 0.956 0.004 0.040
#> GSM531663 1 0.116 0.8556 0.972 0.028 0.000
#> GSM531664 1 0.529 0.6368 0.732 0.268 0.000
#> GSM531666 1 0.529 0.6368 0.732 0.268 0.000
#> GSM531667 3 0.000 0.9049 0.000 0.000 1.000
#> GSM531668 1 0.116 0.8556 0.972 0.028 0.000
#> GSM531669 1 0.116 0.8556 0.972 0.028 0.000
#> GSM531671 1 0.175 0.8032 0.952 0.000 0.048
#> GSM531672 1 0.629 0.1567 0.532 0.468 0.000
#> GSM531673 1 0.116 0.8556 0.972 0.028 0.000
#> GSM531676 2 0.226 0.9272 0.068 0.932 0.000
#> GSM531679 2 0.141 0.9566 0.036 0.964 0.000
#> GSM531681 2 0.141 0.9566 0.036 0.964 0.000
#> GSM531682 2 0.141 0.9566 0.036 0.964 0.000
#> GSM531683 2 0.141 0.9566 0.036 0.964 0.000
#> GSM531684 1 0.334 0.8079 0.880 0.120 0.000
#> GSM531685 2 0.216 0.9314 0.064 0.936 0.000
#> GSM531686 2 0.141 0.9566 0.036 0.964 0.000
#> GSM531687 2 0.141 0.9566 0.036 0.964 0.000
#> GSM531688 2 0.141 0.9566 0.036 0.964 0.000
#> GSM531690 2 0.141 0.9566 0.036 0.964 0.000
#> GSM531693 1 0.627 0.2334 0.548 0.452 0.000
#> GSM531695 2 0.141 0.9566 0.036 0.964 0.000
#> GSM531603 2 0.614 0.2607 0.404 0.596 0.000
#> GSM531609 1 0.000 0.8395 1.000 0.000 0.000
#> GSM531611 2 0.141 0.9566 0.036 0.964 0.000
#> GSM531621 3 0.141 0.8964 0.000 0.036 0.964
#> GSM531622 3 0.000 0.9049 0.000 0.000 1.000
#> GSM531628 1 0.601 0.3657 0.628 0.000 0.372
#> GSM531630 3 0.000 0.9049 0.000 0.000 1.000
#> GSM531633 3 0.141 0.8964 0.000 0.036 0.964
#> GSM531635 3 0.000 0.9049 0.000 0.000 1.000
#> GSM531640 3 0.000 0.9049 0.000 0.000 1.000
#> GSM531649 3 0.625 0.1346 0.444 0.000 0.556
#> GSM531653 1 0.455 0.6713 0.800 0.000 0.200
#> GSM531657 1 0.625 0.2401 0.556 0.444 0.000
#> GSM531665 1 0.116 0.8556 0.972 0.028 0.000
#> GSM531670 1 0.116 0.8556 0.972 0.028 0.000
#> GSM531674 1 0.116 0.8556 0.972 0.028 0.000
#> GSM531675 2 0.141 0.9566 0.036 0.964 0.000
#> GSM531677 2 0.141 0.9566 0.036 0.964 0.000
#> GSM531678 2 0.153 0.9535 0.040 0.960 0.000
#> GSM531680 2 0.141 0.9566 0.036 0.964 0.000
#> GSM531689 2 0.141 0.9566 0.036 0.964 0.000
#> GSM531691 2 0.141 0.9566 0.036 0.964 0.000
#> GSM531692 1 0.319 0.8132 0.888 0.112 0.000
#> GSM531694 2 0.141 0.9566 0.036 0.964 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM531602 2 0.0000 0.9311 0.000 1.000 0.000 0.000
#> GSM531604 4 0.4360 0.6632 0.248 0.008 0.000 0.744
#> GSM531606 4 0.4360 0.6632 0.248 0.008 0.000 0.744
#> GSM531607 2 0.6635 0.1639 0.088 0.524 0.000 0.388
#> GSM531608 3 0.2814 0.7804 0.132 0.000 0.868 0.000
#> GSM531610 4 0.1661 0.7960 0.052 0.004 0.000 0.944
#> GSM531612 2 0.0000 0.9311 0.000 1.000 0.000 0.000
#> GSM531613 2 0.0000 0.9311 0.000 1.000 0.000 0.000
#> GSM531614 4 0.2011 0.7832 0.080 0.000 0.000 0.920
#> GSM531616 3 0.4304 0.8028 0.284 0.000 0.716 0.000
#> GSM531618 4 0.0817 0.8116 0.024 0.000 0.000 0.976
#> GSM531619 3 0.0000 0.7459 0.000 0.000 1.000 0.000
#> GSM531620 1 0.5906 -0.0324 0.528 0.000 0.436 0.036
#> GSM531623 3 0.4250 0.8059 0.276 0.000 0.724 0.000
#> GSM531625 3 0.0000 0.7459 0.000 0.000 1.000 0.000
#> GSM531626 1 0.5519 0.5357 0.684 0.000 0.264 0.052
#> GSM531632 1 0.4679 0.5729 0.648 0.000 0.000 0.352
#> GSM531638 1 0.5376 0.6527 0.736 0.000 0.176 0.088
#> GSM531639 4 0.0336 0.8089 0.008 0.000 0.000 0.992
#> GSM531641 4 0.4999 0.5004 0.012 0.328 0.000 0.660
#> GSM531642 4 0.0336 0.8089 0.008 0.000 0.000 0.992
#> GSM531643 4 0.0817 0.8116 0.024 0.000 0.000 0.976
#> GSM531644 4 0.0817 0.8116 0.024 0.000 0.000 0.976
#> GSM531645 4 0.0817 0.8116 0.024 0.000 0.000 0.976
#> GSM531646 1 0.5355 0.6492 0.736 0.000 0.180 0.084
#> GSM531647 1 0.4277 0.6523 0.720 0.000 0.000 0.280
#> GSM531648 4 0.0817 0.8116 0.024 0.000 0.000 0.976
#> GSM531650 4 0.0817 0.8116 0.024 0.000 0.000 0.976
#> GSM531651 3 0.0000 0.7459 0.000 0.000 1.000 0.000
#> GSM531652 4 0.0817 0.8116 0.024 0.000 0.000 0.976
#> GSM531656 4 0.0817 0.8116 0.024 0.000 0.000 0.976
#> GSM531659 4 0.0336 0.8089 0.008 0.000 0.000 0.992
#> GSM531661 3 0.4304 0.8028 0.284 0.000 0.716 0.000
#> GSM531662 4 0.4992 -0.1610 0.476 0.000 0.000 0.524
#> GSM531663 4 0.0469 0.8121 0.012 0.000 0.000 0.988
#> GSM531664 4 0.4387 0.6214 0.012 0.236 0.000 0.752
#> GSM531666 4 0.4387 0.6214 0.012 0.236 0.000 0.752
#> GSM531667 3 0.4304 0.8028 0.284 0.000 0.716 0.000
#> GSM531668 4 0.0592 0.8105 0.016 0.000 0.000 0.984
#> GSM531669 4 0.0707 0.8118 0.020 0.000 0.000 0.980
#> GSM531671 4 0.4998 -0.2009 0.488 0.000 0.000 0.512
#> GSM531672 4 0.5466 0.2346 0.016 0.436 0.000 0.548
#> GSM531673 4 0.0469 0.8121 0.012 0.000 0.000 0.988
#> GSM531676 2 0.3834 0.8263 0.076 0.848 0.000 0.076
#> GSM531679 2 0.0000 0.9311 0.000 1.000 0.000 0.000
#> GSM531681 2 0.0000 0.9311 0.000 1.000 0.000 0.000
#> GSM531682 2 0.0000 0.9311 0.000 1.000 0.000 0.000
#> GSM531683 2 0.0000 0.9311 0.000 1.000 0.000 0.000
#> GSM531684 4 0.4453 0.6640 0.244 0.012 0.000 0.744
#> GSM531685 2 0.3833 0.8279 0.080 0.848 0.000 0.072
#> GSM531686 2 0.0000 0.9311 0.000 1.000 0.000 0.000
#> GSM531687 2 0.1716 0.8991 0.064 0.936 0.000 0.000
#> GSM531688 2 0.1716 0.8991 0.064 0.936 0.000 0.000
#> GSM531690 2 0.0000 0.9311 0.000 1.000 0.000 0.000
#> GSM531693 4 0.7269 0.2557 0.156 0.356 0.000 0.488
#> GSM531695 2 0.0000 0.9311 0.000 1.000 0.000 0.000
#> GSM531603 2 0.6635 0.1639 0.088 0.524 0.000 0.388
#> GSM531609 4 0.2011 0.7832 0.080 0.000 0.000 0.920
#> GSM531611 2 0.0000 0.9311 0.000 1.000 0.000 0.000
#> GSM531621 3 0.0000 0.7459 0.000 0.000 1.000 0.000
#> GSM531622 3 0.4250 0.8059 0.276 0.000 0.724 0.000
#> GSM531628 1 0.5410 0.6755 0.728 0.000 0.080 0.192
#> GSM531630 3 0.4304 0.8028 0.284 0.000 0.716 0.000
#> GSM531633 3 0.0000 0.7459 0.000 0.000 1.000 0.000
#> GSM531635 3 0.4304 0.8028 0.284 0.000 0.716 0.000
#> GSM531640 3 0.4250 0.8059 0.276 0.000 0.724 0.000
#> GSM531649 1 0.5519 0.5357 0.684 0.000 0.264 0.052
#> GSM531653 1 0.4624 0.5795 0.660 0.000 0.000 0.340
#> GSM531657 4 0.5417 0.3016 0.016 0.412 0.000 0.572
#> GSM531665 4 0.0469 0.8121 0.012 0.000 0.000 0.988
#> GSM531670 4 0.0817 0.8116 0.024 0.000 0.000 0.976
#> GSM531674 4 0.0817 0.8116 0.024 0.000 0.000 0.976
#> GSM531675 2 0.0000 0.9311 0.000 1.000 0.000 0.000
#> GSM531677 2 0.0000 0.9311 0.000 1.000 0.000 0.000
#> GSM531678 2 0.0188 0.9285 0.000 0.996 0.000 0.004
#> GSM531680 2 0.0000 0.9311 0.000 1.000 0.000 0.000
#> GSM531689 2 0.0000 0.9311 0.000 1.000 0.000 0.000
#> GSM531691 2 0.1716 0.8991 0.064 0.936 0.000 0.000
#> GSM531692 4 0.4220 0.6650 0.248 0.004 0.000 0.748
#> GSM531694 2 0.0000 0.9311 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM531602 2 0.0000 0.9243 0.000 1.000 0.000 0.000 0.000
#> GSM531604 5 0.3636 0.8516 0.000 0.000 0.000 0.272 0.728
#> GSM531606 5 0.3636 0.8516 0.000 0.000 0.000 0.272 0.728
#> GSM531607 2 0.6514 -0.0410 0.004 0.516 0.000 0.236 0.244
#> GSM531608 3 0.2732 0.7385 0.160 0.000 0.840 0.000 0.000
#> GSM531610 4 0.5364 0.4644 0.112 0.004 0.000 0.672 0.212
#> GSM531612 2 0.0000 0.9243 0.000 1.000 0.000 0.000 0.000
#> GSM531613 2 0.0000 0.9243 0.000 1.000 0.000 0.000 0.000
#> GSM531614 4 0.5460 0.4350 0.148 0.000 0.000 0.656 0.196
#> GSM531616 3 0.3876 0.7626 0.316 0.000 0.684 0.000 0.000
#> GSM531618 4 0.0771 0.7849 0.020 0.000 0.000 0.976 0.004
#> GSM531619 3 0.1608 0.6799 0.000 0.000 0.928 0.000 0.072
#> GSM531620 1 0.4817 -0.0906 0.572 0.000 0.404 0.024 0.000
#> GSM531623 3 0.3816 0.7666 0.304 0.000 0.696 0.000 0.000
#> GSM531625 3 0.1608 0.6799 0.000 0.000 0.928 0.000 0.072
#> GSM531626 1 0.4192 0.4535 0.736 0.000 0.232 0.032 0.000
#> GSM531632 1 0.3636 0.6320 0.728 0.000 0.000 0.272 0.000
#> GSM531638 1 0.3780 0.5889 0.808 0.000 0.132 0.060 0.000
#> GSM531639 4 0.1205 0.7658 0.004 0.000 0.000 0.956 0.040
#> GSM531641 4 0.5203 0.2101 0.004 0.324 0.000 0.620 0.052
#> GSM531642 4 0.1357 0.7614 0.004 0.000 0.000 0.948 0.048
#> GSM531643 4 0.0771 0.7849 0.020 0.000 0.000 0.976 0.004
#> GSM531644 4 0.0671 0.7861 0.016 0.000 0.000 0.980 0.004
#> GSM531645 4 0.0671 0.7861 0.016 0.000 0.000 0.980 0.004
#> GSM531646 1 0.3714 0.5852 0.812 0.000 0.132 0.056 0.000
#> GSM531647 1 0.3109 0.6625 0.800 0.000 0.000 0.200 0.000
#> GSM531648 4 0.0671 0.7861 0.016 0.000 0.000 0.980 0.004
#> GSM531650 4 0.0671 0.7861 0.016 0.000 0.000 0.980 0.004
#> GSM531651 3 0.1608 0.6799 0.000 0.000 0.928 0.000 0.072
#> GSM531652 4 0.0671 0.7861 0.016 0.000 0.000 0.980 0.004
#> GSM531656 4 0.0771 0.7849 0.020 0.000 0.000 0.976 0.004
#> GSM531659 4 0.1357 0.7614 0.004 0.000 0.000 0.948 0.048
#> GSM531661 3 0.3876 0.7626 0.316 0.000 0.684 0.000 0.000
#> GSM531662 1 0.4610 0.3951 0.556 0.000 0.000 0.432 0.012
#> GSM531663 4 0.0609 0.7799 0.000 0.000 0.000 0.980 0.020
#> GSM531664 4 0.4701 0.4006 0.004 0.232 0.000 0.712 0.052
#> GSM531666 4 0.4701 0.4006 0.004 0.232 0.000 0.712 0.052
#> GSM531667 3 0.3876 0.7626 0.316 0.000 0.684 0.000 0.000
#> GSM531668 4 0.0955 0.7739 0.004 0.000 0.000 0.968 0.028
#> GSM531669 4 0.0912 0.7843 0.012 0.000 0.000 0.972 0.016
#> GSM531671 1 0.4590 0.4230 0.568 0.000 0.000 0.420 0.012
#> GSM531672 4 0.5782 -0.0783 0.004 0.432 0.000 0.488 0.076
#> GSM531673 4 0.0609 0.7799 0.000 0.000 0.000 0.980 0.020
#> GSM531676 2 0.3291 0.7900 0.000 0.840 0.000 0.040 0.120
#> GSM531679 2 0.0000 0.9243 0.000 1.000 0.000 0.000 0.000
#> GSM531681 2 0.0000 0.9243 0.000 1.000 0.000 0.000 0.000
#> GSM531682 2 0.0000 0.9243 0.000 1.000 0.000 0.000 0.000
#> GSM531683 2 0.0000 0.9243 0.000 1.000 0.000 0.000 0.000
#> GSM531684 5 0.3715 0.8480 0.000 0.004 0.000 0.260 0.736
#> GSM531685 2 0.3291 0.7903 0.000 0.840 0.000 0.040 0.120
#> GSM531686 2 0.0000 0.9243 0.000 1.000 0.000 0.000 0.000
#> GSM531687 2 0.1544 0.8821 0.000 0.932 0.000 0.000 0.068
#> GSM531688 2 0.1544 0.8821 0.000 0.932 0.000 0.000 0.068
#> GSM531690 2 0.0000 0.9243 0.000 1.000 0.000 0.000 0.000
#> GSM531693 5 0.6652 0.3924 0.000 0.348 0.000 0.232 0.420
#> GSM531695 2 0.0000 0.9243 0.000 1.000 0.000 0.000 0.000
#> GSM531603 2 0.6514 -0.0410 0.004 0.516 0.000 0.236 0.244
#> GSM531609 4 0.5460 0.4350 0.148 0.000 0.000 0.656 0.196
#> GSM531611 2 0.0000 0.9243 0.000 1.000 0.000 0.000 0.000
#> GSM531621 3 0.1608 0.6799 0.000 0.000 0.928 0.000 0.072
#> GSM531622 3 0.3816 0.7666 0.304 0.000 0.696 0.000 0.000
#> GSM531628 1 0.3527 0.6351 0.828 0.000 0.056 0.116 0.000
#> GSM531630 3 0.3876 0.7626 0.316 0.000 0.684 0.000 0.000
#> GSM531633 3 0.1608 0.6799 0.000 0.000 0.928 0.000 0.072
#> GSM531635 3 0.3876 0.7626 0.316 0.000 0.684 0.000 0.000
#> GSM531640 3 0.3816 0.7666 0.304 0.000 0.696 0.000 0.000
#> GSM531649 1 0.4192 0.4535 0.736 0.000 0.232 0.032 0.000
#> GSM531653 1 0.3689 0.6361 0.740 0.000 0.000 0.256 0.004
#> GSM531657 4 0.5803 -0.0411 0.004 0.408 0.000 0.508 0.080
#> GSM531665 4 0.0609 0.7799 0.000 0.000 0.000 0.980 0.020
#> GSM531670 4 0.0771 0.7849 0.020 0.000 0.000 0.976 0.004
#> GSM531674 4 0.0771 0.7849 0.020 0.000 0.000 0.976 0.004
#> GSM531675 2 0.0000 0.9243 0.000 1.000 0.000 0.000 0.000
#> GSM531677 2 0.0000 0.9243 0.000 1.000 0.000 0.000 0.000
#> GSM531678 2 0.0162 0.9220 0.000 0.996 0.000 0.000 0.004
#> GSM531680 2 0.0000 0.9243 0.000 1.000 0.000 0.000 0.000
#> GSM531689 2 0.0000 0.9243 0.000 1.000 0.000 0.000 0.000
#> GSM531691 2 0.1544 0.8821 0.000 0.932 0.000 0.000 0.068
#> GSM531692 5 0.3636 0.8481 0.000 0.000 0.000 0.272 0.728
#> GSM531694 2 0.0000 0.9243 0.000 1.000 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
#> GSM531602 2 0.0000 0.9207 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531604 5 0.3052 0.6699 0.000 0.000 0.000 0.004 0.780 0.216
#> GSM531606 5 0.3052 0.6699 0.000 0.000 0.000 0.004 0.780 0.216
#> GSM531607 2 0.6294 0.0704 0.008 0.508 0.000 0.016 0.248 0.220
#> GSM531608 3 0.3196 0.6039 0.156 0.000 0.816 0.020 0.008 0.000
#> GSM531610 4 0.3023 0.9093 0.000 0.004 0.000 0.808 0.008 0.180
#> GSM531612 2 0.0260 0.9179 0.008 0.992 0.000 0.000 0.000 0.000
#> GSM531613 2 0.0260 0.9179 0.008 0.992 0.000 0.000 0.000 0.000
#> GSM531614 4 0.2988 0.9559 0.024 0.000 0.000 0.824 0.000 0.152
#> GSM531616 3 0.0146 0.6521 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM531618 6 0.0508 0.8222 0.012 0.000 0.000 0.004 0.000 0.984
#> GSM531619 3 0.6592 0.4371 0.348 0.000 0.448 0.136 0.068 0.000
#> GSM531620 3 0.3448 0.1858 0.280 0.000 0.716 0.000 0.000 0.004
#> GSM531623 3 0.0260 0.6537 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM531625 3 0.6592 0.4371 0.348 0.000 0.448 0.136 0.068 0.000
#> GSM531626 3 0.3975 -0.2899 0.452 0.000 0.544 0.000 0.000 0.004
#> GSM531632 1 0.5183 0.6712 0.604 0.000 0.140 0.000 0.000 0.256
#> GSM531638 1 0.4326 0.4798 0.572 0.000 0.404 0.000 0.000 0.024
#> GSM531639 6 0.1649 0.8039 0.000 0.000 0.000 0.032 0.036 0.932
#> GSM531641 6 0.5397 0.3444 0.008 0.316 0.000 0.032 0.048 0.596
#> GSM531642 6 0.1789 0.7996 0.000 0.000 0.000 0.032 0.044 0.924
#> GSM531643 6 0.0508 0.8222 0.012 0.000 0.000 0.004 0.000 0.984
#> GSM531644 6 0.0405 0.8236 0.008 0.000 0.000 0.004 0.000 0.988
#> GSM531645 6 0.0405 0.8236 0.008 0.000 0.000 0.004 0.000 0.988
#> GSM531646 1 0.4261 0.4715 0.572 0.000 0.408 0.000 0.000 0.020
#> GSM531647 1 0.5083 0.6923 0.632 0.000 0.204 0.000 0.000 0.164
#> GSM531648 6 0.0405 0.8236 0.008 0.000 0.000 0.004 0.000 0.988
#> GSM531650 6 0.0405 0.8236 0.008 0.000 0.000 0.004 0.000 0.988
#> GSM531651 3 0.6592 0.4371 0.348 0.000 0.448 0.136 0.068 0.000
#> GSM531652 6 0.0405 0.8236 0.008 0.000 0.000 0.004 0.000 0.988
#> GSM531656 6 0.0508 0.8222 0.012 0.000 0.000 0.004 0.000 0.984
#> GSM531659 6 0.1789 0.7996 0.000 0.000 0.000 0.032 0.044 0.924
#> GSM531661 3 0.0146 0.6521 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM531662 1 0.4136 0.4869 0.560 0.000 0.000 0.012 0.000 0.428
#> GSM531663 6 0.1168 0.8159 0.000 0.000 0.000 0.028 0.016 0.956
#> GSM531664 6 0.4756 0.5060 0.000 0.232 0.000 0.032 0.048 0.688
#> GSM531666 6 0.4756 0.5060 0.000 0.232 0.000 0.032 0.048 0.688
#> GSM531667 3 0.0146 0.6521 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM531668 6 0.1418 0.8106 0.000 0.000 0.000 0.032 0.024 0.944
#> GSM531669 6 0.0405 0.8229 0.004 0.000 0.000 0.000 0.008 0.988
#> GSM531671 1 0.4116 0.5001 0.572 0.000 0.000 0.012 0.000 0.416
#> GSM531672 6 0.5965 0.0886 0.008 0.424 0.000 0.036 0.072 0.460
#> GSM531673 6 0.1168 0.8159 0.000 0.000 0.000 0.028 0.016 0.956
#> GSM531676 2 0.3312 0.7828 0.020 0.828 0.000 0.000 0.124 0.028
#> GSM531679 2 0.0000 0.9207 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531681 2 0.0000 0.9207 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531682 2 0.0000 0.9207 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531683 2 0.0000 0.9207 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531684 5 0.1956 0.6687 0.000 0.004 0.000 0.008 0.908 0.080
#> GSM531685 2 0.3312 0.7828 0.020 0.828 0.000 0.000 0.124 0.028
#> GSM531686 2 0.0000 0.9207 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531687 2 0.1807 0.8739 0.020 0.920 0.000 0.000 0.060 0.000
#> GSM531688 2 0.1807 0.8739 0.020 0.920 0.000 0.000 0.060 0.000
#> GSM531690 2 0.0000 0.9207 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531693 5 0.5647 0.3472 0.020 0.336 0.000 0.008 0.556 0.080
#> GSM531695 2 0.0000 0.9207 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531603 2 0.6294 0.0704 0.008 0.508 0.000 0.016 0.248 0.220
#> GSM531609 4 0.2988 0.9559 0.024 0.000 0.000 0.824 0.000 0.152
#> GSM531611 2 0.0260 0.9179 0.008 0.992 0.000 0.000 0.000 0.000
#> GSM531621 3 0.6592 0.4371 0.348 0.000 0.448 0.136 0.068 0.000
#> GSM531622 3 0.0260 0.6537 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM531628 1 0.4983 0.5728 0.564 0.000 0.356 0.000 0.000 0.080
#> GSM531630 3 0.0146 0.6521 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM531633 3 0.6592 0.4371 0.348 0.000 0.448 0.136 0.068 0.000
#> GSM531635 3 0.0146 0.6521 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM531640 3 0.0260 0.6537 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM531649 3 0.3975 -0.2899 0.452 0.000 0.544 0.000 0.000 0.004
#> GSM531653 1 0.5214 0.6833 0.624 0.000 0.148 0.004 0.000 0.224
#> GSM531657 6 0.5929 0.1337 0.008 0.400 0.000 0.032 0.076 0.484
#> GSM531665 6 0.1168 0.8159 0.000 0.000 0.000 0.028 0.016 0.956
#> GSM531670 6 0.0508 0.8222 0.012 0.000 0.000 0.004 0.000 0.984
#> GSM531674 6 0.0508 0.8222 0.012 0.000 0.000 0.004 0.000 0.984
#> GSM531675 2 0.0000 0.9207 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531677 2 0.0000 0.9207 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531678 2 0.0146 0.9190 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM531680 2 0.0000 0.9207 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531689 2 0.0000 0.9207 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531691 2 0.1807 0.8739 0.020 0.920 0.000 0.000 0.060 0.000
#> GSM531692 5 0.2070 0.6598 0.000 0.000 0.000 0.012 0.896 0.092
#> GSM531694 2 0.0000 0.9207 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> ATC:hclust 75 0.486 2
#> ATC:hclust 69 0.213 3
#> ATC:hclust 72 0.301 4
#> ATC:hclust 64 0.556 5
#> ATC:hclust 63 0.586 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "kmeans"]
# you can also extract it by
# res = res_list["ATC:kmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 80 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 0.711 0.862 0.935 0.4804 0.497 0.497
#> 3 3 1.000 0.964 0.981 0.3677 0.661 0.424
#> 4 4 0.750 0.704 0.827 0.1107 0.936 0.815
#> 5 5 0.715 0.674 0.786 0.0520 0.972 0.903
#> 6 6 0.720 0.638 0.798 0.0442 0.927 0.731
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
#> GSM531602 2 0.000 0.976 0.000 1.000
#> GSM531604 2 0.000 0.976 0.000 1.000
#> GSM531606 2 0.000 0.976 0.000 1.000
#> GSM531607 2 0.000 0.976 0.000 1.000
#> GSM531608 1 0.000 0.865 1.000 0.000
#> GSM531610 2 0.000 0.976 0.000 1.000
#> GSM531612 2 0.000 0.976 0.000 1.000
#> GSM531613 2 0.000 0.976 0.000 1.000
#> GSM531614 1 0.000 0.865 1.000 0.000
#> GSM531616 1 0.000 0.865 1.000 0.000
#> GSM531618 1 0.943 0.592 0.640 0.360
#> GSM531619 1 0.000 0.865 1.000 0.000
#> GSM531620 1 0.000 0.865 1.000 0.000
#> GSM531623 1 0.000 0.865 1.000 0.000
#> GSM531625 1 0.000 0.865 1.000 0.000
#> GSM531626 1 0.000 0.865 1.000 0.000
#> GSM531632 1 0.000 0.865 1.000 0.000
#> GSM531638 1 0.000 0.865 1.000 0.000
#> GSM531639 2 0.730 0.677 0.204 0.796
#> GSM531641 2 0.000 0.976 0.000 1.000
#> GSM531642 2 0.000 0.976 0.000 1.000
#> GSM531643 1 0.943 0.592 0.640 0.360
#> GSM531644 1 0.943 0.592 0.640 0.360
#> GSM531645 1 0.952 0.568 0.628 0.372
#> GSM531646 1 0.000 0.865 1.000 0.000
#> GSM531647 1 0.000 0.865 1.000 0.000
#> GSM531648 1 0.943 0.592 0.640 0.360
#> GSM531650 1 0.943 0.592 0.640 0.360
#> GSM531651 1 0.000 0.865 1.000 0.000
#> GSM531652 1 0.943 0.592 0.640 0.360
#> GSM531656 1 0.943 0.592 0.640 0.360
#> GSM531659 2 0.000 0.976 0.000 1.000
#> GSM531661 1 0.000 0.865 1.000 0.000
#> GSM531662 1 0.943 0.592 0.640 0.360
#> GSM531663 2 0.584 0.792 0.140 0.860
#> GSM531664 2 0.000 0.976 0.000 1.000
#> GSM531666 2 0.000 0.976 0.000 1.000
#> GSM531667 1 0.000 0.865 1.000 0.000
#> GSM531668 2 0.000 0.976 0.000 1.000
#> GSM531669 2 0.000 0.976 0.000 1.000
#> GSM531671 1 0.000 0.865 1.000 0.000
#> GSM531672 2 0.000 0.976 0.000 1.000
#> GSM531673 2 0.000 0.976 0.000 1.000
#> GSM531676 2 0.000 0.976 0.000 1.000
#> GSM531679 2 0.000 0.976 0.000 1.000
#> GSM531681 2 0.000 0.976 0.000 1.000
#> GSM531682 2 0.000 0.976 0.000 1.000
#> GSM531683 2 0.000 0.976 0.000 1.000
#> GSM531684 2 0.000 0.976 0.000 1.000
#> GSM531685 2 0.000 0.976 0.000 1.000
#> GSM531686 2 0.000 0.976 0.000 1.000
#> GSM531687 2 0.000 0.976 0.000 1.000
#> GSM531688 2 0.000 0.976 0.000 1.000
#> GSM531690 2 0.000 0.976 0.000 1.000
#> GSM531693 2 0.000 0.976 0.000 1.000
#> GSM531695 2 0.000 0.976 0.000 1.000
#> GSM531603 2 0.000 0.976 0.000 1.000
#> GSM531609 2 1.000 -0.237 0.492 0.508
#> GSM531611 2 0.000 0.976 0.000 1.000
#> GSM531621 1 0.000 0.865 1.000 0.000
#> GSM531622 1 0.000 0.865 1.000 0.000
#> GSM531628 1 0.000 0.865 1.000 0.000
#> GSM531630 1 0.000 0.865 1.000 0.000
#> GSM531633 1 0.000 0.865 1.000 0.000
#> GSM531635 1 0.000 0.865 1.000 0.000
#> GSM531640 1 0.000 0.865 1.000 0.000
#> GSM531649 1 0.000 0.865 1.000 0.000
#> GSM531653 1 0.118 0.858 0.984 0.016
#> GSM531657 2 0.000 0.976 0.000 1.000
#> GSM531665 1 0.943 0.592 0.640 0.360
#> GSM531670 1 0.943 0.592 0.640 0.360
#> GSM531674 1 0.943 0.592 0.640 0.360
#> GSM531675 2 0.000 0.976 0.000 1.000
#> GSM531677 2 0.000 0.976 0.000 1.000
#> GSM531678 2 0.000 0.976 0.000 1.000
#> GSM531680 2 0.000 0.976 0.000 1.000
#> GSM531689 2 0.000 0.976 0.000 1.000
#> GSM531691 2 0.000 0.976 0.000 1.000
#> GSM531692 2 0.000 0.976 0.000 1.000
#> GSM531694 2 0.000 0.976 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM531602 2 0.0000 0.978 0.000 1.000 0.000
#> GSM531604 1 0.0892 0.976 0.980 0.020 0.000
#> GSM531606 2 0.6180 0.265 0.416 0.584 0.000
#> GSM531607 2 0.0000 0.978 0.000 1.000 0.000
#> GSM531608 3 0.0892 0.981 0.020 0.000 0.980
#> GSM531610 1 0.0237 0.974 0.996 0.004 0.000
#> GSM531612 2 0.0000 0.978 0.000 1.000 0.000
#> GSM531613 2 0.0000 0.978 0.000 1.000 0.000
#> GSM531614 1 0.0000 0.972 1.000 0.000 0.000
#> GSM531616 3 0.0000 0.997 0.000 0.000 1.000
#> GSM531618 1 0.0983 0.978 0.980 0.004 0.016
#> GSM531619 3 0.0000 0.997 0.000 0.000 1.000
#> GSM531620 3 0.0000 0.997 0.000 0.000 1.000
#> GSM531623 3 0.0000 0.997 0.000 0.000 1.000
#> GSM531625 3 0.0000 0.997 0.000 0.000 1.000
#> GSM531626 3 0.0000 0.997 0.000 0.000 1.000
#> GSM531632 1 0.1753 0.952 0.952 0.000 0.048
#> GSM531638 3 0.1529 0.955 0.040 0.000 0.960
#> GSM531639 1 0.0983 0.978 0.980 0.004 0.016
#> GSM531641 1 0.0892 0.976 0.980 0.020 0.000
#> GSM531642 1 0.0892 0.976 0.980 0.020 0.000
#> GSM531643 1 0.0983 0.978 0.980 0.004 0.016
#> GSM531644 1 0.0983 0.978 0.980 0.004 0.016
#> GSM531645 1 0.0983 0.978 0.980 0.004 0.016
#> GSM531646 3 0.0000 0.997 0.000 0.000 1.000
#> GSM531647 1 0.1289 0.966 0.968 0.000 0.032
#> GSM531648 1 0.0983 0.978 0.980 0.004 0.016
#> GSM531650 1 0.0983 0.978 0.980 0.004 0.016
#> GSM531651 3 0.0000 0.997 0.000 0.000 1.000
#> GSM531652 1 0.0983 0.978 0.980 0.004 0.016
#> GSM531656 1 0.0983 0.978 0.980 0.004 0.016
#> GSM531659 1 0.0892 0.976 0.980 0.020 0.000
#> GSM531661 3 0.0000 0.997 0.000 0.000 1.000
#> GSM531662 1 0.0983 0.978 0.980 0.004 0.016
#> GSM531663 1 0.0892 0.976 0.980 0.020 0.000
#> GSM531664 1 0.0892 0.976 0.980 0.020 0.000
#> GSM531666 1 0.0892 0.976 0.980 0.020 0.000
#> GSM531667 3 0.0000 0.997 0.000 0.000 1.000
#> GSM531668 1 0.0892 0.976 0.980 0.020 0.000
#> GSM531669 1 0.0892 0.976 0.980 0.020 0.000
#> GSM531671 1 0.0892 0.975 0.980 0.000 0.020
#> GSM531672 1 0.0892 0.976 0.980 0.020 0.000
#> GSM531673 1 0.0892 0.976 0.980 0.020 0.000
#> GSM531676 2 0.0000 0.978 0.000 1.000 0.000
#> GSM531679 2 0.0000 0.978 0.000 1.000 0.000
#> GSM531681 2 0.0000 0.978 0.000 1.000 0.000
#> GSM531682 2 0.0000 0.978 0.000 1.000 0.000
#> GSM531683 2 0.0000 0.978 0.000 1.000 0.000
#> GSM531684 2 0.1964 0.919 0.056 0.944 0.000
#> GSM531685 2 0.0000 0.978 0.000 1.000 0.000
#> GSM531686 2 0.0000 0.978 0.000 1.000 0.000
#> GSM531687 2 0.0000 0.978 0.000 1.000 0.000
#> GSM531688 2 0.0000 0.978 0.000 1.000 0.000
#> GSM531690 2 0.0000 0.978 0.000 1.000 0.000
#> GSM531693 1 0.5988 0.425 0.632 0.368 0.000
#> GSM531695 2 0.0000 0.978 0.000 1.000 0.000
#> GSM531603 2 0.0000 0.978 0.000 1.000 0.000
#> GSM531609 1 0.0000 0.972 1.000 0.000 0.000
#> GSM531611 2 0.0000 0.978 0.000 1.000 0.000
#> GSM531621 3 0.0000 0.997 0.000 0.000 1.000
#> GSM531622 3 0.0000 0.997 0.000 0.000 1.000
#> GSM531628 3 0.0000 0.997 0.000 0.000 1.000
#> GSM531630 3 0.0000 0.997 0.000 0.000 1.000
#> GSM531633 3 0.0000 0.997 0.000 0.000 1.000
#> GSM531635 3 0.0000 0.997 0.000 0.000 1.000
#> GSM531640 3 0.0000 0.997 0.000 0.000 1.000
#> GSM531649 3 0.0000 0.997 0.000 0.000 1.000
#> GSM531653 1 0.0892 0.975 0.980 0.000 0.020
#> GSM531657 1 0.0892 0.976 0.980 0.020 0.000
#> GSM531665 1 0.0983 0.978 0.980 0.004 0.016
#> GSM531670 1 0.0983 0.978 0.980 0.004 0.016
#> GSM531674 1 0.0983 0.978 0.980 0.004 0.016
#> GSM531675 2 0.0000 0.978 0.000 1.000 0.000
#> GSM531677 2 0.0000 0.978 0.000 1.000 0.000
#> GSM531678 2 0.0000 0.978 0.000 1.000 0.000
#> GSM531680 2 0.0000 0.978 0.000 1.000 0.000
#> GSM531689 2 0.0000 0.978 0.000 1.000 0.000
#> GSM531691 2 0.0000 0.978 0.000 1.000 0.000
#> GSM531692 1 0.0892 0.976 0.980 0.020 0.000
#> GSM531694 2 0.0000 0.978 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM531602 2 0.0188 0.958 0.000 0.996 0.000 0.004
#> GSM531604 4 0.4632 0.616 0.308 0.004 0.000 0.688
#> GSM531606 4 0.6019 0.673 0.176 0.136 0.000 0.688
#> GSM531607 2 0.5383 0.121 0.012 0.536 0.000 0.452
#> GSM531608 3 0.0592 0.876 0.000 0.000 0.984 0.016
#> GSM531610 4 0.4907 0.162 0.420 0.000 0.000 0.580
#> GSM531612 2 0.0817 0.944 0.000 0.976 0.000 0.024
#> GSM531613 2 0.0707 0.946 0.000 0.980 0.000 0.020
#> GSM531614 1 0.3311 0.580 0.828 0.000 0.000 0.172
#> GSM531616 3 0.0000 0.875 0.000 0.000 1.000 0.000
#> GSM531618 1 0.0000 0.691 1.000 0.000 0.000 0.000
#> GSM531619 3 0.2216 0.858 0.000 0.000 0.908 0.092
#> GSM531620 3 0.2408 0.843 0.000 0.000 0.896 0.104
#> GSM531623 3 0.0592 0.876 0.000 0.000 0.984 0.016
#> GSM531625 3 0.2216 0.858 0.000 0.000 0.908 0.092
#> GSM531626 3 0.2408 0.843 0.000 0.000 0.896 0.104
#> GSM531632 1 0.5314 0.459 0.748 0.000 0.144 0.108
#> GSM531638 3 0.6820 0.446 0.364 0.000 0.528 0.108
#> GSM531639 1 0.1474 0.672 0.948 0.000 0.000 0.052
#> GSM531641 1 0.4790 0.329 0.620 0.000 0.000 0.380
#> GSM531642 1 0.4697 0.370 0.644 0.000 0.000 0.356
#> GSM531643 1 0.0000 0.691 1.000 0.000 0.000 0.000
#> GSM531644 1 0.0000 0.691 1.000 0.000 0.000 0.000
#> GSM531645 1 0.0000 0.691 1.000 0.000 0.000 0.000
#> GSM531646 3 0.6785 0.467 0.352 0.000 0.540 0.108
#> GSM531647 1 0.4605 0.519 0.800 0.000 0.092 0.108
#> GSM531648 1 0.0000 0.691 1.000 0.000 0.000 0.000
#> GSM531650 1 0.0000 0.691 1.000 0.000 0.000 0.000
#> GSM531651 3 0.2216 0.858 0.000 0.000 0.908 0.092
#> GSM531652 1 0.0000 0.691 1.000 0.000 0.000 0.000
#> GSM531656 1 0.0000 0.691 1.000 0.000 0.000 0.000
#> GSM531659 1 0.4877 0.274 0.592 0.000 0.000 0.408
#> GSM531661 3 0.0592 0.876 0.000 0.000 0.984 0.016
#> GSM531662 1 0.1022 0.682 0.968 0.000 0.000 0.032
#> GSM531663 1 0.4477 0.442 0.688 0.000 0.000 0.312
#> GSM531664 1 0.4697 0.368 0.644 0.000 0.000 0.356
#> GSM531666 1 0.4776 0.336 0.624 0.000 0.000 0.376
#> GSM531667 3 0.1716 0.859 0.000 0.000 0.936 0.064
#> GSM531668 1 0.4843 0.302 0.604 0.000 0.000 0.396
#> GSM531669 1 0.4679 0.375 0.648 0.000 0.000 0.352
#> GSM531671 1 0.4879 0.512 0.780 0.000 0.092 0.128
#> GSM531672 1 0.4916 0.230 0.576 0.000 0.000 0.424
#> GSM531673 1 0.4843 0.302 0.604 0.000 0.000 0.396
#> GSM531676 2 0.3074 0.819 0.000 0.848 0.000 0.152
#> GSM531679 2 0.0188 0.958 0.000 0.996 0.000 0.004
#> GSM531681 2 0.0188 0.958 0.000 0.996 0.000 0.004
#> GSM531682 2 0.0000 0.958 0.000 1.000 0.000 0.000
#> GSM531683 2 0.0188 0.958 0.000 0.996 0.000 0.004
#> GSM531684 4 0.5579 0.620 0.060 0.252 0.000 0.688
#> GSM531685 2 0.3024 0.820 0.000 0.852 0.000 0.148
#> GSM531686 2 0.0000 0.958 0.000 1.000 0.000 0.000
#> GSM531687 2 0.0000 0.958 0.000 1.000 0.000 0.000
#> GSM531688 2 0.0000 0.958 0.000 1.000 0.000 0.000
#> GSM531690 2 0.0188 0.958 0.000 0.996 0.000 0.004
#> GSM531693 4 0.5339 0.655 0.272 0.040 0.000 0.688
#> GSM531695 2 0.0000 0.958 0.000 1.000 0.000 0.000
#> GSM531603 4 0.5231 0.537 0.028 0.296 0.000 0.676
#> GSM531609 1 0.4356 0.480 0.708 0.000 0.000 0.292
#> GSM531611 2 0.0817 0.944 0.000 0.976 0.000 0.024
#> GSM531621 3 0.2216 0.858 0.000 0.000 0.908 0.092
#> GSM531622 3 0.0592 0.876 0.000 0.000 0.984 0.016
#> GSM531628 3 0.6867 0.409 0.384 0.000 0.508 0.108
#> GSM531630 3 0.0336 0.875 0.000 0.000 0.992 0.008
#> GSM531633 3 0.2216 0.858 0.000 0.000 0.908 0.092
#> GSM531635 3 0.0336 0.875 0.000 0.000 0.992 0.008
#> GSM531640 3 0.1940 0.863 0.000 0.000 0.924 0.076
#> GSM531649 3 0.2408 0.843 0.000 0.000 0.896 0.104
#> GSM531653 1 0.2469 0.612 0.892 0.000 0.000 0.108
#> GSM531657 1 0.4888 0.265 0.588 0.000 0.000 0.412
#> GSM531665 1 0.3688 0.568 0.792 0.000 0.000 0.208
#> GSM531670 1 0.0188 0.689 0.996 0.000 0.000 0.004
#> GSM531674 1 0.0000 0.691 1.000 0.000 0.000 0.000
#> GSM531675 2 0.0188 0.958 0.000 0.996 0.000 0.004
#> GSM531677 2 0.0000 0.958 0.000 1.000 0.000 0.000
#> GSM531678 2 0.0188 0.958 0.000 0.996 0.000 0.004
#> GSM531680 2 0.0000 0.958 0.000 1.000 0.000 0.000
#> GSM531689 2 0.0188 0.958 0.000 0.996 0.000 0.004
#> GSM531691 2 0.0000 0.958 0.000 1.000 0.000 0.000
#> GSM531692 4 0.4477 0.608 0.312 0.000 0.000 0.688
#> GSM531694 2 0.0188 0.958 0.000 0.996 0.000 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM531602 2 0.0609 0.931 0.000 0.980 0.000 0.020 0.000
#> GSM531604 5 0.2389 0.785 0.116 0.000 0.000 0.004 0.880
#> GSM531606 5 0.2726 0.816 0.052 0.064 0.000 0.000 0.884
#> GSM531607 5 0.5448 0.460 0.000 0.340 0.000 0.076 0.584
#> GSM531608 3 0.3995 0.780 0.000 0.000 0.776 0.180 0.044
#> GSM531610 4 0.6802 -0.430 0.328 0.000 0.000 0.372 0.300
#> GSM531612 2 0.2971 0.862 0.000 0.836 0.000 0.156 0.008
#> GSM531613 2 0.2136 0.910 0.000 0.904 0.000 0.088 0.008
#> GSM531614 1 0.5834 0.306 0.584 0.000 0.000 0.284 0.132
#> GSM531616 3 0.3274 0.787 0.000 0.000 0.780 0.220 0.000
#> GSM531618 1 0.0000 0.645 1.000 0.000 0.000 0.000 0.000
#> GSM531619 3 0.1082 0.751 0.000 0.000 0.964 0.008 0.028
#> GSM531620 3 0.4171 0.613 0.000 0.000 0.604 0.396 0.000
#> GSM531623 3 0.2471 0.801 0.000 0.000 0.864 0.136 0.000
#> GSM531625 3 0.1082 0.751 0.000 0.000 0.964 0.008 0.028
#> GSM531626 3 0.4171 0.613 0.000 0.000 0.604 0.396 0.000
#> GSM531632 1 0.4708 -0.285 0.548 0.000 0.016 0.436 0.000
#> GSM531638 4 0.6660 0.496 0.324 0.000 0.244 0.432 0.000
#> GSM531639 1 0.3309 0.657 0.836 0.000 0.000 0.128 0.036
#> GSM531641 1 0.5618 0.604 0.628 0.000 0.000 0.236 0.136
#> GSM531642 1 0.5504 0.612 0.644 0.000 0.000 0.224 0.132
#> GSM531643 1 0.0290 0.641 0.992 0.000 0.000 0.008 0.000
#> GSM531644 1 0.0000 0.645 1.000 0.000 0.000 0.000 0.000
#> GSM531645 1 0.2648 0.657 0.848 0.000 0.000 0.152 0.000
#> GSM531646 4 0.6687 0.454 0.304 0.000 0.264 0.432 0.000
#> GSM531647 1 0.4242 -0.225 0.572 0.000 0.000 0.428 0.000
#> GSM531648 1 0.0000 0.645 1.000 0.000 0.000 0.000 0.000
#> GSM531650 1 0.0290 0.641 0.992 0.000 0.000 0.008 0.000
#> GSM531651 3 0.1082 0.751 0.000 0.000 0.964 0.008 0.028
#> GSM531652 1 0.0000 0.645 1.000 0.000 0.000 0.000 0.000
#> GSM531656 1 0.0000 0.645 1.000 0.000 0.000 0.000 0.000
#> GSM531659 1 0.6177 0.554 0.556 0.000 0.000 0.212 0.232
#> GSM531661 3 0.3039 0.796 0.000 0.000 0.808 0.192 0.000
#> GSM531662 1 0.3019 0.592 0.864 0.000 0.000 0.048 0.088
#> GSM531663 1 0.5446 0.625 0.660 0.000 0.000 0.164 0.176
#> GSM531664 1 0.5253 0.627 0.676 0.000 0.000 0.200 0.124
#> GSM531666 1 0.5618 0.604 0.628 0.000 0.000 0.236 0.136
#> GSM531667 3 0.3932 0.700 0.000 0.000 0.672 0.328 0.000
#> GSM531668 1 0.5773 0.606 0.616 0.000 0.000 0.168 0.216
#> GSM531669 1 0.4844 0.641 0.720 0.000 0.000 0.172 0.108
#> GSM531671 1 0.5071 -0.243 0.540 0.000 0.000 0.424 0.036
#> GSM531672 1 0.6255 0.537 0.540 0.000 0.000 0.252 0.208
#> GSM531673 1 0.5805 0.604 0.612 0.000 0.000 0.172 0.216
#> GSM531676 2 0.4487 0.767 0.000 0.756 0.000 0.104 0.140
#> GSM531679 2 0.0290 0.932 0.000 0.992 0.000 0.008 0.000
#> GSM531681 2 0.0404 0.932 0.000 0.988 0.000 0.012 0.000
#> GSM531682 2 0.1197 0.928 0.000 0.952 0.000 0.048 0.000
#> GSM531683 2 0.0404 0.932 0.000 0.988 0.000 0.012 0.000
#> GSM531684 5 0.2678 0.802 0.016 0.100 0.000 0.004 0.880
#> GSM531685 2 0.4493 0.766 0.000 0.756 0.000 0.108 0.136
#> GSM531686 2 0.0404 0.932 0.000 0.988 0.000 0.012 0.000
#> GSM531687 2 0.2389 0.905 0.000 0.880 0.000 0.116 0.004
#> GSM531688 2 0.2439 0.906 0.000 0.876 0.000 0.120 0.004
#> GSM531690 2 0.0404 0.932 0.000 0.988 0.000 0.012 0.000
#> GSM531693 5 0.4118 0.787 0.112 0.004 0.000 0.088 0.796
#> GSM531695 2 0.1478 0.924 0.000 0.936 0.000 0.064 0.000
#> GSM531603 5 0.4950 0.754 0.008 0.140 0.000 0.120 0.732
#> GSM531609 1 0.6445 0.386 0.456 0.000 0.000 0.360 0.184
#> GSM531611 2 0.2971 0.862 0.000 0.836 0.000 0.156 0.008
#> GSM531621 3 0.1082 0.751 0.000 0.000 0.964 0.008 0.028
#> GSM531622 3 0.2516 0.801 0.000 0.000 0.860 0.140 0.000
#> GSM531628 4 0.6626 0.501 0.340 0.000 0.228 0.432 0.000
#> GSM531630 3 0.3424 0.778 0.000 0.000 0.760 0.240 0.000
#> GSM531633 3 0.1082 0.751 0.000 0.000 0.964 0.008 0.028
#> GSM531635 3 0.3424 0.778 0.000 0.000 0.760 0.240 0.000
#> GSM531640 3 0.1197 0.781 0.000 0.000 0.952 0.048 0.000
#> GSM531649 3 0.4210 0.593 0.000 0.000 0.588 0.412 0.000
#> GSM531653 1 0.3109 0.385 0.800 0.000 0.000 0.200 0.000
#> GSM531657 1 0.6150 0.561 0.560 0.000 0.000 0.236 0.204
#> GSM531665 1 0.3667 0.633 0.812 0.000 0.000 0.048 0.140
#> GSM531670 1 0.0290 0.641 0.992 0.000 0.000 0.008 0.000
#> GSM531674 1 0.0290 0.641 0.992 0.000 0.000 0.008 0.000
#> GSM531675 2 0.0290 0.932 0.000 0.992 0.000 0.008 0.000
#> GSM531677 2 0.0290 0.932 0.000 0.992 0.000 0.008 0.000
#> GSM531678 2 0.1357 0.922 0.000 0.948 0.000 0.048 0.004
#> GSM531680 2 0.1341 0.926 0.000 0.944 0.000 0.056 0.000
#> GSM531689 2 0.1502 0.919 0.000 0.940 0.000 0.056 0.004
#> GSM531691 2 0.1704 0.922 0.000 0.928 0.000 0.068 0.004
#> GSM531692 5 0.2513 0.784 0.116 0.000 0.000 0.008 0.876
#> GSM531694 2 0.0404 0.932 0.000 0.988 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
#> GSM531602 2 0.0603 0.856 0.004 0.980 0.000 0.016 0.000 0.000
#> GSM531604 5 0.1624 0.804 0.008 0.000 0.000 0.012 0.936 0.044
#> GSM531606 5 0.1237 0.826 0.000 0.020 0.000 0.004 0.956 0.020
#> GSM531607 5 0.5572 0.588 0.016 0.228 0.000 0.116 0.628 0.012
#> GSM531608 3 0.5051 0.610 0.220 0.000 0.652 0.120 0.008 0.000
#> GSM531610 4 0.6093 0.572 0.036 0.000 0.000 0.524 0.136 0.304
#> GSM531612 2 0.3965 0.678 0.000 0.604 0.000 0.388 0.000 0.008
#> GSM531613 2 0.3266 0.775 0.000 0.728 0.000 0.272 0.000 0.000
#> GSM531614 4 0.6636 0.492 0.320 0.000 0.000 0.372 0.028 0.280
#> GSM531616 3 0.3482 0.617 0.316 0.000 0.684 0.000 0.000 0.000
#> GSM531618 6 0.2527 0.654 0.168 0.000 0.000 0.000 0.000 0.832
#> GSM531619 3 0.2331 0.687 0.000 0.000 0.888 0.080 0.032 0.000
#> GSM531620 1 0.3695 0.181 0.624 0.000 0.376 0.000 0.000 0.000
#> GSM531623 3 0.2697 0.706 0.188 0.000 0.812 0.000 0.000 0.000
#> GSM531625 3 0.2331 0.687 0.000 0.000 0.888 0.080 0.032 0.000
#> GSM531626 1 0.3684 0.189 0.628 0.000 0.372 0.000 0.000 0.000
#> GSM531632 1 0.1958 0.642 0.896 0.000 0.004 0.000 0.000 0.100
#> GSM531638 1 0.2088 0.667 0.904 0.000 0.068 0.000 0.000 0.028
#> GSM531639 6 0.1674 0.653 0.068 0.000 0.000 0.004 0.004 0.924
#> GSM531641 6 0.3094 0.538 0.000 0.000 0.000 0.140 0.036 0.824
#> GSM531642 6 0.2384 0.589 0.000 0.000 0.000 0.084 0.032 0.884
#> GSM531643 6 0.2527 0.654 0.168 0.000 0.000 0.000 0.000 0.832
#> GSM531644 6 0.2527 0.654 0.168 0.000 0.000 0.000 0.000 0.832
#> GSM531645 6 0.0547 0.647 0.020 0.000 0.000 0.000 0.000 0.980
#> GSM531646 1 0.2039 0.660 0.904 0.000 0.076 0.000 0.000 0.020
#> GSM531647 1 0.2260 0.608 0.860 0.000 0.000 0.000 0.000 0.140
#> GSM531648 6 0.2527 0.654 0.168 0.000 0.000 0.000 0.000 0.832
#> GSM531650 6 0.2527 0.654 0.168 0.000 0.000 0.000 0.000 0.832
#> GSM531651 3 0.2331 0.687 0.000 0.000 0.888 0.080 0.032 0.000
#> GSM531652 6 0.2527 0.654 0.168 0.000 0.000 0.000 0.000 0.832
#> GSM531656 6 0.2527 0.654 0.168 0.000 0.000 0.000 0.000 0.832
#> GSM531659 6 0.4635 0.431 0.008 0.000 0.000 0.148 0.132 0.712
#> GSM531661 3 0.3360 0.663 0.264 0.000 0.732 0.004 0.000 0.000
#> GSM531662 6 0.6274 0.291 0.272 0.000 0.000 0.096 0.088 0.544
#> GSM531663 6 0.4750 0.440 0.028 0.000 0.000 0.132 0.116 0.724
#> GSM531664 6 0.2462 0.589 0.000 0.000 0.000 0.096 0.028 0.876
#> GSM531666 6 0.3054 0.543 0.000 0.000 0.000 0.136 0.036 0.828
#> GSM531667 3 0.3997 0.206 0.488 0.000 0.508 0.004 0.000 0.000
#> GSM531668 6 0.4464 0.456 0.012 0.000 0.000 0.136 0.116 0.736
#> GSM531669 6 0.2015 0.630 0.016 0.000 0.000 0.056 0.012 0.916
#> GSM531671 1 0.3344 0.569 0.828 0.000 0.000 0.032 0.020 0.120
#> GSM531672 6 0.4687 0.303 0.004 0.000 0.000 0.240 0.084 0.672
#> GSM531673 6 0.4785 0.413 0.020 0.000 0.000 0.148 0.120 0.712
#> GSM531676 2 0.5671 0.604 0.024 0.604 0.000 0.212 0.160 0.000
#> GSM531679 2 0.0146 0.858 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM531681 2 0.0000 0.858 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531682 2 0.2278 0.845 0.004 0.868 0.000 0.128 0.000 0.000
#> GSM531683 2 0.0000 0.858 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531684 5 0.1307 0.827 0.000 0.032 0.000 0.008 0.952 0.008
#> GSM531685 2 0.5811 0.600 0.024 0.576 0.000 0.244 0.156 0.000
#> GSM531686 2 0.0937 0.857 0.000 0.960 0.000 0.040 0.000 0.000
#> GSM531687 2 0.4299 0.766 0.024 0.696 0.000 0.260 0.020 0.000
#> GSM531688 2 0.4383 0.763 0.024 0.680 0.000 0.276 0.020 0.000
#> GSM531690 2 0.0146 0.858 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM531693 5 0.3908 0.786 0.024 0.004 0.000 0.140 0.792 0.040
#> GSM531695 2 0.2994 0.817 0.004 0.788 0.000 0.208 0.000 0.000
#> GSM531603 5 0.4562 0.755 0.016 0.064 0.000 0.148 0.752 0.020
#> GSM531609 4 0.5556 0.542 0.060 0.000 0.000 0.468 0.032 0.440
#> GSM531611 2 0.3965 0.678 0.000 0.604 0.000 0.388 0.000 0.008
#> GSM531621 3 0.2331 0.687 0.000 0.000 0.888 0.080 0.032 0.000
#> GSM531622 3 0.2697 0.706 0.188 0.000 0.812 0.000 0.000 0.000
#> GSM531628 1 0.2129 0.672 0.904 0.000 0.056 0.000 0.000 0.040
#> GSM531630 3 0.3578 0.588 0.340 0.000 0.660 0.000 0.000 0.000
#> GSM531633 3 0.2331 0.687 0.000 0.000 0.888 0.080 0.032 0.000
#> GSM531635 3 0.3578 0.588 0.340 0.000 0.660 0.000 0.000 0.000
#> GSM531640 3 0.1444 0.713 0.072 0.000 0.928 0.000 0.000 0.000
#> GSM531649 1 0.3592 0.240 0.656 0.000 0.344 0.000 0.000 0.000
#> GSM531653 1 0.3862 -0.129 0.524 0.000 0.000 0.000 0.000 0.476
#> GSM531657 6 0.4314 0.425 0.000 0.000 0.000 0.184 0.096 0.720
#> GSM531665 6 0.5849 0.460 0.132 0.000 0.000 0.116 0.112 0.640
#> GSM531670 6 0.2668 0.653 0.168 0.000 0.000 0.004 0.000 0.828
#> GSM531674 6 0.2632 0.653 0.164 0.000 0.000 0.004 0.000 0.832
#> GSM531675 2 0.0146 0.858 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM531677 2 0.0713 0.857 0.000 0.972 0.000 0.028 0.000 0.000
#> GSM531678 2 0.1398 0.846 0.000 0.940 0.000 0.052 0.008 0.000
#> GSM531680 2 0.2340 0.840 0.000 0.852 0.000 0.148 0.000 0.000
#> GSM531689 2 0.1398 0.845 0.000 0.940 0.000 0.052 0.008 0.000
#> GSM531691 2 0.2957 0.836 0.016 0.836 0.000 0.140 0.008 0.000
#> GSM531692 5 0.1806 0.804 0.008 0.000 0.000 0.020 0.928 0.044
#> GSM531694 2 0.0000 0.858 0.000 1.000 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)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> ATC:kmeans 79 0.718 2
#> ATC:kmeans 78 0.281 3
#> ATC:kmeans 62 0.734 4
#> ATC:kmeans 70 0.230 5
#> ATC:kmeans 66 0.388 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "skmeans"]
# you can also extract it by
# res = res_list["ATC:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 80 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 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.970 0.988 0.5064 0.494 0.494
#> 3 3 0.930 0.941 0.976 0.2648 0.822 0.652
#> 4 4 0.856 0.843 0.932 0.1175 0.922 0.784
#> 5 5 0.839 0.776 0.894 0.0338 0.979 0.928
#> 6 6 0.862 0.794 0.882 0.0317 0.941 0.787
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
#> GSM531602 2 0.000 0.990 0.000 1.000
#> GSM531604 2 0.000 0.990 0.000 1.000
#> GSM531606 2 0.000 0.990 0.000 1.000
#> GSM531607 2 0.000 0.990 0.000 1.000
#> GSM531608 1 0.000 0.986 1.000 0.000
#> GSM531610 2 0.000 0.990 0.000 1.000
#> GSM531612 2 0.000 0.990 0.000 1.000
#> GSM531613 2 0.000 0.990 0.000 1.000
#> GSM531614 1 0.000 0.986 1.000 0.000
#> GSM531616 1 0.000 0.986 1.000 0.000
#> GSM531618 1 0.000 0.986 1.000 0.000
#> GSM531619 1 0.000 0.986 1.000 0.000
#> GSM531620 1 0.000 0.986 1.000 0.000
#> GSM531623 1 0.000 0.986 1.000 0.000
#> GSM531625 1 0.000 0.986 1.000 0.000
#> GSM531626 1 0.000 0.986 1.000 0.000
#> GSM531632 1 0.000 0.986 1.000 0.000
#> GSM531638 1 0.000 0.986 1.000 0.000
#> GSM531639 1 0.969 0.344 0.604 0.396
#> GSM531641 2 0.000 0.990 0.000 1.000
#> GSM531642 2 0.000 0.990 0.000 1.000
#> GSM531643 1 0.000 0.986 1.000 0.000
#> GSM531644 1 0.000 0.986 1.000 0.000
#> GSM531645 1 0.000 0.986 1.000 0.000
#> GSM531646 1 0.000 0.986 1.000 0.000
#> GSM531647 1 0.000 0.986 1.000 0.000
#> GSM531648 1 0.000 0.986 1.000 0.000
#> GSM531650 1 0.000 0.986 1.000 0.000
#> GSM531651 1 0.000 0.986 1.000 0.000
#> GSM531652 1 0.000 0.986 1.000 0.000
#> GSM531656 1 0.000 0.986 1.000 0.000
#> GSM531659 2 0.000 0.990 0.000 1.000
#> GSM531661 1 0.000 0.986 1.000 0.000
#> GSM531662 1 0.000 0.986 1.000 0.000
#> GSM531663 2 0.971 0.324 0.400 0.600
#> GSM531664 2 0.000 0.990 0.000 1.000
#> GSM531666 2 0.000 0.990 0.000 1.000
#> GSM531667 1 0.000 0.986 1.000 0.000
#> GSM531668 2 0.000 0.990 0.000 1.000
#> GSM531669 2 0.000 0.990 0.000 1.000
#> GSM531671 1 0.000 0.986 1.000 0.000
#> GSM531672 2 0.000 0.990 0.000 1.000
#> GSM531673 2 0.000 0.990 0.000 1.000
#> GSM531676 2 0.000 0.990 0.000 1.000
#> GSM531679 2 0.000 0.990 0.000 1.000
#> GSM531681 2 0.000 0.990 0.000 1.000
#> GSM531682 2 0.000 0.990 0.000 1.000
#> GSM531683 2 0.000 0.990 0.000 1.000
#> GSM531684 2 0.000 0.990 0.000 1.000
#> GSM531685 2 0.000 0.990 0.000 1.000
#> GSM531686 2 0.000 0.990 0.000 1.000
#> GSM531687 2 0.000 0.990 0.000 1.000
#> GSM531688 2 0.000 0.990 0.000 1.000
#> GSM531690 2 0.000 0.990 0.000 1.000
#> GSM531693 2 0.000 0.990 0.000 1.000
#> GSM531695 2 0.000 0.990 0.000 1.000
#> GSM531603 2 0.000 0.990 0.000 1.000
#> GSM531609 1 0.563 0.841 0.868 0.132
#> GSM531611 2 0.000 0.990 0.000 1.000
#> GSM531621 1 0.000 0.986 1.000 0.000
#> GSM531622 1 0.000 0.986 1.000 0.000
#> GSM531628 1 0.000 0.986 1.000 0.000
#> GSM531630 1 0.000 0.986 1.000 0.000
#> GSM531633 1 0.000 0.986 1.000 0.000
#> GSM531635 1 0.000 0.986 1.000 0.000
#> GSM531640 1 0.000 0.986 1.000 0.000
#> GSM531649 1 0.000 0.986 1.000 0.000
#> GSM531653 1 0.000 0.986 1.000 0.000
#> GSM531657 2 0.000 0.990 0.000 1.000
#> GSM531665 1 0.000 0.986 1.000 0.000
#> GSM531670 1 0.000 0.986 1.000 0.000
#> GSM531674 1 0.000 0.986 1.000 0.000
#> GSM531675 2 0.000 0.990 0.000 1.000
#> GSM531677 2 0.000 0.990 0.000 1.000
#> GSM531678 2 0.000 0.990 0.000 1.000
#> GSM531680 2 0.000 0.990 0.000 1.000
#> GSM531689 2 0.000 0.990 0.000 1.000
#> GSM531691 2 0.000 0.990 0.000 1.000
#> GSM531692 2 0.000 0.990 0.000 1.000
#> GSM531694 2 0.000 0.990 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM531602 2 0.0000 0.980 0.000 1.000 0.000
#> GSM531604 2 0.0000 0.980 0.000 1.000 0.000
#> GSM531606 2 0.0000 0.980 0.000 1.000 0.000
#> GSM531607 2 0.0000 0.980 0.000 1.000 0.000
#> GSM531608 3 0.0000 0.993 0.000 0.000 1.000
#> GSM531610 2 0.0000 0.980 0.000 1.000 0.000
#> GSM531612 2 0.0000 0.980 0.000 1.000 0.000
#> GSM531613 2 0.0000 0.980 0.000 1.000 0.000
#> GSM531614 3 0.0000 0.993 0.000 0.000 1.000
#> GSM531616 3 0.0000 0.993 0.000 0.000 1.000
#> GSM531618 1 0.0000 0.917 1.000 0.000 0.000
#> GSM531619 3 0.0000 0.993 0.000 0.000 1.000
#> GSM531620 3 0.0000 0.993 0.000 0.000 1.000
#> GSM531623 3 0.0000 0.993 0.000 0.000 1.000
#> GSM531625 3 0.0000 0.993 0.000 0.000 1.000
#> GSM531626 3 0.0000 0.993 0.000 0.000 1.000
#> GSM531632 3 0.0000 0.993 0.000 0.000 1.000
#> GSM531638 3 0.0000 0.993 0.000 0.000 1.000
#> GSM531639 1 0.0000 0.917 1.000 0.000 0.000
#> GSM531641 1 0.6126 0.421 0.600 0.400 0.000
#> GSM531642 1 0.4555 0.758 0.800 0.200 0.000
#> GSM531643 1 0.0000 0.917 1.000 0.000 0.000
#> GSM531644 1 0.0000 0.917 1.000 0.000 0.000
#> GSM531645 1 0.0000 0.917 1.000 0.000 0.000
#> GSM531646 3 0.0000 0.993 0.000 0.000 1.000
#> GSM531647 3 0.0000 0.993 0.000 0.000 1.000
#> GSM531648 1 0.0000 0.917 1.000 0.000 0.000
#> GSM531650 1 0.0000 0.917 1.000 0.000 0.000
#> GSM531651 3 0.0000 0.993 0.000 0.000 1.000
#> GSM531652 1 0.0000 0.917 1.000 0.000 0.000
#> GSM531656 1 0.0000 0.917 1.000 0.000 0.000
#> GSM531659 2 0.0000 0.980 0.000 1.000 0.000
#> GSM531661 3 0.0000 0.993 0.000 0.000 1.000
#> GSM531662 3 0.0000 0.993 0.000 0.000 1.000
#> GSM531663 2 0.7378 0.248 0.036 0.560 0.404
#> GSM531664 1 0.4555 0.758 0.800 0.200 0.000
#> GSM531666 1 0.6126 0.421 0.600 0.400 0.000
#> GSM531667 3 0.0000 0.993 0.000 0.000 1.000
#> GSM531668 2 0.4002 0.775 0.160 0.840 0.000
#> GSM531669 1 0.0000 0.917 1.000 0.000 0.000
#> GSM531671 3 0.0000 0.993 0.000 0.000 1.000
#> GSM531672 2 0.0000 0.980 0.000 1.000 0.000
#> GSM531673 2 0.0000 0.980 0.000 1.000 0.000
#> GSM531676 2 0.0000 0.980 0.000 1.000 0.000
#> GSM531679 2 0.0000 0.980 0.000 1.000 0.000
#> GSM531681 2 0.0000 0.980 0.000 1.000 0.000
#> GSM531682 2 0.0000 0.980 0.000 1.000 0.000
#> GSM531683 2 0.0000 0.980 0.000 1.000 0.000
#> GSM531684 2 0.0000 0.980 0.000 1.000 0.000
#> GSM531685 2 0.0000 0.980 0.000 1.000 0.000
#> GSM531686 2 0.0000 0.980 0.000 1.000 0.000
#> GSM531687 2 0.0000 0.980 0.000 1.000 0.000
#> GSM531688 2 0.0000 0.980 0.000 1.000 0.000
#> GSM531690 2 0.0000 0.980 0.000 1.000 0.000
#> GSM531693 2 0.0000 0.980 0.000 1.000 0.000
#> GSM531695 2 0.0000 0.980 0.000 1.000 0.000
#> GSM531603 2 0.0000 0.980 0.000 1.000 0.000
#> GSM531609 3 0.3851 0.807 0.004 0.136 0.860
#> GSM531611 2 0.0000 0.980 0.000 1.000 0.000
#> GSM531621 3 0.0000 0.993 0.000 0.000 1.000
#> GSM531622 3 0.0000 0.993 0.000 0.000 1.000
#> GSM531628 3 0.0000 0.993 0.000 0.000 1.000
#> GSM531630 3 0.0000 0.993 0.000 0.000 1.000
#> GSM531633 3 0.0000 0.993 0.000 0.000 1.000
#> GSM531635 3 0.0000 0.993 0.000 0.000 1.000
#> GSM531640 3 0.0000 0.993 0.000 0.000 1.000
#> GSM531649 3 0.0000 0.993 0.000 0.000 1.000
#> GSM531653 1 0.0000 0.917 1.000 0.000 0.000
#> GSM531657 2 0.0000 0.980 0.000 1.000 0.000
#> GSM531665 3 0.0000 0.993 0.000 0.000 1.000
#> GSM531670 1 0.0237 0.914 0.996 0.000 0.004
#> GSM531674 1 0.0000 0.917 1.000 0.000 0.000
#> GSM531675 2 0.0000 0.980 0.000 1.000 0.000
#> GSM531677 2 0.0000 0.980 0.000 1.000 0.000
#> GSM531678 2 0.0000 0.980 0.000 1.000 0.000
#> GSM531680 2 0.0000 0.980 0.000 1.000 0.000
#> GSM531689 2 0.0000 0.980 0.000 1.000 0.000
#> GSM531691 2 0.0000 0.980 0.000 1.000 0.000
#> GSM531692 2 0.0000 0.980 0.000 1.000 0.000
#> GSM531694 2 0.0000 0.980 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM531602 2 0.0000 0.9112 0.000 1.000 0.000 0.000
#> GSM531604 2 0.3975 0.6511 0.000 0.760 0.000 0.240
#> GSM531606 2 0.1022 0.8855 0.000 0.968 0.000 0.032
#> GSM531607 2 0.0000 0.9112 0.000 1.000 0.000 0.000
#> GSM531608 3 0.0000 0.9814 0.000 0.000 1.000 0.000
#> GSM531610 2 0.4967 0.1327 0.000 0.548 0.000 0.452
#> GSM531612 2 0.4331 0.5589 0.000 0.712 0.000 0.288
#> GSM531613 2 0.4134 0.6078 0.000 0.740 0.000 0.260
#> GSM531614 3 0.0336 0.9744 0.000 0.000 0.992 0.008
#> GSM531616 3 0.0000 0.9814 0.000 0.000 1.000 0.000
#> GSM531618 1 0.0000 0.9391 1.000 0.000 0.000 0.000
#> GSM531619 3 0.0000 0.9814 0.000 0.000 1.000 0.000
#> GSM531620 3 0.0000 0.9814 0.000 0.000 1.000 0.000
#> GSM531623 3 0.0000 0.9814 0.000 0.000 1.000 0.000
#> GSM531625 3 0.0000 0.9814 0.000 0.000 1.000 0.000
#> GSM531626 3 0.0000 0.9814 0.000 0.000 1.000 0.000
#> GSM531632 3 0.0000 0.9814 0.000 0.000 1.000 0.000
#> GSM531638 3 0.0000 0.9814 0.000 0.000 1.000 0.000
#> GSM531639 1 0.0000 0.9391 1.000 0.000 0.000 0.000
#> GSM531641 4 0.5531 0.6863 0.140 0.128 0.000 0.732
#> GSM531642 1 0.6394 0.4128 0.636 0.120 0.000 0.244
#> GSM531643 1 0.0000 0.9391 1.000 0.000 0.000 0.000
#> GSM531644 1 0.0000 0.9391 1.000 0.000 0.000 0.000
#> GSM531645 1 0.0000 0.9391 1.000 0.000 0.000 0.000
#> GSM531646 3 0.0000 0.9814 0.000 0.000 1.000 0.000
#> GSM531647 3 0.0000 0.9814 0.000 0.000 1.000 0.000
#> GSM531648 1 0.0000 0.9391 1.000 0.000 0.000 0.000
#> GSM531650 1 0.0000 0.9391 1.000 0.000 0.000 0.000
#> GSM531651 3 0.0000 0.9814 0.000 0.000 1.000 0.000
#> GSM531652 1 0.0000 0.9391 1.000 0.000 0.000 0.000
#> GSM531656 1 0.0000 0.9391 1.000 0.000 0.000 0.000
#> GSM531659 2 0.4972 0.0839 0.000 0.544 0.000 0.456
#> GSM531661 3 0.0000 0.9814 0.000 0.000 1.000 0.000
#> GSM531662 3 0.3801 0.7386 0.000 0.000 0.780 0.220
#> GSM531663 4 0.0376 0.6917 0.004 0.000 0.004 0.992
#> GSM531664 4 0.6176 0.1680 0.424 0.052 0.000 0.524
#> GSM531666 4 0.5657 0.6737 0.160 0.120 0.000 0.720
#> GSM531667 3 0.0000 0.9814 0.000 0.000 1.000 0.000
#> GSM531668 4 0.1109 0.7051 0.004 0.028 0.000 0.968
#> GSM531669 1 0.4406 0.5450 0.700 0.000 0.000 0.300
#> GSM531671 3 0.0000 0.9814 0.000 0.000 1.000 0.000
#> GSM531672 4 0.4103 0.6429 0.000 0.256 0.000 0.744
#> GSM531673 4 0.0188 0.6946 0.000 0.004 0.000 0.996
#> GSM531676 2 0.0000 0.9112 0.000 1.000 0.000 0.000
#> GSM531679 2 0.0000 0.9112 0.000 1.000 0.000 0.000
#> GSM531681 2 0.0000 0.9112 0.000 1.000 0.000 0.000
#> GSM531682 2 0.0000 0.9112 0.000 1.000 0.000 0.000
#> GSM531683 2 0.0000 0.9112 0.000 1.000 0.000 0.000
#> GSM531684 2 0.0336 0.9052 0.000 0.992 0.000 0.008
#> GSM531685 2 0.0000 0.9112 0.000 1.000 0.000 0.000
#> GSM531686 2 0.0000 0.9112 0.000 1.000 0.000 0.000
#> GSM531687 2 0.0000 0.9112 0.000 1.000 0.000 0.000
#> GSM531688 2 0.0000 0.9112 0.000 1.000 0.000 0.000
#> GSM531690 2 0.0000 0.9112 0.000 1.000 0.000 0.000
#> GSM531693 2 0.0000 0.9112 0.000 1.000 0.000 0.000
#> GSM531695 2 0.0000 0.9112 0.000 1.000 0.000 0.000
#> GSM531603 2 0.0000 0.9112 0.000 1.000 0.000 0.000
#> GSM531609 4 0.6928 0.1920 0.040 0.036 0.436 0.488
#> GSM531611 2 0.4222 0.5876 0.000 0.728 0.000 0.272
#> GSM531621 3 0.0000 0.9814 0.000 0.000 1.000 0.000
#> GSM531622 3 0.0000 0.9814 0.000 0.000 1.000 0.000
#> GSM531628 3 0.0000 0.9814 0.000 0.000 1.000 0.000
#> GSM531630 3 0.0000 0.9814 0.000 0.000 1.000 0.000
#> GSM531633 3 0.0000 0.9814 0.000 0.000 1.000 0.000
#> GSM531635 3 0.0000 0.9814 0.000 0.000 1.000 0.000
#> GSM531640 3 0.0000 0.9814 0.000 0.000 1.000 0.000
#> GSM531649 3 0.0000 0.9814 0.000 0.000 1.000 0.000
#> GSM531653 1 0.0336 0.9317 0.992 0.000 0.008 0.000
#> GSM531657 4 0.4103 0.6429 0.000 0.256 0.000 0.744
#> GSM531665 3 0.3801 0.7386 0.000 0.000 0.780 0.220
#> GSM531670 1 0.0469 0.9274 0.988 0.000 0.012 0.000
#> GSM531674 1 0.0188 0.9366 0.996 0.000 0.000 0.004
#> GSM531675 2 0.0000 0.9112 0.000 1.000 0.000 0.000
#> GSM531677 2 0.0000 0.9112 0.000 1.000 0.000 0.000
#> GSM531678 2 0.0000 0.9112 0.000 1.000 0.000 0.000
#> GSM531680 2 0.0000 0.9112 0.000 1.000 0.000 0.000
#> GSM531689 2 0.0000 0.9112 0.000 1.000 0.000 0.000
#> GSM531691 2 0.0000 0.9112 0.000 1.000 0.000 0.000
#> GSM531692 2 0.3942 0.6560 0.000 0.764 0.000 0.236
#> GSM531694 2 0.0000 0.9112 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM531602 2 0.0000 0.900 0.000 1.000 0.000 0.000 0.000
#> GSM531604 2 0.5957 0.417 0.000 0.588 0.000 0.176 0.236
#> GSM531606 2 0.3772 0.717 0.000 0.792 0.000 0.036 0.172
#> GSM531607 2 0.0000 0.900 0.000 1.000 0.000 0.000 0.000
#> GSM531608 3 0.0404 0.940 0.000 0.000 0.988 0.000 0.012
#> GSM531610 5 0.4417 0.220 0.000 0.148 0.000 0.092 0.760
#> GSM531612 2 0.5240 0.465 0.000 0.672 0.000 0.112 0.216
#> GSM531613 2 0.4152 0.648 0.000 0.772 0.000 0.060 0.168
#> GSM531614 5 0.4497 0.286 0.000 0.000 0.424 0.008 0.568
#> GSM531616 3 0.0000 0.952 0.000 0.000 1.000 0.000 0.000
#> GSM531618 1 0.0000 0.913 1.000 0.000 0.000 0.000 0.000
#> GSM531619 3 0.0000 0.952 0.000 0.000 1.000 0.000 0.000
#> GSM531620 3 0.0000 0.952 0.000 0.000 1.000 0.000 0.000
#> GSM531623 3 0.0000 0.952 0.000 0.000 1.000 0.000 0.000
#> GSM531625 3 0.0000 0.952 0.000 0.000 1.000 0.000 0.000
#> GSM531626 3 0.0000 0.952 0.000 0.000 1.000 0.000 0.000
#> GSM531632 3 0.0000 0.952 0.000 0.000 1.000 0.000 0.000
#> GSM531638 3 0.0000 0.952 0.000 0.000 1.000 0.000 0.000
#> GSM531639 1 0.0404 0.906 0.988 0.000 0.000 0.000 0.012
#> GSM531641 4 0.7512 0.581 0.096 0.168 0.000 0.504 0.232
#> GSM531642 1 0.7162 0.084 0.528 0.084 0.000 0.268 0.120
#> GSM531643 1 0.0000 0.913 1.000 0.000 0.000 0.000 0.000
#> GSM531644 1 0.0000 0.913 1.000 0.000 0.000 0.000 0.000
#> GSM531645 1 0.0000 0.913 1.000 0.000 0.000 0.000 0.000
#> GSM531646 3 0.0000 0.952 0.000 0.000 1.000 0.000 0.000
#> GSM531647 3 0.0162 0.948 0.004 0.000 0.996 0.000 0.000
#> GSM531648 1 0.0000 0.913 1.000 0.000 0.000 0.000 0.000
#> GSM531650 1 0.0000 0.913 1.000 0.000 0.000 0.000 0.000
#> GSM531651 3 0.0000 0.952 0.000 0.000 1.000 0.000 0.000
#> GSM531652 1 0.0000 0.913 1.000 0.000 0.000 0.000 0.000
#> GSM531656 1 0.0000 0.913 1.000 0.000 0.000 0.000 0.000
#> GSM531659 2 0.6290 -0.130 0.000 0.500 0.000 0.332 0.168
#> GSM531661 3 0.0000 0.952 0.000 0.000 1.000 0.000 0.000
#> GSM531662 3 0.4909 0.218 0.000 0.000 0.560 0.412 0.028
#> GSM531663 4 0.1197 0.430 0.000 0.000 0.000 0.952 0.048
#> GSM531664 4 0.7193 0.411 0.324 0.060 0.000 0.480 0.136
#> GSM531666 4 0.7605 0.576 0.128 0.140 0.000 0.500 0.232
#> GSM531667 3 0.0000 0.952 0.000 0.000 1.000 0.000 0.000
#> GSM531668 4 0.3474 0.462 0.008 0.020 0.000 0.824 0.148
#> GSM531669 1 0.5807 0.210 0.560 0.016 0.000 0.360 0.064
#> GSM531671 3 0.0451 0.941 0.000 0.000 0.988 0.004 0.008
#> GSM531672 4 0.6224 0.540 0.000 0.232 0.000 0.548 0.220
#> GSM531673 4 0.1043 0.436 0.000 0.000 0.000 0.960 0.040
#> GSM531676 2 0.0000 0.900 0.000 1.000 0.000 0.000 0.000
#> GSM531679 2 0.0000 0.900 0.000 1.000 0.000 0.000 0.000
#> GSM531681 2 0.0000 0.900 0.000 1.000 0.000 0.000 0.000
#> GSM531682 2 0.0000 0.900 0.000 1.000 0.000 0.000 0.000
#> GSM531683 2 0.0000 0.900 0.000 1.000 0.000 0.000 0.000
#> GSM531684 2 0.3053 0.756 0.000 0.828 0.000 0.008 0.164
#> GSM531685 2 0.0000 0.900 0.000 1.000 0.000 0.000 0.000
#> GSM531686 2 0.0000 0.900 0.000 1.000 0.000 0.000 0.000
#> GSM531687 2 0.0000 0.900 0.000 1.000 0.000 0.000 0.000
#> GSM531688 2 0.0000 0.900 0.000 1.000 0.000 0.000 0.000
#> GSM531690 2 0.0000 0.900 0.000 1.000 0.000 0.000 0.000
#> GSM531693 2 0.0162 0.898 0.000 0.996 0.000 0.000 0.004
#> GSM531695 2 0.0000 0.900 0.000 1.000 0.000 0.000 0.000
#> GSM531603 2 0.0000 0.900 0.000 1.000 0.000 0.000 0.000
#> GSM531609 5 0.4939 0.430 0.012 0.012 0.116 0.100 0.760
#> GSM531611 2 0.4893 0.531 0.000 0.704 0.000 0.088 0.208
#> GSM531621 3 0.0000 0.952 0.000 0.000 1.000 0.000 0.000
#> GSM531622 3 0.0000 0.952 0.000 0.000 1.000 0.000 0.000
#> GSM531628 3 0.0000 0.952 0.000 0.000 1.000 0.000 0.000
#> GSM531630 3 0.0000 0.952 0.000 0.000 1.000 0.000 0.000
#> GSM531633 3 0.0000 0.952 0.000 0.000 1.000 0.000 0.000
#> GSM531635 3 0.0000 0.952 0.000 0.000 1.000 0.000 0.000
#> GSM531640 3 0.0000 0.952 0.000 0.000 1.000 0.000 0.000
#> GSM531649 3 0.0000 0.952 0.000 0.000 1.000 0.000 0.000
#> GSM531653 1 0.0162 0.910 0.996 0.000 0.004 0.000 0.000
#> GSM531657 4 0.6246 0.540 0.000 0.232 0.000 0.544 0.224
#> GSM531665 3 0.4924 0.199 0.000 0.000 0.552 0.420 0.028
#> GSM531670 1 0.1124 0.873 0.960 0.000 0.036 0.000 0.004
#> GSM531674 1 0.0771 0.899 0.976 0.000 0.000 0.020 0.004
#> GSM531675 2 0.0000 0.900 0.000 1.000 0.000 0.000 0.000
#> GSM531677 2 0.0000 0.900 0.000 1.000 0.000 0.000 0.000
#> GSM531678 2 0.0000 0.900 0.000 1.000 0.000 0.000 0.000
#> GSM531680 2 0.0000 0.900 0.000 1.000 0.000 0.000 0.000
#> GSM531689 2 0.0000 0.900 0.000 1.000 0.000 0.000 0.000
#> GSM531691 2 0.0000 0.900 0.000 1.000 0.000 0.000 0.000
#> GSM531692 2 0.5575 0.511 0.000 0.644 0.000 0.168 0.188
#> GSM531694 2 0.0000 0.900 0.000 1.000 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
#> GSM531602 2 0.0000 0.905 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531604 4 0.5166 0.378 0.000 0.364 0.000 0.540 0.096 0.000
#> GSM531606 4 0.3989 0.207 0.000 0.468 0.000 0.528 0.004 0.000
#> GSM531607 2 0.0000 0.905 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531608 3 0.0665 0.976 0.000 0.000 0.980 0.008 0.008 0.004
#> GSM531610 4 0.6753 0.221 0.000 0.068 0.000 0.460 0.288 0.184
#> GSM531612 2 0.3804 0.224 0.000 0.576 0.000 0.000 0.000 0.424
#> GSM531613 2 0.2219 0.751 0.000 0.864 0.000 0.000 0.000 0.136
#> GSM531614 4 0.6975 0.106 0.000 0.000 0.140 0.460 0.272 0.128
#> GSM531616 3 0.0000 0.996 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531618 1 0.0767 0.966 0.976 0.000 0.000 0.004 0.012 0.008
#> GSM531619 3 0.0000 0.996 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531620 3 0.0000 0.996 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531623 3 0.0000 0.996 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531625 3 0.0000 0.996 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531626 3 0.0000 0.996 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531632 3 0.0000 0.996 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531638 3 0.0000 0.996 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531639 1 0.0858 0.952 0.968 0.000 0.000 0.000 0.004 0.028
#> GSM531641 6 0.2908 0.703 0.048 0.104 0.000 0.000 0.000 0.848
#> GSM531642 6 0.4720 0.572 0.308 0.060 0.000 0.000 0.004 0.628
#> GSM531643 1 0.0291 0.967 0.992 0.000 0.000 0.004 0.004 0.000
#> GSM531644 1 0.0405 0.968 0.988 0.000 0.000 0.004 0.000 0.008
#> GSM531645 1 0.0964 0.962 0.968 0.000 0.000 0.004 0.012 0.016
#> GSM531646 3 0.0000 0.996 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531647 3 0.0405 0.984 0.008 0.000 0.988 0.004 0.000 0.000
#> GSM531648 1 0.0870 0.964 0.972 0.000 0.000 0.004 0.012 0.012
#> GSM531650 1 0.0260 0.967 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM531651 3 0.0000 0.996 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531652 1 0.0405 0.968 0.988 0.000 0.000 0.004 0.000 0.008
#> GSM531656 1 0.0291 0.968 0.992 0.000 0.000 0.004 0.004 0.000
#> GSM531659 2 0.4116 0.209 0.000 0.572 0.000 0.000 0.012 0.416
#> GSM531661 3 0.0000 0.996 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531662 5 0.3607 0.561 0.000 0.000 0.348 0.000 0.652 0.000
#> GSM531663 5 0.3288 0.406 0.000 0.000 0.000 0.000 0.724 0.276
#> GSM531664 6 0.3196 0.661 0.156 0.020 0.000 0.008 0.000 0.816
#> GSM531666 6 0.2994 0.705 0.064 0.080 0.000 0.004 0.000 0.852
#> GSM531667 3 0.0000 0.996 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531668 6 0.6175 0.111 0.016 0.004 0.000 0.176 0.312 0.492
#> GSM531669 6 0.5286 0.436 0.348 0.000 0.000 0.012 0.080 0.560
#> GSM531671 3 0.0790 0.961 0.000 0.000 0.968 0.000 0.032 0.000
#> GSM531672 6 0.2821 0.658 0.000 0.152 0.000 0.000 0.016 0.832
#> GSM531673 5 0.3482 0.375 0.000 0.000 0.000 0.000 0.684 0.316
#> GSM531676 2 0.0000 0.905 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531679 2 0.0000 0.905 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531681 2 0.0000 0.905 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531682 2 0.0000 0.905 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531683 2 0.0000 0.905 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531684 2 0.3847 -0.139 0.000 0.544 0.000 0.456 0.000 0.000
#> GSM531685 2 0.0000 0.905 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531686 2 0.0000 0.905 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531687 2 0.0000 0.905 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531688 2 0.0000 0.905 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531690 2 0.0000 0.905 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531693 2 0.0865 0.868 0.000 0.964 0.000 0.036 0.000 0.000
#> GSM531695 2 0.0000 0.905 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531603 2 0.0146 0.902 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM531609 4 0.6731 0.175 0.012 0.000 0.036 0.468 0.288 0.196
#> GSM531611 2 0.3464 0.483 0.000 0.688 0.000 0.000 0.000 0.312
#> GSM531621 3 0.0000 0.996 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531622 3 0.0000 0.996 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531628 3 0.0000 0.996 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531630 3 0.0000 0.996 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531633 3 0.0000 0.996 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531635 3 0.0000 0.996 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531640 3 0.0000 0.996 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531649 3 0.0000 0.996 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531653 1 0.0798 0.957 0.976 0.000 0.012 0.004 0.004 0.004
#> GSM531657 6 0.2790 0.666 0.000 0.140 0.000 0.000 0.020 0.840
#> GSM531665 5 0.3707 0.589 0.000 0.000 0.312 0.000 0.680 0.008
#> GSM531670 1 0.2121 0.905 0.916 0.000 0.040 0.008 0.032 0.004
#> GSM531674 1 0.1888 0.913 0.916 0.000 0.000 0.012 0.068 0.004
#> GSM531675 2 0.0000 0.905 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531677 2 0.0000 0.905 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531678 2 0.0000 0.905 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531680 2 0.0000 0.905 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531689 2 0.0000 0.905 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531691 2 0.0000 0.905 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531692 4 0.4735 0.288 0.000 0.432 0.000 0.520 0.048 0.000
#> GSM531694 2 0.0000 0.905 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> ATC:skmeans 78 0.692 2
#> ATC:skmeans 77 0.520 3
#> ATC:skmeans 75 0.654 4
#> ATC:skmeans 66 0.876 5
#> ATC:skmeans 66 0.847 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "pam"]
# you can also extract it by
# res = res_list["ATC:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 80 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 0.713 0.915 0.951 0.4882 0.494 0.494
#> 3 3 0.907 0.909 0.965 0.3506 0.694 0.463
#> 4 4 0.773 0.832 0.888 0.0838 0.934 0.815
#> 5 5 0.831 0.877 0.925 0.0977 0.867 0.588
#> 6 6 0.866 0.852 0.897 0.0510 0.932 0.697
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
#> GSM531602 2 0.000 0.9022 0.000 1.000
#> GSM531604 2 0.788 0.7935 0.236 0.764
#> GSM531606 2 0.706 0.8423 0.192 0.808
#> GSM531607 2 0.295 0.8897 0.052 0.948
#> GSM531608 1 0.000 0.9878 1.000 0.000
#> GSM531610 2 0.706 0.8423 0.192 0.808
#> GSM531612 2 0.000 0.9022 0.000 1.000
#> GSM531613 2 0.000 0.9022 0.000 1.000
#> GSM531614 1 0.000 0.9878 1.000 0.000
#> GSM531616 1 0.000 0.9878 1.000 0.000
#> GSM531618 1 0.000 0.9878 1.000 0.000
#> GSM531619 1 0.000 0.9878 1.000 0.000
#> GSM531620 1 0.000 0.9878 1.000 0.000
#> GSM531623 1 0.000 0.9878 1.000 0.000
#> GSM531625 1 0.000 0.9878 1.000 0.000
#> GSM531626 1 0.000 0.9878 1.000 0.000
#> GSM531632 1 0.000 0.9878 1.000 0.000
#> GSM531638 1 0.000 0.9878 1.000 0.000
#> GSM531639 1 0.000 0.9878 1.000 0.000
#> GSM531641 2 0.706 0.8423 0.192 0.808
#> GSM531642 2 0.706 0.8423 0.192 0.808
#> GSM531643 1 0.000 0.9878 1.000 0.000
#> GSM531644 1 0.000 0.9878 1.000 0.000
#> GSM531645 1 0.000 0.9878 1.000 0.000
#> GSM531646 1 0.000 0.9878 1.000 0.000
#> GSM531647 1 0.000 0.9878 1.000 0.000
#> GSM531648 1 0.000 0.9878 1.000 0.000
#> GSM531650 1 0.000 0.9878 1.000 0.000
#> GSM531651 1 0.000 0.9878 1.000 0.000
#> GSM531652 1 0.000 0.9878 1.000 0.000
#> GSM531656 1 0.000 0.9878 1.000 0.000
#> GSM531659 2 0.706 0.8423 0.192 0.808
#> GSM531661 1 0.000 0.9878 1.000 0.000
#> GSM531662 1 0.000 0.9878 1.000 0.000
#> GSM531663 1 0.000 0.9878 1.000 0.000
#> GSM531664 2 0.706 0.8423 0.192 0.808
#> GSM531666 2 0.706 0.8423 0.192 0.808
#> GSM531667 1 0.000 0.9878 1.000 0.000
#> GSM531668 2 0.990 0.3923 0.440 0.560
#> GSM531669 2 0.753 0.8174 0.216 0.784
#> GSM531671 1 0.000 0.9878 1.000 0.000
#> GSM531672 2 0.706 0.8423 0.192 0.808
#> GSM531673 1 0.981 0.0798 0.580 0.420
#> GSM531676 2 0.000 0.9022 0.000 1.000
#> GSM531679 2 0.000 0.9022 0.000 1.000
#> GSM531681 2 0.000 0.9022 0.000 1.000
#> GSM531682 2 0.000 0.9022 0.000 1.000
#> GSM531683 2 0.000 0.9022 0.000 1.000
#> GSM531684 2 0.697 0.8440 0.188 0.812
#> GSM531685 2 0.000 0.9022 0.000 1.000
#> GSM531686 2 0.000 0.9022 0.000 1.000
#> GSM531687 2 0.000 0.9022 0.000 1.000
#> GSM531688 2 0.000 0.9022 0.000 1.000
#> GSM531690 2 0.000 0.9022 0.000 1.000
#> GSM531693 2 0.706 0.8423 0.192 0.808
#> GSM531695 2 0.000 0.9022 0.000 1.000
#> GSM531603 2 0.706 0.8423 0.192 0.808
#> GSM531609 1 0.000 0.9878 1.000 0.000
#> GSM531611 2 0.000 0.9022 0.000 1.000
#> GSM531621 1 0.000 0.9878 1.000 0.000
#> GSM531622 1 0.000 0.9878 1.000 0.000
#> GSM531628 1 0.000 0.9878 1.000 0.000
#> GSM531630 1 0.000 0.9878 1.000 0.000
#> GSM531633 1 0.000 0.9878 1.000 0.000
#> GSM531635 1 0.000 0.9878 1.000 0.000
#> GSM531640 1 0.000 0.9878 1.000 0.000
#> GSM531649 1 0.000 0.9878 1.000 0.000
#> GSM531653 1 0.000 0.9878 1.000 0.000
#> GSM531657 2 0.706 0.8423 0.192 0.808
#> GSM531665 1 0.000 0.9878 1.000 0.000
#> GSM531670 1 0.000 0.9878 1.000 0.000
#> GSM531674 1 0.000 0.9878 1.000 0.000
#> GSM531675 2 0.000 0.9022 0.000 1.000
#> GSM531677 2 0.000 0.9022 0.000 1.000
#> GSM531678 2 0.000 0.9022 0.000 1.000
#> GSM531680 2 0.000 0.9022 0.000 1.000
#> GSM531689 2 0.000 0.9022 0.000 1.000
#> GSM531691 2 0.000 0.9022 0.000 1.000
#> GSM531692 2 0.802 0.7831 0.244 0.756
#> GSM531694 2 0.000 0.9022 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM531602 2 0.0000 0.9518 0.000 1.000 0.000
#> GSM531604 1 0.6274 0.0669 0.544 0.456 0.000
#> GSM531606 2 0.4555 0.7684 0.200 0.800 0.000
#> GSM531607 2 0.1860 0.9139 0.052 0.948 0.000
#> GSM531608 3 0.0000 0.9847 0.000 0.000 1.000
#> GSM531610 1 0.0892 0.9346 0.980 0.020 0.000
#> GSM531612 2 0.0000 0.9518 0.000 1.000 0.000
#> GSM531613 2 0.0000 0.9518 0.000 1.000 0.000
#> GSM531614 1 0.0000 0.9536 1.000 0.000 0.000
#> GSM531616 3 0.0000 0.9847 0.000 0.000 1.000
#> GSM531618 1 0.0000 0.9536 1.000 0.000 0.000
#> GSM531619 3 0.0000 0.9847 0.000 0.000 1.000
#> GSM531620 3 0.0000 0.9847 0.000 0.000 1.000
#> GSM531623 3 0.0000 0.9847 0.000 0.000 1.000
#> GSM531625 3 0.0000 0.9847 0.000 0.000 1.000
#> GSM531626 3 0.0000 0.9847 0.000 0.000 1.000
#> GSM531632 1 0.6204 0.2609 0.576 0.000 0.424
#> GSM531638 3 0.5138 0.6361 0.252 0.000 0.748
#> GSM531639 1 0.0000 0.9536 1.000 0.000 0.000
#> GSM531641 1 0.0000 0.9536 1.000 0.000 0.000
#> GSM531642 1 0.0000 0.9536 1.000 0.000 0.000
#> GSM531643 1 0.0000 0.9536 1.000 0.000 0.000
#> GSM531644 1 0.0000 0.9536 1.000 0.000 0.000
#> GSM531645 1 0.0000 0.9536 1.000 0.000 0.000
#> GSM531646 3 0.0000 0.9847 0.000 0.000 1.000
#> GSM531647 1 0.0000 0.9536 1.000 0.000 0.000
#> GSM531648 1 0.0000 0.9536 1.000 0.000 0.000
#> GSM531650 1 0.0000 0.9536 1.000 0.000 0.000
#> GSM531651 3 0.0000 0.9847 0.000 0.000 1.000
#> GSM531652 1 0.0000 0.9536 1.000 0.000 0.000
#> GSM531656 1 0.0000 0.9536 1.000 0.000 0.000
#> GSM531659 1 0.0000 0.9536 1.000 0.000 0.000
#> GSM531661 3 0.0000 0.9847 0.000 0.000 1.000
#> GSM531662 1 0.0000 0.9536 1.000 0.000 0.000
#> GSM531663 1 0.0000 0.9536 1.000 0.000 0.000
#> GSM531664 1 0.0000 0.9536 1.000 0.000 0.000
#> GSM531666 1 0.0000 0.9536 1.000 0.000 0.000
#> GSM531667 3 0.0000 0.9847 0.000 0.000 1.000
#> GSM531668 1 0.0000 0.9536 1.000 0.000 0.000
#> GSM531669 1 0.0000 0.9536 1.000 0.000 0.000
#> GSM531671 1 0.0000 0.9536 1.000 0.000 0.000
#> GSM531672 1 0.0000 0.9536 1.000 0.000 0.000
#> GSM531673 1 0.0000 0.9536 1.000 0.000 0.000
#> GSM531676 2 0.0000 0.9518 0.000 1.000 0.000
#> GSM531679 2 0.0000 0.9518 0.000 1.000 0.000
#> GSM531681 2 0.0000 0.9518 0.000 1.000 0.000
#> GSM531682 2 0.0000 0.9518 0.000 1.000 0.000
#> GSM531683 2 0.0000 0.9518 0.000 1.000 0.000
#> GSM531684 2 0.4002 0.8187 0.160 0.840 0.000
#> GSM531685 2 0.0000 0.9518 0.000 1.000 0.000
#> GSM531686 2 0.0000 0.9518 0.000 1.000 0.000
#> GSM531687 2 0.0000 0.9518 0.000 1.000 0.000
#> GSM531688 2 0.0000 0.9518 0.000 1.000 0.000
#> GSM531690 2 0.0000 0.9518 0.000 1.000 0.000
#> GSM531693 2 0.4178 0.8046 0.172 0.828 0.000
#> GSM531695 2 0.0000 0.9518 0.000 1.000 0.000
#> GSM531603 2 0.3941 0.8231 0.156 0.844 0.000
#> GSM531609 1 0.0000 0.9536 1.000 0.000 0.000
#> GSM531611 2 0.0000 0.9518 0.000 1.000 0.000
#> GSM531621 3 0.0000 0.9847 0.000 0.000 1.000
#> GSM531622 3 0.0000 0.9847 0.000 0.000 1.000
#> GSM531628 1 0.6308 0.0105 0.508 0.000 0.492
#> GSM531630 3 0.0000 0.9847 0.000 0.000 1.000
#> GSM531633 3 0.0000 0.9847 0.000 0.000 1.000
#> GSM531635 3 0.0000 0.9847 0.000 0.000 1.000
#> GSM531640 3 0.0000 0.9847 0.000 0.000 1.000
#> GSM531649 3 0.0000 0.9847 0.000 0.000 1.000
#> GSM531653 1 0.0000 0.9536 1.000 0.000 0.000
#> GSM531657 1 0.0000 0.9536 1.000 0.000 0.000
#> GSM531665 1 0.0000 0.9536 1.000 0.000 0.000
#> GSM531670 1 0.0000 0.9536 1.000 0.000 0.000
#> GSM531674 1 0.0000 0.9536 1.000 0.000 0.000
#> GSM531675 2 0.0000 0.9518 0.000 1.000 0.000
#> GSM531677 2 0.0000 0.9518 0.000 1.000 0.000
#> GSM531678 2 0.0000 0.9518 0.000 1.000 0.000
#> GSM531680 2 0.0000 0.9518 0.000 1.000 0.000
#> GSM531689 2 0.0000 0.9518 0.000 1.000 0.000
#> GSM531691 2 0.0000 0.9518 0.000 1.000 0.000
#> GSM531692 2 0.6140 0.3640 0.404 0.596 0.000
#> GSM531694 2 0.0000 0.9518 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM531602 2 0.0188 0.915 0.000 0.996 0.000 0.004
#> GSM531604 1 0.7879 0.190 0.380 0.332 0.288 0.000
#> GSM531606 2 0.6122 0.642 0.160 0.680 0.160 0.000
#> GSM531607 2 0.4499 0.761 0.048 0.792 0.160 0.000
#> GSM531608 3 0.4661 0.811 0.000 0.000 0.652 0.348
#> GSM531610 1 0.3636 0.832 0.820 0.008 0.172 0.000
#> GSM531612 2 0.0817 0.905 0.000 0.976 0.024 0.000
#> GSM531613 2 0.0188 0.915 0.000 0.996 0.000 0.004
#> GSM531614 1 0.0000 0.870 1.000 0.000 0.000 0.000
#> GSM531616 3 0.4356 0.872 0.000 0.000 0.708 0.292
#> GSM531618 1 0.0000 0.870 1.000 0.000 0.000 0.000
#> GSM531619 4 0.0188 0.993 0.000 0.000 0.004 0.996
#> GSM531620 3 0.4356 0.872 0.000 0.000 0.708 0.292
#> GSM531623 3 0.4522 0.846 0.000 0.000 0.680 0.320
#> GSM531625 4 0.0188 0.993 0.000 0.000 0.004 0.996
#> GSM531626 3 0.4356 0.872 0.000 0.000 0.708 0.292
#> GSM531632 3 0.5772 0.696 0.176 0.000 0.708 0.116
#> GSM531638 3 0.5386 0.832 0.056 0.000 0.708 0.236
#> GSM531639 1 0.0000 0.870 1.000 0.000 0.000 0.000
#> GSM531641 1 0.3123 0.839 0.844 0.000 0.156 0.000
#> GSM531642 1 0.2921 0.845 0.860 0.000 0.140 0.000
#> GSM531643 1 0.0000 0.870 1.000 0.000 0.000 0.000
#> GSM531644 1 0.0000 0.870 1.000 0.000 0.000 0.000
#> GSM531645 1 0.0000 0.870 1.000 0.000 0.000 0.000
#> GSM531646 3 0.4882 0.862 0.020 0.000 0.708 0.272
#> GSM531647 1 0.4679 0.310 0.648 0.000 0.352 0.000
#> GSM531648 1 0.0000 0.870 1.000 0.000 0.000 0.000
#> GSM531650 1 0.0000 0.870 1.000 0.000 0.000 0.000
#> GSM531651 4 0.0188 0.993 0.000 0.000 0.004 0.996
#> GSM531652 1 0.0000 0.870 1.000 0.000 0.000 0.000
#> GSM531656 1 0.0000 0.870 1.000 0.000 0.000 0.000
#> GSM531659 1 0.4331 0.785 0.712 0.000 0.288 0.000
#> GSM531661 3 0.4356 0.872 0.000 0.000 0.708 0.292
#> GSM531662 1 0.3400 0.796 0.820 0.000 0.180 0.000
#> GSM531663 1 0.4331 0.785 0.712 0.000 0.288 0.000
#> GSM531664 1 0.1792 0.863 0.932 0.000 0.068 0.000
#> GSM531666 1 0.3123 0.839 0.844 0.000 0.156 0.000
#> GSM531667 3 0.3172 0.745 0.000 0.000 0.840 0.160
#> GSM531668 1 0.3907 0.814 0.768 0.000 0.232 0.000
#> GSM531669 1 0.2760 0.833 0.872 0.000 0.128 0.000
#> GSM531671 3 0.3528 0.554 0.192 0.000 0.808 0.000
#> GSM531672 1 0.3545 0.834 0.828 0.008 0.164 0.000
#> GSM531673 1 0.4331 0.785 0.712 0.000 0.288 0.000
#> GSM531676 2 0.0188 0.914 0.000 0.996 0.004 0.000
#> GSM531679 2 0.0188 0.915 0.000 0.996 0.000 0.004
#> GSM531681 2 0.0188 0.915 0.000 0.996 0.000 0.004
#> GSM531682 2 0.0188 0.915 0.000 0.996 0.000 0.004
#> GSM531683 2 0.0188 0.915 0.000 0.996 0.000 0.004
#> GSM531684 2 0.5807 0.678 0.132 0.708 0.160 0.000
#> GSM531685 2 0.0469 0.911 0.000 0.988 0.012 0.000
#> GSM531686 2 0.0188 0.915 0.000 0.996 0.000 0.004
#> GSM531687 2 0.0188 0.914 0.000 0.996 0.004 0.000
#> GSM531688 2 0.0188 0.914 0.000 0.996 0.004 0.000
#> GSM531690 2 0.0188 0.915 0.000 0.996 0.000 0.004
#> GSM531693 2 0.5855 0.673 0.136 0.704 0.160 0.000
#> GSM531695 2 0.0188 0.914 0.000 0.996 0.004 0.000
#> GSM531603 2 0.5758 0.682 0.128 0.712 0.160 0.000
#> GSM531609 1 0.0707 0.869 0.980 0.000 0.020 0.000
#> GSM531611 2 0.0817 0.905 0.000 0.976 0.024 0.000
#> GSM531621 4 0.0188 0.993 0.000 0.000 0.004 0.996
#> GSM531622 3 0.4356 0.872 0.000 0.000 0.708 0.292
#> GSM531628 3 0.5291 0.494 0.324 0.000 0.652 0.024
#> GSM531630 3 0.4356 0.872 0.000 0.000 0.708 0.292
#> GSM531633 4 0.0188 0.993 0.000 0.000 0.004 0.996
#> GSM531635 3 0.4356 0.872 0.000 0.000 0.708 0.292
#> GSM531640 4 0.0921 0.965 0.000 0.000 0.028 0.972
#> GSM531649 3 0.4356 0.872 0.000 0.000 0.708 0.292
#> GSM531653 1 0.0000 0.870 1.000 0.000 0.000 0.000
#> GSM531657 1 0.4331 0.785 0.712 0.000 0.288 0.000
#> GSM531665 1 0.4164 0.796 0.736 0.000 0.264 0.000
#> GSM531670 1 0.0000 0.870 1.000 0.000 0.000 0.000
#> GSM531674 1 0.0000 0.870 1.000 0.000 0.000 0.000
#> GSM531675 2 0.0188 0.915 0.000 0.996 0.000 0.004
#> GSM531677 2 0.0188 0.915 0.000 0.996 0.000 0.004
#> GSM531678 2 0.0000 0.915 0.000 1.000 0.000 0.000
#> GSM531680 2 0.0188 0.915 0.000 0.996 0.000 0.004
#> GSM531689 2 0.0188 0.914 0.000 0.996 0.004 0.000
#> GSM531691 2 0.0188 0.914 0.000 0.996 0.004 0.000
#> GSM531692 2 0.7685 0.210 0.256 0.456 0.288 0.000
#> GSM531694 2 0.0188 0.915 0.000 0.996 0.000 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM531602 2 0.0000 0.903 0.000 1.000 0.000 0.000 0.000
#> GSM531604 4 0.1121 0.842 0.044 0.000 0.000 0.956 0.000
#> GSM531606 4 0.0000 0.814 0.000 0.000 0.000 1.000 0.000
#> GSM531607 4 0.0000 0.814 0.000 0.000 0.000 1.000 0.000
#> GSM531608 3 0.2813 0.787 0.000 0.000 0.832 0.000 0.168
#> GSM531610 4 0.2891 0.878 0.176 0.000 0.000 0.824 0.000
#> GSM531612 2 0.3508 0.815 0.000 0.748 0.000 0.252 0.000
#> GSM531613 2 0.0000 0.903 0.000 1.000 0.000 0.000 0.000
#> GSM531614 1 0.0000 0.917 1.000 0.000 0.000 0.000 0.000
#> GSM531616 3 0.0000 0.962 0.000 0.000 1.000 0.000 0.000
#> GSM531618 1 0.0000 0.917 1.000 0.000 0.000 0.000 0.000
#> GSM531619 5 0.0000 0.988 0.000 0.000 0.000 0.000 1.000
#> GSM531620 3 0.0000 0.962 0.000 0.000 1.000 0.000 0.000
#> GSM531623 3 0.1908 0.880 0.000 0.000 0.908 0.000 0.092
#> GSM531625 5 0.0000 0.988 0.000 0.000 0.000 0.000 1.000
#> GSM531626 3 0.0000 0.962 0.000 0.000 1.000 0.000 0.000
#> GSM531632 3 0.0000 0.962 0.000 0.000 1.000 0.000 0.000
#> GSM531638 3 0.0000 0.962 0.000 0.000 1.000 0.000 0.000
#> GSM531639 1 0.0000 0.917 1.000 0.000 0.000 0.000 0.000
#> GSM531641 4 0.2891 0.878 0.176 0.000 0.000 0.824 0.000
#> GSM531642 4 0.3612 0.776 0.268 0.000 0.000 0.732 0.000
#> GSM531643 1 0.0000 0.917 1.000 0.000 0.000 0.000 0.000
#> GSM531644 1 0.0000 0.917 1.000 0.000 0.000 0.000 0.000
#> GSM531645 1 0.0000 0.917 1.000 0.000 0.000 0.000 0.000
#> GSM531646 3 0.0000 0.962 0.000 0.000 1.000 0.000 0.000
#> GSM531647 1 0.3684 0.580 0.720 0.000 0.280 0.000 0.000
#> GSM531648 1 0.0000 0.917 1.000 0.000 0.000 0.000 0.000
#> GSM531650 1 0.0000 0.917 1.000 0.000 0.000 0.000 0.000
#> GSM531651 5 0.0000 0.988 0.000 0.000 0.000 0.000 1.000
#> GSM531652 1 0.0000 0.917 1.000 0.000 0.000 0.000 0.000
#> GSM531656 1 0.0000 0.917 1.000 0.000 0.000 0.000 0.000
#> GSM531659 4 0.2891 0.878 0.176 0.000 0.000 0.824 0.000
#> GSM531661 3 0.0000 0.962 0.000 0.000 1.000 0.000 0.000
#> GSM531662 1 0.2690 0.756 0.844 0.000 0.156 0.000 0.000
#> GSM531663 4 0.2891 0.878 0.176 0.000 0.000 0.824 0.000
#> GSM531664 1 0.4182 0.156 0.600 0.000 0.000 0.400 0.000
#> GSM531666 4 0.3039 0.865 0.192 0.000 0.000 0.808 0.000
#> GSM531667 3 0.0000 0.962 0.000 0.000 1.000 0.000 0.000
#> GSM531668 4 0.2891 0.878 0.176 0.000 0.000 0.824 0.000
#> GSM531669 1 0.3210 0.651 0.788 0.000 0.000 0.212 0.000
#> GSM531671 3 0.0000 0.962 0.000 0.000 1.000 0.000 0.000
#> GSM531672 4 0.2891 0.878 0.176 0.000 0.000 0.824 0.000
#> GSM531673 4 0.2891 0.878 0.176 0.000 0.000 0.824 0.000
#> GSM531676 2 0.2891 0.883 0.000 0.824 0.000 0.176 0.000
#> GSM531679 2 0.0000 0.903 0.000 1.000 0.000 0.000 0.000
#> GSM531681 2 0.0000 0.903 0.000 1.000 0.000 0.000 0.000
#> GSM531682 2 0.0963 0.902 0.000 0.964 0.000 0.036 0.000
#> GSM531683 2 0.0000 0.903 0.000 1.000 0.000 0.000 0.000
#> GSM531684 4 0.0000 0.814 0.000 0.000 0.000 1.000 0.000
#> GSM531685 2 0.3003 0.876 0.000 0.812 0.000 0.188 0.000
#> GSM531686 2 0.0000 0.903 0.000 1.000 0.000 0.000 0.000
#> GSM531687 2 0.2891 0.883 0.000 0.824 0.000 0.176 0.000
#> GSM531688 2 0.2891 0.883 0.000 0.824 0.000 0.176 0.000
#> GSM531690 2 0.0000 0.903 0.000 1.000 0.000 0.000 0.000
#> GSM531693 4 0.0000 0.814 0.000 0.000 0.000 1.000 0.000
#> GSM531695 2 0.2891 0.883 0.000 0.824 0.000 0.176 0.000
#> GSM531603 4 0.0000 0.814 0.000 0.000 0.000 1.000 0.000
#> GSM531609 1 0.1851 0.834 0.912 0.000 0.000 0.088 0.000
#> GSM531611 2 0.3612 0.800 0.000 0.732 0.000 0.268 0.000
#> GSM531621 5 0.0000 0.988 0.000 0.000 0.000 0.000 1.000
#> GSM531622 3 0.0000 0.962 0.000 0.000 1.000 0.000 0.000
#> GSM531628 3 0.3305 0.675 0.224 0.000 0.776 0.000 0.000
#> GSM531630 3 0.0000 0.962 0.000 0.000 1.000 0.000 0.000
#> GSM531633 5 0.0000 0.988 0.000 0.000 0.000 0.000 1.000
#> GSM531635 3 0.0000 0.962 0.000 0.000 1.000 0.000 0.000
#> GSM531640 5 0.1341 0.939 0.000 0.000 0.056 0.000 0.944
#> GSM531649 3 0.0000 0.962 0.000 0.000 1.000 0.000 0.000
#> GSM531653 1 0.0000 0.917 1.000 0.000 0.000 0.000 0.000
#> GSM531657 4 0.2891 0.878 0.176 0.000 0.000 0.824 0.000
#> GSM531665 4 0.4114 0.593 0.376 0.000 0.000 0.624 0.000
#> GSM531670 1 0.0000 0.917 1.000 0.000 0.000 0.000 0.000
#> GSM531674 1 0.0000 0.917 1.000 0.000 0.000 0.000 0.000
#> GSM531675 2 0.0000 0.903 0.000 1.000 0.000 0.000 0.000
#> GSM531677 2 0.0000 0.903 0.000 1.000 0.000 0.000 0.000
#> GSM531678 2 0.2891 0.883 0.000 0.824 0.000 0.176 0.000
#> GSM531680 2 0.0000 0.903 0.000 1.000 0.000 0.000 0.000
#> GSM531689 2 0.2891 0.883 0.000 0.824 0.000 0.176 0.000
#> GSM531691 2 0.2891 0.883 0.000 0.824 0.000 0.176 0.000
#> GSM531692 4 0.1121 0.842 0.044 0.000 0.000 0.956 0.000
#> GSM531694 2 0.0000 0.903 0.000 1.000 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
#> GSM531602 2 0.0146 0.988 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM531604 4 0.0000 0.946 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531606 4 0.2562 0.757 0.000 0.000 0.000 0.828 0.172 0.000
#> GSM531607 5 0.3620 0.504 0.000 0.000 0.000 0.352 0.648 0.000
#> GSM531608 3 0.1531 0.787 0.000 0.000 0.928 0.000 0.004 0.068
#> GSM531610 4 0.0146 0.946 0.004 0.000 0.000 0.996 0.000 0.000
#> GSM531612 5 0.3266 0.782 0.000 0.272 0.000 0.000 0.728 0.000
#> GSM531613 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531614 1 0.0146 0.922 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM531616 3 0.0000 0.844 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531618 1 0.0000 0.924 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM531619 6 0.0000 0.945 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM531620 3 0.2631 0.847 0.000 0.000 0.820 0.000 0.180 0.000
#> GSM531623 3 0.0790 0.823 0.000 0.000 0.968 0.000 0.000 0.032
#> GSM531625 6 0.0000 0.945 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM531626 3 0.2969 0.844 0.000 0.000 0.776 0.000 0.224 0.000
#> GSM531632 3 0.2996 0.843 0.000 0.000 0.772 0.000 0.228 0.000
#> GSM531638 3 0.2996 0.843 0.000 0.000 0.772 0.000 0.228 0.000
#> GSM531639 1 0.0000 0.924 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM531641 4 0.0146 0.946 0.004 0.000 0.000 0.996 0.000 0.000
#> GSM531642 4 0.1814 0.865 0.100 0.000 0.000 0.900 0.000 0.000
#> GSM531643 1 0.0000 0.924 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM531644 1 0.0000 0.924 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM531645 1 0.0000 0.924 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM531646 3 0.2996 0.843 0.000 0.000 0.772 0.000 0.228 0.000
#> GSM531647 1 0.4382 0.613 0.696 0.000 0.076 0.000 0.228 0.000
#> GSM531648 1 0.0000 0.924 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM531650 1 0.0000 0.924 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM531651 6 0.0000 0.945 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM531652 1 0.0000 0.924 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM531656 1 0.0000 0.924 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM531659 4 0.0000 0.946 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531661 3 0.0000 0.844 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531662 1 0.1411 0.869 0.936 0.000 0.060 0.004 0.000 0.000
#> GSM531663 4 0.0000 0.946 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531664 1 0.3756 0.333 0.600 0.000 0.000 0.400 0.000 0.000
#> GSM531666 4 0.0713 0.932 0.028 0.000 0.000 0.972 0.000 0.000
#> GSM531667 3 0.1075 0.849 0.000 0.000 0.952 0.000 0.048 0.000
#> GSM531668 4 0.0146 0.946 0.004 0.000 0.000 0.996 0.000 0.000
#> GSM531669 1 0.3371 0.577 0.708 0.000 0.000 0.292 0.000 0.000
#> GSM531671 3 0.3136 0.842 0.000 0.000 0.768 0.004 0.228 0.000
#> GSM531672 4 0.0146 0.946 0.004 0.000 0.000 0.996 0.000 0.000
#> GSM531673 4 0.0000 0.946 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531676 5 0.3023 0.814 0.000 0.232 0.000 0.000 0.768 0.000
#> GSM531679 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531681 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531682 2 0.1327 0.906 0.000 0.936 0.000 0.000 0.064 0.000
#> GSM531683 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531684 5 0.3607 0.510 0.000 0.000 0.000 0.348 0.652 0.000
#> GSM531685 5 0.3023 0.814 0.000 0.232 0.000 0.000 0.768 0.000
#> GSM531686 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531687 5 0.3023 0.814 0.000 0.232 0.000 0.000 0.768 0.000
#> GSM531688 5 0.3023 0.814 0.000 0.232 0.000 0.000 0.768 0.000
#> GSM531690 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531693 5 0.3023 0.641 0.000 0.000 0.000 0.232 0.768 0.000
#> GSM531695 5 0.3023 0.814 0.000 0.232 0.000 0.000 0.768 0.000
#> GSM531603 5 0.3634 0.496 0.000 0.000 0.000 0.356 0.644 0.000
#> GSM531609 1 0.1010 0.895 0.960 0.000 0.000 0.036 0.004 0.000
#> GSM531611 5 0.3023 0.814 0.000 0.232 0.000 0.000 0.768 0.000
#> GSM531621 6 0.0000 0.945 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM531622 3 0.0000 0.844 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531628 3 0.5940 0.364 0.332 0.000 0.440 0.000 0.228 0.000
#> GSM531630 3 0.0000 0.844 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM531633 6 0.0000 0.945 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM531635 3 0.0547 0.849 0.000 0.000 0.980 0.000 0.020 0.000
#> GSM531640 6 0.3409 0.652 0.000 0.000 0.300 0.000 0.000 0.700
#> GSM531649 3 0.2996 0.843 0.000 0.000 0.772 0.000 0.228 0.000
#> GSM531653 1 0.0000 0.924 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM531657 4 0.0000 0.946 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM531665 4 0.2793 0.703 0.200 0.000 0.000 0.800 0.000 0.000
#> GSM531670 1 0.0000 0.924 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM531674 1 0.0000 0.924 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM531675 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531677 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531678 5 0.3684 0.671 0.000 0.372 0.000 0.000 0.628 0.000
#> GSM531680 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531689 5 0.3607 0.708 0.000 0.348 0.000 0.000 0.652 0.000
#> GSM531691 5 0.3126 0.805 0.000 0.248 0.000 0.000 0.752 0.000
#> GSM531692 4 0.1075 0.912 0.000 0.000 0.000 0.952 0.048 0.000
#> GSM531694 2 0.0000 0.992 0.000 1.000 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)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> ATC:pam 78 0.925 2
#> ATC:pam 76 0.369 3
#> ATC:pam 76 0.502 4
#> ATC:pam 79 0.660 5
#> ATC:pam 77 0.835 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "mclust"]
# you can also extract it by
# res = res_list["ATC:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 80 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 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.369 0.858 0.878 0.3311 0.647 0.647
#> 3 3 0.768 0.901 0.926 0.9242 0.690 0.530
#> 4 4 0.941 0.929 0.975 0.0557 0.915 0.779
#> 5 5 0.794 0.718 0.840 0.1062 0.897 0.693
#> 6 6 0.704 0.553 0.790 0.0628 0.959 0.839
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM531602 2 0.714 0.834 0.196 0.804
#> GSM531604 2 0.714 0.834 0.196 0.804
#> GSM531606 2 0.714 0.834 0.196 0.804
#> GSM531607 2 0.714 0.834 0.196 0.804
#> GSM531608 1 0.714 0.818 0.804 0.196
#> GSM531610 1 0.714 0.818 0.804 0.196
#> GSM531612 2 0.000 0.868 0.000 1.000
#> GSM531613 2 0.163 0.864 0.024 0.976
#> GSM531614 1 0.714 0.818 0.804 0.196
#> GSM531616 1 0.939 0.930 0.644 0.356
#> GSM531618 2 0.000 0.868 0.000 1.000
#> GSM531619 1 0.939 0.930 0.644 0.356
#> GSM531620 1 0.939 0.930 0.644 0.356
#> GSM531623 1 0.939 0.930 0.644 0.356
#> GSM531625 1 0.939 0.930 0.644 0.356
#> GSM531626 1 1.000 0.661 0.500 0.500
#> GSM531632 2 0.000 0.868 0.000 1.000
#> GSM531638 2 0.000 0.868 0.000 1.000
#> GSM531639 2 0.000 0.868 0.000 1.000
#> GSM531641 2 0.000 0.868 0.000 1.000
#> GSM531642 2 0.000 0.868 0.000 1.000
#> GSM531643 2 0.000 0.868 0.000 1.000
#> GSM531644 2 0.000 0.868 0.000 1.000
#> GSM531645 2 0.000 0.868 0.000 1.000
#> GSM531646 2 0.000 0.868 0.000 1.000
#> GSM531647 2 0.000 0.868 0.000 1.000
#> GSM531648 2 0.000 0.868 0.000 1.000
#> GSM531650 2 0.000 0.868 0.000 1.000
#> GSM531651 1 0.939 0.930 0.644 0.356
#> GSM531652 2 0.000 0.868 0.000 1.000
#> GSM531656 2 0.000 0.868 0.000 1.000
#> GSM531659 2 0.000 0.868 0.000 1.000
#> GSM531661 2 0.000 0.868 0.000 1.000
#> GSM531662 2 0.000 0.868 0.000 1.000
#> GSM531663 2 0.000 0.868 0.000 1.000
#> GSM531664 2 0.000 0.868 0.000 1.000
#> GSM531666 2 0.000 0.868 0.000 1.000
#> GSM531667 2 0.000 0.868 0.000 1.000
#> GSM531668 2 0.000 0.868 0.000 1.000
#> GSM531669 2 0.000 0.868 0.000 1.000
#> GSM531671 2 0.000 0.868 0.000 1.000
#> GSM531672 2 0.000 0.868 0.000 1.000
#> GSM531673 2 0.000 0.868 0.000 1.000
#> GSM531676 2 0.714 0.834 0.196 0.804
#> GSM531679 2 0.714 0.834 0.196 0.804
#> GSM531681 2 0.714 0.834 0.196 0.804
#> GSM531682 2 0.714 0.834 0.196 0.804
#> GSM531683 2 0.714 0.834 0.196 0.804
#> GSM531684 2 0.714 0.834 0.196 0.804
#> GSM531685 2 0.714 0.834 0.196 0.804
#> GSM531686 2 0.714 0.834 0.196 0.804
#> GSM531687 2 0.714 0.834 0.196 0.804
#> GSM531688 2 0.714 0.834 0.196 0.804
#> GSM531690 2 0.714 0.834 0.196 0.804
#> GSM531693 2 0.714 0.834 0.196 0.804
#> GSM531695 2 0.714 0.834 0.196 0.804
#> GSM531603 2 0.714 0.834 0.196 0.804
#> GSM531609 1 0.714 0.818 0.804 0.196
#> GSM531611 2 0.000 0.868 0.000 1.000
#> GSM531621 1 0.939 0.930 0.644 0.356
#> GSM531622 1 0.939 0.930 0.644 0.356
#> GSM531628 1 0.939 0.930 0.644 0.356
#> GSM531630 1 0.939 0.930 0.644 0.356
#> GSM531633 1 0.939 0.930 0.644 0.356
#> GSM531635 1 0.939 0.930 0.644 0.356
#> GSM531640 1 0.939 0.930 0.644 0.356
#> GSM531649 2 0.671 0.545 0.176 0.824
#> GSM531653 2 0.000 0.868 0.000 1.000
#> GSM531657 2 0.000 0.868 0.000 1.000
#> GSM531665 2 0.000 0.868 0.000 1.000
#> GSM531670 2 0.000 0.868 0.000 1.000
#> GSM531674 2 0.000 0.868 0.000 1.000
#> GSM531675 2 0.714 0.834 0.196 0.804
#> GSM531677 2 0.714 0.834 0.196 0.804
#> GSM531678 2 0.714 0.834 0.196 0.804
#> GSM531680 2 0.714 0.834 0.196 0.804
#> GSM531689 2 0.714 0.834 0.196 0.804
#> GSM531691 2 0.714 0.834 0.196 0.804
#> GSM531692 2 0.714 0.834 0.196 0.804
#> GSM531694 2 0.714 0.834 0.196 0.804
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM531602 2 0.0892 0.9955 0.020 0.980 0.000
#> GSM531604 2 0.0892 0.9955 0.020 0.980 0.000
#> GSM531606 2 0.0892 0.9955 0.020 0.980 0.000
#> GSM531607 2 0.2625 0.9178 0.084 0.916 0.000
#> GSM531608 3 0.3987 0.8547 0.108 0.020 0.872
#> GSM531610 3 0.5858 0.7587 0.240 0.020 0.740
#> GSM531612 1 0.3742 0.8835 0.892 0.036 0.072
#> GSM531613 1 0.6309 0.0822 0.504 0.496 0.000
#> GSM531614 3 0.3987 0.8547 0.108 0.020 0.872
#> GSM531616 3 0.1411 0.9537 0.036 0.000 0.964
#> GSM531618 1 0.3349 0.9026 0.888 0.004 0.108
#> GSM531619 3 0.1411 0.9537 0.036 0.000 0.964
#> GSM531620 3 0.1411 0.9537 0.036 0.000 0.964
#> GSM531623 3 0.1411 0.9537 0.036 0.000 0.964
#> GSM531625 3 0.1411 0.9537 0.036 0.000 0.964
#> GSM531626 1 0.3686 0.8823 0.860 0.000 0.140
#> GSM531632 1 0.3482 0.8895 0.872 0.000 0.128
#> GSM531638 1 0.3482 0.8895 0.872 0.000 0.128
#> GSM531639 1 0.3116 0.9024 0.892 0.000 0.108
#> GSM531641 1 0.4121 0.8961 0.868 0.024 0.108
#> GSM531642 1 0.3116 0.9024 0.892 0.000 0.108
#> GSM531643 1 0.3116 0.9024 0.892 0.000 0.108
#> GSM531644 1 0.3116 0.9024 0.892 0.000 0.108
#> GSM531645 1 0.3116 0.9024 0.892 0.000 0.108
#> GSM531646 1 0.3482 0.8895 0.872 0.000 0.128
#> GSM531647 1 0.3267 0.8979 0.884 0.000 0.116
#> GSM531648 1 0.3116 0.9024 0.892 0.000 0.108
#> GSM531650 1 0.3116 0.9024 0.892 0.000 0.108
#> GSM531651 3 0.1411 0.9537 0.036 0.000 0.964
#> GSM531652 1 0.3116 0.9024 0.892 0.000 0.108
#> GSM531656 1 0.3116 0.9024 0.892 0.000 0.108
#> GSM531659 1 0.1031 0.8593 0.976 0.024 0.000
#> GSM531661 1 0.5785 0.4561 0.696 0.004 0.300
#> GSM531662 1 0.0592 0.8642 0.988 0.012 0.000
#> GSM531663 1 0.1031 0.8593 0.976 0.024 0.000
#> GSM531664 1 0.3349 0.9026 0.888 0.004 0.108
#> GSM531666 1 0.4121 0.8961 0.868 0.024 0.108
#> GSM531667 1 0.3573 0.7747 0.876 0.004 0.120
#> GSM531668 1 0.1163 0.8569 0.972 0.028 0.000
#> GSM531669 1 0.3349 0.9026 0.888 0.004 0.108
#> GSM531671 1 0.1015 0.8627 0.980 0.012 0.008
#> GSM531672 1 0.1411 0.8515 0.964 0.036 0.000
#> GSM531673 1 0.1031 0.8593 0.976 0.024 0.000
#> GSM531676 2 0.0892 0.9955 0.020 0.980 0.000
#> GSM531679 2 0.0892 0.9955 0.020 0.980 0.000
#> GSM531681 2 0.0892 0.9955 0.020 0.980 0.000
#> GSM531682 2 0.0892 0.9955 0.020 0.980 0.000
#> GSM531683 2 0.0892 0.9955 0.020 0.980 0.000
#> GSM531684 2 0.0892 0.9955 0.020 0.980 0.000
#> GSM531685 2 0.0892 0.9955 0.020 0.980 0.000
#> GSM531686 2 0.0892 0.9955 0.020 0.980 0.000
#> GSM531687 2 0.0892 0.9955 0.020 0.980 0.000
#> GSM531688 2 0.0892 0.9955 0.020 0.980 0.000
#> GSM531690 2 0.0892 0.9955 0.020 0.980 0.000
#> GSM531693 2 0.1753 0.9690 0.048 0.952 0.000
#> GSM531695 2 0.0892 0.9955 0.020 0.980 0.000
#> GSM531603 1 0.6305 0.1256 0.516 0.484 0.000
#> GSM531609 3 0.3987 0.8547 0.108 0.020 0.872
#> GSM531611 1 0.1411 0.8515 0.964 0.036 0.000
#> GSM531621 3 0.1411 0.9537 0.036 0.000 0.964
#> GSM531622 3 0.1411 0.9537 0.036 0.000 0.964
#> GSM531628 3 0.1529 0.9498 0.040 0.000 0.960
#> GSM531630 3 0.1411 0.9537 0.036 0.000 0.964
#> GSM531633 3 0.1411 0.9537 0.036 0.000 0.964
#> GSM531635 3 0.1411 0.9537 0.036 0.000 0.964
#> GSM531640 3 0.1411 0.9537 0.036 0.000 0.964
#> GSM531649 1 0.3482 0.8895 0.872 0.000 0.128
#> GSM531653 1 0.3116 0.9024 0.892 0.000 0.108
#> GSM531657 1 0.1411 0.8515 0.964 0.036 0.000
#> GSM531665 1 0.1031 0.8593 0.976 0.024 0.000
#> GSM531670 1 0.3349 0.9026 0.888 0.004 0.108
#> GSM531674 1 0.3349 0.9026 0.888 0.004 0.108
#> GSM531675 2 0.0892 0.9955 0.020 0.980 0.000
#> GSM531677 2 0.0892 0.9955 0.020 0.980 0.000
#> GSM531678 2 0.0892 0.9955 0.020 0.980 0.000
#> GSM531680 2 0.0892 0.9955 0.020 0.980 0.000
#> GSM531689 2 0.0892 0.9955 0.020 0.980 0.000
#> GSM531691 2 0.0892 0.9955 0.020 0.980 0.000
#> GSM531692 2 0.0892 0.9955 0.020 0.980 0.000
#> GSM531694 2 0.0892 0.9955 0.020 0.980 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM531602 2 0.0000 0.9897 0.000 1.000 0.000 0.000
#> GSM531604 2 0.0000 0.9897 0.000 1.000 0.000 0.000
#> GSM531606 2 0.0000 0.9897 0.000 1.000 0.000 0.000
#> GSM531607 2 0.0336 0.9817 0.008 0.992 0.000 0.000
#> GSM531608 4 0.0000 1.0000 0.000 0.000 0.000 1.000
#> GSM531610 4 0.0000 1.0000 0.000 0.000 0.000 1.000
#> GSM531612 1 0.3356 0.7615 0.824 0.176 0.000 0.000
#> GSM531613 2 0.0336 0.9817 0.008 0.992 0.000 0.000
#> GSM531614 4 0.0000 1.0000 0.000 0.000 0.000 1.000
#> GSM531616 3 0.0000 0.8887 0.000 0.000 1.000 0.000
#> GSM531618 1 0.0000 0.9693 1.000 0.000 0.000 0.000
#> GSM531619 3 0.0000 0.8887 0.000 0.000 1.000 0.000
#> GSM531620 3 0.0921 0.8626 0.028 0.000 0.972 0.000
#> GSM531623 3 0.0000 0.8887 0.000 0.000 1.000 0.000
#> GSM531625 3 0.0000 0.8887 0.000 0.000 1.000 0.000
#> GSM531626 3 0.4999 0.0384 0.492 0.000 0.508 0.000
#> GSM531632 1 0.0000 0.9693 1.000 0.000 0.000 0.000
#> GSM531638 1 0.0336 0.9633 0.992 0.000 0.008 0.000
#> GSM531639 1 0.0000 0.9693 1.000 0.000 0.000 0.000
#> GSM531641 1 0.0000 0.9693 1.000 0.000 0.000 0.000
#> GSM531642 1 0.0000 0.9693 1.000 0.000 0.000 0.000
#> GSM531643 1 0.0000 0.9693 1.000 0.000 0.000 0.000
#> GSM531644 1 0.0000 0.9693 1.000 0.000 0.000 0.000
#> GSM531645 1 0.0000 0.9693 1.000 0.000 0.000 0.000
#> GSM531646 1 0.0188 0.9665 0.996 0.000 0.004 0.000
#> GSM531647 1 0.0000 0.9693 1.000 0.000 0.000 0.000
#> GSM531648 1 0.0000 0.9693 1.000 0.000 0.000 0.000
#> GSM531650 1 0.0000 0.9693 1.000 0.000 0.000 0.000
#> GSM531651 3 0.0000 0.8887 0.000 0.000 1.000 0.000
#> GSM531652 1 0.0000 0.9693 1.000 0.000 0.000 0.000
#> GSM531656 1 0.0000 0.9693 1.000 0.000 0.000 0.000
#> GSM531659 1 0.0000 0.9693 1.000 0.000 0.000 0.000
#> GSM531661 3 0.4843 0.3457 0.396 0.000 0.604 0.000
#> GSM531662 1 0.0188 0.9665 0.996 0.000 0.004 0.000
#> GSM531663 1 0.0000 0.9693 1.000 0.000 0.000 0.000
#> GSM531664 1 0.0000 0.9693 1.000 0.000 0.000 0.000
#> GSM531666 1 0.0000 0.9693 1.000 0.000 0.000 0.000
#> GSM531667 1 0.4072 0.6447 0.748 0.000 0.252 0.000
#> GSM531668 1 0.0000 0.9693 1.000 0.000 0.000 0.000
#> GSM531669 1 0.0000 0.9693 1.000 0.000 0.000 0.000
#> GSM531671 1 0.0336 0.9633 0.992 0.000 0.008 0.000
#> GSM531672 1 0.3539 0.7579 0.820 0.176 0.000 0.004
#> GSM531673 1 0.0000 0.9693 1.000 0.000 0.000 0.000
#> GSM531676 2 0.0000 0.9897 0.000 1.000 0.000 0.000
#> GSM531679 2 0.0000 0.9897 0.000 1.000 0.000 0.000
#> GSM531681 2 0.0000 0.9897 0.000 1.000 0.000 0.000
#> GSM531682 2 0.0000 0.9897 0.000 1.000 0.000 0.000
#> GSM531683 2 0.0000 0.9897 0.000 1.000 0.000 0.000
#> GSM531684 2 0.0000 0.9897 0.000 1.000 0.000 0.000
#> GSM531685 2 0.0000 0.9897 0.000 1.000 0.000 0.000
#> GSM531686 2 0.0000 0.9897 0.000 1.000 0.000 0.000
#> GSM531687 2 0.0000 0.9897 0.000 1.000 0.000 0.000
#> GSM531688 2 0.0000 0.9897 0.000 1.000 0.000 0.000
#> GSM531690 2 0.0000 0.9897 0.000 1.000 0.000 0.000
#> GSM531693 2 0.3266 0.7345 0.168 0.832 0.000 0.000
#> GSM531695 2 0.0000 0.9897 0.000 1.000 0.000 0.000
#> GSM531603 2 0.0336 0.9817 0.008 0.992 0.000 0.000
#> GSM531609 4 0.0000 1.0000 0.000 0.000 0.000 1.000
#> GSM531611 1 0.3569 0.7326 0.804 0.196 0.000 0.000
#> GSM531621 3 0.0000 0.8887 0.000 0.000 1.000 0.000
#> GSM531622 3 0.0000 0.8887 0.000 0.000 1.000 0.000
#> GSM531628 3 0.0921 0.8626 0.028 0.000 0.972 0.000
#> GSM531630 3 0.0000 0.8887 0.000 0.000 1.000 0.000
#> GSM531633 3 0.0000 0.8887 0.000 0.000 1.000 0.000
#> GSM531635 3 0.0000 0.8887 0.000 0.000 1.000 0.000
#> GSM531640 3 0.0000 0.8887 0.000 0.000 1.000 0.000
#> GSM531649 1 0.0336 0.9633 0.992 0.000 0.008 0.000
#> GSM531653 1 0.0000 0.9693 1.000 0.000 0.000 0.000
#> GSM531657 1 0.0000 0.9693 1.000 0.000 0.000 0.000
#> GSM531665 1 0.0000 0.9693 1.000 0.000 0.000 0.000
#> GSM531670 1 0.0000 0.9693 1.000 0.000 0.000 0.000
#> GSM531674 1 0.0000 0.9693 1.000 0.000 0.000 0.000
#> GSM531675 2 0.0000 0.9897 0.000 1.000 0.000 0.000
#> GSM531677 2 0.0000 0.9897 0.000 1.000 0.000 0.000
#> GSM531678 2 0.0000 0.9897 0.000 1.000 0.000 0.000
#> GSM531680 2 0.0000 0.9897 0.000 1.000 0.000 0.000
#> GSM531689 2 0.0000 0.9897 0.000 1.000 0.000 0.000
#> GSM531691 2 0.0000 0.9897 0.000 1.000 0.000 0.000
#> GSM531692 2 0.0000 0.9897 0.000 1.000 0.000 0.000
#> GSM531694 2 0.0000 0.9897 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM531602 2 0.0000 0.927936 0.000 1.000 0.000 0.000 0
#> GSM531604 2 0.1121 0.913901 0.000 0.956 0.000 0.044 0
#> GSM531606 2 0.1121 0.913901 0.000 0.956 0.000 0.044 0
#> GSM531607 2 0.0162 0.927206 0.000 0.996 0.000 0.004 0
#> GSM531608 5 0.0000 1.000000 0.000 0.000 0.000 0.000 1
#> GSM531610 5 0.0000 1.000000 0.000 0.000 0.000 0.000 1
#> GSM531612 4 0.2927 0.532657 0.040 0.092 0.000 0.868 0
#> GSM531613 2 0.4201 0.431082 0.000 0.592 0.000 0.408 0
#> GSM531614 5 0.0000 1.000000 0.000 0.000 0.000 0.000 1
#> GSM531616 3 0.0703 0.975731 0.000 0.000 0.976 0.024 0
#> GSM531618 1 0.3305 0.462474 0.776 0.000 0.000 0.224 0
#> GSM531619 3 0.0290 0.977702 0.000 0.000 0.992 0.008 0
#> GSM531620 3 0.0771 0.974857 0.004 0.000 0.976 0.020 0
#> GSM531623 3 0.0963 0.949382 0.036 0.000 0.964 0.000 0
#> GSM531625 3 0.0290 0.977702 0.000 0.000 0.992 0.008 0
#> GSM531626 1 0.2280 0.583305 0.880 0.000 0.120 0.000 0
#> GSM531632 1 0.0000 0.724425 1.000 0.000 0.000 0.000 0
#> GSM531638 1 0.0290 0.718523 0.992 0.000 0.008 0.000 0
#> GSM531639 1 0.2891 0.545218 0.824 0.000 0.000 0.176 0
#> GSM531641 4 0.4150 0.650737 0.388 0.000 0.000 0.612 0
#> GSM531642 1 0.4138 0.000301 0.616 0.000 0.000 0.384 0
#> GSM531643 1 0.0000 0.724425 1.000 0.000 0.000 0.000 0
#> GSM531644 1 0.0000 0.724425 1.000 0.000 0.000 0.000 0
#> GSM531645 1 0.0000 0.724425 1.000 0.000 0.000 0.000 0
#> GSM531646 1 0.0290 0.718523 0.992 0.000 0.008 0.000 0
#> GSM531647 1 0.0000 0.724425 1.000 0.000 0.000 0.000 0
#> GSM531648 1 0.0000 0.724425 1.000 0.000 0.000 0.000 0
#> GSM531650 1 0.0000 0.724425 1.000 0.000 0.000 0.000 0
#> GSM531651 3 0.0290 0.977702 0.000 0.000 0.992 0.008 0
#> GSM531652 1 0.0000 0.724425 1.000 0.000 0.000 0.000 0
#> GSM531656 1 0.0000 0.724425 1.000 0.000 0.000 0.000 0
#> GSM531659 4 0.4138 0.657096 0.384 0.000 0.000 0.616 0
#> GSM531661 4 0.6506 0.439907 0.344 0.000 0.200 0.456 0
#> GSM531662 1 0.4278 -0.240785 0.548 0.000 0.000 0.452 0
#> GSM531663 4 0.4074 0.666242 0.364 0.000 0.000 0.636 0
#> GSM531664 1 0.4278 -0.240785 0.548 0.000 0.000 0.452 0
#> GSM531666 4 0.4307 0.347749 0.500 0.000 0.000 0.500 0
#> GSM531667 4 0.6299 0.433761 0.380 0.000 0.156 0.464 0
#> GSM531668 4 0.4101 0.665136 0.372 0.000 0.000 0.628 0
#> GSM531669 1 0.4278 -0.240785 0.548 0.000 0.000 0.452 0
#> GSM531671 1 0.4278 -0.240785 0.548 0.000 0.000 0.452 0
#> GSM531672 4 0.2946 0.537925 0.044 0.088 0.000 0.868 0
#> GSM531673 4 0.4126 0.660695 0.380 0.000 0.000 0.620 0
#> GSM531676 2 0.1410 0.909194 0.000 0.940 0.000 0.060 0
#> GSM531679 2 0.0000 0.927936 0.000 1.000 0.000 0.000 0
#> GSM531681 2 0.0000 0.927936 0.000 1.000 0.000 0.000 0
#> GSM531682 2 0.0162 0.927206 0.000 0.996 0.000 0.004 0
#> GSM531683 2 0.0000 0.927936 0.000 1.000 0.000 0.000 0
#> GSM531684 2 0.1270 0.912079 0.000 0.948 0.000 0.052 0
#> GSM531685 2 0.2280 0.878331 0.000 0.880 0.000 0.120 0
#> GSM531686 2 0.0000 0.927936 0.000 1.000 0.000 0.000 0
#> GSM531687 2 0.2280 0.876720 0.000 0.880 0.000 0.120 0
#> GSM531688 2 0.2280 0.876720 0.000 0.880 0.000 0.120 0
#> GSM531690 2 0.0000 0.927936 0.000 1.000 0.000 0.000 0
#> GSM531693 2 0.3309 0.839306 0.036 0.836 0.000 0.128 0
#> GSM531695 2 0.1732 0.893253 0.000 0.920 0.000 0.080 0
#> GSM531603 2 0.4307 0.248174 0.000 0.500 0.000 0.500 0
#> GSM531609 5 0.0000 1.000000 0.000 0.000 0.000 0.000 1
#> GSM531611 4 0.2927 0.532657 0.040 0.092 0.000 0.868 0
#> GSM531621 3 0.0290 0.977702 0.000 0.000 0.992 0.008 0
#> GSM531622 3 0.0703 0.975731 0.000 0.000 0.976 0.024 0
#> GSM531628 3 0.1270 0.922809 0.052 0.000 0.948 0.000 0
#> GSM531630 3 0.0703 0.975731 0.000 0.000 0.976 0.024 0
#> GSM531633 3 0.0290 0.977702 0.000 0.000 0.992 0.008 0
#> GSM531635 3 0.0703 0.975731 0.000 0.000 0.976 0.024 0
#> GSM531640 3 0.0290 0.977702 0.000 0.000 0.992 0.008 0
#> GSM531649 1 0.0880 0.693393 0.968 0.000 0.032 0.000 0
#> GSM531653 1 0.0000 0.724425 1.000 0.000 0.000 0.000 0
#> GSM531657 4 0.3508 0.635691 0.252 0.000 0.000 0.748 0
#> GSM531665 4 0.4138 0.657096 0.384 0.000 0.000 0.616 0
#> GSM531670 1 0.4273 -0.227785 0.552 0.000 0.000 0.448 0
#> GSM531674 1 0.3913 0.188662 0.676 0.000 0.000 0.324 0
#> GSM531675 2 0.0000 0.927936 0.000 1.000 0.000 0.000 0
#> GSM531677 2 0.0000 0.927936 0.000 1.000 0.000 0.000 0
#> GSM531678 2 0.0000 0.927936 0.000 1.000 0.000 0.000 0
#> GSM531680 2 0.0290 0.926961 0.000 0.992 0.000 0.008 0
#> GSM531689 2 0.0290 0.927149 0.000 0.992 0.000 0.008 0
#> GSM531691 2 0.1341 0.910422 0.000 0.944 0.000 0.056 0
#> GSM531692 2 0.2020 0.890191 0.000 0.900 0.000 0.100 0
#> GSM531694 2 0.0000 0.927936 0.000 1.000 0.000 0.000 0
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM531602 2 0.0000 0.6702 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531604 2 0.2969 0.4315 0.000 0.776 0.000 0.000 0.224 0.000
#> GSM531606 2 0.2597 0.4973 0.000 0.824 0.000 0.000 0.176 0.000
#> GSM531607 2 0.0000 0.6702 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531608 6 0.3266 1.0000 0.000 0.000 0.000 0.000 0.272 0.728
#> GSM531610 6 0.3266 1.0000 0.000 0.000 0.000 0.000 0.272 0.728
#> GSM531612 4 0.2915 0.3822 0.008 0.184 0.000 0.808 0.000 0.000
#> GSM531613 2 0.4039 0.1531 0.008 0.568 0.000 0.424 0.000 0.000
#> GSM531614 6 0.3266 1.0000 0.000 0.000 0.000 0.000 0.272 0.728
#> GSM531616 3 0.0713 0.8329 0.000 0.000 0.972 0.000 0.028 0.000
#> GSM531618 1 0.3927 0.4466 0.712 0.000 0.000 0.260 0.004 0.024
#> GSM531619 3 0.2860 0.8265 0.000 0.000 0.852 0.100 0.048 0.000
#> GSM531620 3 0.0146 0.8357 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM531623 3 0.0777 0.8309 0.024 0.000 0.972 0.004 0.000 0.000
#> GSM531625 3 0.2860 0.8265 0.000 0.000 0.852 0.100 0.048 0.000
#> GSM531626 1 0.3795 0.3531 0.632 0.000 0.364 0.004 0.000 0.000
#> GSM531632 1 0.2969 0.6779 0.860 0.000 0.088 0.020 0.000 0.032
#> GSM531638 1 0.2006 0.6603 0.892 0.000 0.104 0.004 0.000 0.000
#> GSM531639 1 0.3555 0.6164 0.780 0.000 0.000 0.044 0.000 0.176
#> GSM531641 4 0.5289 0.5828 0.280 0.000 0.000 0.580 0.000 0.140
#> GSM531642 1 0.3618 0.6133 0.776 0.000 0.000 0.048 0.000 0.176
#> GSM531643 1 0.0547 0.6940 0.980 0.000 0.000 0.020 0.000 0.000
#> GSM531644 1 0.1007 0.6839 0.956 0.000 0.000 0.044 0.000 0.000
#> GSM531645 1 0.3699 0.2394 0.660 0.000 0.000 0.336 0.004 0.000
#> GSM531646 1 0.1765 0.6676 0.904 0.000 0.096 0.000 0.000 0.000
#> GSM531647 1 0.1714 0.6697 0.908 0.000 0.092 0.000 0.000 0.000
#> GSM531648 1 0.3468 0.3687 0.712 0.000 0.000 0.284 0.004 0.000
#> GSM531650 1 0.0000 0.6922 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM531651 3 0.2860 0.8265 0.000 0.000 0.852 0.100 0.048 0.000
#> GSM531652 1 0.0632 0.6899 0.976 0.000 0.000 0.024 0.000 0.000
#> GSM531656 1 0.1141 0.6801 0.948 0.000 0.000 0.052 0.000 0.000
#> GSM531659 4 0.6070 0.6201 0.240 0.000 0.000 0.480 0.008 0.272
#> GSM531661 3 0.6269 0.2863 0.104 0.000 0.556 0.060 0.008 0.272
#> GSM531662 1 0.4610 0.5134 0.664 0.000 0.000 0.056 0.008 0.272
#> GSM531663 4 0.5654 0.6664 0.188 0.000 0.000 0.552 0.004 0.256
#> GSM531664 1 0.4405 0.5396 0.688 0.000 0.000 0.072 0.000 0.240
#> GSM531666 1 0.5841 -0.0221 0.488 0.000 0.000 0.328 0.004 0.180
#> GSM531667 3 0.6361 0.2541 0.120 0.000 0.544 0.056 0.008 0.272
#> GSM531668 4 0.5861 0.6486 0.224 0.000 0.000 0.512 0.004 0.260
#> GSM531669 1 0.4312 0.5223 0.676 0.000 0.000 0.052 0.000 0.272
#> GSM531671 1 0.6007 0.4999 0.580 0.000 0.088 0.052 0.008 0.272
#> GSM531672 4 0.3664 0.4610 0.080 0.108 0.000 0.804 0.000 0.008
#> GSM531673 4 0.5908 0.6411 0.228 0.000 0.000 0.500 0.004 0.268
#> GSM531676 2 0.3833 -0.2819 0.000 0.556 0.000 0.000 0.444 0.000
#> GSM531679 2 0.0000 0.6702 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531681 2 0.0000 0.6702 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531682 2 0.2697 0.4572 0.000 0.812 0.000 0.000 0.188 0.000
#> GSM531683 2 0.0000 0.6702 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531684 2 0.2793 0.4747 0.000 0.800 0.000 0.000 0.200 0.000
#> GSM531685 2 0.4072 -0.3124 0.000 0.544 0.000 0.008 0.448 0.000
#> GSM531686 2 0.0260 0.6660 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM531687 2 0.4072 -0.3124 0.000 0.544 0.000 0.008 0.448 0.000
#> GSM531688 2 0.4072 -0.3124 0.000 0.544 0.000 0.008 0.448 0.000
#> GSM531690 2 0.0000 0.6702 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531693 5 0.7196 0.5443 0.160 0.332 0.000 0.044 0.424 0.040
#> GSM531695 2 0.4032 -0.2388 0.000 0.572 0.000 0.008 0.420 0.000
#> GSM531603 2 0.3934 0.1973 0.008 0.616 0.000 0.376 0.000 0.000
#> GSM531609 6 0.3266 1.0000 0.000 0.000 0.000 0.000 0.272 0.728
#> GSM531611 4 0.2915 0.3822 0.008 0.184 0.000 0.808 0.000 0.000
#> GSM531621 3 0.2812 0.8266 0.000 0.000 0.856 0.096 0.048 0.000
#> GSM531622 3 0.0291 0.8358 0.000 0.000 0.992 0.004 0.004 0.000
#> GSM531628 3 0.1984 0.7746 0.056 0.000 0.912 0.032 0.000 0.000
#> GSM531630 3 0.0713 0.8329 0.000 0.000 0.972 0.000 0.028 0.000
#> GSM531633 3 0.2812 0.8266 0.000 0.000 0.856 0.096 0.048 0.000
#> GSM531635 3 0.0713 0.8329 0.000 0.000 0.972 0.000 0.028 0.000
#> GSM531640 3 0.2812 0.8266 0.000 0.000 0.856 0.096 0.048 0.000
#> GSM531649 1 0.2597 0.6016 0.824 0.000 0.176 0.000 0.000 0.000
#> GSM531653 1 0.0146 0.6923 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM531657 4 0.5055 0.6566 0.184 0.000 0.000 0.652 0.004 0.160
#> GSM531665 4 0.6125 0.6293 0.232 0.000 0.000 0.484 0.012 0.272
#> GSM531670 1 0.4270 0.5325 0.684 0.000 0.000 0.052 0.000 0.264
#> GSM531674 1 0.3964 0.5742 0.724 0.000 0.000 0.044 0.000 0.232
#> GSM531675 2 0.0000 0.6702 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531677 2 0.0000 0.6702 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531678 2 0.0000 0.6702 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM531680 2 0.1765 0.5911 0.000 0.904 0.000 0.000 0.096 0.000
#> GSM531689 2 0.1610 0.6055 0.000 0.916 0.000 0.000 0.084 0.000
#> GSM531691 2 0.3810 -0.2401 0.000 0.572 0.000 0.000 0.428 0.000
#> GSM531692 5 0.3695 0.4604 0.000 0.376 0.000 0.000 0.624 0.000
#> GSM531694 2 0.0000 0.6702 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> ATC:mclust 80 0.220 2
#> ATC:mclust 77 0.130 3
#> ATC:mclust 78 0.168 4
#> ATC:mclust 67 0.248 5
#> ATC:mclust 56 0.439 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "NMF"]
# you can also extract it by
# res = res_list["ATC:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 80 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.949 0.954 0.979 0.4937 0.502 0.502
#> 3 3 0.903 0.892 0.955 0.3257 0.766 0.564
#> 4 4 0.694 0.718 0.858 0.0587 0.835 0.608
#> 5 5 0.532 0.457 0.705 0.0747 0.929 0.805
#> 6 6 0.551 0.381 0.618 0.0514 0.886 0.666
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
#> GSM531602 2 0.0000 0.961 0.000 1.000
#> GSM531604 2 0.8499 0.645 0.276 0.724
#> GSM531606 2 0.3114 0.920 0.056 0.944
#> GSM531607 2 0.0000 0.961 0.000 1.000
#> GSM531608 1 0.0000 0.992 1.000 0.000
#> GSM531610 2 0.0376 0.958 0.004 0.996
#> GSM531612 2 0.0000 0.961 0.000 1.000
#> GSM531613 2 0.0000 0.961 0.000 1.000
#> GSM531614 1 0.0000 0.992 1.000 0.000
#> GSM531616 1 0.0000 0.992 1.000 0.000
#> GSM531618 1 0.0000 0.992 1.000 0.000
#> GSM531619 1 0.0000 0.992 1.000 0.000
#> GSM531620 1 0.0000 0.992 1.000 0.000
#> GSM531623 1 0.0000 0.992 1.000 0.000
#> GSM531625 1 0.0000 0.992 1.000 0.000
#> GSM531626 1 0.0000 0.992 1.000 0.000
#> GSM531632 1 0.0000 0.992 1.000 0.000
#> GSM531638 1 0.0000 0.992 1.000 0.000
#> GSM531639 1 0.0000 0.992 1.000 0.000
#> GSM531641 2 0.2043 0.939 0.032 0.968
#> GSM531642 1 0.3114 0.940 0.944 0.056
#> GSM531643 1 0.0000 0.992 1.000 0.000
#> GSM531644 1 0.0000 0.992 1.000 0.000
#> GSM531645 1 0.0000 0.992 1.000 0.000
#> GSM531646 1 0.0000 0.992 1.000 0.000
#> GSM531647 1 0.0000 0.992 1.000 0.000
#> GSM531648 1 0.0000 0.992 1.000 0.000
#> GSM531650 1 0.0000 0.992 1.000 0.000
#> GSM531651 1 0.0000 0.992 1.000 0.000
#> GSM531652 1 0.0000 0.992 1.000 0.000
#> GSM531656 1 0.0000 0.992 1.000 0.000
#> GSM531659 2 0.8267 0.672 0.260 0.740
#> GSM531661 1 0.0000 0.992 1.000 0.000
#> GSM531662 1 0.0000 0.992 1.000 0.000
#> GSM531663 1 0.4022 0.915 0.920 0.080
#> GSM531664 2 0.9933 0.220 0.452 0.548
#> GSM531666 2 0.0672 0.956 0.008 0.992
#> GSM531667 1 0.0000 0.992 1.000 0.000
#> GSM531668 1 0.1633 0.971 0.976 0.024
#> GSM531669 1 0.0672 0.985 0.992 0.008
#> GSM531671 1 0.0000 0.992 1.000 0.000
#> GSM531672 2 0.0000 0.961 0.000 1.000
#> GSM531673 1 0.4022 0.915 0.920 0.080
#> GSM531676 2 0.0000 0.961 0.000 1.000
#> GSM531679 2 0.0000 0.961 0.000 1.000
#> GSM531681 2 0.0000 0.961 0.000 1.000
#> GSM531682 2 0.0000 0.961 0.000 1.000
#> GSM531683 2 0.0000 0.961 0.000 1.000
#> GSM531684 2 0.0000 0.961 0.000 1.000
#> GSM531685 2 0.0000 0.961 0.000 1.000
#> GSM531686 2 0.0000 0.961 0.000 1.000
#> GSM531687 2 0.0000 0.961 0.000 1.000
#> GSM531688 2 0.0000 0.961 0.000 1.000
#> GSM531690 2 0.0000 0.961 0.000 1.000
#> GSM531693 2 0.4815 0.876 0.104 0.896
#> GSM531695 2 0.0000 0.961 0.000 1.000
#> GSM531603 2 0.0000 0.961 0.000 1.000
#> GSM531609 1 0.0000 0.992 1.000 0.000
#> GSM531611 2 0.0000 0.961 0.000 1.000
#> GSM531621 1 0.0000 0.992 1.000 0.000
#> GSM531622 1 0.0000 0.992 1.000 0.000
#> GSM531628 1 0.0000 0.992 1.000 0.000
#> GSM531630 1 0.0000 0.992 1.000 0.000
#> GSM531633 1 0.0000 0.992 1.000 0.000
#> GSM531635 1 0.0000 0.992 1.000 0.000
#> GSM531640 1 0.0000 0.992 1.000 0.000
#> GSM531649 1 0.0000 0.992 1.000 0.000
#> GSM531653 1 0.0000 0.992 1.000 0.000
#> GSM531657 2 0.5408 0.855 0.124 0.876
#> GSM531665 1 0.0000 0.992 1.000 0.000
#> GSM531670 1 0.0000 0.992 1.000 0.000
#> GSM531674 1 0.0000 0.992 1.000 0.000
#> GSM531675 2 0.0000 0.961 0.000 1.000
#> GSM531677 2 0.0000 0.961 0.000 1.000
#> GSM531678 2 0.0000 0.961 0.000 1.000
#> GSM531680 2 0.0000 0.961 0.000 1.000
#> GSM531689 2 0.0000 0.961 0.000 1.000
#> GSM531691 2 0.0000 0.961 0.000 1.000
#> GSM531692 1 0.4690 0.890 0.900 0.100
#> GSM531694 2 0.0000 0.961 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM531602 2 0.0000 0.9496 0.000 1.000 0.000
#> GSM531604 2 0.5465 0.6034 0.000 0.712 0.288
#> GSM531606 2 0.2878 0.8607 0.000 0.904 0.096
#> GSM531607 2 0.0000 0.9496 0.000 1.000 0.000
#> GSM531608 3 0.0000 0.9712 0.000 0.000 1.000
#> GSM531610 1 0.0475 0.9072 0.992 0.004 0.004
#> GSM531612 1 0.0237 0.9057 0.996 0.004 0.000
#> GSM531613 1 0.2796 0.8365 0.908 0.092 0.000
#> GSM531614 3 0.0000 0.9712 0.000 0.000 1.000
#> GSM531616 3 0.0000 0.9712 0.000 0.000 1.000
#> GSM531618 1 0.6299 0.1770 0.524 0.000 0.476
#> GSM531619 3 0.0000 0.9712 0.000 0.000 1.000
#> GSM531620 3 0.0000 0.9712 0.000 0.000 1.000
#> GSM531623 3 0.0000 0.9712 0.000 0.000 1.000
#> GSM531625 3 0.0000 0.9712 0.000 0.000 1.000
#> GSM531626 3 0.0000 0.9712 0.000 0.000 1.000
#> GSM531632 3 0.0000 0.9712 0.000 0.000 1.000
#> GSM531638 3 0.0000 0.9712 0.000 0.000 1.000
#> GSM531639 1 0.1163 0.9067 0.972 0.000 0.028
#> GSM531641 1 0.0000 0.9071 1.000 0.000 0.000
#> GSM531642 1 0.0000 0.9071 1.000 0.000 0.000
#> GSM531643 1 0.2448 0.8785 0.924 0.000 0.076
#> GSM531644 1 0.1031 0.9078 0.976 0.000 0.024
#> GSM531645 1 0.0237 0.9079 0.996 0.000 0.004
#> GSM531646 3 0.0000 0.9712 0.000 0.000 1.000
#> GSM531647 3 0.1163 0.9504 0.028 0.000 0.972
#> GSM531648 1 0.1031 0.9079 0.976 0.000 0.024
#> GSM531650 1 0.1411 0.9030 0.964 0.000 0.036
#> GSM531651 3 0.0000 0.9712 0.000 0.000 1.000
#> GSM531652 1 0.1031 0.9076 0.976 0.000 0.024
#> GSM531656 1 0.5706 0.5704 0.680 0.000 0.320
#> GSM531659 2 0.8939 0.0184 0.124 0.440 0.436
#> GSM531661 3 0.0000 0.9712 0.000 0.000 1.000
#> GSM531662 3 0.0000 0.9712 0.000 0.000 1.000
#> GSM531663 3 0.1491 0.9507 0.016 0.016 0.968
#> GSM531664 1 0.0000 0.9071 1.000 0.000 0.000
#> GSM531666 1 0.0000 0.9071 1.000 0.000 0.000
#> GSM531667 3 0.0000 0.9712 0.000 0.000 1.000
#> GSM531668 3 0.0424 0.9660 0.008 0.000 0.992
#> GSM531669 1 0.6154 0.3750 0.592 0.000 0.408
#> GSM531671 3 0.0000 0.9712 0.000 0.000 1.000
#> GSM531672 1 0.0000 0.9071 1.000 0.000 0.000
#> GSM531673 3 0.1620 0.9465 0.012 0.024 0.964
#> GSM531676 2 0.0000 0.9496 0.000 1.000 0.000
#> GSM531679 2 0.0000 0.9496 0.000 1.000 0.000
#> GSM531681 2 0.0000 0.9496 0.000 1.000 0.000
#> GSM531682 2 0.0000 0.9496 0.000 1.000 0.000
#> GSM531683 2 0.0000 0.9496 0.000 1.000 0.000
#> GSM531684 2 0.0237 0.9467 0.000 0.996 0.004
#> GSM531685 2 0.0000 0.9496 0.000 1.000 0.000
#> GSM531686 2 0.0000 0.9496 0.000 1.000 0.000
#> GSM531687 2 0.0000 0.9496 0.000 1.000 0.000
#> GSM531688 2 0.0000 0.9496 0.000 1.000 0.000
#> GSM531690 2 0.0000 0.9496 0.000 1.000 0.000
#> GSM531693 2 0.3816 0.8036 0.000 0.852 0.148
#> GSM531695 2 0.0592 0.9414 0.012 0.988 0.000
#> GSM531603 2 0.0000 0.9496 0.000 1.000 0.000
#> GSM531609 1 0.3816 0.8104 0.852 0.000 0.148
#> GSM531611 1 0.0000 0.9071 1.000 0.000 0.000
#> GSM531621 3 0.0000 0.9712 0.000 0.000 1.000
#> GSM531622 3 0.0000 0.9712 0.000 0.000 1.000
#> GSM531628 3 0.0747 0.9603 0.016 0.000 0.984
#> GSM531630 3 0.0000 0.9712 0.000 0.000 1.000
#> GSM531633 3 0.0000 0.9712 0.000 0.000 1.000
#> GSM531635 3 0.0000 0.9712 0.000 0.000 1.000
#> GSM531640 3 0.0000 0.9712 0.000 0.000 1.000
#> GSM531649 3 0.0000 0.9712 0.000 0.000 1.000
#> GSM531653 3 0.5291 0.5965 0.268 0.000 0.732
#> GSM531657 1 0.0892 0.9074 0.980 0.000 0.020
#> GSM531665 3 0.0000 0.9712 0.000 0.000 1.000
#> GSM531670 3 0.0747 0.9603 0.016 0.000 0.984
#> GSM531674 3 0.2261 0.9091 0.068 0.000 0.932
#> GSM531675 2 0.0000 0.9496 0.000 1.000 0.000
#> GSM531677 2 0.0000 0.9496 0.000 1.000 0.000
#> GSM531678 2 0.0000 0.9496 0.000 1.000 0.000
#> GSM531680 2 0.0747 0.9386 0.016 0.984 0.000
#> GSM531689 2 0.0000 0.9496 0.000 1.000 0.000
#> GSM531691 2 0.0000 0.9496 0.000 1.000 0.000
#> GSM531692 3 0.5882 0.4305 0.000 0.348 0.652
#> GSM531694 2 0.0000 0.9496 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM531602 2 0.0188 0.9425 0.000 0.996 0.000 0.004
#> GSM531604 2 0.3215 0.8554 0.092 0.876 0.032 0.000
#> GSM531606 2 0.1059 0.9315 0.012 0.972 0.016 0.000
#> GSM531607 2 0.1936 0.9259 0.028 0.940 0.000 0.032
#> GSM531608 1 0.1867 0.6748 0.928 0.000 0.072 0.000
#> GSM531610 4 0.5345 0.2995 0.428 0.012 0.000 0.560
#> GSM531612 4 0.2282 0.7530 0.052 0.024 0.000 0.924
#> GSM531613 4 0.3312 0.7065 0.052 0.072 0.000 0.876
#> GSM531614 1 0.1970 0.6710 0.932 0.000 0.060 0.008
#> GSM531616 3 0.3172 0.7330 0.160 0.000 0.840 0.000
#> GSM531618 3 0.3074 0.6940 0.000 0.000 0.848 0.152
#> GSM531619 3 0.4994 0.1090 0.480 0.000 0.520 0.000
#> GSM531620 3 0.3528 0.7246 0.192 0.000 0.808 0.000
#> GSM531623 3 0.4222 0.6260 0.272 0.000 0.728 0.000
#> GSM531625 3 0.4522 0.5679 0.320 0.000 0.680 0.000
#> GSM531626 3 0.2921 0.7356 0.140 0.000 0.860 0.000
#> GSM531632 3 0.0921 0.7527 0.028 0.000 0.972 0.000
#> GSM531638 3 0.2704 0.7447 0.124 0.000 0.876 0.000
#> GSM531639 3 0.3583 0.6611 0.004 0.000 0.816 0.180
#> GSM531641 4 0.0657 0.7783 0.012 0.000 0.004 0.984
#> GSM531642 4 0.2773 0.7589 0.004 0.000 0.116 0.880
#> GSM531643 3 0.3105 0.6951 0.004 0.000 0.856 0.140
#> GSM531644 3 0.5158 0.0174 0.004 0.000 0.524 0.472
#> GSM531645 4 0.2271 0.7788 0.008 0.000 0.076 0.916
#> GSM531646 3 0.0336 0.7508 0.008 0.000 0.992 0.000
#> GSM531647 3 0.2197 0.7253 0.004 0.000 0.916 0.080
#> GSM531648 4 0.2469 0.7688 0.000 0.000 0.108 0.892
#> GSM531650 3 0.4905 0.3590 0.004 0.000 0.632 0.364
#> GSM531651 1 0.4989 -0.1950 0.528 0.000 0.472 0.000
#> GSM531652 4 0.4889 0.4524 0.004 0.000 0.360 0.636
#> GSM531656 3 0.3726 0.6340 0.000 0.000 0.788 0.212
#> GSM531659 3 0.5241 0.5985 0.008 0.136 0.768 0.088
#> GSM531661 3 0.3486 0.7069 0.188 0.000 0.812 0.000
#> GSM531662 3 0.3464 0.7377 0.076 0.056 0.868 0.000
#> GSM531663 3 0.2718 0.7336 0.012 0.020 0.912 0.056
#> GSM531664 4 0.5138 0.4009 0.008 0.000 0.392 0.600
#> GSM531666 4 0.2530 0.7683 0.004 0.000 0.100 0.896
#> GSM531667 3 0.4040 0.6491 0.248 0.000 0.752 0.000
#> GSM531668 3 0.3289 0.7445 0.140 0.004 0.852 0.004
#> GSM531669 3 0.2918 0.7103 0.008 0.000 0.876 0.116
#> GSM531671 3 0.2530 0.7497 0.100 0.004 0.896 0.000
#> GSM531672 4 0.2142 0.7572 0.056 0.016 0.000 0.928
#> GSM531673 3 0.2719 0.7343 0.024 0.020 0.916 0.040
#> GSM531676 2 0.0336 0.9414 0.008 0.992 0.000 0.000
#> GSM531679 2 0.0672 0.9414 0.008 0.984 0.000 0.008
#> GSM531681 2 0.0000 0.9425 0.000 1.000 0.000 0.000
#> GSM531682 2 0.0804 0.9408 0.012 0.980 0.000 0.008
#> GSM531683 2 0.0804 0.9410 0.008 0.980 0.000 0.012
#> GSM531684 2 0.0927 0.9333 0.008 0.976 0.016 0.000
#> GSM531685 2 0.0336 0.9414 0.008 0.992 0.000 0.000
#> GSM531686 2 0.2586 0.9107 0.040 0.912 0.000 0.048
#> GSM531687 2 0.0336 0.9414 0.008 0.992 0.000 0.000
#> GSM531688 2 0.0524 0.9416 0.008 0.988 0.000 0.004
#> GSM531690 2 0.2131 0.9223 0.036 0.932 0.000 0.032
#> GSM531693 2 0.2198 0.8828 0.008 0.920 0.072 0.000
#> GSM531695 2 0.2313 0.9188 0.032 0.924 0.000 0.044
#> GSM531603 2 0.3128 0.8878 0.040 0.884 0.000 0.076
#> GSM531609 1 0.5035 0.4375 0.748 0.000 0.056 0.196
#> GSM531611 4 0.2483 0.7468 0.052 0.032 0.000 0.916
#> GSM531621 3 0.4713 0.5039 0.360 0.000 0.640 0.000
#> GSM531622 3 0.3172 0.7276 0.160 0.000 0.840 0.000
#> GSM531628 3 0.3356 0.7328 0.176 0.000 0.824 0.000
#> GSM531630 3 0.3486 0.7165 0.188 0.000 0.812 0.000
#> GSM531633 3 0.4697 0.5105 0.356 0.000 0.644 0.000
#> GSM531635 3 0.3074 0.7358 0.152 0.000 0.848 0.000
#> GSM531640 3 0.4925 0.3362 0.428 0.000 0.572 0.000
#> GSM531649 3 0.2216 0.7496 0.092 0.000 0.908 0.000
#> GSM531653 3 0.2773 0.7114 0.004 0.000 0.880 0.116
#> GSM531657 4 0.1488 0.7833 0.012 0.000 0.032 0.956
#> GSM531665 3 0.3674 0.6961 0.036 0.116 0.848 0.000
#> GSM531670 3 0.2342 0.7238 0.008 0.000 0.912 0.080
#> GSM531674 3 0.2611 0.7185 0.008 0.000 0.896 0.096
#> GSM531675 2 0.0804 0.9408 0.012 0.980 0.000 0.008
#> GSM531677 2 0.2131 0.9223 0.036 0.932 0.000 0.032
#> GSM531678 2 0.0000 0.9425 0.000 1.000 0.000 0.000
#> GSM531680 2 0.2751 0.9051 0.040 0.904 0.000 0.056
#> GSM531689 2 0.0336 0.9414 0.008 0.992 0.000 0.000
#> GSM531691 2 0.0336 0.9414 0.008 0.992 0.000 0.000
#> GSM531692 2 0.7133 0.1643 0.332 0.520 0.148 0.000
#> GSM531694 2 0.0188 0.9421 0.004 0.996 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM531602 2 0.3928 0.5600 0.004 0.700 0.000 0.000 0.296
#> GSM531604 2 0.5342 0.4010 0.000 0.676 0.024 0.056 0.244
#> GSM531606 2 0.4352 0.4363 0.000 0.732 0.020 0.012 0.236
#> GSM531607 2 0.5421 0.3364 0.044 0.584 0.000 0.012 0.360
#> GSM531608 4 0.2859 0.8101 0.000 0.000 0.056 0.876 0.068
#> GSM531610 4 0.2795 0.8216 0.100 0.000 0.000 0.872 0.028
#> GSM531612 1 0.6003 0.1467 0.644 0.024 0.000 0.144 0.188
#> GSM531613 1 0.8293 -0.3018 0.364 0.168 0.000 0.180 0.288
#> GSM531614 4 0.0771 0.8855 0.004 0.000 0.020 0.976 0.000
#> GSM531616 3 0.2490 0.6743 0.004 0.000 0.896 0.080 0.020
#> GSM531618 3 0.4558 0.5031 0.252 0.000 0.708 0.004 0.036
#> GSM531619 3 0.5937 0.4406 0.000 0.000 0.564 0.136 0.300
#> GSM531620 3 0.3059 0.6712 0.004 0.000 0.860 0.108 0.028
#> GSM531623 3 0.5233 0.5341 0.000 0.000 0.636 0.076 0.288
#> GSM531625 3 0.5116 0.5972 0.000 0.000 0.692 0.120 0.188
#> GSM531626 3 0.2037 0.6748 0.004 0.000 0.920 0.012 0.064
#> GSM531632 3 0.2438 0.6419 0.060 0.000 0.900 0.000 0.040
#> GSM531638 3 0.1569 0.6713 0.012 0.000 0.948 0.008 0.032
#> GSM531639 1 0.5541 0.1231 0.496 0.000 0.444 0.004 0.056
#> GSM531641 1 0.4407 0.2022 0.764 0.000 0.016 0.040 0.180
#> GSM531642 1 0.3241 0.4206 0.832 0.000 0.144 0.000 0.024
#> GSM531643 3 0.5683 -0.0418 0.428 0.000 0.500 0.004 0.068
#> GSM531644 1 0.4874 0.1368 0.528 0.000 0.452 0.004 0.016
#> GSM531645 1 0.4222 0.3886 0.792 0.000 0.144 0.020 0.044
#> GSM531646 3 0.1943 0.6497 0.056 0.000 0.924 0.000 0.020
#> GSM531647 3 0.4802 0.4727 0.212 0.000 0.716 0.004 0.068
#> GSM531648 1 0.4871 0.3828 0.648 0.000 0.316 0.008 0.028
#> GSM531650 1 0.5335 0.2058 0.536 0.000 0.416 0.004 0.044
#> GSM531651 3 0.6101 0.4301 0.000 0.000 0.552 0.164 0.284
#> GSM531652 1 0.3992 0.4341 0.712 0.000 0.280 0.004 0.004
#> GSM531656 3 0.4724 0.3896 0.320 0.000 0.652 0.008 0.020
#> GSM531659 3 0.7839 0.1016 0.244 0.156 0.464 0.000 0.136
#> GSM531661 3 0.3790 0.6064 0.000 0.000 0.724 0.004 0.272
#> GSM531662 3 0.4197 0.6171 0.020 0.036 0.788 0.000 0.156
#> GSM531663 3 0.6061 0.5447 0.076 0.016 0.668 0.036 0.204
#> GSM531664 1 0.5834 0.0699 0.472 0.000 0.444 0.004 0.080
#> GSM531666 1 0.3769 0.2365 0.796 0.000 0.028 0.004 0.172
#> GSM531667 3 0.4623 0.5530 0.000 0.000 0.664 0.032 0.304
#> GSM531668 3 0.5798 0.5426 0.080 0.008 0.636 0.012 0.264
#> GSM531669 3 0.6046 0.0680 0.376 0.000 0.512 0.004 0.108
#> GSM531671 3 0.3822 0.6406 0.020 0.020 0.808 0.000 0.152
#> GSM531672 1 0.7452 -0.4250 0.412 0.132 0.028 0.028 0.400
#> GSM531673 3 0.5997 0.5081 0.096 0.036 0.660 0.004 0.204
#> GSM531676 2 0.1851 0.6241 0.000 0.912 0.000 0.000 0.088
#> GSM531679 2 0.3039 0.6373 0.000 0.808 0.000 0.000 0.192
#> GSM531681 2 0.3305 0.6225 0.000 0.776 0.000 0.000 0.224
#> GSM531682 2 0.2074 0.6582 0.000 0.896 0.000 0.000 0.104
#> GSM531683 2 0.3177 0.6285 0.000 0.792 0.000 0.000 0.208
#> GSM531684 2 0.4645 0.4024 0.000 0.672 0.016 0.012 0.300
#> GSM531685 2 0.1908 0.6217 0.000 0.908 0.000 0.000 0.092
#> GSM531686 2 0.3766 0.5614 0.004 0.728 0.000 0.000 0.268
#> GSM531687 2 0.1043 0.6482 0.000 0.960 0.000 0.000 0.040
#> GSM531688 2 0.1908 0.6236 0.000 0.908 0.000 0.000 0.092
#> GSM531690 2 0.5100 0.4488 0.056 0.652 0.000 0.004 0.288
#> GSM531693 2 0.5094 0.4056 0.004 0.688 0.064 0.004 0.240
#> GSM531695 2 0.5599 0.3582 0.120 0.620 0.000 0.000 0.260
#> GSM531603 5 0.6711 -0.2166 0.132 0.388 0.004 0.016 0.460
#> GSM531609 4 0.1124 0.8838 0.036 0.000 0.004 0.960 0.000
#> GSM531611 1 0.6526 0.0829 0.576 0.024 0.000 0.188 0.212
#> GSM531621 3 0.5444 0.5731 0.000 0.000 0.660 0.180 0.160
#> GSM531622 3 0.2505 0.6714 0.000 0.000 0.888 0.020 0.092
#> GSM531628 3 0.4380 0.6444 0.048 0.000 0.788 0.136 0.028
#> GSM531630 3 0.2580 0.6727 0.000 0.000 0.892 0.044 0.064
#> GSM531633 3 0.5210 0.5943 0.000 0.000 0.684 0.184 0.132
#> GSM531635 3 0.2166 0.6752 0.004 0.000 0.912 0.072 0.012
#> GSM531640 3 0.6147 0.4482 0.000 0.000 0.556 0.256 0.188
#> GSM531649 3 0.0807 0.6670 0.012 0.000 0.976 0.000 0.012
#> GSM531653 3 0.5715 0.2187 0.332 0.000 0.576 0.004 0.088
#> GSM531657 5 0.8616 -0.1811 0.284 0.048 0.208 0.072 0.388
#> GSM531665 3 0.4524 0.6162 0.016 0.044 0.768 0.004 0.168
#> GSM531670 3 0.3496 0.6026 0.124 0.000 0.832 0.004 0.040
#> GSM531674 3 0.5786 0.2843 0.284 0.000 0.600 0.004 0.112
#> GSM531675 2 0.3242 0.6233 0.000 0.784 0.000 0.000 0.216
#> GSM531677 2 0.3274 0.6196 0.000 0.780 0.000 0.000 0.220
#> GSM531678 2 0.2329 0.6555 0.000 0.876 0.000 0.000 0.124
#> GSM531680 2 0.5336 0.4070 0.084 0.628 0.000 0.000 0.288
#> GSM531689 2 0.1043 0.6421 0.000 0.960 0.000 0.000 0.040
#> GSM531691 2 0.1732 0.6278 0.000 0.920 0.000 0.000 0.080
#> GSM531692 2 0.6625 0.1141 0.000 0.476 0.112 0.028 0.384
#> GSM531694 2 0.2891 0.6441 0.000 0.824 0.000 0.000 0.176
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM531602 2 0.4037 0.5977 0.008 0.724 0.000 0.032 0.236 0.000
#> GSM531604 2 0.6079 0.2806 0.060 0.472 0.024 0.004 0.416 0.024
#> GSM531606 2 0.6678 0.2008 0.100 0.456 0.040 0.024 0.376 0.004
#> GSM531607 2 0.5244 0.6014 0.020 0.680 0.000 0.160 0.132 0.008
#> GSM531608 6 0.2095 0.8395 0.028 0.000 0.040 0.000 0.016 0.916
#> GSM531610 6 0.3247 0.7462 0.000 0.000 0.000 0.156 0.036 0.808
#> GSM531612 4 0.4808 0.4461 0.028 0.076 0.000 0.760 0.044 0.092
#> GSM531613 4 0.6488 0.3169 0.000 0.232 0.000 0.540 0.092 0.136
#> GSM531614 6 0.0260 0.8865 0.000 0.000 0.008 0.000 0.000 0.992
#> GSM531616 3 0.2585 0.4082 0.048 0.000 0.880 0.000 0.004 0.068
#> GSM531618 3 0.6034 -0.3354 0.184 0.000 0.508 0.292 0.016 0.000
#> GSM531619 3 0.6024 0.2530 0.268 0.000 0.556 0.000 0.136 0.040
#> GSM531620 3 0.3698 0.3851 0.044 0.000 0.796 0.004 0.008 0.148
#> GSM531623 3 0.5577 0.2851 0.272 0.000 0.592 0.000 0.112 0.024
#> GSM531625 3 0.4982 0.4233 0.164 0.000 0.708 0.000 0.060 0.068
#> GSM531626 3 0.1049 0.4568 0.008 0.000 0.960 0.000 0.032 0.000
#> GSM531632 3 0.3921 -0.1329 0.308 0.000 0.676 0.004 0.012 0.000
#> GSM531638 3 0.2278 0.4328 0.052 0.000 0.908 0.008 0.024 0.008
#> GSM531639 1 0.5894 0.7604 0.444 0.000 0.392 0.156 0.008 0.000
#> GSM531641 4 0.2119 0.5185 0.060 0.016 0.008 0.912 0.004 0.000
#> GSM531642 4 0.5278 0.3233 0.284 0.000 0.092 0.608 0.016 0.000
#> GSM531643 1 0.4978 0.7872 0.532 0.000 0.396 0.072 0.000 0.000
#> GSM531644 3 0.5868 -0.7459 0.420 0.000 0.432 0.136 0.012 0.000
#> GSM531645 4 0.5702 0.3066 0.172 0.000 0.172 0.620 0.036 0.000
#> GSM531646 3 0.3357 0.1018 0.224 0.000 0.764 0.004 0.008 0.000
#> GSM531647 3 0.4366 -0.5343 0.440 0.000 0.540 0.004 0.016 0.000
#> GSM531648 4 0.6468 -0.2603 0.228 0.000 0.300 0.444 0.028 0.000
#> GSM531650 1 0.5783 0.7838 0.496 0.000 0.368 0.120 0.016 0.000
#> GSM531651 3 0.6258 0.2551 0.252 0.000 0.552 0.000 0.128 0.068
#> GSM531652 1 0.6317 0.5375 0.376 0.000 0.304 0.312 0.008 0.000
#> GSM531656 3 0.5990 -0.6641 0.368 0.000 0.488 0.112 0.032 0.000
#> GSM531659 3 0.8063 -0.4864 0.280 0.084 0.364 0.056 0.212 0.004
#> GSM531661 3 0.5156 0.3097 0.216 0.000 0.620 0.000 0.164 0.000
#> GSM531662 3 0.5059 0.1182 0.052 0.000 0.540 0.012 0.396 0.000
#> GSM531663 5 0.7601 0.0385 0.064 0.032 0.336 0.196 0.368 0.004
#> GSM531664 1 0.6678 0.7356 0.428 0.000 0.356 0.148 0.068 0.000
#> GSM531666 4 0.4990 0.5057 0.184 0.004 0.044 0.704 0.064 0.000
#> GSM531667 3 0.5509 0.2105 0.292 0.000 0.544 0.000 0.164 0.000
#> GSM531668 3 0.7677 -0.1393 0.104 0.040 0.384 0.120 0.348 0.004
#> GSM531669 1 0.5622 0.7746 0.528 0.000 0.364 0.080 0.028 0.000
#> GSM531671 3 0.4935 0.3043 0.096 0.000 0.660 0.004 0.236 0.004
#> GSM531672 4 0.7288 0.3143 0.076 0.164 0.036 0.484 0.240 0.000
#> GSM531673 5 0.7475 -0.0635 0.108 0.032 0.348 0.120 0.392 0.000
#> GSM531676 2 0.4063 0.6032 0.020 0.692 0.000 0.008 0.280 0.000
#> GSM531679 2 0.0935 0.7357 0.000 0.964 0.000 0.004 0.032 0.000
#> GSM531681 2 0.2750 0.6961 0.000 0.844 0.000 0.020 0.136 0.000
#> GSM531682 2 0.1610 0.7271 0.000 0.916 0.000 0.000 0.084 0.000
#> GSM531683 2 0.1584 0.7309 0.000 0.928 0.000 0.008 0.064 0.000
#> GSM531684 5 0.7164 0.1177 0.252 0.264 0.052 0.000 0.416 0.016
#> GSM531685 2 0.5240 0.5064 0.060 0.588 0.000 0.008 0.332 0.012
#> GSM531686 2 0.1643 0.7273 0.000 0.924 0.000 0.068 0.008 0.000
#> GSM531687 2 0.2442 0.7126 0.000 0.852 0.000 0.004 0.144 0.000
#> GSM531688 2 0.5192 0.5822 0.116 0.648 0.000 0.016 0.220 0.000
#> GSM531690 2 0.4267 0.6378 0.000 0.732 0.000 0.152 0.116 0.000
#> GSM531693 2 0.7242 0.0917 0.268 0.340 0.036 0.012 0.336 0.008
#> GSM531695 2 0.4940 0.6421 0.028 0.704 0.000 0.144 0.124 0.000
#> GSM531603 2 0.7240 0.3046 0.100 0.456 0.004 0.288 0.140 0.012
#> GSM531609 6 0.0632 0.8846 0.000 0.000 0.000 0.024 0.000 0.976
#> GSM531611 4 0.6066 0.3740 0.016 0.112 0.000 0.632 0.068 0.172
#> GSM531621 3 0.4823 0.4532 0.136 0.000 0.724 0.000 0.040 0.100
#> GSM531622 3 0.2513 0.4786 0.060 0.000 0.888 0.000 0.044 0.008
#> GSM531628 3 0.5791 0.0549 0.160 0.000 0.540 0.012 0.000 0.288
#> GSM531630 3 0.1265 0.4537 0.008 0.000 0.948 0.000 0.000 0.044
#> GSM531633 3 0.4418 0.4842 0.084 0.000 0.764 0.000 0.044 0.108
#> GSM531635 3 0.2854 0.4023 0.048 0.000 0.860 0.000 0.004 0.088
#> GSM531640 3 0.5426 0.3916 0.108 0.000 0.644 0.000 0.036 0.212
#> GSM531649 3 0.2214 0.3591 0.092 0.000 0.892 0.004 0.012 0.000
#> GSM531653 1 0.4831 0.7070 0.572 0.000 0.380 0.028 0.020 0.000
#> GSM531657 4 0.8246 0.1661 0.068 0.096 0.176 0.368 0.284 0.008
#> GSM531665 3 0.5580 -0.0211 0.052 0.004 0.488 0.032 0.424 0.000
#> GSM531670 3 0.5257 -0.3179 0.280 0.000 0.624 0.052 0.044 0.000
#> GSM531674 1 0.5184 0.7370 0.496 0.000 0.440 0.036 0.028 0.000
#> GSM531675 2 0.1003 0.7376 0.000 0.964 0.000 0.016 0.020 0.000
#> GSM531677 2 0.0806 0.7354 0.000 0.972 0.000 0.020 0.008 0.000
#> GSM531678 2 0.0937 0.7346 0.000 0.960 0.000 0.000 0.040 0.000
#> GSM531680 2 0.3652 0.6641 0.000 0.768 0.000 0.188 0.044 0.000
#> GSM531689 2 0.1814 0.7227 0.000 0.900 0.000 0.000 0.100 0.000
#> GSM531691 2 0.4099 0.6083 0.024 0.696 0.000 0.008 0.272 0.000
#> GSM531692 5 0.7334 0.2070 0.212 0.188 0.108 0.008 0.476 0.008
#> GSM531694 2 0.1152 0.7358 0.000 0.952 0.000 0.004 0.044 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)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> ATC:NMF 79 1.000 2
#> ATC:NMF 76 0.257 3
#> ATC:NMF 70 0.670 4
#> ATC:NMF 45 0.894 5
#> ATC:NMF 34 0.742 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