Date: 2019-12-25 20:17:21 CET, cola version: 1.3.2
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All available functions which can be applied to this res_list object:
res_list
#> A 'ConsensusPartitionList' object with 24 methods.
#> On a matrix with 10612 rows and 88 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] 10612 88
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 | ||
|---|---|---|---|---|---|---|
| CV:skmeans | 2 | 1.000 | 0.959 | 0.983 | ** | |
| MAD:skmeans | 2 | 1.000 | 0.964 | 0.985 | ** | |
| MAD:NMF | 2 | 0.999 | 0.965 | 0.985 | ** | |
| SD:NMF | 2 | 0.999 | 0.967 | 0.986 | ** | |
| SD:skmeans | 3 | 0.925 | 0.882 | 0.954 | * | 2 |
| ATC:skmeans | 3 | 0.924 | 0.890 | 0.959 | * | |
| ATC:pam | 4 | 0.902 | 0.878 | 0.951 | * | |
| ATC:NMF | 2 | 0.860 | 0.919 | 0.965 | ||
| ATC:mclust | 5 | 0.850 | 0.867 | 0.909 | ||
| MAD:pam | 2 | 0.837 | 0.907 | 0.958 | ||
| MAD:kmeans | 2 | 0.818 | 0.901 | 0.949 | ||
| SD:pam | 2 | 0.813 | 0.901 | 0.953 | ||
| SD:mclust | 3 | 0.784 | 0.923 | 0.947 | ||
| MAD:mclust | 2 | 0.730 | 0.938 | 0.954 | ||
| SD:kmeans | 2 | 0.716 | 0.908 | 0.934 | ||
| CV:pam | 4 | 0.710 | 0.836 | 0.894 | ||
| CV:NMF | 2 | 0.700 | 0.831 | 0.930 | ||
| CV:mclust | 5 | 0.647 | 0.708 | 0.817 | ||
| ATC:kmeans | 2 | 0.599 | 0.808 | 0.900 | ||
| CV:kmeans | 3 | 0.525 | 0.637 | 0.811 | ||
| ATC:hclust | 2 | 0.287 | 0.581 | 0.816 | ||
| CV:hclust | 3 | 0.240 | 0.455 | 0.721 | ||
| MAD:hclust | 3 | 0.225 | 0.529 | 0.743 | ||
| SD:hclust | 3 | 0.202 | 0.516 | 0.726 |
**: 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 0.999 0.967 0.986 0.496 0.504 0.504
#> CV:NMF 2 0.700 0.831 0.930 0.487 0.515 0.515
#> MAD:NMF 2 0.999 0.965 0.985 0.496 0.504 0.504
#> ATC:NMF 2 0.860 0.919 0.965 0.500 0.498 0.498
#> SD:skmeans 2 0.952 0.921 0.972 0.505 0.494 0.494
#> CV:skmeans 2 1.000 0.959 0.983 0.505 0.495 0.495
#> MAD:skmeans 2 1.000 0.964 0.985 0.506 0.495 0.495
#> ATC:skmeans 2 0.482 0.767 0.896 0.503 0.504 0.504
#> SD:mclust 2 0.448 0.842 0.866 0.444 0.504 0.504
#> CV:mclust 2 0.441 0.771 0.870 0.283 0.796 0.796
#> MAD:mclust 2 0.730 0.938 0.954 0.485 0.504 0.504
#> ATC:mclust 2 0.522 0.844 0.910 0.290 0.762 0.762
#> SD:kmeans 2 0.716 0.908 0.934 0.494 0.501 0.501
#> CV:kmeans 2 0.231 0.546 0.778 0.469 0.520 0.520
#> MAD:kmeans 2 0.818 0.901 0.949 0.500 0.501 0.501
#> ATC:kmeans 2 0.599 0.808 0.900 0.479 0.538 0.538
#> SD:pam 2 0.813 0.901 0.953 0.482 0.511 0.511
#> CV:pam 2 0.469 0.569 0.816 0.493 0.495 0.495
#> MAD:pam 2 0.837 0.907 0.958 0.480 0.520 0.520
#> ATC:pam 2 0.562 0.818 0.919 0.500 0.495 0.495
#> SD:hclust 2 0.148 0.492 0.782 0.388 0.645 0.645
#> CV:hclust 2 0.308 0.763 0.865 0.335 0.671 0.671
#> MAD:hclust 2 0.151 0.620 0.807 0.378 0.632 0.632
#> ATC:hclust 2 0.287 0.581 0.816 0.428 0.589 0.589
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 0.597 0.623 0.794 0.313 0.760 0.565
#> CV:NMF 3 0.450 0.599 0.785 0.352 0.742 0.544
#> MAD:NMF 3 0.589 0.581 0.777 0.314 0.752 0.551
#> ATC:NMF 3 0.469 0.440 0.719 0.330 0.639 0.393
#> SD:skmeans 3 0.925 0.882 0.954 0.317 0.782 0.584
#> CV:skmeans 3 0.746 0.851 0.920 0.318 0.742 0.524
#> MAD:skmeans 3 0.847 0.866 0.945 0.316 0.789 0.596
#> ATC:skmeans 3 0.924 0.890 0.959 0.335 0.710 0.482
#> SD:mclust 3 0.784 0.923 0.947 0.421 0.839 0.687
#> CV:mclust 3 0.260 0.579 0.805 1.056 0.460 0.371
#> MAD:mclust 3 0.689 0.761 0.893 0.306 0.828 0.666
#> ATC:mclust 3 0.437 0.744 0.787 1.117 0.526 0.405
#> SD:kmeans 3 0.564 0.741 0.848 0.320 0.762 0.557
#> CV:kmeans 3 0.525 0.637 0.811 0.384 0.732 0.522
#> MAD:kmeans 3 0.538 0.732 0.851 0.311 0.762 0.557
#> ATC:kmeans 3 0.668 0.759 0.872 0.373 0.736 0.535
#> SD:pam 3 0.577 0.761 0.885 0.334 0.826 0.666
#> CV:pam 3 0.438 0.568 0.812 0.266 0.581 0.348
#> MAD:pam 3 0.613 0.793 0.895 0.354 0.809 0.638
#> ATC:pam 3 0.590 0.770 0.857 0.293 0.773 0.577
#> SD:hclust 3 0.202 0.516 0.726 0.488 0.708 0.569
#> CV:hclust 3 0.240 0.455 0.721 0.719 0.737 0.616
#> MAD:hclust 3 0.225 0.529 0.743 0.512 0.769 0.639
#> ATC:hclust 3 0.302 0.417 0.655 0.374 0.714 0.549
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.561 0.630 0.798 0.1034 0.838 0.606
#> CV:NMF 4 0.537 0.623 0.804 0.1249 0.797 0.508
#> MAD:NMF 4 0.528 0.471 0.711 0.1190 0.866 0.650
#> ATC:NMF 4 0.649 0.725 0.859 0.1193 0.721 0.357
#> SD:skmeans 4 0.745 0.855 0.892 0.1153 0.870 0.642
#> CV:skmeans 4 0.647 0.744 0.849 0.1161 0.878 0.659
#> MAD:skmeans 4 0.690 0.784 0.836 0.1173 0.861 0.624
#> ATC:skmeans 4 0.768 0.855 0.913 0.1197 0.853 0.592
#> SD:mclust 4 0.779 0.594 0.837 0.0943 0.952 0.871
#> CV:mclust 4 0.583 0.629 0.734 0.1668 0.820 0.588
#> MAD:mclust 4 0.593 0.588 0.721 0.0824 0.882 0.695
#> ATC:mclust 4 0.415 0.594 0.767 0.1051 0.649 0.318
#> SD:kmeans 4 0.584 0.752 0.809 0.1278 0.906 0.735
#> CV:kmeans 4 0.569 0.707 0.799 0.1217 0.903 0.728
#> MAD:kmeans 4 0.566 0.683 0.771 0.1252 0.906 0.735
#> ATC:kmeans 4 0.541 0.418 0.653 0.1279 0.836 0.562
#> SD:pam 4 0.716 0.720 0.881 0.1290 0.862 0.636
#> CV:pam 4 0.710 0.836 0.894 0.1536 0.862 0.650
#> MAD:pam 4 0.714 0.745 0.890 0.1276 0.851 0.609
#> ATC:pam 4 0.902 0.878 0.951 0.1379 0.686 0.323
#> SD:hclust 4 0.322 0.479 0.670 0.1540 0.870 0.704
#> CV:hclust 4 0.342 0.355 0.683 0.1221 0.880 0.738
#> MAD:hclust 4 0.325 0.454 0.675 0.1612 0.881 0.734
#> ATC:hclust 4 0.453 0.541 0.748 0.1943 0.767 0.477
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.713 0.740 0.862 0.1019 0.852 0.542
#> CV:NMF 5 0.607 0.616 0.792 0.0679 0.899 0.652
#> MAD:NMF 5 0.675 0.699 0.839 0.0894 0.846 0.510
#> ATC:NMF 5 0.590 0.595 0.776 0.0581 0.912 0.686
#> SD:skmeans 5 0.785 0.727 0.859 0.0842 0.883 0.590
#> CV:skmeans 5 0.690 0.590 0.766 0.0795 0.857 0.525
#> MAD:skmeans 5 0.775 0.769 0.872 0.0833 0.859 0.527
#> ATC:skmeans 5 0.782 0.745 0.858 0.0667 0.926 0.713
#> SD:mclust 5 0.590 0.563 0.732 0.1276 0.846 0.550
#> CV:mclust 5 0.647 0.708 0.817 0.0842 0.713 0.327
#> MAD:mclust 5 0.610 0.614 0.768 0.1263 0.757 0.371
#> ATC:mclust 5 0.850 0.867 0.909 0.0976 0.851 0.582
#> SD:kmeans 5 0.668 0.599 0.739 0.0741 0.881 0.599
#> CV:kmeans 5 0.597 0.584 0.747 0.0697 0.937 0.783
#> MAD:kmeans 5 0.639 0.688 0.772 0.0729 0.839 0.495
#> ATC:kmeans 5 0.640 0.685 0.798 0.0681 0.856 0.515
#> SD:pam 5 0.684 0.581 0.791 0.0813 0.895 0.630
#> CV:pam 5 0.656 0.550 0.742 0.0765 0.910 0.708
#> MAD:pam 5 0.655 0.499 0.760 0.0779 0.926 0.737
#> ATC:pam 5 0.822 0.851 0.899 0.0831 0.895 0.626
#> SD:hclust 5 0.450 0.509 0.700 0.1015 0.850 0.579
#> CV:hclust 5 0.440 0.323 0.640 0.1428 0.843 0.629
#> MAD:hclust 5 0.446 0.474 0.638 0.1066 0.807 0.524
#> ATC:hclust 5 0.508 0.562 0.733 0.0668 0.909 0.693
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.726 0.707 0.845 0.0439 0.911 0.612
#> CV:NMF 6 0.733 0.645 0.824 0.0403 0.868 0.485
#> MAD:NMF 6 0.703 0.670 0.822 0.0446 0.913 0.614
#> ATC:NMF 6 0.614 0.592 0.750 0.0393 0.954 0.796
#> SD:skmeans 6 0.768 0.626 0.783 0.0391 0.932 0.678
#> CV:skmeans 6 0.715 0.603 0.768 0.0404 0.920 0.633
#> MAD:skmeans 6 0.764 0.642 0.806 0.0393 0.948 0.743
#> ATC:skmeans 6 0.820 0.775 0.862 0.0393 0.946 0.746
#> SD:mclust 6 0.598 0.448 0.669 0.0369 0.899 0.570
#> CV:mclust 6 0.572 0.530 0.682 0.0573 0.953 0.823
#> MAD:mclust 6 0.599 0.492 0.655 0.0442 0.904 0.623
#> ATC:mclust 6 0.666 0.542 0.793 0.0516 0.859 0.544
#> SD:kmeans 6 0.691 0.576 0.749 0.0423 0.952 0.774
#> CV:kmeans 6 0.646 0.496 0.668 0.0466 0.899 0.603
#> MAD:kmeans 6 0.678 0.562 0.724 0.0429 0.976 0.881
#> ATC:kmeans 6 0.694 0.647 0.771 0.0411 0.946 0.745
#> SD:pam 6 0.663 0.514 0.744 0.0321 0.898 0.577
#> CV:pam 6 0.782 0.802 0.868 0.0592 0.844 0.457
#> MAD:pam 6 0.705 0.467 0.706 0.0340 0.900 0.610
#> ATC:pam 6 0.796 0.718 0.835 0.0363 0.956 0.781
#> SD:hclust 6 0.511 0.541 0.666 0.0514 0.974 0.893
#> CV:hclust 6 0.502 0.411 0.670 0.0450 0.874 0.642
#> MAD:hclust 6 0.511 0.349 0.608 0.0677 0.818 0.448
#> ATC:hclust 6 0.586 0.530 0.718 0.0379 0.972 0.886
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 specimen(p) k
#> SD:NMF 87 3.20e-08 2
#> CV:NMF 79 3.12e-08 2
#> MAD:NMF 87 3.20e-08 2
#> ATC:NMF 85 4.10e-06 2
#> SD:skmeans 83 3.75e-10 2
#> CV:skmeans 86 5.07e-10 2
#> MAD:skmeans 86 9.27e-09 2
#> ATC:skmeans 76 4.23e-08 2
#> SD:mclust 87 4.07e-10 2
#> CV:mclust 82 1.79e-01 2
#> MAD:mclust 87 4.07e-10 2
#> ATC:mclust 87 2.32e-01 2
#> SD:kmeans 88 5.90e-09 2
#> CV:kmeans 66 1.08e-08 2
#> MAD:kmeans 83 5.43e-09 2
#> ATC:kmeans 85 9.69e-06 2
#> SD:pam 85 5.29e-05 2
#> CV:pam 57 7.39e-05 2
#> MAD:pam 85 4.08e-05 2
#> ATC:pam 80 2.20e-05 2
#> SD:hclust 61 4.64e-04 2
#> CV:hclust 80 1.95e-03 2
#> MAD:hclust 70 5.27e-03 2
#> ATC:hclust 63 5.21e-03 2
test_to_known_factors(res_list, k = 3)
#> n specimen(p) k
#> SD:NMF 65 2.79e-05 3
#> CV:NMF 72 5.84e-08 3
#> MAD:NMF 62 3.93e-05 3
#> ATC:NMF 49 1.74e-03 3
#> SD:skmeans 81 8.29e-07 3
#> CV:skmeans 86 9.26e-07 3
#> MAD:skmeans 83 3.28e-07 3
#> ATC:skmeans 82 8.61e-05 3
#> SD:mclust 87 1.26e-07 3
#> CV:mclust 60 3.00e-06 3
#> MAD:mclust 80 1.04e-07 3
#> ATC:mclust 83 1.74e-04 3
#> SD:kmeans 80 2.23e-06 3
#> CV:kmeans 67 5.25e-05 3
#> MAD:kmeans 79 1.28e-06 3
#> ATC:kmeans 82 3.40e-06 3
#> SD:pam 80 1.04e-04 3
#> CV:pam 60 2.61e-04 3
#> MAD:pam 83 4.06e-05 3
#> ATC:pam 84 3.19e-04 3
#> SD:hclust 66 3.01e-07 3
#> CV:hclust 52 4.01e-07 3
#> MAD:hclust 58 8.84e-06 3
#> ATC:hclust 32 1.30e-01 3
test_to_known_factors(res_list, k = 4)
#> n specimen(p) k
#> SD:NMF 72 3.90e-05 4
#> CV:NMF 71 5.06e-05 4
#> MAD:NMF 51 3.25e-06 4
#> ATC:NMF 76 1.92e-04 4
#> SD:skmeans 86 3.60e-05 4
#> CV:skmeans 83 7.32e-06 4
#> MAD:skmeans 84 6.30e-05 4
#> ATC:skmeans 86 7.87e-05 4
#> SD:mclust 57 5.77e-07 4
#> CV:mclust 52 2.28e-06 4
#> MAD:mclust 59 2.34e-06 4
#> ATC:mclust 65 2.87e-04 4
#> SD:kmeans 83 2.02e-05 4
#> CV:kmeans 79 2.94e-06 4
#> MAD:kmeans 76 2.22e-05 4
#> ATC:kmeans 38 5.08e-04 4
#> SD:pam 75 3.25e-05 4
#> CV:pam 84 8.83e-04 4
#> MAD:pam 76 4.47e-05 4
#> ATC:pam 80 1.27e-03 4
#> SD:hclust 47 8.68e-06 4
#> CV:hclust 33 4.12e-05 4
#> MAD:hclust 43 9.54e-04 4
#> ATC:hclust 54 3.35e-03 4
test_to_known_factors(res_list, k = 5)
#> n specimen(p) k
#> SD:NMF 78 1.02e-03 5
#> CV:NMF 73 1.26e-05 5
#> MAD:NMF 76 3.49e-04 5
#> ATC:NMF 67 1.50e-04 5
#> SD:skmeans 76 4.17e-04 5
#> CV:skmeans 64 8.16e-04 5
#> MAD:skmeans 79 2.88e-04 5
#> ATC:skmeans 76 9.13e-05 5
#> SD:mclust 59 1.81e-04 5
#> CV:mclust 82 4.30e-03 5
#> MAD:mclust 73 2.27e-08 5
#> ATC:mclust 84 2.41e-03 5
#> SD:kmeans 62 1.44e-03 5
#> CV:kmeans 64 1.32e-06 5
#> MAD:kmeans 78 1.09e-03 5
#> ATC:kmeans 74 1.42e-04 5
#> SD:pam 67 1.02e-04 5
#> CV:pam 53 2.86e-03 5
#> MAD:pam 52 9.84e-02 5
#> ATC:pam 85 9.13e-04 5
#> SD:hclust 50 5.36e-03 5
#> CV:hclust 34 4.15e-03 5
#> MAD:hclust 48 2.00e-02 5
#> ATC:hclust 60 1.91e-03 5
test_to_known_factors(res_list, k = 6)
#> n specimen(p) k
#> SD:NMF 76 8.28e-05 6
#> CV:NMF 70 1.07e-02 6
#> MAD:NMF 69 1.72e-03 6
#> ATC:NMF 67 2.34e-03 6
#> SD:skmeans 61 2.08e-02 6
#> CV:skmeans 60 2.60e-03 6
#> MAD:skmeans 65 1.49e-02 6
#> ATC:skmeans 80 1.74e-03 6
#> SD:mclust 39 6.52e-04 6
#> CV:mclust 48 4.97e-04 6
#> MAD:mclust 48 2.37e-05 6
#> ATC:mclust 52 1.36e-02 6
#> SD:kmeans 64 1.99e-02 6
#> CV:kmeans 46 1.40e-03 6
#> MAD:kmeans 66 4.54e-02 6
#> ATC:kmeans 68 2.25e-06 6
#> SD:pam 49 6.33e-04 6
#> CV:pam 86 1.32e-02 6
#> MAD:pam 35 3.46e-02 6
#> ATC:pam 75 1.33e-02 6
#> SD:hclust 68 7.71e-04 6
#> CV:hclust 45 1.41e-02 6
#> MAD:hclust 27 7.53e-02 6
#> ATC:hclust 56 5.65e-03 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 10612 rows and 88 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.148 0.492 0.782 0.3880 0.645 0.645
#> 3 3 0.202 0.516 0.726 0.4876 0.708 0.569
#> 4 4 0.322 0.479 0.670 0.1540 0.870 0.704
#> 5 5 0.450 0.509 0.700 0.1015 0.850 0.579
#> 6 6 0.511 0.541 0.666 0.0514 0.974 0.893
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
#> GSM152032 1 0.9129 0.2931 0.672 0.328
#> GSM152033 1 0.2603 0.6611 0.956 0.044
#> GSM152063 2 0.9209 0.5703 0.336 0.664
#> GSM152074 1 0.9460 0.2117 0.636 0.364
#> GSM152080 1 0.9983 -0.0879 0.524 0.476
#> GSM152081 2 0.9866 0.3906 0.432 0.568
#> GSM152083 1 0.9850 0.0512 0.572 0.428
#> GSM152091 1 0.9983 -0.0879 0.524 0.476
#> GSM152108 1 0.7528 0.5020 0.784 0.216
#> GSM152114 1 0.9944 -0.0789 0.544 0.456
#> GSM152035 1 0.9552 0.2231 0.624 0.376
#> GSM152039 2 0.6438 0.6327 0.164 0.836
#> GSM152041 1 0.9209 0.4282 0.664 0.336
#> GSM152044 2 0.8386 0.6292 0.268 0.732
#> GSM152045 1 0.1184 0.6726 0.984 0.016
#> GSM152051 2 0.8386 0.6292 0.268 0.732
#> GSM152054 1 0.7745 0.5202 0.772 0.228
#> GSM152057 2 0.8443 0.6300 0.272 0.728
#> GSM152058 1 0.7219 0.5999 0.800 0.200
#> GSM152067 1 0.9358 0.2396 0.648 0.352
#> GSM152068 2 0.8443 0.6300 0.272 0.728
#> GSM152075 2 0.9933 0.2516 0.452 0.548
#> GSM152076 2 0.6438 0.6327 0.164 0.836
#> GSM152079 2 0.8443 0.6300 0.272 0.728
#> GSM152084 1 0.6887 0.5384 0.816 0.184
#> GSM152089 1 0.9427 0.3816 0.640 0.360
#> GSM152095 2 0.6438 0.6327 0.164 0.836
#> GSM152096 1 0.7219 0.5202 0.800 0.200
#> GSM152097 2 0.0000 0.5930 0.000 1.000
#> GSM152099 2 0.9460 0.4631 0.364 0.636
#> GSM152106 2 0.0000 0.5930 0.000 1.000
#> GSM152107 1 0.9522 0.2248 0.628 0.372
#> GSM152109 1 0.9427 0.2206 0.640 0.360
#> GSM152111 1 0.7299 0.5908 0.796 0.204
#> GSM152112 1 0.9909 -0.0742 0.556 0.444
#> GSM152113 1 0.5946 0.5829 0.856 0.144
#> GSM152115 1 0.9522 0.2248 0.628 0.372
#> GSM152030 2 0.9993 0.2628 0.484 0.516
#> GSM152038 1 0.2043 0.6725 0.968 0.032
#> GSM152042 2 0.9996 0.2462 0.488 0.512
#> GSM152062 1 0.7376 0.5060 0.792 0.208
#> GSM152077 1 0.1414 0.6683 0.980 0.020
#> GSM152088 1 0.9983 -0.0885 0.524 0.476
#> GSM152100 2 0.9933 0.2516 0.452 0.548
#> GSM152102 1 0.9661 0.1961 0.608 0.392
#> GSM152104 2 0.0000 0.5930 0.000 1.000
#> GSM152028 1 0.0000 0.6695 1.000 0.000
#> GSM152029 1 0.1843 0.6738 0.972 0.028
#> GSM152049 1 0.7139 0.5968 0.804 0.196
#> GSM152053 2 0.9996 0.2462 0.488 0.512
#> GSM152059 1 0.2423 0.6720 0.960 0.040
#> GSM152085 1 0.7139 0.5968 0.804 0.196
#> GSM152101 1 0.9522 0.2248 0.628 0.372
#> GSM152105 1 0.1184 0.6724 0.984 0.016
#> GSM152034 1 0.7376 0.5852 0.792 0.208
#> GSM152036 2 0.6531 0.6299 0.168 0.832
#> GSM152040 1 0.2603 0.6736 0.956 0.044
#> GSM152043 1 0.0376 0.6699 0.996 0.004
#> GSM152046 1 0.7950 0.5493 0.760 0.240
#> GSM152047 1 0.0938 0.6720 0.988 0.012
#> GSM152048 1 0.7219 0.5999 0.800 0.200
#> GSM152050 1 0.7219 0.5929 0.800 0.200
#> GSM152052 1 0.2603 0.6741 0.956 0.044
#> GSM152056 1 0.7299 0.5970 0.796 0.204
#> GSM152060 1 0.7950 0.5493 0.760 0.240
#> GSM152065 1 0.0000 0.6695 1.000 0.000
#> GSM152066 1 0.7299 0.5970 0.796 0.204
#> GSM152069 1 0.9427 0.2206 0.640 0.360
#> GSM152070 1 0.0938 0.6720 0.988 0.012
#> GSM152071 1 0.9427 0.2206 0.640 0.360
#> GSM152072 1 0.0938 0.6717 0.988 0.012
#> GSM152073 1 0.6148 0.6263 0.848 0.152
#> GSM152078 1 0.2236 0.6736 0.964 0.036
#> GSM152082 1 0.0000 0.6695 1.000 0.000
#> GSM152086 1 0.7056 0.5998 0.808 0.192
#> GSM152090 1 0.5629 0.6502 0.868 0.132
#> GSM152092 1 0.0000 0.6695 1.000 0.000
#> GSM152093 1 0.5178 0.6597 0.884 0.116
#> GSM152094 1 0.6247 0.6246 0.844 0.156
#> GSM152098 1 0.0376 0.6699 0.996 0.004
#> GSM152110 1 0.7299 0.5970 0.796 0.204
#> GSM152031 1 0.1184 0.6724 0.984 0.016
#> GSM152037 1 0.7299 0.5970 0.796 0.204
#> GSM152055 1 0.7950 0.5493 0.760 0.240
#> GSM152061 1 0.7950 0.5493 0.760 0.240
#> GSM152064 1 0.9129 0.4458 0.672 0.328
#> GSM152087 1 0.6343 0.6229 0.840 0.160
#> GSM152103 1 0.5294 0.6564 0.880 0.120
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM152032 3 0.6955 0.5453 0.332 0.032 0.636
#> GSM152033 1 0.5785 0.4644 0.696 0.004 0.300
#> GSM152063 3 0.8521 0.0877 0.092 0.440 0.468
#> GSM152074 3 0.4974 0.6301 0.236 0.000 0.764
#> GSM152080 3 0.0592 0.5555 0.000 0.012 0.988
#> GSM152081 2 0.8396 0.4908 0.196 0.624 0.180
#> GSM152083 3 0.4353 0.6259 0.156 0.008 0.836
#> GSM152091 3 0.0592 0.5555 0.000 0.012 0.988
#> GSM152108 1 0.8454 -0.1240 0.480 0.088 0.432
#> GSM152114 2 0.9108 0.4644 0.316 0.520 0.164
#> GSM152035 3 0.8622 0.4692 0.296 0.132 0.572
#> GSM152039 2 0.0747 0.6135 0.016 0.984 0.000
#> GSM152041 1 0.7263 0.2922 0.568 0.400 0.032
#> GSM152044 3 0.7004 0.2340 0.020 0.428 0.552
#> GSM152045 1 0.2229 0.6871 0.944 0.012 0.044
#> GSM152051 3 0.7004 0.2340 0.020 0.428 0.552
#> GSM152054 1 0.9046 0.1601 0.528 0.160 0.312
#> GSM152057 3 0.7013 0.2285 0.020 0.432 0.548
#> GSM152058 1 0.5470 0.6513 0.796 0.168 0.036
#> GSM152067 3 0.5327 0.6145 0.272 0.000 0.728
#> GSM152068 3 0.7013 0.2285 0.020 0.432 0.548
#> GSM152075 2 0.8109 0.5402 0.272 0.620 0.108
#> GSM152076 2 0.0747 0.6135 0.016 0.984 0.000
#> GSM152079 3 0.7013 0.2285 0.020 0.432 0.548
#> GSM152084 1 0.7831 0.0580 0.540 0.056 0.404
#> GSM152089 1 0.7337 0.2218 0.540 0.428 0.032
#> GSM152095 2 0.0747 0.6135 0.016 0.984 0.000
#> GSM152096 1 0.7956 -0.0252 0.516 0.060 0.424
#> GSM152097 2 0.4121 0.5088 0.000 0.832 0.168
#> GSM152099 3 0.6402 0.4910 0.040 0.236 0.724
#> GSM152106 2 0.4121 0.5088 0.000 0.832 0.168
#> GSM152107 3 0.7588 0.5732 0.312 0.064 0.624
#> GSM152109 3 0.4887 0.6315 0.228 0.000 0.772
#> GSM152111 1 0.5318 0.6279 0.780 0.204 0.016
#> GSM152112 2 0.8924 0.4386 0.336 0.524 0.140
#> GSM152113 1 0.7207 0.1931 0.584 0.032 0.384
#> GSM152115 3 0.7588 0.5732 0.312 0.064 0.624
#> GSM152030 2 0.8743 0.5246 0.268 0.576 0.156
#> GSM152038 1 0.4750 0.5896 0.784 0.000 0.216
#> GSM152042 2 0.8722 0.5307 0.272 0.576 0.152
#> GSM152062 1 0.7890 -0.0492 0.512 0.056 0.432
#> GSM152077 1 0.5327 0.5005 0.728 0.000 0.272
#> GSM152088 3 0.0983 0.5594 0.004 0.016 0.980
#> GSM152100 2 0.8109 0.5402 0.272 0.620 0.108
#> GSM152102 3 0.8430 0.4900 0.292 0.120 0.588
#> GSM152104 2 0.4121 0.5088 0.000 0.832 0.168
#> GSM152028 1 0.5138 0.5346 0.748 0.000 0.252
#> GSM152029 1 0.1989 0.6869 0.948 0.004 0.048
#> GSM152049 1 0.4912 0.6304 0.796 0.196 0.008
#> GSM152053 2 0.8722 0.5307 0.272 0.576 0.152
#> GSM152059 1 0.2625 0.6795 0.916 0.000 0.084
#> GSM152085 1 0.4808 0.6360 0.804 0.188 0.008
#> GSM152101 3 0.7588 0.5732 0.312 0.064 0.624
#> GSM152105 1 0.4750 0.5885 0.784 0.000 0.216
#> GSM152034 1 0.5201 0.5885 0.760 0.236 0.004
#> GSM152036 2 0.0892 0.6143 0.020 0.980 0.000
#> GSM152040 1 0.4087 0.6861 0.880 0.052 0.068
#> GSM152043 1 0.1643 0.6859 0.956 0.000 0.044
#> GSM152046 1 0.5529 0.5218 0.704 0.296 0.000
#> GSM152047 1 0.2116 0.6869 0.948 0.012 0.040
#> GSM152048 1 0.5470 0.6513 0.796 0.168 0.036
#> GSM152050 1 0.5269 0.6295 0.784 0.200 0.016
#> GSM152052 1 0.5291 0.5310 0.732 0.000 0.268
#> GSM152056 1 0.5635 0.6454 0.784 0.180 0.036
#> GSM152060 1 0.5529 0.5218 0.704 0.296 0.000
#> GSM152065 1 0.5138 0.5346 0.748 0.000 0.252
#> GSM152066 1 0.5635 0.6454 0.784 0.180 0.036
#> GSM152069 3 0.4887 0.6315 0.228 0.000 0.772
#> GSM152070 1 0.1765 0.6866 0.956 0.004 0.040
#> GSM152071 3 0.4887 0.6315 0.228 0.000 0.772
#> GSM152072 1 0.1989 0.6864 0.948 0.004 0.048
#> GSM152073 1 0.4453 0.6582 0.836 0.152 0.012
#> GSM152078 1 0.4654 0.5979 0.792 0.000 0.208
#> GSM152082 1 0.1643 0.6864 0.956 0.000 0.044
#> GSM152086 1 0.5167 0.6367 0.792 0.192 0.016
#> GSM152090 1 0.6613 0.5859 0.740 0.072 0.188
#> GSM152092 1 0.2796 0.6725 0.908 0.000 0.092
#> GSM152093 1 0.6435 0.6123 0.756 0.076 0.168
#> GSM152094 1 0.4228 0.6579 0.844 0.148 0.008
#> GSM152098 1 0.1643 0.6859 0.956 0.000 0.044
#> GSM152110 1 0.5635 0.6454 0.784 0.180 0.036
#> GSM152031 1 0.4654 0.5971 0.792 0.000 0.208
#> GSM152037 1 0.5955 0.6445 0.772 0.180 0.048
#> GSM152055 1 0.5497 0.5269 0.708 0.292 0.000
#> GSM152061 1 0.5529 0.5218 0.704 0.296 0.000
#> GSM152064 1 0.7222 0.3202 0.580 0.388 0.032
#> GSM152087 1 0.4291 0.6562 0.840 0.152 0.008
#> GSM152103 1 0.6458 0.6011 0.752 0.072 0.176
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM152032 3 0.479 0.55142 0.104 0.108 0.788 0.000
#> GSM152033 3 0.549 -0.03392 0.456 0.016 0.528 0.000
#> GSM152063 2 0.775 0.46793 0.012 0.444 0.160 0.384
#> GSM152074 3 0.519 0.46108 0.012 0.268 0.704 0.016
#> GSM152080 2 0.158 0.54322 0.000 0.948 0.048 0.004
#> GSM152081 4 0.695 0.48523 0.132 0.004 0.284 0.580
#> GSM152083 3 0.529 0.00921 0.000 0.484 0.508 0.008
#> GSM152091 2 0.158 0.54322 0.000 0.948 0.048 0.004
#> GSM152108 3 0.802 0.40609 0.244 0.152 0.552 0.052
#> GSM152114 4 0.769 0.42682 0.228 0.000 0.336 0.436
#> GSM152035 2 0.874 0.22331 0.228 0.480 0.220 0.072
#> GSM152039 4 0.128 0.47301 0.024 0.000 0.012 0.964
#> GSM152041 1 0.732 0.29960 0.560 0.016 0.128 0.296
#> GSM152044 2 0.678 0.59507 0.004 0.532 0.088 0.376
#> GSM152045 1 0.376 0.63456 0.828 0.004 0.156 0.012
#> GSM152051 2 0.678 0.59507 0.004 0.532 0.088 0.376
#> GSM152054 1 0.926 -0.18328 0.368 0.196 0.336 0.100
#> GSM152057 2 0.679 0.59379 0.004 0.528 0.088 0.380
#> GSM152058 1 0.404 0.69304 0.836 0.000 0.080 0.084
#> GSM152067 3 0.584 0.48298 0.048 0.276 0.668 0.008
#> GSM152068 2 0.679 0.59379 0.004 0.528 0.088 0.380
#> GSM152075 4 0.752 0.50046 0.252 0.000 0.252 0.496
#> GSM152076 4 0.128 0.47301 0.024 0.000 0.012 0.964
#> GSM152079 2 0.679 0.59379 0.004 0.528 0.088 0.380
#> GSM152084 3 0.521 0.45835 0.288 0.012 0.688 0.012
#> GSM152089 1 0.759 0.21132 0.516 0.016 0.144 0.324
#> GSM152095 4 0.128 0.47301 0.024 0.000 0.012 0.964
#> GSM152096 3 0.541 0.48836 0.268 0.020 0.696 0.016
#> GSM152097 4 0.481 0.22169 0.008 0.200 0.028 0.764
#> GSM152099 2 0.768 0.45425 0.004 0.492 0.272 0.232
#> GSM152106 4 0.481 0.22169 0.008 0.200 0.028 0.764
#> GSM152107 3 0.675 0.53258 0.156 0.184 0.648 0.012
#> GSM152109 3 0.532 0.44290 0.012 0.288 0.684 0.016
#> GSM152111 1 0.324 0.68997 0.872 0.000 0.028 0.100
#> GSM152112 4 0.772 0.41287 0.240 0.000 0.328 0.432
#> GSM152113 3 0.502 0.37333 0.332 0.012 0.656 0.000
#> GSM152115 3 0.675 0.53258 0.156 0.184 0.648 0.012
#> GSM152030 4 0.734 0.51514 0.176 0.000 0.324 0.500
#> GSM152038 1 0.568 0.32117 0.532 0.012 0.448 0.008
#> GSM152042 4 0.739 0.51804 0.184 0.000 0.320 0.496
#> GSM152062 3 0.516 0.49764 0.264 0.016 0.708 0.012
#> GSM152077 3 0.517 -0.12127 0.492 0.004 0.504 0.000
#> GSM152088 2 0.158 0.54554 0.000 0.948 0.048 0.004
#> GSM152100 4 0.752 0.50046 0.252 0.000 0.252 0.496
#> GSM152102 2 0.843 0.22981 0.228 0.508 0.208 0.056
#> GSM152104 4 0.481 0.22169 0.008 0.200 0.028 0.764
#> GSM152028 1 0.526 0.18699 0.544 0.008 0.448 0.000
#> GSM152029 1 0.382 0.63865 0.824 0.008 0.160 0.008
#> GSM152049 1 0.304 0.69166 0.880 0.000 0.020 0.100
#> GSM152053 4 0.739 0.51804 0.184 0.000 0.320 0.496
#> GSM152059 1 0.503 0.59321 0.736 0.016 0.232 0.016
#> GSM152085 1 0.280 0.69472 0.892 0.000 0.016 0.092
#> GSM152101 3 0.675 0.53258 0.156 0.184 0.648 0.012
#> GSM152105 1 0.567 0.31776 0.536 0.012 0.444 0.008
#> GSM152034 1 0.332 0.66848 0.852 0.000 0.012 0.136
#> GSM152036 4 0.139 0.47352 0.028 0.000 0.012 0.960
#> GSM152040 1 0.463 0.62450 0.784 0.012 0.180 0.024
#> GSM152043 1 0.335 0.62898 0.836 0.000 0.160 0.004
#> GSM152046 1 0.398 0.61816 0.796 0.000 0.012 0.192
#> GSM152047 1 0.378 0.63797 0.832 0.004 0.148 0.016
#> GSM152048 1 0.404 0.69304 0.836 0.000 0.080 0.084
#> GSM152050 1 0.314 0.69085 0.876 0.000 0.024 0.100
#> GSM152052 1 0.601 0.19795 0.492 0.020 0.476 0.012
#> GSM152056 1 0.396 0.69267 0.840 0.000 0.068 0.092
#> GSM152060 1 0.398 0.61816 0.796 0.000 0.012 0.192
#> GSM152065 1 0.527 0.18070 0.540 0.008 0.452 0.000
#> GSM152066 1 0.396 0.69267 0.840 0.000 0.068 0.092
#> GSM152069 3 0.532 0.44290 0.012 0.288 0.684 0.016
#> GSM152070 1 0.353 0.63556 0.840 0.004 0.148 0.008
#> GSM152071 3 0.532 0.44290 0.012 0.288 0.684 0.016
#> GSM152072 1 0.373 0.63221 0.832 0.008 0.152 0.008
#> GSM152073 1 0.323 0.69877 0.880 0.000 0.048 0.072
#> GSM152078 1 0.566 0.34489 0.544 0.012 0.436 0.008
#> GSM152082 1 0.331 0.63096 0.840 0.000 0.156 0.004
#> GSM152086 1 0.312 0.69532 0.880 0.000 0.028 0.092
#> GSM152090 1 0.588 0.29438 0.572 0.008 0.396 0.024
#> GSM152092 1 0.409 0.57922 0.764 0.000 0.232 0.004
#> GSM152093 1 0.554 0.34369 0.592 0.000 0.384 0.024
#> GSM152094 1 0.298 0.69743 0.892 0.000 0.040 0.068
#> GSM152098 1 0.335 0.62898 0.836 0.000 0.160 0.004
#> GSM152110 1 0.396 0.69267 0.840 0.000 0.068 0.092
#> GSM152031 1 0.566 0.34002 0.544 0.012 0.436 0.008
#> GSM152037 1 0.430 0.69018 0.820 0.000 0.088 0.092
#> GSM152055 1 0.394 0.62144 0.800 0.000 0.012 0.188
#> GSM152061 1 0.398 0.61816 0.796 0.000 0.012 0.192
#> GSM152064 1 0.722 0.32815 0.576 0.016 0.124 0.284
#> GSM152087 1 0.306 0.69783 0.888 0.000 0.040 0.072
#> GSM152103 1 0.572 0.32916 0.584 0.004 0.388 0.024
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM152032 5 0.5306 -0.0342 0.012 0.020 0.444 0.004 0.520
#> GSM152033 5 0.3653 0.5997 0.164 0.016 0.012 0.000 0.808
#> GSM152063 2 0.6513 0.5066 0.008 0.468 0.000 0.372 0.152
#> GSM152074 3 0.1525 0.7477 0.000 0.012 0.948 0.004 0.036
#> GSM152080 2 0.1408 0.5065 0.000 0.948 0.044 0.000 0.008
#> GSM152081 4 0.7836 0.4788 0.168 0.008 0.184 0.508 0.132
#> GSM152083 3 0.4346 0.4787 0.000 0.304 0.680 0.004 0.012
#> GSM152091 2 0.1408 0.5065 0.000 0.948 0.044 0.000 0.008
#> GSM152108 5 0.4754 0.3814 0.036 0.164 0.000 0.044 0.756
#> GSM152114 5 0.7622 -0.3573 0.208 0.016 0.028 0.348 0.400
#> GSM152035 2 0.7105 0.3467 0.104 0.524 0.008 0.060 0.304
#> GSM152039 4 0.1670 0.4940 0.052 0.000 0.000 0.936 0.012
#> GSM152041 1 0.6251 0.2665 0.600 0.016 0.000 0.200 0.184
#> GSM152044 2 0.5429 0.6190 0.000 0.564 0.000 0.368 0.068
#> GSM152045 1 0.4467 0.5293 0.696 0.004 0.016 0.004 0.280
#> GSM152051 2 0.5429 0.6190 0.000 0.564 0.000 0.368 0.068
#> GSM152054 5 0.7995 0.2411 0.204 0.232 0.016 0.080 0.468
#> GSM152057 2 0.5439 0.6177 0.000 0.560 0.000 0.372 0.068
#> GSM152058 1 0.3081 0.6574 0.832 0.000 0.000 0.012 0.156
#> GSM152067 3 0.2861 0.7486 0.024 0.024 0.888 0.000 0.064
#> GSM152068 2 0.5439 0.6177 0.000 0.560 0.000 0.372 0.068
#> GSM152075 4 0.7308 0.4118 0.292 0.012 0.008 0.400 0.288
#> GSM152076 4 0.1670 0.4940 0.052 0.000 0.000 0.936 0.012
#> GSM152079 2 0.5439 0.6177 0.000 0.560 0.000 0.372 0.068
#> GSM152084 5 0.5011 0.5124 0.088 0.012 0.176 0.000 0.724
#> GSM152089 1 0.6533 0.1969 0.556 0.016 0.000 0.228 0.200
#> GSM152095 4 0.1670 0.4940 0.052 0.000 0.000 0.936 0.012
#> GSM152096 5 0.5258 0.4944 0.072 0.024 0.180 0.004 0.720
#> GSM152097 4 0.4213 0.2716 0.000 0.124 0.008 0.792 0.076
#> GSM152099 3 0.6902 -0.1224 0.000 0.352 0.408 0.232 0.008
#> GSM152106 4 0.4213 0.2716 0.000 0.124 0.008 0.792 0.076
#> GSM152107 3 0.5304 0.6399 0.056 0.016 0.696 0.008 0.224
#> GSM152109 3 0.0992 0.7528 0.000 0.024 0.968 0.000 0.008
#> GSM152111 1 0.1153 0.7022 0.964 0.000 0.004 0.008 0.024
#> GSM152112 4 0.7829 0.3785 0.156 0.012 0.068 0.400 0.364
#> GSM152113 5 0.4937 0.5700 0.112 0.016 0.128 0.000 0.744
#> GSM152115 3 0.5304 0.6399 0.056 0.016 0.696 0.008 0.224
#> GSM152030 4 0.8445 0.4880 0.184 0.024 0.108 0.416 0.268
#> GSM152038 5 0.6529 0.4294 0.368 0.012 0.124 0.004 0.492
#> GSM152042 4 0.8426 0.4873 0.192 0.024 0.100 0.412 0.272
#> GSM152062 5 0.4876 0.4750 0.064 0.012 0.200 0.000 0.724
#> GSM152077 5 0.3109 0.5925 0.200 0.000 0.000 0.000 0.800
#> GSM152088 2 0.1408 0.5077 0.000 0.948 0.044 0.000 0.008
#> GSM152100 4 0.7308 0.4118 0.292 0.012 0.008 0.400 0.288
#> GSM152102 2 0.6943 0.3516 0.104 0.544 0.012 0.044 0.296
#> GSM152104 4 0.4213 0.2716 0.000 0.124 0.008 0.792 0.076
#> GSM152028 5 0.4217 0.5301 0.272 0.004 0.008 0.004 0.712
#> GSM152029 1 0.4946 0.5405 0.700 0.004 0.056 0.004 0.236
#> GSM152049 1 0.1168 0.7021 0.960 0.000 0.000 0.008 0.032
#> GSM152053 4 0.8426 0.4873 0.192 0.024 0.100 0.412 0.272
#> GSM152059 1 0.5707 0.4755 0.676 0.012 0.192 0.008 0.112
#> GSM152085 1 0.1408 0.7046 0.948 0.000 0.000 0.008 0.044
#> GSM152101 3 0.5304 0.6399 0.056 0.016 0.696 0.008 0.224
#> GSM152105 5 0.6434 0.4290 0.356 0.012 0.116 0.004 0.512
#> GSM152034 1 0.1960 0.6923 0.928 0.000 0.004 0.048 0.020
#> GSM152036 4 0.1740 0.4942 0.056 0.000 0.000 0.932 0.012
#> GSM152040 1 0.4540 0.4673 0.676 0.016 0.000 0.008 0.300
#> GSM152043 1 0.4550 0.5258 0.692 0.000 0.028 0.004 0.276
#> GSM152046 1 0.2358 0.6568 0.888 0.000 0.000 0.104 0.008
#> GSM152047 1 0.4516 0.5374 0.704 0.004 0.016 0.008 0.268
#> GSM152048 1 0.3081 0.6574 0.832 0.000 0.000 0.012 0.156
#> GSM152050 1 0.0932 0.7032 0.972 0.000 0.004 0.004 0.020
#> GSM152052 5 0.6752 0.4523 0.320 0.012 0.152 0.008 0.508
#> GSM152056 1 0.2771 0.6686 0.860 0.000 0.000 0.012 0.128
#> GSM152060 1 0.2358 0.6568 0.888 0.000 0.000 0.104 0.008
#> GSM152065 5 0.4143 0.5414 0.260 0.004 0.008 0.004 0.724
#> GSM152066 1 0.2771 0.6686 0.860 0.000 0.000 0.012 0.128
#> GSM152069 3 0.0992 0.7528 0.000 0.024 0.968 0.000 0.008
#> GSM152070 1 0.4445 0.5310 0.700 0.004 0.016 0.004 0.276
#> GSM152071 3 0.0992 0.7528 0.000 0.024 0.968 0.000 0.008
#> GSM152072 1 0.4428 0.5229 0.692 0.004 0.020 0.000 0.284
#> GSM152073 1 0.1768 0.6971 0.924 0.000 0.004 0.000 0.072
#> GSM152078 5 0.6728 0.3973 0.384 0.012 0.132 0.008 0.464
#> GSM152082 1 0.4491 0.5253 0.692 0.000 0.024 0.004 0.280
#> GSM152086 1 0.1365 0.7060 0.952 0.000 0.004 0.004 0.040
#> GSM152090 5 0.5590 0.4028 0.396 0.008 0.056 0.000 0.540
#> GSM152092 1 0.4973 0.3078 0.564 0.000 0.024 0.004 0.408
#> GSM152093 5 0.5170 0.3761 0.412 0.008 0.028 0.000 0.552
#> GSM152094 1 0.1831 0.6946 0.920 0.000 0.004 0.000 0.076
#> GSM152098 1 0.4550 0.5258 0.692 0.000 0.028 0.004 0.276
#> GSM152110 1 0.2771 0.6686 0.860 0.000 0.000 0.012 0.128
#> GSM152031 5 0.6487 0.4134 0.364 0.012 0.120 0.004 0.500
#> GSM152037 1 0.2997 0.6565 0.840 0.000 0.000 0.012 0.148
#> GSM152055 1 0.2304 0.6591 0.892 0.000 0.000 0.100 0.008
#> GSM152061 1 0.2358 0.6568 0.888 0.000 0.000 0.104 0.008
#> GSM152064 1 0.6073 0.3036 0.624 0.016 0.000 0.188 0.172
#> GSM152087 1 0.1768 0.6965 0.924 0.000 0.004 0.000 0.072
#> GSM152103 5 0.5363 0.3901 0.404 0.008 0.040 0.000 0.548
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM152032 1 0.5387 0.0306 0.464 0.004 0.436 0.000 0.096 0.000
#> GSM152033 1 0.2395 0.6093 0.896 0.012 0.004 0.000 0.016 0.072
#> GSM152063 2 0.6955 0.5211 0.076 0.392 0.000 0.368 0.160 0.004
#> GSM152074 3 0.2526 0.7337 0.024 0.004 0.876 0.000 0.096 0.000
#> GSM152080 2 0.0260 0.5264 0.000 0.992 0.008 0.000 0.000 0.000
#> GSM152081 5 0.7817 0.3450 0.080 0.000 0.096 0.208 0.460 0.156
#> GSM152083 3 0.4788 0.4823 0.004 0.288 0.636 0.000 0.072 0.000
#> GSM152091 2 0.0260 0.5264 0.000 0.992 0.008 0.000 0.000 0.000
#> GSM152108 1 0.4897 0.3466 0.700 0.128 0.000 0.000 0.152 0.020
#> GSM152114 5 0.6326 0.6280 0.272 0.000 0.004 0.032 0.516 0.176
#> GSM152035 2 0.6848 0.3111 0.216 0.464 0.000 0.004 0.256 0.060
#> GSM152039 4 0.4791 0.6209 0.004 0.000 0.000 0.564 0.384 0.048
#> GSM152041 6 0.5947 0.0902 0.136 0.000 0.000 0.036 0.264 0.564
#> GSM152044 2 0.5744 0.6099 0.020 0.496 0.000 0.380 0.104 0.000
#> GSM152045 6 0.5330 0.5296 0.220 0.004 0.020 0.000 0.108 0.648
#> GSM152051 2 0.5744 0.6099 0.020 0.496 0.000 0.380 0.104 0.000
#> GSM152054 5 0.7255 0.0156 0.332 0.172 0.000 0.000 0.368 0.128
#> GSM152057 2 0.5778 0.6091 0.020 0.492 0.000 0.380 0.108 0.000
#> GSM152058 6 0.3726 0.5981 0.216 0.000 0.000 0.004 0.028 0.752
#> GSM152067 3 0.1644 0.7436 0.004 0.000 0.920 0.000 0.076 0.000
#> GSM152068 2 0.5778 0.6091 0.020 0.492 0.000 0.380 0.108 0.000
#> GSM152075 5 0.6632 0.6218 0.132 0.000 0.004 0.080 0.512 0.272
#> GSM152076 4 0.4791 0.6209 0.004 0.000 0.000 0.564 0.384 0.048
#> GSM152079 2 0.5778 0.6091 0.020 0.492 0.000 0.380 0.108 0.000
#> GSM152084 1 0.5456 0.4935 0.656 0.000 0.160 0.000 0.144 0.040
#> GSM152089 6 0.6408 -0.0551 0.144 0.000 0.000 0.060 0.284 0.512
#> GSM152095 4 0.4791 0.6209 0.004 0.000 0.000 0.564 0.384 0.048
#> GSM152096 1 0.5724 0.4850 0.648 0.012 0.164 0.000 0.140 0.036
#> GSM152097 4 0.0146 0.5611 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM152099 3 0.6345 -0.0757 0.000 0.328 0.420 0.236 0.016 0.000
#> GSM152106 4 0.0146 0.5611 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM152107 3 0.5146 0.6402 0.104 0.000 0.636 0.000 0.248 0.012
#> GSM152109 3 0.0000 0.7473 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM152111 6 0.1565 0.6862 0.028 0.000 0.004 0.000 0.028 0.940
#> GSM152112 5 0.6323 0.6101 0.196 0.000 0.012 0.080 0.596 0.116
#> GSM152113 1 0.5099 0.5467 0.720 0.008 0.120 0.000 0.100 0.052
#> GSM152115 3 0.5146 0.6402 0.104 0.000 0.636 0.000 0.248 0.012
#> GSM152030 5 0.6553 0.6697 0.132 0.000 0.020 0.096 0.592 0.160
#> GSM152038 1 0.6118 0.5403 0.564 0.000 0.080 0.000 0.092 0.264
#> GSM152042 5 0.6565 0.6764 0.136 0.000 0.016 0.096 0.584 0.168
#> GSM152062 1 0.5296 0.4734 0.656 0.000 0.184 0.000 0.136 0.024
#> GSM152077 1 0.2609 0.6178 0.868 0.000 0.000 0.000 0.036 0.096
#> GSM152088 2 0.0405 0.5282 0.000 0.988 0.008 0.004 0.000 0.000
#> GSM152100 5 0.6632 0.6218 0.132 0.000 0.004 0.080 0.512 0.272
#> GSM152102 2 0.6742 0.3284 0.216 0.492 0.000 0.004 0.228 0.060
#> GSM152104 4 0.0146 0.5611 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM152028 1 0.3168 0.6149 0.792 0.000 0.000 0.000 0.016 0.192
#> GSM152029 6 0.5515 0.5396 0.200 0.004 0.052 0.000 0.088 0.656
#> GSM152049 6 0.1176 0.6856 0.024 0.000 0.000 0.000 0.020 0.956
#> GSM152053 5 0.6565 0.6764 0.136 0.000 0.016 0.096 0.584 0.168
#> GSM152059 6 0.6485 0.3990 0.116 0.004 0.144 0.000 0.160 0.576
#> GSM152085 6 0.1245 0.6879 0.032 0.000 0.000 0.000 0.016 0.952
#> GSM152101 3 0.5146 0.6402 0.104 0.000 0.636 0.000 0.248 0.012
#> GSM152105 1 0.5825 0.5427 0.600 0.000 0.072 0.000 0.080 0.248
#> GSM152034 6 0.2033 0.6796 0.020 0.004 0.004 0.000 0.056 0.916
#> GSM152036 4 0.4845 0.6165 0.004 0.000 0.000 0.560 0.384 0.052
#> GSM152040 6 0.5302 0.4912 0.208 0.004 0.000 0.000 0.172 0.616
#> GSM152043 6 0.5422 0.5278 0.220 0.004 0.032 0.000 0.096 0.648
#> GSM152046 6 0.2313 0.6335 0.012 0.000 0.000 0.004 0.100 0.884
#> GSM152047 6 0.5117 0.5469 0.212 0.004 0.016 0.000 0.100 0.668
#> GSM152048 6 0.3726 0.5981 0.216 0.000 0.000 0.004 0.028 0.752
#> GSM152050 6 0.1405 0.6865 0.024 0.000 0.004 0.000 0.024 0.948
#> GSM152052 1 0.6067 0.5344 0.612 0.000 0.100 0.000 0.128 0.160
#> GSM152056 6 0.3419 0.6227 0.176 0.000 0.000 0.004 0.028 0.792
#> GSM152060 6 0.2313 0.6335 0.012 0.000 0.000 0.004 0.100 0.884
#> GSM152065 1 0.3071 0.6239 0.804 0.000 0.000 0.000 0.016 0.180
#> GSM152066 6 0.3419 0.6227 0.176 0.000 0.000 0.004 0.028 0.792
#> GSM152069 3 0.0000 0.7473 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM152070 6 0.5149 0.5377 0.224 0.004 0.016 0.000 0.096 0.660
#> GSM152071 3 0.0000 0.7473 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM152072 6 0.5389 0.5247 0.224 0.004 0.024 0.000 0.104 0.644
#> GSM152073 6 0.2796 0.6775 0.056 0.004 0.004 0.000 0.064 0.872
#> GSM152078 1 0.6370 0.5216 0.536 0.000 0.088 0.000 0.108 0.268
#> GSM152082 6 0.5374 0.5212 0.236 0.004 0.024 0.000 0.096 0.640
#> GSM152086 6 0.1867 0.6886 0.036 0.000 0.004 0.000 0.036 0.924
#> GSM152090 1 0.6120 0.4391 0.508 0.000 0.048 0.000 0.108 0.336
#> GSM152092 6 0.5738 0.2434 0.408 0.000 0.024 0.000 0.092 0.476
#> GSM152093 1 0.5787 0.4120 0.516 0.000 0.020 0.000 0.116 0.348
#> GSM152094 6 0.2737 0.6755 0.056 0.004 0.004 0.000 0.060 0.876
#> GSM152098 6 0.5422 0.5278 0.220 0.004 0.032 0.000 0.096 0.648
#> GSM152110 6 0.3419 0.6227 0.176 0.000 0.000 0.004 0.028 0.792
#> GSM152031 1 0.5891 0.5378 0.592 0.000 0.076 0.000 0.080 0.252
#> GSM152037 6 0.3610 0.6050 0.200 0.000 0.000 0.004 0.028 0.768
#> GSM152055 6 0.2264 0.6363 0.012 0.000 0.000 0.004 0.096 0.888
#> GSM152061 6 0.2313 0.6335 0.012 0.000 0.000 0.004 0.100 0.884
#> GSM152064 6 0.5760 0.1598 0.132 0.000 0.000 0.032 0.244 0.592
#> GSM152087 6 0.2614 0.6782 0.056 0.004 0.004 0.000 0.052 0.884
#> GSM152103 1 0.5969 0.4266 0.512 0.000 0.032 0.000 0.116 0.340
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 specimen(p) k
#> SD:hclust 61 4.64e-04 2
#> SD:hclust 66 3.01e-07 3
#> SD:hclust 47 8.68e-06 4
#> SD:hclust 50 5.36e-03 5
#> SD:hclust 68 7.71e-04 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "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 10612 rows and 88 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 0.716 0.908 0.934 0.4940 0.501 0.501
#> 3 3 0.564 0.741 0.848 0.3200 0.762 0.557
#> 4 4 0.584 0.752 0.809 0.1278 0.906 0.735
#> 5 5 0.668 0.599 0.739 0.0741 0.881 0.599
#> 6 6 0.691 0.576 0.749 0.0423 0.952 0.774
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
#> GSM152032 2 0.7056 0.846 0.192 0.808
#> GSM152033 1 0.1184 0.930 0.984 0.016
#> GSM152063 2 0.0938 0.932 0.012 0.988
#> GSM152074 2 0.5519 0.893 0.128 0.872
#> GSM152080 2 0.4022 0.913 0.080 0.920
#> GSM152081 2 0.2603 0.935 0.044 0.956
#> GSM152083 2 0.4022 0.913 0.080 0.920
#> GSM152091 2 0.1843 0.934 0.028 0.972
#> GSM152108 2 0.2043 0.934 0.032 0.968
#> GSM152114 1 0.7674 0.781 0.776 0.224
#> GSM152035 2 0.1843 0.934 0.028 0.972
#> GSM152039 2 0.2603 0.935 0.044 0.956
#> GSM152041 2 0.4939 0.890 0.108 0.892
#> GSM152044 2 0.0938 0.932 0.012 0.988
#> GSM152045 1 0.0938 0.932 0.988 0.012
#> GSM152051 2 0.1843 0.934 0.028 0.972
#> GSM152054 2 0.7299 0.833 0.204 0.796
#> GSM152057 2 0.1843 0.934 0.028 0.972
#> GSM152058 1 0.3584 0.923 0.932 0.068
#> GSM152067 2 0.7056 0.846 0.192 0.808
#> GSM152068 2 0.0376 0.935 0.004 0.996
#> GSM152075 2 0.2603 0.935 0.044 0.956
#> GSM152076 2 0.2603 0.935 0.044 0.956
#> GSM152079 2 0.1843 0.934 0.028 0.972
#> GSM152084 1 0.8499 0.619 0.724 0.276
#> GSM152089 2 0.4562 0.905 0.096 0.904
#> GSM152095 2 0.2423 0.935 0.040 0.960
#> GSM152096 2 0.6438 0.867 0.164 0.836
#> GSM152097 2 0.1184 0.931 0.016 0.984
#> GSM152099 2 0.1843 0.934 0.028 0.972
#> GSM152106 2 0.1184 0.931 0.016 0.984
#> GSM152107 2 0.3114 0.935 0.056 0.944
#> GSM152109 2 0.7219 0.837 0.200 0.800
#> GSM152111 1 0.3733 0.922 0.928 0.072
#> GSM152112 2 0.2423 0.938 0.040 0.960
#> GSM152113 1 0.6247 0.814 0.844 0.156
#> GSM152115 2 0.7056 0.846 0.192 0.808
#> GSM152030 2 0.2603 0.935 0.044 0.956
#> GSM152038 1 0.1184 0.930 0.984 0.016
#> GSM152042 2 0.2603 0.935 0.044 0.956
#> GSM152062 1 0.8207 0.659 0.744 0.256
#> GSM152077 1 0.3584 0.923 0.932 0.068
#> GSM152088 2 0.1843 0.934 0.028 0.972
#> GSM152100 2 0.2603 0.935 0.044 0.956
#> GSM152102 2 0.4022 0.913 0.080 0.920
#> GSM152104 2 0.1184 0.931 0.016 0.984
#> GSM152028 1 0.1184 0.930 0.984 0.016
#> GSM152029 1 0.1184 0.930 0.984 0.016
#> GSM152049 1 0.3733 0.922 0.928 0.072
#> GSM152053 2 0.2603 0.935 0.044 0.956
#> GSM152059 1 0.1184 0.930 0.984 0.016
#> GSM152085 1 0.3733 0.922 0.928 0.072
#> GSM152101 2 0.4939 0.911 0.108 0.892
#> GSM152105 1 0.1184 0.930 0.984 0.016
#> GSM152034 1 0.4022 0.917 0.920 0.080
#> GSM152036 2 0.2603 0.935 0.044 0.956
#> GSM152040 1 0.1843 0.930 0.972 0.028
#> GSM152043 1 0.0376 0.931 0.996 0.004
#> GSM152046 1 0.4022 0.917 0.920 0.080
#> GSM152047 1 0.1843 0.930 0.972 0.028
#> GSM152048 1 0.3584 0.923 0.932 0.068
#> GSM152050 1 0.3733 0.922 0.928 0.072
#> GSM152052 1 0.1184 0.930 0.984 0.016
#> GSM152056 1 0.3733 0.922 0.928 0.072
#> GSM152060 1 0.4022 0.917 0.920 0.080
#> GSM152065 1 0.1184 0.930 0.984 0.016
#> GSM152066 1 0.1633 0.931 0.976 0.024
#> GSM152069 1 0.6623 0.794 0.828 0.172
#> GSM152070 1 0.1184 0.930 0.984 0.016
#> GSM152071 1 0.6531 0.800 0.832 0.168
#> GSM152072 1 0.1184 0.930 0.984 0.016
#> GSM152073 1 0.0672 0.931 0.992 0.008
#> GSM152078 1 0.1184 0.930 0.984 0.016
#> GSM152082 1 0.1184 0.930 0.984 0.016
#> GSM152086 1 0.1633 0.931 0.976 0.024
#> GSM152090 1 0.6438 0.805 0.836 0.164
#> GSM152092 1 0.1184 0.930 0.984 0.016
#> GSM152093 1 0.3733 0.922 0.928 0.072
#> GSM152094 1 0.1633 0.931 0.976 0.024
#> GSM152098 1 0.1184 0.930 0.984 0.016
#> GSM152110 1 0.3733 0.922 0.928 0.072
#> GSM152031 1 0.1184 0.930 0.984 0.016
#> GSM152037 1 0.1633 0.931 0.976 0.024
#> GSM152055 1 0.4022 0.917 0.920 0.080
#> GSM152061 1 0.4022 0.917 0.920 0.080
#> GSM152064 1 0.4022 0.917 0.920 0.080
#> GSM152087 1 0.1843 0.930 0.972 0.028
#> GSM152103 1 0.2423 0.920 0.960 0.040
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM152032 3 0.1482 0.784 0.020 0.012 0.968
#> GSM152033 3 0.3551 0.756 0.132 0.000 0.868
#> GSM152063 2 0.2066 0.723 0.000 0.940 0.060
#> GSM152074 3 0.1453 0.776 0.008 0.024 0.968
#> GSM152080 3 0.6111 0.331 0.000 0.396 0.604
#> GSM152081 2 0.7703 0.696 0.104 0.664 0.232
#> GSM152083 3 0.5591 0.480 0.000 0.304 0.696
#> GSM152091 2 0.5431 0.519 0.000 0.716 0.284
#> GSM152108 2 0.5216 0.567 0.000 0.740 0.260
#> GSM152114 1 0.6217 0.524 0.712 0.024 0.264
#> GSM152035 2 0.4702 0.627 0.000 0.788 0.212
#> GSM152039 2 0.7179 0.724 0.104 0.712 0.184
#> GSM152041 2 0.7462 0.714 0.124 0.696 0.180
#> GSM152044 2 0.1031 0.727 0.000 0.976 0.024
#> GSM152045 1 0.5926 0.465 0.644 0.000 0.356
#> GSM152051 2 0.3686 0.692 0.000 0.860 0.140
#> GSM152054 3 0.5223 0.574 0.024 0.176 0.800
#> GSM152057 2 0.3686 0.692 0.000 0.860 0.140
#> GSM152058 1 0.0892 0.909 0.980 0.000 0.020
#> GSM152067 3 0.1182 0.779 0.012 0.012 0.976
#> GSM152068 2 0.2625 0.717 0.000 0.916 0.084
#> GSM152075 2 0.7368 0.717 0.104 0.696 0.200
#> GSM152076 2 0.7179 0.724 0.104 0.712 0.184
#> GSM152079 2 0.3686 0.692 0.000 0.860 0.140
#> GSM152084 3 0.1860 0.787 0.052 0.000 0.948
#> GSM152089 2 0.8318 0.651 0.116 0.600 0.284
#> GSM152095 2 0.7179 0.724 0.104 0.712 0.184
#> GSM152096 3 0.1877 0.776 0.012 0.032 0.956
#> GSM152097 2 0.0592 0.729 0.000 0.988 0.012
#> GSM152099 2 0.3686 0.692 0.000 0.860 0.140
#> GSM152106 2 0.0592 0.729 0.000 0.988 0.012
#> GSM152107 3 0.3528 0.667 0.016 0.092 0.892
#> GSM152109 3 0.1482 0.784 0.020 0.012 0.968
#> GSM152111 1 0.0424 0.900 0.992 0.000 0.008
#> GSM152112 2 0.8179 0.586 0.084 0.564 0.352
#> GSM152113 3 0.2448 0.787 0.076 0.000 0.924
#> GSM152115 3 0.0661 0.773 0.008 0.004 0.988
#> GSM152030 2 0.7778 0.689 0.104 0.656 0.240
#> GSM152038 3 0.2448 0.787 0.076 0.000 0.924
#> GSM152042 2 0.8014 0.662 0.104 0.628 0.268
#> GSM152062 3 0.1860 0.787 0.052 0.000 0.948
#> GSM152077 1 0.0892 0.909 0.980 0.000 0.020
#> GSM152088 2 0.5098 0.575 0.000 0.752 0.248
#> GSM152100 2 0.7276 0.721 0.104 0.704 0.192
#> GSM152102 3 0.6305 0.105 0.000 0.484 0.516
#> GSM152104 2 0.0747 0.728 0.000 0.984 0.016
#> GSM152028 1 0.3192 0.869 0.888 0.000 0.112
#> GSM152029 3 0.6252 0.191 0.444 0.000 0.556
#> GSM152049 1 0.0892 0.909 0.980 0.000 0.020
#> GSM152053 2 0.8075 0.654 0.104 0.620 0.276
#> GSM152059 1 0.3267 0.867 0.884 0.000 0.116
#> GSM152085 1 0.0237 0.902 0.996 0.000 0.004
#> GSM152101 3 0.3528 0.667 0.016 0.092 0.892
#> GSM152105 1 0.3752 0.843 0.856 0.000 0.144
#> GSM152034 1 0.1774 0.881 0.960 0.024 0.016
#> GSM152036 2 0.7179 0.724 0.104 0.712 0.184
#> GSM152040 1 0.1031 0.908 0.976 0.000 0.024
#> GSM152043 1 0.3267 0.867 0.884 0.000 0.116
#> GSM152046 1 0.1620 0.884 0.964 0.024 0.012
#> GSM152047 1 0.0424 0.904 0.992 0.000 0.008
#> GSM152048 1 0.0892 0.909 0.980 0.000 0.020
#> GSM152050 1 0.0424 0.900 0.992 0.000 0.008
#> GSM152052 1 0.4346 0.800 0.816 0.000 0.184
#> GSM152056 1 0.0000 0.904 1.000 0.000 0.000
#> GSM152060 1 0.1774 0.881 0.960 0.024 0.016
#> GSM152065 1 0.6095 0.382 0.608 0.000 0.392
#> GSM152066 1 0.0892 0.909 0.980 0.000 0.020
#> GSM152069 3 0.2200 0.791 0.056 0.004 0.940
#> GSM152070 1 0.3267 0.867 0.884 0.000 0.116
#> GSM152071 3 0.2066 0.791 0.060 0.000 0.940
#> GSM152072 3 0.6045 0.369 0.380 0.000 0.620
#> GSM152073 1 0.2959 0.875 0.900 0.000 0.100
#> GSM152078 3 0.6215 0.242 0.428 0.000 0.572
#> GSM152082 1 0.3267 0.867 0.884 0.000 0.116
#> GSM152086 1 0.0892 0.909 0.980 0.000 0.020
#> GSM152090 3 0.3686 0.749 0.140 0.000 0.860
#> GSM152092 1 0.3267 0.867 0.884 0.000 0.116
#> GSM152093 1 0.0892 0.909 0.980 0.000 0.020
#> GSM152094 1 0.0892 0.909 0.980 0.000 0.020
#> GSM152098 1 0.3267 0.867 0.884 0.000 0.116
#> GSM152110 1 0.0000 0.904 1.000 0.000 0.000
#> GSM152031 1 0.3267 0.867 0.884 0.000 0.116
#> GSM152037 1 0.0892 0.909 0.980 0.000 0.020
#> GSM152055 1 0.1774 0.881 0.960 0.024 0.016
#> GSM152061 1 0.1774 0.881 0.960 0.024 0.016
#> GSM152064 1 0.1337 0.889 0.972 0.012 0.016
#> GSM152087 1 0.0892 0.909 0.980 0.000 0.020
#> GSM152103 3 0.3941 0.736 0.156 0.000 0.844
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM152032 3 0.2593 0.766 0.000 0.080 0.904 0.016
#> GSM152033 3 0.4604 0.705 0.036 0.004 0.784 0.176
#> GSM152063 2 0.1389 0.861 0.000 0.952 0.000 0.048
#> GSM152074 3 0.2662 0.765 0.000 0.084 0.900 0.016
#> GSM152080 2 0.4244 0.748 0.000 0.804 0.160 0.036
#> GSM152081 4 0.5315 0.867 0.016 0.200 0.040 0.744
#> GSM152083 3 0.5352 0.317 0.000 0.388 0.596 0.016
#> GSM152091 2 0.3342 0.814 0.000 0.868 0.100 0.032
#> GSM152108 2 0.4793 0.735 0.008 0.800 0.080 0.112
#> GSM152114 4 0.5459 0.524 0.128 0.004 0.120 0.748
#> GSM152035 2 0.1398 0.865 0.000 0.956 0.040 0.004
#> GSM152039 4 0.4920 0.856 0.028 0.228 0.004 0.740
#> GSM152041 4 0.5512 0.806 0.124 0.128 0.004 0.744
#> GSM152044 2 0.2011 0.836 0.000 0.920 0.000 0.080
#> GSM152045 1 0.6319 0.336 0.604 0.000 0.312 0.084
#> GSM152051 2 0.0376 0.878 0.000 0.992 0.004 0.004
#> GSM152054 3 0.8564 0.501 0.184 0.076 0.512 0.228
#> GSM152057 2 0.0657 0.876 0.000 0.984 0.004 0.012
#> GSM152058 1 0.4937 0.795 0.764 0.000 0.064 0.172
#> GSM152067 3 0.3555 0.764 0.004 0.080 0.868 0.048
#> GSM152068 2 0.0707 0.875 0.000 0.980 0.000 0.020
#> GSM152075 4 0.5057 0.868 0.024 0.200 0.020 0.756
#> GSM152076 4 0.4879 0.861 0.016 0.228 0.012 0.744
#> GSM152079 2 0.0376 0.878 0.000 0.992 0.004 0.004
#> GSM152084 3 0.2984 0.762 0.000 0.028 0.888 0.084
#> GSM152089 4 0.5516 0.708 0.200 0.056 0.012 0.732
#> GSM152095 4 0.4879 0.861 0.016 0.228 0.012 0.744
#> GSM152096 3 0.2706 0.767 0.000 0.080 0.900 0.020
#> GSM152097 2 0.2408 0.814 0.000 0.896 0.000 0.104
#> GSM152099 2 0.0376 0.878 0.000 0.992 0.004 0.004
#> GSM152106 2 0.2408 0.814 0.000 0.896 0.000 0.104
#> GSM152107 3 0.6393 0.466 0.000 0.100 0.616 0.284
#> GSM152109 3 0.3360 0.765 0.004 0.084 0.876 0.036
#> GSM152111 1 0.1474 0.812 0.948 0.000 0.000 0.052
#> GSM152112 4 0.6458 0.748 0.004 0.160 0.176 0.660
#> GSM152113 3 0.3940 0.726 0.020 0.004 0.824 0.152
#> GSM152115 3 0.4036 0.742 0.000 0.076 0.836 0.088
#> GSM152030 4 0.5797 0.853 0.016 0.188 0.072 0.724
#> GSM152038 3 0.2654 0.751 0.000 0.004 0.888 0.108
#> GSM152042 4 0.6231 0.828 0.016 0.172 0.112 0.700
#> GSM152062 3 0.2984 0.762 0.000 0.028 0.888 0.084
#> GSM152077 1 0.5944 0.759 0.700 0.004 0.104 0.192
#> GSM152088 2 0.3307 0.813 0.000 0.868 0.104 0.028
#> GSM152100 4 0.4809 0.865 0.016 0.220 0.012 0.752
#> GSM152102 2 0.4511 0.734 0.000 0.784 0.176 0.040
#> GSM152104 2 0.2149 0.828 0.000 0.912 0.000 0.088
#> GSM152028 1 0.6001 0.747 0.688 0.000 0.128 0.184
#> GSM152029 3 0.6524 0.532 0.316 0.012 0.604 0.068
#> GSM152049 1 0.3552 0.818 0.848 0.000 0.024 0.128
#> GSM152053 4 0.6294 0.823 0.016 0.168 0.120 0.696
#> GSM152059 1 0.2670 0.801 0.908 0.000 0.052 0.040
#> GSM152085 1 0.1118 0.813 0.964 0.000 0.000 0.036
#> GSM152101 3 0.5809 0.587 0.000 0.092 0.692 0.216
#> GSM152105 1 0.7352 0.430 0.496 0.000 0.328 0.176
#> GSM152034 1 0.2868 0.751 0.864 0.000 0.000 0.136
#> GSM152036 4 0.5033 0.858 0.036 0.220 0.004 0.740
#> GSM152040 1 0.2089 0.805 0.932 0.000 0.020 0.048
#> GSM152043 1 0.4621 0.797 0.796 0.000 0.076 0.128
#> GSM152046 1 0.2704 0.762 0.876 0.000 0.000 0.124
#> GSM152047 1 0.2142 0.806 0.928 0.000 0.016 0.056
#> GSM152048 1 0.4937 0.795 0.764 0.000 0.064 0.172
#> GSM152050 1 0.1474 0.812 0.948 0.000 0.000 0.052
#> GSM152052 1 0.7355 0.510 0.536 0.004 0.284 0.176
#> GSM152056 1 0.4746 0.798 0.776 0.000 0.056 0.168
#> GSM152060 1 0.2868 0.751 0.864 0.000 0.000 0.136
#> GSM152065 3 0.7035 0.344 0.244 0.000 0.572 0.184
#> GSM152066 1 0.4663 0.796 0.788 0.000 0.064 0.148
#> GSM152069 3 0.3266 0.766 0.004 0.084 0.880 0.032
#> GSM152070 1 0.3400 0.784 0.872 0.000 0.064 0.064
#> GSM152071 3 0.3266 0.766 0.004 0.084 0.880 0.032
#> GSM152072 3 0.5632 0.695 0.176 0.008 0.732 0.084
#> GSM152073 1 0.2385 0.809 0.920 0.000 0.028 0.052
#> GSM152078 3 0.6699 0.543 0.192 0.008 0.644 0.156
#> GSM152082 1 0.5080 0.781 0.764 0.000 0.092 0.144
#> GSM152086 1 0.2813 0.824 0.896 0.000 0.024 0.080
#> GSM152090 3 0.5235 0.722 0.124 0.028 0.784 0.064
#> GSM152092 1 0.5962 0.749 0.692 0.000 0.128 0.180
#> GSM152093 1 0.4949 0.794 0.760 0.000 0.060 0.180
#> GSM152094 1 0.0336 0.815 0.992 0.000 0.000 0.008
#> GSM152098 1 0.3398 0.784 0.872 0.000 0.068 0.060
#> GSM152110 1 0.4378 0.806 0.796 0.000 0.040 0.164
#> GSM152031 1 0.6678 0.661 0.620 0.000 0.208 0.172
#> GSM152037 1 0.4758 0.794 0.780 0.000 0.064 0.156
#> GSM152055 1 0.2973 0.753 0.856 0.000 0.000 0.144
#> GSM152061 1 0.2868 0.751 0.864 0.000 0.000 0.136
#> GSM152064 1 0.2760 0.763 0.872 0.000 0.000 0.128
#> GSM152087 1 0.0336 0.815 0.992 0.000 0.000 0.008
#> GSM152103 3 0.5390 0.717 0.136 0.028 0.772 0.064
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM152032 3 0.2585 0.76635 0.000 0.024 0.904 0.024 0.048
#> GSM152033 5 0.4531 0.31632 0.008 0.008 0.308 0.004 0.672
#> GSM152063 2 0.1608 0.90442 0.000 0.928 0.000 0.072 0.000
#> GSM152074 3 0.2815 0.76637 0.000 0.028 0.892 0.024 0.056
#> GSM152080 2 0.2927 0.85340 0.000 0.872 0.060 0.000 0.068
#> GSM152081 4 0.1716 0.90090 0.000 0.024 0.016 0.944 0.016
#> GSM152083 3 0.4957 0.48315 0.000 0.296 0.660 0.012 0.032
#> GSM152091 2 0.2790 0.85664 0.000 0.880 0.052 0.000 0.068
#> GSM152108 2 0.5615 0.44801 0.004 0.608 0.056 0.012 0.320
#> GSM152114 5 0.7738 0.22420 0.164 0.016 0.052 0.336 0.432
#> GSM152035 2 0.1799 0.89180 0.000 0.940 0.012 0.020 0.028
#> GSM152039 4 0.1202 0.90343 0.004 0.032 0.000 0.960 0.004
#> GSM152041 4 0.2462 0.87988 0.048 0.020 0.004 0.912 0.016
#> GSM152044 2 0.2189 0.89695 0.000 0.904 0.000 0.084 0.012
#> GSM152045 1 0.6166 0.35992 0.576 0.012 0.092 0.008 0.312
#> GSM152051 2 0.1845 0.90530 0.000 0.928 0.000 0.056 0.016
#> GSM152054 5 0.8770 -0.11091 0.296 0.024 0.240 0.120 0.320
#> GSM152057 2 0.1341 0.90547 0.000 0.944 0.000 0.056 0.000
#> GSM152058 5 0.4560 0.33745 0.484 0.008 0.000 0.000 0.508
#> GSM152067 3 0.2595 0.75365 0.000 0.032 0.888 0.000 0.080
#> GSM152068 2 0.1478 0.90491 0.000 0.936 0.000 0.064 0.000
#> GSM152075 4 0.1554 0.90486 0.004 0.024 0.008 0.952 0.012
#> GSM152076 4 0.1202 0.90343 0.004 0.032 0.000 0.960 0.004
#> GSM152079 2 0.1502 0.90572 0.000 0.940 0.000 0.056 0.004
#> GSM152084 3 0.4074 0.71644 0.000 0.012 0.780 0.028 0.180
#> GSM152089 4 0.6356 0.44722 0.312 0.020 0.024 0.580 0.064
#> GSM152095 4 0.1202 0.90343 0.004 0.032 0.000 0.960 0.004
#> GSM152096 3 0.3556 0.74710 0.000 0.032 0.828 0.008 0.132
#> GSM152097 2 0.2969 0.86889 0.000 0.852 0.000 0.128 0.020
#> GSM152099 2 0.1877 0.90424 0.000 0.924 0.000 0.064 0.012
#> GSM152106 2 0.2969 0.86889 0.000 0.852 0.000 0.128 0.020
#> GSM152107 3 0.5344 0.62058 0.004 0.032 0.708 0.200 0.056
#> GSM152109 3 0.1915 0.76161 0.000 0.032 0.928 0.000 0.040
#> GSM152111 1 0.1485 0.64442 0.948 0.000 0.000 0.032 0.020
#> GSM152112 4 0.4035 0.81783 0.004 0.028 0.080 0.828 0.060
#> GSM152113 5 0.4944 -0.00883 0.000 0.012 0.416 0.012 0.560
#> GSM152115 3 0.4181 0.74128 0.004 0.024 0.816 0.064 0.092
#> GSM152030 4 0.2599 0.88270 0.000 0.024 0.044 0.904 0.028
#> GSM152038 3 0.4462 0.59208 0.000 0.004 0.672 0.016 0.308
#> GSM152042 4 0.2857 0.86942 0.000 0.020 0.064 0.888 0.028
#> GSM152062 3 0.3881 0.71683 0.000 0.008 0.788 0.024 0.180
#> GSM152077 5 0.5564 0.48702 0.328 0.016 0.032 0.012 0.612
#> GSM152088 2 0.2592 0.86125 0.000 0.892 0.056 0.000 0.052
#> GSM152100 4 0.1554 0.90555 0.004 0.024 0.008 0.952 0.012
#> GSM152102 2 0.4005 0.80710 0.004 0.804 0.052 0.004 0.136
#> GSM152104 2 0.2573 0.88750 0.000 0.880 0.000 0.104 0.016
#> GSM152028 5 0.3817 0.53008 0.252 0.004 0.004 0.000 0.740
#> GSM152029 3 0.6957 0.03729 0.360 0.008 0.384 0.000 0.248
#> GSM152049 1 0.4165 0.09245 0.672 0.008 0.000 0.000 0.320
#> GSM152053 4 0.2984 0.86380 0.000 0.020 0.072 0.880 0.028
#> GSM152059 1 0.4040 0.49553 0.712 0.000 0.012 0.000 0.276
#> GSM152085 1 0.0693 0.64629 0.980 0.000 0.000 0.008 0.012
#> GSM152101 3 0.4849 0.69253 0.004 0.024 0.764 0.132 0.076
#> GSM152105 5 0.4404 0.56913 0.152 0.000 0.088 0.000 0.760
#> GSM152034 1 0.2248 0.65120 0.900 0.000 0.000 0.088 0.012
#> GSM152036 4 0.1202 0.90343 0.004 0.032 0.000 0.960 0.004
#> GSM152040 1 0.3421 0.57118 0.788 0.000 0.008 0.000 0.204
#> GSM152043 5 0.4430 0.16850 0.456 0.000 0.004 0.000 0.540
#> GSM152046 1 0.2112 0.65236 0.908 0.000 0.004 0.084 0.004
#> GSM152047 1 0.3132 0.59804 0.820 0.000 0.008 0.000 0.172
#> GSM152048 5 0.4560 0.33745 0.484 0.008 0.000 0.000 0.508
#> GSM152050 1 0.1568 0.64513 0.944 0.000 0.000 0.036 0.020
#> GSM152052 5 0.5150 0.56333 0.228 0.008 0.076 0.000 0.688
#> GSM152056 1 0.4561 -0.36172 0.504 0.008 0.000 0.000 0.488
#> GSM152060 1 0.2011 0.65035 0.908 0.000 0.004 0.088 0.000
#> GSM152065 5 0.3992 0.53669 0.080 0.000 0.124 0.000 0.796
#> GSM152066 5 0.4561 0.32566 0.488 0.008 0.000 0.000 0.504
#> GSM152069 3 0.1915 0.76161 0.000 0.032 0.928 0.000 0.040
#> GSM152070 1 0.4540 0.43541 0.640 0.000 0.020 0.000 0.340
#> GSM152071 3 0.1915 0.76161 0.000 0.032 0.928 0.000 0.040
#> GSM152072 3 0.6547 0.36633 0.140 0.012 0.524 0.004 0.320
#> GSM152073 1 0.3671 0.53859 0.756 0.000 0.008 0.000 0.236
#> GSM152078 5 0.5255 0.34170 0.068 0.004 0.284 0.000 0.644
#> GSM152082 5 0.4348 0.37109 0.316 0.000 0.016 0.000 0.668
#> GSM152086 1 0.4029 0.16508 0.680 0.004 0.000 0.000 0.316
#> GSM152090 3 0.5117 0.65829 0.064 0.012 0.720 0.008 0.196
#> GSM152092 5 0.3612 0.51114 0.268 0.000 0.000 0.000 0.732
#> GSM152093 1 0.4702 -0.33294 0.512 0.008 0.004 0.000 0.476
#> GSM152094 1 0.2233 0.63033 0.892 0.000 0.004 0.000 0.104
#> GSM152098 1 0.4540 0.43436 0.640 0.000 0.020 0.000 0.340
#> GSM152110 1 0.4473 -0.19391 0.580 0.008 0.000 0.000 0.412
#> GSM152031 5 0.3988 0.55621 0.196 0.000 0.036 0.000 0.768
#> GSM152037 5 0.4549 0.36744 0.464 0.008 0.000 0.000 0.528
#> GSM152055 1 0.1851 0.64956 0.912 0.000 0.000 0.088 0.000
#> GSM152061 1 0.2011 0.65035 0.908 0.000 0.004 0.088 0.000
#> GSM152064 1 0.2011 0.64654 0.908 0.000 0.000 0.088 0.004
#> GSM152087 1 0.1704 0.64247 0.928 0.000 0.004 0.000 0.068
#> GSM152103 3 0.5008 0.64580 0.072 0.008 0.720 0.004 0.196
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM152032 3 0.1534 0.7460 0.032 0.004 0.944 0.004 0.016 0.000
#> GSM152033 1 0.4324 0.4788 0.724 0.004 0.192 0.000 0.080 0.000
#> GSM152063 2 0.1049 0.8593 0.000 0.960 0.000 0.032 0.008 0.000
#> GSM152074 3 0.2350 0.7377 0.024 0.004 0.900 0.008 0.064 0.000
#> GSM152080 2 0.3583 0.7469 0.008 0.728 0.004 0.000 0.260 0.000
#> GSM152081 4 0.2765 0.8576 0.000 0.008 0.028 0.876 0.080 0.008
#> GSM152083 3 0.4516 0.5388 0.016 0.240 0.700 0.004 0.040 0.000
#> GSM152091 2 0.3560 0.7495 0.008 0.732 0.004 0.000 0.256 0.000
#> GSM152108 2 0.6630 0.2601 0.344 0.492 0.072 0.040 0.052 0.000
#> GSM152114 1 0.6779 0.4701 0.560 0.004 0.056 0.220 0.032 0.128
#> GSM152035 2 0.2873 0.8279 0.012 0.868 0.016 0.012 0.092 0.000
#> GSM152039 4 0.1982 0.8618 0.004 0.012 0.000 0.924 0.040 0.020
#> GSM152041 4 0.3262 0.7507 0.000 0.004 0.004 0.800 0.012 0.180
#> GSM152044 2 0.1564 0.8542 0.000 0.936 0.000 0.040 0.024 0.000
#> GSM152045 5 0.5835 0.2172 0.132 0.000 0.012 0.000 0.452 0.404
#> GSM152051 2 0.1418 0.8583 0.000 0.944 0.000 0.032 0.024 0.000
#> GSM152054 5 0.7340 0.4949 0.104 0.008 0.156 0.060 0.552 0.120
#> GSM152057 2 0.0790 0.8598 0.000 0.968 0.000 0.032 0.000 0.000
#> GSM152058 1 0.3584 0.5795 0.688 0.000 0.000 0.004 0.000 0.308
#> GSM152067 3 0.3574 0.6927 0.020 0.020 0.804 0.000 0.152 0.004
#> GSM152068 2 0.0790 0.8598 0.000 0.968 0.000 0.032 0.000 0.000
#> GSM152075 4 0.0881 0.8668 0.000 0.008 0.000 0.972 0.008 0.012
#> GSM152076 4 0.1982 0.8618 0.004 0.012 0.000 0.924 0.040 0.020
#> GSM152079 2 0.0790 0.8598 0.000 0.968 0.000 0.032 0.000 0.000
#> GSM152084 3 0.4547 0.7172 0.148 0.008 0.752 0.060 0.032 0.000
#> GSM152089 4 0.6229 0.1872 0.008 0.004 0.012 0.468 0.144 0.364
#> GSM152095 4 0.1982 0.8618 0.004 0.012 0.000 0.924 0.040 0.020
#> GSM152096 3 0.4255 0.7230 0.144 0.016 0.776 0.032 0.032 0.000
#> GSM152097 2 0.3479 0.8028 0.008 0.820 0.000 0.088 0.084 0.000
#> GSM152099 2 0.0935 0.8600 0.000 0.964 0.000 0.032 0.004 0.000
#> GSM152106 2 0.3479 0.8028 0.008 0.820 0.000 0.088 0.084 0.000
#> GSM152107 3 0.4740 0.6469 0.012 0.004 0.724 0.160 0.096 0.004
#> GSM152109 3 0.3019 0.7147 0.032 0.020 0.856 0.000 0.092 0.000
#> GSM152111 6 0.1897 0.5826 0.084 0.000 0.000 0.004 0.004 0.908
#> GSM152112 4 0.3447 0.8047 0.008 0.008 0.064 0.840 0.076 0.004
#> GSM152113 1 0.5677 0.2649 0.588 0.008 0.296 0.032 0.076 0.000
#> GSM152115 3 0.3963 0.6999 0.032 0.000 0.796 0.044 0.124 0.004
#> GSM152030 4 0.2257 0.8518 0.000 0.008 0.040 0.904 0.048 0.000
#> GSM152038 3 0.5063 0.4894 0.324 0.004 0.596 0.004 0.072 0.000
#> GSM152042 4 0.2392 0.8481 0.000 0.008 0.048 0.896 0.048 0.000
#> GSM152062 3 0.4370 0.7191 0.148 0.008 0.764 0.048 0.032 0.000
#> GSM152077 1 0.4133 0.6169 0.808 0.004 0.040 0.036 0.020 0.092
#> GSM152088 2 0.3121 0.7811 0.008 0.796 0.004 0.000 0.192 0.000
#> GSM152100 4 0.0881 0.8667 0.000 0.008 0.000 0.972 0.008 0.012
#> GSM152102 2 0.4874 0.6454 0.024 0.600 0.032 0.000 0.344 0.000
#> GSM152104 2 0.2884 0.8278 0.008 0.864 0.000 0.064 0.064 0.000
#> GSM152028 1 0.3210 0.5971 0.836 0.004 0.000 0.000 0.072 0.088
#> GSM152029 5 0.7386 0.5084 0.124 0.008 0.180 0.000 0.420 0.268
#> GSM152049 6 0.3737 0.0432 0.392 0.000 0.000 0.000 0.000 0.608
#> GSM152053 4 0.2519 0.8435 0.000 0.008 0.056 0.888 0.048 0.000
#> GSM152059 6 0.5830 -0.0459 0.156 0.000 0.008 0.000 0.344 0.492
#> GSM152085 6 0.1285 0.5953 0.052 0.000 0.000 0.000 0.004 0.944
#> GSM152101 3 0.4319 0.6771 0.012 0.004 0.768 0.092 0.120 0.004
#> GSM152105 1 0.3327 0.5837 0.848 0.004 0.064 0.000 0.060 0.024
#> GSM152034 6 0.1889 0.5799 0.004 0.000 0.000 0.020 0.056 0.920
#> GSM152036 4 0.1982 0.8618 0.004 0.012 0.000 0.924 0.040 0.020
#> GSM152040 6 0.5135 0.1436 0.104 0.000 0.000 0.000 0.324 0.572
#> GSM152043 1 0.6078 -0.2335 0.396 0.000 0.000 0.000 0.320 0.284
#> GSM152046 6 0.1983 0.5807 0.000 0.000 0.000 0.020 0.072 0.908
#> GSM152047 6 0.4617 0.2968 0.056 0.000 0.000 0.004 0.296 0.644
#> GSM152048 1 0.3584 0.5795 0.688 0.000 0.000 0.004 0.000 0.308
#> GSM152050 6 0.1908 0.5781 0.096 0.000 0.000 0.004 0.000 0.900
#> GSM152052 1 0.3050 0.6120 0.864 0.000 0.048 0.000 0.040 0.048
#> GSM152056 1 0.3728 0.5422 0.652 0.000 0.000 0.004 0.000 0.344
#> GSM152060 6 0.2123 0.5865 0.008 0.000 0.000 0.020 0.064 0.908
#> GSM152065 1 0.4065 0.4628 0.764 0.004 0.040 0.000 0.176 0.016
#> GSM152066 1 0.3601 0.5759 0.684 0.000 0.000 0.004 0.000 0.312
#> GSM152069 3 0.3140 0.7138 0.036 0.020 0.848 0.000 0.096 0.000
#> GSM152070 6 0.5890 -0.2281 0.172 0.000 0.004 0.000 0.404 0.420
#> GSM152071 3 0.3140 0.7138 0.036 0.020 0.848 0.000 0.096 0.000
#> GSM152072 5 0.6597 0.5564 0.156 0.000 0.252 0.000 0.512 0.080
#> GSM152073 6 0.5683 0.1231 0.184 0.000 0.000 0.000 0.308 0.508
#> GSM152078 1 0.5745 0.2857 0.612 0.004 0.184 0.000 0.176 0.024
#> GSM152082 1 0.5878 -0.0560 0.492 0.004 0.004 0.000 0.340 0.160
#> GSM152086 6 0.4084 0.0507 0.400 0.000 0.000 0.000 0.012 0.588
#> GSM152090 3 0.5301 0.6402 0.232 0.008 0.672 0.032 0.040 0.016
#> GSM152092 1 0.4338 0.4952 0.732 0.004 0.000 0.000 0.164 0.100
#> GSM152093 1 0.5167 0.5507 0.620 0.000 0.020 0.032 0.020 0.308
#> GSM152094 6 0.4198 0.4135 0.060 0.000 0.000 0.000 0.232 0.708
#> GSM152098 6 0.5887 -0.2122 0.172 0.000 0.004 0.000 0.396 0.428
#> GSM152110 1 0.3881 0.4701 0.600 0.000 0.000 0.004 0.000 0.396
#> GSM152031 1 0.4021 0.5565 0.796 0.004 0.032 0.000 0.112 0.056
#> GSM152037 1 0.3489 0.5925 0.708 0.000 0.000 0.004 0.000 0.288
#> GSM152055 6 0.1882 0.5804 0.028 0.000 0.000 0.020 0.024 0.928
#> GSM152061 6 0.2123 0.5865 0.008 0.000 0.000 0.020 0.064 0.908
#> GSM152064 6 0.1390 0.5920 0.032 0.000 0.000 0.016 0.004 0.948
#> GSM152087 6 0.3794 0.4597 0.040 0.000 0.000 0.000 0.216 0.744
#> GSM152103 3 0.5193 0.6252 0.240 0.004 0.672 0.024 0.036 0.024
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n specimen(p) k
#> SD:kmeans 88 5.90e-09 2
#> SD:kmeans 80 2.23e-06 3
#> SD:kmeans 83 2.02e-05 4
#> SD:kmeans 62 1.44e-03 5
#> SD:kmeans 64 1.99e-02 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 10612 rows and 88 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 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 0.952 0.921 0.972 0.5052 0.494 0.494
#> 3 3 0.925 0.882 0.954 0.3174 0.782 0.584
#> 4 4 0.745 0.855 0.892 0.1153 0.870 0.642
#> 5 5 0.785 0.727 0.859 0.0842 0.883 0.590
#> 6 6 0.768 0.626 0.783 0.0391 0.932 0.678
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
#> GSM152032 2 0.0000 0.96335 0.000 1.000
#> GSM152033 1 0.0000 0.97590 1.000 0.000
#> GSM152063 2 0.0000 0.96335 0.000 1.000
#> GSM152074 2 0.0000 0.96335 0.000 1.000
#> GSM152080 2 0.0000 0.96335 0.000 1.000
#> GSM152081 2 0.0000 0.96335 0.000 1.000
#> GSM152083 2 0.0000 0.96335 0.000 1.000
#> GSM152091 2 0.0000 0.96335 0.000 1.000
#> GSM152108 2 0.0000 0.96335 0.000 1.000
#> GSM152114 2 0.9286 0.48876 0.344 0.656
#> GSM152035 2 0.0000 0.96335 0.000 1.000
#> GSM152039 2 0.0000 0.96335 0.000 1.000
#> GSM152041 2 0.5178 0.85144 0.116 0.884
#> GSM152044 2 0.0000 0.96335 0.000 1.000
#> GSM152045 1 0.0000 0.97590 1.000 0.000
#> GSM152051 2 0.0000 0.96335 0.000 1.000
#> GSM152054 2 0.3584 0.90288 0.068 0.932
#> GSM152057 2 0.0000 0.96335 0.000 1.000
#> GSM152058 1 0.0000 0.97590 1.000 0.000
#> GSM152067 2 0.0000 0.96335 0.000 1.000
#> GSM152068 2 0.0000 0.96335 0.000 1.000
#> GSM152075 2 0.0000 0.96335 0.000 1.000
#> GSM152076 2 0.0000 0.96335 0.000 1.000
#> GSM152079 2 0.0000 0.96335 0.000 1.000
#> GSM152084 2 0.0000 0.96335 0.000 1.000
#> GSM152089 2 0.0000 0.96335 0.000 1.000
#> GSM152095 2 0.0000 0.96335 0.000 1.000
#> GSM152096 2 0.0000 0.96335 0.000 1.000
#> GSM152097 2 0.0000 0.96335 0.000 1.000
#> GSM152099 2 0.0000 0.96335 0.000 1.000
#> GSM152106 2 0.0000 0.96335 0.000 1.000
#> GSM152107 2 0.0000 0.96335 0.000 1.000
#> GSM152109 2 0.0000 0.96335 0.000 1.000
#> GSM152111 1 0.0000 0.97590 1.000 0.000
#> GSM152112 2 0.0000 0.96335 0.000 1.000
#> GSM152113 2 0.9815 0.29366 0.420 0.580
#> GSM152115 2 0.0000 0.96335 0.000 1.000
#> GSM152030 2 0.0000 0.96335 0.000 1.000
#> GSM152038 1 0.0000 0.97590 1.000 0.000
#> GSM152042 2 0.0000 0.96335 0.000 1.000
#> GSM152062 2 0.4690 0.86815 0.100 0.900
#> GSM152077 1 0.0000 0.97590 1.000 0.000
#> GSM152088 2 0.0000 0.96335 0.000 1.000
#> GSM152100 2 0.0000 0.96335 0.000 1.000
#> GSM152102 2 0.0000 0.96335 0.000 1.000
#> GSM152104 2 0.0000 0.96335 0.000 1.000
#> GSM152028 1 0.0000 0.97590 1.000 0.000
#> GSM152029 1 0.0000 0.97590 1.000 0.000
#> GSM152049 1 0.0000 0.97590 1.000 0.000
#> GSM152053 2 0.0000 0.96335 0.000 1.000
#> GSM152059 1 0.0000 0.97590 1.000 0.000
#> GSM152085 1 0.0000 0.97590 1.000 0.000
#> GSM152101 2 0.0000 0.96335 0.000 1.000
#> GSM152105 1 0.0000 0.97590 1.000 0.000
#> GSM152034 1 0.0000 0.97590 1.000 0.000
#> GSM152036 2 0.0000 0.96335 0.000 1.000
#> GSM152040 1 0.0000 0.97590 1.000 0.000
#> GSM152043 1 0.0000 0.97590 1.000 0.000
#> GSM152046 1 0.0000 0.97590 1.000 0.000
#> GSM152047 1 0.0000 0.97590 1.000 0.000
#> GSM152048 1 0.0000 0.97590 1.000 0.000
#> GSM152050 1 0.0000 0.97590 1.000 0.000
#> GSM152052 1 0.0000 0.97590 1.000 0.000
#> GSM152056 1 0.0000 0.97590 1.000 0.000
#> GSM152060 1 0.0000 0.97590 1.000 0.000
#> GSM152065 1 0.0000 0.97590 1.000 0.000
#> GSM152066 1 0.0000 0.97590 1.000 0.000
#> GSM152069 2 0.9983 0.09020 0.476 0.524
#> GSM152070 1 0.0000 0.97590 1.000 0.000
#> GSM152071 1 0.9998 -0.00942 0.508 0.492
#> GSM152072 1 0.0000 0.97590 1.000 0.000
#> GSM152073 1 0.0000 0.97590 1.000 0.000
#> GSM152078 1 0.0000 0.97590 1.000 0.000
#> GSM152082 1 0.0000 0.97590 1.000 0.000
#> GSM152086 1 0.0000 0.97590 1.000 0.000
#> GSM152090 1 0.9996 0.00640 0.512 0.488
#> GSM152092 1 0.0000 0.97590 1.000 0.000
#> GSM152093 1 0.0000 0.97590 1.000 0.000
#> GSM152094 1 0.0000 0.97590 1.000 0.000
#> GSM152098 1 0.0000 0.97590 1.000 0.000
#> GSM152110 1 0.0000 0.97590 1.000 0.000
#> GSM152031 1 0.0000 0.97590 1.000 0.000
#> GSM152037 1 0.0000 0.97590 1.000 0.000
#> GSM152055 1 0.0000 0.97590 1.000 0.000
#> GSM152061 1 0.0000 0.97590 1.000 0.000
#> GSM152064 1 0.0000 0.97590 1.000 0.000
#> GSM152087 1 0.0000 0.97590 1.000 0.000
#> GSM152103 1 0.0376 0.97198 0.996 0.004
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM152032 3 0.0000 0.946 0.000 0.000 1.000
#> GSM152033 3 0.0000 0.946 0.000 0.000 1.000
#> GSM152063 2 0.0000 0.931 0.000 1.000 0.000
#> GSM152074 3 0.0000 0.946 0.000 0.000 1.000
#> GSM152080 3 0.3038 0.859 0.000 0.104 0.896
#> GSM152081 2 0.0000 0.931 0.000 1.000 0.000
#> GSM152083 3 0.1529 0.917 0.000 0.040 0.960
#> GSM152091 2 0.0424 0.928 0.000 0.992 0.008
#> GSM152108 2 0.0237 0.930 0.000 0.996 0.004
#> GSM152114 2 0.9086 0.232 0.356 0.496 0.148
#> GSM152035 2 0.0237 0.930 0.000 0.996 0.004
#> GSM152039 2 0.0000 0.931 0.000 1.000 0.000
#> GSM152041 2 0.0000 0.931 0.000 1.000 0.000
#> GSM152044 2 0.0000 0.931 0.000 1.000 0.000
#> GSM152045 1 0.6180 0.235 0.584 0.000 0.416
#> GSM152051 2 0.0237 0.930 0.000 0.996 0.004
#> GSM152054 2 0.6252 0.187 0.000 0.556 0.444
#> GSM152057 2 0.0237 0.930 0.000 0.996 0.004
#> GSM152058 1 0.0000 0.965 1.000 0.000 0.000
#> GSM152067 3 0.0000 0.946 0.000 0.000 1.000
#> GSM152068 2 0.0237 0.930 0.000 0.996 0.004
#> GSM152075 2 0.0000 0.931 0.000 1.000 0.000
#> GSM152076 2 0.0000 0.931 0.000 1.000 0.000
#> GSM152079 2 0.0237 0.930 0.000 0.996 0.004
#> GSM152084 3 0.0000 0.946 0.000 0.000 1.000
#> GSM152089 2 0.0000 0.931 0.000 1.000 0.000
#> GSM152095 2 0.0000 0.931 0.000 1.000 0.000
#> GSM152096 3 0.0000 0.946 0.000 0.000 1.000
#> GSM152097 2 0.0000 0.931 0.000 1.000 0.000
#> GSM152099 2 0.0237 0.930 0.000 0.996 0.004
#> GSM152106 2 0.0000 0.931 0.000 1.000 0.000
#> GSM152107 2 0.6126 0.350 0.000 0.600 0.400
#> GSM152109 3 0.0000 0.946 0.000 0.000 1.000
#> GSM152111 1 0.0000 0.965 1.000 0.000 0.000
#> GSM152112 2 0.0000 0.931 0.000 1.000 0.000
#> GSM152113 3 0.0000 0.946 0.000 0.000 1.000
#> GSM152115 3 0.0592 0.940 0.000 0.012 0.988
#> GSM152030 2 0.0237 0.929 0.000 0.996 0.004
#> GSM152038 3 0.0000 0.946 0.000 0.000 1.000
#> GSM152042 2 0.1411 0.905 0.000 0.964 0.036
#> GSM152062 3 0.0000 0.946 0.000 0.000 1.000
#> GSM152077 1 0.0000 0.965 1.000 0.000 0.000
#> GSM152088 2 0.0237 0.930 0.000 0.996 0.004
#> GSM152100 2 0.0000 0.931 0.000 1.000 0.000
#> GSM152102 2 0.6274 0.148 0.000 0.544 0.456
#> GSM152104 2 0.0000 0.931 0.000 1.000 0.000
#> GSM152028 1 0.0000 0.965 1.000 0.000 0.000
#> GSM152029 3 0.2165 0.900 0.064 0.000 0.936
#> GSM152049 1 0.0000 0.965 1.000 0.000 0.000
#> GSM152053 2 0.1964 0.888 0.000 0.944 0.056
#> GSM152059 1 0.0000 0.965 1.000 0.000 0.000
#> GSM152085 1 0.0000 0.965 1.000 0.000 0.000
#> GSM152101 3 0.6140 0.248 0.000 0.404 0.596
#> GSM152105 1 0.5178 0.656 0.744 0.000 0.256
#> GSM152034 1 0.0000 0.965 1.000 0.000 0.000
#> GSM152036 2 0.0000 0.931 0.000 1.000 0.000
#> GSM152040 1 0.0000 0.965 1.000 0.000 0.000
#> GSM152043 1 0.0000 0.965 1.000 0.000 0.000
#> GSM152046 1 0.0000 0.965 1.000 0.000 0.000
#> GSM152047 1 0.0000 0.965 1.000 0.000 0.000
#> GSM152048 1 0.0000 0.965 1.000 0.000 0.000
#> GSM152050 1 0.0000 0.965 1.000 0.000 0.000
#> GSM152052 1 0.5988 0.436 0.632 0.000 0.368
#> GSM152056 1 0.0000 0.965 1.000 0.000 0.000
#> GSM152060 1 0.0000 0.965 1.000 0.000 0.000
#> GSM152065 3 0.5560 0.552 0.300 0.000 0.700
#> GSM152066 1 0.0000 0.965 1.000 0.000 0.000
#> GSM152069 3 0.0000 0.946 0.000 0.000 1.000
#> GSM152070 1 0.0000 0.965 1.000 0.000 0.000
#> GSM152071 3 0.0000 0.946 0.000 0.000 1.000
#> GSM152072 3 0.1289 0.927 0.032 0.000 0.968
#> GSM152073 1 0.0000 0.965 1.000 0.000 0.000
#> GSM152078 3 0.1529 0.921 0.040 0.000 0.960
#> GSM152082 1 0.0000 0.965 1.000 0.000 0.000
#> GSM152086 1 0.0000 0.965 1.000 0.000 0.000
#> GSM152090 3 0.0000 0.946 0.000 0.000 1.000
#> GSM152092 1 0.0000 0.965 1.000 0.000 0.000
#> GSM152093 1 0.0000 0.965 1.000 0.000 0.000
#> GSM152094 1 0.0000 0.965 1.000 0.000 0.000
#> GSM152098 1 0.0000 0.965 1.000 0.000 0.000
#> GSM152110 1 0.0000 0.965 1.000 0.000 0.000
#> GSM152031 1 0.2625 0.885 0.916 0.000 0.084
#> GSM152037 1 0.0000 0.965 1.000 0.000 0.000
#> GSM152055 1 0.0000 0.965 1.000 0.000 0.000
#> GSM152061 1 0.0000 0.965 1.000 0.000 0.000
#> GSM152064 1 0.0000 0.965 1.000 0.000 0.000
#> GSM152087 1 0.0000 0.965 1.000 0.000 0.000
#> GSM152103 3 0.0424 0.942 0.008 0.000 0.992
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM152032 3 0.0469 0.864 0.000 0.012 0.988 0.000
#> GSM152033 3 0.2888 0.824 0.000 0.124 0.872 0.004
#> GSM152063 2 0.3266 0.925 0.000 0.832 0.000 0.168
#> GSM152074 3 0.0469 0.864 0.000 0.012 0.988 0.000
#> GSM152080 2 0.3597 0.834 0.000 0.836 0.148 0.016
#> GSM152081 4 0.0188 0.933 0.000 0.004 0.000 0.996
#> GSM152083 2 0.4072 0.706 0.000 0.748 0.252 0.000
#> GSM152091 2 0.3907 0.914 0.000 0.836 0.044 0.120
#> GSM152108 2 0.1557 0.849 0.000 0.944 0.000 0.056
#> GSM152114 4 0.4233 0.776 0.032 0.140 0.008 0.820
#> GSM152035 2 0.3450 0.927 0.000 0.836 0.008 0.156
#> GSM152039 4 0.0188 0.933 0.000 0.004 0.000 0.996
#> GSM152041 4 0.1297 0.915 0.020 0.016 0.000 0.964
#> GSM152044 2 0.3266 0.925 0.000 0.832 0.000 0.168
#> GSM152045 1 0.5105 0.617 0.708 0.024 0.264 0.004
#> GSM152051 2 0.3355 0.928 0.000 0.836 0.004 0.160
#> GSM152054 2 0.5346 0.791 0.060 0.780 0.124 0.036
#> GSM152057 2 0.3219 0.927 0.000 0.836 0.000 0.164
#> GSM152058 1 0.3432 0.883 0.848 0.140 0.008 0.004
#> GSM152067 3 0.0592 0.864 0.000 0.016 0.984 0.000
#> GSM152068 2 0.3219 0.927 0.000 0.836 0.000 0.164
#> GSM152075 4 0.0188 0.933 0.000 0.004 0.000 0.996
#> GSM152076 4 0.0188 0.933 0.000 0.004 0.000 0.996
#> GSM152079 2 0.3355 0.928 0.000 0.836 0.004 0.160
#> GSM152084 3 0.3638 0.779 0.000 0.032 0.848 0.120
#> GSM152089 4 0.2412 0.863 0.084 0.008 0.000 0.908
#> GSM152095 4 0.0188 0.933 0.000 0.004 0.000 0.996
#> GSM152096 3 0.4888 0.193 0.000 0.412 0.588 0.000
#> GSM152097 2 0.3444 0.914 0.000 0.816 0.000 0.184
#> GSM152099 2 0.3355 0.928 0.000 0.836 0.004 0.160
#> GSM152106 2 0.3400 0.917 0.000 0.820 0.000 0.180
#> GSM152107 4 0.3402 0.794 0.000 0.004 0.164 0.832
#> GSM152109 3 0.0469 0.864 0.000 0.012 0.988 0.000
#> GSM152111 1 0.0895 0.907 0.976 0.020 0.000 0.004
#> GSM152112 4 0.0592 0.929 0.000 0.000 0.016 0.984
#> GSM152113 3 0.2401 0.842 0.000 0.092 0.904 0.004
#> GSM152115 3 0.4212 0.646 0.000 0.012 0.772 0.216
#> GSM152030 4 0.0376 0.932 0.000 0.004 0.004 0.992
#> GSM152038 3 0.1022 0.863 0.000 0.032 0.968 0.000
#> GSM152042 4 0.0469 0.931 0.000 0.000 0.012 0.988
#> GSM152062 3 0.1356 0.863 0.000 0.032 0.960 0.008
#> GSM152077 1 0.3560 0.881 0.844 0.140 0.012 0.004
#> GSM152088 2 0.3958 0.910 0.000 0.836 0.052 0.112
#> GSM152100 4 0.0188 0.933 0.000 0.004 0.000 0.996
#> GSM152102 2 0.3821 0.858 0.000 0.840 0.120 0.040
#> GSM152104 2 0.3266 0.925 0.000 0.832 0.000 0.168
#> GSM152028 1 0.5192 0.841 0.760 0.160 0.076 0.004
#> GSM152029 3 0.2861 0.824 0.096 0.016 0.888 0.000
#> GSM152049 1 0.2654 0.896 0.888 0.108 0.000 0.004
#> GSM152053 4 0.0469 0.931 0.000 0.000 0.012 0.988
#> GSM152059 1 0.2843 0.865 0.892 0.020 0.088 0.000
#> GSM152085 1 0.0000 0.906 1.000 0.000 0.000 0.000
#> GSM152101 4 0.4795 0.600 0.000 0.012 0.292 0.696
#> GSM152105 3 0.5246 0.749 0.088 0.148 0.760 0.004
#> GSM152034 1 0.1302 0.893 0.956 0.000 0.000 0.044
#> GSM152036 4 0.0188 0.933 0.000 0.004 0.000 0.996
#> GSM152040 1 0.1004 0.903 0.972 0.024 0.004 0.000
#> GSM152043 1 0.3652 0.884 0.856 0.092 0.052 0.000
#> GSM152046 1 0.0592 0.903 0.984 0.000 0.000 0.016
#> GSM152047 1 0.1297 0.903 0.964 0.020 0.000 0.016
#> GSM152048 1 0.3432 0.883 0.848 0.140 0.008 0.004
#> GSM152050 1 0.1042 0.906 0.972 0.020 0.000 0.008
#> GSM152052 3 0.6838 0.523 0.232 0.152 0.612 0.004
#> GSM152056 1 0.3380 0.885 0.852 0.136 0.008 0.004
#> GSM152060 1 0.0817 0.901 0.976 0.000 0.000 0.024
#> GSM152065 3 0.4439 0.790 0.048 0.140 0.808 0.004
#> GSM152066 1 0.3380 0.885 0.852 0.136 0.008 0.004
#> GSM152069 3 0.0469 0.864 0.000 0.012 0.988 0.000
#> GSM152070 1 0.2882 0.864 0.892 0.024 0.084 0.000
#> GSM152071 3 0.0469 0.864 0.000 0.012 0.988 0.000
#> GSM152072 3 0.1520 0.860 0.020 0.024 0.956 0.000
#> GSM152073 1 0.1004 0.905 0.972 0.024 0.004 0.000
#> GSM152078 3 0.2019 0.858 0.024 0.032 0.940 0.004
#> GSM152082 1 0.4953 0.830 0.776 0.120 0.104 0.000
#> GSM152086 1 0.1661 0.906 0.944 0.052 0.000 0.004
#> GSM152090 3 0.1042 0.860 0.000 0.020 0.972 0.008
#> GSM152092 1 0.5136 0.838 0.768 0.144 0.084 0.004
#> GSM152093 1 0.4037 0.877 0.828 0.140 0.008 0.024
#> GSM152094 1 0.0469 0.905 0.988 0.012 0.000 0.000
#> GSM152098 1 0.3080 0.855 0.880 0.024 0.096 0.000
#> GSM152110 1 0.3052 0.888 0.860 0.136 0.000 0.004
#> GSM152031 3 0.7146 0.378 0.292 0.148 0.556 0.004
#> GSM152037 1 0.3432 0.883 0.848 0.140 0.008 0.004
#> GSM152055 1 0.1406 0.903 0.960 0.016 0.000 0.024
#> GSM152061 1 0.0817 0.901 0.976 0.000 0.000 0.024
#> GSM152064 1 0.1488 0.900 0.956 0.012 0.000 0.032
#> GSM152087 1 0.0469 0.905 0.988 0.012 0.000 0.000
#> GSM152103 3 0.0469 0.865 0.000 0.012 0.988 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM152032 3 0.0955 0.8126 0.028 0.004 0.968 0.000 0.000
#> GSM152033 1 0.4009 0.4067 0.684 0.004 0.312 0.000 0.000
#> GSM152063 2 0.0162 0.9419 0.000 0.996 0.000 0.004 0.000
#> GSM152074 3 0.0955 0.8126 0.028 0.004 0.968 0.000 0.000
#> GSM152080 2 0.0162 0.9406 0.000 0.996 0.004 0.000 0.000
#> GSM152081 4 0.0000 0.9526 0.000 0.000 0.000 1.000 0.000
#> GSM152083 2 0.4291 0.0890 0.000 0.536 0.464 0.000 0.000
#> GSM152091 2 0.0162 0.9406 0.000 0.996 0.004 0.000 0.000
#> GSM152108 2 0.0162 0.9389 0.004 0.996 0.000 0.000 0.000
#> GSM152114 1 0.5919 0.2467 0.500 0.000 0.008 0.412 0.080
#> GSM152035 2 0.0000 0.9402 0.000 1.000 0.000 0.000 0.000
#> GSM152039 4 0.0000 0.9526 0.000 0.000 0.000 1.000 0.000
#> GSM152041 4 0.0290 0.9469 0.000 0.000 0.000 0.992 0.008
#> GSM152044 2 0.0162 0.9419 0.000 0.996 0.000 0.004 0.000
#> GSM152045 5 0.4199 0.7130 0.180 0.000 0.056 0.000 0.764
#> GSM152051 2 0.0162 0.9419 0.000 0.996 0.000 0.004 0.000
#> GSM152054 2 0.6579 0.5946 0.156 0.664 0.048 0.044 0.088
#> GSM152057 2 0.0162 0.9419 0.000 0.996 0.000 0.004 0.000
#> GSM152058 1 0.3336 0.7128 0.772 0.000 0.000 0.000 0.228
#> GSM152067 3 0.0671 0.8104 0.016 0.000 0.980 0.000 0.004
#> GSM152068 2 0.0162 0.9419 0.000 0.996 0.000 0.004 0.000
#> GSM152075 4 0.0000 0.9526 0.000 0.000 0.000 1.000 0.000
#> GSM152076 4 0.0000 0.9526 0.000 0.000 0.000 1.000 0.000
#> GSM152079 2 0.0162 0.9419 0.000 0.996 0.000 0.004 0.000
#> GSM152084 3 0.1442 0.8093 0.032 0.004 0.952 0.012 0.000
#> GSM152089 4 0.3139 0.8248 0.012 0.008 0.008 0.860 0.112
#> GSM152095 4 0.0000 0.9526 0.000 0.000 0.000 1.000 0.000
#> GSM152096 3 0.4101 0.4326 0.004 0.332 0.664 0.000 0.000
#> GSM152097 2 0.1410 0.9010 0.000 0.940 0.000 0.060 0.000
#> GSM152099 2 0.0162 0.9419 0.000 0.996 0.000 0.004 0.000
#> GSM152106 2 0.1341 0.9041 0.000 0.944 0.000 0.056 0.000
#> GSM152107 4 0.4331 0.3016 0.000 0.004 0.400 0.596 0.000
#> GSM152109 3 0.0566 0.8139 0.012 0.000 0.984 0.000 0.004
#> GSM152111 5 0.2389 0.7267 0.116 0.000 0.000 0.004 0.880
#> GSM152112 4 0.0290 0.9490 0.000 0.000 0.008 0.992 0.000
#> GSM152113 3 0.4450 0.0933 0.488 0.004 0.508 0.000 0.000
#> GSM152115 3 0.1560 0.8056 0.028 0.004 0.948 0.020 0.000
#> GSM152030 4 0.0162 0.9513 0.000 0.000 0.004 0.996 0.000
#> GSM152038 3 0.3010 0.7243 0.172 0.004 0.824 0.000 0.000
#> GSM152042 4 0.0162 0.9513 0.000 0.000 0.004 0.996 0.000
#> GSM152062 3 0.1041 0.8118 0.032 0.004 0.964 0.000 0.000
#> GSM152077 1 0.2970 0.7246 0.828 0.000 0.004 0.000 0.168
#> GSM152088 2 0.0162 0.9406 0.000 0.996 0.004 0.000 0.000
#> GSM152100 4 0.0000 0.9526 0.000 0.000 0.000 1.000 0.000
#> GSM152102 2 0.0451 0.9343 0.008 0.988 0.004 0.000 0.000
#> GSM152104 2 0.0162 0.9419 0.000 0.996 0.000 0.004 0.000
#> GSM152028 1 0.0865 0.7116 0.972 0.000 0.004 0.000 0.024
#> GSM152029 3 0.6296 -0.0401 0.152 0.000 0.440 0.000 0.408
#> GSM152049 5 0.4201 0.0947 0.408 0.000 0.000 0.000 0.592
#> GSM152053 4 0.0290 0.9490 0.000 0.000 0.008 0.992 0.000
#> GSM152059 5 0.3656 0.7284 0.196 0.000 0.020 0.000 0.784
#> GSM152085 5 0.1121 0.7779 0.044 0.000 0.000 0.000 0.956
#> GSM152101 3 0.4686 0.2284 0.012 0.004 0.588 0.396 0.000
#> GSM152105 1 0.2329 0.6654 0.876 0.000 0.124 0.000 0.000
#> GSM152034 5 0.1043 0.7842 0.000 0.000 0.000 0.040 0.960
#> GSM152036 4 0.0000 0.9526 0.000 0.000 0.000 1.000 0.000
#> GSM152040 5 0.3048 0.7500 0.176 0.000 0.004 0.000 0.820
#> GSM152043 1 0.4235 0.0481 0.576 0.000 0.000 0.000 0.424
#> GSM152046 5 0.0451 0.7880 0.004 0.000 0.000 0.008 0.988
#> GSM152047 5 0.3039 0.7601 0.152 0.000 0.012 0.000 0.836
#> GSM152048 1 0.3336 0.7128 0.772 0.000 0.000 0.000 0.228
#> GSM152050 5 0.2513 0.7249 0.116 0.000 0.000 0.008 0.876
#> GSM152052 1 0.2719 0.7212 0.884 0.000 0.068 0.000 0.048
#> GSM152056 1 0.3534 0.6957 0.744 0.000 0.000 0.000 0.256
#> GSM152060 5 0.0807 0.7858 0.012 0.000 0.000 0.012 0.976
#> GSM152065 1 0.2909 0.6193 0.848 0.000 0.140 0.000 0.012
#> GSM152066 1 0.3424 0.7071 0.760 0.000 0.000 0.000 0.240
#> GSM152069 3 0.0566 0.8139 0.012 0.000 0.984 0.000 0.004
#> GSM152070 5 0.4058 0.7032 0.236 0.000 0.024 0.000 0.740
#> GSM152071 3 0.0566 0.8139 0.012 0.000 0.984 0.000 0.004
#> GSM152072 3 0.4660 0.6322 0.192 0.000 0.728 0.000 0.080
#> GSM152073 5 0.3508 0.7074 0.252 0.000 0.000 0.000 0.748
#> GSM152078 3 0.4574 0.3642 0.412 0.000 0.576 0.000 0.012
#> GSM152082 1 0.3612 0.5271 0.764 0.000 0.008 0.000 0.228
#> GSM152086 5 0.4256 0.0123 0.436 0.000 0.000 0.000 0.564
#> GSM152090 3 0.1059 0.8120 0.020 0.008 0.968 0.000 0.004
#> GSM152092 1 0.2280 0.6607 0.880 0.000 0.000 0.000 0.120
#> GSM152093 1 0.3796 0.6483 0.700 0.000 0.000 0.000 0.300
#> GSM152094 5 0.1908 0.7844 0.092 0.000 0.000 0.000 0.908
#> GSM152098 5 0.3852 0.7110 0.220 0.000 0.020 0.000 0.760
#> GSM152110 1 0.3983 0.5939 0.660 0.000 0.000 0.000 0.340
#> GSM152031 1 0.2278 0.6889 0.908 0.000 0.060 0.000 0.032
#> GSM152037 1 0.3274 0.7167 0.780 0.000 0.000 0.000 0.220
#> GSM152055 5 0.2464 0.7372 0.096 0.000 0.000 0.016 0.888
#> GSM152061 5 0.0807 0.7858 0.012 0.000 0.000 0.012 0.976
#> GSM152064 5 0.2172 0.7520 0.076 0.000 0.000 0.016 0.908
#> GSM152087 5 0.1732 0.7876 0.080 0.000 0.000 0.000 0.920
#> GSM152103 3 0.1331 0.8060 0.040 0.000 0.952 0.000 0.008
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM152032 3 0.0551 0.7483 0.008 0.000 0.984 0.004 0.004 0.000
#> GSM152033 1 0.5440 0.3798 0.552 0.000 0.152 0.000 0.296 0.000
#> GSM152063 2 0.0000 0.9789 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152074 3 0.1781 0.7437 0.008 0.000 0.924 0.008 0.060 0.000
#> GSM152080 2 0.0767 0.9716 0.008 0.976 0.004 0.000 0.012 0.000
#> GSM152081 4 0.1321 0.9244 0.004 0.000 0.020 0.952 0.024 0.000
#> GSM152083 3 0.4258 0.0892 0.004 0.492 0.496 0.004 0.004 0.000
#> GSM152091 2 0.0520 0.9749 0.008 0.984 0.000 0.000 0.008 0.000
#> GSM152108 2 0.1410 0.9422 0.044 0.944 0.004 0.000 0.008 0.000
#> GSM152114 1 0.6323 0.3885 0.580 0.000 0.040 0.256 0.044 0.080
#> GSM152035 2 0.0260 0.9771 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM152039 4 0.0363 0.9333 0.000 0.000 0.000 0.988 0.000 0.012
#> GSM152041 4 0.2711 0.8434 0.012 0.000 0.000 0.860 0.012 0.116
#> GSM152044 2 0.0000 0.9789 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152045 5 0.4469 0.2336 0.012 0.000 0.016 0.000 0.584 0.388
#> GSM152051 2 0.0000 0.9789 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152054 5 0.7057 0.2804 0.028 0.312 0.040 0.072 0.504 0.044
#> GSM152057 2 0.0000 0.9789 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152058 1 0.2003 0.6250 0.884 0.000 0.000 0.000 0.000 0.116
#> GSM152067 3 0.3053 0.7305 0.012 0.000 0.812 0.004 0.172 0.000
#> GSM152068 2 0.0000 0.9789 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152075 4 0.0622 0.9330 0.000 0.000 0.000 0.980 0.012 0.008
#> GSM152076 4 0.0363 0.9333 0.000 0.000 0.000 0.988 0.000 0.012
#> GSM152079 2 0.0000 0.9789 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152084 3 0.2265 0.7360 0.024 0.000 0.900 0.008 0.068 0.000
#> GSM152089 4 0.5061 0.6612 0.008 0.012 0.004 0.688 0.088 0.200
#> GSM152095 4 0.0363 0.9333 0.000 0.000 0.000 0.988 0.000 0.012
#> GSM152096 3 0.4568 0.5123 0.008 0.300 0.648 0.000 0.044 0.000
#> GSM152097 2 0.1387 0.9263 0.000 0.932 0.000 0.068 0.000 0.000
#> GSM152099 2 0.0000 0.9789 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152106 2 0.1327 0.9304 0.000 0.936 0.000 0.064 0.000 0.000
#> GSM152107 3 0.5501 0.3454 0.016 0.000 0.552 0.336 0.096 0.000
#> GSM152109 3 0.2346 0.7385 0.008 0.000 0.868 0.000 0.124 0.000
#> GSM152111 6 0.2431 0.6328 0.132 0.000 0.000 0.000 0.008 0.860
#> GSM152112 4 0.2001 0.8980 0.012 0.000 0.008 0.912 0.068 0.000
#> GSM152113 1 0.5992 0.1339 0.396 0.000 0.372 0.000 0.232 0.000
#> GSM152115 3 0.3622 0.6922 0.020 0.000 0.792 0.024 0.164 0.000
#> GSM152030 4 0.1793 0.9163 0.004 0.000 0.032 0.928 0.036 0.000
#> GSM152038 3 0.5372 0.3785 0.172 0.000 0.604 0.004 0.220 0.000
#> GSM152042 4 0.1719 0.9181 0.004 0.000 0.032 0.932 0.032 0.000
#> GSM152062 3 0.1826 0.7415 0.020 0.000 0.924 0.004 0.052 0.000
#> GSM152077 1 0.1984 0.6171 0.912 0.000 0.000 0.000 0.056 0.032
#> GSM152088 2 0.0405 0.9759 0.008 0.988 0.000 0.000 0.004 0.000
#> GSM152100 4 0.0508 0.9323 0.000 0.000 0.000 0.984 0.004 0.012
#> GSM152102 2 0.1398 0.9455 0.008 0.940 0.000 0.000 0.052 0.000
#> GSM152104 2 0.0260 0.9759 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM152028 1 0.3175 0.5269 0.744 0.000 0.000 0.000 0.256 0.000
#> GSM152029 5 0.5610 0.4128 0.008 0.000 0.252 0.000 0.572 0.168
#> GSM152049 6 0.4405 0.0852 0.472 0.000 0.000 0.000 0.024 0.504
#> GSM152053 4 0.1793 0.9163 0.004 0.000 0.032 0.928 0.036 0.000
#> GSM152059 6 0.4534 -0.0997 0.032 0.000 0.000 0.000 0.476 0.492
#> GSM152085 6 0.2066 0.6564 0.052 0.000 0.000 0.000 0.040 0.908
#> GSM152101 3 0.5595 0.4782 0.016 0.000 0.588 0.256 0.140 0.000
#> GSM152105 1 0.4282 0.4754 0.656 0.000 0.040 0.000 0.304 0.000
#> GSM152034 6 0.1462 0.6340 0.000 0.000 0.000 0.008 0.056 0.936
#> GSM152036 4 0.0508 0.9336 0.000 0.000 0.000 0.984 0.004 0.012
#> GSM152040 6 0.4147 0.0763 0.012 0.000 0.000 0.000 0.436 0.552
#> GSM152043 5 0.5731 0.3366 0.288 0.000 0.000 0.000 0.508 0.204
#> GSM152046 6 0.1075 0.6438 0.000 0.000 0.000 0.000 0.048 0.952
#> GSM152047 6 0.3563 0.3321 0.000 0.000 0.000 0.000 0.336 0.664
#> GSM152048 1 0.2048 0.6242 0.880 0.000 0.000 0.000 0.000 0.120
#> GSM152050 6 0.2704 0.6289 0.140 0.000 0.000 0.000 0.016 0.844
#> GSM152052 1 0.3660 0.5627 0.772 0.000 0.036 0.000 0.188 0.004
#> GSM152056 1 0.3163 0.5258 0.764 0.000 0.000 0.000 0.004 0.232
#> GSM152060 6 0.0725 0.6543 0.012 0.000 0.000 0.000 0.012 0.976
#> GSM152065 1 0.4526 0.2750 0.512 0.000 0.032 0.000 0.456 0.000
#> GSM152066 1 0.2442 0.6128 0.852 0.000 0.000 0.000 0.004 0.144
#> GSM152069 3 0.2389 0.7377 0.008 0.000 0.864 0.000 0.128 0.000
#> GSM152070 5 0.4238 0.3507 0.028 0.000 0.000 0.000 0.628 0.344
#> GSM152071 3 0.2389 0.7377 0.008 0.000 0.864 0.000 0.128 0.000
#> GSM152072 5 0.3551 0.5165 0.000 0.000 0.168 0.000 0.784 0.048
#> GSM152073 6 0.5385 -0.1220 0.112 0.000 0.000 0.000 0.420 0.468
#> GSM152078 5 0.5507 0.2335 0.208 0.000 0.228 0.000 0.564 0.000
#> GSM152082 5 0.4977 0.2580 0.300 0.000 0.004 0.000 0.612 0.084
#> GSM152086 6 0.4852 0.1127 0.452 0.000 0.000 0.000 0.056 0.492
#> GSM152090 3 0.2909 0.7261 0.028 0.000 0.836 0.000 0.136 0.000
#> GSM152092 1 0.4394 0.3114 0.568 0.000 0.004 0.000 0.408 0.020
#> GSM152093 1 0.4634 0.4732 0.688 0.000 0.028 0.000 0.040 0.244
#> GSM152094 6 0.3023 0.5032 0.000 0.000 0.000 0.000 0.232 0.768
#> GSM152098 5 0.4193 0.3401 0.024 0.000 0.000 0.000 0.624 0.352
#> GSM152110 1 0.3508 0.4381 0.704 0.000 0.000 0.000 0.004 0.292
#> GSM152031 1 0.4433 0.3427 0.560 0.000 0.016 0.000 0.416 0.008
#> GSM152037 1 0.1765 0.6275 0.904 0.000 0.000 0.000 0.000 0.096
#> GSM152055 6 0.2442 0.6202 0.144 0.000 0.000 0.000 0.004 0.852
#> GSM152061 6 0.0717 0.6532 0.008 0.000 0.000 0.000 0.016 0.976
#> GSM152064 6 0.2261 0.6376 0.104 0.000 0.000 0.004 0.008 0.884
#> GSM152087 6 0.3110 0.5439 0.012 0.000 0.000 0.000 0.196 0.792
#> GSM152103 3 0.3249 0.7183 0.044 0.000 0.824 0.000 0.128 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 specimen(p) k
#> SD:skmeans 83 3.75e-10 2
#> SD:skmeans 81 8.29e-07 3
#> SD:skmeans 86 3.60e-05 4
#> SD:skmeans 76 4.17e-04 5
#> SD:skmeans 61 2.08e-02 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 10612 rows and 88 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 0.813 0.901 0.953 0.4824 0.511 0.511
#> 3 3 0.577 0.761 0.885 0.3337 0.826 0.666
#> 4 4 0.716 0.720 0.881 0.1290 0.862 0.636
#> 5 5 0.684 0.581 0.791 0.0813 0.895 0.630
#> 6 6 0.663 0.514 0.744 0.0321 0.898 0.577
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
#> GSM152032 2 0.1414 0.9608 0.020 0.980
#> GSM152033 1 0.2043 0.9149 0.968 0.032
#> GSM152063 2 0.0000 0.9601 0.000 1.000
#> GSM152074 2 0.1414 0.9608 0.020 0.980
#> GSM152080 2 0.0376 0.9602 0.004 0.996
#> GSM152081 2 0.1414 0.9609 0.020 0.980
#> GSM152083 2 0.0000 0.9601 0.000 1.000
#> GSM152091 2 0.0000 0.9601 0.000 1.000
#> GSM152108 2 0.5408 0.8531 0.124 0.876
#> GSM152114 1 0.0000 0.9332 1.000 0.000
#> GSM152035 2 0.0000 0.9601 0.000 1.000
#> GSM152039 2 0.5519 0.8578 0.128 0.872
#> GSM152041 1 0.9993 0.1040 0.516 0.484
#> GSM152044 2 0.0000 0.9601 0.000 1.000
#> GSM152045 1 0.6343 0.8027 0.840 0.160
#> GSM152051 2 0.0000 0.9601 0.000 1.000
#> GSM152054 1 0.2948 0.9040 0.948 0.052
#> GSM152057 2 0.0000 0.9601 0.000 1.000
#> GSM152058 1 0.0000 0.9332 1.000 0.000
#> GSM152067 2 0.0376 0.9607 0.004 0.996
#> GSM152068 2 0.0000 0.9601 0.000 1.000
#> GSM152075 2 0.1633 0.9600 0.024 0.976
#> GSM152076 2 0.0000 0.9601 0.000 1.000
#> GSM152079 2 0.0000 0.9601 0.000 1.000
#> GSM152084 2 0.1633 0.9600 0.024 0.976
#> GSM152089 2 0.1633 0.9600 0.024 0.976
#> GSM152095 2 0.0000 0.9601 0.000 1.000
#> GSM152096 2 0.1633 0.9598 0.024 0.976
#> GSM152097 2 0.0000 0.9601 0.000 1.000
#> GSM152099 2 0.0000 0.9601 0.000 1.000
#> GSM152106 2 0.0000 0.9601 0.000 1.000
#> GSM152107 2 0.0376 0.9607 0.004 0.996
#> GSM152109 2 0.1633 0.9600 0.024 0.976
#> GSM152111 2 0.7376 0.7671 0.208 0.792
#> GSM152112 2 0.0938 0.9612 0.012 0.988
#> GSM152113 2 0.7299 0.7728 0.204 0.796
#> GSM152115 2 0.3114 0.9403 0.056 0.944
#> GSM152030 2 0.1414 0.9608 0.020 0.980
#> GSM152038 2 0.8955 0.5684 0.312 0.688
#> GSM152042 2 0.1414 0.9608 0.020 0.980
#> GSM152062 2 0.1633 0.9600 0.024 0.976
#> GSM152077 1 0.0000 0.9332 1.000 0.000
#> GSM152088 2 0.0000 0.9601 0.000 1.000
#> GSM152100 2 0.1843 0.9591 0.028 0.972
#> GSM152102 2 0.0000 0.9601 0.000 1.000
#> GSM152104 2 0.0000 0.9601 0.000 1.000
#> GSM152028 1 0.0000 0.9332 1.000 0.000
#> GSM152029 2 0.3114 0.9443 0.056 0.944
#> GSM152049 1 0.0000 0.9332 1.000 0.000
#> GSM152053 2 0.1633 0.9600 0.024 0.976
#> GSM152059 1 0.6343 0.7905 0.840 0.160
#> GSM152085 1 0.0000 0.9332 1.000 0.000
#> GSM152101 2 0.0376 0.9607 0.004 0.996
#> GSM152105 1 0.0000 0.9332 1.000 0.000
#> GSM152034 2 0.3114 0.9443 0.056 0.944
#> GSM152036 2 0.0672 0.9612 0.008 0.992
#> GSM152040 1 0.0000 0.9332 1.000 0.000
#> GSM152043 1 0.0000 0.9332 1.000 0.000
#> GSM152046 1 0.3431 0.8905 0.936 0.064
#> GSM152047 2 0.3114 0.9443 0.056 0.944
#> GSM152048 1 0.0000 0.9332 1.000 0.000
#> GSM152050 1 0.2603 0.9059 0.956 0.044
#> GSM152052 1 0.9775 0.3075 0.588 0.412
#> GSM152056 1 0.0000 0.9332 1.000 0.000
#> GSM152060 1 0.0000 0.9332 1.000 0.000
#> GSM152065 1 0.0000 0.9332 1.000 0.000
#> GSM152066 1 0.0000 0.9332 1.000 0.000
#> GSM152069 2 0.2603 0.9514 0.044 0.956
#> GSM152070 1 0.4939 0.8478 0.892 0.108
#> GSM152071 2 0.2603 0.9514 0.044 0.956
#> GSM152072 2 0.3114 0.9443 0.056 0.944
#> GSM152073 1 0.0000 0.9332 1.000 0.000
#> GSM152078 2 0.3114 0.9443 0.056 0.944
#> GSM152082 1 0.0000 0.9332 1.000 0.000
#> GSM152086 1 0.0000 0.9332 1.000 0.000
#> GSM152090 2 0.2948 0.9467 0.052 0.948
#> GSM152092 1 0.0000 0.9332 1.000 0.000
#> GSM152093 2 0.6048 0.8526 0.148 0.852
#> GSM152094 1 0.0000 0.9332 1.000 0.000
#> GSM152098 1 0.7056 0.7528 0.808 0.192
#> GSM152110 1 0.0000 0.9332 1.000 0.000
#> GSM152031 1 0.9993 0.0186 0.516 0.484
#> GSM152037 1 0.0000 0.9332 1.000 0.000
#> GSM152055 1 0.0000 0.9332 1.000 0.000
#> GSM152061 1 0.0000 0.9332 1.000 0.000
#> GSM152064 1 0.0000 0.9332 1.000 0.000
#> GSM152087 1 0.0000 0.9332 1.000 0.000
#> GSM152103 2 0.2948 0.9467 0.052 0.948
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM152032 3 0.0000 0.7984 0.000 0.000 1.000
#> GSM152033 1 0.4974 0.6878 0.764 0.000 0.236
#> GSM152063 2 0.0000 0.9610 0.000 1.000 0.000
#> GSM152074 3 0.0237 0.7995 0.004 0.000 0.996
#> GSM152080 2 0.0000 0.9610 0.000 1.000 0.000
#> GSM152081 3 0.1964 0.7769 0.000 0.056 0.944
#> GSM152083 2 0.5363 0.6155 0.000 0.724 0.276
#> GSM152091 2 0.0000 0.9610 0.000 1.000 0.000
#> GSM152108 3 0.8703 0.5993 0.244 0.168 0.588
#> GSM152114 1 0.0000 0.8789 1.000 0.000 0.000
#> GSM152035 2 0.0000 0.9610 0.000 1.000 0.000
#> GSM152039 2 0.4605 0.7450 0.000 0.796 0.204
#> GSM152041 3 0.6308 0.1716 0.492 0.000 0.508
#> GSM152044 2 0.0000 0.9610 0.000 1.000 0.000
#> GSM152045 1 0.5650 0.5481 0.688 0.000 0.312
#> GSM152051 2 0.0000 0.9610 0.000 1.000 0.000
#> GSM152054 1 0.8020 0.4853 0.596 0.084 0.320
#> GSM152057 2 0.0000 0.9610 0.000 1.000 0.000
#> GSM152058 1 0.0000 0.8789 1.000 0.000 0.000
#> GSM152067 3 0.0000 0.7984 0.000 0.000 1.000
#> GSM152068 2 0.0000 0.9610 0.000 1.000 0.000
#> GSM152075 3 0.4605 0.7129 0.204 0.000 0.796
#> GSM152076 3 0.6302 0.0637 0.000 0.480 0.520
#> GSM152079 2 0.0000 0.9610 0.000 1.000 0.000
#> GSM152084 3 0.0592 0.8009 0.012 0.000 0.988
#> GSM152089 3 0.4750 0.7081 0.216 0.000 0.784
#> GSM152095 3 0.6252 0.1852 0.000 0.444 0.556
#> GSM152096 3 0.1905 0.7972 0.016 0.028 0.956
#> GSM152097 2 0.0000 0.9610 0.000 1.000 0.000
#> GSM152099 2 0.0000 0.9610 0.000 1.000 0.000
#> GSM152106 2 0.0000 0.9610 0.000 1.000 0.000
#> GSM152107 3 0.0000 0.7984 0.000 0.000 1.000
#> GSM152109 3 0.0000 0.7984 0.000 0.000 1.000
#> GSM152111 3 0.6244 0.4306 0.440 0.000 0.560
#> GSM152112 3 0.0237 0.7985 0.004 0.000 0.996
#> GSM152113 3 0.4291 0.7262 0.180 0.000 0.820
#> GSM152115 3 0.1411 0.7902 0.036 0.000 0.964
#> GSM152030 3 0.0000 0.7984 0.000 0.000 1.000
#> GSM152038 3 0.5621 0.5085 0.308 0.000 0.692
#> GSM152042 3 0.0000 0.7984 0.000 0.000 1.000
#> GSM152062 3 0.1411 0.7983 0.036 0.000 0.964
#> GSM152077 1 0.0237 0.8770 0.996 0.000 0.004
#> GSM152088 2 0.0000 0.9610 0.000 1.000 0.000
#> GSM152100 3 0.4605 0.7129 0.204 0.000 0.796
#> GSM152102 2 0.2878 0.8733 0.000 0.904 0.096
#> GSM152104 2 0.0000 0.9610 0.000 1.000 0.000
#> GSM152028 1 0.0000 0.8789 1.000 0.000 0.000
#> GSM152029 3 0.3941 0.7540 0.156 0.000 0.844
#> GSM152049 1 0.0000 0.8789 1.000 0.000 0.000
#> GSM152053 3 0.0000 0.7984 0.000 0.000 1.000
#> GSM152059 1 0.5926 0.5006 0.644 0.000 0.356
#> GSM152085 1 0.0000 0.8789 1.000 0.000 0.000
#> GSM152101 3 0.0000 0.7984 0.000 0.000 1.000
#> GSM152105 1 0.4605 0.7170 0.796 0.000 0.204
#> GSM152034 3 0.5835 0.6136 0.340 0.000 0.660
#> GSM152036 3 0.5756 0.6448 0.028 0.208 0.764
#> GSM152040 1 0.4605 0.7170 0.796 0.000 0.204
#> GSM152043 1 0.0000 0.8789 1.000 0.000 0.000
#> GSM152046 1 0.2165 0.8300 0.936 0.000 0.064
#> GSM152047 3 0.5835 0.6136 0.340 0.000 0.660
#> GSM152048 1 0.0000 0.8789 1.000 0.000 0.000
#> GSM152050 1 0.1643 0.8474 0.956 0.000 0.044
#> GSM152052 1 0.5968 0.2349 0.636 0.000 0.364
#> GSM152056 1 0.0000 0.8789 1.000 0.000 0.000
#> GSM152060 1 0.0000 0.8789 1.000 0.000 0.000
#> GSM152065 1 0.4605 0.7170 0.796 0.000 0.204
#> GSM152066 1 0.0000 0.8789 1.000 0.000 0.000
#> GSM152069 3 0.2878 0.7793 0.096 0.000 0.904
#> GSM152070 1 0.3551 0.7771 0.868 0.000 0.132
#> GSM152071 3 0.3340 0.7680 0.120 0.000 0.880
#> GSM152072 3 0.3619 0.7586 0.136 0.000 0.864
#> GSM152073 1 0.0000 0.8789 1.000 0.000 0.000
#> GSM152078 3 0.3619 0.7586 0.136 0.000 0.864
#> GSM152082 1 0.4555 0.7213 0.800 0.000 0.200
#> GSM152086 1 0.0000 0.8789 1.000 0.000 0.000
#> GSM152090 3 0.5706 0.6364 0.320 0.000 0.680
#> GSM152092 1 0.0000 0.8789 1.000 0.000 0.000
#> GSM152093 3 0.6252 0.4261 0.444 0.000 0.556
#> GSM152094 1 0.0000 0.8789 1.000 0.000 0.000
#> GSM152098 1 0.4002 0.7227 0.840 0.000 0.160
#> GSM152110 1 0.0000 0.8789 1.000 0.000 0.000
#> GSM152031 1 0.6274 0.1908 0.544 0.000 0.456
#> GSM152037 1 0.0000 0.8789 1.000 0.000 0.000
#> GSM152055 1 0.0000 0.8789 1.000 0.000 0.000
#> GSM152061 1 0.0000 0.8789 1.000 0.000 0.000
#> GSM152064 1 0.0000 0.8789 1.000 0.000 0.000
#> GSM152087 1 0.0000 0.8789 1.000 0.000 0.000
#> GSM152103 3 0.5785 0.6232 0.332 0.000 0.668
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM152032 3 0.0000 0.7298 0.000 0.000 1.000 0.000
#> GSM152033 1 0.4679 0.4447 0.648 0.000 0.352 0.000
#> GSM152063 2 0.0000 0.9663 0.000 1.000 0.000 0.000
#> GSM152074 3 0.1211 0.7020 0.000 0.000 0.960 0.040
#> GSM152080 2 0.0000 0.9663 0.000 1.000 0.000 0.000
#> GSM152081 3 0.4907 0.2600 0.000 0.000 0.580 0.420
#> GSM152083 2 0.4543 0.5179 0.000 0.676 0.324 0.000
#> GSM152091 2 0.0000 0.9663 0.000 1.000 0.000 0.000
#> GSM152108 3 0.7397 0.4506 0.292 0.200 0.508 0.000
#> GSM152114 1 0.0000 0.8583 1.000 0.000 0.000 0.000
#> GSM152035 2 0.0000 0.9663 0.000 1.000 0.000 0.000
#> GSM152039 4 0.0000 0.8082 0.000 0.000 0.000 1.000
#> GSM152041 1 0.6005 -0.0732 0.500 0.000 0.040 0.460
#> GSM152044 2 0.0000 0.9663 0.000 1.000 0.000 0.000
#> GSM152045 4 0.5851 0.5727 0.272 0.000 0.068 0.660
#> GSM152051 2 0.0000 0.9663 0.000 1.000 0.000 0.000
#> GSM152054 4 0.5466 0.6435 0.040 0.000 0.292 0.668
#> GSM152057 2 0.0000 0.9663 0.000 1.000 0.000 0.000
#> GSM152058 1 0.0000 0.8583 1.000 0.000 0.000 0.000
#> GSM152067 3 0.0000 0.7298 0.000 0.000 1.000 0.000
#> GSM152068 2 0.0000 0.9663 0.000 1.000 0.000 0.000
#> GSM152075 4 0.0000 0.8082 0.000 0.000 0.000 1.000
#> GSM152076 4 0.0000 0.8082 0.000 0.000 0.000 1.000
#> GSM152079 2 0.0000 0.9663 0.000 1.000 0.000 0.000
#> GSM152084 3 0.2611 0.6756 0.008 0.000 0.896 0.096
#> GSM152089 4 0.5466 0.5238 0.292 0.000 0.040 0.668
#> GSM152095 4 0.0000 0.8082 0.000 0.000 0.000 1.000
#> GSM152096 3 0.1114 0.7249 0.008 0.004 0.972 0.016
#> GSM152097 2 0.0000 0.9663 0.000 1.000 0.000 0.000
#> GSM152099 2 0.0000 0.9663 0.000 1.000 0.000 0.000
#> GSM152106 2 0.0592 0.9546 0.000 0.984 0.000 0.016
#> GSM152107 4 0.4356 0.6735 0.000 0.000 0.292 0.708
#> GSM152109 3 0.0000 0.7298 0.000 0.000 1.000 0.000
#> GSM152111 3 0.4967 0.3339 0.452 0.000 0.548 0.000
#> GSM152112 4 0.3907 0.7234 0.000 0.000 0.232 0.768
#> GSM152113 3 0.1022 0.7229 0.032 0.000 0.968 0.000
#> GSM152115 4 0.4356 0.6735 0.000 0.000 0.292 0.708
#> GSM152030 4 0.0000 0.8082 0.000 0.000 0.000 1.000
#> GSM152038 3 0.4304 0.4741 0.284 0.000 0.716 0.000
#> GSM152042 4 0.3444 0.6838 0.000 0.000 0.184 0.816
#> GSM152062 3 0.0592 0.7235 0.000 0.000 0.984 0.016
#> GSM152077 1 0.0469 0.8508 0.988 0.000 0.012 0.000
#> GSM152088 2 0.0000 0.9663 0.000 1.000 0.000 0.000
#> GSM152100 4 0.0000 0.8082 0.000 0.000 0.000 1.000
#> GSM152102 2 0.2623 0.8789 0.000 0.908 0.064 0.028
#> GSM152104 2 0.0000 0.9663 0.000 1.000 0.000 0.000
#> GSM152028 1 0.0000 0.8583 1.000 0.000 0.000 0.000
#> GSM152029 3 0.0921 0.7288 0.028 0.000 0.972 0.000
#> GSM152049 1 0.0000 0.8583 1.000 0.000 0.000 0.000
#> GSM152053 4 0.3400 0.6759 0.000 0.000 0.180 0.820
#> GSM152059 1 0.4985 0.1968 0.532 0.000 0.468 0.000
#> GSM152085 1 0.0000 0.8583 1.000 0.000 0.000 0.000
#> GSM152101 4 0.4008 0.7156 0.000 0.000 0.244 0.756
#> GSM152105 1 0.4522 0.4942 0.680 0.000 0.320 0.000
#> GSM152034 3 0.4978 0.5504 0.324 0.000 0.664 0.012
#> GSM152036 4 0.0000 0.8082 0.000 0.000 0.000 1.000
#> GSM152040 1 0.4522 0.4942 0.680 0.000 0.320 0.000
#> GSM152043 1 0.0000 0.8583 1.000 0.000 0.000 0.000
#> GSM152046 1 0.1637 0.8081 0.940 0.000 0.060 0.000
#> GSM152047 3 0.4605 0.5386 0.336 0.000 0.664 0.000
#> GSM152048 1 0.0000 0.8583 1.000 0.000 0.000 0.000
#> GSM152050 1 0.1211 0.8264 0.960 0.000 0.040 0.000
#> GSM152052 1 0.4941 -0.0258 0.564 0.000 0.436 0.000
#> GSM152056 1 0.0000 0.8583 1.000 0.000 0.000 0.000
#> GSM152060 1 0.0000 0.8583 1.000 0.000 0.000 0.000
#> GSM152065 1 0.4522 0.4942 0.680 0.000 0.320 0.000
#> GSM152066 1 0.0000 0.8583 1.000 0.000 0.000 0.000
#> GSM152069 3 0.0000 0.7298 0.000 0.000 1.000 0.000
#> GSM152070 1 0.2921 0.7332 0.860 0.000 0.140 0.000
#> GSM152071 3 0.0000 0.7298 0.000 0.000 1.000 0.000
#> GSM152072 3 0.0000 0.7298 0.000 0.000 1.000 0.000
#> GSM152073 1 0.0000 0.8583 1.000 0.000 0.000 0.000
#> GSM152078 3 0.0000 0.7298 0.000 0.000 1.000 0.000
#> GSM152082 1 0.4431 0.5178 0.696 0.000 0.304 0.000
#> GSM152086 1 0.0000 0.8583 1.000 0.000 0.000 0.000
#> GSM152090 3 0.4891 0.5636 0.308 0.000 0.680 0.012
#> GSM152092 1 0.0000 0.8583 1.000 0.000 0.000 0.000
#> GSM152093 3 0.4961 0.3438 0.448 0.000 0.552 0.000
#> GSM152094 1 0.0000 0.8583 1.000 0.000 0.000 0.000
#> GSM152098 1 0.3123 0.6913 0.844 0.000 0.156 0.000
#> GSM152110 1 0.0000 0.8583 1.000 0.000 0.000 0.000
#> GSM152031 3 0.5000 -0.1244 0.500 0.000 0.500 0.000
#> GSM152037 1 0.0000 0.8583 1.000 0.000 0.000 0.000
#> GSM152055 1 0.0000 0.8583 1.000 0.000 0.000 0.000
#> GSM152061 1 0.0000 0.8583 1.000 0.000 0.000 0.000
#> GSM152064 1 0.0000 0.8583 1.000 0.000 0.000 0.000
#> GSM152087 1 0.0000 0.8583 1.000 0.000 0.000 0.000
#> GSM152103 3 0.4543 0.5507 0.324 0.000 0.676 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM152032 5 0.4300 -0.3336 0.000 0.000 0.476 0.000 0.524
#> GSM152033 5 0.2520 0.5162 0.048 0.000 0.056 0.000 0.896
#> GSM152063 2 0.0000 0.9724 0.000 1.000 0.000 0.000 0.000
#> GSM152074 5 0.4807 -0.3164 0.000 0.000 0.448 0.020 0.532
#> GSM152080 2 0.0162 0.9699 0.000 0.996 0.004 0.000 0.000
#> GSM152081 3 0.4613 0.4801 0.000 0.000 0.620 0.360 0.020
#> GSM152083 2 0.4010 0.6966 0.000 0.760 0.032 0.000 0.208
#> GSM152091 2 0.0000 0.9724 0.000 1.000 0.000 0.000 0.000
#> GSM152108 3 0.7171 0.3840 0.232 0.208 0.512 0.000 0.048
#> GSM152114 1 0.4283 0.5344 0.544 0.000 0.000 0.000 0.456
#> GSM152035 2 0.0000 0.9724 0.000 1.000 0.000 0.000 0.000
#> GSM152039 4 0.0404 0.8292 0.000 0.000 0.000 0.988 0.012
#> GSM152041 1 0.4264 0.4034 0.744 0.000 0.000 0.212 0.044
#> GSM152044 2 0.0000 0.9724 0.000 1.000 0.000 0.000 0.000
#> GSM152045 4 0.4349 0.7025 0.176 0.000 0.000 0.756 0.068
#> GSM152051 2 0.0000 0.9724 0.000 1.000 0.000 0.000 0.000
#> GSM152054 4 0.4245 0.7701 0.028 0.000 0.016 0.768 0.188
#> GSM152057 2 0.0000 0.9724 0.000 1.000 0.000 0.000 0.000
#> GSM152058 1 0.4283 0.5344 0.544 0.000 0.000 0.000 0.456
#> GSM152067 3 0.3430 0.6528 0.000 0.000 0.776 0.004 0.220
#> GSM152068 2 0.0000 0.9724 0.000 1.000 0.000 0.000 0.000
#> GSM152075 4 0.0404 0.8294 0.000 0.000 0.012 0.988 0.000
#> GSM152076 4 0.0404 0.8292 0.000 0.000 0.000 0.988 0.012
#> GSM152079 2 0.0000 0.9724 0.000 1.000 0.000 0.000 0.000
#> GSM152084 3 0.2570 0.7454 0.000 0.000 0.888 0.028 0.084
#> GSM152089 4 0.3845 0.7194 0.024 0.000 0.208 0.768 0.000
#> GSM152095 4 0.0404 0.8292 0.000 0.000 0.000 0.988 0.012
#> GSM152096 3 0.0162 0.7584 0.000 0.000 0.996 0.004 0.000
#> GSM152097 2 0.0000 0.9724 0.000 1.000 0.000 0.000 0.000
#> GSM152099 2 0.0000 0.9724 0.000 1.000 0.000 0.000 0.000
#> GSM152106 2 0.0290 0.9670 0.000 0.992 0.000 0.008 0.000
#> GSM152107 4 0.3710 0.7790 0.000 0.000 0.024 0.784 0.192
#> GSM152109 3 0.0880 0.7572 0.000 0.000 0.968 0.000 0.032
#> GSM152111 1 0.5039 -0.2142 0.512 0.000 0.456 0.000 0.032
#> GSM152112 4 0.3282 0.7887 0.000 0.000 0.008 0.804 0.188
#> GSM152113 3 0.4449 0.2949 0.004 0.000 0.512 0.000 0.484
#> GSM152115 4 0.3710 0.7790 0.000 0.000 0.024 0.784 0.192
#> GSM152030 4 0.0162 0.8304 0.000 0.000 0.000 0.996 0.004
#> GSM152038 5 0.4197 0.3074 0.028 0.000 0.244 0.000 0.728
#> GSM152042 4 0.4367 0.3786 0.000 0.000 0.416 0.580 0.004
#> GSM152062 3 0.4658 0.4319 0.000 0.000 0.576 0.016 0.408
#> GSM152077 5 0.3857 0.0144 0.312 0.000 0.000 0.000 0.688
#> GSM152088 2 0.0000 0.9724 0.000 1.000 0.000 0.000 0.000
#> GSM152100 4 0.0000 0.8301 0.000 0.000 0.000 1.000 0.000
#> GSM152102 2 0.3530 0.8433 0.040 0.856 0.000 0.044 0.060
#> GSM152104 2 0.0000 0.9724 0.000 1.000 0.000 0.000 0.000
#> GSM152028 5 0.4302 -0.4730 0.480 0.000 0.000 0.000 0.520
#> GSM152029 3 0.0963 0.7572 0.036 0.000 0.964 0.000 0.000
#> GSM152049 1 0.3143 0.5853 0.796 0.000 0.000 0.000 0.204
#> GSM152053 4 0.4211 0.5074 0.000 0.000 0.360 0.636 0.004
#> GSM152059 5 0.4060 0.2998 0.360 0.000 0.000 0.000 0.640
#> GSM152085 1 0.2732 0.5864 0.840 0.000 0.000 0.000 0.160
#> GSM152101 4 0.3318 0.7881 0.000 0.000 0.008 0.800 0.192
#> GSM152105 5 0.1965 0.5131 0.052 0.000 0.024 0.000 0.924
#> GSM152034 3 0.4327 0.5014 0.360 0.000 0.632 0.000 0.008
#> GSM152036 4 0.0510 0.8290 0.000 0.000 0.000 0.984 0.016
#> GSM152040 5 0.4201 -0.0816 0.408 0.000 0.000 0.000 0.592
#> GSM152043 1 0.4552 0.4228 0.524 0.000 0.008 0.000 0.468
#> GSM152046 1 0.0000 0.5149 1.000 0.000 0.000 0.000 0.000
#> GSM152047 3 0.3039 0.7114 0.152 0.000 0.836 0.000 0.012
#> GSM152048 1 0.4283 0.5344 0.544 0.000 0.000 0.000 0.456
#> GSM152050 1 0.3399 0.5845 0.812 0.000 0.020 0.000 0.168
#> GSM152052 1 0.5867 0.1700 0.496 0.000 0.404 0.000 0.100
#> GSM152056 1 0.4283 0.5344 0.544 0.000 0.000 0.000 0.456
#> GSM152060 1 0.0290 0.5190 0.992 0.000 0.000 0.000 0.008
#> GSM152065 5 0.2300 0.5129 0.072 0.000 0.024 0.000 0.904
#> GSM152066 1 0.4283 0.5344 0.544 0.000 0.000 0.000 0.456
#> GSM152069 3 0.0880 0.7572 0.000 0.000 0.968 0.000 0.032
#> GSM152070 5 0.6274 -0.2921 0.424 0.000 0.148 0.000 0.428
#> GSM152071 3 0.0880 0.7572 0.000 0.000 0.968 0.000 0.032
#> GSM152072 3 0.3940 0.6487 0.024 0.000 0.756 0.000 0.220
#> GSM152073 1 0.4182 0.5263 0.600 0.000 0.000 0.000 0.400
#> GSM152078 3 0.4851 0.6383 0.092 0.000 0.712 0.000 0.196
#> GSM152082 5 0.2074 0.4965 0.104 0.000 0.000 0.000 0.896
#> GSM152086 1 0.4273 0.5341 0.552 0.000 0.000 0.000 0.448
#> GSM152090 3 0.2206 0.7484 0.068 0.000 0.912 0.016 0.004
#> GSM152092 1 0.4300 0.4173 0.524 0.000 0.000 0.000 0.476
#> GSM152093 3 0.4351 0.6107 0.100 0.000 0.768 0.000 0.132
#> GSM152094 1 0.4182 0.5263 0.600 0.000 0.000 0.000 0.400
#> GSM152098 5 0.5620 0.2972 0.272 0.000 0.116 0.000 0.612
#> GSM152110 1 0.4283 0.5344 0.544 0.000 0.000 0.000 0.456
#> GSM152031 5 0.1893 0.5141 0.048 0.000 0.024 0.000 0.928
#> GSM152037 5 0.4268 -0.3967 0.444 0.000 0.000 0.000 0.556
#> GSM152055 1 0.1341 0.5184 0.944 0.000 0.000 0.000 0.056
#> GSM152061 1 0.0000 0.5149 1.000 0.000 0.000 0.000 0.000
#> GSM152064 1 0.2648 0.5851 0.848 0.000 0.000 0.000 0.152
#> GSM152087 1 0.2648 0.5851 0.848 0.000 0.000 0.000 0.152
#> GSM152103 3 0.2193 0.7414 0.092 0.000 0.900 0.000 0.008
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM152032 1 0.3563 0.1597 0.664 0.000 0.336 0.000 0.000 0.000
#> GSM152033 1 0.4544 0.4973 0.548 0.000 0.036 0.000 0.000 0.416
#> GSM152063 2 0.0000 0.9516 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152074 1 0.3629 0.1956 0.712 0.000 0.276 0.000 0.012 0.000
#> GSM152080 2 0.0922 0.9408 0.024 0.968 0.004 0.004 0.000 0.000
#> GSM152081 4 0.5655 0.2504 0.016 0.000 0.176 0.592 0.216 0.000
#> GSM152083 2 0.4008 0.5926 0.308 0.672 0.016 0.004 0.000 0.000
#> GSM152091 2 0.0508 0.9477 0.012 0.984 0.000 0.004 0.000 0.000
#> GSM152108 3 0.5721 0.3520 0.000 0.176 0.480 0.000 0.000 0.344
#> GSM152114 6 0.0000 0.6253 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM152035 2 0.0000 0.9516 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152039 4 0.3737 0.3030 0.000 0.000 0.000 0.608 0.392 0.000
#> GSM152041 6 0.6284 0.1232 0.244 0.000 0.000 0.032 0.212 0.512
#> GSM152044 2 0.0000 0.9516 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152045 5 0.3546 0.5873 0.016 0.000 0.000 0.196 0.776 0.012
#> GSM152051 2 0.0000 0.9516 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152054 5 0.3678 0.7117 0.128 0.000 0.000 0.084 0.788 0.000
#> GSM152057 2 0.0000 0.9516 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152058 6 0.0000 0.6253 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM152067 3 0.3769 0.4339 0.356 0.000 0.640 0.000 0.004 0.000
#> GSM152068 2 0.0000 0.9516 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152075 5 0.0260 0.6802 0.000 0.000 0.008 0.000 0.992 0.000
#> GSM152076 4 0.3737 0.3030 0.000 0.000 0.000 0.608 0.392 0.000
#> GSM152079 2 0.0291 0.9502 0.004 0.992 0.000 0.004 0.000 0.000
#> GSM152084 3 0.2257 0.6010 0.116 0.000 0.876 0.000 0.008 0.000
#> GSM152089 5 0.3141 0.6723 0.000 0.000 0.200 0.012 0.788 0.000
#> GSM152095 4 0.3737 0.3030 0.000 0.000 0.000 0.608 0.392 0.000
#> GSM152096 3 0.0146 0.6437 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM152097 2 0.0146 0.9504 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM152099 2 0.0363 0.9482 0.012 0.988 0.000 0.000 0.000 0.000
#> GSM152106 2 0.0725 0.9379 0.000 0.976 0.000 0.012 0.012 0.000
#> GSM152107 5 0.3183 0.7369 0.200 0.000 0.004 0.008 0.788 0.000
#> GSM152109 3 0.2340 0.6200 0.148 0.000 0.852 0.000 0.000 0.000
#> GSM152111 3 0.7698 -0.0922 0.260 0.000 0.292 0.212 0.000 0.236
#> GSM152112 5 0.2762 0.7391 0.196 0.000 0.000 0.000 0.804 0.000
#> GSM152113 1 0.4095 0.0133 0.512 0.000 0.480 0.000 0.000 0.008
#> GSM152115 5 0.2964 0.7355 0.204 0.000 0.004 0.000 0.792 0.000
#> GSM152030 5 0.2902 0.4552 0.004 0.000 0.000 0.196 0.800 0.000
#> GSM152038 1 0.5570 0.5002 0.552 0.000 0.216 0.000 0.000 0.232
#> GSM152042 5 0.3930 0.3948 0.004 0.000 0.420 0.000 0.576 0.000
#> GSM152062 3 0.3975 0.0430 0.452 0.000 0.544 0.000 0.004 0.000
#> GSM152077 6 0.3175 0.1611 0.256 0.000 0.000 0.000 0.000 0.744
#> GSM152088 2 0.0508 0.9477 0.012 0.984 0.000 0.004 0.000 0.000
#> GSM152100 5 0.0458 0.6703 0.000 0.000 0.000 0.016 0.984 0.000
#> GSM152102 2 0.4749 0.6390 0.028 0.708 0.000 0.192 0.072 0.000
#> GSM152104 2 0.0000 0.9516 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152028 6 0.1267 0.5836 0.060 0.000 0.000 0.000 0.000 0.940
#> GSM152029 3 0.0717 0.6503 0.008 0.000 0.976 0.000 0.000 0.016
#> GSM152049 6 0.3534 0.4880 0.244 0.000 0.000 0.016 0.000 0.740
#> GSM152053 5 0.3819 0.4999 0.004 0.000 0.372 0.000 0.624 0.000
#> GSM152059 1 0.5246 -0.0048 0.608 0.000 0.000 0.212 0.000 0.180
#> GSM152085 6 0.5622 0.4325 0.248 0.000 0.000 0.212 0.000 0.540
#> GSM152101 5 0.2793 0.7389 0.200 0.000 0.000 0.000 0.800 0.000
#> GSM152105 1 0.3986 0.4517 0.532 0.000 0.004 0.000 0.000 0.464
#> GSM152034 3 0.5371 0.4354 0.252 0.000 0.620 0.020 0.000 0.108
#> GSM152036 4 0.3862 0.3008 0.004 0.000 0.000 0.608 0.388 0.000
#> GSM152040 6 0.3512 0.5904 0.032 0.000 0.000 0.196 0.000 0.772
#> GSM152043 6 0.4367 0.5631 0.056 0.000 0.024 0.180 0.000 0.740
#> GSM152046 4 0.6078 -0.1784 0.276 0.000 0.000 0.388 0.000 0.336
#> GSM152047 3 0.5159 0.4824 0.020 0.000 0.660 0.208 0.000 0.112
#> GSM152048 6 0.0000 0.6253 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM152050 6 0.6026 0.3635 0.256 0.000 0.192 0.020 0.000 0.532
#> GSM152052 6 0.4379 0.0317 0.028 0.000 0.396 0.000 0.000 0.576
#> GSM152056 6 0.0000 0.6253 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM152060 4 0.6084 -0.1909 0.276 0.000 0.000 0.380 0.000 0.344
#> GSM152065 1 0.3986 0.4517 0.532 0.000 0.004 0.000 0.000 0.464
#> GSM152066 6 0.0000 0.6253 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM152069 3 0.2340 0.6200 0.148 0.000 0.852 0.000 0.000 0.000
#> GSM152070 6 0.5257 0.4757 0.016 0.000 0.140 0.196 0.000 0.648
#> GSM152071 3 0.2340 0.6200 0.148 0.000 0.852 0.000 0.000 0.000
#> GSM152072 3 0.4652 0.4821 0.288 0.000 0.640 0.072 0.000 0.000
#> GSM152073 6 0.3200 0.5976 0.016 0.000 0.000 0.196 0.000 0.788
#> GSM152078 3 0.4681 0.4775 0.232 0.000 0.668 0.000 0.000 0.100
#> GSM152082 6 0.5811 -0.0851 0.336 0.000 0.000 0.196 0.000 0.468
#> GSM152086 6 0.1204 0.6303 0.000 0.000 0.000 0.056 0.000 0.944
#> GSM152090 3 0.2213 0.6415 0.004 0.000 0.888 0.000 0.008 0.100
#> GSM152092 6 0.4008 0.5593 0.064 0.000 0.000 0.196 0.000 0.740
#> GSM152093 3 0.3076 0.5425 0.000 0.000 0.760 0.000 0.000 0.240
#> GSM152094 6 0.3200 0.5976 0.016 0.000 0.000 0.196 0.000 0.788
#> GSM152098 6 0.7195 -0.2229 0.336 0.000 0.104 0.196 0.000 0.364
#> GSM152110 6 0.0000 0.6253 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM152031 1 0.3971 0.4709 0.548 0.000 0.004 0.000 0.000 0.448
#> GSM152037 6 0.1765 0.5447 0.096 0.000 0.000 0.000 0.000 0.904
#> GSM152055 6 0.5563 0.2224 0.260 0.000 0.000 0.192 0.000 0.548
#> GSM152061 4 0.6078 -0.1784 0.276 0.000 0.000 0.388 0.000 0.336
#> GSM152064 6 0.5656 0.4242 0.256 0.000 0.000 0.212 0.000 0.532
#> GSM152087 6 0.5635 0.4302 0.256 0.000 0.000 0.208 0.000 0.536
#> GSM152103 3 0.2350 0.6389 0.020 0.000 0.880 0.000 0.000 0.100
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n specimen(p) k
#> SD:pam 85 5.29e-05 2
#> SD:pam 80 1.04e-04 3
#> SD:pam 75 3.25e-05 4
#> SD:pam 67 1.02e-04 5
#> SD:pam 49 6.33e-04 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "mclust"]
# you can also extract it by
# res = res_list["SD:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 10612 rows and 88 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.448 0.842 0.866 0.4441 0.504 0.504
#> 3 3 0.784 0.923 0.947 0.4209 0.839 0.687
#> 4 4 0.779 0.594 0.837 0.0943 0.952 0.871
#> 5 5 0.590 0.563 0.732 0.1276 0.846 0.550
#> 6 6 0.598 0.448 0.669 0.0369 0.899 0.570
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
#> GSM152032 2 0.952 0.753 0.372 0.628
#> GSM152033 2 0.963 0.739 0.388 0.612
#> GSM152063 2 0.000 0.732 0.000 1.000
#> GSM152074 2 0.936 0.766 0.352 0.648
#> GSM152080 2 0.563 0.771 0.132 0.868
#> GSM152081 2 0.886 0.782 0.304 0.696
#> GSM152083 2 0.443 0.763 0.092 0.908
#> GSM152091 2 0.000 0.732 0.000 1.000
#> GSM152108 2 0.788 0.774 0.236 0.764
#> GSM152114 2 0.963 0.739 0.388 0.612
#> GSM152035 2 0.224 0.745 0.036 0.964
#> GSM152039 2 0.595 0.767 0.144 0.856
#> GSM152041 2 0.949 0.755 0.368 0.632
#> GSM152044 2 0.000 0.732 0.000 1.000
#> GSM152045 1 0.000 0.987 1.000 0.000
#> GSM152051 2 0.000 0.732 0.000 1.000
#> GSM152054 2 0.992 0.636 0.448 0.552
#> GSM152057 2 0.000 0.732 0.000 1.000
#> GSM152058 1 0.000 0.987 1.000 0.000
#> GSM152067 2 0.936 0.765 0.352 0.648
#> GSM152068 2 0.000 0.732 0.000 1.000
#> GSM152075 2 0.895 0.782 0.312 0.688
#> GSM152076 2 0.518 0.767 0.116 0.884
#> GSM152079 2 0.000 0.732 0.000 1.000
#> GSM152084 2 0.963 0.739 0.388 0.612
#> GSM152089 2 0.994 0.629 0.456 0.544
#> GSM152095 2 0.518 0.767 0.116 0.884
#> GSM152096 2 0.821 0.774 0.256 0.744
#> GSM152097 2 0.000 0.732 0.000 1.000
#> GSM152099 2 0.000 0.732 0.000 1.000
#> GSM152106 2 0.000 0.732 0.000 1.000
#> GSM152107 2 0.917 0.776 0.332 0.668
#> GSM152109 2 0.946 0.758 0.364 0.636
#> GSM152111 1 0.000 0.987 1.000 0.000
#> GSM152112 2 0.909 0.779 0.324 0.676
#> GSM152113 2 0.963 0.739 0.388 0.612
#> GSM152115 2 0.943 0.761 0.360 0.640
#> GSM152030 2 0.518 0.767 0.116 0.884
#> GSM152038 2 0.963 0.739 0.388 0.612
#> GSM152042 2 0.886 0.784 0.304 0.696
#> GSM152062 2 0.955 0.750 0.376 0.624
#> GSM152077 2 0.990 0.660 0.440 0.560
#> GSM152088 2 0.000 0.732 0.000 1.000
#> GSM152100 2 0.839 0.786 0.268 0.732
#> GSM152102 2 0.767 0.776 0.224 0.776
#> GSM152104 2 0.000 0.732 0.000 1.000
#> GSM152028 1 0.000 0.987 1.000 0.000
#> GSM152029 1 0.000 0.987 1.000 0.000
#> GSM152049 1 0.000 0.987 1.000 0.000
#> GSM152053 2 0.891 0.784 0.308 0.692
#> GSM152059 1 0.000 0.987 1.000 0.000
#> GSM152085 1 0.000 0.987 1.000 0.000
#> GSM152101 2 0.917 0.776 0.332 0.668
#> GSM152105 1 0.141 0.959 0.980 0.020
#> GSM152034 1 0.000 0.987 1.000 0.000
#> GSM152036 2 0.595 0.767 0.144 0.856
#> GSM152040 1 0.000 0.987 1.000 0.000
#> GSM152043 1 0.000 0.987 1.000 0.000
#> GSM152046 1 0.000 0.987 1.000 0.000
#> GSM152047 1 0.000 0.987 1.000 0.000
#> GSM152048 1 0.000 0.987 1.000 0.000
#> GSM152050 1 0.000 0.987 1.000 0.000
#> GSM152052 1 0.000 0.987 1.000 0.000
#> GSM152056 1 0.000 0.987 1.000 0.000
#> GSM152060 1 0.000 0.987 1.000 0.000
#> GSM152065 1 0.000 0.987 1.000 0.000
#> GSM152066 1 0.000 0.987 1.000 0.000
#> GSM152069 2 0.963 0.739 0.388 0.612
#> GSM152070 1 0.000 0.987 1.000 0.000
#> GSM152071 2 0.963 0.739 0.388 0.612
#> GSM152072 1 0.000 0.987 1.000 0.000
#> GSM152073 1 0.000 0.987 1.000 0.000
#> GSM152078 1 0.000 0.987 1.000 0.000
#> GSM152082 1 0.000 0.987 1.000 0.000
#> GSM152086 1 0.000 0.987 1.000 0.000
#> GSM152090 2 0.963 0.739 0.388 0.612
#> GSM152092 1 0.000 0.987 1.000 0.000
#> GSM152093 1 0.881 0.264 0.700 0.300
#> GSM152094 1 0.000 0.987 1.000 0.000
#> GSM152098 1 0.000 0.987 1.000 0.000
#> GSM152110 1 0.000 0.987 1.000 0.000
#> GSM152031 1 0.000 0.987 1.000 0.000
#> GSM152037 1 0.000 0.987 1.000 0.000
#> GSM152055 1 0.000 0.987 1.000 0.000
#> GSM152061 1 0.000 0.987 1.000 0.000
#> GSM152064 1 0.000 0.987 1.000 0.000
#> GSM152087 1 0.000 0.987 1.000 0.000
#> GSM152103 2 0.975 0.713 0.408 0.592
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM152032 3 0.0000 0.885 0.000 0.000 1.000
#> GSM152033 3 0.1529 0.885 0.040 0.000 0.960
#> GSM152063 2 0.0237 0.928 0.000 0.996 0.004
#> GSM152074 3 0.1031 0.878 0.000 0.024 0.976
#> GSM152080 2 0.3619 0.865 0.000 0.864 0.136
#> GSM152081 3 0.3551 0.879 0.000 0.132 0.868
#> GSM152083 2 0.3816 0.860 0.000 0.852 0.148
#> GSM152091 2 0.3551 0.868 0.000 0.868 0.132
#> GSM152108 3 0.5740 0.828 0.100 0.096 0.804
#> GSM152114 3 0.3551 0.863 0.132 0.000 0.868
#> GSM152035 2 0.4555 0.745 0.000 0.800 0.200
#> GSM152039 3 0.4062 0.863 0.000 0.164 0.836
#> GSM152041 3 0.4172 0.842 0.156 0.004 0.840
#> GSM152044 2 0.0237 0.928 0.000 0.996 0.004
#> GSM152045 1 0.0000 0.993 1.000 0.000 0.000
#> GSM152051 2 0.0237 0.928 0.000 0.996 0.004
#> GSM152054 3 0.3752 0.855 0.144 0.000 0.856
#> GSM152057 2 0.0237 0.928 0.000 0.996 0.004
#> GSM152058 1 0.0000 0.993 1.000 0.000 0.000
#> GSM152067 3 0.1643 0.866 0.000 0.044 0.956
#> GSM152068 2 0.0237 0.928 0.000 0.996 0.004
#> GSM152075 3 0.3551 0.879 0.000 0.132 0.868
#> GSM152076 3 0.4062 0.863 0.000 0.164 0.836
#> GSM152079 2 0.0237 0.928 0.000 0.996 0.004
#> GSM152084 3 0.3482 0.865 0.128 0.000 0.872
#> GSM152089 3 0.3551 0.863 0.132 0.000 0.868
#> GSM152095 3 0.4062 0.863 0.000 0.164 0.836
#> GSM152096 3 0.0000 0.885 0.000 0.000 1.000
#> GSM152097 2 0.0237 0.928 0.000 0.996 0.004
#> GSM152099 2 0.0237 0.928 0.000 0.996 0.004
#> GSM152106 2 0.0237 0.928 0.000 0.996 0.004
#> GSM152107 3 0.0892 0.889 0.000 0.020 0.980
#> GSM152109 3 0.0747 0.881 0.000 0.016 0.984
#> GSM152111 1 0.0237 0.993 0.996 0.004 0.000
#> GSM152112 3 0.3715 0.881 0.004 0.128 0.868
#> GSM152113 3 0.3752 0.855 0.144 0.000 0.856
#> GSM152115 3 0.0000 0.885 0.000 0.000 1.000
#> GSM152030 3 0.3551 0.879 0.000 0.132 0.868
#> GSM152038 3 0.3116 0.874 0.108 0.000 0.892
#> GSM152042 3 0.3551 0.879 0.000 0.132 0.868
#> GSM152062 3 0.1643 0.892 0.044 0.000 0.956
#> GSM152077 1 0.2261 0.921 0.932 0.000 0.068
#> GSM152088 2 0.2448 0.899 0.000 0.924 0.076
#> GSM152100 3 0.3551 0.879 0.000 0.132 0.868
#> GSM152102 2 0.6225 0.426 0.000 0.568 0.432
#> GSM152104 2 0.0237 0.928 0.000 0.996 0.004
#> GSM152028 1 0.0000 0.993 1.000 0.000 0.000
#> GSM152029 1 0.1753 0.942 0.952 0.000 0.048
#> GSM152049 1 0.0237 0.993 0.996 0.004 0.000
#> GSM152053 3 0.3715 0.881 0.004 0.128 0.868
#> GSM152059 1 0.0000 0.993 1.000 0.000 0.000
#> GSM152085 1 0.0237 0.993 0.996 0.004 0.000
#> GSM152101 3 0.0237 0.884 0.000 0.004 0.996
#> GSM152105 1 0.0000 0.993 1.000 0.000 0.000
#> GSM152034 1 0.0237 0.993 0.996 0.004 0.000
#> GSM152036 3 0.4002 0.865 0.000 0.160 0.840
#> GSM152040 1 0.0237 0.993 0.996 0.004 0.000
#> GSM152043 1 0.0000 0.993 1.000 0.000 0.000
#> GSM152046 1 0.0237 0.993 0.996 0.004 0.000
#> GSM152047 1 0.0237 0.993 0.996 0.004 0.000
#> GSM152048 1 0.0237 0.993 0.996 0.004 0.000
#> GSM152050 1 0.0237 0.993 0.996 0.004 0.000
#> GSM152052 1 0.0000 0.993 1.000 0.000 0.000
#> GSM152056 1 0.0237 0.993 0.996 0.004 0.000
#> GSM152060 1 0.0237 0.993 0.996 0.004 0.000
#> GSM152065 1 0.0000 0.993 1.000 0.000 0.000
#> GSM152066 1 0.0000 0.993 1.000 0.000 0.000
#> GSM152069 3 0.0892 0.887 0.020 0.000 0.980
#> GSM152070 1 0.0000 0.993 1.000 0.000 0.000
#> GSM152071 3 0.1031 0.886 0.024 0.000 0.976
#> GSM152072 1 0.2165 0.927 0.936 0.000 0.064
#> GSM152073 1 0.0000 0.993 1.000 0.000 0.000
#> GSM152078 1 0.0424 0.986 0.992 0.000 0.008
#> GSM152082 1 0.0000 0.993 1.000 0.000 0.000
#> GSM152086 1 0.0237 0.993 0.996 0.004 0.000
#> GSM152090 3 0.3686 0.858 0.140 0.000 0.860
#> GSM152092 1 0.0000 0.993 1.000 0.000 0.000
#> GSM152093 1 0.0000 0.993 1.000 0.000 0.000
#> GSM152094 1 0.0237 0.993 0.996 0.004 0.000
#> GSM152098 1 0.0000 0.993 1.000 0.000 0.000
#> GSM152110 1 0.0237 0.993 0.996 0.004 0.000
#> GSM152031 1 0.0000 0.993 1.000 0.000 0.000
#> GSM152037 1 0.0000 0.993 1.000 0.000 0.000
#> GSM152055 1 0.0237 0.993 0.996 0.004 0.000
#> GSM152061 1 0.0237 0.993 0.996 0.004 0.000
#> GSM152064 1 0.0237 0.993 0.996 0.004 0.000
#> GSM152087 1 0.0237 0.993 0.996 0.004 0.000
#> GSM152103 3 0.4121 0.833 0.168 0.000 0.832
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM152032 3 0.2125 0.40191 0.000 0.004 0.920 0.076
#> GSM152033 3 0.0592 0.45503 0.016 0.000 0.984 0.000
#> GSM152063 2 0.0524 0.88770 0.000 0.988 0.004 0.008
#> GSM152074 3 0.2845 0.40597 0.000 0.028 0.896 0.076
#> GSM152080 2 0.4955 0.65787 0.000 0.556 0.000 0.444
#> GSM152081 3 0.5856 -0.83241 0.000 0.032 0.504 0.464
#> GSM152083 2 0.2089 0.86018 0.000 0.932 0.048 0.020
#> GSM152091 2 0.4955 0.65787 0.000 0.556 0.000 0.444
#> GSM152108 3 0.3899 0.32528 0.000 0.108 0.840 0.052
#> GSM152114 3 0.1811 0.43240 0.020 0.004 0.948 0.028
#> GSM152035 2 0.4452 0.52232 0.000 0.732 0.260 0.008
#> GSM152039 4 0.6660 1.00000 0.000 0.084 0.452 0.464
#> GSM152041 3 0.6351 -0.66624 0.032 0.020 0.560 0.388
#> GSM152044 2 0.0336 0.88914 0.000 0.992 0.000 0.008
#> GSM152045 1 0.1584 0.94239 0.952 0.000 0.036 0.012
#> GSM152051 2 0.0000 0.88889 0.000 1.000 0.000 0.000
#> GSM152054 3 0.6087 0.29218 0.236 0.004 0.672 0.088
#> GSM152057 2 0.0336 0.88914 0.000 0.992 0.000 0.008
#> GSM152058 1 0.2521 0.94042 0.912 0.000 0.024 0.064
#> GSM152067 3 0.5070 0.31524 0.000 0.008 0.620 0.372
#> GSM152068 2 0.0188 0.88920 0.000 0.996 0.000 0.004
#> GSM152075 3 0.5856 -0.83241 0.000 0.032 0.504 0.464
#> GSM152076 4 0.6660 1.00000 0.000 0.084 0.452 0.464
#> GSM152079 2 0.0000 0.88889 0.000 1.000 0.000 0.000
#> GSM152084 3 0.0376 0.44925 0.000 0.004 0.992 0.004
#> GSM152089 3 0.7857 -0.00906 0.268 0.004 0.452 0.276
#> GSM152095 4 0.6660 1.00000 0.000 0.084 0.452 0.464
#> GSM152096 3 0.1209 0.43671 0.000 0.004 0.964 0.032
#> GSM152097 2 0.0469 0.88755 0.000 0.988 0.000 0.012
#> GSM152099 2 0.0000 0.88889 0.000 1.000 0.000 0.000
#> GSM152106 2 0.0336 0.88914 0.000 0.992 0.000 0.008
#> GSM152107 3 0.4699 -0.29478 0.000 0.004 0.676 0.320
#> GSM152109 3 0.4699 0.33068 0.000 0.004 0.676 0.320
#> GSM152111 1 0.0469 0.95339 0.988 0.000 0.000 0.012
#> GSM152112 3 0.5774 -0.82238 0.000 0.028 0.508 0.464
#> GSM152113 3 0.0336 0.45503 0.008 0.000 0.992 0.000
#> GSM152115 3 0.2530 0.37280 0.000 0.004 0.896 0.100
#> GSM152030 3 0.5856 -0.83241 0.000 0.032 0.504 0.464
#> GSM152038 3 0.0657 0.45512 0.012 0.000 0.984 0.004
#> GSM152042 3 0.5856 -0.83241 0.000 0.032 0.504 0.464
#> GSM152062 3 0.0336 0.45013 0.000 0.000 0.992 0.008
#> GSM152077 3 0.6371 0.05651 0.428 0.000 0.508 0.064
#> GSM152088 2 0.2704 0.84330 0.000 0.876 0.000 0.124
#> GSM152100 3 0.6147 -0.88385 0.000 0.048 0.488 0.464
#> GSM152102 2 0.7006 0.54651 0.000 0.528 0.132 0.340
#> GSM152104 2 0.0336 0.88914 0.000 0.992 0.000 0.008
#> GSM152028 1 0.2722 0.93656 0.904 0.000 0.032 0.064
#> GSM152029 1 0.2179 0.91746 0.924 0.000 0.064 0.012
#> GSM152049 1 0.1059 0.95495 0.972 0.000 0.016 0.012
#> GSM152053 3 0.5597 -0.80132 0.000 0.020 0.516 0.464
#> GSM152059 1 0.0469 0.95399 0.988 0.000 0.000 0.012
#> GSM152085 1 0.0000 0.95482 1.000 0.000 0.000 0.000
#> GSM152101 3 0.5057 -0.34420 0.000 0.012 0.648 0.340
#> GSM152105 1 0.3071 0.92706 0.888 0.000 0.044 0.068
#> GSM152034 1 0.0336 0.95371 0.992 0.000 0.000 0.008
#> GSM152036 4 0.6660 1.00000 0.000 0.084 0.452 0.464
#> GSM152040 1 0.0469 0.95339 0.988 0.000 0.000 0.012
#> GSM152043 1 0.2021 0.94987 0.936 0.000 0.024 0.040
#> GSM152046 1 0.0188 0.95444 0.996 0.000 0.000 0.004
#> GSM152047 1 0.0657 0.95263 0.984 0.000 0.004 0.012
#> GSM152048 1 0.2142 0.94537 0.928 0.000 0.016 0.056
#> GSM152050 1 0.1059 0.95505 0.972 0.000 0.016 0.012
#> GSM152052 1 0.2131 0.94993 0.932 0.000 0.036 0.032
#> GSM152056 1 0.1888 0.94942 0.940 0.000 0.016 0.044
#> GSM152060 1 0.0000 0.95482 1.000 0.000 0.000 0.000
#> GSM152065 1 0.3056 0.92913 0.888 0.000 0.040 0.072
#> GSM152066 1 0.2060 0.94698 0.932 0.000 0.016 0.052
#> GSM152069 3 0.5026 0.33308 0.016 0.000 0.672 0.312
#> GSM152070 1 0.0592 0.95478 0.984 0.000 0.000 0.016
#> GSM152071 3 0.5496 0.32548 0.036 0.000 0.652 0.312
#> GSM152072 1 0.1284 0.95023 0.964 0.000 0.012 0.024
#> GSM152073 1 0.0524 0.95433 0.988 0.000 0.004 0.008
#> GSM152078 1 0.2089 0.94007 0.932 0.000 0.048 0.020
#> GSM152082 1 0.2101 0.94613 0.928 0.000 0.012 0.060
#> GSM152086 1 0.0927 0.95608 0.976 0.000 0.008 0.016
#> GSM152090 3 0.0469 0.45441 0.012 0.000 0.988 0.000
#> GSM152092 1 0.2021 0.95086 0.936 0.000 0.024 0.040
#> GSM152093 1 0.5873 0.20167 0.548 0.000 0.416 0.036
#> GSM152094 1 0.0336 0.95371 0.992 0.000 0.000 0.008
#> GSM152098 1 0.0672 0.95613 0.984 0.000 0.008 0.008
#> GSM152110 1 0.1406 0.95468 0.960 0.000 0.016 0.024
#> GSM152031 1 0.2660 0.93836 0.908 0.000 0.036 0.056
#> GSM152037 1 0.2521 0.94042 0.912 0.000 0.024 0.064
#> GSM152055 1 0.1297 0.95470 0.964 0.000 0.016 0.020
#> GSM152061 1 0.0188 0.95444 0.996 0.000 0.000 0.004
#> GSM152064 1 0.0469 0.95339 0.988 0.000 0.000 0.012
#> GSM152087 1 0.0188 0.95494 0.996 0.000 0.000 0.004
#> GSM152103 3 0.1118 0.44590 0.036 0.000 0.964 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM152032 3 0.0290 0.4793 0.000 0.000 0.992 0.008 0.000
#> GSM152033 3 0.5470 0.4329 0.296 0.000 0.612 0.000 0.092
#> GSM152063 2 0.0162 0.8354 0.000 0.996 0.000 0.004 0.000
#> GSM152074 3 0.0451 0.4777 0.000 0.004 0.988 0.008 0.000
#> GSM152080 2 0.5009 0.5628 0.000 0.496 0.012 0.480 0.012
#> GSM152081 4 0.5439 0.6811 0.000 0.060 0.432 0.508 0.000
#> GSM152083 2 0.3796 0.4948 0.000 0.700 0.300 0.000 0.000
#> GSM152091 2 0.5009 0.5628 0.000 0.496 0.012 0.480 0.012
#> GSM152108 3 0.3617 0.3383 0.012 0.088 0.840 0.060 0.000
#> GSM152114 3 0.3282 0.4660 0.012 0.000 0.860 0.044 0.084
#> GSM152035 2 0.1628 0.7864 0.000 0.936 0.056 0.008 0.000
#> GSM152039 4 0.6140 0.6566 0.000 0.356 0.140 0.504 0.000
#> GSM152041 4 0.8106 0.6081 0.008 0.204 0.256 0.432 0.100
#> GSM152044 2 0.0000 0.8376 0.000 1.000 0.000 0.000 0.000
#> GSM152045 5 0.1965 0.6857 0.096 0.000 0.000 0.000 0.904
#> GSM152051 2 0.0000 0.8376 0.000 1.000 0.000 0.000 0.000
#> GSM152054 3 0.6402 0.2195 0.020 0.000 0.456 0.100 0.424
#> GSM152057 2 0.0000 0.8376 0.000 1.000 0.000 0.000 0.000
#> GSM152058 1 0.2848 0.7368 0.868 0.000 0.028 0.000 0.104
#> GSM152067 3 0.6250 0.3561 0.000 0.004 0.540 0.156 0.300
#> GSM152068 2 0.0000 0.8376 0.000 1.000 0.000 0.000 0.000
#> GSM152075 4 0.4744 0.6487 0.000 0.016 0.476 0.508 0.000
#> GSM152076 4 0.6163 0.6607 0.000 0.352 0.144 0.504 0.000
#> GSM152079 2 0.0000 0.8376 0.000 1.000 0.000 0.000 0.000
#> GSM152084 3 0.2407 0.4951 0.012 0.000 0.896 0.004 0.088
#> GSM152089 5 0.6129 0.1178 0.012 0.008 0.068 0.412 0.500
#> GSM152095 4 0.6140 0.6566 0.000 0.356 0.140 0.504 0.000
#> GSM152096 3 0.1329 0.4912 0.032 0.000 0.956 0.008 0.004
#> GSM152097 2 0.0290 0.8324 0.000 0.992 0.000 0.008 0.000
#> GSM152099 2 0.0162 0.8360 0.000 0.996 0.004 0.000 0.000
#> GSM152106 2 0.0000 0.8376 0.000 1.000 0.000 0.000 0.000
#> GSM152107 3 0.4735 -0.2898 0.004 0.032 0.668 0.296 0.000
#> GSM152109 3 0.6186 0.3609 0.004 0.000 0.548 0.148 0.300
#> GSM152111 5 0.3707 0.4900 0.284 0.000 0.000 0.000 0.716
#> GSM152112 4 0.5315 0.6612 0.004 0.040 0.456 0.500 0.000
#> GSM152113 3 0.4247 0.5029 0.132 0.000 0.776 0.000 0.092
#> GSM152115 3 0.1918 0.4781 0.036 0.000 0.928 0.036 0.000
#> GSM152030 4 0.4744 0.6487 0.000 0.016 0.476 0.508 0.000
#> GSM152038 3 0.5584 0.4251 0.324 0.000 0.584 0.000 0.092
#> GSM152042 4 0.4746 0.6437 0.000 0.016 0.480 0.504 0.000
#> GSM152062 3 0.2349 0.4953 0.012 0.000 0.900 0.004 0.084
#> GSM152077 3 0.5779 0.2543 0.220 0.000 0.628 0.004 0.148
#> GSM152088 2 0.4538 0.6467 0.000 0.636 0.012 0.348 0.004
#> GSM152100 4 0.5849 0.6921 0.000 0.100 0.392 0.508 0.000
#> GSM152102 2 0.7061 0.4338 0.000 0.500 0.032 0.236 0.232
#> GSM152104 2 0.0000 0.8376 0.000 1.000 0.000 0.000 0.000
#> GSM152028 1 0.0000 0.7455 1.000 0.000 0.000 0.000 0.000
#> GSM152029 5 0.3760 0.6532 0.188 0.000 0.028 0.000 0.784
#> GSM152049 1 0.4182 0.4926 0.600 0.000 0.000 0.000 0.400
#> GSM152053 3 0.4803 -0.6610 0.004 0.012 0.496 0.488 0.000
#> GSM152059 5 0.4565 0.5524 0.408 0.000 0.000 0.012 0.580
#> GSM152085 5 0.2377 0.7136 0.128 0.000 0.000 0.000 0.872
#> GSM152101 3 0.5888 -0.3976 0.000 0.136 0.576 0.288 0.000
#> GSM152105 1 0.0955 0.7345 0.968 0.000 0.028 0.000 0.004
#> GSM152034 5 0.2329 0.7120 0.124 0.000 0.000 0.000 0.876
#> GSM152036 4 0.6140 0.6566 0.000 0.356 0.140 0.504 0.000
#> GSM152040 5 0.2424 0.7133 0.132 0.000 0.000 0.000 0.868
#> GSM152043 1 0.0609 0.7529 0.980 0.000 0.000 0.000 0.020
#> GSM152046 5 0.2127 0.7112 0.108 0.000 0.000 0.000 0.892
#> GSM152047 5 0.2127 0.7132 0.108 0.000 0.000 0.000 0.892
#> GSM152048 1 0.3366 0.6784 0.768 0.000 0.000 0.000 0.232
#> GSM152050 1 0.4242 0.4798 0.572 0.000 0.000 0.000 0.428
#> GSM152052 1 0.3274 0.5718 0.780 0.000 0.000 0.000 0.220
#> GSM152056 1 0.4150 0.5373 0.612 0.000 0.000 0.000 0.388
#> GSM152060 5 0.2127 0.7112 0.108 0.000 0.000 0.000 0.892
#> GSM152065 1 0.0162 0.7478 0.996 0.000 0.000 0.000 0.004
#> GSM152066 1 0.2280 0.7409 0.880 0.000 0.000 0.000 0.120
#> GSM152069 3 0.6743 0.3278 0.020 0.000 0.464 0.148 0.368
#> GSM152070 5 0.4505 0.5791 0.384 0.000 0.000 0.012 0.604
#> GSM152071 3 0.6765 0.3080 0.020 0.000 0.444 0.148 0.388
#> GSM152072 5 0.4109 0.5791 0.288 0.000 0.012 0.000 0.700
#> GSM152073 5 0.3949 0.6316 0.332 0.000 0.000 0.000 0.668
#> GSM152078 5 0.4360 0.5651 0.300 0.000 0.020 0.000 0.680
#> GSM152082 1 0.2561 0.5990 0.856 0.000 0.000 0.000 0.144
#> GSM152086 1 0.3366 0.6544 0.768 0.000 0.000 0.000 0.232
#> GSM152090 3 0.5250 0.5182 0.108 0.000 0.668 0.000 0.224
#> GSM152092 1 0.0609 0.7529 0.980 0.000 0.000 0.000 0.020
#> GSM152093 5 0.6602 -0.0248 0.216 0.000 0.360 0.000 0.424
#> GSM152094 5 0.3242 0.6970 0.216 0.000 0.000 0.000 0.784
#> GSM152098 5 0.4632 0.4809 0.448 0.000 0.000 0.012 0.540
#> GSM152110 1 0.4210 0.5070 0.588 0.000 0.000 0.000 0.412
#> GSM152031 1 0.0290 0.7497 0.992 0.000 0.000 0.000 0.008
#> GSM152037 1 0.0510 0.7531 0.984 0.000 0.000 0.000 0.016
#> GSM152055 1 0.4242 0.4895 0.572 0.000 0.000 0.000 0.428
#> GSM152061 5 0.2127 0.7112 0.108 0.000 0.000 0.000 0.892
#> GSM152064 5 0.3534 0.5364 0.256 0.000 0.000 0.000 0.744
#> GSM152087 5 0.3424 0.6867 0.240 0.000 0.000 0.000 0.760
#> GSM152103 3 0.5672 0.4320 0.088 0.000 0.544 0.000 0.368
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM152032 3 0.5273 0.4020 0.000 0.032 0.568 0.352 0.048 0.000
#> GSM152033 5 0.7157 0.3136 0.140 0.000 0.212 0.196 0.452 0.000
#> GSM152063 2 0.2030 0.8004 0.000 0.908 0.064 0.028 0.000 0.000
#> GSM152074 3 0.5329 0.4051 0.000 0.040 0.568 0.348 0.044 0.000
#> GSM152080 2 0.5937 0.4533 0.000 0.480 0.308 0.000 0.208 0.004
#> GSM152081 4 0.1461 0.5600 0.000 0.044 0.016 0.940 0.000 0.000
#> GSM152083 2 0.3977 0.6485 0.000 0.760 0.096 0.144 0.000 0.000
#> GSM152091 2 0.5937 0.4533 0.000 0.480 0.308 0.000 0.208 0.004
#> GSM152108 4 0.5817 0.0977 0.008 0.084 0.252 0.608 0.048 0.000
#> GSM152114 4 0.5838 0.0109 0.008 0.000 0.120 0.500 0.364 0.008
#> GSM152035 2 0.4200 0.6518 0.000 0.760 0.136 0.092 0.012 0.000
#> GSM152039 4 0.3938 0.4828 0.000 0.228 0.000 0.728 0.044 0.000
#> GSM152041 4 0.7779 0.1561 0.004 0.128 0.044 0.432 0.272 0.120
#> GSM152044 2 0.0713 0.8333 0.000 0.972 0.000 0.000 0.028 0.000
#> GSM152045 6 0.6377 -0.1744 0.152 0.000 0.040 0.000 0.360 0.448
#> GSM152051 2 0.0725 0.8372 0.000 0.976 0.012 0.012 0.000 0.000
#> GSM152054 5 0.7674 0.4018 0.064 0.012 0.236 0.032 0.436 0.220
#> GSM152057 2 0.0891 0.8358 0.000 0.968 0.024 0.008 0.000 0.000
#> GSM152058 1 0.2936 0.6328 0.836 0.000 0.004 0.004 0.012 0.144
#> GSM152067 3 0.1956 0.4376 0.000 0.000 0.908 0.008 0.004 0.080
#> GSM152068 2 0.0520 0.8362 0.000 0.984 0.008 0.000 0.008 0.000
#> GSM152075 4 0.0779 0.5579 0.000 0.008 0.008 0.976 0.008 0.000
#> GSM152076 4 0.4132 0.4881 0.000 0.212 0.016 0.736 0.036 0.000
#> GSM152079 2 0.0891 0.8358 0.000 0.968 0.024 0.008 0.000 0.000
#> GSM152084 4 0.6124 -0.1245 0.008 0.000 0.156 0.416 0.412 0.008
#> GSM152089 5 0.7324 0.3380 0.012 0.004 0.064 0.232 0.408 0.280
#> GSM152095 4 0.3860 0.4848 0.000 0.236 0.000 0.728 0.036 0.000
#> GSM152096 3 0.5586 0.3487 0.012 0.012 0.544 0.356 0.076 0.000
#> GSM152097 2 0.1141 0.8282 0.000 0.948 0.000 0.000 0.052 0.000
#> GSM152099 2 0.0806 0.8366 0.000 0.972 0.020 0.008 0.000 0.000
#> GSM152106 2 0.1141 0.8282 0.000 0.948 0.000 0.000 0.052 0.000
#> GSM152107 4 0.5485 -0.1976 0.000 0.032 0.436 0.484 0.044 0.004
#> GSM152109 3 0.1956 0.4375 0.000 0.000 0.908 0.008 0.004 0.080
#> GSM152111 6 0.3807 0.3489 0.368 0.000 0.000 0.000 0.004 0.628
#> GSM152112 4 0.1718 0.5545 0.000 0.024 0.020 0.936 0.020 0.000
#> GSM152113 5 0.7093 0.2547 0.108 0.000 0.176 0.296 0.420 0.000
#> GSM152115 3 0.5310 0.2739 0.016 0.000 0.500 0.432 0.044 0.008
#> GSM152030 4 0.1026 0.5568 0.000 0.008 0.012 0.968 0.008 0.004
#> GSM152038 5 0.7340 0.3239 0.168 0.000 0.204 0.180 0.444 0.004
#> GSM152042 4 0.0779 0.5568 0.000 0.008 0.008 0.976 0.000 0.008
#> GSM152062 4 0.6394 -0.1320 0.008 0.000 0.220 0.384 0.380 0.008
#> GSM152077 4 0.7789 -0.0219 0.080 0.000 0.080 0.456 0.200 0.184
#> GSM152088 2 0.5330 0.5975 0.000 0.612 0.176 0.000 0.208 0.004
#> GSM152100 4 0.1951 0.5552 0.000 0.076 0.016 0.908 0.000 0.000
#> GSM152102 3 0.6534 -0.2049 0.000 0.360 0.468 0.008 0.092 0.072
#> GSM152104 2 0.1141 0.8282 0.000 0.948 0.000 0.000 0.052 0.000
#> GSM152028 1 0.1649 0.6263 0.932 0.000 0.000 0.000 0.032 0.036
#> GSM152029 5 0.6814 0.2280 0.208 0.000 0.056 0.000 0.400 0.336
#> GSM152049 1 0.3984 0.3924 0.596 0.000 0.000 0.000 0.008 0.396
#> GSM152053 4 0.1780 0.5434 0.000 0.008 0.044 0.932 0.008 0.008
#> GSM152059 6 0.5371 0.4934 0.316 0.000 0.032 0.000 0.064 0.588
#> GSM152085 6 0.3163 0.5986 0.232 0.000 0.000 0.000 0.004 0.764
#> GSM152101 3 0.5938 0.2188 0.000 0.092 0.496 0.372 0.040 0.000
#> GSM152105 1 0.2032 0.6438 0.920 0.000 0.020 0.000 0.036 0.024
#> GSM152034 6 0.3547 0.4789 0.300 0.000 0.000 0.000 0.004 0.696
#> GSM152036 4 0.4124 0.4875 0.000 0.224 0.012 0.728 0.036 0.000
#> GSM152040 6 0.2823 0.6147 0.204 0.000 0.000 0.000 0.000 0.796
#> GSM152043 1 0.1141 0.6573 0.948 0.000 0.000 0.000 0.000 0.052
#> GSM152046 6 0.3819 0.6021 0.172 0.000 0.000 0.000 0.064 0.764
#> GSM152047 6 0.4866 0.4009 0.116 0.000 0.000 0.000 0.236 0.648
#> GSM152048 1 0.3314 0.5730 0.740 0.000 0.000 0.000 0.004 0.256
#> GSM152050 1 0.3915 0.3448 0.584 0.000 0.000 0.000 0.004 0.412
#> GSM152052 1 0.5336 0.2780 0.584 0.000 0.000 0.000 0.160 0.256
#> GSM152056 1 0.3819 0.4276 0.624 0.000 0.000 0.000 0.004 0.372
#> GSM152060 6 0.3819 0.5984 0.172 0.000 0.000 0.000 0.064 0.764
#> GSM152065 1 0.1921 0.6250 0.916 0.000 0.000 0.000 0.032 0.052
#> GSM152066 1 0.2668 0.6310 0.828 0.000 0.000 0.000 0.004 0.168
#> GSM152069 3 0.4176 0.3464 0.000 0.000 0.752 0.008 0.160 0.080
#> GSM152070 6 0.5385 0.4946 0.320 0.000 0.032 0.000 0.064 0.584
#> GSM152071 3 0.4768 0.2109 0.000 0.000 0.668 0.008 0.244 0.080
#> GSM152072 5 0.6791 0.2191 0.212 0.000 0.052 0.000 0.392 0.344
#> GSM152073 6 0.4166 0.5321 0.324 0.000 0.028 0.000 0.000 0.648
#> GSM152078 5 0.6791 0.3049 0.204 0.000 0.048 0.004 0.436 0.308
#> GSM152082 1 0.3602 0.4025 0.760 0.000 0.000 0.000 0.032 0.208
#> GSM152086 1 0.3245 0.5900 0.764 0.000 0.000 0.000 0.008 0.228
#> GSM152090 5 0.7431 0.3145 0.124 0.000 0.172 0.268 0.424 0.012
#> GSM152092 1 0.1950 0.6403 0.912 0.000 0.000 0.000 0.024 0.064
#> GSM152093 4 0.8176 -0.2803 0.184 0.000 0.032 0.296 0.280 0.208
#> GSM152094 6 0.2902 0.6252 0.196 0.000 0.000 0.000 0.004 0.800
#> GSM152098 6 0.5255 0.4058 0.396 0.000 0.032 0.000 0.040 0.532
#> GSM152110 1 0.3937 0.3592 0.572 0.000 0.000 0.000 0.004 0.424
#> GSM152031 1 0.2106 0.6361 0.904 0.000 0.000 0.000 0.032 0.064
#> GSM152037 1 0.1464 0.6579 0.944 0.000 0.000 0.004 0.016 0.036
#> GSM152055 1 0.4584 0.2978 0.556 0.000 0.000 0.000 0.040 0.404
#> GSM152061 6 0.3786 0.6008 0.168 0.000 0.000 0.000 0.064 0.768
#> GSM152064 6 0.4098 0.4003 0.292 0.000 0.000 0.000 0.032 0.676
#> GSM152087 6 0.3601 0.5659 0.312 0.000 0.000 0.000 0.004 0.684
#> GSM152103 5 0.7703 0.4218 0.132 0.000 0.180 0.100 0.492 0.096
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n specimen(p) k
#> SD:mclust 87 4.07e-10 2
#> SD:mclust 87 1.26e-07 3
#> SD:mclust 57 5.77e-07 4
#> SD:mclust 59 1.81e-04 5
#> SD:mclust 39 6.52e-04 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "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 10612 rows and 88 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 0.999 0.967 0.986 0.4957 0.504 0.504
#> 3 3 0.597 0.623 0.794 0.3127 0.760 0.565
#> 4 4 0.561 0.630 0.798 0.1034 0.838 0.606
#> 5 5 0.713 0.740 0.862 0.1019 0.852 0.542
#> 6 6 0.726 0.707 0.845 0.0439 0.911 0.612
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
#> GSM152032 2 0.3431 0.924 0.064 0.936
#> GSM152033 1 0.0000 0.989 1.000 0.000
#> GSM152063 2 0.0000 0.980 0.000 1.000
#> GSM152074 2 0.0000 0.980 0.000 1.000
#> GSM152080 2 0.0000 0.980 0.000 1.000
#> GSM152081 2 0.0000 0.980 0.000 1.000
#> GSM152083 2 0.0000 0.980 0.000 1.000
#> GSM152091 2 0.0000 0.980 0.000 1.000
#> GSM152108 2 0.0000 0.980 0.000 1.000
#> GSM152114 1 0.0000 0.989 1.000 0.000
#> GSM152035 2 0.0000 0.980 0.000 1.000
#> GSM152039 2 0.0000 0.980 0.000 1.000
#> GSM152041 2 0.9393 0.450 0.356 0.644
#> GSM152044 2 0.0000 0.980 0.000 1.000
#> GSM152045 1 0.0000 0.989 1.000 0.000
#> GSM152051 2 0.0000 0.980 0.000 1.000
#> GSM152054 1 0.8861 0.558 0.696 0.304
#> GSM152057 2 0.0000 0.980 0.000 1.000
#> GSM152058 1 0.0000 0.989 1.000 0.000
#> GSM152067 2 0.0000 0.980 0.000 1.000
#> GSM152068 2 0.0000 0.980 0.000 1.000
#> GSM152075 2 0.0000 0.980 0.000 1.000
#> GSM152076 2 0.0000 0.980 0.000 1.000
#> GSM152079 2 0.0000 0.980 0.000 1.000
#> GSM152084 1 0.4298 0.901 0.912 0.088
#> GSM152089 2 0.4690 0.886 0.100 0.900
#> GSM152095 2 0.0000 0.980 0.000 1.000
#> GSM152096 2 0.0000 0.980 0.000 1.000
#> GSM152097 2 0.0000 0.980 0.000 1.000
#> GSM152099 2 0.0000 0.980 0.000 1.000
#> GSM152106 2 0.0000 0.980 0.000 1.000
#> GSM152107 2 0.0000 0.980 0.000 1.000
#> GSM152109 2 0.2043 0.954 0.032 0.968
#> GSM152111 1 0.0000 0.989 1.000 0.000
#> GSM152112 2 0.0000 0.980 0.000 1.000
#> GSM152113 1 0.0376 0.985 0.996 0.004
#> GSM152115 2 0.6887 0.777 0.184 0.816
#> GSM152030 2 0.0000 0.980 0.000 1.000
#> GSM152038 1 0.0000 0.989 1.000 0.000
#> GSM152042 2 0.0000 0.980 0.000 1.000
#> GSM152062 1 0.3733 0.919 0.928 0.072
#> GSM152077 1 0.0000 0.989 1.000 0.000
#> GSM152088 2 0.0000 0.980 0.000 1.000
#> GSM152100 2 0.0000 0.980 0.000 1.000
#> GSM152102 2 0.0000 0.980 0.000 1.000
#> GSM152104 2 0.0000 0.980 0.000 1.000
#> GSM152028 1 0.0000 0.989 1.000 0.000
#> GSM152029 1 0.0000 0.989 1.000 0.000
#> GSM152049 1 0.0000 0.989 1.000 0.000
#> GSM152053 2 0.0000 0.980 0.000 1.000
#> GSM152059 1 0.0000 0.989 1.000 0.000
#> GSM152085 1 0.0000 0.989 1.000 0.000
#> GSM152101 2 0.0000 0.980 0.000 1.000
#> GSM152105 1 0.0000 0.989 1.000 0.000
#> GSM152034 1 0.0000 0.989 1.000 0.000
#> GSM152036 2 0.0000 0.980 0.000 1.000
#> GSM152040 1 0.0000 0.989 1.000 0.000
#> GSM152043 1 0.0000 0.989 1.000 0.000
#> GSM152046 1 0.0000 0.989 1.000 0.000
#> GSM152047 1 0.0000 0.989 1.000 0.000
#> GSM152048 1 0.0000 0.989 1.000 0.000
#> GSM152050 1 0.0000 0.989 1.000 0.000
#> GSM152052 1 0.0000 0.989 1.000 0.000
#> GSM152056 1 0.0000 0.989 1.000 0.000
#> GSM152060 1 0.0000 0.989 1.000 0.000
#> GSM152065 1 0.0000 0.989 1.000 0.000
#> GSM152066 1 0.0000 0.989 1.000 0.000
#> GSM152069 1 0.0376 0.985 0.996 0.004
#> GSM152070 1 0.0000 0.989 1.000 0.000
#> GSM152071 1 0.0000 0.989 1.000 0.000
#> GSM152072 1 0.0000 0.989 1.000 0.000
#> GSM152073 1 0.0000 0.989 1.000 0.000
#> GSM152078 1 0.0000 0.989 1.000 0.000
#> GSM152082 1 0.0000 0.989 1.000 0.000
#> GSM152086 1 0.0000 0.989 1.000 0.000
#> GSM152090 1 0.3431 0.927 0.936 0.064
#> GSM152092 1 0.0000 0.989 1.000 0.000
#> GSM152093 1 0.0000 0.989 1.000 0.000
#> GSM152094 1 0.0000 0.989 1.000 0.000
#> GSM152098 1 0.0000 0.989 1.000 0.000
#> GSM152110 1 0.0000 0.989 1.000 0.000
#> GSM152031 1 0.0000 0.989 1.000 0.000
#> GSM152037 1 0.0000 0.989 1.000 0.000
#> GSM152055 1 0.0000 0.989 1.000 0.000
#> GSM152061 1 0.0000 0.989 1.000 0.000
#> GSM152064 1 0.0000 0.989 1.000 0.000
#> GSM152087 1 0.0000 0.989 1.000 0.000
#> GSM152103 1 0.0000 0.989 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM152032 3 0.0000 0.7160 0.000 0.000 1.000
#> GSM152033 3 0.6215 0.2646 0.428 0.000 0.572
#> GSM152063 2 0.6252 0.3217 0.000 0.556 0.444
#> GSM152074 3 0.0000 0.7160 0.000 0.000 1.000
#> GSM152080 3 0.0237 0.7154 0.000 0.004 0.996
#> GSM152081 2 0.0000 0.7608 0.000 1.000 0.000
#> GSM152083 3 0.0237 0.7154 0.000 0.004 0.996
#> GSM152091 3 0.6045 0.1790 0.000 0.380 0.620
#> GSM152108 3 0.0592 0.7137 0.000 0.012 0.988
#> GSM152114 1 0.3623 0.8146 0.896 0.072 0.032
#> GSM152035 3 0.5785 0.3052 0.000 0.332 0.668
#> GSM152039 2 0.0237 0.7592 0.004 0.996 0.000
#> GSM152041 2 0.1643 0.7277 0.044 0.956 0.000
#> GSM152044 2 0.6180 0.3775 0.000 0.584 0.416
#> GSM152045 1 0.0000 0.8494 1.000 0.000 0.000
#> GSM152051 3 0.6008 0.2044 0.000 0.372 0.628
#> GSM152054 2 0.8387 -0.0441 0.428 0.488 0.084
#> GSM152057 3 0.4504 0.5627 0.000 0.196 0.804
#> GSM152058 1 0.0000 0.8494 1.000 0.000 0.000
#> GSM152067 3 0.0000 0.7160 0.000 0.000 1.000
#> GSM152068 2 0.6307 0.2085 0.000 0.512 0.488
#> GSM152075 2 0.0000 0.7608 0.000 1.000 0.000
#> GSM152076 2 0.0000 0.7608 0.000 1.000 0.000
#> GSM152079 3 0.4605 0.5525 0.000 0.204 0.796
#> GSM152084 3 0.5098 0.5718 0.248 0.000 0.752
#> GSM152089 2 0.0892 0.7485 0.020 0.980 0.000
#> GSM152095 2 0.0000 0.7608 0.000 1.000 0.000
#> GSM152096 3 0.0000 0.7160 0.000 0.000 1.000
#> GSM152097 2 0.5529 0.5591 0.000 0.704 0.296
#> GSM152099 3 0.4062 0.5998 0.000 0.164 0.836
#> GSM152106 2 0.0592 0.7577 0.000 0.988 0.012
#> GSM152107 3 0.1411 0.7034 0.000 0.036 0.964
#> GSM152109 3 0.0000 0.7160 0.000 0.000 1.000
#> GSM152111 1 0.5327 0.6408 0.728 0.272 0.000
#> GSM152112 3 0.6286 -0.1215 0.000 0.464 0.536
#> GSM152113 3 0.6225 0.2536 0.432 0.000 0.568
#> GSM152115 3 0.0237 0.7150 0.004 0.000 0.996
#> GSM152030 2 0.5621 0.5456 0.000 0.692 0.308
#> GSM152038 3 0.6244 0.2319 0.440 0.000 0.560
#> GSM152042 2 0.6286 0.2740 0.000 0.536 0.464
#> GSM152062 3 0.5678 0.4913 0.316 0.000 0.684
#> GSM152077 1 0.0747 0.8445 0.984 0.000 0.016
#> GSM152088 3 0.3192 0.6495 0.000 0.112 0.888
#> GSM152100 2 0.0000 0.7608 0.000 1.000 0.000
#> GSM152102 3 0.1031 0.7091 0.000 0.024 0.976
#> GSM152104 2 0.4399 0.6606 0.000 0.812 0.188
#> GSM152028 1 0.0592 0.8462 0.988 0.000 0.012
#> GSM152029 1 0.4452 0.6728 0.808 0.000 0.192
#> GSM152049 1 0.0000 0.8494 1.000 0.000 0.000
#> GSM152053 3 0.5591 0.3802 0.000 0.304 0.696
#> GSM152059 1 0.0000 0.8494 1.000 0.000 0.000
#> GSM152085 1 0.3267 0.7879 0.884 0.116 0.000
#> GSM152101 3 0.1031 0.7091 0.000 0.024 0.976
#> GSM152105 1 0.1860 0.8226 0.948 0.000 0.052
#> GSM152034 1 0.5926 0.5300 0.644 0.356 0.000
#> GSM152036 2 0.0237 0.7592 0.004 0.996 0.000
#> GSM152040 1 0.0000 0.8494 1.000 0.000 0.000
#> GSM152043 1 0.0237 0.8487 0.996 0.000 0.004
#> GSM152046 1 0.6215 0.4116 0.572 0.428 0.000
#> GSM152047 1 0.5497 0.6168 0.708 0.292 0.000
#> GSM152048 1 0.0000 0.8494 1.000 0.000 0.000
#> GSM152050 1 0.3879 0.7601 0.848 0.152 0.000
#> GSM152052 1 0.3116 0.7753 0.892 0.000 0.108
#> GSM152056 1 0.0892 0.8442 0.980 0.020 0.000
#> GSM152060 1 0.6180 0.4344 0.584 0.416 0.000
#> GSM152065 1 0.2711 0.7944 0.912 0.000 0.088
#> GSM152066 1 0.0000 0.8494 1.000 0.000 0.000
#> GSM152069 3 0.2796 0.6725 0.092 0.000 0.908
#> GSM152070 1 0.0237 0.8487 0.996 0.000 0.004
#> GSM152071 3 0.5621 0.5019 0.308 0.000 0.692
#> GSM152072 1 0.6079 0.2841 0.612 0.000 0.388
#> GSM152073 1 0.0000 0.8494 1.000 0.000 0.000
#> GSM152078 1 0.6225 0.1515 0.568 0.000 0.432
#> GSM152082 1 0.0747 0.8446 0.984 0.000 0.016
#> GSM152086 1 0.0000 0.8494 1.000 0.000 0.000
#> GSM152090 3 0.6111 0.3346 0.396 0.000 0.604
#> GSM152092 1 0.0592 0.8462 0.988 0.000 0.012
#> GSM152093 1 0.0000 0.8494 1.000 0.000 0.000
#> GSM152094 1 0.0424 0.8476 0.992 0.008 0.000
#> GSM152098 1 0.0237 0.8487 0.996 0.000 0.004
#> GSM152110 1 0.1643 0.8335 0.956 0.044 0.000
#> GSM152031 1 0.1031 0.8404 0.976 0.000 0.024
#> GSM152037 1 0.0237 0.8487 0.996 0.000 0.004
#> GSM152055 1 0.6180 0.4344 0.584 0.416 0.000
#> GSM152061 1 0.6235 0.3952 0.564 0.436 0.000
#> GSM152064 1 0.6180 0.4344 0.584 0.416 0.000
#> GSM152087 1 0.0000 0.8494 1.000 0.000 0.000
#> GSM152103 1 0.6308 -0.0576 0.508 0.000 0.492
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM152032 3 0.2704 0.6645 0.000 0.124 0.876 0.000
#> GSM152033 3 0.7313 -0.2549 0.380 0.156 0.464 0.000
#> GSM152063 2 0.2928 0.7804 0.000 0.880 0.012 0.108
#> GSM152074 3 0.2345 0.6483 0.000 0.100 0.900 0.000
#> GSM152080 2 0.1722 0.7621 0.000 0.944 0.048 0.008
#> GSM152081 4 0.2589 0.7281 0.000 0.000 0.116 0.884
#> GSM152083 3 0.4994 0.2898 0.000 0.480 0.520 0.000
#> GSM152091 2 0.2021 0.7896 0.000 0.932 0.012 0.056
#> GSM152108 2 0.4655 0.4509 0.004 0.684 0.312 0.000
#> GSM152114 3 0.8356 -0.1118 0.312 0.080 0.496 0.112
#> GSM152035 2 0.3899 0.7295 0.000 0.840 0.108 0.052
#> GSM152039 4 0.0000 0.8148 0.000 0.000 0.000 1.000
#> GSM152041 4 0.0188 0.8129 0.004 0.000 0.000 0.996
#> GSM152044 2 0.5548 0.4490 0.000 0.588 0.024 0.388
#> GSM152045 1 0.2465 0.7649 0.924 0.012 0.044 0.020
#> GSM152051 2 0.3013 0.7870 0.000 0.888 0.032 0.080
#> GSM152054 2 0.8958 0.0901 0.316 0.404 0.068 0.212
#> GSM152057 2 0.3367 0.7794 0.000 0.864 0.028 0.108
#> GSM152058 1 0.5478 0.7265 0.696 0.056 0.248 0.000
#> GSM152067 3 0.4483 0.6275 0.004 0.284 0.712 0.000
#> GSM152068 2 0.3149 0.7858 0.000 0.880 0.032 0.088
#> GSM152075 4 0.0000 0.8148 0.000 0.000 0.000 1.000
#> GSM152076 4 0.0000 0.8148 0.000 0.000 0.000 1.000
#> GSM152079 2 0.2773 0.7888 0.000 0.900 0.028 0.072
#> GSM152084 3 0.2363 0.6388 0.024 0.056 0.920 0.000
#> GSM152089 4 0.3774 0.6868 0.168 0.008 0.004 0.820
#> GSM152095 4 0.0000 0.8148 0.000 0.000 0.000 1.000
#> GSM152096 2 0.2149 0.7209 0.000 0.912 0.088 0.000
#> GSM152097 4 0.2647 0.7189 0.000 0.120 0.000 0.880
#> GSM152099 2 0.5464 0.5480 0.000 0.716 0.212 0.072
#> GSM152106 4 0.1792 0.7678 0.000 0.068 0.000 0.932
#> GSM152107 3 0.4252 0.6474 0.000 0.252 0.744 0.004
#> GSM152109 3 0.4164 0.6432 0.000 0.264 0.736 0.000
#> GSM152111 1 0.3539 0.7107 0.820 0.000 0.004 0.176
#> GSM152112 3 0.6171 0.6020 0.004 0.232 0.668 0.096
#> GSM152113 1 0.7221 0.3423 0.436 0.140 0.424 0.000
#> GSM152115 3 0.4262 0.6549 0.008 0.236 0.756 0.000
#> GSM152030 3 0.5550 0.1862 0.000 0.020 0.552 0.428
#> GSM152038 3 0.4633 0.4449 0.172 0.048 0.780 0.000
#> GSM152042 3 0.5747 0.6232 0.000 0.196 0.704 0.100
#> GSM152062 3 0.1059 0.6089 0.012 0.016 0.972 0.000
#> GSM152077 1 0.6483 0.6153 0.584 0.092 0.324 0.000
#> GSM152088 2 0.2830 0.7823 0.000 0.900 0.040 0.060
#> GSM152100 4 0.0000 0.8148 0.000 0.000 0.000 1.000
#> GSM152102 2 0.1985 0.7600 0.004 0.940 0.040 0.016
#> GSM152104 4 0.4008 0.5214 0.000 0.244 0.000 0.756
#> GSM152028 1 0.5757 0.7198 0.684 0.076 0.240 0.000
#> GSM152029 1 0.3621 0.7262 0.860 0.072 0.068 0.000
#> GSM152049 1 0.2081 0.7904 0.916 0.000 0.084 0.000
#> GSM152053 3 0.3856 0.6623 0.000 0.136 0.832 0.032
#> GSM152059 1 0.0188 0.7830 0.996 0.004 0.000 0.000
#> GSM152085 1 0.1109 0.7749 0.968 0.004 0.000 0.028
#> GSM152101 3 0.4252 0.6486 0.004 0.252 0.744 0.000
#> GSM152105 1 0.5344 0.6986 0.668 0.032 0.300 0.000
#> GSM152034 1 0.4401 0.4987 0.724 0.004 0.000 0.272
#> GSM152036 4 0.0000 0.8148 0.000 0.000 0.000 1.000
#> GSM152040 1 0.0844 0.7788 0.980 0.004 0.004 0.012
#> GSM152043 1 0.0336 0.7844 0.992 0.000 0.008 0.000
#> GSM152046 1 0.5119 0.1912 0.556 0.004 0.000 0.440
#> GSM152047 1 0.3289 0.6835 0.852 0.004 0.004 0.140
#> GSM152048 1 0.5343 0.7335 0.708 0.052 0.240 0.000
#> GSM152050 1 0.3545 0.7197 0.828 0.000 0.008 0.164
#> GSM152052 1 0.6167 0.6934 0.648 0.096 0.256 0.000
#> GSM152056 1 0.4867 0.7468 0.736 0.032 0.232 0.000
#> GSM152060 1 0.5147 0.1404 0.536 0.004 0.000 0.460
#> GSM152065 1 0.5727 0.7266 0.692 0.080 0.228 0.000
#> GSM152066 1 0.4468 0.7531 0.752 0.016 0.232 0.000
#> GSM152069 3 0.6219 0.5331 0.068 0.344 0.588 0.000
#> GSM152070 1 0.0376 0.7822 0.992 0.004 0.004 0.000
#> GSM152071 3 0.6439 0.5750 0.180 0.172 0.648 0.000
#> GSM152072 1 0.3266 0.7236 0.868 0.024 0.108 0.000
#> GSM152073 1 0.0000 0.7837 1.000 0.000 0.000 0.000
#> GSM152078 1 0.4171 0.7761 0.828 0.084 0.088 0.000
#> GSM152082 1 0.0524 0.7852 0.988 0.004 0.008 0.000
#> GSM152086 1 0.1389 0.7902 0.952 0.000 0.048 0.000
#> GSM152090 1 0.7325 0.1649 0.528 0.208 0.264 0.000
#> GSM152092 1 0.3324 0.7846 0.852 0.012 0.136 0.000
#> GSM152093 1 0.4212 0.7640 0.772 0.000 0.216 0.012
#> GSM152094 1 0.0188 0.7830 0.996 0.004 0.000 0.000
#> GSM152098 1 0.0376 0.7822 0.992 0.004 0.004 0.000
#> GSM152110 1 0.5340 0.7539 0.736 0.016 0.212 0.036
#> GSM152031 1 0.3831 0.7669 0.792 0.004 0.204 0.000
#> GSM152037 1 0.4567 0.7479 0.740 0.016 0.244 0.000
#> GSM152055 4 0.5325 -0.0785 0.468 0.004 0.004 0.524
#> GSM152061 4 0.5151 -0.0190 0.464 0.004 0.000 0.532
#> GSM152064 1 0.4948 0.2781 0.560 0.000 0.000 0.440
#> GSM152087 1 0.0188 0.7830 0.996 0.004 0.000 0.000
#> GSM152103 1 0.4467 0.6964 0.788 0.040 0.172 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM152032 3 0.1124 0.8420 0.036 0.004 0.960 0.000 0.000
#> GSM152033 1 0.0865 0.8753 0.972 0.000 0.024 0.000 0.004
#> GSM152063 2 0.0510 0.8501 0.000 0.984 0.000 0.016 0.000
#> GSM152074 3 0.2011 0.8267 0.088 0.004 0.908 0.000 0.000
#> GSM152080 2 0.0162 0.8507 0.004 0.996 0.000 0.000 0.000
#> GSM152081 4 0.4213 0.4411 0.000 0.000 0.308 0.680 0.012
#> GSM152083 2 0.4538 0.3960 0.016 0.620 0.364 0.000 0.000
#> GSM152091 2 0.0324 0.8515 0.000 0.992 0.004 0.004 0.000
#> GSM152108 1 0.1756 0.8553 0.940 0.036 0.008 0.016 0.000
#> GSM152114 1 0.0854 0.8834 0.976 0.000 0.008 0.012 0.004
#> GSM152035 2 0.1518 0.8423 0.016 0.952 0.020 0.012 0.000
#> GSM152039 4 0.0404 0.7801 0.000 0.000 0.000 0.988 0.012
#> GSM152041 4 0.0510 0.7803 0.000 0.000 0.000 0.984 0.016
#> GSM152044 2 0.2020 0.7939 0.000 0.900 0.000 0.100 0.000
#> GSM152045 5 0.1662 0.8152 0.004 0.004 0.056 0.000 0.936
#> GSM152051 2 0.0290 0.8515 0.000 0.992 0.000 0.008 0.000
#> GSM152054 2 0.8741 0.0431 0.324 0.324 0.044 0.080 0.228
#> GSM152057 2 0.1743 0.8364 0.028 0.940 0.004 0.028 0.000
#> GSM152058 1 0.0794 0.8962 0.972 0.000 0.000 0.000 0.028
#> GSM152067 3 0.2450 0.8293 0.000 0.028 0.896 0.000 0.076
#> GSM152068 2 0.0404 0.8511 0.000 0.988 0.000 0.012 0.000
#> GSM152075 4 0.0451 0.7778 0.008 0.000 0.004 0.988 0.000
#> GSM152076 4 0.0324 0.7788 0.000 0.000 0.004 0.992 0.004
#> GSM152079 2 0.0290 0.8515 0.000 0.992 0.000 0.008 0.000
#> GSM152084 3 0.2233 0.8147 0.104 0.000 0.892 0.000 0.004
#> GSM152089 4 0.5205 0.4901 0.000 0.012 0.036 0.616 0.336
#> GSM152095 4 0.0613 0.7784 0.000 0.004 0.008 0.984 0.004
#> GSM152096 2 0.4066 0.5285 0.324 0.672 0.004 0.000 0.000
#> GSM152097 4 0.2966 0.6426 0.000 0.184 0.000 0.816 0.000
#> GSM152099 2 0.3861 0.5958 0.000 0.728 0.264 0.008 0.000
#> GSM152106 4 0.1410 0.7503 0.000 0.060 0.000 0.940 0.000
#> GSM152107 3 0.0771 0.8428 0.000 0.020 0.976 0.000 0.004
#> GSM152109 3 0.1195 0.8411 0.000 0.028 0.960 0.000 0.012
#> GSM152111 5 0.4221 0.7859 0.112 0.000 0.000 0.108 0.780
#> GSM152112 3 0.2200 0.8293 0.008 0.004 0.924 0.032 0.032
#> GSM152113 1 0.0693 0.8814 0.980 0.000 0.012 0.000 0.008
#> GSM152115 3 0.1278 0.8431 0.016 0.004 0.960 0.000 0.020
#> GSM152030 3 0.4728 0.5208 0.040 0.000 0.664 0.296 0.000
#> GSM152038 1 0.3074 0.7051 0.804 0.000 0.196 0.000 0.000
#> GSM152042 3 0.1568 0.8364 0.000 0.020 0.944 0.036 0.000
#> GSM152062 3 0.4276 0.3916 0.380 0.000 0.616 0.000 0.004
#> GSM152077 1 0.0290 0.8858 0.992 0.000 0.008 0.000 0.000
#> GSM152088 2 0.0162 0.8513 0.000 0.996 0.000 0.004 0.000
#> GSM152100 4 0.0740 0.7772 0.008 0.004 0.008 0.980 0.000
#> GSM152102 2 0.1646 0.8287 0.004 0.944 0.032 0.000 0.020
#> GSM152104 4 0.4304 -0.0202 0.000 0.484 0.000 0.516 0.000
#> GSM152028 1 0.1197 0.8994 0.952 0.000 0.000 0.000 0.048
#> GSM152029 5 0.1690 0.8472 0.024 0.024 0.008 0.000 0.944
#> GSM152049 5 0.3885 0.6878 0.268 0.000 0.000 0.008 0.724
#> GSM152053 3 0.1728 0.8415 0.036 0.004 0.940 0.020 0.000
#> GSM152059 5 0.1270 0.8530 0.052 0.000 0.000 0.000 0.948
#> GSM152085 5 0.2171 0.8496 0.064 0.000 0.000 0.024 0.912
#> GSM152101 3 0.1285 0.8373 0.004 0.004 0.956 0.000 0.036
#> GSM152105 1 0.0671 0.8939 0.980 0.000 0.004 0.000 0.016
#> GSM152034 5 0.1768 0.8269 0.004 0.000 0.000 0.072 0.924
#> GSM152036 4 0.0510 0.7798 0.000 0.000 0.000 0.984 0.016
#> GSM152040 5 0.1900 0.8355 0.024 0.004 0.032 0.004 0.936
#> GSM152043 5 0.1544 0.8525 0.068 0.000 0.000 0.000 0.932
#> GSM152046 5 0.3280 0.7328 0.012 0.000 0.000 0.176 0.812
#> GSM152047 5 0.0960 0.8388 0.004 0.000 0.016 0.008 0.972
#> GSM152048 1 0.1197 0.8994 0.952 0.000 0.000 0.000 0.048
#> GSM152050 5 0.4364 0.7632 0.088 0.000 0.000 0.148 0.764
#> GSM152052 1 0.1341 0.8984 0.944 0.000 0.000 0.000 0.056
#> GSM152056 1 0.2233 0.8754 0.892 0.000 0.000 0.004 0.104
#> GSM152060 5 0.4384 0.4730 0.016 0.000 0.000 0.324 0.660
#> GSM152065 1 0.3193 0.8442 0.852 0.004 0.032 0.000 0.112
#> GSM152066 1 0.2516 0.8482 0.860 0.000 0.000 0.000 0.140
#> GSM152069 3 0.4965 0.5347 0.000 0.052 0.644 0.000 0.304
#> GSM152070 5 0.1547 0.8362 0.016 0.004 0.032 0.000 0.948
#> GSM152071 3 0.4518 0.5177 0.004 0.016 0.660 0.000 0.320
#> GSM152072 5 0.1983 0.8172 0.008 0.008 0.060 0.000 0.924
#> GSM152073 5 0.1544 0.8520 0.068 0.000 0.000 0.000 0.932
#> GSM152078 5 0.4517 0.4635 0.372 0.008 0.004 0.000 0.616
#> GSM152082 5 0.2470 0.8422 0.104 0.000 0.012 0.000 0.884
#> GSM152086 5 0.3455 0.7641 0.208 0.000 0.000 0.008 0.784
#> GSM152090 5 0.6269 0.5183 0.124 0.024 0.260 0.000 0.592
#> GSM152092 1 0.3551 0.7495 0.772 0.000 0.008 0.000 0.220
#> GSM152093 1 0.2873 0.8450 0.856 0.000 0.000 0.016 0.128
#> GSM152094 5 0.1121 0.8525 0.044 0.000 0.000 0.000 0.956
#> GSM152098 5 0.0486 0.8422 0.004 0.004 0.004 0.000 0.988
#> GSM152110 1 0.3016 0.8486 0.848 0.000 0.000 0.020 0.132
#> GSM152031 1 0.3774 0.5961 0.704 0.000 0.000 0.000 0.296
#> GSM152037 1 0.1410 0.8972 0.940 0.000 0.000 0.000 0.060
#> GSM152055 4 0.3910 0.6187 0.032 0.000 0.000 0.772 0.196
#> GSM152061 4 0.4658 0.2669 0.016 0.000 0.000 0.576 0.408
#> GSM152064 4 0.4803 -0.0430 0.012 0.004 0.000 0.496 0.488
#> GSM152087 5 0.1430 0.8529 0.052 0.000 0.000 0.004 0.944
#> GSM152103 5 0.5087 0.6539 0.264 0.008 0.056 0.000 0.672
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM152032 3 0.0508 0.8356 0.012 0.000 0.984 0.000 0.004 0.000
#> GSM152033 1 0.1152 0.8293 0.952 0.004 0.000 0.000 0.044 0.000
#> GSM152063 2 0.0146 0.8781 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM152074 3 0.2060 0.7863 0.084 0.000 0.900 0.000 0.016 0.000
#> GSM152080 2 0.0000 0.8777 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152081 4 0.4110 0.4915 0.004 0.000 0.296 0.680 0.008 0.012
#> GSM152083 2 0.3296 0.7257 0.008 0.792 0.188 0.000 0.012 0.000
#> GSM152091 2 0.0000 0.8777 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152108 1 0.1682 0.8183 0.928 0.052 0.000 0.000 0.020 0.000
#> GSM152114 1 0.1628 0.8449 0.940 0.000 0.004 0.008 0.036 0.012
#> GSM152035 2 0.1666 0.8614 0.008 0.936 0.000 0.020 0.036 0.000
#> GSM152039 4 0.1267 0.7933 0.000 0.000 0.000 0.940 0.060 0.000
#> GSM152041 4 0.2933 0.7511 0.004 0.000 0.000 0.796 0.200 0.000
#> GSM152044 2 0.1010 0.8696 0.000 0.960 0.000 0.036 0.004 0.000
#> GSM152045 5 0.1340 0.6834 0.000 0.000 0.008 0.004 0.948 0.040
#> GSM152051 2 0.0146 0.8780 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM152054 5 0.2239 0.6717 0.072 0.000 0.000 0.020 0.900 0.008
#> GSM152057 2 0.1296 0.8671 0.000 0.948 0.004 0.044 0.004 0.000
#> GSM152058 1 0.0790 0.8494 0.968 0.000 0.000 0.000 0.000 0.032
#> GSM152067 3 0.2915 0.7779 0.000 0.000 0.808 0.000 0.184 0.008
#> GSM152068 2 0.0405 0.8775 0.000 0.988 0.000 0.008 0.004 0.000
#> GSM152075 4 0.2595 0.7704 0.004 0.000 0.000 0.836 0.160 0.000
#> GSM152076 4 0.1267 0.7933 0.000 0.000 0.000 0.940 0.060 0.000
#> GSM152079 2 0.0260 0.8779 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM152084 3 0.4606 0.7045 0.112 0.000 0.712 0.000 0.168 0.008
#> GSM152089 5 0.1477 0.6749 0.000 0.000 0.004 0.048 0.940 0.008
#> GSM152095 4 0.1814 0.7896 0.000 0.000 0.000 0.900 0.100 0.000
#> GSM152096 2 0.2362 0.7778 0.136 0.860 0.000 0.000 0.004 0.000
#> GSM152097 4 0.1908 0.7304 0.000 0.096 0.000 0.900 0.004 0.000
#> GSM152099 2 0.3448 0.6062 0.000 0.716 0.280 0.004 0.000 0.000
#> GSM152106 4 0.0603 0.7744 0.000 0.016 0.000 0.980 0.004 0.000
#> GSM152107 3 0.2703 0.7842 0.000 0.000 0.824 0.004 0.172 0.000
#> GSM152109 3 0.2454 0.8136 0.000 0.004 0.876 0.000 0.104 0.016
#> GSM152111 6 0.2507 0.8087 0.016 0.000 0.000 0.056 0.036 0.892
#> GSM152112 5 0.2511 0.6538 0.000 0.000 0.056 0.064 0.880 0.000
#> GSM152113 1 0.1908 0.8032 0.900 0.004 0.000 0.000 0.096 0.000
#> GSM152115 5 0.3103 0.5720 0.008 0.000 0.208 0.000 0.784 0.000
#> GSM152030 3 0.3779 0.5367 0.008 0.000 0.708 0.276 0.008 0.000
#> GSM152038 1 0.2404 0.8054 0.884 0.000 0.080 0.000 0.036 0.000
#> GSM152042 3 0.0520 0.8359 0.000 0.000 0.984 0.008 0.008 0.000
#> GSM152062 1 0.5400 0.1198 0.504 0.000 0.376 0.000 0.120 0.000
#> GSM152077 1 0.0520 0.8431 0.984 0.000 0.000 0.000 0.008 0.008
#> GSM152088 2 0.0000 0.8777 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152100 4 0.3330 0.6709 0.000 0.000 0.000 0.716 0.284 0.000
#> GSM152102 2 0.4080 0.1544 0.008 0.536 0.000 0.000 0.456 0.000
#> GSM152104 2 0.3807 0.4842 0.000 0.628 0.000 0.368 0.004 0.000
#> GSM152028 1 0.0622 0.8443 0.980 0.000 0.000 0.000 0.008 0.012
#> GSM152029 6 0.2122 0.8039 0.000 0.008 0.008 0.000 0.084 0.900
#> GSM152049 6 0.2668 0.7341 0.168 0.000 0.000 0.004 0.000 0.828
#> GSM152053 3 0.0779 0.8298 0.008 0.000 0.976 0.008 0.008 0.000
#> GSM152059 6 0.0291 0.8300 0.004 0.000 0.000 0.000 0.004 0.992
#> GSM152085 6 0.0806 0.8290 0.008 0.000 0.000 0.020 0.000 0.972
#> GSM152101 5 0.3482 0.3670 0.000 0.000 0.316 0.000 0.684 0.000
#> GSM152105 1 0.1845 0.8465 0.916 0.000 0.004 0.000 0.008 0.072
#> GSM152034 6 0.1426 0.8314 0.000 0.000 0.008 0.016 0.028 0.948
#> GSM152036 4 0.0146 0.7818 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM152040 5 0.2742 0.6685 0.012 0.000 0.000 0.008 0.852 0.128
#> GSM152043 6 0.1643 0.8245 0.008 0.000 0.000 0.000 0.068 0.924
#> GSM152046 6 0.3658 0.6187 0.000 0.000 0.000 0.216 0.032 0.752
#> GSM152047 6 0.2048 0.7770 0.000 0.000 0.000 0.000 0.120 0.880
#> GSM152048 1 0.1398 0.8502 0.940 0.000 0.000 0.000 0.008 0.052
#> GSM152050 6 0.2446 0.7781 0.012 0.000 0.000 0.124 0.000 0.864
#> GSM152052 1 0.2340 0.8005 0.852 0.000 0.000 0.000 0.000 0.148
#> GSM152056 1 0.2118 0.8321 0.888 0.000 0.000 0.008 0.000 0.104
#> GSM152060 4 0.5114 0.1963 0.000 0.000 0.000 0.468 0.080 0.452
#> GSM152065 5 0.4097 -0.0234 0.492 0.000 0.000 0.000 0.500 0.008
#> GSM152066 1 0.2744 0.8018 0.840 0.000 0.000 0.000 0.016 0.144
#> GSM152069 6 0.5758 0.2274 0.000 0.012 0.348 0.000 0.132 0.508
#> GSM152070 5 0.3864 0.1075 0.000 0.000 0.000 0.000 0.520 0.480
#> GSM152071 6 0.5541 0.3379 0.000 0.004 0.304 0.000 0.144 0.548
#> GSM152072 5 0.3850 0.4088 0.000 0.004 0.004 0.000 0.652 0.340
#> GSM152073 6 0.0405 0.8299 0.004 0.000 0.000 0.000 0.008 0.988
#> GSM152078 6 0.2805 0.7079 0.184 0.000 0.000 0.000 0.004 0.812
#> GSM152082 6 0.4007 0.6228 0.052 0.000 0.000 0.000 0.220 0.728
#> GSM152086 6 0.1501 0.8112 0.076 0.000 0.000 0.000 0.000 0.924
#> GSM152090 6 0.3190 0.7916 0.016 0.012 0.052 0.000 0.060 0.860
#> GSM152092 1 0.4716 0.6063 0.668 0.000 0.000 0.000 0.224 0.108
#> GSM152093 1 0.3956 0.7810 0.792 0.000 0.000 0.024 0.072 0.112
#> GSM152094 6 0.0692 0.8314 0.004 0.000 0.000 0.000 0.020 0.976
#> GSM152098 6 0.1765 0.8089 0.000 0.000 0.000 0.000 0.096 0.904
#> GSM152110 1 0.2594 0.8416 0.888 0.000 0.000 0.036 0.020 0.056
#> GSM152031 1 0.3996 0.1325 0.512 0.000 0.000 0.000 0.004 0.484
#> GSM152037 1 0.1196 0.8504 0.952 0.000 0.000 0.000 0.008 0.040
#> GSM152055 4 0.3462 0.7560 0.004 0.000 0.000 0.816 0.080 0.100
#> GSM152061 4 0.4621 0.5741 0.000 0.000 0.000 0.632 0.064 0.304
#> GSM152064 4 0.4503 0.6543 0.000 0.000 0.000 0.696 0.100 0.204
#> GSM152087 6 0.0603 0.8310 0.004 0.000 0.000 0.000 0.016 0.980
#> GSM152103 6 0.3330 0.7623 0.116 0.000 0.012 0.000 0.044 0.828
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 specimen(p) k
#> SD:NMF 87 3.20e-08 2
#> SD:NMF 65 2.79e-05 3
#> SD:NMF 72 3.90e-05 4
#> SD:NMF 78 1.02e-03 5
#> SD:NMF 76 8.28e-05 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "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 10612 rows and 88 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.308 0.763 0.865 0.335 0.671 0.671
#> 3 3 0.240 0.455 0.721 0.719 0.737 0.616
#> 4 4 0.342 0.355 0.683 0.122 0.880 0.738
#> 5 5 0.440 0.323 0.640 0.143 0.843 0.629
#> 6 6 0.502 0.411 0.670 0.045 0.874 0.642
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
#> GSM152032 1 0.242 0.8514 0.960 0.040
#> GSM152033 1 0.163 0.8561 0.976 0.024
#> GSM152063 2 0.795 0.7574 0.240 0.760
#> GSM152074 1 0.260 0.8465 0.956 0.044
#> GSM152080 1 0.653 0.7724 0.832 0.168
#> GSM152081 1 0.975 0.2449 0.592 0.408
#> GSM152083 1 0.469 0.8015 0.900 0.100
#> GSM152091 1 0.653 0.7724 0.832 0.168
#> GSM152108 1 0.278 0.8602 0.952 0.048
#> GSM152114 1 0.671 0.7873 0.824 0.176
#> GSM152035 1 0.184 0.8637 0.972 0.028
#> GSM152039 2 0.430 0.7382 0.088 0.912
#> GSM152041 2 0.999 0.1756 0.484 0.516
#> GSM152044 2 0.802 0.7570 0.244 0.756
#> GSM152045 1 0.141 0.8586 0.980 0.020
#> GSM152051 2 0.802 0.7570 0.244 0.756
#> GSM152054 1 0.141 0.8574 0.980 0.020
#> GSM152057 2 0.802 0.7570 0.244 0.756
#> GSM152058 1 0.634 0.8122 0.840 0.160
#> GSM152067 1 0.204 0.8581 0.968 0.032
#> GSM152068 2 0.802 0.7570 0.244 0.756
#> GSM152075 2 0.991 0.3128 0.444 0.556
#> GSM152076 2 0.430 0.7382 0.088 0.912
#> GSM152079 2 0.802 0.7570 0.244 0.756
#> GSM152084 1 0.541 0.8348 0.876 0.124
#> GSM152089 1 0.913 0.5324 0.672 0.328
#> GSM152095 2 0.443 0.7397 0.092 0.908
#> GSM152096 1 0.689 0.7760 0.816 0.184
#> GSM152097 2 0.563 0.7529 0.132 0.868
#> GSM152099 2 0.802 0.7570 0.244 0.756
#> GSM152106 2 0.141 0.7155 0.020 0.980
#> GSM152107 1 0.518 0.8288 0.884 0.116
#> GSM152109 1 0.204 0.8559 0.968 0.032
#> GSM152111 1 0.584 0.8319 0.860 0.140
#> GSM152112 1 0.584 0.7991 0.860 0.140
#> GSM152113 1 0.204 0.8666 0.968 0.032
#> GSM152115 1 0.184 0.8605 0.972 0.028
#> GSM152030 1 0.978 0.1943 0.588 0.412
#> GSM152038 1 0.141 0.8638 0.980 0.020
#> GSM152042 1 0.990 0.0789 0.560 0.440
#> GSM152062 1 0.506 0.8431 0.888 0.112
#> GSM152077 1 0.295 0.8593 0.948 0.052
#> GSM152088 2 0.996 0.3302 0.464 0.536
#> GSM152100 2 0.988 0.3272 0.436 0.564
#> GSM152102 1 0.184 0.8637 0.972 0.028
#> GSM152104 2 0.163 0.7185 0.024 0.976
#> GSM152028 1 0.141 0.8629 0.980 0.020
#> GSM152029 1 0.278 0.8651 0.952 0.048
#> GSM152049 1 0.644 0.8054 0.836 0.164
#> GSM152053 1 0.988 0.1341 0.564 0.436
#> GSM152059 1 0.295 0.8643 0.948 0.052
#> GSM152085 1 0.653 0.8038 0.832 0.168
#> GSM152101 1 0.184 0.8605 0.972 0.028
#> GSM152105 1 0.204 0.8656 0.968 0.032
#> GSM152034 1 0.730 0.7687 0.796 0.204
#> GSM152036 2 0.443 0.7382 0.092 0.908
#> GSM152040 1 0.141 0.8586 0.980 0.020
#> GSM152043 1 0.118 0.8593 0.984 0.016
#> GSM152046 1 0.730 0.7687 0.796 0.204
#> GSM152047 1 0.141 0.8608 0.980 0.020
#> GSM152048 1 0.634 0.8122 0.840 0.160
#> GSM152050 1 0.563 0.8345 0.868 0.132
#> GSM152052 1 0.242 0.8663 0.960 0.040
#> GSM152056 1 0.634 0.8122 0.840 0.160
#> GSM152060 1 0.730 0.7687 0.796 0.204
#> GSM152065 1 0.141 0.8562 0.980 0.020
#> GSM152066 1 0.574 0.8309 0.864 0.136
#> GSM152069 1 0.204 0.8559 0.968 0.032
#> GSM152070 1 0.118 0.8593 0.984 0.016
#> GSM152071 1 0.204 0.8559 0.968 0.032
#> GSM152072 1 0.141 0.8586 0.980 0.020
#> GSM152073 1 0.518 0.8476 0.884 0.116
#> GSM152078 1 0.242 0.8663 0.960 0.040
#> GSM152082 1 0.118 0.8593 0.984 0.016
#> GSM152086 1 0.584 0.8319 0.860 0.140
#> GSM152090 1 0.402 0.8611 0.920 0.080
#> GSM152092 1 0.118 0.8593 0.984 0.016
#> GSM152093 1 0.469 0.8550 0.900 0.100
#> GSM152094 1 0.541 0.8421 0.876 0.124
#> GSM152098 1 0.118 0.8593 0.984 0.016
#> GSM152110 1 0.634 0.8122 0.840 0.160
#> GSM152031 1 0.204 0.8656 0.968 0.032
#> GSM152037 1 0.574 0.8309 0.864 0.136
#> GSM152055 1 0.730 0.7687 0.796 0.204
#> GSM152061 1 0.730 0.7687 0.796 0.204
#> GSM152064 1 0.722 0.7743 0.800 0.200
#> GSM152087 1 0.506 0.8460 0.888 0.112
#> GSM152103 1 0.388 0.8615 0.924 0.076
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM152032 3 0.3851 0.6483 0.136 0.004 0.860
#> GSM152033 3 0.6045 0.3817 0.380 0.000 0.620
#> GSM152063 2 0.5201 0.7205 0.004 0.760 0.236
#> GSM152074 3 0.3340 0.6427 0.120 0.000 0.880
#> GSM152080 3 0.4634 0.4133 0.012 0.164 0.824
#> GSM152081 1 0.9912 -0.0471 0.396 0.284 0.320
#> GSM152083 3 0.4745 0.5967 0.080 0.068 0.852
#> GSM152091 3 0.4634 0.4133 0.012 0.164 0.824
#> GSM152108 3 0.6659 0.5409 0.304 0.028 0.668
#> GSM152114 3 0.8793 0.1336 0.436 0.112 0.452
#> GSM152035 3 0.7184 0.1575 0.472 0.024 0.504
#> GSM152039 2 0.5276 0.6648 0.128 0.820 0.052
#> GSM152041 1 0.8328 0.1059 0.520 0.396 0.084
#> GSM152044 2 0.5244 0.7201 0.004 0.756 0.240
#> GSM152045 1 0.5810 0.3724 0.664 0.000 0.336
#> GSM152051 2 0.5244 0.7201 0.004 0.756 0.240
#> GSM152054 1 0.6079 0.2718 0.612 0.000 0.388
#> GSM152057 2 0.5244 0.7201 0.004 0.756 0.240
#> GSM152058 1 0.3947 0.6140 0.884 0.040 0.076
#> GSM152067 3 0.5588 0.5580 0.276 0.004 0.720
#> GSM152068 2 0.5244 0.7201 0.004 0.756 0.240
#> GSM152075 2 0.9111 0.0585 0.424 0.436 0.140
#> GSM152076 2 0.5276 0.6648 0.128 0.820 0.052
#> GSM152079 2 0.5420 0.7182 0.008 0.752 0.240
#> GSM152084 3 0.8000 0.2971 0.408 0.064 0.528
#> GSM152089 1 0.7676 0.4416 0.672 0.216 0.112
#> GSM152095 2 0.5343 0.6634 0.132 0.816 0.052
#> GSM152096 3 0.8712 0.4703 0.312 0.132 0.556
#> GSM152097 2 0.3412 0.7198 0.000 0.876 0.124
#> GSM152099 2 0.5244 0.7201 0.004 0.756 0.240
#> GSM152106 2 0.0237 0.6965 0.000 0.996 0.004
#> GSM152107 1 0.8211 0.0596 0.520 0.076 0.404
#> GSM152109 3 0.3918 0.6477 0.140 0.004 0.856
#> GSM152111 1 0.3832 0.6239 0.888 0.036 0.076
#> GSM152112 1 0.8604 0.1792 0.540 0.112 0.348
#> GSM152113 1 0.6819 -0.0621 0.512 0.012 0.476
#> GSM152115 1 0.6483 0.0791 0.544 0.004 0.452
#> GSM152030 1 0.9901 -0.0386 0.404 0.300 0.296
#> GSM152038 1 0.6274 0.0746 0.544 0.000 0.456
#> GSM152042 1 0.9926 -0.0334 0.388 0.328 0.284
#> GSM152062 3 0.7868 0.2773 0.420 0.056 0.524
#> GSM152077 3 0.6659 0.5392 0.304 0.028 0.668
#> GSM152088 2 0.6495 0.4212 0.004 0.536 0.460
#> GSM152100 2 0.9068 0.0639 0.420 0.444 0.136
#> GSM152102 3 0.7184 0.1575 0.472 0.024 0.504
#> GSM152104 2 0.0424 0.6985 0.000 0.992 0.008
#> GSM152028 1 0.6168 0.1944 0.588 0.000 0.412
#> GSM152029 1 0.5517 0.5339 0.728 0.004 0.268
#> GSM152049 1 0.2806 0.6156 0.928 0.040 0.032
#> GSM152053 1 0.9948 -0.0491 0.384 0.312 0.304
#> GSM152059 1 0.4293 0.5924 0.832 0.004 0.164
#> GSM152085 1 0.2681 0.6150 0.932 0.040 0.028
#> GSM152101 1 0.6483 0.0791 0.544 0.004 0.452
#> GSM152105 1 0.5678 0.4367 0.684 0.000 0.316
#> GSM152034 1 0.3589 0.5852 0.900 0.048 0.052
#> GSM152036 2 0.5343 0.6631 0.132 0.816 0.052
#> GSM152040 1 0.4931 0.5213 0.768 0.000 0.232
#> GSM152043 1 0.4235 0.5643 0.824 0.000 0.176
#> GSM152046 1 0.3484 0.5876 0.904 0.048 0.048
#> GSM152047 1 0.4291 0.5605 0.820 0.000 0.180
#> GSM152048 1 0.3947 0.6140 0.884 0.040 0.076
#> GSM152050 1 0.4092 0.6241 0.876 0.036 0.088
#> GSM152052 1 0.6260 0.1750 0.552 0.000 0.448
#> GSM152056 1 0.3947 0.6140 0.884 0.040 0.076
#> GSM152060 1 0.3589 0.5852 0.900 0.048 0.052
#> GSM152065 1 0.6291 0.0673 0.532 0.000 0.468
#> GSM152066 1 0.4094 0.6129 0.872 0.028 0.100
#> GSM152069 3 0.3851 0.6485 0.136 0.004 0.860
#> GSM152070 1 0.4399 0.5532 0.812 0.000 0.188
#> GSM152071 3 0.3851 0.6485 0.136 0.004 0.860
#> GSM152072 1 0.5810 0.3733 0.664 0.000 0.336
#> GSM152073 1 0.3587 0.6214 0.892 0.020 0.088
#> GSM152078 1 0.6252 0.1779 0.556 0.000 0.444
#> GSM152082 1 0.4291 0.5613 0.820 0.000 0.180
#> GSM152086 1 0.3832 0.6239 0.888 0.036 0.076
#> GSM152090 1 0.6717 0.3461 0.628 0.020 0.352
#> GSM152092 1 0.4750 0.5479 0.784 0.000 0.216
#> GSM152093 1 0.7262 0.3410 0.624 0.044 0.332
#> GSM152094 1 0.3805 0.6221 0.884 0.024 0.092
#> GSM152098 1 0.4291 0.5613 0.820 0.000 0.180
#> GSM152110 1 0.3856 0.6144 0.888 0.040 0.072
#> GSM152031 1 0.5678 0.4367 0.684 0.000 0.316
#> GSM152037 1 0.4172 0.6114 0.868 0.028 0.104
#> GSM152055 1 0.3589 0.5852 0.900 0.048 0.052
#> GSM152061 1 0.3589 0.5852 0.900 0.048 0.052
#> GSM152064 1 0.3998 0.5954 0.884 0.060 0.056
#> GSM152087 1 0.3502 0.6222 0.896 0.020 0.084
#> GSM152103 1 0.6777 0.3247 0.616 0.020 0.364
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM152032 3 0.305 0.2371 0.028 0.056 0.900 0.016
#> GSM152033 3 0.475 0.4378 0.304 0.008 0.688 0.000
#> GSM152063 4 0.520 0.5018 0.004 0.360 0.008 0.628
#> GSM152074 3 0.183 0.2710 0.024 0.032 0.944 0.000
#> GSM152080 2 0.211 0.4259 0.000 0.932 0.024 0.044
#> GSM152081 1 0.807 -0.1633 0.356 0.004 0.304 0.336
#> GSM152083 3 0.474 -0.0360 0.012 0.240 0.740 0.008
#> GSM152091 2 0.211 0.4259 0.000 0.932 0.024 0.044
#> GSM152108 3 0.495 0.5042 0.232 0.004 0.736 0.028
#> GSM152114 3 0.834 0.2503 0.388 0.044 0.416 0.152
#> GSM152035 3 0.753 0.2923 0.396 0.144 0.452 0.008
#> GSM152039 4 0.194 0.4962 0.076 0.000 0.000 0.924
#> GSM152041 1 0.624 0.0693 0.504 0.004 0.044 0.448
#> GSM152044 4 0.521 0.5001 0.004 0.364 0.008 0.624
#> GSM152045 1 0.530 0.1541 0.600 0.008 0.388 0.004
#> GSM152051 4 0.521 0.5001 0.004 0.364 0.008 0.624
#> GSM152054 1 0.557 -0.0236 0.540 0.020 0.440 0.000
#> GSM152057 4 0.521 0.5001 0.004 0.364 0.008 0.624
#> GSM152058 1 0.292 0.5977 0.896 0.008 0.080 0.016
#> GSM152067 3 0.822 -0.1045 0.208 0.372 0.400 0.020
#> GSM152068 4 0.521 0.5001 0.004 0.364 0.008 0.624
#> GSM152075 4 0.699 0.0887 0.384 0.004 0.104 0.508
#> GSM152076 4 0.194 0.4962 0.076 0.000 0.000 0.924
#> GSM152079 4 0.535 0.4983 0.008 0.364 0.008 0.620
#> GSM152084 3 0.788 0.3436 0.340 0.048 0.508 0.104
#> GSM152089 1 0.618 0.3030 0.660 0.028 0.040 0.272
#> GSM152095 4 0.201 0.4957 0.080 0.000 0.000 0.920
#> GSM152096 3 0.928 0.3588 0.260 0.208 0.420 0.112
#> GSM152097 4 0.436 0.5112 0.000 0.248 0.008 0.744
#> GSM152099 4 0.521 0.5001 0.004 0.364 0.008 0.624
#> GSM152106 4 0.281 0.5115 0.000 0.132 0.000 0.868
#> GSM152107 1 0.734 -0.2061 0.444 0.016 0.440 0.100
#> GSM152109 2 0.722 0.4297 0.068 0.464 0.440 0.028
#> GSM152111 1 0.259 0.6091 0.920 0.036 0.032 0.012
#> GSM152112 1 0.755 -0.1450 0.472 0.012 0.380 0.136
#> GSM152113 3 0.678 0.1147 0.452 0.056 0.476 0.016
#> GSM152115 3 0.590 0.1890 0.452 0.012 0.520 0.016
#> GSM152030 1 0.804 -0.1684 0.368 0.004 0.288 0.340
#> GSM152038 1 0.649 -0.0445 0.496 0.060 0.440 0.004
#> GSM152042 4 0.800 -0.1225 0.352 0.004 0.264 0.380
#> GSM152062 3 0.785 0.3440 0.348 0.048 0.504 0.100
#> GSM152077 3 0.492 0.5030 0.228 0.004 0.740 0.028
#> GSM152088 2 0.505 -0.2738 0.000 0.588 0.004 0.408
#> GSM152100 4 0.686 0.0939 0.388 0.004 0.092 0.516
#> GSM152102 3 0.753 0.2923 0.396 0.144 0.452 0.008
#> GSM152104 4 0.287 0.5121 0.000 0.136 0.000 0.864
#> GSM152028 1 0.616 0.0731 0.536 0.052 0.412 0.000
#> GSM152029 1 0.571 0.4713 0.716 0.156 0.128 0.000
#> GSM152049 1 0.185 0.6085 0.948 0.008 0.024 0.020
#> GSM152053 4 0.805 -0.1308 0.344 0.004 0.292 0.360
#> GSM152059 1 0.409 0.5593 0.828 0.116 0.056 0.000
#> GSM152085 1 0.196 0.6079 0.944 0.008 0.024 0.024
#> GSM152101 3 0.591 0.1805 0.456 0.012 0.516 0.016
#> GSM152105 1 0.595 0.3852 0.656 0.076 0.268 0.000
#> GSM152034 1 0.220 0.5850 0.920 0.000 0.008 0.072
#> GSM152036 4 0.220 0.4953 0.080 0.000 0.004 0.916
#> GSM152040 1 0.448 0.4039 0.712 0.004 0.284 0.000
#> GSM152043 1 0.418 0.5025 0.784 0.016 0.200 0.000
#> GSM152046 1 0.212 0.5864 0.924 0.000 0.008 0.068
#> GSM152047 1 0.412 0.4829 0.772 0.008 0.220 0.000
#> GSM152048 1 0.292 0.5977 0.896 0.008 0.080 0.016
#> GSM152050 1 0.257 0.6096 0.916 0.028 0.052 0.004
#> GSM152052 1 0.691 0.1049 0.520 0.116 0.364 0.000
#> GSM152056 1 0.292 0.5977 0.896 0.008 0.080 0.016
#> GSM152060 1 0.220 0.5850 0.920 0.000 0.008 0.072
#> GSM152065 3 0.515 0.1656 0.460 0.004 0.536 0.000
#> GSM152066 1 0.349 0.5901 0.860 0.008 0.116 0.016
#> GSM152069 2 0.713 0.4297 0.068 0.464 0.444 0.024
#> GSM152070 1 0.419 0.4718 0.764 0.008 0.228 0.000
#> GSM152071 2 0.713 0.4297 0.068 0.464 0.444 0.024
#> GSM152072 1 0.514 0.1565 0.600 0.008 0.392 0.000
#> GSM152073 1 0.267 0.6043 0.908 0.048 0.044 0.000
#> GSM152078 1 0.687 0.1144 0.524 0.112 0.364 0.000
#> GSM152082 1 0.421 0.4978 0.780 0.016 0.204 0.000
#> GSM152086 1 0.259 0.6091 0.920 0.036 0.032 0.012
#> GSM152090 1 0.702 0.2575 0.592 0.080 0.300 0.028
#> GSM152092 1 0.473 0.4855 0.752 0.032 0.216 0.000
#> GSM152093 1 0.696 0.2503 0.612 0.060 0.284 0.044
#> GSM152094 1 0.305 0.6050 0.900 0.048 0.040 0.012
#> GSM152098 1 0.421 0.4978 0.780 0.016 0.204 0.000
#> GSM152110 1 0.285 0.5989 0.900 0.008 0.076 0.016
#> GSM152031 1 0.595 0.3852 0.656 0.076 0.268 0.000
#> GSM152037 1 0.355 0.5877 0.856 0.008 0.120 0.016
#> GSM152055 1 0.220 0.5850 0.920 0.000 0.008 0.072
#> GSM152061 1 0.220 0.5850 0.920 0.000 0.008 0.072
#> GSM152064 1 0.291 0.5850 0.900 0.004 0.032 0.064
#> GSM152087 1 0.259 0.6072 0.912 0.040 0.048 0.000
#> GSM152103 1 0.729 0.2255 0.572 0.084 0.308 0.036
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM152032 3 0.4941 0.0911 0.012 0.004 0.636 0.016 0.332
#> GSM152033 3 0.3599 0.3375 0.020 0.000 0.824 0.140 0.016
#> GSM152063 2 0.0833 0.7540 0.004 0.976 0.000 0.004 0.016
#> GSM152074 3 0.4477 0.1286 0.008 0.000 0.688 0.016 0.288
#> GSM152080 5 0.6913 0.3300 0.000 0.348 0.004 0.276 0.372
#> GSM152081 1 0.9771 -0.3851 0.312 0.184 0.152 0.172 0.180
#> GSM152083 3 0.6488 -0.0453 0.000 0.200 0.564 0.016 0.220
#> GSM152091 5 0.6913 0.3300 0.000 0.348 0.004 0.276 0.372
#> GSM152108 3 0.3759 0.3081 0.100 0.024 0.840 0.008 0.028
#> GSM152114 3 0.8851 -0.0880 0.284 0.044 0.380 0.148 0.144
#> GSM152035 3 0.7017 0.2703 0.024 0.044 0.520 0.336 0.076
#> GSM152039 2 0.5792 0.4821 0.084 0.536 0.000 0.376 0.004
#> GSM152041 1 0.8070 -0.3507 0.444 0.224 0.032 0.252 0.048
#> GSM152044 2 0.0771 0.7544 0.004 0.976 0.000 0.000 0.020
#> GSM152045 3 0.7415 0.1741 0.224 0.000 0.416 0.320 0.040
#> GSM152051 2 0.0771 0.7544 0.004 0.976 0.000 0.000 0.020
#> GSM152054 3 0.7042 0.2501 0.096 0.004 0.520 0.312 0.068
#> GSM152057 2 0.0771 0.7544 0.004 0.976 0.000 0.000 0.020
#> GSM152058 1 0.2890 0.5581 0.872 0.004 0.104 0.004 0.016
#> GSM152067 5 0.5730 0.3766 0.072 0.012 0.132 0.064 0.720
#> GSM152068 2 0.0771 0.7544 0.004 0.976 0.000 0.000 0.020
#> GSM152075 1 0.8917 -0.5522 0.316 0.252 0.080 0.296 0.056
#> GSM152076 2 0.5792 0.4821 0.084 0.536 0.000 0.376 0.004
#> GSM152079 2 0.0898 0.7519 0.008 0.972 0.000 0.000 0.020
#> GSM152084 3 0.8511 0.0413 0.240 0.020 0.408 0.120 0.212
#> GSM152089 1 0.8045 -0.3115 0.412 0.068 0.072 0.376 0.072
#> GSM152095 2 0.5829 0.4765 0.088 0.536 0.000 0.372 0.004
#> GSM152096 3 0.9275 0.0564 0.180 0.196 0.392 0.100 0.132
#> GSM152097 2 0.2068 0.7394 0.000 0.904 0.000 0.092 0.004
#> GSM152099 2 0.0771 0.7544 0.004 0.976 0.000 0.000 0.020
#> GSM152106 2 0.3612 0.6997 0.000 0.764 0.000 0.228 0.008
#> GSM152107 3 0.9036 -0.1307 0.124 0.040 0.296 0.284 0.256
#> GSM152109 5 0.3084 0.6142 0.036 0.016 0.064 0.004 0.880
#> GSM152111 1 0.2006 0.5722 0.916 0.000 0.000 0.012 0.072
#> GSM152112 4 0.8912 -0.2616 0.172 0.036 0.272 0.364 0.156
#> GSM152113 3 0.7358 0.2427 0.248 0.004 0.532 0.112 0.104
#> GSM152115 3 0.7926 0.1951 0.084 0.004 0.416 0.300 0.196
#> GSM152030 1 0.9679 -0.3736 0.308 0.204 0.216 0.156 0.116
#> GSM152038 3 0.7231 0.2080 0.304 0.000 0.500 0.096 0.100
#> GSM152042 1 0.9721 -0.4133 0.312 0.208 0.152 0.192 0.136
#> GSM152062 3 0.8281 0.0650 0.220 0.016 0.452 0.128 0.184
#> GSM152077 3 0.3641 0.3053 0.112 0.024 0.840 0.008 0.016
#> GSM152088 2 0.4772 0.4751 0.000 0.740 0.004 0.108 0.148
#> GSM152100 4 0.8913 0.1443 0.304 0.240 0.072 0.320 0.064
#> GSM152102 3 0.7017 0.2703 0.024 0.044 0.520 0.336 0.076
#> GSM152104 2 0.3582 0.7017 0.000 0.768 0.000 0.224 0.008
#> GSM152028 3 0.7069 0.1443 0.336 0.000 0.488 0.112 0.064
#> GSM152029 1 0.4995 0.4725 0.688 0.008 0.020 0.020 0.264
#> GSM152049 1 0.1200 0.5700 0.964 0.000 0.012 0.008 0.016
#> GSM152053 1 0.9792 -0.4143 0.300 0.208 0.152 0.180 0.160
#> GSM152059 1 0.3443 0.5373 0.816 0.000 0.012 0.008 0.164
#> GSM152085 1 0.1314 0.5690 0.960 0.000 0.012 0.012 0.016
#> GSM152101 3 0.7944 0.1910 0.084 0.004 0.412 0.300 0.200
#> GSM152105 1 0.6321 0.3911 0.592 0.000 0.264 0.032 0.112
#> GSM152034 1 0.1768 0.5426 0.924 0.000 0.000 0.072 0.004
#> GSM152036 2 0.5932 0.4763 0.088 0.536 0.000 0.368 0.008
#> GSM152040 1 0.7549 -0.1891 0.376 0.000 0.304 0.280 0.040
#> GSM152043 1 0.6706 0.2035 0.564 0.000 0.204 0.200 0.032
#> GSM152046 1 0.1704 0.5441 0.928 0.000 0.000 0.068 0.004
#> GSM152047 1 0.6819 0.1051 0.516 0.000 0.228 0.236 0.020
#> GSM152048 1 0.2994 0.5558 0.864 0.004 0.112 0.004 0.016
#> GSM152050 1 0.2585 0.5755 0.896 0.000 0.036 0.004 0.064
#> GSM152052 1 0.6473 0.2270 0.468 0.000 0.364 0.004 0.164
#> GSM152056 1 0.2890 0.5581 0.872 0.004 0.104 0.004 0.016
#> GSM152060 1 0.1768 0.5426 0.924 0.000 0.000 0.072 0.004
#> GSM152065 3 0.5780 0.2939 0.068 0.000 0.616 0.292 0.024
#> GSM152066 1 0.3666 0.5508 0.828 0.004 0.132 0.020 0.016
#> GSM152069 5 0.2971 0.6162 0.032 0.016 0.072 0.000 0.880
#> GSM152070 1 0.6858 0.0867 0.508 0.000 0.236 0.236 0.020
#> GSM152071 5 0.2971 0.6162 0.032 0.016 0.072 0.000 0.880
#> GSM152072 3 0.7425 0.1905 0.216 0.000 0.428 0.312 0.044
#> GSM152073 1 0.2362 0.5700 0.900 0.000 0.008 0.008 0.084
#> GSM152078 1 0.6447 0.2319 0.472 0.000 0.364 0.004 0.160
#> GSM152082 1 0.6756 0.1887 0.556 0.000 0.204 0.208 0.032
#> GSM152086 1 0.2006 0.5722 0.916 0.000 0.000 0.012 0.072
#> GSM152090 1 0.6998 0.3621 0.556 0.004 0.212 0.044 0.184
#> GSM152092 1 0.6963 0.1784 0.540 0.000 0.232 0.184 0.044
#> GSM152093 1 0.7120 0.2995 0.540 0.008 0.280 0.068 0.104
#> GSM152094 1 0.2305 0.5707 0.896 0.000 0.000 0.012 0.092
#> GSM152098 1 0.6756 0.1887 0.556 0.000 0.204 0.208 0.032
#> GSM152110 1 0.2837 0.5590 0.876 0.004 0.100 0.004 0.016
#> GSM152031 1 0.6321 0.3911 0.592 0.000 0.264 0.032 0.112
#> GSM152037 1 0.3711 0.5488 0.824 0.004 0.136 0.020 0.016
#> GSM152055 1 0.1768 0.5426 0.924 0.000 0.000 0.072 0.004
#> GSM152061 1 0.1768 0.5426 0.924 0.000 0.000 0.072 0.004
#> GSM152064 1 0.2744 0.5288 0.896 0.008 0.004 0.052 0.040
#> GSM152087 1 0.2017 0.5734 0.912 0.000 0.008 0.000 0.080
#> GSM152103 1 0.7067 0.3509 0.544 0.004 0.184 0.044 0.224
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM152032 1 0.4576 -0.03698 0.616 0.000 0.344 0.004 0.032 0.004
#> GSM152033 1 0.4209 -0.12536 0.560 0.000 0.004 0.004 0.428 0.004
#> GSM152063 2 0.0458 0.69772 0.016 0.984 0.000 0.000 0.000 0.000
#> GSM152074 1 0.4308 0.02128 0.676 0.000 0.280 0.004 0.040 0.000
#> GSM152080 4 0.5404 0.36896 0.016 0.292 0.064 0.612 0.016 0.000
#> GSM152081 1 0.8861 0.19713 0.268 0.156 0.212 0.116 0.004 0.244
#> GSM152083 1 0.6044 -0.00262 0.572 0.200 0.196 0.004 0.028 0.000
#> GSM152091 4 0.5404 0.36896 0.016 0.292 0.064 0.612 0.016 0.000
#> GSM152108 1 0.3692 0.32066 0.800 0.012 0.004 0.000 0.144 0.040
#> GSM152114 1 0.7886 0.36488 0.472 0.032 0.180 0.076 0.036 0.204
#> GSM152035 5 0.4427 0.52961 0.096 0.028 0.004 0.108 0.764 0.000
#> GSM152039 2 0.6332 0.45850 0.052 0.500 0.012 0.348 0.000 0.088
#> GSM152041 6 0.8554 -0.11025 0.080 0.204 0.072 0.200 0.040 0.404
#> GSM152044 2 0.0363 0.69845 0.012 0.988 0.000 0.000 0.000 0.000
#> GSM152045 5 0.2631 0.62545 0.012 0.000 0.000 0.004 0.856 0.128
#> GSM152051 2 0.0363 0.69845 0.012 0.988 0.000 0.000 0.000 0.000
#> GSM152054 5 0.1586 0.60528 0.040 0.004 0.004 0.000 0.940 0.012
#> GSM152057 2 0.0363 0.69845 0.012 0.988 0.000 0.000 0.000 0.000
#> GSM152058 6 0.2794 0.61377 0.144 0.000 0.012 0.004 0.000 0.840
#> GSM152067 3 0.3766 0.62157 0.000 0.000 0.720 0.000 0.256 0.024
#> GSM152068 2 0.0363 0.69845 0.012 0.988 0.000 0.000 0.000 0.000
#> GSM152075 6 0.9326 -0.33631 0.164 0.224 0.092 0.224 0.044 0.252
#> GSM152076 2 0.6332 0.45850 0.052 0.500 0.012 0.348 0.000 0.088
#> GSM152079 2 0.0508 0.69522 0.012 0.984 0.000 0.000 0.000 0.004
#> GSM152084 1 0.7665 0.30990 0.444 0.008 0.268 0.048 0.064 0.168
#> GSM152089 6 0.8947 -0.15953 0.096 0.056 0.072 0.176 0.284 0.316
#> GSM152095 2 0.6374 0.45580 0.056 0.500 0.012 0.344 0.000 0.088
#> GSM152096 1 0.8430 0.27172 0.452 0.188 0.132 0.044 0.068 0.116
#> GSM152097 2 0.2092 0.67487 0.000 0.876 0.000 0.124 0.000 0.000
#> GSM152099 2 0.0363 0.69845 0.012 0.988 0.000 0.000 0.000 0.000
#> GSM152106 2 0.4369 0.61017 0.012 0.700 0.020 0.256 0.012 0.000
#> GSM152107 5 0.7217 0.26362 0.072 0.032 0.280 0.036 0.516 0.064
#> GSM152109 3 0.1232 0.86648 0.016 0.000 0.956 0.004 0.000 0.024
#> GSM152111 6 0.2237 0.63757 0.036 0.000 0.068 0.000 0.000 0.896
#> GSM152112 5 0.7572 0.35964 0.132 0.020 0.160 0.076 0.540 0.072
#> GSM152113 1 0.7613 0.26078 0.428 0.004 0.116 0.016 0.236 0.200
#> GSM152115 5 0.3851 0.53019 0.032 0.000 0.176 0.008 0.776 0.008
#> GSM152030 1 0.8627 0.22255 0.340 0.180 0.144 0.100 0.004 0.232
#> GSM152038 1 0.7349 0.22082 0.400 0.000 0.108 0.004 0.232 0.256
#> GSM152042 1 0.9023 0.16560 0.264 0.180 0.176 0.136 0.008 0.236
#> GSM152062 1 0.7796 0.32653 0.460 0.008 0.236 0.048 0.104 0.144
#> GSM152077 1 0.3766 0.33277 0.800 0.012 0.004 0.000 0.132 0.052
#> GSM152088 2 0.4057 0.36189 0.008 0.740 0.016 0.220 0.016 0.000
#> GSM152100 4 0.9464 -0.26014 0.152 0.212 0.092 0.240 0.064 0.240
#> GSM152102 5 0.4380 0.53287 0.092 0.028 0.004 0.108 0.768 0.000
#> GSM152104 2 0.4347 0.61175 0.012 0.704 0.020 0.252 0.012 0.000
#> GSM152028 1 0.7063 0.13188 0.364 0.000 0.068 0.000 0.280 0.288
#> GSM152029 6 0.4924 0.50546 0.048 0.000 0.276 0.000 0.028 0.648
#> GSM152049 6 0.1553 0.63991 0.032 0.000 0.012 0.008 0.004 0.944
#> GSM152053 1 0.8975 0.17548 0.272 0.180 0.184 0.120 0.008 0.236
#> GSM152059 6 0.3851 0.58336 0.032 0.000 0.164 0.000 0.024 0.780
#> GSM152085 6 0.1396 0.63932 0.024 0.000 0.012 0.008 0.004 0.952
#> GSM152101 5 0.3884 0.52785 0.032 0.000 0.180 0.008 0.772 0.008
#> GSM152105 6 0.6365 0.38696 0.268 0.000 0.112 0.000 0.084 0.536
#> GSM152034 6 0.2596 0.61007 0.032 0.000 0.016 0.044 0.012 0.896
#> GSM152036 2 0.6404 0.45405 0.056 0.500 0.012 0.340 0.000 0.092
#> GSM152040 5 0.3954 0.51417 0.012 0.000 0.008 0.000 0.688 0.292
#> GSM152043 6 0.4962 -0.07249 0.016 0.000 0.036 0.000 0.428 0.520
#> GSM152046 6 0.2528 0.61164 0.032 0.000 0.016 0.040 0.012 0.900
#> GSM152047 5 0.4954 0.18745 0.016 0.000 0.020 0.008 0.500 0.456
#> GSM152048 6 0.2975 0.61039 0.148 0.000 0.012 0.004 0.004 0.832
#> GSM152050 6 0.2794 0.63622 0.080 0.000 0.060 0.000 0.000 0.860
#> GSM152052 6 0.6008 0.15823 0.408 0.000 0.160 0.000 0.012 0.420
#> GSM152056 6 0.2794 0.61377 0.144 0.000 0.012 0.004 0.000 0.840
#> GSM152060 6 0.2596 0.61007 0.032 0.000 0.016 0.044 0.012 0.896
#> GSM152065 5 0.3514 0.54000 0.208 0.000 0.004 0.000 0.768 0.020
#> GSM152066 6 0.3587 0.60226 0.164 0.000 0.012 0.004 0.024 0.796
#> GSM152069 3 0.1629 0.87046 0.028 0.000 0.940 0.004 0.004 0.024
#> GSM152070 5 0.4719 0.21360 0.016 0.000 0.020 0.000 0.516 0.448
#> GSM152071 3 0.1549 0.87199 0.024 0.000 0.944 0.004 0.004 0.024
#> GSM152072 5 0.2581 0.62854 0.020 0.000 0.000 0.000 0.860 0.120
#> GSM152073 6 0.2973 0.63176 0.040 0.000 0.084 0.000 0.016 0.860
#> GSM152078 6 0.5986 0.16391 0.408 0.000 0.156 0.000 0.012 0.424
#> GSM152082 6 0.4893 -0.10455 0.012 0.000 0.036 0.000 0.440 0.512
#> GSM152086 6 0.2237 0.63757 0.036 0.000 0.068 0.000 0.000 0.896
#> GSM152090 6 0.6445 0.29230 0.260 0.000 0.208 0.020 0.012 0.500
#> GSM152092 6 0.5696 -0.05695 0.056 0.000 0.048 0.000 0.396 0.500
#> GSM152093 6 0.6613 0.11225 0.364 0.000 0.108 0.032 0.032 0.464
#> GSM152094 6 0.2509 0.63356 0.036 0.000 0.088 0.000 0.000 0.876
#> GSM152098 6 0.4893 -0.10455 0.012 0.000 0.036 0.000 0.440 0.512
#> GSM152110 6 0.2755 0.61528 0.140 0.000 0.012 0.004 0.000 0.844
#> GSM152031 6 0.6365 0.38696 0.268 0.000 0.112 0.000 0.084 0.536
#> GSM152037 6 0.3622 0.59929 0.168 0.000 0.012 0.004 0.024 0.792
#> GSM152055 6 0.2569 0.61010 0.036 0.000 0.016 0.044 0.008 0.896
#> GSM152061 6 0.2596 0.61007 0.032 0.000 0.016 0.044 0.012 0.896
#> GSM152064 6 0.3018 0.60137 0.040 0.004 0.048 0.024 0.008 0.876
#> GSM152087 6 0.2685 0.63553 0.044 0.000 0.080 0.000 0.004 0.872
#> GSM152103 6 0.6497 0.26508 0.216 0.000 0.264 0.020 0.012 0.488
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 specimen(p) k
#> CV:hclust 80 1.95e-03 2
#> CV:hclust 52 4.01e-07 3
#> CV:hclust 33 4.12e-05 4
#> CV:hclust 34 4.15e-03 5
#> CV:hclust 45 1.41e-02 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 10612 rows and 88 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.231 0.546 0.778 0.4694 0.520 0.520
#> 3 3 0.525 0.637 0.811 0.3843 0.732 0.522
#> 4 4 0.569 0.707 0.799 0.1217 0.903 0.728
#> 5 5 0.597 0.584 0.747 0.0697 0.937 0.783
#> 6 6 0.646 0.496 0.668 0.0466 0.899 0.603
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
#> GSM152032 1 0.9775 0.02574 0.588 0.412
#> GSM152033 1 0.9710 0.06083 0.600 0.400
#> GSM152063 2 0.0000 0.71460 0.000 1.000
#> GSM152074 1 0.9775 0.02574 0.588 0.412
#> GSM152080 2 0.8207 0.56608 0.256 0.744
#> GSM152081 2 0.9170 0.41660 0.332 0.668
#> GSM152083 2 0.8207 0.56608 0.256 0.744
#> GSM152091 2 0.7674 0.59288 0.224 0.776
#> GSM152108 2 0.3274 0.70391 0.060 0.940
#> GSM152114 1 0.9896 0.33007 0.560 0.440
#> GSM152035 2 0.7674 0.59288 0.224 0.776
#> GSM152039 2 0.7376 0.59907 0.208 0.792
#> GSM152041 2 0.9209 0.39761 0.336 0.664
#> GSM152044 2 0.0672 0.71505 0.008 0.992
#> GSM152045 1 0.6148 0.54546 0.848 0.152
#> GSM152051 2 0.0672 0.71648 0.008 0.992
#> GSM152054 2 0.9970 0.35423 0.468 0.532
#> GSM152057 2 0.0672 0.71648 0.008 0.992
#> GSM152058 1 0.7883 0.65931 0.764 0.236
#> GSM152067 1 0.9815 -0.00889 0.580 0.420
#> GSM152068 2 0.0672 0.71648 0.008 0.992
#> GSM152075 2 0.8661 0.50640 0.288 0.712
#> GSM152076 2 0.7745 0.58310 0.228 0.772
#> GSM152079 2 0.0672 0.71648 0.008 0.992
#> GSM152084 1 0.9775 0.19300 0.588 0.412
#> GSM152089 2 0.7950 0.55439 0.240 0.760
#> GSM152095 2 0.7745 0.58310 0.228 0.772
#> GSM152096 2 0.8861 0.54047 0.304 0.696
#> GSM152097 2 0.0376 0.71375 0.004 0.996
#> GSM152099 2 0.0672 0.71648 0.008 0.992
#> GSM152106 2 0.0376 0.71375 0.004 0.996
#> GSM152107 2 0.9686 0.44563 0.396 0.604
#> GSM152109 1 0.9754 0.03945 0.592 0.408
#> GSM152111 1 0.8207 0.64911 0.744 0.256
#> GSM152112 2 0.9661 0.47948 0.392 0.608
#> GSM152113 1 0.9393 0.15251 0.644 0.356
#> GSM152115 1 0.9754 0.00409 0.592 0.408
#> GSM152030 2 0.8909 0.48332 0.308 0.692
#> GSM152038 1 0.1633 0.65315 0.976 0.024
#> GSM152042 2 0.9170 0.41660 0.332 0.668
#> GSM152062 1 0.9358 0.16073 0.648 0.352
#> GSM152077 1 0.7950 0.65730 0.760 0.240
#> GSM152088 2 0.0672 0.71648 0.008 0.992
#> GSM152100 2 0.5059 0.67881 0.112 0.888
#> GSM152102 2 0.8386 0.56056 0.268 0.732
#> GSM152104 2 0.0376 0.71375 0.004 0.996
#> GSM152028 1 0.0376 0.66538 0.996 0.004
#> GSM152029 1 0.0376 0.66538 0.996 0.004
#> GSM152049 1 0.7883 0.65931 0.764 0.236
#> GSM152053 2 0.9170 0.43033 0.332 0.668
#> GSM152059 1 0.0000 0.66622 1.000 0.000
#> GSM152085 1 0.8016 0.65680 0.756 0.244
#> GSM152101 2 0.9996 0.30967 0.488 0.512
#> GSM152105 1 0.0376 0.66538 0.996 0.004
#> GSM152034 1 0.8207 0.64911 0.744 0.256
#> GSM152036 2 0.8016 0.56499 0.244 0.756
#> GSM152040 1 0.0672 0.66565 0.992 0.008
#> GSM152043 1 0.0672 0.66565 0.992 0.008
#> GSM152046 1 0.8207 0.64911 0.744 0.256
#> GSM152047 1 0.5737 0.66978 0.864 0.136
#> GSM152048 1 0.7883 0.65931 0.764 0.236
#> GSM152050 1 0.8207 0.64911 0.744 0.256
#> GSM152052 1 0.1414 0.66865 0.980 0.020
#> GSM152056 1 0.8144 0.65071 0.748 0.252
#> GSM152060 1 0.8207 0.64911 0.744 0.256
#> GSM152065 1 0.4298 0.59795 0.912 0.088
#> GSM152066 1 0.7883 0.65931 0.764 0.236
#> GSM152069 1 0.9754 0.03945 0.592 0.408
#> GSM152070 1 0.0376 0.66538 0.996 0.004
#> GSM152071 1 0.9710 0.06099 0.600 0.400
#> GSM152072 1 0.5519 0.56038 0.872 0.128
#> GSM152073 1 0.0000 0.66622 1.000 0.000
#> GSM152078 1 0.0376 0.66538 0.996 0.004
#> GSM152082 1 0.0376 0.66538 0.996 0.004
#> GSM152086 1 0.7950 0.65844 0.760 0.240
#> GSM152090 1 0.9710 0.42642 0.600 0.400
#> GSM152092 1 0.0376 0.66538 0.996 0.004
#> GSM152093 1 0.8081 0.65174 0.752 0.248
#> GSM152094 1 0.7950 0.65885 0.760 0.240
#> GSM152098 1 0.0376 0.66538 0.996 0.004
#> GSM152110 1 0.8207 0.64911 0.744 0.256
#> GSM152031 1 0.0376 0.66538 0.996 0.004
#> GSM152037 1 0.7815 0.66051 0.768 0.232
#> GSM152055 1 0.8207 0.64911 0.744 0.256
#> GSM152061 1 0.8207 0.64911 0.744 0.256
#> GSM152064 1 0.8207 0.64911 0.744 0.256
#> GSM152087 1 0.7883 0.66018 0.764 0.236
#> GSM152103 1 0.8386 0.62906 0.732 0.268
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM152032 3 0.1525 0.7843 0.032 0.004 0.964
#> GSM152033 3 0.1647 0.7846 0.036 0.004 0.960
#> GSM152063 2 0.1647 0.6635 0.004 0.960 0.036
#> GSM152074 3 0.1289 0.7844 0.032 0.000 0.968
#> GSM152080 2 0.6359 0.1104 0.004 0.592 0.404
#> GSM152081 2 0.9574 0.4256 0.392 0.412 0.196
#> GSM152083 3 0.6291 0.1382 0.000 0.468 0.532
#> GSM152091 2 0.4682 0.5248 0.004 0.804 0.192
#> GSM152108 2 0.7014 0.4985 0.080 0.712 0.208
#> GSM152114 1 0.4465 0.6786 0.820 0.004 0.176
#> GSM152035 2 0.4733 0.5198 0.004 0.800 0.196
#> GSM152039 2 0.8803 0.5463 0.320 0.544 0.136
#> GSM152041 2 0.9062 0.4250 0.412 0.452 0.136
#> GSM152044 2 0.1765 0.6632 0.004 0.956 0.040
#> GSM152045 3 0.3832 0.7419 0.100 0.020 0.880
#> GSM152051 2 0.2063 0.6628 0.008 0.948 0.044
#> GSM152054 3 0.2527 0.7505 0.020 0.044 0.936
#> GSM152057 2 0.2063 0.6628 0.008 0.948 0.044
#> GSM152058 1 0.0424 0.8452 0.992 0.000 0.008
#> GSM152067 3 0.1170 0.7779 0.016 0.008 0.976
#> GSM152068 2 0.2063 0.6628 0.008 0.948 0.044
#> GSM152075 2 0.9172 0.4463 0.396 0.456 0.148
#> GSM152076 2 0.8902 0.5443 0.320 0.536 0.144
#> GSM152079 2 0.2063 0.6628 0.008 0.948 0.044
#> GSM152084 3 0.2400 0.7726 0.064 0.004 0.932
#> GSM152089 3 0.9331 -0.0483 0.344 0.176 0.480
#> GSM152095 2 0.8902 0.5443 0.320 0.536 0.144
#> GSM152096 3 0.6451 0.2183 0.004 0.436 0.560
#> GSM152097 2 0.0983 0.6636 0.004 0.980 0.016
#> GSM152099 2 0.1878 0.6628 0.004 0.952 0.044
#> GSM152106 2 0.0237 0.6601 0.004 0.996 0.000
#> GSM152107 3 0.0829 0.7676 0.004 0.012 0.984
#> GSM152109 3 0.1525 0.7843 0.032 0.004 0.964
#> GSM152111 1 0.0000 0.8443 1.000 0.000 0.000
#> GSM152112 3 0.3752 0.7095 0.020 0.096 0.884
#> GSM152113 3 0.1411 0.7842 0.036 0.000 0.964
#> GSM152115 3 0.0848 0.7732 0.008 0.008 0.984
#> GSM152030 2 0.9625 0.4377 0.388 0.408 0.204
#> GSM152038 3 0.2356 0.7722 0.072 0.000 0.928
#> GSM152042 2 0.9625 0.4377 0.388 0.408 0.204
#> GSM152062 3 0.1647 0.7845 0.036 0.004 0.960
#> GSM152077 1 0.1643 0.8283 0.956 0.000 0.044
#> GSM152088 2 0.2063 0.6628 0.008 0.948 0.044
#> GSM152100 2 0.8902 0.5443 0.320 0.536 0.144
#> GSM152102 3 0.6111 0.3311 0.000 0.396 0.604
#> GSM152104 2 0.1129 0.6637 0.004 0.976 0.020
#> GSM152028 1 0.5835 0.4708 0.660 0.000 0.340
#> GSM152029 3 0.6302 0.0801 0.480 0.000 0.520
#> GSM152049 1 0.0747 0.8431 0.984 0.000 0.016
#> GSM152053 2 0.9673 0.4313 0.388 0.400 0.212
#> GSM152059 1 0.4702 0.6695 0.788 0.000 0.212
#> GSM152085 1 0.0000 0.8443 1.000 0.000 0.000
#> GSM152101 3 0.0848 0.7732 0.008 0.008 0.984
#> GSM152105 1 0.5926 0.4642 0.644 0.000 0.356
#> GSM152034 1 0.2187 0.8175 0.948 0.028 0.024
#> GSM152036 2 0.8971 0.5286 0.336 0.520 0.144
#> GSM152040 1 0.6057 0.4834 0.656 0.004 0.340
#> GSM152043 1 0.5560 0.5369 0.700 0.000 0.300
#> GSM152046 1 0.2187 0.8175 0.948 0.028 0.024
#> GSM152047 1 0.1163 0.8368 0.972 0.000 0.028
#> GSM152048 1 0.0592 0.8448 0.988 0.000 0.012
#> GSM152050 1 0.0000 0.8443 1.000 0.000 0.000
#> GSM152052 1 0.1289 0.8387 0.968 0.000 0.032
#> GSM152056 1 0.0424 0.8452 0.992 0.000 0.008
#> GSM152060 1 0.2187 0.8175 0.948 0.028 0.024
#> GSM152065 3 0.4682 0.6884 0.192 0.004 0.804
#> GSM152066 1 0.0424 0.8452 0.992 0.000 0.008
#> GSM152069 3 0.1525 0.7843 0.032 0.004 0.964
#> GSM152070 3 0.6330 0.3432 0.396 0.004 0.600
#> GSM152071 3 0.1525 0.7843 0.032 0.004 0.964
#> GSM152072 3 0.4682 0.6919 0.192 0.004 0.804
#> GSM152073 1 0.5397 0.5728 0.720 0.000 0.280
#> GSM152078 1 0.6204 0.2590 0.576 0.000 0.424
#> GSM152082 3 0.6204 0.2664 0.424 0.000 0.576
#> GSM152086 1 0.0424 0.8452 0.992 0.000 0.008
#> GSM152090 1 0.4465 0.7010 0.820 0.004 0.176
#> GSM152092 1 0.5835 0.4708 0.660 0.000 0.340
#> GSM152093 1 0.0424 0.8452 0.992 0.000 0.008
#> GSM152094 1 0.0000 0.8443 1.000 0.000 0.000
#> GSM152098 3 0.6274 0.1660 0.456 0.000 0.544
#> GSM152110 1 0.0237 0.8444 0.996 0.000 0.004
#> GSM152031 1 0.5706 0.5100 0.680 0.000 0.320
#> GSM152037 1 0.0424 0.8452 0.992 0.000 0.008
#> GSM152055 1 0.2318 0.8137 0.944 0.028 0.028
#> GSM152061 1 0.2187 0.8175 0.948 0.028 0.024
#> GSM152064 1 0.2187 0.8159 0.948 0.024 0.028
#> GSM152087 1 0.0237 0.8449 0.996 0.000 0.004
#> GSM152103 1 0.3482 0.7684 0.872 0.000 0.128
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM152032 3 0.2803 0.6907 0.008 0.012 0.900 0.080
#> GSM152033 3 0.3326 0.7161 0.008 0.004 0.856 0.132
#> GSM152063 2 0.0336 0.8684 0.000 0.992 0.000 0.008
#> GSM152074 3 0.2660 0.6926 0.008 0.012 0.908 0.072
#> GSM152080 2 0.4907 0.7417 0.000 0.764 0.176 0.060
#> GSM152081 4 0.8285 0.7888 0.128 0.172 0.128 0.572
#> GSM152083 2 0.6100 0.5610 0.000 0.624 0.304 0.072
#> GSM152091 2 0.3239 0.8288 0.000 0.880 0.068 0.052
#> GSM152108 2 0.6157 0.6852 0.084 0.732 0.136 0.048
#> GSM152114 1 0.7362 -0.2103 0.444 0.000 0.160 0.396
#> GSM152035 2 0.2983 0.8343 0.000 0.892 0.068 0.040
#> GSM152039 4 0.5935 0.8078 0.080 0.256 0.000 0.664
#> GSM152041 4 0.6363 0.7956 0.172 0.172 0.000 0.656
#> GSM152044 2 0.0336 0.8684 0.000 0.992 0.000 0.008
#> GSM152045 3 0.5839 0.6135 0.044 0.000 0.604 0.352
#> GSM152051 2 0.0188 0.8737 0.000 0.996 0.004 0.000
#> GSM152054 3 0.5468 0.6182 0.012 0.008 0.616 0.364
#> GSM152057 2 0.0188 0.8737 0.000 0.996 0.004 0.000
#> GSM152058 1 0.1398 0.8310 0.956 0.000 0.040 0.004
#> GSM152067 3 0.4303 0.6973 0.008 0.004 0.768 0.220
#> GSM152068 2 0.0188 0.8737 0.000 0.996 0.004 0.000
#> GSM152075 4 0.6315 0.8194 0.128 0.184 0.008 0.680
#> GSM152076 4 0.5873 0.8093 0.076 0.256 0.000 0.668
#> GSM152079 2 0.0188 0.8737 0.000 0.996 0.004 0.000
#> GSM152084 3 0.7391 0.1977 0.156 0.012 0.556 0.276
#> GSM152089 4 0.4824 0.6032 0.084 0.024 0.080 0.812
#> GSM152095 4 0.5873 0.8093 0.076 0.256 0.000 0.668
#> GSM152096 2 0.6089 0.5284 0.000 0.608 0.328 0.064
#> GSM152097 2 0.1302 0.8428 0.000 0.956 0.000 0.044
#> GSM152099 2 0.0188 0.8737 0.000 0.996 0.004 0.000
#> GSM152106 2 0.1302 0.8428 0.000 0.956 0.000 0.044
#> GSM152107 3 0.6380 0.1759 0.012 0.048 0.576 0.364
#> GSM152109 3 0.2473 0.7030 0.000 0.012 0.908 0.080
#> GSM152111 1 0.0672 0.8323 0.984 0.000 0.008 0.008
#> GSM152112 4 0.4690 0.0791 0.000 0.012 0.276 0.712
#> GSM152113 3 0.2983 0.7128 0.016 0.012 0.896 0.076
#> GSM152115 3 0.4718 0.6836 0.008 0.004 0.716 0.272
#> GSM152030 4 0.8274 0.7854 0.120 0.176 0.132 0.572
#> GSM152038 3 0.2271 0.7164 0.008 0.000 0.916 0.076
#> GSM152042 4 0.8281 0.7830 0.120 0.172 0.136 0.572
#> GSM152062 3 0.2438 0.6997 0.016 0.012 0.924 0.048
#> GSM152077 1 0.4008 0.7713 0.820 0.000 0.148 0.032
#> GSM152088 2 0.1724 0.8596 0.000 0.948 0.032 0.020
#> GSM152100 4 0.5753 0.8120 0.072 0.248 0.000 0.680
#> GSM152102 3 0.7686 0.2958 0.000 0.336 0.436 0.228
#> GSM152104 2 0.0469 0.8657 0.000 0.988 0.000 0.012
#> GSM152028 1 0.4552 0.7570 0.800 0.000 0.128 0.072
#> GSM152029 1 0.5966 0.5572 0.648 0.000 0.280 0.072
#> GSM152049 1 0.0469 0.8320 0.988 0.000 0.000 0.012
#> GSM152053 4 0.8275 0.7755 0.112 0.168 0.148 0.572
#> GSM152059 1 0.3071 0.8178 0.888 0.000 0.068 0.044
#> GSM152085 1 0.1389 0.8259 0.952 0.000 0.000 0.048
#> GSM152101 3 0.4718 0.6854 0.008 0.004 0.716 0.272
#> GSM152105 1 0.4535 0.7146 0.744 0.000 0.240 0.016
#> GSM152034 1 0.4053 0.7013 0.768 0.000 0.004 0.228
#> GSM152036 4 0.5880 0.8132 0.088 0.232 0.000 0.680
#> GSM152040 1 0.6594 0.4927 0.620 0.000 0.140 0.240
#> GSM152043 1 0.2919 0.8193 0.896 0.000 0.060 0.044
#> GSM152046 1 0.3982 0.7102 0.776 0.000 0.004 0.220
#> GSM152047 1 0.3278 0.7985 0.864 0.000 0.020 0.116
#> GSM152048 1 0.1489 0.8308 0.952 0.000 0.044 0.004
#> GSM152050 1 0.0657 0.8320 0.984 0.000 0.004 0.012
#> GSM152052 1 0.3249 0.7955 0.852 0.000 0.140 0.008
#> GSM152056 1 0.1109 0.8326 0.968 0.000 0.028 0.004
#> GSM152060 1 0.4053 0.7013 0.768 0.000 0.004 0.228
#> GSM152065 3 0.5593 0.6796 0.080 0.000 0.708 0.212
#> GSM152066 1 0.1004 0.8330 0.972 0.000 0.024 0.004
#> GSM152069 3 0.2402 0.7045 0.000 0.012 0.912 0.076
#> GSM152070 3 0.7756 0.3768 0.328 0.000 0.424 0.248
#> GSM152071 3 0.2402 0.7045 0.000 0.012 0.912 0.076
#> GSM152072 3 0.5889 0.6724 0.100 0.000 0.688 0.212
#> GSM152073 1 0.3090 0.8159 0.888 0.000 0.056 0.056
#> GSM152078 1 0.5300 0.5981 0.664 0.000 0.308 0.028
#> GSM152082 3 0.7561 0.3199 0.348 0.000 0.452 0.200
#> GSM152086 1 0.0657 0.8330 0.984 0.000 0.012 0.004
#> GSM152090 1 0.5082 0.6627 0.720 0.004 0.248 0.028
#> GSM152092 1 0.4599 0.7580 0.800 0.000 0.112 0.088
#> GSM152093 1 0.1975 0.8271 0.936 0.000 0.048 0.016
#> GSM152094 1 0.1211 0.8271 0.960 0.000 0.000 0.040
#> GSM152098 3 0.7745 0.2725 0.372 0.000 0.396 0.232
#> GSM152110 1 0.0927 0.8325 0.976 0.000 0.016 0.008
#> GSM152031 1 0.3647 0.7890 0.832 0.000 0.152 0.016
#> GSM152037 1 0.1305 0.8326 0.960 0.000 0.036 0.004
#> GSM152055 1 0.4040 0.6662 0.752 0.000 0.000 0.248
#> GSM152061 1 0.4053 0.7013 0.768 0.000 0.004 0.228
#> GSM152064 1 0.3942 0.6905 0.764 0.000 0.000 0.236
#> GSM152087 1 0.1489 0.8276 0.952 0.000 0.004 0.044
#> GSM152103 1 0.4885 0.6731 0.728 0.004 0.248 0.020
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM152032 3 0.1739 0.5976 0.000 0.024 0.940 0.004 0.032
#> GSM152033 3 0.5156 0.2050 0.016 0.008 0.572 0.008 0.396
#> GSM152063 2 0.1478 0.8577 0.000 0.936 0.000 0.064 0.000
#> GSM152074 3 0.2544 0.5899 0.000 0.028 0.900 0.008 0.064
#> GSM152080 2 0.4447 0.7073 0.000 0.800 0.080 0.048 0.072
#> GSM152081 4 0.5090 0.6745 0.036 0.040 0.212 0.712 0.000
#> GSM152083 2 0.5893 0.0471 0.000 0.468 0.456 0.016 0.060
#> GSM152091 2 0.3003 0.7757 0.000 0.880 0.016 0.040 0.064
#> GSM152108 2 0.8057 0.0189 0.068 0.396 0.356 0.024 0.156
#> GSM152114 4 0.7781 0.1016 0.332 0.004 0.240 0.372 0.052
#> GSM152035 2 0.4943 0.7192 0.000 0.764 0.100 0.048 0.088
#> GSM152039 4 0.2692 0.7603 0.016 0.092 0.000 0.884 0.008
#> GSM152041 4 0.2464 0.7579 0.048 0.044 0.004 0.904 0.000
#> GSM152044 2 0.1638 0.8571 0.000 0.932 0.000 0.064 0.004
#> GSM152045 5 0.5677 0.5549 0.068 0.000 0.172 0.064 0.696
#> GSM152051 2 0.1410 0.8589 0.000 0.940 0.000 0.060 0.000
#> GSM152054 5 0.5715 0.4465 0.004 0.016 0.208 0.104 0.668
#> GSM152057 2 0.1410 0.8589 0.000 0.940 0.000 0.060 0.000
#> GSM152058 1 0.4160 0.7187 0.816 0.000 0.084 0.036 0.064
#> GSM152067 5 0.5170 0.1949 0.004 0.000 0.440 0.032 0.524
#> GSM152068 2 0.1410 0.8589 0.000 0.940 0.000 0.060 0.000
#> GSM152075 4 0.2627 0.7598 0.044 0.044 0.012 0.900 0.000
#> GSM152076 4 0.2727 0.7619 0.016 0.092 0.004 0.884 0.004
#> GSM152079 2 0.1410 0.8589 0.000 0.940 0.000 0.060 0.000
#> GSM152084 3 0.4874 0.4699 0.072 0.008 0.736 0.180 0.004
#> GSM152089 4 0.4915 0.6066 0.052 0.004 0.024 0.744 0.176
#> GSM152095 4 0.2727 0.7619 0.016 0.092 0.004 0.884 0.004
#> GSM152096 3 0.5639 0.0634 0.000 0.400 0.536 0.012 0.052
#> GSM152097 2 0.2616 0.8328 0.000 0.880 0.000 0.100 0.020
#> GSM152099 2 0.1410 0.8589 0.000 0.940 0.000 0.060 0.000
#> GSM152106 2 0.2761 0.8291 0.000 0.872 0.000 0.104 0.024
#> GSM152107 3 0.5267 -0.1571 0.000 0.016 0.492 0.472 0.020
#> GSM152109 3 0.5149 0.4463 0.000 0.044 0.696 0.028 0.232
#> GSM152111 1 0.1153 0.7273 0.964 0.000 0.004 0.024 0.008
#> GSM152112 4 0.6225 0.1350 0.000 0.004 0.136 0.516 0.344
#> GSM152113 3 0.4484 0.4575 0.044 0.000 0.752 0.012 0.192
#> GSM152115 5 0.4988 0.3346 0.004 0.000 0.416 0.024 0.556
#> GSM152030 4 0.5374 0.6518 0.044 0.040 0.232 0.684 0.000
#> GSM152038 3 0.3320 0.5512 0.008 0.000 0.828 0.012 0.152
#> GSM152042 4 0.5385 0.6549 0.036 0.040 0.232 0.688 0.004
#> GSM152062 3 0.2157 0.5907 0.016 0.004 0.928 0.028 0.024
#> GSM152077 1 0.6530 0.4375 0.524 0.000 0.340 0.032 0.104
#> GSM152088 2 0.0968 0.8273 0.000 0.972 0.004 0.012 0.012
#> GSM152100 4 0.2645 0.7605 0.008 0.096 0.012 0.884 0.000
#> GSM152102 5 0.6424 0.3031 0.000 0.200 0.156 0.036 0.608
#> GSM152104 2 0.2362 0.8472 0.000 0.900 0.000 0.076 0.024
#> GSM152028 1 0.6307 0.5681 0.596 0.000 0.160 0.020 0.224
#> GSM152029 1 0.6509 0.3835 0.592 0.008 0.176 0.016 0.208
#> GSM152049 1 0.1686 0.7272 0.944 0.000 0.008 0.020 0.028
#> GSM152053 4 0.5159 0.6484 0.028 0.040 0.244 0.688 0.000
#> GSM152059 1 0.2621 0.6914 0.876 0.000 0.008 0.004 0.112
#> GSM152085 1 0.2540 0.7000 0.888 0.000 0.000 0.024 0.088
#> GSM152101 5 0.4813 0.3759 0.004 0.000 0.376 0.020 0.600
#> GSM152105 1 0.6375 0.5405 0.568 0.000 0.292 0.028 0.112
#> GSM152034 1 0.5082 0.5597 0.684 0.000 0.000 0.220 0.096
#> GSM152036 4 0.2518 0.7585 0.016 0.080 0.000 0.896 0.008
#> GSM152040 5 0.4872 0.1374 0.436 0.000 0.000 0.024 0.540
#> GSM152043 1 0.3124 0.6783 0.844 0.000 0.016 0.004 0.136
#> GSM152046 1 0.5073 0.5695 0.688 0.000 0.000 0.212 0.100
#> GSM152047 1 0.4069 0.6464 0.788 0.000 0.000 0.076 0.136
#> GSM152048 1 0.4160 0.7187 0.816 0.000 0.084 0.036 0.064
#> GSM152050 1 0.1243 0.7271 0.960 0.000 0.004 0.028 0.008
#> GSM152052 1 0.5508 0.6440 0.688 0.004 0.216 0.028 0.064
#> GSM152056 1 0.4039 0.7208 0.824 0.000 0.080 0.036 0.060
#> GSM152060 1 0.5130 0.5590 0.680 0.000 0.000 0.220 0.100
#> GSM152065 5 0.3988 0.5271 0.036 0.000 0.196 0.000 0.768
#> GSM152066 1 0.3973 0.7208 0.828 0.000 0.080 0.036 0.056
#> GSM152069 3 0.5302 0.4459 0.004 0.044 0.692 0.028 0.232
#> GSM152070 5 0.4860 0.5379 0.228 0.000 0.064 0.004 0.704
#> GSM152071 3 0.5302 0.4459 0.004 0.044 0.692 0.028 0.232
#> GSM152072 5 0.5077 0.5572 0.088 0.000 0.212 0.004 0.696
#> GSM152073 1 0.2439 0.6910 0.876 0.000 0.000 0.004 0.120
#> GSM152078 1 0.6695 0.5374 0.560 0.004 0.264 0.028 0.144
#> GSM152082 5 0.5405 0.4994 0.272 0.000 0.084 0.004 0.640
#> GSM152086 1 0.1507 0.7306 0.952 0.000 0.012 0.024 0.012
#> GSM152090 1 0.5123 0.4922 0.600 0.008 0.364 0.024 0.004
#> GSM152092 1 0.6299 0.5647 0.588 0.000 0.164 0.016 0.232
#> GSM152093 1 0.4204 0.7165 0.812 0.000 0.096 0.040 0.052
#> GSM152094 1 0.2006 0.7073 0.916 0.000 0.000 0.012 0.072
#> GSM152098 5 0.5333 0.4922 0.300 0.000 0.068 0.004 0.628
#> GSM152110 1 0.3947 0.7252 0.832 0.000 0.064 0.044 0.060
#> GSM152031 1 0.5982 0.6199 0.640 0.000 0.212 0.024 0.124
#> GSM152037 1 0.4103 0.7199 0.820 0.000 0.080 0.036 0.064
#> GSM152055 1 0.5254 0.5232 0.644 0.000 0.000 0.272 0.084
#> GSM152061 1 0.5130 0.5590 0.680 0.000 0.000 0.220 0.100
#> GSM152064 1 0.5110 0.5677 0.680 0.000 0.000 0.224 0.096
#> GSM152087 1 0.1956 0.7050 0.916 0.000 0.000 0.008 0.076
#> GSM152103 1 0.5313 0.4508 0.568 0.008 0.392 0.024 0.008
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM152032 3 0.0665 0.5614 0.000 0.000 0.980 0.004 0.008 0.008
#> GSM152033 3 0.6545 0.2592 0.092 0.000 0.484 0.004 0.332 0.088
#> GSM152063 2 0.1007 0.9014 0.000 0.956 0.000 0.044 0.000 0.000
#> GSM152074 3 0.2942 0.5444 0.004 0.000 0.856 0.004 0.036 0.100
#> GSM152080 2 0.5779 0.6092 0.000 0.668 0.100 0.028 0.048 0.156
#> GSM152081 4 0.4956 0.6844 0.052 0.000 0.236 0.680 0.012 0.020
#> GSM152083 3 0.5812 0.3017 0.000 0.308 0.572 0.012 0.032 0.076
#> GSM152091 2 0.3688 0.7821 0.000 0.820 0.008 0.020 0.048 0.104
#> GSM152108 3 0.8859 0.3532 0.288 0.168 0.312 0.028 0.100 0.104
#> GSM152114 1 0.5496 0.2004 0.592 0.000 0.160 0.240 0.000 0.008
#> GSM152035 2 0.5639 0.6355 0.000 0.680 0.076 0.012 0.108 0.124
#> GSM152039 4 0.2001 0.7844 0.012 0.028 0.000 0.924 0.004 0.032
#> GSM152041 4 0.1554 0.7848 0.044 0.004 0.004 0.940 0.000 0.008
#> GSM152044 2 0.1007 0.9014 0.000 0.956 0.000 0.044 0.000 0.000
#> GSM152045 5 0.3306 0.6215 0.000 0.000 0.052 0.020 0.840 0.088
#> GSM152051 2 0.1010 0.9010 0.000 0.960 0.004 0.036 0.000 0.000
#> GSM152054 5 0.3744 0.5447 0.004 0.004 0.076 0.040 0.828 0.048
#> GSM152057 2 0.1226 0.9014 0.000 0.952 0.004 0.040 0.000 0.004
#> GSM152058 1 0.0405 0.5037 0.988 0.000 0.000 0.004 0.000 0.008
#> GSM152067 5 0.5518 0.2807 0.000 0.000 0.308 0.012 0.564 0.116
#> GSM152068 2 0.1082 0.9018 0.000 0.956 0.004 0.040 0.000 0.000
#> GSM152075 4 0.1608 0.7864 0.036 0.004 0.016 0.940 0.004 0.000
#> GSM152076 4 0.2001 0.7844 0.012 0.028 0.000 0.924 0.004 0.032
#> GSM152079 2 0.1082 0.9018 0.000 0.956 0.004 0.040 0.000 0.000
#> GSM152084 3 0.5046 0.4838 0.200 0.000 0.676 0.108 0.008 0.008
#> GSM152089 4 0.4934 0.5762 0.008 0.004 0.004 0.696 0.180 0.108
#> GSM152095 4 0.1857 0.7855 0.012 0.028 0.000 0.928 0.000 0.032
#> GSM152096 3 0.5786 0.3354 0.020 0.320 0.580 0.008 0.036 0.036
#> GSM152097 2 0.3117 0.8431 0.000 0.848 0.000 0.100 0.020 0.032
#> GSM152099 2 0.1082 0.9018 0.000 0.956 0.004 0.040 0.000 0.000
#> GSM152106 2 0.3483 0.8256 0.000 0.820 0.000 0.120 0.020 0.040
#> GSM152107 4 0.5526 0.2767 0.008 0.000 0.440 0.472 0.068 0.012
#> GSM152109 3 0.5930 0.3903 0.004 0.024 0.628 0.016 0.172 0.156
#> GSM152111 1 0.3619 -0.1461 0.680 0.000 0.000 0.004 0.000 0.316
#> GSM152112 5 0.5241 0.1022 0.000 0.000 0.072 0.420 0.500 0.008
#> GSM152113 3 0.6591 0.4467 0.288 0.000 0.536 0.032 0.080 0.064
#> GSM152115 5 0.3702 0.4916 0.000 0.000 0.264 0.004 0.720 0.012
#> GSM152030 4 0.5363 0.6488 0.080 0.000 0.244 0.644 0.012 0.020
#> GSM152038 3 0.5091 0.5375 0.128 0.004 0.728 0.008 0.056 0.076
#> GSM152042 4 0.4895 0.6759 0.048 0.000 0.252 0.672 0.008 0.020
#> GSM152062 3 0.3851 0.5608 0.120 0.000 0.808 0.032 0.012 0.028
#> GSM152077 1 0.6109 0.0788 0.576 0.000 0.284 0.032 0.036 0.072
#> GSM152088 2 0.1457 0.8639 0.000 0.948 0.004 0.016 0.004 0.028
#> GSM152100 4 0.1363 0.7868 0.004 0.028 0.004 0.952 0.012 0.000
#> GSM152102 5 0.5551 0.4067 0.000 0.120 0.072 0.012 0.688 0.108
#> GSM152104 2 0.2283 0.8869 0.000 0.904 0.000 0.056 0.020 0.020
#> GSM152028 1 0.5626 0.3927 0.660 0.004 0.072 0.000 0.092 0.172
#> GSM152029 6 0.6483 0.2152 0.208 0.004 0.120 0.000 0.104 0.564
#> GSM152049 1 0.3584 -0.1188 0.688 0.000 0.000 0.004 0.000 0.308
#> GSM152053 4 0.4967 0.6766 0.048 0.000 0.248 0.672 0.012 0.020
#> GSM152059 6 0.4594 0.4018 0.468 0.004 0.004 0.000 0.020 0.504
#> GSM152085 1 0.4184 -0.4390 0.556 0.000 0.000 0.004 0.008 0.432
#> GSM152101 5 0.3314 0.5162 0.000 0.000 0.224 0.000 0.764 0.012
#> GSM152105 1 0.4663 0.3877 0.672 0.000 0.244 0.004 0.000 0.080
#> GSM152034 6 0.6066 0.6638 0.376 0.000 0.000 0.148 0.020 0.456
#> GSM152036 4 0.2014 0.7855 0.016 0.024 0.000 0.924 0.004 0.032
#> GSM152040 5 0.5329 0.3622 0.096 0.004 0.000 0.000 0.520 0.380
#> GSM152043 6 0.4836 0.3937 0.440 0.004 0.004 0.000 0.036 0.516
#> GSM152046 6 0.6014 0.6634 0.376 0.000 0.000 0.140 0.020 0.464
#> GSM152047 6 0.5095 0.5367 0.352 0.000 0.000 0.016 0.056 0.576
#> GSM152048 1 0.0405 0.5037 0.988 0.000 0.000 0.004 0.000 0.008
#> GSM152050 1 0.3636 -0.1580 0.676 0.000 0.000 0.004 0.000 0.320
#> GSM152052 1 0.3088 0.4985 0.832 0.000 0.120 0.000 0.000 0.048
#> GSM152056 1 0.0692 0.4971 0.976 0.000 0.000 0.004 0.000 0.020
#> GSM152060 6 0.6095 0.6619 0.380 0.000 0.000 0.152 0.020 0.448
#> GSM152065 5 0.4836 0.5619 0.088 0.000 0.080 0.000 0.736 0.096
#> GSM152066 1 0.0790 0.4917 0.968 0.000 0.000 0.000 0.000 0.032
#> GSM152069 3 0.5930 0.3903 0.004 0.024 0.628 0.016 0.172 0.156
#> GSM152070 5 0.4556 0.5708 0.036 0.004 0.004 0.000 0.636 0.320
#> GSM152071 3 0.5930 0.3903 0.004 0.024 0.628 0.016 0.172 0.156
#> GSM152072 5 0.3840 0.6107 0.008 0.000 0.076 0.004 0.796 0.116
#> GSM152073 6 0.4466 0.4056 0.476 0.004 0.000 0.000 0.020 0.500
#> GSM152078 1 0.5303 0.4285 0.664 0.004 0.140 0.000 0.020 0.172
#> GSM152082 5 0.5563 0.4951 0.080 0.004 0.016 0.000 0.524 0.376
#> GSM152086 1 0.3052 0.1516 0.780 0.000 0.000 0.004 0.000 0.216
#> GSM152090 1 0.4892 0.3786 0.644 0.000 0.280 0.004 0.008 0.064
#> GSM152092 1 0.6227 0.2798 0.560 0.004 0.060 0.000 0.116 0.260
#> GSM152093 1 0.2112 0.4970 0.916 0.000 0.036 0.020 0.000 0.028
#> GSM152094 1 0.3966 -0.4006 0.552 0.000 0.000 0.000 0.004 0.444
#> GSM152098 5 0.5232 0.4943 0.076 0.004 0.004 0.000 0.548 0.368
#> GSM152110 1 0.1320 0.4875 0.948 0.000 0.000 0.016 0.000 0.036
#> GSM152031 1 0.4553 0.4507 0.720 0.004 0.104 0.000 0.004 0.168
#> GSM152037 1 0.0146 0.5066 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM152055 6 0.6250 0.6098 0.396 0.000 0.000 0.180 0.020 0.404
#> GSM152061 6 0.6095 0.6619 0.380 0.000 0.000 0.152 0.020 0.448
#> GSM152064 6 0.6103 0.6296 0.400 0.000 0.000 0.164 0.016 0.420
#> GSM152087 1 0.4253 -0.4365 0.524 0.000 0.000 0.000 0.016 0.460
#> GSM152103 1 0.5109 0.3850 0.608 0.000 0.308 0.004 0.008 0.072
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 specimen(p) k
#> CV:kmeans 66 1.08e-08 2
#> CV:kmeans 67 5.25e-05 3
#> CV:kmeans 79 2.94e-06 4
#> CV:kmeans 64 1.32e-06 5
#> CV:kmeans 46 1.40e-03 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "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 10612 rows and 88 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.959 0.983 0.5053 0.495 0.495
#> 3 3 0.746 0.851 0.920 0.3182 0.742 0.524
#> 4 4 0.647 0.744 0.849 0.1161 0.878 0.659
#> 5 5 0.690 0.590 0.766 0.0795 0.857 0.525
#> 6 6 0.715 0.603 0.768 0.0404 0.920 0.633
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
#> GSM152032 2 0.0000 0.991 0.000 1.000
#> GSM152033 2 0.1633 0.968 0.024 0.976
#> GSM152063 2 0.0000 0.991 0.000 1.000
#> GSM152074 2 0.0000 0.991 0.000 1.000
#> GSM152080 2 0.0000 0.991 0.000 1.000
#> GSM152081 2 0.0000 0.991 0.000 1.000
#> GSM152083 2 0.0000 0.991 0.000 1.000
#> GSM152091 2 0.0000 0.991 0.000 1.000
#> GSM152108 2 0.0000 0.991 0.000 1.000
#> GSM152114 1 0.8763 0.595 0.704 0.296
#> GSM152035 2 0.0000 0.991 0.000 1.000
#> GSM152039 2 0.0000 0.991 0.000 1.000
#> GSM152041 1 0.9491 0.438 0.632 0.368
#> GSM152044 2 0.0000 0.991 0.000 1.000
#> GSM152045 2 0.9286 0.461 0.344 0.656
#> GSM152051 2 0.0000 0.991 0.000 1.000
#> GSM152054 2 0.0000 0.991 0.000 1.000
#> GSM152057 2 0.0000 0.991 0.000 1.000
#> GSM152058 1 0.0000 0.973 1.000 0.000
#> GSM152067 2 0.0000 0.991 0.000 1.000
#> GSM152068 2 0.0000 0.991 0.000 1.000
#> GSM152075 2 0.0000 0.991 0.000 1.000
#> GSM152076 2 0.0000 0.991 0.000 1.000
#> GSM152079 2 0.0000 0.991 0.000 1.000
#> GSM152084 2 0.0000 0.991 0.000 1.000
#> GSM152089 2 0.0000 0.991 0.000 1.000
#> GSM152095 2 0.0000 0.991 0.000 1.000
#> GSM152096 2 0.0000 0.991 0.000 1.000
#> GSM152097 2 0.0000 0.991 0.000 1.000
#> GSM152099 2 0.0000 0.991 0.000 1.000
#> GSM152106 2 0.0000 0.991 0.000 1.000
#> GSM152107 2 0.0000 0.991 0.000 1.000
#> GSM152109 2 0.0000 0.991 0.000 1.000
#> GSM152111 1 0.0000 0.973 1.000 0.000
#> GSM152112 2 0.0000 0.991 0.000 1.000
#> GSM152113 2 0.0000 0.991 0.000 1.000
#> GSM152115 2 0.0000 0.991 0.000 1.000
#> GSM152030 2 0.0000 0.991 0.000 1.000
#> GSM152038 1 0.0000 0.973 1.000 0.000
#> GSM152042 2 0.0000 0.991 0.000 1.000
#> GSM152062 2 0.0000 0.991 0.000 1.000
#> GSM152077 1 0.0000 0.973 1.000 0.000
#> GSM152088 2 0.0000 0.991 0.000 1.000
#> GSM152100 2 0.0000 0.991 0.000 1.000
#> GSM152102 2 0.0000 0.991 0.000 1.000
#> GSM152104 2 0.0000 0.991 0.000 1.000
#> GSM152028 1 0.0000 0.973 1.000 0.000
#> GSM152029 1 0.0000 0.973 1.000 0.000
#> GSM152049 1 0.0000 0.973 1.000 0.000
#> GSM152053 2 0.0000 0.991 0.000 1.000
#> GSM152059 1 0.0000 0.973 1.000 0.000
#> GSM152085 1 0.0000 0.973 1.000 0.000
#> GSM152101 2 0.0000 0.991 0.000 1.000
#> GSM152105 1 0.0000 0.973 1.000 0.000
#> GSM152034 1 0.0000 0.973 1.000 0.000
#> GSM152036 2 0.0000 0.991 0.000 1.000
#> GSM152040 1 0.0000 0.973 1.000 0.000
#> GSM152043 1 0.0000 0.973 1.000 0.000
#> GSM152046 1 0.0000 0.973 1.000 0.000
#> GSM152047 1 0.0000 0.973 1.000 0.000
#> GSM152048 1 0.0000 0.973 1.000 0.000
#> GSM152050 1 0.0000 0.973 1.000 0.000
#> GSM152052 1 0.0000 0.973 1.000 0.000
#> GSM152056 1 0.0000 0.973 1.000 0.000
#> GSM152060 1 0.0000 0.973 1.000 0.000
#> GSM152065 1 0.0000 0.973 1.000 0.000
#> GSM152066 1 0.0000 0.973 1.000 0.000
#> GSM152069 2 0.0000 0.991 0.000 1.000
#> GSM152070 1 0.0000 0.973 1.000 0.000
#> GSM152071 2 0.1843 0.963 0.028 0.972
#> GSM152072 1 0.8661 0.599 0.712 0.288
#> GSM152073 1 0.0000 0.973 1.000 0.000
#> GSM152078 1 0.0000 0.973 1.000 0.000
#> GSM152082 1 0.0000 0.973 1.000 0.000
#> GSM152086 1 0.0000 0.973 1.000 0.000
#> GSM152090 1 0.6623 0.789 0.828 0.172
#> GSM152092 1 0.0000 0.973 1.000 0.000
#> GSM152093 1 0.0000 0.973 1.000 0.000
#> GSM152094 1 0.0000 0.973 1.000 0.000
#> GSM152098 1 0.0000 0.973 1.000 0.000
#> GSM152110 1 0.0000 0.973 1.000 0.000
#> GSM152031 1 0.0000 0.973 1.000 0.000
#> GSM152037 1 0.0000 0.973 1.000 0.000
#> GSM152055 1 0.0000 0.973 1.000 0.000
#> GSM152061 1 0.0000 0.973 1.000 0.000
#> GSM152064 1 0.0000 0.973 1.000 0.000
#> GSM152087 1 0.0000 0.973 1.000 0.000
#> GSM152103 1 0.0376 0.969 0.996 0.004
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM152032 3 0.0892 0.827 0.000 0.020 0.980
#> GSM152033 3 0.1529 0.825 0.000 0.040 0.960
#> GSM152063 2 0.0237 0.934 0.000 0.996 0.004
#> GSM152074 3 0.0892 0.827 0.000 0.020 0.980
#> GSM152080 3 0.5363 0.649 0.000 0.276 0.724
#> GSM152081 2 0.4682 0.811 0.004 0.804 0.192
#> GSM152083 3 0.2261 0.814 0.000 0.068 0.932
#> GSM152091 2 0.2066 0.904 0.000 0.940 0.060
#> GSM152108 2 0.1643 0.916 0.000 0.956 0.044
#> GSM152114 1 0.7772 0.573 0.672 0.132 0.196
#> GSM152035 2 0.1964 0.907 0.000 0.944 0.056
#> GSM152039 2 0.1529 0.927 0.000 0.960 0.040
#> GSM152041 2 0.2269 0.922 0.016 0.944 0.040
#> GSM152044 2 0.0237 0.934 0.000 0.996 0.004
#> GSM152045 3 0.4062 0.773 0.164 0.000 0.836
#> GSM152051 2 0.0237 0.934 0.000 0.996 0.004
#> GSM152054 3 0.4178 0.743 0.000 0.172 0.828
#> GSM152057 2 0.0237 0.934 0.000 0.996 0.004
#> GSM152058 1 0.0000 0.957 1.000 0.000 0.000
#> GSM152067 3 0.0237 0.823 0.000 0.004 0.996
#> GSM152068 2 0.0237 0.934 0.000 0.996 0.004
#> GSM152075 2 0.1765 0.926 0.004 0.956 0.040
#> GSM152076 2 0.1529 0.927 0.000 0.960 0.040
#> GSM152079 2 0.0237 0.934 0.000 0.996 0.004
#> GSM152084 3 0.1411 0.809 0.000 0.036 0.964
#> GSM152089 2 0.2959 0.896 0.000 0.900 0.100
#> GSM152095 2 0.1529 0.927 0.000 0.960 0.040
#> GSM152096 3 0.4842 0.710 0.000 0.224 0.776
#> GSM152097 2 0.0237 0.934 0.000 0.996 0.004
#> GSM152099 2 0.0237 0.934 0.000 0.996 0.004
#> GSM152106 2 0.0237 0.934 0.000 0.996 0.004
#> GSM152107 3 0.6008 0.202 0.000 0.372 0.628
#> GSM152109 3 0.1031 0.827 0.000 0.024 0.976
#> GSM152111 1 0.0000 0.957 1.000 0.000 0.000
#> GSM152112 2 0.5678 0.573 0.000 0.684 0.316
#> GSM152113 3 0.1411 0.826 0.000 0.036 0.964
#> GSM152115 3 0.0237 0.823 0.000 0.004 0.996
#> GSM152030 2 0.4733 0.808 0.004 0.800 0.196
#> GSM152038 3 0.0424 0.826 0.008 0.000 0.992
#> GSM152042 2 0.4682 0.811 0.004 0.804 0.192
#> GSM152062 3 0.0237 0.823 0.000 0.004 0.996
#> GSM152077 1 0.2165 0.904 0.936 0.000 0.064
#> GSM152088 2 0.0237 0.934 0.000 0.996 0.004
#> GSM152100 2 0.1529 0.927 0.000 0.960 0.040
#> GSM152102 3 0.4504 0.735 0.000 0.196 0.804
#> GSM152104 2 0.0237 0.934 0.000 0.996 0.004
#> GSM152028 1 0.1289 0.933 0.968 0.000 0.032
#> GSM152029 3 0.6111 0.490 0.396 0.000 0.604
#> GSM152049 1 0.0000 0.957 1.000 0.000 0.000
#> GSM152053 2 0.4733 0.808 0.004 0.800 0.196
#> GSM152059 1 0.0237 0.955 0.996 0.000 0.004
#> GSM152085 1 0.0000 0.957 1.000 0.000 0.000
#> GSM152101 3 0.0237 0.823 0.000 0.004 0.996
#> GSM152105 1 0.2959 0.877 0.900 0.000 0.100
#> GSM152034 1 0.0000 0.957 1.000 0.000 0.000
#> GSM152036 2 0.1765 0.926 0.004 0.956 0.040
#> GSM152040 1 0.4555 0.707 0.800 0.000 0.200
#> GSM152043 1 0.0592 0.950 0.988 0.000 0.012
#> GSM152046 1 0.0000 0.957 1.000 0.000 0.000
#> GSM152047 1 0.0000 0.957 1.000 0.000 0.000
#> GSM152048 1 0.0000 0.957 1.000 0.000 0.000
#> GSM152050 1 0.0000 0.957 1.000 0.000 0.000
#> GSM152052 1 0.0000 0.957 1.000 0.000 0.000
#> GSM152056 1 0.0000 0.957 1.000 0.000 0.000
#> GSM152060 1 0.0000 0.957 1.000 0.000 0.000
#> GSM152065 3 0.4399 0.757 0.188 0.000 0.812
#> GSM152066 1 0.0000 0.957 1.000 0.000 0.000
#> GSM152069 3 0.1529 0.825 0.000 0.040 0.960
#> GSM152070 3 0.5926 0.558 0.356 0.000 0.644
#> GSM152071 3 0.1289 0.827 0.000 0.032 0.968
#> GSM152072 3 0.4452 0.754 0.192 0.000 0.808
#> GSM152073 1 0.0237 0.955 0.996 0.000 0.004
#> GSM152078 3 0.6079 0.502 0.388 0.000 0.612
#> GSM152082 3 0.6062 0.511 0.384 0.000 0.616
#> GSM152086 1 0.0000 0.957 1.000 0.000 0.000
#> GSM152090 1 0.5618 0.746 0.796 0.048 0.156
#> GSM152092 1 0.2959 0.861 0.900 0.000 0.100
#> GSM152093 1 0.0000 0.957 1.000 0.000 0.000
#> GSM152094 1 0.0000 0.957 1.000 0.000 0.000
#> GSM152098 3 0.6062 0.511 0.384 0.000 0.616
#> GSM152110 1 0.0000 0.957 1.000 0.000 0.000
#> GSM152031 1 0.0237 0.955 0.996 0.000 0.004
#> GSM152037 1 0.0000 0.957 1.000 0.000 0.000
#> GSM152055 1 0.0000 0.957 1.000 0.000 0.000
#> GSM152061 1 0.0000 0.957 1.000 0.000 0.000
#> GSM152064 1 0.0000 0.957 1.000 0.000 0.000
#> GSM152087 1 0.0000 0.957 1.000 0.000 0.000
#> GSM152103 1 0.4921 0.767 0.816 0.020 0.164
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM152032 3 0.1042 0.7735 0.000 0.020 0.972 0.008
#> GSM152033 3 0.3768 0.7395 0.008 0.120 0.848 0.024
#> GSM152063 2 0.0817 0.9399 0.000 0.976 0.000 0.024
#> GSM152074 3 0.0927 0.7746 0.000 0.016 0.976 0.008
#> GSM152080 2 0.2334 0.8833 0.000 0.908 0.088 0.004
#> GSM152081 4 0.5339 0.8198 0.000 0.100 0.156 0.744
#> GSM152083 2 0.2737 0.8703 0.000 0.888 0.104 0.008
#> GSM152091 2 0.1635 0.9181 0.000 0.948 0.044 0.008
#> GSM152108 2 0.2616 0.9136 0.036 0.920 0.016 0.028
#> GSM152114 4 0.6992 0.5684 0.248 0.000 0.176 0.576
#> GSM152035 2 0.1820 0.9292 0.000 0.944 0.036 0.020
#> GSM152039 4 0.2469 0.8615 0.000 0.108 0.000 0.892
#> GSM152041 4 0.2408 0.8608 0.000 0.104 0.000 0.896
#> GSM152044 2 0.0817 0.9399 0.000 0.976 0.000 0.024
#> GSM152045 3 0.3873 0.6745 0.000 0.000 0.772 0.228
#> GSM152051 2 0.0707 0.9415 0.000 0.980 0.000 0.020
#> GSM152054 3 0.5228 0.6902 0.000 0.120 0.756 0.124
#> GSM152057 2 0.0707 0.9415 0.000 0.980 0.000 0.020
#> GSM152058 1 0.0188 0.8195 0.996 0.000 0.000 0.004
#> GSM152067 3 0.1488 0.7731 0.000 0.012 0.956 0.032
#> GSM152068 2 0.0707 0.9415 0.000 0.980 0.000 0.020
#> GSM152075 4 0.2469 0.8615 0.000 0.108 0.000 0.892
#> GSM152076 4 0.2469 0.8615 0.000 0.108 0.000 0.892
#> GSM152079 2 0.0592 0.9412 0.000 0.984 0.000 0.016
#> GSM152084 3 0.6102 -0.3262 0.012 0.024 0.492 0.472
#> GSM152089 4 0.2282 0.8151 0.000 0.052 0.024 0.924
#> GSM152095 4 0.2469 0.8615 0.000 0.108 0.000 0.892
#> GSM152096 2 0.2466 0.8763 0.000 0.900 0.096 0.004
#> GSM152097 2 0.0817 0.9399 0.000 0.976 0.000 0.024
#> GSM152099 2 0.0707 0.9415 0.000 0.980 0.000 0.020
#> GSM152106 2 0.0817 0.9399 0.000 0.976 0.000 0.024
#> GSM152107 4 0.5793 0.5309 0.000 0.036 0.384 0.580
#> GSM152109 3 0.1004 0.7746 0.000 0.024 0.972 0.004
#> GSM152111 1 0.0469 0.8204 0.988 0.000 0.000 0.012
#> GSM152112 4 0.4104 0.7332 0.000 0.028 0.164 0.808
#> GSM152113 3 0.2861 0.7561 0.004 0.092 0.892 0.012
#> GSM152115 3 0.1576 0.7683 0.000 0.004 0.948 0.048
#> GSM152030 4 0.5369 0.8145 0.000 0.096 0.164 0.740
#> GSM152038 3 0.0469 0.7775 0.000 0.000 0.988 0.012
#> GSM152042 4 0.5427 0.8150 0.000 0.100 0.164 0.736
#> GSM152062 3 0.1174 0.7720 0.000 0.020 0.968 0.012
#> GSM152077 1 0.2131 0.8028 0.932 0.000 0.036 0.032
#> GSM152088 2 0.0000 0.9370 0.000 1.000 0.000 0.000
#> GSM152100 4 0.2469 0.8615 0.000 0.108 0.000 0.892
#> GSM152102 2 0.4574 0.7140 0.000 0.756 0.220 0.024
#> GSM152104 2 0.0817 0.9399 0.000 0.976 0.000 0.024
#> GSM152028 1 0.5543 0.2456 0.612 0.000 0.360 0.028
#> GSM152029 3 0.6521 0.6021 0.256 0.020 0.648 0.076
#> GSM152049 1 0.0469 0.8204 0.988 0.000 0.000 0.012
#> GSM152053 4 0.5412 0.8133 0.000 0.096 0.168 0.736
#> GSM152059 1 0.2053 0.8098 0.924 0.000 0.004 0.072
#> GSM152085 1 0.1867 0.8127 0.928 0.000 0.000 0.072
#> GSM152101 3 0.1489 0.7700 0.000 0.004 0.952 0.044
#> GSM152105 1 0.5355 0.3097 0.620 0.000 0.360 0.020
#> GSM152034 1 0.4454 0.6642 0.692 0.000 0.000 0.308
#> GSM152036 4 0.2408 0.8608 0.000 0.104 0.000 0.896
#> GSM152040 3 0.6875 0.2917 0.388 0.000 0.504 0.108
#> GSM152043 1 0.5850 0.5239 0.676 0.000 0.244 0.080
#> GSM152046 1 0.4406 0.6728 0.700 0.000 0.000 0.300
#> GSM152047 1 0.5489 0.7071 0.700 0.000 0.060 0.240
#> GSM152048 1 0.0188 0.8195 0.996 0.000 0.000 0.004
#> GSM152050 1 0.1118 0.8214 0.964 0.000 0.000 0.036
#> GSM152052 1 0.1396 0.8099 0.960 0.004 0.032 0.004
#> GSM152056 1 0.0188 0.8195 0.996 0.000 0.000 0.004
#> GSM152060 1 0.4454 0.6642 0.692 0.000 0.000 0.308
#> GSM152065 3 0.4290 0.7355 0.164 0.000 0.800 0.036
#> GSM152066 1 0.0188 0.8195 0.996 0.000 0.000 0.004
#> GSM152069 3 0.1109 0.7746 0.000 0.028 0.968 0.004
#> GSM152070 3 0.6167 0.6060 0.256 0.000 0.648 0.096
#> GSM152071 3 0.1004 0.7746 0.000 0.024 0.972 0.004
#> GSM152072 3 0.4152 0.7386 0.160 0.000 0.808 0.032
#> GSM152073 1 0.2329 0.8074 0.916 0.000 0.012 0.072
#> GSM152078 3 0.5751 0.5053 0.352 0.012 0.616 0.020
#> GSM152082 3 0.6167 0.6060 0.256 0.000 0.648 0.096
#> GSM152086 1 0.0000 0.8195 1.000 0.000 0.000 0.000
#> GSM152090 1 0.6094 0.5929 0.692 0.084 0.212 0.012
#> GSM152092 1 0.6537 -0.0611 0.500 0.000 0.424 0.076
#> GSM152093 1 0.1174 0.8151 0.968 0.000 0.012 0.020
#> GSM152094 1 0.1637 0.8135 0.940 0.000 0.000 0.060
#> GSM152098 3 0.6219 0.5938 0.264 0.000 0.640 0.096
#> GSM152110 1 0.1211 0.8181 0.960 0.000 0.000 0.040
#> GSM152031 1 0.4406 0.6420 0.780 0.000 0.192 0.028
#> GSM152037 1 0.0188 0.8195 0.996 0.000 0.000 0.004
#> GSM152055 1 0.4356 0.6559 0.708 0.000 0.000 0.292
#> GSM152061 1 0.4477 0.6597 0.688 0.000 0.000 0.312
#> GSM152064 1 0.4776 0.5611 0.624 0.000 0.000 0.376
#> GSM152087 1 0.1637 0.8135 0.940 0.000 0.000 0.060
#> GSM152103 1 0.4822 0.6529 0.756 0.024 0.212 0.008
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM152032 3 0.1697 0.66990 0.060 0.008 0.932 0.000 0.000
#> GSM152033 3 0.4645 0.60366 0.376 0.008 0.608 0.008 0.000
#> GSM152063 2 0.0404 0.95586 0.000 0.988 0.000 0.012 0.000
#> GSM152074 3 0.2286 0.67982 0.108 0.004 0.888 0.000 0.000
#> GSM152080 2 0.0609 0.94164 0.000 0.980 0.020 0.000 0.000
#> GSM152081 4 0.2894 0.83014 0.008 0.008 0.124 0.860 0.000
#> GSM152083 2 0.1851 0.89113 0.000 0.912 0.088 0.000 0.000
#> GSM152091 2 0.0000 0.95184 0.000 1.000 0.000 0.000 0.000
#> GSM152108 2 0.1732 0.90233 0.080 0.920 0.000 0.000 0.000
#> GSM152114 1 0.7047 0.38673 0.508 0.000 0.052 0.300 0.140
#> GSM152035 2 0.0290 0.95474 0.000 0.992 0.000 0.008 0.000
#> GSM152039 4 0.0290 0.87423 0.000 0.008 0.000 0.992 0.000
#> GSM152041 4 0.0290 0.87423 0.000 0.008 0.000 0.992 0.000
#> GSM152044 2 0.0404 0.95586 0.000 0.988 0.000 0.012 0.000
#> GSM152045 3 0.7419 0.50028 0.296 0.004 0.496 0.116 0.088
#> GSM152051 2 0.0404 0.95586 0.000 0.988 0.000 0.012 0.000
#> GSM152054 3 0.7338 0.56400 0.288 0.080 0.516 0.108 0.008
#> GSM152057 2 0.0404 0.95586 0.000 0.988 0.000 0.012 0.000
#> GSM152058 1 0.4242 0.59158 0.572 0.000 0.000 0.000 0.428
#> GSM152067 3 0.3205 0.67509 0.176 0.004 0.816 0.004 0.000
#> GSM152068 2 0.0404 0.95586 0.000 0.988 0.000 0.012 0.000
#> GSM152075 4 0.0290 0.87423 0.000 0.008 0.000 0.992 0.000
#> GSM152076 4 0.0290 0.87423 0.000 0.008 0.000 0.992 0.000
#> GSM152079 2 0.0404 0.95586 0.000 0.988 0.000 0.012 0.000
#> GSM152084 3 0.5592 0.20145 0.084 0.004 0.600 0.312 0.000
#> GSM152089 4 0.4237 0.74669 0.076 0.012 0.052 0.824 0.036
#> GSM152095 4 0.0290 0.87423 0.000 0.008 0.000 0.992 0.000
#> GSM152096 2 0.1478 0.91371 0.000 0.936 0.064 0.000 0.000
#> GSM152097 2 0.0703 0.95037 0.000 0.976 0.000 0.024 0.000
#> GSM152099 2 0.0404 0.95586 0.000 0.988 0.000 0.012 0.000
#> GSM152106 2 0.0963 0.94290 0.000 0.964 0.000 0.036 0.000
#> GSM152107 4 0.4640 0.42661 0.016 0.000 0.400 0.584 0.000
#> GSM152109 3 0.0451 0.68298 0.004 0.008 0.988 0.000 0.000
#> GSM152111 5 0.3607 0.16622 0.244 0.000 0.000 0.004 0.752
#> GSM152112 4 0.5070 0.58430 0.124 0.004 0.160 0.712 0.000
#> GSM152113 3 0.4462 0.60876 0.308 0.016 0.672 0.004 0.000
#> GSM152115 3 0.4527 0.65261 0.272 0.004 0.696 0.028 0.000
#> GSM152030 4 0.3556 0.81283 0.032 0.008 0.132 0.828 0.000
#> GSM152038 3 0.3231 0.66847 0.196 0.000 0.800 0.004 0.000
#> GSM152042 4 0.3053 0.82646 0.012 0.008 0.128 0.852 0.000
#> GSM152062 3 0.1831 0.66835 0.076 0.004 0.920 0.000 0.000
#> GSM152077 1 0.4506 0.59617 0.676 0.000 0.028 0.000 0.296
#> GSM152088 2 0.0162 0.95332 0.000 0.996 0.000 0.004 0.000
#> GSM152100 4 0.0290 0.87423 0.000 0.008 0.000 0.992 0.000
#> GSM152102 2 0.6028 0.40325 0.192 0.612 0.188 0.008 0.000
#> GSM152104 2 0.0510 0.95435 0.000 0.984 0.000 0.016 0.000
#> GSM152028 1 0.3622 0.43990 0.820 0.000 0.056 0.000 0.124
#> GSM152029 5 0.6149 0.29796 0.116 0.008 0.340 0.000 0.536
#> GSM152049 5 0.3837 -0.02404 0.308 0.000 0.000 0.000 0.692
#> GSM152053 4 0.3336 0.81372 0.016 0.008 0.144 0.832 0.000
#> GSM152059 5 0.2540 0.54837 0.088 0.000 0.024 0.000 0.888
#> GSM152085 5 0.0510 0.54107 0.016 0.000 0.000 0.000 0.984
#> GSM152101 3 0.4244 0.65638 0.268 0.004 0.712 0.016 0.000
#> GSM152105 1 0.4618 0.46817 0.724 0.000 0.208 0.000 0.068
#> GSM152034 5 0.2127 0.55587 0.000 0.000 0.000 0.108 0.892
#> GSM152036 4 0.0290 0.87423 0.000 0.008 0.000 0.992 0.000
#> GSM152040 5 0.5855 0.38809 0.356 0.000 0.084 0.008 0.552
#> GSM152043 5 0.4820 0.48490 0.240 0.000 0.056 0.004 0.700
#> GSM152046 5 0.2068 0.55802 0.004 0.000 0.000 0.092 0.904
#> GSM152047 5 0.4805 0.49525 0.268 0.000 0.032 0.012 0.688
#> GSM152048 1 0.4242 0.59158 0.572 0.000 0.000 0.000 0.428
#> GSM152050 5 0.3455 0.26145 0.208 0.000 0.000 0.008 0.784
#> GSM152052 1 0.5831 0.57768 0.604 0.000 0.160 0.000 0.236
#> GSM152056 1 0.4249 0.58778 0.568 0.000 0.000 0.000 0.432
#> GSM152060 5 0.2513 0.54916 0.008 0.000 0.000 0.116 0.876
#> GSM152065 3 0.5159 0.54329 0.472 0.000 0.496 0.008 0.024
#> GSM152066 1 0.4287 0.55718 0.540 0.000 0.000 0.000 0.460
#> GSM152069 3 0.0451 0.68298 0.004 0.008 0.988 0.000 0.000
#> GSM152070 5 0.6884 0.13542 0.348 0.000 0.228 0.008 0.416
#> GSM152071 3 0.0693 0.68225 0.012 0.008 0.980 0.000 0.000
#> GSM152072 3 0.6158 0.53850 0.348 0.004 0.540 0.008 0.100
#> GSM152073 5 0.2674 0.54633 0.140 0.000 0.004 0.000 0.856
#> GSM152078 1 0.6264 -0.01400 0.460 0.004 0.408 0.000 0.128
#> GSM152082 5 0.7017 -0.00476 0.352 0.000 0.276 0.008 0.364
#> GSM152086 5 0.4171 -0.31434 0.396 0.000 0.000 0.000 0.604
#> GSM152090 3 0.7186 -0.37775 0.344 0.020 0.392 0.000 0.244
#> GSM152092 1 0.6017 -0.04709 0.572 0.000 0.132 0.004 0.292
#> GSM152093 1 0.5075 0.53971 0.512 0.000 0.020 0.008 0.460
#> GSM152094 5 0.0703 0.54694 0.024 0.000 0.000 0.000 0.976
#> GSM152098 5 0.6630 0.25418 0.336 0.000 0.180 0.008 0.476
#> GSM152110 1 0.4656 0.50622 0.508 0.000 0.000 0.012 0.480
#> GSM152031 1 0.5610 0.46025 0.640 0.000 0.180 0.000 0.180
#> GSM152037 1 0.4242 0.59158 0.572 0.000 0.000 0.000 0.428
#> GSM152055 5 0.5237 0.33350 0.160 0.000 0.000 0.156 0.684
#> GSM152061 5 0.2513 0.54916 0.008 0.000 0.000 0.116 0.876
#> GSM152064 5 0.4170 0.46168 0.048 0.000 0.000 0.192 0.760
#> GSM152087 5 0.0609 0.55392 0.020 0.000 0.000 0.000 0.980
#> GSM152103 3 0.6772 -0.32274 0.404 0.016 0.420 0.000 0.160
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM152032 3 0.3073 0.582358 0.080 0.000 0.840 0.000 0.080 0.000
#> GSM152033 5 0.6481 0.000908 0.272 0.008 0.312 0.000 0.400 0.008
#> GSM152063 2 0.0000 0.947720 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152074 3 0.4965 0.489954 0.156 0.000 0.664 0.004 0.176 0.000
#> GSM152080 2 0.1610 0.895450 0.000 0.916 0.084 0.000 0.000 0.000
#> GSM152081 4 0.3601 0.767874 0.016 0.004 0.084 0.824 0.072 0.000
#> GSM152083 2 0.3534 0.698133 0.016 0.740 0.244 0.000 0.000 0.000
#> GSM152091 2 0.0260 0.945342 0.000 0.992 0.008 0.000 0.000 0.000
#> GSM152108 2 0.3989 0.770913 0.128 0.788 0.052 0.000 0.032 0.000
#> GSM152114 1 0.5313 0.405275 0.640 0.000 0.048 0.268 0.020 0.024
#> GSM152035 2 0.0653 0.939905 0.004 0.980 0.012 0.000 0.004 0.000
#> GSM152039 4 0.0291 0.824956 0.000 0.004 0.000 0.992 0.000 0.004
#> GSM152041 4 0.0291 0.824956 0.000 0.004 0.000 0.992 0.000 0.004
#> GSM152044 2 0.0000 0.947720 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152045 5 0.4486 0.533124 0.000 0.000 0.068 0.092 0.764 0.076
#> GSM152051 2 0.0000 0.947720 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152054 5 0.4357 0.508259 0.000 0.040 0.088 0.104 0.768 0.000
#> GSM152057 2 0.0000 0.947720 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152058 1 0.3023 0.647811 0.768 0.000 0.000 0.000 0.000 0.232
#> GSM152067 5 0.4083 0.103140 0.000 0.000 0.460 0.008 0.532 0.000
#> GSM152068 2 0.0000 0.947720 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152075 4 0.0582 0.824008 0.004 0.004 0.004 0.984 0.000 0.004
#> GSM152076 4 0.0291 0.824956 0.000 0.004 0.000 0.992 0.000 0.004
#> GSM152079 2 0.0000 0.947720 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152084 3 0.5666 0.460390 0.084 0.000 0.640 0.196 0.080 0.000
#> GSM152089 4 0.5326 0.328243 0.000 0.008 0.012 0.572 0.344 0.064
#> GSM152095 4 0.0291 0.824956 0.000 0.004 0.000 0.992 0.000 0.004
#> GSM152096 2 0.3110 0.774363 0.012 0.792 0.196 0.000 0.000 0.000
#> GSM152097 2 0.0547 0.937802 0.000 0.980 0.000 0.020 0.000 0.000
#> GSM152099 2 0.0000 0.947720 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152106 2 0.0547 0.937324 0.000 0.980 0.000 0.020 0.000 0.000
#> GSM152107 4 0.5961 0.361779 0.016 0.000 0.284 0.524 0.176 0.000
#> GSM152109 3 0.1957 0.562263 0.000 0.000 0.888 0.000 0.112 0.000
#> GSM152111 6 0.3714 0.532627 0.264 0.000 0.008 0.000 0.008 0.720
#> GSM152112 4 0.4508 0.305663 0.000 0.000 0.036 0.568 0.396 0.000
#> GSM152113 3 0.6282 0.214820 0.272 0.012 0.436 0.000 0.280 0.000
#> GSM152115 5 0.3450 0.418536 0.008 0.000 0.208 0.012 0.772 0.000
#> GSM152030 4 0.4122 0.748709 0.032 0.004 0.092 0.792 0.080 0.000
#> GSM152038 3 0.5843 0.313759 0.220 0.000 0.516 0.000 0.260 0.004
#> GSM152042 4 0.3786 0.761378 0.020 0.004 0.092 0.812 0.072 0.000
#> GSM152062 3 0.3976 0.573984 0.088 0.000 0.776 0.008 0.128 0.000
#> GSM152077 1 0.2620 0.556579 0.888 0.000 0.052 0.000 0.028 0.032
#> GSM152088 2 0.0146 0.946216 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM152100 4 0.0551 0.822401 0.000 0.008 0.000 0.984 0.004 0.004
#> GSM152102 5 0.4740 0.176429 0.004 0.412 0.032 0.004 0.548 0.000
#> GSM152104 2 0.0000 0.947720 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152028 1 0.5077 0.289303 0.660 0.000 0.068 0.000 0.240 0.032
#> GSM152029 3 0.6348 0.112118 0.024 0.000 0.452 0.000 0.204 0.320
#> GSM152049 6 0.3938 0.415759 0.324 0.000 0.000 0.000 0.016 0.660
#> GSM152053 4 0.3737 0.764082 0.020 0.004 0.088 0.816 0.072 0.000
#> GSM152059 6 0.4376 0.664135 0.100 0.000 0.028 0.000 0.112 0.760
#> GSM152085 6 0.1152 0.769476 0.044 0.000 0.000 0.000 0.004 0.952
#> GSM152101 5 0.3311 0.427265 0.004 0.000 0.204 0.012 0.780 0.000
#> GSM152105 1 0.4473 0.366883 0.740 0.000 0.160 0.000 0.076 0.024
#> GSM152034 6 0.1080 0.774977 0.004 0.000 0.000 0.032 0.004 0.960
#> GSM152036 4 0.0405 0.823713 0.000 0.004 0.000 0.988 0.000 0.008
#> GSM152040 5 0.4465 0.405361 0.036 0.000 0.000 0.004 0.628 0.332
#> GSM152043 6 0.5464 0.426389 0.120 0.000 0.020 0.000 0.248 0.612
#> GSM152046 6 0.1194 0.775118 0.008 0.000 0.000 0.032 0.004 0.956
#> GSM152047 6 0.4011 0.543316 0.028 0.000 0.000 0.012 0.228 0.732
#> GSM152048 1 0.3163 0.648278 0.764 0.000 0.000 0.000 0.004 0.232
#> GSM152050 6 0.3043 0.646119 0.196 0.000 0.004 0.000 0.004 0.796
#> GSM152052 1 0.3434 0.583886 0.808 0.000 0.140 0.000 0.004 0.048
#> GSM152056 1 0.3076 0.642381 0.760 0.000 0.000 0.000 0.000 0.240
#> GSM152060 6 0.1370 0.774317 0.012 0.000 0.000 0.036 0.004 0.948
#> GSM152065 5 0.4913 0.448991 0.180 0.000 0.124 0.000 0.684 0.012
#> GSM152066 1 0.3360 0.618408 0.732 0.000 0.000 0.000 0.004 0.264
#> GSM152069 3 0.2092 0.560992 0.000 0.000 0.876 0.000 0.124 0.000
#> GSM152070 5 0.4150 0.522403 0.036 0.000 0.012 0.000 0.724 0.228
#> GSM152071 3 0.1957 0.568328 0.000 0.000 0.888 0.000 0.112 0.000
#> GSM152072 5 0.3612 0.524174 0.016 0.000 0.148 0.000 0.800 0.036
#> GSM152073 6 0.4586 0.618089 0.104 0.000 0.008 0.000 0.176 0.712
#> GSM152078 1 0.6760 -0.129160 0.380 0.000 0.320 0.000 0.260 0.040
#> GSM152082 5 0.6287 0.441770 0.188 0.000 0.052 0.000 0.548 0.212
#> GSM152086 1 0.4332 0.338117 0.564 0.000 0.004 0.000 0.016 0.416
#> GSM152090 3 0.5322 0.249123 0.308 0.004 0.604 0.004 0.016 0.064
#> GSM152092 5 0.6757 0.236208 0.380 0.000 0.064 0.000 0.388 0.168
#> GSM152093 1 0.4952 0.599558 0.672 0.000 0.036 0.028 0.012 0.252
#> GSM152094 6 0.2333 0.757812 0.060 0.000 0.004 0.000 0.040 0.896
#> GSM152098 5 0.5361 0.438376 0.072 0.000 0.032 0.000 0.608 0.288
#> GSM152110 1 0.3996 0.513456 0.636 0.000 0.000 0.008 0.004 0.352
#> GSM152031 1 0.5836 0.309821 0.624 0.000 0.188 0.000 0.120 0.068
#> GSM152037 1 0.3023 0.647525 0.768 0.000 0.000 0.000 0.000 0.232
#> GSM152055 6 0.4165 0.618721 0.160 0.000 0.000 0.100 0.000 0.740
#> GSM152061 6 0.1370 0.774317 0.012 0.000 0.000 0.036 0.004 0.948
#> GSM152064 6 0.3325 0.703957 0.084 0.000 0.000 0.096 0.000 0.820
#> GSM152087 6 0.1924 0.763020 0.028 0.000 0.004 0.000 0.048 0.920
#> GSM152103 3 0.4743 0.336124 0.292 0.000 0.648 0.000 0.024 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 specimen(p) k
#> CV:skmeans 86 5.07e-10 2
#> CV:skmeans 86 9.26e-07 3
#> CV:skmeans 83 7.32e-06 4
#> CV:skmeans 64 8.16e-04 5
#> CV:skmeans 60 2.60e-03 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "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 10612 rows and 88 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 0.469 0.569 0.816 0.4927 0.495 0.495
#> 3 3 0.438 0.568 0.812 0.2664 0.581 0.348
#> 4 4 0.710 0.836 0.894 0.1536 0.862 0.650
#> 5 5 0.656 0.550 0.742 0.0765 0.910 0.708
#> 6 6 0.782 0.802 0.868 0.0592 0.844 0.457
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
#> GSM152032 2 0.1843 0.716 0.028 0.972
#> GSM152033 1 0.6973 0.649 0.812 0.188
#> GSM152063 2 0.2778 0.723 0.048 0.952
#> GSM152074 2 0.9000 0.264 0.316 0.684
#> GSM152080 2 0.9686 0.444 0.396 0.604
#> GSM152081 2 0.3733 0.723 0.072 0.928
#> GSM152083 2 0.0000 0.712 0.000 1.000
#> GSM152091 2 0.9635 0.486 0.388 0.612
#> GSM152108 1 0.0672 0.769 0.992 0.008
#> GSM152114 1 0.0000 0.774 1.000 0.000
#> GSM152035 2 0.1184 0.717 0.016 0.984
#> GSM152039 2 0.4022 0.722 0.080 0.920
#> GSM152041 1 0.9993 -0.352 0.516 0.484
#> GSM152044 2 0.2778 0.723 0.048 0.952
#> GSM152045 1 0.9044 0.492 0.680 0.320
#> GSM152051 2 0.4022 0.723 0.080 0.920
#> GSM152054 1 0.3431 0.758 0.936 0.064
#> GSM152057 2 0.2778 0.723 0.048 0.952
#> GSM152058 1 0.0000 0.774 1.000 0.000
#> GSM152067 2 0.1843 0.716 0.028 0.972
#> GSM152068 2 0.2778 0.723 0.048 0.952
#> GSM152075 1 0.9795 0.295 0.584 0.416
#> GSM152076 2 0.3733 0.724 0.072 0.928
#> GSM152079 2 0.2778 0.723 0.048 0.952
#> GSM152084 1 0.9998 0.240 0.508 0.492
#> GSM152089 2 0.9998 0.371 0.492 0.508
#> GSM152095 2 0.3879 0.723 0.076 0.924
#> GSM152096 2 0.9754 0.435 0.408 0.592
#> GSM152097 2 0.2778 0.723 0.048 0.952
#> GSM152099 2 0.0000 0.712 0.000 1.000
#> GSM152106 2 0.2778 0.723 0.048 0.952
#> GSM152107 2 0.1843 0.716 0.028 0.972
#> GSM152109 2 0.1843 0.716 0.028 0.972
#> GSM152111 1 0.9881 -0.234 0.564 0.436
#> GSM152112 1 0.9988 0.263 0.520 0.480
#> GSM152113 1 0.3431 0.759 0.936 0.064
#> GSM152115 1 0.9993 0.256 0.516 0.484
#> GSM152030 1 0.9815 0.285 0.580 0.420
#> GSM152038 1 0.9970 0.280 0.532 0.468
#> GSM152042 2 0.1843 0.716 0.028 0.972
#> GSM152062 2 0.9998 -0.242 0.492 0.508
#> GSM152077 1 0.0000 0.774 1.000 0.000
#> GSM152088 2 0.9661 0.499 0.392 0.608
#> GSM152100 1 0.9795 0.302 0.584 0.416
#> GSM152102 2 0.7815 0.588 0.232 0.768
#> GSM152104 2 0.3431 0.725 0.064 0.936
#> GSM152028 1 0.2778 0.762 0.952 0.048
#> GSM152029 2 0.9833 0.419 0.424 0.576
#> GSM152049 1 0.1184 0.764 0.984 0.016
#> GSM152053 1 0.9996 0.249 0.512 0.488
#> GSM152059 2 0.9977 0.329 0.472 0.528
#> GSM152085 1 0.0000 0.774 1.000 0.000
#> GSM152101 2 0.0000 0.712 0.000 1.000
#> GSM152105 1 0.2778 0.762 0.952 0.048
#> GSM152034 2 0.9833 0.479 0.424 0.576
#> GSM152036 2 0.3879 0.723 0.076 0.924
#> GSM152040 1 0.2603 0.763 0.956 0.044
#> GSM152043 1 0.3431 0.758 0.936 0.064
#> GSM152046 1 1.0000 -0.376 0.504 0.496
#> GSM152047 2 0.9998 0.371 0.492 0.508
#> GSM152048 1 0.0000 0.774 1.000 0.000
#> GSM152050 1 0.9044 0.163 0.680 0.320
#> GSM152052 1 0.9996 -0.360 0.512 0.488
#> GSM152056 1 0.0000 0.774 1.000 0.000
#> GSM152060 1 0.0000 0.774 1.000 0.000
#> GSM152065 1 0.3879 0.752 0.924 0.076
#> GSM152066 1 0.0000 0.774 1.000 0.000
#> GSM152069 2 0.6048 0.674 0.148 0.852
#> GSM152070 1 0.3431 0.758 0.936 0.064
#> GSM152071 2 0.9522 0.490 0.372 0.628
#> GSM152072 2 0.9850 0.413 0.428 0.572
#> GSM152073 1 0.0000 0.774 1.000 0.000
#> GSM152078 2 0.9896 0.391 0.440 0.560
#> GSM152082 1 0.2778 0.762 0.952 0.048
#> GSM152086 1 0.0000 0.774 1.000 0.000
#> GSM152090 2 0.9977 0.410 0.472 0.528
#> GSM152092 1 0.2778 0.762 0.952 0.048
#> GSM152093 2 1.0000 0.356 0.500 0.500
#> GSM152094 1 0.0000 0.774 1.000 0.000
#> GSM152098 1 0.3733 0.755 0.928 0.072
#> GSM152110 1 0.0000 0.774 1.000 0.000
#> GSM152031 1 0.3114 0.761 0.944 0.056
#> GSM152037 1 0.0000 0.774 1.000 0.000
#> GSM152055 1 0.0000 0.774 1.000 0.000
#> GSM152061 1 0.0000 0.774 1.000 0.000
#> GSM152064 1 0.0000 0.774 1.000 0.000
#> GSM152087 1 0.0000 0.774 1.000 0.000
#> GSM152103 2 0.9977 0.410 0.472 0.528
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM152032 3 0.3340 0.58372 0.000 0.120 0.880
#> GSM152033 3 0.5859 0.51271 0.344 0.000 0.656
#> GSM152063 2 0.0237 0.91399 0.000 0.996 0.004
#> GSM152074 3 0.0237 0.59262 0.000 0.004 0.996
#> GSM152080 2 0.0000 0.91629 0.000 1.000 0.000
#> GSM152081 1 0.6521 0.16875 0.504 0.004 0.492
#> GSM152083 3 0.6302 0.15040 0.000 0.480 0.520
#> GSM152091 2 0.0000 0.91629 0.000 1.000 0.000
#> GSM152108 1 0.4692 0.59770 0.820 0.012 0.168
#> GSM152114 1 0.0000 0.77239 1.000 0.000 0.000
#> GSM152035 2 0.3116 0.85250 0.000 0.892 0.108
#> GSM152039 3 0.9549 0.00365 0.276 0.240 0.484
#> GSM152041 1 0.3764 0.73872 0.892 0.068 0.040
#> GSM152044 2 0.0000 0.91629 0.000 1.000 0.000
#> GSM152045 3 0.5497 0.54981 0.292 0.000 0.708
#> GSM152051 2 0.0000 0.91629 0.000 1.000 0.000
#> GSM152054 3 0.6295 0.37537 0.472 0.000 0.528
#> GSM152057 2 0.3267 0.84462 0.000 0.884 0.116
#> GSM152058 1 0.0000 0.77239 1.000 0.000 0.000
#> GSM152067 3 0.3267 0.58447 0.000 0.116 0.884
#> GSM152068 2 0.0000 0.91629 0.000 1.000 0.000
#> GSM152075 1 0.6305 0.18863 0.516 0.000 0.484
#> GSM152076 3 0.9543 0.00913 0.280 0.236 0.484
#> GSM152079 2 0.0000 0.91629 0.000 1.000 0.000
#> GSM152084 3 0.2682 0.61889 0.076 0.004 0.920
#> GSM152089 1 0.3500 0.73218 0.880 0.116 0.004
#> GSM152095 1 0.7377 0.20491 0.516 0.032 0.452
#> GSM152096 2 0.9391 0.07322 0.284 0.504 0.212
#> GSM152097 2 0.3340 0.84243 0.000 0.880 0.120
#> GSM152099 2 0.3340 0.84242 0.000 0.880 0.120
#> GSM152106 2 0.0000 0.91629 0.000 1.000 0.000
#> GSM152107 3 0.0000 0.59235 0.000 0.000 1.000
#> GSM152109 3 0.3340 0.58372 0.000 0.120 0.880
#> GSM152111 1 0.3038 0.73969 0.896 0.104 0.000
#> GSM152112 3 0.0000 0.59235 0.000 0.000 1.000
#> GSM152113 3 0.6305 0.36105 0.484 0.000 0.516
#> GSM152115 3 0.0000 0.59235 0.000 0.000 1.000
#> GSM152030 1 0.6307 0.18256 0.512 0.000 0.488
#> GSM152038 3 0.3349 0.62177 0.108 0.004 0.888
#> GSM152042 3 0.0237 0.59262 0.000 0.004 0.996
#> GSM152062 3 0.3375 0.62195 0.100 0.008 0.892
#> GSM152077 1 0.0424 0.76739 0.992 0.000 0.008
#> GSM152088 2 0.0000 0.91629 0.000 1.000 0.000
#> GSM152100 1 0.6307 0.18255 0.512 0.000 0.488
#> GSM152102 3 0.6008 0.21460 0.000 0.372 0.628
#> GSM152104 2 0.0000 0.91629 0.000 1.000 0.000
#> GSM152028 1 0.5988 0.04305 0.632 0.000 0.368
#> GSM152029 1 0.8880 -0.19132 0.464 0.120 0.416
#> GSM152049 1 0.0000 0.77239 1.000 0.000 0.000
#> GSM152053 3 0.0237 0.59262 0.000 0.004 0.996
#> GSM152059 1 0.8139 0.28551 0.616 0.108 0.276
#> GSM152085 1 0.0000 0.77239 1.000 0.000 0.000
#> GSM152101 3 0.0000 0.59235 0.000 0.000 1.000
#> GSM152105 3 0.6305 0.36105 0.484 0.000 0.516
#> GSM152034 1 0.3340 0.73144 0.880 0.120 0.000
#> GSM152036 3 0.8561 -0.08996 0.420 0.096 0.484
#> GSM152040 1 0.6309 -0.36560 0.500 0.000 0.500
#> GSM152043 1 0.6229 0.13408 0.652 0.008 0.340
#> GSM152046 1 0.3267 0.73368 0.884 0.116 0.000
#> GSM152047 1 0.3267 0.73368 0.884 0.116 0.000
#> GSM152048 1 0.0000 0.77239 1.000 0.000 0.000
#> GSM152050 1 0.2537 0.75000 0.920 0.080 0.000
#> GSM152052 1 0.3116 0.73741 0.892 0.108 0.000
#> GSM152056 1 0.0000 0.77239 1.000 0.000 0.000
#> GSM152060 1 0.0000 0.77239 1.000 0.000 0.000
#> GSM152065 3 0.6274 0.39927 0.456 0.000 0.544
#> GSM152066 1 0.0000 0.77239 1.000 0.000 0.000
#> GSM152069 3 0.6788 0.58497 0.136 0.120 0.744
#> GSM152070 3 0.6680 0.35462 0.484 0.008 0.508
#> GSM152071 3 0.8759 0.38543 0.360 0.120 0.520
#> GSM152072 3 0.8731 0.37649 0.368 0.116 0.516
#> GSM152073 1 0.0000 0.77239 1.000 0.000 0.000
#> GSM152078 3 0.8880 0.28002 0.416 0.120 0.464
#> GSM152082 3 0.6305 0.36105 0.484 0.000 0.516
#> GSM152086 1 0.0000 0.77239 1.000 0.000 0.000
#> GSM152090 1 0.3340 0.73144 0.880 0.120 0.000
#> GSM152092 1 0.5363 0.32160 0.724 0.000 0.276
#> GSM152093 1 0.3192 0.73644 0.888 0.112 0.000
#> GSM152094 1 0.0000 0.77239 1.000 0.000 0.000
#> GSM152098 3 0.6682 0.34697 0.488 0.008 0.504
#> GSM152110 1 0.0000 0.77239 1.000 0.000 0.000
#> GSM152031 3 0.6516 0.36612 0.480 0.004 0.516
#> GSM152037 1 0.0000 0.77239 1.000 0.000 0.000
#> GSM152055 1 0.0000 0.77239 1.000 0.000 0.000
#> GSM152061 1 0.0000 0.77239 1.000 0.000 0.000
#> GSM152064 1 0.0000 0.77239 1.000 0.000 0.000
#> GSM152087 1 0.0000 0.77239 1.000 0.000 0.000
#> GSM152103 1 0.3340 0.73144 0.880 0.120 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM152032 3 0.3024 0.7944 0.000 0.000 0.852 0.148
#> GSM152033 3 0.1637 0.8222 0.060 0.000 0.940 0.000
#> GSM152063 2 0.0000 0.9573 0.000 1.000 0.000 0.000
#> GSM152074 3 0.3486 0.7796 0.000 0.000 0.812 0.188
#> GSM152080 2 0.0000 0.9573 0.000 1.000 0.000 0.000
#> GSM152081 4 0.0469 0.9722 0.000 0.000 0.012 0.988
#> GSM152083 3 0.3975 0.6909 0.000 0.240 0.760 0.000
#> GSM152091 2 0.0000 0.9573 0.000 1.000 0.000 0.000
#> GSM152108 1 0.4972 0.2384 0.544 0.000 0.456 0.000
#> GSM152114 1 0.2149 0.8781 0.912 0.000 0.088 0.000
#> GSM152035 2 0.0000 0.9573 0.000 1.000 0.000 0.000
#> GSM152039 4 0.1807 0.9337 0.052 0.000 0.008 0.940
#> GSM152041 1 0.0336 0.8910 0.992 0.000 0.000 0.008
#> GSM152044 2 0.0000 0.9573 0.000 1.000 0.000 0.000
#> GSM152045 3 0.4050 0.8200 0.144 0.000 0.820 0.036
#> GSM152051 2 0.0000 0.9573 0.000 1.000 0.000 0.000
#> GSM152054 3 0.3074 0.8206 0.152 0.000 0.848 0.000
#> GSM152057 2 0.0000 0.9573 0.000 1.000 0.000 0.000
#> GSM152058 1 0.2081 0.8797 0.916 0.000 0.084 0.000
#> GSM152067 3 0.2814 0.7980 0.000 0.000 0.868 0.132
#> GSM152068 2 0.0000 0.9573 0.000 1.000 0.000 0.000
#> GSM152075 4 0.0336 0.9719 0.000 0.000 0.008 0.992
#> GSM152076 4 0.0000 0.9704 0.000 0.000 0.000 1.000
#> GSM152079 2 0.0336 0.9506 0.000 0.992 0.008 0.000
#> GSM152084 4 0.2924 0.9143 0.016 0.000 0.100 0.884
#> GSM152089 1 0.3803 0.8043 0.836 0.000 0.032 0.132
#> GSM152095 4 0.2021 0.9350 0.040 0.000 0.024 0.936
#> GSM152096 2 0.7714 0.0883 0.244 0.440 0.316 0.000
#> GSM152097 2 0.0000 0.9573 0.000 1.000 0.000 0.000
#> GSM152099 2 0.0188 0.9540 0.000 0.996 0.000 0.004
#> GSM152106 2 0.0000 0.9573 0.000 1.000 0.000 0.000
#> GSM152107 3 0.3400 0.7885 0.000 0.000 0.820 0.180
#> GSM152109 3 0.3311 0.7772 0.000 0.000 0.828 0.172
#> GSM152111 1 0.0817 0.8881 0.976 0.000 0.024 0.000
#> GSM152112 4 0.0469 0.9722 0.000 0.000 0.012 0.988
#> GSM152113 3 0.2814 0.8256 0.132 0.000 0.868 0.000
#> GSM152115 3 0.3444 0.7817 0.000 0.000 0.816 0.184
#> GSM152030 4 0.0469 0.9722 0.000 0.000 0.012 0.988
#> GSM152038 3 0.3157 0.8000 0.004 0.000 0.852 0.144
#> GSM152042 4 0.0469 0.9722 0.000 0.000 0.012 0.988
#> GSM152062 3 0.3219 0.7902 0.000 0.000 0.836 0.164
#> GSM152077 1 0.3123 0.8312 0.844 0.000 0.156 0.000
#> GSM152088 2 0.0000 0.9573 0.000 1.000 0.000 0.000
#> GSM152100 4 0.0000 0.9704 0.000 0.000 0.000 1.000
#> GSM152102 3 0.3942 0.6930 0.000 0.236 0.764 0.000
#> GSM152104 2 0.0000 0.9573 0.000 1.000 0.000 0.000
#> GSM152028 1 0.4697 0.5291 0.644 0.000 0.356 0.000
#> GSM152029 3 0.4916 0.3757 0.424 0.000 0.576 0.000
#> GSM152049 1 0.2081 0.8797 0.916 0.000 0.084 0.000
#> GSM152053 4 0.0469 0.9722 0.000 0.000 0.012 0.988
#> GSM152059 1 0.3172 0.7758 0.840 0.000 0.160 0.000
#> GSM152085 1 0.0000 0.8908 1.000 0.000 0.000 0.000
#> GSM152101 4 0.1474 0.9412 0.000 0.000 0.052 0.948
#> GSM152105 3 0.2469 0.8144 0.108 0.000 0.892 0.000
#> GSM152034 1 0.2830 0.8603 0.900 0.000 0.060 0.040
#> GSM152036 4 0.0707 0.9602 0.020 0.000 0.000 0.980
#> GSM152040 3 0.2760 0.8223 0.128 0.000 0.872 0.000
#> GSM152043 1 0.4916 0.1705 0.576 0.000 0.424 0.000
#> GSM152046 1 0.1118 0.8845 0.964 0.000 0.036 0.000
#> GSM152047 1 0.4285 0.7733 0.804 0.000 0.040 0.156
#> GSM152048 1 0.2081 0.8797 0.916 0.000 0.084 0.000
#> GSM152050 1 0.0000 0.8908 1.000 0.000 0.000 0.000
#> GSM152052 1 0.2081 0.8797 0.916 0.000 0.084 0.000
#> GSM152056 1 0.2081 0.8797 0.916 0.000 0.084 0.000
#> GSM152060 1 0.1211 0.8860 0.960 0.000 0.040 0.000
#> GSM152065 3 0.1474 0.8262 0.052 0.000 0.948 0.000
#> GSM152066 1 0.1211 0.8884 0.960 0.000 0.040 0.000
#> GSM152069 3 0.3144 0.8230 0.044 0.000 0.884 0.072
#> GSM152070 3 0.4406 0.6770 0.300 0.000 0.700 0.000
#> GSM152071 3 0.2840 0.8280 0.056 0.000 0.900 0.044
#> GSM152072 3 0.2530 0.8246 0.112 0.000 0.888 0.000
#> GSM152073 1 0.1557 0.8889 0.944 0.000 0.056 0.000
#> GSM152078 3 0.4661 0.5520 0.348 0.000 0.652 0.000
#> GSM152082 3 0.3219 0.8114 0.164 0.000 0.836 0.000
#> GSM152086 1 0.2081 0.8797 0.916 0.000 0.084 0.000
#> GSM152090 1 0.1807 0.8714 0.940 0.000 0.052 0.008
#> GSM152092 1 0.3311 0.7923 0.828 0.000 0.172 0.000
#> GSM152093 1 0.0336 0.8907 0.992 0.000 0.008 0.000
#> GSM152094 1 0.1118 0.8845 0.964 0.000 0.036 0.000
#> GSM152098 3 0.4605 0.6174 0.336 0.000 0.664 0.000
#> GSM152110 1 0.1637 0.8857 0.940 0.000 0.060 0.000
#> GSM152031 3 0.2281 0.8175 0.096 0.000 0.904 0.000
#> GSM152037 1 0.2081 0.8797 0.916 0.000 0.084 0.000
#> GSM152055 1 0.2081 0.8797 0.916 0.000 0.084 0.000
#> GSM152061 1 0.1118 0.8845 0.964 0.000 0.036 0.000
#> GSM152064 1 0.1118 0.8845 0.964 0.000 0.036 0.000
#> GSM152087 1 0.1118 0.8845 0.964 0.000 0.036 0.000
#> GSM152103 1 0.1118 0.8848 0.964 0.000 0.036 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM152032 5 0.1894 0.6160 0.000 0.000 0.008 0.072 0.920
#> GSM152033 5 0.3675 0.6147 0.024 0.000 0.188 0.000 0.788
#> GSM152063 2 0.0000 0.9669 0.000 1.000 0.000 0.000 0.000
#> GSM152074 5 0.2852 0.6256 0.000 0.000 0.000 0.172 0.828
#> GSM152080 2 0.2516 0.8663 0.000 0.860 0.140 0.000 0.000
#> GSM152081 4 0.1341 0.9266 0.000 0.000 0.000 0.944 0.056
#> GSM152083 5 0.3508 0.5277 0.000 0.252 0.000 0.000 0.748
#> GSM152091 2 0.0290 0.9632 0.000 0.992 0.008 0.000 0.000
#> GSM152108 3 0.6660 -0.1976 0.288 0.000 0.444 0.000 0.268
#> GSM152114 1 0.4262 0.4969 0.560 0.000 0.440 0.000 0.000
#> GSM152035 2 0.0000 0.9669 0.000 1.000 0.000 0.000 0.000
#> GSM152039 4 0.2732 0.8540 0.088 0.000 0.020 0.884 0.008
#> GSM152041 1 0.4874 0.5074 0.632 0.000 0.328 0.040 0.000
#> GSM152044 2 0.0000 0.9669 0.000 1.000 0.000 0.000 0.000
#> GSM152045 5 0.5177 0.4142 0.468 0.000 0.020 0.012 0.500
#> GSM152051 2 0.0000 0.9669 0.000 1.000 0.000 0.000 0.000
#> GSM152054 5 0.3242 0.6065 0.216 0.000 0.000 0.000 0.784
#> GSM152057 2 0.0000 0.9669 0.000 1.000 0.000 0.000 0.000
#> GSM152058 1 0.4268 0.4949 0.556 0.000 0.444 0.000 0.000
#> GSM152067 5 0.5086 0.0243 0.000 0.000 0.396 0.040 0.564
#> GSM152068 2 0.0000 0.9669 0.000 1.000 0.000 0.000 0.000
#> GSM152075 4 0.1270 0.9266 0.000 0.000 0.000 0.948 0.052
#> GSM152076 4 0.0609 0.9127 0.000 0.000 0.020 0.980 0.000
#> GSM152079 2 0.3366 0.8144 0.000 0.828 0.140 0.000 0.032
#> GSM152084 4 0.3474 0.8345 0.004 0.000 0.008 0.796 0.192
#> GSM152089 1 0.5659 0.3647 0.704 0.000 0.148 0.056 0.092
#> GSM152095 4 0.4007 0.8119 0.076 0.000 0.072 0.824 0.028
#> GSM152096 3 0.7330 0.2535 0.072 0.148 0.492 0.000 0.288
#> GSM152097 2 0.0000 0.9669 0.000 1.000 0.000 0.000 0.000
#> GSM152099 2 0.1544 0.9163 0.000 0.932 0.000 0.068 0.000
#> GSM152106 2 0.0000 0.9669 0.000 1.000 0.000 0.000 0.000
#> GSM152107 5 0.3123 0.6302 0.000 0.000 0.004 0.184 0.812
#> GSM152109 3 0.4878 0.2211 0.000 0.000 0.536 0.024 0.440
#> GSM152111 1 0.3491 0.5433 0.768 0.000 0.228 0.000 0.004
#> GSM152112 4 0.1410 0.9262 0.000 0.000 0.000 0.940 0.060
#> GSM152113 5 0.3991 0.6087 0.048 0.000 0.172 0.000 0.780
#> GSM152115 5 0.2773 0.6278 0.000 0.000 0.000 0.164 0.836
#> GSM152030 4 0.1341 0.9266 0.000 0.000 0.000 0.944 0.056
#> GSM152038 5 0.3445 0.6382 0.000 0.000 0.036 0.140 0.824
#> GSM152042 4 0.1341 0.9266 0.000 0.000 0.000 0.944 0.056
#> GSM152062 5 0.2690 0.6300 0.000 0.000 0.000 0.156 0.844
#> GSM152077 1 0.5223 0.4441 0.512 0.000 0.444 0.000 0.044
#> GSM152088 2 0.1043 0.9418 0.000 0.960 0.040 0.000 0.000
#> GSM152100 4 0.0771 0.9121 0.000 0.000 0.020 0.976 0.004
#> GSM152102 5 0.6417 0.4224 0.280 0.216 0.000 0.000 0.504
#> GSM152104 2 0.0000 0.9669 0.000 1.000 0.000 0.000 0.000
#> GSM152028 3 0.6647 -0.2825 0.304 0.000 0.444 0.000 0.252
#> GSM152029 1 0.5798 0.2057 0.604 0.000 0.148 0.000 0.248
#> GSM152049 1 0.4268 0.4949 0.556 0.000 0.444 0.000 0.000
#> GSM152053 4 0.1341 0.9266 0.000 0.000 0.000 0.944 0.056
#> GSM152059 1 0.2561 0.4225 0.856 0.000 0.000 0.000 0.144
#> GSM152085 1 0.3774 0.5325 0.704 0.000 0.296 0.000 0.000
#> GSM152101 4 0.2648 0.8432 0.000 0.000 0.000 0.848 0.152
#> GSM152105 5 0.3795 0.6002 0.028 0.000 0.192 0.000 0.780
#> GSM152034 1 0.5390 0.3744 0.720 0.000 0.148 0.092 0.040
#> GSM152036 4 0.1648 0.8950 0.040 0.000 0.020 0.940 0.000
#> GSM152040 5 0.5697 0.4416 0.404 0.000 0.084 0.000 0.512
#> GSM152043 1 0.4300 -0.1830 0.524 0.000 0.000 0.000 0.476
#> GSM152046 1 0.0000 0.5337 1.000 0.000 0.000 0.000 0.000
#> GSM152047 1 0.2674 0.4443 0.856 0.000 0.140 0.004 0.000
#> GSM152048 1 0.4268 0.4949 0.556 0.000 0.444 0.000 0.000
#> GSM152050 1 0.3857 0.5288 0.688 0.000 0.312 0.000 0.000
#> GSM152052 3 0.4219 -0.4719 0.416 0.000 0.584 0.000 0.000
#> GSM152056 1 0.4268 0.4949 0.556 0.000 0.444 0.000 0.000
#> GSM152060 1 0.0162 0.5344 0.996 0.000 0.004 0.000 0.000
#> GSM152065 5 0.3995 0.6326 0.060 0.000 0.152 0.000 0.788
#> GSM152066 1 0.4201 0.5090 0.592 0.000 0.408 0.000 0.000
#> GSM152069 3 0.4878 0.2293 0.024 0.000 0.536 0.000 0.440
#> GSM152070 1 0.4210 -0.2307 0.588 0.000 0.000 0.000 0.412
#> GSM152071 3 0.5077 0.2256 0.036 0.000 0.536 0.000 0.428
#> GSM152072 5 0.5965 0.0261 0.112 0.000 0.392 0.000 0.496
#> GSM152073 1 0.1197 0.5351 0.952 0.000 0.048 0.000 0.000
#> GSM152078 5 0.4127 0.3777 0.312 0.000 0.008 0.000 0.680
#> GSM152082 5 0.5100 0.4335 0.448 0.000 0.036 0.000 0.516
#> GSM152086 1 0.4268 0.4949 0.556 0.000 0.444 0.000 0.000
#> GSM152090 1 0.8087 0.1461 0.416 0.000 0.216 0.240 0.128
#> GSM152092 1 0.5227 0.3792 0.676 0.000 0.116 0.000 0.208
#> GSM152093 1 0.5399 0.4007 0.496 0.000 0.448 0.000 0.056
#> GSM152094 1 0.0000 0.5337 1.000 0.000 0.000 0.000 0.000
#> GSM152098 1 0.4262 -0.2000 0.560 0.000 0.000 0.000 0.440
#> GSM152110 1 0.4235 0.5038 0.576 0.000 0.424 0.000 0.000
#> GSM152031 5 0.3929 0.5870 0.028 0.000 0.208 0.000 0.764
#> GSM152037 1 0.4268 0.4949 0.556 0.000 0.444 0.000 0.000
#> GSM152055 1 0.4268 0.4949 0.556 0.000 0.444 0.000 0.000
#> GSM152061 1 0.0000 0.5337 1.000 0.000 0.000 0.000 0.000
#> GSM152064 1 0.1568 0.5409 0.944 0.000 0.036 0.020 0.000
#> GSM152087 1 0.0000 0.5337 1.000 0.000 0.000 0.000 0.000
#> GSM152103 1 0.6553 0.1118 0.456 0.000 0.216 0.000 0.328
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM152032 5 0.3066 0.716 0.000 0.000 0.124 0.044 0.832 0.000
#> GSM152033 5 0.2631 0.741 0.180 0.000 0.000 0.000 0.820 0.000
#> GSM152063 2 0.0000 0.965 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152074 5 0.2300 0.733 0.000 0.000 0.000 0.144 0.856 0.000
#> GSM152080 2 0.3464 0.559 0.000 0.688 0.312 0.000 0.000 0.000
#> GSM152081 4 0.1204 0.822 0.000 0.000 0.000 0.944 0.056 0.000
#> GSM152083 5 0.3052 0.640 0.000 0.216 0.004 0.000 0.780 0.000
#> GSM152091 2 0.0000 0.965 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152108 1 0.1444 0.840 0.928 0.000 0.000 0.000 0.072 0.000
#> GSM152114 1 0.0000 0.918 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM152035 2 0.0000 0.965 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152039 4 0.4122 0.766 0.000 0.000 0.008 0.764 0.124 0.104
#> GSM152041 1 0.4627 0.727 0.756 0.000 0.008 0.040 0.120 0.076
#> GSM152044 2 0.0000 0.965 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152045 6 0.1901 0.825 0.000 0.000 0.008 0.004 0.076 0.912
#> GSM152051 2 0.0000 0.965 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152054 5 0.2597 0.698 0.000 0.000 0.000 0.000 0.824 0.176
#> GSM152057 2 0.0000 0.965 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152058 1 0.0000 0.918 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM152067 3 0.2001 0.873 0.000 0.000 0.912 0.040 0.048 0.000
#> GSM152068 2 0.0000 0.965 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152075 4 0.1075 0.822 0.000 0.000 0.000 0.952 0.048 0.000
#> GSM152076 4 0.3845 0.776 0.000 0.000 0.008 0.788 0.120 0.084
#> GSM152079 2 0.1204 0.918 0.000 0.944 0.056 0.000 0.000 0.000
#> GSM152084 4 0.3263 0.717 0.000 0.000 0.176 0.800 0.020 0.004
#> GSM152089 6 0.6352 0.681 0.100 0.000 0.044 0.092 0.128 0.636
#> GSM152095 4 0.4470 0.757 0.000 0.000 0.024 0.748 0.124 0.104
#> GSM152096 3 0.2948 0.820 0.000 0.060 0.848 0.000 0.092 0.000
#> GSM152097 2 0.0000 0.965 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152099 2 0.1082 0.927 0.000 0.956 0.000 0.040 0.004 0.000
#> GSM152106 2 0.0146 0.963 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM152107 5 0.0632 0.726 0.000 0.000 0.000 0.024 0.976 0.000
#> GSM152109 3 0.0260 0.910 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM152111 1 0.4098 0.518 0.676 0.000 0.032 0.000 0.000 0.292
#> GSM152112 4 0.1267 0.821 0.000 0.000 0.000 0.940 0.060 0.000
#> GSM152113 5 0.3202 0.745 0.176 0.000 0.000 0.000 0.800 0.024
#> GSM152115 5 0.2300 0.732 0.000 0.000 0.000 0.144 0.856 0.000
#> GSM152030 4 0.1204 0.822 0.000 0.000 0.000 0.944 0.056 0.000
#> GSM152038 5 0.2822 0.751 0.040 0.000 0.000 0.108 0.852 0.000
#> GSM152042 4 0.1204 0.822 0.000 0.000 0.000 0.944 0.056 0.000
#> GSM152062 5 0.2623 0.736 0.000 0.000 0.016 0.132 0.852 0.000
#> GSM152077 1 0.0260 0.913 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM152088 2 0.0363 0.957 0.000 0.988 0.012 0.000 0.000 0.000
#> GSM152100 4 0.3111 0.789 0.000 0.000 0.008 0.836 0.124 0.032
#> GSM152102 6 0.4796 0.637 0.000 0.172 0.008 0.000 0.128 0.692
#> GSM152104 2 0.0000 0.965 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152028 1 0.0632 0.900 0.976 0.000 0.000 0.000 0.024 0.000
#> GSM152029 6 0.4392 0.741 0.060 0.000 0.176 0.000 0.024 0.740
#> GSM152049 1 0.0000 0.918 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM152053 4 0.1204 0.822 0.000 0.000 0.000 0.944 0.056 0.000
#> GSM152059 6 0.1610 0.862 0.084 0.000 0.000 0.000 0.000 0.916
#> GSM152085 1 0.2562 0.783 0.828 0.000 0.000 0.000 0.000 0.172
#> GSM152101 4 0.2823 0.683 0.000 0.000 0.000 0.796 0.204 0.000
#> GSM152105 5 0.3482 0.649 0.316 0.000 0.000 0.000 0.684 0.000
#> GSM152034 6 0.6109 0.614 0.100 0.000 0.148 0.144 0.000 0.608
#> GSM152036 4 0.3989 0.772 0.000 0.000 0.008 0.776 0.120 0.096
#> GSM152040 6 0.2432 0.818 0.024 0.000 0.000 0.000 0.100 0.876
#> GSM152043 5 0.4389 0.555 0.052 0.000 0.000 0.000 0.660 0.288
#> GSM152046 6 0.1814 0.859 0.100 0.000 0.000 0.000 0.000 0.900
#> GSM152047 6 0.1610 0.862 0.084 0.000 0.000 0.000 0.000 0.916
#> GSM152048 1 0.0000 0.918 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM152050 1 0.3062 0.784 0.816 0.000 0.024 0.000 0.000 0.160
#> GSM152052 1 0.0000 0.918 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM152056 1 0.0000 0.918 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM152060 6 0.1765 0.862 0.096 0.000 0.000 0.000 0.000 0.904
#> GSM152065 5 0.3204 0.751 0.144 0.000 0.004 0.000 0.820 0.032
#> GSM152066 1 0.0713 0.906 0.972 0.000 0.000 0.000 0.000 0.028
#> GSM152069 3 0.0260 0.910 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM152070 6 0.2221 0.844 0.032 0.000 0.000 0.000 0.072 0.896
#> GSM152071 3 0.0260 0.910 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM152072 3 0.3190 0.773 0.000 0.000 0.820 0.000 0.044 0.136
#> GSM152073 6 0.1863 0.860 0.104 0.000 0.000 0.000 0.000 0.896
#> GSM152078 5 0.5998 0.558 0.072 0.000 0.124 0.000 0.604 0.200
#> GSM152082 6 0.2212 0.814 0.008 0.000 0.000 0.000 0.112 0.880
#> GSM152086 1 0.0000 0.918 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM152090 4 0.5825 0.297 0.288 0.000 0.224 0.488 0.000 0.000
#> GSM152092 6 0.5516 0.518 0.244 0.000 0.000 0.000 0.196 0.560
#> GSM152093 1 0.3229 0.777 0.816 0.000 0.140 0.000 0.000 0.044
#> GSM152094 6 0.1814 0.859 0.100 0.000 0.000 0.000 0.000 0.900
#> GSM152098 6 0.2393 0.847 0.040 0.000 0.004 0.000 0.064 0.892
#> GSM152110 1 0.0632 0.908 0.976 0.000 0.000 0.000 0.000 0.024
#> GSM152031 5 0.3717 0.543 0.384 0.000 0.000 0.000 0.616 0.000
#> GSM152037 1 0.0000 0.918 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM152055 1 0.0000 0.918 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM152061 6 0.1610 0.862 0.084 0.000 0.000 0.000 0.000 0.916
#> GSM152064 6 0.3979 0.685 0.256 0.000 0.000 0.036 0.000 0.708
#> GSM152087 6 0.1814 0.859 0.100 0.000 0.000 0.000 0.000 0.900
#> GSM152103 5 0.6684 0.418 0.228 0.000 0.204 0.004 0.504 0.060
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 specimen(p) k
#> CV:pam 57 7.39e-05 2
#> CV:pam 60 2.61e-04 3
#> CV:pam 84 8.83e-04 4
#> CV:pam 53 2.86e-03 5
#> CV:pam 86 1.32e-02 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 10612 rows and 88 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 5.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.441 0.771 0.870 0.2825 0.796 0.796
#> 3 3 0.260 0.579 0.805 1.0557 0.460 0.371
#> 4 4 0.583 0.629 0.734 0.1668 0.820 0.588
#> 5 5 0.647 0.708 0.817 0.0842 0.713 0.327
#> 6 6 0.572 0.530 0.682 0.0573 0.953 0.823
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM152032 2 0.0376 0.8611 0.004 0.996
#> GSM152033 2 0.0000 0.8614 0.000 1.000
#> GSM152063 2 0.4022 0.8242 0.080 0.920
#> GSM152074 2 0.0376 0.8611 0.004 0.996
#> GSM152080 2 0.4022 0.8239 0.080 0.920
#> GSM152081 2 0.0672 0.8615 0.008 0.992
#> GSM152083 2 0.3879 0.8266 0.076 0.924
#> GSM152091 2 0.3879 0.8267 0.076 0.924
#> GSM152108 2 0.2043 0.8510 0.032 0.968
#> GSM152114 2 0.1184 0.8600 0.016 0.984
#> GSM152035 2 0.3274 0.8364 0.060 0.940
#> GSM152039 2 0.0938 0.8615 0.012 0.988
#> GSM152041 2 0.4161 0.8314 0.084 0.916
#> GSM152044 2 0.4431 0.8150 0.092 0.908
#> GSM152045 2 0.4298 0.8298 0.088 0.912
#> GSM152051 2 0.4431 0.8150 0.092 0.908
#> GSM152054 2 0.0672 0.8606 0.008 0.992
#> GSM152057 2 0.4431 0.8150 0.092 0.908
#> GSM152058 1 0.8016 0.7718 0.756 0.244
#> GSM152067 2 0.0376 0.8611 0.004 0.996
#> GSM152068 2 0.4431 0.8150 0.092 0.908
#> GSM152075 2 0.0376 0.8611 0.004 0.996
#> GSM152076 2 0.0938 0.8615 0.012 0.988
#> GSM152079 2 0.4431 0.8150 0.092 0.908
#> GSM152084 2 0.0376 0.8611 0.004 0.996
#> GSM152089 2 0.2423 0.8513 0.040 0.960
#> GSM152095 2 0.0938 0.8615 0.012 0.988
#> GSM152096 2 0.2423 0.8472 0.040 0.960
#> GSM152097 2 0.4431 0.8150 0.092 0.908
#> GSM152099 2 0.4431 0.8150 0.092 0.908
#> GSM152106 2 0.4431 0.8150 0.092 0.908
#> GSM152107 2 0.0376 0.8611 0.004 0.996
#> GSM152109 2 0.0376 0.8611 0.004 0.996
#> GSM152111 1 0.5294 0.8494 0.880 0.120
#> GSM152112 2 0.0672 0.8615 0.008 0.992
#> GSM152113 2 0.0376 0.8611 0.004 0.996
#> GSM152115 2 0.0376 0.8611 0.004 0.996
#> GSM152030 2 0.0376 0.8611 0.004 0.996
#> GSM152038 2 0.0376 0.8611 0.004 0.996
#> GSM152042 2 0.0376 0.8611 0.004 0.996
#> GSM152062 2 0.0376 0.8611 0.004 0.996
#> GSM152077 2 0.6148 0.7793 0.152 0.848
#> GSM152088 2 0.4431 0.8150 0.092 0.908
#> GSM152100 2 0.0376 0.8611 0.004 0.996
#> GSM152102 2 0.2423 0.8472 0.040 0.960
#> GSM152104 2 0.4431 0.8150 0.092 0.908
#> GSM152028 2 0.5737 0.8021 0.136 0.864
#> GSM152029 2 0.5178 0.8135 0.116 0.884
#> GSM152049 1 0.4562 0.8561 0.904 0.096
#> GSM152053 2 0.0376 0.8611 0.004 0.996
#> GSM152059 2 0.8443 0.6333 0.272 0.728
#> GSM152085 2 0.9993 -0.0568 0.484 0.516
#> GSM152101 2 0.0376 0.8611 0.004 0.996
#> GSM152105 2 0.6712 0.7631 0.176 0.824
#> GSM152034 2 0.8713 0.5860 0.292 0.708
#> GSM152036 2 0.0672 0.8617 0.008 0.992
#> GSM152040 2 0.6531 0.7754 0.168 0.832
#> GSM152043 2 0.8909 0.5637 0.308 0.692
#> GSM152046 2 0.9552 0.3796 0.376 0.624
#> GSM152047 2 0.5842 0.7991 0.140 0.860
#> GSM152048 1 0.4431 0.8564 0.908 0.092
#> GSM152050 1 0.9170 0.6544 0.668 0.332
#> GSM152052 2 0.6048 0.7922 0.148 0.852
#> GSM152056 1 0.4431 0.8564 0.908 0.092
#> GSM152060 2 0.8661 0.6004 0.288 0.712
#> GSM152065 2 0.4939 0.8174 0.108 0.892
#> GSM152066 1 0.4431 0.8564 0.908 0.092
#> GSM152069 2 0.0672 0.8606 0.008 0.992
#> GSM152070 2 0.6531 0.7757 0.168 0.832
#> GSM152071 2 0.0000 0.8614 0.000 1.000
#> GSM152072 2 0.4939 0.8174 0.108 0.892
#> GSM152073 2 0.8608 0.6124 0.284 0.716
#> GSM152078 2 0.5178 0.8140 0.116 0.884
#> GSM152082 2 0.5294 0.8121 0.120 0.880
#> GSM152086 1 0.4431 0.8564 0.908 0.092
#> GSM152090 2 0.0376 0.8611 0.004 0.996
#> GSM152092 2 0.7139 0.7451 0.196 0.804
#> GSM152093 2 0.9881 0.1049 0.436 0.564
#> GSM152094 1 0.8861 0.6979 0.696 0.304
#> GSM152098 2 0.6801 0.7641 0.180 0.820
#> GSM152110 2 0.8661 0.5923 0.288 0.712
#> GSM152031 2 0.8327 0.6458 0.264 0.736
#> GSM152037 1 0.9754 0.4577 0.592 0.408
#> GSM152055 2 0.9491 0.4010 0.368 0.632
#> GSM152061 2 0.8555 0.6147 0.280 0.720
#> GSM152064 2 0.7453 0.7243 0.212 0.788
#> GSM152087 2 0.9580 0.3739 0.380 0.620
#> GSM152103 2 0.4161 0.8322 0.084 0.916
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM152032 3 0.0237 0.5622 0.000 0.004 0.996
#> GSM152033 3 0.0237 0.5622 0.000 0.004 0.996
#> GSM152063 2 0.3482 0.9810 0.000 0.872 0.128
#> GSM152074 3 0.0237 0.5622 0.000 0.004 0.996
#> GSM152080 3 0.6154 -0.0964 0.000 0.408 0.592
#> GSM152081 3 0.6299 0.1148 0.476 0.000 0.524
#> GSM152083 3 0.6111 -0.0688 0.000 0.396 0.604
#> GSM152091 2 0.3551 0.9777 0.000 0.868 0.132
#> GSM152108 3 0.6669 0.1257 0.468 0.008 0.524
#> GSM152114 3 0.6299 0.1148 0.476 0.000 0.524
#> GSM152035 2 0.4291 0.9200 0.000 0.820 0.180
#> GSM152039 3 0.6513 -0.0925 0.004 0.476 0.520
#> GSM152041 3 0.6672 0.1177 0.472 0.008 0.520
#> GSM152044 2 0.3482 0.9810 0.000 0.872 0.128
#> GSM152045 3 0.4654 0.4885 0.208 0.000 0.792
#> GSM152051 2 0.3267 0.9755 0.000 0.884 0.116
#> GSM152054 3 0.0237 0.5622 0.000 0.004 0.996
#> GSM152057 2 0.3192 0.9741 0.000 0.888 0.112
#> GSM152058 1 0.0000 0.8165 1.000 0.000 0.000
#> GSM152067 3 0.0237 0.5622 0.000 0.004 0.996
#> GSM152068 2 0.3192 0.9741 0.000 0.888 0.112
#> GSM152075 3 0.6672 0.1177 0.472 0.008 0.520
#> GSM152076 3 0.6513 -0.0925 0.004 0.476 0.520
#> GSM152079 2 0.3192 0.9741 0.000 0.888 0.112
#> GSM152084 3 0.6295 0.1221 0.472 0.000 0.528
#> GSM152089 3 0.6295 0.1221 0.472 0.000 0.528
#> GSM152095 3 0.6672 -0.0827 0.008 0.472 0.520
#> GSM152096 3 0.1860 0.5312 0.000 0.052 0.948
#> GSM152097 2 0.3482 0.9810 0.000 0.872 0.128
#> GSM152099 2 0.3482 0.9810 0.000 0.872 0.128
#> GSM152106 2 0.3551 0.9761 0.000 0.868 0.132
#> GSM152107 3 0.5497 0.4300 0.292 0.000 0.708
#> GSM152109 3 0.0237 0.5622 0.000 0.004 0.996
#> GSM152111 1 0.0000 0.8165 1.000 0.000 0.000
#> GSM152112 3 0.0000 0.5625 0.000 0.000 1.000
#> GSM152113 3 0.3941 0.5656 0.156 0.000 0.844
#> GSM152115 3 0.0237 0.5622 0.000 0.004 0.996
#> GSM152030 3 0.6509 0.1210 0.472 0.004 0.524
#> GSM152038 3 0.4002 0.5180 0.160 0.000 0.840
#> GSM152042 3 0.6299 0.1148 0.476 0.000 0.524
#> GSM152062 3 0.2878 0.5703 0.096 0.000 0.904
#> GSM152077 1 0.6305 -0.0187 0.516 0.000 0.484
#> GSM152088 2 0.3192 0.9741 0.000 0.888 0.112
#> GSM152100 3 0.6509 -0.0897 0.004 0.472 0.524
#> GSM152102 3 0.3192 0.4758 0.000 0.112 0.888
#> GSM152104 2 0.3482 0.9810 0.000 0.872 0.128
#> GSM152028 1 0.3686 0.8486 0.860 0.000 0.140
#> GSM152029 1 0.4842 0.7322 0.776 0.000 0.224
#> GSM152049 1 0.0000 0.8165 1.000 0.000 0.000
#> GSM152053 3 0.6295 0.1221 0.472 0.000 0.528
#> GSM152059 1 0.3619 0.8504 0.864 0.000 0.136
#> GSM152085 1 0.3340 0.8517 0.880 0.000 0.120
#> GSM152101 3 0.0237 0.5622 0.000 0.004 0.996
#> GSM152105 1 0.3686 0.8486 0.860 0.000 0.140
#> GSM152034 1 0.3784 0.8511 0.864 0.004 0.132
#> GSM152036 3 0.7372 -0.0277 0.032 0.448 0.520
#> GSM152040 1 0.3686 0.8486 0.860 0.000 0.140
#> GSM152043 1 0.3619 0.8504 0.864 0.000 0.136
#> GSM152046 1 0.4196 0.8184 0.864 0.112 0.024
#> GSM152047 1 0.3686 0.8486 0.860 0.000 0.140
#> GSM152048 1 0.0000 0.8165 1.000 0.000 0.000
#> GSM152050 1 0.0000 0.8165 1.000 0.000 0.000
#> GSM152052 1 0.3816 0.8424 0.852 0.000 0.148
#> GSM152056 1 0.0000 0.8165 1.000 0.000 0.000
#> GSM152060 1 0.4196 0.8184 0.864 0.112 0.024
#> GSM152065 3 0.6045 0.2298 0.380 0.000 0.620
#> GSM152066 1 0.0000 0.8165 1.000 0.000 0.000
#> GSM152069 3 0.0237 0.5622 0.000 0.004 0.996
#> GSM152070 3 0.6079 0.2150 0.388 0.000 0.612
#> GSM152071 3 0.0000 0.5625 0.000 0.000 1.000
#> GSM152072 3 0.5098 0.4462 0.248 0.000 0.752
#> GSM152073 1 0.3619 0.8504 0.864 0.000 0.136
#> GSM152078 1 0.4346 0.8038 0.816 0.000 0.184
#> GSM152082 3 0.6079 0.2150 0.388 0.000 0.612
#> GSM152086 1 0.0000 0.8165 1.000 0.000 0.000
#> GSM152090 3 0.6295 0.1221 0.472 0.000 0.528
#> GSM152092 1 0.3686 0.8486 0.860 0.000 0.140
#> GSM152093 1 0.2796 0.8445 0.908 0.000 0.092
#> GSM152094 1 0.0000 0.8165 1.000 0.000 0.000
#> GSM152098 3 0.6140 0.1867 0.404 0.000 0.596
#> GSM152110 1 0.3619 0.8504 0.864 0.000 0.136
#> GSM152031 1 0.3686 0.8486 0.860 0.000 0.140
#> GSM152037 1 0.0237 0.8187 0.996 0.000 0.004
#> GSM152055 1 0.4196 0.8184 0.864 0.112 0.024
#> GSM152061 1 0.4443 0.8341 0.864 0.084 0.052
#> GSM152064 1 0.3784 0.8511 0.864 0.004 0.132
#> GSM152087 1 0.3619 0.8504 0.864 0.000 0.136
#> GSM152103 1 0.6309 -0.0579 0.504 0.000 0.496
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM152032 3 0.2189 0.4089 0.004 0.020 0.932 0.044
#> GSM152033 3 0.1229 0.4217 0.004 0.008 0.968 0.020
#> GSM152063 2 0.0657 0.9119 0.004 0.984 0.000 0.012
#> GSM152074 3 0.2125 0.4091 0.004 0.012 0.932 0.052
#> GSM152080 2 0.4584 0.6125 0.004 0.696 0.300 0.000
#> GSM152081 3 0.8493 0.3572 0.296 0.028 0.412 0.264
#> GSM152083 2 0.4584 0.6125 0.004 0.696 0.300 0.000
#> GSM152091 2 0.1305 0.8868 0.004 0.960 0.036 0.000
#> GSM152108 3 0.7186 0.4542 0.260 0.044 0.612 0.084
#> GSM152114 3 0.7613 0.4135 0.340 0.000 0.448 0.212
#> GSM152035 2 0.2795 0.8244 0.004 0.896 0.088 0.012
#> GSM152039 4 0.5143 0.6425 0.000 0.256 0.036 0.708
#> GSM152041 3 0.8656 0.2782 0.276 0.036 0.400 0.288
#> GSM152044 2 0.0779 0.9108 0.004 0.980 0.000 0.016
#> GSM152045 3 0.7589 0.2153 0.196 0.000 0.404 0.400
#> GSM152051 2 0.1247 0.9013 0.004 0.968 0.016 0.012
#> GSM152054 3 0.4008 0.3999 0.000 0.000 0.756 0.244
#> GSM152057 2 0.0188 0.9130 0.004 0.996 0.000 0.000
#> GSM152058 1 0.0336 0.8647 0.992 0.000 0.000 0.008
#> GSM152067 3 0.4193 0.3962 0.000 0.000 0.732 0.268
#> GSM152068 2 0.0188 0.9130 0.004 0.996 0.000 0.000
#> GSM152075 4 0.8174 0.0959 0.256 0.040 0.188 0.516
#> GSM152076 4 0.5143 0.6425 0.000 0.256 0.036 0.708
#> GSM152079 2 0.0524 0.9117 0.004 0.988 0.000 0.008
#> GSM152084 3 0.7597 0.4309 0.308 0.000 0.468 0.224
#> GSM152089 4 0.7307 -0.2478 0.156 0.000 0.376 0.468
#> GSM152095 4 0.5143 0.6425 0.000 0.256 0.036 0.708
#> GSM152096 3 0.2441 0.3819 0.004 0.068 0.916 0.012
#> GSM152097 2 0.1489 0.8954 0.004 0.952 0.000 0.044
#> GSM152099 2 0.0376 0.9125 0.004 0.992 0.004 0.000
#> GSM152106 2 0.1576 0.8914 0.004 0.948 0.000 0.048
#> GSM152107 3 0.7232 0.4569 0.268 0.008 0.568 0.156
#> GSM152109 3 0.1822 0.4124 0.004 0.008 0.944 0.044
#> GSM152111 1 0.0524 0.8641 0.988 0.004 0.000 0.008
#> GSM152112 3 0.4955 0.1635 0.000 0.000 0.556 0.444
#> GSM152113 3 0.7634 0.4435 0.284 0.008 0.512 0.196
#> GSM152115 3 0.4193 0.3962 0.000 0.000 0.732 0.268
#> GSM152030 3 0.8635 0.3679 0.316 0.040 0.412 0.232
#> GSM152038 3 0.7651 0.3847 0.288 0.008 0.508 0.196
#> GSM152042 3 0.8050 0.4117 0.320 0.012 0.440 0.228
#> GSM152062 3 0.7830 0.4349 0.284 0.008 0.480 0.228
#> GSM152077 3 0.7485 0.3936 0.380 0.000 0.440 0.180
#> GSM152088 2 0.0188 0.9130 0.004 0.996 0.000 0.000
#> GSM152100 4 0.7387 0.5994 0.000 0.256 0.224 0.520
#> GSM152102 3 0.5590 0.3492 0.000 0.064 0.692 0.244
#> GSM152104 2 0.1305 0.9007 0.004 0.960 0.000 0.036
#> GSM152028 1 0.1792 0.8490 0.932 0.000 0.068 0.000
#> GSM152029 1 0.6944 0.1607 0.588 0.000 0.216 0.196
#> GSM152049 1 0.0524 0.8641 0.988 0.004 0.000 0.008
#> GSM152053 3 0.7626 0.4300 0.304 0.000 0.464 0.232
#> GSM152059 1 0.1118 0.8630 0.964 0.000 0.036 0.000
#> GSM152085 1 0.1004 0.8652 0.972 0.000 0.004 0.024
#> GSM152101 3 0.4193 0.3962 0.000 0.000 0.732 0.268
#> GSM152105 1 0.1940 0.8468 0.924 0.000 0.076 0.000
#> GSM152034 1 0.2335 0.8557 0.920 0.000 0.020 0.060
#> GSM152036 4 0.6970 0.6303 0.000 0.256 0.168 0.576
#> GSM152040 1 0.5947 0.6027 0.688 0.000 0.112 0.200
#> GSM152043 1 0.1722 0.8612 0.944 0.000 0.048 0.008
#> GSM152046 1 0.2334 0.8470 0.908 0.000 0.004 0.088
#> GSM152047 1 0.2179 0.8550 0.924 0.000 0.064 0.012
#> GSM152048 1 0.0712 0.8646 0.984 0.004 0.004 0.008
#> GSM152050 1 0.0376 0.8656 0.992 0.000 0.004 0.004
#> GSM152052 1 0.2197 0.8405 0.916 0.000 0.080 0.004
#> GSM152056 1 0.0524 0.8641 0.988 0.004 0.000 0.008
#> GSM152060 1 0.2593 0.8362 0.892 0.000 0.004 0.104
#> GSM152065 1 0.7264 0.3367 0.512 0.000 0.168 0.320
#> GSM152066 1 0.0524 0.8641 0.988 0.004 0.000 0.008
#> GSM152069 3 0.1339 0.4140 0.004 0.008 0.964 0.024
#> GSM152070 1 0.6626 0.5044 0.624 0.000 0.160 0.216
#> GSM152071 3 0.0859 0.4197 0.004 0.008 0.980 0.008
#> GSM152072 3 0.7613 0.2344 0.212 0.000 0.448 0.340
#> GSM152073 1 0.1474 0.8586 0.948 0.000 0.052 0.000
#> GSM152078 1 0.5962 0.4779 0.692 0.000 0.128 0.180
#> GSM152082 1 0.6862 0.4735 0.596 0.000 0.176 0.228
#> GSM152086 1 0.0524 0.8641 0.988 0.004 0.000 0.008
#> GSM152090 3 0.7559 0.4182 0.336 0.000 0.460 0.204
#> GSM152092 1 0.1867 0.8476 0.928 0.000 0.072 0.000
#> GSM152093 1 0.1452 0.8552 0.956 0.000 0.036 0.008
#> GSM152094 1 0.0188 0.8653 0.996 0.000 0.000 0.004
#> GSM152098 1 0.6586 0.5108 0.628 0.000 0.156 0.216
#> GSM152110 1 0.1452 0.8638 0.956 0.000 0.036 0.008
#> GSM152031 1 0.1302 0.8608 0.956 0.000 0.044 0.000
#> GSM152037 1 0.0524 0.8650 0.988 0.000 0.004 0.008
#> GSM152055 1 0.2675 0.8397 0.892 0.000 0.008 0.100
#> GSM152061 1 0.2593 0.8362 0.892 0.000 0.004 0.104
#> GSM152064 1 0.2596 0.8511 0.908 0.000 0.024 0.068
#> GSM152087 1 0.1109 0.8662 0.968 0.000 0.028 0.004
#> GSM152103 3 0.7584 0.4092 0.348 0.000 0.448 0.204
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM152032 3 0.4437 0.7470 0.068 0.000 0.780 0.016 0.136
#> GSM152033 3 0.1877 0.8010 0.064 0.000 0.924 0.000 0.012
#> GSM152063 2 0.0609 0.9790 0.000 0.980 0.000 0.020 0.000
#> GSM152074 3 0.4375 0.7482 0.064 0.000 0.784 0.016 0.136
#> GSM152080 3 0.4599 0.4586 0.020 0.356 0.624 0.000 0.000
#> GSM152081 4 0.5818 0.5317 0.092 0.000 0.072 0.696 0.140
#> GSM152083 3 0.4599 0.4586 0.020 0.356 0.624 0.000 0.000
#> GSM152091 2 0.0609 0.9629 0.020 0.980 0.000 0.000 0.000
#> GSM152108 1 0.5042 0.5914 0.652 0.008 0.308 0.020 0.012
#> GSM152114 1 0.4695 0.6555 0.700 0.000 0.260 0.024 0.016
#> GSM152035 2 0.1728 0.9281 0.020 0.940 0.036 0.000 0.004
#> GSM152039 4 0.0290 0.6460 0.000 0.000 0.008 0.992 0.000
#> GSM152041 4 0.5142 0.5444 0.076 0.000 0.188 0.716 0.020
#> GSM152044 2 0.0609 0.9790 0.000 0.980 0.000 0.020 0.000
#> GSM152045 5 0.3972 0.7166 0.212 0.000 0.008 0.016 0.764
#> GSM152051 2 0.0324 0.9766 0.000 0.992 0.004 0.000 0.004
#> GSM152054 5 0.3935 0.5938 0.024 0.000 0.200 0.004 0.772
#> GSM152057 2 0.0000 0.9790 0.000 1.000 0.000 0.000 0.000
#> GSM152058 1 0.1557 0.7833 0.940 0.000 0.052 0.008 0.000
#> GSM152067 5 0.2672 0.6393 0.024 0.000 0.064 0.016 0.896
#> GSM152068 2 0.0000 0.9790 0.000 1.000 0.000 0.000 0.000
#> GSM152075 4 0.0740 0.6497 0.008 0.000 0.008 0.980 0.004
#> GSM152076 4 0.0290 0.6460 0.000 0.000 0.008 0.992 0.000
#> GSM152079 2 0.0162 0.9781 0.000 0.996 0.000 0.000 0.004
#> GSM152084 1 0.5198 0.6565 0.700 0.000 0.220 0.028 0.052
#> GSM152089 4 0.7425 0.0566 0.068 0.000 0.160 0.464 0.308
#> GSM152095 4 0.0290 0.6460 0.000 0.000 0.008 0.992 0.000
#> GSM152096 3 0.3704 0.7918 0.068 0.060 0.848 0.016 0.008
#> GSM152097 2 0.0609 0.9790 0.000 0.980 0.000 0.020 0.000
#> GSM152099 2 0.0510 0.9682 0.016 0.984 0.000 0.000 0.000
#> GSM152106 2 0.0703 0.9766 0.000 0.976 0.000 0.024 0.000
#> GSM152107 1 0.8987 0.1574 0.424 0.204 0.144 0.072 0.156
#> GSM152109 3 0.2741 0.8017 0.064 0.000 0.892 0.012 0.032
#> GSM152111 1 0.1764 0.7779 0.928 0.000 0.064 0.008 0.000
#> GSM152112 5 0.3414 0.6248 0.024 0.000 0.056 0.060 0.860
#> GSM152113 1 0.4940 0.6006 0.656 0.000 0.304 0.020 0.020
#> GSM152115 5 0.2537 0.6387 0.024 0.000 0.056 0.016 0.904
#> GSM152030 1 0.5864 0.6397 0.688 0.000 0.116 0.056 0.140
#> GSM152038 1 0.5841 0.5664 0.628 0.000 0.260 0.020 0.092
#> GSM152042 1 0.5860 0.6391 0.692 0.000 0.100 0.068 0.140
#> GSM152062 1 0.6164 0.5713 0.640 0.000 0.184 0.036 0.140
#> GSM152077 1 0.4739 0.6698 0.712 0.000 0.240 0.020 0.028
#> GSM152088 2 0.0000 0.9790 0.000 1.000 0.000 0.000 0.000
#> GSM152100 4 0.0740 0.6500 0.008 0.000 0.008 0.980 0.004
#> GSM152102 5 0.6100 0.5378 0.056 0.080 0.200 0.004 0.660
#> GSM152104 2 0.0609 0.9790 0.000 0.980 0.000 0.020 0.000
#> GSM152028 1 0.0162 0.7903 0.996 0.000 0.004 0.000 0.000
#> GSM152029 1 0.2418 0.7816 0.912 0.000 0.044 0.020 0.024
#> GSM152049 1 0.1764 0.7779 0.928 0.000 0.064 0.008 0.000
#> GSM152053 1 0.6475 0.5879 0.640 0.000 0.088 0.132 0.140
#> GSM152059 1 0.0000 0.7904 1.000 0.000 0.000 0.000 0.000
#> GSM152085 1 0.4639 -0.0578 0.612 0.000 0.020 0.368 0.000
#> GSM152101 5 0.2537 0.6387 0.024 0.000 0.056 0.016 0.904
#> GSM152105 1 0.0451 0.7912 0.988 0.000 0.004 0.000 0.008
#> GSM152034 4 0.4480 0.5845 0.400 0.000 0.004 0.592 0.004
#> GSM152036 4 0.0451 0.6463 0.000 0.000 0.008 0.988 0.004
#> GSM152040 5 0.4299 0.6457 0.388 0.000 0.000 0.004 0.608
#> GSM152043 1 0.0162 0.7903 0.996 0.000 0.004 0.000 0.000
#> GSM152046 4 0.5422 0.6199 0.348 0.000 0.000 0.580 0.072
#> GSM152047 4 0.4692 0.4983 0.460 0.000 0.004 0.528 0.008
#> GSM152048 1 0.1764 0.7779 0.928 0.000 0.064 0.008 0.000
#> GSM152050 1 0.1202 0.7885 0.960 0.000 0.032 0.004 0.004
#> GSM152052 1 0.0404 0.7916 0.988 0.000 0.012 0.000 0.000
#> GSM152056 1 0.1764 0.7779 0.928 0.000 0.064 0.008 0.000
#> GSM152060 4 0.5382 0.6266 0.336 0.000 0.000 0.592 0.072
#> GSM152065 5 0.4635 0.6969 0.320 0.000 0.008 0.016 0.656
#> GSM152066 1 0.1764 0.7779 0.928 0.000 0.064 0.008 0.000
#> GSM152069 3 0.1478 0.8005 0.064 0.000 0.936 0.000 0.000
#> GSM152070 5 0.4302 0.6879 0.344 0.000 0.004 0.004 0.648
#> GSM152071 3 0.2037 0.7953 0.064 0.000 0.920 0.012 0.004
#> GSM152072 5 0.4394 0.7185 0.256 0.000 0.012 0.016 0.716
#> GSM152073 1 0.0000 0.7904 1.000 0.000 0.000 0.000 0.000
#> GSM152078 1 0.1967 0.7856 0.932 0.000 0.036 0.020 0.012
#> GSM152082 5 0.4367 0.6625 0.372 0.000 0.008 0.000 0.620
#> GSM152086 1 0.1764 0.7779 0.928 0.000 0.064 0.008 0.000
#> GSM152090 1 0.4560 0.6540 0.700 0.000 0.268 0.020 0.012
#> GSM152092 1 0.0324 0.7906 0.992 0.000 0.004 0.004 0.000
#> GSM152093 1 0.2623 0.7841 0.884 0.000 0.096 0.004 0.016
#> GSM152094 1 0.1478 0.7779 0.936 0.000 0.064 0.000 0.000
#> GSM152098 5 0.4331 0.6332 0.400 0.000 0.004 0.000 0.596
#> GSM152110 1 0.1885 0.7892 0.932 0.000 0.044 0.004 0.020
#> GSM152031 1 0.0000 0.7904 1.000 0.000 0.000 0.000 0.000
#> GSM152037 1 0.1557 0.7833 0.940 0.000 0.052 0.008 0.000
#> GSM152055 4 0.4934 0.6115 0.364 0.000 0.000 0.600 0.036
#> GSM152061 4 0.5353 0.6292 0.328 0.000 0.000 0.600 0.072
#> GSM152064 4 0.4871 0.5919 0.384 0.000 0.012 0.592 0.012
#> GSM152087 1 0.0404 0.7898 0.988 0.000 0.012 0.000 0.000
#> GSM152103 1 0.4675 0.6604 0.704 0.000 0.256 0.020 0.020
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM152032 3 0.3023 0.7092 0.008 0.004 0.808 0.000 0.180 0.000
#> GSM152033 3 0.0632 0.7535 0.000 0.000 0.976 0.000 0.024 0.000
#> GSM152063 2 0.2482 0.8857 0.000 0.848 0.004 0.148 0.000 0.000
#> GSM152074 3 0.2562 0.7120 0.000 0.000 0.828 0.000 0.172 0.000
#> GSM152080 3 0.3955 0.3885 0.000 0.384 0.608 0.000 0.008 0.000
#> GSM152081 6 0.7656 0.3210 0.196 0.000 0.064 0.072 0.212 0.456
#> GSM152083 3 0.3955 0.3885 0.000 0.384 0.608 0.000 0.008 0.000
#> GSM152091 2 0.3243 0.8661 0.000 0.844 0.016 0.076 0.064 0.000
#> GSM152108 1 0.6980 0.4457 0.412 0.068 0.348 0.000 0.164 0.008
#> GSM152114 1 0.4606 0.5860 0.640 0.000 0.312 0.000 0.032 0.016
#> GSM152035 2 0.3813 0.8343 0.000 0.812 0.040 0.072 0.076 0.000
#> GSM152039 4 0.4056 0.4545 0.004 0.000 0.000 0.576 0.004 0.416
#> GSM152041 6 0.7299 0.2758 0.104 0.000 0.236 0.156 0.024 0.480
#> GSM152044 2 0.2482 0.8856 0.000 0.848 0.000 0.148 0.004 0.000
#> GSM152045 5 0.7087 0.4317 0.096 0.000 0.068 0.396 0.400 0.040
#> GSM152051 2 0.0000 0.8949 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152054 5 0.5855 0.3914 0.000 0.000 0.192 0.396 0.412 0.000
#> GSM152057 2 0.0000 0.8949 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152058 1 0.0748 0.6678 0.976 0.000 0.000 0.004 0.004 0.016
#> GSM152067 5 0.4569 0.4310 0.000 0.000 0.040 0.396 0.564 0.000
#> GSM152068 2 0.0000 0.8949 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152075 6 0.5837 -0.1723 0.076 0.000 0.016 0.412 0.016 0.480
#> GSM152076 4 0.4056 0.4545 0.004 0.000 0.000 0.576 0.004 0.416
#> GSM152079 2 0.0000 0.8949 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152084 1 0.6161 0.5016 0.452 0.000 0.284 0.000 0.256 0.008
#> GSM152089 6 0.7952 -0.0448 0.016 0.000 0.180 0.224 0.260 0.320
#> GSM152095 4 0.4056 0.4545 0.004 0.000 0.000 0.576 0.004 0.416
#> GSM152096 3 0.2976 0.7443 0.008 0.128 0.844 0.000 0.016 0.004
#> GSM152097 2 0.3011 0.8671 0.000 0.800 0.000 0.192 0.004 0.004
#> GSM152099 2 0.0260 0.8915 0.000 0.992 0.008 0.000 0.000 0.000
#> GSM152106 2 0.3074 0.8616 0.000 0.792 0.000 0.200 0.004 0.004
#> GSM152107 5 0.7328 -0.3697 0.368 0.012 0.136 0.064 0.400 0.020
#> GSM152109 3 0.1267 0.7654 0.000 0.000 0.940 0.000 0.060 0.000
#> GSM152111 1 0.1889 0.6614 0.920 0.000 0.020 0.004 0.000 0.056
#> GSM152112 5 0.4334 0.4306 0.000 0.000 0.024 0.408 0.568 0.000
#> GSM152113 1 0.6105 0.4614 0.408 0.000 0.384 0.000 0.200 0.008
#> GSM152115 5 0.4237 0.4310 0.000 0.000 0.020 0.396 0.584 0.000
#> GSM152030 1 0.5828 0.5233 0.604 0.000 0.136 0.000 0.216 0.044
#> GSM152038 5 0.7039 -0.2574 0.284 0.000 0.268 0.004 0.388 0.056
#> GSM152042 1 0.6596 0.4604 0.468 0.000 0.144 0.000 0.320 0.068
#> GSM152062 1 0.6242 0.3560 0.376 0.000 0.244 0.000 0.372 0.008
#> GSM152077 1 0.4681 0.6016 0.664 0.000 0.280 0.004 0.032 0.020
#> GSM152088 2 0.0000 0.8949 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152100 4 0.4714 0.4061 0.004 0.000 0.008 0.548 0.024 0.416
#> GSM152102 4 0.7225 -0.4332 0.004 0.124 0.148 0.404 0.320 0.000
#> GSM152104 2 0.2838 0.8717 0.000 0.808 0.000 0.188 0.004 0.000
#> GSM152028 1 0.5048 0.5537 0.604 0.000 0.068 0.000 0.316 0.012
#> GSM152029 1 0.5537 0.6269 0.620 0.000 0.140 0.000 0.216 0.024
#> GSM152049 1 0.1080 0.6608 0.960 0.000 0.000 0.004 0.004 0.032
#> GSM152053 1 0.7325 0.3652 0.408 0.000 0.084 0.048 0.364 0.096
#> GSM152059 1 0.1745 0.6853 0.920 0.000 0.012 0.000 0.068 0.000
#> GSM152085 1 0.3528 0.3490 0.700 0.000 0.000 0.000 0.004 0.296
#> GSM152101 5 0.4237 0.4310 0.000 0.000 0.020 0.396 0.584 0.000
#> GSM152105 1 0.3253 0.6838 0.832 0.000 0.068 0.000 0.096 0.004
#> GSM152034 6 0.5160 0.4709 0.324 0.000 0.068 0.000 0.016 0.592
#> GSM152036 4 0.4158 0.4520 0.004 0.000 0.000 0.572 0.008 0.416
#> GSM152040 5 0.7556 0.4379 0.188 0.000 0.040 0.168 0.480 0.124
#> GSM152043 1 0.6064 0.5501 0.580 0.000 0.068 0.000 0.240 0.112
#> GSM152046 6 0.1863 0.4480 0.104 0.000 0.000 0.000 0.000 0.896
#> GSM152047 6 0.6128 0.4249 0.316 0.000 0.068 0.000 0.088 0.528
#> GSM152048 1 0.1377 0.6736 0.952 0.000 0.016 0.004 0.004 0.024
#> GSM152050 1 0.3450 0.6064 0.820 0.000 0.056 0.004 0.004 0.116
#> GSM152052 1 0.2519 0.6851 0.884 0.000 0.068 0.000 0.044 0.004
#> GSM152056 1 0.1010 0.6610 0.960 0.000 0.000 0.004 0.000 0.036
#> GSM152060 6 0.1765 0.4465 0.096 0.000 0.000 0.000 0.000 0.904
#> GSM152065 5 0.7626 0.4450 0.144 0.000 0.076 0.168 0.500 0.112
#> GSM152066 1 0.0748 0.6684 0.976 0.000 0.000 0.004 0.004 0.016
#> GSM152069 3 0.0260 0.7581 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM152070 5 0.7243 0.4437 0.220 0.000 0.016 0.176 0.480 0.108
#> GSM152071 3 0.0146 0.7573 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM152072 4 0.7695 -0.5480 0.136 0.000 0.072 0.376 0.348 0.068
#> GSM152073 1 0.4591 0.6070 0.704 0.000 0.012 0.000 0.208 0.076
#> GSM152078 1 0.4761 0.6443 0.688 0.000 0.088 0.000 0.212 0.012
#> GSM152082 5 0.5658 0.3042 0.172 0.000 0.072 0.000 0.648 0.108
#> GSM152086 1 0.1080 0.6619 0.960 0.000 0.000 0.004 0.004 0.032
#> GSM152090 1 0.5265 0.5694 0.572 0.000 0.328 0.000 0.092 0.008
#> GSM152092 1 0.5907 0.5634 0.592 0.000 0.068 0.000 0.248 0.092
#> GSM152093 1 0.2971 0.6711 0.848 0.000 0.116 0.000 0.012 0.024
#> GSM152094 1 0.0922 0.6659 0.968 0.000 0.000 0.004 0.004 0.024
#> GSM152098 5 0.6971 0.4240 0.224 0.000 0.016 0.132 0.520 0.108
#> GSM152110 1 0.5574 0.4812 0.604 0.000 0.140 0.000 0.020 0.236
#> GSM152031 1 0.2445 0.6859 0.872 0.000 0.020 0.000 0.108 0.000
#> GSM152037 1 0.1511 0.6796 0.940 0.000 0.044 0.000 0.004 0.012
#> GSM152055 6 0.3633 0.4937 0.148 0.000 0.056 0.000 0.004 0.792
#> GSM152061 6 0.1908 0.4504 0.096 0.000 0.000 0.000 0.004 0.900
#> GSM152064 6 0.5180 0.4784 0.316 0.000 0.072 0.000 0.016 0.596
#> GSM152087 1 0.3667 0.5867 0.776 0.000 0.008 0.000 0.032 0.184
#> GSM152103 1 0.5051 0.5856 0.600 0.000 0.316 0.000 0.076 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 specimen(p) k
#> CV:mclust 82 1.79e-01 2
#> CV:mclust 60 3.00e-06 3
#> CV:mclust 52 2.28e-06 4
#> CV:mclust 82 4.30e-03 5
#> CV:mclust 48 4.97e-04 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "NMF"]
# you can also extract it by
# res = res_list["CV:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 10612 rows and 88 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 0.700 0.831 0.930 0.4869 0.515 0.515
#> 3 3 0.450 0.599 0.785 0.3521 0.742 0.544
#> 4 4 0.537 0.623 0.804 0.1249 0.797 0.508
#> 5 5 0.607 0.616 0.792 0.0679 0.899 0.652
#> 6 6 0.733 0.645 0.824 0.0403 0.868 0.485
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
#> GSM152032 2 0.9881 0.0992 0.436 0.564
#> GSM152033 1 0.8813 0.6123 0.700 0.300
#> GSM152063 2 0.0000 0.9394 0.000 1.000
#> GSM152074 1 0.9754 0.4087 0.592 0.408
#> GSM152080 2 0.0000 0.9394 0.000 1.000
#> GSM152081 2 0.0376 0.9366 0.004 0.996
#> GSM152083 2 0.0000 0.9394 0.000 1.000
#> GSM152091 2 0.0000 0.9394 0.000 1.000
#> GSM152108 2 0.0000 0.9394 0.000 1.000
#> GSM152114 2 0.9998 -0.0712 0.492 0.508
#> GSM152035 2 0.0000 0.9394 0.000 1.000
#> GSM152039 2 0.0000 0.9394 0.000 1.000
#> GSM152041 2 0.8327 0.6080 0.264 0.736
#> GSM152044 2 0.0000 0.9394 0.000 1.000
#> GSM152045 1 0.0000 0.9072 1.000 0.000
#> GSM152051 2 0.0000 0.9394 0.000 1.000
#> GSM152054 1 0.9608 0.4606 0.616 0.384
#> GSM152057 2 0.0000 0.9394 0.000 1.000
#> GSM152058 1 0.0000 0.9072 1.000 0.000
#> GSM152067 1 0.9710 0.4284 0.600 0.400
#> GSM152068 2 0.0000 0.9394 0.000 1.000
#> GSM152075 2 0.0000 0.9394 0.000 1.000
#> GSM152076 2 0.0000 0.9394 0.000 1.000
#> GSM152079 2 0.0000 0.9394 0.000 1.000
#> GSM152084 1 0.9358 0.5267 0.648 0.352
#> GSM152089 2 0.5294 0.8251 0.120 0.880
#> GSM152095 2 0.0000 0.9394 0.000 1.000
#> GSM152096 2 0.0672 0.9336 0.008 0.992
#> GSM152097 2 0.0000 0.9394 0.000 1.000
#> GSM152099 2 0.0000 0.9394 0.000 1.000
#> GSM152106 2 0.0000 0.9394 0.000 1.000
#> GSM152107 2 0.0376 0.9366 0.004 0.996
#> GSM152109 1 0.9710 0.4284 0.600 0.400
#> GSM152111 1 0.0000 0.9072 1.000 0.000
#> GSM152112 2 0.0000 0.9394 0.000 1.000
#> GSM152113 1 0.8081 0.6833 0.752 0.248
#> GSM152115 1 0.9635 0.4541 0.612 0.388
#> GSM152030 2 0.0000 0.9394 0.000 1.000
#> GSM152038 1 0.0000 0.9072 1.000 0.000
#> GSM152042 2 0.0000 0.9394 0.000 1.000
#> GSM152062 1 0.9000 0.5879 0.684 0.316
#> GSM152077 1 0.0000 0.9072 1.000 0.000
#> GSM152088 2 0.0000 0.9394 0.000 1.000
#> GSM152100 2 0.0000 0.9394 0.000 1.000
#> GSM152102 2 0.4298 0.8530 0.088 0.912
#> GSM152104 2 0.0000 0.9394 0.000 1.000
#> GSM152028 1 0.0000 0.9072 1.000 0.000
#> GSM152029 1 0.0000 0.9072 1.000 0.000
#> GSM152049 1 0.0000 0.9072 1.000 0.000
#> GSM152053 2 0.0000 0.9394 0.000 1.000
#> GSM152059 1 0.0000 0.9072 1.000 0.000
#> GSM152085 1 0.0000 0.9072 1.000 0.000
#> GSM152101 2 0.9491 0.3269 0.368 0.632
#> GSM152105 1 0.0000 0.9072 1.000 0.000
#> GSM152034 1 0.0376 0.9046 0.996 0.004
#> GSM152036 2 0.1184 0.9265 0.016 0.984
#> GSM152040 1 0.0000 0.9072 1.000 0.000
#> GSM152043 1 0.0000 0.9072 1.000 0.000
#> GSM152046 1 0.0000 0.9072 1.000 0.000
#> GSM152047 1 0.0000 0.9072 1.000 0.000
#> GSM152048 1 0.0000 0.9072 1.000 0.000
#> GSM152050 1 0.0000 0.9072 1.000 0.000
#> GSM152052 1 0.0000 0.9072 1.000 0.000
#> GSM152056 1 0.0000 0.9072 1.000 0.000
#> GSM152060 1 0.0000 0.9072 1.000 0.000
#> GSM152065 1 0.0000 0.9072 1.000 0.000
#> GSM152066 1 0.0000 0.9072 1.000 0.000
#> GSM152069 1 0.9710 0.4284 0.600 0.400
#> GSM152070 1 0.0000 0.9072 1.000 0.000
#> GSM152071 1 0.7376 0.7299 0.792 0.208
#> GSM152072 1 0.0000 0.9072 1.000 0.000
#> GSM152073 1 0.0000 0.9072 1.000 0.000
#> GSM152078 1 0.0000 0.9072 1.000 0.000
#> GSM152082 1 0.0000 0.9072 1.000 0.000
#> GSM152086 1 0.0000 0.9072 1.000 0.000
#> GSM152090 1 0.9358 0.5159 0.648 0.352
#> GSM152092 1 0.0000 0.9072 1.000 0.000
#> GSM152093 1 0.0376 0.9046 0.996 0.004
#> GSM152094 1 0.0000 0.9072 1.000 0.000
#> GSM152098 1 0.0000 0.9072 1.000 0.000
#> GSM152110 1 0.0000 0.9072 1.000 0.000
#> GSM152031 1 0.0000 0.9072 1.000 0.000
#> GSM152037 1 0.0000 0.9072 1.000 0.000
#> GSM152055 1 0.0000 0.9072 1.000 0.000
#> GSM152061 1 0.0000 0.9072 1.000 0.000
#> GSM152064 1 0.2236 0.8800 0.964 0.036
#> GSM152087 1 0.0000 0.9072 1.000 0.000
#> GSM152103 1 0.6438 0.7751 0.836 0.164
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM152032 3 0.1411 0.6805 0.036 0.000 0.964
#> GSM152033 3 0.5497 0.5855 0.292 0.000 0.708
#> GSM152063 2 0.6180 0.3967 0.000 0.584 0.416
#> GSM152074 3 0.3267 0.6843 0.116 0.000 0.884
#> GSM152080 3 0.2537 0.6323 0.000 0.080 0.920
#> GSM152081 2 0.2152 0.7379 0.036 0.948 0.016
#> GSM152083 3 0.1163 0.6625 0.000 0.028 0.972
#> GSM152091 3 0.4346 0.5365 0.000 0.184 0.816
#> GSM152108 3 0.4291 0.5421 0.000 0.180 0.820
#> GSM152114 2 0.9083 0.3249 0.280 0.540 0.180
#> GSM152035 3 0.3340 0.6035 0.000 0.120 0.880
#> GSM152039 2 0.0424 0.7433 0.008 0.992 0.000
#> GSM152041 2 0.2959 0.6709 0.100 0.900 0.000
#> GSM152044 2 0.6180 0.4019 0.000 0.584 0.416
#> GSM152045 1 0.7265 0.5504 0.684 0.076 0.240
#> GSM152051 3 0.6274 -0.1162 0.000 0.456 0.544
#> GSM152054 3 0.4842 0.6504 0.224 0.000 0.776
#> GSM152057 3 0.6095 0.1013 0.000 0.392 0.608
#> GSM152058 1 0.3192 0.7708 0.888 0.112 0.000
#> GSM152067 3 0.3551 0.6823 0.132 0.000 0.868
#> GSM152068 2 0.6308 0.2130 0.000 0.508 0.492
#> GSM152075 2 0.1289 0.7326 0.032 0.968 0.000
#> GSM152076 2 0.0237 0.7440 0.004 0.996 0.000
#> GSM152079 3 0.6299 -0.1824 0.000 0.476 0.524
#> GSM152084 3 0.5327 0.6107 0.272 0.000 0.728
#> GSM152089 2 0.1315 0.7426 0.020 0.972 0.008
#> GSM152095 2 0.0983 0.7457 0.004 0.980 0.016
#> GSM152096 3 0.1031 0.6643 0.000 0.024 0.976
#> GSM152097 2 0.5497 0.5977 0.000 0.708 0.292
#> GSM152099 3 0.5733 0.2852 0.000 0.324 0.676
#> GSM152106 2 0.4178 0.6942 0.000 0.828 0.172
#> GSM152107 3 0.3412 0.6006 0.000 0.124 0.876
#> GSM152109 3 0.3340 0.6837 0.120 0.000 0.880
#> GSM152111 1 0.5760 0.6402 0.672 0.328 0.000
#> GSM152112 3 0.6008 0.2283 0.000 0.372 0.628
#> GSM152113 3 0.5733 0.5341 0.324 0.000 0.676
#> GSM152115 3 0.4887 0.6492 0.228 0.000 0.772
#> GSM152030 2 0.4654 0.6643 0.000 0.792 0.208
#> GSM152038 3 0.6302 0.1672 0.480 0.000 0.520
#> GSM152042 2 0.3879 0.7117 0.000 0.848 0.152
#> GSM152062 3 0.5098 0.6377 0.248 0.000 0.752
#> GSM152077 1 0.2301 0.7593 0.936 0.004 0.060
#> GSM152088 3 0.6154 0.0511 0.000 0.408 0.592
#> GSM152100 2 0.2066 0.7375 0.000 0.940 0.060
#> GSM152102 3 0.0424 0.6694 0.000 0.008 0.992
#> GSM152104 2 0.5621 0.5794 0.000 0.692 0.308
#> GSM152028 1 0.2448 0.7461 0.924 0.000 0.076
#> GSM152029 1 0.3116 0.7239 0.892 0.000 0.108
#> GSM152049 1 0.3816 0.7582 0.852 0.148 0.000
#> GSM152053 2 0.6026 0.4855 0.000 0.624 0.376
#> GSM152059 1 0.0424 0.7776 0.992 0.008 0.000
#> GSM152085 1 0.4974 0.7137 0.764 0.236 0.000
#> GSM152101 3 0.1289 0.6805 0.032 0.000 0.968
#> GSM152105 1 0.2796 0.7373 0.908 0.000 0.092
#> GSM152034 1 0.6280 0.4652 0.540 0.460 0.000
#> GSM152036 2 0.1860 0.7180 0.052 0.948 0.000
#> GSM152040 1 0.0747 0.7797 0.984 0.016 0.000
#> GSM152043 1 0.0424 0.7777 0.992 0.008 0.000
#> GSM152046 1 0.6140 0.5539 0.596 0.404 0.000
#> GSM152047 1 0.3686 0.7665 0.860 0.140 0.000
#> GSM152048 1 0.2261 0.7800 0.932 0.068 0.000
#> GSM152050 1 0.5926 0.6121 0.644 0.356 0.000
#> GSM152052 1 0.2165 0.7551 0.936 0.000 0.064
#> GSM152056 1 0.4796 0.7225 0.780 0.220 0.000
#> GSM152060 1 0.5948 0.6092 0.640 0.360 0.000
#> GSM152065 1 0.5882 0.3303 0.652 0.000 0.348
#> GSM152066 1 0.2356 0.7794 0.928 0.072 0.000
#> GSM152069 3 0.3879 0.6771 0.152 0.000 0.848
#> GSM152070 1 0.2711 0.7385 0.912 0.000 0.088
#> GSM152071 3 0.5138 0.6350 0.252 0.000 0.748
#> GSM152072 1 0.6309 -0.1490 0.504 0.000 0.496
#> GSM152073 1 0.0000 0.7753 1.000 0.000 0.000
#> GSM152078 1 0.4002 0.6738 0.840 0.000 0.160
#> GSM152082 1 0.2796 0.7359 0.908 0.000 0.092
#> GSM152086 1 0.4504 0.7350 0.804 0.196 0.000
#> GSM152090 1 0.7804 0.5334 0.664 0.120 0.216
#> GSM152092 1 0.2796 0.7364 0.908 0.000 0.092
#> GSM152093 1 0.5404 0.6944 0.740 0.256 0.004
#> GSM152094 1 0.4235 0.7521 0.824 0.176 0.000
#> GSM152098 1 0.2165 0.7520 0.936 0.000 0.064
#> GSM152110 1 0.5621 0.6614 0.692 0.308 0.000
#> GSM152031 1 0.1529 0.7637 0.960 0.000 0.040
#> GSM152037 1 0.1031 0.7805 0.976 0.024 0.000
#> GSM152055 1 0.6204 0.5252 0.576 0.424 0.000
#> GSM152061 1 0.6111 0.5647 0.604 0.396 0.000
#> GSM152064 1 0.6299 0.4351 0.524 0.476 0.000
#> GSM152087 1 0.2625 0.7778 0.916 0.084 0.000
#> GSM152103 1 0.4605 0.6233 0.796 0.000 0.204
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM152032 2 0.6316 0.3430 0.080 0.596 0.324 0.000
#> GSM152033 3 0.4856 0.6023 0.084 0.136 0.780 0.000
#> GSM152063 2 0.4382 0.5941 0.000 0.704 0.000 0.296
#> GSM152074 3 0.6693 0.0243 0.088 0.424 0.488 0.000
#> GSM152080 2 0.1059 0.7603 0.000 0.972 0.016 0.012
#> GSM152081 4 0.2999 0.7370 0.004 0.000 0.132 0.864
#> GSM152083 2 0.1978 0.7453 0.000 0.928 0.068 0.004
#> GSM152091 2 0.1970 0.7755 0.000 0.932 0.008 0.060
#> GSM152108 2 0.5659 0.5978 0.076 0.740 0.168 0.016
#> GSM152114 1 0.6581 0.6126 0.700 0.056 0.160 0.084
#> GSM152035 2 0.3761 0.7496 0.000 0.852 0.080 0.068
#> GSM152039 4 0.0188 0.7885 0.000 0.004 0.000 0.996
#> GSM152041 4 0.0921 0.7796 0.028 0.000 0.000 0.972
#> GSM152044 2 0.4250 0.6162 0.000 0.724 0.000 0.276
#> GSM152045 3 0.4605 0.6494 0.108 0.000 0.800 0.092
#> GSM152051 2 0.2469 0.7711 0.000 0.892 0.000 0.108
#> GSM152054 3 0.3103 0.6743 0.008 0.072 0.892 0.028
#> GSM152057 2 0.2081 0.7773 0.000 0.916 0.000 0.084
#> GSM152058 1 0.1631 0.7988 0.956 0.016 0.020 0.008
#> GSM152067 3 0.2530 0.6613 0.000 0.112 0.888 0.000
#> GSM152068 2 0.2921 0.7506 0.000 0.860 0.000 0.140
#> GSM152075 4 0.0000 0.7883 0.000 0.000 0.000 1.000
#> GSM152076 4 0.0188 0.7885 0.000 0.004 0.000 0.996
#> GSM152079 2 0.2216 0.7755 0.000 0.908 0.000 0.092
#> GSM152084 2 0.7609 -0.0362 0.200 0.404 0.396 0.000
#> GSM152089 4 0.5755 0.0991 0.028 0.000 0.444 0.528
#> GSM152095 4 0.0336 0.7873 0.000 0.008 0.000 0.992
#> GSM152096 2 0.0967 0.7568 0.004 0.976 0.016 0.004
#> GSM152097 4 0.3726 0.5907 0.000 0.212 0.000 0.788
#> GSM152099 2 0.2266 0.7772 0.000 0.912 0.004 0.084
#> GSM152106 4 0.2011 0.7476 0.000 0.080 0.000 0.920
#> GSM152107 3 0.5594 0.5086 0.000 0.180 0.720 0.100
#> GSM152109 2 0.4467 0.6547 0.040 0.788 0.172 0.000
#> GSM152111 1 0.2530 0.7885 0.888 0.000 0.000 0.112
#> GSM152112 3 0.4552 0.6383 0.000 0.072 0.800 0.128
#> GSM152113 3 0.6033 0.5154 0.116 0.204 0.680 0.000
#> GSM152115 3 0.1474 0.6760 0.000 0.052 0.948 0.000
#> GSM152030 4 0.6919 0.5749 0.060 0.068 0.216 0.656
#> GSM152038 3 0.4731 0.6093 0.160 0.060 0.780 0.000
#> GSM152042 4 0.3697 0.7361 0.000 0.048 0.100 0.852
#> GSM152062 3 0.6673 0.4082 0.140 0.252 0.608 0.000
#> GSM152077 1 0.5442 0.5002 0.672 0.040 0.288 0.000
#> GSM152088 2 0.1637 0.7752 0.000 0.940 0.000 0.060
#> GSM152100 4 0.1182 0.7797 0.000 0.016 0.016 0.968
#> GSM152102 3 0.4677 0.4665 0.000 0.316 0.680 0.004
#> GSM152104 2 0.4985 0.2144 0.000 0.532 0.000 0.468
#> GSM152028 1 0.2480 0.7843 0.904 0.008 0.088 0.000
#> GSM152029 1 0.3962 0.7520 0.832 0.044 0.124 0.000
#> GSM152049 1 0.1610 0.8041 0.952 0.000 0.016 0.032
#> GSM152053 4 0.6005 0.4243 0.036 0.008 0.356 0.600
#> GSM152059 1 0.1557 0.7952 0.944 0.000 0.056 0.000
#> GSM152085 1 0.3243 0.7849 0.876 0.000 0.036 0.088
#> GSM152101 3 0.1824 0.6738 0.000 0.060 0.936 0.004
#> GSM152105 1 0.4669 0.6344 0.764 0.036 0.200 0.000
#> GSM152034 1 0.5894 0.3911 0.568 0.000 0.040 0.392
#> GSM152036 4 0.0188 0.7879 0.004 0.000 0.000 0.996
#> GSM152040 3 0.4606 0.5786 0.264 0.000 0.724 0.012
#> GSM152043 1 0.3123 0.7425 0.844 0.000 0.156 0.000
#> GSM152046 1 0.5256 0.6258 0.692 0.000 0.036 0.272
#> GSM152047 1 0.6646 0.0994 0.488 0.000 0.428 0.084
#> GSM152048 1 0.1339 0.7993 0.964 0.008 0.024 0.004
#> GSM152050 1 0.3356 0.7520 0.824 0.000 0.000 0.176
#> GSM152052 1 0.2706 0.7698 0.900 0.080 0.020 0.000
#> GSM152056 1 0.2156 0.8036 0.928 0.004 0.008 0.060
#> GSM152060 1 0.5750 0.6512 0.696 0.000 0.088 0.216
#> GSM152065 3 0.2704 0.6879 0.124 0.000 0.876 0.000
#> GSM152066 1 0.0927 0.7993 0.976 0.008 0.016 0.000
#> GSM152069 2 0.5026 0.4324 0.016 0.672 0.312 0.000
#> GSM152070 3 0.4331 0.5483 0.288 0.000 0.712 0.000
#> GSM152071 2 0.6216 0.4671 0.108 0.652 0.240 0.000
#> GSM152072 3 0.3681 0.6702 0.176 0.008 0.816 0.000
#> GSM152073 1 0.2408 0.7769 0.896 0.000 0.104 0.000
#> GSM152078 1 0.2670 0.7922 0.908 0.052 0.040 0.000
#> GSM152082 3 0.4543 0.4891 0.324 0.000 0.676 0.000
#> GSM152086 1 0.1576 0.8051 0.948 0.004 0.000 0.048
#> GSM152090 1 0.6086 0.2834 0.548 0.412 0.008 0.032
#> GSM152092 1 0.2760 0.7745 0.872 0.000 0.128 0.000
#> GSM152093 1 0.1854 0.8000 0.948 0.008 0.024 0.020
#> GSM152094 1 0.2142 0.7949 0.928 0.000 0.056 0.016
#> GSM152098 3 0.5165 0.0273 0.484 0.000 0.512 0.004
#> GSM152110 1 0.4401 0.6487 0.724 0.000 0.004 0.272
#> GSM152031 1 0.1151 0.7980 0.968 0.024 0.008 0.000
#> GSM152037 1 0.1042 0.7987 0.972 0.008 0.020 0.000
#> GSM152055 4 0.5143 -0.0850 0.456 0.000 0.004 0.540
#> GSM152061 1 0.6871 0.2313 0.480 0.000 0.104 0.416
#> GSM152064 4 0.4485 0.5242 0.248 0.000 0.012 0.740
#> GSM152087 1 0.2124 0.7911 0.924 0.000 0.068 0.008
#> GSM152103 1 0.4770 0.5602 0.700 0.288 0.012 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM152032 3 0.2196 0.6834 0.004 0.056 0.916 0.000 0.024
#> GSM152033 3 0.4483 0.5523 0.012 0.008 0.672 0.000 0.308
#> GSM152063 2 0.3561 0.6610 0.000 0.740 0.000 0.260 0.000
#> GSM152074 3 0.2332 0.6899 0.004 0.016 0.904 0.000 0.076
#> GSM152080 2 0.0798 0.7690 0.008 0.976 0.016 0.000 0.000
#> GSM152081 4 0.3132 0.6763 0.000 0.000 0.172 0.820 0.008
#> GSM152083 2 0.4066 0.5398 0.000 0.672 0.324 0.000 0.004
#> GSM152091 2 0.0703 0.7842 0.000 0.976 0.000 0.024 0.000
#> GSM152108 3 0.5724 0.5902 0.024 0.132 0.676 0.000 0.168
#> GSM152114 3 0.5721 0.2346 0.344 0.000 0.576 0.068 0.012
#> GSM152035 2 0.7045 0.4131 0.000 0.540 0.220 0.052 0.188
#> GSM152039 4 0.0000 0.7991 0.000 0.000 0.000 1.000 0.000
#> GSM152041 4 0.0510 0.7910 0.016 0.000 0.000 0.984 0.000
#> GSM152044 2 0.3395 0.6833 0.000 0.764 0.000 0.236 0.000
#> GSM152045 5 0.1493 0.7355 0.028 0.000 0.000 0.024 0.948
#> GSM152051 2 0.1768 0.7843 0.000 0.924 0.004 0.072 0.000
#> GSM152054 5 0.1942 0.7010 0.000 0.012 0.068 0.000 0.920
#> GSM152057 2 0.4117 0.7445 0.000 0.788 0.096 0.116 0.000
#> GSM152058 1 0.4668 0.5628 0.688 0.000 0.276 0.008 0.028
#> GSM152067 5 0.4854 0.6011 0.016 0.072 0.172 0.000 0.740
#> GSM152068 2 0.2338 0.7714 0.000 0.884 0.004 0.112 0.000
#> GSM152075 4 0.0162 0.7985 0.000 0.000 0.004 0.996 0.000
#> GSM152076 4 0.0000 0.7991 0.000 0.000 0.000 1.000 0.000
#> GSM152079 2 0.1557 0.7860 0.000 0.940 0.008 0.052 0.000
#> GSM152084 3 0.1716 0.6868 0.016 0.024 0.944 0.000 0.016
#> GSM152089 5 0.3895 0.5176 0.000 0.000 0.000 0.320 0.680
#> GSM152095 4 0.0000 0.7991 0.000 0.000 0.000 1.000 0.000
#> GSM152096 2 0.0771 0.7774 0.004 0.976 0.020 0.000 0.000
#> GSM152097 4 0.4084 0.3513 0.000 0.328 0.004 0.668 0.000
#> GSM152099 2 0.2305 0.7812 0.000 0.896 0.012 0.092 0.000
#> GSM152106 4 0.2773 0.6631 0.000 0.164 0.000 0.836 0.000
#> GSM152107 3 0.6998 0.0184 0.000 0.028 0.452 0.168 0.352
#> GSM152109 2 0.5939 0.4360 0.056 0.604 0.300 0.000 0.040
#> GSM152111 1 0.1205 0.7662 0.956 0.000 0.004 0.040 0.000
#> GSM152112 5 0.5241 0.6133 0.000 0.012 0.088 0.204 0.696
#> GSM152113 3 0.4584 0.5964 0.020 0.016 0.708 0.000 0.256
#> GSM152115 5 0.3086 0.6304 0.000 0.004 0.180 0.000 0.816
#> GSM152030 3 0.4211 0.5112 0.008 0.008 0.728 0.252 0.004
#> GSM152038 3 0.3710 0.6553 0.024 0.000 0.784 0.000 0.192
#> GSM152042 4 0.4037 0.5409 0.000 0.004 0.288 0.704 0.004
#> GSM152062 3 0.2193 0.6744 0.000 0.028 0.912 0.000 0.060
#> GSM152077 3 0.4657 0.6298 0.152 0.000 0.740 0.000 0.108
#> GSM152088 2 0.0451 0.7793 0.004 0.988 0.000 0.008 0.000
#> GSM152100 4 0.2796 0.7054 0.000 0.008 0.008 0.868 0.116
#> GSM152102 5 0.4021 0.6199 0.000 0.168 0.052 0.000 0.780
#> GSM152104 2 0.3837 0.5923 0.000 0.692 0.000 0.308 0.000
#> GSM152028 1 0.6309 0.1865 0.492 0.000 0.340 0.000 0.168
#> GSM152029 1 0.5988 0.4182 0.612 0.272 0.024 0.000 0.092
#> GSM152049 1 0.1493 0.7660 0.948 0.000 0.024 0.028 0.000
#> GSM152053 3 0.3732 0.5959 0.000 0.000 0.792 0.176 0.032
#> GSM152059 1 0.0880 0.7615 0.968 0.000 0.000 0.000 0.032
#> GSM152085 1 0.1568 0.7614 0.944 0.000 0.000 0.020 0.036
#> GSM152101 5 0.2233 0.7014 0.000 0.004 0.104 0.000 0.892
#> GSM152105 3 0.5036 -0.0409 0.452 0.000 0.516 0.000 0.032
#> GSM152034 1 0.4017 0.6879 0.788 0.000 0.000 0.148 0.064
#> GSM152036 4 0.0290 0.7970 0.000 0.000 0.000 0.992 0.008
#> GSM152040 5 0.1792 0.7318 0.084 0.000 0.000 0.000 0.916
#> GSM152043 1 0.3333 0.6132 0.788 0.000 0.004 0.000 0.208
#> GSM152046 1 0.3983 0.6980 0.784 0.000 0.000 0.164 0.052
#> GSM152047 5 0.5509 0.4176 0.360 0.000 0.000 0.076 0.564
#> GSM152048 1 0.4887 0.5326 0.668 0.000 0.284 0.004 0.044
#> GSM152050 1 0.2813 0.7288 0.832 0.000 0.000 0.168 0.000
#> GSM152052 1 0.3239 0.7101 0.828 0.004 0.156 0.000 0.012
#> GSM152056 1 0.5282 0.6477 0.716 0.000 0.172 0.084 0.028
#> GSM152060 1 0.4393 0.6897 0.756 0.000 0.000 0.168 0.076
#> GSM152065 5 0.2233 0.6962 0.016 0.000 0.080 0.000 0.904
#> GSM152066 1 0.1956 0.7556 0.916 0.000 0.076 0.008 0.000
#> GSM152069 2 0.5267 0.6338 0.036 0.732 0.120 0.000 0.112
#> GSM152070 5 0.2966 0.6908 0.184 0.000 0.000 0.000 0.816
#> GSM152071 2 0.7589 0.2795 0.192 0.480 0.244 0.000 0.084
#> GSM152072 5 0.1662 0.7363 0.056 0.004 0.004 0.000 0.936
#> GSM152073 1 0.1608 0.7468 0.928 0.000 0.000 0.000 0.072
#> GSM152078 1 0.1469 0.7624 0.948 0.016 0.036 0.000 0.000
#> GSM152082 5 0.4166 0.5232 0.348 0.000 0.004 0.000 0.648
#> GSM152086 1 0.1830 0.7640 0.932 0.000 0.040 0.028 0.000
#> GSM152090 1 0.5119 0.3352 0.576 0.388 0.028 0.000 0.008
#> GSM152092 1 0.5490 0.5500 0.644 0.000 0.128 0.000 0.228
#> GSM152093 1 0.4796 0.6825 0.740 0.000 0.164 0.088 0.008
#> GSM152094 1 0.1043 0.7601 0.960 0.000 0.000 0.000 0.040
#> GSM152098 5 0.4415 0.3287 0.444 0.000 0.004 0.000 0.552
#> GSM152110 1 0.5920 0.5082 0.592 0.000 0.072 0.312 0.024
#> GSM152031 1 0.1410 0.7600 0.940 0.000 0.060 0.000 0.000
#> GSM152037 1 0.4250 0.6007 0.720 0.000 0.252 0.000 0.028
#> GSM152055 4 0.4310 0.1362 0.392 0.000 0.000 0.604 0.004
#> GSM152061 1 0.5895 0.1613 0.460 0.000 0.000 0.440 0.100
#> GSM152064 4 0.4206 0.4445 0.272 0.000 0.000 0.708 0.020
#> GSM152087 1 0.1197 0.7572 0.952 0.000 0.000 0.000 0.048
#> GSM152103 1 0.4373 0.6577 0.764 0.176 0.052 0.000 0.008
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM152032 3 0.1958 0.8464 0.100 0.000 0.896 0.000 0.004 0.000
#> GSM152033 1 0.3915 0.2955 0.696 0.008 0.012 0.000 0.284 0.000
#> GSM152063 2 0.1152 0.9341 0.004 0.952 0.000 0.044 0.000 0.000
#> GSM152074 1 0.4408 0.1046 0.636 0.000 0.320 0.000 0.044 0.000
#> GSM152080 2 0.0603 0.9400 0.000 0.980 0.016 0.000 0.000 0.004
#> GSM152081 4 0.3163 0.5084 0.000 0.000 0.232 0.764 0.000 0.004
#> GSM152083 2 0.2706 0.8547 0.124 0.852 0.024 0.000 0.000 0.000
#> GSM152091 2 0.0000 0.9467 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152108 1 0.2579 0.5703 0.872 0.088 0.000 0.000 0.040 0.000
#> GSM152114 1 0.3590 0.6474 0.812 0.000 0.012 0.064 0.000 0.112
#> GSM152035 2 0.3852 0.7395 0.064 0.760 0.000 0.000 0.176 0.000
#> GSM152039 4 0.0260 0.7240 0.000 0.000 0.008 0.992 0.000 0.000
#> GSM152041 4 0.0260 0.7227 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM152044 2 0.1219 0.9319 0.004 0.948 0.000 0.048 0.000 0.000
#> GSM152045 5 0.0508 0.8042 0.000 0.000 0.000 0.004 0.984 0.012
#> GSM152051 2 0.0146 0.9471 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM152054 5 0.0777 0.8020 0.024 0.000 0.000 0.004 0.972 0.000
#> GSM152057 2 0.0858 0.9406 0.028 0.968 0.000 0.004 0.000 0.000
#> GSM152058 1 0.3738 0.5524 0.680 0.000 0.004 0.004 0.000 0.312
#> GSM152067 3 0.3791 0.7226 0.000 0.004 0.768 0.000 0.180 0.048
#> GSM152068 2 0.0291 0.9470 0.004 0.992 0.000 0.004 0.000 0.000
#> GSM152075 4 0.0405 0.7240 0.000 0.000 0.008 0.988 0.000 0.004
#> GSM152076 4 0.0260 0.7240 0.000 0.000 0.008 0.992 0.000 0.000
#> GSM152079 2 0.0146 0.9471 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM152084 3 0.1333 0.8658 0.048 0.000 0.944 0.008 0.000 0.000
#> GSM152089 5 0.4274 0.4483 0.000 0.000 0.004 0.336 0.636 0.024
#> GSM152095 4 0.0363 0.7229 0.000 0.000 0.012 0.988 0.000 0.000
#> GSM152096 2 0.0000 0.9467 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152097 4 0.3872 0.2661 0.000 0.392 0.004 0.604 0.000 0.000
#> GSM152099 2 0.1642 0.9239 0.004 0.936 0.028 0.032 0.000 0.000
#> GSM152106 4 0.3817 0.1560 0.000 0.432 0.000 0.568 0.000 0.000
#> GSM152107 3 0.1793 0.8614 0.036 0.000 0.928 0.032 0.004 0.000
#> GSM152109 3 0.1500 0.8504 0.000 0.012 0.936 0.000 0.000 0.052
#> GSM152111 6 0.2163 0.7373 0.092 0.000 0.000 0.016 0.000 0.892
#> GSM152112 5 0.2850 0.7528 0.016 0.000 0.016 0.112 0.856 0.000
#> GSM152113 1 0.2455 0.5595 0.872 0.012 0.000 0.000 0.112 0.004
#> GSM152115 5 0.1584 0.7874 0.064 0.000 0.008 0.000 0.928 0.000
#> GSM152030 4 0.6378 0.0232 0.300 0.000 0.300 0.388 0.000 0.012
#> GSM152038 1 0.3424 0.5045 0.812 0.000 0.096 0.000 0.092 0.000
#> GSM152042 3 0.2191 0.8181 0.004 0.000 0.876 0.120 0.000 0.000
#> GSM152062 3 0.1364 0.8653 0.048 0.000 0.944 0.004 0.004 0.000
#> GSM152077 1 0.1007 0.6491 0.956 0.000 0.000 0.000 0.000 0.044
#> GSM152088 2 0.0291 0.9449 0.000 0.992 0.004 0.000 0.000 0.004
#> GSM152100 4 0.0717 0.7181 0.000 0.000 0.008 0.976 0.016 0.000
#> GSM152102 5 0.2361 0.7529 0.028 0.088 0.000 0.000 0.884 0.000
#> GSM152104 2 0.1610 0.9035 0.000 0.916 0.000 0.084 0.000 0.000
#> GSM152028 1 0.3290 0.6300 0.776 0.000 0.000 0.000 0.016 0.208
#> GSM152029 6 0.3276 0.6715 0.000 0.028 0.100 0.000 0.032 0.840
#> GSM152049 6 0.2946 0.6923 0.160 0.000 0.004 0.012 0.000 0.824
#> GSM152053 3 0.3647 0.7619 0.052 0.000 0.788 0.156 0.004 0.000
#> GSM152059 6 0.0260 0.7541 0.000 0.000 0.000 0.000 0.008 0.992
#> GSM152085 6 0.1511 0.7554 0.044 0.000 0.000 0.012 0.004 0.940
#> GSM152101 5 0.0964 0.8006 0.012 0.000 0.016 0.004 0.968 0.000
#> GSM152105 1 0.2527 0.6476 0.832 0.000 0.000 0.000 0.000 0.168
#> GSM152034 6 0.1675 0.7426 0.000 0.000 0.008 0.032 0.024 0.936
#> GSM152036 4 0.0291 0.7233 0.000 0.000 0.004 0.992 0.004 0.000
#> GSM152040 5 0.0458 0.8030 0.000 0.000 0.000 0.000 0.984 0.016
#> GSM152043 6 0.1588 0.7325 0.000 0.000 0.004 0.000 0.072 0.924
#> GSM152046 6 0.2264 0.7360 0.000 0.000 0.004 0.096 0.012 0.888
#> GSM152047 6 0.3937 0.1375 0.000 0.000 0.004 0.000 0.424 0.572
#> GSM152048 1 0.3721 0.5563 0.684 0.000 0.004 0.004 0.000 0.308
#> GSM152050 6 0.4075 0.6450 0.076 0.000 0.000 0.184 0.000 0.740
#> GSM152052 1 0.3854 0.2314 0.536 0.000 0.000 0.000 0.000 0.464
#> GSM152056 1 0.4275 0.4190 0.592 0.000 0.004 0.016 0.000 0.388
#> GSM152060 6 0.4102 0.6048 0.000 0.000 0.004 0.232 0.044 0.720
#> GSM152065 5 0.1349 0.7978 0.056 0.000 0.000 0.000 0.940 0.004
#> GSM152066 6 0.3819 0.3020 0.372 0.000 0.004 0.000 0.000 0.624
#> GSM152069 3 0.3987 0.7742 0.000 0.084 0.788 0.000 0.020 0.108
#> GSM152070 5 0.2854 0.6800 0.000 0.000 0.000 0.000 0.792 0.208
#> GSM152071 3 0.3020 0.7853 0.000 0.008 0.824 0.000 0.012 0.156
#> GSM152072 5 0.1010 0.7958 0.000 0.000 0.004 0.000 0.960 0.036
#> GSM152073 6 0.1633 0.7525 0.024 0.000 0.000 0.000 0.044 0.932
#> GSM152078 6 0.2773 0.7063 0.152 0.000 0.004 0.000 0.008 0.836
#> GSM152082 5 0.3756 0.4152 0.004 0.000 0.000 0.000 0.644 0.352
#> GSM152086 6 0.2902 0.6590 0.196 0.000 0.000 0.004 0.000 0.800
#> GSM152090 6 0.4358 0.6322 0.020 0.096 0.116 0.004 0.000 0.764
#> GSM152092 5 0.6025 -0.2302 0.244 0.000 0.000 0.000 0.384 0.372
#> GSM152093 6 0.5425 0.0219 0.396 0.000 0.012 0.084 0.000 0.508
#> GSM152094 6 0.0458 0.7566 0.016 0.000 0.000 0.000 0.000 0.984
#> GSM152098 6 0.3782 0.2735 0.000 0.000 0.004 0.000 0.360 0.636
#> GSM152110 1 0.5771 0.3792 0.500 0.000 0.004 0.168 0.000 0.328
#> GSM152031 6 0.3076 0.5991 0.240 0.000 0.000 0.000 0.000 0.760
#> GSM152037 1 0.3727 0.4368 0.612 0.000 0.000 0.000 0.000 0.388
#> GSM152055 4 0.4286 0.3369 0.028 0.000 0.004 0.648 0.000 0.320
#> GSM152061 4 0.5027 -0.0601 0.000 0.000 0.004 0.488 0.060 0.448
#> GSM152064 4 0.3559 0.5211 0.000 0.000 0.004 0.744 0.012 0.240
#> GSM152087 6 0.0935 0.7560 0.032 0.000 0.000 0.000 0.004 0.964
#> GSM152103 6 0.4129 0.6822 0.144 0.012 0.080 0.000 0.000 0.764
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 specimen(p) k
#> CV:NMF 79 3.12e-08 2
#> CV:NMF 72 5.84e-08 3
#> CV:NMF 71 5.06e-05 4
#> CV:NMF 73 1.26e-05 5
#> CV:NMF 70 1.07e-02 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 10612 rows and 88 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 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 0.151 0.620 0.807 0.3779 0.632 0.632
#> 3 3 0.225 0.529 0.743 0.5124 0.769 0.639
#> 4 4 0.325 0.454 0.675 0.1612 0.881 0.734
#> 5 5 0.446 0.474 0.638 0.1066 0.807 0.524
#> 6 6 0.511 0.349 0.608 0.0677 0.818 0.448
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
#> GSM152032 1 0.7376 0.640 0.792 0.208
#> GSM152033 1 0.2778 0.745 0.952 0.048
#> GSM152063 2 0.9129 0.573 0.328 0.672
#> GSM152074 1 0.7602 0.611 0.780 0.220
#> GSM152080 1 0.8763 0.488 0.704 0.296
#> GSM152081 2 0.9608 0.450 0.384 0.616
#> GSM152083 1 0.8081 0.568 0.752 0.248
#> GSM152091 1 0.8763 0.488 0.704 0.296
#> GSM152108 1 0.6712 0.688 0.824 0.176
#> GSM152114 1 0.8763 0.567 0.704 0.296
#> GSM152035 1 0.8443 0.590 0.728 0.272
#> GSM152039 2 0.2778 0.658 0.048 0.952
#> GSM152041 1 0.9881 0.257 0.564 0.436
#> GSM152044 2 0.8608 0.627 0.284 0.716
#> GSM152045 1 0.2043 0.751 0.968 0.032
#> GSM152051 2 0.8608 0.627 0.284 0.716
#> GSM152054 1 0.7602 0.672 0.780 0.220
#> GSM152057 2 0.8555 0.630 0.280 0.720
#> GSM152058 1 0.6148 0.712 0.848 0.152
#> GSM152067 1 0.7602 0.611 0.780 0.220
#> GSM152068 2 0.8555 0.630 0.280 0.720
#> GSM152075 2 0.9909 0.204 0.444 0.556
#> GSM152076 2 0.2778 0.658 0.048 0.952
#> GSM152079 2 0.8555 0.630 0.280 0.720
#> GSM152084 1 0.6712 0.686 0.824 0.176
#> GSM152089 1 0.9977 0.103 0.528 0.472
#> GSM152095 2 0.2778 0.658 0.048 0.952
#> GSM152096 1 0.6531 0.687 0.832 0.168
#> GSM152097 2 0.0000 0.640 0.000 1.000
#> GSM152099 2 0.9909 0.368 0.444 0.556
#> GSM152106 2 0.0000 0.640 0.000 1.000
#> GSM152107 1 0.7528 0.616 0.784 0.216
#> GSM152109 1 0.7602 0.611 0.780 0.220
#> GSM152111 1 0.7219 0.668 0.800 0.200
#> GSM152112 2 0.9933 0.180 0.452 0.548
#> GSM152113 1 0.5294 0.724 0.880 0.120
#> GSM152115 1 0.7528 0.616 0.784 0.216
#> GSM152030 2 0.9775 0.383 0.412 0.588
#> GSM152038 1 0.4298 0.752 0.912 0.088
#> GSM152042 2 0.9754 0.383 0.408 0.592
#> GSM152062 1 0.6531 0.687 0.832 0.168
#> GSM152077 1 0.3114 0.751 0.944 0.056
#> GSM152088 1 0.8813 0.478 0.700 0.300
#> GSM152100 2 0.9922 0.188 0.448 0.552
#> GSM152102 1 0.8443 0.590 0.728 0.272
#> GSM152104 2 0.0000 0.640 0.000 1.000
#> GSM152028 1 0.0000 0.746 1.000 0.000
#> GSM152029 1 0.3114 0.752 0.944 0.056
#> GSM152049 1 0.6438 0.701 0.836 0.164
#> GSM152053 2 0.9754 0.383 0.408 0.592
#> GSM152059 1 0.4690 0.747 0.900 0.100
#> GSM152085 1 0.5946 0.718 0.856 0.144
#> GSM152101 1 0.7528 0.616 0.784 0.216
#> GSM152105 1 0.1414 0.751 0.980 0.020
#> GSM152034 1 0.7674 0.630 0.776 0.224
#> GSM152036 2 0.2778 0.658 0.048 0.952
#> GSM152040 1 0.5519 0.746 0.872 0.128
#> GSM152043 1 0.0938 0.749 0.988 0.012
#> GSM152046 1 0.9044 0.461 0.680 0.320
#> GSM152047 1 0.2043 0.751 0.968 0.032
#> GSM152048 1 0.6148 0.712 0.848 0.152
#> GSM152050 1 0.7139 0.667 0.804 0.196
#> GSM152052 1 0.4298 0.749 0.912 0.088
#> GSM152056 1 0.6148 0.712 0.848 0.152
#> GSM152060 1 0.9044 0.461 0.680 0.320
#> GSM152065 1 0.0000 0.746 1.000 0.000
#> GSM152066 1 0.6148 0.712 0.848 0.152
#> GSM152069 1 0.7602 0.611 0.780 0.220
#> GSM152070 1 0.2043 0.751 0.968 0.032
#> GSM152071 1 0.7602 0.611 0.780 0.220
#> GSM152072 1 0.1843 0.751 0.972 0.028
#> GSM152073 1 0.5737 0.725 0.864 0.136
#> GSM152078 1 0.4022 0.748 0.920 0.080
#> GSM152082 1 0.0000 0.746 1.000 0.000
#> GSM152086 1 0.6247 0.707 0.844 0.156
#> GSM152090 1 0.7056 0.713 0.808 0.192
#> GSM152092 1 0.0000 0.746 1.000 0.000
#> GSM152093 1 0.6048 0.744 0.852 0.148
#> GSM152094 1 0.5737 0.725 0.864 0.136
#> GSM152098 1 0.1414 0.750 0.980 0.020
#> GSM152110 1 0.6343 0.706 0.840 0.160
#> GSM152031 1 0.4298 0.752 0.912 0.088
#> GSM152037 1 0.2948 0.755 0.948 0.052
#> GSM152055 1 0.9044 0.461 0.680 0.320
#> GSM152061 1 0.9044 0.461 0.680 0.320
#> GSM152064 1 0.9732 0.338 0.596 0.404
#> GSM152087 1 0.5294 0.735 0.880 0.120
#> GSM152103 1 0.6801 0.723 0.820 0.180
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM152032 3 0.7138 0.5815 0.312 0.044 0.644
#> GSM152033 1 0.5968 0.4356 0.636 0.000 0.364
#> GSM152063 2 0.8562 0.3679 0.108 0.540 0.352
#> GSM152074 3 0.4291 0.7381 0.180 0.000 0.820
#> GSM152080 3 0.0592 0.5810 0.000 0.012 0.988
#> GSM152081 2 0.9087 0.3466 0.224 0.552 0.224
#> GSM152083 3 0.3845 0.6997 0.116 0.012 0.872
#> GSM152091 3 0.0592 0.5810 0.000 0.012 0.988
#> GSM152108 1 0.8466 0.1542 0.508 0.092 0.400
#> GSM152114 1 0.9452 0.2204 0.496 0.220 0.284
#> GSM152035 3 0.8790 0.2953 0.328 0.132 0.540
#> GSM152039 2 0.0237 0.5745 0.004 0.996 0.000
#> GSM152041 1 0.8619 0.2549 0.524 0.368 0.108
#> GSM152044 2 0.6955 0.3234 0.016 0.492 0.492
#> GSM152045 1 0.3193 0.7080 0.896 0.004 0.100
#> GSM152051 2 0.6955 0.3234 0.016 0.492 0.492
#> GSM152054 1 0.9075 0.1737 0.472 0.140 0.388
#> GSM152057 2 0.6954 0.3340 0.016 0.500 0.484
#> GSM152058 1 0.4569 0.7141 0.860 0.072 0.068
#> GSM152067 3 0.5178 0.7217 0.256 0.000 0.744
#> GSM152068 2 0.6954 0.3340 0.016 0.500 0.484
#> GSM152075 2 0.9122 0.3695 0.280 0.536 0.184
#> GSM152076 2 0.0237 0.5745 0.004 0.996 0.000
#> GSM152079 2 0.6954 0.3340 0.016 0.500 0.484
#> GSM152084 1 0.7913 0.0260 0.492 0.056 0.452
#> GSM152089 2 0.9189 -0.0639 0.416 0.436 0.148
#> GSM152095 2 0.0237 0.5745 0.004 0.996 0.000
#> GSM152096 1 0.7755 0.0207 0.492 0.048 0.460
#> GSM152097 2 0.2165 0.5685 0.000 0.936 0.064
#> GSM152099 3 0.8073 0.0892 0.080 0.344 0.576
#> GSM152106 2 0.2165 0.5685 0.000 0.936 0.064
#> GSM152107 3 0.6053 0.7132 0.260 0.020 0.720
#> GSM152109 3 0.4002 0.7385 0.160 0.000 0.840
#> GSM152111 1 0.3845 0.6873 0.872 0.116 0.012
#> GSM152112 2 0.9243 0.3555 0.288 0.520 0.192
#> GSM152113 1 0.7337 0.1901 0.540 0.032 0.428
#> GSM152115 3 0.6053 0.7132 0.260 0.020 0.720
#> GSM152030 2 0.9463 0.2860 0.256 0.500 0.244
#> GSM152038 1 0.4178 0.6791 0.828 0.000 0.172
#> GSM152042 2 0.9364 0.3044 0.268 0.512 0.220
#> GSM152062 1 0.7755 0.0207 0.492 0.048 0.460
#> GSM152077 1 0.6497 0.4663 0.648 0.016 0.336
#> GSM152088 3 0.0747 0.5791 0.000 0.016 0.984
#> GSM152100 2 0.9145 0.3609 0.284 0.532 0.184
#> GSM152102 3 0.8738 0.3006 0.328 0.128 0.544
#> GSM152104 2 0.2165 0.5685 0.000 0.936 0.064
#> GSM152028 1 0.5138 0.6135 0.748 0.000 0.252
#> GSM152029 1 0.2356 0.7174 0.928 0.000 0.072
#> GSM152049 1 0.4206 0.7093 0.872 0.088 0.040
#> GSM152053 2 0.9364 0.3044 0.268 0.512 0.220
#> GSM152059 1 0.3038 0.6982 0.896 0.000 0.104
#> GSM152085 1 0.3370 0.7122 0.904 0.072 0.024
#> GSM152101 3 0.6053 0.7132 0.260 0.020 0.720
#> GSM152105 1 0.4002 0.6931 0.840 0.000 0.160
#> GSM152034 1 0.4453 0.6540 0.836 0.152 0.012
#> GSM152036 2 0.0237 0.5745 0.004 0.996 0.000
#> GSM152040 1 0.6939 0.6231 0.712 0.072 0.216
#> GSM152043 1 0.3267 0.7101 0.884 0.000 0.116
#> GSM152046 1 0.5216 0.5062 0.740 0.260 0.000
#> GSM152047 1 0.2959 0.7084 0.900 0.000 0.100
#> GSM152048 1 0.4569 0.7141 0.860 0.072 0.068
#> GSM152050 1 0.3771 0.6878 0.876 0.112 0.012
#> GSM152052 1 0.4654 0.6520 0.792 0.000 0.208
#> GSM152056 1 0.4569 0.7141 0.860 0.072 0.068
#> GSM152060 1 0.5216 0.5062 0.740 0.260 0.000
#> GSM152065 1 0.5098 0.6171 0.752 0.000 0.248
#> GSM152066 1 0.4569 0.7141 0.860 0.072 0.068
#> GSM152069 3 0.4002 0.7385 0.160 0.000 0.840
#> GSM152070 1 0.2959 0.7084 0.900 0.000 0.100
#> GSM152071 3 0.4002 0.7385 0.160 0.000 0.840
#> GSM152072 1 0.2959 0.7074 0.900 0.000 0.100
#> GSM152073 1 0.3780 0.7165 0.892 0.064 0.044
#> GSM152078 1 0.4002 0.6861 0.840 0.000 0.160
#> GSM152082 1 0.3412 0.7048 0.876 0.000 0.124
#> GSM152086 1 0.3765 0.7074 0.888 0.084 0.028
#> GSM152090 1 0.7262 0.4326 0.624 0.044 0.332
#> GSM152092 1 0.3686 0.6987 0.860 0.000 0.140
#> GSM152093 1 0.7199 0.5693 0.676 0.064 0.260
#> GSM152094 1 0.3780 0.7165 0.892 0.064 0.044
#> GSM152098 1 0.2878 0.7118 0.904 0.000 0.096
#> GSM152110 1 0.4544 0.7121 0.860 0.084 0.056
#> GSM152031 1 0.3686 0.6970 0.860 0.000 0.140
#> GSM152037 1 0.4551 0.7167 0.844 0.024 0.132
#> GSM152055 1 0.5216 0.5062 0.740 0.260 0.000
#> GSM152061 1 0.5216 0.5062 0.740 0.260 0.000
#> GSM152064 1 0.8494 0.3339 0.556 0.336 0.108
#> GSM152087 1 0.3896 0.7235 0.888 0.052 0.060
#> GSM152103 1 0.7012 0.4918 0.652 0.040 0.308
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM152032 3 0.6390 0.4055 0.136 0.132 0.704 0.028
#> GSM152033 1 0.7540 0.2050 0.444 0.192 0.364 0.000
#> GSM152063 4 0.7619 0.3001 0.020 0.372 0.124 0.484
#> GSM152074 3 0.2060 0.4689 0.016 0.052 0.932 0.000
#> GSM152080 2 0.4193 0.3983 0.000 0.732 0.268 0.000
#> GSM152081 4 0.7563 0.3180 0.120 0.028 0.308 0.544
#> GSM152083 3 0.4188 0.1564 0.004 0.244 0.752 0.000
#> GSM152091 2 0.4193 0.3983 0.000 0.732 0.268 0.000
#> GSM152108 3 0.8929 0.0936 0.316 0.304 0.332 0.048
#> GSM152114 1 0.9746 -0.0580 0.332 0.200 0.296 0.172
#> GSM152035 2 0.8899 0.2112 0.232 0.456 0.236 0.076
#> GSM152039 4 0.0376 0.5475 0.004 0.004 0.000 0.992
#> GSM152041 1 0.8760 0.2513 0.468 0.212 0.068 0.252
#> GSM152044 4 0.7119 0.3048 0.000 0.388 0.132 0.480
#> GSM152045 1 0.4334 0.6705 0.804 0.032 0.160 0.004
#> GSM152051 4 0.7119 0.3048 0.000 0.388 0.132 0.480
#> GSM152054 2 0.9098 -0.0536 0.344 0.356 0.228 0.072
#> GSM152057 4 0.7106 0.3136 0.000 0.380 0.132 0.488
#> GSM152058 1 0.3963 0.6926 0.860 0.056 0.060 0.024
#> GSM152067 3 0.3243 0.4864 0.088 0.036 0.876 0.000
#> GSM152068 4 0.7106 0.3136 0.000 0.380 0.132 0.488
#> GSM152075 4 0.9427 0.2140 0.204 0.188 0.176 0.432
#> GSM152076 4 0.0376 0.5475 0.004 0.004 0.000 0.992
#> GSM152079 4 0.7106 0.3136 0.000 0.380 0.132 0.488
#> GSM152084 3 0.8259 0.2725 0.288 0.180 0.492 0.040
#> GSM152089 1 0.9452 0.0101 0.328 0.244 0.104 0.324
#> GSM152095 4 0.0376 0.5475 0.004 0.004 0.000 0.992
#> GSM152096 3 0.8120 0.2765 0.284 0.184 0.500 0.032
#> GSM152097 4 0.1792 0.5404 0.000 0.068 0.000 0.932
#> GSM152099 3 0.7879 -0.2739 0.000 0.288 0.380 0.332
#> GSM152106 4 0.1792 0.5404 0.000 0.068 0.000 0.932
#> GSM152107 3 0.3036 0.4952 0.080 0.020 0.892 0.008
#> GSM152109 3 0.2450 0.4560 0.016 0.072 0.912 0.000
#> GSM152111 1 0.3432 0.6853 0.884 0.036 0.020 0.060
#> GSM152112 4 0.9503 0.2032 0.196 0.192 0.192 0.420
#> GSM152113 3 0.8063 0.0822 0.352 0.184 0.444 0.020
#> GSM152115 3 0.3036 0.4952 0.080 0.020 0.892 0.008
#> GSM152030 4 0.8044 0.2576 0.128 0.040 0.364 0.468
#> GSM152038 1 0.5582 0.6250 0.724 0.108 0.168 0.000
#> GSM152042 4 0.8136 0.2772 0.136 0.044 0.340 0.480
#> GSM152062 3 0.8104 0.2832 0.280 0.184 0.504 0.032
#> GSM152077 1 0.7846 0.2456 0.464 0.184 0.340 0.012
#> GSM152088 2 0.4372 0.3951 0.000 0.728 0.268 0.004
#> GSM152100 4 0.9454 0.2077 0.200 0.192 0.180 0.428
#> GSM152102 2 0.8846 0.2134 0.232 0.460 0.236 0.072
#> GSM152104 4 0.1792 0.5404 0.000 0.068 0.000 0.932
#> GSM152028 1 0.6708 0.5090 0.596 0.132 0.272 0.000
#> GSM152029 1 0.3542 0.6928 0.852 0.028 0.120 0.000
#> GSM152049 1 0.3398 0.7018 0.888 0.028 0.048 0.036
#> GSM152053 4 0.8136 0.2772 0.136 0.044 0.340 0.480
#> GSM152059 1 0.4205 0.6677 0.820 0.056 0.124 0.000
#> GSM152085 1 0.2715 0.7046 0.916 0.016 0.036 0.032
#> GSM152101 3 0.3036 0.4952 0.080 0.020 0.892 0.008
#> GSM152105 1 0.5147 0.6507 0.740 0.060 0.200 0.000
#> GSM152034 1 0.4212 0.6622 0.844 0.044 0.024 0.088
#> GSM152036 4 0.0376 0.5475 0.004 0.004 0.000 0.992
#> GSM152040 1 0.7610 0.4943 0.584 0.168 0.216 0.032
#> GSM152043 1 0.4194 0.6739 0.800 0.028 0.172 0.000
#> GSM152046 1 0.5076 0.5566 0.756 0.072 0.000 0.172
#> GSM152047 1 0.4244 0.6703 0.804 0.036 0.160 0.000
#> GSM152048 1 0.3963 0.6926 0.860 0.056 0.060 0.024
#> GSM152050 1 0.3353 0.6857 0.888 0.036 0.020 0.056
#> GSM152052 1 0.6075 0.5895 0.680 0.128 0.192 0.000
#> GSM152056 1 0.3963 0.6926 0.860 0.056 0.060 0.024
#> GSM152060 1 0.5118 0.5541 0.752 0.072 0.000 0.176
#> GSM152065 1 0.6685 0.5134 0.600 0.132 0.268 0.000
#> GSM152066 1 0.3963 0.6926 0.860 0.056 0.060 0.024
#> GSM152069 3 0.2450 0.4560 0.016 0.072 0.912 0.000
#> GSM152070 1 0.4244 0.6703 0.804 0.036 0.160 0.000
#> GSM152071 3 0.2450 0.4560 0.016 0.072 0.912 0.000
#> GSM152072 1 0.4152 0.6702 0.808 0.032 0.160 0.000
#> GSM152073 1 0.3852 0.7012 0.864 0.040 0.072 0.024
#> GSM152078 1 0.5496 0.6325 0.732 0.108 0.160 0.000
#> GSM152082 1 0.4281 0.6658 0.792 0.028 0.180 0.000
#> GSM152086 1 0.3410 0.6990 0.888 0.036 0.044 0.032
#> GSM152090 1 0.7926 0.2108 0.480 0.144 0.348 0.028
#> GSM152092 1 0.4720 0.6568 0.768 0.044 0.188 0.000
#> GSM152093 1 0.7996 0.4096 0.532 0.156 0.272 0.040
#> GSM152094 1 0.3852 0.7012 0.864 0.040 0.072 0.024
#> GSM152098 1 0.3862 0.6776 0.824 0.024 0.152 0.000
#> GSM152110 1 0.3943 0.6956 0.864 0.048 0.048 0.040
#> GSM152031 1 0.4919 0.6564 0.772 0.076 0.152 0.000
#> GSM152037 1 0.4807 0.6871 0.788 0.052 0.152 0.008
#> GSM152055 1 0.5118 0.5541 0.752 0.072 0.000 0.176
#> GSM152061 1 0.5118 0.5541 0.752 0.072 0.000 0.176
#> GSM152064 1 0.8566 0.3156 0.504 0.204 0.068 0.224
#> GSM152087 1 0.3684 0.7073 0.868 0.036 0.080 0.016
#> GSM152103 1 0.7700 0.3099 0.516 0.136 0.324 0.024
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM152032 5 0.5396 0.1014 0.056 0.000 0.444 0.000 0.500
#> GSM152033 5 0.4235 0.4483 0.184 0.008 0.040 0.000 0.768
#> GSM152063 4 0.7488 -0.1788 0.024 0.276 0.008 0.412 0.280
#> GSM152074 3 0.2079 0.8326 0.000 0.020 0.916 0.000 0.064
#> GSM152080 2 0.0963 0.5048 0.000 0.964 0.036 0.000 0.000
#> GSM152081 4 0.7538 0.4112 0.080 0.012 0.244 0.524 0.140
#> GSM152083 3 0.3934 0.5189 0.000 0.276 0.716 0.000 0.008
#> GSM152091 2 0.0963 0.5048 0.000 0.964 0.036 0.000 0.000
#> GSM152108 5 0.4260 0.5377 0.068 0.100 0.020 0.004 0.808
#> GSM152114 5 0.6486 0.4463 0.204 0.000 0.068 0.108 0.620
#> GSM152035 5 0.6806 0.2250 0.100 0.388 0.016 0.020 0.476
#> GSM152039 4 0.0854 0.5736 0.008 0.000 0.004 0.976 0.012
#> GSM152041 1 0.7354 0.0277 0.496 0.060 0.012 0.116 0.316
#> GSM152044 2 0.5503 0.5627 0.000 0.484 0.024 0.468 0.024
#> GSM152045 1 0.4840 0.4567 0.640 0.000 0.040 0.000 0.320
#> GSM152051 2 0.5503 0.5627 0.000 0.484 0.024 0.468 0.024
#> GSM152054 5 0.6834 0.4154 0.184 0.200 0.032 0.008 0.576
#> GSM152057 2 0.5644 0.5611 0.000 0.476 0.024 0.468 0.032
#> GSM152058 1 0.3652 0.5804 0.784 0.000 0.004 0.012 0.200
#> GSM152067 3 0.3454 0.8484 0.036 0.016 0.848 0.000 0.100
#> GSM152068 2 0.5644 0.5611 0.000 0.476 0.024 0.468 0.032
#> GSM152075 5 0.7960 0.0614 0.224 0.024 0.040 0.304 0.408
#> GSM152076 4 0.0854 0.5736 0.008 0.000 0.004 0.976 0.012
#> GSM152079 2 0.5644 0.5611 0.000 0.476 0.024 0.468 0.032
#> GSM152084 5 0.4801 0.5293 0.084 0.000 0.184 0.004 0.728
#> GSM152089 5 0.7744 0.2456 0.308 0.060 0.008 0.188 0.436
#> GSM152095 4 0.0854 0.5736 0.008 0.000 0.004 0.976 0.012
#> GSM152096 5 0.4502 0.5304 0.076 0.000 0.180 0.000 0.744
#> GSM152097 4 0.1798 0.5172 0.000 0.064 0.004 0.928 0.004
#> GSM152099 2 0.7353 0.3401 0.000 0.352 0.300 0.324 0.024
#> GSM152106 4 0.1798 0.5172 0.000 0.064 0.004 0.928 0.004
#> GSM152107 3 0.3433 0.8410 0.032 0.004 0.832 0.000 0.132
#> GSM152109 3 0.1280 0.8505 0.008 0.024 0.960 0.000 0.008
#> GSM152111 1 0.2270 0.6275 0.908 0.000 0.004 0.016 0.072
#> GSM152112 5 0.7978 0.0817 0.216 0.024 0.044 0.300 0.416
#> GSM152113 5 0.4723 0.5240 0.136 0.000 0.128 0.000 0.736
#> GSM152115 3 0.3433 0.8410 0.032 0.004 0.832 0.000 0.132
#> GSM152030 4 0.7972 0.3944 0.092 0.004 0.240 0.436 0.228
#> GSM152038 1 0.5868 0.3659 0.580 0.020 0.056 0.004 0.340
#> GSM152042 4 0.7997 0.4003 0.100 0.004 0.216 0.440 0.240
#> GSM152062 5 0.4537 0.5268 0.076 0.000 0.184 0.000 0.740
#> GSM152077 5 0.3880 0.4372 0.204 0.004 0.020 0.000 0.772
#> GSM152088 2 0.1124 0.5059 0.000 0.960 0.036 0.004 0.000
#> GSM152100 5 0.7878 0.0800 0.220 0.024 0.036 0.300 0.420
#> GSM152102 5 0.6811 0.2215 0.100 0.392 0.016 0.020 0.472
#> GSM152104 4 0.1798 0.5172 0.000 0.064 0.004 0.928 0.004
#> GSM152028 5 0.5122 0.1179 0.352 0.004 0.032 0.004 0.608
#> GSM152029 1 0.4186 0.5887 0.768 0.000 0.044 0.004 0.184
#> GSM152049 1 0.2909 0.6212 0.848 0.000 0.000 0.012 0.140
#> GSM152053 4 0.7997 0.4003 0.100 0.004 0.216 0.440 0.240
#> GSM152059 1 0.4795 0.5791 0.780 0.040 0.096 0.004 0.080
#> GSM152085 1 0.2284 0.6407 0.896 0.000 0.004 0.004 0.096
#> GSM152101 3 0.3433 0.8410 0.032 0.004 0.832 0.000 0.132
#> GSM152105 1 0.5277 0.3415 0.548 0.004 0.032 0.004 0.412
#> GSM152034 1 0.2745 0.6064 0.892 0.004 0.004 0.036 0.064
#> GSM152036 4 0.0693 0.5734 0.008 0.000 0.000 0.980 0.012
#> GSM152040 5 0.6163 0.0322 0.424 0.044 0.036 0.004 0.492
#> GSM152043 1 0.4971 0.4712 0.628 0.000 0.036 0.004 0.332
#> GSM152046 1 0.4311 0.5038 0.808 0.012 0.012 0.076 0.092
#> GSM152047 1 0.4854 0.4595 0.648 0.000 0.044 0.000 0.308
#> GSM152048 1 0.3652 0.5804 0.784 0.000 0.004 0.012 0.200
#> GSM152050 1 0.2206 0.6285 0.912 0.000 0.004 0.016 0.068
#> GSM152052 1 0.6366 0.3007 0.532 0.044 0.056 0.004 0.364
#> GSM152056 1 0.3652 0.5804 0.784 0.000 0.004 0.012 0.200
#> GSM152060 1 0.4369 0.5004 0.804 0.012 0.012 0.080 0.092
#> GSM152065 5 0.5136 0.1094 0.356 0.004 0.032 0.004 0.604
#> GSM152066 1 0.3652 0.5804 0.784 0.000 0.004 0.012 0.200
#> GSM152069 3 0.1280 0.8505 0.008 0.024 0.960 0.000 0.008
#> GSM152070 1 0.4854 0.4595 0.648 0.000 0.044 0.000 0.308
#> GSM152071 3 0.1280 0.8505 0.008 0.024 0.960 0.000 0.008
#> GSM152072 1 0.4823 0.4584 0.644 0.000 0.040 0.000 0.316
#> GSM152073 1 0.2464 0.6287 0.888 0.000 0.016 0.000 0.096
#> GSM152078 1 0.5766 0.3840 0.588 0.024 0.044 0.004 0.340
#> GSM152082 1 0.5012 0.4369 0.600 0.000 0.032 0.004 0.364
#> GSM152086 1 0.1892 0.6359 0.916 0.000 0.004 0.000 0.080
#> GSM152090 5 0.5940 0.4048 0.284 0.000 0.144 0.000 0.572
#> GSM152092 1 0.5088 0.4005 0.572 0.000 0.032 0.004 0.392
#> GSM152093 5 0.5172 0.3110 0.332 0.000 0.048 0.004 0.616
#> GSM152094 1 0.2464 0.6287 0.888 0.000 0.016 0.000 0.096
#> GSM152098 1 0.4867 0.4847 0.652 0.000 0.036 0.004 0.308
#> GSM152110 1 0.3525 0.6031 0.816 0.000 0.004 0.024 0.156
#> GSM152031 1 0.5485 0.4561 0.640 0.020 0.044 0.004 0.292
#> GSM152037 1 0.4817 0.4576 0.608 0.000 0.016 0.008 0.368
#> GSM152055 1 0.4422 0.4986 0.800 0.012 0.012 0.080 0.096
#> GSM152061 1 0.4369 0.5004 0.804 0.012 0.012 0.080 0.092
#> GSM152064 1 0.6949 0.1109 0.540 0.060 0.004 0.104 0.292
#> GSM152087 1 0.2723 0.6322 0.864 0.000 0.012 0.000 0.124
#> GSM152103 5 0.5952 0.3370 0.324 0.000 0.128 0.000 0.548
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM152032 1 0.5481 -0.042765 0.468 0.000 0.420 0.004 0.108 0.000
#> GSM152033 1 0.2308 0.405820 0.880 0.000 0.004 0.000 0.108 0.008
#> GSM152063 4 0.7468 0.123382 0.072 0.196 0.000 0.424 0.276 0.032
#> GSM152074 3 0.2290 0.801937 0.020 0.000 0.892 0.004 0.084 0.000
#> GSM152080 2 0.0000 0.523957 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152081 4 0.7567 0.198427 0.052 0.000 0.184 0.444 0.252 0.068
#> GSM152083 3 0.3788 0.484695 0.004 0.280 0.704 0.000 0.012 0.000
#> GSM152091 2 0.0000 0.523957 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152108 1 0.4551 0.175072 0.668 0.040 0.000 0.004 0.280 0.008
#> GSM152114 1 0.6772 -0.145142 0.448 0.000 0.028 0.028 0.344 0.152
#> GSM152035 2 0.7242 0.029061 0.308 0.324 0.000 0.020 0.308 0.040
#> GSM152039 4 0.2384 0.529783 0.000 0.000 0.000 0.888 0.064 0.048
#> GSM152041 6 0.6049 -0.293808 0.080 0.008 0.000 0.044 0.344 0.524
#> GSM152044 4 0.5162 0.231007 0.004 0.456 0.008 0.480 0.052 0.000
#> GSM152045 1 0.5355 0.118629 0.468 0.000 0.000 0.000 0.108 0.424
#> GSM152051 4 0.5162 0.231007 0.004 0.456 0.008 0.480 0.052 0.000
#> GSM152054 5 0.6780 0.046385 0.372 0.132 0.000 0.000 0.408 0.088
#> GSM152057 4 0.5255 0.235643 0.004 0.448 0.008 0.480 0.060 0.000
#> GSM152058 6 0.4264 0.431089 0.352 0.000 0.000 0.000 0.028 0.620
#> GSM152067 3 0.2886 0.834717 0.064 0.000 0.860 0.000 0.072 0.004
#> GSM152068 4 0.5255 0.235643 0.004 0.448 0.008 0.480 0.060 0.000
#> GSM152075 5 0.7194 0.678539 0.104 0.000 0.008 0.176 0.452 0.260
#> GSM152076 4 0.2384 0.529783 0.000 0.000 0.000 0.888 0.064 0.048
#> GSM152079 4 0.5255 0.235643 0.004 0.448 0.008 0.480 0.060 0.000
#> GSM152084 1 0.5425 0.261983 0.648 0.000 0.144 0.004 0.184 0.020
#> GSM152089 5 0.7311 0.580729 0.164 0.008 0.000 0.112 0.404 0.312
#> GSM152095 4 0.2384 0.529783 0.000 0.000 0.000 0.888 0.064 0.048
#> GSM152096 1 0.5171 0.268403 0.668 0.000 0.144 0.004 0.172 0.012
#> GSM152097 4 0.0405 0.533790 0.000 0.008 0.000 0.988 0.004 0.000
#> GSM152099 2 0.6972 -0.139540 0.004 0.344 0.284 0.324 0.044 0.000
#> GSM152106 4 0.0405 0.533790 0.000 0.008 0.000 0.988 0.004 0.000
#> GSM152107 3 0.3393 0.827919 0.068 0.000 0.820 0.000 0.108 0.004
#> GSM152109 3 0.0725 0.839473 0.012 0.000 0.976 0.000 0.012 0.000
#> GSM152111 6 0.3700 0.545435 0.152 0.000 0.000 0.000 0.068 0.780
#> GSM152112 5 0.7454 0.684218 0.120 0.000 0.016 0.176 0.436 0.252
#> GSM152113 1 0.4474 0.339388 0.740 0.000 0.088 0.004 0.156 0.012
#> GSM152115 3 0.3393 0.827919 0.068 0.000 0.820 0.000 0.108 0.004
#> GSM152030 4 0.8033 0.067560 0.088 0.000 0.168 0.364 0.304 0.076
#> GSM152038 1 0.6364 -0.046511 0.456 0.000 0.028 0.000 0.192 0.324
#> GSM152042 4 0.8031 0.040463 0.088 0.000 0.152 0.368 0.308 0.084
#> GSM152062 1 0.5205 0.263223 0.664 0.000 0.148 0.004 0.172 0.012
#> GSM152077 1 0.3381 0.407358 0.808 0.000 0.000 0.004 0.148 0.040
#> GSM152088 2 0.0146 0.522456 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM152100 5 0.7275 0.687946 0.116 0.000 0.008 0.176 0.444 0.256
#> GSM152102 2 0.7239 0.036105 0.308 0.332 0.000 0.020 0.300 0.040
#> GSM152104 4 0.0405 0.533790 0.000 0.008 0.000 0.988 0.004 0.000
#> GSM152028 1 0.2214 0.418230 0.888 0.000 0.000 0.000 0.016 0.096
#> GSM152029 6 0.5451 0.199457 0.340 0.000 0.000 0.000 0.136 0.524
#> GSM152049 6 0.3670 0.497148 0.284 0.000 0.000 0.000 0.012 0.704
#> GSM152053 4 0.8031 0.040463 0.088 0.000 0.152 0.368 0.308 0.084
#> GSM152059 6 0.6013 0.363827 0.120 0.000 0.044 0.000 0.284 0.552
#> GSM152085 6 0.4099 0.512154 0.244 0.000 0.000 0.000 0.048 0.708
#> GSM152101 3 0.3393 0.827919 0.068 0.000 0.820 0.000 0.108 0.004
#> GSM152105 1 0.5064 0.247315 0.632 0.000 0.016 0.000 0.076 0.276
#> GSM152034 6 0.3172 0.552800 0.128 0.000 0.000 0.000 0.048 0.824
#> GSM152036 4 0.2325 0.530401 0.000 0.000 0.000 0.892 0.060 0.048
#> GSM152040 1 0.6208 0.219605 0.436 0.008 0.000 0.000 0.276 0.280
#> GSM152043 1 0.5205 0.103661 0.496 0.000 0.000 0.000 0.092 0.412
#> GSM152046 6 0.2278 0.451490 0.000 0.000 0.000 0.004 0.128 0.868
#> GSM152047 1 0.5357 0.105189 0.464 0.000 0.000 0.000 0.108 0.428
#> GSM152048 6 0.4264 0.431089 0.352 0.000 0.000 0.000 0.028 0.620
#> GSM152050 6 0.3681 0.545316 0.156 0.000 0.000 0.000 0.064 0.780
#> GSM152052 1 0.6586 -0.000173 0.444 0.000 0.036 0.000 0.248 0.272
#> GSM152056 6 0.4264 0.431089 0.352 0.000 0.000 0.000 0.028 0.620
#> GSM152060 6 0.2320 0.445988 0.000 0.000 0.000 0.004 0.132 0.864
#> GSM152065 1 0.2263 0.416997 0.884 0.000 0.000 0.000 0.016 0.100
#> GSM152066 6 0.4264 0.431089 0.352 0.000 0.000 0.000 0.028 0.620
#> GSM152069 3 0.0725 0.839473 0.012 0.000 0.976 0.000 0.012 0.000
#> GSM152070 1 0.5357 0.105189 0.464 0.000 0.000 0.000 0.108 0.428
#> GSM152071 3 0.0725 0.839473 0.012 0.000 0.976 0.000 0.012 0.000
#> GSM152072 1 0.5353 0.118922 0.472 0.000 0.000 0.000 0.108 0.420
#> GSM152073 6 0.4381 0.461326 0.236 0.000 0.000 0.000 0.072 0.692
#> GSM152078 1 0.6401 -0.054225 0.448 0.000 0.028 0.000 0.200 0.324
#> GSM152082 1 0.5117 0.176710 0.548 0.000 0.000 0.000 0.092 0.360
#> GSM152086 6 0.4039 0.512494 0.208 0.000 0.000 0.000 0.060 0.732
#> GSM152090 1 0.6108 0.358973 0.608 0.000 0.100 0.000 0.140 0.152
#> GSM152092 1 0.4970 0.208981 0.580 0.000 0.000 0.000 0.084 0.336
#> GSM152093 1 0.5605 0.344526 0.604 0.000 0.020 0.000 0.152 0.224
#> GSM152094 6 0.4381 0.461326 0.236 0.000 0.000 0.000 0.072 0.692
#> GSM152098 1 0.5224 0.070506 0.468 0.000 0.000 0.000 0.092 0.440
#> GSM152110 6 0.4289 0.475269 0.304 0.000 0.000 0.004 0.032 0.660
#> GSM152031 6 0.6362 0.118447 0.376 0.000 0.024 0.000 0.192 0.408
#> GSM152037 1 0.4408 0.105740 0.608 0.000 0.000 0.000 0.036 0.356
#> GSM152055 6 0.2420 0.448560 0.004 0.000 0.000 0.004 0.128 0.864
#> GSM152061 6 0.2320 0.445988 0.000 0.000 0.000 0.004 0.132 0.864
#> GSM152064 6 0.5880 -0.195916 0.080 0.008 0.000 0.036 0.324 0.552
#> GSM152087 6 0.4557 0.448282 0.268 0.000 0.000 0.000 0.072 0.660
#> GSM152103 1 0.6152 0.377416 0.596 0.000 0.088 0.000 0.136 0.180
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n specimen(p) k
#> MAD:hclust 70 5.27e-03 2
#> MAD:hclust 58 8.84e-06 3
#> MAD:hclust 43 9.54e-04 4
#> MAD:hclust 48 2.00e-02 5
#> MAD:hclust 27 7.53e-02 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 10612 rows and 88 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 0.818 0.901 0.949 0.4996 0.501 0.501
#> 3 3 0.538 0.732 0.851 0.3110 0.762 0.557
#> 4 4 0.566 0.683 0.771 0.1252 0.906 0.735
#> 5 5 0.639 0.688 0.772 0.0729 0.839 0.495
#> 6 6 0.678 0.562 0.724 0.0429 0.976 0.881
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
#> GSM152032 2 0.5059 0.893 0.112 0.888
#> GSM152033 1 0.0938 0.931 0.988 0.012
#> GSM152063 2 0.0938 0.963 0.012 0.988
#> GSM152074 2 0.4815 0.901 0.104 0.896
#> GSM152080 2 0.2423 0.943 0.040 0.960
#> GSM152081 2 0.0938 0.963 0.012 0.988
#> GSM152083 2 0.2423 0.943 0.040 0.960
#> GSM152091 2 0.0000 0.962 0.000 1.000
#> GSM152108 2 0.0938 0.959 0.012 0.988
#> GSM152114 1 0.6623 0.799 0.828 0.172
#> GSM152035 2 0.0000 0.962 0.000 1.000
#> GSM152039 2 0.0938 0.963 0.012 0.988
#> GSM152041 2 0.7745 0.702 0.228 0.772
#> GSM152044 2 0.0938 0.963 0.012 0.988
#> GSM152045 1 0.0672 0.931 0.992 0.008
#> GSM152051 2 0.0000 0.962 0.000 1.000
#> GSM152054 2 0.5737 0.870 0.136 0.864
#> GSM152057 2 0.0000 0.962 0.000 1.000
#> GSM152058 1 0.2043 0.925 0.968 0.032
#> GSM152067 2 0.4815 0.901 0.104 0.896
#> GSM152068 2 0.0672 0.963 0.008 0.992
#> GSM152075 2 0.0938 0.963 0.012 0.988
#> GSM152076 2 0.0938 0.963 0.012 0.988
#> GSM152079 2 0.0000 0.962 0.000 1.000
#> GSM152084 1 0.9754 0.355 0.592 0.408
#> GSM152089 2 0.0938 0.963 0.012 0.988
#> GSM152095 2 0.0938 0.963 0.012 0.988
#> GSM152096 2 0.4939 0.897 0.108 0.892
#> GSM152097 2 0.0938 0.963 0.012 0.988
#> GSM152099 2 0.0000 0.962 0.000 1.000
#> GSM152106 2 0.0938 0.963 0.012 0.988
#> GSM152107 2 0.0000 0.962 0.000 1.000
#> GSM152109 2 0.5059 0.893 0.112 0.888
#> GSM152111 1 0.2043 0.925 0.968 0.032
#> GSM152112 2 0.0938 0.963 0.012 0.988
#> GSM152113 1 0.8267 0.661 0.740 0.260
#> GSM152115 2 0.4815 0.901 0.104 0.896
#> GSM152030 2 0.0938 0.963 0.012 0.988
#> GSM152038 1 0.1184 0.930 0.984 0.016
#> GSM152042 2 0.0938 0.963 0.012 0.988
#> GSM152062 1 0.9661 0.399 0.608 0.392
#> GSM152077 1 0.2043 0.925 0.968 0.032
#> GSM152088 2 0.0000 0.962 0.000 1.000
#> GSM152100 2 0.0938 0.963 0.012 0.988
#> GSM152102 2 0.2423 0.943 0.040 0.960
#> GSM152104 2 0.0938 0.963 0.012 0.988
#> GSM152028 1 0.0938 0.931 0.988 0.012
#> GSM152029 1 0.0938 0.931 0.988 0.012
#> GSM152049 1 0.2043 0.925 0.968 0.032
#> GSM152053 2 0.0938 0.963 0.012 0.988
#> GSM152059 1 0.0938 0.931 0.988 0.012
#> GSM152085 1 0.2043 0.925 0.968 0.032
#> GSM152101 2 0.2043 0.946 0.032 0.968
#> GSM152105 1 0.0938 0.931 0.988 0.012
#> GSM152034 1 0.2423 0.921 0.960 0.040
#> GSM152036 2 0.0938 0.963 0.012 0.988
#> GSM152040 1 0.0000 0.931 1.000 0.000
#> GSM152043 1 0.0672 0.931 0.992 0.008
#> GSM152046 1 0.2423 0.921 0.960 0.040
#> GSM152047 1 0.0000 0.931 1.000 0.000
#> GSM152048 1 0.2043 0.925 0.968 0.032
#> GSM152050 1 0.2043 0.925 0.968 0.032
#> GSM152052 1 0.0938 0.931 0.988 0.012
#> GSM152056 1 0.2043 0.925 0.968 0.032
#> GSM152060 1 0.2423 0.921 0.960 0.040
#> GSM152065 1 0.0938 0.931 0.988 0.012
#> GSM152066 1 0.0000 0.931 1.000 0.000
#> GSM152069 1 0.9460 0.468 0.636 0.364
#> GSM152070 1 0.0938 0.931 0.988 0.012
#> GSM152071 1 0.9460 0.468 0.636 0.364
#> GSM152072 1 0.0938 0.931 0.988 0.012
#> GSM152073 1 0.0938 0.931 0.988 0.012
#> GSM152078 1 0.0938 0.931 0.988 0.012
#> GSM152082 1 0.0938 0.931 0.988 0.012
#> GSM152086 1 0.0000 0.931 1.000 0.000
#> GSM152090 1 0.9393 0.491 0.644 0.356
#> GSM152092 1 0.0938 0.931 0.988 0.012
#> GSM152093 1 0.2043 0.925 0.968 0.032
#> GSM152094 1 0.0000 0.931 1.000 0.000
#> GSM152098 1 0.0938 0.931 0.988 0.012
#> GSM152110 1 0.2043 0.925 0.968 0.032
#> GSM152031 1 0.0938 0.931 0.988 0.012
#> GSM152037 1 0.0000 0.931 1.000 0.000
#> GSM152055 1 0.2423 0.921 0.960 0.040
#> GSM152061 1 0.2423 0.921 0.960 0.040
#> GSM152064 1 0.2423 0.921 0.960 0.040
#> GSM152087 1 0.0000 0.931 1.000 0.000
#> GSM152103 1 0.2236 0.920 0.964 0.036
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM152032 3 0.0983 0.766 0.016 0.004 0.980
#> GSM152033 3 0.4121 0.730 0.168 0.000 0.832
#> GSM152063 2 0.2796 0.758 0.000 0.908 0.092
#> GSM152074 3 0.1525 0.756 0.004 0.032 0.964
#> GSM152080 3 0.6026 0.319 0.000 0.376 0.624
#> GSM152081 2 0.6500 0.744 0.100 0.760 0.140
#> GSM152083 3 0.5178 0.529 0.000 0.256 0.744
#> GSM152091 2 0.5678 0.549 0.000 0.684 0.316
#> GSM152108 2 0.6339 0.441 0.008 0.632 0.360
#> GSM152114 1 0.6416 0.587 0.708 0.032 0.260
#> GSM152035 2 0.4974 0.664 0.000 0.764 0.236
#> GSM152039 2 0.5492 0.762 0.104 0.816 0.080
#> GSM152041 2 0.6025 0.740 0.140 0.784 0.076
#> GSM152044 2 0.1964 0.764 0.000 0.944 0.056
#> GSM152045 1 0.6451 0.392 0.608 0.008 0.384
#> GSM152051 2 0.4399 0.715 0.000 0.812 0.188
#> GSM152054 3 0.6507 0.413 0.028 0.284 0.688
#> GSM152057 2 0.4062 0.728 0.000 0.836 0.164
#> GSM152058 1 0.0892 0.892 0.980 0.000 0.020
#> GSM152067 3 0.1031 0.757 0.000 0.024 0.976
#> GSM152068 2 0.3412 0.748 0.000 0.876 0.124
#> GSM152075 2 0.6250 0.747 0.104 0.776 0.120
#> GSM152076 2 0.5492 0.762 0.104 0.816 0.080
#> GSM152079 2 0.4399 0.715 0.000 0.812 0.188
#> GSM152084 3 0.3276 0.768 0.068 0.024 0.908
#> GSM152089 2 0.6974 0.734 0.104 0.728 0.168
#> GSM152095 2 0.5505 0.766 0.096 0.816 0.088
#> GSM152096 3 0.1337 0.766 0.016 0.012 0.972
#> GSM152097 2 0.1529 0.767 0.000 0.960 0.040
#> GSM152099 2 0.4399 0.715 0.000 0.812 0.188
#> GSM152106 2 0.1643 0.766 0.000 0.956 0.044
#> GSM152107 3 0.4912 0.572 0.008 0.196 0.796
#> GSM152109 3 0.1170 0.764 0.008 0.016 0.976
#> GSM152111 1 0.0983 0.884 0.980 0.016 0.004
#> GSM152112 2 0.7039 0.605 0.040 0.648 0.312
#> GSM152113 3 0.2878 0.768 0.096 0.000 0.904
#> GSM152115 3 0.1643 0.750 0.000 0.044 0.956
#> GSM152030 2 0.7007 0.717 0.100 0.724 0.176
#> GSM152038 3 0.3038 0.764 0.104 0.000 0.896
#> GSM152042 2 0.7298 0.695 0.100 0.700 0.200
#> GSM152062 3 0.3276 0.768 0.068 0.024 0.908
#> GSM152077 1 0.1289 0.889 0.968 0.000 0.032
#> GSM152088 2 0.5497 0.588 0.000 0.708 0.292
#> GSM152100 2 0.5492 0.762 0.104 0.816 0.080
#> GSM152102 3 0.6274 0.093 0.000 0.456 0.544
#> GSM152104 2 0.1643 0.766 0.000 0.956 0.044
#> GSM152028 1 0.3482 0.843 0.872 0.000 0.128
#> GSM152029 3 0.6192 0.242 0.420 0.000 0.580
#> GSM152049 1 0.0592 0.892 0.988 0.000 0.012
#> GSM152053 2 0.7388 0.686 0.100 0.692 0.208
#> GSM152059 1 0.3482 0.846 0.872 0.000 0.128
#> GSM152085 1 0.0661 0.887 0.988 0.008 0.004
#> GSM152101 3 0.4912 0.572 0.008 0.196 0.796
#> GSM152105 1 0.4750 0.757 0.784 0.000 0.216
#> GSM152034 1 0.2599 0.858 0.932 0.052 0.016
#> GSM152036 2 0.5492 0.762 0.104 0.816 0.080
#> GSM152040 1 0.1753 0.886 0.952 0.000 0.048
#> GSM152043 1 0.3412 0.845 0.876 0.000 0.124
#> GSM152046 1 0.2599 0.858 0.932 0.052 0.016
#> GSM152047 1 0.1905 0.873 0.956 0.028 0.016
#> GSM152048 1 0.0892 0.892 0.980 0.000 0.020
#> GSM152050 1 0.0983 0.884 0.980 0.016 0.004
#> GSM152052 1 0.4702 0.762 0.788 0.000 0.212
#> GSM152056 1 0.0592 0.892 0.988 0.000 0.012
#> GSM152060 1 0.2599 0.858 0.932 0.052 0.016
#> GSM152065 1 0.6302 0.112 0.520 0.000 0.480
#> GSM152066 1 0.0747 0.892 0.984 0.000 0.016
#> GSM152069 3 0.1643 0.775 0.044 0.000 0.956
#> GSM152070 1 0.3482 0.846 0.872 0.000 0.128
#> GSM152071 3 0.1643 0.775 0.044 0.000 0.956
#> GSM152072 3 0.5948 0.393 0.360 0.000 0.640
#> GSM152073 1 0.3192 0.854 0.888 0.000 0.112
#> GSM152078 3 0.6126 0.285 0.400 0.000 0.600
#> GSM152082 1 0.3482 0.845 0.872 0.000 0.128
#> GSM152086 1 0.0592 0.892 0.988 0.000 0.012
#> GSM152090 3 0.4002 0.735 0.160 0.000 0.840
#> GSM152092 1 0.3482 0.843 0.872 0.000 0.128
#> GSM152093 1 0.0892 0.892 0.980 0.000 0.020
#> GSM152094 1 0.0892 0.891 0.980 0.000 0.020
#> GSM152098 1 0.3482 0.846 0.872 0.000 0.128
#> GSM152110 1 0.0475 0.890 0.992 0.004 0.004
#> GSM152031 1 0.4291 0.799 0.820 0.000 0.180
#> GSM152037 1 0.0892 0.892 0.980 0.000 0.020
#> GSM152055 1 0.2280 0.859 0.940 0.052 0.008
#> GSM152061 1 0.2599 0.858 0.932 0.052 0.016
#> GSM152064 1 0.1999 0.870 0.952 0.036 0.012
#> GSM152087 1 0.0892 0.891 0.980 0.000 0.020
#> GSM152103 3 0.4121 0.727 0.168 0.000 0.832
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM152032 3 0.3399 0.716 0.000 0.092 0.868 0.040
#> GSM152033 3 0.5593 0.616 0.048 0.004 0.688 0.260
#> GSM152063 2 0.1792 0.776 0.000 0.932 0.000 0.068
#> GSM152074 3 0.3587 0.710 0.000 0.104 0.856 0.040
#> GSM152080 2 0.4840 0.642 0.000 0.732 0.240 0.028
#> GSM152081 4 0.6029 0.811 0.008 0.272 0.060 0.660
#> GSM152083 3 0.5344 0.472 0.000 0.300 0.668 0.032
#> GSM152091 2 0.4549 0.707 0.000 0.776 0.188 0.036
#> GSM152108 2 0.5833 0.566 0.000 0.692 0.096 0.212
#> GSM152114 4 0.6979 0.177 0.180 0.012 0.184 0.624
#> GSM152035 2 0.2227 0.796 0.000 0.928 0.036 0.036
#> GSM152039 4 0.5421 0.789 0.020 0.308 0.008 0.664
#> GSM152041 4 0.6557 0.714 0.152 0.196 0.004 0.648
#> GSM152044 2 0.2081 0.765 0.000 0.916 0.000 0.084
#> GSM152045 1 0.6567 0.395 0.616 0.000 0.256 0.128
#> GSM152051 2 0.0000 0.814 0.000 1.000 0.000 0.000
#> GSM152054 3 0.9453 0.304 0.256 0.116 0.384 0.244
#> GSM152057 2 0.0336 0.812 0.000 0.992 0.000 0.008
#> GSM152058 1 0.5132 0.752 0.748 0.000 0.068 0.184
#> GSM152067 3 0.3117 0.705 0.000 0.092 0.880 0.028
#> GSM152068 2 0.0469 0.812 0.000 0.988 0.000 0.012
#> GSM152075 4 0.5959 0.814 0.012 0.276 0.048 0.664
#> GSM152076 4 0.5701 0.803 0.008 0.308 0.032 0.652
#> GSM152079 2 0.0000 0.814 0.000 1.000 0.000 0.000
#> GSM152084 3 0.3791 0.711 0.008 0.032 0.852 0.108
#> GSM152089 4 0.7075 0.607 0.200 0.108 0.044 0.648
#> GSM152095 4 0.5701 0.803 0.008 0.308 0.032 0.652
#> GSM152096 3 0.3307 0.713 0.000 0.104 0.868 0.028
#> GSM152097 2 0.2345 0.747 0.000 0.900 0.000 0.100
#> GSM152099 2 0.0336 0.812 0.000 0.992 0.000 0.008
#> GSM152106 2 0.2345 0.747 0.000 0.900 0.000 0.100
#> GSM152107 3 0.7020 0.243 0.000 0.136 0.532 0.332
#> GSM152109 3 0.2546 0.710 0.000 0.092 0.900 0.008
#> GSM152111 1 0.1118 0.768 0.964 0.000 0.000 0.036
#> GSM152112 4 0.7226 0.690 0.004 0.232 0.196 0.568
#> GSM152113 3 0.5235 0.656 0.024 0.016 0.728 0.232
#> GSM152115 3 0.5292 0.646 0.000 0.088 0.744 0.168
#> GSM152030 4 0.6608 0.790 0.008 0.268 0.100 0.624
#> GSM152038 3 0.3484 0.701 0.008 0.004 0.844 0.144
#> GSM152042 4 0.6955 0.766 0.008 0.248 0.140 0.604
#> GSM152062 3 0.3791 0.711 0.008 0.032 0.852 0.108
#> GSM152077 1 0.6315 0.693 0.652 0.004 0.100 0.244
#> GSM152088 2 0.4387 0.702 0.000 0.776 0.200 0.024
#> GSM152100 4 0.5701 0.805 0.008 0.308 0.032 0.652
#> GSM152102 2 0.5664 0.612 0.000 0.696 0.228 0.076
#> GSM152104 2 0.2149 0.761 0.000 0.912 0.000 0.088
#> GSM152028 1 0.6300 0.700 0.640 0.000 0.108 0.252
#> GSM152029 3 0.6470 0.332 0.388 0.008 0.548 0.056
#> GSM152049 1 0.4508 0.765 0.780 0.000 0.036 0.184
#> GSM152053 4 0.6917 0.759 0.008 0.236 0.144 0.612
#> GSM152059 1 0.2483 0.766 0.916 0.000 0.032 0.052
#> GSM152085 1 0.1022 0.769 0.968 0.000 0.000 0.032
#> GSM152101 3 0.6273 0.483 0.000 0.100 0.636 0.264
#> GSM152105 1 0.7786 0.323 0.424 0.000 0.308 0.268
#> GSM152034 1 0.3074 0.701 0.848 0.000 0.000 0.152
#> GSM152036 4 0.5520 0.793 0.020 0.304 0.012 0.664
#> GSM152040 1 0.3143 0.751 0.876 0.000 0.024 0.100
#> GSM152043 1 0.5392 0.748 0.724 0.000 0.072 0.204
#> GSM152046 1 0.3024 0.705 0.852 0.000 0.000 0.148
#> GSM152047 1 0.3335 0.741 0.856 0.000 0.016 0.128
#> GSM152048 1 0.5132 0.752 0.748 0.000 0.068 0.184
#> GSM152050 1 0.1118 0.768 0.964 0.000 0.000 0.036
#> GSM152052 1 0.7396 0.482 0.516 0.000 0.268 0.216
#> GSM152056 1 0.4880 0.758 0.760 0.000 0.052 0.188
#> GSM152060 1 0.3074 0.701 0.848 0.000 0.000 0.152
#> GSM152065 3 0.7520 0.254 0.228 0.000 0.492 0.280
#> GSM152066 1 0.4893 0.754 0.768 0.000 0.064 0.168
#> GSM152069 3 0.2382 0.717 0.004 0.080 0.912 0.004
#> GSM152070 1 0.3587 0.743 0.860 0.000 0.052 0.088
#> GSM152071 3 0.2382 0.717 0.004 0.080 0.912 0.004
#> GSM152072 3 0.5798 0.605 0.208 0.000 0.696 0.096
#> GSM152073 1 0.2363 0.767 0.920 0.000 0.024 0.056
#> GSM152078 3 0.6967 0.354 0.244 0.000 0.580 0.176
#> GSM152082 1 0.5787 0.726 0.680 0.000 0.076 0.244
#> GSM152086 1 0.3037 0.781 0.880 0.000 0.020 0.100
#> GSM152090 3 0.4254 0.693 0.108 0.024 0.836 0.032
#> GSM152092 1 0.6192 0.709 0.652 0.000 0.104 0.244
#> GSM152093 1 0.5279 0.747 0.736 0.000 0.072 0.192
#> GSM152094 1 0.1209 0.771 0.964 0.000 0.004 0.032
#> GSM152098 1 0.3453 0.748 0.868 0.000 0.052 0.080
#> GSM152110 1 0.4801 0.759 0.764 0.000 0.048 0.188
#> GSM152031 1 0.7538 0.477 0.492 0.000 0.260 0.248
#> GSM152037 1 0.5007 0.751 0.760 0.000 0.068 0.172
#> GSM152055 1 0.3074 0.701 0.848 0.000 0.000 0.152
#> GSM152061 1 0.3074 0.701 0.848 0.000 0.000 0.152
#> GSM152064 1 0.2868 0.716 0.864 0.000 0.000 0.136
#> GSM152087 1 0.0707 0.773 0.980 0.000 0.000 0.020
#> GSM152103 3 0.5199 0.658 0.168 0.024 0.768 0.040
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM152032 3 0.339 0.7932 0.076 0.032 0.860 0.032 0.000
#> GSM152033 1 0.355 0.4506 0.776 0.004 0.216 0.004 0.000
#> GSM152063 2 0.239 0.8988 0.004 0.880 0.000 0.116 0.000
#> GSM152074 3 0.363 0.7919 0.076 0.036 0.848 0.040 0.000
#> GSM152080 2 0.375 0.7886 0.064 0.812 0.124 0.000 0.000
#> GSM152081 4 0.128 0.9188 0.004 0.020 0.016 0.960 0.000
#> GSM152083 3 0.463 0.7103 0.044 0.168 0.760 0.028 0.000
#> GSM152091 2 0.366 0.8076 0.064 0.828 0.104 0.004 0.000
#> GSM152108 1 0.597 -0.0430 0.480 0.448 0.044 0.024 0.004
#> GSM152114 1 0.637 0.5526 0.624 0.008 0.028 0.212 0.128
#> GSM152035 2 0.251 0.8693 0.020 0.908 0.028 0.044 0.000
#> GSM152039 4 0.159 0.9158 0.004 0.052 0.000 0.940 0.004
#> GSM152041 4 0.379 0.8074 0.016 0.024 0.008 0.828 0.124
#> GSM152044 2 0.281 0.8833 0.004 0.844 0.000 0.152 0.000
#> GSM152045 5 0.637 0.5892 0.188 0.056 0.124 0.000 0.632
#> GSM152051 2 0.234 0.8994 0.000 0.884 0.004 0.112 0.000
#> GSM152054 5 0.898 0.3029 0.264 0.200 0.124 0.048 0.364
#> GSM152057 2 0.223 0.8991 0.000 0.884 0.000 0.116 0.000
#> GSM152058 1 0.457 0.6477 0.596 0.004 0.000 0.008 0.392
#> GSM152067 3 0.196 0.7721 0.020 0.048 0.928 0.000 0.004
#> GSM152068 2 0.223 0.8991 0.000 0.884 0.000 0.116 0.000
#> GSM152075 4 0.127 0.9194 0.012 0.024 0.000 0.960 0.004
#> GSM152076 4 0.159 0.9158 0.004 0.052 0.000 0.940 0.004
#> GSM152079 2 0.234 0.8994 0.000 0.884 0.004 0.112 0.000
#> GSM152084 3 0.498 0.7145 0.268 0.008 0.676 0.048 0.000
#> GSM152089 5 0.791 0.0770 0.060 0.072 0.068 0.384 0.416
#> GSM152095 4 0.159 0.9158 0.004 0.052 0.000 0.940 0.004
#> GSM152096 3 0.435 0.7687 0.180 0.032 0.768 0.020 0.000
#> GSM152097 2 0.328 0.8553 0.008 0.804 0.000 0.188 0.000
#> GSM152099 2 0.249 0.8959 0.000 0.872 0.004 0.124 0.000
#> GSM152106 2 0.328 0.8553 0.008 0.804 0.000 0.188 0.000
#> GSM152107 3 0.556 0.5920 0.040 0.052 0.668 0.240 0.000
#> GSM152109 3 0.267 0.7856 0.060 0.044 0.892 0.000 0.004
#> GSM152111 5 0.228 0.6920 0.040 0.004 0.008 0.028 0.920
#> GSM152112 4 0.378 0.8225 0.040 0.032 0.092 0.836 0.000
#> GSM152113 1 0.452 0.0840 0.624 0.000 0.360 0.016 0.000
#> GSM152115 3 0.489 0.7329 0.072 0.072 0.772 0.084 0.000
#> GSM152030 4 0.167 0.9070 0.008 0.016 0.032 0.944 0.000
#> GSM152038 3 0.470 0.6822 0.304 0.004 0.664 0.028 0.000
#> GSM152042 4 0.200 0.8972 0.012 0.012 0.048 0.928 0.000
#> GSM152062 3 0.477 0.7152 0.264 0.004 0.688 0.044 0.000
#> GSM152077 1 0.451 0.6869 0.744 0.000 0.024 0.024 0.208
#> GSM152088 2 0.348 0.8126 0.056 0.840 0.100 0.004 0.000
#> GSM152100 4 0.157 0.9190 0.008 0.044 0.000 0.944 0.004
#> GSM152102 2 0.456 0.7233 0.108 0.760 0.128 0.000 0.004
#> GSM152104 2 0.297 0.8796 0.008 0.836 0.000 0.156 0.000
#> GSM152028 1 0.364 0.6689 0.776 0.004 0.008 0.000 0.212
#> GSM152029 5 0.669 0.2703 0.144 0.020 0.356 0.000 0.480
#> GSM152049 1 0.484 0.5675 0.524 0.004 0.004 0.008 0.460
#> GSM152053 4 0.207 0.8946 0.012 0.012 0.052 0.924 0.000
#> GSM152059 5 0.353 0.6951 0.152 0.012 0.016 0.000 0.820
#> GSM152085 5 0.112 0.7114 0.028 0.004 0.000 0.004 0.964
#> GSM152101 3 0.531 0.6837 0.060 0.068 0.732 0.140 0.000
#> GSM152105 1 0.332 0.6719 0.844 0.000 0.056 0.000 0.100
#> GSM152034 5 0.205 0.7303 0.000 0.008 0.004 0.072 0.916
#> GSM152036 4 0.159 0.9158 0.004 0.052 0.000 0.940 0.004
#> GSM152040 5 0.457 0.6876 0.152 0.036 0.032 0.004 0.776
#> GSM152043 1 0.509 0.4374 0.568 0.020 0.012 0.000 0.400
#> GSM152046 5 0.180 0.7315 0.000 0.004 0.004 0.064 0.928
#> GSM152047 5 0.408 0.7171 0.108 0.020 0.028 0.020 0.824
#> GSM152048 1 0.457 0.6477 0.596 0.004 0.000 0.008 0.392
#> GSM152050 5 0.215 0.6923 0.040 0.004 0.004 0.028 0.924
#> GSM152052 1 0.405 0.6877 0.780 0.000 0.056 0.000 0.164
#> GSM152056 1 0.474 0.6391 0.584 0.004 0.004 0.008 0.400
#> GSM152060 5 0.209 0.7256 0.004 0.004 0.004 0.072 0.916
#> GSM152065 1 0.378 0.5758 0.832 0.016 0.088 0.000 0.064
#> GSM152066 1 0.473 0.6425 0.588 0.004 0.004 0.008 0.396
#> GSM152069 3 0.293 0.7854 0.076 0.044 0.876 0.000 0.004
#> GSM152070 5 0.496 0.6502 0.196 0.040 0.036 0.000 0.728
#> GSM152071 3 0.293 0.7854 0.076 0.044 0.876 0.000 0.004
#> GSM152072 3 0.754 0.1204 0.232 0.056 0.444 0.000 0.268
#> GSM152073 5 0.339 0.6942 0.148 0.012 0.012 0.000 0.828
#> GSM152078 1 0.579 0.3497 0.616 0.012 0.276 0.000 0.096
#> GSM152082 1 0.457 0.5633 0.688 0.028 0.004 0.000 0.280
#> GSM152086 5 0.459 -0.0875 0.348 0.004 0.004 0.008 0.636
#> GSM152090 3 0.562 0.6660 0.232 0.016 0.676 0.016 0.060
#> GSM152092 1 0.409 0.6391 0.736 0.016 0.004 0.000 0.244
#> GSM152093 1 0.489 0.6494 0.596 0.004 0.004 0.016 0.380
#> GSM152094 5 0.229 0.7263 0.072 0.012 0.008 0.000 0.908
#> GSM152098 5 0.490 0.6527 0.188 0.040 0.036 0.000 0.736
#> GSM152110 1 0.481 0.6081 0.552 0.004 0.004 0.008 0.432
#> GSM152031 1 0.380 0.6717 0.808 0.004 0.044 0.000 0.144
#> GSM152037 1 0.448 0.6635 0.628 0.004 0.000 0.008 0.360
#> GSM152055 5 0.240 0.7169 0.008 0.008 0.004 0.076 0.904
#> GSM152061 5 0.209 0.7256 0.004 0.004 0.004 0.072 0.916
#> GSM152064 5 0.239 0.7155 0.012 0.008 0.004 0.068 0.908
#> GSM152087 5 0.197 0.7278 0.060 0.012 0.004 0.000 0.924
#> GSM152103 3 0.526 0.6564 0.240 0.012 0.684 0.004 0.060
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM152032 3 0.127 0.7384 0.036 0.000 0.952 0.008 0.000 0.004
#> GSM152033 1 0.498 0.4896 0.700 0.000 0.144 0.012 0.136 0.008
#> GSM152063 2 0.193 0.8796 0.000 0.912 0.000 0.068 0.020 0.000
#> GSM152074 3 0.216 0.7287 0.020 0.004 0.916 0.008 0.048 0.004
#> GSM152080 2 0.335 0.7724 0.004 0.780 0.008 0.000 0.204 0.004
#> GSM152081 4 0.322 0.8542 0.000 0.012 0.036 0.848 0.096 0.008
#> GSM152083 3 0.336 0.6856 0.012 0.112 0.836 0.004 0.032 0.004
#> GSM152091 2 0.310 0.7772 0.004 0.788 0.004 0.000 0.204 0.000
#> GSM152108 1 0.738 0.0795 0.400 0.364 0.064 0.056 0.116 0.000
#> GSM152114 1 0.661 0.5238 0.600 0.004 0.032 0.156 0.064 0.144
#> GSM152035 2 0.242 0.8367 0.004 0.884 0.008 0.008 0.096 0.000
#> GSM152039 4 0.266 0.8484 0.000 0.012 0.000 0.876 0.084 0.028
#> GSM152041 4 0.448 0.5539 0.020 0.000 0.000 0.660 0.024 0.296
#> GSM152044 2 0.220 0.8764 0.004 0.900 0.000 0.080 0.012 0.004
#> GSM152045 5 0.592 0.3729 0.132 0.000 0.016 0.000 0.440 0.412
#> GSM152051 2 0.184 0.8817 0.000 0.920 0.008 0.064 0.008 0.000
#> GSM152054 5 0.680 0.3771 0.068 0.100 0.032 0.040 0.624 0.136
#> GSM152057 2 0.147 0.8813 0.000 0.932 0.004 0.064 0.000 0.000
#> GSM152058 1 0.324 0.6077 0.732 0.000 0.000 0.000 0.000 0.268
#> GSM152067 3 0.273 0.7057 0.004 0.016 0.860 0.000 0.116 0.004
#> GSM152068 2 0.139 0.8812 0.000 0.932 0.000 0.068 0.000 0.000
#> GSM152075 4 0.149 0.8587 0.004 0.008 0.012 0.952 0.012 0.012
#> GSM152076 4 0.281 0.8505 0.000 0.012 0.004 0.872 0.084 0.028
#> GSM152079 2 0.158 0.8814 0.000 0.928 0.008 0.064 0.000 0.000
#> GSM152084 3 0.586 0.6719 0.176 0.004 0.636 0.112 0.072 0.000
#> GSM152089 6 0.625 -0.0845 0.004 0.000 0.008 0.384 0.204 0.400
#> GSM152095 4 0.281 0.8505 0.000 0.012 0.004 0.872 0.084 0.028
#> GSM152096 3 0.603 0.6783 0.176 0.020 0.640 0.080 0.084 0.000
#> GSM152097 2 0.411 0.7947 0.004 0.768 0.000 0.124 0.100 0.004
#> GSM152099 2 0.184 0.8813 0.000 0.920 0.008 0.064 0.008 0.000
#> GSM152106 2 0.411 0.7947 0.004 0.768 0.000 0.124 0.100 0.004
#> GSM152107 3 0.499 0.5901 0.004 0.004 0.660 0.224 0.108 0.000
#> GSM152109 3 0.274 0.7131 0.016 0.020 0.876 0.000 0.084 0.004
#> GSM152111 6 0.228 0.5547 0.096 0.000 0.000 0.008 0.008 0.888
#> GSM152112 4 0.371 0.7652 0.000 0.008 0.084 0.800 0.108 0.000
#> GSM152113 1 0.636 0.0725 0.516 0.000 0.288 0.060 0.136 0.000
#> GSM152115 3 0.414 0.6836 0.008 0.000 0.756 0.080 0.156 0.000
#> GSM152030 4 0.244 0.8409 0.004 0.008 0.060 0.896 0.032 0.000
#> GSM152038 3 0.573 0.5092 0.312 0.000 0.552 0.024 0.112 0.000
#> GSM152042 4 0.269 0.8310 0.004 0.008 0.072 0.880 0.036 0.000
#> GSM152062 3 0.568 0.6746 0.180 0.004 0.652 0.096 0.068 0.000
#> GSM152077 1 0.438 0.6182 0.796 0.004 0.024 0.048 0.044 0.084
#> GSM152088 2 0.270 0.8006 0.004 0.836 0.004 0.000 0.156 0.000
#> GSM152100 4 0.127 0.8599 0.004 0.008 0.004 0.960 0.012 0.012
#> GSM152102 2 0.441 0.6170 0.008 0.620 0.016 0.004 0.352 0.000
#> GSM152104 2 0.286 0.8622 0.004 0.864 0.000 0.088 0.040 0.004
#> GSM152028 1 0.302 0.5705 0.848 0.000 0.004 0.000 0.096 0.052
#> GSM152029 5 0.737 0.4775 0.136 0.004 0.176 0.000 0.408 0.276
#> GSM152049 1 0.411 0.3412 0.540 0.000 0.000 0.004 0.004 0.452
#> GSM152053 4 0.280 0.8248 0.004 0.008 0.080 0.872 0.036 0.000
#> GSM152059 6 0.574 -0.1976 0.196 0.000 0.000 0.000 0.304 0.500
#> GSM152085 6 0.162 0.5681 0.064 0.000 0.000 0.004 0.004 0.928
#> GSM152101 3 0.445 0.6579 0.000 0.004 0.724 0.124 0.148 0.000
#> GSM152105 1 0.229 0.5892 0.904 0.000 0.040 0.000 0.044 0.012
#> GSM152034 6 0.184 0.5661 0.000 0.000 0.000 0.028 0.052 0.920
#> GSM152036 4 0.278 0.8503 0.000 0.008 0.004 0.872 0.084 0.032
#> GSM152040 6 0.553 -0.2659 0.124 0.000 0.000 0.004 0.360 0.512
#> GSM152043 1 0.551 0.0952 0.560 0.000 0.000 0.000 0.248 0.192
#> GSM152046 6 0.191 0.5677 0.000 0.000 0.000 0.028 0.056 0.916
#> GSM152047 6 0.487 0.1272 0.084 0.000 0.000 0.004 0.276 0.636
#> GSM152048 1 0.324 0.6077 0.732 0.000 0.000 0.000 0.000 0.268
#> GSM152050 6 0.242 0.5482 0.108 0.000 0.000 0.008 0.008 0.876
#> GSM152052 1 0.332 0.6158 0.844 0.000 0.028 0.000 0.068 0.060
#> GSM152056 1 0.360 0.5718 0.684 0.000 0.000 0.004 0.000 0.312
#> GSM152060 6 0.199 0.5709 0.004 0.000 0.000 0.028 0.052 0.916
#> GSM152065 1 0.390 0.4757 0.764 0.000 0.040 0.000 0.184 0.012
#> GSM152066 1 0.345 0.5996 0.716 0.000 0.000 0.000 0.004 0.280
#> GSM152069 3 0.284 0.7137 0.016 0.020 0.868 0.000 0.092 0.004
#> GSM152070 5 0.604 0.3479 0.184 0.000 0.008 0.000 0.408 0.400
#> GSM152071 3 0.284 0.7137 0.016 0.020 0.868 0.000 0.092 0.004
#> GSM152072 5 0.667 0.5368 0.168 0.000 0.172 0.000 0.536 0.124
#> GSM152073 6 0.578 -0.2121 0.200 0.000 0.000 0.000 0.312 0.488
#> GSM152078 1 0.588 0.1453 0.548 0.000 0.156 0.000 0.276 0.020
#> GSM152082 1 0.520 0.1139 0.584 0.000 0.008 0.000 0.320 0.088
#> GSM152086 6 0.447 -0.0519 0.412 0.000 0.000 0.004 0.024 0.560
#> GSM152090 3 0.697 0.5831 0.236 0.008 0.540 0.068 0.120 0.028
#> GSM152092 1 0.393 0.4675 0.756 0.000 0.000 0.000 0.172 0.072
#> GSM152093 1 0.519 0.5864 0.652 0.000 0.004 0.052 0.040 0.252
#> GSM152094 6 0.423 0.3806 0.084 0.000 0.000 0.000 0.192 0.724
#> GSM152098 6 0.606 -0.4823 0.188 0.000 0.008 0.000 0.400 0.404
#> GSM152110 1 0.365 0.5607 0.672 0.000 0.000 0.004 0.000 0.324
#> GSM152031 1 0.355 0.5354 0.812 0.000 0.028 0.000 0.132 0.028
#> GSM152037 1 0.317 0.6147 0.744 0.000 0.000 0.000 0.000 0.256
#> GSM152055 6 0.205 0.5615 0.044 0.000 0.000 0.032 0.008 0.916
#> GSM152061 6 0.199 0.5709 0.004 0.000 0.000 0.028 0.052 0.916
#> GSM152064 6 0.168 0.5669 0.028 0.000 0.000 0.028 0.008 0.936
#> GSM152087 6 0.417 0.4131 0.092 0.000 0.000 0.000 0.172 0.736
#> GSM152103 3 0.673 0.5259 0.288 0.008 0.524 0.036 0.116 0.028
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n specimen(p) k
#> MAD:kmeans 83 5.43e-09 2
#> MAD:kmeans 79 1.28e-06 3
#> MAD:kmeans 76 2.22e-05 4
#> MAD:kmeans 78 1.09e-03 5
#> MAD:kmeans 66 4.54e-02 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 10612 rows and 88 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.964 0.985 0.5056 0.495 0.495
#> 3 3 0.847 0.866 0.945 0.3157 0.789 0.596
#> 4 4 0.690 0.784 0.836 0.1173 0.861 0.624
#> 5 5 0.775 0.769 0.872 0.0833 0.859 0.527
#> 6 6 0.764 0.642 0.806 0.0393 0.948 0.743
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
#> GSM152032 2 0.000 0.978 0.000 1.000
#> GSM152033 1 0.000 0.991 1.000 0.000
#> GSM152063 2 0.000 0.978 0.000 1.000
#> GSM152074 2 0.000 0.978 0.000 1.000
#> GSM152080 2 0.000 0.978 0.000 1.000
#> GSM152081 2 0.000 0.978 0.000 1.000
#> GSM152083 2 0.000 0.978 0.000 1.000
#> GSM152091 2 0.000 0.978 0.000 1.000
#> GSM152108 2 0.000 0.978 0.000 1.000
#> GSM152114 1 0.958 0.356 0.620 0.380
#> GSM152035 2 0.000 0.978 0.000 1.000
#> GSM152039 2 0.000 0.978 0.000 1.000
#> GSM152041 2 0.929 0.478 0.344 0.656
#> GSM152044 2 0.000 0.978 0.000 1.000
#> GSM152045 1 0.000 0.991 1.000 0.000
#> GSM152051 2 0.000 0.978 0.000 1.000
#> GSM152054 2 0.163 0.959 0.024 0.976
#> GSM152057 2 0.000 0.978 0.000 1.000
#> GSM152058 1 0.000 0.991 1.000 0.000
#> GSM152067 2 0.000 0.978 0.000 1.000
#> GSM152068 2 0.000 0.978 0.000 1.000
#> GSM152075 2 0.000 0.978 0.000 1.000
#> GSM152076 2 0.000 0.978 0.000 1.000
#> GSM152079 2 0.000 0.978 0.000 1.000
#> GSM152084 2 0.000 0.978 0.000 1.000
#> GSM152089 2 0.000 0.978 0.000 1.000
#> GSM152095 2 0.000 0.978 0.000 1.000
#> GSM152096 2 0.000 0.978 0.000 1.000
#> GSM152097 2 0.000 0.978 0.000 1.000
#> GSM152099 2 0.000 0.978 0.000 1.000
#> GSM152106 2 0.000 0.978 0.000 1.000
#> GSM152107 2 0.000 0.978 0.000 1.000
#> GSM152109 2 0.000 0.978 0.000 1.000
#> GSM152111 1 0.000 0.991 1.000 0.000
#> GSM152112 2 0.000 0.978 0.000 1.000
#> GSM152113 2 0.827 0.663 0.260 0.740
#> GSM152115 2 0.000 0.978 0.000 1.000
#> GSM152030 2 0.000 0.978 0.000 1.000
#> GSM152038 1 0.000 0.991 1.000 0.000
#> GSM152042 2 0.000 0.978 0.000 1.000
#> GSM152062 2 0.295 0.935 0.052 0.948
#> GSM152077 1 0.000 0.991 1.000 0.000
#> GSM152088 2 0.000 0.978 0.000 1.000
#> GSM152100 2 0.000 0.978 0.000 1.000
#> GSM152102 2 0.000 0.978 0.000 1.000
#> GSM152104 2 0.000 0.978 0.000 1.000
#> GSM152028 1 0.000 0.991 1.000 0.000
#> GSM152029 1 0.000 0.991 1.000 0.000
#> GSM152049 1 0.000 0.991 1.000 0.000
#> GSM152053 2 0.000 0.978 0.000 1.000
#> GSM152059 1 0.000 0.991 1.000 0.000
#> GSM152085 1 0.000 0.991 1.000 0.000
#> GSM152101 2 0.000 0.978 0.000 1.000
#> GSM152105 1 0.000 0.991 1.000 0.000
#> GSM152034 1 0.000 0.991 1.000 0.000
#> GSM152036 2 0.000 0.978 0.000 1.000
#> GSM152040 1 0.000 0.991 1.000 0.000
#> GSM152043 1 0.000 0.991 1.000 0.000
#> GSM152046 1 0.000 0.991 1.000 0.000
#> GSM152047 1 0.000 0.991 1.000 0.000
#> GSM152048 1 0.000 0.991 1.000 0.000
#> GSM152050 1 0.000 0.991 1.000 0.000
#> GSM152052 1 0.000 0.991 1.000 0.000
#> GSM152056 1 0.000 0.991 1.000 0.000
#> GSM152060 1 0.000 0.991 1.000 0.000
#> GSM152065 1 0.000 0.991 1.000 0.000
#> GSM152066 1 0.000 0.991 1.000 0.000
#> GSM152069 2 0.416 0.905 0.084 0.916
#> GSM152070 1 0.000 0.991 1.000 0.000
#> GSM152071 2 0.443 0.897 0.092 0.908
#> GSM152072 1 0.000 0.991 1.000 0.000
#> GSM152073 1 0.000 0.991 1.000 0.000
#> GSM152078 1 0.000 0.991 1.000 0.000
#> GSM152082 1 0.000 0.991 1.000 0.000
#> GSM152086 1 0.000 0.991 1.000 0.000
#> GSM152090 2 0.469 0.889 0.100 0.900
#> GSM152092 1 0.000 0.991 1.000 0.000
#> GSM152093 1 0.000 0.991 1.000 0.000
#> GSM152094 1 0.000 0.991 1.000 0.000
#> GSM152098 1 0.000 0.991 1.000 0.000
#> GSM152110 1 0.000 0.991 1.000 0.000
#> GSM152031 1 0.000 0.991 1.000 0.000
#> GSM152037 1 0.000 0.991 1.000 0.000
#> GSM152055 1 0.000 0.991 1.000 0.000
#> GSM152061 1 0.000 0.991 1.000 0.000
#> GSM152064 1 0.000 0.991 1.000 0.000
#> GSM152087 1 0.000 0.991 1.000 0.000
#> GSM152103 1 0.000 0.991 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM152032 3 0.0000 0.9244 0.000 0.000 1.000
#> GSM152033 3 0.0237 0.9230 0.004 0.000 0.996
#> GSM152063 2 0.0237 0.9444 0.000 0.996 0.004
#> GSM152074 3 0.0000 0.9244 0.000 0.000 1.000
#> GSM152080 3 0.4504 0.7486 0.000 0.196 0.804
#> GSM152081 2 0.0000 0.9447 0.000 1.000 0.000
#> GSM152083 3 0.2261 0.8765 0.000 0.068 0.932
#> GSM152091 2 0.0592 0.9428 0.000 0.988 0.012
#> GSM152108 2 0.0592 0.9428 0.000 0.988 0.012
#> GSM152114 1 0.9789 0.0141 0.396 0.368 0.236
#> GSM152035 2 0.0237 0.9444 0.000 0.996 0.004
#> GSM152039 2 0.0000 0.9447 0.000 1.000 0.000
#> GSM152041 2 0.1163 0.9214 0.028 0.972 0.000
#> GSM152044 2 0.0000 0.9447 0.000 1.000 0.000
#> GSM152045 1 0.6192 0.2018 0.580 0.000 0.420
#> GSM152051 2 0.0592 0.9428 0.000 0.988 0.012
#> GSM152054 2 0.6180 0.2447 0.000 0.584 0.416
#> GSM152057 2 0.0592 0.9428 0.000 0.988 0.012
#> GSM152058 1 0.0000 0.9402 1.000 0.000 0.000
#> GSM152067 3 0.0424 0.9205 0.000 0.008 0.992
#> GSM152068 2 0.0237 0.9444 0.000 0.996 0.004
#> GSM152075 2 0.0000 0.9447 0.000 1.000 0.000
#> GSM152076 2 0.0000 0.9447 0.000 1.000 0.000
#> GSM152079 2 0.0592 0.9428 0.000 0.988 0.012
#> GSM152084 3 0.0000 0.9244 0.000 0.000 1.000
#> GSM152089 2 0.0000 0.9447 0.000 1.000 0.000
#> GSM152095 2 0.0000 0.9447 0.000 1.000 0.000
#> GSM152096 3 0.0000 0.9244 0.000 0.000 1.000
#> GSM152097 2 0.0000 0.9447 0.000 1.000 0.000
#> GSM152099 2 0.0592 0.9428 0.000 0.988 0.012
#> GSM152106 2 0.0000 0.9447 0.000 1.000 0.000
#> GSM152107 2 0.5178 0.6781 0.000 0.744 0.256
#> GSM152109 3 0.0000 0.9244 0.000 0.000 1.000
#> GSM152111 1 0.0000 0.9402 1.000 0.000 0.000
#> GSM152112 2 0.0424 0.9423 0.000 0.992 0.008
#> GSM152113 3 0.0000 0.9244 0.000 0.000 1.000
#> GSM152115 3 0.2165 0.8801 0.000 0.064 0.936
#> GSM152030 2 0.1163 0.9293 0.000 0.972 0.028
#> GSM152038 3 0.0237 0.9230 0.004 0.000 0.996
#> GSM152042 2 0.3192 0.8539 0.000 0.888 0.112
#> GSM152062 3 0.0000 0.9244 0.000 0.000 1.000
#> GSM152077 1 0.0592 0.9313 0.988 0.000 0.012
#> GSM152088 2 0.0592 0.9428 0.000 0.988 0.012
#> GSM152100 2 0.0000 0.9447 0.000 1.000 0.000
#> GSM152102 2 0.6192 0.2414 0.000 0.580 0.420
#> GSM152104 2 0.0000 0.9447 0.000 1.000 0.000
#> GSM152028 1 0.0000 0.9402 1.000 0.000 0.000
#> GSM152029 3 0.3619 0.8235 0.136 0.000 0.864
#> GSM152049 1 0.0000 0.9402 1.000 0.000 0.000
#> GSM152053 2 0.3192 0.8539 0.000 0.888 0.112
#> GSM152059 1 0.0000 0.9402 1.000 0.000 0.000
#> GSM152085 1 0.0000 0.9402 1.000 0.000 0.000
#> GSM152101 3 0.6235 0.1371 0.000 0.436 0.564
#> GSM152105 1 0.5760 0.5183 0.672 0.000 0.328
#> GSM152034 1 0.0237 0.9383 0.996 0.004 0.000
#> GSM152036 2 0.0000 0.9447 0.000 1.000 0.000
#> GSM152040 1 0.0000 0.9402 1.000 0.000 0.000
#> GSM152043 1 0.0000 0.9402 1.000 0.000 0.000
#> GSM152046 1 0.0237 0.9383 0.996 0.004 0.000
#> GSM152047 1 0.0237 0.9383 0.996 0.004 0.000
#> GSM152048 1 0.0000 0.9402 1.000 0.000 0.000
#> GSM152050 1 0.0000 0.9402 1.000 0.000 0.000
#> GSM152052 1 0.5621 0.5572 0.692 0.000 0.308
#> GSM152056 1 0.0000 0.9402 1.000 0.000 0.000
#> GSM152060 1 0.0237 0.9383 0.996 0.004 0.000
#> GSM152065 3 0.5058 0.6650 0.244 0.000 0.756
#> GSM152066 1 0.0000 0.9402 1.000 0.000 0.000
#> GSM152069 3 0.0000 0.9244 0.000 0.000 1.000
#> GSM152070 1 0.0000 0.9402 1.000 0.000 0.000
#> GSM152071 3 0.0000 0.9244 0.000 0.000 1.000
#> GSM152072 3 0.3412 0.8336 0.124 0.000 0.876
#> GSM152073 1 0.0000 0.9402 1.000 0.000 0.000
#> GSM152078 3 0.3340 0.8376 0.120 0.000 0.880
#> GSM152082 1 0.0000 0.9402 1.000 0.000 0.000
#> GSM152086 1 0.0000 0.9402 1.000 0.000 0.000
#> GSM152090 3 0.0000 0.9244 0.000 0.000 1.000
#> GSM152092 1 0.0000 0.9402 1.000 0.000 0.000
#> GSM152093 1 0.0000 0.9402 1.000 0.000 0.000
#> GSM152094 1 0.0000 0.9402 1.000 0.000 0.000
#> GSM152098 1 0.0000 0.9402 1.000 0.000 0.000
#> GSM152110 1 0.0000 0.9402 1.000 0.000 0.000
#> GSM152031 1 0.5397 0.6067 0.720 0.000 0.280
#> GSM152037 1 0.0000 0.9402 1.000 0.000 0.000
#> GSM152055 1 0.0237 0.9383 0.996 0.004 0.000
#> GSM152061 1 0.0237 0.9383 0.996 0.004 0.000
#> GSM152064 1 0.0237 0.9383 0.996 0.004 0.000
#> GSM152087 1 0.0000 0.9402 1.000 0.000 0.000
#> GSM152103 3 0.0237 0.9231 0.004 0.000 0.996
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM152032 3 0.1118 0.805 0.000 0.036 0.964 0.000
#> GSM152033 3 0.4155 0.731 0.004 0.240 0.756 0.000
#> GSM152063 2 0.4431 0.865 0.000 0.696 0.000 0.304
#> GSM152074 3 0.1302 0.802 0.000 0.044 0.956 0.000
#> GSM152080 2 0.5530 0.714 0.000 0.712 0.212 0.076
#> GSM152081 4 0.0524 0.864 0.000 0.004 0.008 0.988
#> GSM152083 2 0.4961 0.270 0.000 0.552 0.448 0.000
#> GSM152091 2 0.5394 0.850 0.000 0.712 0.060 0.228
#> GSM152108 2 0.3278 0.713 0.000 0.864 0.020 0.116
#> GSM152114 4 0.6675 0.534 0.060 0.240 0.044 0.656
#> GSM152035 2 0.4483 0.873 0.000 0.712 0.004 0.284
#> GSM152039 4 0.0000 0.864 0.000 0.000 0.000 1.000
#> GSM152041 4 0.1211 0.847 0.040 0.000 0.000 0.960
#> GSM152044 2 0.4454 0.862 0.000 0.692 0.000 0.308
#> GSM152045 1 0.5281 0.667 0.756 0.048 0.180 0.016
#> GSM152051 2 0.4331 0.873 0.000 0.712 0.000 0.288
#> GSM152054 2 0.6495 0.716 0.088 0.720 0.096 0.096
#> GSM152057 2 0.4331 0.873 0.000 0.712 0.000 0.288
#> GSM152058 1 0.4932 0.789 0.728 0.240 0.032 0.000
#> GSM152067 3 0.1637 0.798 0.000 0.060 0.940 0.000
#> GSM152068 2 0.4331 0.873 0.000 0.712 0.000 0.288
#> GSM152075 4 0.0188 0.864 0.004 0.000 0.000 0.996
#> GSM152076 4 0.0000 0.864 0.000 0.000 0.000 1.000
#> GSM152079 2 0.4331 0.873 0.000 0.712 0.000 0.288
#> GSM152084 3 0.3453 0.770 0.000 0.052 0.868 0.080
#> GSM152089 4 0.4083 0.739 0.100 0.068 0.000 0.832
#> GSM152095 4 0.0000 0.864 0.000 0.000 0.000 1.000
#> GSM152096 3 0.3172 0.702 0.000 0.160 0.840 0.000
#> GSM152097 2 0.4543 0.847 0.000 0.676 0.000 0.324
#> GSM152099 2 0.4331 0.873 0.000 0.712 0.000 0.288
#> GSM152106 2 0.4522 0.851 0.000 0.680 0.000 0.320
#> GSM152107 4 0.4546 0.653 0.000 0.012 0.256 0.732
#> GSM152109 3 0.1211 0.803 0.000 0.040 0.960 0.000
#> GSM152111 1 0.0937 0.856 0.976 0.012 0.000 0.012
#> GSM152112 4 0.1398 0.858 0.000 0.004 0.040 0.956
#> GSM152113 3 0.3311 0.774 0.000 0.172 0.828 0.000
#> GSM152115 3 0.4867 0.553 0.000 0.032 0.736 0.232
#> GSM152030 4 0.0895 0.862 0.000 0.004 0.020 0.976
#> GSM152038 3 0.1389 0.811 0.000 0.048 0.952 0.000
#> GSM152042 4 0.2125 0.838 0.000 0.004 0.076 0.920
#> GSM152062 3 0.1635 0.809 0.000 0.044 0.948 0.008
#> GSM152077 1 0.5137 0.782 0.716 0.244 0.040 0.000
#> GSM152088 2 0.5466 0.845 0.000 0.712 0.068 0.220
#> GSM152100 4 0.0000 0.864 0.000 0.000 0.000 1.000
#> GSM152102 2 0.5581 0.784 0.000 0.728 0.132 0.140
#> GSM152104 2 0.4477 0.859 0.000 0.688 0.000 0.312
#> GSM152028 1 0.6052 0.745 0.640 0.284 0.076 0.000
#> GSM152029 3 0.4035 0.739 0.176 0.020 0.804 0.000
#> GSM152049 1 0.4011 0.816 0.784 0.208 0.008 0.000
#> GSM152053 4 0.2197 0.835 0.000 0.004 0.080 0.916
#> GSM152059 1 0.1545 0.849 0.952 0.040 0.008 0.000
#> GSM152085 1 0.0188 0.855 0.996 0.000 0.000 0.004
#> GSM152101 4 0.5699 0.397 0.000 0.032 0.380 0.588
#> GSM152105 3 0.6262 0.622 0.092 0.280 0.628 0.000
#> GSM152034 1 0.0921 0.850 0.972 0.000 0.000 0.028
#> GSM152036 4 0.0000 0.864 0.000 0.000 0.000 1.000
#> GSM152040 1 0.2099 0.845 0.936 0.044 0.012 0.008
#> GSM152043 1 0.4149 0.831 0.804 0.168 0.028 0.000
#> GSM152046 1 0.0707 0.852 0.980 0.000 0.000 0.020
#> GSM152047 1 0.2075 0.845 0.936 0.044 0.004 0.016
#> GSM152048 1 0.4932 0.789 0.728 0.240 0.032 0.000
#> GSM152050 1 0.0937 0.856 0.976 0.012 0.000 0.012
#> GSM152052 3 0.7644 0.292 0.272 0.260 0.468 0.000
#> GSM152056 1 0.4808 0.794 0.736 0.236 0.028 0.000
#> GSM152060 1 0.0817 0.851 0.976 0.000 0.000 0.024
#> GSM152065 3 0.5864 0.668 0.072 0.264 0.664 0.000
#> GSM152066 1 0.4932 0.789 0.728 0.240 0.032 0.000
#> GSM152069 3 0.1022 0.806 0.000 0.032 0.968 0.000
#> GSM152070 1 0.2761 0.826 0.904 0.048 0.048 0.000
#> GSM152071 3 0.1022 0.806 0.000 0.032 0.968 0.000
#> GSM152072 3 0.4153 0.760 0.132 0.048 0.820 0.000
#> GSM152073 1 0.1722 0.849 0.944 0.048 0.008 0.000
#> GSM152078 3 0.3694 0.785 0.032 0.124 0.844 0.000
#> GSM152082 1 0.5394 0.788 0.712 0.228 0.060 0.000
#> GSM152086 1 0.2408 0.849 0.896 0.104 0.000 0.000
#> GSM152090 3 0.1909 0.809 0.008 0.048 0.940 0.004
#> GSM152092 1 0.5864 0.762 0.664 0.264 0.072 0.000
#> GSM152093 1 0.4900 0.791 0.732 0.236 0.032 0.000
#> GSM152094 1 0.0469 0.856 0.988 0.012 0.000 0.000
#> GSM152098 1 0.2761 0.826 0.904 0.048 0.048 0.000
#> GSM152110 1 0.4678 0.798 0.744 0.232 0.024 0.000
#> GSM152031 3 0.7606 0.311 0.248 0.276 0.476 0.000
#> GSM152037 1 0.4964 0.788 0.724 0.244 0.032 0.000
#> GSM152055 1 0.1151 0.853 0.968 0.008 0.000 0.024
#> GSM152061 1 0.0817 0.851 0.976 0.000 0.000 0.024
#> GSM152064 1 0.1004 0.852 0.972 0.004 0.000 0.024
#> GSM152087 1 0.0469 0.856 0.988 0.012 0.000 0.000
#> GSM152103 3 0.2256 0.813 0.020 0.056 0.924 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM152032 3 0.0613 0.8328 0.008 0.004 0.984 0.004 0.000
#> GSM152033 1 0.4768 0.4763 0.656 0.000 0.304 0.000 0.040
#> GSM152063 2 0.0794 0.9649 0.000 0.972 0.000 0.028 0.000
#> GSM152074 3 0.0613 0.8328 0.008 0.004 0.984 0.004 0.000
#> GSM152080 2 0.0290 0.9539 0.000 0.992 0.008 0.000 0.000
#> GSM152081 4 0.0000 0.9305 0.000 0.000 0.000 1.000 0.000
#> GSM152083 3 0.3990 0.5391 0.000 0.308 0.688 0.004 0.000
#> GSM152091 2 0.0324 0.9564 0.000 0.992 0.004 0.004 0.000
#> GSM152108 2 0.1485 0.9357 0.032 0.948 0.020 0.000 0.000
#> GSM152114 1 0.3675 0.6377 0.772 0.000 0.004 0.216 0.008
#> GSM152035 2 0.0898 0.9629 0.000 0.972 0.008 0.020 0.000
#> GSM152039 4 0.0162 0.9309 0.000 0.004 0.000 0.996 0.000
#> GSM152041 4 0.1653 0.8948 0.028 0.004 0.000 0.944 0.024
#> GSM152044 2 0.0880 0.9634 0.000 0.968 0.000 0.032 0.000
#> GSM152045 5 0.2053 0.7845 0.024 0.012 0.028 0.004 0.932
#> GSM152051 2 0.0794 0.9649 0.000 0.972 0.000 0.028 0.000
#> GSM152054 2 0.4187 0.7240 0.008 0.764 0.032 0.000 0.196
#> GSM152057 2 0.0794 0.9649 0.000 0.972 0.000 0.028 0.000
#> GSM152058 1 0.1043 0.7697 0.960 0.000 0.000 0.000 0.040
#> GSM152067 3 0.0932 0.8325 0.004 0.020 0.972 0.000 0.004
#> GSM152068 2 0.0794 0.9649 0.000 0.972 0.000 0.028 0.000
#> GSM152075 4 0.0000 0.9305 0.000 0.000 0.000 1.000 0.000
#> GSM152076 4 0.0162 0.9309 0.000 0.004 0.000 0.996 0.000
#> GSM152079 2 0.0794 0.9649 0.000 0.972 0.000 0.028 0.000
#> GSM152084 3 0.0798 0.8317 0.016 0.000 0.976 0.008 0.000
#> GSM152089 4 0.5083 0.6823 0.000 0.148 0.004 0.712 0.136
#> GSM152095 4 0.0162 0.9309 0.000 0.004 0.000 0.996 0.000
#> GSM152096 3 0.2865 0.7742 0.008 0.132 0.856 0.004 0.000
#> GSM152097 2 0.2179 0.8957 0.000 0.888 0.000 0.112 0.000
#> GSM152099 2 0.0794 0.9649 0.000 0.972 0.000 0.028 0.000
#> GSM152106 2 0.1608 0.9352 0.000 0.928 0.000 0.072 0.000
#> GSM152107 4 0.4182 0.2981 0.000 0.000 0.400 0.600 0.000
#> GSM152109 3 0.0671 0.8331 0.004 0.016 0.980 0.000 0.000
#> GSM152111 5 0.3835 0.7384 0.260 0.000 0.000 0.008 0.732
#> GSM152112 4 0.0880 0.9163 0.000 0.000 0.032 0.968 0.000
#> GSM152113 3 0.4789 0.2802 0.392 0.000 0.584 0.000 0.024
#> GSM152115 3 0.3168 0.7547 0.016 0.004 0.856 0.116 0.008
#> GSM152030 4 0.0404 0.9273 0.000 0.000 0.012 0.988 0.000
#> GSM152038 3 0.2172 0.7987 0.076 0.000 0.908 0.000 0.016
#> GSM152042 4 0.0703 0.9214 0.000 0.000 0.024 0.976 0.000
#> GSM152062 3 0.0671 0.8315 0.016 0.000 0.980 0.004 0.000
#> GSM152077 1 0.0510 0.7728 0.984 0.000 0.016 0.000 0.000
#> GSM152088 2 0.0451 0.9559 0.000 0.988 0.008 0.004 0.000
#> GSM152100 4 0.0162 0.9309 0.000 0.004 0.000 0.996 0.000
#> GSM152102 2 0.0404 0.9539 0.000 0.988 0.012 0.000 0.000
#> GSM152104 2 0.0880 0.9634 0.000 0.968 0.000 0.032 0.000
#> GSM152028 1 0.3093 0.7403 0.824 0.000 0.008 0.000 0.168
#> GSM152029 5 0.5015 0.3960 0.016 0.028 0.304 0.000 0.652
#> GSM152049 1 0.3210 0.6095 0.788 0.000 0.000 0.000 0.212
#> GSM152053 4 0.0703 0.9214 0.000 0.000 0.024 0.976 0.000
#> GSM152059 5 0.1731 0.7889 0.040 0.008 0.012 0.000 0.940
#> GSM152085 5 0.3246 0.8014 0.184 0.000 0.000 0.008 0.808
#> GSM152101 3 0.4596 -0.0588 0.000 0.004 0.500 0.492 0.004
#> GSM152105 1 0.4487 0.7020 0.756 0.000 0.104 0.000 0.140
#> GSM152034 5 0.3459 0.8125 0.116 0.000 0.000 0.052 0.832
#> GSM152036 4 0.0162 0.9309 0.000 0.004 0.000 0.996 0.000
#> GSM152040 5 0.1517 0.7960 0.028 0.012 0.004 0.004 0.952
#> GSM152043 1 0.4434 0.3694 0.536 0.004 0.000 0.000 0.460
#> GSM152046 5 0.3370 0.8120 0.148 0.000 0.000 0.028 0.824
#> GSM152047 5 0.0902 0.8062 0.004 0.008 0.004 0.008 0.976
#> GSM152048 1 0.1121 0.7695 0.956 0.000 0.000 0.000 0.044
#> GSM152050 5 0.3992 0.7270 0.268 0.000 0.000 0.012 0.720
#> GSM152052 1 0.2694 0.7655 0.884 0.000 0.040 0.000 0.076
#> GSM152056 1 0.1478 0.7639 0.936 0.000 0.000 0.000 0.064
#> GSM152060 5 0.3454 0.8095 0.156 0.000 0.000 0.028 0.816
#> GSM152065 1 0.5461 0.6376 0.680 0.008 0.140 0.000 0.172
#> GSM152066 1 0.1410 0.7654 0.940 0.000 0.000 0.000 0.060
#> GSM152069 3 0.0671 0.8331 0.004 0.016 0.980 0.000 0.000
#> GSM152070 5 0.1830 0.7760 0.052 0.012 0.004 0.000 0.932
#> GSM152071 3 0.0671 0.8331 0.004 0.016 0.980 0.000 0.000
#> GSM152072 3 0.5579 0.4307 0.040 0.024 0.588 0.000 0.348
#> GSM152073 5 0.2136 0.7580 0.088 0.008 0.000 0.000 0.904
#> GSM152078 3 0.6624 0.2174 0.304 0.016 0.516 0.000 0.164
#> GSM152082 1 0.4536 0.6000 0.640 0.008 0.008 0.000 0.344
#> GSM152086 1 0.4256 -0.0342 0.564 0.000 0.000 0.000 0.436
#> GSM152090 3 0.1356 0.8306 0.012 0.028 0.956 0.004 0.000
#> GSM152092 1 0.3689 0.6898 0.740 0.004 0.000 0.000 0.256
#> GSM152093 1 0.1671 0.7578 0.924 0.000 0.000 0.000 0.076
#> GSM152094 5 0.1410 0.8199 0.060 0.000 0.000 0.000 0.940
#> GSM152098 5 0.1956 0.7744 0.052 0.012 0.008 0.000 0.928
#> GSM152110 1 0.1908 0.7479 0.908 0.000 0.000 0.000 0.092
#> GSM152031 1 0.4409 0.7106 0.752 0.000 0.072 0.000 0.176
#> GSM152037 1 0.0703 0.7727 0.976 0.000 0.000 0.000 0.024
#> GSM152055 5 0.4223 0.7421 0.248 0.000 0.000 0.028 0.724
#> GSM152061 5 0.3454 0.8095 0.156 0.000 0.000 0.028 0.816
#> GSM152064 5 0.3929 0.7777 0.208 0.000 0.000 0.028 0.764
#> GSM152087 5 0.1792 0.8215 0.084 0.000 0.000 0.000 0.916
#> GSM152103 3 0.2228 0.8153 0.044 0.020 0.920 0.000 0.016
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM152032 3 0.0551 0.7841 0.004 0.000 0.984 0.004 0.008 0.000
#> GSM152033 1 0.5990 0.3203 0.500 0.000 0.224 0.008 0.268 0.000
#> GSM152063 2 0.0000 0.9686 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152074 3 0.1820 0.7826 0.016 0.000 0.928 0.012 0.044 0.000
#> GSM152080 2 0.0291 0.9650 0.000 0.992 0.004 0.000 0.004 0.000
#> GSM152081 4 0.1241 0.8781 0.004 0.004 0.004 0.960 0.020 0.008
#> GSM152083 3 0.4075 0.5377 0.004 0.312 0.668 0.004 0.012 0.000
#> GSM152091 2 0.0146 0.9667 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM152108 2 0.3069 0.8390 0.096 0.852 0.032 0.000 0.020 0.000
#> GSM152114 1 0.5012 0.5477 0.724 0.000 0.040 0.164 0.040 0.032
#> GSM152035 2 0.0260 0.9655 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM152039 4 0.0603 0.8803 0.000 0.004 0.000 0.980 0.000 0.016
#> GSM152041 4 0.4326 0.6613 0.028 0.000 0.000 0.724 0.032 0.216
#> GSM152044 2 0.0000 0.9686 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152045 5 0.4311 0.2469 0.008 0.000 0.004 0.004 0.556 0.428
#> GSM152051 2 0.0000 0.9686 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152054 5 0.6182 0.0852 0.012 0.404 0.012 0.016 0.468 0.088
#> GSM152057 2 0.0000 0.9686 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152058 1 0.1501 0.6715 0.924 0.000 0.000 0.000 0.000 0.076
#> GSM152067 3 0.3030 0.7709 0.008 0.000 0.816 0.000 0.168 0.008
#> GSM152068 2 0.0000 0.9686 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152075 4 0.0870 0.8803 0.000 0.004 0.000 0.972 0.012 0.012
#> GSM152076 4 0.0603 0.8803 0.000 0.004 0.000 0.980 0.000 0.016
#> GSM152079 2 0.0000 0.9686 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152084 3 0.1913 0.7793 0.016 0.000 0.924 0.016 0.044 0.000
#> GSM152089 4 0.6534 0.3416 0.000 0.092 0.000 0.484 0.104 0.320
#> GSM152095 4 0.0603 0.8803 0.000 0.004 0.000 0.980 0.000 0.016
#> GSM152096 3 0.3527 0.7255 0.008 0.132 0.808 0.000 0.052 0.000
#> GSM152097 2 0.2260 0.8390 0.000 0.860 0.000 0.140 0.000 0.000
#> GSM152099 2 0.0000 0.9686 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152106 2 0.1610 0.9001 0.000 0.916 0.000 0.084 0.000 0.000
#> GSM152107 4 0.5157 -0.0241 0.004 0.000 0.440 0.484 0.072 0.000
#> GSM152109 3 0.2320 0.7781 0.004 0.000 0.864 0.000 0.132 0.000
#> GSM152111 6 0.2882 0.6813 0.180 0.000 0.000 0.000 0.008 0.812
#> GSM152112 4 0.1851 0.8527 0.004 0.000 0.012 0.924 0.056 0.004
#> GSM152113 3 0.5927 0.2441 0.284 0.000 0.508 0.008 0.200 0.000
#> GSM152115 3 0.4516 0.6931 0.016 0.000 0.748 0.084 0.144 0.008
#> GSM152030 4 0.1147 0.8745 0.004 0.004 0.004 0.960 0.028 0.000
#> GSM152038 3 0.4700 0.5959 0.112 0.000 0.700 0.008 0.180 0.000
#> GSM152042 4 0.1067 0.8755 0.004 0.004 0.004 0.964 0.024 0.000
#> GSM152062 3 0.1332 0.7835 0.012 0.000 0.952 0.008 0.028 0.000
#> GSM152077 1 0.2201 0.6406 0.904 0.000 0.036 0.000 0.056 0.004
#> GSM152088 2 0.0146 0.9667 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM152100 4 0.0748 0.8797 0.000 0.004 0.000 0.976 0.004 0.016
#> GSM152102 2 0.1296 0.9377 0.000 0.952 0.000 0.004 0.032 0.012
#> GSM152104 2 0.0000 0.9686 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152028 1 0.3778 0.5020 0.696 0.000 0.016 0.000 0.288 0.000
#> GSM152029 5 0.5089 0.4662 0.004 0.000 0.176 0.000 0.648 0.172
#> GSM152049 1 0.3647 0.3811 0.640 0.000 0.000 0.000 0.000 0.360
#> GSM152053 4 0.1147 0.8745 0.004 0.004 0.004 0.960 0.028 0.000
#> GSM152059 5 0.4524 0.2736 0.024 0.000 0.004 0.000 0.520 0.452
#> GSM152085 6 0.2309 0.7369 0.084 0.000 0.000 0.000 0.028 0.888
#> GSM152101 3 0.5778 0.2097 0.004 0.000 0.496 0.368 0.124 0.008
#> GSM152105 1 0.4352 0.4941 0.668 0.000 0.052 0.000 0.280 0.000
#> GSM152034 6 0.1296 0.7290 0.004 0.000 0.000 0.012 0.032 0.952
#> GSM152036 4 0.0547 0.8794 0.000 0.000 0.000 0.980 0.000 0.020
#> GSM152040 6 0.4089 -0.1749 0.008 0.000 0.000 0.000 0.468 0.524
#> GSM152043 5 0.5705 0.1710 0.380 0.000 0.000 0.000 0.456 0.164
#> GSM152046 6 0.0993 0.7371 0.012 0.000 0.000 0.000 0.024 0.964
#> GSM152047 6 0.3684 0.1773 0.000 0.000 0.000 0.000 0.372 0.628
#> GSM152048 1 0.1700 0.6717 0.916 0.000 0.000 0.000 0.004 0.080
#> GSM152050 6 0.3190 0.6460 0.220 0.000 0.000 0.000 0.008 0.772
#> GSM152052 1 0.3758 0.5579 0.740 0.000 0.024 0.000 0.232 0.004
#> GSM152056 1 0.2491 0.6435 0.836 0.000 0.000 0.000 0.000 0.164
#> GSM152060 6 0.1088 0.7442 0.024 0.000 0.000 0.000 0.016 0.960
#> GSM152065 1 0.4979 0.2376 0.492 0.000 0.056 0.004 0.448 0.000
#> GSM152066 1 0.1910 0.6650 0.892 0.000 0.000 0.000 0.000 0.108
#> GSM152069 3 0.2362 0.7770 0.004 0.000 0.860 0.000 0.136 0.000
#> GSM152070 5 0.4482 0.4718 0.048 0.000 0.000 0.000 0.628 0.324
#> GSM152071 3 0.2362 0.7770 0.004 0.000 0.860 0.000 0.136 0.000
#> GSM152072 5 0.3661 0.5209 0.016 0.000 0.108 0.004 0.816 0.056
#> GSM152073 5 0.5224 0.2549 0.092 0.000 0.000 0.000 0.468 0.440
#> GSM152078 5 0.5096 0.3193 0.152 0.000 0.184 0.000 0.656 0.008
#> GSM152082 5 0.4908 0.1776 0.348 0.000 0.004 0.000 0.584 0.064
#> GSM152086 1 0.4569 0.1942 0.564 0.000 0.000 0.000 0.040 0.396
#> GSM152090 3 0.3053 0.7658 0.024 0.000 0.828 0.004 0.144 0.000
#> GSM152092 1 0.4594 0.2639 0.544 0.000 0.008 0.000 0.424 0.024
#> GSM152093 1 0.3411 0.6379 0.804 0.000 0.012 0.000 0.024 0.160
#> GSM152094 6 0.3314 0.5289 0.012 0.000 0.000 0.000 0.224 0.764
#> GSM152098 5 0.4406 0.4623 0.040 0.000 0.000 0.000 0.624 0.336
#> GSM152110 1 0.2793 0.6212 0.800 0.000 0.000 0.000 0.000 0.200
#> GSM152031 1 0.4676 0.2927 0.528 0.000 0.028 0.000 0.436 0.008
#> GSM152037 1 0.1219 0.6693 0.948 0.000 0.000 0.000 0.004 0.048
#> GSM152055 6 0.2772 0.6744 0.180 0.000 0.000 0.000 0.004 0.816
#> GSM152061 6 0.1088 0.7442 0.024 0.000 0.000 0.000 0.016 0.960
#> GSM152064 6 0.2501 0.7140 0.108 0.000 0.000 0.004 0.016 0.872
#> GSM152087 6 0.3176 0.6250 0.032 0.000 0.000 0.000 0.156 0.812
#> GSM152103 3 0.3521 0.7498 0.044 0.000 0.796 0.000 0.156 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 specimen(p) k
#> MAD:skmeans 86 9.27e-09 2
#> MAD:skmeans 83 3.28e-07 3
#> MAD:skmeans 84 6.30e-05 4
#> MAD:skmeans 79 2.88e-04 5
#> MAD:skmeans 65 1.49e-02 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 10612 rows and 88 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 0.837 0.907 0.958 0.4800 0.520 0.520
#> 3 3 0.613 0.793 0.895 0.3542 0.809 0.638
#> 4 4 0.714 0.745 0.890 0.1276 0.851 0.609
#> 5 5 0.655 0.499 0.760 0.0779 0.926 0.737
#> 6 6 0.705 0.467 0.706 0.0340 0.900 0.610
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
#> GSM152032 2 0.0672 0.957 0.008 0.992
#> GSM152033 1 0.0000 0.949 1.000 0.000
#> GSM152063 2 0.0000 0.959 0.000 1.000
#> GSM152074 2 0.0000 0.959 0.000 1.000
#> GSM152080 2 0.1184 0.953 0.016 0.984
#> GSM152081 2 0.0000 0.959 0.000 1.000
#> GSM152083 2 0.0000 0.959 0.000 1.000
#> GSM152091 2 0.0000 0.959 0.000 1.000
#> GSM152108 2 0.5946 0.823 0.144 0.856
#> GSM152114 1 0.0000 0.949 1.000 0.000
#> GSM152035 2 0.0000 0.959 0.000 1.000
#> GSM152039 2 0.0000 0.959 0.000 1.000
#> GSM152041 2 0.9323 0.465 0.348 0.652
#> GSM152044 2 0.0000 0.959 0.000 1.000
#> GSM152045 1 0.6801 0.779 0.820 0.180
#> GSM152051 2 0.0000 0.959 0.000 1.000
#> GSM152054 1 0.6801 0.783 0.820 0.180
#> GSM152057 2 0.0000 0.959 0.000 1.000
#> GSM152058 1 0.0000 0.949 1.000 0.000
#> GSM152067 2 0.0000 0.959 0.000 1.000
#> GSM152068 2 0.0000 0.959 0.000 1.000
#> GSM152075 2 0.0672 0.957 0.008 0.992
#> GSM152076 2 0.0000 0.959 0.000 1.000
#> GSM152079 2 0.0000 0.959 0.000 1.000
#> GSM152084 2 0.0672 0.957 0.008 0.992
#> GSM152089 2 0.0000 0.959 0.000 1.000
#> GSM152095 2 0.0000 0.959 0.000 1.000
#> GSM152096 2 0.0672 0.957 0.008 0.992
#> GSM152097 2 0.0000 0.959 0.000 1.000
#> GSM152099 2 0.0000 0.959 0.000 1.000
#> GSM152106 2 0.0000 0.959 0.000 1.000
#> GSM152107 2 0.0000 0.959 0.000 1.000
#> GSM152109 2 0.0672 0.957 0.008 0.992
#> GSM152111 2 0.2778 0.934 0.048 0.952
#> GSM152112 2 0.0000 0.959 0.000 1.000
#> GSM152113 2 0.5629 0.853 0.132 0.868
#> GSM152115 2 0.4161 0.893 0.084 0.916
#> GSM152030 2 0.0000 0.959 0.000 1.000
#> GSM152038 2 0.8813 0.568 0.300 0.700
#> GSM152042 2 0.0000 0.959 0.000 1.000
#> GSM152062 2 0.0672 0.957 0.008 0.992
#> GSM152077 1 0.0000 0.949 1.000 0.000
#> GSM152088 2 0.0000 0.959 0.000 1.000
#> GSM152100 2 0.0000 0.959 0.000 1.000
#> GSM152102 2 0.0000 0.959 0.000 1.000
#> GSM152104 2 0.0000 0.959 0.000 1.000
#> GSM152028 1 0.0000 0.949 1.000 0.000
#> GSM152029 2 0.2236 0.943 0.036 0.964
#> GSM152049 1 0.0000 0.949 1.000 0.000
#> GSM152053 2 0.0672 0.957 0.008 0.992
#> GSM152059 1 0.9686 0.342 0.604 0.396
#> GSM152085 1 0.0000 0.949 1.000 0.000
#> GSM152101 2 0.0000 0.959 0.000 1.000
#> GSM152105 1 0.0000 0.949 1.000 0.000
#> GSM152034 2 0.2236 0.943 0.036 0.964
#> GSM152036 2 0.0000 0.959 0.000 1.000
#> GSM152040 1 0.0000 0.949 1.000 0.000
#> GSM152043 1 0.0000 0.949 1.000 0.000
#> GSM152046 1 0.7883 0.689 0.764 0.236
#> GSM152047 2 0.2236 0.943 0.036 0.964
#> GSM152048 1 0.0000 0.949 1.000 0.000
#> GSM152050 1 0.7745 0.701 0.772 0.228
#> GSM152052 2 0.9608 0.379 0.384 0.616
#> GSM152056 1 0.0000 0.949 1.000 0.000
#> GSM152060 1 0.0000 0.949 1.000 0.000
#> GSM152065 1 0.0000 0.949 1.000 0.000
#> GSM152066 1 0.0000 0.949 1.000 0.000
#> GSM152069 2 0.1184 0.954 0.016 0.984
#> GSM152070 1 0.0000 0.949 1.000 0.000
#> GSM152071 2 0.1633 0.950 0.024 0.976
#> GSM152072 2 0.2236 0.943 0.036 0.964
#> GSM152073 1 0.0000 0.949 1.000 0.000
#> GSM152078 2 0.2236 0.943 0.036 0.964
#> GSM152082 1 0.0000 0.949 1.000 0.000
#> GSM152086 1 0.0000 0.949 1.000 0.000
#> GSM152090 2 0.2236 0.943 0.036 0.964
#> GSM152092 1 0.0000 0.949 1.000 0.000
#> GSM152093 2 0.8443 0.636 0.272 0.728
#> GSM152094 1 0.0000 0.949 1.000 0.000
#> GSM152098 1 0.2423 0.918 0.960 0.040
#> GSM152110 1 0.0000 0.949 1.000 0.000
#> GSM152031 1 0.9044 0.517 0.680 0.320
#> GSM152037 1 0.0000 0.949 1.000 0.000
#> GSM152055 1 0.0000 0.949 1.000 0.000
#> GSM152061 1 0.0000 0.949 1.000 0.000
#> GSM152064 1 0.0000 0.949 1.000 0.000
#> GSM152087 1 0.0000 0.949 1.000 0.000
#> GSM152103 2 0.2236 0.943 0.036 0.964
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM152032 3 0.0000 0.832 0.000 0.000 1.000
#> GSM152033 1 0.4062 0.792 0.836 0.000 0.164
#> GSM152063 2 0.0000 0.908 0.000 1.000 0.000
#> GSM152074 3 0.0000 0.832 0.000 0.000 1.000
#> GSM152080 2 0.1643 0.910 0.000 0.956 0.044
#> GSM152081 3 0.3038 0.786 0.000 0.104 0.896
#> GSM152083 2 0.5678 0.598 0.000 0.684 0.316
#> GSM152091 2 0.1289 0.916 0.000 0.968 0.032
#> GSM152108 3 0.6001 0.773 0.176 0.052 0.772
#> GSM152114 1 0.0000 0.902 1.000 0.000 0.000
#> GSM152035 2 0.0000 0.908 0.000 1.000 0.000
#> GSM152039 2 0.2261 0.871 0.000 0.932 0.068
#> GSM152041 3 0.6057 0.627 0.340 0.004 0.656
#> GSM152044 2 0.1031 0.916 0.000 0.976 0.024
#> GSM152045 1 0.6931 0.504 0.640 0.032 0.328
#> GSM152051 2 0.1031 0.916 0.000 0.976 0.024
#> GSM152054 1 0.9756 0.139 0.428 0.332 0.240
#> GSM152057 2 0.1289 0.916 0.000 0.968 0.032
#> GSM152058 1 0.0000 0.902 1.000 0.000 0.000
#> GSM152067 3 0.0000 0.832 0.000 0.000 1.000
#> GSM152068 2 0.1289 0.916 0.000 0.968 0.032
#> GSM152075 3 0.5298 0.782 0.164 0.032 0.804
#> GSM152076 2 0.5621 0.551 0.000 0.692 0.308
#> GSM152079 2 0.1289 0.916 0.000 0.968 0.032
#> GSM152084 3 0.0000 0.832 0.000 0.000 1.000
#> GSM152089 3 0.5298 0.782 0.164 0.032 0.804
#> GSM152095 2 0.6045 0.381 0.000 0.620 0.380
#> GSM152096 3 0.0000 0.832 0.000 0.000 1.000
#> GSM152097 2 0.0000 0.908 0.000 1.000 0.000
#> GSM152099 2 0.0000 0.908 0.000 1.000 0.000
#> GSM152106 2 0.0892 0.915 0.000 0.980 0.020
#> GSM152107 3 0.1289 0.826 0.000 0.032 0.968
#> GSM152109 3 0.0000 0.832 0.000 0.000 1.000
#> GSM152111 3 0.5098 0.742 0.248 0.000 0.752
#> GSM152112 3 0.1289 0.826 0.000 0.032 0.968
#> GSM152113 3 0.2448 0.824 0.076 0.000 0.924
#> GSM152115 3 0.3713 0.795 0.076 0.032 0.892
#> GSM152030 3 0.1411 0.825 0.000 0.036 0.964
#> GSM152038 3 0.5397 0.523 0.280 0.000 0.720
#> GSM152042 3 0.0000 0.832 0.000 0.000 1.000
#> GSM152062 3 0.0000 0.832 0.000 0.000 1.000
#> GSM152077 1 0.1529 0.882 0.960 0.000 0.040
#> GSM152088 2 0.1289 0.916 0.000 0.968 0.032
#> GSM152100 3 0.5731 0.770 0.088 0.108 0.804
#> GSM152102 2 0.3686 0.806 0.000 0.860 0.140
#> GSM152104 2 0.1289 0.916 0.000 0.968 0.032
#> GSM152028 1 0.0000 0.902 1.000 0.000 0.000
#> GSM152029 3 0.2261 0.828 0.068 0.000 0.932
#> GSM152049 1 0.0000 0.902 1.000 0.000 0.000
#> GSM152053 3 0.1289 0.826 0.000 0.032 0.968
#> GSM152059 3 0.6286 0.118 0.464 0.000 0.536
#> GSM152085 1 0.0000 0.902 1.000 0.000 0.000
#> GSM152101 3 0.1289 0.826 0.000 0.032 0.968
#> GSM152105 1 0.4062 0.792 0.836 0.000 0.164
#> GSM152034 3 0.4931 0.756 0.232 0.000 0.768
#> GSM152036 3 0.6228 0.394 0.004 0.372 0.624
#> GSM152040 1 0.4062 0.792 0.836 0.000 0.164
#> GSM152043 1 0.0000 0.902 1.000 0.000 0.000
#> GSM152046 1 0.4931 0.594 0.768 0.000 0.232
#> GSM152047 3 0.4931 0.756 0.232 0.000 0.768
#> GSM152048 1 0.0000 0.902 1.000 0.000 0.000
#> GSM152050 1 0.4842 0.613 0.776 0.000 0.224
#> GSM152052 3 0.6026 0.564 0.376 0.000 0.624
#> GSM152056 1 0.0000 0.902 1.000 0.000 0.000
#> GSM152060 1 0.0000 0.902 1.000 0.000 0.000
#> GSM152065 1 0.4062 0.792 0.836 0.000 0.164
#> GSM152066 1 0.0000 0.902 1.000 0.000 0.000
#> GSM152069 3 0.0237 0.833 0.004 0.000 0.996
#> GSM152070 1 0.3482 0.821 0.872 0.000 0.128
#> GSM152071 3 0.2066 0.830 0.060 0.000 0.940
#> GSM152072 3 0.2261 0.828 0.068 0.000 0.932
#> GSM152073 1 0.0000 0.902 1.000 0.000 0.000
#> GSM152078 3 0.2261 0.828 0.068 0.000 0.932
#> GSM152082 1 0.3941 0.799 0.844 0.000 0.156
#> GSM152086 1 0.0000 0.902 1.000 0.000 0.000
#> GSM152090 3 0.4931 0.756 0.232 0.000 0.768
#> GSM152092 1 0.0000 0.902 1.000 0.000 0.000
#> GSM152093 3 0.6302 0.294 0.480 0.000 0.520
#> GSM152094 1 0.0000 0.902 1.000 0.000 0.000
#> GSM152098 1 0.1643 0.876 0.956 0.000 0.044
#> GSM152110 1 0.0000 0.902 1.000 0.000 0.000
#> GSM152031 1 0.5327 0.665 0.728 0.000 0.272
#> GSM152037 1 0.0000 0.902 1.000 0.000 0.000
#> GSM152055 1 0.0000 0.902 1.000 0.000 0.000
#> GSM152061 1 0.0000 0.902 1.000 0.000 0.000
#> GSM152064 1 0.0000 0.902 1.000 0.000 0.000
#> GSM152087 1 0.0000 0.902 1.000 0.000 0.000
#> GSM152103 3 0.4931 0.756 0.232 0.000 0.768
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM152032 3 0.0000 0.772 0.000 0.000 1.000 0.000
#> GSM152033 1 0.4697 0.490 0.644 0.000 0.356 0.000
#> GSM152063 2 0.0000 0.950 0.000 1.000 0.000 0.000
#> GSM152074 3 0.0707 0.761 0.000 0.000 0.980 0.020
#> GSM152080 2 0.0000 0.950 0.000 1.000 0.000 0.000
#> GSM152081 4 0.4941 0.191 0.000 0.000 0.436 0.564
#> GSM152083 2 0.4697 0.479 0.000 0.644 0.356 0.000
#> GSM152091 2 0.0000 0.950 0.000 1.000 0.000 0.000
#> GSM152108 3 0.6731 0.569 0.248 0.148 0.604 0.000
#> GSM152114 1 0.0000 0.844 1.000 0.000 0.000 0.000
#> GSM152035 2 0.0000 0.950 0.000 1.000 0.000 0.000
#> GSM152039 4 0.0000 0.895 0.000 0.000 0.000 1.000
#> GSM152041 1 0.7706 -0.251 0.412 0.000 0.364 0.224
#> GSM152044 2 0.0000 0.950 0.000 1.000 0.000 0.000
#> GSM152045 4 0.5427 0.725 0.100 0.000 0.164 0.736
#> GSM152051 2 0.0000 0.950 0.000 1.000 0.000 0.000
#> GSM152054 4 0.3108 0.847 0.016 0.000 0.112 0.872
#> GSM152057 2 0.0000 0.950 0.000 1.000 0.000 0.000
#> GSM152058 1 0.0000 0.844 1.000 0.000 0.000 0.000
#> GSM152067 3 0.0188 0.770 0.000 0.000 0.996 0.004
#> GSM152068 2 0.0000 0.950 0.000 1.000 0.000 0.000
#> GSM152075 4 0.0000 0.895 0.000 0.000 0.000 1.000
#> GSM152076 4 0.0000 0.895 0.000 0.000 0.000 1.000
#> GSM152079 2 0.0000 0.950 0.000 1.000 0.000 0.000
#> GSM152084 3 0.4522 0.407 0.000 0.000 0.680 0.320
#> GSM152089 4 0.3523 0.801 0.112 0.000 0.032 0.856
#> GSM152095 4 0.0000 0.895 0.000 0.000 0.000 1.000
#> GSM152096 3 0.1118 0.753 0.000 0.000 0.964 0.036
#> GSM152097 2 0.0000 0.950 0.000 1.000 0.000 0.000
#> GSM152099 2 0.0000 0.950 0.000 1.000 0.000 0.000
#> GSM152106 2 0.0000 0.950 0.000 1.000 0.000 0.000
#> GSM152107 4 0.2530 0.855 0.000 0.000 0.112 0.888
#> GSM152109 3 0.0592 0.766 0.000 0.000 0.984 0.016
#> GSM152111 3 0.4713 0.539 0.360 0.000 0.640 0.000
#> GSM152112 4 0.1118 0.891 0.000 0.000 0.036 0.964
#> GSM152113 3 0.0707 0.764 0.020 0.000 0.980 0.000
#> GSM152115 4 0.2530 0.855 0.000 0.000 0.112 0.888
#> GSM152030 4 0.0000 0.895 0.000 0.000 0.000 1.000
#> GSM152038 3 0.3688 0.572 0.208 0.000 0.792 0.000
#> GSM152042 4 0.3764 0.708 0.000 0.000 0.216 0.784
#> GSM152062 3 0.0000 0.772 0.000 0.000 1.000 0.000
#> GSM152077 1 0.3074 0.730 0.848 0.000 0.152 0.000
#> GSM152088 2 0.0000 0.950 0.000 1.000 0.000 0.000
#> GSM152100 4 0.0000 0.895 0.000 0.000 0.000 1.000
#> GSM152102 2 0.6074 0.491 0.000 0.648 0.084 0.268
#> GSM152104 2 0.0000 0.950 0.000 1.000 0.000 0.000
#> GSM152028 1 0.0000 0.844 1.000 0.000 0.000 0.000
#> GSM152029 3 0.0000 0.772 0.000 0.000 1.000 0.000
#> GSM152049 1 0.0000 0.844 1.000 0.000 0.000 0.000
#> GSM152053 4 0.0817 0.891 0.000 0.000 0.024 0.976
#> GSM152059 3 0.4679 0.293 0.352 0.000 0.648 0.000
#> GSM152085 1 0.0000 0.844 1.000 0.000 0.000 0.000
#> GSM152101 4 0.1637 0.883 0.000 0.000 0.060 0.940
#> GSM152105 1 0.4697 0.490 0.644 0.000 0.356 0.000
#> GSM152034 3 0.5331 0.564 0.332 0.000 0.644 0.024
#> GSM152036 4 0.0000 0.895 0.000 0.000 0.000 1.000
#> GSM152040 1 0.4643 0.508 0.656 0.000 0.344 0.000
#> GSM152043 1 0.0000 0.844 1.000 0.000 0.000 0.000
#> GSM152046 1 0.3266 0.661 0.832 0.000 0.168 0.000
#> GSM152047 3 0.4697 0.544 0.356 0.000 0.644 0.000
#> GSM152048 1 0.0000 0.844 1.000 0.000 0.000 0.000
#> GSM152050 1 0.3172 0.673 0.840 0.000 0.160 0.000
#> GSM152052 3 0.4961 0.368 0.448 0.000 0.552 0.000
#> GSM152056 1 0.0000 0.844 1.000 0.000 0.000 0.000
#> GSM152060 1 0.0000 0.844 1.000 0.000 0.000 0.000
#> GSM152065 1 0.4697 0.490 0.644 0.000 0.356 0.000
#> GSM152066 1 0.0000 0.844 1.000 0.000 0.000 0.000
#> GSM152069 3 0.0000 0.772 0.000 0.000 1.000 0.000
#> GSM152070 1 0.3688 0.672 0.792 0.000 0.208 0.000
#> GSM152071 3 0.0000 0.772 0.000 0.000 1.000 0.000
#> GSM152072 3 0.0000 0.772 0.000 0.000 1.000 0.000
#> GSM152073 1 0.0000 0.844 1.000 0.000 0.000 0.000
#> GSM152078 3 0.0000 0.772 0.000 0.000 1.000 0.000
#> GSM152082 1 0.4304 0.586 0.716 0.000 0.284 0.000
#> GSM152086 1 0.0000 0.844 1.000 0.000 0.000 0.000
#> GSM152090 3 0.5331 0.564 0.332 0.000 0.644 0.024
#> GSM152092 1 0.0000 0.844 1.000 0.000 0.000 0.000
#> GSM152093 1 0.4866 0.071 0.596 0.000 0.404 0.000
#> GSM152094 1 0.0000 0.844 1.000 0.000 0.000 0.000
#> GSM152098 1 0.1389 0.814 0.952 0.000 0.048 0.000
#> GSM152110 1 0.0000 0.844 1.000 0.000 0.000 0.000
#> GSM152031 1 0.4888 0.391 0.588 0.000 0.412 0.000
#> GSM152037 1 0.0000 0.844 1.000 0.000 0.000 0.000
#> GSM152055 1 0.0000 0.844 1.000 0.000 0.000 0.000
#> GSM152061 1 0.0000 0.844 1.000 0.000 0.000 0.000
#> GSM152064 1 0.0000 0.844 1.000 0.000 0.000 0.000
#> GSM152087 1 0.0000 0.844 1.000 0.000 0.000 0.000
#> GSM152103 3 0.4697 0.544 0.356 0.000 0.644 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM152032 3 0.3796 0.60954 0.000 0.000 0.700 0.000 0.300
#> GSM152033 1 0.6234 0.20426 0.524 0.000 0.172 0.000 0.304
#> GSM152063 2 0.0000 0.94301 0.000 1.000 0.000 0.000 0.000
#> GSM152074 3 0.4836 0.57505 0.000 0.000 0.652 0.044 0.304
#> GSM152080 2 0.0000 0.94301 0.000 1.000 0.000 0.000 0.000
#> GSM152081 4 0.4655 0.28065 0.000 0.000 0.328 0.644 0.028
#> GSM152083 2 0.6301 0.22629 0.000 0.516 0.184 0.000 0.300
#> GSM152091 2 0.0000 0.94301 0.000 1.000 0.000 0.000 0.000
#> GSM152108 3 0.5789 0.41389 0.260 0.124 0.612 0.000 0.004
#> GSM152114 1 0.1106 0.50648 0.964 0.000 0.012 0.024 0.000
#> GSM152035 2 0.0000 0.94301 0.000 1.000 0.000 0.000 0.000
#> GSM152039 4 0.0794 0.72139 0.000 0.000 0.000 0.972 0.028
#> GSM152041 1 0.8018 -0.12433 0.444 0.000 0.144 0.204 0.208
#> GSM152044 2 0.0000 0.94301 0.000 1.000 0.000 0.000 0.000
#> GSM152045 4 0.7682 -0.01678 0.196 0.000 0.068 0.392 0.344
#> GSM152051 2 0.0000 0.94301 0.000 1.000 0.000 0.000 0.000
#> GSM152054 4 0.4517 0.48905 0.000 0.000 0.008 0.556 0.436
#> GSM152057 2 0.0000 0.94301 0.000 1.000 0.000 0.000 0.000
#> GSM152058 1 0.0794 0.50547 0.972 0.000 0.000 0.000 0.028
#> GSM152067 3 0.3109 0.64524 0.000 0.000 0.800 0.000 0.200
#> GSM152068 2 0.0000 0.94301 0.000 1.000 0.000 0.000 0.000
#> GSM152075 4 0.0963 0.71792 0.000 0.000 0.036 0.964 0.000
#> GSM152076 4 0.0794 0.72139 0.000 0.000 0.000 0.972 0.028
#> GSM152079 2 0.0000 0.94301 0.000 1.000 0.000 0.000 0.000
#> GSM152084 3 0.2890 0.56834 0.004 0.000 0.836 0.160 0.000
#> GSM152089 4 0.6082 0.43603 0.000 0.000 0.312 0.540 0.148
#> GSM152095 4 0.0794 0.72139 0.000 0.000 0.000 0.972 0.028
#> GSM152096 3 0.0162 0.66862 0.000 0.000 0.996 0.004 0.000
#> GSM152097 2 0.0510 0.93121 0.000 0.984 0.000 0.000 0.016
#> GSM152099 2 0.0000 0.94301 0.000 1.000 0.000 0.000 0.000
#> GSM152106 2 0.0000 0.94301 0.000 1.000 0.000 0.000 0.000
#> GSM152107 4 0.5887 0.51213 0.000 0.000 0.156 0.592 0.252
#> GSM152109 3 0.1043 0.65534 0.000 0.000 0.960 0.040 0.000
#> GSM152111 5 0.4996 0.09784 0.032 0.000 0.420 0.000 0.548
#> GSM152112 4 0.3812 0.65112 0.000 0.000 0.024 0.772 0.204
#> GSM152113 3 0.4269 0.60820 0.016 0.000 0.684 0.000 0.300
#> GSM152115 4 0.5819 0.51930 0.000 0.000 0.148 0.600 0.252
#> GSM152030 4 0.0162 0.72290 0.000 0.000 0.000 0.996 0.004
#> GSM152038 3 0.5804 0.52469 0.120 0.000 0.576 0.000 0.304
#> GSM152042 4 0.3932 0.52797 0.000 0.000 0.328 0.672 0.000
#> GSM152062 3 0.4325 0.60771 0.012 0.000 0.684 0.004 0.300
#> GSM152077 1 0.2891 0.40716 0.824 0.000 0.000 0.000 0.176
#> GSM152088 2 0.0000 0.94301 0.000 1.000 0.000 0.000 0.000
#> GSM152100 4 0.0000 0.72286 0.000 0.000 0.000 1.000 0.000
#> GSM152102 2 0.4040 0.60580 0.000 0.724 0.000 0.016 0.260
#> GSM152104 2 0.0000 0.94301 0.000 1.000 0.000 0.000 0.000
#> GSM152028 1 0.0000 0.51231 1.000 0.000 0.000 0.000 0.000
#> GSM152029 3 0.2929 0.56228 0.000 0.000 0.820 0.000 0.180
#> GSM152049 1 0.3109 0.32311 0.800 0.000 0.000 0.000 0.200
#> GSM152053 4 0.3661 0.58423 0.000 0.000 0.276 0.724 0.000
#> GSM152059 5 0.3060 0.30798 0.128 0.000 0.024 0.000 0.848
#> GSM152085 1 0.4088 0.07001 0.632 0.000 0.000 0.000 0.368
#> GSM152101 4 0.5470 0.55666 0.000 0.000 0.112 0.636 0.252
#> GSM152105 1 0.6234 0.20426 0.524 0.000 0.172 0.000 0.304
#> GSM152034 3 0.5412 0.40705 0.004 0.000 0.644 0.088 0.264
#> GSM152036 4 0.0794 0.72139 0.000 0.000 0.000 0.972 0.028
#> GSM152040 5 0.4196 0.00466 0.356 0.000 0.004 0.000 0.640
#> GSM152043 1 0.3353 0.37230 0.796 0.000 0.008 0.000 0.196
#> GSM152046 5 0.3949 0.48833 0.332 0.000 0.000 0.000 0.668
#> GSM152047 3 0.4225 0.29679 0.004 0.000 0.632 0.000 0.364
#> GSM152048 1 0.0794 0.50547 0.972 0.000 0.000 0.000 0.028
#> GSM152050 1 0.5252 0.04500 0.616 0.000 0.068 0.000 0.316
#> GSM152052 1 0.6024 -0.04986 0.532 0.000 0.336 0.000 0.132
#> GSM152056 1 0.0794 0.50547 0.972 0.000 0.000 0.000 0.028
#> GSM152060 5 0.3949 0.48833 0.332 0.000 0.000 0.000 0.668
#> GSM152065 1 0.6326 0.18052 0.492 0.000 0.172 0.000 0.336
#> GSM152066 1 0.0000 0.51231 1.000 0.000 0.000 0.000 0.000
#> GSM152069 3 0.0000 0.66948 0.000 0.000 1.000 0.000 0.000
#> GSM152070 1 0.4549 -0.03185 0.528 0.000 0.008 0.000 0.464
#> GSM152071 3 0.0000 0.66948 0.000 0.000 1.000 0.000 0.000
#> GSM152072 3 0.4114 0.57589 0.000 0.000 0.624 0.000 0.376
#> GSM152073 1 0.3999 0.10845 0.656 0.000 0.000 0.000 0.344
#> GSM152078 3 0.3966 0.60225 0.000 0.000 0.664 0.000 0.336
#> GSM152082 1 0.4321 0.20062 0.600 0.000 0.004 0.000 0.396
#> GSM152086 1 0.2516 0.43324 0.860 0.000 0.000 0.000 0.140
#> GSM152090 3 0.2488 0.59809 0.004 0.000 0.872 0.124 0.000
#> GSM152092 1 0.3143 0.36536 0.796 0.000 0.000 0.000 0.204
#> GSM152093 3 0.4227 0.26827 0.420 0.000 0.580 0.000 0.000
#> GSM152094 1 0.4015 0.09985 0.652 0.000 0.000 0.000 0.348
#> GSM152098 1 0.4800 0.03039 0.604 0.000 0.028 0.000 0.368
#> GSM152110 1 0.0000 0.51231 1.000 0.000 0.000 0.000 0.000
#> GSM152031 1 0.6234 0.20426 0.524 0.000 0.172 0.000 0.304
#> GSM152037 1 0.0162 0.51211 0.996 0.000 0.000 0.000 0.004
#> GSM152055 1 0.3857 0.17040 0.688 0.000 0.000 0.000 0.312
#> GSM152061 5 0.3949 0.48833 0.332 0.000 0.000 0.000 0.668
#> GSM152064 1 0.4294 -0.20200 0.532 0.000 0.000 0.000 0.468
#> GSM152087 5 0.4304 0.23881 0.484 0.000 0.000 0.000 0.516
#> GSM152103 3 0.3086 0.55835 0.004 0.000 0.816 0.000 0.180
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM152032 3 0.0363 4.78e-01 0.000 0.000 0.988 0.012 0.000 0.000
#> GSM152033 3 0.3998 -8.23e-02 0.492 0.000 0.504 0.000 0.000 0.004
#> GSM152063 2 0.0000 9.60e-01 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152074 3 0.2393 4.33e-01 0.000 0.000 0.892 0.064 0.040 0.004
#> GSM152080 2 0.0000 9.60e-01 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152081 4 0.2660 8.85e-01 0.000 0.000 0.048 0.868 0.084 0.000
#> GSM152083 3 0.3995 -1.67e-01 0.000 0.480 0.516 0.004 0.000 0.000
#> GSM152091 2 0.0000 9.60e-01 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152108 3 0.8316 2.71e-01 0.228 0.124 0.388 0.000 0.108 0.152
#> GSM152114 1 0.0363 5.72e-01 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM152035 2 0.0000 9.60e-01 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152039 4 0.1501 9.72e-01 0.000 0.000 0.000 0.924 0.076 0.000
#> GSM152041 1 0.8260 -9.29e-02 0.324 0.000 0.052 0.256 0.140 0.228
#> GSM152044 2 0.0000 9.60e-01 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152045 5 0.5664 2.72e-01 0.060 0.000 0.048 0.000 0.540 0.352
#> GSM152051 2 0.0000 9.60e-01 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152054 5 0.4311 5.22e-01 0.000 0.008 0.040 0.000 0.692 0.260
#> GSM152057 2 0.0000 9.60e-01 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152058 1 0.0713 5.69e-01 0.972 0.000 0.000 0.000 0.000 0.028
#> GSM152067 3 0.2313 4.82e-01 0.000 0.000 0.884 0.012 0.004 0.100
#> GSM152068 2 0.0000 9.60e-01 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152075 5 0.2996 5.27e-01 0.000 0.000 0.000 0.228 0.772 0.000
#> GSM152076 4 0.1501 9.72e-01 0.000 0.000 0.000 0.924 0.076 0.000
#> GSM152079 2 0.0000 9.60e-01 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152084 3 0.6014 4.38e-01 0.004 0.000 0.468 0.000 0.292 0.236
#> GSM152089 5 0.1760 5.57e-01 0.000 0.000 0.048 0.020 0.928 0.004
#> GSM152095 4 0.1501 9.72e-01 0.000 0.000 0.000 0.924 0.076 0.000
#> GSM152096 3 0.5753 4.52e-01 0.000 0.000 0.512 0.000 0.252 0.236
#> GSM152097 2 0.1910 8.54e-01 0.000 0.892 0.000 0.108 0.000 0.000
#> GSM152099 2 0.0000 9.60e-01 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152106 2 0.0547 9.44e-01 0.000 0.980 0.000 0.020 0.000 0.000
#> GSM152107 5 0.3812 6.22e-01 0.000 0.000 0.264 0.024 0.712 0.000
#> GSM152109 3 0.6071 4.53e-01 0.000 0.000 0.500 0.012 0.252 0.236
#> GSM152111 6 0.2573 4.04e-01 0.024 0.000 0.112 0.000 0.000 0.864
#> GSM152112 5 0.3265 6.33e-01 0.000 0.000 0.248 0.004 0.748 0.000
#> GSM152113 3 0.0777 4.80e-01 0.024 0.000 0.972 0.000 0.004 0.000
#> GSM152115 5 0.3244 6.25e-01 0.000 0.000 0.268 0.000 0.732 0.000
#> GSM152030 5 0.3727 2.78e-01 0.000 0.000 0.000 0.388 0.612 0.000
#> GSM152038 3 0.3426 4.12e-01 0.116 0.000 0.816 0.064 0.000 0.004
#> GSM152042 5 0.3715 3.66e-01 0.000 0.000 0.048 0.000 0.764 0.188
#> GSM152062 3 0.1059 4.75e-01 0.016 0.000 0.964 0.000 0.016 0.004
#> GSM152077 1 0.2300 4.65e-01 0.856 0.000 0.144 0.000 0.000 0.000
#> GSM152088 2 0.0000 9.60e-01 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152100 5 0.3351 4.85e-01 0.000 0.000 0.000 0.288 0.712 0.000
#> GSM152102 2 0.5061 4.49e-01 0.000 0.620 0.000 0.000 0.128 0.252
#> GSM152104 2 0.0000 9.60e-01 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152028 1 0.0000 5.73e-01 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM152029 3 0.6101 4.29e-01 0.000 0.000 0.472 0.008 0.252 0.268
#> GSM152049 1 0.2912 3.98e-01 0.784 0.000 0.000 0.000 0.000 0.216
#> GSM152053 5 0.0547 5.72e-01 0.000 0.000 0.020 0.000 0.980 0.000
#> GSM152059 6 0.5572 3.38e-01 0.072 0.000 0.236 0.064 0.000 0.628
#> GSM152085 1 0.3843 8.01e-02 0.548 0.000 0.000 0.000 0.000 0.452
#> GSM152101 5 0.3151 6.32e-01 0.000 0.000 0.252 0.000 0.748 0.000
#> GSM152105 3 0.3998 -8.23e-02 0.492 0.000 0.504 0.000 0.000 0.004
#> GSM152034 6 0.6051 -2.85e-01 0.004 0.000 0.284 0.000 0.252 0.460
#> GSM152036 4 0.1501 9.72e-01 0.000 0.000 0.000 0.924 0.076 0.000
#> GSM152040 6 0.5937 -3.99e-02 0.352 0.000 0.220 0.000 0.000 0.428
#> GSM152043 1 0.3834 4.11e-01 0.728 0.000 0.004 0.000 0.024 0.244
#> GSM152046 6 0.3076 4.12e-01 0.240 0.000 0.000 0.000 0.000 0.760
#> GSM152047 6 0.3499 8.72e-02 0.000 0.000 0.320 0.000 0.000 0.680
#> GSM152048 1 0.0713 5.69e-01 0.972 0.000 0.000 0.000 0.000 0.028
#> GSM152050 1 0.6654 -5.18e-02 0.416 0.000 0.036 0.000 0.252 0.296
#> GSM152052 1 0.6367 4.02e-02 0.520 0.000 0.284 0.064 0.000 0.132
#> GSM152056 1 0.0713 5.69e-01 0.972 0.000 0.000 0.000 0.000 0.028
#> GSM152060 6 0.3076 4.12e-01 0.240 0.000 0.000 0.000 0.000 0.760
#> GSM152065 3 0.3998 -8.23e-02 0.492 0.000 0.504 0.000 0.000 0.004
#> GSM152066 1 0.0000 5.73e-01 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM152069 3 0.6071 4.53e-01 0.000 0.000 0.500 0.012 0.252 0.236
#> GSM152070 1 0.5282 5.19e-02 0.484 0.000 0.100 0.000 0.000 0.416
#> GSM152071 3 0.6071 4.53e-01 0.000 0.000 0.500 0.012 0.252 0.236
#> GSM152072 3 0.3440 4.03e-01 0.000 0.000 0.776 0.028 0.000 0.196
#> GSM152073 1 0.3789 1.64e-01 0.584 0.000 0.000 0.000 0.000 0.416
#> GSM152078 3 0.2106 4.58e-01 0.000 0.000 0.904 0.064 0.000 0.032
#> GSM152082 1 0.5190 2.82e-01 0.596 0.000 0.132 0.000 0.000 0.272
#> GSM152086 1 0.2664 4.80e-01 0.816 0.000 0.000 0.000 0.000 0.184
#> GSM152090 3 0.5812 4.45e-01 0.000 0.000 0.496 0.000 0.268 0.236
#> GSM152092 1 0.3266 3.93e-01 0.728 0.000 0.000 0.000 0.000 0.272
#> GSM152093 1 0.7733 -3.51e-01 0.264 0.000 0.248 0.000 0.252 0.236
#> GSM152094 1 0.3797 1.57e-01 0.580 0.000 0.000 0.000 0.000 0.420
#> GSM152098 1 0.4509 9.54e-02 0.532 0.000 0.032 0.000 0.000 0.436
#> GSM152110 1 0.0000 5.73e-01 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM152031 3 0.5060 -3.75e-06 0.428 0.000 0.504 0.064 0.000 0.004
#> GSM152037 1 0.0146 5.73e-01 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM152055 1 0.3499 2.82e-01 0.680 0.000 0.000 0.000 0.000 0.320
#> GSM152061 6 0.3076 4.12e-01 0.240 0.000 0.000 0.000 0.000 0.760
#> GSM152064 6 0.3823 9.44e-02 0.436 0.000 0.000 0.000 0.000 0.564
#> GSM152087 6 0.3747 2.13e-01 0.396 0.000 0.000 0.000 0.000 0.604
#> GSM152103 3 0.5874 4.30e-01 0.000 0.000 0.480 0.000 0.252 0.268
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 specimen(p) k
#> MAD:pam 85 4.08e-05 2
#> MAD:pam 83 4.06e-05 3
#> MAD:pam 76 4.47e-05 4
#> MAD:pam 52 9.84e-02 5
#> MAD:pam 35 3.46e-02 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 10612 rows and 88 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 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 0.730 0.938 0.954 0.4854 0.504 0.504
#> 3 3 0.689 0.761 0.893 0.3060 0.828 0.666
#> 4 4 0.593 0.588 0.721 0.0824 0.882 0.695
#> 5 5 0.610 0.614 0.768 0.1263 0.757 0.371
#> 6 6 0.599 0.492 0.655 0.0442 0.904 0.623
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
#> GSM152032 2 0.4939 0.925 0.108 0.892
#> GSM152033 2 0.7453 0.834 0.212 0.788
#> GSM152063 2 0.0000 0.926 0.000 1.000
#> GSM152074 2 0.4690 0.928 0.100 0.900
#> GSM152080 2 0.2778 0.935 0.048 0.952
#> GSM152081 2 0.2948 0.936 0.052 0.948
#> GSM152083 2 0.2948 0.936 0.052 0.948
#> GSM152091 2 0.0000 0.926 0.000 1.000
#> GSM152108 2 0.4815 0.926 0.104 0.896
#> GSM152114 2 0.5842 0.906 0.140 0.860
#> GSM152035 2 0.1633 0.932 0.024 0.976
#> GSM152039 2 0.0000 0.926 0.000 1.000
#> GSM152041 2 0.4298 0.931 0.088 0.912
#> GSM152044 2 0.0000 0.926 0.000 1.000
#> GSM152045 1 0.0000 0.988 1.000 0.000
#> GSM152051 2 0.0000 0.926 0.000 1.000
#> GSM152054 2 0.7674 0.817 0.224 0.776
#> GSM152057 2 0.0000 0.926 0.000 1.000
#> GSM152058 1 0.0000 0.988 1.000 0.000
#> GSM152067 2 0.4690 0.928 0.100 0.900
#> GSM152068 2 0.0000 0.926 0.000 1.000
#> GSM152075 2 0.3114 0.936 0.056 0.944
#> GSM152076 2 0.0000 0.926 0.000 1.000
#> GSM152079 2 0.0000 0.926 0.000 1.000
#> GSM152084 2 0.5294 0.918 0.120 0.880
#> GSM152089 2 0.7056 0.854 0.192 0.808
#> GSM152095 2 0.0000 0.926 0.000 1.000
#> GSM152096 2 0.4939 0.925 0.108 0.892
#> GSM152097 2 0.0000 0.926 0.000 1.000
#> GSM152099 2 0.0000 0.926 0.000 1.000
#> GSM152106 2 0.0000 0.926 0.000 1.000
#> GSM152107 2 0.3733 0.934 0.072 0.928
#> GSM152109 2 0.4939 0.925 0.108 0.892
#> GSM152111 1 0.0000 0.988 1.000 0.000
#> GSM152112 2 0.2948 0.936 0.052 0.948
#> GSM152113 2 0.6438 0.886 0.164 0.836
#> GSM152115 2 0.4690 0.928 0.100 0.900
#> GSM152030 2 0.0000 0.926 0.000 1.000
#> GSM152038 2 0.6531 0.882 0.168 0.832
#> GSM152042 2 0.3114 0.936 0.056 0.944
#> GSM152062 2 0.5408 0.916 0.124 0.876
#> GSM152077 2 0.8207 0.772 0.256 0.744
#> GSM152088 2 0.0000 0.926 0.000 1.000
#> GSM152100 2 0.0938 0.929 0.012 0.988
#> GSM152102 2 0.4431 0.930 0.092 0.908
#> GSM152104 2 0.0000 0.926 0.000 1.000
#> GSM152028 1 0.0000 0.988 1.000 0.000
#> GSM152029 1 0.0672 0.980 0.992 0.008
#> GSM152049 1 0.0000 0.988 1.000 0.000
#> GSM152053 2 0.3274 0.935 0.060 0.940
#> GSM152059 1 0.0000 0.988 1.000 0.000
#> GSM152085 1 0.0000 0.988 1.000 0.000
#> GSM152101 2 0.3584 0.935 0.068 0.932
#> GSM152105 1 0.0000 0.988 1.000 0.000
#> GSM152034 1 0.0000 0.988 1.000 0.000
#> GSM152036 2 0.0000 0.926 0.000 1.000
#> GSM152040 1 0.0000 0.988 1.000 0.000
#> GSM152043 1 0.0000 0.988 1.000 0.000
#> GSM152046 1 0.0000 0.988 1.000 0.000
#> GSM152047 1 0.0000 0.988 1.000 0.000
#> GSM152048 1 0.0000 0.988 1.000 0.000
#> GSM152050 1 0.0000 0.988 1.000 0.000
#> GSM152052 1 0.0000 0.988 1.000 0.000
#> GSM152056 1 0.0000 0.988 1.000 0.000
#> GSM152060 1 0.0000 0.988 1.000 0.000
#> GSM152065 1 0.0000 0.988 1.000 0.000
#> GSM152066 1 0.0000 0.988 1.000 0.000
#> GSM152069 2 0.5737 0.909 0.136 0.864
#> GSM152070 1 0.0000 0.988 1.000 0.000
#> GSM152071 2 0.5842 0.906 0.140 0.860
#> GSM152072 1 0.0376 0.984 0.996 0.004
#> GSM152073 1 0.0000 0.988 1.000 0.000
#> GSM152078 1 0.0000 0.988 1.000 0.000
#> GSM152082 1 0.0000 0.988 1.000 0.000
#> GSM152086 1 0.0000 0.988 1.000 0.000
#> GSM152090 2 0.6048 0.900 0.148 0.852
#> GSM152092 1 0.0000 0.988 1.000 0.000
#> GSM152093 1 0.9580 0.263 0.620 0.380
#> GSM152094 1 0.0000 0.988 1.000 0.000
#> GSM152098 1 0.0000 0.988 1.000 0.000
#> GSM152110 1 0.0000 0.988 1.000 0.000
#> GSM152031 1 0.0000 0.988 1.000 0.000
#> GSM152037 1 0.0000 0.988 1.000 0.000
#> GSM152055 1 0.0000 0.988 1.000 0.000
#> GSM152061 1 0.0000 0.988 1.000 0.000
#> GSM152064 1 0.0000 0.988 1.000 0.000
#> GSM152087 1 0.0000 0.988 1.000 0.000
#> GSM152103 2 0.7299 0.844 0.204 0.796
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM152032 3 0.1163 0.6792 0.000 0.028 0.972
#> GSM152033 3 0.6140 0.3311 0.404 0.000 0.596
#> GSM152063 2 0.0000 0.7805 0.000 1.000 0.000
#> GSM152074 3 0.2959 0.6371 0.000 0.100 0.900
#> GSM152080 2 0.5497 0.5778 0.000 0.708 0.292
#> GSM152081 3 0.5497 0.5663 0.000 0.292 0.708
#> GSM152083 2 0.5621 0.5635 0.000 0.692 0.308
#> GSM152091 2 0.5058 0.6289 0.000 0.756 0.244
#> GSM152108 3 0.2959 0.6994 0.100 0.000 0.900
#> GSM152114 3 0.5291 0.6258 0.268 0.000 0.732
#> GSM152035 2 0.5178 0.6034 0.000 0.744 0.256
#> GSM152039 2 0.6307 -0.0934 0.000 0.512 0.488
#> GSM152041 3 0.7265 0.6423 0.160 0.128 0.712
#> GSM152044 2 0.0000 0.7805 0.000 1.000 0.000
#> GSM152045 1 0.0237 0.9915 0.996 0.000 0.004
#> GSM152051 2 0.0000 0.7805 0.000 1.000 0.000
#> GSM152054 3 0.5621 0.5908 0.308 0.000 0.692
#> GSM152057 2 0.0000 0.7805 0.000 1.000 0.000
#> GSM152058 1 0.0000 0.9950 1.000 0.000 0.000
#> GSM152067 3 0.5098 0.3824 0.000 0.248 0.752
#> GSM152068 2 0.0000 0.7805 0.000 1.000 0.000
#> GSM152075 3 0.5497 0.5663 0.000 0.292 0.708
#> GSM152076 2 0.6305 -0.0812 0.000 0.516 0.484
#> GSM152079 2 0.0000 0.7805 0.000 1.000 0.000
#> GSM152084 3 0.3686 0.6917 0.140 0.000 0.860
#> GSM152089 3 0.5291 0.6258 0.268 0.000 0.732
#> GSM152095 2 0.5621 0.4079 0.000 0.692 0.308
#> GSM152096 3 0.0000 0.6800 0.000 0.000 1.000
#> GSM152097 2 0.0000 0.7805 0.000 1.000 0.000
#> GSM152099 2 0.0424 0.7776 0.000 0.992 0.008
#> GSM152106 2 0.0000 0.7805 0.000 1.000 0.000
#> GSM152107 3 0.2165 0.6788 0.000 0.064 0.936
#> GSM152109 3 0.2711 0.6306 0.000 0.088 0.912
#> GSM152111 1 0.0000 0.9950 1.000 0.000 0.000
#> GSM152112 3 0.5497 0.5663 0.000 0.292 0.708
#> GSM152113 3 0.4654 0.6638 0.208 0.000 0.792
#> GSM152115 3 0.1031 0.6803 0.000 0.024 0.976
#> GSM152030 3 0.5497 0.5663 0.000 0.292 0.708
#> GSM152038 3 0.4504 0.6253 0.196 0.000 0.804
#> GSM152042 3 0.5497 0.5663 0.000 0.292 0.708
#> GSM152062 3 0.0237 0.6825 0.004 0.000 0.996
#> GSM152077 1 0.1031 0.9720 0.976 0.000 0.024
#> GSM152088 2 0.4235 0.6814 0.000 0.824 0.176
#> GSM152100 3 0.5497 0.5663 0.000 0.292 0.708
#> GSM152102 3 0.6280 -0.2160 0.000 0.460 0.540
#> GSM152104 2 0.0000 0.7805 0.000 1.000 0.000
#> GSM152028 1 0.0000 0.9950 1.000 0.000 0.000
#> GSM152029 1 0.1163 0.9648 0.972 0.000 0.028
#> GSM152049 1 0.0000 0.9950 1.000 0.000 0.000
#> GSM152053 3 0.5497 0.5663 0.000 0.292 0.708
#> GSM152059 1 0.0000 0.9950 1.000 0.000 0.000
#> GSM152085 1 0.0000 0.9950 1.000 0.000 0.000
#> GSM152101 3 0.3551 0.6062 0.000 0.132 0.868
#> GSM152105 1 0.0000 0.9950 1.000 0.000 0.000
#> GSM152034 1 0.0000 0.9950 1.000 0.000 0.000
#> GSM152036 2 0.6308 -0.1059 0.000 0.508 0.492
#> GSM152040 1 0.0000 0.9950 1.000 0.000 0.000
#> GSM152043 1 0.0000 0.9950 1.000 0.000 0.000
#> GSM152046 1 0.0000 0.9950 1.000 0.000 0.000
#> GSM152047 1 0.0000 0.9950 1.000 0.000 0.000
#> GSM152048 1 0.0000 0.9950 1.000 0.000 0.000
#> GSM152050 1 0.0000 0.9950 1.000 0.000 0.000
#> GSM152052 1 0.0000 0.9950 1.000 0.000 0.000
#> GSM152056 1 0.0000 0.9950 1.000 0.000 0.000
#> GSM152060 1 0.0000 0.9950 1.000 0.000 0.000
#> GSM152065 1 0.0000 0.9950 1.000 0.000 0.000
#> GSM152066 1 0.0000 0.9950 1.000 0.000 0.000
#> GSM152069 3 0.0661 0.6819 0.008 0.004 0.988
#> GSM152070 1 0.0000 0.9950 1.000 0.000 0.000
#> GSM152071 3 0.3425 0.6574 0.112 0.004 0.884
#> GSM152072 1 0.2537 0.9042 0.920 0.000 0.080
#> GSM152073 1 0.0000 0.9950 1.000 0.000 0.000
#> GSM152078 1 0.0237 0.9915 0.996 0.000 0.004
#> GSM152082 1 0.0000 0.9950 1.000 0.000 0.000
#> GSM152086 1 0.0000 0.9950 1.000 0.000 0.000
#> GSM152090 3 0.5291 0.6258 0.268 0.000 0.732
#> GSM152092 1 0.0000 0.9950 1.000 0.000 0.000
#> GSM152093 1 0.1031 0.9720 0.976 0.000 0.024
#> GSM152094 1 0.0000 0.9950 1.000 0.000 0.000
#> GSM152098 1 0.0000 0.9950 1.000 0.000 0.000
#> GSM152110 1 0.0000 0.9950 1.000 0.000 0.000
#> GSM152031 1 0.0000 0.9950 1.000 0.000 0.000
#> GSM152037 1 0.0000 0.9950 1.000 0.000 0.000
#> GSM152055 1 0.0000 0.9950 1.000 0.000 0.000
#> GSM152061 1 0.0000 0.9950 1.000 0.000 0.000
#> GSM152064 1 0.0000 0.9950 1.000 0.000 0.000
#> GSM152087 1 0.0000 0.9950 1.000 0.000 0.000
#> GSM152103 3 0.6111 0.4946 0.396 0.000 0.604
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM152032 4 0.7009 -0.3730 0.000 0.120 0.392 0.488
#> GSM152033 3 0.7185 0.4717 0.176 0.000 0.540 0.284
#> GSM152063 2 0.4746 0.7111 0.000 0.632 0.000 0.368
#> GSM152074 4 0.7345 -0.2888 0.000 0.172 0.336 0.492
#> GSM152080 2 0.5881 0.3416 0.000 0.544 0.420 0.036
#> GSM152081 4 0.0188 0.5803 0.000 0.004 0.000 0.996
#> GSM152083 2 0.5630 0.4659 0.000 0.724 0.136 0.140
#> GSM152091 2 0.5881 0.3416 0.000 0.544 0.420 0.036
#> GSM152108 3 0.5510 0.4702 0.000 0.016 0.504 0.480
#> GSM152114 4 0.7043 -0.5143 0.120 0.000 0.424 0.456
#> GSM152035 4 0.5512 -0.1514 0.000 0.492 0.016 0.492
#> GSM152039 4 0.3172 0.4510 0.000 0.160 0.000 0.840
#> GSM152041 4 0.3030 0.4806 0.076 0.004 0.028 0.892
#> GSM152044 2 0.4661 0.7338 0.000 0.652 0.000 0.348
#> GSM152045 1 0.2597 0.8812 0.904 0.008 0.084 0.004
#> GSM152051 2 0.4605 0.7339 0.000 0.664 0.000 0.336
#> GSM152054 1 0.7998 -0.1866 0.452 0.016 0.340 0.192
#> GSM152057 2 0.4661 0.7338 0.000 0.652 0.000 0.348
#> GSM152058 1 0.2814 0.8627 0.868 0.000 0.132 0.000
#> GSM152067 3 0.7764 0.1474 0.000 0.356 0.404 0.240
#> GSM152068 2 0.4643 0.7343 0.000 0.656 0.000 0.344
#> GSM152075 4 0.0000 0.5805 0.000 0.000 0.000 1.000
#> GSM152076 4 0.3172 0.4510 0.000 0.160 0.000 0.840
#> GSM152079 2 0.4477 0.7269 0.000 0.688 0.000 0.312
#> GSM152084 3 0.5137 0.5261 0.004 0.000 0.544 0.452
#> GSM152089 4 0.5980 -0.0552 0.396 0.000 0.044 0.560
#> GSM152095 4 0.3311 0.4241 0.000 0.172 0.000 0.828
#> GSM152096 4 0.7044 -0.4411 0.000 0.120 0.428 0.452
#> GSM152097 2 0.4661 0.7338 0.000 0.652 0.000 0.348
#> GSM152099 2 0.4560 0.7185 0.000 0.700 0.004 0.296
#> GSM152106 2 0.4661 0.7338 0.000 0.652 0.000 0.348
#> GSM152107 4 0.4188 0.3881 0.000 0.064 0.112 0.824
#> GSM152109 3 0.6921 0.3988 0.000 0.160 0.580 0.260
#> GSM152111 1 0.1452 0.8820 0.956 0.036 0.008 0.000
#> GSM152112 4 0.0336 0.5772 0.000 0.000 0.008 0.992
#> GSM152113 3 0.5257 0.5329 0.008 0.000 0.548 0.444
#> GSM152115 4 0.6919 -0.3341 0.000 0.116 0.368 0.516
#> GSM152030 4 0.0000 0.5805 0.000 0.000 0.000 1.000
#> GSM152038 3 0.6443 0.5500 0.076 0.000 0.548 0.376
#> GSM152042 4 0.0336 0.5772 0.000 0.000 0.008 0.992
#> GSM152062 3 0.5137 0.5261 0.004 0.000 0.544 0.452
#> GSM152077 1 0.7618 0.1087 0.472 0.000 0.244 0.284
#> GSM152088 2 0.4874 0.5189 0.000 0.764 0.180 0.056
#> GSM152100 4 0.0000 0.5805 0.000 0.000 0.000 1.000
#> GSM152102 2 0.7072 0.2419 0.000 0.524 0.336 0.140
#> GSM152104 2 0.4661 0.7338 0.000 0.652 0.000 0.348
#> GSM152028 1 0.3545 0.8452 0.828 0.008 0.164 0.000
#> GSM152029 1 0.3860 0.8571 0.852 0.032 0.104 0.012
#> GSM152049 1 0.1356 0.8860 0.960 0.032 0.008 0.000
#> GSM152053 4 0.0817 0.5660 0.000 0.000 0.024 0.976
#> GSM152059 1 0.1042 0.8871 0.972 0.020 0.008 0.000
#> GSM152085 1 0.1452 0.8820 0.956 0.036 0.008 0.000
#> GSM152101 4 0.6565 0.1167 0.000 0.224 0.148 0.628
#> GSM152105 1 0.3569 0.8229 0.804 0.000 0.196 0.000
#> GSM152034 1 0.1452 0.8820 0.956 0.036 0.008 0.000
#> GSM152036 4 0.3123 0.4576 0.000 0.156 0.000 0.844
#> GSM152040 1 0.1256 0.8847 0.964 0.028 0.008 0.000
#> GSM152043 1 0.2868 0.8582 0.864 0.000 0.136 0.000
#> GSM152046 1 0.1545 0.8818 0.952 0.040 0.008 0.000
#> GSM152047 1 0.1811 0.8826 0.948 0.028 0.020 0.004
#> GSM152048 1 0.1637 0.8843 0.940 0.000 0.060 0.000
#> GSM152050 1 0.1584 0.8851 0.952 0.036 0.012 0.000
#> GSM152052 1 0.3196 0.8526 0.856 0.008 0.136 0.000
#> GSM152056 1 0.1936 0.8853 0.940 0.032 0.028 0.000
#> GSM152060 1 0.1545 0.8818 0.952 0.040 0.008 0.000
#> GSM152065 1 0.3486 0.8281 0.812 0.000 0.188 0.000
#> GSM152066 1 0.1211 0.8868 0.960 0.000 0.040 0.000
#> GSM152069 3 0.7815 0.4652 0.048 0.148 0.576 0.228
#> GSM152070 1 0.1042 0.8871 0.972 0.020 0.008 0.000
#> GSM152071 3 0.8141 0.4654 0.088 0.148 0.576 0.188
#> GSM152072 1 0.3780 0.8438 0.832 0.016 0.148 0.004
#> GSM152073 1 0.1174 0.8874 0.968 0.012 0.020 0.000
#> GSM152078 1 0.3355 0.8454 0.836 0.000 0.160 0.004
#> GSM152082 1 0.3545 0.8452 0.828 0.008 0.164 0.000
#> GSM152086 1 0.0672 0.8877 0.984 0.008 0.008 0.000
#> GSM152090 3 0.6755 0.4957 0.092 0.000 0.460 0.448
#> GSM152092 1 0.3024 0.8513 0.852 0.000 0.148 0.000
#> GSM152093 1 0.7129 0.3429 0.560 0.000 0.196 0.244
#> GSM152094 1 0.0657 0.8868 0.984 0.012 0.004 0.000
#> GSM152098 1 0.1820 0.8855 0.944 0.020 0.036 0.000
#> GSM152110 1 0.1488 0.8864 0.956 0.032 0.012 0.000
#> GSM152031 1 0.3172 0.8470 0.840 0.000 0.160 0.000
#> GSM152037 1 0.3219 0.8459 0.836 0.000 0.164 0.000
#> GSM152055 1 0.1929 0.8833 0.940 0.036 0.024 0.000
#> GSM152061 1 0.1545 0.8818 0.952 0.040 0.008 0.000
#> GSM152064 1 0.1452 0.8820 0.956 0.036 0.008 0.000
#> GSM152087 1 0.0469 0.8869 0.988 0.012 0.000 0.000
#> GSM152103 3 0.7821 0.3674 0.260 0.000 0.396 0.344
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM152032 3 0.3961 0.6416 0.000 0.000 0.736 0.248 0.016
#> GSM152033 1 0.7219 0.1589 0.484 0.000 0.256 0.220 0.040
#> GSM152063 2 0.1205 0.7694 0.000 0.956 0.040 0.004 0.000
#> GSM152074 3 0.4848 0.6231 0.000 0.060 0.732 0.192 0.016
#> GSM152080 4 0.3607 0.8446 0.000 0.244 0.004 0.752 0.000
#> GSM152081 3 0.3177 0.5134 0.000 0.208 0.792 0.000 0.000
#> GSM152083 2 0.5422 0.1663 0.000 0.568 0.372 0.056 0.004
#> GSM152091 4 0.3508 0.8457 0.000 0.252 0.000 0.748 0.000
#> GSM152108 3 0.4070 0.6627 0.004 0.016 0.776 0.192 0.012
#> GSM152114 3 0.6605 0.5981 0.128 0.000 0.604 0.208 0.060
#> GSM152035 2 0.1469 0.7627 0.000 0.948 0.036 0.016 0.000
#> GSM152039 2 0.3876 0.6194 0.000 0.684 0.316 0.000 0.000
#> GSM152041 3 0.8172 -0.0765 0.052 0.324 0.368 0.024 0.232
#> GSM152044 2 0.0162 0.7735 0.000 0.996 0.000 0.000 0.004
#> GSM152045 5 0.3586 0.6964 0.264 0.000 0.000 0.000 0.736
#> GSM152051 2 0.0324 0.7735 0.000 0.992 0.004 0.004 0.000
#> GSM152054 5 0.6397 0.5278 0.124 0.004 0.024 0.256 0.592
#> GSM152057 2 0.0290 0.7746 0.000 0.992 0.008 0.000 0.000
#> GSM152058 1 0.1892 0.7869 0.916 0.000 0.004 0.000 0.080
#> GSM152067 5 0.8281 -0.1182 0.000 0.176 0.172 0.280 0.372
#> GSM152068 2 0.0324 0.7735 0.000 0.992 0.004 0.004 0.000
#> GSM152075 3 0.2848 0.5763 0.000 0.156 0.840 0.004 0.000
#> GSM152076 2 0.3876 0.6194 0.000 0.684 0.316 0.000 0.000
#> GSM152079 2 0.0324 0.7735 0.000 0.992 0.004 0.004 0.000
#> GSM152084 3 0.4834 0.6396 0.016 0.000 0.716 0.224 0.044
#> GSM152089 5 0.6833 0.3719 0.016 0.132 0.204 0.044 0.604
#> GSM152095 2 0.3876 0.6194 0.000 0.684 0.316 0.000 0.000
#> GSM152096 3 0.4236 0.6423 0.008 0.000 0.728 0.248 0.016
#> GSM152097 2 0.1041 0.7689 0.000 0.964 0.032 0.000 0.004
#> GSM152099 2 0.0451 0.7710 0.000 0.988 0.004 0.008 0.000
#> GSM152106 2 0.0162 0.7735 0.000 0.996 0.000 0.000 0.004
#> GSM152107 3 0.2853 0.6369 0.000 0.072 0.876 0.052 0.000
#> GSM152109 5 0.6481 0.1960 0.000 0.000 0.184 0.408 0.408
#> GSM152111 5 0.3039 0.6447 0.192 0.000 0.000 0.000 0.808
#> GSM152112 3 0.2890 0.5732 0.000 0.160 0.836 0.004 0.000
#> GSM152113 3 0.6101 0.5988 0.100 0.000 0.636 0.224 0.040
#> GSM152115 3 0.4035 0.6524 0.008 0.000 0.756 0.220 0.016
#> GSM152030 3 0.2806 0.5803 0.000 0.152 0.844 0.004 0.000
#> GSM152038 1 0.7176 0.1976 0.504 0.000 0.228 0.224 0.044
#> GSM152042 3 0.2806 0.5803 0.000 0.152 0.844 0.004 0.000
#> GSM152062 3 0.4629 0.6393 0.008 0.000 0.724 0.224 0.044
#> GSM152077 3 0.4632 0.2160 0.448 0.000 0.540 0.000 0.012
#> GSM152088 4 0.3752 0.8203 0.000 0.292 0.000 0.708 0.000
#> GSM152100 3 0.3969 0.3241 0.000 0.304 0.692 0.004 0.000
#> GSM152102 4 0.6455 0.5975 0.000 0.240 0.004 0.528 0.228
#> GSM152104 2 0.0162 0.7735 0.000 0.996 0.000 0.000 0.004
#> GSM152028 1 0.0000 0.7886 1.000 0.000 0.000 0.000 0.000
#> GSM152029 5 0.3969 0.6802 0.304 0.000 0.004 0.000 0.692
#> GSM152049 1 0.3336 0.7136 0.772 0.000 0.000 0.000 0.228
#> GSM152053 3 0.2806 0.5803 0.000 0.152 0.844 0.004 0.000
#> GSM152059 5 0.4029 0.6753 0.316 0.000 0.000 0.004 0.680
#> GSM152085 5 0.2179 0.7060 0.112 0.000 0.000 0.000 0.888
#> GSM152101 2 0.5504 0.2150 0.000 0.488 0.448 0.064 0.000
#> GSM152105 1 0.0162 0.7874 0.996 0.000 0.004 0.000 0.000
#> GSM152034 5 0.2020 0.7051 0.100 0.000 0.000 0.000 0.900
#> GSM152036 2 0.3876 0.6194 0.000 0.684 0.316 0.000 0.000
#> GSM152040 5 0.2377 0.7091 0.128 0.000 0.000 0.000 0.872
#> GSM152043 1 0.0000 0.7886 1.000 0.000 0.000 0.000 0.000
#> GSM152046 5 0.1270 0.6925 0.052 0.000 0.000 0.000 0.948
#> GSM152047 5 0.1732 0.7095 0.080 0.000 0.000 0.000 0.920
#> GSM152048 1 0.2280 0.7736 0.880 0.000 0.000 0.000 0.120
#> GSM152050 1 0.3837 0.6429 0.692 0.000 0.000 0.000 0.308
#> GSM152052 1 0.2813 0.6107 0.832 0.000 0.000 0.000 0.168
#> GSM152056 1 0.3366 0.7082 0.768 0.000 0.000 0.000 0.232
#> GSM152060 5 0.1341 0.6948 0.056 0.000 0.000 0.000 0.944
#> GSM152065 1 0.0000 0.7886 1.000 0.000 0.000 0.000 0.000
#> GSM152066 1 0.1732 0.7867 0.920 0.000 0.000 0.000 0.080
#> GSM152069 5 0.6504 0.2859 0.004 0.000 0.172 0.352 0.472
#> GSM152070 5 0.4066 0.6704 0.324 0.000 0.000 0.004 0.672
#> GSM152071 5 0.6471 0.2929 0.004 0.000 0.168 0.348 0.480
#> GSM152072 5 0.3913 0.6686 0.324 0.000 0.000 0.000 0.676
#> GSM152073 5 0.3999 0.6570 0.344 0.000 0.000 0.000 0.656
#> GSM152078 5 0.4030 0.6503 0.352 0.000 0.000 0.000 0.648
#> GSM152082 1 0.2020 0.7129 0.900 0.000 0.000 0.000 0.100
#> GSM152086 1 0.2020 0.7818 0.900 0.000 0.000 0.000 0.100
#> GSM152090 3 0.8357 0.2221 0.160 0.000 0.360 0.224 0.256
#> GSM152092 1 0.0000 0.7886 1.000 0.000 0.000 0.000 0.000
#> GSM152093 1 0.5797 0.4456 0.592 0.000 0.276 0.000 0.132
#> GSM152094 5 0.2852 0.7081 0.172 0.000 0.000 0.000 0.828
#> GSM152098 5 0.3983 0.6617 0.340 0.000 0.000 0.000 0.660
#> GSM152110 1 0.3661 0.6759 0.724 0.000 0.000 0.000 0.276
#> GSM152031 1 0.0000 0.7886 1.000 0.000 0.000 0.000 0.000
#> GSM152037 1 0.0000 0.7886 1.000 0.000 0.000 0.000 0.000
#> GSM152055 1 0.3876 0.6380 0.684 0.000 0.000 0.000 0.316
#> GSM152061 5 0.1270 0.6925 0.052 0.000 0.000 0.000 0.948
#> GSM152064 5 0.3003 0.6436 0.188 0.000 0.000 0.000 0.812
#> GSM152087 5 0.3003 0.7005 0.188 0.000 0.000 0.000 0.812
#> GSM152103 5 0.7509 0.4661 0.252 0.000 0.072 0.196 0.480
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM152032 3 0.2523 0.4743 0.000 0.036 0.896 0.048 0.016 0.004
#> GSM152033 3 0.4549 0.4696 0.248 0.000 0.688 0.048 0.000 0.016
#> GSM152063 2 0.2320 0.6517 0.000 0.864 0.000 0.132 0.004 0.000
#> GSM152074 3 0.3147 0.4523 0.000 0.092 0.852 0.036 0.016 0.004
#> GSM152080 5 0.5089 0.8698 0.000 0.260 0.004 0.112 0.624 0.000
#> GSM152081 4 0.5447 0.7635 0.000 0.152 0.264 0.580 0.004 0.000
#> GSM152083 2 0.5272 0.0383 0.000 0.504 0.420 0.060 0.016 0.000
#> GSM152091 5 0.5089 0.8698 0.000 0.260 0.004 0.112 0.624 0.000
#> GSM152108 3 0.3895 0.1703 0.008 0.008 0.708 0.272 0.004 0.000
#> GSM152114 3 0.5094 0.0996 0.100 0.000 0.628 0.264 0.000 0.008
#> GSM152035 2 0.3452 0.6160 0.000 0.828 0.040 0.112 0.016 0.004
#> GSM152039 2 0.5984 0.3058 0.000 0.536 0.040 0.344 0.064 0.016
#> GSM152041 4 0.9321 0.1540 0.192 0.160 0.176 0.312 0.112 0.048
#> GSM152044 2 0.2339 0.6288 0.000 0.896 0.000 0.020 0.072 0.012
#> GSM152045 6 0.5071 0.5032 0.156 0.000 0.012 0.016 0.116 0.700
#> GSM152051 2 0.1493 0.6381 0.000 0.936 0.004 0.056 0.004 0.000
#> GSM152054 6 0.6637 0.1790 0.032 0.028 0.264 0.076 0.032 0.568
#> GSM152057 2 0.1753 0.6362 0.000 0.912 0.000 0.084 0.004 0.000
#> GSM152058 1 0.0405 0.6595 0.988 0.000 0.000 0.008 0.000 0.004
#> GSM152067 3 0.8578 -0.1381 0.000 0.176 0.356 0.140 0.192 0.136
#> GSM152068 2 0.1010 0.6358 0.000 0.960 0.000 0.036 0.004 0.000
#> GSM152075 4 0.5298 0.7789 0.000 0.100 0.348 0.548 0.000 0.004
#> GSM152076 2 0.6062 0.2803 0.000 0.496 0.040 0.384 0.064 0.016
#> GSM152079 2 0.1674 0.6384 0.000 0.924 0.004 0.068 0.004 0.000
#> GSM152084 3 0.3166 0.3504 0.008 0.000 0.800 0.184 0.000 0.008
#> GSM152089 6 0.9181 0.2490 0.176 0.080 0.132 0.248 0.056 0.308
#> GSM152095 2 0.5936 0.3168 0.000 0.540 0.040 0.344 0.060 0.016
#> GSM152096 3 0.2660 0.4901 0.004 0.008 0.872 0.100 0.016 0.000
#> GSM152097 2 0.2554 0.6334 0.000 0.880 0.000 0.020 0.088 0.012
#> GSM152099 2 0.1845 0.6392 0.000 0.916 0.004 0.072 0.008 0.000
#> GSM152106 2 0.2554 0.6280 0.000 0.880 0.000 0.020 0.088 0.012
#> GSM152107 4 0.5867 0.6078 0.000 0.112 0.380 0.488 0.016 0.004
#> GSM152109 3 0.6830 0.3155 0.000 0.008 0.540 0.140 0.176 0.136
#> GSM152111 6 0.5963 0.5451 0.320 0.000 0.000 0.000 0.240 0.440
#> GSM152112 4 0.5127 0.7788 0.000 0.112 0.300 0.588 0.000 0.000
#> GSM152113 3 0.4121 0.4743 0.088 0.000 0.788 0.084 0.000 0.040
#> GSM152115 3 0.2753 0.4513 0.012 0.004 0.876 0.088 0.016 0.004
#> GSM152030 4 0.5166 0.7789 0.000 0.100 0.348 0.552 0.000 0.000
#> GSM152038 3 0.4424 0.4687 0.252 0.000 0.692 0.044 0.000 0.012
#> GSM152042 4 0.5083 0.7872 0.000 0.100 0.320 0.580 0.000 0.000
#> GSM152062 3 0.2174 0.4655 0.008 0.000 0.896 0.088 0.000 0.008
#> GSM152077 3 0.6619 -0.0601 0.368 0.000 0.400 0.196 0.004 0.032
#> GSM152088 5 0.5303 0.8327 0.000 0.312 0.004 0.112 0.572 0.000
#> GSM152100 4 0.5621 0.6614 0.000 0.216 0.216 0.564 0.000 0.004
#> GSM152102 5 0.7680 0.6762 0.000 0.260 0.020 0.200 0.396 0.124
#> GSM152104 2 0.2449 0.6290 0.000 0.888 0.000 0.020 0.080 0.012
#> GSM152028 1 0.4093 0.6563 0.736 0.000 0.000 0.056 0.004 0.204
#> GSM152029 6 0.2965 0.4783 0.108 0.000 0.012 0.016 0.008 0.856
#> GSM152049 1 0.3148 0.5455 0.840 0.000 0.000 0.004 0.092 0.064
#> GSM152053 4 0.5176 0.7764 0.000 0.100 0.352 0.548 0.000 0.000
#> GSM152059 6 0.2333 0.4643 0.120 0.000 0.000 0.004 0.004 0.872
#> GSM152085 6 0.5891 0.5634 0.300 0.000 0.000 0.000 0.232 0.468
#> GSM152101 2 0.6576 -0.0561 0.000 0.408 0.312 0.256 0.020 0.004
#> GSM152105 1 0.3786 0.6702 0.772 0.000 0.000 0.052 0.004 0.172
#> GSM152034 6 0.5894 0.5662 0.284 0.000 0.000 0.000 0.244 0.472
#> GSM152036 2 0.6012 0.2975 0.000 0.524 0.040 0.356 0.064 0.016
#> GSM152040 6 0.5805 0.5786 0.276 0.000 0.000 0.000 0.228 0.496
#> GSM152043 1 0.2915 0.6711 0.808 0.000 0.000 0.008 0.000 0.184
#> GSM152046 6 0.6340 0.5684 0.252 0.000 0.000 0.024 0.248 0.476
#> GSM152047 6 0.6384 0.5825 0.224 0.000 0.012 0.016 0.244 0.504
#> GSM152048 1 0.0984 0.6489 0.968 0.000 0.000 0.008 0.012 0.012
#> GSM152050 1 0.4624 0.3519 0.700 0.000 0.000 0.004 0.184 0.112
#> GSM152052 6 0.4984 -0.3497 0.464 0.000 0.000 0.048 0.008 0.480
#> GSM152056 1 0.3598 0.4996 0.804 0.000 0.000 0.004 0.112 0.080
#> GSM152060 6 0.6340 0.5684 0.252 0.000 0.000 0.024 0.248 0.476
#> GSM152065 1 0.4361 0.6315 0.708 0.000 0.004 0.052 0.004 0.232
#> GSM152066 1 0.1644 0.6752 0.932 0.000 0.000 0.012 0.004 0.052
#> GSM152069 3 0.6267 0.3684 0.000 0.000 0.592 0.132 0.124 0.152
#> GSM152070 6 0.2871 0.4294 0.192 0.000 0.000 0.004 0.000 0.804
#> GSM152071 3 0.6267 0.3684 0.000 0.000 0.592 0.132 0.124 0.152
#> GSM152072 6 0.3227 0.4627 0.132 0.000 0.012 0.016 0.008 0.832
#> GSM152073 6 0.3725 0.3201 0.316 0.000 0.000 0.000 0.008 0.676
#> GSM152078 6 0.3471 0.4589 0.120 0.000 0.036 0.016 0.004 0.824
#> GSM152082 1 0.4507 0.5878 0.660 0.000 0.000 0.052 0.004 0.284
#> GSM152086 1 0.2101 0.6488 0.912 0.000 0.000 0.008 0.028 0.052
#> GSM152090 3 0.5348 0.4543 0.056 0.000 0.652 0.224 0.000 0.068
#> GSM152092 1 0.3924 0.6550 0.740 0.000 0.000 0.052 0.000 0.208
#> GSM152093 1 0.6762 0.3278 0.556 0.000 0.216 0.112 0.024 0.092
#> GSM152094 6 0.5624 0.5797 0.264 0.000 0.000 0.000 0.200 0.536
#> GSM152098 6 0.2994 0.4148 0.208 0.000 0.000 0.004 0.000 0.788
#> GSM152110 1 0.4391 0.4082 0.728 0.000 0.000 0.004 0.160 0.108
#> GSM152031 1 0.4059 0.6372 0.720 0.000 0.000 0.052 0.000 0.228
#> GSM152037 1 0.3213 0.6746 0.808 0.000 0.000 0.032 0.000 0.160
#> GSM152055 1 0.4963 0.2453 0.648 0.000 0.000 0.004 0.236 0.112
#> GSM152061 6 0.6340 0.5684 0.252 0.000 0.000 0.024 0.248 0.476
#> GSM152064 6 0.5944 0.5505 0.304 0.000 0.000 0.000 0.244 0.452
#> GSM152087 6 0.5761 0.5019 0.396 0.000 0.000 0.000 0.172 0.432
#> GSM152103 3 0.6528 0.1932 0.068 0.000 0.460 0.076 0.016 0.380
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 specimen(p) k
#> MAD:mclust 87 4.07e-10 2
#> MAD:mclust 80 1.04e-07 3
#> MAD:mclust 59 2.34e-06 4
#> MAD:mclust 73 2.27e-08 5
#> MAD:mclust 48 2.37e-05 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "NMF"]
# you can also extract it by
# res = res_list["MAD:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 10612 rows and 88 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 0.999 0.965 0.985 0.4958 0.504 0.504
#> 3 3 0.589 0.581 0.777 0.3137 0.752 0.551
#> 4 4 0.528 0.471 0.711 0.1190 0.866 0.650
#> 5 5 0.675 0.699 0.839 0.0894 0.846 0.510
#> 6 6 0.703 0.670 0.822 0.0446 0.913 0.614
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
#> GSM152032 2 0.3879 0.911 0.076 0.924
#> GSM152033 1 0.0000 0.988 1.000 0.000
#> GSM152063 2 0.0000 0.980 0.000 1.000
#> GSM152074 2 0.1184 0.969 0.016 0.984
#> GSM152080 2 0.0000 0.980 0.000 1.000
#> GSM152081 2 0.0000 0.980 0.000 1.000
#> GSM152083 2 0.0000 0.980 0.000 1.000
#> GSM152091 2 0.0000 0.980 0.000 1.000
#> GSM152108 2 0.0376 0.977 0.004 0.996
#> GSM152114 1 0.0376 0.985 0.996 0.004
#> GSM152035 2 0.0000 0.980 0.000 1.000
#> GSM152039 2 0.0000 0.980 0.000 1.000
#> GSM152041 2 0.9775 0.297 0.412 0.588
#> GSM152044 2 0.0000 0.980 0.000 1.000
#> GSM152045 1 0.0000 0.988 1.000 0.000
#> GSM152051 2 0.0000 0.980 0.000 1.000
#> GSM152054 1 0.8713 0.587 0.708 0.292
#> GSM152057 2 0.0000 0.980 0.000 1.000
#> GSM152058 1 0.0000 0.988 1.000 0.000
#> GSM152067 2 0.0938 0.972 0.012 0.988
#> GSM152068 2 0.0000 0.980 0.000 1.000
#> GSM152075 2 0.0000 0.980 0.000 1.000
#> GSM152076 2 0.0000 0.980 0.000 1.000
#> GSM152079 2 0.0000 0.980 0.000 1.000
#> GSM152084 1 0.5178 0.869 0.884 0.116
#> GSM152089 2 0.2043 0.956 0.032 0.968
#> GSM152095 2 0.0000 0.980 0.000 1.000
#> GSM152096 2 0.1184 0.969 0.016 0.984
#> GSM152097 2 0.0000 0.980 0.000 1.000
#> GSM152099 2 0.0000 0.980 0.000 1.000
#> GSM152106 2 0.0000 0.980 0.000 1.000
#> GSM152107 2 0.0000 0.980 0.000 1.000
#> GSM152109 2 0.1414 0.966 0.020 0.980
#> GSM152111 1 0.0000 0.988 1.000 0.000
#> GSM152112 2 0.0000 0.980 0.000 1.000
#> GSM152113 1 0.0376 0.985 0.996 0.004
#> GSM152115 2 0.6048 0.825 0.148 0.852
#> GSM152030 2 0.0000 0.980 0.000 1.000
#> GSM152038 1 0.0000 0.988 1.000 0.000
#> GSM152042 2 0.0000 0.980 0.000 1.000
#> GSM152062 1 0.4161 0.906 0.916 0.084
#> GSM152077 1 0.0000 0.988 1.000 0.000
#> GSM152088 2 0.0000 0.980 0.000 1.000
#> GSM152100 2 0.0000 0.980 0.000 1.000
#> GSM152102 2 0.0000 0.980 0.000 1.000
#> GSM152104 2 0.0000 0.980 0.000 1.000
#> GSM152028 1 0.0000 0.988 1.000 0.000
#> GSM152029 1 0.0000 0.988 1.000 0.000
#> GSM152049 1 0.0000 0.988 1.000 0.000
#> GSM152053 2 0.0000 0.980 0.000 1.000
#> GSM152059 1 0.0000 0.988 1.000 0.000
#> GSM152085 1 0.0000 0.988 1.000 0.000
#> GSM152101 2 0.0000 0.980 0.000 1.000
#> GSM152105 1 0.0000 0.988 1.000 0.000
#> GSM152034 1 0.0000 0.988 1.000 0.000
#> GSM152036 2 0.0000 0.980 0.000 1.000
#> GSM152040 1 0.0000 0.988 1.000 0.000
#> GSM152043 1 0.0000 0.988 1.000 0.000
#> GSM152046 1 0.0000 0.988 1.000 0.000
#> GSM152047 1 0.0000 0.988 1.000 0.000
#> GSM152048 1 0.0000 0.988 1.000 0.000
#> GSM152050 1 0.0000 0.988 1.000 0.000
#> GSM152052 1 0.0000 0.988 1.000 0.000
#> GSM152056 1 0.0000 0.988 1.000 0.000
#> GSM152060 1 0.0000 0.988 1.000 0.000
#> GSM152065 1 0.0000 0.988 1.000 0.000
#> GSM152066 1 0.0000 0.988 1.000 0.000
#> GSM152069 1 0.0938 0.978 0.988 0.012
#> GSM152070 1 0.0000 0.988 1.000 0.000
#> GSM152071 1 0.0376 0.985 0.996 0.004
#> GSM152072 1 0.0000 0.988 1.000 0.000
#> GSM152073 1 0.0000 0.988 1.000 0.000
#> GSM152078 1 0.0000 0.988 1.000 0.000
#> GSM152082 1 0.0000 0.988 1.000 0.000
#> GSM152086 1 0.0000 0.988 1.000 0.000
#> GSM152090 1 0.3584 0.924 0.932 0.068
#> GSM152092 1 0.0000 0.988 1.000 0.000
#> GSM152093 1 0.0000 0.988 1.000 0.000
#> GSM152094 1 0.0000 0.988 1.000 0.000
#> GSM152098 1 0.0000 0.988 1.000 0.000
#> GSM152110 1 0.0000 0.988 1.000 0.000
#> GSM152031 1 0.0000 0.988 1.000 0.000
#> GSM152037 1 0.0000 0.988 1.000 0.000
#> GSM152055 1 0.0000 0.988 1.000 0.000
#> GSM152061 1 0.0000 0.988 1.000 0.000
#> GSM152064 1 0.0000 0.988 1.000 0.000
#> GSM152087 1 0.0000 0.988 1.000 0.000
#> GSM152103 1 0.0000 0.988 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM152032 3 0.0000 0.76289 0.000 0.000 1.000
#> GSM152033 1 0.6302 0.13286 0.520 0.000 0.480
#> GSM152063 3 0.6302 0.21023 0.000 0.480 0.520
#> GSM152074 3 0.0000 0.76289 0.000 0.000 1.000
#> GSM152080 3 0.0000 0.76289 0.000 0.000 1.000
#> GSM152081 2 0.1289 0.67320 0.000 0.968 0.032
#> GSM152083 3 0.0000 0.76289 0.000 0.000 1.000
#> GSM152091 3 0.6204 0.34167 0.000 0.424 0.576
#> GSM152108 3 0.0237 0.76303 0.000 0.004 0.996
#> GSM152114 1 0.3587 0.77025 0.892 0.088 0.020
#> GSM152035 3 0.5733 0.51441 0.000 0.324 0.676
#> GSM152039 2 0.0000 0.69111 0.000 1.000 0.000
#> GSM152041 2 0.0424 0.68857 0.008 0.992 0.000
#> GSM152044 2 0.6291 -0.13500 0.000 0.532 0.468
#> GSM152045 1 0.0237 0.82704 0.996 0.000 0.004
#> GSM152051 3 0.5810 0.49876 0.000 0.336 0.664
#> GSM152054 2 0.7658 0.31268 0.356 0.588 0.056
#> GSM152057 3 0.3619 0.71147 0.000 0.136 0.864
#> GSM152058 1 0.0000 0.82737 1.000 0.000 0.000
#> GSM152067 3 0.0000 0.76289 0.000 0.000 1.000
#> GSM152068 3 0.6267 0.27994 0.000 0.452 0.548
#> GSM152075 2 0.0000 0.69111 0.000 1.000 0.000
#> GSM152076 2 0.0000 0.69111 0.000 1.000 0.000
#> GSM152079 3 0.4291 0.67754 0.000 0.180 0.820
#> GSM152084 3 0.5733 0.39819 0.324 0.000 0.676
#> GSM152089 2 0.0000 0.69111 0.000 1.000 0.000
#> GSM152095 2 0.0000 0.69111 0.000 1.000 0.000
#> GSM152096 3 0.0000 0.76289 0.000 0.000 1.000
#> GSM152097 2 0.6062 0.12008 0.000 0.616 0.384
#> GSM152099 3 0.3116 0.72771 0.000 0.108 0.892
#> GSM152106 2 0.2261 0.64310 0.000 0.932 0.068
#> GSM152107 3 0.0592 0.76138 0.000 0.012 0.988
#> GSM152109 3 0.0000 0.76289 0.000 0.000 1.000
#> GSM152111 1 0.6215 0.15919 0.572 0.428 0.000
#> GSM152112 3 0.5706 0.51751 0.000 0.320 0.680
#> GSM152113 1 0.6308 0.09540 0.508 0.000 0.492
#> GSM152115 3 0.0237 0.76104 0.004 0.000 0.996
#> GSM152030 2 0.6168 0.04203 0.000 0.588 0.412
#> GSM152038 1 0.6309 0.08200 0.504 0.000 0.496
#> GSM152042 3 0.6045 0.42986 0.000 0.380 0.620
#> GSM152062 3 0.6045 0.26894 0.380 0.000 0.620
#> GSM152077 1 0.0424 0.82585 0.992 0.000 0.008
#> GSM152088 3 0.2711 0.73693 0.000 0.088 0.912
#> GSM152100 2 0.0000 0.69111 0.000 1.000 0.000
#> GSM152102 3 0.0237 0.76303 0.000 0.004 0.996
#> GSM152104 2 0.5016 0.42819 0.000 0.760 0.240
#> GSM152028 1 0.0237 0.82704 0.996 0.000 0.004
#> GSM152029 1 0.4062 0.70748 0.836 0.000 0.164
#> GSM152049 1 0.0237 0.82640 0.996 0.004 0.000
#> GSM152053 3 0.3412 0.71996 0.000 0.124 0.876
#> GSM152059 1 0.0000 0.82737 1.000 0.000 0.000
#> GSM152085 1 0.4654 0.62141 0.792 0.208 0.000
#> GSM152101 3 0.0237 0.76298 0.000 0.004 0.996
#> GSM152105 1 0.1289 0.81409 0.968 0.000 0.032
#> GSM152034 1 0.6299 0.00913 0.524 0.476 0.000
#> GSM152036 2 0.0000 0.69111 0.000 1.000 0.000
#> GSM152040 1 0.0237 0.82661 0.996 0.004 0.000
#> GSM152043 1 0.0000 0.82737 1.000 0.000 0.000
#> GSM152046 2 0.6309 0.00857 0.496 0.504 0.000
#> GSM152047 1 0.6168 0.20319 0.588 0.412 0.000
#> GSM152048 1 0.0000 0.82737 1.000 0.000 0.000
#> GSM152050 1 0.4504 0.64087 0.804 0.196 0.000
#> GSM152052 1 0.0892 0.82057 0.980 0.000 0.020
#> GSM152056 1 0.1753 0.79930 0.952 0.048 0.000
#> GSM152060 2 0.6309 -0.00424 0.500 0.500 0.000
#> GSM152065 1 0.1964 0.79835 0.944 0.000 0.056
#> GSM152066 1 0.0000 0.82737 1.000 0.000 0.000
#> GSM152069 3 0.4178 0.62393 0.172 0.000 0.828
#> GSM152070 1 0.0000 0.82737 1.000 0.000 0.000
#> GSM152071 3 0.5859 0.35547 0.344 0.000 0.656
#> GSM152072 1 0.5591 0.53128 0.696 0.000 0.304
#> GSM152073 1 0.0000 0.82737 1.000 0.000 0.000
#> GSM152078 1 0.5465 0.55536 0.712 0.000 0.288
#> GSM152082 1 0.0237 0.82704 0.996 0.000 0.004
#> GSM152086 1 0.0237 0.82640 0.996 0.004 0.000
#> GSM152090 3 0.6168 0.17156 0.412 0.000 0.588
#> GSM152092 1 0.0237 0.82704 0.996 0.000 0.004
#> GSM152093 1 0.0424 0.82472 0.992 0.008 0.000
#> GSM152094 1 0.1031 0.81567 0.976 0.024 0.000
#> GSM152098 1 0.0000 0.82737 1.000 0.000 0.000
#> GSM152110 1 0.1964 0.79361 0.944 0.056 0.000
#> GSM152031 1 0.0424 0.82585 0.992 0.000 0.008
#> GSM152037 1 0.0000 0.82737 1.000 0.000 0.000
#> GSM152055 1 0.6307 -0.03197 0.512 0.488 0.000
#> GSM152061 2 0.6308 0.02054 0.492 0.508 0.000
#> GSM152064 2 0.6302 0.05071 0.480 0.520 0.000
#> GSM152087 1 0.0237 0.82640 0.996 0.004 0.000
#> GSM152103 1 0.6267 0.21259 0.548 0.000 0.452
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM152032 3 0.7002 0.393 0.268 0.164 0.568 0.000
#> GSM152033 1 0.5168 0.260 0.712 0.040 0.248 0.000
#> GSM152063 2 0.3573 0.655 0.028 0.864 0.008 0.100
#> GSM152074 3 0.6954 0.389 0.280 0.152 0.568 0.000
#> GSM152080 2 0.0804 0.658 0.000 0.980 0.008 0.012
#> GSM152081 4 0.4465 0.583 0.000 0.056 0.144 0.800
#> GSM152083 3 0.4999 0.237 0.000 0.492 0.508 0.000
#> GSM152091 2 0.1970 0.671 0.000 0.932 0.008 0.060
#> GSM152108 2 0.7282 0.115 0.416 0.436 0.148 0.000
#> GSM152114 1 0.6162 0.273 0.708 0.032 0.192 0.068
#> GSM152035 2 0.4413 0.604 0.140 0.812 0.008 0.040
#> GSM152039 4 0.0188 0.738 0.000 0.004 0.000 0.996
#> GSM152041 4 0.0000 0.738 0.000 0.000 0.000 1.000
#> GSM152044 2 0.4855 0.442 0.000 0.644 0.004 0.352
#> GSM152045 1 0.6348 0.630 0.516 0.008 0.432 0.044
#> GSM152051 2 0.1489 0.670 0.000 0.952 0.004 0.044
#> GSM152054 2 0.9053 0.265 0.212 0.472 0.200 0.116
#> GSM152057 2 0.2987 0.641 0.000 0.880 0.016 0.104
#> GSM152058 1 0.1486 0.619 0.960 0.024 0.008 0.008
#> GSM152067 3 0.5000 0.203 0.000 0.496 0.504 0.000
#> GSM152068 2 0.1824 0.669 0.000 0.936 0.004 0.060
#> GSM152075 4 0.0336 0.738 0.000 0.008 0.000 0.992
#> GSM152076 4 0.0336 0.738 0.000 0.008 0.000 0.992
#> GSM152079 2 0.1489 0.670 0.000 0.952 0.004 0.044
#> GSM152084 3 0.6240 0.357 0.368 0.064 0.568 0.000
#> GSM152089 4 0.4871 0.640 0.012 0.040 0.168 0.780
#> GSM152095 4 0.0336 0.738 0.000 0.008 0.000 0.992
#> GSM152096 2 0.5052 0.447 0.244 0.720 0.036 0.000
#> GSM152097 4 0.3975 0.518 0.000 0.240 0.000 0.760
#> GSM152099 2 0.5109 0.383 0.000 0.736 0.212 0.052
#> GSM152106 4 0.2704 0.657 0.000 0.124 0.000 0.876
#> GSM152107 3 0.5360 0.299 0.000 0.436 0.552 0.012
#> GSM152109 3 0.4989 0.268 0.000 0.472 0.528 0.000
#> GSM152111 1 0.7575 0.435 0.484 0.000 0.252 0.264
#> GSM152112 3 0.6627 0.223 0.000 0.412 0.504 0.084
#> GSM152113 1 0.4998 0.339 0.748 0.052 0.200 0.000
#> GSM152115 3 0.6553 0.360 0.100 0.316 0.584 0.000
#> GSM152030 3 0.8948 0.185 0.172 0.080 0.376 0.372
#> GSM152038 1 0.5671 -0.138 0.572 0.028 0.400 0.000
#> GSM152042 3 0.7130 0.233 0.000 0.396 0.472 0.132
#> GSM152062 3 0.5756 0.336 0.400 0.032 0.568 0.000
#> GSM152077 1 0.3653 0.485 0.844 0.028 0.128 0.000
#> GSM152088 2 0.1305 0.667 0.000 0.960 0.004 0.036
#> GSM152100 4 0.0592 0.734 0.000 0.016 0.000 0.984
#> GSM152102 2 0.2945 0.650 0.056 0.904 0.024 0.016
#> GSM152104 4 0.4008 0.515 0.000 0.244 0.000 0.756
#> GSM152028 1 0.1109 0.622 0.968 0.028 0.004 0.000
#> GSM152029 3 0.7246 -0.551 0.408 0.144 0.448 0.000
#> GSM152049 1 0.5062 0.674 0.680 0.000 0.300 0.020
#> GSM152053 3 0.7457 0.396 0.216 0.208 0.564 0.012
#> GSM152059 1 0.5193 0.658 0.580 0.000 0.412 0.008
#> GSM152085 1 0.6562 0.608 0.516 0.000 0.404 0.080
#> GSM152101 3 0.4925 0.301 0.000 0.428 0.572 0.000
#> GSM152105 1 0.2413 0.574 0.916 0.020 0.064 0.000
#> GSM152034 3 0.7834 -0.409 0.284 0.000 0.408 0.308
#> GSM152036 4 0.0000 0.738 0.000 0.000 0.000 1.000
#> GSM152040 1 0.5902 0.644 0.540 0.004 0.428 0.028
#> GSM152043 1 0.5050 0.660 0.588 0.000 0.408 0.004
#> GSM152046 4 0.7285 0.238 0.308 0.000 0.176 0.516
#> GSM152047 3 0.7721 -0.523 0.380 0.004 0.424 0.192
#> GSM152048 1 0.1229 0.623 0.968 0.020 0.004 0.008
#> GSM152050 1 0.7518 0.466 0.496 0.000 0.260 0.244
#> GSM152052 1 0.1388 0.623 0.960 0.028 0.012 0.000
#> GSM152056 1 0.1396 0.635 0.960 0.004 0.004 0.032
#> GSM152060 4 0.6356 0.389 0.320 0.000 0.084 0.596
#> GSM152065 1 0.3342 0.633 0.868 0.032 0.100 0.000
#> GSM152066 1 0.0592 0.642 0.984 0.000 0.016 0.000
#> GSM152069 2 0.6393 -0.211 0.064 0.480 0.456 0.000
#> GSM152070 1 0.5276 0.652 0.560 0.004 0.432 0.004
#> GSM152071 3 0.5939 0.232 0.084 0.248 0.668 0.000
#> GSM152072 1 0.5590 0.634 0.524 0.020 0.456 0.000
#> GSM152073 1 0.5060 0.659 0.584 0.000 0.412 0.004
#> GSM152078 1 0.5626 0.665 0.588 0.028 0.384 0.000
#> GSM152082 1 0.4855 0.666 0.600 0.000 0.400 0.000
#> GSM152086 1 0.5217 0.667 0.608 0.000 0.380 0.012
#> GSM152090 2 0.7851 -0.115 0.356 0.376 0.268 0.000
#> GSM152092 1 0.3351 0.663 0.844 0.008 0.148 0.000
#> GSM152093 1 0.1936 0.642 0.940 0.000 0.032 0.028
#> GSM152094 1 0.5517 0.654 0.568 0.000 0.412 0.020
#> GSM152098 1 0.5260 0.655 0.568 0.004 0.424 0.004
#> GSM152110 1 0.1576 0.632 0.948 0.004 0.000 0.048
#> GSM152031 1 0.2401 0.658 0.904 0.004 0.092 0.000
#> GSM152037 1 0.0336 0.632 0.992 0.000 0.008 0.000
#> GSM152055 4 0.5090 0.469 0.324 0.000 0.016 0.660
#> GSM152061 4 0.5453 0.482 0.304 0.000 0.036 0.660
#> GSM152064 4 0.5894 0.263 0.392 0.000 0.040 0.568
#> GSM152087 1 0.5691 0.651 0.564 0.000 0.408 0.028
#> GSM152103 1 0.6426 0.614 0.568 0.080 0.352 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM152032 3 0.2179 0.7879 0.112 0.000 0.888 0.000 0.000
#> GSM152033 1 0.2193 0.7814 0.900 0.000 0.092 0.000 0.008
#> GSM152063 2 0.0798 0.8330 0.000 0.976 0.008 0.016 0.000
#> GSM152074 3 0.2020 0.7937 0.100 0.000 0.900 0.000 0.000
#> GSM152080 2 0.0000 0.8339 0.000 1.000 0.000 0.000 0.000
#> GSM152081 4 0.4171 0.2378 0.000 0.000 0.396 0.604 0.000
#> GSM152083 3 0.4331 0.3641 0.004 0.400 0.596 0.000 0.000
#> GSM152091 2 0.0162 0.8338 0.000 0.996 0.004 0.000 0.000
#> GSM152108 1 0.2359 0.7886 0.904 0.060 0.036 0.000 0.000
#> GSM152114 1 0.1364 0.8228 0.952 0.000 0.012 0.036 0.000
#> GSM152035 2 0.1877 0.8040 0.000 0.924 0.064 0.012 0.000
#> GSM152039 4 0.0000 0.7901 0.000 0.000 0.000 1.000 0.000
#> GSM152041 4 0.0000 0.7901 0.000 0.000 0.000 1.000 0.000
#> GSM152044 2 0.2074 0.7739 0.000 0.896 0.000 0.104 0.000
#> GSM152045 5 0.2228 0.7782 0.004 0.004 0.092 0.000 0.900
#> GSM152051 2 0.0162 0.8342 0.000 0.996 0.000 0.004 0.000
#> GSM152054 2 0.7826 0.3565 0.228 0.460 0.084 0.004 0.224
#> GSM152057 2 0.1168 0.8258 0.008 0.960 0.000 0.032 0.000
#> GSM152058 1 0.0290 0.8390 0.992 0.000 0.000 0.000 0.008
#> GSM152067 3 0.3840 0.7804 0.000 0.076 0.808 0.000 0.116
#> GSM152068 2 0.0404 0.8335 0.000 0.988 0.000 0.012 0.000
#> GSM152075 4 0.0162 0.7891 0.000 0.000 0.004 0.996 0.000
#> GSM152076 4 0.0000 0.7901 0.000 0.000 0.000 1.000 0.000
#> GSM152079 2 0.0162 0.8342 0.000 0.996 0.000 0.004 0.000
#> GSM152084 3 0.3534 0.6298 0.256 0.000 0.744 0.000 0.000
#> GSM152089 4 0.5982 0.5140 0.000 0.028 0.076 0.600 0.296
#> GSM152095 4 0.0162 0.7891 0.000 0.000 0.004 0.996 0.000
#> GSM152096 2 0.4273 0.1665 0.448 0.552 0.000 0.000 0.000
#> GSM152097 4 0.2424 0.7111 0.000 0.132 0.000 0.868 0.000
#> GSM152099 2 0.4305 -0.1702 0.000 0.512 0.488 0.000 0.000
#> GSM152106 4 0.1410 0.7617 0.000 0.060 0.000 0.940 0.000
#> GSM152107 3 0.1831 0.7954 0.000 0.076 0.920 0.004 0.000
#> GSM152109 3 0.2416 0.7896 0.000 0.100 0.888 0.000 0.012
#> GSM152111 5 0.4704 0.7786 0.152 0.000 0.000 0.112 0.736
#> GSM152112 3 0.2801 0.7696 0.004 0.004 0.884 0.024 0.084
#> GSM152113 1 0.2139 0.7988 0.916 0.000 0.052 0.000 0.032
#> GSM152115 3 0.1788 0.7888 0.008 0.004 0.932 0.000 0.056
#> GSM152030 3 0.4587 0.6685 0.068 0.000 0.728 0.204 0.000
#> GSM152038 1 0.3424 0.6257 0.760 0.000 0.240 0.000 0.000
#> GSM152042 3 0.2592 0.7942 0.000 0.056 0.892 0.052 0.000
#> GSM152062 1 0.4300 0.0552 0.524 0.000 0.476 0.000 0.000
#> GSM152077 1 0.0703 0.8289 0.976 0.000 0.024 0.000 0.000
#> GSM152088 2 0.0162 0.8327 0.000 0.996 0.004 0.000 0.000
#> GSM152100 4 0.0000 0.7901 0.000 0.000 0.000 1.000 0.000
#> GSM152102 2 0.3362 0.7375 0.000 0.844 0.080 0.000 0.076
#> GSM152104 4 0.4300 0.0506 0.000 0.476 0.000 0.524 0.000
#> GSM152028 1 0.0609 0.8410 0.980 0.000 0.000 0.000 0.020
#> GSM152029 5 0.2504 0.8370 0.040 0.064 0.000 0.000 0.896
#> GSM152049 1 0.4307 -0.1774 0.504 0.000 0.000 0.000 0.496
#> GSM152053 3 0.2241 0.7984 0.076 0.008 0.908 0.008 0.000
#> GSM152059 5 0.2179 0.8524 0.112 0.000 0.000 0.000 0.888
#> GSM152085 5 0.2519 0.8522 0.100 0.000 0.000 0.016 0.884
#> GSM152101 3 0.2124 0.7724 0.000 0.004 0.900 0.000 0.096
#> GSM152105 1 0.0579 0.8382 0.984 0.000 0.008 0.000 0.008
#> GSM152034 5 0.2522 0.8050 0.012 0.000 0.000 0.108 0.880
#> GSM152036 4 0.0000 0.7901 0.000 0.000 0.000 1.000 0.000
#> GSM152040 5 0.2449 0.7848 0.012 0.004 0.080 0.004 0.900
#> GSM152043 5 0.2230 0.8532 0.116 0.000 0.000 0.000 0.884
#> GSM152046 5 0.4054 0.6657 0.028 0.000 0.000 0.224 0.748
#> GSM152047 5 0.1043 0.8107 0.000 0.000 0.040 0.000 0.960
#> GSM152048 1 0.0510 0.8406 0.984 0.000 0.000 0.000 0.016
#> GSM152050 5 0.4588 0.7851 0.136 0.000 0.000 0.116 0.748
#> GSM152052 1 0.1341 0.8338 0.944 0.000 0.000 0.000 0.056
#> GSM152056 1 0.2074 0.8290 0.920 0.000 0.000 0.036 0.044
#> GSM152060 4 0.5052 0.2359 0.036 0.000 0.000 0.552 0.412
#> GSM152065 1 0.4868 0.6633 0.720 0.004 0.084 0.000 0.192
#> GSM152066 1 0.1851 0.8129 0.912 0.000 0.000 0.000 0.088
#> GSM152069 3 0.5632 0.6069 0.000 0.140 0.628 0.000 0.232
#> GSM152070 5 0.1892 0.7885 0.000 0.004 0.080 0.000 0.916
#> GSM152071 3 0.5354 0.4742 0.028 0.028 0.620 0.000 0.324
#> GSM152072 5 0.2170 0.7812 0.004 0.004 0.088 0.000 0.904
#> GSM152073 5 0.2074 0.8541 0.104 0.000 0.000 0.000 0.896
#> GSM152078 5 0.3642 0.7647 0.232 0.008 0.000 0.000 0.760
#> GSM152082 5 0.2773 0.8451 0.112 0.000 0.020 0.000 0.868
#> GSM152086 5 0.3579 0.7585 0.240 0.000 0.000 0.004 0.756
#> GSM152090 5 0.6927 0.5361 0.168 0.052 0.224 0.000 0.556
#> GSM152092 1 0.3810 0.7125 0.792 0.000 0.040 0.000 0.168
#> GSM152093 1 0.1597 0.8363 0.940 0.000 0.000 0.012 0.048
#> GSM152094 5 0.2020 0.8537 0.100 0.000 0.000 0.000 0.900
#> GSM152098 5 0.0609 0.8366 0.020 0.000 0.000 0.000 0.980
#> GSM152110 1 0.1992 0.8288 0.924 0.000 0.000 0.044 0.032
#> GSM152031 1 0.4088 0.3106 0.632 0.000 0.000 0.000 0.368
#> GSM152037 1 0.0794 0.8405 0.972 0.000 0.000 0.000 0.028
#> GSM152055 4 0.2932 0.7310 0.032 0.000 0.000 0.864 0.104
#> GSM152061 4 0.4326 0.5594 0.028 0.000 0.000 0.708 0.264
#> GSM152064 4 0.4871 0.3373 0.024 0.000 0.004 0.604 0.368
#> GSM152087 5 0.2179 0.8538 0.100 0.000 0.000 0.004 0.896
#> GSM152103 5 0.5175 0.6816 0.272 0.036 0.024 0.000 0.668
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM152032 3 0.0547 0.7102 0.020 0.000 0.980 0.000 0.000 0.000
#> GSM152033 1 0.1327 0.8185 0.936 0.000 0.000 0.000 0.064 0.000
#> GSM152063 2 0.0837 0.8926 0.004 0.972 0.000 0.020 0.004 0.000
#> GSM152074 3 0.2432 0.6615 0.100 0.000 0.876 0.000 0.024 0.000
#> GSM152080 2 0.0000 0.8924 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152081 4 0.4509 0.1571 0.000 0.000 0.436 0.532 0.032 0.000
#> GSM152083 3 0.4850 0.1921 0.016 0.440 0.516 0.000 0.028 0.000
#> GSM152091 2 0.0146 0.8928 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM152108 1 0.2201 0.8068 0.900 0.048 0.000 0.000 0.052 0.000
#> GSM152114 1 0.2159 0.8302 0.904 0.000 0.000 0.012 0.072 0.012
#> GSM152035 2 0.2554 0.8374 0.012 0.880 0.000 0.020 0.088 0.000
#> GSM152039 4 0.0260 0.7981 0.000 0.000 0.000 0.992 0.008 0.000
#> GSM152041 4 0.1701 0.7895 0.000 0.000 0.000 0.920 0.072 0.008
#> GSM152044 2 0.1913 0.8582 0.000 0.908 0.000 0.080 0.012 0.000
#> GSM152045 5 0.2890 0.6747 0.004 0.000 0.004 0.028 0.856 0.108
#> GSM152051 2 0.0260 0.8947 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM152054 5 0.4113 0.6569 0.112 0.044 0.000 0.036 0.796 0.012
#> GSM152057 2 0.1950 0.8772 0.008 0.924 0.004 0.044 0.020 0.000
#> GSM152058 1 0.0865 0.8431 0.964 0.000 0.000 0.000 0.000 0.036
#> GSM152067 3 0.2791 0.6776 0.000 0.008 0.852 0.000 0.124 0.016
#> GSM152068 2 0.0508 0.8943 0.000 0.984 0.000 0.012 0.004 0.000
#> GSM152075 4 0.0951 0.7984 0.000 0.000 0.008 0.968 0.020 0.004
#> GSM152076 4 0.0000 0.7973 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM152079 2 0.0260 0.8947 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM152084 3 0.4295 0.5834 0.160 0.000 0.728 0.000 0.112 0.000
#> GSM152089 5 0.3592 0.6337 0.000 0.012 0.004 0.156 0.800 0.028
#> GSM152095 4 0.0858 0.7964 0.000 0.000 0.004 0.968 0.028 0.000
#> GSM152096 2 0.3714 0.4430 0.340 0.656 0.000 0.000 0.004 0.000
#> GSM152097 4 0.2740 0.7184 0.000 0.120 0.000 0.852 0.028 0.000
#> GSM152099 3 0.4147 0.2315 0.000 0.436 0.552 0.012 0.000 0.000
#> GSM152106 4 0.1789 0.7703 0.000 0.044 0.000 0.924 0.032 0.000
#> GSM152107 3 0.1152 0.7088 0.000 0.000 0.952 0.004 0.044 0.000
#> GSM152109 3 0.2274 0.6967 0.000 0.008 0.892 0.000 0.088 0.012
#> GSM152111 6 0.3170 0.7993 0.036 0.000 0.000 0.052 0.056 0.856
#> GSM152112 5 0.4474 0.5880 0.000 0.000 0.188 0.108 0.704 0.000
#> GSM152113 1 0.1863 0.7994 0.896 0.000 0.000 0.000 0.104 0.000
#> GSM152115 5 0.3650 0.5561 0.008 0.000 0.272 0.004 0.716 0.000
#> GSM152030 3 0.3915 0.4732 0.004 0.000 0.704 0.272 0.020 0.000
#> GSM152038 1 0.4179 0.6962 0.760 0.000 0.144 0.000 0.084 0.012
#> GSM152042 3 0.0653 0.7116 0.004 0.000 0.980 0.004 0.012 0.000
#> GSM152062 1 0.4903 0.0645 0.476 0.000 0.464 0.000 0.060 0.000
#> GSM152077 1 0.0632 0.8336 0.976 0.000 0.000 0.000 0.024 0.000
#> GSM152088 2 0.0000 0.8924 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152100 4 0.1714 0.7720 0.000 0.000 0.000 0.908 0.092 0.000
#> GSM152102 5 0.4046 0.3604 0.004 0.368 0.000 0.008 0.620 0.000
#> GSM152104 2 0.4319 0.4769 0.000 0.620 0.000 0.348 0.032 0.000
#> GSM152028 1 0.0520 0.8398 0.984 0.000 0.000 0.000 0.008 0.008
#> GSM152029 6 0.2912 0.7642 0.000 0.028 0.012 0.000 0.104 0.856
#> GSM152049 6 0.4443 0.5005 0.328 0.000 0.000 0.012 0.024 0.636
#> GSM152053 3 0.0551 0.7070 0.004 0.000 0.984 0.004 0.008 0.000
#> GSM152059 6 0.0291 0.8076 0.004 0.000 0.000 0.000 0.004 0.992
#> GSM152085 6 0.0964 0.8077 0.012 0.000 0.000 0.016 0.004 0.968
#> GSM152101 5 0.3907 0.3573 0.000 0.000 0.408 0.004 0.588 0.000
#> GSM152105 1 0.1408 0.8435 0.944 0.000 0.000 0.000 0.020 0.036
#> GSM152034 6 0.1882 0.7998 0.000 0.000 0.008 0.012 0.060 0.920
#> GSM152036 4 0.0972 0.7940 0.000 0.000 0.000 0.964 0.028 0.008
#> GSM152040 5 0.4082 0.6643 0.028 0.000 0.000 0.028 0.752 0.192
#> GSM152043 6 0.2737 0.7940 0.044 0.000 0.004 0.000 0.084 0.868
#> GSM152046 6 0.3189 0.6802 0.000 0.000 0.000 0.184 0.020 0.796
#> GSM152047 6 0.2913 0.6616 0.000 0.000 0.004 0.004 0.180 0.812
#> GSM152048 1 0.1297 0.8428 0.948 0.000 0.000 0.000 0.012 0.040
#> GSM152050 6 0.2540 0.7791 0.020 0.000 0.000 0.104 0.004 0.872
#> GSM152052 1 0.2482 0.7842 0.848 0.000 0.000 0.000 0.004 0.148
#> GSM152056 1 0.2834 0.8004 0.852 0.000 0.000 0.008 0.020 0.120
#> GSM152060 4 0.4833 0.2773 0.000 0.000 0.000 0.516 0.056 0.428
#> GSM152065 5 0.3890 0.2763 0.400 0.000 0.000 0.000 0.596 0.004
#> GSM152066 1 0.3578 0.7502 0.784 0.000 0.000 0.000 0.052 0.164
#> GSM152069 3 0.5628 0.4112 0.000 0.016 0.564 0.000 0.124 0.296
#> GSM152070 5 0.3706 0.4519 0.000 0.000 0.000 0.000 0.620 0.380
#> GSM152071 3 0.5777 0.2648 0.000 0.016 0.500 0.000 0.120 0.364
#> GSM152072 5 0.3986 0.4321 0.004 0.004 0.004 0.000 0.648 0.340
#> GSM152073 6 0.0405 0.8081 0.008 0.000 0.000 0.000 0.004 0.988
#> GSM152078 6 0.2846 0.7692 0.140 0.016 0.000 0.000 0.004 0.840
#> GSM152082 6 0.4535 0.4761 0.060 0.000 0.000 0.000 0.296 0.644
#> GSM152086 6 0.2149 0.7883 0.104 0.000 0.000 0.004 0.004 0.888
#> GSM152090 6 0.5679 0.6445 0.052 0.036 0.132 0.000 0.092 0.688
#> GSM152092 1 0.5142 0.1420 0.488 0.000 0.000 0.000 0.428 0.084
#> GSM152093 1 0.4184 0.7613 0.768 0.000 0.000 0.016 0.108 0.108
#> GSM152094 6 0.0865 0.8061 0.000 0.000 0.000 0.000 0.036 0.964
#> GSM152098 6 0.2191 0.7535 0.000 0.000 0.004 0.000 0.120 0.876
#> GSM152110 1 0.2231 0.8355 0.908 0.000 0.000 0.016 0.048 0.028
#> GSM152031 6 0.3950 0.2387 0.432 0.000 0.000 0.000 0.004 0.564
#> GSM152037 1 0.1492 0.8407 0.940 0.000 0.000 0.000 0.036 0.024
#> GSM152055 4 0.3306 0.7238 0.008 0.000 0.000 0.820 0.036 0.136
#> GSM152061 4 0.4167 0.4584 0.000 0.000 0.000 0.612 0.020 0.368
#> GSM152064 4 0.4596 0.5960 0.000 0.000 0.000 0.672 0.088 0.240
#> GSM152087 6 0.0653 0.8086 0.004 0.000 0.000 0.004 0.012 0.980
#> GSM152103 6 0.5130 0.6986 0.148 0.048 0.020 0.000 0.064 0.720
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 specimen(p) k
#> MAD:NMF 87 3.20e-08 2
#> MAD:NMF 62 3.93e-05 3
#> MAD:NMF 51 3.25e-06 4
#> MAD:NMF 76 3.49e-04 5
#> MAD:NMF 69 1.72e-03 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "hclust"]
# you can also extract it by
# res = res_list["ATC:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 10612 rows and 88 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.287 0.581 0.816 0.4277 0.589 0.589
#> 3 3 0.302 0.417 0.655 0.3744 0.714 0.549
#> 4 4 0.453 0.541 0.748 0.1943 0.767 0.477
#> 5 5 0.508 0.562 0.733 0.0668 0.909 0.693
#> 6 6 0.586 0.530 0.718 0.0379 0.972 0.886
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
#> GSM152032 1 0.4022 0.7137 0.920 0.080
#> GSM152033 1 0.0000 0.7341 1.000 0.000
#> GSM152063 2 0.0376 0.7858 0.004 0.996
#> GSM152074 1 0.0000 0.7341 1.000 0.000
#> GSM152080 1 0.8443 0.5906 0.728 0.272
#> GSM152081 2 0.8861 0.5202 0.304 0.696
#> GSM152083 1 0.4022 0.7137 0.920 0.080
#> GSM152091 1 0.9754 0.3571 0.592 0.408
#> GSM152108 2 0.9998 -0.1736 0.492 0.508
#> GSM152114 1 0.9998 0.1311 0.508 0.492
#> GSM152035 1 0.9000 0.5260 0.684 0.316
#> GSM152039 2 0.0376 0.7867 0.004 0.996
#> GSM152041 2 0.8327 0.5863 0.264 0.736
#> GSM152044 2 0.0000 0.7860 0.000 1.000
#> GSM152045 1 0.0376 0.7351 0.996 0.004
#> GSM152051 2 0.0376 0.7858 0.004 0.996
#> GSM152054 1 0.1633 0.7376 0.976 0.024
#> GSM152057 2 0.0376 0.7858 0.004 0.996
#> GSM152058 1 0.9944 0.2516 0.544 0.456
#> GSM152067 1 0.2778 0.7234 0.952 0.048
#> GSM152068 2 0.0376 0.7858 0.004 0.996
#> GSM152075 2 0.7950 0.6208 0.240 0.760
#> GSM152076 2 0.0376 0.7867 0.004 0.996
#> GSM152079 2 0.0376 0.7858 0.004 0.996
#> GSM152084 1 0.6048 0.7073 0.852 0.148
#> GSM152089 2 0.9881 0.0557 0.436 0.564
#> GSM152095 2 0.0376 0.7867 0.004 0.996
#> GSM152096 1 0.6048 0.7073 0.852 0.148
#> GSM152097 2 0.0000 0.7860 0.000 1.000
#> GSM152099 2 0.0376 0.7858 0.004 0.996
#> GSM152106 2 0.0000 0.7860 0.000 1.000
#> GSM152107 1 0.6343 0.7022 0.840 0.160
#> GSM152109 1 0.3879 0.7129 0.924 0.076
#> GSM152111 1 0.9963 0.2315 0.536 0.464
#> GSM152112 1 0.6247 0.7030 0.844 0.156
#> GSM152113 1 0.6048 0.7073 0.852 0.148
#> GSM152115 1 0.0938 0.7363 0.988 0.012
#> GSM152030 2 0.8763 0.5335 0.296 0.704
#> GSM152038 1 0.0672 0.7366 0.992 0.008
#> GSM152042 2 0.9087 0.4651 0.324 0.676
#> GSM152062 1 0.6048 0.7073 0.852 0.148
#> GSM152077 1 0.9909 0.2652 0.556 0.444
#> GSM152088 2 0.6887 0.6559 0.184 0.816
#> GSM152100 2 0.7950 0.6208 0.240 0.760
#> GSM152102 1 0.1843 0.7374 0.972 0.028
#> GSM152104 2 0.0000 0.7860 0.000 1.000
#> GSM152028 1 0.0000 0.7341 1.000 0.000
#> GSM152029 1 0.5059 0.7176 0.888 0.112
#> GSM152049 1 0.9933 0.2612 0.548 0.452
#> GSM152053 2 0.9087 0.4651 0.324 0.676
#> GSM152059 1 0.2236 0.7378 0.964 0.036
#> GSM152085 1 0.9922 0.2700 0.552 0.448
#> GSM152101 1 0.1843 0.7366 0.972 0.028
#> GSM152105 1 0.0672 0.7366 0.992 0.008
#> GSM152034 1 0.9970 0.2186 0.532 0.468
#> GSM152036 2 0.0376 0.7867 0.004 0.996
#> GSM152040 1 0.4939 0.7167 0.892 0.108
#> GSM152043 1 0.5408 0.7069 0.876 0.124
#> GSM152046 1 0.9977 0.2071 0.528 0.472
#> GSM152047 1 0.5059 0.7152 0.888 0.112
#> GSM152048 1 0.9944 0.2516 0.544 0.456
#> GSM152050 1 0.9963 0.2315 0.536 0.464
#> GSM152052 1 0.1843 0.7379 0.972 0.028
#> GSM152056 1 0.9944 0.2516 0.544 0.456
#> GSM152060 1 0.9977 0.2071 0.528 0.472
#> GSM152065 1 0.0000 0.7341 1.000 0.000
#> GSM152066 1 0.9427 0.4364 0.640 0.360
#> GSM152069 1 0.3879 0.7129 0.924 0.076
#> GSM152070 1 0.0000 0.7341 1.000 0.000
#> GSM152071 1 0.3879 0.7129 0.924 0.076
#> GSM152072 1 0.0000 0.7341 1.000 0.000
#> GSM152073 1 0.5946 0.6980 0.856 0.144
#> GSM152078 1 0.0672 0.7366 0.992 0.008
#> GSM152082 1 0.0000 0.7341 1.000 0.000
#> GSM152086 1 0.9754 0.3518 0.592 0.408
#> GSM152090 1 0.6048 0.7066 0.852 0.148
#> GSM152092 1 0.4022 0.7268 0.920 0.080
#> GSM152093 1 0.9988 0.1697 0.520 0.480
#> GSM152094 1 0.6247 0.6907 0.844 0.156
#> GSM152098 1 0.0000 0.7341 1.000 0.000
#> GSM152110 1 0.9944 0.2527 0.544 0.456
#> GSM152031 1 0.0672 0.7366 0.992 0.008
#> GSM152037 1 0.9427 0.4364 0.640 0.360
#> GSM152055 1 0.9977 0.2071 0.528 0.472
#> GSM152061 1 0.9977 0.2071 0.528 0.472
#> GSM152064 2 1.0000 -0.1415 0.496 0.504
#> GSM152087 1 0.6247 0.6907 0.844 0.156
#> GSM152103 1 0.6048 0.7066 0.852 0.148
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM152032 3 0.3607 0.6301 0.112 0.008 0.880
#> GSM152033 1 0.6126 0.0188 0.600 0.000 0.400
#> GSM152063 2 0.2590 0.7344 0.004 0.924 0.072
#> GSM152074 1 0.6308 -0.2128 0.508 0.000 0.492
#> GSM152080 3 0.4555 0.4129 0.000 0.200 0.800
#> GSM152081 2 0.6825 0.2077 0.488 0.500 0.012
#> GSM152083 3 0.3607 0.6301 0.112 0.008 0.880
#> GSM152091 3 0.5810 0.2229 0.000 0.336 0.664
#> GSM152108 1 0.9212 0.2378 0.516 0.304 0.180
#> GSM152114 1 0.6082 0.4025 0.692 0.296 0.012
#> GSM152035 3 0.9722 0.4279 0.312 0.244 0.444
#> GSM152039 2 0.4261 0.7353 0.140 0.848 0.012
#> GSM152041 2 0.7029 0.3365 0.440 0.540 0.020
#> GSM152044 2 0.0424 0.7428 0.008 0.992 0.000
#> GSM152045 1 0.6079 0.0336 0.612 0.000 0.388
#> GSM152051 2 0.2590 0.7344 0.004 0.924 0.072
#> GSM152054 1 0.6931 -0.2161 0.528 0.016 0.456
#> GSM152057 2 0.2590 0.7344 0.004 0.924 0.072
#> GSM152058 1 0.5365 0.4698 0.744 0.252 0.004
#> GSM152067 3 0.4605 0.6126 0.204 0.000 0.796
#> GSM152068 2 0.2590 0.7344 0.004 0.924 0.072
#> GSM152075 2 0.6950 0.4020 0.408 0.572 0.020
#> GSM152076 2 0.4261 0.7353 0.140 0.848 0.012
#> GSM152079 2 0.2590 0.7344 0.004 0.924 0.072
#> GSM152084 3 0.7114 0.5781 0.388 0.028 0.584
#> GSM152089 2 0.9964 -0.0291 0.328 0.372 0.300
#> GSM152095 2 0.4261 0.7353 0.140 0.848 0.012
#> GSM152096 3 0.7099 0.5833 0.384 0.028 0.588
#> GSM152097 2 0.1529 0.7544 0.040 0.960 0.000
#> GSM152099 2 0.2590 0.7344 0.004 0.924 0.072
#> GSM152106 2 0.1529 0.7544 0.040 0.960 0.000
#> GSM152107 3 0.7379 0.5814 0.376 0.040 0.584
#> GSM152109 3 0.1753 0.6346 0.048 0.000 0.952
#> GSM152111 1 0.5178 0.4617 0.744 0.256 0.000
#> GSM152112 3 0.7584 0.3403 0.472 0.040 0.488
#> GSM152113 3 0.7099 0.5833 0.384 0.028 0.588
#> GSM152115 1 0.6500 -0.1958 0.532 0.004 0.464
#> GSM152030 2 0.6822 0.2327 0.480 0.508 0.012
#> GSM152038 1 0.5254 0.2849 0.736 0.000 0.264
#> GSM152042 1 0.7919 -0.2232 0.480 0.464 0.056
#> GSM152062 3 0.7099 0.5833 0.384 0.028 0.588
#> GSM152077 1 0.7277 0.4490 0.660 0.280 0.060
#> GSM152088 2 0.5138 0.5379 0.000 0.748 0.252
#> GSM152100 2 0.6950 0.4020 0.408 0.572 0.020
#> GSM152102 3 0.7295 0.2482 0.480 0.028 0.492
#> GSM152104 2 0.1529 0.7544 0.040 0.960 0.000
#> GSM152028 1 0.5497 0.2498 0.708 0.000 0.292
#> GSM152029 3 0.6247 0.5851 0.376 0.004 0.620
#> GSM152049 1 0.5325 0.4742 0.748 0.248 0.004
#> GSM152053 1 0.7919 -0.2232 0.480 0.464 0.056
#> GSM152059 1 0.4654 0.3333 0.792 0.000 0.208
#> GSM152085 1 0.5285 0.4779 0.752 0.244 0.004
#> GSM152101 1 0.6822 -0.2600 0.508 0.012 0.480
#> GSM152105 1 0.5254 0.2849 0.736 0.000 0.264
#> GSM152034 1 0.5803 0.4552 0.736 0.248 0.016
#> GSM152036 2 0.4261 0.7353 0.140 0.848 0.012
#> GSM152040 1 0.5850 0.4126 0.772 0.040 0.188
#> GSM152043 1 0.5947 0.4360 0.776 0.052 0.172
#> GSM152046 1 0.5698 0.4504 0.736 0.252 0.012
#> GSM152047 1 0.5746 0.4196 0.780 0.040 0.180
#> GSM152048 1 0.5365 0.4698 0.744 0.252 0.004
#> GSM152050 1 0.5178 0.4617 0.744 0.256 0.000
#> GSM152052 1 0.5178 0.2813 0.744 0.000 0.256
#> GSM152056 1 0.5365 0.4698 0.744 0.252 0.004
#> GSM152060 1 0.5698 0.4504 0.736 0.252 0.012
#> GSM152065 1 0.5882 0.1441 0.652 0.000 0.348
#> GSM152066 1 0.5402 0.5330 0.792 0.180 0.028
#> GSM152069 3 0.1860 0.6368 0.052 0.000 0.948
#> GSM152070 1 0.5529 0.2432 0.704 0.000 0.296
#> GSM152071 3 0.1860 0.6368 0.052 0.000 0.948
#> GSM152072 1 0.6095 0.0309 0.608 0.000 0.392
#> GSM152073 1 0.4137 0.4648 0.872 0.032 0.096
#> GSM152078 1 0.5254 0.2849 0.736 0.000 0.264
#> GSM152082 1 0.5529 0.2412 0.704 0.000 0.296
#> GSM152086 1 0.5061 0.5063 0.784 0.208 0.008
#> GSM152090 3 0.7143 0.5737 0.396 0.028 0.576
#> GSM152092 1 0.4749 0.4038 0.816 0.012 0.172
#> GSM152093 1 0.6420 0.4207 0.688 0.288 0.024
#> GSM152094 1 0.4289 0.4716 0.868 0.040 0.092
#> GSM152098 1 0.5465 0.2547 0.712 0.000 0.288
#> GSM152110 1 0.5098 0.4718 0.752 0.248 0.000
#> GSM152031 1 0.5254 0.2849 0.736 0.000 0.264
#> GSM152037 1 0.5402 0.5330 0.792 0.180 0.028
#> GSM152055 1 0.5698 0.4504 0.736 0.252 0.012
#> GSM152061 1 0.5698 0.4504 0.736 0.252 0.012
#> GSM152064 1 0.6262 0.4017 0.696 0.284 0.020
#> GSM152087 1 0.4289 0.4716 0.868 0.040 0.092
#> GSM152103 3 0.7143 0.5737 0.396 0.028 0.576
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM152032 4 0.4790 0.4533 0.000 0.000 0.380 0.620
#> GSM152033 3 0.2281 0.4924 0.000 0.000 0.904 0.096
#> GSM152063 2 0.2921 0.7939 0.000 0.860 0.000 0.140
#> GSM152074 3 0.3400 0.4003 0.000 0.000 0.820 0.180
#> GSM152080 4 0.2345 0.3545 0.000 0.100 0.000 0.900
#> GSM152081 1 0.4993 0.6053 0.728 0.244 0.008 0.020
#> GSM152083 4 0.4790 0.4533 0.000 0.000 0.380 0.620
#> GSM152091 4 0.3942 0.1090 0.000 0.236 0.000 0.764
#> GSM152108 1 0.8048 0.4626 0.588 0.088 0.156 0.168
#> GSM152114 1 0.3094 0.7783 0.900 0.032 0.048 0.020
#> GSM152035 4 0.8508 0.1925 0.056 0.152 0.368 0.424
#> GSM152039 2 0.4524 0.6665 0.204 0.768 0.000 0.028
#> GSM152041 1 0.5886 0.4764 0.640 0.316 0.016 0.028
#> GSM152044 2 0.1637 0.7921 0.000 0.940 0.000 0.060
#> GSM152045 3 0.3796 0.4914 0.056 0.000 0.848 0.096
#> GSM152051 2 0.2921 0.7939 0.000 0.860 0.000 0.140
#> GSM152054 3 0.5840 0.2902 0.060 0.004 0.672 0.264
#> GSM152057 2 0.2921 0.7939 0.000 0.860 0.000 0.140
#> GSM152058 1 0.0336 0.7978 0.992 0.000 0.008 0.000
#> GSM152067 4 0.4967 0.3719 0.000 0.000 0.452 0.548
#> GSM152068 2 0.2921 0.7939 0.000 0.860 0.000 0.140
#> GSM152075 1 0.6031 0.4016 0.608 0.348 0.016 0.028
#> GSM152076 2 0.4524 0.6665 0.204 0.768 0.000 0.028
#> GSM152079 2 0.2921 0.7939 0.000 0.860 0.000 0.140
#> GSM152084 4 0.7568 0.4389 0.148 0.008 0.408 0.436
#> GSM152089 2 0.9996 -0.1968 0.252 0.256 0.236 0.256
#> GSM152095 2 0.4524 0.6665 0.204 0.768 0.000 0.028
#> GSM152096 4 0.7536 0.4434 0.144 0.008 0.408 0.440
#> GSM152097 2 0.0000 0.7876 0.000 1.000 0.000 0.000
#> GSM152099 2 0.2921 0.7939 0.000 0.860 0.000 0.140
#> GSM152106 2 0.0000 0.7876 0.000 1.000 0.000 0.000
#> GSM152107 4 0.7633 0.4475 0.144 0.012 0.392 0.452
#> GSM152109 4 0.4382 0.5202 0.000 0.000 0.296 0.704
#> GSM152111 1 0.0564 0.7993 0.988 0.004 0.004 0.004
#> GSM152112 3 0.7108 0.1097 0.124 0.020 0.608 0.248
#> GSM152113 4 0.7536 0.4434 0.144 0.008 0.408 0.440
#> GSM152115 3 0.5184 0.3473 0.060 0.000 0.736 0.204
#> GSM152030 1 0.5055 0.5966 0.720 0.252 0.008 0.020
#> GSM152038 3 0.3636 0.5921 0.172 0.000 0.820 0.008
#> GSM152042 1 0.5882 0.6120 0.708 0.212 0.016 0.064
#> GSM152062 4 0.7536 0.4434 0.144 0.008 0.408 0.440
#> GSM152077 1 0.4952 0.7122 0.796 0.028 0.132 0.044
#> GSM152088 2 0.4564 0.6134 0.000 0.672 0.000 0.328
#> GSM152100 1 0.6031 0.4016 0.608 0.348 0.016 0.028
#> GSM152102 3 0.6226 0.1906 0.056 0.008 0.616 0.320
#> GSM152104 2 0.0000 0.7876 0.000 1.000 0.000 0.000
#> GSM152028 3 0.2737 0.6028 0.104 0.000 0.888 0.008
#> GSM152029 3 0.7120 -0.4208 0.128 0.000 0.436 0.436
#> GSM152049 1 0.0469 0.7977 0.988 0.000 0.012 0.000
#> GSM152053 1 0.5882 0.6120 0.708 0.212 0.016 0.064
#> GSM152059 3 0.4748 0.5163 0.268 0.000 0.716 0.016
#> GSM152085 1 0.0592 0.7964 0.984 0.000 0.016 0.000
#> GSM152101 3 0.5572 0.3018 0.060 0.004 0.708 0.228
#> GSM152105 3 0.3636 0.5921 0.172 0.000 0.820 0.008
#> GSM152034 1 0.0657 0.7989 0.984 0.000 0.004 0.012
#> GSM152036 2 0.4524 0.6665 0.204 0.768 0.000 0.028
#> GSM152040 3 0.5168 0.1131 0.492 0.000 0.504 0.004
#> GSM152043 1 0.4985 -0.0481 0.532 0.000 0.468 0.000
#> GSM152046 1 0.0336 0.7989 0.992 0.000 0.000 0.008
#> GSM152047 3 0.5000 0.0952 0.500 0.000 0.500 0.000
#> GSM152048 1 0.0336 0.7978 0.992 0.000 0.008 0.000
#> GSM152050 1 0.0564 0.7993 0.988 0.004 0.004 0.004
#> GSM152052 3 0.4888 0.5178 0.224 0.000 0.740 0.036
#> GSM152056 1 0.0336 0.7978 0.992 0.000 0.008 0.000
#> GSM152060 1 0.0336 0.7989 0.992 0.000 0.000 0.008
#> GSM152065 3 0.2111 0.5468 0.024 0.000 0.932 0.044
#> GSM152066 1 0.2589 0.7182 0.884 0.000 0.116 0.000
#> GSM152069 4 0.4406 0.5208 0.000 0.000 0.300 0.700
#> GSM152070 3 0.2345 0.6013 0.100 0.000 0.900 0.000
#> GSM152071 4 0.4406 0.5208 0.000 0.000 0.300 0.700
#> GSM152072 3 0.2730 0.5168 0.016 0.000 0.896 0.088
#> GSM152073 1 0.4837 0.2604 0.648 0.000 0.348 0.004
#> GSM152078 3 0.3636 0.5921 0.172 0.000 0.820 0.008
#> GSM152082 3 0.2216 0.5984 0.092 0.000 0.908 0.000
#> GSM152086 1 0.1637 0.7706 0.940 0.000 0.060 0.000
#> GSM152090 4 0.7539 0.4335 0.144 0.008 0.416 0.432
#> GSM152092 3 0.4992 0.1780 0.476 0.000 0.524 0.000
#> GSM152093 1 0.3877 0.7623 0.860 0.032 0.084 0.024
#> GSM152094 1 0.4781 0.2922 0.660 0.000 0.336 0.004
#> GSM152098 3 0.2469 0.6024 0.108 0.000 0.892 0.000
#> GSM152110 1 0.0779 0.7984 0.980 0.004 0.016 0.000
#> GSM152031 3 0.3636 0.5921 0.172 0.000 0.820 0.008
#> GSM152037 1 0.2589 0.7182 0.884 0.000 0.116 0.000
#> GSM152055 1 0.0336 0.7989 0.992 0.000 0.000 0.008
#> GSM152061 1 0.0336 0.7989 0.992 0.000 0.000 0.008
#> GSM152064 1 0.2432 0.7890 0.928 0.028 0.020 0.024
#> GSM152087 1 0.4781 0.2922 0.660 0.000 0.336 0.004
#> GSM152103 4 0.7539 0.4335 0.144 0.008 0.416 0.432
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM152032 4 0.4171 0.627955 0.000 0.000 0.112 0.784 0.104
#> GSM152033 5 0.4908 0.245680 0.000 0.000 0.320 0.044 0.636
#> GSM152063 2 0.1851 0.809608 0.000 0.912 0.088 0.000 0.000
#> GSM152074 5 0.6367 0.181982 0.000 0.000 0.232 0.248 0.520
#> GSM152080 4 0.5813 0.458200 0.000 0.084 0.184 0.680 0.052
#> GSM152081 1 0.4793 0.582136 0.708 0.216 0.076 0.000 0.000
#> GSM152083 4 0.4171 0.627955 0.000 0.000 0.112 0.784 0.104
#> GSM152091 4 0.7385 0.281470 0.000 0.212 0.264 0.472 0.052
#> GSM152108 1 0.6602 0.345708 0.552 0.064 0.308 0.000 0.076
#> GSM152114 1 0.2800 0.740484 0.888 0.016 0.072 0.000 0.024
#> GSM152035 3 0.6607 0.242812 0.008 0.196 0.620 0.048 0.128
#> GSM152039 2 0.5275 0.663617 0.200 0.684 0.112 0.004 0.000
#> GSM152041 1 0.5570 0.455435 0.620 0.292 0.080 0.000 0.008
#> GSM152044 2 0.0162 0.804182 0.000 0.996 0.004 0.000 0.000
#> GSM152045 5 0.5421 -0.150434 0.008 0.000 0.448 0.040 0.504
#> GSM152051 2 0.1851 0.809608 0.000 0.912 0.088 0.000 0.000
#> GSM152054 3 0.5716 0.418435 0.008 0.000 0.628 0.108 0.256
#> GSM152057 2 0.1851 0.809608 0.000 0.912 0.088 0.000 0.000
#> GSM152058 1 0.0290 0.768220 0.992 0.000 0.000 0.000 0.008
#> GSM152067 4 0.5237 0.515352 0.000 0.000 0.156 0.684 0.160
#> GSM152068 2 0.1851 0.809608 0.000 0.912 0.088 0.000 0.000
#> GSM152075 1 0.5564 0.393307 0.596 0.328 0.068 0.000 0.008
#> GSM152076 2 0.5275 0.663617 0.200 0.684 0.112 0.004 0.000
#> GSM152079 2 0.1851 0.809608 0.000 0.912 0.088 0.000 0.000
#> GSM152084 3 0.7996 0.501943 0.104 0.000 0.396 0.296 0.204
#> GSM152089 3 0.8726 0.216177 0.212 0.232 0.416 0.064 0.076
#> GSM152095 2 0.5275 0.663617 0.200 0.684 0.112 0.004 0.000
#> GSM152096 3 0.7962 0.504749 0.100 0.000 0.400 0.296 0.204
#> GSM152097 2 0.1638 0.795364 0.000 0.932 0.064 0.004 0.000
#> GSM152099 2 0.1851 0.809608 0.000 0.912 0.088 0.000 0.000
#> GSM152106 2 0.1638 0.795364 0.000 0.932 0.064 0.004 0.000
#> GSM152107 3 0.7788 0.486036 0.100 0.004 0.460 0.284 0.152
#> GSM152109 4 0.2677 0.663101 0.000 0.000 0.016 0.872 0.112
#> GSM152111 1 0.0162 0.769134 0.996 0.000 0.004 0.000 0.000
#> GSM152112 3 0.6650 0.445333 0.068 0.012 0.608 0.072 0.240
#> GSM152113 3 0.7962 0.504749 0.100 0.000 0.400 0.296 0.204
#> GSM152115 3 0.5963 0.391153 0.008 0.000 0.560 0.100 0.332
#> GSM152030 1 0.4850 0.573406 0.700 0.224 0.076 0.000 0.000
#> GSM152038 5 0.3320 0.696761 0.164 0.000 0.004 0.012 0.820
#> GSM152042 1 0.5169 0.586772 0.688 0.184 0.128 0.000 0.000
#> GSM152062 3 0.7962 0.504749 0.100 0.000 0.400 0.296 0.204
#> GSM152077 1 0.4283 0.668868 0.780 0.004 0.136 0.000 0.080
#> GSM152088 2 0.5017 0.609486 0.000 0.724 0.112 0.156 0.008
#> GSM152100 1 0.5564 0.393307 0.596 0.328 0.068 0.000 0.008
#> GSM152102 3 0.5810 0.383181 0.008 0.000 0.632 0.136 0.224
#> GSM152104 2 0.1638 0.795364 0.000 0.932 0.064 0.004 0.000
#> GSM152028 5 0.2720 0.687802 0.096 0.000 0.020 0.004 0.880
#> GSM152029 4 0.8181 -0.353154 0.112 0.000 0.280 0.356 0.252
#> GSM152049 1 0.0451 0.768630 0.988 0.000 0.004 0.000 0.008
#> GSM152053 1 0.5169 0.586772 0.688 0.184 0.128 0.000 0.000
#> GSM152059 5 0.4065 0.606126 0.264 0.000 0.000 0.016 0.720
#> GSM152085 1 0.0579 0.768125 0.984 0.000 0.008 0.000 0.008
#> GSM152101 3 0.5798 0.424087 0.008 0.000 0.596 0.096 0.300
#> GSM152105 5 0.3320 0.696761 0.164 0.000 0.004 0.012 0.820
#> GSM152034 1 0.0865 0.768991 0.972 0.000 0.024 0.000 0.004
#> GSM152036 2 0.5275 0.663617 0.200 0.684 0.112 0.004 0.000
#> GSM152040 1 0.5440 0.000548 0.476 0.000 0.048 0.004 0.472
#> GSM152043 1 0.5303 0.107526 0.516 0.000 0.040 0.004 0.440
#> GSM152046 1 0.0566 0.769354 0.984 0.000 0.012 0.000 0.004
#> GSM152047 1 0.5381 0.016164 0.484 0.000 0.044 0.004 0.468
#> GSM152048 1 0.0290 0.768220 0.992 0.000 0.000 0.000 0.008
#> GSM152050 1 0.0162 0.769134 0.996 0.000 0.004 0.000 0.000
#> GSM152052 5 0.4862 0.602863 0.220 0.000 0.004 0.068 0.708
#> GSM152056 1 0.0290 0.768220 0.992 0.000 0.000 0.000 0.008
#> GSM152060 1 0.0566 0.769354 0.984 0.000 0.012 0.000 0.004
#> GSM152065 5 0.3398 0.535314 0.024 0.000 0.144 0.004 0.828
#> GSM152066 1 0.2928 0.701775 0.872 0.000 0.032 0.004 0.092
#> GSM152069 4 0.2727 0.663407 0.000 0.000 0.016 0.868 0.116
#> GSM152070 5 0.2249 0.689445 0.096 0.000 0.008 0.000 0.896
#> GSM152071 4 0.2727 0.663407 0.000 0.000 0.016 0.868 0.116
#> GSM152072 5 0.5033 0.264676 0.016 0.000 0.292 0.032 0.660
#> GSM152073 1 0.5037 0.339262 0.636 0.000 0.036 0.008 0.320
#> GSM152078 5 0.3320 0.696761 0.164 0.000 0.004 0.012 0.820
#> GSM152082 5 0.2351 0.686601 0.088 0.000 0.016 0.000 0.896
#> GSM152086 1 0.1800 0.744519 0.932 0.000 0.020 0.000 0.048
#> GSM152090 3 0.8080 0.488342 0.108 0.000 0.376 0.300 0.216
#> GSM152092 5 0.5318 0.013366 0.460 0.000 0.040 0.004 0.496
#> GSM152093 1 0.3627 0.724237 0.848 0.016 0.092 0.008 0.036
#> GSM152094 1 0.4984 0.366554 0.648 0.000 0.036 0.008 0.308
#> GSM152098 5 0.2358 0.691035 0.104 0.000 0.008 0.000 0.888
#> GSM152110 1 0.0451 0.769075 0.988 0.000 0.004 0.000 0.008
#> GSM152031 5 0.3320 0.696761 0.164 0.000 0.004 0.012 0.820
#> GSM152037 1 0.2928 0.701775 0.872 0.000 0.032 0.004 0.092
#> GSM152055 1 0.0566 0.769354 0.984 0.000 0.012 0.000 0.004
#> GSM152061 1 0.0566 0.769354 0.984 0.000 0.012 0.000 0.004
#> GSM152064 1 0.2251 0.758084 0.916 0.024 0.052 0.000 0.008
#> GSM152087 1 0.4984 0.366554 0.648 0.000 0.036 0.008 0.308
#> GSM152103 3 0.8080 0.488342 0.108 0.000 0.376 0.300 0.216
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM152032 3 0.2944 0.64458 0.004 0.000 0.856 0.072 0.068 0.000
#> GSM152033 1 0.5647 0.11092 0.488 0.000 0.028 0.076 0.408 0.000
#> GSM152063 2 0.0000 0.82088 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152074 3 0.7378 0.17673 0.308 0.000 0.324 0.112 0.256 0.000
#> GSM152080 3 0.6482 0.38183 0.056 0.064 0.500 0.348 0.032 0.000
#> GSM152081 6 0.4651 0.51528 0.000 0.124 0.000 0.172 0.004 0.700
#> GSM152083 3 0.2944 0.64458 0.004 0.000 0.856 0.072 0.068 0.000
#> GSM152091 4 0.7548 -0.37849 0.056 0.272 0.292 0.348 0.032 0.000
#> GSM152108 6 0.6611 0.33900 0.008 0.132 0.000 0.088 0.224 0.548
#> GSM152114 6 0.2635 0.70823 0.004 0.008 0.000 0.068 0.036 0.884
#> GSM152035 5 0.5405 0.25760 0.020 0.284 0.004 0.084 0.608 0.000
#> GSM152039 4 0.5753 0.64654 0.000 0.384 0.000 0.444 0.000 0.172
#> GSM152041 6 0.5510 0.35295 0.000 0.164 0.000 0.220 0.012 0.604
#> GSM152044 2 0.2416 0.71215 0.000 0.844 0.000 0.156 0.000 0.000
#> GSM152045 5 0.5142 0.13750 0.292 0.000 0.024 0.064 0.620 0.000
#> GSM152051 2 0.0000 0.82088 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152054 5 0.2906 0.37775 0.028 0.004 0.052 0.040 0.876 0.000
#> GSM152057 2 0.0000 0.82088 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152058 6 0.0260 0.75490 0.008 0.000 0.000 0.000 0.000 0.992
#> GSM152067 3 0.3724 0.55033 0.028 0.000 0.772 0.012 0.188 0.000
#> GSM152068 2 0.0000 0.82088 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152075 6 0.5700 0.27143 0.000 0.196 0.000 0.216 0.012 0.576
#> GSM152076 4 0.5753 0.64654 0.000 0.384 0.000 0.444 0.000 0.172
#> GSM152079 2 0.0000 0.82088 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152084 5 0.8567 0.43461 0.108 0.076 0.296 0.048 0.376 0.096
#> GSM152089 5 0.8121 0.07381 0.004 0.248 0.036 0.148 0.372 0.192
#> GSM152095 4 0.5753 0.64654 0.000 0.384 0.000 0.444 0.000 0.172
#> GSM152096 5 0.8536 0.43717 0.108 0.076 0.296 0.048 0.380 0.092
#> GSM152097 2 0.3050 0.63445 0.000 0.764 0.000 0.236 0.000 0.000
#> GSM152099 2 0.0000 0.82088 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152106 2 0.3050 0.63445 0.000 0.764 0.000 0.236 0.000 0.000
#> GSM152107 5 0.8176 0.42707 0.064 0.080 0.288 0.048 0.428 0.092
#> GSM152109 3 0.0692 0.66673 0.020 0.000 0.976 0.000 0.004 0.000
#> GSM152111 6 0.0260 0.75449 0.000 0.000 0.000 0.008 0.000 0.992
#> GSM152112 5 0.6257 0.40453 0.156 0.092 0.044 0.004 0.644 0.060
#> GSM152113 5 0.8536 0.43717 0.108 0.076 0.296 0.048 0.380 0.092
#> GSM152115 5 0.3983 0.37691 0.164 0.000 0.056 0.012 0.768 0.000
#> GSM152030 6 0.4713 0.50517 0.000 0.124 0.000 0.180 0.004 0.692
#> GSM152038 1 0.2615 0.72626 0.852 0.000 0.004 0.008 0.000 0.136
#> GSM152042 6 0.5255 0.50932 0.000 0.140 0.000 0.140 0.040 0.680
#> GSM152062 5 0.8536 0.43717 0.108 0.076 0.296 0.048 0.380 0.092
#> GSM152077 6 0.4073 0.64955 0.016 0.000 0.000 0.084 0.124 0.776
#> GSM152088 2 0.3516 0.57248 0.000 0.812 0.096 0.088 0.004 0.000
#> GSM152100 6 0.5700 0.27143 0.000 0.196 0.000 0.216 0.012 0.576
#> GSM152102 5 0.3512 0.35368 0.028 0.004 0.056 0.076 0.836 0.000
#> GSM152104 2 0.3050 0.63445 0.000 0.764 0.000 0.236 0.000 0.000
#> GSM152028 1 0.3052 0.71392 0.864 0.000 0.004 0.020 0.044 0.068
#> GSM152029 3 0.8160 -0.31439 0.188 0.072 0.360 0.000 0.276 0.104
#> GSM152049 6 0.0405 0.75554 0.008 0.000 0.000 0.000 0.004 0.988
#> GSM152053 6 0.5255 0.50932 0.000 0.140 0.000 0.140 0.040 0.680
#> GSM152059 1 0.3806 0.63354 0.736 0.000 0.012 0.004 0.008 0.240
#> GSM152085 6 0.0665 0.75482 0.008 0.000 0.000 0.004 0.008 0.980
#> GSM152101 5 0.4146 0.38486 0.160 0.012 0.060 0.004 0.764 0.000
#> GSM152105 1 0.2615 0.72626 0.852 0.000 0.004 0.008 0.000 0.136
#> GSM152034 6 0.0964 0.75418 0.004 0.000 0.000 0.016 0.012 0.968
#> GSM152036 4 0.5753 0.64654 0.000 0.384 0.000 0.444 0.000 0.172
#> GSM152040 6 0.5415 -0.02327 0.444 0.000 0.000 0.008 0.088 0.460
#> GSM152043 6 0.5192 0.10529 0.416 0.000 0.000 0.008 0.068 0.508
#> GSM152046 6 0.0603 0.75400 0.004 0.000 0.000 0.016 0.000 0.980
#> GSM152047 6 0.5338 -0.00725 0.444 0.000 0.000 0.008 0.080 0.468
#> GSM152048 6 0.0260 0.75490 0.008 0.000 0.000 0.000 0.000 0.992
#> GSM152050 6 0.0260 0.75449 0.000 0.000 0.000 0.008 0.000 0.992
#> GSM152052 1 0.4800 0.60852 0.716 0.000 0.056 0.024 0.012 0.192
#> GSM152056 6 0.0260 0.75490 0.008 0.000 0.000 0.000 0.000 0.992
#> GSM152060 6 0.0603 0.75400 0.004 0.000 0.000 0.016 0.000 0.980
#> GSM152065 1 0.4516 0.53584 0.704 0.000 0.012 0.064 0.220 0.000
#> GSM152066 6 0.2721 0.69773 0.088 0.000 0.000 0.004 0.040 0.868
#> GSM152069 3 0.0777 0.66747 0.024 0.000 0.972 0.000 0.004 0.000
#> GSM152070 1 0.4311 0.70196 0.792 0.000 0.012 0.064 0.064 0.068
#> GSM152071 3 0.0777 0.66747 0.024 0.000 0.972 0.000 0.004 0.000
#> GSM152072 1 0.5528 0.19723 0.488 0.000 0.028 0.064 0.420 0.000
#> GSM152073 6 0.4702 0.30572 0.332 0.000 0.000 0.004 0.052 0.612
#> GSM152078 1 0.2615 0.72626 0.852 0.000 0.004 0.008 0.000 0.136
#> GSM152082 1 0.4022 0.70076 0.812 0.000 0.012 0.064 0.052 0.060
#> GSM152086 6 0.1844 0.73710 0.048 0.000 0.000 0.004 0.024 0.924
#> GSM152090 5 0.8610 0.41995 0.124 0.076 0.300 0.040 0.360 0.100
#> GSM152092 1 0.5216 0.01686 0.476 0.000 0.000 0.008 0.068 0.448
#> GSM152093 6 0.3469 0.69468 0.016 0.008 0.004 0.068 0.060 0.844
#> GSM152094 6 0.4659 0.33307 0.320 0.000 0.000 0.004 0.052 0.624
#> GSM152098 1 0.4305 0.70496 0.792 0.000 0.012 0.068 0.056 0.072
#> GSM152110 6 0.0436 0.75516 0.004 0.000 0.000 0.004 0.004 0.988
#> GSM152031 1 0.2615 0.72626 0.852 0.000 0.004 0.008 0.000 0.136
#> GSM152037 6 0.2721 0.69773 0.088 0.000 0.000 0.004 0.040 0.868
#> GSM152055 6 0.0603 0.75400 0.004 0.000 0.000 0.016 0.000 0.980
#> GSM152061 6 0.0603 0.75400 0.004 0.000 0.000 0.016 0.000 0.980
#> GSM152064 6 0.2108 0.72957 0.000 0.016 0.000 0.056 0.016 0.912
#> GSM152087 6 0.4659 0.33307 0.320 0.000 0.000 0.004 0.052 0.624
#> GSM152103 5 0.8610 0.41995 0.124 0.076 0.300 0.040 0.360 0.100
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n specimen(p) k
#> ATC:hclust 63 0.00521 2
#> ATC:hclust 32 0.13036 3
#> ATC:hclust 54 0.00335 4
#> ATC:hclust 60 0.00191 5
#> ATC:hclust 56 0.00565 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 10612 rows and 88 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.599 0.808 0.900 0.4793 0.538 0.538
#> 3 3 0.668 0.759 0.872 0.3729 0.736 0.535
#> 4 4 0.541 0.418 0.653 0.1279 0.836 0.562
#> 5 5 0.640 0.685 0.798 0.0681 0.856 0.515
#> 6 6 0.694 0.647 0.771 0.0411 0.946 0.745
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
#> GSM152032 1 0.2778 0.831 0.952 0.048
#> GSM152033 1 0.0376 0.844 0.996 0.004
#> GSM152063 2 0.0000 0.948 0.000 1.000
#> GSM152074 1 0.2778 0.831 0.952 0.048
#> GSM152080 2 0.9323 0.455 0.348 0.652
#> GSM152081 2 0.0376 0.947 0.004 0.996
#> GSM152083 2 0.9323 0.455 0.348 0.652
#> GSM152091 2 0.0000 0.948 0.000 1.000
#> GSM152108 2 0.0000 0.948 0.000 1.000
#> GSM152114 1 0.9710 0.557 0.600 0.400
#> GSM152035 2 0.0000 0.948 0.000 1.000
#> GSM152039 2 0.0376 0.947 0.004 0.996
#> GSM152041 2 0.0376 0.947 0.004 0.996
#> GSM152044 2 0.0000 0.948 0.000 1.000
#> GSM152045 1 0.0000 0.845 1.000 0.000
#> GSM152051 2 0.0000 0.948 0.000 1.000
#> GSM152054 1 0.2603 0.833 0.956 0.044
#> GSM152057 2 0.0000 0.948 0.000 1.000
#> GSM152058 1 0.8207 0.718 0.744 0.256
#> GSM152067 1 0.2778 0.831 0.952 0.048
#> GSM152068 2 0.0000 0.948 0.000 1.000
#> GSM152075 2 0.0376 0.947 0.004 0.996
#> GSM152076 2 0.0376 0.947 0.004 0.996
#> GSM152079 2 0.0000 0.948 0.000 1.000
#> GSM152084 1 0.6801 0.782 0.820 0.180
#> GSM152089 2 0.0000 0.948 0.000 1.000
#> GSM152095 2 0.0000 0.948 0.000 1.000
#> GSM152096 2 0.9993 0.117 0.484 0.516
#> GSM152097 2 0.0000 0.948 0.000 1.000
#> GSM152099 2 0.0000 0.948 0.000 1.000
#> GSM152106 2 0.0000 0.948 0.000 1.000
#> GSM152107 2 0.0000 0.948 0.000 1.000
#> GSM152109 1 0.2778 0.831 0.952 0.048
#> GSM152111 1 0.9393 0.613 0.644 0.356
#> GSM152112 2 0.3114 0.883 0.056 0.944
#> GSM152113 1 0.2603 0.833 0.956 0.044
#> GSM152115 1 0.2778 0.831 0.952 0.048
#> GSM152030 2 0.0376 0.947 0.004 0.996
#> GSM152038 1 0.0000 0.845 1.000 0.000
#> GSM152042 2 0.0376 0.947 0.004 0.996
#> GSM152062 1 0.2423 0.835 0.960 0.040
#> GSM152077 1 0.8207 0.718 0.744 0.256
#> GSM152088 2 0.0000 0.948 0.000 1.000
#> GSM152100 2 0.0000 0.948 0.000 1.000
#> GSM152102 1 0.7745 0.640 0.772 0.228
#> GSM152104 2 0.0000 0.948 0.000 1.000
#> GSM152028 1 0.0000 0.845 1.000 0.000
#> GSM152029 1 0.0000 0.845 1.000 0.000
#> GSM152049 1 0.8955 0.664 0.688 0.312
#> GSM152053 2 0.0376 0.947 0.004 0.996
#> GSM152059 1 0.0000 0.845 1.000 0.000
#> GSM152085 1 0.8499 0.700 0.724 0.276
#> GSM152101 1 0.7745 0.640 0.772 0.228
#> GSM152105 1 0.0000 0.845 1.000 0.000
#> GSM152034 1 0.9393 0.613 0.644 0.356
#> GSM152036 2 0.0376 0.947 0.004 0.996
#> GSM152040 1 0.0000 0.845 1.000 0.000
#> GSM152043 1 0.0000 0.845 1.000 0.000
#> GSM152046 1 0.9323 0.624 0.652 0.348
#> GSM152047 1 0.0000 0.845 1.000 0.000
#> GSM152048 1 0.8207 0.718 0.744 0.256
#> GSM152050 1 0.9323 0.624 0.652 0.348
#> GSM152052 1 0.0000 0.845 1.000 0.000
#> GSM152056 1 0.9323 0.624 0.652 0.348
#> GSM152060 1 0.9323 0.624 0.652 0.348
#> GSM152065 1 0.0000 0.845 1.000 0.000
#> GSM152066 1 0.4298 0.820 0.912 0.088
#> GSM152069 1 0.2778 0.831 0.952 0.048
#> GSM152070 1 0.0000 0.845 1.000 0.000
#> GSM152071 1 0.1843 0.838 0.972 0.028
#> GSM152072 1 0.0376 0.844 0.996 0.004
#> GSM152073 1 0.0000 0.845 1.000 0.000
#> GSM152078 1 0.0000 0.845 1.000 0.000
#> GSM152082 1 0.0000 0.845 1.000 0.000
#> GSM152086 1 0.7602 0.744 0.780 0.220
#> GSM152090 1 0.9686 0.567 0.604 0.396
#> GSM152092 1 0.0000 0.845 1.000 0.000
#> GSM152093 1 0.9460 0.600 0.636 0.364
#> GSM152094 1 0.1184 0.843 0.984 0.016
#> GSM152098 1 0.0000 0.845 1.000 0.000
#> GSM152110 1 0.9323 0.624 0.652 0.348
#> GSM152031 1 0.0000 0.845 1.000 0.000
#> GSM152037 1 0.0000 0.845 1.000 0.000
#> GSM152055 1 0.9323 0.624 0.652 0.348
#> GSM152061 1 0.9323 0.624 0.652 0.348
#> GSM152064 1 0.9460 0.600 0.636 0.364
#> GSM152087 1 0.0000 0.845 1.000 0.000
#> GSM152103 1 0.4562 0.823 0.904 0.096
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM152032 3 0.0000 0.885 0.000 0.000 1.000
#> GSM152033 3 0.1411 0.878 0.036 0.000 0.964
#> GSM152063 2 0.0592 0.810 0.000 0.988 0.012
#> GSM152074 3 0.0000 0.885 0.000 0.000 1.000
#> GSM152080 3 0.5254 0.631 0.000 0.264 0.736
#> GSM152081 2 0.6111 0.614 0.396 0.604 0.000
#> GSM152083 3 0.4750 0.693 0.000 0.216 0.784
#> GSM152091 2 0.1753 0.799 0.000 0.952 0.048
#> GSM152108 2 0.7671 0.732 0.300 0.628 0.072
#> GSM152114 1 0.1529 0.830 0.960 0.040 0.000
#> GSM152035 2 0.2356 0.781 0.000 0.928 0.072
#> GSM152039 2 0.4796 0.797 0.220 0.780 0.000
#> GSM152041 2 0.5678 0.733 0.316 0.684 0.000
#> GSM152044 2 0.0424 0.811 0.000 0.992 0.008
#> GSM152045 3 0.1529 0.877 0.040 0.000 0.960
#> GSM152051 2 0.1529 0.803 0.000 0.960 0.040
#> GSM152054 3 0.0892 0.883 0.020 0.000 0.980
#> GSM152057 2 0.1529 0.803 0.000 0.960 0.040
#> GSM152058 1 0.0000 0.841 1.000 0.000 0.000
#> GSM152067 3 0.0000 0.885 0.000 0.000 1.000
#> GSM152068 2 0.1529 0.803 0.000 0.960 0.040
#> GSM152075 2 0.5650 0.737 0.312 0.688 0.000
#> GSM152076 2 0.4796 0.797 0.220 0.780 0.000
#> GSM152079 2 0.1529 0.803 0.000 0.960 0.040
#> GSM152084 1 0.6252 0.233 0.556 0.000 0.444
#> GSM152089 2 0.5958 0.746 0.300 0.692 0.008
#> GSM152095 2 0.4796 0.797 0.220 0.780 0.000
#> GSM152096 3 0.2625 0.831 0.000 0.084 0.916
#> GSM152097 2 0.0000 0.812 0.000 1.000 0.000
#> GSM152099 2 0.1529 0.803 0.000 0.960 0.040
#> GSM152106 2 0.0000 0.812 0.000 1.000 0.000
#> GSM152107 3 0.9596 -0.241 0.200 0.384 0.416
#> GSM152109 3 0.0000 0.885 0.000 0.000 1.000
#> GSM152111 1 0.1529 0.830 0.960 0.040 0.000
#> GSM152112 3 0.8727 0.268 0.148 0.280 0.572
#> GSM152113 3 0.0237 0.885 0.004 0.000 0.996
#> GSM152115 3 0.0747 0.884 0.016 0.000 0.984
#> GSM152030 2 0.5678 0.733 0.316 0.684 0.000
#> GSM152038 3 0.1529 0.877 0.040 0.000 0.960
#> GSM152042 2 0.5678 0.733 0.316 0.684 0.000
#> GSM152062 3 0.0237 0.885 0.004 0.000 0.996
#> GSM152077 1 0.0000 0.841 1.000 0.000 0.000
#> GSM152088 2 0.1529 0.803 0.000 0.960 0.040
#> GSM152100 2 0.4796 0.797 0.220 0.780 0.000
#> GSM152102 3 0.0000 0.885 0.000 0.000 1.000
#> GSM152104 2 0.0000 0.812 0.000 1.000 0.000
#> GSM152028 1 0.6008 0.479 0.628 0.000 0.372
#> GSM152029 3 0.2356 0.848 0.072 0.000 0.928
#> GSM152049 1 0.0424 0.841 0.992 0.008 0.000
#> GSM152053 2 0.5882 0.692 0.348 0.652 0.000
#> GSM152059 1 0.5859 0.534 0.656 0.000 0.344
#> GSM152085 1 0.0424 0.841 0.992 0.008 0.000
#> GSM152101 3 0.0000 0.885 0.000 0.000 1.000
#> GSM152105 1 0.5948 0.504 0.640 0.000 0.360
#> GSM152034 1 0.1529 0.830 0.960 0.040 0.000
#> GSM152036 2 0.5016 0.787 0.240 0.760 0.000
#> GSM152040 1 0.4887 0.687 0.772 0.000 0.228
#> GSM152043 1 0.4654 0.709 0.792 0.000 0.208
#> GSM152046 1 0.1529 0.830 0.960 0.040 0.000
#> GSM152047 1 0.2878 0.808 0.904 0.000 0.096
#> GSM152048 1 0.0000 0.841 1.000 0.000 0.000
#> GSM152050 1 0.1529 0.830 0.960 0.040 0.000
#> GSM152052 1 0.5859 0.535 0.656 0.000 0.344
#> GSM152056 1 0.0747 0.839 0.984 0.016 0.000
#> GSM152060 1 0.1529 0.830 0.960 0.040 0.000
#> GSM152065 3 0.1529 0.877 0.040 0.000 0.960
#> GSM152066 1 0.0000 0.841 1.000 0.000 0.000
#> GSM152069 3 0.0000 0.885 0.000 0.000 1.000
#> GSM152070 3 0.2537 0.849 0.080 0.000 0.920
#> GSM152071 3 0.0000 0.885 0.000 0.000 1.000
#> GSM152072 3 0.1529 0.877 0.040 0.000 0.960
#> GSM152073 1 0.5529 0.602 0.704 0.000 0.296
#> GSM152078 3 0.2448 0.852 0.076 0.000 0.924
#> GSM152082 3 0.4178 0.737 0.172 0.000 0.828
#> GSM152086 1 0.0000 0.841 1.000 0.000 0.000
#> GSM152090 1 0.1753 0.824 0.952 0.000 0.048
#> GSM152092 1 0.5988 0.487 0.632 0.000 0.368
#> GSM152093 1 0.1411 0.832 0.964 0.036 0.000
#> GSM152094 1 0.1411 0.834 0.964 0.000 0.036
#> GSM152098 3 0.6225 0.103 0.432 0.000 0.568
#> GSM152110 1 0.0892 0.838 0.980 0.020 0.000
#> GSM152031 1 0.5882 0.527 0.652 0.000 0.348
#> GSM152037 1 0.1643 0.832 0.956 0.000 0.044
#> GSM152055 1 0.1529 0.830 0.960 0.040 0.000
#> GSM152061 1 0.1529 0.830 0.960 0.040 0.000
#> GSM152064 1 0.1529 0.830 0.960 0.040 0.000
#> GSM152087 1 0.0892 0.839 0.980 0.000 0.020
#> GSM152103 1 0.4062 0.780 0.836 0.000 0.164
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM152032 2 0.4981 0.25201 0.000 0.536 0.464 0.000
#> GSM152033 3 0.3074 0.37003 0.000 0.152 0.848 0.000
#> GSM152063 4 0.4967 0.50562 0.000 0.452 0.000 0.548
#> GSM152074 3 0.4999 -0.26426 0.000 0.492 0.508 0.000
#> GSM152080 2 0.2282 0.39876 0.000 0.924 0.052 0.024
#> GSM152081 4 0.4697 0.35863 0.356 0.000 0.000 0.644
#> GSM152083 2 0.4155 0.41043 0.000 0.756 0.240 0.004
#> GSM152091 2 0.4679 -0.25528 0.000 0.648 0.000 0.352
#> GSM152108 4 0.8076 0.25467 0.156 0.380 0.028 0.436
#> GSM152114 1 0.4509 0.54952 0.708 0.004 0.000 0.288
#> GSM152035 2 0.4643 -0.24724 0.000 0.656 0.000 0.344
#> GSM152039 4 0.1637 0.61009 0.060 0.000 0.000 0.940
#> GSM152041 4 0.3764 0.56673 0.216 0.000 0.000 0.784
#> GSM152044 4 0.4804 0.52875 0.000 0.384 0.000 0.616
#> GSM152045 3 0.2814 0.39295 0.000 0.132 0.868 0.000
#> GSM152051 4 0.4981 0.49534 0.000 0.464 0.000 0.536
#> GSM152054 3 0.4103 0.23280 0.000 0.256 0.744 0.000
#> GSM152057 4 0.4967 0.50562 0.000 0.452 0.000 0.548
#> GSM152058 1 0.0188 0.80917 0.996 0.004 0.000 0.000
#> GSM152067 2 0.5000 0.19050 0.000 0.504 0.496 0.000
#> GSM152068 4 0.4967 0.50562 0.000 0.452 0.000 0.548
#> GSM152075 4 0.3649 0.57337 0.204 0.000 0.000 0.796
#> GSM152076 4 0.1637 0.61009 0.060 0.000 0.000 0.940
#> GSM152079 4 0.4977 0.49916 0.000 0.460 0.000 0.540
#> GSM152084 2 0.9014 0.20554 0.276 0.436 0.084 0.204
#> GSM152089 4 0.6898 0.41437 0.164 0.224 0.004 0.608
#> GSM152095 4 0.1637 0.61009 0.060 0.000 0.000 0.940
#> GSM152096 2 0.4372 0.39976 0.000 0.728 0.268 0.004
#> GSM152097 4 0.4624 0.54484 0.000 0.340 0.000 0.660
#> GSM152099 4 0.4994 0.47862 0.000 0.480 0.000 0.520
#> GSM152106 4 0.4624 0.54484 0.000 0.340 0.000 0.660
#> GSM152107 2 0.5994 0.38173 0.000 0.636 0.068 0.296
#> GSM152109 2 0.5000 0.18957 0.000 0.500 0.500 0.000
#> GSM152111 1 0.2281 0.79396 0.904 0.000 0.000 0.096
#> GSM152112 2 0.8007 0.23507 0.016 0.416 0.184 0.384
#> GSM152113 2 0.4994 0.23427 0.000 0.520 0.480 0.000
#> GSM152115 3 0.4250 0.18966 0.000 0.276 0.724 0.000
#> GSM152030 4 0.3649 0.57337 0.204 0.000 0.000 0.796
#> GSM152038 3 0.1716 0.44442 0.000 0.064 0.936 0.000
#> GSM152042 4 0.4452 0.52250 0.260 0.008 0.000 0.732
#> GSM152062 2 0.4998 0.22493 0.000 0.512 0.488 0.000
#> GSM152077 1 0.1004 0.81379 0.972 0.004 0.000 0.024
#> GSM152088 2 0.4866 -0.35295 0.000 0.596 0.000 0.404
#> GSM152100 4 0.1637 0.61009 0.060 0.000 0.000 0.940
#> GSM152102 3 0.4996 -0.23028 0.000 0.484 0.516 0.000
#> GSM152104 4 0.4624 0.54484 0.000 0.340 0.000 0.660
#> GSM152028 3 0.3945 0.48914 0.216 0.004 0.780 0.000
#> GSM152029 2 0.6708 0.05837 0.088 0.464 0.448 0.000
#> GSM152049 1 0.0188 0.80917 0.996 0.004 0.000 0.000
#> GSM152053 4 0.4643 0.38440 0.344 0.000 0.000 0.656
#> GSM152059 3 0.5168 0.00189 0.492 0.004 0.504 0.000
#> GSM152085 1 0.0188 0.80874 0.996 0.000 0.004 0.000
#> GSM152101 3 0.4994 -0.22499 0.000 0.480 0.520 0.000
#> GSM152105 3 0.5085 0.29636 0.376 0.008 0.616 0.000
#> GSM152034 1 0.2654 0.78523 0.888 0.000 0.004 0.108
#> GSM152036 4 0.2921 0.59478 0.140 0.000 0.000 0.860
#> GSM152040 3 0.5168 -0.08733 0.496 0.004 0.500 0.000
#> GSM152043 1 0.4697 0.37612 0.644 0.000 0.356 0.000
#> GSM152046 1 0.1824 0.81227 0.936 0.000 0.004 0.060
#> GSM152047 1 0.4781 0.43176 0.660 0.004 0.336 0.000
#> GSM152048 1 0.0188 0.80917 0.996 0.004 0.000 0.000
#> GSM152050 1 0.2081 0.80131 0.916 0.000 0.000 0.084
#> GSM152052 1 0.5466 0.10423 0.548 0.016 0.436 0.000
#> GSM152056 1 0.1004 0.81379 0.972 0.004 0.000 0.024
#> GSM152060 1 0.1824 0.81227 0.936 0.000 0.004 0.060
#> GSM152065 3 0.1004 0.48049 0.024 0.004 0.972 0.000
#> GSM152066 1 0.1489 0.78458 0.952 0.004 0.044 0.000
#> GSM152069 3 0.5000 -0.26903 0.000 0.496 0.504 0.000
#> GSM152070 3 0.2266 0.49918 0.084 0.004 0.912 0.000
#> GSM152071 3 0.5000 -0.26903 0.000 0.496 0.504 0.000
#> GSM152072 3 0.3123 0.36882 0.000 0.156 0.844 0.000
#> GSM152073 3 0.5000 -0.03584 0.500 0.000 0.500 0.000
#> GSM152078 3 0.3370 0.48860 0.080 0.048 0.872 0.000
#> GSM152082 3 0.2149 0.49988 0.088 0.000 0.912 0.000
#> GSM152086 1 0.1398 0.78703 0.956 0.004 0.040 0.000
#> GSM152090 1 0.7046 0.35759 0.524 0.340 0.000 0.136
#> GSM152092 3 0.4535 0.41354 0.292 0.004 0.704 0.000
#> GSM152093 1 0.2944 0.76891 0.868 0.004 0.000 0.128
#> GSM152094 1 0.2868 0.70936 0.864 0.000 0.136 0.000
#> GSM152098 3 0.3400 0.49686 0.180 0.000 0.820 0.000
#> GSM152110 1 0.2266 0.80127 0.912 0.004 0.000 0.084
#> GSM152031 3 0.5288 0.05745 0.472 0.008 0.520 0.000
#> GSM152037 1 0.3494 0.66869 0.824 0.004 0.172 0.000
#> GSM152055 1 0.2334 0.79929 0.908 0.000 0.004 0.088
#> GSM152061 1 0.1824 0.81227 0.936 0.000 0.004 0.060
#> GSM152064 1 0.4088 0.64210 0.764 0.000 0.004 0.232
#> GSM152087 1 0.2973 0.70136 0.856 0.000 0.144 0.000
#> GSM152103 1 0.6819 0.12802 0.500 0.424 0.060 0.016
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM152032 3 0.1197 0.72471 0.000 0.000 0.952 0.000 0.048
#> GSM152033 5 0.5405 0.45020 0.000 0.000 0.256 0.104 0.640
#> GSM152063 2 0.0162 0.90172 0.000 0.996 0.000 0.004 0.000
#> GSM152074 3 0.2843 0.71058 0.000 0.000 0.876 0.048 0.076
#> GSM152080 3 0.4305 0.48544 0.000 0.296 0.688 0.012 0.004
#> GSM152081 4 0.5768 0.67358 0.268 0.076 0.024 0.632 0.000
#> GSM152083 3 0.2865 0.68492 0.000 0.132 0.856 0.008 0.004
#> GSM152091 2 0.2927 0.80681 0.000 0.872 0.068 0.060 0.000
#> GSM152108 4 0.8171 -0.01177 0.128 0.148 0.316 0.400 0.008
#> GSM152114 1 0.4000 0.68387 0.788 0.000 0.028 0.172 0.012
#> GSM152035 2 0.3844 0.72826 0.000 0.804 0.064 0.132 0.000
#> GSM152039 4 0.4773 0.64523 0.012 0.256 0.012 0.704 0.016
#> GSM152041 4 0.4686 0.74477 0.160 0.104 0.000 0.736 0.000
#> GSM152044 2 0.1830 0.87352 0.000 0.932 0.004 0.052 0.012
#> GSM152045 5 0.5783 0.43847 0.000 0.000 0.228 0.160 0.612
#> GSM152051 2 0.0290 0.90142 0.000 0.992 0.000 0.008 0.000
#> GSM152054 5 0.6401 0.11101 0.000 0.000 0.336 0.184 0.480
#> GSM152057 2 0.0162 0.90172 0.000 0.996 0.000 0.004 0.000
#> GSM152058 1 0.0955 0.86205 0.968 0.000 0.000 0.004 0.028
#> GSM152067 3 0.2491 0.71238 0.000 0.000 0.896 0.036 0.068
#> GSM152068 2 0.0162 0.90172 0.000 0.996 0.000 0.004 0.000
#> GSM152075 4 0.5085 0.74758 0.152 0.112 0.012 0.724 0.000
#> GSM152076 4 0.4773 0.64523 0.012 0.256 0.012 0.704 0.016
#> GSM152079 2 0.0290 0.90142 0.000 0.992 0.000 0.008 0.000
#> GSM152084 3 0.7163 0.41381 0.192 0.012 0.524 0.244 0.028
#> GSM152089 4 0.5004 0.65311 0.084 0.076 0.076 0.764 0.000
#> GSM152095 4 0.4773 0.64523 0.012 0.256 0.012 0.704 0.016
#> GSM152096 3 0.4142 0.68758 0.004 0.120 0.800 0.072 0.004
#> GSM152097 2 0.3459 0.80066 0.000 0.832 0.016 0.136 0.016
#> GSM152099 2 0.0693 0.89651 0.000 0.980 0.008 0.012 0.000
#> GSM152106 2 0.3459 0.80066 0.000 0.832 0.016 0.136 0.016
#> GSM152107 3 0.5540 0.45138 0.012 0.056 0.592 0.340 0.000
#> GSM152109 3 0.2110 0.71601 0.000 0.000 0.912 0.016 0.072
#> GSM152111 1 0.1251 0.85752 0.956 0.000 0.000 0.036 0.008
#> GSM152112 4 0.5831 0.29359 0.016 0.028 0.244 0.660 0.052
#> GSM152113 3 0.4973 0.69216 0.032 0.008 0.756 0.152 0.052
#> GSM152115 3 0.6349 0.00487 0.000 0.000 0.424 0.160 0.416
#> GSM152030 4 0.5855 0.74294 0.184 0.124 0.028 0.664 0.000
#> GSM152038 5 0.4032 0.63166 0.004 0.000 0.192 0.032 0.772
#> GSM152042 4 0.5910 0.72095 0.220 0.092 0.036 0.652 0.000
#> GSM152062 3 0.4551 0.69846 0.028 0.004 0.780 0.144 0.044
#> GSM152077 1 0.2095 0.84422 0.928 0.000 0.020 0.028 0.024
#> GSM152088 2 0.1444 0.87180 0.000 0.948 0.040 0.012 0.000
#> GSM152100 4 0.3878 0.68120 0.016 0.236 0.000 0.748 0.000
#> GSM152102 3 0.5808 0.61853 0.000 0.016 0.656 0.176 0.152
#> GSM152104 2 0.3413 0.80436 0.000 0.836 0.016 0.132 0.016
#> GSM152028 5 0.1591 0.74811 0.052 0.000 0.004 0.004 0.940
#> GSM152029 3 0.5692 0.58783 0.052 0.000 0.676 0.060 0.212
#> GSM152049 1 0.0510 0.86384 0.984 0.000 0.000 0.000 0.016
#> GSM152053 4 0.5863 0.71224 0.228 0.084 0.036 0.652 0.000
#> GSM152059 5 0.3935 0.68302 0.220 0.000 0.008 0.012 0.760
#> GSM152085 1 0.1195 0.86109 0.960 0.000 0.000 0.012 0.028
#> GSM152101 3 0.5608 0.62032 0.000 0.008 0.664 0.176 0.152
#> GSM152105 5 0.3552 0.72364 0.164 0.000 0.012 0.012 0.812
#> GSM152034 1 0.2951 0.82496 0.860 0.000 0.000 0.112 0.028
#> GSM152036 4 0.5256 0.70143 0.064 0.188 0.012 0.720 0.016
#> GSM152040 5 0.3197 0.73620 0.116 0.000 0.008 0.024 0.852
#> GSM152043 5 0.4152 0.56829 0.296 0.000 0.000 0.012 0.692
#> GSM152046 1 0.2628 0.83603 0.884 0.000 0.000 0.088 0.028
#> GSM152047 1 0.5548 -0.01002 0.480 0.000 0.008 0.048 0.464
#> GSM152048 1 0.0955 0.86205 0.968 0.000 0.000 0.004 0.028
#> GSM152050 1 0.0865 0.86172 0.972 0.000 0.000 0.024 0.004
#> GSM152052 5 0.4799 0.45597 0.360 0.000 0.012 0.012 0.616
#> GSM152056 1 0.0671 0.86332 0.980 0.000 0.000 0.004 0.016
#> GSM152060 1 0.2628 0.83603 0.884 0.000 0.000 0.088 0.028
#> GSM152065 5 0.2954 0.70526 0.004 0.000 0.064 0.056 0.876
#> GSM152066 1 0.1628 0.84923 0.936 0.000 0.000 0.008 0.056
#> GSM152069 3 0.2172 0.71471 0.000 0.000 0.908 0.016 0.076
#> GSM152070 5 0.2536 0.72195 0.004 0.000 0.044 0.052 0.900
#> GSM152071 3 0.2172 0.71471 0.000 0.000 0.908 0.016 0.076
#> GSM152072 5 0.5505 0.38969 0.000 0.000 0.304 0.092 0.604
#> GSM152073 5 0.3596 0.69321 0.212 0.000 0.000 0.012 0.776
#> GSM152078 5 0.3224 0.73042 0.044 0.000 0.080 0.012 0.864
#> GSM152082 5 0.2060 0.73338 0.012 0.000 0.036 0.024 0.928
#> GSM152086 1 0.1205 0.85680 0.956 0.000 0.000 0.004 0.040
#> GSM152090 3 0.7285 0.27299 0.332 0.008 0.452 0.180 0.028
#> GSM152092 5 0.2249 0.74448 0.096 0.000 0.000 0.008 0.896
#> GSM152093 1 0.3395 0.77184 0.848 0.000 0.028 0.108 0.016
#> GSM152094 1 0.3355 0.72945 0.804 0.000 0.000 0.012 0.184
#> GSM152098 5 0.2060 0.74142 0.024 0.000 0.036 0.012 0.928
#> GSM152110 1 0.1644 0.84959 0.940 0.000 0.004 0.048 0.008
#> GSM152031 5 0.3840 0.69818 0.196 0.000 0.008 0.016 0.780
#> GSM152037 1 0.3612 0.65977 0.764 0.000 0.000 0.008 0.228
#> GSM152055 1 0.2136 0.83744 0.904 0.000 0.000 0.088 0.008
#> GSM152061 1 0.2628 0.83603 0.884 0.000 0.000 0.088 0.028
#> GSM152064 1 0.3170 0.76670 0.828 0.000 0.008 0.160 0.004
#> GSM152087 1 0.3427 0.71966 0.796 0.000 0.000 0.012 0.192
#> GSM152103 3 0.6860 0.43602 0.296 0.008 0.544 0.112 0.040
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM152032 3 0.1918 0.7330 0.008 0.000 0.904 0.000 0.088 0.000
#> GSM152033 1 0.6641 0.1547 0.436 0.000 0.236 0.040 0.288 0.000
#> GSM152063 2 0.0436 0.8995 0.004 0.988 0.000 0.004 0.004 0.000
#> GSM152074 3 0.2386 0.7216 0.028 0.000 0.896 0.012 0.064 0.000
#> GSM152080 3 0.4806 0.5378 0.000 0.220 0.684 0.016 0.080 0.000
#> GSM152081 4 0.4774 0.7287 0.000 0.008 0.000 0.696 0.160 0.136
#> GSM152083 3 0.3559 0.6898 0.004 0.084 0.816 0.004 0.092 0.000
#> GSM152091 2 0.2288 0.8488 0.000 0.900 0.016 0.016 0.068 0.000
#> GSM152108 5 0.6635 0.3867 0.020 0.056 0.096 0.152 0.628 0.048
#> GSM152114 6 0.5284 0.4985 0.008 0.000 0.000 0.124 0.256 0.612
#> GSM152035 2 0.3528 0.5823 0.000 0.700 0.000 0.004 0.296 0.000
#> GSM152039 4 0.2355 0.7527 0.000 0.112 0.008 0.876 0.000 0.004
#> GSM152041 4 0.3868 0.7886 0.000 0.012 0.000 0.792 0.096 0.100
#> GSM152044 2 0.1836 0.8777 0.004 0.928 0.008 0.048 0.012 0.000
#> GSM152045 5 0.6562 0.0577 0.328 0.000 0.196 0.040 0.436 0.000
#> GSM152051 2 0.0363 0.8991 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM152054 5 0.6283 0.2246 0.244 0.000 0.200 0.036 0.520 0.000
#> GSM152057 2 0.0260 0.8999 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM152058 6 0.2051 0.8394 0.036 0.000 0.000 0.008 0.040 0.916
#> GSM152067 3 0.1333 0.7275 0.008 0.000 0.944 0.000 0.048 0.000
#> GSM152068 2 0.0291 0.8997 0.000 0.992 0.000 0.004 0.004 0.000
#> GSM152075 4 0.3903 0.7923 0.000 0.016 0.000 0.792 0.108 0.084
#> GSM152076 4 0.2355 0.7527 0.000 0.112 0.008 0.876 0.000 0.004
#> GSM152079 2 0.0260 0.8999 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM152084 5 0.7267 0.3522 0.072 0.008 0.208 0.084 0.544 0.084
#> GSM152089 5 0.4779 -0.1588 0.000 0.016 0.000 0.436 0.524 0.024
#> GSM152095 4 0.2355 0.7527 0.000 0.112 0.008 0.876 0.000 0.004
#> GSM152096 3 0.5262 0.2379 0.000 0.080 0.536 0.008 0.376 0.000
#> GSM152097 2 0.3499 0.7829 0.004 0.780 0.008 0.196 0.012 0.000
#> GSM152099 2 0.0458 0.8983 0.000 0.984 0.000 0.000 0.016 0.000
#> GSM152106 2 0.3499 0.7829 0.004 0.780 0.008 0.196 0.012 0.000
#> GSM152107 5 0.6417 0.3530 0.012 0.016 0.216 0.180 0.560 0.016
#> GSM152109 3 0.0547 0.7582 0.020 0.000 0.980 0.000 0.000 0.000
#> GSM152111 6 0.0806 0.8454 0.000 0.000 0.000 0.020 0.008 0.972
#> GSM152112 5 0.4555 0.3163 0.008 0.008 0.052 0.208 0.720 0.004
#> GSM152113 5 0.5850 0.2970 0.096 0.000 0.276 0.024 0.588 0.016
#> GSM152115 5 0.6427 0.1379 0.172 0.000 0.320 0.040 0.468 0.000
#> GSM152030 4 0.4541 0.7714 0.000 0.020 0.000 0.732 0.160 0.088
#> GSM152038 1 0.3546 0.7024 0.824 0.000 0.096 0.024 0.056 0.000
#> GSM152042 4 0.4892 0.6643 0.000 0.012 0.000 0.648 0.268 0.072
#> GSM152062 5 0.5968 0.2242 0.080 0.000 0.340 0.028 0.536 0.016
#> GSM152077 6 0.3917 0.7496 0.040 0.000 0.000 0.024 0.156 0.780
#> GSM152088 2 0.1605 0.8737 0.000 0.940 0.012 0.016 0.032 0.000
#> GSM152100 4 0.3703 0.7872 0.000 0.092 0.000 0.796 0.108 0.004
#> GSM152102 5 0.5573 0.1512 0.096 0.004 0.316 0.016 0.568 0.000
#> GSM152104 2 0.3371 0.7975 0.004 0.796 0.008 0.180 0.012 0.000
#> GSM152028 1 0.1750 0.7626 0.932 0.000 0.000 0.016 0.040 0.012
#> GSM152029 3 0.6765 0.1981 0.204 0.000 0.504 0.004 0.216 0.072
#> GSM152049 6 0.1167 0.8463 0.020 0.000 0.000 0.008 0.012 0.960
#> GSM152053 4 0.4921 0.6680 0.000 0.012 0.000 0.648 0.264 0.076
#> GSM152059 1 0.2700 0.7214 0.836 0.000 0.000 0.004 0.004 0.156
#> GSM152085 6 0.0551 0.8450 0.004 0.000 0.000 0.008 0.004 0.984
#> GSM152101 5 0.5397 0.1572 0.088 0.000 0.328 0.016 0.568 0.000
#> GSM152105 1 0.2936 0.7352 0.856 0.000 0.000 0.004 0.060 0.080
#> GSM152034 6 0.2340 0.8249 0.000 0.000 0.004 0.056 0.044 0.896
#> GSM152036 4 0.2151 0.7610 0.000 0.072 0.008 0.904 0.000 0.016
#> GSM152040 1 0.3093 0.7367 0.852 0.000 0.000 0.012 0.076 0.060
#> GSM152043 1 0.3302 0.6490 0.760 0.000 0.000 0.004 0.004 0.232
#> GSM152046 6 0.2344 0.8235 0.000 0.000 0.004 0.052 0.048 0.896
#> GSM152047 6 0.5731 0.2942 0.324 0.000 0.000 0.012 0.136 0.528
#> GSM152048 6 0.2051 0.8394 0.036 0.000 0.000 0.008 0.040 0.916
#> GSM152050 6 0.0508 0.8452 0.000 0.000 0.000 0.012 0.004 0.984
#> GSM152052 1 0.4455 0.6527 0.756 0.000 0.024 0.008 0.064 0.148
#> GSM152056 6 0.1838 0.8411 0.020 0.000 0.000 0.012 0.040 0.928
#> GSM152060 6 0.2344 0.8235 0.000 0.000 0.004 0.052 0.048 0.896
#> GSM152065 1 0.4030 0.6683 0.776 0.000 0.040 0.032 0.152 0.000
#> GSM152066 6 0.2445 0.8326 0.060 0.000 0.000 0.008 0.040 0.892
#> GSM152069 3 0.0692 0.7586 0.020 0.000 0.976 0.000 0.004 0.000
#> GSM152070 1 0.3627 0.6957 0.808 0.000 0.028 0.032 0.132 0.000
#> GSM152071 3 0.0692 0.7586 0.020 0.000 0.976 0.000 0.004 0.000
#> GSM152072 1 0.6744 0.0642 0.396 0.000 0.300 0.040 0.264 0.000
#> GSM152073 1 0.2700 0.7222 0.836 0.000 0.000 0.004 0.004 0.156
#> GSM152078 1 0.2259 0.7555 0.912 0.000 0.036 0.004 0.024 0.024
#> GSM152082 1 0.2688 0.7394 0.884 0.000 0.020 0.024 0.068 0.004
#> GSM152086 6 0.1757 0.8404 0.052 0.000 0.000 0.008 0.012 0.928
#> GSM152090 5 0.7967 0.2931 0.072 0.004 0.208 0.084 0.436 0.196
#> GSM152092 1 0.0748 0.7636 0.976 0.000 0.000 0.004 0.004 0.016
#> GSM152093 6 0.4789 0.6186 0.020 0.000 0.000 0.072 0.220 0.688
#> GSM152094 6 0.2848 0.7536 0.176 0.000 0.000 0.008 0.000 0.816
#> GSM152098 1 0.2051 0.7581 0.920 0.000 0.004 0.020 0.044 0.012
#> GSM152110 6 0.2239 0.8307 0.008 0.000 0.000 0.020 0.072 0.900
#> GSM152031 1 0.3065 0.7259 0.844 0.000 0.000 0.004 0.052 0.100
#> GSM152037 6 0.4354 0.6241 0.268 0.000 0.000 0.008 0.040 0.684
#> GSM152055 6 0.2344 0.8235 0.000 0.000 0.004 0.052 0.048 0.896
#> GSM152061 6 0.2344 0.8235 0.000 0.000 0.004 0.052 0.048 0.896
#> GSM152064 6 0.3221 0.7727 0.000 0.000 0.000 0.096 0.076 0.828
#> GSM152087 6 0.2848 0.7530 0.176 0.000 0.000 0.008 0.000 0.816
#> GSM152103 5 0.7568 0.2429 0.100 0.004 0.260 0.024 0.440 0.172
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 specimen(p) k
#> ATC:kmeans 85 9.69e-06 2
#> ATC:kmeans 82 3.40e-06 3
#> ATC:kmeans 38 5.08e-04 4
#> ATC:kmeans 74 1.42e-04 5
#> ATC:kmeans 68 2.25e-06 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "skmeans"]
# you can also extract it by
# res = res_list["ATC:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 10612 rows and 88 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 0.482 0.767 0.896 0.5031 0.504 0.504
#> 3 3 0.924 0.890 0.959 0.3350 0.710 0.482
#> 4 4 0.768 0.855 0.913 0.1197 0.853 0.592
#> 5 5 0.782 0.745 0.858 0.0667 0.926 0.713
#> 6 6 0.820 0.775 0.862 0.0393 0.946 0.746
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
#> GSM152032 2 0.9732 0.311 0.404 0.596
#> GSM152033 1 0.0000 0.829 1.000 0.000
#> GSM152063 2 0.0000 0.924 0.000 1.000
#> GSM152074 1 0.9710 0.330 0.600 0.400
#> GSM152080 2 0.7139 0.727 0.196 0.804
#> GSM152081 2 0.0000 0.924 0.000 1.000
#> GSM152083 2 0.7139 0.727 0.196 0.804
#> GSM152091 2 0.0000 0.924 0.000 1.000
#> GSM152108 2 0.0000 0.924 0.000 1.000
#> GSM152114 2 0.3733 0.846 0.072 0.928
#> GSM152035 2 0.0000 0.924 0.000 1.000
#> GSM152039 2 0.0000 0.924 0.000 1.000
#> GSM152041 2 0.0000 0.924 0.000 1.000
#> GSM152044 2 0.0000 0.924 0.000 1.000
#> GSM152045 1 0.0000 0.829 1.000 0.000
#> GSM152051 2 0.0000 0.924 0.000 1.000
#> GSM152054 1 0.7815 0.633 0.768 0.232
#> GSM152057 2 0.0000 0.924 0.000 1.000
#> GSM152058 1 0.6973 0.749 0.812 0.188
#> GSM152067 1 0.9710 0.330 0.600 0.400
#> GSM152068 2 0.0000 0.924 0.000 1.000
#> GSM152075 2 0.0000 0.924 0.000 1.000
#> GSM152076 2 0.0000 0.924 0.000 1.000
#> GSM152079 2 0.0000 0.924 0.000 1.000
#> GSM152084 2 0.8713 0.579 0.292 0.708
#> GSM152089 2 0.0000 0.924 0.000 1.000
#> GSM152095 2 0.0000 0.924 0.000 1.000
#> GSM152096 2 0.7139 0.727 0.196 0.804
#> GSM152097 2 0.0000 0.924 0.000 1.000
#> GSM152099 2 0.0000 0.924 0.000 1.000
#> GSM152106 2 0.0000 0.924 0.000 1.000
#> GSM152107 2 0.0938 0.915 0.012 0.988
#> GSM152109 1 0.9732 0.319 0.596 0.404
#> GSM152111 1 0.9635 0.470 0.612 0.388
#> GSM152112 2 0.0000 0.924 0.000 1.000
#> GSM152113 1 0.9686 0.340 0.604 0.396
#> GSM152115 1 0.9661 0.349 0.608 0.392
#> GSM152030 2 0.0000 0.924 0.000 1.000
#> GSM152038 1 0.0000 0.829 1.000 0.000
#> GSM152042 2 0.0000 0.924 0.000 1.000
#> GSM152062 1 0.9686 0.340 0.604 0.396
#> GSM152077 1 0.6973 0.749 0.812 0.188
#> GSM152088 2 0.0000 0.924 0.000 1.000
#> GSM152100 2 0.0000 0.924 0.000 1.000
#> GSM152102 2 0.7299 0.718 0.204 0.796
#> GSM152104 2 0.0000 0.924 0.000 1.000
#> GSM152028 1 0.0000 0.829 1.000 0.000
#> GSM152029 1 0.0000 0.829 1.000 0.000
#> GSM152049 1 0.7139 0.743 0.804 0.196
#> GSM152053 2 0.0000 0.924 0.000 1.000
#> GSM152059 1 0.0000 0.829 1.000 0.000
#> GSM152085 1 0.7056 0.746 0.808 0.192
#> GSM152101 2 0.7219 0.723 0.200 0.800
#> GSM152105 1 0.0000 0.829 1.000 0.000
#> GSM152034 1 0.9710 0.445 0.600 0.400
#> GSM152036 2 0.0000 0.924 0.000 1.000
#> GSM152040 1 0.0000 0.829 1.000 0.000
#> GSM152043 1 0.0000 0.829 1.000 0.000
#> GSM152046 1 0.7139 0.743 0.804 0.196
#> GSM152047 1 0.0000 0.829 1.000 0.000
#> GSM152048 1 0.6973 0.749 0.812 0.188
#> GSM152050 1 0.7139 0.743 0.804 0.196
#> GSM152052 1 0.0000 0.829 1.000 0.000
#> GSM152056 1 0.7139 0.743 0.804 0.196
#> GSM152060 1 0.7139 0.743 0.804 0.196
#> GSM152065 1 0.0000 0.829 1.000 0.000
#> GSM152066 1 0.0000 0.829 1.000 0.000
#> GSM152069 1 0.9686 0.340 0.604 0.396
#> GSM152070 1 0.0000 0.829 1.000 0.000
#> GSM152071 1 0.6801 0.699 0.820 0.180
#> GSM152072 1 0.0000 0.829 1.000 0.000
#> GSM152073 1 0.0000 0.829 1.000 0.000
#> GSM152078 1 0.0000 0.829 1.000 0.000
#> GSM152082 1 0.0000 0.829 1.000 0.000
#> GSM152086 1 0.0938 0.825 0.988 0.012
#> GSM152090 2 0.0000 0.924 0.000 1.000
#> GSM152092 1 0.0000 0.829 1.000 0.000
#> GSM152093 1 0.9909 0.343 0.556 0.444
#> GSM152094 1 0.0000 0.829 1.000 0.000
#> GSM152098 1 0.0000 0.829 1.000 0.000
#> GSM152110 1 0.7139 0.743 0.804 0.196
#> GSM152031 1 0.0000 0.829 1.000 0.000
#> GSM152037 1 0.0000 0.829 1.000 0.000
#> GSM152055 1 0.7139 0.743 0.804 0.196
#> GSM152061 1 0.7139 0.743 0.804 0.196
#> GSM152064 2 0.9754 0.110 0.408 0.592
#> GSM152087 1 0.0000 0.829 1.000 0.000
#> GSM152103 1 0.7815 0.651 0.768 0.232
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM152032 3 0.0000 0.9172 0.000 0.000 1.000
#> GSM152033 3 0.0000 0.9172 0.000 0.000 1.000
#> GSM152063 2 0.0000 0.9939 0.000 1.000 0.000
#> GSM152074 3 0.0000 0.9172 0.000 0.000 1.000
#> GSM152080 3 0.0000 0.9172 0.000 0.000 1.000
#> GSM152081 2 0.0000 0.9939 0.000 1.000 0.000
#> GSM152083 3 0.0000 0.9172 0.000 0.000 1.000
#> GSM152091 2 0.0000 0.9939 0.000 1.000 0.000
#> GSM152108 2 0.0000 0.9939 0.000 1.000 0.000
#> GSM152114 1 0.3816 0.7862 0.852 0.148 0.000
#> GSM152035 2 0.0747 0.9802 0.000 0.984 0.016
#> GSM152039 2 0.0000 0.9939 0.000 1.000 0.000
#> GSM152041 2 0.0000 0.9939 0.000 1.000 0.000
#> GSM152044 2 0.0000 0.9939 0.000 1.000 0.000
#> GSM152045 3 0.0000 0.9172 0.000 0.000 1.000
#> GSM152051 2 0.0000 0.9939 0.000 1.000 0.000
#> GSM152054 3 0.0000 0.9172 0.000 0.000 1.000
#> GSM152057 2 0.0000 0.9939 0.000 1.000 0.000
#> GSM152058 1 0.0000 0.9475 1.000 0.000 0.000
#> GSM152067 3 0.0000 0.9172 0.000 0.000 1.000
#> GSM152068 2 0.0000 0.9939 0.000 1.000 0.000
#> GSM152075 2 0.0000 0.9939 0.000 1.000 0.000
#> GSM152076 2 0.0000 0.9939 0.000 1.000 0.000
#> GSM152079 2 0.0000 0.9939 0.000 1.000 0.000
#> GSM152084 3 0.0592 0.9080 0.000 0.012 0.988
#> GSM152089 2 0.0000 0.9939 0.000 1.000 0.000
#> GSM152095 2 0.0000 0.9939 0.000 1.000 0.000
#> GSM152096 3 0.0000 0.9172 0.000 0.000 1.000
#> GSM152097 2 0.0000 0.9939 0.000 1.000 0.000
#> GSM152099 2 0.0000 0.9939 0.000 1.000 0.000
#> GSM152106 2 0.0000 0.9939 0.000 1.000 0.000
#> GSM152107 2 0.0000 0.9939 0.000 1.000 0.000
#> GSM152109 3 0.0000 0.9172 0.000 0.000 1.000
#> GSM152111 1 0.0000 0.9475 1.000 0.000 0.000
#> GSM152112 2 0.2448 0.9199 0.000 0.924 0.076
#> GSM152113 3 0.0000 0.9172 0.000 0.000 1.000
#> GSM152115 3 0.0000 0.9172 0.000 0.000 1.000
#> GSM152030 2 0.0000 0.9939 0.000 1.000 0.000
#> GSM152038 3 0.0000 0.9172 0.000 0.000 1.000
#> GSM152042 2 0.0000 0.9939 0.000 1.000 0.000
#> GSM152062 3 0.0000 0.9172 0.000 0.000 1.000
#> GSM152077 1 0.0000 0.9475 1.000 0.000 0.000
#> GSM152088 2 0.0000 0.9939 0.000 1.000 0.000
#> GSM152100 2 0.0000 0.9939 0.000 1.000 0.000
#> GSM152102 3 0.0000 0.9172 0.000 0.000 1.000
#> GSM152104 2 0.0000 0.9939 0.000 1.000 0.000
#> GSM152028 3 0.6274 0.2035 0.456 0.000 0.544
#> GSM152029 3 0.0000 0.9172 0.000 0.000 1.000
#> GSM152049 1 0.0000 0.9475 1.000 0.000 0.000
#> GSM152053 2 0.0000 0.9939 0.000 1.000 0.000
#> GSM152059 1 0.5016 0.6341 0.760 0.000 0.240
#> GSM152085 1 0.0000 0.9475 1.000 0.000 0.000
#> GSM152101 3 0.0000 0.9172 0.000 0.000 1.000
#> GSM152105 3 0.6309 0.0661 0.496 0.000 0.504
#> GSM152034 1 0.0000 0.9475 1.000 0.000 0.000
#> GSM152036 2 0.0000 0.9939 0.000 1.000 0.000
#> GSM152040 1 0.0000 0.9475 1.000 0.000 0.000
#> GSM152043 1 0.0000 0.9475 1.000 0.000 0.000
#> GSM152046 1 0.0000 0.9475 1.000 0.000 0.000
#> GSM152047 1 0.0000 0.9475 1.000 0.000 0.000
#> GSM152048 1 0.0000 0.9475 1.000 0.000 0.000
#> GSM152050 1 0.0000 0.9475 1.000 0.000 0.000
#> GSM152052 1 0.6244 0.1224 0.560 0.000 0.440
#> GSM152056 1 0.0000 0.9475 1.000 0.000 0.000
#> GSM152060 1 0.0000 0.9475 1.000 0.000 0.000
#> GSM152065 3 0.0000 0.9172 0.000 0.000 1.000
#> GSM152066 1 0.0000 0.9475 1.000 0.000 0.000
#> GSM152069 3 0.0000 0.9172 0.000 0.000 1.000
#> GSM152070 3 0.0000 0.9172 0.000 0.000 1.000
#> GSM152071 3 0.0000 0.9172 0.000 0.000 1.000
#> GSM152072 3 0.0000 0.9172 0.000 0.000 1.000
#> GSM152073 1 0.0747 0.9332 0.984 0.000 0.016
#> GSM152078 3 0.0000 0.9172 0.000 0.000 1.000
#> GSM152082 3 0.4555 0.7207 0.200 0.000 0.800
#> GSM152086 1 0.0000 0.9475 1.000 0.000 0.000
#> GSM152090 2 0.2448 0.9146 0.076 0.924 0.000
#> GSM152092 3 0.6280 0.1911 0.460 0.000 0.540
#> GSM152093 1 0.0000 0.9475 1.000 0.000 0.000
#> GSM152094 1 0.0000 0.9475 1.000 0.000 0.000
#> GSM152098 3 0.6111 0.3671 0.396 0.000 0.604
#> GSM152110 1 0.0000 0.9475 1.000 0.000 0.000
#> GSM152031 1 0.6225 0.1509 0.568 0.000 0.432
#> GSM152037 1 0.0000 0.9475 1.000 0.000 0.000
#> GSM152055 1 0.0000 0.9475 1.000 0.000 0.000
#> GSM152061 1 0.0000 0.9475 1.000 0.000 0.000
#> GSM152064 1 0.0000 0.9475 1.000 0.000 0.000
#> GSM152087 1 0.0000 0.9475 1.000 0.000 0.000
#> GSM152103 3 0.4235 0.7529 0.176 0.000 0.824
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM152032 3 0.2345 0.882 0.000 0.000 0.900 0.100
#> GSM152033 4 0.4072 0.603 0.000 0.000 0.252 0.748
#> GSM152063 2 0.0592 0.931 0.000 0.984 0.016 0.000
#> GSM152074 3 0.2589 0.881 0.000 0.000 0.884 0.116
#> GSM152080 3 0.2216 0.846 0.000 0.092 0.908 0.000
#> GSM152081 2 0.4998 0.815 0.128 0.780 0.088 0.004
#> GSM152083 3 0.2266 0.850 0.000 0.084 0.912 0.004
#> GSM152091 2 0.2647 0.848 0.000 0.880 0.120 0.000
#> GSM152108 2 0.0921 0.928 0.000 0.972 0.028 0.000
#> GSM152114 1 0.2795 0.851 0.896 0.012 0.088 0.004
#> GSM152035 2 0.1118 0.924 0.000 0.964 0.036 0.000
#> GSM152039 2 0.2334 0.928 0.000 0.908 0.088 0.004
#> GSM152041 2 0.2795 0.922 0.012 0.896 0.088 0.004
#> GSM152044 2 0.0592 0.931 0.000 0.984 0.016 0.000
#> GSM152045 4 0.1716 0.811 0.000 0.000 0.064 0.936
#> GSM152051 2 0.0817 0.929 0.000 0.976 0.024 0.000
#> GSM152054 4 0.4193 0.574 0.000 0.000 0.268 0.732
#> GSM152057 2 0.0817 0.929 0.000 0.976 0.024 0.000
#> GSM152058 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM152067 3 0.2589 0.881 0.000 0.000 0.884 0.116
#> GSM152068 2 0.0817 0.929 0.000 0.976 0.024 0.000
#> GSM152075 2 0.2334 0.928 0.000 0.908 0.088 0.004
#> GSM152076 2 0.2334 0.928 0.000 0.908 0.088 0.004
#> GSM152079 2 0.0817 0.929 0.000 0.976 0.024 0.000
#> GSM152084 3 0.0336 0.842 0.000 0.000 0.992 0.008
#> GSM152089 2 0.1940 0.930 0.000 0.924 0.076 0.000
#> GSM152095 2 0.2334 0.928 0.000 0.908 0.088 0.004
#> GSM152096 3 0.2216 0.846 0.000 0.092 0.908 0.000
#> GSM152097 2 0.0188 0.932 0.000 0.996 0.004 0.000
#> GSM152099 2 0.0817 0.929 0.000 0.976 0.024 0.000
#> GSM152106 2 0.0188 0.932 0.000 0.996 0.004 0.000
#> GSM152107 3 0.3907 0.574 0.000 0.232 0.768 0.000
#> GSM152109 3 0.2408 0.883 0.000 0.000 0.896 0.104
#> GSM152111 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM152112 2 0.3547 0.877 0.000 0.840 0.144 0.016
#> GSM152113 3 0.2760 0.875 0.000 0.000 0.872 0.128
#> GSM152115 4 0.4543 0.462 0.000 0.000 0.324 0.676
#> GSM152030 2 0.2334 0.928 0.000 0.908 0.088 0.004
#> GSM152038 4 0.1022 0.831 0.000 0.000 0.032 0.968
#> GSM152042 2 0.2334 0.928 0.000 0.908 0.088 0.004
#> GSM152062 3 0.2469 0.882 0.000 0.000 0.892 0.108
#> GSM152077 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM152088 2 0.2589 0.852 0.000 0.884 0.116 0.000
#> GSM152100 2 0.2334 0.928 0.000 0.908 0.088 0.004
#> GSM152102 3 0.3975 0.762 0.000 0.000 0.760 0.240
#> GSM152104 2 0.0469 0.931 0.000 0.988 0.012 0.000
#> GSM152028 4 0.0469 0.845 0.012 0.000 0.000 0.988
#> GSM152029 3 0.3400 0.841 0.000 0.000 0.820 0.180
#> GSM152049 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM152053 2 0.2334 0.928 0.000 0.908 0.088 0.004
#> GSM152059 4 0.3400 0.755 0.180 0.000 0.000 0.820
#> GSM152085 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM152101 3 0.3726 0.799 0.000 0.000 0.788 0.212
#> GSM152105 4 0.1302 0.841 0.044 0.000 0.000 0.956
#> GSM152034 1 0.0188 0.950 0.996 0.000 0.000 0.004
#> GSM152036 2 0.2334 0.928 0.000 0.908 0.088 0.004
#> GSM152040 4 0.2345 0.821 0.100 0.000 0.000 0.900
#> GSM152043 4 0.3649 0.726 0.204 0.000 0.000 0.796
#> GSM152046 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM152047 4 0.2408 0.819 0.104 0.000 0.000 0.896
#> GSM152048 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM152050 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM152052 4 0.5543 0.415 0.360 0.000 0.028 0.612
#> GSM152056 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM152060 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM152065 4 0.0188 0.842 0.000 0.000 0.004 0.996
#> GSM152066 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM152069 3 0.2530 0.882 0.000 0.000 0.888 0.112
#> GSM152070 4 0.0188 0.842 0.000 0.000 0.004 0.996
#> GSM152071 3 0.2530 0.882 0.000 0.000 0.888 0.112
#> GSM152072 4 0.4331 0.536 0.000 0.000 0.288 0.712
#> GSM152073 4 0.2469 0.817 0.108 0.000 0.000 0.892
#> GSM152078 4 0.0188 0.842 0.000 0.000 0.004 0.996
#> GSM152082 4 0.0188 0.843 0.004 0.000 0.000 0.996
#> GSM152086 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM152090 3 0.4770 0.618 0.012 0.288 0.700 0.000
#> GSM152092 4 0.0592 0.845 0.016 0.000 0.000 0.984
#> GSM152093 1 0.0524 0.944 0.988 0.000 0.008 0.004
#> GSM152094 1 0.4222 0.629 0.728 0.000 0.000 0.272
#> GSM152098 4 0.0469 0.845 0.012 0.000 0.000 0.988
#> GSM152110 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM152031 4 0.2921 0.798 0.140 0.000 0.000 0.860
#> GSM152037 1 0.4072 0.662 0.748 0.000 0.000 0.252
#> GSM152055 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM152061 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM152064 1 0.0564 0.944 0.988 0.004 0.004 0.004
#> GSM152087 1 0.3873 0.702 0.772 0.000 0.000 0.228
#> GSM152103 3 0.3898 0.822 0.008 0.092 0.852 0.048
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM152032 3 0.0771 0.7657 0.000 0.004 0.976 0.000 0.020
#> GSM152033 5 0.5557 0.0423 0.000 0.068 0.460 0.000 0.472
#> GSM152063 2 0.2471 0.8798 0.000 0.864 0.000 0.136 0.000
#> GSM152074 3 0.1582 0.7602 0.000 0.028 0.944 0.000 0.028
#> GSM152080 3 0.4278 0.2385 0.000 0.452 0.548 0.000 0.000
#> GSM152081 4 0.0162 0.9449 0.004 0.000 0.000 0.996 0.000
#> GSM152083 3 0.2891 0.6763 0.000 0.176 0.824 0.000 0.000
#> GSM152091 2 0.2236 0.8489 0.000 0.908 0.024 0.068 0.000
#> GSM152108 2 0.2286 0.8699 0.000 0.888 0.004 0.108 0.000
#> GSM152114 1 0.3920 0.6216 0.724 0.004 0.004 0.268 0.000
#> GSM152035 2 0.1638 0.8421 0.000 0.932 0.004 0.064 0.000
#> GSM152039 4 0.0162 0.9478 0.000 0.004 0.000 0.996 0.000
#> GSM152041 4 0.0451 0.9422 0.008 0.004 0.000 0.988 0.000
#> GSM152044 2 0.2561 0.8755 0.000 0.856 0.000 0.144 0.000
#> GSM152045 5 0.5916 0.3320 0.000 0.120 0.336 0.000 0.544
#> GSM152051 2 0.2424 0.8811 0.000 0.868 0.000 0.132 0.000
#> GSM152054 3 0.6062 -0.0381 0.000 0.120 0.464 0.000 0.416
#> GSM152057 2 0.2424 0.8811 0.000 0.868 0.000 0.132 0.000
#> GSM152058 1 0.0000 0.9131 1.000 0.000 0.000 0.000 0.000
#> GSM152067 3 0.1725 0.7536 0.000 0.044 0.936 0.000 0.020
#> GSM152068 2 0.2424 0.8811 0.000 0.868 0.000 0.132 0.000
#> GSM152075 4 0.0000 0.9479 0.000 0.000 0.000 1.000 0.000
#> GSM152076 4 0.0162 0.9478 0.000 0.004 0.000 0.996 0.000
#> GSM152079 2 0.2424 0.8811 0.000 0.868 0.000 0.132 0.000
#> GSM152084 3 0.2311 0.7543 0.004 0.020 0.920 0.040 0.016
#> GSM152089 4 0.3177 0.7557 0.000 0.208 0.000 0.792 0.000
#> GSM152095 4 0.0162 0.9478 0.000 0.004 0.000 0.996 0.000
#> GSM152096 3 0.4126 0.3896 0.000 0.380 0.620 0.000 0.000
#> GSM152097 2 0.4074 0.6069 0.000 0.636 0.000 0.364 0.000
#> GSM152099 2 0.2424 0.8811 0.000 0.868 0.000 0.132 0.000
#> GSM152106 2 0.4015 0.6360 0.000 0.652 0.000 0.348 0.000
#> GSM152107 3 0.6175 0.3122 0.000 0.332 0.516 0.152 0.000
#> GSM152109 3 0.0798 0.7662 0.000 0.008 0.976 0.000 0.016
#> GSM152111 1 0.0324 0.9132 0.992 0.000 0.000 0.004 0.004
#> GSM152112 4 0.5869 0.5881 0.000 0.160 0.164 0.656 0.020
#> GSM152113 3 0.2036 0.7512 0.000 0.024 0.920 0.000 0.056
#> GSM152115 3 0.5988 0.1196 0.000 0.120 0.516 0.000 0.364
#> GSM152030 4 0.0000 0.9479 0.000 0.000 0.000 1.000 0.000
#> GSM152038 5 0.4003 0.5605 0.000 0.008 0.288 0.000 0.704
#> GSM152042 4 0.0000 0.9479 0.000 0.000 0.000 1.000 0.000
#> GSM152062 3 0.0865 0.7652 0.000 0.004 0.972 0.000 0.024
#> GSM152077 1 0.0451 0.9100 0.988 0.000 0.000 0.004 0.008
#> GSM152088 2 0.2707 0.8657 0.000 0.876 0.024 0.100 0.000
#> GSM152100 4 0.0404 0.9412 0.000 0.012 0.000 0.988 0.000
#> GSM152102 3 0.4711 0.6286 0.000 0.148 0.736 0.000 0.116
#> GSM152104 2 0.3636 0.7477 0.000 0.728 0.000 0.272 0.000
#> GSM152028 5 0.0693 0.8317 0.008 0.000 0.012 0.000 0.980
#> GSM152029 3 0.3487 0.6186 0.000 0.008 0.780 0.000 0.212
#> GSM152049 1 0.0000 0.9131 1.000 0.000 0.000 0.000 0.000
#> GSM152053 4 0.0000 0.9479 0.000 0.000 0.000 1.000 0.000
#> GSM152059 5 0.1851 0.7949 0.088 0.000 0.000 0.000 0.912
#> GSM152085 1 0.0510 0.9113 0.984 0.000 0.000 0.000 0.016
#> GSM152101 3 0.4312 0.6492 0.000 0.124 0.772 0.000 0.104
#> GSM152105 5 0.1670 0.8219 0.052 0.000 0.012 0.000 0.936
#> GSM152034 1 0.1018 0.9083 0.968 0.000 0.000 0.016 0.016
#> GSM152036 4 0.0162 0.9478 0.000 0.004 0.000 0.996 0.000
#> GSM152040 5 0.1419 0.8268 0.012 0.016 0.016 0.000 0.956
#> GSM152043 5 0.2074 0.7821 0.104 0.000 0.000 0.000 0.896
#> GSM152046 1 0.0798 0.9110 0.976 0.000 0.000 0.008 0.016
#> GSM152047 5 0.1904 0.8224 0.020 0.028 0.016 0.000 0.936
#> GSM152048 1 0.0000 0.9131 1.000 0.000 0.000 0.000 0.000
#> GSM152050 1 0.0324 0.9132 0.992 0.000 0.000 0.004 0.004
#> GSM152052 5 0.4359 0.6646 0.188 0.004 0.052 0.000 0.756
#> GSM152056 1 0.0000 0.9131 1.000 0.000 0.000 0.000 0.000
#> GSM152060 1 0.0798 0.9110 0.976 0.000 0.000 0.008 0.016
#> GSM152065 5 0.2144 0.7984 0.000 0.020 0.068 0.000 0.912
#> GSM152066 1 0.0162 0.9124 0.996 0.000 0.000 0.000 0.004
#> GSM152069 3 0.0798 0.7662 0.000 0.008 0.976 0.000 0.016
#> GSM152070 5 0.1386 0.8238 0.000 0.016 0.032 0.000 0.952
#> GSM152071 3 0.0798 0.7662 0.000 0.008 0.976 0.000 0.016
#> GSM152072 5 0.5507 0.0722 0.000 0.064 0.456 0.000 0.480
#> GSM152073 5 0.0880 0.8269 0.032 0.000 0.000 0.000 0.968
#> GSM152078 5 0.0955 0.8295 0.004 0.000 0.028 0.000 0.968
#> GSM152082 5 0.0771 0.8308 0.004 0.000 0.020 0.000 0.976
#> GSM152086 1 0.0162 0.9124 0.996 0.000 0.000 0.000 0.004
#> GSM152090 2 0.5002 -0.1376 0.016 0.488 0.488 0.008 0.000
#> GSM152092 5 0.0798 0.8320 0.008 0.000 0.016 0.000 0.976
#> GSM152093 1 0.1202 0.8970 0.960 0.004 0.004 0.032 0.000
#> GSM152094 1 0.4201 0.3835 0.592 0.000 0.000 0.000 0.408
#> GSM152098 5 0.0579 0.8316 0.008 0.000 0.008 0.000 0.984
#> GSM152110 1 0.0162 0.9129 0.996 0.000 0.000 0.004 0.000
#> GSM152031 5 0.1830 0.8129 0.068 0.000 0.008 0.000 0.924
#> GSM152037 1 0.3816 0.5662 0.696 0.000 0.000 0.000 0.304
#> GSM152055 1 0.0693 0.9118 0.980 0.000 0.000 0.008 0.012
#> GSM152061 1 0.0798 0.9110 0.976 0.000 0.000 0.008 0.016
#> GSM152064 1 0.3280 0.7676 0.812 0.000 0.000 0.176 0.012
#> GSM152087 1 0.4126 0.4435 0.620 0.000 0.000 0.000 0.380
#> GSM152103 3 0.5235 0.4798 0.016 0.304 0.640 0.000 0.040
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM152032 3 0.1863 0.7969 0.016 0.004 0.920 0.000 0.060 0.000
#> GSM152033 5 0.4980 0.6077 0.280 0.004 0.092 0.000 0.624 0.000
#> GSM152063 2 0.0146 0.9771 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM152074 3 0.4373 0.4902 0.028 0.004 0.624 0.000 0.344 0.000
#> GSM152080 3 0.3470 0.6605 0.000 0.248 0.740 0.000 0.012 0.000
#> GSM152081 4 0.0582 0.9441 0.000 0.004 0.004 0.984 0.004 0.004
#> GSM152083 3 0.2733 0.7913 0.000 0.080 0.864 0.000 0.056 0.000
#> GSM152091 2 0.0405 0.9718 0.000 0.988 0.004 0.000 0.008 0.000
#> GSM152108 2 0.0291 0.9732 0.004 0.992 0.000 0.000 0.004 0.000
#> GSM152114 6 0.6815 0.1769 0.060 0.000 0.052 0.400 0.060 0.428
#> GSM152035 2 0.0458 0.9693 0.000 0.984 0.000 0.000 0.016 0.000
#> GSM152039 4 0.0260 0.9465 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM152041 4 0.0260 0.9465 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM152044 2 0.0458 0.9724 0.000 0.984 0.000 0.016 0.000 0.000
#> GSM152045 5 0.2842 0.8183 0.104 0.000 0.044 0.000 0.852 0.000
#> GSM152051 2 0.0146 0.9771 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM152054 5 0.2688 0.8361 0.068 0.000 0.064 0.000 0.868 0.000
#> GSM152057 2 0.0146 0.9771 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM152058 6 0.2747 0.8274 0.076 0.000 0.008 0.004 0.036 0.876
#> GSM152067 3 0.3717 0.4450 0.000 0.000 0.616 0.000 0.384 0.000
#> GSM152068 2 0.0146 0.9771 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM152075 4 0.0291 0.9467 0.000 0.004 0.004 0.992 0.000 0.000
#> GSM152076 4 0.0146 0.9470 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM152079 2 0.0146 0.9771 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM152084 3 0.2024 0.7839 0.020 0.008 0.924 0.012 0.036 0.000
#> GSM152089 4 0.5705 0.3091 0.000 0.308 0.000 0.504 0.188 0.000
#> GSM152095 4 0.0260 0.9465 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM152096 3 0.2704 0.7562 0.000 0.140 0.844 0.000 0.016 0.000
#> GSM152097 2 0.1863 0.8958 0.000 0.896 0.000 0.104 0.000 0.000
#> GSM152099 2 0.0146 0.9771 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM152106 2 0.1556 0.9210 0.000 0.920 0.000 0.080 0.000 0.000
#> GSM152107 3 0.6612 0.3694 0.000 0.260 0.484 0.200 0.056 0.000
#> GSM152109 3 0.1918 0.7947 0.008 0.000 0.904 0.000 0.088 0.000
#> GSM152111 6 0.0665 0.8407 0.008 0.000 0.004 0.000 0.008 0.980
#> GSM152112 5 0.3650 0.5408 0.000 0.004 0.008 0.272 0.716 0.000
#> GSM152113 3 0.3810 0.6869 0.036 0.004 0.752 0.000 0.208 0.000
#> GSM152115 5 0.2573 0.8284 0.024 0.000 0.112 0.000 0.864 0.000
#> GSM152030 4 0.0551 0.9449 0.000 0.004 0.008 0.984 0.004 0.000
#> GSM152038 1 0.4259 0.6284 0.716 0.004 0.060 0.000 0.220 0.000
#> GSM152042 4 0.0551 0.9449 0.000 0.004 0.008 0.984 0.004 0.000
#> GSM152062 3 0.2651 0.7919 0.036 0.004 0.872 0.000 0.088 0.000
#> GSM152077 6 0.3673 0.7796 0.148 0.000 0.008 0.008 0.036 0.800
#> GSM152088 2 0.0260 0.9725 0.000 0.992 0.008 0.000 0.000 0.000
#> GSM152100 4 0.0363 0.9437 0.000 0.012 0.000 0.988 0.000 0.000
#> GSM152102 5 0.2234 0.8169 0.004 0.000 0.124 0.000 0.872 0.000
#> GSM152104 2 0.0937 0.9554 0.000 0.960 0.000 0.040 0.000 0.000
#> GSM152028 1 0.1714 0.8119 0.908 0.000 0.000 0.000 0.092 0.000
#> GSM152029 3 0.2688 0.7747 0.068 0.000 0.868 0.000 0.064 0.000
#> GSM152049 6 0.1697 0.8405 0.036 0.000 0.004 0.004 0.020 0.936
#> GSM152053 4 0.0551 0.9449 0.000 0.004 0.008 0.984 0.004 0.000
#> GSM152059 1 0.1787 0.7923 0.920 0.000 0.004 0.000 0.008 0.068
#> GSM152085 6 0.1261 0.8314 0.024 0.000 0.000 0.000 0.024 0.952
#> GSM152101 5 0.2278 0.8134 0.004 0.000 0.128 0.000 0.868 0.000
#> GSM152105 1 0.1346 0.7968 0.952 0.000 0.016 0.000 0.024 0.008
#> GSM152034 6 0.2109 0.8221 0.024 0.000 0.004 0.024 0.028 0.920
#> GSM152036 4 0.0146 0.9470 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM152040 1 0.3271 0.7241 0.760 0.000 0.000 0.000 0.232 0.008
#> GSM152043 1 0.1918 0.7846 0.904 0.000 0.000 0.000 0.008 0.088
#> GSM152046 6 0.1341 0.8304 0.024 0.000 0.000 0.000 0.028 0.948
#> GSM152047 1 0.4946 0.5419 0.616 0.000 0.000 0.000 0.284 0.100
#> GSM152048 6 0.2635 0.8298 0.068 0.000 0.008 0.004 0.036 0.884
#> GSM152050 6 0.0405 0.8391 0.004 0.000 0.000 0.000 0.008 0.988
#> GSM152052 1 0.3935 0.6971 0.808 0.000 0.092 0.004 0.052 0.044
#> GSM152056 6 0.2392 0.8324 0.064 0.000 0.004 0.004 0.032 0.896
#> GSM152060 6 0.1341 0.8304 0.024 0.000 0.000 0.000 0.028 0.948
#> GSM152065 1 0.3151 0.7040 0.748 0.000 0.000 0.000 0.252 0.000
#> GSM152066 6 0.2692 0.8290 0.072 0.000 0.008 0.004 0.036 0.880
#> GSM152069 3 0.2212 0.7877 0.008 0.000 0.880 0.000 0.112 0.000
#> GSM152070 1 0.3266 0.6911 0.728 0.000 0.000 0.000 0.272 0.000
#> GSM152071 3 0.2212 0.7877 0.008 0.000 0.880 0.000 0.112 0.000
#> GSM152072 5 0.3806 0.7850 0.152 0.000 0.076 0.000 0.772 0.000
#> GSM152073 1 0.1856 0.8105 0.920 0.000 0.000 0.000 0.048 0.032
#> GSM152078 1 0.2747 0.7989 0.860 0.000 0.044 0.000 0.096 0.000
#> GSM152082 1 0.1863 0.8093 0.896 0.000 0.000 0.000 0.104 0.000
#> GSM152086 6 0.2329 0.8370 0.048 0.000 0.008 0.004 0.036 0.904
#> GSM152090 3 0.3156 0.7399 0.012 0.052 0.860 0.000 0.064 0.012
#> GSM152092 1 0.1765 0.8117 0.904 0.000 0.000 0.000 0.096 0.000
#> GSM152093 6 0.5300 0.7500 0.064 0.000 0.056 0.084 0.064 0.732
#> GSM152094 6 0.4602 -0.0317 0.484 0.000 0.004 0.000 0.028 0.484
#> GSM152098 1 0.2053 0.8094 0.888 0.000 0.000 0.000 0.108 0.004
#> GSM152110 6 0.1649 0.8395 0.036 0.000 0.000 0.000 0.032 0.932
#> GSM152031 1 0.1086 0.7954 0.964 0.000 0.012 0.000 0.012 0.012
#> GSM152037 1 0.4932 -0.0833 0.516 0.000 0.008 0.004 0.036 0.436
#> GSM152055 6 0.0692 0.8359 0.004 0.000 0.000 0.000 0.020 0.976
#> GSM152061 6 0.1341 0.8304 0.024 0.000 0.000 0.000 0.028 0.948
#> GSM152064 6 0.3780 0.6256 0.004 0.000 0.000 0.248 0.020 0.728
#> GSM152087 6 0.4331 0.0533 0.464 0.000 0.000 0.000 0.020 0.516
#> GSM152103 3 0.2520 0.7568 0.012 0.020 0.896 0.000 0.060 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 specimen(p) k
#> ATC:skmeans 76 4.23e-08 2
#> ATC:skmeans 82 8.61e-05 3
#> ATC:skmeans 86 7.87e-05 4
#> ATC:skmeans 76 9.13e-05 5
#> ATC:skmeans 80 1.74e-03 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "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 10612 rows and 88 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 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 0.562 0.818 0.919 0.4999 0.495 0.495
#> 3 3 0.590 0.770 0.857 0.2931 0.773 0.577
#> 4 4 0.902 0.878 0.951 0.1379 0.686 0.323
#> 5 5 0.822 0.851 0.899 0.0831 0.895 0.626
#> 6 6 0.796 0.718 0.835 0.0363 0.956 0.781
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
#> GSM152032 2 0.4939 0.8431 0.108 0.892
#> GSM152033 1 0.0000 0.8745 1.000 0.000
#> GSM152063 2 0.0000 0.9351 0.000 1.000
#> GSM152074 1 0.9732 0.3842 0.596 0.404
#> GSM152080 2 0.0376 0.9349 0.004 0.996
#> GSM152081 2 0.0376 0.9349 0.004 0.996
#> GSM152083 2 0.4939 0.8431 0.108 0.892
#> GSM152091 2 0.0000 0.9351 0.000 1.000
#> GSM152108 2 0.3114 0.9014 0.056 0.944
#> GSM152114 2 0.3584 0.8910 0.068 0.932
#> GSM152035 2 0.0000 0.9351 0.000 1.000
#> GSM152039 2 0.0000 0.9351 0.000 1.000
#> GSM152041 2 0.3584 0.8910 0.068 0.932
#> GSM152044 2 0.0000 0.9351 0.000 1.000
#> GSM152045 1 0.0000 0.8745 1.000 0.000
#> GSM152051 2 0.0000 0.9351 0.000 1.000
#> GSM152054 1 0.0000 0.8745 1.000 0.000
#> GSM152057 2 0.0000 0.9351 0.000 1.000
#> GSM152058 1 0.4815 0.8308 0.896 0.104
#> GSM152067 1 0.9580 0.4408 0.620 0.380
#> GSM152068 2 0.0000 0.9351 0.000 1.000
#> GSM152075 2 0.0376 0.9349 0.004 0.996
#> GSM152076 2 0.0000 0.9351 0.000 1.000
#> GSM152079 2 0.0000 0.9351 0.000 1.000
#> GSM152084 2 0.0376 0.9349 0.004 0.996
#> GSM152089 2 0.1633 0.9243 0.024 0.976
#> GSM152095 2 0.0000 0.9351 0.000 1.000
#> GSM152096 2 0.0376 0.9349 0.004 0.996
#> GSM152097 2 0.0000 0.9351 0.000 1.000
#> GSM152099 2 0.0000 0.9351 0.000 1.000
#> GSM152106 2 0.0000 0.9351 0.000 1.000
#> GSM152107 2 0.0376 0.9349 0.004 0.996
#> GSM152109 1 0.9988 0.1509 0.520 0.480
#> GSM152111 2 0.8608 0.5707 0.284 0.716
#> GSM152112 2 0.7376 0.6879 0.208 0.792
#> GSM152113 2 0.9963 0.0656 0.464 0.536
#> GSM152115 1 0.2948 0.8540 0.948 0.052
#> GSM152030 2 0.0376 0.9349 0.004 0.996
#> GSM152038 1 0.1633 0.8666 0.976 0.024
#> GSM152042 2 0.0376 0.9349 0.004 0.996
#> GSM152062 2 0.4939 0.8431 0.108 0.892
#> GSM152077 2 0.9000 0.5119 0.316 0.684
#> GSM152088 2 0.0000 0.9351 0.000 1.000
#> GSM152100 2 0.0000 0.9351 0.000 1.000
#> GSM152102 1 0.4161 0.8377 0.916 0.084
#> GSM152104 2 0.0000 0.9351 0.000 1.000
#> GSM152028 1 0.0000 0.8745 1.000 0.000
#> GSM152029 1 0.9427 0.4720 0.640 0.360
#> GSM152049 1 0.4939 0.8289 0.892 0.108
#> GSM152053 2 0.0376 0.9349 0.004 0.996
#> GSM152059 1 0.0000 0.8745 1.000 0.000
#> GSM152085 1 0.5842 0.8016 0.860 0.140
#> GSM152101 2 0.9044 0.5333 0.320 0.680
#> GSM152105 1 0.0000 0.8745 1.000 0.000
#> GSM152034 2 0.0376 0.9349 0.004 0.996
#> GSM152036 2 0.0000 0.9351 0.000 1.000
#> GSM152040 1 0.0000 0.8745 1.000 0.000
#> GSM152043 1 0.0000 0.8745 1.000 0.000
#> GSM152046 1 0.4815 0.8308 0.896 0.104
#> GSM152047 1 0.2603 0.8579 0.956 0.044
#> GSM152048 1 0.3733 0.8480 0.928 0.072
#> GSM152050 2 0.6247 0.7980 0.156 0.844
#> GSM152052 1 0.9000 0.5354 0.684 0.316
#> GSM152056 1 0.4815 0.8308 0.896 0.104
#> GSM152060 1 0.4815 0.8308 0.896 0.104
#> GSM152065 1 0.0000 0.8745 1.000 0.000
#> GSM152066 1 0.0000 0.8745 1.000 0.000
#> GSM152069 1 0.9580 0.4408 0.620 0.380
#> GSM152070 1 0.0000 0.8745 1.000 0.000
#> GSM152071 1 0.9552 0.4475 0.624 0.376
#> GSM152072 1 0.2603 0.8579 0.956 0.044
#> GSM152073 1 0.0000 0.8745 1.000 0.000
#> GSM152078 1 0.0000 0.8745 1.000 0.000
#> GSM152082 1 0.0000 0.8745 1.000 0.000
#> GSM152086 1 0.4815 0.8308 0.896 0.104
#> GSM152090 2 0.0376 0.9349 0.004 0.996
#> GSM152092 1 0.0000 0.8745 1.000 0.000
#> GSM152093 2 0.1633 0.9243 0.024 0.976
#> GSM152094 1 0.0000 0.8745 1.000 0.000
#> GSM152098 1 0.0000 0.8745 1.000 0.000
#> GSM152110 1 0.9922 0.2195 0.552 0.448
#> GSM152031 1 0.0000 0.8745 1.000 0.000
#> GSM152037 1 0.0000 0.8745 1.000 0.000
#> GSM152055 1 0.8861 0.5743 0.696 0.304
#> GSM152061 1 0.4815 0.8308 0.896 0.104
#> GSM152064 2 0.4562 0.8673 0.096 0.904
#> GSM152087 1 0.0000 0.8745 1.000 0.000
#> GSM152103 2 0.1843 0.9225 0.028 0.972
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM152032 3 0.5363 0.745 0.276 0.000 0.724
#> GSM152033 1 0.0000 0.780 1.000 0.000 0.000
#> GSM152063 2 0.0000 0.962 0.000 1.000 0.000
#> GSM152074 1 0.6026 -0.108 0.624 0.000 0.376
#> GSM152080 3 0.5859 0.475 0.000 0.344 0.656
#> GSM152081 3 0.0747 0.778 0.016 0.000 0.984
#> GSM152083 3 0.7416 0.719 0.276 0.068 0.656
#> GSM152091 2 0.0000 0.962 0.000 1.000 0.000
#> GSM152108 3 0.0747 0.778 0.016 0.000 0.984
#> GSM152114 3 0.0000 0.775 0.000 0.000 1.000
#> GSM152035 2 0.1411 0.939 0.000 0.964 0.036
#> GSM152039 2 0.2261 0.924 0.000 0.932 0.068
#> GSM152041 3 0.0000 0.775 0.000 0.000 1.000
#> GSM152044 2 0.0000 0.962 0.000 1.000 0.000
#> GSM152045 1 0.0000 0.780 1.000 0.000 0.000
#> GSM152051 2 0.0000 0.962 0.000 1.000 0.000
#> GSM152054 1 0.1643 0.746 0.956 0.000 0.044
#> GSM152057 2 0.0000 0.962 0.000 1.000 0.000
#> GSM152058 1 0.5363 0.776 0.724 0.000 0.276
#> GSM152067 3 0.5859 0.710 0.344 0.000 0.656
#> GSM152068 2 0.0000 0.962 0.000 1.000 0.000
#> GSM152075 3 0.0000 0.775 0.000 0.000 1.000
#> GSM152076 2 0.2261 0.924 0.000 0.932 0.068
#> GSM152079 2 0.0000 0.962 0.000 1.000 0.000
#> GSM152084 3 0.4796 0.765 0.220 0.000 0.780
#> GSM152089 3 0.0000 0.775 0.000 0.000 1.000
#> GSM152095 2 0.4291 0.805 0.000 0.820 0.180
#> GSM152096 3 0.5363 0.745 0.276 0.000 0.724
#> GSM152097 2 0.0000 0.962 0.000 1.000 0.000
#> GSM152099 2 0.0000 0.962 0.000 1.000 0.000
#> GSM152106 2 0.0000 0.962 0.000 1.000 0.000
#> GSM152107 3 0.5363 0.745 0.276 0.000 0.724
#> GSM152109 3 0.5859 0.710 0.344 0.000 0.656
#> GSM152111 3 0.0000 0.775 0.000 0.000 1.000
#> GSM152112 3 0.6280 0.519 0.460 0.000 0.540
#> GSM152113 3 0.5363 0.745 0.276 0.000 0.724
#> GSM152115 1 0.1643 0.746 0.956 0.000 0.044
#> GSM152030 3 0.0237 0.775 0.000 0.004 0.996
#> GSM152038 1 0.0000 0.780 1.000 0.000 0.000
#> GSM152042 3 0.0000 0.775 0.000 0.000 1.000
#> GSM152062 3 0.5363 0.745 0.276 0.000 0.724
#> GSM152077 3 0.5678 0.225 0.316 0.000 0.684
#> GSM152088 2 0.0000 0.962 0.000 1.000 0.000
#> GSM152100 2 0.2356 0.922 0.000 0.928 0.072
#> GSM152102 1 0.2711 0.704 0.912 0.000 0.088
#> GSM152104 2 0.0000 0.962 0.000 1.000 0.000
#> GSM152028 1 0.0000 0.780 1.000 0.000 0.000
#> GSM152029 3 0.5882 0.707 0.348 0.000 0.652
#> GSM152049 1 0.6008 0.682 0.628 0.000 0.372
#> GSM152053 3 0.3340 0.772 0.120 0.000 0.880
#> GSM152059 1 0.3340 0.799 0.880 0.000 0.120
#> GSM152085 1 0.5905 0.710 0.648 0.000 0.352
#> GSM152101 3 0.6260 0.549 0.448 0.000 0.552
#> GSM152105 1 0.0000 0.780 1.000 0.000 0.000
#> GSM152034 3 0.0000 0.775 0.000 0.000 1.000
#> GSM152036 2 0.4605 0.783 0.000 0.796 0.204
#> GSM152040 1 0.4887 0.790 0.772 0.000 0.228
#> GSM152043 1 0.3941 0.800 0.844 0.000 0.156
#> GSM152046 1 0.5363 0.776 0.724 0.000 0.276
#> GSM152047 1 0.4291 0.798 0.820 0.000 0.180
#> GSM152048 1 0.5363 0.776 0.724 0.000 0.276
#> GSM152050 3 0.0000 0.775 0.000 0.000 1.000
#> GSM152052 3 0.6045 0.493 0.380 0.000 0.620
#> GSM152056 1 0.5363 0.776 0.724 0.000 0.276
#> GSM152060 1 0.5363 0.776 0.724 0.000 0.276
#> GSM152065 1 0.0000 0.780 1.000 0.000 0.000
#> GSM152066 1 0.5363 0.776 0.724 0.000 0.276
#> GSM152069 3 0.5905 0.703 0.352 0.000 0.648
#> GSM152070 1 0.0000 0.780 1.000 0.000 0.000
#> GSM152071 3 0.5859 0.710 0.344 0.000 0.656
#> GSM152072 1 0.0000 0.780 1.000 0.000 0.000
#> GSM152073 1 0.3340 0.799 0.880 0.000 0.120
#> GSM152078 1 0.0000 0.780 1.000 0.000 0.000
#> GSM152082 1 0.0000 0.780 1.000 0.000 0.000
#> GSM152086 1 0.5363 0.776 0.724 0.000 0.276
#> GSM152090 3 0.0000 0.775 0.000 0.000 1.000
#> GSM152092 1 0.3340 0.799 0.880 0.000 0.120
#> GSM152093 3 0.0000 0.775 0.000 0.000 1.000
#> GSM152094 1 0.5363 0.776 0.724 0.000 0.276
#> GSM152098 1 0.0000 0.780 1.000 0.000 0.000
#> GSM152110 1 0.6180 0.626 0.584 0.000 0.416
#> GSM152031 1 0.0000 0.780 1.000 0.000 0.000
#> GSM152037 1 0.5363 0.776 0.724 0.000 0.276
#> GSM152055 1 0.5785 0.725 0.668 0.000 0.332
#> GSM152061 1 0.5363 0.776 0.724 0.000 0.276
#> GSM152064 3 0.0000 0.775 0.000 0.000 1.000
#> GSM152087 1 0.5363 0.776 0.724 0.000 0.276
#> GSM152103 3 0.3879 0.769 0.152 0.000 0.848
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM152032 3 0.0000 0.974 0.000 0.000 1.000 0.000
#> GSM152033 3 0.0000 0.974 0.000 0.000 1.000 0.000
#> GSM152063 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM152074 3 0.0000 0.974 0.000 0.000 1.000 0.000
#> GSM152080 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM152081 4 0.0000 0.935 0.000 0.000 0.000 1.000
#> GSM152083 3 0.2345 0.864 0.000 0.100 0.900 0.000
#> GSM152091 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM152108 4 0.5613 0.310 0.380 0.000 0.028 0.592
#> GSM152114 1 0.0000 0.887 1.000 0.000 0.000 0.000
#> GSM152035 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM152039 4 0.0000 0.935 0.000 0.000 0.000 1.000
#> GSM152041 1 0.4746 0.380 0.632 0.000 0.000 0.368
#> GSM152044 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM152045 3 0.0000 0.974 0.000 0.000 1.000 0.000
#> GSM152051 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM152054 3 0.0000 0.974 0.000 0.000 1.000 0.000
#> GSM152057 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM152058 1 0.0000 0.887 1.000 0.000 0.000 0.000
#> GSM152067 3 0.0000 0.974 0.000 0.000 1.000 0.000
#> GSM152068 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM152075 4 0.0000 0.935 0.000 0.000 0.000 1.000
#> GSM152076 4 0.0000 0.935 0.000 0.000 0.000 1.000
#> GSM152079 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM152084 4 0.0895 0.925 0.020 0.000 0.004 0.976
#> GSM152089 4 0.4790 0.328 0.380 0.000 0.000 0.620
#> GSM152095 4 0.0000 0.935 0.000 0.000 0.000 1.000
#> GSM152096 4 0.0921 0.920 0.000 0.028 0.000 0.972
#> GSM152097 2 0.0469 0.990 0.000 0.988 0.000 0.012
#> GSM152099 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM152106 2 0.0469 0.990 0.000 0.988 0.000 0.012
#> GSM152107 4 0.0817 0.920 0.000 0.000 0.024 0.976
#> GSM152109 3 0.0000 0.974 0.000 0.000 1.000 0.000
#> GSM152111 1 0.0188 0.885 0.996 0.000 0.000 0.004
#> GSM152112 4 0.0469 0.929 0.000 0.000 0.012 0.988
#> GSM152113 3 0.0000 0.974 0.000 0.000 1.000 0.000
#> GSM152115 3 0.0000 0.974 0.000 0.000 1.000 0.000
#> GSM152030 4 0.0000 0.935 0.000 0.000 0.000 1.000
#> GSM152038 3 0.0000 0.974 0.000 0.000 1.000 0.000
#> GSM152042 4 0.0000 0.935 0.000 0.000 0.000 1.000
#> GSM152062 3 0.0000 0.974 0.000 0.000 1.000 0.000
#> GSM152077 1 0.0000 0.887 1.000 0.000 0.000 0.000
#> GSM152088 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM152100 4 0.0000 0.935 0.000 0.000 0.000 1.000
#> GSM152102 3 0.0000 0.974 0.000 0.000 1.000 0.000
#> GSM152104 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM152028 3 0.0000 0.974 0.000 0.000 1.000 0.000
#> GSM152029 3 0.0000 0.974 0.000 0.000 1.000 0.000
#> GSM152049 1 0.0000 0.887 1.000 0.000 0.000 0.000
#> GSM152053 4 0.0188 0.934 0.000 0.000 0.004 0.996
#> GSM152059 1 0.4817 0.458 0.612 0.000 0.388 0.000
#> GSM152085 1 0.0000 0.887 1.000 0.000 0.000 0.000
#> GSM152101 3 0.0188 0.970 0.000 0.000 0.996 0.004
#> GSM152105 3 0.0000 0.974 0.000 0.000 1.000 0.000
#> GSM152034 4 0.0707 0.926 0.020 0.000 0.000 0.980
#> GSM152036 4 0.0000 0.935 0.000 0.000 0.000 1.000
#> GSM152040 1 0.3486 0.755 0.812 0.000 0.188 0.000
#> GSM152043 1 0.4585 0.562 0.668 0.000 0.332 0.000
#> GSM152046 1 0.0000 0.887 1.000 0.000 0.000 0.000
#> GSM152047 1 0.3569 0.745 0.804 0.000 0.196 0.000
#> GSM152048 1 0.0000 0.887 1.000 0.000 0.000 0.000
#> GSM152050 1 0.0000 0.887 1.000 0.000 0.000 0.000
#> GSM152052 1 0.4817 0.458 0.612 0.000 0.388 0.000
#> GSM152056 1 0.0000 0.887 1.000 0.000 0.000 0.000
#> GSM152060 1 0.0000 0.887 1.000 0.000 0.000 0.000
#> GSM152065 3 0.0000 0.974 0.000 0.000 1.000 0.000
#> GSM152066 1 0.0000 0.887 1.000 0.000 0.000 0.000
#> GSM152069 3 0.0000 0.974 0.000 0.000 1.000 0.000
#> GSM152070 3 0.0000 0.974 0.000 0.000 1.000 0.000
#> GSM152071 3 0.0000 0.974 0.000 0.000 1.000 0.000
#> GSM152072 3 0.0000 0.974 0.000 0.000 1.000 0.000
#> GSM152073 1 0.4817 0.458 0.612 0.000 0.388 0.000
#> GSM152078 3 0.0000 0.974 0.000 0.000 1.000 0.000
#> GSM152082 3 0.0000 0.974 0.000 0.000 1.000 0.000
#> GSM152086 1 0.0000 0.887 1.000 0.000 0.000 0.000
#> GSM152090 4 0.0817 0.923 0.024 0.000 0.000 0.976
#> GSM152092 3 0.4996 -0.140 0.484 0.000 0.516 0.000
#> GSM152093 1 0.0188 0.885 0.996 0.000 0.000 0.004
#> GSM152094 1 0.0000 0.887 1.000 0.000 0.000 0.000
#> GSM152098 3 0.0000 0.974 0.000 0.000 1.000 0.000
#> GSM152110 1 0.0000 0.887 1.000 0.000 0.000 0.000
#> GSM152031 3 0.0000 0.974 0.000 0.000 1.000 0.000
#> GSM152037 1 0.0000 0.887 1.000 0.000 0.000 0.000
#> GSM152055 1 0.0000 0.887 1.000 0.000 0.000 0.000
#> GSM152061 1 0.0000 0.887 1.000 0.000 0.000 0.000
#> GSM152064 1 0.2149 0.821 0.912 0.000 0.000 0.088
#> GSM152087 1 0.0000 0.887 1.000 0.000 0.000 0.000
#> GSM152103 1 0.4830 0.354 0.608 0.000 0.000 0.392
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM152032 3 0.1671 0.8653 0.000 0.000 0.924 0.000 0.076
#> GSM152033 3 0.2773 0.8854 0.000 0.000 0.836 0.000 0.164
#> GSM152063 2 0.0000 0.9722 0.000 1.000 0.000 0.000 0.000
#> GSM152074 3 0.2424 0.8838 0.000 0.000 0.868 0.000 0.132
#> GSM152080 2 0.3696 0.7860 0.000 0.772 0.212 0.016 0.000
#> GSM152081 4 0.1399 0.9087 0.028 0.000 0.000 0.952 0.020
#> GSM152083 3 0.0162 0.8234 0.000 0.000 0.996 0.004 0.000
#> GSM152091 2 0.0000 0.9722 0.000 1.000 0.000 0.000 0.000
#> GSM152108 4 0.4262 0.1719 0.440 0.000 0.000 0.560 0.000
#> GSM152114 1 0.0162 0.9331 0.996 0.000 0.000 0.004 0.000
#> GSM152035 2 0.0794 0.9522 0.000 0.972 0.000 0.028 0.000
#> GSM152039 4 0.3035 0.8906 0.000 0.032 0.000 0.856 0.112
#> GSM152041 1 0.4624 0.6603 0.744 0.000 0.000 0.144 0.112
#> GSM152044 2 0.0000 0.9722 0.000 1.000 0.000 0.000 0.000
#> GSM152045 5 0.2179 0.8011 0.000 0.000 0.112 0.000 0.888
#> GSM152051 2 0.0000 0.9722 0.000 1.000 0.000 0.000 0.000
#> GSM152054 3 0.3612 0.8043 0.000 0.000 0.732 0.000 0.268
#> GSM152057 2 0.0000 0.9722 0.000 1.000 0.000 0.000 0.000
#> GSM152058 1 0.0000 0.9357 1.000 0.000 0.000 0.000 0.000
#> GSM152067 3 0.0000 0.8258 0.000 0.000 1.000 0.000 0.000
#> GSM152068 2 0.0000 0.9722 0.000 1.000 0.000 0.000 0.000
#> GSM152075 4 0.1732 0.9105 0.000 0.000 0.000 0.920 0.080
#> GSM152076 4 0.2179 0.9059 0.000 0.000 0.000 0.888 0.112
#> GSM152079 2 0.0000 0.9722 0.000 1.000 0.000 0.000 0.000
#> GSM152084 4 0.0000 0.9094 0.000 0.000 0.000 1.000 0.000
#> GSM152089 4 0.2020 0.8989 0.000 0.000 0.000 0.900 0.100
#> GSM152095 4 0.2179 0.9059 0.000 0.000 0.000 0.888 0.112
#> GSM152096 4 0.3201 0.8396 0.000 0.052 0.096 0.852 0.000
#> GSM152097 2 0.2127 0.8984 0.000 0.892 0.000 0.000 0.108
#> GSM152099 2 0.0000 0.9722 0.000 1.000 0.000 0.000 0.000
#> GSM152106 2 0.1121 0.9475 0.000 0.956 0.000 0.000 0.044
#> GSM152107 4 0.0162 0.9094 0.000 0.000 0.004 0.996 0.000
#> GSM152109 3 0.0609 0.8113 0.000 0.000 0.980 0.020 0.000
#> GSM152111 1 0.0162 0.9328 0.996 0.000 0.000 0.004 0.000
#> GSM152112 4 0.0609 0.9065 0.000 0.000 0.020 0.980 0.000
#> GSM152113 3 0.2848 0.8868 0.000 0.000 0.840 0.004 0.156
#> GSM152115 3 0.2690 0.8862 0.000 0.000 0.844 0.000 0.156
#> GSM152030 4 0.1197 0.9106 0.000 0.000 0.000 0.952 0.048
#> GSM152038 3 0.3210 0.8631 0.000 0.000 0.788 0.000 0.212
#> GSM152042 4 0.0000 0.9094 0.000 0.000 0.000 1.000 0.000
#> GSM152062 3 0.2848 0.8868 0.000 0.000 0.840 0.004 0.156
#> GSM152077 1 0.0000 0.9357 1.000 0.000 0.000 0.000 0.000
#> GSM152088 2 0.0000 0.9722 0.000 1.000 0.000 0.000 0.000
#> GSM152100 4 0.2127 0.9067 0.000 0.000 0.000 0.892 0.108
#> GSM152102 3 0.2732 0.8862 0.000 0.000 0.840 0.000 0.160
#> GSM152104 2 0.0000 0.9722 0.000 1.000 0.000 0.000 0.000
#> GSM152028 5 0.3586 0.5630 0.000 0.000 0.264 0.000 0.736
#> GSM152029 5 0.4100 0.6933 0.000 0.000 0.192 0.044 0.764
#> GSM152049 1 0.0000 0.9357 1.000 0.000 0.000 0.000 0.000
#> GSM152053 4 0.0000 0.9094 0.000 0.000 0.000 1.000 0.000
#> GSM152059 5 0.2628 0.8407 0.088 0.000 0.028 0.000 0.884
#> GSM152085 1 0.4242 0.0913 0.572 0.000 0.000 0.000 0.428
#> GSM152101 3 0.4548 0.8353 0.000 0.000 0.748 0.096 0.156
#> GSM152105 3 0.3210 0.8631 0.000 0.000 0.788 0.000 0.212
#> GSM152034 4 0.1478 0.8886 0.064 0.000 0.000 0.936 0.000
#> GSM152036 4 0.2179 0.9059 0.000 0.000 0.000 0.888 0.112
#> GSM152040 5 0.2536 0.8261 0.128 0.000 0.004 0.000 0.868
#> GSM152043 5 0.2597 0.8400 0.092 0.000 0.024 0.000 0.884
#> GSM152046 1 0.0000 0.9357 1.000 0.000 0.000 0.000 0.000
#> GSM152047 5 0.3810 0.7738 0.168 0.000 0.000 0.040 0.792
#> GSM152048 1 0.0000 0.9357 1.000 0.000 0.000 0.000 0.000
#> GSM152050 1 0.0000 0.9357 1.000 0.000 0.000 0.000 0.000
#> GSM152052 5 0.4501 0.6602 0.276 0.000 0.008 0.020 0.696
#> GSM152056 1 0.0000 0.9357 1.000 0.000 0.000 0.000 0.000
#> GSM152060 1 0.0000 0.9357 1.000 0.000 0.000 0.000 0.000
#> GSM152065 3 0.3210 0.8631 0.000 0.000 0.788 0.000 0.212
#> GSM152066 1 0.0000 0.9357 1.000 0.000 0.000 0.000 0.000
#> GSM152069 3 0.0000 0.8258 0.000 0.000 1.000 0.000 0.000
#> GSM152070 5 0.2179 0.8011 0.000 0.000 0.112 0.000 0.888
#> GSM152071 3 0.0000 0.8258 0.000 0.000 1.000 0.000 0.000
#> GSM152072 3 0.2561 0.8808 0.000 0.000 0.856 0.000 0.144
#> GSM152073 5 0.2628 0.8407 0.088 0.000 0.028 0.000 0.884
#> GSM152078 3 0.3210 0.8631 0.000 0.000 0.788 0.000 0.212
#> GSM152082 5 0.2179 0.8011 0.000 0.000 0.112 0.000 0.888
#> GSM152086 1 0.0000 0.9357 1.000 0.000 0.000 0.000 0.000
#> GSM152090 4 0.1410 0.8900 0.060 0.000 0.000 0.940 0.000
#> GSM152092 5 0.2654 0.8358 0.064 0.000 0.048 0.000 0.888
#> GSM152093 1 0.1197 0.8978 0.952 0.000 0.000 0.048 0.000
#> GSM152094 5 0.3612 0.6687 0.268 0.000 0.000 0.000 0.732
#> GSM152098 5 0.2179 0.8011 0.000 0.000 0.112 0.000 0.888
#> GSM152110 1 0.0000 0.9357 1.000 0.000 0.000 0.000 0.000
#> GSM152031 3 0.4242 0.4735 0.000 0.000 0.572 0.000 0.428
#> GSM152037 1 0.3242 0.6562 0.784 0.000 0.000 0.000 0.216
#> GSM152055 1 0.0000 0.9357 1.000 0.000 0.000 0.000 0.000
#> GSM152061 1 0.0000 0.9357 1.000 0.000 0.000 0.000 0.000
#> GSM152064 1 0.1732 0.8634 0.920 0.000 0.000 0.080 0.000
#> GSM152087 5 0.3612 0.6687 0.268 0.000 0.000 0.000 0.732
#> GSM152103 4 0.4330 0.7664 0.152 0.000 0.028 0.784 0.036
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM152032 1 0.2179 0.7520 0.900 0.000 0.064 0.000 0.036 0.000
#> GSM152033 1 0.3490 0.7029 0.724 0.000 0.008 0.000 0.268 0.000
#> GSM152063 2 0.0000 0.9120 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152074 1 0.1500 0.7574 0.936 0.000 0.012 0.000 0.052 0.000
#> GSM152080 2 0.5936 0.4699 0.272 0.576 0.076 0.076 0.000 0.000
#> GSM152081 4 0.5934 0.3931 0.000 0.000 0.328 0.444 0.000 0.228
#> GSM152083 1 0.1901 0.7179 0.912 0.000 0.008 0.076 0.004 0.000
#> GSM152091 2 0.0000 0.9120 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152108 3 0.3383 0.4851 0.004 0.000 0.728 0.000 0.000 0.268
#> GSM152114 6 0.2378 0.7483 0.000 0.000 0.152 0.000 0.000 0.848
#> GSM152035 2 0.0000 0.9120 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152039 4 0.1719 0.7300 0.000 0.016 0.060 0.924 0.000 0.000
#> GSM152041 4 0.3857 0.0461 0.000 0.000 0.000 0.532 0.000 0.468
#> GSM152044 2 0.0000 0.9120 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152045 5 0.0547 0.8458 0.020 0.000 0.000 0.000 0.980 0.000
#> GSM152051 2 0.0000 0.9120 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152054 1 0.4837 0.6756 0.624 0.000 0.088 0.000 0.288 0.000
#> GSM152057 2 0.0000 0.9120 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152058 6 0.0000 0.9283 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM152067 1 0.2039 0.7027 0.904 0.000 0.000 0.076 0.020 0.000
#> GSM152068 2 0.0000 0.9120 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152075 4 0.3409 0.6608 0.000 0.000 0.300 0.700 0.000 0.000
#> GSM152076 4 0.1501 0.7402 0.000 0.000 0.076 0.924 0.000 0.000
#> GSM152079 2 0.0000 0.9120 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152084 3 0.0000 0.7193 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM152089 3 0.3821 0.5202 0.000 0.000 0.740 0.220 0.040 0.000
#> GSM152095 4 0.1501 0.7402 0.000 0.000 0.076 0.924 0.000 0.000
#> GSM152096 3 0.1794 0.7097 0.024 0.012 0.936 0.008 0.020 0.000
#> GSM152097 2 0.3833 0.3124 0.000 0.556 0.000 0.444 0.000 0.000
#> GSM152099 2 0.0000 0.9120 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152106 2 0.3151 0.6628 0.000 0.748 0.000 0.252 0.000 0.000
#> GSM152107 3 0.0146 0.7201 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM152109 1 0.5533 -0.1757 0.468 0.000 0.436 0.076 0.020 0.000
#> GSM152111 6 0.0146 0.9249 0.000 0.000 0.004 0.000 0.000 0.996
#> GSM152112 3 0.4576 -0.0201 0.400 0.000 0.560 0.000 0.040 0.000
#> GSM152113 1 0.4122 0.6926 0.724 0.000 0.212 0.000 0.064 0.000
#> GSM152115 1 0.2006 0.7550 0.892 0.000 0.004 0.000 0.104 0.000
#> GSM152030 4 0.3531 0.6406 0.000 0.000 0.328 0.672 0.000 0.000
#> GSM152038 1 0.3309 0.6946 0.720 0.000 0.000 0.000 0.280 0.000
#> GSM152042 3 0.0146 0.7183 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM152062 1 0.4122 0.6926 0.724 0.000 0.212 0.000 0.064 0.000
#> GSM152077 6 0.0000 0.9283 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM152088 2 0.0000 0.9120 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152100 4 0.4210 0.6488 0.000 0.000 0.288 0.672 0.040 0.000
#> GSM152102 1 0.4421 0.7263 0.716 0.000 0.128 0.000 0.156 0.000
#> GSM152104 2 0.0000 0.9120 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152028 5 0.2883 0.6208 0.212 0.000 0.000 0.000 0.788 0.000
#> GSM152029 3 0.4829 0.3575 0.080 0.000 0.612 0.000 0.308 0.000
#> GSM152049 6 0.0000 0.9283 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM152053 3 0.1196 0.7067 0.000 0.000 0.952 0.000 0.040 0.008
#> GSM152059 5 0.1444 0.8799 0.000 0.000 0.000 0.000 0.928 0.072
#> GSM152085 6 0.3804 0.2012 0.000 0.000 0.000 0.000 0.424 0.576
#> GSM152101 1 0.4704 0.6497 0.664 0.000 0.236 0.000 0.100 0.000
#> GSM152105 1 0.3309 0.6946 0.720 0.000 0.000 0.000 0.280 0.000
#> GSM152034 3 0.2823 0.5674 0.000 0.000 0.796 0.000 0.000 0.204
#> GSM152036 4 0.1501 0.7402 0.000 0.000 0.076 0.924 0.000 0.000
#> GSM152040 5 0.1501 0.8785 0.000 0.000 0.000 0.000 0.924 0.076
#> GSM152043 5 0.1588 0.8795 0.000 0.000 0.004 0.000 0.924 0.072
#> GSM152046 6 0.0146 0.9259 0.000 0.000 0.000 0.000 0.004 0.996
#> GSM152047 5 0.2488 0.8522 0.000 0.000 0.044 0.000 0.880 0.076
#> GSM152048 6 0.0000 0.9283 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM152050 6 0.0000 0.9283 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM152052 5 0.5162 0.1989 0.000 0.000 0.408 0.000 0.504 0.088
#> GSM152056 6 0.0000 0.9283 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM152060 6 0.0000 0.9283 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM152065 1 0.3309 0.6946 0.720 0.000 0.000 0.000 0.280 0.000
#> GSM152066 6 0.0000 0.9283 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM152069 1 0.2039 0.7027 0.904 0.000 0.000 0.076 0.020 0.000
#> GSM152070 5 0.1267 0.8452 0.060 0.000 0.000 0.000 0.940 0.000
#> GSM152071 1 0.2039 0.7027 0.904 0.000 0.000 0.076 0.020 0.000
#> GSM152072 1 0.2801 0.7353 0.860 0.000 0.000 0.072 0.068 0.000
#> GSM152073 5 0.1444 0.8799 0.000 0.000 0.000 0.000 0.928 0.072
#> GSM152078 1 0.3309 0.6946 0.720 0.000 0.000 0.000 0.280 0.000
#> GSM152082 5 0.1267 0.8452 0.060 0.000 0.000 0.000 0.940 0.000
#> GSM152086 6 0.0000 0.9283 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM152090 3 0.0865 0.7222 0.000 0.000 0.964 0.000 0.000 0.036
#> GSM152092 5 0.1387 0.8796 0.000 0.000 0.000 0.000 0.932 0.068
#> GSM152093 3 0.3862 0.1624 0.000 0.000 0.524 0.000 0.000 0.476
#> GSM152094 5 0.2340 0.8221 0.000 0.000 0.000 0.000 0.852 0.148
#> GSM152098 5 0.1267 0.8452 0.060 0.000 0.000 0.000 0.940 0.000
#> GSM152110 6 0.0000 0.9283 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM152031 1 0.3857 0.3605 0.532 0.000 0.000 0.000 0.468 0.000
#> GSM152037 6 0.3499 0.4352 0.000 0.000 0.000 0.000 0.320 0.680
#> GSM152055 6 0.0000 0.9283 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM152061 6 0.0146 0.9259 0.000 0.000 0.000 0.000 0.004 0.996
#> GSM152064 6 0.0858 0.9005 0.000 0.000 0.028 0.000 0.004 0.968
#> GSM152087 5 0.2340 0.8221 0.000 0.000 0.000 0.000 0.852 0.148
#> GSM152103 3 0.1196 0.7221 0.008 0.000 0.952 0.000 0.000 0.040
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n specimen(p) k
#> ATC:pam 80 0.000022 2
#> ATC:pam 84 0.000319 3
#> ATC:pam 80 0.001273 4
#> ATC:pam 85 0.000913 5
#> ATC:pam 75 0.013315 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 10612 rows and 88 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 5.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.522 0.844 0.910 0.2899 0.762 0.762
#> 3 3 0.437 0.744 0.787 1.1172 0.526 0.405
#> 4 4 0.415 0.594 0.767 0.1051 0.649 0.318
#> 5 5 0.850 0.867 0.909 0.0976 0.851 0.582
#> 6 6 0.666 0.542 0.793 0.0516 0.859 0.544
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM152032 2 0.0000 0.893 0.000 1.000
#> GSM152033 2 0.0000 0.893 0.000 1.000
#> GSM152063 2 0.0376 0.892 0.004 0.996
#> GSM152074 2 0.0000 0.893 0.000 1.000
#> GSM152080 2 0.0000 0.893 0.000 1.000
#> GSM152081 2 0.7950 0.756 0.240 0.760
#> GSM152083 2 0.0000 0.893 0.000 1.000
#> GSM152091 2 0.0376 0.892 0.004 0.996
#> GSM152108 2 0.0000 0.893 0.000 1.000
#> GSM152114 2 0.8909 0.661 0.308 0.692
#> GSM152035 2 0.0376 0.892 0.004 0.996
#> GSM152039 2 0.7299 0.793 0.204 0.796
#> GSM152041 2 0.8081 0.752 0.248 0.752
#> GSM152044 2 0.0376 0.892 0.004 0.996
#> GSM152045 2 0.2236 0.868 0.036 0.964
#> GSM152051 2 0.0376 0.892 0.004 0.996
#> GSM152054 2 0.2236 0.868 0.036 0.964
#> GSM152057 2 0.0376 0.892 0.004 0.996
#> GSM152058 1 0.2423 0.924 0.960 0.040
#> GSM152067 2 0.0000 0.893 0.000 1.000
#> GSM152068 2 0.0376 0.892 0.004 0.996
#> GSM152075 2 0.8016 0.756 0.244 0.756
#> GSM152076 2 0.7376 0.789 0.208 0.792
#> GSM152079 2 0.0376 0.892 0.004 0.996
#> GSM152084 2 0.0000 0.893 0.000 1.000
#> GSM152089 2 0.0000 0.893 0.000 1.000
#> GSM152095 2 0.6531 0.821 0.168 0.832
#> GSM152096 2 0.0000 0.893 0.000 1.000
#> GSM152097 2 0.0376 0.892 0.004 0.996
#> GSM152099 2 0.0376 0.892 0.004 0.996
#> GSM152106 2 0.0376 0.892 0.004 0.996
#> GSM152107 2 0.0000 0.893 0.000 1.000
#> GSM152109 2 0.0000 0.893 0.000 1.000
#> GSM152111 1 0.4815 0.882 0.896 0.104
#> GSM152112 2 0.2236 0.868 0.036 0.964
#> GSM152113 2 0.0000 0.893 0.000 1.000
#> GSM152115 2 0.2236 0.868 0.036 0.964
#> GSM152030 2 0.8081 0.752 0.248 0.752
#> GSM152038 2 0.0000 0.893 0.000 1.000
#> GSM152042 2 0.6048 0.831 0.148 0.852
#> GSM152062 2 0.0000 0.893 0.000 1.000
#> GSM152077 2 0.8955 0.655 0.312 0.688
#> GSM152088 2 0.0376 0.892 0.004 0.996
#> GSM152100 2 0.0376 0.892 0.004 0.996
#> GSM152102 2 0.2236 0.868 0.036 0.964
#> GSM152104 2 0.0376 0.892 0.004 0.996
#> GSM152028 2 0.5408 0.843 0.124 0.876
#> GSM152029 2 0.0000 0.893 0.000 1.000
#> GSM152049 1 0.2423 0.924 0.960 0.040
#> GSM152053 2 0.6801 0.809 0.180 0.820
#> GSM152059 2 0.8144 0.745 0.252 0.748
#> GSM152085 1 0.4298 0.897 0.912 0.088
#> GSM152101 2 0.2236 0.868 0.036 0.964
#> GSM152105 2 0.5842 0.836 0.140 0.860
#> GSM152034 2 0.8207 0.740 0.256 0.744
#> GSM152036 2 0.7883 0.764 0.236 0.764
#> GSM152040 2 0.5946 0.833 0.144 0.856
#> GSM152043 2 0.8443 0.720 0.272 0.728
#> GSM152046 2 0.8443 0.720 0.272 0.728
#> GSM152047 2 0.5946 0.833 0.144 0.856
#> GSM152048 1 0.2423 0.924 0.960 0.040
#> GSM152050 1 0.2423 0.924 0.960 0.040
#> GSM152052 2 0.0672 0.890 0.008 0.992
#> GSM152056 1 0.2423 0.924 0.960 0.040
#> GSM152060 2 0.8327 0.731 0.264 0.736
#> GSM152065 2 0.0000 0.893 0.000 1.000
#> GSM152066 1 0.2423 0.924 0.960 0.040
#> GSM152069 2 0.0000 0.893 0.000 1.000
#> GSM152070 2 0.0000 0.893 0.000 1.000
#> GSM152071 2 0.0000 0.893 0.000 1.000
#> GSM152072 2 0.0000 0.893 0.000 1.000
#> GSM152073 2 0.8081 0.748 0.248 0.752
#> GSM152078 2 0.0000 0.893 0.000 1.000
#> GSM152082 2 0.0000 0.893 0.000 1.000
#> GSM152086 1 0.2423 0.924 0.960 0.040
#> GSM152090 2 0.0000 0.893 0.000 1.000
#> GSM152092 2 0.5842 0.835 0.140 0.860
#> GSM152093 2 0.8386 0.724 0.268 0.732
#> GSM152094 1 0.2948 0.919 0.948 0.052
#> GSM152098 2 0.2043 0.883 0.032 0.968
#> GSM152110 2 0.8207 0.740 0.256 0.744
#> GSM152031 2 0.5842 0.837 0.140 0.860
#> GSM152037 1 0.8207 0.667 0.744 0.256
#> GSM152055 2 0.8327 0.731 0.264 0.736
#> GSM152061 2 0.8327 0.731 0.264 0.736
#> GSM152064 2 0.8016 0.752 0.244 0.756
#> GSM152087 1 0.9460 0.391 0.636 0.364
#> GSM152103 2 0.0000 0.893 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM152032 3 0.5223 0.720 0.024 0.176 0.800
#> GSM152033 3 0.0237 0.735 0.000 0.004 0.996
#> GSM152063 2 0.2711 0.789 0.000 0.912 0.088
#> GSM152074 3 0.4749 0.720 0.012 0.172 0.816
#> GSM152080 3 0.5775 0.665 0.012 0.260 0.728
#> GSM152081 2 0.8951 0.372 0.396 0.476 0.128
#> GSM152083 3 0.5737 0.668 0.012 0.256 0.732
#> GSM152091 2 0.2625 0.790 0.000 0.916 0.084
#> GSM152108 3 0.8098 0.635 0.140 0.216 0.644
#> GSM152114 1 0.3267 0.860 0.884 0.000 0.116
#> GSM152035 3 0.6308 0.202 0.000 0.492 0.508
#> GSM152039 2 0.7248 0.727 0.184 0.708 0.108
#> GSM152041 2 0.8250 0.601 0.292 0.600 0.108
#> GSM152044 2 0.2625 0.790 0.000 0.916 0.084
#> GSM152045 3 0.1411 0.721 0.000 0.036 0.964
#> GSM152051 2 0.2625 0.790 0.000 0.916 0.084
#> GSM152054 3 0.1411 0.721 0.000 0.036 0.964
#> GSM152057 2 0.2625 0.790 0.000 0.916 0.084
#> GSM152058 1 0.0000 0.936 1.000 0.000 0.000
#> GSM152067 3 0.2066 0.738 0.000 0.060 0.940
#> GSM152068 2 0.2625 0.790 0.000 0.916 0.084
#> GSM152075 2 0.7610 0.697 0.216 0.676 0.108
#> GSM152076 2 0.7248 0.727 0.184 0.708 0.108
#> GSM152079 2 0.2625 0.790 0.000 0.916 0.084
#> GSM152084 3 0.5560 0.675 0.300 0.000 0.700
#> GSM152089 3 0.6400 0.489 0.052 0.208 0.740
#> GSM152095 2 0.7316 0.729 0.184 0.704 0.112
#> GSM152096 3 0.4968 0.712 0.012 0.188 0.800
#> GSM152097 2 0.2496 0.789 0.004 0.928 0.068
#> GSM152099 2 0.2625 0.790 0.000 0.916 0.084
#> GSM152106 2 0.2496 0.789 0.004 0.928 0.068
#> GSM152107 3 0.6542 0.711 0.060 0.204 0.736
#> GSM152109 3 0.4749 0.720 0.012 0.172 0.816
#> GSM152111 1 0.0237 0.937 0.996 0.000 0.004
#> GSM152112 3 0.1411 0.721 0.000 0.036 0.964
#> GSM152113 3 0.5911 0.748 0.156 0.060 0.784
#> GSM152115 3 0.1411 0.721 0.000 0.036 0.964
#> GSM152030 2 0.8048 0.657 0.264 0.628 0.108
#> GSM152038 3 0.5138 0.731 0.252 0.000 0.748
#> GSM152042 2 0.8674 0.602 0.296 0.568 0.136
#> GSM152062 3 0.5875 0.747 0.160 0.056 0.784
#> GSM152077 1 0.1411 0.936 0.964 0.000 0.036
#> GSM152088 2 0.2860 0.789 0.004 0.912 0.084
#> GSM152100 2 0.7777 0.742 0.164 0.676 0.160
#> GSM152102 3 0.1411 0.721 0.000 0.036 0.964
#> GSM152104 2 0.2261 0.787 0.000 0.932 0.068
#> GSM152028 3 0.6264 0.616 0.380 0.004 0.616
#> GSM152029 3 0.6979 0.736 0.128 0.140 0.732
#> GSM152049 1 0.0000 0.936 1.000 0.000 0.000
#> GSM152053 2 0.9975 0.245 0.312 0.368 0.320
#> GSM152059 3 0.6126 0.593 0.400 0.000 0.600
#> GSM152085 1 0.1031 0.939 0.976 0.000 0.024
#> GSM152101 3 0.1411 0.721 0.000 0.036 0.964
#> GSM152105 3 0.6111 0.599 0.396 0.000 0.604
#> GSM152034 1 0.3120 0.898 0.908 0.012 0.080
#> GSM152036 2 0.7365 0.726 0.188 0.700 0.112
#> GSM152040 3 0.5363 0.697 0.276 0.000 0.724
#> GSM152043 1 0.5956 0.318 0.672 0.004 0.324
#> GSM152046 1 0.1832 0.935 0.956 0.008 0.036
#> GSM152047 3 0.5815 0.684 0.304 0.004 0.692
#> GSM152048 1 0.0000 0.936 1.000 0.000 0.000
#> GSM152050 1 0.0000 0.936 1.000 0.000 0.000
#> GSM152052 3 0.6008 0.631 0.372 0.000 0.628
#> GSM152056 1 0.0000 0.936 1.000 0.000 0.000
#> GSM152060 1 0.1832 0.935 0.956 0.008 0.036
#> GSM152065 3 0.2261 0.739 0.068 0.000 0.932
#> GSM152066 1 0.0000 0.936 1.000 0.000 0.000
#> GSM152069 3 0.4390 0.728 0.012 0.148 0.840
#> GSM152070 3 0.2261 0.739 0.068 0.000 0.932
#> GSM152071 3 0.4749 0.720 0.012 0.172 0.816
#> GSM152072 3 0.0237 0.735 0.000 0.004 0.996
#> GSM152073 3 0.6330 0.596 0.396 0.004 0.600
#> GSM152078 3 0.5835 0.664 0.340 0.000 0.660
#> GSM152082 3 0.4293 0.744 0.164 0.004 0.832
#> GSM152086 1 0.0000 0.936 1.000 0.000 0.000
#> GSM152090 3 0.5560 0.675 0.300 0.000 0.700
#> GSM152092 3 0.6079 0.608 0.388 0.000 0.612
#> GSM152093 1 0.2356 0.910 0.928 0.000 0.072
#> GSM152094 1 0.0000 0.936 1.000 0.000 0.000
#> GSM152098 3 0.5956 0.675 0.324 0.004 0.672
#> GSM152110 1 0.1647 0.936 0.960 0.004 0.036
#> GSM152031 3 0.6111 0.600 0.396 0.000 0.604
#> GSM152037 1 0.0747 0.939 0.984 0.000 0.016
#> GSM152055 1 0.1832 0.935 0.956 0.008 0.036
#> GSM152061 1 0.2173 0.932 0.944 0.008 0.048
#> GSM152064 1 0.3377 0.883 0.896 0.012 0.092
#> GSM152087 1 0.1289 0.936 0.968 0.000 0.032
#> GSM152103 3 0.6875 0.718 0.244 0.056 0.700
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM152032 2 0.5742 0.584 0.000 0.648 0.300 0.052
#> GSM152033 3 0.0524 0.815 0.000 0.004 0.988 0.008
#> GSM152063 4 0.6165 0.451 0.008 0.380 0.040 0.572
#> GSM152074 2 0.5742 0.584 0.000 0.648 0.300 0.052
#> GSM152080 2 0.3569 0.630 0.000 0.804 0.196 0.000
#> GSM152081 1 0.7047 0.346 0.440 0.000 0.120 0.440
#> GSM152083 2 0.3569 0.630 0.000 0.804 0.196 0.000
#> GSM152091 2 0.5371 0.500 0.000 0.732 0.080 0.188
#> GSM152108 1 0.9123 0.456 0.476 0.156 0.200 0.168
#> GSM152114 1 0.3959 0.734 0.840 0.000 0.068 0.092
#> GSM152035 2 0.7611 0.343 0.004 0.424 0.400 0.172
#> GSM152039 4 0.1489 0.663 0.044 0.000 0.004 0.952
#> GSM152041 4 0.5119 -0.257 0.440 0.000 0.004 0.556
#> GSM152044 4 0.5000 0.219 0.000 0.500 0.000 0.500
#> GSM152045 3 0.0188 0.816 0.000 0.000 0.996 0.004
#> GSM152051 2 0.3610 0.436 0.000 0.800 0.000 0.200
#> GSM152054 3 0.0469 0.817 0.000 0.000 0.988 0.012
#> GSM152057 2 0.3610 0.436 0.000 0.800 0.000 0.200
#> GSM152058 1 0.0000 0.739 1.000 0.000 0.000 0.000
#> GSM152067 3 0.3257 0.631 0.000 0.152 0.844 0.004
#> GSM152068 2 0.3610 0.436 0.000 0.800 0.000 0.200
#> GSM152075 4 0.2266 0.636 0.084 0.000 0.004 0.912
#> GSM152076 4 0.1489 0.663 0.044 0.000 0.004 0.952
#> GSM152079 2 0.3610 0.436 0.000 0.800 0.000 0.200
#> GSM152084 1 0.6576 0.618 0.632 0.000 0.200 0.168
#> GSM152089 3 0.6442 0.486 0.124 0.000 0.632 0.244
#> GSM152095 4 0.1489 0.663 0.044 0.000 0.004 0.952
#> GSM152096 2 0.5849 0.588 0.004 0.656 0.288 0.052
#> GSM152097 4 0.4543 0.526 0.000 0.324 0.000 0.676
#> GSM152099 2 0.3610 0.436 0.000 0.800 0.000 0.200
#> GSM152106 4 0.4643 0.510 0.000 0.344 0.000 0.656
#> GSM152107 2 0.8935 0.420 0.148 0.472 0.264 0.116
#> GSM152109 2 0.5742 0.584 0.000 0.648 0.300 0.052
#> GSM152111 1 0.0188 0.739 0.996 0.000 0.004 0.000
#> GSM152112 3 0.0469 0.817 0.000 0.000 0.988 0.012
#> GSM152113 1 0.9165 0.436 0.468 0.156 0.212 0.164
#> GSM152115 3 0.0336 0.817 0.000 0.000 0.992 0.008
#> GSM152030 1 0.6737 0.432 0.532 0.000 0.100 0.368
#> GSM152038 1 0.6316 0.531 0.596 0.000 0.324 0.080
#> GSM152042 1 0.6664 0.624 0.616 0.000 0.152 0.232
#> GSM152062 1 0.9646 0.204 0.380 0.244 0.212 0.164
#> GSM152077 1 0.2300 0.739 0.920 0.000 0.016 0.064
#> GSM152088 2 0.3123 0.459 0.000 0.844 0.000 0.156
#> GSM152100 4 0.3962 0.533 0.044 0.000 0.124 0.832
#> GSM152102 3 0.0336 0.815 0.000 0.000 0.992 0.008
#> GSM152104 4 0.4916 0.388 0.000 0.424 0.000 0.576
#> GSM152028 1 0.4697 0.607 0.696 0.000 0.296 0.008
#> GSM152029 2 0.9636 0.201 0.252 0.380 0.204 0.164
#> GSM152049 1 0.0000 0.739 1.000 0.000 0.000 0.000
#> GSM152053 1 0.7398 0.453 0.456 0.000 0.168 0.376
#> GSM152059 1 0.3569 0.698 0.804 0.000 0.196 0.000
#> GSM152085 1 0.0000 0.739 1.000 0.000 0.000 0.000
#> GSM152101 3 0.0336 0.815 0.000 0.000 0.992 0.008
#> GSM152105 1 0.3569 0.698 0.804 0.000 0.196 0.000
#> GSM152034 1 0.4898 0.597 0.716 0.000 0.024 0.260
#> GSM152036 4 0.1489 0.663 0.044 0.000 0.004 0.952
#> GSM152040 3 0.6278 0.530 0.228 0.000 0.652 0.120
#> GSM152043 1 0.3047 0.735 0.872 0.000 0.116 0.012
#> GSM152046 1 0.4559 0.639 0.792 0.040 0.004 0.164
#> GSM152047 3 0.7261 0.101 0.340 0.000 0.500 0.160
#> GSM152048 1 0.0000 0.739 1.000 0.000 0.000 0.000
#> GSM152050 1 0.0000 0.739 1.000 0.000 0.000 0.000
#> GSM152052 1 0.3688 0.694 0.792 0.000 0.208 0.000
#> GSM152056 1 0.0000 0.739 1.000 0.000 0.000 0.000
#> GSM152060 1 0.5011 0.589 0.748 0.040 0.004 0.208
#> GSM152065 3 0.3435 0.760 0.100 0.000 0.864 0.036
#> GSM152066 1 0.0000 0.739 1.000 0.000 0.000 0.000
#> GSM152069 2 0.5742 0.584 0.000 0.648 0.300 0.052
#> GSM152070 3 0.3107 0.772 0.080 0.000 0.884 0.036
#> GSM152071 2 0.5742 0.584 0.000 0.648 0.300 0.052
#> GSM152072 3 0.0336 0.817 0.000 0.000 0.992 0.008
#> GSM152073 1 0.3933 0.696 0.792 0.000 0.200 0.008
#> GSM152078 1 0.5219 0.670 0.728 0.000 0.216 0.056
#> GSM152082 3 0.3581 0.749 0.116 0.000 0.852 0.032
#> GSM152086 1 0.0000 0.739 1.000 0.000 0.000 0.000
#> GSM152090 1 0.6570 0.617 0.632 0.000 0.204 0.164
#> GSM152092 1 0.4524 0.688 0.768 0.000 0.204 0.028
#> GSM152093 1 0.2197 0.748 0.928 0.000 0.048 0.024
#> GSM152094 1 0.0000 0.739 1.000 0.000 0.000 0.000
#> GSM152098 1 0.5673 0.474 0.596 0.000 0.372 0.032
#> GSM152110 1 0.4542 0.630 0.752 0.000 0.020 0.228
#> GSM152031 1 0.3569 0.698 0.804 0.000 0.196 0.000
#> GSM152037 1 0.0000 0.739 1.000 0.000 0.000 0.000
#> GSM152055 1 0.5011 0.589 0.748 0.040 0.004 0.208
#> GSM152061 1 0.5011 0.589 0.748 0.040 0.004 0.208
#> GSM152064 1 0.5754 0.546 0.636 0.000 0.048 0.316
#> GSM152087 1 0.0000 0.739 1.000 0.000 0.000 0.000
#> GSM152103 1 0.7795 0.574 0.584 0.048 0.204 0.164
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM152032 3 0.1992 0.983 0.044 0.000 0.924 0.000 0.032
#> GSM152033 5 0.1443 0.856 0.044 0.000 0.004 0.004 0.948
#> GSM152063 2 0.1787 0.882 0.044 0.936 0.004 0.016 0.000
#> GSM152074 3 0.1992 0.983 0.044 0.000 0.924 0.000 0.032
#> GSM152080 3 0.3016 0.959 0.044 0.040 0.884 0.000 0.032
#> GSM152081 4 0.1617 0.897 0.020 0.020 0.000 0.948 0.012
#> GSM152083 3 0.3016 0.959 0.044 0.040 0.884 0.000 0.032
#> GSM152091 2 0.3016 0.852 0.044 0.884 0.040 0.000 0.032
#> GSM152108 1 0.4053 0.864 0.840 0.060 0.024 0.044 0.032
#> GSM152114 1 0.1901 0.931 0.932 0.000 0.004 0.040 0.024
#> GSM152035 2 0.5485 0.121 0.044 0.496 0.008 0.000 0.452
#> GSM152039 4 0.1644 0.899 0.008 0.048 0.004 0.940 0.000
#> GSM152041 4 0.1012 0.904 0.012 0.020 0.000 0.968 0.000
#> GSM152044 2 0.1626 0.882 0.044 0.940 0.000 0.016 0.000
#> GSM152045 5 0.0000 0.860 0.000 0.000 0.000 0.000 1.000
#> GSM152051 2 0.1978 0.891 0.044 0.928 0.024 0.004 0.000
#> GSM152054 5 0.0000 0.860 0.000 0.000 0.000 0.000 1.000
#> GSM152057 2 0.1978 0.891 0.044 0.928 0.024 0.004 0.000
#> GSM152058 1 0.1626 0.921 0.940 0.000 0.044 0.016 0.000
#> GSM152067 5 0.5167 0.216 0.044 0.000 0.404 0.000 0.552
#> GSM152068 2 0.1978 0.891 0.044 0.928 0.024 0.004 0.000
#> GSM152075 4 0.1408 0.900 0.008 0.044 0.000 0.948 0.000
#> GSM152076 4 0.1644 0.899 0.008 0.048 0.004 0.940 0.000
#> GSM152079 2 0.1978 0.891 0.044 0.928 0.024 0.004 0.000
#> GSM152084 1 0.2122 0.918 0.924 0.000 0.008 0.036 0.032
#> GSM152089 5 0.5915 0.338 0.056 0.012 0.008 0.380 0.544
#> GSM152095 4 0.1644 0.899 0.008 0.048 0.004 0.940 0.000
#> GSM152096 3 0.2675 0.973 0.044 0.012 0.904 0.008 0.032
#> GSM152097 2 0.0510 0.853 0.000 0.984 0.000 0.016 0.000
#> GSM152099 2 0.1907 0.890 0.044 0.928 0.028 0.000 0.000
#> GSM152106 2 0.0510 0.853 0.000 0.984 0.000 0.016 0.000
#> GSM152107 2 0.5945 0.541 0.240 0.656 0.056 0.016 0.032
#> GSM152109 3 0.1992 0.983 0.044 0.000 0.924 0.000 0.032
#> GSM152111 1 0.1626 0.921 0.940 0.000 0.044 0.016 0.000
#> GSM152112 5 0.0290 0.859 0.000 0.000 0.008 0.000 0.992
#> GSM152113 1 0.2696 0.908 0.900 0.000 0.040 0.028 0.032
#> GSM152115 5 0.0000 0.860 0.000 0.000 0.000 0.000 1.000
#> GSM152030 1 0.2460 0.912 0.900 0.024 0.000 0.072 0.004
#> GSM152038 1 0.2351 0.918 0.916 0.000 0.028 0.020 0.036
#> GSM152042 1 0.2580 0.920 0.900 0.020 0.000 0.064 0.016
#> GSM152062 1 0.2617 0.909 0.904 0.000 0.036 0.028 0.032
#> GSM152077 1 0.1205 0.931 0.956 0.000 0.000 0.040 0.004
#> GSM152088 2 0.1907 0.890 0.044 0.928 0.028 0.000 0.000
#> GSM152100 4 0.1883 0.891 0.012 0.048 0.008 0.932 0.000
#> GSM152102 5 0.0162 0.860 0.000 0.000 0.004 0.000 0.996
#> GSM152104 2 0.0510 0.853 0.000 0.984 0.000 0.016 0.000
#> GSM152028 1 0.2067 0.928 0.928 0.000 0.028 0.032 0.012
#> GSM152029 1 0.2987 0.894 0.884 0.000 0.056 0.028 0.032
#> GSM152049 1 0.1626 0.921 0.940 0.000 0.044 0.016 0.000
#> GSM152053 4 0.4970 0.443 0.340 0.008 0.000 0.624 0.028
#> GSM152059 1 0.1299 0.935 0.960 0.000 0.020 0.008 0.012
#> GSM152085 1 0.2074 0.918 0.920 0.000 0.044 0.036 0.000
#> GSM152101 5 0.0162 0.860 0.000 0.000 0.004 0.000 0.996
#> GSM152105 1 0.1012 0.934 0.968 0.000 0.020 0.000 0.012
#> GSM152034 4 0.2411 0.870 0.108 0.000 0.000 0.884 0.008
#> GSM152036 4 0.1484 0.899 0.008 0.048 0.000 0.944 0.000
#> GSM152040 5 0.2248 0.837 0.088 0.000 0.000 0.012 0.900
#> GSM152043 1 0.1686 0.931 0.944 0.000 0.020 0.028 0.008
#> GSM152046 4 0.1768 0.895 0.072 0.000 0.004 0.924 0.000
#> GSM152047 5 0.5136 0.585 0.080 0.000 0.000 0.260 0.660
#> GSM152048 1 0.2074 0.918 0.920 0.000 0.044 0.036 0.000
#> GSM152050 1 0.1626 0.921 0.940 0.000 0.044 0.016 0.000
#> GSM152052 1 0.1168 0.931 0.960 0.000 0.000 0.008 0.032
#> GSM152056 1 0.1626 0.921 0.940 0.000 0.044 0.016 0.000
#> GSM152060 4 0.1697 0.897 0.060 0.000 0.008 0.932 0.000
#> GSM152065 5 0.1924 0.854 0.064 0.000 0.008 0.004 0.924
#> GSM152066 1 0.1626 0.921 0.940 0.000 0.044 0.016 0.000
#> GSM152069 3 0.1992 0.983 0.044 0.000 0.924 0.000 0.032
#> GSM152070 5 0.1924 0.854 0.064 0.000 0.008 0.004 0.924
#> GSM152071 3 0.1992 0.983 0.044 0.000 0.924 0.000 0.032
#> GSM152072 5 0.1443 0.856 0.044 0.000 0.004 0.004 0.948
#> GSM152073 1 0.1799 0.930 0.940 0.000 0.020 0.028 0.012
#> GSM152078 1 0.1202 0.929 0.960 0.000 0.004 0.004 0.032
#> GSM152082 5 0.2666 0.841 0.076 0.000 0.012 0.020 0.892
#> GSM152086 1 0.1626 0.921 0.940 0.000 0.044 0.016 0.000
#> GSM152090 1 0.2234 0.922 0.920 0.000 0.012 0.036 0.032
#> GSM152092 1 0.1885 0.930 0.936 0.000 0.020 0.032 0.012
#> GSM152093 1 0.0898 0.936 0.972 0.000 0.000 0.020 0.008
#> GSM152094 1 0.1408 0.922 0.948 0.000 0.044 0.008 0.000
#> GSM152098 1 0.4244 0.764 0.780 0.000 0.024 0.028 0.168
#> GSM152110 4 0.2848 0.822 0.156 0.000 0.000 0.840 0.004
#> GSM152031 1 0.1299 0.935 0.960 0.000 0.020 0.008 0.012
#> GSM152037 1 0.1648 0.924 0.940 0.000 0.040 0.020 0.000
#> GSM152055 4 0.1697 0.897 0.060 0.000 0.008 0.932 0.000
#> GSM152061 4 0.1697 0.897 0.060 0.000 0.008 0.932 0.000
#> GSM152064 4 0.2104 0.891 0.060 0.000 0.000 0.916 0.024
#> GSM152087 1 0.1836 0.924 0.932 0.000 0.032 0.036 0.000
#> GSM152103 1 0.2256 0.922 0.920 0.000 0.016 0.032 0.032
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM152032 3 0.0363 0.8506 0.000 0.000 0.988 0.000 0.012 0.000
#> GSM152033 5 0.4531 0.2038 0.464 0.000 0.032 0.000 0.504 0.000
#> GSM152063 2 0.1285 0.8433 0.000 0.944 0.004 0.052 0.000 0.000
#> GSM152074 3 0.0363 0.8506 0.000 0.000 0.988 0.000 0.012 0.000
#> GSM152080 3 0.3586 0.6405 0.000 0.268 0.720 0.000 0.012 0.000
#> GSM152081 4 0.4464 0.4137 0.028 0.000 0.000 0.624 0.008 0.340
#> GSM152083 3 0.3586 0.6405 0.000 0.268 0.720 0.000 0.012 0.000
#> GSM152091 2 0.2189 0.8099 0.008 0.912 0.044 0.004 0.032 0.000
#> GSM152108 6 0.7682 0.2283 0.144 0.132 0.012 0.236 0.020 0.456
#> GSM152114 6 0.3269 0.5969 0.052 0.000 0.000 0.108 0.008 0.832
#> GSM152035 2 0.4318 0.4568 0.008 0.632 0.020 0.000 0.340 0.000
#> GSM152039 4 0.0000 0.7451 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM152041 4 0.2402 0.7224 0.012 0.000 0.000 0.868 0.000 0.120
#> GSM152044 2 0.1152 0.8452 0.000 0.952 0.004 0.044 0.000 0.000
#> GSM152045 5 0.0363 0.7812 0.012 0.000 0.000 0.000 0.988 0.000
#> GSM152051 2 0.0000 0.8503 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152054 5 0.0260 0.7826 0.008 0.000 0.000 0.000 0.992 0.000
#> GSM152057 2 0.0000 0.8503 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152058 6 0.0000 0.6631 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM152067 3 0.4109 0.3199 0.012 0.000 0.576 0.000 0.412 0.000
#> GSM152068 2 0.0000 0.8503 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM152075 4 0.1644 0.7413 0.004 0.000 0.000 0.920 0.000 0.076
#> GSM152076 4 0.0000 0.7451 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM152079 2 0.0146 0.8504 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM152084 6 0.6384 0.3479 0.244 0.000 0.012 0.224 0.016 0.504
#> GSM152089 5 0.6779 -0.1383 0.048 0.000 0.000 0.264 0.420 0.268
#> GSM152095 4 0.0000 0.7451 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM152096 3 0.2497 0.8058 0.040 0.032 0.896 0.000 0.032 0.000
#> GSM152097 2 0.2584 0.7998 0.004 0.848 0.004 0.144 0.000 0.000
#> GSM152099 2 0.0146 0.8504 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM152106 2 0.2584 0.7998 0.004 0.848 0.004 0.144 0.000 0.000
#> GSM152107 2 0.8429 -0.2571 0.120 0.320 0.024 0.224 0.032 0.280
#> GSM152109 3 0.0363 0.8506 0.000 0.000 0.988 0.000 0.012 0.000
#> GSM152111 6 0.0000 0.6631 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM152112 5 0.0260 0.7826 0.008 0.000 0.000 0.000 0.992 0.000
#> GSM152113 6 0.6736 0.3184 0.244 0.000 0.016 0.224 0.032 0.484
#> GSM152115 5 0.0363 0.7812 0.012 0.000 0.000 0.000 0.988 0.000
#> GSM152030 6 0.4569 0.1811 0.040 0.000 0.000 0.396 0.000 0.564
#> GSM152038 1 0.2298 0.5340 0.912 0.000 0.024 0.008 0.032 0.024
#> GSM152042 6 0.5698 0.3261 0.112 0.000 0.004 0.308 0.016 0.560
#> GSM152062 1 0.8005 0.0497 0.336 0.000 0.132 0.224 0.032 0.276
#> GSM152077 6 0.0972 0.6582 0.008 0.000 0.000 0.028 0.000 0.964
#> GSM152088 2 0.0146 0.8504 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM152100 4 0.1268 0.7201 0.036 0.004 0.000 0.952 0.008 0.000
#> GSM152102 5 0.0260 0.7826 0.008 0.000 0.000 0.000 0.992 0.000
#> GSM152104 2 0.2584 0.7998 0.004 0.848 0.004 0.144 0.000 0.000
#> GSM152028 1 0.2911 0.5514 0.832 0.000 0.000 0.000 0.024 0.144
#> GSM152029 6 0.7564 0.1012 0.300 0.000 0.096 0.224 0.016 0.364
#> GSM152049 6 0.0000 0.6631 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM152053 4 0.5167 0.3265 0.060 0.000 0.000 0.564 0.016 0.360
#> GSM152059 6 0.3563 0.3529 0.336 0.000 0.000 0.000 0.000 0.664
#> GSM152085 6 0.0000 0.6631 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM152101 5 0.0260 0.7826 0.008 0.000 0.000 0.000 0.992 0.000
#> GSM152105 6 0.3684 0.2774 0.372 0.000 0.000 0.000 0.000 0.628
#> GSM152034 6 0.4136 0.0728 0.012 0.000 0.000 0.428 0.000 0.560
#> GSM152036 4 0.0000 0.7451 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM152040 1 0.6733 0.2078 0.408 0.000 0.000 0.048 0.212 0.332
#> GSM152043 6 0.3151 0.5092 0.252 0.000 0.000 0.000 0.000 0.748
#> GSM152046 6 0.4173 0.3787 0.028 0.000 0.008 0.272 0.000 0.692
#> GSM152047 6 0.7350 -0.1357 0.316 0.000 0.000 0.252 0.108 0.324
#> GSM152048 6 0.0000 0.6631 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM152050 6 0.0000 0.6631 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM152052 6 0.3885 0.4240 0.300 0.000 0.004 0.000 0.012 0.684
#> GSM152056 6 0.0000 0.6631 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM152060 6 0.4684 0.3263 0.036 0.000 0.008 0.300 0.008 0.648
#> GSM152065 1 0.3850 0.2919 0.716 0.000 0.004 0.000 0.260 0.020
#> GSM152066 6 0.0000 0.6631 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM152069 3 0.0363 0.8506 0.000 0.000 0.988 0.000 0.012 0.000
#> GSM152070 1 0.3879 0.2538 0.688 0.000 0.000 0.000 0.292 0.020
#> GSM152071 3 0.0363 0.8506 0.000 0.000 0.988 0.000 0.012 0.000
#> GSM152072 5 0.4186 0.4718 0.312 0.000 0.032 0.000 0.656 0.000
#> GSM152073 6 0.3717 0.2717 0.384 0.000 0.000 0.000 0.000 0.616
#> GSM152078 1 0.6206 0.1489 0.512 0.000 0.012 0.116 0.028 0.332
#> GSM152082 1 0.3023 0.4944 0.836 0.000 0.000 0.000 0.120 0.044
#> GSM152086 6 0.0000 0.6631 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM152090 6 0.6214 0.3905 0.204 0.000 0.012 0.228 0.016 0.540
#> GSM152092 1 0.3699 0.3774 0.660 0.000 0.000 0.000 0.004 0.336
#> GSM152093 6 0.1141 0.6523 0.052 0.000 0.000 0.000 0.000 0.948
#> GSM152094 6 0.1814 0.6251 0.100 0.000 0.000 0.000 0.000 0.900
#> GSM152098 1 0.2265 0.5425 0.896 0.000 0.000 0.000 0.052 0.052
#> GSM152110 6 0.3565 0.3638 0.004 0.000 0.000 0.304 0.000 0.692
#> GSM152031 6 0.3563 0.3529 0.336 0.000 0.000 0.000 0.000 0.664
#> GSM152037 6 0.0146 0.6621 0.004 0.000 0.000 0.000 0.000 0.996
#> GSM152055 6 0.4684 0.3263 0.036 0.000 0.008 0.300 0.008 0.648
#> GSM152061 6 0.4684 0.3263 0.036 0.000 0.008 0.300 0.008 0.648
#> GSM152064 4 0.4496 0.2782 0.020 0.000 0.000 0.564 0.008 0.408
#> GSM152087 6 0.0000 0.6631 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM152103 6 0.6194 0.3957 0.204 0.000 0.012 0.224 0.016 0.544
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 specimen(p) k
#> ATC:mclust 87 0.231505 2
#> ATC:mclust 83 0.000174 3
#> ATC:mclust 65 0.000287 4
#> ATC:mclust 84 0.002409 5
#> ATC:mclust 52 0.013567 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 10612 rows and 88 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.860 0.919 0.965 0.4997 0.498 0.498
#> 3 3 0.469 0.440 0.719 0.3301 0.639 0.393
#> 4 4 0.649 0.725 0.859 0.1193 0.721 0.357
#> 5 5 0.590 0.595 0.776 0.0581 0.912 0.686
#> 6 6 0.614 0.592 0.750 0.0393 0.954 0.796
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
#> GSM152032 2 0.644 0.800 0.164 0.836
#> GSM152033 1 0.000 0.959 1.000 0.000
#> GSM152063 2 0.000 0.966 0.000 1.000
#> GSM152074 1 0.000 0.959 1.000 0.000
#> GSM152080 2 0.000 0.966 0.000 1.000
#> GSM152081 2 0.000 0.966 0.000 1.000
#> GSM152083 2 0.000 0.966 0.000 1.000
#> GSM152091 2 0.000 0.966 0.000 1.000
#> GSM152108 2 0.000 0.966 0.000 1.000
#> GSM152114 2 0.204 0.940 0.032 0.968
#> GSM152035 2 0.000 0.966 0.000 1.000
#> GSM152039 2 0.000 0.966 0.000 1.000
#> GSM152041 2 0.000 0.966 0.000 1.000
#> GSM152044 2 0.000 0.966 0.000 1.000
#> GSM152045 1 0.000 0.959 1.000 0.000
#> GSM152051 2 0.000 0.966 0.000 1.000
#> GSM152054 1 0.295 0.917 0.948 0.052
#> GSM152057 2 0.000 0.966 0.000 1.000
#> GSM152058 1 0.000 0.959 1.000 0.000
#> GSM152067 1 0.904 0.544 0.680 0.320
#> GSM152068 2 0.000 0.966 0.000 1.000
#> GSM152075 2 0.000 0.966 0.000 1.000
#> GSM152076 2 0.000 0.966 0.000 1.000
#> GSM152079 2 0.000 0.966 0.000 1.000
#> GSM152084 2 0.833 0.645 0.264 0.736
#> GSM152089 2 0.000 0.966 0.000 1.000
#> GSM152095 2 0.000 0.966 0.000 1.000
#> GSM152096 2 0.000 0.966 0.000 1.000
#> GSM152097 2 0.000 0.966 0.000 1.000
#> GSM152099 2 0.000 0.966 0.000 1.000
#> GSM152106 2 0.000 0.966 0.000 1.000
#> GSM152107 2 0.000 0.966 0.000 1.000
#> GSM152109 2 0.671 0.784 0.176 0.824
#> GSM152111 1 0.653 0.790 0.832 0.168
#> GSM152112 2 0.000 0.966 0.000 1.000
#> GSM152113 1 0.886 0.575 0.696 0.304
#> GSM152115 1 0.000 0.959 1.000 0.000
#> GSM152030 2 0.000 0.966 0.000 1.000
#> GSM152038 1 0.000 0.959 1.000 0.000
#> GSM152042 2 0.000 0.966 0.000 1.000
#> GSM152062 1 0.260 0.924 0.956 0.044
#> GSM152077 1 0.000 0.959 1.000 0.000
#> GSM152088 2 0.000 0.966 0.000 1.000
#> GSM152100 2 0.000 0.966 0.000 1.000
#> GSM152102 2 0.000 0.966 0.000 1.000
#> GSM152104 2 0.000 0.966 0.000 1.000
#> GSM152028 1 0.000 0.959 1.000 0.000
#> GSM152029 1 0.574 0.829 0.864 0.136
#> GSM152049 1 0.000 0.959 1.000 0.000
#> GSM152053 2 0.000 0.966 0.000 1.000
#> GSM152059 1 0.000 0.959 1.000 0.000
#> GSM152085 1 0.000 0.959 1.000 0.000
#> GSM152101 2 0.118 0.954 0.016 0.984
#> GSM152105 1 0.000 0.959 1.000 0.000
#> GSM152034 1 0.978 0.313 0.588 0.412
#> GSM152036 2 0.000 0.966 0.000 1.000
#> GSM152040 1 0.000 0.959 1.000 0.000
#> GSM152043 1 0.000 0.959 1.000 0.000
#> GSM152046 1 0.000 0.959 1.000 0.000
#> GSM152047 1 0.000 0.959 1.000 0.000
#> GSM152048 1 0.000 0.959 1.000 0.000
#> GSM152050 1 0.000 0.959 1.000 0.000
#> GSM152052 1 0.000 0.959 1.000 0.000
#> GSM152056 1 0.000 0.959 1.000 0.000
#> GSM152060 1 0.000 0.959 1.000 0.000
#> GSM152065 1 0.000 0.959 1.000 0.000
#> GSM152066 1 0.000 0.959 1.000 0.000
#> GSM152069 1 0.118 0.947 0.984 0.016
#> GSM152070 1 0.000 0.959 1.000 0.000
#> GSM152071 1 0.000 0.959 1.000 0.000
#> GSM152072 1 0.000 0.959 1.000 0.000
#> GSM152073 1 0.000 0.959 1.000 0.000
#> GSM152078 1 0.000 0.959 1.000 0.000
#> GSM152082 1 0.000 0.959 1.000 0.000
#> GSM152086 1 0.000 0.959 1.000 0.000
#> GSM152090 2 0.000 0.966 0.000 1.000
#> GSM152092 1 0.000 0.959 1.000 0.000
#> GSM152093 1 0.955 0.413 0.624 0.376
#> GSM152094 1 0.000 0.959 1.000 0.000
#> GSM152098 1 0.000 0.959 1.000 0.000
#> GSM152110 1 0.000 0.959 1.000 0.000
#> GSM152031 1 0.000 0.959 1.000 0.000
#> GSM152037 1 0.000 0.959 1.000 0.000
#> GSM152055 1 0.000 0.959 1.000 0.000
#> GSM152061 1 0.000 0.959 1.000 0.000
#> GSM152064 2 0.929 0.473 0.344 0.656
#> GSM152087 1 0.000 0.959 1.000 0.000
#> GSM152103 2 0.781 0.701 0.232 0.768
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM152032 3 0.0237 0.692689 0.004 0.000 0.996
#> GSM152033 1 0.6252 0.104053 0.556 0.000 0.444
#> GSM152063 2 0.6309 -0.305897 0.000 0.500 0.500
#> GSM152074 3 0.2959 0.646595 0.100 0.000 0.900
#> GSM152080 3 0.3116 0.668518 0.000 0.108 0.892
#> GSM152081 2 0.0747 0.658164 0.016 0.984 0.000
#> GSM152083 3 0.0747 0.692066 0.000 0.016 0.984
#> GSM152091 3 0.5397 0.568174 0.000 0.280 0.720
#> GSM152108 2 0.6095 0.026088 0.000 0.608 0.392
#> GSM152114 2 0.4002 0.588538 0.160 0.840 0.000
#> GSM152035 3 0.4346 0.632483 0.000 0.184 0.816
#> GSM152039 2 0.0000 0.654399 0.000 1.000 0.000
#> GSM152041 2 0.2356 0.645833 0.072 0.928 0.000
#> GSM152044 2 0.6299 -0.251657 0.000 0.524 0.476
#> GSM152045 1 0.4235 0.587208 0.824 0.000 0.176
#> GSM152051 3 0.6267 0.359298 0.000 0.452 0.548
#> GSM152054 1 0.7049 0.080645 0.528 0.020 0.452
#> GSM152057 3 0.6252 0.372480 0.000 0.444 0.556
#> GSM152058 1 0.6280 0.075505 0.540 0.460 0.000
#> GSM152067 3 0.0892 0.690667 0.020 0.000 0.980
#> GSM152068 3 0.6274 0.352787 0.000 0.456 0.544
#> GSM152075 2 0.1031 0.658093 0.024 0.976 0.000
#> GSM152076 2 0.0000 0.654399 0.000 1.000 0.000
#> GSM152079 3 0.6274 0.352787 0.000 0.456 0.544
#> GSM152084 3 0.9364 0.158532 0.172 0.372 0.456
#> GSM152089 2 0.0424 0.651434 0.000 0.992 0.008
#> GSM152095 2 0.0237 0.653032 0.000 0.996 0.004
#> GSM152096 3 0.1964 0.685313 0.000 0.056 0.944
#> GSM152097 2 0.3879 0.508773 0.000 0.848 0.152
#> GSM152099 3 0.5882 0.501356 0.000 0.348 0.652
#> GSM152106 2 0.3879 0.508894 0.000 0.848 0.152
#> GSM152107 3 0.5397 0.567728 0.000 0.280 0.720
#> GSM152109 3 0.0592 0.692128 0.012 0.000 0.988
#> GSM152111 2 0.5733 0.402112 0.324 0.676 0.000
#> GSM152112 2 0.6252 -0.054970 0.000 0.556 0.444
#> GSM152113 3 0.5591 0.406901 0.304 0.000 0.696
#> GSM152115 3 0.6307 0.020213 0.488 0.000 0.512
#> GSM152030 2 0.0424 0.651170 0.000 0.992 0.008
#> GSM152038 1 0.5760 0.354289 0.672 0.000 0.328
#> GSM152042 2 0.0747 0.646952 0.000 0.984 0.016
#> GSM152062 3 0.6302 0.040271 0.480 0.000 0.520
#> GSM152077 1 0.5988 0.291034 0.632 0.368 0.000
#> GSM152088 3 0.6095 0.447181 0.000 0.392 0.608
#> GSM152100 2 0.0747 0.646952 0.000 0.984 0.016
#> GSM152102 3 0.0424 0.692896 0.000 0.008 0.992
#> GSM152104 2 0.5650 0.209217 0.000 0.688 0.312
#> GSM152028 1 0.1289 0.703330 0.968 0.000 0.032
#> GSM152029 3 0.6008 0.289780 0.372 0.000 0.628
#> GSM152049 1 0.6305 0.001349 0.516 0.484 0.000
#> GSM152053 2 0.1753 0.622504 0.000 0.952 0.048
#> GSM152059 1 0.0424 0.702109 0.992 0.008 0.000
#> GSM152085 1 0.6308 -0.026609 0.508 0.492 0.000
#> GSM152101 3 0.0475 0.693136 0.004 0.004 0.992
#> GSM152105 1 0.1163 0.704434 0.972 0.000 0.028
#> GSM152034 2 0.5016 0.516938 0.240 0.760 0.000
#> GSM152036 2 0.0747 0.657621 0.016 0.984 0.000
#> GSM152040 1 0.2625 0.662396 0.916 0.084 0.000
#> GSM152043 1 0.0592 0.700742 0.988 0.012 0.000
#> GSM152046 2 0.6274 0.136608 0.456 0.544 0.000
#> GSM152047 1 0.5291 0.467764 0.732 0.268 0.000
#> GSM152048 1 0.6079 0.255964 0.612 0.388 0.000
#> GSM152050 2 0.6204 0.209906 0.424 0.576 0.000
#> GSM152052 1 0.0000 0.704081 1.000 0.000 0.000
#> GSM152056 2 0.6291 0.102733 0.468 0.532 0.000
#> GSM152060 2 0.6291 0.102973 0.468 0.532 0.000
#> GSM152065 1 0.4399 0.573077 0.812 0.000 0.188
#> GSM152066 1 0.6168 0.201841 0.588 0.412 0.000
#> GSM152069 3 0.2165 0.669589 0.064 0.000 0.936
#> GSM152070 1 0.2625 0.671751 0.916 0.000 0.084
#> GSM152071 3 0.5254 0.467889 0.264 0.000 0.736
#> GSM152072 1 0.6260 0.095713 0.552 0.000 0.448
#> GSM152073 1 0.0000 0.704081 1.000 0.000 0.000
#> GSM152078 1 0.4121 0.595962 0.832 0.000 0.168
#> GSM152082 1 0.2356 0.680158 0.928 0.000 0.072
#> GSM152086 1 0.6305 0.000653 0.516 0.484 0.000
#> GSM152090 2 0.6126 0.090280 0.004 0.644 0.352
#> GSM152092 1 0.1031 0.704961 0.976 0.000 0.024
#> GSM152093 2 0.5363 0.473631 0.276 0.724 0.000
#> GSM152094 1 0.5560 0.420025 0.700 0.300 0.000
#> GSM152098 1 0.0592 0.705407 0.988 0.000 0.012
#> GSM152110 2 0.6286 0.115080 0.464 0.536 0.000
#> GSM152031 1 0.0592 0.705407 0.988 0.000 0.012
#> GSM152037 1 0.0747 0.699307 0.984 0.016 0.000
#> GSM152055 2 0.6267 0.146745 0.452 0.548 0.000
#> GSM152061 2 0.6280 0.125777 0.460 0.540 0.000
#> GSM152064 2 0.4931 0.525841 0.232 0.768 0.000
#> GSM152087 1 0.2711 0.659876 0.912 0.088 0.000
#> GSM152103 3 0.7824 0.589694 0.212 0.124 0.664
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM152032 2 0.1706 0.842 0.016 0.948 0.036 0.000
#> GSM152033 3 0.0804 0.826 0.008 0.012 0.980 0.000
#> GSM152063 4 0.4941 0.128 0.000 0.436 0.000 0.564
#> GSM152074 3 0.4245 0.725 0.020 0.196 0.784 0.000
#> GSM152080 2 0.0336 0.868 0.000 0.992 0.008 0.000
#> GSM152081 4 0.0469 0.840 0.012 0.000 0.000 0.988
#> GSM152083 2 0.0469 0.865 0.000 0.988 0.012 0.000
#> GSM152091 2 0.1022 0.879 0.000 0.968 0.000 0.032
#> GSM152108 2 0.5774 0.635 0.004 0.692 0.068 0.236
#> GSM152114 1 0.3597 0.772 0.836 0.016 0.000 0.148
#> GSM152035 2 0.6465 0.101 0.000 0.516 0.412 0.072
#> GSM152039 4 0.0188 0.840 0.004 0.000 0.000 0.996
#> GSM152041 4 0.1211 0.835 0.040 0.000 0.000 0.960
#> GSM152044 2 0.3726 0.718 0.000 0.788 0.000 0.212
#> GSM152045 3 0.0592 0.824 0.000 0.000 0.984 0.016
#> GSM152051 2 0.1474 0.876 0.000 0.948 0.000 0.052
#> GSM152054 3 0.1118 0.819 0.000 0.000 0.964 0.036
#> GSM152057 2 0.1389 0.877 0.000 0.952 0.000 0.048
#> GSM152058 1 0.0707 0.836 0.980 0.000 0.000 0.020
#> GSM152067 3 0.3123 0.766 0.000 0.156 0.844 0.000
#> GSM152068 2 0.2011 0.860 0.000 0.920 0.000 0.080
#> GSM152075 4 0.0000 0.840 0.000 0.000 0.000 1.000
#> GSM152076 4 0.0000 0.840 0.000 0.000 0.000 1.000
#> GSM152079 2 0.1211 0.878 0.000 0.960 0.000 0.040
#> GSM152084 1 0.5977 0.263 0.528 0.432 0.000 0.040
#> GSM152089 4 0.2921 0.738 0.000 0.000 0.140 0.860
#> GSM152095 4 0.0336 0.840 0.000 0.008 0.000 0.992
#> GSM152096 2 0.0000 0.869 0.000 1.000 0.000 0.000
#> GSM152097 4 0.2973 0.767 0.000 0.144 0.000 0.856
#> GSM152099 2 0.0921 0.879 0.000 0.972 0.000 0.028
#> GSM152106 4 0.2216 0.805 0.000 0.092 0.000 0.908
#> GSM152107 2 0.1824 0.872 0.000 0.936 0.004 0.060
#> GSM152109 2 0.4820 0.454 0.012 0.692 0.296 0.000
#> GSM152111 1 0.3196 0.783 0.856 0.008 0.000 0.136
#> GSM152112 3 0.4431 0.561 0.000 0.000 0.696 0.304
#> GSM152113 3 0.4964 0.662 0.028 0.256 0.716 0.000
#> GSM152115 3 0.0469 0.826 0.000 0.012 0.988 0.000
#> GSM152030 4 0.2830 0.818 0.040 0.060 0.000 0.900
#> GSM152038 3 0.3324 0.769 0.136 0.012 0.852 0.000
#> GSM152042 4 0.4903 0.640 0.028 0.248 0.000 0.724
#> GSM152062 3 0.6757 0.561 0.192 0.196 0.612 0.000
#> GSM152077 1 0.4095 0.747 0.804 0.000 0.024 0.172
#> GSM152088 2 0.0469 0.875 0.000 0.988 0.000 0.012
#> GSM152100 4 0.0336 0.838 0.000 0.000 0.008 0.992
#> GSM152102 3 0.1557 0.817 0.000 0.056 0.944 0.000
#> GSM152104 4 0.4431 0.545 0.000 0.304 0.000 0.696
#> GSM152028 1 0.4431 0.565 0.696 0.000 0.304 0.000
#> GSM152029 1 0.4428 0.624 0.720 0.276 0.004 0.000
#> GSM152049 1 0.1022 0.834 0.968 0.000 0.000 0.032
#> GSM152053 4 0.0524 0.839 0.000 0.008 0.004 0.988
#> GSM152059 1 0.0817 0.836 0.976 0.000 0.024 0.000
#> GSM152085 1 0.2611 0.814 0.896 0.000 0.008 0.096
#> GSM152101 3 0.1211 0.821 0.000 0.040 0.960 0.000
#> GSM152105 1 0.0921 0.836 0.972 0.000 0.028 0.000
#> GSM152034 1 0.5143 0.236 0.540 0.000 0.004 0.456
#> GSM152036 4 0.0336 0.838 0.000 0.000 0.008 0.992
#> GSM152040 3 0.4050 0.739 0.036 0.000 0.820 0.144
#> GSM152043 1 0.1211 0.835 0.960 0.000 0.040 0.000
#> GSM152046 1 0.4991 0.413 0.608 0.000 0.004 0.388
#> GSM152047 3 0.5078 0.580 0.028 0.000 0.700 0.272
#> GSM152048 1 0.1929 0.837 0.940 0.000 0.024 0.036
#> GSM152050 1 0.3123 0.770 0.844 0.000 0.000 0.156
#> GSM152052 1 0.1388 0.832 0.960 0.028 0.012 0.000
#> GSM152056 1 0.2469 0.804 0.892 0.000 0.000 0.108
#> GSM152060 1 0.5628 0.306 0.556 0.000 0.024 0.420
#> GSM152065 3 0.0779 0.825 0.016 0.004 0.980 0.000
#> GSM152066 1 0.0469 0.836 0.988 0.000 0.000 0.012
#> GSM152069 3 0.4916 0.350 0.000 0.424 0.576 0.000
#> GSM152070 3 0.0336 0.825 0.008 0.000 0.992 0.000
#> GSM152071 3 0.7098 0.299 0.132 0.376 0.492 0.000
#> GSM152072 3 0.0672 0.826 0.008 0.008 0.984 0.000
#> GSM152073 1 0.1474 0.832 0.948 0.000 0.052 0.000
#> GSM152078 1 0.2021 0.827 0.936 0.024 0.040 0.000
#> GSM152082 3 0.1792 0.808 0.068 0.000 0.932 0.000
#> GSM152086 1 0.0592 0.836 0.984 0.000 0.000 0.016
#> GSM152090 1 0.5159 0.463 0.624 0.364 0.000 0.012
#> GSM152092 1 0.3074 0.767 0.848 0.000 0.152 0.000
#> GSM152093 1 0.2198 0.820 0.920 0.008 0.000 0.072
#> GSM152094 1 0.1297 0.838 0.964 0.000 0.020 0.016
#> GSM152098 1 0.4679 0.501 0.648 0.000 0.352 0.000
#> GSM152110 4 0.4155 0.626 0.240 0.000 0.004 0.756
#> GSM152031 1 0.0817 0.836 0.976 0.000 0.024 0.000
#> GSM152037 1 0.0817 0.836 0.976 0.000 0.024 0.000
#> GSM152055 4 0.4792 0.474 0.312 0.000 0.008 0.680
#> GSM152061 4 0.5432 0.454 0.316 0.000 0.032 0.652
#> GSM152064 4 0.2647 0.781 0.120 0.000 0.000 0.880
#> GSM152087 1 0.1211 0.835 0.960 0.000 0.040 0.000
#> GSM152103 1 0.3710 0.725 0.804 0.192 0.000 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM152032 3 0.4010 0.6417 0.000 0.088 0.796 0.000 0.116
#> GSM152033 3 0.4114 0.3189 0.000 0.000 0.624 0.000 0.376
#> GSM152063 4 0.4300 -0.0908 0.000 0.476 0.000 0.524 0.000
#> GSM152074 3 0.3274 0.5726 0.000 0.000 0.780 0.000 0.220
#> GSM152080 2 0.1018 0.7908 0.000 0.968 0.016 0.000 0.016
#> GSM152081 4 0.1195 0.7327 0.000 0.012 0.028 0.960 0.000
#> GSM152083 2 0.3530 0.6622 0.000 0.784 0.204 0.000 0.012
#> GSM152091 2 0.0671 0.7945 0.000 0.980 0.016 0.000 0.004
#> GSM152108 3 0.4639 0.6448 0.000 0.056 0.788 0.084 0.072
#> GSM152114 3 0.6495 0.1382 0.216 0.000 0.480 0.304 0.000
#> GSM152035 2 0.6350 0.3821 0.000 0.552 0.024 0.108 0.316
#> GSM152039 4 0.0451 0.7355 0.000 0.000 0.004 0.988 0.008
#> GSM152041 4 0.1978 0.7239 0.024 0.004 0.044 0.928 0.000
#> GSM152044 2 0.4473 0.5114 0.000 0.656 0.020 0.324 0.000
#> GSM152045 5 0.1978 0.7645 0.004 0.000 0.024 0.044 0.928
#> GSM152051 2 0.2362 0.8001 0.000 0.900 0.024 0.076 0.000
#> GSM152054 5 0.3051 0.7570 0.000 0.000 0.120 0.028 0.852
#> GSM152057 2 0.3485 0.7672 0.000 0.828 0.048 0.124 0.000
#> GSM152058 1 0.5493 0.6131 0.628 0.000 0.264 0.108 0.000
#> GSM152067 5 0.4403 0.5743 0.004 0.240 0.032 0.000 0.724
#> GSM152068 2 0.2361 0.7952 0.000 0.892 0.012 0.096 0.000
#> GSM152075 4 0.0867 0.7369 0.000 0.008 0.008 0.976 0.008
#> GSM152076 4 0.0451 0.7365 0.000 0.004 0.000 0.988 0.008
#> GSM152079 2 0.1725 0.8058 0.000 0.936 0.020 0.044 0.000
#> GSM152084 3 0.4469 0.6063 0.048 0.044 0.800 0.104 0.004
#> GSM152089 4 0.4610 0.2622 0.000 0.000 0.016 0.596 0.388
#> GSM152095 4 0.0290 0.7371 0.000 0.008 0.000 0.992 0.000
#> GSM152096 2 0.0613 0.8026 0.000 0.984 0.004 0.008 0.004
#> GSM152097 4 0.2886 0.6809 0.000 0.148 0.008 0.844 0.000
#> GSM152099 2 0.2046 0.8050 0.000 0.916 0.016 0.068 0.000
#> GSM152106 4 0.3010 0.6613 0.000 0.172 0.004 0.824 0.000
#> GSM152107 2 0.5118 0.7007 0.000 0.716 0.128 0.148 0.008
#> GSM152109 2 0.3327 0.7193 0.000 0.828 0.028 0.000 0.144
#> GSM152111 1 0.4621 0.6874 0.744 0.004 0.076 0.176 0.000
#> GSM152112 5 0.3884 0.5535 0.000 0.000 0.004 0.288 0.708
#> GSM152113 3 0.4461 0.6217 0.000 0.036 0.760 0.020 0.184
#> GSM152115 5 0.2852 0.7275 0.000 0.000 0.172 0.000 0.828
#> GSM152030 4 0.5133 0.2788 0.012 0.024 0.384 0.580 0.000
#> GSM152038 3 0.4118 0.4094 0.004 0.000 0.660 0.000 0.336
#> GSM152042 4 0.3666 0.6735 0.012 0.032 0.132 0.824 0.000
#> GSM152062 3 0.2660 0.6403 0.000 0.000 0.864 0.008 0.128
#> GSM152077 3 0.3738 0.6496 0.052 0.000 0.844 0.064 0.040
#> GSM152088 2 0.0162 0.8011 0.000 0.996 0.000 0.004 0.000
#> GSM152100 4 0.1591 0.7218 0.000 0.004 0.004 0.940 0.052
#> GSM152102 5 0.3067 0.7489 0.000 0.012 0.140 0.004 0.844
#> GSM152104 4 0.4367 0.3032 0.000 0.372 0.008 0.620 0.000
#> GSM152028 1 0.5555 0.4795 0.640 0.000 0.140 0.000 0.220
#> GSM152029 1 0.5483 0.3870 0.616 0.316 0.016 0.000 0.052
#> GSM152049 1 0.3169 0.7346 0.856 0.000 0.084 0.060 0.000
#> GSM152053 3 0.5673 0.1569 0.000 0.020 0.512 0.428 0.040
#> GSM152059 1 0.0000 0.7324 1.000 0.000 0.000 0.000 0.000
#> GSM152085 1 0.1168 0.7376 0.960 0.000 0.000 0.032 0.008
#> GSM152101 5 0.1471 0.7675 0.000 0.020 0.024 0.004 0.952
#> GSM152105 3 0.4817 0.0938 0.404 0.000 0.572 0.000 0.024
#> GSM152034 1 0.5526 0.4798 0.608 0.000 0.004 0.308 0.080
#> GSM152036 4 0.1894 0.7103 0.000 0.000 0.008 0.920 0.072
#> GSM152040 5 0.4651 0.6863 0.104 0.000 0.012 0.120 0.764
#> GSM152043 1 0.0404 0.7300 0.988 0.000 0.000 0.000 0.012
#> GSM152046 1 0.4564 0.4766 0.612 0.000 0.000 0.372 0.016
#> GSM152047 5 0.4758 0.6397 0.088 0.000 0.008 0.160 0.744
#> GSM152048 1 0.5750 0.6143 0.616 0.000 0.228 0.156 0.000
#> GSM152050 1 0.5144 0.5669 0.640 0.000 0.068 0.292 0.000
#> GSM152052 1 0.2732 0.7103 0.840 0.000 0.160 0.000 0.000
#> GSM152056 1 0.5952 0.5757 0.584 0.000 0.164 0.252 0.000
#> GSM152060 1 0.5019 0.3124 0.532 0.000 0.000 0.436 0.032
#> GSM152065 5 0.3318 0.7273 0.012 0.000 0.180 0.000 0.808
#> GSM152066 1 0.3639 0.7186 0.812 0.000 0.144 0.044 0.000
#> GSM152069 2 0.5226 0.4951 0.012 0.636 0.044 0.000 0.308
#> GSM152070 5 0.3825 0.7393 0.136 0.000 0.060 0.000 0.804
#> GSM152071 2 0.6676 0.4300 0.080 0.568 0.076 0.000 0.276
#> GSM152072 5 0.2388 0.7713 0.028 0.000 0.072 0.000 0.900
#> GSM152073 1 0.0609 0.7265 0.980 0.000 0.000 0.000 0.020
#> GSM152078 1 0.1280 0.7326 0.960 0.008 0.024 0.000 0.008
#> GSM152082 5 0.5441 0.5505 0.324 0.000 0.080 0.000 0.596
#> GSM152086 1 0.2409 0.7381 0.900 0.000 0.068 0.032 0.000
#> GSM152090 1 0.4595 0.1498 0.504 0.488 0.004 0.004 0.000
#> GSM152092 1 0.2074 0.6890 0.896 0.000 0.000 0.000 0.104
#> GSM152093 1 0.5896 0.6024 0.596 0.000 0.236 0.168 0.000
#> GSM152094 1 0.0162 0.7318 0.996 0.000 0.000 0.000 0.004
#> GSM152098 1 0.4557 0.0195 0.584 0.000 0.012 0.000 0.404
#> GSM152110 4 0.3905 0.5406 0.232 0.000 0.012 0.752 0.004
#> GSM152031 1 0.1908 0.7299 0.908 0.000 0.092 0.000 0.000
#> GSM152037 1 0.3231 0.6880 0.800 0.000 0.196 0.004 0.000
#> GSM152055 4 0.4613 0.2210 0.360 0.000 0.000 0.620 0.020
#> GSM152061 4 0.5799 0.1723 0.360 0.000 0.004 0.548 0.088
#> GSM152064 4 0.3443 0.6333 0.164 0.000 0.008 0.816 0.012
#> GSM152087 1 0.0290 0.7310 0.992 0.000 0.000 0.000 0.008
#> GSM152103 1 0.5783 0.5720 0.632 0.232 0.128 0.008 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM152032 1 0.5785 0.1651 0.496 0.048 0.392 0.000 0.064 0.000
#> GSM152033 1 0.4335 0.1090 0.508 0.000 0.020 0.000 0.472 0.000
#> GSM152063 2 0.3579 0.7717 0.008 0.784 0.020 0.184 0.004 0.000
#> GSM152074 1 0.5150 0.4230 0.608 0.000 0.256 0.000 0.136 0.000
#> GSM152080 2 0.0865 0.8538 0.000 0.964 0.036 0.000 0.000 0.000
#> GSM152081 4 0.3514 0.6970 0.032 0.000 0.108 0.824 0.000 0.036
#> GSM152083 2 0.4410 0.6815 0.096 0.744 0.144 0.000 0.016 0.000
#> GSM152091 2 0.0653 0.8671 0.000 0.980 0.012 0.004 0.004 0.000
#> GSM152108 1 0.3824 0.5507 0.820 0.064 0.016 0.020 0.080 0.000
#> GSM152114 1 0.5788 0.3199 0.632 0.004 0.052 0.192 0.000 0.120
#> GSM152035 2 0.4029 0.7355 0.032 0.780 0.008 0.024 0.156 0.000
#> GSM152039 4 0.0767 0.7270 0.004 0.008 0.012 0.976 0.000 0.000
#> GSM152041 4 0.3348 0.7068 0.048 0.008 0.060 0.852 0.000 0.032
#> GSM152044 2 0.2996 0.8108 0.008 0.832 0.016 0.144 0.000 0.000
#> GSM152045 5 0.2726 0.7550 0.004 0.000 0.052 0.056 0.880 0.008
#> GSM152051 2 0.1194 0.8741 0.004 0.956 0.008 0.032 0.000 0.000
#> GSM152054 5 0.2571 0.7336 0.060 0.004 0.024 0.020 0.892 0.000
#> GSM152057 2 0.1666 0.8717 0.008 0.936 0.020 0.036 0.000 0.000
#> GSM152058 6 0.5291 0.4657 0.424 0.000 0.040 0.032 0.000 0.504
#> GSM152067 3 0.4500 0.5353 0.000 0.088 0.688 0.000 0.224 0.000
#> GSM152068 2 0.1332 0.8739 0.008 0.952 0.012 0.028 0.000 0.000
#> GSM152075 4 0.1628 0.7279 0.008 0.004 0.036 0.940 0.000 0.012
#> GSM152076 4 0.1138 0.7240 0.004 0.012 0.024 0.960 0.000 0.000
#> GSM152079 2 0.1116 0.8741 0.004 0.960 0.008 0.028 0.000 0.000
#> GSM152084 3 0.5825 0.2708 0.280 0.008 0.596 0.072 0.004 0.040
#> GSM152089 4 0.5281 0.4164 0.004 0.004 0.172 0.636 0.184 0.000
#> GSM152095 4 0.1526 0.7255 0.008 0.004 0.036 0.944 0.000 0.008
#> GSM152096 2 0.0603 0.8656 0.004 0.980 0.016 0.000 0.000 0.000
#> GSM152097 4 0.4441 0.5189 0.016 0.240 0.044 0.700 0.000 0.000
#> GSM152099 2 0.3275 0.7818 0.008 0.820 0.140 0.032 0.000 0.000
#> GSM152106 4 0.4877 -0.0947 0.008 0.464 0.040 0.488 0.000 0.000
#> GSM152107 3 0.4332 0.5820 0.024 0.052 0.792 0.092 0.040 0.000
#> GSM152109 3 0.4145 0.5722 0.004 0.220 0.724 0.000 0.052 0.000
#> GSM152111 6 0.4298 0.6895 0.084 0.000 0.048 0.092 0.000 0.776
#> GSM152112 5 0.5348 0.5169 0.016 0.000 0.104 0.272 0.608 0.000
#> GSM152113 1 0.3075 0.5706 0.844 0.004 0.020 0.000 0.120 0.012
#> GSM152115 5 0.2941 0.7042 0.064 0.000 0.076 0.004 0.856 0.000
#> GSM152030 4 0.5410 0.5477 0.164 0.012 0.128 0.672 0.000 0.024
#> GSM152038 1 0.5120 0.4821 0.600 0.000 0.120 0.000 0.280 0.000
#> GSM152042 3 0.5289 0.1944 0.032 0.004 0.520 0.412 0.000 0.032
#> GSM152062 1 0.5520 0.2127 0.496 0.000 0.396 0.004 0.100 0.004
#> GSM152077 1 0.2671 0.5475 0.892 0.000 0.008 0.040 0.024 0.036
#> GSM152088 2 0.0260 0.8670 0.000 0.992 0.008 0.000 0.000 0.000
#> GSM152100 4 0.1655 0.7158 0.004 0.012 0.044 0.936 0.004 0.000
#> GSM152102 5 0.3066 0.7243 0.056 0.048 0.016 0.012 0.868 0.000
#> GSM152104 2 0.3883 0.6966 0.004 0.728 0.028 0.240 0.000 0.000
#> GSM152028 6 0.6370 0.2029 0.248 0.000 0.016 0.000 0.320 0.416
#> GSM152029 6 0.4805 0.5431 0.000 0.160 0.120 0.000 0.016 0.704
#> GSM152049 6 0.2880 0.7127 0.108 0.000 0.024 0.012 0.000 0.856
#> GSM152053 3 0.6105 0.2116 0.132 0.004 0.436 0.412 0.008 0.008
#> GSM152059 6 0.1503 0.6985 0.008 0.000 0.016 0.000 0.032 0.944
#> GSM152085 6 0.1844 0.7098 0.012 0.000 0.028 0.024 0.004 0.932
#> GSM152101 5 0.4096 0.6524 0.012 0.004 0.200 0.036 0.748 0.000
#> GSM152105 1 0.4471 0.1956 0.648 0.000 0.020 0.000 0.020 0.312
#> GSM152034 6 0.4731 0.4082 0.000 0.008 0.036 0.340 0.004 0.612
#> GSM152036 4 0.1749 0.7243 0.004 0.004 0.044 0.932 0.000 0.016
#> GSM152040 5 0.3995 0.6898 0.000 0.000 0.032 0.028 0.768 0.172
#> GSM152043 6 0.1693 0.7029 0.000 0.000 0.032 0.012 0.020 0.936
#> GSM152046 6 0.4077 0.6056 0.000 0.000 0.044 0.228 0.004 0.724
#> GSM152047 5 0.5690 0.5974 0.000 0.000 0.052 0.124 0.632 0.192
#> GSM152048 6 0.5394 0.5186 0.368 0.000 0.036 0.040 0.004 0.552
#> GSM152050 6 0.5048 0.6087 0.064 0.000 0.044 0.212 0.000 0.680
#> GSM152052 6 0.4487 0.6077 0.316 0.000 0.020 0.000 0.020 0.644
#> GSM152056 6 0.6004 0.5868 0.252 0.000 0.048 0.128 0.000 0.572
#> GSM152060 6 0.4780 0.3784 0.000 0.000 0.036 0.372 0.012 0.580
#> GSM152065 5 0.2772 0.7301 0.068 0.000 0.020 0.000 0.876 0.036
#> GSM152066 6 0.4003 0.6871 0.192 0.000 0.028 0.012 0.008 0.760
#> GSM152069 3 0.4732 0.5922 0.004 0.136 0.724 0.000 0.120 0.016
#> GSM152070 5 0.2831 0.7246 0.000 0.000 0.024 0.000 0.840 0.136
#> GSM152071 3 0.4826 0.5889 0.008 0.108 0.736 0.000 0.116 0.032
#> GSM152072 5 0.2395 0.7491 0.020 0.000 0.076 0.000 0.892 0.012
#> GSM152073 6 0.1594 0.6939 0.000 0.000 0.016 0.000 0.052 0.932
#> GSM152078 6 0.3023 0.7075 0.084 0.004 0.012 0.000 0.040 0.860
#> GSM152082 5 0.5087 0.5309 0.028 0.000 0.052 0.000 0.620 0.300
#> GSM152086 6 0.2841 0.7113 0.092 0.000 0.032 0.012 0.000 0.864
#> GSM152090 6 0.6445 0.4657 0.068 0.272 0.080 0.024 0.000 0.556
#> GSM152092 6 0.4193 0.5180 0.028 0.000 0.008 0.000 0.276 0.688
#> GSM152093 6 0.6246 0.4609 0.360 0.000 0.060 0.100 0.000 0.480
#> GSM152094 6 0.1167 0.7060 0.000 0.000 0.020 0.008 0.012 0.960
#> GSM152098 6 0.4224 0.4068 0.004 0.000 0.036 0.000 0.276 0.684
#> GSM152110 4 0.5443 0.5323 0.080 0.004 0.048 0.656 0.000 0.212
#> GSM152031 6 0.3201 0.6994 0.140 0.000 0.008 0.000 0.028 0.824
#> GSM152037 6 0.4606 0.5915 0.312 0.000 0.020 0.004 0.020 0.644
#> GSM152055 4 0.4492 0.5633 0.004 0.000 0.044 0.700 0.012 0.240
#> GSM152061 4 0.5178 0.3273 0.004 0.000 0.040 0.592 0.028 0.336
#> GSM152064 4 0.3546 0.6758 0.012 0.000 0.036 0.812 0.004 0.136
#> GSM152087 6 0.0881 0.7083 0.000 0.000 0.012 0.008 0.008 0.972
#> GSM152103 6 0.6226 0.3985 0.116 0.344 0.040 0.004 0.000 0.496
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 specimen(p) k
#> ATC:NMF 85 4.10e-06 2
#> ATC:NMF 49 1.74e-03 3
#> ATC:NMF 76 1.92e-04 4
#> ATC:NMF 67 1.50e-04 5
#> ATC:NMF 67 2.34e-03 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
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